History of Econometrics in France (Routledge Studies in the History of Economics, Vol. 85)

A History of E conometrics in France

Whereas it is usually taken for granted that econometrics rose during the twentieth century, this book shows how econometric ideas emerged and spread in France between 1830 and 1930 and progressively became institutionalized. Philippe Le Gall explains how econometric ideas developed from and were inspired by philosophical worldviews and scientific paradigms from the nineteenth century. Le Gall explores the methodology of French authors like Cournot, Briaune and Regnault and demonstrates how they were influenced by the natural sciences of their time, rooted as they were in a worldview where natural order and laws played a central role. As an organized community emerged at the start of the twentieth century, Le Gall shows how these econometric ideas intermingled with new worldviews associated with the complexity of the economy. “This engaging and most scholarly book by Philippe Le Gall reshapes the historical narrative in distinctive ways.” – Mary S. Morgan This book is essential reading for postgraduate students and researchers in the history of economic thought, economic methodology and the history of science as well as econometricians at all levels. Philippe Le Gall is Professor of Economics at the University of Angers, France, and a member of the research groups History and Methodology of Economics (University of Amsterdam, The Netherlands) and ENS Cachan–EconomiX (France).

Routledge Studies in the History of E conomics 1 E conomics as Literature Willie Henderson

13 Ancient E conomic Thought Edited by B. B. Price

2 Socialism and Marginalism in E conomics 1870-1930 Edited by Ian Steedman

14 The Political E conomy of Social Credit and Guild Socialism Frances Hutchinson and Brian Burkitt

3 Hayek’s Political E conomy The socio-economics of order Steve Fleetwood

15 E conomic Careers Economics and economists in Britain 1930-1970 Keith Tribe

4 On the Origins of Classical E conomics Distribution and value from William Petty to Adam Smith Tony Aspromourgos

16 Understanding ‘Classical’ E conomics Studies in the long-period theory Heinz Kurz and Neri Salvadori

5 The E conomics of Joan Robinson Edited by Maria Cristina Marcuzzo, Luigi Pasinetti and Alesandro Roncaglia

17 History of E nvironmental E conomic Thought E. Kula

6 The E volutionist E conomics of Léon Walras Albert Jolink

18 E conomic Thought in Communist and Post-Communist E urope Edited by Hans-Jürgen Wagener

7 Keynes and the ‘Classics’ A study in language, epistemology and mistaken identities Michel Verdon

19 Studies in the History of French Political E conomy From Bodin to Walras Edited by Gilbert Faccarello

8 The History of Game Theory, Vol 1 From the beginnings to 1945 Robert W. Dimand and Mary Ann Dimand

20 The E conomics of John Rae Edited by O. Hamouda, C. Lee and D. Mair

9 The E conomics of W. S. Jevons Sandra Peart 10 Gandhi’s E conomic Thought Ajit K Dasgupta 11 E quilibrium and E conomic Theory Edited by Giovanni Caravale 12 Austrian E conomics in Debate Edited by Willem Keizer, Bert Tieben and Rudy van Zijp

21 Keynes and the N eoclassical Synthesis Einsteinian versus Newtonian macroeconomics Teodoro Dario Togati 22 Historical Perspectives on Macroeconomics Sixty years after the ‘General Theory’ Edited by Philippe Fontaine and Albert Jolink 23 The Founding of Institutional E conomics The leisure class and sovereignty Edited by Warren J. Samuels

24 E volution of Austrian E conomics From Menger to Lachmann Sandye Gloria 25 Marx’s Concept of Money: the God of Commodities Anitra Nelson 26 The E conomics of James Steuart Edited by Ramón Tortajada 27 The Development of E conomics in E urope since 1945 Edited by A. W. Bob Coats 28 The Canon in the History of E conomics Critical essays Edited by Michalis Psalidopoulos 29 Money and Growth Selected papers of Allyn Abbott Young Edited by Perry G. Mehrling and Roger J. Sandilands 30 The Social E conomics of JeanBaptiste Say Markets & virtue Evelyn L. Forget 31 The Foundations of Laissez-Faire The economics of Pierre de Boisguilbert Gilbert Faccarello 32 John Ruskin’s Political E conomy Willie Henderson 33 Contributions to the History of E conomic Thought Essays in honour of RDC Black Edited by Antoin E Murphy and Renee Prendergast

36 E conomics as the Art of Thought Essays in memory of G L S Shackle Edited by Stephen F Frowen and Peter Earl 37 The Decline of Ricardian E conomics Politics and economics in PostRicardian theory Susan Pashkoff 38 Piero Sraffa His life, thought and cultural heritage Alessandro Roncaglia 39 E quilibrium and Disequilibrium in E conomic Theory The Marshall-Walras divide Michel de Vroey 40 The German Historical School The historical and ethical approach to economics Edited by Yuichi Shionoya 41 Reflections on the Classical Canon in E conomics Essays in honor of Samuel Hollander Edited by Sandra Peart and Evelyn Forget 42 Piero Sraffa’s Political E conomy A centenary estimate Edited by Terenzio Cozzi and Roberto Marchionatti 43 The Contribution of Joseph Schumpeter to E conomics Economic development and institutional change Richard Arena and Cecile Dangel 44 On the Development of Long-run N eo-Classical Theory Tom Kompas

34 Towards an Unknown Marx A commentary on the manuscripts of 1861-63 Enrique Dussel

45 F.A. Hayek as a Political E conomist Economic analysis and values Edited by Jack Birner, Pierre Garrouste and Thierry Aimar

35 E conomics and Interdisciplinary E xchange Edited by Guido Erreygers

46 Pareto, E conomics and Society The mechanical analogy Michael McLure

47 The Cambridge Controversies in Capital Theory A study in the logic of theory development Jack Birner

57 Classics and Moderns in E conomics Volume I Essays on nineteenth and twentieth century economic thought Peter Groenewegen

48 E conomics Broadly Considered Essays in honor of Warren J Samuels Edited by Steven G Medema, Jeff Biddle and John B Davis

58 Classics and Moderns in E conomics Volume II Essays on nineteenth and twentieth century economic thought Peter Groenewegen

49 Physicians and Political E conomy Six studies of the work of doctoreconomists Edited by Peter Groenewegen 50 The Spread of Political E conomy and the Professionalisation of E conomists Economic societies in Europe, America and Japan in the Nineteenth Century Massimo Augello and Marco Guidi 51 Historians of E conomics & E conomic Thought The construction of disciplinary memory Steven G Medema and Warren J Samuels 52 Competing E conomic Theories Essays in memory of Giovanni Caravale Sergio Nisticò and Domenico Tosato 53 E conomic Thought and Policy in Less Developed E urope The 19th century Edited by Michalis Psalidopoulos and MariaEugenia Almedia Mata 54 Family Fictions and Family Facts Harriet Martineau, Adolphe Quetelet and the population question in England 1798-1859 Brian Cooper

59 Marshall’s E volutionary E conomics Tiziano Raffaelli 60 Money, Time and Rationality in Max Weber Austrian connections Stephen D. Parsons 61 Classical Macroeconomics Some modern variations and distortions James C.W. Ahiakpor 62 The Historical School of E conomics in E ngland and Japan Tamotsu Nishizawa 63 Classical E conomics and Modern Theory Heinz D. Kurz and Neri Salvadori 64 A Bibliography of Female E conomic Thought to 1940 Kirsten K. Madden, Janet A. Sietz and Michele Pujol 65 E conomics, E conomists and E xpectations From microfoundations to macroeconomics Warren Young, Robert Leeson and William Darity Jnr.

55 E ighteeth-Century E conomics Peter Groenewegen

66 The Political E conomy of Public Finance in Britain, 1767-1873 Takuo Dome

56 The Rise of Political E conomy in the Scottish E nlightenment Edited by Tatsuya Sakamoto and Hideo Tanaka

67 E ssays in the History of E conomics Warren J. Samuels, Willie Henderson, Kirk D. Johnson and Marianne Johnson

68 History and Political E conomy Essays in honour of P.D. Groenewegen Edited by Tony Aspromourgos and John Lodewijks 69 The Tradition of Free Trade Lars Magnusson 70 E volution of the Market Process Austrian and Swedish economics Edited by Michel Bellet, Sandye GloriaPalermo & Abdallah Zouache 71 Consumption as an Investment The fear of goods from Hesiod to Adam Smith Cosimo Perrotta 72 Jean-Baptiste Say and the Classical Canon in E conomics The British connection in French classicism Samuel Hollander 73 Knut Wicksell on Poverty No place is too exalted Knut Wicksell 74 E conomists in Cambridge A study through their correspondence 1907-1946 Edited by M.C. Marcuzzo and A. Rosselli 75 The E xperiment in the History of E conomics Edited by Philippe Fontaine and Robert Leonard 76 At the Origins of Mathematical E conomics The economics of A.N. Isnard (17481803) Richard van den Berg

77 Money and E xchange Folktales and reality Sasan Fayazmanesh 78 E conomic Development and Social Change Historical roots and modern perspectives George Stathakis and Gianni Vaggi 79 E thical Codes and income distribution A study of John Bates Clark and Thorstein Veblen Guglielmo Forges Davanzati 80 E valuating Adam Smith Creating the Wealth of Nations Willie Henderson 81 Civil Happiness Economics and human flourishing in historical perspective Luigino Bruni 82 N ew Voices on Adam Smith Edited by Leonidas Montes and Eric Schliesser 83 Making Chicago Price Theory Milton Friedman – George Stigler Correspondence, 1945-1957 Edited by J. Daniel Hammond and Claire H. Hammond 84 William Stanley Jevons and the Cutting E dge of E conomics Bert Mosselmans 85 A History of E conometrics in France From nature to models Philippe Le Gall

A History of E conometrics in France From Nature to Models

Philippe Le Gall With a Foreword by Mary S. Morgan

First published 2007 by Routledge 2 Park Square, Milton Park, Abingdon, OX14 4RN Simultaneously published in the USA and Canada by Routledge 270 Madison Ave, New York, NY 10016 Routledge is an imprint of the Taylor & Francis Group, an Informa Business © 2007 Philippe Le Gall This edition published in the Taylor & Francis e-Library, 2007. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Library of Congress Cataloging-in-Publication Data Le Gall, Philippe.A history of econometrics in France : from nature to models / Philippe Le Gall. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-415-32255-3 (hb) 1. Econometrics. 2. Economics--Study and teaching--France--History. I. Title. HB139.L4 2007 330.01'5195--dc22 2006027070 ISBN 0-203-30040-8 Master e-book ISBN ISBN10: 0-415-32255-3 (hbk) ISBN10: 0-203-30040-8 (ebk) ISBN13: 978-0-415-32255-3 (hbk) ISBN13: 978-0-203-30040-4 (ebk)

Be patient, for the world is broad and wide. – Edwin Abbott, Flatland. A romance of many dimensions

Contents Illustrations Foreword (by Mary S. Morgan) Acknowledgements 1. Introduction: Unifying econometrics

xi xiii xviii 1

1.1. An investigation into nineteenth century French “political economies” 1.2. “Natural econometrics” in context: Isolated econometricians in a unified world 1.3. The methodology of natural econometrics 1.4. The “unity of orchestration” in uncertainty 1.5. The outline of the book

6 10 14 18

PART I. N ATURAL E CON OME TRICS AN D THE “ SYSTE M OF THE WORLD”

21

2. The secrets of the beehive: Cournot’s “law of sales” as natural econometrics

25

2.1. The “law of sales”: Optimizing the return of the “commercial machinery” 2.1.1. Economics and the large numbers 2.1.2. The market in a “very advanced state of civilization” 2.1.3. The construction of the “law of sales” The search for “less sterile principles” A mathematical law A case of statistical thinking: The inference of the “law of sales” from observed averages 2.1.4. The search for the price maximizing wealth

3

28 29 31 33 33 34 37 41

2.2. The validation of the “law of sales”: Cournot’s “philosophical probability” 2.2.1. “Philosophical probability” 2.2.2. The simplicity of laws 2.2.3. “Induction”: The empirical investigation 2.2.4. Analogical thinking

44 45 46 48 49

2.3. Cournot’s worldview

52

2.3.1. Causality and chance 2.3.2. The “end of history”: Why economics becomes “social physics” 2.3.3. “The hand of God” 2.3.4. The foundations of Cournot’s worldview

53 56 61 63

Conclusion

65

3. The formation of agricultural prices, economic cycles, and natural order: Briaune’s social meteorology

67

3.1. The economy as a body: Briaune’s search for causal chains 3.1.1. Causalities in the “social body” 3.1.2. Agricultural prices and the economic environment

71 71 75

3.2. On the use of statistics and mathematics 3.2.1. Observation: “extracting facts from their obscurity” 3.2.2. Briaune’s use of statistical instruments and mathematics

76 77 77

3.3. The “law of proportionality” 3.3.1. The relation between price and supplying 3.3.2. The test of the law

80 80 83

3.4. The lasting of the reserve: On “auctions” and “double proportionality” 3.4.1. The law of “double proportionality” 3.4.2. The test of the law of “double proportionality”

85 86 90

3.5. A question of atmosphere: Briaune’s “social meteorology” 3.5.1. The weather influence 3.5.2. The bible of econometricians 3.5.3. Fourteen-year agricultural cycles 3.5.4. Forecasting and economic policy 3.5.5. Back to the postulates of natural econometrics

96 96 97 100 101 104

Conclusion

105

4. N atural laws on the Stock market: Regnault’s “financial physics”

107

4.1. Into the “temple of modern society”: A first approach of Regnault’s agenda, instruments, and worldview 110 4.2. Regnault’s worldview: Determinism, unity, and God’s design 4.2.1. An orderly world

115 115

4.2.2. Analogies, transfers, and reductionism: Regnault’s unified world

119

4.3. Instruments for exploring the social world: Regnault’s use of statistics and mathematics 4.3.1. Observation, averages, and time-series analysis 4.3.2. From observation and statistics to mathematical laws

121 121 125

4.4. Short-term speculation: The random walk as a trompe-l’œil 4.4.1. The random walk Information and price movements The “law of deviations” The test of the theoretical results 4.4.2. On ruin: Transaction costs as the visible hand of God Risks, costs, and inequalities The “invisible enemy” and the “law of ruin”

127 127 128 130 135 137 138 139

4.5. From vices to virtues: On long-term speculation 4.5.1. The search for constant causes 4.5.2. The determination of the mean price 4.5.3. Coupon payment and seasonal effects 4.5.4. The discovery of “attraction centers” 4.5.5. The “law of attraction”

142 143 145 146 148 151

4.6. Science as a means to reach the “end of history”

153

Conclusion

157

PART II. T HE RISE OF TWE N TIE TH CE N TURY E CON OME TRICS AN D THE “ UN ITY OF ORCHE STRATION ” 159 5. Statistical socioeconomics for the masses: March attacks

163

5.1. On numbers and measurement: Delineating statistics 5.1.1. Statistics as “une langue commune” 5.1.2. Objective foundations of statistics

167 167 172

5.2. Graphs, coefficients, barometers: March’s measurement implements 5.2.1. Fechner and Pearson revisited: New instruments for the comparison of socioeconomic time series 5.2.2. March and business cycles: On barometric indexation

175 182

5.3. A break in determinism: March’s worldview 5.3.1. On correlation, causality, and historical time

188 188

175

5.3.2. Measuring and taming the world

195

5.4. Early signs of institutionalization: March’s boundary work 5.4.1. A rising institutionalization of econometrics 5.4.2. On scientific conventions

200 201 203

Conclusion

205

6. “If we assume that…”: Lenoir and the artificial worlds of econometrics

207

6.1. Well behaved in the artificial world 6.1.1. The artificial world 6.1.2. The construction of aggregate demand curves Indifference curves Demand curves 6.1.3. The construction of aggregate supply curves

213 214 216 217 225 230

6.2. From the artificial world to the real world: The empirical estimation of demand and supply curves 6.2.1. Lenoir’s statistical instruments: The rising autonomy of correlation The use of graphs Graphs, mathematical statistics, and causality: An undisciplined disciple Lenoir on time-series analysis 6.2.2. The statistical estimation of demand and supply curves 6.2.3. The identification issue

235 235 235 236 239 241 245

Conclusion

252

7. Conclusion: From nature to models

255

7.1. Natural econometrics: An encompassing story? 7.1.1. The rise of barometers and unification 7.1.2. Jevons’s “mechanical reasoning” 7.1.3. On Moore’s star system

257 257 261 263

7.2. The changing shape of econometrics 7.2.1. Modeling, observing, and confessing 7.2.2. Which part of truth?

265 266 267

References Index

269 286

Illustrations Figures 1.1 2.1 2.2 3.1 4.1 4.2 4.3 5.1 5.2 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17 7.1

Natural econometrics Cournot’s “law of sales” Jevons’s drawing of an alleged price law graph The agricultural prices, 1804-1855 The evolution of monthly mean values of the price of the French 3% bond The distribution of the monthly prices of the French 3% bond, 1825-1862 Regnault’s “circles of action” for France and England March’s barometer Prices and the increasing rate of the stock of gold and silver “Elementary actions” “Indifference directions” Indifference curves in the general case Elliptic indifference curves Convex indifference curves A better bundle A worse bundle The “total indifference curve” Individual demand curves The aggregate demand curve “Indifference directions” of the producer The “indifference curves” of the producer An individual supply curve The distribution of individual supply curves The aggregate supply curve The short-term components in consumption and price of coal Identification Babson’s barometer

12 35 41 102 147 150 156 184 187 217 219 220 221 222 223 223 224 226 228 231 232 233 233 234 243 247 258

Tables 3.1 The annual mean price of wheat and the economic and political environment 3.2 String calculation for the period 1860-1846

75 84

3.3 The theoretical price obtained by auctions in the case of an initial shortage of 120 days 3.4 Observed price and theoretical price obtained from “auctions,” 1816-1817 3.5 Observed price and theoretical price obtained from “auctions,” 1846-1847 4.1 Deviations and differences inferior or equal to one month 4.2 The chances to lose or to gain an amount of 14000F 5.1 Variations in marriages, birth and death rates in France (18731902) 5.2 Variations in various indices of the Banque de France (18741902) 5.3 Correlations between births and marriages in England 5.4 Correlations between the short-term movements of marriage and births (England, 1851-1901)

89 92 93 134 140 177 178 180 181

Foreword Economists think of econometrics as a twentieth century development. Their instincts are right in the sense that it is during this period that methods of measuring economic relations using statistical techniques became widespread throughout the discipline of economics. And they are right in the sense that this involved not just the simple adoption of existing statistical methods to economic data but also the concurrent development of an original econometric approach: a combination of conceptual work (the development of ideas about models, about identification, and about structures) and technical work in statistical theory and methods (particularly for time series data, in the treatment of errors, and for methods of model testing etc.). This highly sophisticated work – conceptual and technical – by econometricians effectively engineered a branch of statistics especially for their own usage (just as psychometrics was developed for psychology). Such accounts of econometrics understood as a twentieth century phenomenon inevitably focussed on what seemed new in that period compared to previous times. Thus the traditional story of econometrics has been shaped around a sequence consisting of first the development of concepts and techniques in the 1910s and 1920s; then the foundation of the institutional base in the form of the Econometric Society in the 1930s, and the development of modelling notions by Tinbergen and Frisch around that same time. Econometrics is thought to have come of age with the union of mathematics, statistics and economics in the work of Haavelmo and The Cowles Commission in the 1940s; but the subsequent breaking apart of this utopian approach created three foci in the latter half of the century: mathematical modelling as a way of doing theoretical economics; applied econometrics using statistically based models and methods; and technical econometric theory. Older developments, such as political arithmetic in seventeenth century Britain, or mathematical economics in eighteenth century France, have usually

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been seen as separate, isolated, and unconnected examples of a prehistory, sometimes making their way into histories of statistics or of mathematical economics, but rarely being taken seriously as forms of econometrics. Even recognised mid-nineteenth century pioneers of econometrics, such as Cournot in France and Jevons in Britain, have not been fully integrated into the conventional narrative, given rather the status of revered ancestors at the beginning of those histories. This engaging and most scholarly book by Philippe Le Gall reshapes this historical narrative in distinctive ways. The canvas is a French one, yet his history promises a wider relevance by virtue of the generic quality of the ideas and analysis put forward. Le Gall’s most significant conceptual contribution to the literature on the history of econometrics is his designation of the “natural econometrician”, an economist of the nineteenth century whose world view was that of a natural scientist. A natural econometrician denotes a scientist whose ontology is of a unified world, and whose social laws – like natural laws – were taken to be mathematical. For such a scientist, these natural, mathematically written, laws of economics could be unveiled by an astute and careful handling of statistical numbers, both in tables and in graphical form, rather than by the application of analytical statistical techniques (which mostly came later). Le Gall’s account provides a specialized companion to more broad ranging histories of statistics in the economic and related realms provided by Theodore Porter and others.1 These nineteenth century practitioners of natural econometrics were never institutionalised, and they did not constitute a movement in nineteenth century France, though Cournot is numbered in their set. But, in labelling them as natural econometricians, Le Gall is able to integrate these apparently isolated figures into a narrative of the Theodore M. Porter (1995) Trust in Numbers: The Pursuit of Objectivity and Science in Public Life (Princeton University Press); Alain Desrosières (1998) The Politics of Large Numbers: A History of Statistical Reasoning (Harvard University Press), Judy L. Klein (1997) Statistical Visions in Time: A History of Time Series Analysis, 1662–1938 (Cambridge University Press); Roy Weintraub (2002) How Economics Became a Mathematical Science (Duke University Press).

1

Foreword

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mainstream sciences of their day. So, in this account, we see how the rest of economics appears out of joint with the physical sciences, not these individuals with economics. The pioneers of natural econometrics, such as Cournot and Jevons,2 still stand as giants in the development of “modern” economics, an economics predicated on sharing both philosophy and methodology with the natural sciences. But this book enables us to integrate them into a story in which they are the most impressive members of a group of economists who shared these scientific approaches and values. This label of “natural econometrician” is more widely suggestive, for it does not just re-position these particular French economists as natural scientists, but encourages us to speculate about how far we can construct a broader category of such “natural (social) scientists” within the nineteenth century social sciences. Having established its validity, the category of natural econometrics allows Le Gall to redefine the major historical divide in the history of econometrics as lying between the natural econometricians of the nineteenth century (for whom statistics unveils the mathematical laws that govern the economy), and the instrument-based econometricians of the twentieth century (for whom mathematically and/or statistically formulated tools provide instruments to interrogate a confusing and hidden economic world). This has implications which offer a different shape compared to the conventional story, but do not substantially alter its timing. Whereas the conventional accounts tend to place the breakthrough concept of econometric modelling (models as a matching device between theory and data) in late 1920s and 1930s and sets their originators against the contemporaneous non-model building, empiricist, statistical economists; then sees the fully unified version of econometrics (maths, stats and economics) in the 1940s, and a subsequent break into mathematical modelling and applied statistical econometrics after the 1950s, Le Gall’s categorization suggests a different Harro Maas (2005) William Stanley Jevons and the Making of Modern Economics (Cambridge University Press) offers a treatment of Jevons which parallels this account of the French econometricians, thus speaking to the broader validity of Le Gall’s conceptual and historical claims.

2

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landscape. With his categories, the cut comes a little earlier – natural econometrics gives way to various different instrument-based approaches in econometrics as early as the 1910s. But much more significant is that he shows how these different approaches are based on a world view shared by statistical empirical economists and mathematical model builders alike. In Le Gall’s account, the category of those with an instrument-based world view incorporates both the statistical analysis of March (on business cycles, comparable to the work of Babson and Mitchell in the USA) and the idealized mathematical model building prior to statistical data matching of Lenoir (comparable not just to Edgeworth’s work in mathematical economics but to the work of American and other European econometricians in the 1930s and 1940s). This account is particularly satisfying because it integrates into one group all those economists who considered themselves to be econometricians in the first half of the twentieth century, integrated under their world view in which mathematics, models and statistics are instruments to help find a way into a complex and secret economic world. This original account rests on the attention Le Gall gives to the “world views” of his heroes, that is, to their philosophical beliefs about the constitution of economic laws and relations and to the ways in which these philosophies are carried through into methodologies and methods. This depth of scholarly attention means that we understand these earlier natural econometricians, well-known or otherwise, not as unsophisticated figures using folklore methods that scarcely pass any test of scientificity, but as coherent scientists, using methods appropriate to their expressed philosophies of science. Le Gall, in giving countenance to nineteenth natural econometrics not only provides us with a new account in the history of econometrics of that century, but one that reflects a searching light onto the conventional histories of twentieth century econometrics. Understanding the twentieth century history of econometrics as the development of various different instrumentbased kinds of work enables us to see that history in a far more integrated way than before. Although Le Gall’s history does not go through into the latter half of the twentieth century, using his

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categories we can see the later more strongly “instrumentalist” economics, based on the ideas of Friedman and then Lucas, as the natural off-spring of the earlier twentieth century move to instrument-based econometrics evident in the French economics of March and Lenoir as much as in that of the more well-known figures of Tinbergen and Frisch. Le Gall, in valuing a group of French nineteenth and twentieth century economists as econometricians, invites us to re-evaluate not only the history of econometrics but the broader history of economics. Mary S. Morgan London School of Economics and University of Amsterdam

Acknowledgements This book owes immensely to the support of colleagues and friends. I would like first to thank Mary Morgan and Claude Ménard, who both permanently constitute for me models of researchers. In their work and in their high research standards, I have always found an invaluable source of intellectual stimulation. This book does not only result from discussions with them, it also results from the confidence they placed in me and from their guidance since more than 15 years now. This has been a privilege that I will never forget. I must also say that I have learned a lot from Mary Morgan’s comments on the first draft of the book, and the definitive shape of Chapter 6 owes much to her questions. Thanks also go to Michel De Vroey. From discussions with him a long time ago, I have extracted essential views on the nature of research in economics and in history of economic thought. During the recent years, my greatest debt is to Franck Jovanovic. Although our respective fields of interest differ in many respects, we share many fundamental questionings. This complementary dynamic has led to an academic partnership in full swing from 1998 onwards. A series of papers co-written contributed to shape this book. More generally, the present form of From Nature to Models owes much to his encouragement and to endless discussions to make things fit better. His curiosity and constant questioning sometimes put me in the corner but led me to surpass. I warmly thank him for that invaluable opportunity. Ideas presented in the book also benefited from enlightening discussions over time with many other colleagues. First, I would like to thank Harro Maas, a very precious colleague and friend. I am also grateful to Marcel Boumans, Yves Breton, Eric Chancellier, Loïc Charles, John B. Davis, Gérard Debreu, Michèle Favreau, Philippe Fontaine, Bob Hébert, Judy Klein, Ted Porter, and Margaret Schabas. I would particularly like to thank Jean-Pascal Simonin for all the information and the material on French political economy he spontaneously brought to me, for help and explanations when it was

Acknowledgements

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necessary, and also for his permanent and enthusiastic search for historical puzzles. And of course, I do not forget that he made me discover the work of Jean-Edmond Briaune, one of the heroes of this book. Members of the History and Methodology of Economics group at the University of Amsterdam have sometimes been – willing – guinea pigs for my experiments, I confess. Discussions of preliminary chapters greatly stimulated my work and exerted a decisive influence on the clarification of my thoughts and of the rationale behind this book, and I warmly thank my Amsterdam colleagues for that. Thanks also go to members of the GEAPE (University of Angers) and the History of Social Science group (Ecole Normale Supérieure de Cachan). In both groups, I have presented preliminary chapters or papers that were in a way or in another related to this book. Discussions and comments contributed to polish several of my arguments. I warmly thank people from Routledge, and in particular Terry Clague and Rob Langham: from the very beginning, the project benefited from their enthusiasm. I do not forget Emma Hart and Thomas Sutton, whose help I mostly appreciated. I also acknowledge permission to use previously published material in this essay: Chapter 4. Parts from “Does God Practice a Random walk? The ‘Financial Physics’ of a 19th Century Forerunner, Jules Regnault,” in the European Journal of the History of Economic Thought 8(3), 2001, 332–62, Routledge (written with Franck Jovanovic). Chapter 5. Parts from “March to Numbers. The Statistical Style of Lucien March,” in History of Political Economy 33 (annual supplement: The Age of Economic Measurement, edited by Judy L. Klein and Mary S. Morgan), 2001, 86–110, Duke University Press (written with Franck Jovanovic). My thanks also go to David Hendry, Mary Morgan, and Cambridge University Press for giving me the permission to use translations of Marcel Lenoir’s book contained in Chapter 17 of The Foundations of Econometric Analysis, edited by David F. Hendry and Mary S. Morgan, Cambridge University Press, 1995. Every effort has been made to contact copyright holders for their permission to reprint material in this book. The publishers would be grateful to hear from any copyright holder who is not here acknowledged and will undertake to rectify any errors or omissions in future editions of this book.

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Acknowledgements

Last, but not least, the constant support of my family, parents, and friends was a permanent gift while writing this book. Karine and Maud, I love you. But I cannot find words to express my feelings for Paola, Frank, and Florian: life is simply beautiful with you. I must add a final qualification. This book was directly written in English, which is not my primary language. It has sometimes been difficult to express in this language some subtleties I had in mind. I nevertheless take full responsibility for eventual unclear wording and all translations (indicated as “tr”). The usual caveat applies more than ever.

1. Introduction: Unifying econometrics She felt heat, and wet. Something rough scraped along her face, like sandpaper. It happened again, this roughness on her cheek. Sarah Harding coughed. Something dripped on her neck. She smelled an odd, sweetish odor, like fermenting African beer. There was a deep hissing sound. Then the rough scraping again, starting at her neck, moving up her cheek. Slowly, she opened her eyes and stared up into the face of a horse. The big, dull eye of the horse peered down at her, with soft eyelashes. The horse was licking her with its tongue. It was almost pleasant, she thought, almost reassuring. Lying on her back in the mud, with a horse – It wasn’t a horse. The head was too narrow, she suddenly saw, the snout too tapered, the proportions all wrong. She turned to look and saw that it was a small head, leading to a surprisingly thick neck, and a heavy body – She jumped up, scrambling to her knees. “Oh my God!” Her sudden movement startled the big animal, which snorted in alarm, and moved slowly away. It walked a few steps down the muddy shore and then turned back, looking at her reproachfully. But she could see it now: small head, thick neck, huge lumbering body, with a double raw of pentagonal plates running along the crest of the back. A dragging tail, with spikes in it. Harding blinked. It couldn’t be. – Michael Crichton, The Lost World

It is generally taken for granted that econometrics took-off at the end of the 1920s and the early 1930s, with Ragnar Frisch in the cockpit. At that time, the label “econometrics” was coined,1 and a scientific community emerged and organized at the institutional level – witness “Experience has shown that each of these three view-points, that of statistics, economic theory, and mathematics, is a necessary, but not by itself a sufficient, condition for a real understanding of the quantitative relations in modern economic life. It is the unification of all three that is powerful. And it is this unification that constitutes econometrics” (Frisch 1933a: 2).

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the creation of the Econometric Society, the Cowles Commission, and Econometrica – which actively promoted practices that, under various forms, deeply shaped twentieth century economics and economic policy. But in which respect does this moment represent the launching of econometrics? Although it has often been taken for granted in existing histories, this starting point raises several problems. It is indeed the one identified by econometricians of the Econometric Society and of the Cowles Commission themselves, witness the linear “official” and canonical history written by Christ (1952), with the rhetoric and persuasion it conceals.2 On historical grounds, however, the practice the term “econometrics” covers – or can cover – was more ancient, and of a rather different nature than the approaches that developed from the 1930s. For instance, in Britain, William Stanley Jevons had in mind a union of economic theory and statistics (Morgan 1990), and he practiced it (Maas 2005, Maas and Morgan 2002); in the United States of America, a different kind of association was thought and experimented by Henry Ludwell Moore as early as 1908 (Morgan 1990, Le Gall 1999), despite subsequent attempts to portray his work as “folkloric” (Mirowski 1990, Wulwick 1992 and 1995); in France, a late nineteenth century author such as Emile Cheysson was seen by Hébert (1986)3 as practicing econometrics;4 and in several studies, Niels Kærgaard A canon refers here to a doctrinal history, which aims at serving (even legitimating) a community of scientists. Most often, rhetoric and persuasion play a large role in canons, which carry the ideas of a linear progress and an imperfect past, both summarized by Israel (2000: 142 tr) as follows: “science only accepts history as a mythical and apologetic story of its glorious route to the present days.” In the field of econometrics, two examples can be mentioned. First, Carl Christ’s “official” history was certainly an efficient weapon in the battle with the N.B.E.R. (on the Koopmans–Vining controversy, see Mirowski 1989a). Second, several economists involved in the foundation of the Econometric Society and of the Cowles Commission identified prestigious ancestors as supports, for instance Cournot (see Roy 1933 and Schumpeter 1933). Yet, the ancestor was also seen as somewhat backward: twentieth century econometricians would give birth to the dreams of Cournot, who would have missed the conception and the practice of econometrics. 3 See also Ekelund and Hébert (1999). 4 In addition, we should not forget the work of the Physiocrats, which sometimes leaves room for observation and calculus (see Perrot 1992). 2

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suggested that an econometric thought was existing in Denmark during the very early twentieth century.5 The aim of this book is precisely to show that this standard, canonical starting point of econometrics is just the tip of the iceberg. My investigation is based on the basic idea that the institutional rise of econometrics, whose most visible expression is the birth of the Econometric Society, is clearly distinct from the scientific rise and development of econometric ideas, which occurred during the nineteenth century. It will then be possible to analyze the way twentieth century econometrics progressively became extricated from previous practices by a succession of methodological, theoretical, and philosophical shifts or breaks, and consequently to identify the way the nineteenth century practices as well as the twentieth century practices rely on idiosyncratic foundations. It is in that sense that I shall follow here an archaeological path that, in several respects, owes much to Michel Foucault and Georges Canguilhem.6 I thus invite the reader to discover and to become familiar with this “lost world” of econometric ideas, and our case study is France. 1.1. AN IN VE STIGATION IN TO N IN E TE E N TH CE N TURY F RE N CH “ POLITICAL E CON OMIE S” The history of French contributions to econometrics has received scant attention, even in France. From the existing stories, we learn that econometrics would rise in the country during the early twentieth century in the hands of several statisticians of the Statistique Générale de la France;7 it would slowly develop from the 1930s (Bungener and Joel 1989), and would only become a standard practice during the 1970s (Artus, Deleau and Malgrange 1986).8 It would then gain See for instance Kærgaard (1984 and 1995). Although our work combines archaeology and the history of ideas, that Foucault ([1969] 2002) dissociates. 7 See Desrosières (1993). The Statistique Générale de la France (created in 1833) was the main statistical bureau of the time. It became the Institut National de la Statistique et des Etudes Economiques (INSEE) after World War Two. 8 According to these stories, it would have taken time for this style of modeling to win acceptance as a tool of public policy: France would have preferred a social accounting approach, based on the analysis of national accounts without reference to explicit models. Universities would have long 5 6

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academic recognition and would develop in universities and statistical bureaus. Yet, econometric ideas are not in France a twentieth century phenomenon: although it then took a specific shape, the early twentieth century econometrics is rather the continuation of a practice that developed during the nineteenth century. Actually, the rise of econometric ideas in the country covers a long period, from the 1830s to the 1930s. In the 1830s, the first combinations of economic theory, mathematics, and statistics (in the sense of data and instruments) were thought and elaborated; in the early 1930s, French economists were rather massively (at least comparatively) involved in the creation of the Econometric Society and French was one of the two official languages of the Econometric Society.9 Between these two decades, different styles of econometric ideas took shape and were experimented by scholars who belonged to different schools, traditions, and intellectual milieus. A brief account of what economics was in France during the nineteenth century is here helpful.10 At that time, the “political economy” landscape was made up of several schools or groups, and two of them deserve attention here. First, the “liberal school,” which shared much (at least at the political and the ideological levels) with the British classical school.11 It can mainly be characterized as an ignored mainstream econometrics, and French economists would have remained impervious to the Cowles methods and statistical inference, seen as a conservative practice based on the observation of the past (see Malinvaud 1991). 9 And of Econometrica, whose first volume was published in 1933. Ragnar Frisch stayed in Paris during the mid-1920s and met several French economists interested in the constitution of such a society (for instance François Divisia). In October 1934, the Econometric Society was including 463 members, and the three most represented countries were the United States (151), Italy (42), and France (41) (see Econometrica 1934: 448). 10 According to Le Van-Lemesle (2004), economics was fully institutionalized in France in 1877, when compulsory courses of economics were introduced in law universities (although we should not forget that other forms of institutionalization were previously existing). It then gained autonomy during the early twentieth century, although it was still dependent on law departments. Bernard Lassudrie-Duchêne ironically mentions that during the 1930s, “economists had a little bit the feeling they were the professors of gymnastics of universities” (1994, 2 tr). 11 See Breton and Lutfalla (1991) and Le Van-Lemesle (2004).

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organized political lobby devoted to the promotion of economic liberalism. However, at the methodological level, this school brought few innovations: the approach was largely descriptive, even atheoretical,12 and it ignored, even sometimes harshly rejected, the use of mathematics and statistical instruments. In the emblematic and influential work of Jean-Baptiste Say, for instance, and despite his admiration for experimental methods (Steiner 2005), Ménard (1980) mainly sees a “resistance to statistics,” and in it, there is no temptation to use mathematics.13 During the nineteenth century, French political economy was also characterized by another group: the “econo-engineers.”14 It took the shape of a so-called “élite” group associated with the grandes écoles.15 Their methodology deserves attention: engineers were scientifically well trained, and recurrently used algebra, sophisticated graphs and statistics to solve concrete economic questions, for instance tariff, “optimal price,” or surplus. Authors such as Jules Dupuit or Emile Cheysson are key figures of this tradition: for instance, Cheysson’s courbe des débouchés can, in a sense, nicely illustrates pre-1930 econometrics (Ekelund and Hébert 1999, Hébert 1986). However, the knowledge of French nineteenth century economics is often dependent on retrospective biases. For instance, the focus on engineers often finds a justification in the present shape of economics (with for instance mathematics as a dominant language or the importance of microeconomic issues). To put it differently, attention easily focuses on what is rather familiar with the present state of affairs.16 However, this predilection masks radical difference – the kind of difference Michel Foucault identifies in the preface of The In that respect, a large part of early nineteenth century economic thought ignored the level of abstraction we can find in the Physiocracy. 13 But the majority of nineteenth economists were not well trained in mathematics, science, or statistics. This (but also political issues) contributes to explain that until the first half of the twentieth century, mathematical economics was highly controversial. See Breton (1992) and Zylberberg (1990). 14 See Ekelund and Hébert (1999), Etner (1987), Kurita (1989), Picon (1992), Simonin and Vatin (2002), and Zylberberg (1990). 15 The Ecole Polytechnique, the Ecole des Mines, the Ecole des Ponts et Chaussées, the Conservatoire National des Arts et Métiers. 16 This echoes the idea that “an analogy becomes fertile only if it highlights a difference” (Ménard 1989: 93). 12

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Order of Things: This book first arose out of a passage in Borges, out of the laughter that shattered, as I read the passage, all the familiar landmarks of my thought – our thought, the thought that bears the stamp of our age and our geography – breaking up all the ordered surfaces and all the planes with which we are accustomed the tame the wild profusion of existing things, and continuing long afterwards to disturb and threaten with collapse our age-old distinction between the Same and the Other. This passage quotes a ‘certain Chinese encyclopaedia’ in which it is written that ‘animals are divided into: (a) belonging to the Emperor, (b) embalmed, (c) tame, (d) sucking pigs, (e) sirens, (f) fabulous, (g) stray dogs, (h) included in the present classification, (i) frenzied, (j) innumerable, (k) drawn with a very fine camelhair brush, (l) et cetera, (m) having just broken the water pitcher, (n) that from a long way off look like flies’. In the wonderment of this taxonomy, the thing we apprehend in one great leap, the thing that, by means of the fable, is demonstrated as the exotic charm of another system of thought, is the limitation of our own, the stark impossibility of thinking that. (Foucault [1966] 1994: xv) Precisely, the French nineteenth century economic thought conceals idiosyncratic pieces of work that received scant attention and remain unexplored, probably because they are somewhat puzzling to contemporary economists. 1.2. “N ATURAL E CON OME TRICS” IN CON TE XT : I SOLATE D E CON OME TRICIAN S IN A UN IFIE D WORLD The first aim of this book is to show that several nineteenth century French scholars combined economics, mathematics, and statistics, and practiced econometrics. Yet, in comparison with the twentieth century approaches, these combinations took a very specific shape: they were conceived as a means of identifying and measuring an alleged natural order ruling the social world. I label natural econometrics this style of econometric ideas. Natural econometrics refers to the application of scientific tools, views, and methodologies (associated with the use of mathematics and statistics) to solve economic questions, and this

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application was made possible by a worldview in which the belief in natural order was pivotal. Natural econometricians often remained on the fringe of dominant groups or schools, from which they never gained a real and immediate recognition for this aspect of their work. In addition, they elaborated independently their approach, they worked on separate domains, and they are the product of different educations, trainings, and backgrounds – no scientific community existed and the field had no proper existence. Although it is thus impossible to see natural econometrics as an organized, self-conscious movement that would characterize nineteenth century French economic thought, these authors shared a common approach, which was carried by the scientific and philosophical context. Two contextual factors allowed this emergence. First, about 1800, reflections on the application of mathematics (with Lacroix and Poisson17) and of statistical instruments (with Condorcet, Laplace, and Quételet18) to social issues developed. As previously mentioned, such reflections were often ignored by dominant French economists of the nineteenth century (see Breton 1992), but they strongly influenced some econo-engineers as well as several authors who were on the fringe of traditional groups, lobbies or schools, and who were belonging to rather impervious communities. As illustrations, the nineteenth century opened with sound applications of mathematics to economic questions (e.g. Canard 1801, Bicquilley [1804] 1995, and later on Cournot [1838] 1927), and in the mid-century, we see a rising interest in the application of probability and statistical instruments19 (especially the average) to socioeconomic issues (Cournot [1838] 1927 and [1843] 1984, Dufau 1840). In addition, and more importantly, between the 1830s and the 1860s, three authors20 explored the combination of statistics (in the sense of data and instruments) and mathematics to See Ménard (1978: 99). See especially Armatte (1991), Klein (1997), Perrot (1992), and Porter (1986). 19 This was an important break: for Moreau de Jonnès, the influential director of the Statistique Générale de la France, statistics was mainly understood as the gathering of data. He developed strong arguments against the use of the average. See Armatte (1991). 20 These authors were not engineers. In this respect, our story complements the now traditional focus on econo-engineers. 17 18

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study economic questions. The first one is the polymath Antoine Augustin Cournot (1801–1877), whose work on demand (the “law of sales,” elaborated in 1838) is based on a union of mathematics, statistics, and economics, and belongs to econometrics. Although they remain neglected by the present time, the works of two other authors are masterpieces of nineteenth century econometrics. First, in two books respectively published in 1840 and 1857, Jean-Edmond Briaune (1798–1885) – an agronomist – investigated economic cycles and the relationship between the prices and the quantities of agricultural goods with the help of mathematics and statistics. Second, in 1863, Jules Regnault (1834–1894) – a broker – analyzed stock price behavior in his Calcul des Chances et Philosophie de la Bourse (1863), a book that aimed at erecting a “financial physics” strongly inspired from Adolphe Quételet’s “social physics.” Despite differences, Cournot, Briaune, and Regnault share many methodological views. All three followed methodological paths explored in the natural sciences, especially astronomy and mechanics, and they were led to use mathematics or statistics in economic analysis. A second contextual factor matters here. The econometric perspective we can find in the work of Cournot, Briaune and Regnault was thought and practiced in close association with an idiosyncratic worldview that cannot be understood independently from its context. As Israel (1996) explains, from the seventeenth century to the nineteenth century, science largely developed within the frame of a unified paradigm: various kinds of natural and social phenomena were perceived as being parts of a deterministic and unified “system of the world,” to use the words of Laplace.21 This idea enlightens the intensive use by economists of the eighteenth and the nineteenth centuries of analogies with the natural sciences,22 but also the study of economic phenomena in close relation with an alleged natural order that would rule the social and the natural phenomena. This applies to the work of the Physiocrats (Banzhaf 2000 and Steiner 1998) and of numerous nineteenth century 21 Newton and Laplace are central figures here. See for instance Clark (1992) and Hahn (2004). 22 See Cohen (1985, 1993a and 1993b), Ingrao and Israel (1990), Israel (1996 and 2000), Le Gall (2002b), Maas (2005), Ménard (1978), Mirowski (1989b and 1994), Schabas (1990), and Vatin (1993).

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economists (Raynaud 1936: 56–7). Cournot, Briaune and Regnault share such a belief. In the Recherches of 1838, Cournot writes that “the progress of nations in the commercial system is a fact in the face of which all discussion of its desirability becomes idle; [we are here down] to observe, and not to criticise, the irresistible laws of nature” ([1838] 1927: §2, translation revised); Briaune pays similar attention to “natural law[s]” (1857: 120 tr) and to “the natural order of facts” (1840: 14, footnote 6 tr); and Regnault only focuses on the identification of “general and immutable laws” (1863: 7 tr). For all three, as for some scientists of the Enlightenment23 and some French economists of the eighteenth century (for instance the Physiocrats24), the economy and the society would be characterized by a specific organization: a self-regulating natural order.25 Natural order plays here the role of a “metasocial reference” (Steiner 1998: 96 tr); for our three authors, it is a model of social organization made up of a bounded set of immutable mechanisms and mathematical laws which would work together toward a finality – a harmonious state of societies, predetermined and preprogrammed. Science was then defined as the knowledge of such an order: the society, and more generally Nature, would be a harmonious text written in mathematics and numbers that scientists have to decipher with appropriate instruments. In addition, such a text was considered the work of a “magnificent arithmetician” (Rohrbasser 2001: 7 tr): this natural order goes hand in hand with “the idea that the social and the physical universe are ordered according to God’s blueprint” (Clark 1992: 31). From the seventeenth century to the nineteenth century, such an idea was shared by many scientists and economists (see Israel 1996):26 the world would obey principles secretly elaborated by God, principles 23 “The creation of a natural social science, an explanation of social activities based on the operation of nature and determined by natural laws, was clearly the aim of the Enlightenment” (Clark 1992: 14). 24 See Banzhaf (2000: 525–6), Meyssonnier (1989: Chapter 2), Perrot (1992), and Steiner (1998). On Quesnay’s methodology, see also Charles (2003 and 2004). 25 The eighteenth century also saw the development of the search for natural laws and natural order within the political sphere (see Larrère 2006). 26 The association of statistical thinking with religion was well established by the eighteenth century political arithmetician Johann Peter SüƢmilch (see Rohrbasser 2001).

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that scientists should progressively unveil and that man should, of course, respect – only God would know how things should be for global harmony and happiness. The natural order is thus here a divine order: the discovery of mathematical laws from statistics was assimilated to the knowledge of God’s design, since for such authors “order and number necessarily lead to God” (Rohrbasser 2001: 9 tr). The econometric perspective of Cournot, Briaune, and Regnault cannot be separated from that context. Each of them, and this is not an accident, brought to the fore relations that they considered laws, even natural laws, ruling the social world: the “law of sales” in the case of Cournot; laws of attraction of prices to the average or gravitation of prices around the average in the case of Regnault and Briaune. All three explored economic issues on the basis of new scientific paths and methodologies, largely inspired from the natural sciences, and such explorations were conducted in a unified perspective that was based on the belief that the social and the natural phenomena obey the same natural order. More explicitly, the associations of mathematics and statistics they thought or experimented were means of identifying and measuring natural laws that would rule the socioeconomic world. 1.3. T HE ME THODOLOGY OF N ATURAL E CON OMETRICS In the work of Cournot, Briaune, and Regnault, we thus find the constitutive elements of econometrics – statistics, mathematics, economic analysis. But their arrangement, their shape, and their goal are founded on specific philosophical views: the use by these authors of mathematics and statistics was associated with the quest of an alleged natural order. Ultimately, natural econometrics is the product of beliefs and postulates carried by the context, postulates meaning here elements that are accepted uncritically as the foundations on which scientists practice their investigations and that form a worldview. Postulates take here the shape of the alleged existence, at the ontological level,27 of a world that would be regular, mathematical, orderly (most often in a mechanical sense), deterministic, unified, and of a divine origin. It is from these postulates that data were interpreted and that the world I refer to ontology as the “investigation of the nature, structure and constitution of reality” (Davis 1998: 343). 27

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was read and understood. Such a worldview enlightens the methodological framework of natural econometricians: the use of mathematics is associated with the idea that the world would be intrinsically mathematical and unified – and this would explain why the various sciences use (or should use) mathematics and why mathematical laws that are identified by natural scientists would own counterparts in the social sciences. Statistics was then used for discovering, measuring, and testing (or verifying) such laws. It is in that sense that mathematics and statistics are inseparable methodologies for Cournot, Regnault, and Briaune: with statistics, it would be possible to unveil and to measure the natural and mathematical laws that rule the world. What is particularly striking in natural econometrics is the fact that the elaboration of a law does not ultimately rely on what we would now consider economic assumptions or even views. Instead, the investigations are based on the belief that the economy is part of the more general28 and mathematical “system of the world.” In that sense, we reach here the raison d’être of natural econometrics: it results from a philosophical quest of the whole world. The constitutive steps of natural econometrics highlight this feature (figure 1.1). As previously emphasized, the underlying worldview results from postulates that take the shape of the alleged existence of a world that would be regular, mathematical, orderly, deterministic, unified, and divinely designed. This worldview contains the elements from which scientific activity is seen as possible. It determines the language (mathematics) and the instruments (mainly statistical ones, e.g. time-series decomposition, averaging procedures) to be used. The worldview also permits references (grounded on the image of a world that would be unified at the ontological level) to results (such as laws and principles) elaborated or used in the natural sciences (e.g. attraction, gravitation) and that could be used for analyzing the economy – they are even the prisms through which the economic world is read and understood. From these elements (at least some of them), the shape and the measurement of economic laws are obtained. Then, verifications of various kinds (and not exclusively of a statistical nature) are realized. Ultimately, the economic laws are then seen as offering a supplementary knowledge of the “system of the world,” in accordance with the initial postulates For instance, economics is not restricted here to the study of the market process. 28

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– the results were seen as confirming and widening the range of application of the initial postulates, they would “demonstrate” their fruitfulness. Finally, the economic laws could open the way for applications, for instance norms for economic policy or individual behavior in conformity with natural order, if the latter is not fully respected. Philosophical worldview (postulates)

Observation, Statistical instruments

Non-economic laws (natural sciences)

Mathematics

Economic laws

Verifications (quantitative, qualitative “tests”)

Knowledge of the world and the natural order

Norms for economic policy and individual behavior Figure 1.1 Natural econometrics.

The step of what would nowadays be the domain of “testing”, and which is rather verification in natural econometrics,29 illuminates In natural econometrics, we find rather confirmations than refutations in the Popperian style. But as explained by Kim, De Marchi and Morgan (1995), econometric tests rarely fit the Popperian guidelines. A nice analysis of econometric tests can also be found in McCloskey and Ziliak (2004). 29

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the way the approach fully depends on philosophical postulates of that kind.30 In the work of Cournot, Briaune, and Regnault, we can find two categories of tests or verifications: quantitative (statistical) verifications, but also qualitative verifications. Cournot’s work is a nice illustration of this idea. The criteria he used (and that, for him, should rule any scientific work) are “induction” (it covers interpolation and extrapolation), simplicity, analogy, and beauty. These criteria, which are included into what he calls “philosophical probability,”31 are rooted in a set of postulates, in a worldview: There is thus, independently of the proof called apodictic, or of the formal demonstration, a certainty that we call philosophical or rational (…). [I]t results from a judgment of reason that estimates various suppositions or assumptions, and admits some of them because of the order and the rational link [enchaînement] they introduce in the system of our knowledge, and rejects the other ones because they are incompatible with this rational order whose realization is searched (…) by human intelligence. Reason thus legitimates some natural and instinctive beliefs, whereas other ones are rejected as biases [préjugés] or illusions of senses; and finally our whole knowledge is based on this philosophical certainty, because no truths can be demonstrated independently of initial notions or truths, which are accepted and nondemonstrable. (Cournot [1843] 1984: §231 tr) “Philosophical probability” is thus a set of criteria that rule science but that cannot be demonstrated: it belongs to the domain of

30 For instance, these authors “tested” their results on the basis of philosophical arguments that originate in the belief that the world was unified and ruled by a natural order. However, the reference to noneconomic laws (e.g. attraction) also occurred before the elaboration of an economic law, and was a prism for the reading of data. In that perspective, these elements were as much a conclusion of research as they were a starting point. 31 Cournot constantly looked for a correspondence between the order in knowledge and the order in the real world. What he labeled “philosophical probability” is seen as offering foundations to such an agreement (see section 2.2).

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postulates.32 During the nineteenth century, we thus find in the work of isolated French scholars the very idea and the practice of econometrics – despite the word was not, of course, used at that time – and in their hands the association of economic theory, statistics, and mathematics was fully dependent on such philosophical views. Econometric ideas were thus well on their way at the time, although they took an idiosyncratic shape. At that stage, the question is: How did the early twentieth century style of econometrics become extricated from this natural econometrics? 1.4. T HE “ UN ITY OF ORCHE STRATION ” IN UN CE RTAIN TY During the early twentieth century, we find in France – as in other countries – a rising interest in British mathematical statistics. This interest is particularly apparent in the communities of actuaries33 and engineers. Lucien March, Henri Bunle, Marcel Lenoir are indeed to be included into the set of authors (e.g. George Udny Yule, Arthur Bowley, Henry Ludwell Moore) who used at that time new statistical instruments34 to analyze socioeconomic issues such as the relationships between price and quantity or between economic variables (e.g. unemployment) and social variables (e.g. the marriage rate).35 Actually, the simultaneous use of such methods and this common agenda illustrate fundamental changes in French econometrics, at two levels. At the institutional level, a “unity of orchestration,” to use the words of Margaret Morrison,36 is emerging: the period saw the development of a small homogenous community, in France and at Even in the work of Karl Popper, that we often see as a champion of testing procedures, we find postulates: “My dream programme is metaphysical. It is non-testable: it is irrefutable (and irrefutability, we should remember, is not a virtue but a vice). It is based upon the metaphysical (rather than the ‘scientific’) idea of indeterminism” (Popper 1992: 198–9). 33 For instance Hermann Laurent. See Breton (1998) and Le Gall (1997). 34 Mainly correlation, regression, and sometimes more sophisticated instruments such as the periodogram, which is an ancestor of spectral methods (see Cargill 1974). 35 See Armatte (1995), Klein (1997), Klein and Morgan (2001), MacKenzie (1981), Morgan (1990 and 1997), and Porter (1986). 36 See Morrison (2000). 32

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the international level. This is perfectly clear at two levels. First, several of these French econometricians (Lenoir, Bunle, and later Louis Dugé de Bernonville and Michel Huber) belonged to the same institution, the Statistique Générale de la France; they worked in close association; and they benefited from the training and experience of their mentor, March, who was head of this institution. In addition, from the 1920s, econometric ideas began to gain recognition, and they stimulated the publication of textbooks (e.g. Aftalion 1928, March 1930a) presenting, explaining, and supporting the approach. Second, this small “national community” is part of an international process: it is closely related to scholars from other countries, to international associations or journals that made possible the diffusion and the development of the approach (for instance the International Statistical Institute). What is emerging during the period, in Western Europe and in the United States, is this “unity of orchestration,” and this constitutes a decisive step for econometrics. As a rather homogenous and self-conscious community, econometricians were now beginning to share instruments, results, theoretical references, agendas, and a common knowledge could emerge and spread. This progressively opened the way for what we commonly consider the starting point of econometrics: the second half of the 1920s and the early 1930s, with the institutional organization of the Econometric Society, but also a research program shared by several authors, e.g. the estimation of relations between price and quantity and investigations on business cycles (see Morgan 1990). At the methodological and philosophical level, now, these early twentieth century studies represent a break in the foundations of econometrics: the approach became narrower – i.e. econometric studies focused on the analysis of economic issues independently from the whole “system of the world” – and also largely independent from the postulates that framed natural econometrics. In short, they reveal the collapse of the very foundations of natural econometrics. The turn of the century science knew major evolutions that contribute to explain the shift from natural econometrics to the early twentieth century style of econometrics. First, a break in determinism, which occurred in the natural sciences (e.g. the rise of quantum theory) but also (although less apparently) in the social sciences.37 As Ménard (1987) explains that in several respects, economics was not severely affected by the “probabilistic revolution.” However, branches of 37

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the contributors of the volumes The Probabilistic Revolution emphasize,38 at the turn of the century the deterministic framework left progressively room for probability,39 and this deeply affected scientific instruments and theories (e.g. causality40). Second, and perhaps more importantly here, between approximately 1900 and the 1930s, science was characterized by a major evolution: the rise of instrumentalist approaches. This is clear from Giorgio Israel’s studies: what he labels “mechanical analogies” progressively left room for “mathematical analogies.”41 More explicitly, during the eighteenth and nineteenth centuries, a style of mathematical modeling developed, which relied on the idea that “science has to afford a unitary and objective picture of the Universe” (Israel 1996: 19 tr): the universe was considered a well-ordered and deterministic machine functioning on the basis of perfect rules. Various phenomena were understood as ontologically ruled by similar principles. Within this unitary paradigm, forms of reductionism could thus develop: they aimed at reducing “the description of facts to a system of principles and methods considered the ontological or epistemological core of science” (1996: 149 tr), and a unitary picture of the world was possible.42 However, and in many respects this largely encompasses the episode of the “probabilistic revolution,” the early twentieth century saw the development of another approach, more instrumentalist in substance: what Israel labels “mathematical analogies” refers to the use in modeling of tools that were mainly selected for their capacity to reproduce efficiently phenomena,43 and this selection became largely economics such as financial economics knew such a shift during the 1930s (Jovanovic 2002a), and Chancellier and Jovanovic (2002) show the way a postulate – unpredictability – played a major role during the early years of the Cowles Commission. 38 See Krüger, Gigenrenzer and Morgan (1987) and Krüger, Daston and Heidelberger (1987). 39 Although chance was often perfectly tamed (Hacking 1990). 40 See Cartwright (1983 and 1989) and McKim and Turner (1997). 41 See especially Israel (1996, 2000, and 2001). 42 See also Cartwright (1999) and Morrison (2000). 43 An example discussed by Israel (1996) is Van Der Pol’s theory of oscillations. The argument perfectly applies to pieces of econometric modeling of the 1930s, for instance Philippe Le Corbeiller’s analysis of cycles (Le Corbeiller 1933; see Le Gall 1994) or Frisch’s “rocking horse” model (Frisch 1933b). For an analysis of the analogies between Van Der

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independent from ontological considerations. The generalization of the practice contributes to the emergence of a fragmentary paradigm, in which the various sciences and even the various sub-fields of disciplines were only related by common tools and languages. Both the “probabilistic revolution” and the decline of ontology – although Israel’s hypothesis cannot be transposed literally to econometrics – contribute to the understanding of a major evolution and shift that affected econometrics in France during the early twentieth century, when natural econometrics left room for another style of econometrics. The major figure in this transition is the statistician and engineer Lucien March (1859–1933), mainly known as the promoter of correlation in France during the early twentieth century. In many respects, March represents the collapse of the worldview and of the postulates that supported natural econometrics: he got rid of determinism, simplicity, and ontological unification. Instead, his postulate was the existence of a complex and uncertain social world, that social scientists could not fully reach. From this, he developed a predilection for a style of analysis in which the observation and the measurement of uncertainty play a major role. In addition, although his own work is dominated by an ontological perspective, it rapidly paved the way for an approach in which statistics and mathematics were used independently from ontological claims. This is perfectly clear from the work of two statisticians that March trained: Henri Bunle and, most importantly, Marcel Lenoir (1881–1927). Although March turned to measurement, seen as a means of observing a complex social world, Lenoir followed another methodological path. Given the collapse of the worldview associated with natural econometrics, given also some changes in the standards of scientific practice, econometricians began to ground their work on another foundation: small mathematical models depicting artificial worlds. “The scale (…) is of humans, not of God,” Deirdre McCloskey wrote in another context (2002: 334). This is, in a sense, the shift Lenoir illustrates in the history of econometric ideas in France: with models, econometricians get a new power: the possibility of constructing autonomous “small worlds,” in which kinds of experiments could be realized and from which they escape from the alleged complexity and out of reach nature of the economy. Three Pol’s oscillations and Frisch’s model, see Boumans (1999 and 2005), Le Gall (1993 and 2002a), and Morgan (1990).

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shifts appear here. At the theoretical level, economic analysis became strictly centered on the functioning of the market. At the philosophical level, the ontological claim vanished, but the model could be used to offer possible explanations to some features of the real world. At the methodological level, finally, the aim was not to extract mathematical laws from observation; rather, it was to estimate and to quantify laws that could be explained by preliminary investigations operated in the frame of the model. In sum, mathematical models defined as local and artificial worlds became the econometrician’s yardsticks; they became the explanatory framework to which the econometrician refers. 1.5. T HE OUTLIN E OF THE BOOK The main arguments exposed in this book can thus be summarized as follows: in France, econometric ideas rose and developed during the nineteenth century in the hands of isolated authors (who were however products of their time), and the style of econometrics they practiced finds its foundations in a worldview in which determinism, ontological unification, God’s design, and natural order play a central role. Within such a frame, natural econometricians used statistical and mathematical tools of the time to solve economic questions of their time. Then, around 1900, the worldview that supported natural econometrics collapsed, and another style of econometrics could progressively emerge, a more local and narrower style associated with mathematical modeling and in which ontological claims and unification declined. At the institutional level, this shift was accompanied by the rise of a community; scientific conventions emerged and led to a progressive organization of the field. This book thus offers an archaeology of econometrics at two levels: an analysis of the way early twentieth century econometric ideas became extricated from nineteenth century natural econometrics; and an identification of some of the methodological and philosophical foundations of the various styles of econometrics that developed from the 1830s to the 1920s. Such an archaeological path leads to the identification of possibilities for econometric ideas to rise, to develop, and to transform, possibilities that took the shape of scientific and philosophical factors. Yet, the book aims at no exhaustiveness: it does not take the shape of a full history of econometrics, but should rather be understood as an essay on the

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foundations of econometric ideas in France during the period scrutinized. Authors and theories were selected in order to illustrate the rise and the decline of natural econometrics.44 The book is organized in two parts and six chapters. Part I (Natural econometrics and the “system of the world”) explores the shape natural econometrics took in the hands of three authors: Antoine-Augustin Cournot (Chapter 2, The secrets of the beehive: Cournot’s “law of sales” as natural econometrics), Jean-Edmond Briaune (Chapter 3, The formation of agricultural prices, economic cycles, and natural order: Briaune’s social meteorology), and Jules Regnault (Chapter 4, Natural laws on the stock market: Regnault’s “financial physics”). Although their approach and the issues they grasped sometimes differ, all three illustrate the core of natural econometrics. At the methodological level, they identified mathematical laws with the help of observation and statistical instruments (the most important one being the average); at the philosophical level, their search for laws was closely dependent on a postulate: the society would be governed, as exactly as the natural world, by a divine natural order. For all three, econometrics was a means of unveiling, measuring, and identifying such an order. Part II (The rise of twentieth century econometrics and the “unity of orchestration”) exposes the style of econometrics that rose during the early twentieth century. This style developed on the basis of another postulate: the complexity and the out of reach nature of the social world. In Chapter 5 (Statistical socioeconomics for the masses: March attacks), we explain that Lucien March represents a shift, even a break, at three levels: at the methodological level, he imported and contributed to the diffusion in France of what became the early conventional tools (regression, correlation); at the institutional level, he contributed to the emergence of a small community; and at the philosophical level, he separated econometric ideas from the deterministic and unified framework dominated by the belief in natural order, and we shall explain in particular the way this break led him to develop an agenda dominated by measurement. By contrast, Marcel Lenoir (Chapter 6, 44 Our selection process led us to eliminate the work of scholars such as Louis Bachelier, Emile Cheysson, François Divisia, Jules Dupuit, Hermann Laurent, among others. In many respects, these authors should certainly have a role in a more exhaustive history, for instance a history of instruments.

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“If we assume that…”: Lenoir and the artificial worlds of econometrics) clearly got rid of that perspective, and he developed a predilection for the construction of models depicting artificial worlds. These models afford an explanatory framework that fully orientates the applied work. Finally, Chapter 7 (From nature to models) presents concluding comments.

Part I. N atural econometrics and the “system of the world” De toutes les sciences naturelles, l’Astronomie est celle qui présente la plus longue suite de découvertes. Il y a extrêmement loin, de la première vue du ciel, à la vue générale par laquelle on embrasse aujourd’hui, les états passés et futurs du systême du monde. Pour y parvenir, il a fallu observer les astres, pendant un grand nombre de siècles; reconnoître dans leurs apparences, les mouvemens réels de la terre; s’élever aux loix des mouvemens planétaires, et de ces loix, au principe de la pesanteur universelle; redescendre enfin, de ce principe, à l’explication complète de tous les phénomènes célestes, jusque dans leurs moindres détails. Voilà ce que l’esprit humain a fait dans l’astronomie. L’exposition de ces découvertes, et de la manière la plus simple dont elles ont pu naître les unes des autres, aura le double avantage d’offrir un grand ensemble de vérités importantes, et la vraie méthode qu’il faut suivre dans la recherche des loix de la nature. ȥ Pierre-Simon Laplace, Exposition du Systême du Monde.

The next three chapters are explorations into an unfamiliar region of the history of economic ideas: the rise and the development of natural econometrics in France, from the 1830s to the 1860s. Despite differences, for instance relative to the way they use mathematics,1 Antoine Augustin Cournot, Jean-Edmond Briaune, and Jules Regnault share much at the methodological and the philosophical levels. All three drew inspiration from scientific programs of the period (mainly those defined by Laplace and Quételet), and analyzed economic issues with the help of statistics (data and instruments) and mathematics. Such a use of statistics and mathematics is closely dependent on their image of the economy and the society: both would be made up with causal, deterministic, divine Some of these differences originate in specific training (for instance Cournot was well trained in that field). Individual education is a rather important data at a time when no institutional field supported econometric ideas.

1

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and mathematical laws and structures (most often of a mechanical nature), and our three authors conceived statistics as a means to discover such laws and structures. In addition, these laws were understood as being parts of a general natural order, which would rule the social world as exactly as the natural world – the whole world was considered mathematically and mechanically organized and structured, and originating in a divine design. In that perspective, Cournot, Briaune, and Regnault aimed at discovering the secrets of the “system of the world” and at making Nature confess. In the hands of these scholars, observation and statistical instruments play a central role. For Cournot, Briaune, and Regnault, science originates in observation. To my knowledge, none of them was directly involved in the collection of measures. But “from about 1830,” as Theodore Porter shows, “there occurred an enormous increase in the acquisition and use of quantitative information about nature, technology, and society alike” (Porter 2001: 14). They could thus use data collected by administrations and institutions, for instance the Ministry of Agriculture or Paris Stock Exchange. Yet, for all three observed data were systematically associated with imperfection. Imperfection does not refer here to a bad quality of observed data, but rather to the functioning of the social world: although it is not chaos, this world would incorporate perturbation – for instance historical accidents or dissenting behaviors originating in ignorance – or, more radically, it is seen as having not reached yet its final and harmonious form. This explains that for these authors, statistical instruments had to be used in order to unveil the signs of constancy, order, and perfection in data. Here the statistical instrument par excellence is the average – these authors share much with Quételet in that perspective2 – from which accidents and imperfection could be eliminated. From averages, these scholars thought that timeless, invariant laws could be inferred and discovered: the “law of sales,” which relates price and quantity (Cournot); the “laws of proportionality,” which connect price to supplying (Briaune); and the “law of attraction” governing stock “Quételet proposed an identification of greatness with the mean,” Theodore Porter writes (1986: 102): the average was “not just a mathematical abstraction, but a moral ideal” (1986: 103). By contrast, any deviation from the average was considered an error, or a vice in the moral sense.

2

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price behavior (Regnault). It is at this stage that statistics and mathematics become inseparable. From observation and from the use of statistical instruments, all three thought that it could be possible to identify mathematical laws ruling the society. In other words, for natural econometricians statistics plays an active role: it was considered a means to discover mathematical relationships and laws. Indeed, Cournot, Briaune, and Regnault believed that the social world – just like the natural world – would be a text written in mathematics, a text that it could be possible to decipher with the help of appropriate statistical instruments. In sum, we shall see in the next three chapters that for these three authors, the use of averages was seen as a means to unveil mathematical laws that would govern the society. We can perceive here the way the methodology of natural econometricians and an idiosyncratic worldview are closely intertwined. These authors rooted their explorations of the economy in the belief that the social world would be, just like the natural world, ruled by a natural order. As we shall see in a more detailed way in the next chapters, the use of statistics and mathematics is here based on a particular image of the society. First, the society would be governed by a finite set of mathematical and mechanical3 laws. This idea legitimates two kinds of unity: an ontological unity – the whole “system of the world” would be made up with a set of laws that apply to society and nature – and a methodological unity – this worldview explains these authors’ search for economic translations of laws at work in the natural sciences. In other words, reductionism is here legitimated by the unity of phenomena supposed to prevail in the real world. Second, this ontological unity would find its roots in God’s design. In fine, natural econometricians saw statistics and mathematics as means for knowing laws they considered divine laws, and such laws were positively interpreted: they would work for harmony, at the individual and at the collective levels. For them, the social scientist would be an observer and a discoverer of God’s secret workshop, of a world they consider finite and harmonious. This explains a pivotal feature of natural econometrics: the task of the natural econometrician is to discover in observed data such a hidden order that, once identified, could lead societies to a stable and In that sense, a “mechanical reasoning” feeds off natural econometrics, à la Jevons (see Maas 2005).

3

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harmonious state, in full conformity with natural order and God’s design. Not surprisingly, for Cournot, Briaune, and Regnault, statistics and mathematics were means for identifying an “end of history,” the moment when no deviations from the natural laws occur and when historical time has no room anymore, when the economy becomes a timeless, ahistorical system. The next three chapters are illustrations of this idiosyncratic interweaving of econometric ideas and a worldview dominated by the belief in a divine natural order. However, it is important to keep in mind that although econometric ideas emerged and took shape in the hands of Cournot, Briaune, and Regnault, this emergence never led to the constitution of a disciplinary field at the institutional level: natural econometrics remains a story of rather isolated figures. Basically, these authors can be considered innovators, in the sense that they largely break with the common practice and methodology of political economy of their time. Yet, they also perfectly fit into scientific paradigms of the period. It is in this mismatch that the historical originality of natural econometrics lies.

2. T he secrets of the beehive: Cournot’s “law of sales” as natural econometrics The question has sometimes been asked why Cournot’s reputation has not been equal to the merit of his work, and why with friends, opportunities, and ability, theoretical and practical, of the first order, he did not rise to a higher rank in French scientific and political history. The complete answer to this question would require an analysis of his many-sided publications (…). But, so far as purely personal causes are concerned, a partial answer may be given: it was his masterful independence and absolute truthfulness, together with an invincible repugnance to self-advertisement and the exploitation of friends. – Henry Ludwell Moore, “The Personality of Antoine-Augustin Cournot”

Science is for Antoine-Augustin Cournot1 “the knowledge logically organized” ([1851] 1975: §3082 tr), and it “can only take shape once facts have been gathered in a sufficiently large number, in such a way that from their comparison, a generality and a ruling principle can emerge” ([1851] 1975: §307 tr). In addition, he proclaimed “the marvelous alliance of abstract speculations and observations judiciously discussed” ([1872] 1973: p.174 tr). Mathematics and statistics play a crucial role here. Mathematics would ensure “the logical linking of propositions,” of course ([1851] 1975: §308 tr). But the use of mathematics also results from a philosophical view: for him, mathematics aims at capturing an order that would be at work in the Antoine-Augustin Cournot (1801–1877) was trained in science at the University of Paris (his dissertation in mechanics was defended in 1829) and in law. He became a professor of mechanics in 1834 and during a large part of his life, he held administrative positions. More detailed biographical elements can be found in Bottinelli (1913), Ménard (1978), Moore (1905a and 1905b), and Vatin (1998). 2 Given the large number of the French editions of Cournot’s books, I shall refer to paragraph numbers and not to page numbers, except when specified otherwise. 1

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real world. However, the discovery of order would need observation, and the aim of statistics is precisely “to penetrate as much as possible the knowledge of the thing itself”3 ([1843] 1984: §106 tr). Mathematics and statistics would thus be complementary tools: the former mainly retranscribes and captures order, and the latter aims at discovering it. In this chapter, I show that this methodology underlies the economic analysis of the market that Cournot developed in the Recherches sur les Principes Mathématiques de la Théorie des Richesses 4 ([1838] 1927), and that Cournot can be portrayed as a natural econometrician. Straightaway, it should be noticed that the analysis of his economic work raises difficulties, mainly because it is now often read through the sole prism of neoclassicism or game theory. However, a very different picture emerges from a contextual perspective, in particular as soon as it is recognized that Cournot’s economic work can hardly be understood “all things being equal,” given the multiple relations that tie it to other parts of his works.5 Cournot is indeed a polymath: his writings cover mechanics, mathematics, statistics, probability, philosophy, economics and history, and in the mid-nineteenth century, he became a leading figure in French science and philosophy. Although they concern, at least at first sight, impervious fields, Cournot’s various works are closely related by an epistemological agenda – the majority of his books deal with the foundations of knowledge – and a philosophical agenda, constructed in the 1830s: the search for an order underlying the society and nature, and in particular the way the society would obey (at least in some circumstances) a natural, mathematical and divine order. In addition, at the methodological level, Cournot thought (like Briaune and Regnault6) that statistics was a means of “pénétrer autant que possible dans la connaissance de la chose en soi.” This book will be referred to under the title Recherches. English translation: Researches into the Mathematical Principles of the Theory of Wealth, 1927. 5 The fact that the various parts of Cournot’s work are connected and intertwined has been shown by several historians of science, and notably Ménard (1978) and Martin (1996). Note also that to our knowledge, the unique book of Cournot translated into English is the Recherches of 1838, and that consequently the economic literature in English often ignores a large part of Cournot’s thought. Incidentally, note that a useful list of the work published on Cournot is given in Martin (1998). 6 See Chapters 3 and 4. 3 4

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unveiling such an order. We shall see that this particularly applies to his famous “law of sales,” constructed in the Recherches ([1838] 1927): this mathematical law is associated by Cournot with a natural order and, in sharp opposition to a now commonly accepted idea,7 it is inserted into a statistical thinking in which averages play a central role. In the Recherches, Cournot mainly focused on the study of a social order that would be relative to “a very advanced state of civilization” ([1838] 1927: §20) and to a “practically stationary condition” ([1838] 1927: §21). As he explains in some of his subsequent books, these elliptical wordings apply to a state where “the society tends to be arranged like the beehive”8 ([1861] 1982: §541 tr) and where the study of the economy would be the concern of “social physics” ([1872] 1973: p.325 tr). In addition, in the Recherches he even saw the economy as being governed by natural laws: The progress of nations in the commercial system is a fact in the face of which all discussion of its desirability becomes idle; [we are here down] to observe, and not to criticise, the irresistible laws of nature. (Cournot [1838] 1927: §2; translation revised) This image of the society and, more generally, this worldview, which rose in the Recherches ([1838] 1927) and developed in subsequent books, mainly the Exposition de la Théorie des Chances et des Probabilités 9 ([1843] 1984), the Essai sur les Fondements de nos Connaissances et sur les Caractères de la Critique Philosophique 10 ([1851] 1975), and the Traité de l’Enchaînement des Idées Fondamentales dans les Sciences et dans l’Histoire 11 ([1861] 1982), exert a strong influence on Cournot’s methodology: statistics was used to unveil an alleged mathematical, mechanical and Although his demonstration was qualified, Ménard (1980) claimed that Cournot’s work was an example of the nineteenth century “resistance to statistics.” This idea was more abruptly used in subsequent studies, for instance Stigler (1986). 8 And, he remarks, human societies are in the long term constituted as “a kind of geometrical regularity, an idea or rather an image of which is what we have called the ‘geometry of bees’” ([1872] 1973: p.148 tr). 9 This book will be referred to under the title Exposition. 10 This book will be referred to under the title Essai. 11 This book will be referred to under the title Traité. 7

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natural order ruling the society. In this chapter, this association of a methodology (the joint use of mathematics and statistics) and a worldview (a social world ruled by natural order) is analyzed on the basis of the “law of sales.” That law12 takes the shape of a mathematical relationship, this is well known, but it also exemplifies the fact that for Cournot, political economy “recognizes as its guide experience or rather observation” ([1838] 1927: §5): in his mind, this mathematical law could only be unveiled by statistics, i.e. inferred from observations and statistical instruments. This explains why it incorporates statistical arguments such as averages – and it is in this sense that econometric ideas can be found here. But there is more. This mathematical law extracted from data would be, for Cournot, a natural law, associated with a mathematical causal order that would prevail in a final and harmonious “state of civilization.” The nature, the foundations, and the validation of the “law of sales” cannot be separated from a worldview based on the perception of a natural order that would rule the world. Cournot thus developed, in the first half of the nineteenth century, econometric ideas that closely depend on such a worldview. In sum, he illustrates the emergence of natural econometrics. Three results are suggested in this chapter. First, the “law of sales” combines, in an original way, statistics and mathematics. Second, the validation of the law is rooted in criteria defined by what Cournot calls “philosophical probability.” These criteria, which are statistical but which are also of a qualitative nature – among them, simplicity, beauty, and analogy – help to understand the kind of scientific results in which Cournot was interested. Third, the very foundation of the “law of sales” is a worldview – in which the criteria that define “philosophical probability” are rooted – based on reductionism and on the idea that on the long term, the study of the economy, which would reach a final state in full conformity with natural order, would be the matter of a “social physics.” 2.1. T HE “ LAW OF SALE S”: O PTIMIZIN G THE RE TURN OF THE “ COMME RCIAL MACHIN E RY” No consensus can be found in the literature relative to the “law of As Ménard (1978: 134–5) explains, the “law of sales” is the most important step of the Recherches. 12

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sales.” According to Henry Schultz, it would be a theoretical relationship of a Marshallian nature – he mentions “the Cournot– Marshall law of demand” (Schultz 1938: 7) – whereas Léon Walras interprets it as an empirical relationship.13 More recently,14 Ekelund and Hébert (2002) find neoclassical arguments in it, whereas Guitton (1978) and Mirowski (1990) suggest that it would be an empirical and phenomenological regularity. We shall thus reconsider the arguments given by Cournot, and it will be possible to explain that the “law of sales” is a mathematical and macroeconomic relationship that, in Cournot’s mind, should be inferred from observed averages. 2.1.1. E conomics and the large numbers It is first necessary to begin with Cournot’s general views on economics. The point here is that he does not exactly follow a microeconomic path – and this may constitute some itching powder for retrospective analyses of Cournot’s work on demand at the light of neoclassicism; rather, he approaches the economy in a global, macroeconomic perspective. His definition of economics is enlightening. For instance, Chapter XII of the Traité contains the exposition of a comparison between law and economics, and for Cournot, “law concerns the private interests, whereas the economic science merely applies to the society as a whole [prise en corps]” (Cournot [1861] 1982: §472 tr). More precisely, Let us indeed see the conditions under which the theoretical idea of wealth, as well as all consequences that can be deduced from it, are realized or are tending to be realized. It is necessary in all respects to apply what the geometers have called the law of large numbers. It is necessary to have a large number of sellers and buyers for the determination of a price [prix courant ], or for each good to own a determined value. You want to calculate the 13 “Our method is identical, because mine is yours, but you work in the perspective of the law of large numbers and you follow the route which leads to numerical applications; I remain above this law, on the ground of the rigorous data of pure theory” (letter from Walras to Cournot, 20 March 1874, in Jaffé 1965 tr). 14 Fry and Ekelund (1971) offer a (now ancient) synthesis of these contrasted interpretations.

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influence, on the price of a good, of the assessment [l’assiette] or the suppression of a tax, of the rise or the fall in the production costs, of the appearance or the disappearance of an outlet [débouché ]? It is clear that we can take into account differences neither in individual pleasure [fantaisie] nor in the exaggeration of the hopes and fears relative to the humor of everyone, and it is necessary to consider a period or a territory sufficiently considerable for a compensation of all the effects of these irregular causes; and in such a way that in the mean values, only the mark of regular, permanent causes, or [of the causes] that concern the main relations between things, remains. Consequently, political economy is the name generally given by the present time to the science that analyzes the laws of production, distribution, and consumption of wealth. Economists, in contrast to most lawyers [jurisconsultes], have been led to analyze their subject from that point of view which dominates the sphere of private interests; it was not a choice, but a necessity; because every science presupposes an abstract conception or an idea, and the essential condition of the idea from which the speculations of the economist begin is the consideration of masses or of the large number. (Cournot [1861] 1982: §472 tr) Another element supports Cournot’s macroeconomic perspective. Cournot recurrently claims that individuals are subordinated to a totality (the society, the group) and that they cannot constitute the foundation of economic reasoning. For instance, in the Exposition, he writes that: The acts of living, intelligent, and moral beings cannot be explained, in the current state of our knowledge, and we can boldly proclaim that they will never be explained by the mechanics of geometers. Consequently, they do not belong, by a geometrical or mechanical dimension, to the domain of numbers; but they are placed in it (…). (Cournot [1843] 1984: §45 tr)

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Not surprisingly, Cournot rarely discussed individual behavior.15 In his work, we find no reference to individual utility, no systematic analysis of individual choices, and one may guess that he would not have appreciated the calculus of pleasures and pains developed by authors such as Stanley Jevons or Francis Ysidro Edgeworth. By contrast, he thought that it was only possible to identify regularities produced by a large number of agents on a market. As we shall see below in a more detailed way, the economy is mainly considered here a system, and only the study of “masses” matters. This explains why, in a previous quotation, Cournot focuses on the determination of “mean values” from which, remember, “only the mark of regular, permanent causes, or [of the causes] that concern the main relations between things, remains” (Cournot [1861] 1982: §472 tr). With mean values, individual factors compensate, and the idiosyncratic laws of the system under scrutiny could be revealed. 2.1.2. The market in a “very advanced state of civilization” In his 1838 book, Cournot analyzes the functioning of such a system: a perfectly organized market. At first glance, the relationship between this analysis and the real markets seems distant, and it is necessary to remember the main steps of his reasoning. The Recherches open with the analysis of Cournot’s central concept: wealth. Wealth would originate in the development of the market,16 defined as “the entire territory of which the parts are so 15 Of course, Chapter 4 of the Recherches contains an assumption relative to the functioning of the market: “We shall invoke but a single axiom, or, if you prefer, make but a single hypothesis, i.e. that each one seeks to derive the greatest possible value from his goods or his labour” ([1838] 1927: §20). In a retrospective perspective, we could see in this “axiom” the neoclassical assumption of individual rationality (although Cournot never referred to utility value). However, such an “axiom” owns here specific foundations: for Cournot, the development of the market and of the society educates individuals, in the sense of the individual rationality. The latter then becomes the result of the system, and is not a founding assumption (see Ménard 1978). We shall analyze this idea in section 2.3. 16 “The idea which the word wealth presents to us to-day, and which is relative to our state of civilization, could not have been grasped by men of Teutonic stock, either at the epoch of the Conquest, or even at much later periods, when the feudal law existed in full vigour. Property, power, the

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united by the relations of unrestricted commerce that prices there take the same level throughout, with ease and rapidity” ([1838] 1927: §23, footnote). In such a frame, “wealth” and “value” are considered synonymous: “we ought to absolutely identify the sense of the word wealth with that which is presented to us by the words exchangeable values” ([1838] 1927: §2). What Cournot was interested in is “the functioning of the market as the place where prices form and where value gets its meaning, through the act of exchange (…). It is from the market that the economic system exists, but it is also from it that the theory can be constituted (…)” (Ménard 1978: 19–20 tr). This, Cournot explains, applies to a market in a “very advanced state of civilization”: To lay the foundations of the theory of exchangeable values, we shall not accompany most speculative writers back to the cradle of the human race;17 we shall undertake to explain neither the origin of property nor that of exchange or division of labour. All this doubtless belongs to the history of mankind, but it has no influence on a theory which could only become applicable at a very advanced state of civilization, at a period when (to use the language of [geometers]) the influence of the initial conditions is entirely gone. (Cournot [1838] 1927: §20; translation revised) In this “very advanced state,” the notions of utility and of scarcity are seen as “accessory,” as “variable, and by nature indeterminate” ideas, “ill suited for the foundation of a scientific theory” ([1838] 1927: §3): Cournot rejects any investigation into value theory. Only distinctions between masters, servants and slaves, abundance, and poverty, rights and privileges, all these are found among the most savage tribes, and seem to flow necessarily from the natural laws which preside over aggregations of individuals and of families; but such an idea of wealth as we draw from our advanced state of civilization, and such as is necessary to give rise to a theory, can only be slowly developed as a consequence of the progress of commercial relations, and of the gradual reaction of those relations on civil institutions” (Cournot [1838] 1927: §1). 17 He rejects here any discussion concerning the origins or the foundations of value as well as a large part of the theoretical framework of authors such as Adam Smith.

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the optimization of wealth in this “very advanced state” of societies would matter. 2.1.3. The construction of the “law of sales” Now let me turn to the way Cournot constructed the “law of sales.” I shall suggest that, in conformity with his ideal in science, Cournot mobilized here mathematical and statistical arguments. More precisely, we shall see that in his mind, it is from observed averages that the true shape of the law could be identified. The search for “less sterile principles” In Chapter 4 of the Recherches, Cournot analyzes a market in such a “very advanced state,” and he focuses on “sales,” i.e. the effective demand for a good immediately followed by the act of exchange: “sales” and demand are “synonymous, and we do not see for what reason theory need take account of any demand which does not result in a sale” (Cournot [1838] 1927: §20). His aim was the determination of a relationship between sales and prices, and he harshly challenges previous analyses: It has been said almost unanimously that “the price of goods is in the inverse ratio of the quantity offered, and in the direct ratio of the quantity demanded.” It has never been considered that the statistics necessary for accurate numerical estimation might be lacking, whether of the quantity offered or of the quantity demanded, and that this might prevent deducing from this principle general consequences capable of useful application. But wherein does the principle itself consist? Does it mean that in case a double quantity of any article is offered for sale, the price will fall one-half? Then it should be more simply expressed, and it should only be said that the price is in the inverse ratio of the quantity offered. But the principle thus made intelligible would be false; for, in general, that 100 units of an article have been sold at 20 francs is no reason that 200 units would sell at 10 francs in the same lapse of time and under the same circumstances. Sometimes less would be marketed; often much more.

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Furthermore, what is meant by the quantity demanded? Undoubtedly it is not that which is actually marketed at the demand of buyers, for then the generally absurd consequence would result from the pretended principle, that the more of an article is marketed the dearer it is. If by demand only a vague desire of possession of the article is understood, without reference to the limited price which every buyer supposes in his demand, there is scarcely an article for which the demand cannot be considered indefinite; but if the price is to be considered at which each buyer is willing to buy, and the price at which each seller is willing to sell, what becomes of the pretended principle? It is not, we repeat, an erroneous proposition – it is a proposition devoid of meaning. Consequently all those who have united to proclaim it have likewise united to make no use of it. Let us try to adhere to less sterile principles. (Cournot [1838] 1927: §20) For him, the “law of sales” would precisely offer “less sterile principles.” A mathematical law It is well known that for Cournot, demand and price are related by a mathematical function: Let us admit therefore that the sales or the annual demand D is, for each article, a particular function F(p) of the price p of such article. To know the form of this function would be to know what we call the law of demand or of sales. (Cournot [1838] 1927: §21) We find here the mathematical expression of the law, D = F(p). Of course, one of Cournot’s historical originalities is here the introduction of a mathematical function to relate quantity (sales) to price, i.e. the introduction of “the unknown law of demand into analytical combinations, by means of an indeterminate symbol” ([1838] 1927: §21). In the general case that Cournot studies,18 the Cournot ([1838] 1927: §20) constructed a typology of goods based on the value of the elasticity of demand, to use a contemporary word. His typology 18

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result is a downward-sloping curve (figure 2.1).

Figure 2.1 Cournot’s “law of sales.” Source: Cournot (1838: §24).

Cournot focused on three properties of the “law of sales”: it is monotonously decreasing, derivable, and continuous. Continuity19 deserves particular attention here. As Ménard (1978) and Martin (1996) show, continuity owns for Cournot a philosophical status: the real world is seen as perfectly continuous. In Cournot’s own words, “the continuous magnitudes are (…) in nature” ([1851] 1975: §186 tr). Similarly, from a general law of nature, continuity is the rule and discontinuity the exception, in the intellectual and moral order as well as in the physical order (…). (Cournot [1851] 1975: §197 tr) More precisely, for Cournot the aim of science is to discover, to capture the order that would be at work in the real world. The latter, is based on examples but no data was explicitly used. In Chapter 6, we shall see the way Marcel Lenoir dealt with this issue. 19 Continuity was defined as follows: “We will assume that the function F(p), which expresses the law of demand or of the market, is a continuous function, i.e. a function which does not pass suddenly from one value to another, but which takes in passing all intermediate values” ([1838] 1927: §22).

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supposed continuous, would have to stimulate the development of tools with which continuity could be thought. Not surprising, then, the infinitesimal calculus is seen as “a pivotal discovery”: according to Cournot, “its proper virtue is to capture directly the fact of continuity within the variation of magnitudes; it is thus in accordance with the nature of things” ([1851] 1975: §201 tr).20 Continuity is precisely the most interesting property of the “law of sales.” In particular, its economic interpretation is based on large numbers: [T]he wider the market extends, and the more the combinations of needs, of fortunes, or even of caprices, are varied among consumers, the closer the function F(p) will come to varying with p in a continuous manner. However little may be the variation of p, there will be some consumers so placed that the slight rise or fall of the article will affect their consumptions, and will lead them to deprive themselves in some way or to reduce their manufacturing output, or to substitute something else for the article that has grown dearer, as, for instance, coal for wood or anthracite for soft coal. [As an illustration, the thermometer of the Stock Exchange] shows by very slight variations of [the price, le cours] the fleeting variations in the estimate of the chances which affect government bonds, variations which are not a sufficient motive for buying or selling to most of those who have their fortunes invested in [government] bonds. (Cournot [1838] 1927: §22; translation revised) Continuity in the economic affairs could be admitted on a perfect market where a large number of agents transact. Cournot could then write that “just as friction wears down roughnesses and softens outlines, so the wear of commerce tends to suppress these exceptional cases, at the same time that commercial machinery moderates variations in prices and tends to maintain them between limits which facilitate the application of theory” ([1838] 1927: §22). On such a market, the individual particularities compensate, and a property relative to a system could be revealed: remember that Cournot is only interested in the study of this “commercial machinery.” 20

See also Poincaré (1905).

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A case of statistical thinking: The inference of the “law of sales” from observed averages Although it is nowadays admitted that, at the methodological level, Cournot’s main contribution to economics lies in his use of mathematics, statistics is an essential component of his work. For him, the aim of statistics would be “to find order” ([1843] 1984: §106 tr), and it would be a universal approach: This theory [statistics] applies to the facts of the physical and natural order, as well as to those of the social and political order. In that sense, phenomena that are achieved in the celestial spaces can be subject to the rules and the investigations of statistics, just like the perturbations of atmosphere, the perturbations of animal economics, and just like the more complex facts that rise, in the state of society, from the frictions of individuals and peoples. (Cournot [1843] 1984: §105 tr) As we can see, Cournot is far from excluding statistics from economics. In the Recherches, he even claims that “Political Economy (…) recognizes as its guide experience or rather observation” ([1838] 1927: §5). In the Recherches, we can find the general idea that the mathematical and the statistical analyses of the “law of sales” should go hand in hand. For instance, Cournot explains that: Unknown functions may none the less possess properties or general characteristics which are known; as, for instance, to be indefinitely increasing or decreasing, or periodical, or only real between certain limits. Nevertheless such data, however imperfect they may seem, by reason of their very generality and by means of analytical symbols, may lead up to relations equally general which would have been difficult to discover without this help. Thus without knowing the law of decrease of the capillary forces, and starting solely from the principle that these forces are inappreciable at appreciable distances, [geometers] have demonstrated the general laws of the phenomena of capillarity, and these laws have been confirmed by observation.

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On the other hand, by showing what determinate relations exist between unknown quantities, analysis reduces these unknown quantities to the smallest possible number, and guides the observer to the best observations for discovering their values. It reduces and cöordinates statistical documents; and it diminishes the labour of statisticians at the same time that it throws light on them (…). Who doubts that in the field of social economy there is a mass of figures thus mutually connected by assignable relations, by means of which the easiest to determine empirically might be chosen, so as to deduce all the others from it by means of theory? (Cournot [1838] 1927: §21; translation revised) This quote highlights Cournot’s ideal in science, the association of mathematics and statistics. The variables D and p are mathematically related, but they also act as guide for the observer and the statistician, and from observation the slope of the law D = F(p) could be identified. And this is precisely the path Cournot followed. Two steps of his reasoning deserve attention here. First, averages play an important role in the way Cournot constructs his law. More precisely, sales and price are defined as annual averages relative to the market or a country: [T]he price of an article may vary notably in the course of a year, and, strictly speaking, the law of demand may also vary in the same interval, if the country experiences a movement of progress or decadence. For greater accuracy, therefore, in the expression F(p), p must be held to denote the annual average price, and the curve which represents function F to be in itself an average of all the curves which would represent this function at different times of the year. (Cournot [1838] 1927: §23)21 The mathematical relation thus directly incorporates a measurement In addition, “to define with accuracy the quantity D, or the function F(p) which is the expression of it, we have supposed that D represented the quantity sold annually throughout the extent of the country or of the market under consideration” (Cournot [1838] 1927: §23). 21

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process, and one may think that Cournot is particularly interested in the observed prices and quantities on a market. Moreover, as averages determined on a market, and a fortiori on a perfectly organized market, D and p are relative to a large number of agents.22 Although he harshly criticized Quételet’s results on technical grounds,23 Cournot discussed averaging procedures at length in the Exposition de la Théorie des Chances et des Probabilités ([1843] 1984). From averages relative to sufficiently homogenous and large populations, the identification of order would be possible. This would be particularly helpful in economics, whose raison d’être is for him, remember, the determination of laws within populations including a large number of individuals. In economics, only the study of “masses” and the identification of regularities and laws from mean results – when individual factors compensate – would matter: It is clear that we can take into account differences neither in individual pleasure [fantaisie] nor in the exaggeration of the hopes and fears relative to the humor of everyone, and it is necessary to consider a period or a territory sufficiently considerable for a compensation of all the effects of these irregular causes; and in such a way that in the mean values, only the mark of regular, permanent causes, or [of the causes] that concern the main relations between things, remains. (Cournot [1861] 1982: §472 tr) This enlightens the important role that averages play in the Recherches, and this idea finds an illustration in the market that he analyzes in Chapter 4 of the Recherches: it includes a large number of agents, and with averages, it would be possible to identify its significant properties – witness the possible inference of the “law of sales” from observed averages. Second, and precisely, in accordance with his general views on statistics, Cournot thought that it should be from observed data that the true shape of the curve could be identified: 22 In that sense, Moore’s “laws of demand” share much with Cournot’s “law of sales” (see Le Gall 1999 and Mirowski 1990). 23 Cournot explained that the “average man” would be an “impossible man” ([1843] 1984: §123 tr). However, he recognizes that Quételet’s work is “worthy” ([1843] 1984: §123 tr). See Armatte (1991: 96).

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Observation must therefore be depended on for furnishing the means of drawing up between proper limits a table of the corresponding values of D and p; after which, by the wellknown methods of interpolation or by graphic processes, an empiric formula or a curve can be made to represent the function in question.24 (Cournot [1838] 1927: §21) In other words, from the empirical yearly mean values of p and D, the shape of the curve could be identified, and we see here the way Cournot believed that a mathematical relationship could be extracted from observed data: what he has in mind is the inference of the law from observation, as Jevons did later (see Maas and Morgan 2002: 114–5 and Maas 2005: Chapter 9;25 see figure 2.2). In Cournot’s definition of the “law of sales,” averages are thus associated with a measurement process: from observation and empirical yearly averages, the law could be identified, and then its genuine mathematical expression could be determined, i.e. its genuine “algebraic formula” ([1838] 1927: §21).26 However, we face a serious puzzle here: the “law of sales” describes no real market and Cournot used no data in Chapter 4 of the Recherches. Before solving this puzzle Cournot explains that the construction of the “law of sales” would be similar to the inference of a law of mortality from observed data: “it is impossible a priori to assign an algebraic form to the law of mortality; it is equally impossible to formulate the function expressing the subdivision of population by ages in a stationary population; but these two functions are connected by so simple a relation, that, as soon as statistics have permitted the construction of a table of mortality, it will be possible, without recourse to new observations, to deduce from this table one expressing the proportion of the various ages in the midst of a stationary population, or even of a population for which the annual excess of deaths over births is known” ([1838] 1927: §21). 25 As Maas (2005: 235–6) explains, “With modern eyes, we may be inclined to take Jevons’s drawing as a very rudimentary fitting of a curve to the data. However, in Jevons’s use of the graphical method, the goal was not to fit the graph to the data, but to obtain an idea of the class of functions to which the ‘rational function’ belonged – that is, to obtain an idea of the causal explanation of the phenomena behind the observed data.” 26 In the Recherches, remember that Cournot only exposed its general expression, D = F(p). 24

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in section 3 of this chapter, let me explain the usefulness Cournot attributed to the “law of sales.”

Figure 2.2 Jevons’s drawing of an alleged price law graph (no date). Horizontal axis: price; vertical axis: quantity. Source: Maas and Morgan (2002: 115).

2.1.4. The search for the price maximizing wealth Cournot considers the economy “a system to be maximized ” (Ménard 1978: 18 tr),27 and the “law of sales” is precisely the instrument from which the price maximizing the value of wealth, pF(p), could be determined. For Cournot, the market would be a “commercial machinery” ([1838] 1927: §22), whose return could and should be maximized. The following analogy with mechanics sheds some light on this idea: In the act of exchange, as in the transmission of power by machinery, there is friction to be overcome, losses which must be borne, and limits which cannot be exceeded. (Cournot [1838] 1927: §2) As we shall see in the next two sections, a “mechanical reasoning” feeds off his economic analysis, to use once more the words of Maas (2005).

27

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The “law of sales” is indeed the instrument from which the maximum of the value of sales pF(p) could be determined. Cournot drew no figure here, although it is possible to imagine it from the arguments he gave: This function would equal zero if p equals zero, since the consumption of any article remains finite even on the hypothesis that it is absolutely free (…). The function pF(p) disappears also when p becomes infinite (…). Since the function pF(p) at first increases [when p increases], and then decreases (…), there is therefore a value of p which makes this function a maximum, and which is given by the equation, (I) F(p) + pFȨ(p) = 0, in which FȨ, according to Lagrange’s [notion], denotes the differential coefficient of function F. If we lay out the curve anb [see figure 2.1], of which the abscissas oq and the ordinates qn represent the variables p and D, the root of equation (I) will be the abscissa of the point n from which the triangle ont, formed by the tangent nt and the radius vector on, is isosceles, so that we have oq = qt. (Cournot [1838] 1927: §24; translation revised) We reach here the aim of Chapter 4 of the Recherches: the determination of the price maximizing the value of sales, and thus the receipts. In §25 of the Recherches, Cournot algebraically verifies that in the general case, a maximum of the function pF(p) exists. Does this mean that statistics is of no help here? We suspect not. The construction of a table, where these values could be found, would be the work best calculated for preparing for the practical and rigorous solution of questions relating to the theory of wealth. (Cournot [1838] 1927: §24) More precisely, his idea is to encourage the statistical path and to combine it to mathematics:

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But even if it were impossible to obtain from [statistical registers] the value of p which should render the product pF(p) a maximum, it would be easy to [know], at least for all articles to which the attempt has been made to extend commercial statistics, whether current prices are above or below this value. Suppose that when the price becomes p + ƅp, the annual consumption as shown by statistics, such as customhouse records, becomes D–ƅD. According as ª 'D D «  p ¬« 'p

, or

'D Dº ! » 'p p »¼

,

the increase in price, ƅp, will increase or diminish the product pF(p); and, consequently, it will be known whether the two values p and p + ƅp (assuming ƅp to be a small fraction of p) fall above or below the value which makes the product under consideration a maximum. Commercial statistics should therefore be required to separate articles of high economic importance into two categories, according as their current prices are above or below the value which makes a maximum of pF(p). (Cournot [1838] 1927: §24; translation revised) From these developments, the very meaning and nature of the “law of sales” can be unveiled. Cournot affords here instructions relative to the kind of data observers of the social world should collect. He wrote, remember, that “by showing what determinate relations exist between unknown quantities, analysis reduces these unknown quantities to the smallest possible number, and guides the observer to the best observations for discovering their values. It reduces and cöordinates statistical documents; and it diminishes the labour of statisticians at the same time that it throws light on them” (Cournot [1838] 1927: §21). Then, from the observation of the yearly mean values of p and D, the slope of the curve relative to the market under consideration could be determined, and the price maximizing wealth could be identified. Let us take stock. Cournot’s previous developments are not applied econometrics but should rather be understood as the preparation for an econometric work. Very oddly, the Recherches contain no empirical investigations of real markets and Cournot’s developments only depict a general case. A key to this puzzle is to be found in the fact that Cournot faced a lack of data. At first sight, this

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lack is justified in a very intriguing way: France “has not yet reached a practically stationary condition” ([1838] 1927: §21), he writes. We shall explain this argument in section 2.3.28 For the moment, let me rather remind that from the previous analysis, we can see that, at least in mind, mathematics and statistics are for Cournot complementary paths: the structure of the “law of sales” is mathematical, its variables are defined as averages, and it would be from observation that the genuine shape of the law could be identified. Then, the law could and should pave the way for “governmental applications” ([1838] 1927, preface: p.5). Yet, an important question remains unanswered: How was the “law of sales” validated by Cournot? Answers, we believe, can be found in his epistemological framework, which affords first keys to identify the worldview from which the law cannot be separated. 2.2. T HE VALIDATION OF THE “ LAW OF SALE S”: COURN OT ’S “ PHILOSOPHICAL PROBABILITY” For Cournot, “the powers [les facultés] by which we acquire our knowledge are, or seem to be, subject to error: senses own their illusions; the attention lies dormant; the memory is capricious; errors of calculus or of reasoning escape us many times one after another. We thus rightly mistrust ourselves, and we consider accepted truths only those which have been controlled” ([1843] 1984: §226 tr). In the perspective of the history of econometrics, this idea deserves attention: we indeed find in Cournot’s work a testing procedure, or at least a validation process, defined by what Cournot calls “philosophical probability.” Such a procedure incorporates two kinds of tests. The empirical confrontation of a law plays a key role in it, but it should be noticed that it also include other criteria, such as simplicity and analogy, which are qualitative and which directly echo Cournot’s worldview. The “law of sales” is precisely based on several of these criteria.

28 In short, Cournot rooted his analysis of the “law of sales” in a historical argument, according to which the society is converging toward “perfection.” Then, in this future state of societies, the law could be inferred from observed data and from the determination of averages, and it could be the instrument for maximizing the return of the “commercial machinery.”

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2.2.1. “Philosophical probability” The Exposition ([1843] 1984) – written before 183829 – is devoted to two kinds of probability: mathematical probability and what Cournot labels “philosophical probability.” What is the nature of “philosophical probability”? For Cournot, knowledge can only be based on probable judgments, on probabilities “which are not relative to [qui ne se résolvent pas] an enumeration of chances, and whose discussion does not properly belong to the doctrine of mathematical probabilities” ([1843] 1984: §113 tr). However, they “motivate a mass of our judgments, and even the most important judgments” ([1843] 1984: §240, #8 tr). From them, we could “evaluate in each particular case the value of the motives [motifs] that lead us to believe, to refuse or to suspend our assent [assentiment]” ([1843] 1984: §227 tr): the issue is here that of the “foundations of knowledge,” if we refer to the title of his 1851 book. Cournot constantly looked for a correspondence between the order in knowledge and the order in the real world: science aims at identifying the “reason of things” in the real world and, in the case of a success, “the objective reason is found, the subjective reason is satisfied”30 ([1875] 1987: p.161 tr). “Philosophical probability” precisely frames and controls knowledge in such a perspective, and it offers foundations to such an agreement: This probability that we call philosophical, and that, in certain particular applications, is called analogy and induction, is related both to the notion of chance [hasard ] and to the sentiment of order and simplicity of the laws that express it (…). We can neither number [nombrer ] the possible laws, nor grade [échelonner ] them as magnitudes [grandeurs] on the basis of this property of form which constitutes their degree of simplicity, and which gives, to various degrees, to our theoretical conceptions the unity, the symmetry, the elegance, and the beauty. (Cournot [1861] 1982: §64 tr) “Philosophical probability” includes, as we can see here, criteria such as unity, beauty, simplicity, analogy, and “induction,” as Cournot See Moore (1905b). For Cournot, “reason” covers the functioning of the real world as well as the faculty to understand it. 29 30

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labels empirical validation. For him, these criteria should apply to every scientific work. It can be noted that one of them is quantitative – “induction” is based on observation – unlike the other ones (simplicity, analogy, and beauty).31 Cournot sees these criteria as reflecting beliefs relative to the way the world functions. In addition, since these criteria reflect beliefs, no absolute certainty prevails: There is thus, independently of the proof called apodictic, or of the formal demonstration, a certainty that we call philosophical or rational (…). [I]t results from a judgment of reason that estimates various suppositions or assumptions, and admits some of them because of the order and the rational link [enchaînement] they introduce in the system of our knowledge, and rejects the other ones because they are incompatible with this rational order whose realization is searched (…) by human intelligence. Reason thus legitimates some natural and instinctive beliefs, whereas other ones are rejected as biases [préjugés] or illusions of senses; and finally our whole knowledge is based on this philosophical certainty, because no truths can be demonstrated independently of initial notions or truths, which are accepted and non-demonstrable. (Cournot [1843] 1984: §231 tr) Philosophical probability is thus a set of criteria that rule science but that cannot be demonstrated: it belongs to the domain of postulates. Let us now analyze these criteria and identify the way they apply to the “law of sales.” 2.2.2. The simplicity of laws For Cournot, one aim of science and of “natural philosophy” is to “untangle the relative or apparent movements,” and here would arise “the idea of the simplicity of laws, and consequently the very idea of law” ([1861] 1982: §57 tr). In addition, it is “a principle of human reason, (…) without which no science could be possible, to search in simplicity the explanation or the reason of complexity” ([1861] 1982:

This means that a law is here accepted on the basis of criteria that escape quantification and quantitative rules. 31

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§57 tr).32 Why does simplicity matter so much for Cournot? Basically, for him, the real world would be made up of simple laws, and this is why simplicity is for him a regulating principle of science. He then formulates the general statement: Generally, any scientific theory, imagined in order to relate a certain number of facts discovered by observation, can be compared to the curve drawn from a mathematical definition, under the constraint to make it pass through a certain number of points given in advance. The judgment that reason passes on the intrinsic value of this theory is a probable judgment, whose probability depends on the one hand on the simplicity of the theoretical formula, on the other hand on the number of facts or the sets of facts that it relates (…). If more complication is needed as soon as new facts from observation occur, it becomes less and less probable as a law of nature (…): it rapidly becomes an artificial construction,33 which finally collapses when, by more and more complication, it even loses the utility of an artificial system, which is to help the work of thought and to guide research.34 (Cournot [1851] 1975: §45 tr) Such a criterion perfectly fits the “law of sales.” First, its mathematical formulation – D = F(p) – is a model of simplicity. This simplicity reflects the structure of the market Cournot considers in the Recherches : such a market would be analogous to a mechanical system, free from friction, and functioning in a perfect and rational way. Cournot’s framework excludes here historical path 32 Simplicity as a ruling principle has often been explicitly proclaimed in science (e.g. Laplace 1796). See for instance Morrison (2000: Chapter 1) in the case of Kepler. 33 We can understand here that Cournot was only interested in the identification of laws that would be at work in the real world, and that he disliked what he considered “artificial” constructions. In Chapter 6, we shall see that Marcel Lenoir developed another strategy, based on another philosophical basis. 34 Simplicity is also associated with harmony and beauty, which are for Cournot features of the real world (see for instance 1851: §67). Scientists had thus to capture and to incorporate these criteria in their own constructions. On the role of such criteria in science, see McAllister (1996).

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dependencies, accidents, chance, and complex psychological phenomena. Second, remember that in a previous quotation Cournot deduced “the very idea of law” from simplicity: he had a good reason to coin the relation between demand and price the law of sales. 2.2.3. “Induction”: The empirical investigation For Cournot, simplicity is closely associated with empirical investigation, labeled “induction.” “Induction,” as well as experiment and more generally observation, plays a key role in each of his books (e.g. [1861] 1982: §121). It covers interpolation35 and extrapolation,36 and both determine the empirical validation of a law. But this idea applies only partially to the “law of sales.” The law, as previously seen,37 could be inferred from observed data and then, from it, the price maximizing the value of sales could be determined. Yet, “induction” was not completely used: Cournot puts forward a lack of data.38 But such an argument does not only apply to economics. Cournot explained that interpolation and extrapolation remain difficult to practice outside an experimental environment, since data always remain “fragmentary”: [W]e understand that, reduced as we are in our role of observers catching only a glimpse of fragments of the general order, we can easily be wrong in our partial applications of this ruling idea.39 When only a few vestiges of an important edifice remain, the architect who attempts to renovate it can easily be mistaken about the inductions he draws from them concerning the general plan of the edifice. He will think that a wall passes by a certain number of markers, and for him their alignment will not be reasonably considered the product of fortuitous crossings; 35 That is, “the induction which applies to points bounded by the limits of observation” ([1851] 1975: §46 tr). 36 That is, “the induction which includes points that go beyond these limits” ([1851] 1975: §46 tr). 37 See section 2.1.3. 38 See section 2.1.4. In addition, although Cournot recurrently refers to the possibility of forecasting (see for instance [1851] 1975: §302), the Recherches contain no exercise of that kind. 39 That is, the “idea of unity, of simplicity in the economy of natural laws” ([1851] 1975: §52 tr).

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and if other vestiges are discovered, one will be led to change the plan of the initial renovation, and we shall recognize that the observed alignment is the product of chance. (Cournot [1851] 1975: §52 tr) The previous excerpt enlightens methodological features of the “law of sales.” The social scientist is looking for “markers” – i.e. observed mean values of p and D – from which the law could be drawn and identified. But the central idea here is that of the exteriority, and thus of the precariousness, of the social scientist.40 In addition, interpolation and extrapolation face a serious problem: structural changes can occur. The world – and especially the social world – would not be invariant but would be characterized by the emergence of novelty,41 at least, as we shall see soon,42 until it reaches a stable state – remember that for Cournot France “has not yet reached a practically stationary condition” ([1838] 1927: §21). “Induction” is constrained by this problem: past data could not be exhaustively collected and forecasting remains uncertain. 2.2.4. Analogical thinking Analogy is the third important criterion associated with “philosophical probability.” It is defined as “links or similarities in the sense that they indicate links” ([1851] 1975: §49 tr). Cournot adds, “in the analogical judgment, the view of the mind only turns towards links and the reason of similarities: similarities have no value if they do not refer to links in the order of facts, where analogy applies” ([1851] 1975: §49). The importance of analogical thinking relies on the fact that, for Cournot, various phenomena would own a “common origin” to be identified: In the analogical judgment, the aim is no more, as in induction, to pass from the observation of facts to the elaboration of a link which unifies them or to a law which rules them, but to go back 40 Similar ideas and words can be found in the work of Lucien March (see section 5.3.2). 41 As we shall see below, this novelty originates in chance that would exist during transitory moments of history. 42 See sections 2.3.1 and 2.3.2.

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to the common origin [anneau commun] or to the common ancestor in order to find, in the community of descent, the reason of similarities or of common characteristics. (Cournot [1875] 1987: p.190 tr) Analogy is thus associated with this fundamental idea: the alleged existence of a common root which would tie up various phenomena and which would be a feature of the kind of order at work in the whole real world.43 Such a criterion plays an important role in the Recherches. As previously noticed, the market Cournot analyzes shares much with mechanics: he considered the economy a mechanical system, a “commercial machinery,” whose return could and should be maximized. Claude Ménard44 precisely shows how the prism of mechanics exerted a strong influence on the way Cournot elaborated his economic work: It is from Cournot’s Recherches of 1838 that one should date the systematic importation of the physics metaphor into economics, in conjunction with its powerful engine of analysis, the differential calculus. We can trace exactly (…) the systematic determinants of this operation. In 1834, Cournot published a French translation of the work of Kater and Lardner, The Elements of Mechanics, appending a chapter of his own on “the measurement of force and the work of machines.” In it, there are philosophical reflections on the idea of force in physics, technical considerations on the work output of machines, considerations of standards of measurement which had been 43 It can be noticed that Cournot dealt cautiously with analogy: analogy could be treacherous, in the sense that it could result from accidents. Consequently, the analysis of analogies could not be separated from the search for rational explanations that aim at demonstrating that analogies do not result from fortuitous causes, from chance (see section 2.3). Incidentally, we see here a distinction between constant causes and accidental causes. For Cournot, “[i]f nature has conformed to a plan, it is necessary to discover the general lines of this plan and to separate the main characteristics from the accidental characteristics” (Mentré 1908: 172 tr). “Induction” and analogy thus share something: they can face chance and have to deal with it. 44 See especially Ménard (1978).

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just proposed, such as ho[r]se power, and remarks on the problem of maximization of work output juxtaposed with minimization of work input. In a brief passage (# 405), he suggests possible comparisons between these questions and those posed in political economy. Four years later Cournot began the Recherches with a redefinition of political economy. The act of exchange is assimilated to the transmission of motion by machines, where “there is friction to overcome, losses to suffer, limits which cannot be exceeded.”45 (Ménard 1989: 85–6) However, analogy does not only refer to a common language used by various sciences: for Cournot, analogical reasoning finds its raison d’être in the way he perceived the constitution and the order of the real world. It is well known that economists intensively used different kinds of analogies during the nineteenth century, and that branches of economics developed at that time with the help of a privileged referent: the natural sciences, and more explicitly mechanics.46 But some of these references took a particular shape, as Israel (1996 and 2000) demonstrates: the “mechanical analogies”47 that spread during the nineteenth century consist in reducing every phenomenon to a mechanistic principle, in order to devise a unitary picture of the world. The natural phenomena and the human phenomena were seen as unified, and physics, considered the most prestigious discipline, would offer a possible reading of the human and social world – society and nature would obey similar principles. In many respects, Cournot followed that path: the references to mechanics that can be found in the Recherches are related to the search for “a common origin.” For Cournot, the economy could be read at the light of mechanics because the social and the natural phenomena would own a common origin of a mechanical nature and would thus share essential features. This explains, as we shall see below, that for In Ménard’s article, translation from Cournot by Pamela Cook. See for instance Ingrao and Israel (1990), Le Gall (2002b), Maas (2005), Ménard (1978), and Schabas (1990). 47 On the role of such analogies in the history of twentieth century econometrics, see Le Gall (2002a). 45 46

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Cournot economics is basically a “social physics.”48 At that stage, we can see that Cournot brings to the fore several criteria that do not reduce to number and on which the validation of scientific work would be grounded – and this particularly applies to the “law of sales.” But why did Cournot select these criteria? The answer can be found in the worldview that underlies his thought and work, and which highlights the nature and the meaning of the “law of sales.” 2.3. COURN OT ’S WORLDVIE W Cournot’s work is grounded on the belief that ideas are attempts to capture an alleged order which rules the real world ([1851] 1975: §90), a world which is external to us.49 Of course, “philosophical probability” plays an important role here: it evaluates the “representative value of our ideas (…), separates [fait la part] the constitution of the external world from the configuration of the mirror that reflects it” ([1872] 1973: p.101 tr). In other words, two notions of order are here at work: a logical order, which is produced by science – its discourses, theories, and laws – and is “relative to certain views of our mind” ([1861] 1982: §45 tr), and a “rational order,” seen as ruling the real world.50 “Philosophical probability” helps to found a correspondence between both ([1851] 1975: §399) and to ensure that science captures “correctly” features of the order in the real world. It is precisely Cournot’s image of the real world that has now to be identified. From the postulates and more generally the worldview that rule his whole work, it will be possible to understand his vision of science, and also the nature and the foundations of the “law of sales.”

48 When societies “function or become close to functioning as a mechanism where all the springs, all the cogwheels can be defined, measured, adjusted with a precision continuously increasing, and kept in a state of regular order, [we have] thus what we can call (…) a social physics” ([1872] 1973: p.148 tr). 49 See Cournot ([1851] 1975: §90 and [1861] 1982: §200). 50 “The rational order is relative to the things considered themselves; the logical order is relative to the construction of propositions, to the shapes and the order of language which is for us the instrument of thought and the means to express it” (Cournot [1861] 1982: §42 tr).

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2.3.1. Causality and chance Cournot is often remembered for his contribution to probability theory.51 In France, he contributed to make popular the basic distinction between objective probability and subjective probability, and several of his books contain theoretical developments and applications in this field. He was particularly interested in objective probability, and there was a good reason for that: at a time when determinism – as it had been exposed by Laplace – reached its apogee, a main feature of Cournot’s thought is to be found in its probabilistic nature. At least during some transitory periods of history, forms of chance would indeed characterize the world, and Cournot thus believed that the calculus of probability, in its objective form, had a wide range of application. A brief detour by causality is necessary to understand Cournot’s conception of chance. Cournot does not reject causality: he recalls that “no phenomena or event is produced without a cause: it is the sovereign and regulating principle of human reason, in the investigation of the real facts,” and this is “an absolute and necessary rule” ([1843] 1984: §39 tr). Every event would be generated by – at least – one cause that would itself be the effect of another cause. It would thus be possible to see events as belonging to causal chains or series: We return from an effect to its immediate cause; this cause is in turn conceived as an effect, and so on; and it is impossible for the understanding [l’entendement ] to conceive a limit to this law of regression in the order of phenomena. The current effect becomes, or can become, in turn the cause of a subsequent effect, and so on at infinitum.52 (Cournot [1843] 1984: §39 tr) From this principle, he identifies two kinds of series that can exist in the universe: the first ones are solidaires, the other ones are “independent.” The concept of série solidaire deserves little explanation: it On the history of probability, see Callens (1997), Coumet (1970), Daston (1988) and Hacking (1975). 52 Cournot often used an analogy with genealogy trees to expose this idea (see for instance [1843] 1984: §39). 51

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concerns phenomena that are causally dependent. Yet, it can be remarked that in Chapter 6 of the Traité, Cournot analyzed this concept of solidarité in a mathematical perspective. For him, this solidarité can be represented by a mathematical function: the function is the variable “whose changes of magnitude result from those of another variable magnitude that, at least in a relative sense, takes the status of independent variable” (Cournot [1861] 1982: §52 tr). The “law of sales” precisely describes such a série solidaire. The concept of “independent” series is also intuitive. Two examples given by Cournot are clear illustrations of it: Nobody can seriously think that while stamping on the ground he disturbs the sailor who travels on the antipodes, or that he shocks the system of Jupiter’s satellites. (Cournot [1843] 1984: §40 tr) It is not impossible that an event that happened in China or in Japan exerts a certain influence on facts that happen in Paris or in London; but generally, it is certain that the way a bourgeois from Paris organizes his day is not influenced by what happens at the same time in a city of China where Europeans have never been. There is here something like two small worlds, and in each of them we can observe a relation [un enchaînement] from causes to effects that develop simultaneously, without any connection between them, and without any significant mutual influence. (Cournot [1851] 1975: §30 tr) “Independent” series are thus causal chains that do not intersect. At this stage, Cournot depicts a world including what he calls “small worlds”: each of them is ruled by causality, and they follow independent paths. In some circumstances, however, some of these “small worlds” intersect: independent series can cross. This crossing is a key to the understanding of a major feature of Cournot’s worldview: although the world is ruled by causality, it is not completely deterministic and chance exists. Chance would even be an essential component of the functioning of the world: “chance [hasard ] rules the world, or more appropriately it plays a role, and a notable role, in the government of the world” ([1843] 1984: §45 tr). Chance is defined from the

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previous elements as “the combination of independent causes, for the production of a determined event” ([1843] 1984: §240, #1 tr).53 More explicitly, [T]he idea of chance [hasard ] is the idea of a crossing of facts which are rationally independent, a crossing which is in itself only a pure fact, to which no law or no reason can be attributed. (Cournot [1861] 1982: §59 tr) We can see here that for Cournot, chance is not relative to the ignorance of true causes: it has no subjective foundations54 ([1851] 1975: §31–2). Against Laplace, he claims that a superior intelligence would find no determinism where we see chance. Chance is thus “the fortuitous, unpredictable collision of structured systems [ensembles], events and processes that were previously making their own way without any interference” (SaintSernin 1995: 10 tr). Yet, chance takes several shapes in Cournot’s work: it can depict an event – a collision – that has no major importance on a system, but also a more serious shock that affects the system and leads to a structural change. This is particularly important: as long as chance exists, the world can be characterized by the emergence of novelty. Then, historical time matters, and science has to deal with what Cournot labels “the historical data,” or more simply “history”55 – this “material of continuous weft, on which the accident embroiders its variations and laces” (Mentré 1908: 443 tr). Two points can be deduced from this idea. First, historical time reflects at the same time shocks between independent “small worlds” and regularities produced by causal laws – in other 53 One famous example nicely illustrates this idea: “A tile falls from a roof, whether I walk or whether I do not walk in the street; there is no connection, no solidarity, no dependency between the causes that lead to the fall of the tile and those that led me to go outside home to post a letter. The tile falls on my head, and the old logician is definitely out of order: this crossing is fortuitous, or occurs by chance [par hasard ]” (Cournot [1875] 1987: p.175 tr). 54 In Chapter 4, we shall see that by contrast, Jules Regnault associated ignorance and chance. 55 “A certain mix of necessary laws and accidental or providential facts is what motivates the use of the word history, in the order of Nature as in the order of humanity” (Cournot [1861] 1982: §524 tr).

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words, data include irregular and constant factors that the scientist has to identify and to separate.56 Second, from the fact that deterministic causal chains can be perturbed, the existence of chance constitutes an obstacle to the knowledge of the past and to forecasting, i.e. to “induction,” as previously seen in section 2.2.3. This coexistence of chance and causality explains the nature of Cournot’s economics. In the real world, independent “small worlds,” free from chance and historical time, would exist and could be isolated. It would thus be possible to apply the idea of causal relationship within the frame of each of these “small worlds.” The “law of sales” illustrates this situation. It takes the shape of a causal relationship between demand and price within a “small world”: the “commercial machinery.” The law is deterministic in nature, although two kinds of chance can be thought in it. First, a chance relative to individual behavior, but such a chance is neutralized at two levels: all the individuals have a close behavior, and more importantly here, the variables that define the law are annual averages, which neutralize individual particularities. Second, the “law of sales” could be subject to more global kinds of chance, which are relative to the system or to the society as a whole.57 But Cournot also neutralizes this kind of chance: his analysis, remember, only applies to “a very advanced state of civilization” ([1838] 1927: §20), and the “law of sales” relies on a theory of social history according to which perfectly organized markets would triumph in the long term. 2.3.2. The “end of history”: Why economics becomes “social physics” For Cournot, the world is indeed far from chaos ruled by chance: 56 This explains the importance for Cournot of what we can retrospectively label time-series decomposition, and averages play an important role here. However, we shall see in Chapters 3 and 4 that Briaune and Regnault analyzed more precisely that issue. We can note that in Chapter 2 of the Recherches, Cournot mentions the idea of a decomposition of data as functions of time: “as in astronomy, it is necessary to recognize secular variations, which are independent of periodic variations” ([1838] 1927: §11). 57 Structural shocks could delay the emergence of a stable state of societies. Ménard (1978) explains the way Cournot was influenced by the political disorders that occurred in France in the mid nineteenth century (not to speak of the French Revolution of 1789).

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chance is tamed in the long term, and the society would reach a final state, which would be both harmonious and stable. This alleged “end of history” contains the solution to our previous puzzle: Why is the “law of sales” based on no observed data, although Cournot had in mind its inference from data? The evolution of societies would be characterized by the succession of three periods: the “chaotic” or “prehistoric” period, ruled by chance; the “historical” period, a purely transitory period during which the organization of society develops; and finally the “post historical” period, during which chance vanishes. These three periods are exposed by Cournot as follows: 1. a chaotic period, of undefined length a parte ante, during which the phenomena would have followed each other without any regular law, until the appearance of a combination which gives a beginning to the formation of a regular order, by the play of internal forces and mutual reactions between the various elements of the system; 2. a period that we can label genetic, during which the system gradually got closer to the final conditions of stability, permanence or regularity to which it had finally to arrive; 3. and a final period, of undefined length a parte post, unless causes exterior to the system and that we cannot guess ruin its order and economy. (Cournot [1861] 1982: §194 tr) The “prehistoric” period is characterized by the domination of instinct over reason, by the domination of “vitalisme,” if we refer to the title of Cournot’s 1875 book. During that period, societies are viewed as organisms whose action would be irregular. But a time would come when these primitive forms generate mechanisms capable of organization. We would then enter the second and transitory period, characterized by the rise of institutions and traditions, mainly by the way of politics and religion. The improvement in organization would then progressively pave the way for the third period, which originates in the “movement, often hidden, of the civilizing trend which has waited until our epoch to begin to reveal to every eye its irresistible strength” ([1861] 1982: §541 tr). This “final” period is crucial to understand Cournot’s economic analysis. During this period, indeed, “the general conditions of

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civilization progressively prevail over the individual causes that can accelerate or trouble the course [of history]” (Mentré 1908: 452 tr). More precisely, Cournot notices that during the century in which he lives the notion of society gains in precision and tightens the links between individuals. Human rights are respected [s’imposent au respect], juridical regimes are more accurately defined, civil institutions more flexible. The spirit of association is developing. Economic interests are more and more important in the scales of the contradictory concerns of the human decision. They dominate almost per se the rivalries; the passions of another kind decline. In every occasion the points of view of the economist tend to dominate. (Bompaire 1931: 97 tr) This highlights the foundations of the “law of sales” and of the situation of “unlimited competition” that Cournot appreciates.58 During this period, the individual has no influence on society or on the market; instincts leave room for experience, logic, and calculus; mechanism and order characterize society; and the regularities produced by the whole acts of individuals – i.e. by the system – become significant. A rational era would then open: [History] progressively leads humanity to a final state in which, as far as the domain of the organization of societies is concerned, the elements of the civilization strictly speaking have been taking a dominating influence on the other elements of human nature (by the help of the continuous intervention of experience and general reason), and consequently all the original distinctions tend to disappear, the influence of previous historical facts tends to weaken, and the society tends to be arranged like the beehive, according to quasi geometrical

Cournot also had a predilection for “unlimited competition” on the supply side, although he mainly remains known for his analysis of monopoly or duopoly. 58

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conditions, whose essential conditions can be noticed by experience and demonstrated by the theory.59 (Cournot [1861] 1982: §541 tr) It would then be possible to speak of social sciences, of social physics, of social arithmetic. There are here facts to gather methodically and in time, ratios, laws to discover by a patient investigation, theories to devise by the appropriate use of reasoning, sometimes, or experience, other times. Such sciences include, as the physical or the natural sciences, an indefinite progress, whatever the vicissitudes of systems in philosophy, morals, politics; and even their true nature, their real impact will be revealed the more the importance of moral and political influences will decrease and then clear the structure and the mechanism of societies. (Cournot [1872] 1973: p.325 tr) This “final” period is characterized by the “masses”; “the individual instincts cancel each other, and only the global effect [effet d’ensemble] remains” (Mentré 1908: 462 tr).60 We are brought back to the foundations of the “law of sales.” Chapter 4 of the Recherches opens with a pivotal precision: Cournot analyzes an epoch in which “the influence of the initial conditions is entirely gone” ([1838] 1927: §20), and his construction of the law only applies to “a very advanced state of civilization” ([1838] 1927: §20). This is, precisely, the perfect market the era of “social physics” would lead to, this “territory of which the parts are so united by the relations of unrestricted commerce that prices there take the same Similarly, “an increase in the perfection of human societies, specifically labeled civilization, tends towards the substitution of living organism for the calculated or calculable mechanism, of instinct for reason, of the movement of life for the stability [fixité] of arithmetical and logical combinations” ([1861] 1982: §212 tr). 60 As Ménard (1978: 203 tr) notes, “it is then possible to understand more precisely the way man can, as a social product, be considered a point of the system.” We then also understand why, for Cournot, the axiom “each one seeks to derive the greatest possible value from his goods or his labour” ([1838] 1927: §20) results from the system, and why the macrostructure creates the microstructure. 59

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level throughout, with ease and rapidity” (Cournot [1838] 1927: §23, footnote), with a large number of individuals transacting: The extension of commerce and the development of commercial facilities tend to bring the actual condition of affairs nearer and nearer to this order of abstract conceptions, on which alone theoretical calculations can be based, in the same way as the skillful engineer approaches nearer to theoretical conditions by diminishing friction through polished bearings and accurate gearing. (Cournot [1838] 1927: §2) During this “final” period, observation would make sense: then, remember, there would be “facts to gather methodically” and “ratios, laws to discover” ([1872] 1973: p.325 tr) – then, averages could reveal the mathematical regularities of the “commercial machinery” and the “law of sales” could be fully identified from observed data. This is also the moment when “it is possible to calculate the precise results of a regular mechanism” (Cournot [1861] 1982: §542 tr), i.e. the moment when the “law of sales” can become the instrument for maximizing the return of the “commercial machinery.” We can now understand why Cournot used no data in the Recherches, although his reasoning leaves a central room for statistics and is econometric in substance: he thought that by 1838 France “has not yet reached a practically stationary condition” ([1838] 1927: §21), and the “law of sales” thus depicts the society’s destiny. The use of empirical averages would only be relative to a future final state, once societies would be in a stable state,61 in accordance with natural order. It is thus in this “final” state of societies that the combination of mathematics and statistics – Cournot’s ideal in science – could take shape. Then, the mechanical and mathematical nature of the economy would triumph; then, the range of application of statistics would open. In that sense, the “law of sales” “supposes history – and moreover an oriented history – but it can only be obtained by the suppression of history” (Ménard 1978: 191 tr). In that respect, Cournot is a typical author of his time: as numerous economists of See also Cournot ([1863] 1981: Chapter VI). The idea that Cournot’s Recherches leaves no room for statistics thus only deals with the tip of the iceberg.

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the end of the eighteenth century and of the nineteenth century, he puts forward a finite history (Foucault ([1966] 1994). But in turn, another question immediately emerges: How can this convergence toward the “final” state be explained? 2.3.3. “The hand of God” In the Recherches, remember, Cournot writes that “the progress of nations in the commercial system is a fact in the face of which all discussion of its desirability becomes idle; [we are here down] to observe, and not to criticise, the irresistible laws of nature” ([1838] 1927: §2, translation revised). Basically, for Cournot, scientific instruments are attempts to discover nature and natural order, to identify and to understand “the heart or the substance of things [which] is for us full of obscurity and mysteries” ([1851] 1975: §1 tr). More explicitly, he explained that “it is not in accordance with a law of our intelligence that Nature has realized on a gigantic scale the grandiose phenomena to which the laws of general mechanics especially apply” ([1861] 1982: §514 tr). Behind this conviction, we find a certain subordination of the scientist to reality. Cournot’s approach owns an essential contemplative dimension: science is the study of a world that could only be contemplated and discovered by the elaboration of theories and instruments that could capture laws at work in the real world. To understand such a belief, we need to take into account his religious beliefs.62 Indeed, God plays an important role in Cournot’s worldview – as in the one of many scientists and economists of the eighteenth and the nineteenth centuries63 and of other natural econometricians, as we shall see in the next two chapters. Cournot recurrently refers to the “general plan of nature” (e.g. [1851] 1975: §66 tr), to the “general plan of creation” (e.g. [1851] 1975: §170 tr), to the “general organization [ordonnance] of the world” (e.g. [1851] 1975: §67 tr), and he perceives in them “the hand of God” ([1861] 1982: §332 tr). For instance, he writes in the Essai : [T]he more the number of general laws and independent facts reduces according to the progress in our positive knowledge, 62 63

These beliefs were clearly underlined by Moore (1905a and 1905b). See Clark (1992), Israel (1996), and Rohrbasser (2001).

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the more the fundamental harmonies and applications distinct from the principle of finality will reduce similarly; also, the more every fundamental harmony, taken in particular, will get value and convincing strength in its witness in favor of the finality of causes and of an intelligent coordination, because we necessarily evaluate the perfection of a system on the basis of the simplicity of principles and the fruitfulness [fécondité] of consequences; in such a way that, if it was possible for us to go back to a unique principle which would explain everything, this unique principle or this essential decree would be the highest expression of wisdom and supreme power. (Cournot [1851] 1975: §67 tr) Although temporarily ruled by chance, the world of Cournot is far from being forgotten by God.64 This world is characterized by the cohabitation of combinations, conjunctions, and independent causal chains. But it is not ruled by chaos: it remains ruled by causality and by a finality of a historical kind. Cournot had good reasons to refer to the expression “Man fidgets and God guides him” ([1861] 1982: §331 tr) – an expression that can also be found in Regnault (186365): he guides us in a world where God permanently acts and where history leads progressively societies to perfection, in accordance with In that perspective, Cournot is a rather original author: he incorporates an objective chance within such a worldview. But in the long term, chance is tamed: chance and God are not incompatible. For instance, he writes in the Exposition that: “It is true to say (…) that chance [le hasard] rules the world, or rather that it plays a role, and a noticeable role, in the government of the world; there is here no contradiction with [ce qui ne répugne en aucune façon à] the idea of a supreme and providential direction: the providential direction is only the concern of average and general results, secured by the very laws of chance; or the supreme cause arranges the details and particular facts to coordinate them in aims that surpass our sciences and our theories” ([1843] 1984: §45 tr). As he explains in the Considérations, “From the fact that Nature shakes incessantly the cup of chance [le cornet du hasard], and from the fact that the continuous crossing of chains of conditions and secondary causes, independent the ones the others, perpetually gives birth to what we call chances [chances] or fortuitous combinations, it cannot be deduced that God does not hold in his hands the ones and the others, and that it was not possible for him to realize them from an identical initial decree” ([1872] 1973: p.9 tr). 65 See Chapter 3. 64

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God’s design. Man is then, for Cournot, the “intelligent witness” of the “marvels” of the world, of which “he only has, most often, an imperfect knowledge” ([1851] 1975: §66 tr). We see here the idea that man – as well as the scientist – acts within the frame of an order which would be exterior to him66 and of which he would be the “concessionaire.”67 Such an idea applies to the “law of sales”: on the perfect market Cournot analyzes, the economic agent does not exist without the whole, without a structure that would historically triumph, and his influence is negligible. Otherwise stated, man himself is not the standard: the “secret workshop” of God68 is the unique yardstick. Ultimately, Cournot’s economic analysis relies on beliefs that belong to the domain of faith. 2.3.4. The foundations of Cournot’s worldview We can now understand why “philosophical probability” indicates that knowledge is only probable. Cournot never abruptly postulated a correspondence of knowledge with reality. “Philosophical probability” only offers probable answers: a scientific construction is one reflect, philosophically probable, of the real world.69 This leads to Cournot’s conception of truth. Truth, for Cournot, belongs to the domain of probability. As he writes in the Traité, “the truth in ideas and in the expression of ideas is in general something that admits approximation” ([1861] 1982: §50 tr). More explicitly, What are we looking for, what do we have to look for, in speculation as in practice? The truth, i.e. apparently the conformity of the notion that we have of things with the things themselves, the resemblance of an image with its type. But, if there are cases in which the truth consists of getting a precise point, a rigorous number, from which we cannot deviate 66 An order which is “independent of the way we conceive [ideas]” (Cournot [1851] 1975: §90 tr). 67 “From the king of Creation that he was or he believed he was, man rose or came down (as he wishes to hear) to the role of concessionaire of a planet” (Cournot [1872] 1973: p.422 tr). 68 Goethe 1830, in Saint-Sernin (1995: 142 tr). 69 See for instance Cournot ([1861] 1982: §404).

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without committing a demonstrable error, it happens far more frequently that the calculus leaves room for an estimation that could only be rigorously exact by an infinitely improbable chance [hasard ], and for which we do not even possess any rule [procédés] of regular approximation. (…) Getting in their whole truth, as far as it can be given to man, the understandable relations between things, choosing the sensible images the less imperfectly appropriate to the expression of such links, this will not be most often the handiwork of a calculator [calculateur ] who walks confidently, who applies methods, who combines or develops formulae, who links propositions; but the handiwork of an artist, a particular sense of whom, given by nature, improved by use and study, guides and supports the hand in the sketch of the plan as well as for the touch of details. (Cournot [1851] 1975: §405 tr) For Cournot, the search for truth should rule scientific work. This idea of truth is associated with the fact that “our representations are modeled on [se règlent sur ] phenomena, and not phenomena on our representations” ([1851] 1975: §394 tr): the aim is to get the conviction that ideas and science tell something about the real world, that theories and laws “capture” the real world. But for him, the search for truth relies on the criteria given by “philosophical probability.” This means that science thus ultimately depends on a set of beliefs and postulates, given by a worldview: [T]here will always exist the belief in a superior principle of order, harmony, unity, from which the phenomena and the laws that we can scientifically study are only the products or the manifestations, and which itself escapes from any sensible perception, from any scientific investigation. This belief will always persist, whether it is associated with dogmas and a religious symbol, whether it becomes free from them and is only relative to a judgment of reason applied to the contemplation of the marvels of Nature itself. (Cournot [1861] 1982: §195 tr) Science, for Cournot, is indeed founded ultimately on a set of postulates that does not belong to science but from which science is possible. In other words, science is based on ideas that “do not

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themselves fall within the scope of experience, do not constitute properly science, but the philosophy of science” ([1861] 1982: §404 tr). Science is the mistress of philosophy, of an “order of superior considerations” ([1851] 1975: §48 tr), an order that “does not have to be proved” and that “glides over the sciences” ([1861] 1982: §404 tr). If science is based on demonstrations, it relies ultimately on a worldview which belongs to the domain of a belief or of “culture” ([1861] 1982: §518 tr), and its foundation itself remains probable. CON CLUSION As this chapter shows, in the “law of sales” we find, at the methodological level, an association of the various ingredients of econometrics – mathematics, statistics, and economics. In this respect, Cournot’s methodology is in full conformity with his scientific ideal – the constant association of statistics and mathematics. Of course, one conclusion of this chapter is that, as far as the “law of sales” is concerned, Cournot did not fully practice this association: he considered imperfect the observed data of his time, in the sense that the law would only apply to a future state of the economy. In the next two chapters, we shall see the way JeanEdmond Briaune and Jules Regnault bypassed this problem. However, the way Cournot explained that it should be from observation and statistical instruments – mainly the average – that the mathematical relation between annual mean prices and quantities could be identified, and also the way this law could and should pave the way for the determination of optimal price, lead us to think that Cournot can be portrayed as an econometrician. What is even more interesting here is the way the “law of sales” is constructed. In this chapter, we have also suggested that, at the theoretical and the methodological levels, it gets its meaning from several postulates, from a worldview. The law cannot be separated from Cournot’s theory of social history: it depicts an “end of history,” a final state of the society when the market becomes perfectly organized, when the deterministic, mechanical, and mathematical nature of the social world triumphs, when the social world does not differ from the natural world, when God’s design and the natural order to which it corresponds prevail and can be fully revealed. The various instruments Cournot used, the criteria defining “philosophical probability,” which largely apply to the “law of sales,”

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and the economic knowledge he affords, cannot be separated from this worldview, and Cournot can be portrayed as a natural econometrician. As a whole, the “law of sales” is a statistical and mathematical instrument, depicting a natural order that would rule the social world and, more generally, the “system of the world.” Cournot’s economic and econometric work cannot be separated from his more general views on history, science, and philosophy of science; it cannot be separated from the more general worldview that guides his lifework. In that respect, his econometric ideas are mainly to be understood as the servants of a philosophical quest, in which a divine natural order plays a central role.

3. T he formation of agricultural prices, economic cycles, and natural order: Briaune’s social meteorology That the nation should be given instruction in the general laws of the natural order, which constitute the form of government which is self-evidently the most perfect. The study of human jurisprudence is not sufficient to make a statesman; it is necessary that those who are destined for administrative positions should be obliged to make a study of the natural order which is most advantageous to men combined together in society. It is also necessary that the practical knowledge and insight which the nation acquires through experience and reflection and insight should be brought together in the general science of government, so that the sovereign authority, always guided by what is self evident, should institute the best laws and cause them to be scrupulously observed, in order to pride for the security of all and to attain to the greatest degree of prosperity possible for the society. – François Quesnay, The General Maxims for the Economic Government of an Agricultural Kingdom The primary purpose of this Essay is to show that a known natural cause originates an agricultural cycle which in turn generates other economic cycles. – Henry Ludwell Moore, Generating Economic Cycles

One ideal in nineteenth century science was unity: the least secrets of the world would vanish once the hidden connections between the natural and the social phenomena would be unveiled and once a small set of identical laws governing nature as well as society would be discovered. We can see the triumph of such an ideal in the work of natural scientists (e.g. Laplace) and social scientists (e.g. Cournot, Regnault, Jevons): with the help of appropriate instruments, scientists could discover patiently the unitary “system of the world.” Unity operated at two basic levels. First, it consisted in seeing the social phenomena and the natural phenomena as intrinsically ruled by similar laws (e.g. gravitation, attraction), and this legitimated

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reductionism. Second, unity also took the shape of a direct linkage of social and natural phenomena, in such a way that the discovery of physical causes would give the ultimate explanation of social phenomena. One of the most spectacular illustrations of this second kind of unity was the construction of direct bridges between the natural world and the social world on the basis of a driving belt: agriculture. The agenda of a rather large body of work that spread during the nineteenth century and even during the early twentieth century was the search for exogenous causes (e.g. celestial movements, weather regularities) affecting agriculture and propagating in the economy. Such causes could in particular contribute to explain the cyclical movements in economic variables. We find this idea at least from the 1820s (with the work of George MacKenzie1) to the 1920s, with an interdisciplinary conference that was held in 19232 and in which Henry Ludwell Moore was involved (Moore 1923b). The most famous episodes of these “social meteorologies,” even of these “social astronomies,” are Jevons’ search for the influence of sunspot periodicities on agriculture and Moore’s identification of Venus’s movements as causing agricultural and industrial cycles.3 In this chapter, I shall focus on one of these linkages that spread in France during the nineteenth century.4 This linkage was “George MacKenzie’s hypothesis was that the preponderance of either solar east winds, solar west winds, lunar east winds, or lunar west winds in Britain determined the fate of the wheat crop for that season and that the nature of the winds and the price of wheat moved in a fifty-four-year cycle” (Klein 1997: 113). 2 See The Geographical Review (1923), and more specifically Clements (1923), Marvin (1923), and Moore (1923b). 3 See Jevons (1884) and Moore (1923a). On Jevons’ search for cyclical movements, see Maas (2005), Mirowski (1984), and Morgan (1990). In particular, Maas explains the way Jevons’s investigation is the product of the “mechanical reasoning” which characterizes his whole thought. On Moore’s investigations, see Morgan (1990) and Le Gall (1999). Many other authors were involved in this kind of social meteorology or astronomy, for instance William Beveridge (see Beveridge 1920) or Arthur Schuster (see Schuster 1898 and 1906). 4 See for instance Ducrotoy (1862). His aim was to identify “the constant and immutable order of the general laws of Nature” (1862: 11 tr). In particular, he showed the way the variations in agricultural prices would 1

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elaborated by the agronomist and farmer Jean-Edmond Briaune (1798–1885),5 nowadays a neglected and rather unknown figure. Two books he published deserve particular attention: Des Crises Commerciales, de leurs Causes et de leurs Remèdes 6 (1840), and most importantly Du Prix des Grains, du Libre Echange et des Réserves 7 (1857). In both books, Briaune analyzed economic and social crises that, for him, originate in the rise of agricultural prices: any considerable “disequilibrium” in agriculture would exert an influence on the industrial, the financial, and even the political spheres, and it could end up with general social crises. His agenda also includes the definition of economic policy rules; once the nature of economic crises is identified, means of controlling them could be devised. This led him to become involved in a typical debate of the period in agriculture: free trade vs. protectionism (Simonin 2006c and 2006d). The core of Briaune’s economic work is a set of mathematical laws relating supplying to price – that define what he labeled, in a general way, “the law of proportionality.” It stipulates that prices stir and gravitate around the mean price, positively interpreted as the “normal” price, according to the volume of supplying. Two features originate in variations in temperature. It can be noticed that from the deterministic laws he identified, he deduced the possibility of forecasts. 5 Jean-Edmond Briaune, whose work was rediscovered in 2003 by JeanPascal Simonin, was trained in law, and he became a lawyer. He rapidly switched to agronomy that he taught at the Institut Royal Agronomique of Grignon (near Versailles), of which he was head in the early 1830s. He was a leading figure in the community of mid nineteenth century French agronomists; he was also a farmer in the département de l’Indre (in central France) and got particularly interested in experimental farming. In particular, Briaune (1831, 1857) linked experimental farming and political economy, as David Ricardo did (see Morgan 2005). He published numerous articles on various issues (agricultural techniques, teaching, local institutions), and also two books that investigate more directly economic analysis, Des Crises Commerciales, de leurs Causes et de leurs Remèdes (1840) and Du Prix des Grains, du Libre Echange et des Réserves (1857). A full biography of Briaune can be found in Simonin (2006b), and Briaune’s various contributions are analyzed in the book edited by Simonin (2006a). In the English-speaking literature, Briaune’s name is (to my knowledge) only mentioned in Joseph Schumpeter’s History of Economic Analysis ([1954] 1994: 745). 6 This book will be referred to under the title Des Crises Commerciales. 7 This book will be referred to under the title Du Prix des Grains.

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of that law deserve special attention. First, at the methodological level, Briaune largely used statistics (in the sense of observed data and instruments, the most important being the average) and he claimed that the “law of proportionality” was a mathematical law. He also empirically checked its adequacy with observed data – stressing the need for a “concordance of theory with facts” (1857: 86 tr). We thus find in Briaune’s work the various components of econometrics. At this stage, it can be noted that Briaune’s methodology shares much with that of Cournot: the mathematical “law of proportionality” was inferred from observation. Second, the “law of proportionality” was dependent on a worldview in which, once more, determinism, unity, God’s design, and natural order – the “natural order of facts” (1840: 15, footnote 5 tr), in Briaune’s words – play a key role. This is particularly apparent in his investigations of the origins of agricultural crises: he wondered about the existence of periodic fluctuations in crops and prices – and thus periodic crises affecting the whole social world – and he identified the weather and “physical causes” as the culprits (1857: 122 tr). He thus ended up with a “social meteorology,” which was “demonstrating” that the economy was ruled by a regular and deterministic rhythm imposed by the natural world. In Briaune’s mind, these two laws – the “law of proportionality” and the fourteen-year cycles he found in his data – were natural laws, interpreted as parts of the natural order which would rule identically, and in an entangled way, society and nature, a natural order that would find its origins in God’s design. In this chapter, I shall focus on the way Briaune used instruments (mathematics and statistics) to analyze economic issues (the formation of agricultural prices and economic cycles) in an idiosyncratic perspective: the measurement and the identification of natural laws (mathematical in substance) ruling the economy. It is in that respect that his work belongs to natural econometrics. The chapter is organized as follows. Section 3.1 analyzes Briaune’s general views of the economy, seen as a “social body,” and in particular his emphasis on the search for causal chains ruling its functioning. Then, section 3.2 presents the methodological foundations of his approach, namely the use of statistics and mathematics. Sections 3.3 and 3.4 are devoted to an analysis of the mathematical relationships associating price and quantity that Briaune elaborated, the “laws of proportionality.” I shall also explain here the way statistics played a pivotal role in the construction and in

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the “test” of these mathematical laws. Finally, section 3.5 presents Briaune’s search for the cyclical movements that would affect the economy. This search led him to elaborate a “social meteorology”: the economy, and more generally the social world, would be ruled by a periodic meteorological cycle originating in the natural world and seen as the expression of an immutable natural order. In this section, I shall also analyze some of the economic policies Briaune advocated, which were considered means for respecting natural order. 3.1. T HE E CON OMY AS A BODY: B RIAUN E ’S SE ARCH FOR CAUSAL CHAIN S

In Briaune’s two books, economic crises are – at least metaphorically – approached in a physiological perspective: he saw the economy (and more generally the society) as a “body,” characterized by interdependencies and the existence of “symptoms” and “diseases.” These crises would arise in agriculture, and they would then propagate in the whole structure of the “body.” In that respect, one feature of Briaune’s work is the search for causal chains and for a causal structure. 3.1.1. Causalities in the “social body” For Briaune, the society would indeed be a “social body” (1840: 11 tr), whose various parts are interdependent. More precisely, the society would be constituted by interrelated organs and, at least in “normal” situations,8 its whole functioning would be characterized by a harmonious “equilibrium” – the structure would indeed work for the “common well-being” (1840: 18 tr). However, as any body, the society could also be affected by “symptoms,” “diseases,” and crises, in the physiological sense. From the first page of Des Crises Commerciales, the economy is analyzed in that perspective: The social body is, like the human body, subject to diseases [;] some of them can originate in external accidents and only induce a temporary trouble in the vital functions, whereas the We shall explain below this idea, which is connected to the way Briaune considered the average and its relation with natural order.

8

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other ones, caused by organic vices and becoming chronic, exert an influence on the constitution and the development of individuals and societies.9 (Briaune 1840: 1 tr) In many respects, such a representation of the economy shares much with the physiological analysis devised by Nicolas-François Canard,10 with the analogies with blood circulation developed by Quesnay (who also aimed at identifying and restoring a natural order), with Clément Juglar’s comparison of cycles and “diseases,”11 and even with the physiological basis of some early business barometers.12 For Briaune, the central part of the “social body” is agriculture – a central role that finds a justification in the importance of agriculture in the French economy of the time13 – and the “equilibrium” of the whole society would depend on agriculture. In particular, any agricultural “disease” would propagate into the whole society: agricultural crises would generate economic, financial, and even political crises. In that respect, agricultural crises would be “the most serious question of our social order” (1857: vii tr). The most interesting point here is that Briaune’s analysis of the economy and of the society is characterized by the search for causalities – in the sense of causal chains and even a causal structure.14 As in Cournot’s work, causality is here a pivotal concept. The ideas of harm and pain, in the medical sense, are recurrent in Briaune’s writings. See also (1840: 11). 10 See Canard (1801). 11 See Juglar (1862). 12 See Chancellier (2006a), who analyzes the physiological bases of the business barometers elaborated by Alfred de Foville, Franz Xaver Neumann-Spallart, and A. Julin. 13 During the period, the French economy was largely dominated by agriculture: in 1850, more than 60% of the working population was in agriculture (Asselain 1985: 54). 14 In Du Prix des Grains, he suggests the way an agricultural crisis generates, through causal relations, a general social crisis: “Then, in the trade of a superior order, stores are congested and it does not send any demand to plants. Deprived of their selling, they are forced to stop, to reduce wages that were already insufficient, and to reduce the number of their workers. New aggravation of the food crisis, new obstacle to the commercial movement, new stop of manufacturing labor. Thus, every effect becoming a cause, if the high price persists we reach from reactions to reactions the last 9

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However, whereas Cournot’s “law of sales” was relative to one série solidaire within one “small world,”15 Briaune has a predilection for the identification and the study of more global causal chains that could take into account the various interdependencies of the “social body.” In addition, he was only interested in timeless and ahistorical mechanisms – not to say laws – that could afford general explanations of the way the economy functions, and from which its deep structure could be unveiled and understood. This interest explains the way he rejected former explanations of the early nineteenth century crises. These explanations, he thought, were ad hoc and partial in the sense that they would not focus on the search for an ahistorical explanatory frame – they would not focus on the search for constant causes: The current crisis has been attributed to the excess of manufacturing, of credit, or to speculation on the stock market. (…) [I]f such are the true causes, they must have exerted an influence on the crises of 1811, of 1817, of 1827;16 because this periodic recurrence of the same harm necessarily leads to the existence of identical and permanent causes. Yet, nobody could see in these previous crises the alleged origin of the current crisis; and it is (…) somewhat illogical to see the origin of such effects (…) in different kinds of accidents. Against the general principle that searches the same cause in a series of identical effects, irrefutable proofs would be necessary, and such proofs are still to be afforded.17 (Briaune 1840: 4–5 tr) limits of the commercial crisis” (Briaune 1857: 6–7 tr). The last manifestation of the crisis would then be financial, even political. Briaune’s aim is then to reduce the ignorance relative to agricultural and commercial crises in order to maintain a political stability. Indeed, a “truth which spreads in masses calms the passions, stimulates foresight, and protects from misfortunes, the consequences of our faults and our ignorance; its first aim is to protect from harm, then to overcome it, finally to avoid it, or perhaps to solve it” (1840: 17 tr). 15 See section 2.3.1. 16 We can note that in his 1840 book, Briaune had not yet in mind a fourteen-year periodicity of crises (see section 3.5). 17 As Besomi (2006) explains, Briaune is to be included into the set of nineteenth century authors who shifted from crises to cycles.

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By contrast, Briaune was interested in universal explanations: to him, what matters are only immutable causal chains – the social world, ruled by an immutable natural order, would indeed be subject to no real evolution – and the search for causes that repeat regularly, not to say periodically, and that lead to similar effects.18 In accordance with this representation of the economy, Briaune was mainly interested in the search for the constant causes that would lead to crises. In this respect, he believed that such crises are rooted in a unique cause, the rise in the price of cereals: The excess in production begins where consumption stops; consequently, the rise in the one or the fall in the other leads to the same results, congestion (…). From these truths, it follows that if consumption suddenly stops, manufacturing leads to a congestion in stores, the congestion leads to a fall in the value of its goods, this fall alters the safety of security [gage], consequently credit; finally the realization of operations leads to the bankruptcy of the manufacturer or the ruin of the creditor; and, as everything is tied up, the harm develops in a geometric proportion until the cause stops.19 (…) [E]verything leads to wonder about the existence in our industrial society of a cause that, during more or less close epochs, stops instantly consumption. This cause, the common sense and the facts indicate that it is the periodic rise in the price of cereals. (Briaune 1840: 5–6 tr) Then, he tried to show this pivotal role of agricultural prices as well as the central role agriculture plays in the economic and the social world. This was his agenda in Des Crises Commerciales, although the “demonstration” remains very general.

From this, we can also guess that Briaune is looking for deterministic laws ruling the economy, as we shall see below. 19 See also Briaune (1840: 12). 18

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3.1.2. Agricultural prices and the economic environment In Des Crises Commerciales, Briaune constructed a table (see table 3.1), in which he compares the annual mean price of the hectoliter of wheat with the general economic and social environment between 1808 and 1840. From it, he concluded that: Years

Mean price of the hectoliter 1808 16 f. 58 1809 14 98 1810 19 68 1811 26 19 1812 34 33 1813 22 58 1814 17 33 1815 19 53 1816 28 31 1817 36 16 1818 24 65 1819 18 43 1819 to 20 16 60 21 18 65 22 15 08 23 17 20 24 15 86 25 14 80 26 15 23 27 15 97 28 20 44 29 22 34 29 21 29 31 22 41 32 23 89 33 18 13 34 15 08 35 15 07 36 15 28 37 16 46 38 17 91 39 21 50 40 23 13

Commercial and political observations

Commercial crisis Continuation The Restoration, weak business take off The Cent-Jours, invasion Beginning of the crisis Commercial crisis Business take off Commercial development Idem Idem Idem Idem Idem Idem Idem Beginning of the crisis Crisis Crisis Extreme intensity Continuation Business take off, cholera, armed riots Commercial prosperity Idem Idem Idem Idem Crisis Continuation of the crisis

Table 3.1 The annual mean price of wheat and the economic and political environment (1808–1840). Source: Briaune (1840: 13 tr).

reason, facts, everything demonstrates that the prosperity of trade is closely linked to the price of food, and that the rise in the price of wheat is the true cause of these commercial crises

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that periodically come back and ruin families, paralyze labor and demoralize the industry. (Briaune 1840: 16 tr) For him, the conjunction of political and agricultural crises would not be “a simple effect of chance” (1857: 13 tr): the history of the French political crises led him claiming that “in front of so strong and so recurrent proofs, it is difficult to deny the danger of the high price of grains” (1857, 25 tr). Yet, in the 1840 book, the demonstration Briaune offers is rather weak and it remains largely descriptive. This weakness probably motivated the analysis he conducted in Du Prix des Grains, in which he selected instruments from which the question of agricultural prices could be enlightened: he then turned to mathematics and statistics, and it is at this stage that he became involved in econometric ideas. 3.2. ON THE USE OF STATISTICS AN D MATHE MATICS Briaune’s agenda spread in three directions: we can only hope to find [the solution] through the knowledge of three general facts that dominate this question, namely: national production, the relation between price and supplying, and the mode of alternation of good and bad crops. As long as these facts are ignored or badly known, we can only walk randomly toward the solution desired. (Briaune 1857: 43 tr) In each of these directions, his aim is to identify “economic laws more or less ignored until now” (1857: vii tr). It is precisely in the identification of such laws that the methodological originality of Briaune fully appears. In particular, his investigations of “the relation between price and supplying” are based on observation (as well as on postulates that we shall present and discuss below) and, with the help of statistical instruments (in particular the average), they aim at identifying and measuring mathematical laws that would explain the formation of agricultural prices.

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3.2.1. Observation: “extracting facts from their obscurity” 20 In his books, Briaune explicitly referred to no statisticians. However, his writings share much with the nineteenth century statistical fevers21 exemplified by Quételet’s “social physics.” Briaune’s 1857 book is indeed characterized by a constant use and analysis of observations. From “the progress in statistics” (1857: 52 tr), it would be possible “to shed a totally new light on the most serious question of our social order, food” (1857: vii tr). In addition, for a theory to be accepted, “the sanction of practical facts is necessary” (1857: 85 tr).22 His motto is then: In economics, as in every study, it is necessary to stay among facts; otherwise, we do not rise in space, we fall into the void (…). We do not have to stay among assumptions and abstractions, but among the facts as history and the practice of life present them. (Briaune 1857: 68 tr) More precisely, observation operates at two levels: to use contemporary words, it would help the formulation of “stylized facts” that, in association with postulates, should contribute to open the way to general explanations, and from observation the validity of such explanations could be checked and confirmed. But Briaune never thought that laws could be discovered from a passive observation of data: in contrast to a part of French statistical economists of the time, who had a predilection for the pure collection of data, his aim is to use statistical procedures: then, it would be possible to make data “talk” (1840: 14, footnote 6 tr). 3.2.2. Briaune’s use of statistical instruments and mathematics During the nineteenth century, the statistical instrument par excellence Briaune (1857: 43). See Porter (1986 and 2001) and Klein and Morgan (2001). 22 The same idea (though it was exposed in a less sophisticated way) can be found in Des Crises Commerciales: “It is thus by the incontestable proof of facts that the demonstration of the most important truths are obtained (…). [T]hen we have to recognize the evidence of facts or to deny light” (1840: 12–3 tr). 20 21

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in socioeconomics was the average,23 which was, as Quételet’s work exemplifies, tied to the search for order, constant causes, and laws. In this respect, Briaune is a typical product of this context. The main statistical instrument he used is indeed “the law of averages” (1857: 77 tr) and, in many respects, he follows Quételet’s views on the average: the mean value would be “very close to truth” (1857: 45 tr), it is positively tied to equilibrium, harmony, and moderation, and seen as the sign of stability and order. This explains why the mean price is positively interpreted by Briaune as the “desirable price,” as “the expression of a normal supplying” (1857: 77 tr).24 By contrast, any variation from the average was considered an accident, a vice, or an error.25 However, it is necessary to dig deeper here. Two features of the average matter here. First, with statistics and in particular with the average, Briaune thought that it was possible to identify an order26 and more particularly “the natural order of facts” (1840: 14, footnote 6 tr). Second, although he is less explicit on that point than other authors (e.g. Regnault, see Chapter 4), the use of the average is closely associated with what we would label now time-series decomposition. The average was considered an instrument for operating a separation of the long-term constant causes and the accidental causes that concern the short term. It would reveal and catch the constant causes around which accidental causes stir but compensate27 in the long term. In sum, the average is here, as in the work of other nineteenth century scientists,28 a moral and philosophical ideal: it is associated with the harmonious laws that would rule the world in the long term. Last, but not least, mathematics is an important component of Briaune’s methodology. In Du Prix des Grains, he put a great emphasis on the mathematical nature of his “law of proportionality” 23 See Armatte (1991), Boumans (forthcoming), Le Gall (2006c), and Porter (1986). As Chapters 2 and 4 show, the average was also the favorite statistical instrument of Cournot and Regnault. 24 The fact that Briaune referred once to an “intrinsic value” (1857: 87 tr) illustrates the idea of a stable price around which observed prices stir. 25 Note that it is only with Francis Galton and Karl Pearson that deviations became positively interpreted. See MacKenzie (1981) and Porter (1986). 26 Such an order was of course ruled by causality, as seen above. 27 See Briaune (1857: 45, 51, and 120). 28 See Porter (1986).

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of price to supplying: this proportionality of price (…) can be proved so rigorously by the application of economic laws that it would be possible to translate its demonstration in a purely mathematical language. (Briaune 1857: 85 tr) In addition, his empirical verifications led him claiming that this mathematical law would be “the very painting of practical facts and of the actions they determine” (1857: 104 tr). This last quotation illustrates an important feature of Briaune’s thought. Although he rarely discussed methodological and philosophical issues, at least in comparison with Cournot and Regnault, he considered the real social world structured and governed by mathematical schemes, and for him the “law of proportionality” owns an ontological dimension.29 Yet, Briaune’s use of mathematics deserves more attention. In his 1857 book, Briaune used algebra; parts of his reasoning are mathematical; and, as we shall see in sections 3.3 and 3.4, his empirical comparisons of theoretical and observed results show that his “law of proportionality” is a mathematical relationship. However, mathematical relations never explicitly appeared in his work.30 Two explanations can be given here. First, he considered Du Prix des Grains a pedagogical book, which should work for the diffusion of knowledge and the reduction of ignorance (that of the government, of agronomists and economists, and of farmers; see Favreau 2006). Several years before the publication of that book, he precisely wrote: I always welcome books that make science without xs and without formulae. To notice a scientific fact, it is necessary to submit it to scientists and to speak their language; by contrast, to popularize, it is necessary to speak the language of everybody. (Briaune 1848, 541 tr) Second, and the same will largely apply to Regnault (see Chapter 4), mathematics is never ultimately a tool for demonstration here. Rather, Briaune tried to prove results on the basis of other 29 30

We analyze this point in more details in section 3.4.2. In Chapter 4, we show that the same applies to Regnault.

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foundations: from his worldview, he believed that the world was mathematically written and that the role of observation was to reveal its constitutive mathematical laws. In addition, from his unified conception of the world, he felt free to offer economic translations of laws such as gravitation and attraction without mathematical demonstrations or proofs as such. 3.3. T HE “ LAW OF PROPORTION ALITY” In Du Prix des Grains (1857), Briaune’s goal is to identify a macroeconomic law applying to the wheat market and relating price to supplying. The result, the “law of proportionality,” offers a nice illustration of Briaune’s econometric perspective: it is a mathematical law, obtained with the help of observation and statistical instruments. I shall first expose the way the law was constructed, and then I shall turn to its statistical test. 3.3.1. The relation between price and supplying The “law of proportionality” was constructed in three main steps. In a first step, Briaune determined the mean price of wheat (18.40F).31 This price would correspond to “a normal supplying” (1857: 75 tr), sufficient to satisfy demand. At this stage, it should be noted that this “normal supplying” takes into account a stock that he labels a “floating reserve” (1857: 74 tr). Relying on observation, Briaune explained that the estimated amount of the reserve is 60 days. Such an amount (i.e. a supplying of 365 + 60 = 425 days32) would make possible the satisfaction of demand and thus the “normality” of prices, represented by the mean price. In a second step, Briaune looked for a general relation between price and supplying, “a proportionality of prices to each day of surplus or of deficit in supplying, by the application of economic The data Briaune used are the monthly prices of wheat for agricultural years stretching from 1804–1805 to 1854–1855. This mean value, which would represent a harmonious and “normal” state, is determined after the elimination of years for which price is seen as exceptional. A reason for such elimination is probably Briaune’s distaste for high deviations. 32 Briaune explained that “a normal supplying has to present a quantity of wheat to be sold which is sufficient for 14 months of food of the nonproducers” (1857: 75 tr). 31

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laws” (1857: 78 tr). He indeed applied to the formation of the price of wheat a “universally recognized” and “elementary principle of political economy”: “the price of goods rises or falls in proportion to the quantity supplied and demanded” (1857: 67 tr). But he exposed the principle in a now unfamiliar way: For each good of a recognized usefulness, supply and demand have a natural tendency toward each other. But such a tendency is not always equal, and each of them progresses in direct proportion to its mass and in inverse proportion to the one that comes toward it. In this progression, as they move forward, supply reduces the estimation of the good and demand increases it. These constant truths in economics strike anybody who sets foot on a market and who observes a transaction. (Briaune 1857: 79 tr) The reasoning is based on a move of supply and demand toward their meeting point, toward the equilibrium, and this move would be a function of the magnitude – the “mass” – of each quantity. Then, in a third step, he quantified such a move, and he proceeded as follows. The “normal” price – i.e. the mean price for Briaune – would occur when supplying is exactly sufficient to satisfy demand (425 days). In this case, he explains that the price would result from an identical move of supply and demand: As the sum of the quantities supplied and of the quantities demanded was in both cases equivalent to 425 days of food, supply and demand had thus covered, in proportion to their equal masses, an identical distance, exactly proportional, that is, 425 degrees that form the total sum of 850.33 (Briaune 1857: 79 tr)

Briaune’s reasoning can be visualized as the move of points on a onedimensional figure: Supply Demand

33

0

425 p=18.40 However, such a figure cannot be found in his book.

0

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One “degree” represents one day. Since a “normal” supply and demand of 425 would lead to the price of 18.40, Briaune deduced – using a rule of three – that one “degree” represents a variation of 18.40 425

0.043 in price (1857: 79). In addition, since any variation of

one “degree” in supply would induce a similar variation in demand, the total variation in price would be 0.043 u 2 = 0.086. From this, he proposed a general rule for the determination of the price as a function of the volume of supplying: As we see, the calculation will be relatively the same with two, three, four, or a more considerable number of days of surplus; and the price of the hectoliter will continue to decrease 0 fr. 086m per day of surplus in the normal supplying.34 (Briaune 1857: 81 tr) The theoretical price is thus: p = 18.40 – [0.086 u De], De denoting the days of excess in the reserve. In a similar way, in case of shortage, we have: p = 18.40 + [0.086 u Ds], Ds denoting the days of shortage in the reserve.35 These relations give what Briaune labels the “law of proportionality.”36 These relations deserve two comments. First, at the methodological level, we see here the way the mathematical “law of proportionality” directly incorporates a statistical component, the observed mean value. Second, at the analytical level, the law “m” refers to the French word millième, i.e. “thousandth.” The cases in which supplying is lower than 365 days are examined in section 3.4. 36 As explained in section 3.2.2, Briaune presented the law in a literary way, although he clearly explained the way it is a mathematical law: he indeed wrote, remember, that “this proportionality of price (…) can be proved so rigorously by the application of economic laws that it would be possible to translate its demonstration in a purely mathematical language” (1857: 85 tr). 34 35

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stipulates that prices stir and gravitate around the mean value – considered a stable value – according to supplying. The “law of proportionality” depicts, at least implicitly, a kind of gravitation of observed prices around the mean value.37 3.3.2. The test of the law Briaune put a particular emphasis on the need for verifying this result: “[F]or this theory of proportionality of the price of wheat to become included among economic laws, the sanction of practical facts is necessary (…). [I]f these (…) proofs are given, the agreement of theory and facts is complete” (1857: 85–6 tr). More precisely, he mentioned at least one “test”: “[The sanction of practical facts] will be obtained if [facts] demonstrate (…) [t]hat each day of deficit in this reserve leads to an increase [of ] 0 fr. 086m until its lasting” (1857: 85–6 tr). This test enlightens Briaune’s confrontation of theory to facts. It includes two steps. First, Briaune operates several historical verifications of the matching of theoretical price to observed price. For instance, The year 1831–32 followed five bad crops that have consumed the surplus of 1827 and import (…). [F]rom August 1831 to March 1832 the prices remained constant at 22 fr. 50 c. This high price was thus caused by the difficulty in satisfying in time consumption. Then, as lofts were emptying, this difficulty was growing, prices rose from March to the harvest in such a way that the mean price was 23 fr. 25 c., as close as possible from the final price of 23 fr. 56 c. given by the formula. (Briaune 1857: 90–1 tr) This historical verification relies on no formal testing procedure: in this respect, it can seem rather flimsy. Yet, one has to wait the first decades of the twentieth century to find in econometrics more formal procedures.38 Anyway, we can also note in Briaune’s statement a very enthusiastic assessment of his theoretical law. His views on economic cycles afford more light on this idea (see section 3.5). 38 For instance Moore’s tests of peaks on a periodogram (Moore 1914); see Cargill (1974) and Le Gall (1999). 37

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The starting point is the year 1840–41, leaving at the end of July a normal floating reserve of 60 days with 150,000 hect. per day 9,000,000 hectol. If the harvest of 1841 had been equal to consumption of one year, (…) the supplying would have remained complete and the mean price at 18 fr. 40 c. From the mercuriales it was 19 fr. 30 c.; and the difference of 0 fr. 90 c. between both prices indicates, from the formula, a shortage of 10 days plus a part of the reserve, due in part to the harvest and to a weak export. It was thus reduced of 1,575,000 and was, on August 1, 1842 7,425,000 Import, which was zero the previous year, brought in 1842–43 a supplement of 1,200,000 The reserve was 8,625,000 The deficit would thus have been of only 3 days and half if the harvest of 1842 had been equal to the needs for food. But the price indicates a difference of 21 days below a normal supplying; 17 days and half have once more to be deduced from the reserve or 2,625,000 and it was reduced on August 1, 1843 to 6,000,000 Import of the year added 3,098,000 and the reserve was 9,098,000 But the price of 20 fr. 63 c. indicates a shortage of 26 days, including some re-exportation; and the harvest of 1843 led to a decrease of the reserve of 3,900,000 On August 1, 1844, its amount was only 5,198,000 Import added 780,000 The mean price of the year 1844–45 was 18 fr. 60 c., indicating a normal supplying apart from 2 days and a fraction. Consequently, the harvest of 1844 brought an overabundance of 18 days or 2,700,000 and the reserve was on August 1, 1845 8,678,000 In addition, import of 1845–46 in our harbors was 3,000,000 That is, on August 1, 1845 11,678,000 On August 1, 1846, prices reached 22 fr. 92 c., indicating that the reserve was reduced to 5 days and a quarter and that the harvest of 1845 led, as a lot of informed men claimed, to a shortage of more than 71 days, that is 10,891,000 and the reserve was reduced on August 1, 1846 to 787,000

Table 3.2 String calculation for the period 1840–1846. Source: Briaune (1857: 93–6 tr).

Second, Briaune realized a more sophisticated “test.” He indeed proposed a string calculation from 1840–1841 to 1845–1846 (table 3.2). He proceeded as follows. For the first year, he deduced from the observed price – the “mercuriales” – the theoretical volume of the reserve. Then, from one year to another, he computed the theoretical volume of the reserve given the theoretical volume of the reserve for

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the previous year and the observed values of price, imports, and exports. He finally compared the result with the observed volume for the final year: in August 1846, the theoretical volume of the reserve represents 5.25 days, and this would exactly correspond with the observed data. From this “test,” he concluded that the theoretical relation – in his words, “the formula given by the theory” (1857: 92 tr) – was reproducing correctly observed data; it would be a “certified law” (1857: 118 tr). His conclusion was indeed quite enthusiastic: An economic truth has perhaps never been established in a more certain, a more concrete, and a more incontestable way. (Briaune 1857: 98 tr) He could then see the “law of proportionality” as capturing the true functioning of the world: for him, remember, “the theoretical explanation has been the very painting of practical facts and of the actions they determine” (1857: 104 tr). 3.4. T HE LASTIN G OF THE RE SE RVE : ON “ AUCTION S” AN D “ DOUBLE PROPORTION ALITY” In the situations analyzed previously, the quantity of wheat was sufficient for the satisfaction of usual consumers: any shortage was only affecting the reserve, and the quantity offered for consumption was remaining at least greater than 365 days.39 By contrast, Briaune explained that as soon as this quantity becomes lower than 365 days, and the price greater than 23.56, some consumers have to be excluded from the market: [W]hen shortage occurs, a fraction [of consumers] has necessarily to be pushed from the use of wheat to that of inferior grains, and it will be this fraction that, at the end of sacrifices, can no more reduce on other needs. The means that in anarchy would be strength (…) is in the social state the use of fortune. (Briaune 1857: 105 tr) In these situations, demand (from consumers) was of course always satisfied. 39

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This exclusion takes the shape of what Briaune labels “auctions,” and it leads to the formulation of an extended version of the previous “law of proportionality”: the law of “double proportionality,” which was also “tested.” 3.4.1. The law of “double proportionality” For Briaune, when the price of wheat becomes greater than 23.56, some of the usual consumers are excluded from the market. He thinks that this exclusion results from a competition between consumers, which he labels “auctions.” These consumers would have to turn to “inferior” grains, i.e. grains of a lower quality, which are however substitutes for wheat – and this is an illustration of the way the various parts of the “social body” are interdependent.40 The result is a generalization of “auctions”: the consumers who are excluded from the market of wheat turn to markets of inferior crops; in turn, these markets know an auction that “from degree to degree leads poorest people at the bottom of the alimentary scale” (1857: 105–6 tr). The prices of grains are thus determined sequentially from wheat to inferior grains: “any determined price becomes the basis of an auction that, in turn, becomes the basis of another one” (1857: 106 tr). He indeed deals with the determination of the price within the frame of interdependent agricultural markets, with substitution effects between them. The idea of such an interdependence recurrently appears in Du Prix des Grains. For instance, “[w]heat (…) constitutes the most considerable part of the mass of grains put on sale. On the other side, man prefers it to the other ones and abstains from it only if it is difficult to get it (…). However, all of the cereals can be used for the consumption of humans, even those that are usually left for domestic animals. The latter, at one or two exceptions, can do without grains, and consequently there is, during the worst years, a mass of starches consumable by humans largely superior to their needs. In France, for instance, where annual consumption of wheat is currently 65 million hectoliters, weighting in average 5 billion kilograms, animals are given more than one billion and a half of wheat, rye, barley, corn and oats, not mentioning buckwheat and potatoes. In this state of affairs, the demand for wheat can thus always diminish, if we accept to go down one step in the scale of cereals; and its price, which rules that of other grains, does not rise by the necessity of living, but by the preference of taste, habits and the desire for well-being” (Briaune 1857: 68–9 tr). 40

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In such situations, two effects would contribute to the determination of the price – in Briaune’s own words, a “double proportionality” would exist. The first “proportionality” refers to a “supplying effect,” which is measured by an extended version the previous “law of proportionality.” It corresponds to the rise in price resulting from the reduction of crops, and given by the formula: P = 18.40 + [0.086 u 60] + [0.086 u DCs ],

DCs denoting the shortage in consumption (60 refers to the shortage in the reserve). The second “proportionality” refers to an “exclusion effect” that would occur as soon as supplying is lower than 365 days. Briaune explained this effect – in a rather convoluted way – as follows: The reason of the last proportionality is easy to understand (…). This number [the number of consumers to be excluded] is in direct proportion to the sum of days of shortage in food, and the day can be taken as its exact expression. But as the exclusion has no absolute character, and is only a necessity on each market, if we take one market per month, the auction needs only to exclude a number of consumers proportional to the monthly shortage or the twelfth of the year. Indeed, if this shortage is 60 days, with the preservation of 5 days per month of the consumption in excess, the equilibrium is reached back at the end of the year. The auction only acts with a strict necessity and progresses consequently as 5 times 0 fr. 086, then the next month as 5 times 0 fr. 086 more than the first one, and so forth. (Briaune 1857: 106–7 tr) An example can shed some light on this idea. Consider an initial situation characterized by a shortage of 120 days (a shortage of food of 60 days, a strict lasting of the reserve, and no imports41); at the beginning of the agricultural year, the price would be: P = 18.40 + [0.086 u 60] + [0.086 u 60].

41

Imports can indeed lead to an interruption of auctions.

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In this case, the theoretical price of wheat is thus 28.72. However, this price is only the initial price, at the very beginning of the agricultural year: in the previous quote, Briaune writes that “if this shortage is 60 days, with the preservation of 5 days per month of the consumption in excess, the equilibrium is reached back at the end of the year” (1857: 106–7 tr). Since the available quantity corresponds to 305 days, annual consumption has to decrease of 60 days, i.e. 5 days per month. It is on that basis that an “exclusion effect” would occur during the agricultural year: an “auction” between potential consumers should lead to a progressive exclusion of consumers which would correspond to 5 days per month of consumption, in such a way that demand could adjust to supply. In addition, Briaune assumed that “every consumer excluded from his usual food comes back on the following market42 by calculus and taste” (Briaune 1857: 106). During each month of the year, a more and more considerable number of consumers would thus have to be excluded. Table 3.3 presents the evolution of “auctions” during one year, on the basis of the previous initial conditions (a shortage of 120 days). Initially, in September the theoretical price is 28.72. During the next month (October), consumption has to be 5 down. An “auction” occurs, leading to the theoretical price POct : POct = 28.72 + [0.086 u 5] = 28.72 + 0.43 = 29.15. In November, the monthly consumption has again to be 5 down. In comparison with September, the drop in consumption is thus 10. However, the theoretical price of November is not PNov = 28.72 + [0.086 u 10]: the basis of the new “auction” is now POct , and the theoretical price of November would thus be: PNov = 29.15 + [0.086 u 5] + 0.43 = 29.15 + 0.86 = 30.01. The same phenomena would occur during each of the next months,43 until July, when “auctions” would stop:

That is, the market of the next month. For instance, the theoretical price PDec = 30.01 + [0.086 u 5] + 0.86 = 31.30. 42 43

for

December

is:

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Table 3.3 The theoretical price (“prix définitif”) obtained by auctions in the case of an initial shortage of 120 days.44 Source: Briaune (1857: 109).

In the south of France, harvest is made in July, in the north that of rye and of barley of winter begins. During the epochs of high price, the new resources are rapidly employed; and by mid-July the auction becomes useless (…). Consequently, the price of July is composed of two numbers, one formed by the law of the year, the other one simply proportional to the shortage of food and of supplying of approximately ten days needed for preparation. (Briaune 1857: 108 tr) The preceding principle would thus give, for the first half of July, a In this table, several “definitive prices” seem to be wrong. From March, the prices I found are 40.76, 44.20, 48.07, 52.37 and 57.10.

44

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price of 57.10. During the second half of July, the perspective of the new harvest would make auctions stop: then, the theoretical price would only be a function of supplying. With a shortage of food of 60 and a shortage of the reserve of 10, the price during the second half of July would be: PJuly2 = 18,40 + [0.086 u 60] + [0.086 u 10] = 18.40 + 5.16 + 0.86 = 24.42. Briaune could then determine the mean price of July (40.77). For these situations of shortage, Briaune thus constructed a theoretical process explaining the way an adjustment of demand to supply would be possible from the exclusion of consumers and a variation in price. The next step is the “test” of this relation – the aim is to “evaluate its exactness and precision,” in Briaune’s words (1857: 110 tr). 3.4.2. The test of the law of “double proportionality” Once more, the “test” of the law of “double proportionality” takes the shape of historical verifications. These comparisons of theoretical and observed prices are here relative to two agricultural years characterized by high prices of wheat, 1816–1817 and 1846– 1847. However, in the latter case there was a surprise in store for Briaune. The first agricultural year is characterized by a mean observed price of 35.79, corresponding to “an excess of 17 fr. 39 c. from the normal price45 and of 12 fr. 23 c. from a supplying deprived from the two months of the floating reserve”46 (1857: 111 tr). From this excess of price, Briaune deduced the existence of a theoretical shortage of 52 days47 (in addition to the lasting of the reserve), to which 14 days of observed imports have to be added, that is 66 days 45 The “normal price,” remember, is for Briaune the mean price (18.40), corresponding to a supplying of 425 days. 46 In this case, supplying is 365 and the price is 23.56. 47 This determination was based on a rule of three. For another similar year, he concluded that a shortage of 60 in food was corresponding to a rise in price of 14.05. He deduced that a rise in price of 12.23 corresponds to a shortage of approximately 52 days.

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or 5.5 days per month. Before the “auction,” the theoretical price is then: P = 18.40 + [0.086 u 60] + [0.086 u 66] = 29.23. As table 3.4 shows, this theoretical result is “exactly the price of the first month of the period” (1857: 111 tr): “the appreciation of the shortage has been exact from the very beginning of the year” (1857: 110 tr). Now, the theoretical role of auctions during the next months had to be determined: “The number of consumers to be excluded being proportional to 5 days, 0050es per month,48 the first factor of the auction was 5.50 multiplied by the formula of 0 fr. 086 c., second factor, and it began in September” (1857: 111–2). Briaune then represents the “auction” relative to the whole year (see table 3.4). From the last two columns of this table, it is possible to compare the prix resultant (the theoretical price) with the prix de la mercuriale (the observed price). Once more, no formal “test” can be found here. Briaune just compared the theoretical and the observed prices, as well as the mean theoretical price (36.10) and the mean observed price (35.79) for this agricultural year, and he concluded that the match was rather good: This weak difference of 0 fr. 31 c. only represents one day 1/3 of food on the whole year, according to the double proportionality of shortage and auction. (Briaune 1857: 114 tr) The second year examined, 1846–1847, was a very different case study, and it enlightens Briaune’s methodology and even the very status he attributed to his law. Briaune’s idea was, as in the previous case study, to verify that the “auctions” permitted, month after month, the adjustment of demand to supply. However, he faced a serious puzzle. As the last two columns of table 3.5 show, the monthly theoretical prices (the prix résultant) and the monthly observed prices (the mercuriale) do not match, although the mean theoretical price and the mean observed price remain close 48

“00es” refers to hundredth.

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(respectively 30.86 and 30.77). In table 3.5, we can see that from August 1846 to January 1847, the theoretical price is superior to the observed price, whereas the opposite occurs from February 1847 to July 1847.

Table 3.4 Observed price (“prix de la mercuriale”) and theoretical price (“prix résultant”) obtained from “auctions,” 1816–1817. Source: Briaune (1857: 113).

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Table 3.5 Observed price (“mercuriale”) and theoretical price (“prix résultant”) obtained from “auctions,” 1846–1847. Source: Briaune (1857: 117).

Does this mean that the theory was imperfect? Briaune suspected not. He separated this agricultural year into what he considered two homogenous sub-periods: the first half of the year, during which observed prices are lower than expected and imports

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are weak, and the second half of the year, during which observed prices are higher than expected and imports are high. The mean observed prices of both sub-periods are respectively 26.77 and 34.77, presenting respective differences of 3.21 and 11.21 with a situation where the reserve is zero (with a price of 23.56). Briaune exposed that situation as follows: A comparison of these differences shows that 3 fr. 23 c.49 is the 14 , which, with an import expression of a shortage of 25 days 100 es 96 100es

, and that 11 fr. 21 c. is the

expression of a shortage of 32 days

, which, with an import

of 42 days

Thus, during the first

of 12 days

82 100 es

, gives 37 days

20 100es

, gives 75 days

90 100es 10 . 100es

semester the shortage had been evaluated at less than six weeks, and during the second [semester] it has been estimated at more than two months. Between these two contradictory expressions, whose total is 113 days, the mean expression of the annual 50 . shortage would be 56 100 es But since the auction brought it to 75 during the last six months, a shortage necessarily widened during the first semester, independently of the one of the year, due to a too large relative consumption. Indeed, in the first evaluation of the shortage at only 38 days for the year, only 19 for six months, 25 . Consequently, since the there was an error of 9 days 100 es auction had not excluded from wheat a proportional 25 . But as this consumption, the shortage increased of 9 days 100 es aggravation was relative to the second half of the year, the 50 auction led to a shortage of 37 days 100 for six months or 75 es days for the whole year, although in reality its amount was only 66 days, including the too large initial consumption. (Briaune 1857: 115–6 tr) What Briaune explains here is that it is not the theory which is imperfect, but rather the real world: the real market would have wrongly appreciated the deficit. The market underestimated the deficit, and thus the mass of consumers to be excluded was smaller than 49

In fact, 3.21.

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necessary – and the real price was too weak in comparison with the theoretical price. Then, from February, a correction occurred, and it was necessary to exclude the mass of consumers that should have been excluded during the first half of the year. This correction corresponds to an observed price higher than the theoretical price. But at the end of July, the observed price was finally close to the theoretical price. Briaune’s conclusion could finally be very optimistic: the difference of 0 fr. 09 c. that exists between theory and the mercuriale gives, according to the proportions of scarcities, onethird a day of supplying. It was impossible to be more exact. (Briaune 1857: 118 tr) The main point here, we believe, is this final judgment: the theoretical law was not rejected. Despite observed discrepancies caused by an “abnormal incident” (1857: 114 tr) – actually an error originating in ignorance, in Briaune’s opinion – “the proportionality is the expression of commercial facts” (1857: 115 tr). This must be related to the way he previously explained that the mathematical “law of proportionality” would be “the very painting of practical facts and of the actions they determine” (1857: 104 tr): the theory would capture the true mechanisms of the economy, although accidents and errors of appreciation can happen in the real world. At that stage, this result deserves two comments. First, despite the lack of formal statistical procedure, we clearly find here empirical “tests” – or verifications – of a mathematical relationship. From the favorable results of these “tests,” Briaune concluded that his theory would own the status of a law : in this long application of the theory of proportionality of prices to the excesses and shortages in supplying, the principle and the formulae never failed. In the more varied situations, it was always in conformity with the real numbers (…). At that stage, it is not a theory, it is a certified law. (Briaune 1857: 118 tr) Briaune did not use the word “law” by chance: for him, the law of proportionality was representing a timeless, ahistorical and deterministic causal chain ruling the economy and the “social body,”

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and it would even own the status of a natural law. Briaune thought that he had unveiled a part of the causal structure of the economy and consequently of the social world. Second, we can find here the idea that the deviations from a deterministic relation are interpreted as subjective errors and, in this sense, Briaune follows Laplace’s views. In Briaune’s mind, a means for reducing such errors was education,50 in the sense that the government and individuals should know the natural laws governing the society; for Briaune, science was defined as the discovery and the diffusion of natural order. 3.5. A QUE STION OF ATMOSPHE RE : B RIAUN E ’S “ SOCIAL ME TE OROLOGY” But as such, the “laws of proportionality” are not Briaune’s ultimate aim. In fact, he was particularly interested in showing that within the social world, universal laws such as gravitation have room. Once the “laws of proportionality” were obtained, he wondered about an order ruling the way prices stir around the average; about the existence of a cyclical movement of agricultural prices around the average; and about the causes of such potential movements. The discovery of the culprit – a weather cycle affecting crops and thus prices – led him to shape a kind of “social meteorology,” which also had a flavor of “social astronomy”: the “laws of proportionality” were associated with a natural cause that could explain periodic oscillations in prices, and more generally recurrent economic crises and political disorders. This search illuminates the meaning of his econometric work: Briaune believed that the society and nature were entangled, that the society was part of the unified “system of the world” and was ruled by a unified natural order. 3.5.1. The weather influence Briaune’s starting point is here a basic idea, the influence of weather on crops and thus – given the “law of proportionality” – on prices: Those who write on agriculture only talk about man and progress; those who practice it only talk about God and the weather. The first ones only consider the attempt, the others the 50

We shall find a similar idea in Regnault’s work (see Chapter 4).

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event. Man prepares harvests, and the seasons decide, and whereas labor for preparation remains rather constant, the atmospheric action varies constantly. (Briaune 1857: 119 tr) In this quote, we can identify several postulates that underlie Briaune’s work, for instance the action of God, that we shall analyze more completely in section 3.5.2. More importantly for the moment, Briaune’s investigation illustrates his constant focus on causality and deterministic causal chains. He thought that agriculture is affected by a cause: an “atmospheric action” or an “atmospheric fecundity” (1857: 141 tr).51 In addition, he thought that this alleged cause was far from following a random process: he had in mind an “atmospheric period” (1857: 123 tr), i.e. a periodic cyclical movement. [T]his variability is due to the laws that conserve and restrict beings, and consequently (…) it has to be subject to some balance [pondération] in its effects and to a certain periodic equality in its movements. (Briaune 1857: 119 tr) The alleged existence of weather cycles, and consequently agricultural cycles, is thus the starting point guiding his work here. Actually, we reach here Briaune’s ultimate aim: the identification of a “fact” that “summarizes all the physical causes that act on crops” (1857: 122 tr), of a “natural law” ruling the atmosphere (1857: 120) and consequently agriculture as well as the whole socioeconomic world. In other words, the agenda is a linkage of the natural world and the socioeconomic world.52 3.5.2. The bible of econometricians How did Briaune identify a cyclical movement in weather and “[I]t would be necessary for observation to reduce all the other circumstances of fertilization, season, humidity, and heat to a unique fact, or at least to a principal, dominant, and essential fact” (Briaune 1857: 119–20 tr). 52 He thus focused on the search for a forced cycle, in Van Der Pol’s words. 51

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agriculture? The answer to this question enlightens beautifully the foundations of his methodology. He could have begun with a statistical analysis of observed prices, from which potential movements could have been identified. However, since he was looking for a “natural law” ruling the natural and the social worlds, he first tried to gather preliminary “proofs” of the existence of a potential immutable weather cycle in order to focus only on significant movements and constant causes,53 and to read his data with these movements in mind. Briaune’s analysis of data is based on an unexpected reference: the Bible. God plays an important role in his writings, as in those of Cournot and Regnault. In the Prix des Grains, we find recurrent references to “Providence” (1857: 11 tr) and “God” (1857: 17 tr) and, like Cournot and Regnault, Briaune thought that the world obeys principles and laws elaborated by God and which form the natural order. For instance, he wrote that: [The forces] of nature, fatally ruled by God, produce by their concordance this admirable harmony of the material universe in front of which the mind bows and humbles. (Briaune 1874: 4 tr) This explains why Briaune referred to the Bible in his analysis of cycles. He indeed thought that the Bible could offer a key to the identification of the period of the cycles affecting the weather and agriculture: he refers to “the Nile floods in Egypt, whose height has always given a certain sign of the various degrees of abundance or of scarcity” (1857: 120 tr). In addition, he notes, “as simple as this fact is in itself, it could only be remarked by observation and the comparison of a rather long series of floods and crops” (1857: 120 tr). For Briaune, the holy book was based on an accumulation of observed data that are universal, in the sense of atemporal,54 and “But when we want to pass from this philosophical feeling to the study of the causes of fecundity and of sterility, we get lost in their multiplicity, their combinations, their necessary linking and their apparent contradictions” (1857: 119 tr). 54 Once more, Briaune’s predilection for ahistorical deterministic causal chains explains the fact that for him, past observations follow schemes that would still be at work at his time. 53

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here precisely lie his first “observations”: What reason indicates as the consequence of the observation of the Nile floods and the signs of abundance or scarcities resulting from the level of the waters, is formally recorded in the most ancient book of the world, the Bible; and whatever our judgment on the holy book, the fact of the seven years of abundance and the seven years of scarcity cannot be denied. For the one who believes, the divine intervention relative to Joseph and Abraham’s race reveals in the dream of the Pharaoh, in its explanation, in the elevation of Joseph; as for the alternation of the seven years, the fact can be part of the common law without being for that reason less indisputable, and even be extraordinary without being supernatural yet. For the one who sees the Bible as a simple story in which truth and error are mingled and merge, the periodicity that it tells remains a fact that he must accept. Indeed, either Moses sincerely related the life of Joseph, or he more or less distorted the events, or he completely invented them. In the first case, no objection is possible. In the two others, he would have spoken, as do all those who want to lie to the masses, by relying on an initial, constant, and popular truth, in order to give some likelihood to the fictions they want to deduce from it. Thus, from the very fact that the story related by Moses would be false, the fourteen-year period and the alternation of the seven opposite years on which it relies would remain true. Moreover, his story is in accordance with what we know about the Egyptian constitution. By which means could the kings become owners of the soil in another way than the capture of crops bought at a low price and sold at an extremely high price? How did the idea of such an operation come to them if not by the observation of the alternation and equality of good and bad years? How finally would it be possible for this equality to exist if the alternation was not to be found in some periodicity. History and reason thus testify the bi-septennial periodicity on which the whole story of Moses relies. (Briaune 1857: 121–2 tr) For Briaune, the Bible would reveal here the existence of a universal cycle: “[i]f this periodicity was existing in Egypt, it exists everywhere;

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because the very nature of the law is its generality although its initials vary according to climates” (1857: 122 tr). He then tried to discover such a period in his data – “the mercuriales are the tables in which the facts of our food history are printed” (1857: 122–3 tr). This is a nice illustration of the way natural econometricians inserted their results in alleged universal laws and read observed data through the prism of postulates dominated by the belief in a divine natural order. 3.5.3. Fourteen-year agricultural cycles In his search for cyclical movements, Briaune used annual data (1804–1855), and every crop was considered “good” or “bad” (1857: 126 tr). The criterion he used is the price: a price above or below the mean price was interpreted as the sign for a bad or a good crop. At this stage, his agenda was the discovery of an order in this set of bad and good crops, and he suggested two results. First, a compensation: [I]f good [years] are separated from bad [years], we find that the number of the former is 28 and that of the latter is 30. Consequently, we get this first conclusion (…), the favors and the rigors of the sky balance [se pondèrent] in the production of wheat. (Briaune 1857: 128–9 tr) Second, he looked for “a constant periodicity” (1857: 120 tr). He studied the succession of “bad” and “good” years, and he found three fourteen-year cycles “until the crop of 1846. Then a new period begins and will end in 1859–60”55 (1857: 129 tr). He concluded that: Confronted with such precise facts, it should thus be recognized that the success of crops depends on an atmospheric fecundity, whose revolution occurs in 14 years and whose start should differ according to the various climates. (Briaune 1857: 141 tr) He visualized this alleged regular order in figure 3.1, the unique We shall analyze in section 3.5.4 the idea of forecasting contained in this sentence. 55

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graph that appears in Du Prix des Grains.56 Two curves appear on it. The first one (in broken lines) is relative to annual observed mean prices. The second one, which separates “good crops from those which are insufficient” (1857: 340 tr), corresponds to a kind of smoothing process with a fourteen-year periodicity (peaks occur in 1804, 1818, 1832, 1846). But its construction remains rudimentary and quite mysterious: Briaune gives no data, and he does not explain the formal nature of this smoothing process. We can notice that in 1829, George MacKenzie (one of the first social astronomers) followed a similar perspective, but used a formal smoothing procedure (Klein 1997: 115). Anyway, from this graph Briaune concluded that a regular cycle could be found in the maze of historical data and events. Despite its somewhat fragile basis, this fourteen-year cycle plays a major role in Briaune’s analysis: it is a complement to the “law of proportionality,” which affords no information on the way prices gravitate in an orderly way around the mean price. With that cycle, Briaune believed that he successfully demonstrated that there was an order in the way prices stir around the average, and such an order was working for unity at two levels: at the methodological level, he was able to bring to the fore a gravitation process ruling the economy, just like it rules some natural phenomena; at a more philosophical level, he showed that the social world and the natural world were perfectly connected, and that the economy and the society follow the immutable order of the physical world – their rhythm would even be given by a physical time. 3.5.4. Forecasting and economic policy Briaune finally focused on two consequences of this deterministic and natural law ruling agriculture. First, from the existence of this periodicity, he deduced the possibility of forecasts. one part of a period being ended, it is easy to calculate the proportion of good and bad years during the rest of the period and to find a probabilistic basis for supplying. (Briaune 1857: 141 tr) 56

Briaune indeed had a more important predilection for tables.

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Figure 3.1 The agricultural prices, 1804–1855. This figure shows annual observed mean prices (broken line) and a smoothing curve of a fourteen-year period. Source: Briaune (1857: 340).

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In addition, remember that in a previous quote, Briaune wrote: “a new period begins and will end in 1859–60” (1857: 129 tr). Of course, this agricultural year 1859–1860 is posterior to Briaune’s observations and to the publication of Du Prix des Grains. Such a forecasting largely originates in the intrinsic determinism of the world as Briaune sees it: “the future is only the continuation of the past, and consequently there are probabilities that the common sense can try to calculate” (1857: 191 tr). Second, the knowledge of this periodicity has obvious consequences for economic policy. Of course, the fourteen-year cycle was considered an immutable law that would impose upon men: deviations from the mean and “desirable” price would occur periodically and, in addition, Briaune believed that “no agricultural progress can prevent a nation from the periodic inequality of crops” (1857: 141 tr). However, he thought that the periodical deviations in prices could be smoothed, even cancelled, and the solution would lie in international trade between countries that are not simultaneously affected by similar atmospheric constraints. For instance: Bad weather, even if it is moderate, affects rather equally the British islands, France, Belgium, and Northern Germany; and when it is more intense, its effects spread to the whole Europe, with the exception of Russia. Thus in the circumstances where importation seems the most necessary, considerable excesses can only be found in the latter country and in the United States. Egypt, Algeria, Sicily, Spain can only furnish secondary help. (Briaune 1857: 191 tr) Not surprisingly, then, England would have as main commercial partners the United States, Canada, or Russia. International trade would thus be a means of maintaining a “normal” supplying and of eliminating variations in agricultural prices – of ensuring that no deviations from the “desirable” price occur. Of course, we are now brought back to Briaune’s predilection for stable states. In addition, we are also brought back to a Physiocratic idea: the government should only operate on the basis of the constraints given by natural

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order.57 3.5.5. Back to the postulates of natural econometrics At that stage, the very foundations of Briaune’s economic analysis become fully apparent. He mobilized statistical and mathematical instruments in close association with postulates that form a worldview oriented toward the knowledge of a divine natural order ruling, in a unified way, the social and the natural worlds. First, Briaune’s investigations are an illustration of the determinism that was dominant in the science of the time. His work and his thought are hymns to determinism – he believed, remember, that “the future is only the continuation of the past” (1857: 191 tr). This explains that objective chance has no room in Briaune’s world: a deterministic law relating price to quantity would permanently be at work – it would be “the very painting of practical facts” (1857: 104 tr), remember – and observed prices fluctuate regularly and periodically around a harmonious equilibrium represented by the average. Of course, accidents can happen in the real world, but they are seen as resulting from wrong estimations: they are basically considered subjective errors, and the manifestation of ignorance. In sum, Briaune believed that the economy – and the “social body” – was a perfect clockwork, that man has to identify. The second major postulate is unity. Just like Cournot (and Regnault, as we shall see in the next chapter), he thought that social and natural phenomena obey similar laws (e.g. gravitation). But he also claimed that economic phenomena are physically dependent on natural phenomena. Here is precisely his very goal: the identification of a “natural law” that would rule the atmosphere and would propagate into the whole “social body.” In that respect, Briaune’s work illustrates physical determinism, which explains “all our reactions, including what appear to us as beliefs based on arguments, as due to purely physical conditions” (Popper 1979: 224). In that sense, he aimed at the reinforcement of the deterministic paradigm by showing that a direct linkage to physical deterministic phenomena of a fourteen-year period could explain movements in the economic world. It can also be remarked that from this unification, the We find a similar idea in the work of Moore, one of the last “social astronomers” (see Le Gall 1999). 57

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economy was seen as governed by a physical time, the immutable, regular time of the natural world.58 The rhythm of the socioeconomic world becomes naturalized and, despite accidents, historical time does not really matter. The third major postulate is the belief in a harmonious and stable natural order, in an “end of history,” that the society could and should reach. Briaune’s views differ here from Cournot’s. In Cournot’s work, a historical “progress” would naturally lead societies to an “end of history,” the moment when the society finds a final harmonious form in accordance with natural order. In the case of Briaune – and the same applies to Regnault – men could reach this state through scientific knowledge: the aim of science is to identify the natural laws and, from knowledge and education, men can devise the means to reach a final and quiet state of societies, in accordance with natural order. The final postulate that shapes Briaune’s worldview is, of course, God’s design. As seen above, a prism conditioned his search for agricultural cyclical movements and his reading of data: the fourteen-year period found in the Bible. More generally, religious beliefs underlie Briaune’s writings.59 We find here the idea that science aims at unveiling the divine creation and the divine order. Once more, we see the way economic analysis depends here on views that belong to the domain of faith. CON CLUSION Briaune’s work enlightens pivotal features of natural econometrics. Within the frame of postulates associated with a worldview, statistics is used to unveil and to measure mathematical laws ruling the economy and, once validated and accepted, these laws were seen as part of the natural order that would rule the “system of the world.” In Briaune’s Du Prix des Grains, we find econometric ideas: his methodology is based on the combination of statistics (observation 58 On historical time, physical time, and logical time in statistical economics, see Granger (1955), Klein (1995 and 1997), Maas and Morgan (2002), and Morgan (1997). 59 For instance, “There is indeed something vast and indefinite in this power of art that, covering the ground of rich harvests, seems to belong to the society of the Creator [semble entrer en société du Créateur ]” (1857: 158 tr). For Quesnay, the soil is a divine gift, and the same applies to Briaune.

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and instruments) and mathematics, and “tests” (rather verifications) are recurrently used. But these econometric ideas – the instruments used as well as the interpretation of results – find their roots in an underlying worldview. Three examples illustrate this close association. First, in his reading of observed data he presupposes the existence of cycles, and more importantly the existence of the periodic cycles that he found in the Bible. Second, he constantly (although often not explicitly) saw crude data as the sum of two components, the constant causes (given by the “laws of proportionality” and weather cycles) and the accidental causes. His goal and his use of instruments were then perfectly matched: from his conception of an orderly, causal and deterministic social world, he could put emphasis on the sole constant causes. In that perspective, the major statistical instrument he used was the average, from which the compensation of errors and accidents was possible and the constant causes could be identified. The average was considered an instrument from which deterministic laws and the alleged structure of the world could be discovered. Third, the association of the “laws of proportionality” with weather cycles aimed at showing that the society was in full swing with nature, and that the whole “system of the world” was unified and was obeying similar principles and laws – and that, of course, there was no major differences between the natural and the social sciences. Ultimately, the “proofs” Briaune referred to are philosophical ones. His whole work is oriented toward the identification and the measurement of a deterministic, orderly, divine, and natural order that would rule the social world. We find here one feature of the nineteenth century social sciences: the positioning of man vis-à-vis the natural laws.60 Briaune, as well as the other natural econometricians, acts like a “revelator of the world,” to use the words of Gusdorf (1956: 43 tr).

60

See for instance Ménard (1983) in the case of Malthus.

4. N atural laws on the Stock market: Regnault’s “financial physics” In all probability, when Jules [Regnault] and Odilon [his brother ] arrived in Paris, their financial resources were low (…). When he died, his fortune was estimated at 1 026 510.03 francs (more than 3.8 million euros 2004). – Franck Jovanovic, “A nineteenth-century random walk: Jules Regnault and the origins of scientific financial economics”

In 1863, a broker, Jules Regnault,1 published the Calcul des Chances et Philosophie de la Bourse,2 a book devoted to stock prices behavior. The book was not written by accident: it was stimulated by a recurrent question in France, the legislation of financial markets and the morality of speculation.3 Economists were progressively involved in these debates,4 although they adopted different methodological positions. On the one hand, “traditional economists” – the liberal economists belonging to the French Classical tradition, for instance Alphonse Courtois – claimed the usefulness of the stock market as a whole. Their approach was literary and descriptive, and left no room Jules Regnault (1834–1894) spent his formative years in Belgium, where he was strongly influenced by Adolphe Quételet. Then, in 1862, he became a broker at the Paris Stock Exchange. The first biography of Regnault can be found in Jovanovic (2005 and 2006a). On Regnault’s work, see Jovanovic (2000, 2001, 2002a, 2006a, and 2006c), Jovanovic and Le Gall (2001b and 2002), and Taqqu (2001). 2 This book will be referred to under the title Calcul des Chances. 3 As Jovanovic (2002a and 2006a) and Jovanovic and Le Gall (2001b) show, from the eighteenth century to the second half of the nineteenth century, the legislation on this issue fluctuated and reflected oppositions between on one side economic and financial needs – especially those of governments – and on the other side the “morality” of speculation and of the stock market. Future markets were officially recognized in the country in 1885, although the French jurisprudence implicitly recognized future operations from 1860. 4 The Journal des Economistes regularly published debates of that kind (see for instance the Journal des Economistes, 1857, 47: 308–14). 1

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for mathematics, statistical procedures, or probability. On the other hand, we can find scholars who were on the fringe of the academic milieu and who had a predilection for other methodologies. Henri Lefèvre,5 an actuary trained in natural science, opted for calculus and geometry to understand the nature of some financial operations, and Regnault had a predilection for the joint use of statistics and mathematics. Regnault’s agenda is very explicit: the construction of a “science of the Stock market” (1863: 47 tr). Such a “science” aims at identifying “new laws of the variations of the Stock market” (1863: 7 tr) that should offer answers to the debates of the time: the agenda is “to demonstrate the dangers of gambling [jeu], and at the same time to discover the aim that Speculation should propose” (1863: 1 tr). Regnault’s Calcul des Chances offers two basic demonstrations. The first one is relative to short-term speculation – “gambling”, in Regnault’s words (“agiotage” or “jeu”). “Gambling” designates for Regnault the practice based on the search for immediate gains – at the time of Regnault, the word agiotage was related to short operations, made “without any resource, credit or capital” (1863: 102 tr). Regnault offers two results here. One the one hand, he showed that in the short term, stock prices follow a random walk – a result that Louis Bachelier mathematically refined in 1900.6 Yet, on the other hand, the extension of the analysis led him to “demonstrate” that short-term speculation would inexorably lead to ruin: the random walk is a trompe-l’œil. The second demonstration is relative to long-term speculation (“speculation” or “true speculation,” in Regnault’s words), which corresponds to financial operations relative to the long term and that are linked to the economic needs of companies or of the country. Regnault shows that in the long term, stock prices would follow patterns: for instance, they would be attracted toward mean and “normal” values, labeled “attraction centers.” For him, such patterns are the manifestation of natural laws from which agents could not escape. Although Regnault’s book gained recognition within the small circle of financiers and actuaries7 of the end of the nineteenth See Lefèvre (1870, 1874, and 1885). On Lefèvre, see Jovanovic (2006b). See Jovanovic (2000, 2002a, and 2005); Jovanovic and Le Gall (2002). On Bachelier, see also Dimand (1993), Mandelbrot and Hudson (2004), or Taqqu (2001). 7 See Jovanovic (2002a, 2002b, and 2005). 5 6

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century and of the early twentieth century (e.g. Louis Bachelier, Emile Dormoy, Maurice Gherardt, and Hermann Laurent), it remains largely unrecognized by the present time, at least until its recent rediscovery by Franck Jovanovic. Yet, it is a masterpiece of the history of economic analysis, financial economics, and econometrics. At the theoretical level, we find in this book the first representation of stock price fluctuations as a random walk, thirty-seven years before Louis Bachelier, to whom this paternity was commonly attributed in canonical histories.8 At the methodological level, Regnault used and combined statistics and mathematics, at a time when such choices were far from being a standard: from observation and statistical instruments (in particular the average), he identified several mathematical laws ruling the price of bonds, and these laws were statistically tested. In that perspective, Regnault is a major figure in the rise and the development of econometric ideas in France during the nineteenth century. However, for the contemporary reader, the Calcul des Chances may seem weird, in the sense that its reading mainly suggests the difference with our usual analyses, a kind of difference similar to the one created by the Chinese encyclopaedia that Michel Foucault mentions in the preface of The Order of Things.9 In Regnault’s book we indeed find: (a) “the experience of the Infinite” (1863: 4 tr); (b) the “laws of universal attraction” (1863: 7 tr); (c) “the observation of past events” (1863: 13 tr); (d) “the thermometer of public opinion” (1863: 24 tr); (e) “social economics” (1863: 33 tr); (f) “a so attractive and so perfidious Stock market” (1863: 35 tr); (g) “a mathematical law that rules the variations and the mean deviation of Stock prices” (1863: 50 tr); (h) “man [who] fidgets, God [who] guides him” (1863: 52 tr); (i) “the revolutions of planets” (1863: 98 tr); (j) “supply and demand” (1863: 101 tr); (k) “A sphere, a ball, a wheel, a hoop, struck by a body that moves in space, [which] get a movement of rotation and at the same time a movement of translation” (1863: 143 tr); (l) et cætera; (m) “the heart [that] has irregular and convulsive movements” (1863: 210 tr); (n) “extreme things (…) [which] are always fatal, to peoples and to individuals” (1863: 210 tr). Yet, there is an order underlying this bizarre classification, and this order is a typical product of the See for instance Fama (1970). On the construction of canonical histories in financial economics, see Jovanovic (2004a). 9 See section 1.1. 8

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intellectual and scientific context of the time. In particular, Regnault’s work is dependent on a worldview in which, once more, determinism, unity, and God’s design are essential: to him, science aims at revealing exact laws, analogous to those that would rule the natural world, and included in a unified natural order ruling the “system of the world.” In that respect, his association of economic analysis, mathematics, and statistics clearly belongs to natural econometrics. The aim of this chapter is to show that natural econometrics finds an apogee in the Calcul des Chances, in which Regnault aimed at the construction of a “financial physics” largely inspired from Quételet’s “social physics.”10 Regnault’s agenda, at the theoretical and the methodological levels, is presented in section 4.1. Then, in section 4.2, Regnault’s worldview is analyzed, and I focus on the postulates of natural econometrics that can be discovered in his book. Regnault’s use of statistics and mathematics is scrutinized in section 4.3. In sections 4.4 and 4.5, Regnault’s analysis of short-term speculation and of long-term speculation is presented, and I particularly put emphasis on the way Regnault identified laws that, he thought, were part of a natural order ruling the world. Finally, section 4.6 explains the way the existence of natural laws was seen as a means of identifying a stable “end of history,” à la Cournot and à la Briaune. 4.1. I N TO THE “ TE MPLE OF MODE RN SOCIE TY”: A FIRST APPROACH OF R E GN AULT ’S AGE N DA, IN STRUME N TS, AN D WORLDVIE W

Given the fact that Regnault’s work remains largely ignored, it is useful to begin with the way he exposed his general goal in the Calcul des Chances’s introduction. We shall find in it his whole agenda, at the theoretical, methodological, and philosophical levels. [1]11 The Stock market is the temple of modern society: it is there that all the large interests of a century eminently positive and industrial are intended to converge; but the Stock market is also the official sanctuary of gambling, and it is there that 10 11

See especially Quételet (1835). In brackets are the page numbers.

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fortunes and existences swallow up. We believe that we do a service to the whole society in trying to analyze its chances [chances], to demonstrate the dangers of gambling, at the same time to discover the aim that Speculation should propose. Morals, under its various forms, was not absent, until now, to attack the abuses of speculation and to try to correct them; but morals, in order to persuade, has to bring conviction. Man, slave to his passions, indifferent to what does not affect him, turns to good or to evil according to his own interest; it is not by abstract and idle discourses, meaningless words, that it can be expected to [2] reform his bad instincts; the truths that are convincing have to be obvious, irrefutable. Is it not better to demonstrate to the gambler how, given the way things are, he will inexorably be ruined at a given day, rather than to make him feel that if he gets rich, it can only result from stripping his fellow? Yet, this truth can be proved to him, because it can be expected. Nothing in nature is arranged arbitrarily and happens without having been prepared by an anterior cause, whether we know it or whether we do not know it. If we were perfectly familiar with this so simple truth, we would be less frequently seduced by the marvelous, we would conform less frequently to the unexpected and to what we generally call chance [hasard ]. There is no chance [hasard ]12, instead there is our ignorance; it is ignorance that makes us misjudge the necessary connection between all the effects and maintains our illusions and our errors; this is the first cause for all our excesses, all our passions, all our misfortunes. It is true that we shall never reach a full knowledge of all causes, and that when we estimate a fact we cannot see most of them; in the case of an isolated fact, no forecasting is possible, or only a very reduced possibility, but in the case of a set of facts there is often a certainty almost complete for or against, and the limits of doubt (between which [3] our estimation, or the quantity of error that can affect it, varies) tend to diminish, according to precise ratios, as the number of facts increases, In a footnote, Regnault quotes here (in English) David Hume: “Though there be no such thing as chance in the world, our ignorance of the real cause of any event has the same influence on the understanding.” 12

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because the particular causes that affect each fact considered separately cancel in a large number and then reveal the general laws; thus, we cannot predict with certainty, even if we know his constitution, the age at which a person should die, but on the basis of a large number of persons, it can be said, very accurately, how many of them will reach or not a given age. Very expert is the one who, on the Stock market, while seeing an operation begin, could predict if it will lead to a benefit or to a loss; but it is not necessary to be a seer to predict what will happen in a continual series of operations. Particular events can deceive our forecasts, but it is necessary to rise above the consideration of these events to see only the set of last results, which can never mislead. It is to J. Bernoulli that we owe the demonstration of this beautiful theorem that he saw, rightly, more important and more useful than the discovery of the quadrature of the circle. “By multiplying indefinitely observations and experiments, the ratio [rapport ] of events of various natures that must happen, becomes close to that of their respective possibilities within limits whose interval becomes narrower and becomes smaller than any ascribable quantity.” [4] It is here a very remarkable phenomenon to see the events that seem to be the most dependent on unknown, unappreciable causes, presenting, by multiplying and combining in an infinite way under our eyes, a tendency to reach fix, appreciable ratios, in such a way that, if we conceive on either sides of these ratios an interval as small as we want, the probability for the mean result of observations to fall within this interval only differs in the end from certainty in a quantity inferior to any magnitude wished. All the numbers presented by the theory of probability only present a final state, oscillate in a series of continual vibrations around the natural state, progressively diminishing these vibrations as they concern a larger number of facts, and become rigorously exact as soon as we suppose their number infinitely large. We would thus know the future, if we had the experience of the Infinite. It is this idea of Infinite, finally evoked, that makes that every mathematical theory is necessarily moral and philosophical, and that, to understand its true scope, it is

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necessary to get rid of special influences, of stingy, temporary considerations. The whole science of chances [hasards] is ultimately a matter of a determination in a general way of all the events of the same kind, of grouping and reducing them in a limited number of facts, distinct events perfectly defined, all equally possible. And each group of events of the same kind being clearly delimited, it remains to determine, according to the nature of their production, [5] or to the careful appreciation of facts previously accomplished in each order of events, the number of favorable or opposite chances in the arrival of each of them. Once these ratios are well established, once the number of chances [chances] of each of the possible events is determined by an exact analysis, the final word of human science is pronounced, and there is nothing else to learn. Nature acts and irresistibly demonstrates by its effects the exactitude of these ratios. A lot of well enlightened minds are annoyed that we dare allow calculus to enter into questions that can be considered as belonging to the moral order; but the moral world is ruled by the same laws as the physical world: all our wills, all our determinations, all our enterprises, are not ruled by chance [hasard ], but are based only on an enumeration of favorable or unfavorable chances [chances], because we all aspire to happiness and success, and for that we can only decide on the basis of probabilities [;] but as we are not all instructed equally, we follow different routes, and vice is the route to error, unfortunately too frequently followed. Calculus indicates nothing more than the reasonable man already knows, but it is because common sense and reflection are not always sufficient for numbering exactly all the possible chances [chances], that calculus is sometimes necessary. Is it not right that if it was said: “Here is an urn that contains one white ball and one hundred black balls, you draw one, if white you double [6] your fortune, but if black, you are ruined”; is it not right that there would be no man in the world, except if we suppose him crazy, to desire such a convention? Well! we demonstrate in an irrefutable way that in the most part of the conditions of gambling on the Stock

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market, the urn of fate, for one white ball, contains more that one hundred billion black balls. (Regnault 1863: 1–6 tr) At the theoretical level, Regnault’s agenda is the understanding of the way the stock market includes heterogeneous types of behaviors, practices and views – the stock market would correspond both to a “sanctuary of gambling” and to a “temple of modern society.” What Regnault is delineating here is the basic distinction that structures his book: short-term speculation vs. long-term speculation. Whereas, he claims, the former would lead to ruin, the latter would be associated with – and would serve – “the large interests of a century eminently positive and industrial” and the financial needs necessary for economic development. In that respect, his aim is to identify the nature and the consequences of these kinds of speculation, and then to reduce ignorance and “the quantity of error.” His theoretical contribution is, of course, closely associated with the methodological path he followed. To reach that analytical aim, Regnault found necessary to escape from “idle discourses” and to search for “irrefutable” truths and “general laws.” This search should, he thought, rely on a “set of facts” – including observed data – as well as on the introduction of calculus13 in the “moral order.” His methodology combines here statistics (data and instruments) and mathematics, and it is in that respect that Regnault’s methodological agenda is the concern of econometric ideas. Regnault is particularly wise to write that “every mathematical theory is necessarily moral and philosophical.” Actually, his whole work, and in particular the econometric path he followed, fully depends on a worldview and on metaphysical convictions – witness this reference to the “experience of the Infinite.” In the previous quote, Regnault recurrently refers to “Nature” – e.g. “the natural course of things,” the “natural state” – in an ontological perspective – “Nature acts and irresistibly demonstrates by its effects the exactitude of these ratios.” References to an order are also to be found here – witness the focus on causality, determinism and the rejection of objective chance, the search for “fix, appreciable ratios” In Regnault’s introduction, this mainly concerns the calculus of probability. Algebra is introduced in next parts of the book.

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and “general laws.” In addition, we also find the conviction that “the moral world is ruled by the same laws as the physical world.” All this delineates the set of postulates, the frame from which Regnault’s econometric ideas took shape: God’s design, unification, natural order, and determinism. 4.2. R E GN AULT ’S WORLDVIE W: DE TE RMIN ISM , UN ITY, AN D GOD’S DE SIGN Two components of Regnault’s worldview exert a decisive influence on his methodology and his financial analyses. First, for him the world would be ruled by deterministic, immutable and divine laws, considered components of a natural order. Second, a unified picture of the world is here omnipresent: Regnault believed that the society and nature obey similar principles, and that it could be possible to operate financial translations of laws discovered by natural scientists. 4.2.1. An orderly world In the Calcul des Chances, Regnault only focused on the identification of “general and immutable laws” (1863: 7 tr), of a natural order that, he believed, was governing the society. Three features of this worldview can be mentioned here. The first feature of Regnault’s worldview is determinism. Regnault indeed believed that the terms “scientific” and “deterministic” were synonymous and inseparable, and he undoubtedly had good reasons to refer to Laplace’s Essai Philosophique in the early pages of his book (1863: 7). For Regnault, “[t]he future inexorably follows from the past, as the effect invariably derives from the cause” (1863: 140 tr), and: Everything in nature is ruled by common, general, and immutable laws, without which no thing, no phenomenon could be produced or maintained, and the most general laws are also the simplest ones.14 (Regnault 1863: 7 tr)

We find here the criterion of simplicity, also present in Cournot’s methodology (see section 2.2.2).

14

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His focus on determinism contributes to explain the central role causality and forecasting play in his book, but also his belief that probability is only of a subjective nature. Just like Cournot and Briaune, Regnault devoted long developments to causality. In the introduction of his Calcul des Chances, he explains, remember, that “Nothing in nature is arranged arbitrarily and happens without having been prepared by an anterior cause, whether we know it or whether we do not know it”15 (1863: 2 tr). In addition, “anytime, anywhere, the same causes reproduce the same effects” (1863: 135 tr). However, the way Regnault grasps causality has to be unpacked. He indeed identified two kinds of causes: All the causes that contribute to the formation of any event, are divided in two basic categories: constant and accidental. The constant causes are those whose action is continuous and regular, always in the same direction and with a constant intensity. The accidental causes are those whose action is neither continuous nor regular, and which are produced without any apparent law, and fortuitously, in one direction or another. (Regnault 1863: 11 tr) The issue lurking behind this distinction is, as we shall see below,16 time-series decomposition: accidental causes, which would occur in an irregular and non-predictable way, would be perturbations, relative to specific circumstances and to the short term, whereas the constant causes would be the only ones significant in the long term, independently from particular circumstances.17 These constant causes would be related to deterministic laws at work in the real world, although they remain masked by the accidental causes. For Regnault, science, which aimed at identifying the true laws that rule the world, has thus to unveil these constant causes. From the alleged existence of deterministic laws, Regnault This idea refers to a subjective evaluation of probabilities (see below). See section 4.3.1. 17 Let me remind that such a distinction can be found in Laplace and Quételet (see Porter 1986: 108), and was also operated by Cournot and Briaune (see Chapters 2 and 3). 15 16

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inferred the possibility of forecasting: Knowledge, or rather the intuition of future facts, this precious faculty from which men who own it to the supreme degree were considered supernatural beings, and that was pretentiously called divination, when its true name is experience, this faculty is nothing else than the fruit of a careful study of past facts: it is one of the truths that can never be repeated too frequently. The future inexorably follows from the past, as the effect invariably derives from the cause. (Regnault 1863: 140 tr)18 We also see here – and this will be developed below – that for Regnault, the scientific method par excellence is based on observation: from an appropriate analysis of past facts, and facts in a sufficient number, it would be possible to discover the true mechanisms that would rule the world – and then what the future has in store. Another consequence of Regnault’s belief in determinism is the subjective nature19 of probability: probability is useful only because individuals would have bounded knowledge. This imperfection of knowledge has one major consequence: individuals try to tame the future through the elaboration of probabilities that are, of course, of a subjective nature; “all our calculus”, Regnault writes, “can have no other basis than personal observation” (1863: 18 tr)20. Yet, another idea 18 Regnault adds: “The discovery of the future has always exerted a large attraction on men, because by teaching them how to direct their actions in the sense of expected events, this discovery is the path that leads to wisdom and that should give them the greatest sum of calm and happiness, whose possession is the tendency in the whole nature (…). Every speculation, from that of the gambler who buys today to sell tomorrow at a price a little bit higher, to that of the capitalist who invests his funds with the hope of a future increase of capital, perhaps in a very distant future, every speculation, we say, is only the more or less intelligent search for the causes that, in the past, are the source and the foundation of the laws of the future” (1863: 140–1 tr). 19 In that respect, objective chance does not exist for Regnault – his conception of the society shares nothing with Cournot’s “historical period” (see section 2.3.2). 20 Let me remind that, in the early pages of the introduction of the Calcul des Chances, Regnault put a particular emphasis on information.

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is lurking here: the use of probability should progressively decline, in the sense that the more science progresses and discovers the true laws ruling the society, the more ignorance reduces. Just like Briaune, Regnault believed that the society was made up with a limited set of immutable laws, and that their identification should progressively lead to a state of perfect knowledge, which means for Regnault a harmonious and stable state of societies.21 The second feature of Regnault’s worldview is his belief in the mechanical organization of the world. Regnault claims that the society would be nothing but “a huge machine in which all the springs are connected together” (1863: 202 tr). From this viewpoint, he fully shares Cournot’s description of the “final” state of societies22 – when societies “function or become close to functioning as a mechanism where all the springs, all the cogwheels can be defined, measured, adjusted with a precision continuously increasing, and kept in a state of regular order, [we have] thus what we can call (…) a social physics” (Cournot: [1872] 1973: p.148 tr). Here the society is thus perceived as made up of precision clocks that are regular, orderly, and highly predictable. Finally, Regnault’s worldview cannot be separated from the belief in an alleged divine origin of the world – once more, a belief he shares with Cournot and Briaune. Regnault is very wordy on this point. To him, the order and the structure of the universe – from the revolution of planets to the formation of prices on the stock market (1863: 98) – would result from God’s design. He refers to the existence of “superior and providential laws” (1863: 185 tr) that each man should respect and that would inexorably impose upon men: Man has never to pretend that he rules the course of events; they rule themselves in a far better way than what he could do, and nature cares respecting without him that the order prevailing at all its manifestations is never perturbed. (Regnault 1863: 186 tr) In addition, he wrote this beautiful passage:

21 22

See section 4.6. See section 2.3.2.

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What a subject for amazement and admiration is offered by the views of Providence, what reflections are suggested to us by the marvelous order that characterizes the least details of the most hidden events! What! The variations of the Stock market are ruled by immutable mathematical laws! Events that are generated by the caprice of men, the most unpredictable shocks of the political movements, the most cleverly studied financial combinations, the result of a multitude of events that are not related together, all these effects are tied up in an admirable set, and chance [hasard] is now a meaningless word! And now, you, the princes of the Earth, have to learn and to be humble, you who in your pride, are dreaming of holding in your hands the People’s destiny; you, the kings of finance, who have at your disposal the wealth and the credit of nations, you are nothing else than frail and docile instruments in the hands of the One who masters the whole causes and the whole effects in an identical order, and who, according to the expression of the Bible, has measured, calculated, evaluated and distributed everything according to a perfect order. Man fidgets, God guides him.23 (Regnault 1863: 51–2 tr) In both quotes we find the idea of an active God, directing the action of men who are submitted to a natural order: men should respect this order – i.e. they must act in conformity with the natural laws and thus with the constant causes – otherwise, as we shall see below, their behavior is a vice and ends up in ruin – ruin, which would originate in the search for immediate gains, is nothing but a divine punishment in Regnault’s mind. 4.2.2. Analogies, transfers, and reductionism: Regnault’s unified world A final feature of Regnault’s worldview deserves attention: unity, which operates at the methodological and at the philosophical levels. A vast number of nineteenth century social scientists approached the economy at the light of the natural sciences. Like Cournot, but also like Briaune, Regnault believed that the various 23

Cournot, remember, wrote the same words (see section 2.3.3).

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components of the universe – the physical world as well as the social world – were ruled by analogous laws.24 Two illustrations of that belief can be given here: A society should be represented as a huge machine in which all the springs are connected together; credit is the functioning of these springs, and the general interest rate, at which we can borrow in this society, represents well enough the loss of force [force vive] caused by the functioning of the machine; the more perfect the mechanism, the more the loss necessarily diminishes. (Regnault 1863: 202 tr) The variations of the Stock market, as well as the Earth in the curve it describes around the Sun, are ruled by the laws of universal attraction; under some conditions, the capitalist can be sure to realize proportional profits with the same certainty as he is waiting for the regular return of seasons. (Regnault 1863: 7 tr) For Regnault, more generally, “the moral world is ruled by the same laws as the physical world” (1863: 5 tr) and “the state of a society is submitted to the same physical laws as those that rule the organized bodies” (1863: 168–9 tr). This unified conception of the world means that some laws would permanently act, in space and through time, at different levels. Thus, various disciplinary fields share – or rather should share – principles, concepts, instruments, methods, and laws and, as we shall see in more details in sections 4.4 and 4.5, this is why Regnault permanently looked for financial translations of laws already identified in the natural sciences. Such analogies probably aim at persuasion and are in this respect an important part of his discourse.25 But more importantly, Regnault’s use of analogies results from a unified representation of the world: the laws identified by natural scientists – in particular physicists and astronomers – could be transposed to the economic domain simply because the social I refer here to I. Bernard Cohen’s and Claude Ménard’s definition of analogy (see Cohen 1993a and Ménard 1989). 25 On analogies as rhetoric devices, see Cohen (1993a), McCloskey (1998), and Ménard (1989). 24

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phenomena would be analogous26 with the natural phenomena. Such a belief brings us back to the idea that both kinds of phenomena would own a common origin: as divinely designed, they would obey the same rules. 4.3. I N STRUME N TS FOR E XPLORIN G THE SOCIAL WORLD: R E GN AULT ’S USE OF STATISTICS AN D MATHE MATICS The Calcul des Chances is a hymn to a statistical analysis of the social world. The influence of Adolphe Quételet is central here. During his formative years in Belgium, Regnault was trained – at least indirectly – by Quételet,27 and the latter was one of the few authors explicitly mentioned in Regnault’s book. Regnault enthusiastically put forward the way the knowledge of the society benefited from the statistical approaches initiated by Quételet’s “social physics,” and his basic aim was to erect a “financial physics.” For him, the usefulness of statistics is advocated at two levels: the role of observation, and the use of statistical instruments. From them, it would be possible to unveil mathematical laws, and it is in that sense that statistics and mathematics are for him complementary instruments. 4.3.1. Observation, averages, and time-series analysis Regnault’s methodology – just like Briaune’s – is based on observation: “I begin to relate everything to observation,” he claimed (1863: 16 tr). Basically, and from that viewpoint Regnault also shares much with Cournot, statistics is considered a universal methodology; with it, it would be possible to discover constant causes and laws: Statistics (…) succeeded to subject its laws, not only to material things, whose functioning could to a certain point belong to the domain of mechanics, but most importantly, it has also included within such a rigorous system the moral facts, even those which are apparently the least likely to belong to a stable or normal 26 In this perspective, Regnault (1863: 28) relied on Pierre Cabanis’s analyses of relations between the social sciences and the natural sciences (see Cabanis 1843). 27 Quételet’s influence on Regnault is analyzed in Jovanovic (2002a, 2004b, and 2006a).

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state. Births, marriages, diseases, suicides, crimes, etc., can change from year to year under the influence of accidental causes, but over a rather long series of years, they will follow each other in the most regular way (…). Even more surprisingly, our mistakes, our distractions, our biases, and even our caprices are ruled by the law of probabilities. What is more indiscernible, uncontrollable, than the human mind? Yet, the phenomena that produce it (…) appear as more regular than the physical phenomena when men are free, that is, when they are not disturbed by private causes of personal interest.28 (Regnault 1863: 156–7 tr) However, observed data do not immediately and passively reveal their secrets. For that, scientists would have to use instruments. Regnault actively promoted the virtues of the average, an instrument discussed at length in the Calcul des Chances and from which, he believed, order – even natural order – could be identified. Just like other nineteenth century scientists, Regnault considered the average “not just a mathematical abstraction, but a moral ideal” (Porter 1986: 103), even a philosophical ideal. This explains that, like Briaune, Regnault interpreted very positively a mean result: an average is here synonymous with “order” and “equilibrium” (1863: 26 tr). This order would be associated with constant causes (1863: 150), with “general laws” (1863: 3 tr), even with “this inexorable Fatality that presides over the laws of the physical and moral world” (1863: 157 tr). By contrast, any deviation from the average was considered an “illusion” (1863: 36 tr), an error or a vice in the moral sense: It seems that nature wants to show us that every deviation is harmful, and that the happiness of societies and of individuals consists in a stable and quiet state. (Regnault 1863: 163 tr) And it is not by accident that the final sentence of Regnault’s book is: “The extreme things are always fatal, to peoples and to We can note here Regnault’s conception of individual freedom: men become free as soon as they act in conformity with natural laws and thus with God’s instructions.

28

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individuals” (1863: 210 tr). However, Regnault’s analysis of the average is more sophisticated than Briaune’s. In particular, he precisely coupled the average with time-series decomposition – a major issue in statistical economics and econometrics29 – and he also referred here to the “law of error.” Basically, Regnault thought that economic data would include two components: a systematic component, associated with a constant cause, and an error term, associated with accidental causes. Rather interestingly, since we can find here an illustration of the role unity plays in his worldview, this idea finds its origin in an analogy he perceived with some problems that arise in the natural sciences:30 When we study the natural laws of motion, in mechanics, physics, astronomy, etc., we soon see that motion is subject to laws that are always made up of two simple, separate, and crucial movements. A projectile [which is] thrown describes a parabola, that is, it moves horizontally under the action of the projection, and vertically under the action of the centripetal force. A sphere, a ball, a wheel, a hoop, struck by a body that moves in space, get a movement of rotation and at the same time a movement of translation. The magnetized needle, under the influence of the magnetic force, moves according to the laws of inclination and of declination. The Earth, in its path through space, is ruled by two well separate movements: The first one on itself, in one day; The other one around the Sun, in one year. In order to represent the compound movement of these various bodies, it is necessary to study separately, to decompose the two simple movements that constitute it. This is the method we follow.

See Klein (1997) and Morgan (1997). Cournot brought to the fore a rather similar idea: for him, remember, “as in astronomy, it is necessary to recognize secular variations, which are independent of periodic variations” ([1838] 1927: §11). 29 30

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The variations of the Stock market, subject, as the movements of the Earth, to the laws of universal gravitation, can also be decomposed into: Diurnal and annual, that is, the short and the long period. (Regnault 1863: 142–3 tr) For Regnault, given the nature of socioeconomic data, such a timeseries decomposition was associated with the distinction between accidental causes and constant causes: When we study the laws of the rise and of the fall, it is necessary to distinguish the two principles of the movement in prices: The first one, produced by accidental causes: The second one, produced by constant causes. (Regnault 1863: 143 tr) The short-term components are generated by accidental causes. They occur in an irregular and non-predictable way: “no forecasting is possible; the accidental causes occur without any order, indifferently favorable or opposite” (1863: 143 tr). However, they would own a major property, compensation: For the one who does not focus on tiny agitation, on petty preoccupations of every day, but rises higher and looks for the final result of everything, the accidental causes do not exist. He knows that they have to cancel each other after some time. (Regnault 1863: 146 tr) Regnault sees the principle of compensation as the “first natural law” (1863: 206 tr), and averages reveal this property: on the basis of a sufficient number of observations, an average cancels the accidental causes and would reveal the constant causes, i.e. the long term and systematic components. In addition, and the same can be found in Quételet’s work, the

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use of the average is closely associated with the “law of error,”31 as the following example explains:32 We can have a true idea of what happens in the case an event is announced, in observing what would happen if a large number of people, placed at a certain distance from a high edifice from which they could not get closer, have to measure approximately and visually the height from the basis to the top. Among the remarkable properties given by the set of observations, it is demonstrated: 1. That in adding all the evaluations obtained, and in dividing by the number of observers, we shall have a mean height, only differing from the true height in a mean deviation, that will be all the more reduced that the number of observations will increase, and will diminish in proportion to the square root of this increase. 2. The numbers given by each observer will not appear randomly and without order, but will form a group, according to a certain law, in the most symmetrical way on the two sides of the mean value; if we divide in equal parts the distance from this value to the extreme points, the numerical value of each group would progressively diminish as we would go away from the mean value. (Regnault 1863: 25 tr) As we shall see below, in his analysis of long-term speculation, Regnault used that idea.33 4.3.2. From observation and statistics to mathematical laws In his book, Regnault did not only use statistics, he also determined several mathematical laws, for instance, the “great mathematical law of deviations” (1863: 173 tr):

31 The label “normal law” only appeared with Wilhelm Lexis and Francis Galton (see Armatte 1991 and Porter 1986). 32 This was a usual example at the time. For instance, Porter (1986: 107) shows the way Quételet used it. 33 See section 4.5.4.

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Thus, a mathematical law exists and it rules the variations as well as the mean deviation of the prices on the Stock market[;] this law apparently has never been suspected until now, so we shall formulate it for the first time: THE DEVIATION OF THE PRICES IS IN DIRECT PROPORTION TO THE SQUARE ROOT OF TIMES.34 (Regnault 1863: 50 tr) Regnault’s use of mathematics, which shares much with Cournot’s and particularly Briaune’s, owns two features. First, Regnault believed that the society (as well as the whole “system of the world”) was a harmonious text written in mathematics and numbers by a “magnificent arithmetician” (Rohrbasser 2001: 7 tr) – namely God – that scientists have to decipher with appropriate instruments. He associated “constant mathematical laws” with “the views of Providence” (1863: 51 tr), with “the marvelous order that characterizes the least details of the most hidden events” (1863: 51–2 tr), and he explained that “Nature acts and irresistibly demonstrates by its effects the exactitude of these ratios” (1863: 5 tr). For him, mathematics would reflect the true functioning of the world – its underlying and hidden structure. This idea finds roots in an ancient methodological and philosophical attitude: Galileo’s idea according to which “the book of Nature is ‘written in mathematical language’” (Rohrbasser 2001: 97 tr) as well as Descartes’s “view of the universe as a mathematical system” (Clark 1992: 23). This refers to a mathematical vision of the world, an idea that accompanied the development of the natural sciences from Galileo to Fourier (see Israel 1996) and which was shared by Cournot and Briaune. We then suspect that Regnault has good reasons to write in the early pages of his book: “every mathematical theory is necessarily moral and philosophical” (1863: 4 tr). Second, although Regnault’s reasoning is mathematical (as his empirical verifications of laws show), the most part of his results were exposed in a literary way – he thus proceeded like Briaune and like Quételet (see Jovanovic 2002a and 2006a). Such a use of “L’ÉCART DES COURS EST EN RAISON DIRECTE DE LA RACINE CARRÉE DES TEMPS.” We shall analyze below (section 4.4) that law, which was

34

obtained from observation and which plays a major role in Regnault’s analysis of short-term speculation.

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mathematics is particularly instructive. It reveals that, in the case of France, the emergence of mathematical economics is more complex than what is often assumed. Indeed, mathematical economics did not only rise with the use of mathematics as a demonstration device. From that restricted – and perhaps also somewhat retrospective – point of view, authors such as Cournot,35 Léon Walras, or econoengineers such as Jules Dupuit, are important landmarks. However, as Regnault’s and Briaune’s work illustrate, the rise of mathematical economics should not be restricted to the early use of mathematics as a demonstration device: during the nineteenth century, mathematics was also used in close association with the idea that the structure of the world, elaborated by a divine programmer, was mathematical. The “proofs” in which authors such as Regnault and Briaune were interested were not mathematical ones. Rather, the identification of mathematical laws relied on two complementary elements: first, from their belief in a unified world, these authors felt free to operate economic translations of laws already identified in the natural sciences; second, with statistics, mathematical laws could be unveiled. It is in this kind of joint use of mathematics and statistics that one distinctive feature of natural econometrics can be found. 4.4. SHORT - TE RM SPE CULATION : T HE RAN DOM WALK AS A TROMPE - L ’ŒIL

Regnault’s first demonstration is relative to stock price behavior in the short term, and it aims at showing that short-term speculation inexorably leads to ruin. Regnault proceeded in two main steps. First, he represented price behavior as a symmetrical random walk and he elaborated the mathematical “law of deviations,” which was tested. Second, he introduced brokerage fees in the analysis and he could “demonstrate” the ruin of gamblers. 4.4.1. The random walk In a first step, Regnault approached the short-term variations in stock prices in a probabilistic perspective. More precisely, he saw price behavior as similar to the binomial probabilistic model of “a game of heads or tails” (1863: 34 tr): 35

At least for historians who read his work retrospectively.

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On the stock market, the whole mechanism of gambling comes down to two opposite chances [chances]: the rise and the fall. Each one can always occur with an equal facility. (Regnault 1863: 34 tr) On that basis, he showed, in a very pioneering way, that price behavior took the shape of a random walk36 – although he never used the word. This was undoubtedly an important step in the construction of financial theory. Louis Bachelier was to follow this path37 – in his dissertation, Bachelier (1900) offered a formalization of the Brownian motion and thus initiated the mathematical theory of stochastic processes in continuous time (Mandelbrot 1966) – and the random walk was also used in the construction and the test of informational efficiency theory that was built during the 1960s and the 1970s (e.g. Fama 1970). In the theory of efficient markets, we find a close relation between price and information, and despite strong differences,38 such a relation can also be found in Regnault’s analysis. Information and price movements An important issue at work in Regnault’s book is indeed information. The short-term speculator would only be interested in immediate profits – more precisely in profits made during a period which is shorter than the “liquidation,” i.e. the settlement period.39 He thus tries to benefit from any variation of prices – and thus, in Regnault’s mind, from accidental causes. At this stage, Regnault associated these causes with the new information that would arrive on the market. In addition, he claimed that at every moment of time, the price contains the whole information: When the gambler buys or sells, expecting a rise or a fall of Although, as we shall explain below, the random walk was associated with an attraction process to the mean values, which appears in Regnault’s analysis of long-term speculation. See section 4.5 and Jovanovic (2006a). 37 See Jovanovic (2000 and 2002a) on the way Bachelier was influenced by Regnault. 38 For instance, whereas Regnault saw random very negatively, in Fama and the efficient market theory we can find a positive interpretation of it. 39 In the opposite case, the speculator has to pay the “report ”. 36

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prices, he thinks that prices are below or above their true value: (…) in order to determinate that, it is necessary for him to perceive in the current situation a cause of rise or fall which is not taken into account at this moment. In vain he could pretend that it is only in future and distant consequences that he sees these reasons for rise or fall; we know that these consequences, if they exist, are contained in the current price (…). (Regnault 1863: 29–30 tr) Then, Regnault identified two properties of price variations. First, he explained that “[o]n the stock market, the whole possible events can only determine two opposite effects, the rise and the fall ” (1863: 15 tr), and that the probability for the price to rise is equal to the probability for the price to fall, i.e. ½. If such was not the case, agents could arbitrage40 and choose systematically the strategy that would have the highest probability: In all the games of chance [hasard ] that contain two opposite chances [chances], relative equality precisely results from the possibility for the speculator to choose one chance or the other as he wants: these two conditions cannot be separated, because if one of the two possibilities would generate a greater advantage than the other one, it would be constantly chosen. (Regnault 1863: 41 tr) Second, Regnault claimed that, like in a game of heads or tails, the movements of stock prices would be independent: When I toss up, it is certain that each toss is completely independent from the previous ones (…). In a similar way, the gambler on the Stock market always attempts to conjecture what has to happen on the basis of what has already happened, in such a way that after three or four days of fall, he will be led to believe in rise for the next day, or other times he sees a motive for the continuation of the movement, although a complete independence is after all existing between these various effects. (Regnault 1863: 38 tr) 40

A word explicitly used by Regnault (1863: 40).

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Otherwise stated, at every moment stock prices can rise or fall with the same probability (½), independently of the previous prices. Consequently, the expected profits for each agent are zero. From these two assumptions (equiprobability and independence of variations), Regnault could represent price behavior as a random walk. The “law of deviations” Then, Regnault analyzed the way prices vary through time, and he discovered a relation – that can also be found in Bachelier (1900)41 – between the mean deviation of prices and time.42 When an agent is involved in a new operation, he is in an uncertain situation. He can choose a given deviation – i.e. the profit he wishes or the loss that he is ready to support – but the time of the operation remains uncertain. He can also choose a given period, but then the deviation is undetermined:

As noticed in Jovanovic (2006a: 200), “if stock prices follow a random walk, because of the independence of this process, the deviation of the 41

prices increases with the square root of time, Ƴ ( nƴ ) n

12

Ƴ (ƴ ) , where n is a

multiple reference scale. It is precisely what Regnault finds for the 3 percent French bond.” 42 Regnault also calculated a “probable” deviation (in fact the median deviation). The difference between both deviations was seen as a measure of the instability of the market: “We can note (…) the remarkable ratio that links the probable deviation to the mean deviation, approximately 2/3, a ratio that we frequently find, for instance the one which links the probable life to the mean life. Moreover, this ratio is not constant, it is used for giving a measure of the regularity of the movement in prices, and depending on whether this movement is following less violent shocks (…), the probable deviation gets closer to the mean deviation; they could even be identical if the movement in prices was perfectly regular and continuous. And just like the tendency of the probable life to get closer to the mean life is a sign of the progress of the well-being and of the civilization in a country, the ratio of deviations for prices, which tends to get closer to unity (…), is an exact measure of the morality of speculation (…)” (1863: 53 tr). This refers to Regnault’s conception of social history, that we shall analyze in section 4.6.

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[W]hen a speculator begins an operation, most often he is not decided to sell precisely at a given day and at a given hour; what mainly influences him is the benefit or the loss that the operation will present at one moment, always undetermined in advance; according to his character and his habits, he will content himself with approximately a certain benefit, and a certain loss will be sufficient for determining him to sell. But although he acts this way, and could stay a more or less long time without making operations, although there is no apparent regularity in the intervals of time necessary to bring the deviation of selling [l’écart de liquidation] that suits him, it would be indifferent to him to substitute the fix deviation that he researches between his purchase or selling prices for a certain equal time between each of his operations and his selling, although, by this way, he only has irregular differences, sometimes stronger, sometimes weaker. (Regnault 1863: 48 tr) In the latter case, a mean deviation for a given period can be calculated, and Regnault looked for a relation between time and that deviation. To this end, he identified from observation43 two elements. First, for a given period of time, the mean deviations are approximately equal: If we follow carefully the variations of the Stock market during a very long period of time, beginning with a recording of the price of a security for a very large number of days chosen indifferently, then calculate the deviation of price between these prices and the prices corresponding to an epoch equally distant from these dates, a distance of one month for example, and then repeat the same experiment several times, we shall always obtain sums of deviations or averages that are sensibly equal. In such a way that various speculators who would have invariably followed this principle, choosing always one month, or more The bond Regnault analyzed is the French 3% (the “Rente”), then the most important bond related to the French public debt. At the time of Regnault, approximately 450 securities were quoted in the Bourse de Paris and among them approximately 160 (French and foreign) bonds.

43

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generally any given interval of time between each of their operations and its selling, and who would have speculated separately during a very long time, would all have obtained a similar result, would have obtained in average equal deviations between their purchase prices and their selling prices. We can conclude that deviations are equal for equal times. (Regnault 1863: 49 tr) Second, the shorter the period of time considered, the smaller the deviations. From observation, Regnault could clarify this relation between time and deviations: [I]f we search for the link that can unite these different deviations to the different times during which they occurred, we can see that for a period half inferior, the deviation diminishes, not of the half, but in a proportion which is sensibly to the first as 1 is to 1.41; for a period three times inferior, the deviation diminishes in a proportion which is as 1 to 1.73, for a period of four times inferior, in a proportion 1 to 2. (Regnault 1863: 50 tr) From these elements, he proposed the following general result – his “great mathematical law of deviations” (1863: 173 tr): Thus, a mathematical law exists and it rules the variations as well as the mean deviation of the prices on the Stock market[;] this law apparently has never been suspected until now, so we shall formulate it for the first time: THE DEVIATION OF THE PRICES IS IN DIRECT PROPORTION TO THE SQUARE ROOT OF TIMES.44 (Regnault 1863: 50 tr) This law thus stipulates that an individual cannot anticipate in an exact way the future price of a security, but he can anticipate a mean deviation for a given period of time. Regnault then determined (for the period stretching from 1825 to 1862) the mean deviation and the “probable” deviation – i.e. the “L’ÉCART DES COURS EST EN RAISON DIRECTE DE LA RACINE CARRÉE DES TEMPS.”

44

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median deviation – of the Rente 3% for one month, and he found the following results: From the observations realized until the recent period on the variations of the Rente 3% since its creation, the mean deviation of prices, for one month, can be fixed at 1 fr. 55 c. The probable deviation, at 1 fr. 10 c. That is, if a speculator realizes for a long time operations that he would sell regularly every month, the mean deviation between his purchase and selling prices, or the sum of the differences divided by the number of operations, would be approximately 1 fr. 55 c., and in the total number of his operations, there would be one half of them that would be sold [liquidées] with a deviation superior to 1 fr. 10 c. and one half with an inferior deviation. (Regnault 1863: 52–3 tr) Then, he deduced from these two monthly deviations the probable and the mean deviations relative to other periods inferior to one month (see columns 2 and 3, table 4.1). For these periods, the mean deviation D(x) was determined as follows:45 D (x )

1.55 , 30 x

x denoting the period considered (inferior to 30 days).

45 The mathematical formulation does not appear explicitly in Regnault’s book, he only gave a literary presentation of it: “To obtain the mean deviation of liquidation for any number of days, we begin by dividing the number of the days in a month, 30, by this number of days; we have thus the ratio of times; we take the square root of this ratio, and we divide the mean deviation of the month, 1.55, by this square root” (1863: 56 tr).

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Table 4.1 Deviations and differences inferior or equal to one month. In this table we find the period of transaction considered (“temps moyen de liquidation”), the probable and mean deviations (“écarts probables” and “écarts moyens”), the absolute value of the mean deviations relative to an operation of 1500F (“différences brutes sur 1500F de Rente”), the net gains and the net losses of the speculator (“différences nettes en gain,” “différences nettes en perte”), and the ratio between them (“Le gain = 1, la perte =”). Source: Regnault (1863: 55).

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From these deviations, he deduced the gains and the losses of a speculator who would operate with 1500F of the Rente 3%. The fourth column of table 4.1 gives the “gross differences” (the différences brutes ), i.e. the absolute values of the mean deviations relative to this operation of 1500F.46 Although we shall analyze below this issue, the next columns of this table incorporate brokerage fees: with the two brokerage fees associated with each operation – their amount is 20F – Regnault could obtain the gains and the losses of the operation (columns 5 and 6) and the ratio between them (column 747). The test of the theoretical results In the two previous chapters, we have seen that natural econometricians devised and used a set of procedures to “test” or to verify their results. These “tests” were quantitative – they consist in a comparison of theoretical results with observed data – and qualitative – this was particularly apparent from Cournot’s “philosophical probability.” In the Calcul des Chances, Regnault used both kinds of testing procedures.48 The first one is based on a comparison with existing scientific laws, and this was a means to ensure that his law was a universal law, in accordance with one of his initial postulates: a unified world. The second procedure takes the shape of a comparison of the theoretical results with observation. The first test, of a qualitative nature, is rooted in the unified worldview to which Regnault adheres. We have seen above that he believed that some laws were ruling a large set of phenomena in the world and, from this unified worldview, a unified methodological framework for all the sciences was proclaimed. Precisely, Regnault’s first test consists in checking that the “law of deviations” is the financial translation of a more general natural law:

46

Following a convention of the time (Jovanovic 2002a), these differences

are determined as follows:

1500 D( x ) . 3

In column 7 of table 4.1, the ratios are always greater than one, and this means that the probability of loss is superior to the probability of gain when brokerage fees are taken into account. This point is analyzed in section 4.4.2. 48 Although Regnault’s qualitative tests are less sophisticated than the ones of Cournot. 47

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The price, in its variations, is constantly in search for its true price, or an absolute price, that we can represent as the center of a circle, whose radius will represent the deviation that can equally appear in one or the other direction and on each point of the surface, in a period of time consequently equal to this surface, and the whole points of its circumference will represent the limits of deviation. In all its variations, the price is only moving away or getting closer to the center, and from the first notions of geometry, we know that the radius or the deviations are in proportion to the square roots of areas or of times. (Regnault 1863: 51 tr) Following Jovanovic (2002a), it is also important to remark here that similar laws were suggested by Quételet (1846 and 1848), for instance between weight and height or between height and heartbeats: “The number of heartbeats would be in direct proportion to the square root of height” (Quételet 1848: 48 tr). From these analogies, Regnault could explain that the “law of deviations” was nothing but a general law, even a natural law. It should however be noted that he had probably in mind such general laws while devising his own financial laws, and that he read, at least partially, his data from such initial beliefs. Then, Regnault empirically tested his theoretical results. For instance, he analyzed the relation between time and the means of extreme deviations of the Rente for various periods (a month, a quarter, and a year). From observation, he found that the monthly mean deviation was 2.73 and that the yearly mean deviation was 9.50. He then showed that “[t]he deviations follow here, once more, in their extreme variations, the great mathematical law of direct deviations given by the immediate difference of prices [cours] from one time to another: the magnitude of deviations is in direct proportion to the square root of times”49 (1863: 173–4 tr). He thus verified that 9.50 (the observed mean deviation) was close to 2.73 12 9.45 (the theoretical mean deviation).50 His conclusion was very enthusiastic, in a Briaunian style:

“la grandeur des écarts est en raison directe de la racine carrée des temps.” A similar test can be found in Bachelier (1900). See Jovanovic and Le Gall (2002).

49 50

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Is there a more striking example of a matching of theory and experience! (Regnault 1863: 175 tr)51 More generally, these developments enlighten the econometric nature of Regnault’s analysis of short-term speculation: we have here a mathematical relation grounded on statistics, which is verified with observed data, and which is fully dependent on the belief in a unified world.52 4.4.2. On ruin: Transaction costs as the visible hand of God However, the previous developments do not suffice to depict Regnault’s full analysis of short-term speculation. Indeed, he extended the previous analysis and introduced transaction costs, from which the inexorable ruin of the short-term speculator could be demonstrated. Regnault could then show that this kind of behavior is harmful and vain.

It can be noted that if there is a mismatch between theoretical and observed results, Regnault does not lose faith in his laws: he thought that their exactitude could be revealed through the use a wider set of observed data. See for instance Regnault (1863: 57–8). 52 These results opened the way for probability rules. On the basis of the extreme monthly deviations, Regnault found that “For an identical time, the probabilities vary in direct proportion to the square of deviations [Pour un même temps, les probabilités varient en raison directe des carrés des écarts]” (1863: 177 tr). For an initial price of 75F and a settlement period of one month, Regnault (1863, 177) found the following rules: 51

1 on 10 (10%)

for 0.865 10

2.73

or 77 fr. 73

1 on 15 (7%)

for 0.865 15

3.35

or 78 fr. 35

1 on 20 (5%)

for 0.865 20

3.87

or 78 fr. 87

1 on 25 (4%)

for 0.865 25

4.32

or 79 fr. 32

1 on 50 (2%)

for 0.865 50

6.12

or 81 fr. 12

1 on 100 (1%)

for 0.865 100

8.65

or 83 fr. 65

For example, there is thus a probability of 1% for the price of the Rente to reach 83.65F in one month. In Regnault’s book, a lot of similar examples can be found.

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Risks, costs, and inequalities At this stage of his “demonstration,” Regnault focused on the costs that affect the speculator when trading: the risk of dealing with an informed trader, the risk that the order will not be executed, and the risk that agents manipulate prices or information.53 However, these risks were considered negligible – they could be avoided or reduced, and were seen as exceptions. For instance, the risk that an agent deals with an informed trader could be reduced by an appropriate choice of bonds – those whose market is large:54 Other things the same, the unfavorable chances [chances] are thus largely reduced on a large market, where the business is very large, and they proportionally increase on a small and especially an easily influenced market. (Regnault 1863: 43–4 tr) By contrast, a fourth element plays a key role in Regnault’s analysis of short-term speculation: the brokerage fees that concern every operation.55 Let us remind ourselves that without any brokerage fee, the expected profits are zero. However, when a brokerage fee exists, [t]he equal chances to win or to lose different amounts of money [leave room for] unequal chances to lose or to win an identical amount of money. (Regnault 1863: 212 tr) The main consequence of the introduction of these fees lies precisely in the fact that the probability to lose a given amount becomes At least in a retrospective perspective, this kind of risk raises three interesting problems. First, personal information and informational asymmetries disturb the functioning of the Stock market and modify equity (1863: 42). Second, Regnault mentioned mimetic behaviors (1863: 97). Third, he also considered the use of erroneous information in order to influence the market. 54 Similarly, the manipulation of information was considered marginal (1863: 97–8), and the risk that the order will not be executed (1863: 43–4) could be reduced by a change in the limits of the order price. 55 “[W]hat mainly contributes to establish inequality is the transmission right or the brokerage fee [courtage] withdrawn from every operation” (Regnault 1863: 45 tr). 53

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greater than the probability to win that amount, and the expected profits become negative. Regnault thus had in his hands the elements that could pave the way for a “law of ruin.” The “invisible enemy” and the “law of ruin” Once brokerage fees are taken into account, the gambler would face an “invisible enemy whose chances of gain and loss are inverse to his own” (1863: 71–2 tr). In addition, Regnault explained that this inequality increases exponentially with the number of transactions: In every unfair game, the repetition of throws [coups] leads to a very rapid increase, and in proportions truly unbelievable, of the probabilities of loss of the disadvantaged player; on the Stock market, this increase is even more rapid (…). (Regnault 1863: 88–9 tr) This increase of losses is represented in table 4.2, which visualizes, in a very striking way, the dangers of ruin.56 In this table, we can find the chances to lose or to gain an amount of 14000F. In the first three columns, which come from table 4.1, we find the mean time of transaction (from 0.5 day to 30 days), the “gross differences” on 1500F of Rente, and the ratio between loss and gain on these differences. The next column gives the number of chances to lose an amount of 14000F for one chance to gain that amount when operating with 1500F. The next four columns give similar results when an agent operates with 3000F, 6000F, 12000F, and 30000F.

56 For Regnault, “The speculator who would only operate with 1500 fr. of Rente, and who would sell each of his operations during the same day, for one chance of gain that he would have to earn a probable amount of 14000 fr., would have a number of chances of loss expressed by eighteen digits. The one who, only operating with 1500, would always sell the following day each of his operations, would have a number of chances of loss expressed by the same number of digits, but even more considerable, 689 000 000 000 000 000, approximately (…). These are real impossibilities. Even if we do ten thousand experiments or ten thousand drawings per day, an event of this kind would not appear once in a billion of centuries” (1863: 82 tr).

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Table 4.2 The chances to lose or to gain an amount of 14000F. In the table we find the periods considered (“temps moyen de liquidation”), the absolute value of the mean deviations relative to an operation of 1500F (“différences brutes sur 1500F de Rente”), the ratio between losses and gains (“gain = 1, perte =”), and chances of loss for one chance of gain (“pour une chance de Gain, les chances de Perte”) when operating with 1500F, 3000F, 6000F, 12000F, and 30000F. Source: Regnault (1863: 78–9).

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Regnault put forward three additional laws. First, “the chances of loss are increasing with the power given by the amount of wealth ”57 (1863: 91 tr). Second, “the chances of loss are increasing with the power given by the inverse ratio of amounts ”58 (1863: 91 tr). Third, he identified a specific element – time – that would exert an influence on the chance to lose on the stock market: “THE CHANCES OF LOSS ARE INCREASING WITH THE POWER GIVEN BY THE INVERSE RATIO OF TIMES”59 (1863: 91 tr). Thus, “[t]he one who sells in a time half inferior, squared the number of his chances of loss, the one who sells in a time three, four, or five times inferior, increases them with the power three, four, five, etc.” (1863: 91–2 tr). He could then bring to the fore the following results: In sum, in order to compare exactly the more or the less [important] chances [chances] to lose or to gain on the Stock market, three elements have to be considered. 1. The more gambling continues for a long time, or in other words, the more the amounts to lose or to gain are important; 2. The smaller the amounts on which we operate; 3. The shorter the mean time of settlement, And the more the chances of loss are important. By contrast: 1. The smaller the amounts to lose or to gain; 2. The bigger the amounts on which we operate; 3. The more the mean time of settlement is distant, And the less the chances of loss are important. The probability of loss is in these three cases superior to 1/2, [it] can pass, when we make these three elements vary, and when we combine them appropriately, by all the degrees wanted between 1/2 and unity, from the doubt to the certainty almost absolute.

57 “Les chances de perte s’élèvent à la puissance donnée par le rapport direct des fortunes.” 58 “Les chances de perte s’élèvent à la puissance donnée par le rapport inverse des quotités.” 59 “LES CHANCES DE PERTE S’ÉLÈVENT À LA PUISSANCE DONNÉE PAR LE RAPPORT INVERSE DES TEMPS.”

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For the rise or the fall that we can exert over each of these elements, the law of variation of chances to lose is always that of the extraction of roots, or of the rising of powers. (Regnault 1863: 93 tr) Regnault could thus “demonstrate” that gambling inexorably leads to ruin.60 The short-term speculator, who constantly wants to benefit from the variations that result from accidental causes, has to transact rapidly and frequently. However, rapid trades generate only small profits – according to the “law of deviations” – and frequent trades lead him to lose his capital – because of brokerage fees. Since profits cannot compensate for brokerage fees, the ruin of short-term speculators could not be avoided. In sum, Regnault demonstrates here that short term speculation, based on accidental causes, was nothing but a vice: “the frequency of operations is an abuse; and since the unique motivation of each exchange is and has to be usefulness, each time this usefulness disappears, there is an error or a bad use” (1863: 105 tr). In fact, what Regnault demonstrated here is that ruin is a divine punishment: individuals cannot defeat the divine natural laws that would operate in the long term, and they should thus respect God’s design. The identification of such natural laws was precisely the aim of his analysis of long-term speculation. 4.5. F ROM VICE S TO VIRTUE S: O N LON G- TE RM SPE CULATION Regnault’s second “demonstration” aims at identifying the deterministic laws that rule the stock market in the long term and at showing the way long-term speculation would represent a social usefulness. Once more, the analytical, the methodological, and the philosophical levels are perfectly entangled. For Regnault, the accidental causes compensate in the long term, and the underlying order that would rule the stock market could be discovered. With the help of statistics (especially the average), and in conformity with his worldview, he brought to the fore laws, in particular a mathematical Regnault thought that he could even predict the exact moment of ruin (see 1863: 95). In full accordance with his worldview, he wrote: “Alas! why does he [the gambler] ignore that his imminent ruin, predicted as exactly as the revolutions of planets in their orbits, is an unavoidable, necessary effect of chances and of their combinations!” (1863: 98 tr).

60

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143

“law of attraction.” 4.5.1. The search for constant causes As seen above, Regnault believed that laws associated with constant causes were permanently acting in the social world, although masked by accidental causes. He thus put particular emphasis on the identification of such constant causes. For instance, he first looked for a “special” constant cause61 that would contribute to the formation of “the true price of the bond” (1863: 111 tr). This identification resulted from the main feature of a bond: the payment for an interest, defined as “the representation of the risk capital incurs” (1863: 124 tr). Regnault believed that “the interest rate is the most important element in the composition of a security” (1863: 120 tr). This focus on interest deserves two comments. First, risk is considered a source of instability, and Regnault thus claimed his predilection for bonds offering low interest: agents have “to avoid carefully too large risks that can compromise [their] capital” (1863: 123 tr), since “numerous dubious companies offer unjustified dividends (…) as a misleading lure [appât trompeur]” (1863: 124 tr). Second, a similar idea can be found in his distaste for variable interest securities: this variability was seen, once more, as offering some basis for gambling.62 Both ideas contribute to understand Regnault’s focus on the French 3% bond: the identification of constant causes was certainly eased by the constant nature of the interest, and Regnault claimed the morality of such a bond. The knowledge of such a constant cause was delineating the outlines of a moral behavior leading to social usefulness. Whereas 61 Two kinds of constant causes were differentiated: “general” (générales) vs. “special” (spéciales) constant causes. The first ones are relative to events that concern the whole general conditions (for instance the whole security market): “They encompass all of a political, commercial and financial situation, they lead to a rise or a fall in the general interest rate, or exert an indirect influence on prices via imposition taxes (…) or any financial measure whose main effect is an acceleration or a reduction of the circulation of securities” (1863: 111 tr). By contrast, “special” constant causes are only relative to a particular security (1863: 111). 62 In section 4.6, we shall show the way Regnault, in conformity with his worldview, devised means for reducing variability of stock prices.

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short-term speculation would be largely independent of interest and capital, and consequently would lead to a “ghost market” which would be non-significant as a game practiced “in a gambling-den” can be (1863: 108 tr),63 long-term speculation was undoubtedly seen as a fruitful path: it would be associated with constant causes – the only significant causes, in Regnault’s mind; it would generate trust;64 and it would be a moral practice, in the sense that it was associated with labor from two points of view. First, an agent has to spend a considerable amount of time and labor to choose appropriate securities, i.e. to identify those which would have “serious” economic counterparts. Second, these counterparts were precisely seen as sets of labor: profits result from “an accumulation of Labor, of Savings and of Production” (1863: 103 tr). Securities are here basically seen as portions of capital that have to be cultivated, as sets of labor forces:65 The only possible wealth is the one which is the product of labor; any other one is purely chimerical, or is only a move of wealth that, to enrich a few ones, impoverishes necessarily other ones; in the estimation of public wealth, there is no durable rise except the one which results from capital; every fictitious rise or fall, that escapes the regular action of serious supply and demand, since it has for unique effect the ruin of few individuals from which a few others benefit, does not diminish, does not add an atom to the amount of this wealth. (Regnault 1863: 137 tr) Such a belief was also closely linked to what Regnault considered the raison d’être of men: labor. “True speculation” was thus defined as “an 63 An anecdote is worth noting: despite his condemnation of “gamblingdens,” the powers of evil triumphed: nowadays his own house of Enghienles-Bains (a bourgeois city in the north of Paris) belongs to a casino company. 64 Regnault mentions the creation of “a moral value [valeur morale] that we label trust or creditworthy [crédit] and that can be perfectly measured [susceptible d’une appréciation chiffrée] just like concrete and material wealth” (1863: 109 tr). 65 In that sense, he remains close to the Classical paradigm: he believed that “[t]he price of goods results from several elements; labor is its real and closest measure” (1863: 111 tr).

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accumulation of the fruits of Labor” (1863: 6 tr). Whereas shortterm speculation was based on the search for immediate profits and had no economic counterparts, long-term speculation was associated with the development of capital and labor, and was seen as delineating a moral behavior. In that sense, it should be clear that Regnault approached the stock market with a harsh condemnation of the search for immediate individual interest in mind: collective interest – i.e. behaviors that would be in conformity with natural order, as we shall see below – should prevail. Now let us turn to Regnault’s concrete analysis of long-term speculation, constructed in four steps and in which nice econometric ideas can be found. 4.5.2. The determination of the mean price Regnault started his analysis of stock prices over the long term with the determination of the mean price of the Rente 3%. He advocated the usefulness of Quételet’s analyses, and he considered the average the most fruitful statistical instrument, since it unveils the constant causes: From a look at [the data], it can be seen immediately that the variations of the Rente occurred in very wide limits, since it oscillates from the price of 86 fr. 65, in July 1840, to that of 32 fr. 50, in April 1848, with a deviation of 54 fr. 15 between both prices. The revolutions that modify and change the face of the social order, the scourges that distress humanity, the disruptions, the various crises that perturb the regular course of events, seem to appear without any visible order and should, it seems, leave no room for the reasoned appreciation of things whose economy is disturbed by so hard, so unexpected shocks. However, and this is the important fact on which we call attention, although the accidental causes that led to so large variations of the price of the Rente are considered resulting from a blind chance [hasard aveugle] and have between them no precise systematic connections, although their effects have been so powerful that it is tempting to neglect all the secondary causes, when we widen the range of our observations a little bit, it is easy to perceive that all these fortuitous anomalies soon

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compensate and destruct each other, cancel each other and vanish almost entirely to reveal the sole weak causes, but of a constant nature. It is the use of averages that gives us the demonstration of this fact. (Regnault 1863: 150 tr) Regnault proceeded as follows:66 for each month, during the period stretching from May 1825 to October 1862, he identified from daily quotations the highest and the lowest prices, from which he computed the highest and lowest monthly mean prices; from them, he obtained monthly mean prices; finally, he determined the general mean price (72.48F):67 The [monthly] mean value varies from 72.20 at the lowest level, to 73.05 at the highest [level], with a deviation of only 0.85 c. between these two prices. The general mean value, considered between these quantities, gives the price of 72.48. Thus, during a relatively short period, which only covers thirty-seven to thirty-eight years, during which the variations occurred each year in a very different way in the course of each month, the results already appear with striking evidence. (Regnault 1863: 152 tr) As we shall see below, this positive appreciation finds its roots in the fact that for him, the average and order were coupled. 4.5.3. Coupon payment and seasonal effects Regnault then wanted to verify that monthly mean prices were increasing regularly between the coupon payments,68 the very feature Regnault’s data are presented on pp. 148–9 of his book. However, in his book Regnault determined other “mean values” (in his own words), including for him the median value (73.40). See Jovanovic and Le Gall (2001b: 351–2). 68 That is, the money that the holder of the bond gets twice a year. Regnault remarked that the maximum price of the French bond precedes the days of 66 67

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of the French 3% bond: Within the interval defined by the payment of two coupons, prices should regularly increase, under the influence of the interest, and define a perfectly straight line, as we can see in figure [4.1]. (Regnault 1863: 153 tr)

Figure 4.1 The evolution of monthly mean values of the price of the French 3% bond (observed mean values: thick curves; theoretical values: thin lines). Source: Regnault (1863: 153).

In other words, Regnault defines here a “normal” pattern that should characterize monthly mean prices. He examined its robustness, and compared the regular increase of the price between coupon payment and the observed monthly mean prices. Like Briaune, he did not use formal testing procedures; however, he proceeded like some turn of the century econometricians69 and he used a graphical approach. The observed and the theoretical values are plotted in figure 4.1. Although Regnault noted the existence of systematic deviations of

its coupon payment (June 6 and December 6), whereas its minimum price happens on the following day. 69 See Morgan (1997).

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observed data from the straight lines,70 he found that the two curves were matched, and he concluded that: Among the most capricious variations, the price of the Rente is thus ultimately and solely influenced by the constant causes; the main one, clearly identified, is the amount of interest; (…) this cause, apparently so weak, should inexorably triumph over the other ones. (Regnault 1863: 154 tr) Such an analysis deserves two comments. First, Regnault discovered well-shaped seasonal effects:71 the lowest monthly averages occurred in June and December and the highest monthly mean values occurred in May and November. Second, with averages, the accidental causes disappear, and only the long-term constant causes – only order – would remain: The accidental causes have completely disappeared, and in general, so powerful are their effects, so bizarre, so irregular are their apparitions, they will always cancel almost fully after a certain time, to reveal only the effect of regular and constant causes, even though this effect is so weak. (Regnault 1863: 154 tr) In other words, stock prices are far from obeying a random process: with the help of statistical instruments, an underlying order could be identified. However, he thought that more significant forms of order could be discovered in data. 4.5.4. The discovery of “attraction centers” Given the stormy history of France during the period considered (at He hypothesized that these deviations originate in the existence of constant causes other than the interest, although he never analyzed them carefully. 71 Seasonal effects were also put forward by Quételet, for instance in his analysis of crimes (Quételet 1835). Note also that in a paper read to the British Association for the Advancement of Science in 1862, Jevons took a similar approach to seasonal fluctuations. This paper is reproduced and analyzed in Hendry and Morgan (1995). 70

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the economic, social, and political levels), Regnault suspected that the mean price previously determined (72.48) results from heterogeneous sub-periods. Once more, the analysis was based on a visual approach. In figure 4.2 Regnault represented the frequencies of the monthly prices of the Rente 3% from May 1825 to October 1862.72 He remarked that: It is around this price of 73.4073 that the evolutions of the Rente stir, however not randomly and without order, but according to a certain disposition, whose regularity is the consequence of the curious properties of the theory of deviations, which completes the theory of averages. It is not enough that, under the influence of disturbing causes, an event varies in the most regular way, the order of succession in which this event appears is also ruled by the certain laws of combinations. The largest number of these returns is located around the mean value, then decreases symmetrically on the two sides, as the deviation increases. The same phenomenon always appears with changes that are mainly relative to the deep nature of things or events. If we consider a large number of prices of the Rente at different epochs separated by an identical interval of time, by making a record of all these prices by order, from the lowest to the highest, we see that the negotiations have been more or less frequent on the different prices, according to a certain order, and grouping preferentially on some prices; it is this disposition well noticed of the prices to move around a certain equilibrium state that we visualize in figure [4.2]. (Regnault 1863: 166 tr)

However, in this figure Regnault mentions that the period considered stretches from 1825 to 1863. 73 This refers to what Regnault labeled the “probable price,” i.e. the median price. 72

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Figure 4.2 The distribution of the monthly prices of the French 3% bond, 1825–1862. Horizontal axis: the price of the French Rente 3% (from 32 to 86F). Source: Regnault (1863: 167).

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From that figure Regnault identified four peaks, that he labeled “attraction centers” or “attraction axes” (1863: 168 tr). Then, he explained how each of them would be associated with specific historical circumstances and he looked for the price that the Rente should reach in a “normal” state, i.e. the price that the bond should reach during quiet and prosperous periods. The first “attraction center” (46F) would be mainly generated by the year 1848, characterized by a political revolution, and the second one (57F) was associated with political disorders (1830–1831 and 1849–1851). These “attraction centers” would thus represent “abnormal” moments of French history, and this is why Regnault considered them “deviations” (1863: 169 tr). The third one (70F) would correspond with periods of “transition toward the great industrial and commercial movement” (1863: 169 tr), 1825–1832 and 1854– 1862, and should be considered an “unstable state” (1863: 170 tr). Finally, the fourth one (80F) occurred during a “long period” (1863: 170), the years 1833–1847 and 1852–1853, that Regnault considered prosperous – during these years the Rente was at its “apogee” (1863: 169 tr). This price was seen as a “normal” one, as the average relative to a harmonious state of the economy and the society. Then, he focused on the distribution of prices around these “attraction centers.” He noted that their frequency “decreases symmetrically on the two sides” (1863: 166 tr), and he concluded that: (…) [T]he so capricious fluctuations of the public bonds, that seem to stir in a confused way according to the inconsistency of the most varied and unexpected events, move by contrast with an admirable symmetry around some attraction or gravity axes, and follow in that respect the universal laws that rule the world. (Regnault 1863: 168 tr) Regnault interpreted this distribution as the manifestation of a “force” (1863: 188 tr). Here he had in his hands the elements from which he identified a “law of attraction.” 4.5.5. The “law of attraction” Precisely, the final step of Regnault’s reasoning was the identification

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of a law that rules stock prices in the long term: it took the shape of a kind of attraction mechanism that would constantly move the price toward the average. In the first part of his book, Regnault elaborated the “law of deviations,” according to which, remember, “THE DEVIATION OF THE PRICES IS IN DIRECT PROPORTION TO THE SQUARE ROOT OF TIMES” and is also independent from the price itself. This law could

not contribute to the explanation of a possible relation between the observed price and the mean price. However, on the basis of the preceding steps, he could put forward the existence of a complementary mathematical law: a “law of attraction,” which stipulates that: The price, in all its deviations, is permanently attracted to its mean price, in direct proportion to the square of its distance.74 (Regnault 1863: 187 tr) In spite of its apparent randomness, revealed by Regnault’s analysis of the short term, the price of the French 3% bond would thus be attracted in the long term toward a mean value – deviations from that price would be nothing but temporary. At the methodological level, the construction of that law enlightens natural econometrics. In Regnault’s mind, it is indeed a mathematical law – although it was, once more, literary exposed – and it was inferred from two connected elements: statistics, and in particular the use of averages; and his worldview, in particular his unified conception of the world. For him, remember, “the moral world is ruled by the same laws as the physical world” (1863: 5 tr), and he could believe that attraction mechanisms were also at work on the stock market.75 Although Regnault dealt rather cautiously with this “law of attraction” – he confessed that he ignored “the measure of this force, and the very moment when it has to be at work” (1863: 188

74 “La valeur, dans tous ses écarts, est sans cesse attirée vers son prix moyen, en raison directe du carré de son éloignement.” 75 This is also an illustration of the fact that “at the apogee of classical mechanics (…), there existed no scientific project or political utopia which did not seek a secret principle of attraction” (Ménard 1989: 90).

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tr)76 – its identification was his ultimate aim. He could indeed “demonstrate” that stock prices obey a law that imposes upon men, and the full meaning of his whole book becomes apparent here. In the Calcul des Chances, he showed that the short-term speculator was only focusing on accidental causes, i.e. on deviations. But he would act that way because he is “blind” (1863: 198 tr): he ignores that “the extreme things are always fatal, to peoples and to individuals” (1863: 210 tr) – he ignores that he will be ruined since natural laws and constant causes cannot be defeated. By contrast, the “true speculator” focuses “less on the current circumstances than on a future more or less distant” (1863: 198 tr). The “law of attraction” precisely served two purposes. First, it was affording an answer to one of the questions motivating the Calcul des Chances: “For a given price, is it preferable to buy or to sell at this price? ” (1863: 142 tr). Second, it aims more generally at educating individuals: they should learn that “[t]ime always takes care to bring back the price to its true value and to correct the deviations of speculation” (1863: 205 tr), that “nothing in the world could stop a just return of things” (1863: 137 tr), that in some circumstances “it is necessary to WAIT” (1863: 198 tr). The knowledge of such a natural law was indeed an important feature of Regnault’s work, as we shall see now: it should lead to a state of certainty, a stable state in accordance with natural order and God’s design – an “end of history.” 4.6. SCIE N CE AS A ME AN S TO RE ACH THE “ E N D OF HISTORY” From the discovery of the laws that rule stock prices in the long term, it could be possible, through education, to reach a stable state of the stock market (and more generally of the society, in Regnault’s mind), a harmonious state that would be dominated by the taming of risks and deviations, at the individual and at the collective levels. In contrast with short-term speculation, long-term speculation would be based on no accidental causes and would generate no The analysis of this law was mainly based on a unique example, that of 1848: “Why, when the Rente fell at the price of 32.50 in 1848, did it increase so rapidly and with so much vigor, although it stayed quoted during several years at the extreme prices of 85 and 86? Because the distance to the mean value was three times more considerable in the first case, the Rente (…) had a force nine times more considerable to rise than to fall” (1863: 188 tr). 76

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deviations: It is Gambling, that is, the speculation with all its abuses, which represents the expansive, indefinite force of the movement of prices. It is Capital, that is, the useful speculation that, as the unique and true principle of that movement, represents its restrictive and definite force. All the efforts of Gambling tend to increase the deviations of the variation of prices. All the efforts of Capital tend, by contrast, to narrow them. (Regnault 1863: 135 tr) Regnault thought that “useful speculation,” since it is associated with laws that could not be defeated (the “law of ruin” and the “law of attraction”), would inexorably triumph. More precisely, In this constant fight between Gambling and Capital, the advantage must finally go to the latter. If a rise that, under the sole influence of capital, has been of 10 francs on the price of a bond, but has been exaggerated under the influence of gambling in an artificial rise of 30 francs, sooner or later there will necessarily be, and by this unique fact, a backward movement that, making the price decrease of 20 francs, will only leave the natural rise due to capital. And if gambling, acting in an opposite way, had brought a decline of 30 francs, it is absolutely necessary, sooner or later, that a rising reaction of 40 francs occurs. The sum of reaction, always equal to the sum of action in all the effects of nature, has also to exist in all the results given exclusively by gambling, because the effect of selling or buying short always calls for an opposite effect. The reaction that always happens after a considerable movement, more or less sharp, more or less prompt, because of the causes that led the movement, can never be equal to the action immediately, because the first cause is not destroyed; for the reaction to be complete, it is necessary that the cause does not exist anymore. This is, however, only a matter of time. The reaction would be obtained in the interval of a unique liquidation, if short

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buyer and short seller had no facility to continue indefinitely their fictitious operations, by the mean of reports. The most deplorable error that could be made would be to overemphasize the alleged power of gambling, to attribute to it any efficiency, to imagine that it can operate in one direction without any forced reaction in the other direction. The governments can tolerate gambling [agiotage] when, by a fictitious rise of public bonds,77 they hope ensure for a moment the success of their policy, [but] they will never stop, and nothing in the world could stop a just return of things, a return all the more disastrous that the illusion has been important and has lasted for a long time. (Regnault 1863: 135–7 tr) Of course, in the real world deviations and dissenting behaviors – gambling – exist. However, both would basically originate in ignorance or vice.78 Ultimately, the Calcul des Chances thus aims at educating agents who transact on the stock market as well as the political authorities.79 We find here the idea, which also underlies Briaune’s thought, that the raison d’être of science is to afford means for reaching a stable and harmonious state of societies, a state where there is no room for perturbations, a state exclusively ruled by natural order and God’s instructions. The knowledge and the respect of these laws should indeed help reaching a stable state of the stock market and of the society, a harmonious “end of history” in which deviations, vices, errors are fully tamed. As Regnault explains,

This refers to episodes of French financial history mentioned in the introduction of this chapter. 78 In Regnault’s mind, the pursuit of self-interest is a kind of vice. For him, individuals are strictly dependent on the natural laws and only get freedom within the frame of a knowledge and a respect of these laws – “this inexorable Fatality that presides over the laws of the physical and moral world” (1863: 157 tr). With the Calcul des Chances, we are in a sense brought back to François Quesnay’s Tableau Economique: individuals should act in conformity with the immutable natural order. 79 This is why Regnault believes that the use of subjective probability should progressively decline, as the deterministic laws ruling the Stock market are unveiled (see section 4.2.1). 77

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The peoples advance in civilization, in morality, in well-being, only as the varying social elements oscillate in narrower limits; as the political quietness strengthens, the important shocks disappear; then trust develops, and with it the power of Association and of Credit. The extreme things are always fatal, to peoples and to individuals. (Regnault 1863: 210 tr)

Figure 4.3 Regnault’s “circles of action” for France and England. The radius is given by the ratio between the mean deviation and the “probable” deviation of bond prices. The smaller the ratio, the more a country is considered advanced. Source: Regnault (1863: 195).

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Here we can note that Regnault precisely afforded an index of the advancement of countries, given by the ratio between the mean deviation and the “probable” (i.e. median) deviation of prices, and from which international comparisons could be achieved. For instance, he compared the French 3% bond with a similar British bond, and this comparison would reveal “the hugeness of the variations of the French Rente” (1863: 193 tr). He visualized that ratio in both countries as concentric circles that he labels “circles of action” (see figure 4.3), each circle being “a precise measure of the risks incurred” (1863: 194 tr). In addition, with this index the convergence toward the “end of history” could be checked. Like Cournot and Briaune, Regnault was delineating here the outlines of finitude. CON CLUSION With Jules Regnault’s Calcul des Chances, natural econometrics reaches its apogee in France. Regnault’s agenda is the combination of statistics and mathematics in order to analyze an economic issue, the functioning of the stock market, and he could identify laws explaining stock price behavior. In addition, this combination is fully dependent on a worldview: the belief in a divine and unified natural order. As this chapter shows, such a worldview exerts a strong influence on Regnault’s methodology and analytical results. For him, the world was governed by a small set of mathematical laws devised by God, which remain masked by various kinds of perturbations. Such laws could be unveiled by scientists with the help of observation and appropriate statistical instruments (the average, which is here closely linked to time-series decomposition). In addition, several laws Regnault devised were conceived as translations of universal laws already identified by natural scientists, and this was of course a consequence of his belief in a unified world, the belief that nature and society share an identical origin and follow the same rules, and that the natural and the social sciences should speak the same language. Then, once laws are identified, they are considered means to reorientate individual behaviors, to define the behaviors that are in conformity with the natural and divine order. The laws are the keys from which a stable state of societies – an “end of history” – could be reached, the moment when societies would

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strictly follow the alleged perfect rules elaborated by God. From the previous chapters, we can see that although econometrics as a discipline had of course no existence during the nineteenth century, econometric ideas have a clear existence at that time in France: Cournot, Briaune, and Regnault devised or practiced associations of observed data, statistical instruments, mathematics, and economic analysis. In several respects, we can find in the work of these authors several major features of early twentieth century econometrics, for instance time-series decomposition, testing procedures, the measurement of laws or relationships between price and quantity, the analysis of business cycles, and the definition of economic policy rules. Yet, in many respects, what I label natural econometrics is only to be understood as a typical product of the nineteenth century. Indeed, the shape and the goal of these pieces of econometrics remain idiosyncratic: in the hands of natural econometricians, mathematics, statistics, and economic analysis are only used to discover the structure of an alleged natural order, which would be divinely designed, unified, and mathematical in substance. Despite differences, Cournot, Briaune, and Regnault tried to identify the causal structure (most often considered mechanical) of a finite “system of the world.” In fine, as the previous chapters demonstrate, the econometric ideas that rose in France during the nineteenth century are mainly to be considered as a part of that philosophical program and quest: the discovery of such a finite world.80

As Ricardian economics and its subsequent developments also illustrate (see Foucault [1966] 1994 and Ventelou 2001). For instance, “What is essential is that at the beginning of the nineteenth century a new arrangement of knowledge was constituted, which accommodated simultaneously the history of economics (in relation to the forms of production), the finitude of human existence (in relation to scarcity and labour), and the fulfilment to an end to History – whether in the form of an indefinite deceleration or in that of a radical reverse” (Foucault [1966] 1994: 262).

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Part II. T he rise of twentieth century econometrics and the “unity of orchestration” Orchestration requires diversity in order to sustain itself; even the state of perfect harmony cannot be achieved without the necessary independence of each member of the group. In that sense the orchestration is self-directed from within, rather than imposed from without. ȥ Margaret Morrison, Unifying Scientific Theories The image should stand out from the frame. ȥ Michel Foucault, The Order of Things

Man has killed God; this is, in a sense, what happened in the field of econometric ideas around the turn of the century. In the hands of natural econometricians, the natural and the social world, man, and God were inextricably linked in a single history, and this entanglement had to be broken for early twentieth century econometric ideas to rise. At that time, indeed, the idea of mathematical models, representing narrow and artificial worlds but which could orientate the applied work, emerged: econometricians refer now to a reduced and reframed explanatory frame, independent from any unification of the natural world and the society, from natural order, from God’s design, and from an alleged and within reach “system of the world.” Around 1900, econometric ideas in France began to become associated with a new worldview, in which we find both the complexity of the social world and kinds of indeterminism. Of course, and we shall go back over this issue, the “probabilistic revolution,” or at least the “erosion of determinism,” in Ian Hacking’s words,1 played a key role here. The emergence of this association of a new worldview with econometric ideas in France is a 1

See Hacking (1990).

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two-step process. The statistician Lucien March is first a central figure in the emergence of this new worldview. It is now rather well known that March largely contributed to develop and to make popular in France instruments such as correlation. Yet, he does not only deserve attention in that perspective. As an answer to complexity and uncertainty – two pivotal components of his own image of the society and the economy – he developed a research path dominated by the observation and the measurement of socioeconomic phenomena: to him, only measurement could capture, though imperfectly, this new image of the social world. Although March kept from natural econometricians the pivotal importance of observation and statistics as well as the focus on macrostructures, his philosophical views led him to operate two decisive breaks vis-à-vis natural econometrics: the abandonment of determinism and its underlying ideal of certainty, and the impossibility of ontological correspondences between the real world and the scientific work – in the sense that the real world was just supposed complex and out of reach. But other scholars deduced more radical conclusions from this new image of the economy. As the case of Marcel Lenoir illustrates, econometricians began to deal with the alleged complexity and uncertainty of the economy through the development of abstract mathematical models, based on economic theory. These models, centered on the market process, and which were microfounded in the case of Lenoir, took the shape of artificial worlds that the economist constructs. The econometrician becomes here the architect and the deviser of these “small worlds,” in the words of Cournot,2 whereas the natural econometrician can merely be portrayed as an observer of the “system of the world.” These models correspond to another relation of econometric ideas with the real world. The real world would be out of reach, but it could be possible to erect idealized explanatory frames, based on assumptions, from which empirical investigations could be achieved. In other words, these models may tell something about the real world, but they are deliberately considered independent from the real world – and in that sense, the ontological claim of natural econometricians knew a severe decline. This has an important consequence at the 2

See section 2.3.1.

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methodological level. Whereas natural econometricians believed they could capture the set of mathematical laws ruling the society with the help of observation and statistical instruments, here statistics is acquiring a more passive role in econometric research: relationships are not extracted from data3 anymore, they are rather given by the model, which orientates the statistical work. In the next two chapters, we shall see some apparent continuities at work in the history of econometric ideas from the 1830s to the 1920s, for instance, the focus on time-series decomposition or the elaboration of relationships between price and quantity. However, as a whole, the comparison of these early twentieth century econometric ideas with natural econometrics reveals an incommensurability: the causal structure which is now built is deliberately seen as artificial and is fully understood as being independent from the whole “system of the world,” even from the real economic world; the concept of time and the way to depict individual behavior acquire a new meaning; the reasons for using statistics and mathematics strongly differ; and of course the ideas of ontological unification and God’s design fully vanish. Econometrics now offers and generates another knowledge of the economic world: space is cleared for autonomous, malleable, and possible images of the economic world. But there is more. The two following chapters also show that another pivotal evolution was at work during the early twentieth century, this time at the institutional level. Indeed, whereas natural econometrics is mainly to be considered a set of ideas and practices without any institutional support, the development of econometrics in France during the early twentieth century saw the rise of a “unity of orchestration.” This unity covers a common research program (including at least the application of British mathematical statistics to economic issues), the definition of scientific conventions (i.e. the elaboration of scientific norms), publication policies, and the emergence of a small community that was in full swing with scholars from other Western countries. It is here that econometric ideas and the existence of econometrics as a field with a proper identity begin to intersect: during the first three decades of the twentieth century, Of course, some of the philosophical postulates on which natural econometrics is based also played a key role in the determination of these relationships.

3

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the bases of another style of econometrics could rise and could develop as a common research program.

5. Statistical socioeconomics for the masses: March attacks Science needs (…) pictures. They largely determine its problem situations. A new picture, a new way of looking at things, a new interpretation may change the situation in science completely (…). But these pictures are not only much-needed tools of scientific discovery, or guides to it, they also help us to decide whether a scientific hypothesis is to be taken seriously; whether it is a potential discovery, and how its acceptance would affect the problem situation in science, and perhaps even the picture itself. ȥ Karl Popper, Quantum Theory and the Schism in Physics

Around the turn of the century, statistics knew several evolutions. In France, as in several Western countries, a large scale measurement of the socioeconomic world developed, partially motivated by the economic crisis of the years 1873–1897 (Breton, Broder and Lutfalla 1997, Topalov 1999); the need for answers and reforms called for a systematic measurement of the economy, then achieved in governmental agencies (Porter 2001). At the methodological level, new instruments (e.g. correlation1) were shaped, especially by British statisticians and biometricians (MacKenzie 1981, Porter 1986). These instruments were rather well suited to the analysis of economic issues, and after a necessary adaptation and transformation (Morgan 1997, Klein 1997), they rapidly became used for the measurement of relations between price and quantity (Epstein 1987, Morgan 1990). Yet, a more decisive scientific and philosophical evolution, even a break, occurred during the period: the “erosion of determinism.” Scientists progressively got rid of the belief that the laws ruling phenomena are simple or deterministic. The great unified and deterministic edifice of nineteenth century science progressively

Although the term and the method were used as early as 1846 by the astronomer Auguste Bravais (see Porter 1986: 273–4).

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cracked,2 even collapsed, and this break sometimes left room for more pragmatic and more local scientific styles (Israel 1996 and 2000). This break, anyway, deeply affected the way scientists perceived their instruments, their concepts, their theories, and even their goals. Let us mention for instance the way error was perceived – it lost (at least partially) its negative meaning (Armatte 1991) and opened the door to objective chance and to random shocks.3 The development of econometrics in France during the period did not escape from these evolutions and breaks, as the work of Lucien March (1859–1933) shows. March is the architect of the most important achievements in the field of early twentieth century French econometrics and statistical economics. He entered the Ecole Polytechnique in 1878, he became an engineer in the Corps des Mines, and from 1899 to 1920 he was head of the Statistique Générale de la France, the main government statistical agency of the time.4 March finds no easy home in our contemporary schemes, in the sense that he breaks with our standard classifications. He reshaped the French statistical system; he imported the new statistical instruments devised by British biometricians,5 investigated the field of time-series analysis, contributed to the spread of eugenics in France, and promoted lectures in advanced statistics at a time when they were scarce. In addition, March approached during his lifework an impressive category of socioeconomic issues (demography, education, life standards, business cycles, the distribution of wages, money), and he published numerous papers on the application of statistical procedures and theory to socioeconomics. Last, but not least, he developed a philosophy of See Cartwright (1999), Krüger, Gigenrenzer and Morgan (1987), Krüger, Daston and Heidelberger (1987), and Morrison (2000). 3 In econometrics, random shocks became central in the work of Moore (1929), Frisch (1933b), and Tinbergen (1939). In addition, “errors” referred to intrinsically stochastic features of the real work in Haavelmo (1944). See Le Gall (2002a and 2002c), Morgan (1990 and 1998), and Spanos (1989). 4 The work achieved at the Statistique Générale de la France during the early twentieth century is impressive, in two directions: the collection of data and the elaboration of explanations of what has been measured. On the rather meandering history of the Statistique Générale, which is characterized by a successive dependency on various ministries and administrations, see Marietti (1947). 5 See MacKenzie (1981) and Porter (1986). 2

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science based on measure that – in some respects – illustrates the importance of the state in developing measurement (Porter 2001). March’s style is precisely to be found in a methodological agenda: the definition, the practice, and the promotion of the application of statistics to socioeconomics as the unique path to measure the social world, and his style can be seen as a constant statistical expertise to approach social issues. My focus on March is not only motivated by the fact that his full contribution to the history of statistics has received scant attention or that he imported, devised, or manipulated statistical instruments that became the core of subsequent developments in econometrics. More importantly, the historical significance of March’s work in econometrics is to be found in an epistemological and philosophical frame that underlies his whole work. March is indeed far from promoting the use of an efficient toolbox for social scientists, in a pragmatic perspective. Rather, he rooted his statistical work in a worldview in which uncertainty, random, and historical processes play a key role: his statistical style can be seen as permanent attempts and trials to measure such a world. Otherwise stated, March is an illustration of a break in the analytical style of econometric ideas in France, and more appropriately a break in their foundations and their underlying worldviews. He got rid of the philosophical foundations of natural econometrics and its underlying postulates; instead, his work is based on a worldview in which the main postulates are the uncertainty, the complexity, and the inaccessibility of the social world. However, this break in the foundations and the nature of econometric ideas is not the unique raison-d’être of this chapter. At the institutional level, the end of the nineteenth century saw the development of the professionalization and of the institutionalization of economics in France (Breton and Lutfalla 1991, Le Van-Lemesle 2004). Research in economics and statistics became more organized, and societies such as the Société de Statistique de Paris played a key role in that perspective. March is precisely a French statistician of the early twentieth century who developed great talents in the promotion and the institutionalization of the field. He largely promoted the need for conventional instruments and for a harmonization of measurement processes in

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national statistical bureaus;6 he trained statisticians who played a key role in the subsequent developments of econometrics (e.g. Marcel Lenoir7); and he promoted the creation of appropriate courses for postgraduate students. This is an additional break in the history of econometrics in the country. Natural econometricians founded no academic schools, trained no disciples, and never benefited from large-audience tribunes (e.g. journals), at least for the econometric aspect of their work – they were isolated scholars. By contrast, with March, the rise of a small scientific community in the field becomes apparent. In sum, with March econometrics knows in France a double turn: a rising institutionalization, and a break in its analytical content and its philosophical foundations. In this chapter, March’s role in the history of econometrics is analyzed in four steps. Section 5.1 presents the way March saw statistics – its nature, properties and range of application. Statistics was considered an objective and scientific way to deal with complex phenomena and collections of heterogeneous facts. In section 5.2, I focus on the way he contributed to statistics in two directions: the statistical methods and their application to economics. It will be emphasized that his work is characterized by the search for methods from which regularities could be discovered in a complex and moving world, and also that he constantly put forward the limits of his own results. Section 5.3 sheds light on March’s worldview that assigns a precise role to statistics. It was a means of approaching, measuring and taming a social world characterized by an epistemic uncertainty, and his work is only meaningful in the frame of this epistemology that draws the scope and the limits of statistics. Finally, section 5.4 suggests the way March promoted an institutionalization and even, in some respects, an early normalization in the field, especially through the definition of scientific conventions.

This harmonization has often been advocated by nineteenth century social scientists, for instance Quételet or, in France (and at the very end of the century), Emile Cheysson. 7 See Chapter 6. 6

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5.1. O N N UMBE RS AN D ME ASURE ME N T : DE LIN E ATIN G STATISTICS From the very beginning of his scientific career, March carefully tried to identify the nature and the frontiers of statistics – and in that respect, he follows the agenda of authors such as Emile Cheysson or Frédéric Le Play.8 At a time when the application of statistical procedures to the social sciences was controversial in France (Ménard 1980) and when statistics was even derided (Porter 1995), March suggested that it was however a path based on precise and scientific criteria, a path that various disciplines should follow. 5.1.1. Statistics as “ une langue commune” March thought that the identification of the territory of statistics resulted from the identification of the limits of the experimental method: [T]he methods that suit the experimental sciences, and that are based on the possibility to isolate one circumstance among all those that coexist in a phenomena, badly apply to the observational sciences, in which a fact can never (…) be reproduced in the way it has been produced, and where the invariability of the adjacent circumstances, with the exception of one, is never realized. (March 1924: 341 tr) Thus, “when we do not control the main circumstances of observation, the statistical method is to be applied” (1930a: 9 tr), and the scientist can only observe the facts “as they appear” to him (1930a: 11 tr). Statistics was thus considered a substitute for the experimental method. March shared here the views of other social scientists of the time: Morgan (1990) indeed suggests that the use of statistics, especially by economists and econometricians of the turn of the century, was based on similar arguments and that more generally this problem “arose in other social sciences and in natural sciences where controlled experiments were not possible” (1990: 9).9 On the relation between statistics and economics in France at the turn of the century, see Breton (1991). 9 See also Boumans (forthcoming). 8

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Although these views were not original, March’s arguments deserve attention. In various textbooks, he explained that, in contrast to the experimental method, statistics would be concerned with complex phenomena and heterogeneous collections. March was here moving away from the ideas of simplicity and order that mattered so much for natural econometricians: these facts are generally subject to complex influences that it remains impossible to separate or to make vary at will. They arise from the shock of circumstances that we do not master, often from intentional facts whose scattering and capriciousness disconcert (…). The phenomena that are studied are often influenced not only by causes that operate in the scope of observation (for instance, in the case of wages, the health of workers compared); but also by causes that largely preceded observation (for instance those relative to heredity, habits and traditions in human societies). In sum, the complexity of the range of observation is particularly important when the study is concerned with collections of living beings, or of social facts. (March 1930a: 14–5 tr) At that stage, March’s thought moved in two directions. First, given its complexity, the human world could only be observed, and its knowledge was requiring data. This would particularly apply to economics, as he wrote in his 1921 essay: Political economy, as every science, needs precision, measures, numerical ratios. It has thus been possible to say rightfully that statistics is the essential complement of the economic science. The phenomena we observe and we range in the study of production, circulation, distribution and consumption of wealth cannot be correctly described, the consequences of every change in their fundamental conditions cannot be correctly appreciated without the intervention of numerical data borrowed from statistics. Political economy has probably some roots in the analysis of desires, aspirations, needs, inherent to human nature and the social feature of humanity. But such an analysis can only develop in a scientific frame if it is based on

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observations that can be compared by universally accepted forms, i.e. measures.10 (March 1921: 137 tr) Straightaway, it can be remarked that such a requirement can be illustrated by the institutional role March played in France at the turn of the century. In 1892, he joined the Office du Travail, which had been created the previous year to study the various elements of labor.11 At that time, the Statistique Générale de la France was a department of the Office du Travail. That precise linkage was not by chance: it was necessary for the Office to get precise information on national economic structure as well as on individuals, and such information could be collected through censuses that fell within the scope of the Statistique Générale de la France. The latter reported regularly on demography and economics (industrial structures, wages, and so forth) and collected numbers for various ministries and administrations, and some of these results were published in the associated review, the Bulletin de la Statistique Générale de la France. The work the agency achieved during this period was impressive, especially concerning the collection of data, and a large part of the work is to be attributed to March (Huber 1937). But March’s conception of observation requires more precision. To him, social scientists had “to describe carefully and to delimit as exactly as possible the facts (…) to be observed” (1924: 331 tr). Consequently, statistics and measurement were closely associated: “[t]he method of statistics intervenes when we want to measure” (1908: 290 tr). In his historical survey of the development of statistics, he precisely explains that “the development of a lot of sciences has followed the creation or the improvement of instruments of measure that made possible immediate and objective determinations of the 10 For March, the most substantive work in political economy was rooted in observation: “Most economists have been wise observers of the things of their time: Turgot saw the peasants of Limousin live and hire, and his conclusion was what has been called later la loi d’airain; Stuart Mill saw the development of the large scale British industry and heard employers asserting to their workers that they could not increase wages without a reduction of their capital. Von Thunen probably saw employers reducing the rate of wages as new workers were accepting these reductions and were forcing the workers previously recruited to accept them” (1912c: 371 tr). 11 On the history of the Office du Travail, see Luciani (1992).

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characteristics studied” (1924: 326 tr). Otherwise stated, just like he defined statistics on a basis of exclusion, he identified its range of application through the elimination of non-measurable phenomena, such as those of psychology (1924: 332).12 Yet, statistics had a wide range of application, as March’s applied work illustrates. It mainly concerned demography and economics, and is a hymn to statistics: it was constantly based on measurable phenomena or on phenomena that he contributed to make measurable, such as unemployment (Reynaud-Cressent 1984, Topalov 1994). Perhaps less known is his involvement in eugenics. From an institutional point of view, he contributed to the creation in 1912 of a French society devoted to the promotion of eugenics, the Société Française d’Eugénique, and in various papers, he remained open about his eugenic beliefs.13 From a methodological point of view, this involvement is perfectly understandable given the other issues he tackled: eugenics involved a quantification and a measurement of the hereditary make-up of individuals, “a reduction of people to numbers” (MacKenzie 1981: 34). Second, March saw such a gathering of data and measurements as a unique means to analyze the social world. Some regularities could then be unveiled, and statistics aimed precisely toward the Statistics “has to eliminate as much as possible the psychological elements, that cannot be expressed by numbers” (1924: 332 tr). As we shall see below, this does not mean that non-measurable or qualitative factors were of no importance, but rather that they are excluded from the range of statistics. 13 See for instance March (1912d and 1929). See Carol (1995) on March’s involvement in eugenics. Despite the institutional role he played in French eugenics, his papers are often ambiguous. On the one hand, he clearly and explicitly concluded that hereditary particularities were existing (e.g. 1929: 40). He also mentioned the “social value” of individuals (e.g. 1912d: 588 tr) and analyzed the issue of artificial selection. In addition, he wrote a very laudatory obituary of Galton (March 1911a), in which he paid tribute to Galton’s eugenics. But on the other hand, March largely focused on the need for care, on the virtues of a country lifestyle and traditional way of life (1929: 221–2). The decrease of birth rates in France was a constant preoccupation for him (e.g. 1912d and 1929), and it would originate in “moral” and “economic” causes (1929: 100–1 tr). His 228-page essay on demography (March 1929) is in essence a monograph devoted to a full analysis of demographic issues and a search for explanations of the fall in birth rates. 12

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discovery of signs of constancy, of order within chaos of complex phenomena: Because the human mind does not easily understand a complex or variable group, it can only exert its power for generalization through the reduction of complexity to more simple notions, of variability to something constant. The method of statistics tends toward that. (March 1924: 327 tr) The statistical theory helps to understand how the regularity rises in average results, and it explains to a certain extent these results. (March 1910a: 486 tr) As such, this idea was not highly original either. Here March exemplifies the nineteenth century use of statistical methods in which relationships were extracted from varying measurements – as the previous chapters show – although it should obviously be remarked that he got rid of the belief that Nature was basically a simple machine. March thus saw statistics as closely associated with observation and measurement. It was offering means of reducing heterogeneous data and identifying regularities in mass phenomena. In “Statistique,” a masterly paper published in 1924, statistics was defined as la pléthométrie.14 It was also “une langue commune” (1924: 363), applying to large territories and to a large diversity of objects. Just like Karl Pearson, March believed that statistics “provided the proper discipline to reasoning in almost every area of human activity” (Porter 1995: 20). The foundations of such an ambition now need to be explored.

“Through the diversity of objects and of phenomena of nature, human observation remarks uniformity, regularity (…). When the quantitative study is relative to the counting of objective facts or mental representations, it belongs to statistics. The latter includes a particular discipline, appropriate to observation and the comparison of mass facts: it could appropriately be labeled pléthométrie” (March 1910a: 447 tr).

14

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5.1.2. Objective foundations of statistics March exposed the way statistics could extract regularities in a way that could achieve a scientific status. Statistics was defined as a threestep process including observation, the determination of results, and finally interpretation and forecasting. This final step was believed to be unduly influenced by personal and subjective judgments and was thus excluded from the range of science.15 By contrast, the scientific status of the two preceding steps was based on their objectivity: in his whole work, March constantly warned off “the dangers of subjective appreciations” (1912c: 371 tr), and statistics would help in “reducing the conjectures, in gaining precision in the objective dimension of the results of observation, and consequently in increasing the scientific value of these results” (1924: 364 tr). The scientific dimension of the first step, that of observation, would originate in the elaboration of nomenclatures and in the training of collectors. Both were seen as making statistics objective, in the sense that they contribute to “the elimination of particular and personal influences” (1924: 337 tr). Nomenclatures as such deserve little attention, but it should be remarked that March believed that they became objective tools as soon as their structure was detailed in such a way that it minimizes the collectors’ doubts, and he stressed the need for the precise description and narrowing of facts to be observed and measured (1924: 331 tr). Interestingly, he also advocated the need for homogenous nomenclatures at the international level: they would be “universal conventions” (1930a: 5 tr), standardized tools that exclude judgment. In that sense, he had in mind a kind of objectivity associated with distance, one that transcends frontiers and hints at Porter’s similar analysis of quantification as “a technology of distance” (1995: ix). The search for objectivity in the collection of data was also at work on the side of collectors: “the observer has to indicate no personal tendency; his impartiality has to be absolute” (1924: 330 tr). March stressed the need for the training of collectors, who have to be “impartial,” “honest,” “competent” (1924: 328 tr), well trained, and “educated” Although helpful, forecasting was excluded from science: it only “relies on a science” and is “un art ” (1931: 475 tr). Otherwise stated, “[t]he scientific work stops when the elements from observation have been gathered, coordinated, enlightened” (1931: 476 tr). See also March (1910a: 447). 15

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(1924: 330 tr) – such a “morality” was thought as leading to a reduction of errors in the collection of data. Thus he thought that careful and objective measurement was a prerequisite for scientific work in statistics. The whole aims at the elimination – or at least the minimization – of errors of observation.16 The second step was that of the determination of results, i.e. the extraction of constant results from measurements. Once more, objectivity was at work: aggregate results aimed at identifying what individual cases share in common (1924: 342) while transcending personal behaviors. To reach this goal, the statistician had to use appropriate instruments: graphs, index numbers, the correlation coefficient and the principle of compensation,17 associated with the normal law. The latter here deserves attention. March recognized that this law was helpful and that “the use of mathematical processes – more or less elementary – offers an objective value” (1909: 255 tr). But in sharp contrast to Regnault,18 he also believed that it was “an ideal model” (1909: 255 tr) or a “bold assumption” (1912c: 378 tr). A nice illustration of March’s views is a debate on the status and the use of the normal law that occurred at the 1909 International Statistical Institute conference. While Wilhelm Lexis claimed that the Gaussian law was a “natural law” (Bulletin de l’Institut International de Statistique 1909: 54 tr), even a “genuine natural law” (Bulletin de l’Institut International de Statistique 1909: 95 tr), March thought that it was rather to be considered an “adaptation (…) of natural facts to a conventional process. It owns no universal feature, because it is far from reality in the case of some groups of phenomena, and for these groups it could be very interesting to use more appropriate shapes” (Bulletin de l’Institut International de Statistique 1909: 95 tr). For March, more generally, “the natural facts are not ruled by simple laws; most often, their distribution (…) differs from this limit form” (1909: 256 tr).19 Of course, March expresses here the very idea of complexity of the world. This may explain that he often claimed that other kinds of 16 Such errors cover both inattention and appreciation; see March (1921: 139–40). March is the first of our authors to focus on precision in the measurement process. 17 This principle was essential to him (March 1924: 335–6, 352; 1921: 144– 5). 18 See section 4.3.1. 19 See also March (1921: 163).

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distribution were available for use (1908: 293).20 How, then, could March recognize the usefulness of the normal law? The key to this puzzle is to be found in his belief that science needs conventions, as we shall see more completely below: the Gaussian law would be “precious since (…) it establishes the practical unity of [a] group” (1909: 255–6 tr) – it was a “frame” that sets precise limits (1910a: 485 tr). Similar arguments were developed about the correlation coefficient and index numbers. Although these instruments could – and should – be criticized, they were parts of the conventional language of science and make possible the coordination of scientific activities; such routines work toward objectivity.21 These two steps in March’s process of statistics would form an objective and a scientific path from the heterogeneous, individual and complex facts toward aggregate results. This statistical path deserves two comments. First, March constantly insisted on the need for identifying – and also for overcoming – the limits of every component of these steps. It is striking to note that his whole work leaves space for criticism, for what he labeled “scientific criticism” (1924: 323 tr) – which was, for instance, associated with the search for more realistic conventions. Second, he stressed the need for the elaboration of a precise and simple vocabulary, from which any confusion could be banished. For instance, “one has to regret that words such as probability, correlation, that possess a well determined meaning in the mathematical language and in logic, are used differently in statistics” (1909: 262 tr). As we shall see below,22 he harshly criticized the assimilation of correlation with causality practiced by several statistical economists of the early twentieth century.23 Otherwise stated, March claimed that we cannot demand too much of the instruments used in statistics or ask for more than their assumptions stipulate. He also stressed the need for a simple March recurrently mentioned the existence of asymmetric distributions, which however differ from Pareto’s. See for instance March (1908: 293–4; 1909: 255; and 1921: 159). His own work on wages (March 1898) also shows his interest in such distributions. 21 He thought that statistical instruments such as correlation are objective in the sense that the results are independent from the user. He thus has in mind “mechanical” processes that work toward neutrality and objectivity (1921: 169 tr). 22 See section 5.3.1. 23 This would in particular apply to Henry L. Moore (see section 5.3.1). 20

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vocabulary in order to avoid any misunderstanding: he hoped that statistical instruments could be used by non-specialists, for instance businessmen. 5.2. GRAPHS, COE FFICIE N TS, BAROME TE RS: M ARCH ’S ME ASURE ME N T IMPLE ME N TS Now it is necessary to dig deeper and to analyze the way March approached and practiced statistics in his concrete work. His contribution to the elaboration of statistical tools for the social sciences as well as his economic work, especially on business cycles, perfectly illustrates how he extracted regularities from heterogeneous data and how he pressed the limits of such attempts. 5.2.1. Fechner and Pearson revisited: N ew instruments for the comparison of socioeconomic time series Today March remains known for his study devoted to the comparison of socioeconomic variables, Les Représentations Graphiques et la Statistique Comparative 24 (1905). This work aimed at presenting two kinds of instruments that he considered useful for such an enterprise: graphic representations and mathematical indices, which he labeled indices de dépendance and would give “a numerical precision to the visual impression” (1905: 22 tr). His analysis of these indices deserves special attention.25 The paper opened with Gustav Fechner’s indices, which March pedagogically exposed. March presented two coefficients of dependency devised by Fechner. The first one is: i

c d , where c is c d

the “number of agreements” (i.e. cases in which the two series move in the same direction) and d is the “number of disagreements” (i.e. the opposite case). However, “this index does not take into account the magnitude of the compared variations” (1905: 26 tr). March also referred to another coefficient, defined as: I=

C D , where C is the C+D

sum of the products of the values of both variables when their variation reveals an “agreement” and D is the sum of the products of 24 25

This study will be referred to under the title Les Représentations. For March such indices were connected to graphs (see section 5.3.1).

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the values of both variables when their variation reveals a “disagreement.” Although March recognized the limits of these indices,26 he applied them to socioeconomic data, as the two following case studies show. In the first case study, March investigated the relationship between marriage and birth27 in France from 1873 to 1902 (annual data). As we can see in table 5.1, he uses the symbol “+” to represent a positive variation from one year to another, “–” for a negative variation, “0” for a constant evolution. He then identified the positive associations (+ +, – –), called “concordances” or “agreements,” the negative associations (“discordances” or “disagreements,” + –, – +), and cases in which one of the variations is zero (+ 0, 0 +, – 0, 0 –), i.e. “indifferences.” He could then calculate Fechner i-ratios. He concluded that “every variation in the number of marriages, from one year to another, is most often accompanied with a variation in the number of births in the same direction” (March 1905, 21 tr). In the second case study, he investigated the relationship between the annual change of several financial indices from 1874 to 1902 (table 5.2). He found several cases in which “the indice de dépendance has a significant value” (1905: 24 tr); for instance he noticed the existence of an inverse relationship between reserves and the discount rate. Then he presented “improvements” to Fechner’s indices and moved toward Karl Pearson’s coefficient of correlation.28 But the use of these indices led him to face a problem relative to time: In the previous studies, we have always supposed that we dealt with annual changes. But it frequently happens that, in the changes that affect statistical facts, we can distinguish various phases. We shall distinguish yearly changes, changes relative to several years (for instance decennial changes), secular changes and of course changes relative to periods inferior to one year. (March 1905: 32 tr) They do not “sufficiently take into account the magnitude of the compared variations” (1905: 27 tr). 27 Such relationships were commonly studied at that time (Morgan 1997). 28 Although he had a strong predilection for Fechner’s simplest index. In various studies published in the 1920s, he still used it: he thought that major tendencies could be shown even by such a crude and simple index. See for instance (March 1928: 47; 1921: 168–9). 26

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Table 5.1 Variations in marriages (“mariages”), birth (“naissances”), and death (“décès”) rates in France (1873–1902). Source: March (1905: 20).

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Table 5.2 Variations in the following indices of the Banque de France: reserves (“encaisses”); discount rate (“taux de l’escompte”); discount (“escompte”); and the movements (“mouvements”), the balance (“solde”), and the transfers (“virements”) in accounts (“comptes courants”), between 1874 and 1902. Source: March (1905: 23).

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March thus recognized here that using an instrument devised outside the social sciences required adaptation. Actually the correlation coefficient could not be immediately used by economists, since economic laws did not deal with variability within the population (like in biometrics), “[r]ather, socioeconomic data often consisted of single observations (…) connected together to form a series which exhibited variability over time. Available correlation techniques were not designed with such time-series data in mind” (Morgan 1997: 49). The question of which of the several units of time should be correlated had thus to find an answer. “The earliest writers saw the time-correlation problem as isolating the different components and correlating only similar components of two or more variables. It was usually of greater interest to economists to investigate correlation of short-term oscillations, in particular the movement through the trade or business cycle. Economic statisticians recognized that the correlation coefficients of unmanipulated observations only indicated a relationship between the secular changes” (Klein 1997: 229). As March stated, For a more exhaustive analysis of the conditions of dependency between two statistical series, it is thus necessary to calculate the coefficient of dependency between annual changes as well as a coefficient of dependency for a longer period, for instance the one that corresponds to decennial changes. (March 1905: 32 tr)29 On this point, the 1905 study contains new techniques that could solve the time problem. March determined the correlation of longterm changes on the basis of ten-year averages. He applied the method to the relationship between the marriage and the birth rates in England (1851–1901) and found a coefficient of 0.16. He concluded that: The coefficient is positive and weak; the circumstances that determine the movements in marriages and births on the long period seem to be of small influence. (March 1905: 33 tr) 29

See also March (1929: 34).

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He also determined the correlation between the annual values of both variables and he found a coefficient of 0.072. He concluded that “no significant relations seem to be existing between the marriages during a year and the births during the same year” (1905: 33 tr). But he also introduced lags in the analysis. He considered births and the lagged values (from a one-year to a five-year lag) of marriages (table 5.3) but again found no significant relation: “the influences that rule the ones seem very different from the influences that rule the other ones” (1905: 34). Incidentally, it can be remarked that March is here opening correlation hunting in France, although for the moment he comes home empty-handed.

Table 5.3 Correlations between births and marriages in England. Marriages are considered with no lag (“même année”) and with a lag from one year to five years. Source: March (1905: 33).

But the 1905 paper also contained a new method of time-series decomposition, which was close to those independently developed by Reginald Hooker in 1901 and John Norton in 1902.30 The method aimed at isolating short-term changes defined as the deviations from a trending factor: In order to offer a greater precision to the analysis, we have to decompose the changes that are studied (…). [W]e can determine the coefficient of dependency: 1. for two of these courbes interpolées or courbes moyennes; 2. for the deviations between the observed numbers and these courbes moyennes. (March 1905: 34 tr) He applied this decomposition to the study of the relationship 30

On Hooker’s and Norton’s methods, see Klein (1997).

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between marriage and birth rates. The correlation between the courbes moyennes was weak (0.07), a result March explained on the basis of the existence of three historical sub-periods: From 1851 to 1873, births and marriages varied inversely, marriages were decreasing while births were increasing. From 1873 to 1886, both coefficients varied in the same direction, marriages were still decreasing and births were beginning to decrease. After 1886, changes are again opposite, births were still decreasing while marriages were again increasing. (March 1905: 34 tr) By contrast, the correlation of the short term components gave more significant results: the highest correlation was found when considering births and marriages with a two-year or a three-year lag (respectively 0.341 and 0.329, see table 5.4). He concluded that “the influence of marriages on births becomes rather sensible when we compare marriages with births that occurred two or three years later, and when the influence of long-term changes has been eliminated” (1905: 36 tr).31

Table 5.4 Correlations between the short-term movements of marriage and birth, marriages being considered the same year and with a one-year from a four-year lag (England, 1851–1901). Source: March (1905: 36).

Les Représentations undoubtedly deserve a special place in the history of econometric ideas and of time-series analysis. Several of March used the same method to correlate unemployment with birth. See (1905: 36). 31

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March’s other contributions also illustrate the intersection of his work with econometrics, for instance his parametric estimation of a distribution of wages (March 1898). However, a reduction of March’s economic work to the use of such instruments would be misleading. In large parts of his own work, he rarely used correlation – and more generally British mathematical statistics, he saw as an “insufficiently advanced science” (Bulletin de l’Institut International de Statistique 1909: 93 tr). To him, spurious correlations were existing32 and, as we shall see in section 5.3, he had a predilection for instruments that capture, identify and respect the very circumstances in which the phenomena are considered. More explicitly, historical time was important to him; however, correlation does not take it into account. March thus moved toward other statistical strategies, as his construction of a business barometer suggests.33 5.2.2. March and business cycles: On barometric indexation In the 1920s, March attacked the challenging task of measuring business cycles. Following a direction practiced since the end of the nineteenth century in several countries, he constructed a French business barometer34 based on index numbers and considered an equivalent to the Harvard barometer. Although his postulate was that business cycles would be complex in the sense that they would result from “innumerable and very different economic facts” (1923: 252 tr), he believed that they could be analyzed with the help of index numbers, “instruments of observation and analysis” and “instruments of measurement” (1923: 277 tr). But such numbers would also be “conventions” (1923: 253 tr) or instruments of international comparison. March thus adopted indices that were counterparts of those on which some of the See for example March (1923: 272; 1928: 57). March’s research path can here be contrasted with that of Hooker. Around 1900 both examined similar problems, but March’s work took an almost opposite direction and became concerned with historical time. This helps explain why the correlation coefficient was of little importance in the papers he published after 1905. On Hooker see Klein (1997) and Morgan (1990 and 1997). 34 Barometers defined as “time-series representations of cyclical activity” (Morgan 1990, 57). On the history of business barometers, see Armatte (1992), Chancellier (2006a, 2006c), Klein (1997), and Morgan (1990). 32 33

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previously constructed barometers were based: the price of financial securities35 (A), the wholesale prices (B1), the British wholesale prices (B2) and the Banque de France discount rate (C). He ended up with “ABC” curves in Warren Persons’ Harvard style. His barometer (figure 5.1) visualizes the cycles in France, England, and the United States. It suggests the ways the various curves are related in cycles – their “successions,” in March’s own words. It also suggests a kind of international regularity: March remarked that “the three ABC curves in United Kingdom reveal the same pattern [than in the United States]: the oscillations of the curve of securities precede those of the curve of prices, which are themselves followed by the oscillation of the curve of discount rate” (1923: 277 tr). These successions, however, were less apparent in the case of France. March’s index numbers approach remains at times ambiguous. On the one hand, he seems to view them as physical measurements of variables (1923: 277), as in the price index work of Wesley Clair Mitchell and Irving Fisher,36 and the purpose was to get measures of their movement through time. On the other hand, the important thing about March’s measurement approach was not the numbers as such37 but rather the search for graphic indicators that could establish facts about economic phenomena and make possible the discovery of regularities, in the style of Mitchell’s business cycle work. Then the existence of such regularities had to be verified by the indices de dépendance: During the 1910s and the 1920s, the statisticians of the Statistique Générale de la France became interested in the influence of the stock market fluctuations on economic activity, and Marcel Lenoir led the study of that issue. In a first step, he developed in 1919 long-term indices relative to the French stock market. This included the construction of two indices: an index relative to bonds (including 17 securities) and an index relative to stocks (including 186 securities, decomposed in 25 sector-based subindices). In a second step, he constructed after 1919 indices complementary to those previously mentioned and some monthly indices as well. This work by Lenoir illustrates the role of the Statistique Générale de la France in constructing instruments that make possible the observation of the economy. 36 See Banzhaf (2001). 37 Compared to the point of the exercises discussed by Boumans (2001) and Banzhaf (2001), the numbers themselves were not the issue. 35

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Figure 5.1 March’s barometer. The three figures are relative to France, United Kingdom, and the United States. In each figure are visualized: the price of financial securities (dotted lines); wholesale prices (black thick lines); and the discount or interest rate (double black lines). The French barometer also includes wholesale prices in England (thin black line). Source: March (1923: 276).

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These movements can be usefully compared (…) in order to search for possible links. (March 1923: 267 tr)38 This means that March believed that graphs and indices were two complementary technologies that should be used hand in hand, and this idea will be more fully exposed below. March’s views on cycle deserve two comments. First, he thought that index numbers could not be considered “precise” (1923: 277 tr) and could not take into account the whole range of circumstances – this was to him a major difference between measurement in economics and measurement in some of the natural sciences (1923: 277–8). However, he believed that a large variety of indices could help in narrowing uncertainties (1923: 278–9). Second, the complexity of business cycles was grounded in the belief that their origins could not be traced back to a single cause: cyclical fluctuations are (…) complex. They cover phenomena of very different origins: meteorological accidents (dryness, frost, flooding, etc.), social accidents (wars, strikes), or monetary phenomena. (March 1923: 271 tr) March did not use the term “fluctuation” by chance. He rejected the possibility of strictly periodic cycles because economic conditions would change in such a way that the length of cycles was expected to vary; business cycles were seen as recurrent but not strictly periodic. From that point of view, his cycle approach strongly differs from Briaune’s, Jevons’s, and Moore’s social meteorologies or astronomies. Moreover, some of the phenomena influencing economic conditions could not be quantified and measured (March 1923: 270). This meant to him that institutions, history, and so forth, were significant and consequently that partial and simple theories or schemes were to be considered cautiously.39 He made here no use of correlation. This perhaps explains why March did not infer forecasts from the barometer. He had good reasons to write: “can we expect that one day, a 38 39

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Similar conclusions can be drawn from his work on the quantity theory of money. A paper he published in 1912 aimed at testing statistically and graphically this relation (data covered the 1783–1910 period). Yet, he doubted the relevance of such a simple relationship and believed that “other factors” have to be taken into account (1912a: 114 tr).40 He found it necessary from the start to take into account the whole range of circumstances and he developed a taste for a statistical approach that left no room for abstraction and that could respect the alleged complexity of the real world. Note that he believed that statistics made possible the derivation of empirical regularities in the social world; yet, such regularities could not be considered laws – the very idea of law, which was playing a major role in the work of natural econometricians, was largely banished from March’s vocabulary. The relation between price and gold and silver was investigated in more details and in a different way in the 1923 paper on business cycles. March considered the nine-year averages of wholesale prices in Britain, the United States, and France between 1796 and 1921, and the increasing rate of the annual stock of gold and silver (between 1800 and 1920). The analysis of figure 5.2 led him to the following conclusion: If both curves are considered [with the same time axis], they do not offer a lot of concordances, but if we shift the curve of prices of about ten years (…) we get a remarkable parallelism. skillful combination of numerical indices makes automatic the interpretation of their movements? It does not seem so” (1931: 475 tr). 40 This approach of monetary issues can here be contrasted with the episodes in the quantitative assessment of the value of money analyzed by Hoover and Dowell (2001) (and in a different way by Humphrey 2001). A common concern of the authors they study was the search for causes, and some of them referred to John Stuart Mill’s emphasis on a single main cause – although Mill thought that no one such cause could be extricated empirically from a multitude of significant causes (Peart 2001). Mill thought that “abstractions were necessary to the scientific pretensions of political economy because they would reveal the true nature of economic activity to us,” although “he did not think that that was all you needed in order to explain things in the economy” (Morgan 2000: 153). On Mill’s isolation of economic phenomena, see also Zouboulakis (1990) and Le Gall and Robert (1999).

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This means that the oscillations in the curve of the monetary stock have predicted with an interval of approximately ten years the moment when the maximum of the curve of prices reaches an exceptional peak: this is an example of the possibilities of statistical forecasting. (March 1923: 268 tr)

Figure 5.2 Prices and the increasing rate of the stock of gold and silver. The three upper curves represent prices in England (curve #1), in the United States (curve #2), and in France (curve #3). The lower curve represents the increasing rate of the annual stock of gold and silver (in France). Source: March (1923: 269).

However, he immediately tempered this optimistic opinion. Such a result, he believed, would be dependent on the historical context: “This is only a limited and provisory law” (1923: 269 tr). In other words, constancy could only be admitted within the limits of the period considered, and forecasting could only be accepted for the

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very short term, because structural changes can occur: “Within the field of social facts, more than in any other one, long-term forecasts cannot own a scientific value, because circumstances that escape any measure can occur: climatic changes, revolutions, wars; but also because the observed law often depends on other laws that do not possess the same shape” (1923: 270 tr).41 In sum, March’s work on economic cycle and on the quantity theory shows that he became more interested in the composition problem – the interweaving of phenomena, which was to him the fundamental issue in the social sciences – than in the decomposition problem, although he remains known for his technical contribution to the latter. We also see that March, even while he practiced statistics, which he saw as a methodological path to observe the social world, constantly put forward the limits of his exercises. To understand such a combination, we should examine the association he made between statistics and his epistemological views. 5.3. A BRE AK IN DE TE RMIN ISM : M ARCH ’S WORLDVIE W March’s statistical work cannot be separated from his epistemological views, and the various limits he put forward – those in measurement and statistics – in his theoretical and applied work originate in a specific worldview. In that perspective, March’s thought represents a break in the foundations of econometric ideas in France: March does not see the social world as ruled by a simple, unified, and deterministic natural order, but rather as intrinsically complex, characterized by epistemic uncertainty – a kind of “lost,” evasive, and out of reach world, in constant evolution. He believed science and statistics offered a means of approaching and taming this world and of allowing decision making in human societies. 5.3.1. On correlation, causality, and historical time The nature of March’s worldview can first be approached through his work on correlation. March indeed carefully delineated the range of application of the method of correlation: it was an instrument that took no account of the time dimension – it was consequently to him A similar idea can be found in March (1931), a paper which was certainly influenced by the occurrence of the 1929 crisis. 41

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a restricted instrument, even an inappropriate instrument – and could not be considered to measure causal relationships. For him, a correlation coefficient cannot be sufficient to analyze the relation between variables: it makes possible the quantification of the intensity of their association, but it leads to a loss of information in the sense that it negates historical time.42 March precisely thought that history mattered within the social world, that the various circumstances could never be considered constant: “economic laws, like every general formula, remain valid only during a certain period and under precise circumstances” (1912a: 112 tr). This was of pivotal importance to him. An explanation can be found in his initial conviction that the social sciences strongly differ from the natural sciences, and that both sciences have to follow separate methodological routes: experiments for the natural sciences, statistics for the social sciences. This disciplinary cleavage, this break in methodological unification that was so important for natural econometricians, finds its raison d’être in the irreducible fact that the social phenomena are time-loaded.43 For March, historical time matters, whereas natural econometricians were mainly interested in a physical time or believed that in the long term, historical time was tamed and even vanished once society reaches an “end of history.” As seen above, the range of application of statistics was identified and defined on a basis of exclusion, and we find here the key to understand the role of historical time: In a laboratory of physics, we generally deal with numbers that we can make vary as little as we want and in a reversible way. For instance, we compare the expansion of a metal with the temperature of an environment in which it is placed (…). Out of the laboratory of physical experiments, we do not obtain relations that can so simply be expressed by the unique consideration of the corresponding elements. We cannot make phenomena vary as little as we want, in a continuous way, so to speak, and reversible way. We have to content ourselves with See Morgan (1997) on such an analysis of correlation. Only few timeless laws were seen as existing in the social world, for example the proportion of males and females (see March 1924: 338). In some respects, March shares much with nineteenth century descriptive and historical approaches, e.g. that of Clément Juglar (see Juglar 1862).

42 43

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spontaneous and sporadic observations, which follow an imposed evolution. (March 1928: 45–6 tr)44 This should not be a surprise: we have previously seen that in the case of the barometer he precisely thought that events and conjunctions never repeat identically – the social world includes an irreducible component, historical time, that correlation does not fully capture,45 despite adaptation of the instrument to the features of the recipient field. This can explain why, as a whole, March rarely used correlation in his applied studies: he had a more developed taste for instruments that retranscribe and capture historical time: graphs. In that direction, Morgan explains the way “the arguments based on graphs were employed to justify explanations of specific historical time series” (1997: 73). She indeed suggests that “while the introduction of the correlation coefficient could be regarded as in some sense a technical advance, most economic statisticians continued [at the turn of the century] to use graphic methods extensively (…). The correlation coefficient is informative only about the overall relationship; it does not allow you to retrieve what has happened to the two individual series over extended periods of time of the sort that can easily be gained from visual inspection of the time-series graph. Correlation does not tell you much. It does not tell you the history of the variable or help you to explain what has happened, nor even help you to predict a time series; it is a complementary, not a replacement, technology” (1997: 74–5). The argument perfectly fits March’s methodological strategy. For him, unlike correlation, graphs visualize the economic movements over time: From the point of view of descriptive statistics, [graphs] present (…) the schematic picture of the facts that can be measured. From the point of view of comparative (or analytical) statistics, they show the reciprocal relations between facts and can help in the discovery of what is constant in these relations. Moreover,

See also March (1924: 341 and 1921: 167). This idea can also be found in his review of Moore’s Laws of Wages (March 1912c: 375). 44 45

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they make easier the comparison of the various phases of a phenomenon, they reveal irregularities and anomalies. (March 1905: 4 tr) Graphs play an important role in March’s methodology, and he wrote very enthusiastic comments on earlier writers who followed this path, for instance William Playfair.46 The 1905 opus precisely opens with the following words, full of poetry – although March’s prose traditionally remains austere: We often use graphical representations to guide the mind, in the practice of arts or in scientific studies. They offer to statistics a support whose usefulness was perceived by the first researchers: Playfair’s atlas dates from 1786. Nowadays, when financial resources allow it, we accompany the dry tables of numbers by cartogrammes and diagrams that enlighten the exposition or the analysis of numerical facts, just like the image gives colors to a story or supports a theory, and the reader always receives it with satisfaction, just like we celebrate the sunbeam that, through a light haze, reveals the outlines of things. (March 1905: 3 tr) As such, graphs were seen as instruments that could suggest inquiries: they were tools of discovery, for instance “of relationships” (1905: 4 tr), although various curves can be related to various influences (1905: 17). March especially set rules for the construction of graphs that visualize phenomena dependent on time – graphs which are the most useful, he claimed (1905: 11) – focusing for instance on the choice of scales, units, and colors in order to avoid any immediate “fallacious” conclusion. But March’s methodology obviously goes beyond this. In the 1905 study, whose title was suggestive – Les Représentations Graphiques et la Statistique Comparative – he proclaimed that correlation and graphs should not be separated.47 If that study is today known for On Playfair, see Klein (2001), Maas and Morgan (2002), and Nikolow (2001). 47 However, in his 1923 paper on barometers, he made no use of correlation. 46

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including pioneering ideas about correlation, it also contains long developments on graphs that remain neglected. His idea is that the conclusions drawn from graphs can gain in precision – or rather can be confirmed – with the use of mathematical indices, and in a prim fashion correlation:48 From the juxtaposition of curves it is possible to be aware of the accordance or the discordance of movements; but the comparison remains a little bit vague and imprecise. In order to give to it the status of a measure, we calculate average coefficients that synthesize the agreement of observed variations, while taking into account or not the importance of these variations. (March 1908: 295 tr) Similarly, the parallelism of curves is not sufficient to demonstrate the rigid relationship between the facts [which are] represented. It supports links, gives verification, suggests opinions, but offers no certainty. The graphical or numerical representations we use in statistics constitute excellent research instruments: they do not prevent from thinking; they support and precise the judgment: strictly speaking, they do not condition it, they do not fix its formula. (March 1905: 17 tr) Otherwise stated, the originality lies here in the association of both instruments providing a “control” for each other: The alliance of graphic processes and of calculus makes possible a precise analysis of the links between facts, as far as we can evaluate the appearances and the particularities that can be measured. The result is a method of investigation and of control that should be recommended. (March 1905: 40 tr)49 48 49

See March (1910a: 477; 1928: 46; and 1931: 473–4). See also March (1909: 261).

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If correlation was thus associated as a complement to graphs, it was dissociated from causality.50 March indeed pointed out a basic difference between the indices de dépendance – including Pearson’s correlation coefficient – and causality, a difference that he carefully explained from the early 1910s through to his 1930 blueprint, Les Principes de la Méthode Statistique. His arguments largely originate in Karl Pearson’s positivist thought, as his translation into French of the third edition of The Grammar of Science suggests – a book he enthusiastically presented in the Journal de la Société de Statistique de Paris (March 1912b). That book, as well as the rest of Pearson’s work, was an indictment of causality. Pearson believed that we cannot gain access to causes; instead, we perceive correlations: Nowhere do we find perfect lawlikeness, he stressed. Everywhere we find correlations. That is, even in mechanics there is always some unexplained variation. This should cause us no distress. The possibility of science depends only in the most general way on the nature of the phenomena being investigated. A correlation, after all, is not a deep truth about the world, but a convenient way of summarizing experience. Pearson’s conception of science was more a social than a natural philosophy. The key to science he found not in the world, but in an ordered method of investigation. For Pearson, scientific knowledge depended on a correct approach, and this meant, first of all, the taming of human subjectivity. (Porter 1995: 21) March and Pearson were led to believe that causality was a “pure concept” or a “conceptual limit” whose realism had to be questioned in each particular case. This idea was expressed by March in his Of course with correlation, no dependency is explicit – just a corelationship. Yet, at the turn of the century, several scholars read causality into it. In his review of Laws of Wages: An Essay in Statistical Economics (Moore 1911), March harshly criticized Moore’s assimilation of correlation and causality (see 1912c: 368). However, as we shall see in Chapter 6, these scholars had sometimes good reasons to associate correlation and causality: their worldview was supporting such an association. Note also that before the 1910s, March sometimes deduced causality from high correlation (e.g. 1905: 36).

50

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preface to Pearson’s book: The author of the Grammar adopts Hume’s idea, according to which no internal necessity, and consequently no absolute, is existing between cause and effect. The succeeding events never reappear in an identical way; the notion of causality is once more a borderline notion [notion-limite] that goes beyond sensible experience. A more or less close statistical agreement is only existing between the changes of the cause and those of the effect. (March 1912b: v tr) This concept of notion-limite indicates that for March there was an epistemological barrier to grasping all causal influences in concrete cases. Along with Pearson, March claimed that causal relationships were just simple and particular “images” of the world (1931: 475 tr) – “simplicity of nature is ultimately a simplification introduced by a mysterious power, the mental mechanism” (March 1912b: iv tr) – that should leave room for recognition that the universe was not so simple and was rather inaccessible.51 Consequently, the general case became a “space in between”: absolute independence and dependence were just borderline cases, whereas the general rule was the continuum of intermediate situations, i.e. “the various degrees of association” (Pearson 1912: 200 tr). Correlation was precisely the adequate instrument for measuring the association between two variables, but there was no possibility it could help one infer the existence of a causal relation.52 Both the alliance of correlation and graphs and the dissociation of causality from correlation find their explanations in a worldview Of course, we can see here the incommensurability with the worldview of natural econometricians. 52 Two points here deserve attention. First, in order to avoid alleged confusions generated by previous studies (such as Moore’s, in March’s opinion), March rejected the use of the word “correlation” in his applied work and he had a predilection for the words covariation or concomittance, which were to him free of notions of causality – yet, in the 1905 paper, March still used the word dépendance for “euphony reasons” (1905: 18 tr). Second, this differentiation of causality and correlation strongly influenced the subsequent early twentieth century French econometricians (see Chapter 6). 51

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that reserves a particular place for history and that denies the possibility of the successful search for causal relationships. In that perspective, March breaks with the worldview that accompanied natural econometrics. 5.3.2. Measuring and taming the world A key to March’s worldview is to be found in his belief in the “variability” and the “complexity” of the world, to use his own words. Although some regularities and even a certain determinism could be unveiled by statistics (1924: 351), he thought that Nature – and especially the human world – was characterized by permanent change, by epistemic uncertainty. March often referred to the concept of “Nature.” But at the difference of natural econometricians, Nature was not seen here as continuous (1909: 259) nor mechanical, nor deterministic – he only mentioned the existence of “some determinism” (1924: 351 tr) – nor simple – “economic facts are complex, heterogeneous, interdependent” (1912c: 367 tr).53 At least three features of his own representation of the social world deserve attention here. First, man would permanently act on reality and social facts would depend on human will that could not be understood.54 Second, the social world would be dependent on endogenous and exogenous uncertainties – not to say shocks – which, he believed, do not obey precise laws. March thus got rid of the belief in a social world only punctuated by exogenous and periodic physical causes, à la Briaune. Third, a large variety of phenomena would be tied up55 in such a way that their knowledge would be out of reach – and here we find an explanation of his rejection of the search for causal relationships and causal structures. As a whole, Nature was for March in constant evolution, history matters, and temporal “variability” would be permanently at work.56 In sum, three features of the worldview underlying natural econometrics are vanishing here: the simplicity and order of the See also March (1923: 280; 1931: 475–6; and 1930b: 268). See March (1924: 350). 55 “Common influences always exist,” he claimed (1911b: 421 tr). 56 In several respects, March’s view of the society shares much with Cournot’s “historical period,” in which the complexity generated by chance was playing an important role. 53 54

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world, determinism, and even the very idea of law, as this concept was understood by natural econometricians. In addition, whereas natural econometricians thought it was possible to unveil the true underlying mechanisms of the world (at least the most important ones), although the correspondence between the real world and knowledge was only considered probable for Cournot, March thought that the functioning of the universe was basically out of reach. The gap between the functioning of the real world and knowledge was not only to be found in imperfect observation.57 More generally, to him, “certainty or scientific evidence results from an accordance between thought and itself (…). Scientific certainty only exists in the world of concepts” (March 1912b: iii tr). For March, there is no clear and well-defined structure to identify and to discover – he rejected the idea that “Nature aims at realizing a determined type” (1909: 256 tr). In addition, he was more generally delineating a frontier between the real and inaccessible world and any theoretical world, where certainty can prevail but has no realistic counterpart. Theoretical worlds were certain in the sense that they obey formal rules of logic, but given the inaccessibility of the real world, they could never be satisfying: “a theory is only fully satisfying if it takes into account the whole facts to which it is relative” (1909: 258 tr). In that perspective, one may guess that he did not appreciate Lenoir’s methodological path, based on models that deliberately represent artificial worlds (see Chapter 6). However, here there was no renouncement of studying reality per se. Of course, knowledge would always afford in fine an unfaithful image of the real world,58 and the social scientist would always be in a precarious posture – “in the analysis of complex observations, we often grope” (1924: 350 tr).59 The world could not be exhaustively understood or captured, but it could be approximately observed and measured. Here we understand the pivotal role of statistics for March: it was the unique way to analyze reality, and his claim that “the See March (1909: 261). “Nature is diverse; it is generally by a conception of mind, and for the convenience of classifications, that we see uniformities in it. The diversity is particularly important in the case of economic phenomena; the association of multiple factors intensifies it but, in a sense, makes it less sensible” (March 1921: 156 tr). 59 Such an idea was also clearly formulated by Cournot, although for other reasons (see section 2.2.3). 57 58

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analysis of complex facts, produced by human societies, has to rely on patient and prolonged observation” (1924: 321 tr) finds here a full explanation. More precisely, with the help and the development of observation, of measurement, and of statistical instruments, social phenomena could be studied, and we can thus understand why March’s worldview paved the way for his favorite method of inquiry, monographs that open the door to a large variety of indicators: In physical meteorology, we never obtain the best forecasts on the basis of a single look at the barometer, but on the basis of an additional observation of the thermometer, of the hydrometer and of the weather vane. It is doubtful that a single index that would be a synthesis of these four observations could be more useful than four indications taken separately (…). Similarly, in the observation of business movement, we have to avoid referring to a unique index. (March 1923: 281 tr) More generally, the usefulness of monographs in the study of socioeconomic issues was recurrently championed by March (e.g. 1924: 337): from monographs it would be possible to “penetrate into the details of the phenomena studied, to scrutinize the sequence of its manifestations” (1921: 145 tr). Illustrations can be found in his studies on the influence of price variations on the movements of domestic spending (March 1910b), on demography (March 1929), or on business cycles (March 1923): all of them are detailed studies that aim at analyzing the various dimensions, ramifications, and contextual foundations of these issues. For instance, his studies on demography were often associated with an analysis of the general economic context of the countries he scrutinized, of race and climate (1929), or of socio-professional categories (1912d: 590).60 In that perspective, March follows – with other techniques – the path intensively practiced in France by Frédéric Le Play and Emile Cheysson during the late nineteenth century,61 and this is an important feature of his expertise – this also constitutes a Similarly, he regrets that in Laws of Wages Moore neglected “the circumstances of a psychological, political, financial order” which would exert an influence on economic phenomena (1912c: 382 tr). 61 See Le Gall (1997). 60

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supplementary confirmation that to him, only the composition problem matters.62 Not surprisingly, large parts of these studies are incorporating various and complementary instruments, indices, and information that, as seen above, control each other. In particular, the social scientist, March claimed, could not restrict to the use of a small set of indices to understand and approach, at least partly, the very nature of things and the relationships at work between the phenomena studied (March 1912c: 371). Explorations of the social world should rely on a large set of variables and a large set of tools and information.63 This toolbox and these measures should help to know – although imperfectly – the context that produces the phenomena under scrutiny.64 Such an epistemological view was a watershed. March was rejecting nineteenth century beliefs and postulates, and in a more formal fashion the idea that the mathematical structure of the social world could be fully unveiled from statistics. March even often rejected the use of mathematics in economics, which was considered incompatible with the alleged complexity of the real world. This led to a reorientation of statistical work: statistics was not a means to unveil mathematical and natural laws, but it should now aim at approaching and measuring an evasive Nature. In a sense March’s thought also illustrates the way the development of statistics began to tame chance at the turn of the century; statistics made chance amenable to analysis and brought it under control – as Hacking emphasized when he showed how Francis Galton’s tools represent “a fundamental transition in the conception of statistical laws” (Hacking 1990: 180– 1). Moreover, although the “erosion of determinism” in science See section 5.2.2. See March (1928: 58; 1931: 477; 1930b: 269; and 1924: 348). 64 However, March also developed a more pessimistic idea: “the unknown and the known increase jointly” (1912b: v tr). This is orthogonal to the ideal of finitude on which natural econometrics relied. Moreover, the social scientist could never be certain that he has reached reality: the regularities he extracted could have been different in another context and with other tools; in other words, we find here the idea that on the basis of other instruments and other scientific conventions, the image of the real world would have been different. March wrote: “Reality is just a trace [vestige] in the immense range of possibilities” (1924: 346 tr); in that sense, statistics was only the expression of possibilities – it afforded means to study facts, but it remains impossible to infer that we have reached reality. 62 63

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around the turn of the century made room for kinds of instrumentalism – in the sense that the aim of science became detached from ontological claims65 – March never rejected the study of reality: he, along with nineteenth century scientists, maintained the idea that science should reveal something about reality. This explains why he remained opposed to the development of instrumental models and why he kept from natural econometricians a methodological orientation: the importance of measurement, of observation, and of statistics. Nevertheless, the social world was seen as intrinsically complicated, making the task of science and statistics immensely difficult. Statistics, in taming chance, had become a means to measure the world. But it was also a means to improve the human lot and environment. These views originate in March’s perception of forecasting. Straightaway it should be noted that a form of paradox characterizes forecasting: it is the ultimate aim of statistics but at the same time it marks the end of science. Indeed, and as seen previously,66 March believed that forecasting was a subjective exercise: the various users of statistical studies (businessmen or governments) have to interpret statistical regularities according to their own aims. It was taken for granted that statistics was offering a fragile knowledge relative to a complex object. Forecasting was thus based on conjectures relative to what has happened and to what will happen and necessary involved “personal judgment” (1923: 280 tr). In March’s words, it was “un art ” (1931: 475) characterized by “la liberté de se déterminer ” (1930b: 269) – and was the moment when science stops. Once more, this idea is to be contrasted with the appreciation of forecasting found in the work of natural econometricians. For them, the discovery of laws was synonymous with the discovery of what the future had in store.67 In March’s See Israel (1996 and 2000). See section 5.1.2. 67 We understand here why March excluded forecasting from science: his belief in an uncertain and complex social world was not compatible with reliable forecasts. More explicitly, forecasting is based on a principle: “the things do not vary suddenly without reason ‘nature non facit altus’” (1931: 475 tr). But March thought that structural homogeneity cannot be admitted more generally, and he shares this idea with some scholars of the 1930s, for instance at the Cowles Commission but also John Maynard Keynes, who based their work on a postulate: unpredictability (see Chancellier and 65 66

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statistical work we see now both tamed chance and cracks in determinism. But this “end of science” does not reduce the usefulness of forecasting, and March’s barometer is here an enlightening case study. Although the label is somewhat misleading,68 the barometer was also an instrument of prediction, and in his 1931 paper he discussed at length forecasting, especially as it could be extracted from graphs – although he immediately stressed on its dangers (1931: 474). It would be a tool to be used by governments and businessmen: for instance, forecasting based on an analysis of the curves could aid in reasoning and decision making within the firm. An illustration can be found in the fact that it makes possible the determination of the moment when “the prices will be the most attractive” (1931: 473 tr). More generally, forecasting would be a means to lessen risks, to dominate the environment: “administrer c’est prévoir ” (1930a: x) was March’s motto. Statistics was thus seen as a means of measuring but also taming and shaping the social world. 5.4. E ARLY SIGN S OF IN STITUTION ALIZATION : M ARCH ’S BOUN DARY WORK

March represents a decisive step in the history of econometric ideas in France, but also in the professionalization and the institutionalization of the field. Whereas natural econometricians Jovanovic 2002, and Jovanovic 2002a). In his 1931 paper (written after the 1929 crisis), March explained this attitude. In particular, he developed the idea that the forecast of turning points of fluctuations was impossible, and he stressed once more the need for a large variety of indices and indicators as well as the fact that “the points to be observed are not necessarily the same for all the periods” (1931: 478 tr). Given the state of knowledge and tools, and given the complexity of the social world, we understand why, although useful in principle, accurate forecasting was intrinsically out of reach: “The complexity of facts that belong to political economy cannot lead, by the theory, to forecasts analogous with those that are made possible by the laws of the physical world. We thus often recognize that political economy can only indicate the more or less powerful trends that rule the facts relative to it” (1921: 138 tr). 68 The visual language of the graphs provides not just an indicator of where the economy is going (as a barometer), but a whole picture of what it has gone through. March’s “barometer” was not just an instrument of observation but also more nearly an instrument of current indication and prediction.

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were isolated scholars, March’s work (at least in the domain of statistical instruments) is fully inserted into a rising international research program. In addition, March’s significance at the institutional level lies in his efforts in organizing and developing the field in France, as well as in his search for scientific conventions from which a “unity of orchestration” could be possible. 5.4.1. A rising institutionalization of econometrics Several attempts to organize econometrics at the institutional level occurred during the early twentieth century. As Carl Christ relates, Irving Fisher – then vice president of the American Association for the Advancement of Science – tried in 1912 “to organize a society to promote research in quantitative and mathematical economics” (Christ 1952: 5). Yet, Christ continues, “Wesley C. Mitchell, Henry L. Moore, and a few others had been interested but they were too few.” At the same moment, Moore was also achieving an important boundary work at Columbia University,69 where he proclaimed as early as 1908 “the statistical complement of pure economics.” The context was favorable to such an institutionalization. Since the turn of the century, several researchers became interested in the same agenda: the application of British mathematical statistics to socioeconomic data. Authors such as Arthur Bowley, Reginald Hooker, Henry Ludwell Moore, John Norton, George Udny Yule,

Moore moved in 1902 from Smith College to Columbia University, where he became Professor of Political Economy from 1906 to 1929. That move was not pure chance. As Camic and Xie (1994) explain, the turn of the century was a period of major reorganization of scientific activity in the United States. At that time, American universities engaged in a harsh competition (relative to money, students, and prestige) and each university had to demonstrate its legitimacy as scientific center, and these struggles explain major innovations to differentiate from other universities. Camic and Xie argue that Columbia University developed “as a favorable setting for the advance of statistical methods” (1994: 778). They focus on the joint adoption and use of statistical methods by Boas in anthropology, McKeen Cattell in psychology, Giddings in sociology, and Moore in economics: their statistical framework was – at least partly – the product of local and scientific circumstances. 69

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and of course March,70 played a key role in that perspective. In addition, since the end of the nineteenth century, several journals and societies became open to statistical economics and econometric ideas. For instance, Moore’s 1908 programmatic paper was published in the Quarterly Journal of Economics and key papers by Hooker and Yule appeared in the columns of the Journal of the Royal Statistical Society71 or of the Economic Journal. In France, the Journal de la Société de Statistique de Paris, the Bulletin de la Statistique Générale de la France, and later on the Revue d’Economie Politique, played a notable role in that direction. March was an important figure in this international spread of econometrics during the early twentieth century. He was perfectly familiar with the latest developments in statistical theory as well as their use in socioeconomics. For instance, his writings show that he knew – and mastered well – the work of Galton, Pearson, Edgeworth, Pareto, Norton, Moore, or Yule. In turn, some of these scholars (e.g. Yule 1909) recognized his own contributions to the field, especially his work on correlation and time-series decomposition. This connection was reinforced by the various national or international institutions to which March belonged.72 The 1909 ISI conference that was held in Paris (July 4–10) was an important moment of that institutionalization process: Bertillon, Borel, Bowley, Cheysson, Edgeworth, de Foville, Guillaume, Huber, Julin, Lenoir, Lexis, Neymarck, Raffalovitch, Yule attended the conference. This shows that a common agenda was developing in the domain of the application of statistical instruments to economic issues and data, i.e. a collective recognition and promotion of a research direction. A separate, distinct field was slowly emerging and was progressively acquiring the first signs of professionalization and institutionalization. The approach was requiring idiosyncratic knowledge, training, skills and savoir-faire, it initiated followers and imitators, and it was gaining a proper identity; to put it more directly, the new approach was acquiring an identity through the rise of a 70 And also Hermann Laurent, in the case of France (see Breton 1998 and Le Gall 1997). 71 March also published a paper in this journal (March 1912e). 72 For instance, he became president of the Société de Statistique de Paris in 1907 and was a member of the International Statistical Institute.

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professionalization. In the case of France, March is the most visible illustration of the fact that developments in the field of econometrics are no more the product of isolated researchers, without any collective dynamic and agenda. For instance, he created an exam to recruit statisticians at the Statistique Générale de la France (Dugé de Bernonville, Bunle, Lenoir, were recruited that way), he trained statisticians (Lenoir), he promoted the teaching of probability theory in French universities, at a time when such courses were absent from the academic scene and when the kind of statistics generally taught remained largely descriptive.73 5.4.2. On scientific conventions In the context of such an emerging institutionalization, March deserves particular attention for the organization of research and future research in the field. His “boundary work” includes reflections on the concepts of statistical economics, the general directions to follow, and the definition of its foundations.74 March’s basic claim was that a correct practice of applied analysis – and of science – needs a precise and deep knowledge of the theoretical foundations of instruments. He often warns that “the observation, the implementation, and the interpretation of statistical data are (…) founded on a theory” (1911b: 416 tr). Similarly, he explains that “the statistical logic is mainly necessary to the statistician to force him to reason with method and precision” (1911b: 426 tr). Not surprisingly, a large part of his work was devoted to theoretical statistics.75 But although it is technically advanced, this work is rather pedagogically exposed, witness his 1930

He contributed in the 1920s to the creation of the Institut Supérieur de l’Université de Paris (see Desrosières 1998). Note also that during the 1909 conference of the International Statistical Institute, a committee for the teaching of statistics was created. It included (among others) Bertillon, Bowley, Edgeworth, Faure, de Foville, Lexis, Yule, and March. 74 Of course, what is particularly interesting here is that a rising field is malleable: its instruments, foundations, and orientation are not as rigid as in a more mature and ancient field. 75 See for instance March (1905, 1909, 1910a, 1911b, 1928, and 1931). 73

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textbook, Les Principes de la Méthode Statistique76. Remember that mathematical statistics was far from being a common knowledge at that time. March’s aim here was to familiarize economists and statisticians with the foundations of statistics – its range of application, its underlying assumptions, and its limits. March also stressed the need for the elaboration of a common culture for researchers in the field, and this was a means of defining the scientific rules for a collective and objective work in a rising field. Of course, this was possible by the training of disciples, the involvement in societies and journals, the organization of conferences, and so forth. One aspect of March’s work in these directions deserves particular attention: his focus on the language used and on the tools and the instruments that can define the methodological core of the field. An illustration can be found in March’s emphasis on the need for conventions, at a twofold level. First, at the measurement level, he asked for uniform statistical measures, definitions, and categories.77 For instance, he stressed the need for “international agreements” and “uniform rules” in the measurement of the causes of death and rates of stillbirths (1929: 58 and 103 tr) and more generally for a coordination of the various national statistical bureaus (1930b: 282). Second, at the methodological level, he called for standardized instruments. What will become some of the standard instruments of the subsequent years and decades were not uniformly understood and labeled at the turn of the century: March remarked the existence of several words that designate the same tools.78 In addition, although he recognized that “[n]o tools for comparison (…) could be universal” (1921: 149 tr), he thought that uniformity and agreement were necessary for a proper and objective collective work: “It should be important, in application, whose conclusions are intended for the public, that the tools for comparison and the words are uniform and free from risks of ambiguity, as far as possible” (March 1908: 296 tr). For instance From around 1930, the publication of books in which econometrics plays a central role developed. Let us mention Aftalion (1928), Guitton (1938), Marchal (1943), and even Pirou (1943). 77 See the introduction of this chapter. It can be noticed that March’s innovating work on the definition and the measurement of unemployment deserves attention in that perspective (see Topalov 1994). 78 For instance the “normal value” of Lexis and the “modal value” of Karl Pearson. 76

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he asked for a normalized use of units for graphs (1905: 8), tests of the fit of observation to a normal distribution (1921: 162–3), choice of indices for the construction of barometers, and average processes – he considered the arithmetic average “a universal instrument of numerical comparison” (1924: 352–3 tr). Finally, as seen in section 5.3.1, he discussed at length the way the word “correlation” should be understood, and he also proposed the rejection of the word “probability” in descriptive statistics (1908: 291 and 296).79 March’s work is thus deeply characterized by the desire to define conventions, and he was particularly interested in a unitary language. Of course he recognized that conventional tools and concepts cannot always be perfect or the most appropriate – remember his opinion about the normal distribution80 – but such limits were counterbalanced by what he calls “the desire for unity” (1909: 256 tr). This is undoubtedly an important turn in the history of econometrics in France: the institutional rise of the field calls for a need for common references, for conventions. A new face of unity emerges: a unity of orchestration, in the words of Morrison (2000: 24), which designates here the definition of social conventions in a scientific community. CON CLUSION In our archaeology, March is the first author to meet two requirements: he is a pivotal author in the history of econometric ideas (instruments and practice), but also in the rise of econometrics as a discipline. In both domains, he represents an important shift, even a break, that will exert an influence on the subsequent developments in the field. The most important shift is to be found in the domain of the worldview that underlies econometric ideas: March illustrates a break with the worldview on which natural econometrics was based. For March, uncertainty, complexity, and indeterminism were central features of the world, and in his worldview we find no references to the postulates from which natural econometrics rose. It is then not surprising to see that March fully escaped from the ideal of finitude that could be found in the hands of natural econometricians. Instead, 79 80

See also March (1909: 262). See section 5.1.2.

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he claimed that social scientists can never completely master the way the social world was functioning and that this world is dominated by epistemic uncertainty. Of course, the idea of a regular, mechanistic, mathematical and divine natural order cannot be found here. This philosophical shift leads to a reorientation of the econometric work. Whereas natural econometricians saw statistics as a means of discovering and measuring alleged mathematical and natural laws at work in a regular social world, March’s statistical style can be understood as the search for tools and indicators that make possible the approximate measurement of a changing and uncertain social world. But as a whole, March’s legacy in French econometrics remains ambiguous. At the institutional level, he certainly largely contributed to improvements in the statistical system and to an organization of labor in the field, from which other social scientists benefited. At the scientific level, the instruments he used, devised, and adapted also clearly paved the way for subsequent developments in the field. At the epistemological level, however, March’s influence is more obscure. For him, measurement was the most appropriate research path for dealing with uncertainty and indeterminism.81 But it is precisely the abandonment of this focus on measurement as such that characterizes subsequent developments in the field. From the fact that the real world was out of reach, other scholars deduced an orthogonal conclusion: the target was not and could not be the real world, but it could be artificial worlds, devised by the econometrician himself. If the real world was considered out of reach, the elaboration of experimental “pseudo-realities” was seen as a means for econometricians to bring back certainty, simplicity, determinism, and finitude in research. This is exemplified by the work of March’s undisciplined disciple: Marcel Lenoir.

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To some respects in the early N.B.E.R. style.

6. “If we assume that…”: Lenoir and the artificial worlds of econometrics A design of experiments (a prescription of what the physicists call a “crucial experiment”) is an essential appendix to any quantitative theory. And we usually have some such experiments in mind when we construct the theories, although – unfortunately – most economists do not describe their designs of experiments explicitly. If they did, they would see that the experiments they have in mind may be grouped into two different classes, namely, (1) experiments that we should like to make to see if certain real economic phenomena – when artificially isolated from “other influences” – would verify certain hypotheses, and (2) the stream of experiments that Nature is steadily turning out from her own enormous laboratory, and which we merely watch as passive observers. – Trygve Haavelmo, “The Probability Approach in Econometrics” Vulgarity in economics would more appropriately be defined as criticizing or caricaturing an abstract (and hence potentially useful) model because it leaves something out. – Robert E. Lucas, “Methods and Problems in Business Cycle Theory”

During the early twentieth century, correlation hunting, motivated by the search for good fits, was declared opened. The period saw, in several Western countries, the development of pragmatic studies devoted to the search for relationships between several socioeconomic indicators, for instance between demographic variables (such as the marriage rate or the birth rate) and economic variables1 (such as unemployment). In France, in a study published in 1911 in the Journal de la Société de Statistique de Paris, Henri Bunle – a statistician of the Statistique Générale de la France – zealously correlated variables such as marriages, the price of wheat, or foreign Authors such as Reginald Hooker, Robert Lehfeldt, and George Udny Yule sometimes used British mathematical statistics in that perspective. See Klein (1997) and Morgan (1990, 1997).

1

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trade. Bunle was very proud of his high coefficients. However, during the same period, other scholars sounded very doubtful as to the robustness of such a hunting, and they claimed that applied econometrics should be based on solid foundations given by economic theory. In his Statistique Mathématique (1908), Hermann Laurent (1841–1908),2 an influent actuary, carefully exposed central tools of mathematical statistics and econometrics – for instance the least squares – and he explained the way “statistics is a means of verifying economic theories” (1908: 176 tr). Yet, he thought that the true expression and explanation of “the natural laws of economic phenomena” (1908: 1 tr) was still to be identified, and this perhaps contributes to explain that his work contains very few concrete applications of these statistical techniques to economic data. Although his answer strongly differs, another author shared that need for theoretical foundations: Marcel Lenoir (1881–1927),3 a student of March and a statistician of the Statistique Générale de la France. Lenoir is another rather familiar figure of the history of econometrics: it is now well known that his Etudes sur la Formation et le Mouvement des Prix 4 (1913) are a masterpiece of early twentieth century applied econometrics and contain one of the first On Laurent, see Breton (1998), Le Gall (1997), and Zylberberg (1990). Lenoir was a former student of the Ecole Polytechnique and an engineer from the Ecole des Mines. In 1908, he joined the Statistique Générale de la France – March was head of the bureau at that time – and in 1913, he defended at the Université de Paris his PhD dissertation, the Etudes sur la Formation et le Mouvement des Prix. At the Statistique Générale, he mainly worked on statistical and descriptive studies elaborated for the government (see for instance Lenoir 1919). Some parts of his work on the construction of price and wage index numbers (Lenoir 1923, 1924, 1925, and 1926) were published annually during the 1920s in the Revue d’Economie Politique, a rather open-minded journal (Pénin 1996). Lenoir also frequently published similar papers in the Bulletin de la Statistique Générale de la France. Note furthermore that he reviewed several books in the Revue d’Economie Politique, for instance François Simiand’s Statistique et Expérience. Remarques de Méthodes (Lenoir 1922a) and Arthur Bowley’s Prices and Wages in the United Kingdom, 1914– 1920 (Lenoir 1922b). These reviews were working for the spread of ideas and the construction of the field. In 1926, Lenoir joined the Statistique Générale department of Hanoï, where he published the first Annuaire Statistique de l’Indochine. He died in that country one year later. A biography of Lenoir, though incomplete, can be found in Huber (1928). 4 This book will be referred to under the title Etudes. 2 3

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expositions of the identification problem. Some parts of the Etudes gained a certain recognition, and this illustrates the rising “unity of orchestration” during the early twentieth century. The book circulated within the small group of French statistical economists of the 1920s – it was for instance quoted in Aftalion (1928) or in several works of March – and was also known outside France. According to Kærgaard, Andersen and Topp (1998: 335), the Danish economist Edvard Mackeprang had read Lenoir, although he did not refer to him while describing the identification problem in 1924. During the 1930s, Henry Schultz (1938) has claimed to draw inspiration from Lenoir’s statistical investigations and from his indifference curves analysis.5 Yet, despite Schultz’s reference to Lenoir, it is often ignored that the Etudes are also a masterpiece of theoretical microeconomics.6 The book offers a mathematical and graphical analysis of the formation of prices that ends up in the construction of aggregate demand and supply curves and an analysis of economic equilibrium. It is precisely here that the historical significance of Lenoir’s work lies. The statistical estimations of relationships between price and quantity that can be found in the applied part of the Etudes, “Mouvement des prix (études statistiques),” are rooted in a preliminary theoretical investigation of the market process, achieved in the first part of the book, “Formation du prix (étude théorique).” In that respect, the Etudes represent a decisive step in the development of econometric ideas in France. Lenoir shared March’s postulate about the complexity of the real social world – the “maze of facts,” in his own words (1913: 2 tr) – but his strategy took an opposite direction: econometrics should rely on models, whose foundations are based on economic theory. With Lenoir’s Etudes, econometrics thus gained new foundations and took a new shape: applied econometrics became rooted in the construction of preliminary models that represent reduced-scale maps of the Afterwards, if we except George Stigler’s history of empirical studies of demand (Stigler 1954), no references to Lenoir can be found until the growing interest the history of econometrics knew in the 1980s and 1990s, exemplified by Breton (1992), Chaigneau and Le Gall (1998), Christ (1985), Hendry and Morgan (1995), Morgan (1990), and Zylberberg (1990). 6 To my knowledge, the unique historical investigation of Lenoir’s theoretical analysis can be found in Chaigneau and Le Gall (1998), in which the role Lenoir played in the history of the so-called “Edgeworth box diagram” is analyzed. 5

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economy and depict artificial worlds, and with them it could be possible to experiment on paper some mechanisms that could explain the formation of economic phenomena in a ceteris paribus perspective.7 As Mary Morgan notes, “[e]conomics is now a modeling discipline and has been for the last few decades. That is to say that economists’ discourse is concerned with ‘models’ rather than with ‘theories’, in theoretical work, in applied work, and in giving policy advice” (2002b: 42). On historical grounds, mathematical models mainly began to develop in economics during the 1930s and 1940s,8 with the emblematic work achieved by Ragnar Frisch, Jan Tinbergen, or Trygve Haavelmo.9 An economic model can be understood as an experimental frame10 constructed by the economist11 and with which he can realize some “pen-and-paper experiments” (Morgan 2002b: 43). He seeks to explore mechanisms – most often expressed mathematically – relating a set of variables in an environment under control, ceteris paribus.12 Thus, “the mathematical modeler creates an Although artificial, the model with which the econometrician reasons can of course shed light on the complex real world and it can afford possible interpretations of it, as we shall see below in more details. 8 However, other kinds of models developed previously. As Morgan (forthcoming: Chapter 1) explains, graphical models developed at the end of the nineteenth century, and we could even say that François Quesnay’s Tableau Economique is a kind of economic model (see Le Gall 2006b). 9 See in particular Boumans (1992 and 2005) and Morgan (1990). 10 Following Morgan, “[t]he term experiment refers here to the combination of the external and internal dynamics, the activity of asking questions about a circumscribed and limited model world and deriving answers about the world. This is a process in which scientist and model are jointly active participants, neither is passive” (2002b: 43–4). 11 As we shall see in this chapter, here econometricians become free from the constraints of the belief in natural order, and from this, a new power emerges: they get the power of constructing artificial worlds they can control and in which they can actively experiment. 12 One of the most recent forms of economic model can be found in Robert Lucas’s work: models would be “fully articulated, artificial economic systems that can serve as laboratories in which policies that would be prohibitively expensive to experiment with in actual economies can be tested out at much lower cost” (Lucas 1980: 696). Lucas’s views about models remain specific, with a particular focus on mimicking – the idea according to which a model is “an explicit set of instructions for building a 7

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artificial world ” (Morgan 2002b: 49), in which he actively uses and manipulates the relations and the structure he devises in order to answer some questions13 about the real world, about the world defined by the model, or about some aspects of the underlying economic theories.14 In Haavelmo’s words, a model thus refers to “experiments that we should like to make to see if certain real economic phenomena – when artificially isolated from ‘other influences’ – would verify certain hypotheses” (1944: 14). In this chapter, we shall explain the way such a methodology was inaugurated during the 1910s by Lenoir, although he never used the word “model.”15 Straightaway, it has to be remarked that in comparison with Frisch’s or Tinbergen’s models of the 1930s, Lenoir’s is less formal: it is not a purely mathematical model – graphical reasoning also plays an important role in it – and it does not obey the formal rules that were elaborated or used by economists of the 1930s and the 1940s. In addition, as we shall see below, the very correspondence between the model and observed data was rather loose, at least retrospectively. Yet, Lenoir’s applied analysis is based on explanations provided by a preliminary model founded on economic theory. We can immediately see the breaks Lenoir induces in our history of econometric ideas. A first break occurred with March’s views: although both share a similar worldview and, as we shall see in

parallel or analogue system – a mechanical, imitation economy” (Lucas 1980: 697). On Lucas’s methodology and epistemology, see Boumans (1997 and 2005), De Vroey (2004), and De Vroey and Hoover (2005). 13 On this aspect of models, see Morgan (2002a and 2002b). 14 Recent literature shows that models are specific constructions, which can act as “mediators” between economic theory and the real world (Morgan and Morrison 1999) and which possess their own rules and properties. On the nature of economic models, see Boumans (2005), Boumans and Morgan (2001), Granger (1955 and 2003), and Morgan (2002a, 2002b, 2003, forthcoming). 15 To my knowledge, that word, in the sense that it covers the previously mentioned features, was used in France for the first time in Guillaume and Guillaume (1932: 62–3). Georges Guillaume advocates the use of models on the basis of a comparison with Niels Bohr’s model of the atom. It can be noticed that Tinbergen also transferred the word from physics (see Boumans 1992, Morgan 1990 and forthcoming).

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this chapter, similar statistical instruments, Lenoir16 does not see statistics and measurement as the ultimate path for knowing the social world. But, of course, Lenoir also breaks with natural econometricians, at three levels. The first difference is relative to the way tools and instruments are used. In natural econometrics, mathematical laws were unveiled by statistics, and natural econometricians did not focus very much on the mathematical demonstration of the laws they obtained – actually, their mathematical shape was rather grounded on philosophical postulates and they believed that mathematics was God’s language. By contrast, for Lenoir, statistical relationships are dependent on a preliminary explanatory frame, given by the model, in which observation plays no direct role and mathematics17 (and also graphs) was a demonstration device. The second difference is relative to the world to which econometricians refer, in the sense of the explanatory frame to which they refer. Whereas natural econometricians had in mind the broad and unified “system of the world,” Lenoir referred to a narrow world, given by the model.18 Lenoir’s theoretical investigations only mobilized a small set of economic concepts – e.g. demand, supply, price, individual rationality – independently from any reference to other aspects of the social world, not to speak of the natural world or God. The third difference concerns ontology. Whereas natural econometricians thought they could identify the true mechanisms ruling the world – in their mind, there was an isomorphism between the real world and the laws obtained – Lenoir took for granted the complex and out of reach nature of the economy – in that perspective, he follows March – and he rejected the possibility of ontological correspondences between the real world and the model. For instance, determinism and simplicity were introduced in the model only for practical purposes. However, although the model depicts an artificial world, it can orientate the applied work and can explain the relationships that were statistically At least in the Etudes. Which was for him free from any ontological content, it was rather an efficient tool working for precision. 18 In several respects, Lenoir’s aim is to devise “small worlds” à la Cournot (see section 2.3.1), but free from any ontological content. For Lenoir, these “small worlds” are deliberately considered artificial, whereas for Cournot the “small world” represented by the perfect market would historically triumph. 16 17

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estimated. In that sense, the model can enlighten some features of the real world.19 This chapter thus explains the way Lenoir represents the rise of a new posture of the econometrician. The econometrician is not anymore the discoverer of a finite and accessible world. He is not either the measurer of a complex world. Instead, he becomes the deviser of artificial worlds, to be understood as “plausible” or “maybe” worlds from which the real world could be partly understood. In section 6.1, I analyze the model constructed by Lenoir. Within the frame of a static world peopled with maximizing individuals, Lenoir constructed aggregate demand and supply curves. Section 6.2 examines the statistical estimation of these aggregate curves, as well as the statistical instruments used, which mainly originate in March’s work – and this is a supplementary illustration of the “unity of orchestration” previously brought to the fore.20 I shall also focus on the correspondences Lenoir constructed between the model and the real world, and his discovery of the identification problem played a major role in that direction. 6.1. WE LL BE HAVE D IN THE ARTIFICIAL WORLD Lenoir’s starting point is the basic claim that the price is determined by supply and demand. But he immediately notes that supply and demand are “complex” (1913: 5 tr) – we find here a postulate and a worldview he shares with March. Yet, in contrast with March, Lenoir thought that economic knowledge does not only result from observation and measurement, but also – and mainly – from “pure economics” (1913: 2 tr). The historical originality of the approach lies in this claim: ultimately, economic theory would be the instrument from which one could escape from the alleged It is important to note here that the artificial nature of models does not necessarily imply an instrumentalist “as if ” perspective, if we refer to Milton Friedman’s 1953 essay, according to which a model is an instrument not meant to capture some kind of representation of aspects of the real world. Lenoir’s model is not artificial in that sense. It is rather a “maybe” model, i.e. an idealized hypothesis about a version of the complex and out of reach world; it is a kind of reduced-scale map, a schematic but usable instrument to get around the real world. On the “as if” and the “maybe” perspectives, see Ménard (2005). 20 See the introduction of Part II and Chapter 5. 19

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“complexity” of the real world. The first aim of the Etudes is thus to construct, on the basis of principles of economic theory and, at the methodological level, of an intensive use of graphs and mathematics,21 a theoretical model relying on several assumptions and which could explain the formation of prices. More precisely, Lenoir’s agenda is the analysis of individual behavior from which individual demand and supply curves, and then aggregate demand and supply curves, could be obtained. 6.1.1. The artificial world Whereas natural econometricians combined statistics, mathematics, and economics in the frame of a general quest of the unified “system of the world,” whereas they thought – from the postulates to which they adhered – that they could collect, gather, and capture exhaustively a finite world, Lenoir deliberately based his approach on the construction of a preliminary, narrow and artificial, explanatory frame. The model does not aim at offering a faithful image of the real world; rather, it aims at identifying some mechanisms offering a plausible explanation of stylized facts. The foundations of Lenoir’s work are to be found in the theoretical part of his book. The way he saw economic theory as a “guide” for empirical inquiries is here illuminating: From the static point of view, one has to examine, on a given market, at a given time, how equilibrium is reached through the opposite action of a group of purchasers and a group of sellers, how the price that ensures this equilibrium is determined. (…)

Lenoir advocated “the precious help that the use of curves and of their analytical representation can bring to economic theory” (1913: 5 tr) and, in that perspective, he claimed a methodological continuity with previous “masters” (1913: 6 tr): “Cournot has been a precursor, but his researches, published in 1838, passed unnoticed. It is only thirty-five years later that the simultaneous work of Stanley Jevons and Léon Walras definitively introduced this method in the economic science. It will be sufficient for us to mention the names of Edgeworth and Marshall in England, of Pareto in Italy, of Irving Fisher in America, of Auspitz and Lieben in Germany, of Cheysson and Colson in France, to remind the generality of the movement which imposed a notion now universally adopted” (1913: 5–6 tr).

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In fact, it is from a daily observation that we get a knowledge of the mechanism of exchange, a constant observation of men and things, and which does not express itself in tables of numbers but comes down to abstract notions. By this way economists have been able to discern the general laws of the functioning of a market. Later on, it is not with the help of a more complete documentation, but with the use of a more precise psychological analysis that it has been possible to clarify the modalities of these laws. The result, “pure economics,” does not probably cover the whole economic science, and does not aim at forecasting the whole economic phenomena, but it is a guide in the maze of facts, it enlightens its connections (…). It was thus necessary, in these researches on price, to present first a brief analysis of exchange from the psychological fact which is its first cause. Our aim is not to construct a new theory of prices, following so many brilliant authors. We have only tried to clarify its critical points (…). The theoretical study achieved in the first part initially provides guidance for these researches, through some critical connections. And when observation has verified some agreements of numerical series, it is again theory that helps to analyze them, that provides guidance in the search for the sequence of causes that these agreements can detect. (Lenoir 1913: 2–3 tr) For Lenoir, econometrics is thus founded on a set of “abstract notions” (concepts and relationships) which belong to “pure economics.” From them, “general laws of the functioning of a market” could be identified and could shed light on the real world. The model is here deliberately viewed as depicting an artificial world. In the previous quote, we can see that Lenoir’s aim is the analysis of a static world, despite the real economic phenomena constantly change through time and are time-related and timeloaded. In addition, we find in the first part of the Etudes the following and recurrent expressions:22 “Let us consider an individual with two variable economic elements, x, y” (1913: 7 tr); “Let us assume that …” (1913: 13 tr); “Until now, we have only considered individuals, either an isolated individual, or two individuals together” 22

Our emphasis in the seven following quotes.

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(1913: 33 tr); “Let us consider a group of N consumers of the commodity x …” (1913: 33 tr); “If we suppose that all the individual curves have similar shapes …” (1913: 34–5 tr); “If we want the complete curve, we always need a hypothetical extrapolation” (1913: 41 tr); “… in what will follow, as in what has preceded, the individual, here the producer, is considered at a given moment, in a given economic environment (…). Moreover, in general we shall suppose that the quantities produced of commodities are sold, and admit consequently that there are no variations in stocks” (1913: 43 tr). Of course, such expressions illustrate a deep feature of Lenoir’s methodology: the reasoning in “a circumscribed and limited model world” (Morgan 2002b: 43), in which Lenoir analyzes a narrow set of issues in an environment under control – an environment deliberately defined by the econometrician himself. The economic framework constructed in the Etudes thus breaks with any desire to represent faithfully the real economic world, or even parts of it: given the alleged complexity and out of reach nature of the real world, an artificial “small world,” in which the economist wishes to reason, is defined. For example, Lenoir’s economic framework is deterministic for practical reasons – no ontological determinism is claimed here. It is also a world in which simplicity is introduced and advocated, in the sense that the situations analyzed in the model concern pure markets, whereas, remember, the real economic world is considered “complex”.23 In the model, the economist thus wants to isolate and to explore pure situations, ceteris paribus and, as we shall see more precisely below, to conceive “pen-and-paper” experiments: the model is malleable, and the economist can consider various kinds of situations by making assumptions vary according to what he wants to demonstrate. 6.1.2. The construction of aggregate demand curves Lenoir treated the demand side in two main steps. First, on the basis We see here the way Lenoir represents a shift in comparison with March: both believed that the real economy is uncertain and complex, but Lenoir circumvents the problem and focuses on a model in which simplicity can be brought back. We also see here the way Lenoir’s approach of the market differs from Cournot’s: for Cournot, the perfect market, the “commercial machinery,” was not yet existing but would prevail in the long term (see section 2.3.2).

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of an analysis of individual behavior and indifference curves, he defined individual demand curves. Second, he used an aggregation procedure and obtained demand curves relative to a market. Indifference curves Lenoir started with the definition of his framework. He considered one individual and two goods, x and y. The quantity of x and y can vary continuously.24 The individual is also supposed free, i.e. he only acts “if he wants to” (1913: 8 tr). Lenoir represented the possible “elementary actions” from any point A (figure 6.1), an “elementary action” being defined as an infinitely small variation of x and y. However, it is supposed that the individual “will have to abandon some of one good to get some of the other one” (1913: 8 tr): in figure 6.1, the individual only acts in the directions aȨAb (northwest) or bȨAa (southeast).

Figure 6.1 “Elementary actions.” In A, the individual has to abandon some of y to get more x. Source: Lenoir (1913: 8).

Contrary to Cournot (see section 2.1.3), continuity was just for Lenoir a useful assumption: “this continuity, as every continuity, is a theoretical abstraction that cannot in general be realized practically” (1913: 7 tr). 24

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Two pivotal notions are then introduced. First, if we consider any action or direction, for instance Au1 (forming an angle ơ1 with Aa), “the individual, in order to increase x of dx, has to reduce y of dy1; he pays dx with dy1: the price of x in y is then for him

dy 1 dx

tgơ 1 ”

(1913: 8 tr). To use our contemporary vocabulary,25 this price is the marginal rate of substitution, measuring the rate at which the individual is just willing to substitute one good for the other. Second, individual behavior is exclusively described by preferences26 or rather, in Lenoir’s words, “tastes”: if we refer to the action Au1, “the individual will realize it or not, according to his relative tastes for x and y” (1913: 8 tr). Lenoir formulated the following general statement: We thus see that all the directions of the angle aAbȨ can be divided into two groups: one including all the directions for which the individual will act, the other [including] all those for which he will have a predilection for refraining, and all the directions of the first group are located above all the directions of the second group (that is, their angle with Aa is smaller) (…). A certain direction Au0 of the angle aAbȨ is thus existing and separates the two groups, and for which we cannot say whether the individual will act or will refrain. We shall label it: indifference direction. For every direction located above Au0 (with a smaller angle with Aa), the individual will act; for every direction located below (with a greater angle with Aa), the individual will refrain. To the indifference direction Au0 corresponds the indifference price of x in y p 0

dy 0 dx

tgơ 0 .

(Lenoir 1913: 9 tr)

In every point A, an individual is characterized by the existence of At several occasions, I shall explain Lenoir’s reasoning and concepts on the basis of phrasing used in Varian (2003). 26 With individual rationality, this is in Lenoir’s model the unique characterization of the individual. We can see a deep change in comparison with the frame of natural econometrics, in which individuals were considered dependent on natural order and God. It can also be noticed that there is no utility concept in the Etudes. 25

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two “indifference directions,” Au0 (acquirement of x) and Av0 (acquirement of y), as figure 6.2 shows.

Figure 6.2 “Indifference directions.” The broken line u0Av0 separates worse bundles (shaded area) from better bundles. Source: Lenoir (1913: 10).

The next step is the deduction of indifference curves from indifference directions: From these indifference directions, [which are] such as one of them with an angular coefficient

dy dx

 p( x , y ) passes through

any point xy, we can deduce, under some conditions, a series of indifference curves by integrating this equation. One, and only one, of these indifference curves passes through any point of the plane and in this point it is tangent to the indifference direction defined above. (Lenoir 1913: 11 tr) Lenoir considered different shapes for indifference curves, these

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shapes being kinds of mental explorations of his model.27

Figure 6.3 Indifference curves in the general case. Source: Lenoir (1913: 12).

First – and this would be “the general case” (1913: 12 tr) – he assumed that “an indifference curve C (figure [6.3]) admits a certain number of tangents parallel to Ox in the points AȨ, AȨȨ, AȨȨȨ of abscissa XȨ, XȨȨ, XȨȨȨ, …, and a certain number of tangents parallel to Oy in the points BȨ, BȨȨ, BȨȨȨ of ordinate YȨ, YȨȨ, YȨȨȨ, …” (1913: 12 tr). In the points AȨ, AȨȨ, AȨȨȨ, the individual “is not willing to abandon a part of his amount of y to make x vary,” and in the points BȨ, BȨȨ, BȨȨȨ, the individual “is not willing to abandon a part of his amount of x to make y vary” (1913: 12 tr). Therefore, Lenoir designated “the points AȨ, AȨȨ, AȨȨȨ, …, as the points de satiété for x, and the points BȨ, BȨȨ, BȨȨȨ, …, as the points de satiété for y” (1913: 12 tr), that is bliss points. In figure 6.3 he supposed the existence of a total bliss point, the point ƹ of “satiété totale” (1913: 12), which is the situation where “the As Morgan (2002b: 46) explains, model reasoning “involves a kind of thought experiment.”

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individual is fully satisfied” (1913: 13 tr).28 Incidentally, we can see here the way Lenoir’s model reasoning incorporates idiosyncratic concepts: the bliss point is here a landmark but it could not be observed as such. Second, Lenoir presented the case of “closed curves enveloping each other around the point ƹ’’ (1913: 13 tr), i.e. elliptic indifference curves (figure 6.4).

Figure 6.4 Elliptic indifference curves. Source: Lenoir (1913: 13).

Third, Lenoir proposed a more simple shape, which was downward sloping to the right and convex to the origin (figure 6.5).

Schultz (1938) used this part of Lenoir’s analysis. See Chaigneau and Le Gall (1998: 169–70).

28

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Figure 6.5 Convex indifference curves. Source: Lenoir (1913: 16).

This is precisely the shape he kept in the subsequent developments of the Etudes. Why did he operate this choice? He noted that “experience suggests some kinds of simple shapes” (1913: 11 tr), but this was a broad statement and no data was used to support it. In addition, he explained that “there is only a very small part of an indifference curve that corresponds to reality, during a time that excludes a too considerable variation in the taste of the individual as well as in the other economic factors” (1913: 12 tr). This enlightens three features of Lenoir’s methodology. First, we can find here a property of model reasoning: independently from observation, the economist makes assumptions about some characteristics of the model.29 Second, the choice of such a shape results from Lenoir’s predilection for simplicity inside the artificial world, which depicts a pure world. In addition, this simple shape was sufficient for the following steps of his demonstration. Third, we can see here the break Lenoir illustrates in our story. In comparison with March, he tried to bring back simplicity in research, although both share a similar worldview; and in comparison with natural econometricians, 29

See Morgan (2002b: 55–6).

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especially Cournot, Lenoir does not consider that simplicity applies to the real world: he selects simple shapes in his model because it is a useful and sufficient assumption.

Figure 6.6 A2 is a better bundle. Source: Lenoir (1913: 18).

Figure 6.7 A2 is a worse bundle. Source: Lenoir (1913: 18).

Let us now follow the last step of Lenoir’s analysis of indifference curves: the way the individual maximizes his satisfaction. Let A1 (x1, y1) the initial situation, and A2 (x2, y2) the final situation, with x1 < x2 and y2 < y1 (figures 6.6 and 6.7). Then,

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In order to make a decision, the individual analyzes his situation in A2 [and] his tastes in A2. However, in A2, the individual tends to act following every direction that penetrates inside the indifference curve passing through this point, tends to increase x and to reduce y as long as the possible price of x in y is inferior to the indifference price (…). If, thus, the extension of A1A2 penetrates inside the indifference curve, and this shows that the price of x in y of the operation A1A2 is inferior to the indifference price in A2, the individual, in A2, would like to extend again the operation A1A2. This is the assumption admitted in figure [6.6]. In this case, for the individual in situation A1, the operation A1A2 appears desirable, and he realizes it. If, by contrast (figure [6.7]), the extension of the vector A1A2 passes outside the indifference curve in A2, and this shows that the price of x in y of the operation A1A2 is superior to the indifference price in A2, the individual in A2 would not like to extend the operation A1A2, but would rather be inclined to an opposite operation, if it is possible. In this case, the individual in situation A1 does not find desirable the operation A1A2, and he does not realize it. (Lenoir 1913: 17–8 tr)

Figure 6.8 The “total indifference curve” D. Source: Lenoir (1913: 19).

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Lenoir focused on the case in which “A1A2 is tangent in A2 to the indifference curve,” when “the individual stops” (1913: 18 tr). From “any point A,” he obtained a set of optimal bundles, which delineate a curve D, called by Lenoir “total indifference curve,” and which is, in the contemporary vocabulary, the price offer curve. With downward slopping and convex indifference curves, he obtained the curve D represented in figure 6.8. At that stage, Lenoir’s reasoning spread in two directions. First, he extended his initial hypothetical frame and considered a market with two individuals trading (and still two goods). This situation was analyzed in the frame of a box diagram.30 Second, and this is more important here, he moved to the construction of aggregate demand curves. Demand curves In the previous developments, the quantities of x and y are supposed to vary jointly. In Chapter 3 of the Etudes, Lenoir revised his framework: now he supposed that the market of y is held fixed.31 This was a means of posing a ceteris paribus condition, and we can see here both his search for the study of simple and pure situations within the frame of the model, independently from features of the real world, and the malleability of model, in which the economist can consider various kinds of situations by making assumptions vary according to what he wants to demonstrate.32 In this revised frame, Lenoir easily obtained individual demand curves, that he labeled, in a rather treacherous way, “indifference curves,” noted ǐ. Individual demand curves are visualized in figure 6.9.

See Chaigneau and Le Gall (1998). “In the previous developments, we have supposed, and this is the general case, that the indifference direction of the individual in the point xy depends on x and y (…). In what will follow, we shall make an assumption that will largely simplify the following parts of our study: we shall assume that the indifference direction of the individual, in the point xy, only depends on one of the variables, namely x” (Lenoir 1913: 25 tr). 32 See section 6.1.1. 30 31

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Figure 6.9 Individual demand curves ǐ.

Source: Lenoir (1913: 34).

Yet, Lenoir’s ultimate goal was the construction of an “indifference curve” or a “demand curve” for a group of individuals, for a market: Until now, we have only considered individuals, either an isolated individual, or two individuals together. We shall extend the definition and the use of indifference curves to the case in which the commodity considered is consumed, or purchased, or sold, or produced by groups of individuals. This extension is possible, and is easily achieved, under the assumption we have considered, according to which the commodity is exchanged against money, the total quantity of money owned by each individual being of no influence. (Lenoir 1913: 33 tr) Here Lenoir considers a market with N consumers of x, other things being equal. He stated that an “indifference curve” or a “curve of total demand” (1913: 34 tr) relative to the whole group of N consumers could be obtained from individuals curves: The definition of the indifference curve of the group will be analogous: this curve ǐ will be the location of points M, of coordinates Ɠx,p, such as the total consumption of the group being Ɠx, this consumption will increase, will diminish, or will

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remain constant, depending on whether the possible price of transactions (by assumption, the unique price in the market) is inferior, superior, or equal to p. The consumption Ɠx is the sum of the individual consumptions x1 + x2 + x3 +…+ xn. (Lenoir 1913: 34 tr)33 Once more, the result depends on several assumptions. First, Lenoir supposed that for each individual, a maximum indifference price34 exists, a price for which consumption in x is zero; second, N is an “infinitely large number” (1913: 35 tr); third, individual indifference curves – i.e. demand curves – are linear. Then, the variations in consumption of any individual are proportional to the variations in prices. The maximum prices of consumption of the various individuals are spaced in a continuous way from p1 to p2 (…). The individual curves thus determined are uniformly distributed, that is, the number dn of individuals whose maximum indifference price lies between p and p + dp is the same whatever p (lying between p1 and p2). If N is the total number of individuals considered, we have dn

N

dp . p 2  p1

(Lenoir 1913: 35–6 tr) Hence, the shape of the aggregate curve (figure 6.10) could be “easily” deduced (1913: 36 tr):35

33 Similarly, a mean curve could be constructed: “we can also consider the mean demand curve, (…) for which any point of ordinate p has as abscissa 6x ” (1913: 34 tr). x N 34 The maximum indifference price is the price from which an individual is not willing to purchase the commodity x. Lenoir assumed that this price differs from one individual to another (see figure 6.10). The price p1 is “the lowest of the maximum indifference prices’’ (1913: 36 tr), i.e. the price for which the quantity demanded by one of the N individuals is zero. The price p2 is the greatest maximum indifference price, i.e. the price for which none of the N individuals are willing to purchase x. 35 Yet, Lenoir’s exposition was rather terse. A demonstration is given in Chaigneau and Le Gall (1998).

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Let x be the mean indifference consumption at price p. As long as p is inferior to p1, all the individuals consume, and the average curve is rectilinear, as the individual curves; it is the straight line of equation: x X

p log

1

p2 p1

p 2  p1

.

From p1 to p2, the mean curve bends, having a convexity turned to the origin, so that it arrives in p2 where it is tangent to Op. In this region, its equation is: x X

p 2  p(1  log

p2 p

)

p 2  p1

(Lenoir 1913: 36 tr)

Figure 6.10 The aggregate demand curve obtained from individual demand curves that are supposed linear and spaced uniformly from Xp1 to Xp2. Source: Lenoir (1913: 36).

For Lenoir, the aggregate curve36 thus obtained is the curve which is “generally considered under the name demand curve or, from the point

This kind of aggregation procedure was innovating: “one has to wait until René Roy in the 1930s for this problem to be anew considered” (Zylberberg 1990: 129 tr).

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of view of the producer who furnishes x, the courbe des débouchés”37 (1913: 40 tr). From this analysis, Lenoir had in his hands a demand curve relative to the market. This aggregate demand curve, he warned, was of course determined inside the controlled environment of the model, and it depends on the assumptions made: The demand curve just previously defined, like the indifference curves from which we got it, applies to a set of individuals with constant tastes, in a constant economic environment, conditions that we can only supposed realized, even approximately, during a rather short period of time, a period during which the prices and the consumptions do not vary a lot. (Lenoir 1913: 40 tr) However, this curve could be used to analyze the real world. At this stage, Lenoir’s challenge was indeed to turn to a statistical investigation of the way price and quantity are related on real markets. In Lenoir’s mind, the model depicts an idealized, simplified world, but it could provide “guidance” (1913: 3 tr) about the analysis of the complex real world. But the artificial world and the real world remain separate entities, and Lenoir put some emphasis on the gap between them: It is only about such curves that experience can afford some information. From some statistics, indeed, it is possible to follow, simultaneously, price and consumption. But the experimental drawing of a demand curve seems difficult. It is only about a very small part of such a curve that experience can inform. (Lenoir 1913: 40 tr) We shall turn to Lenoir’s applied analysis in section 6.2. For the moment, we have to examine the way he analyzed supply in order to have in his hands a full analysis of the market.

This probably refers to Emile Cheysson’s eponym curve (see Cheysson 1887 and 1911). On Cheysson’s curve, see Ekelund and Hébert (1999), Hébert (1986), and Zylberberg (1990).

37

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6.1.3. The construction of aggregate supply curves To my knowledge, Lenoir’s analysis of the supply side has never been exposed in the literature. It follows the same path as his analysis of the demand side: the aim was to construct an aggregate supply curve from individual supply curves.38 However, as a prolegomenon, it should be noted that for the contemporary reader, his analysis of the supply side may sometimes be both counterintuitive and obscure, and this is especially due to the vocabulary Lenoir used. For instance, he labeled cost curves “indifference curves”39 and he sometimes afforded results that were not carefully demonstrated. Of course, Lenoir’s explanatory framework is given, once more, by an artificial world, which aimed at analyzing and understanding supply in pure, idealized situations. At the individual level, Lenoir considered a producer “at a given moment, in a given economic environment” (1913: 43 tr). In this world, only one commodity and money are considered: the two variables on which he focused are x, a commodity, and y, “the quantities of numerate got in payment” (1913: 43 tr), i.e. the gross receipts. In addition, it is assumed that no fix capital is existing – this applies to a producer who is “for instance an isolated worker with negligible tools” (1913: 44 tr). Given these assumptions, Lenoir claimed that: The simultaneous variations in the variables x and y which are possible for the individual, and which can be used for the determination of indifference curves, are thus the variations the individual can produce or not, as he wishes, almost instantaneously. (Lenoir 1913: 43 tr) Oddly enough, we can see here that Lenoir wants to construct “indifference curves” that would characterize the behavior of the producer. Following Lenoir, an “indifference direction” could be defined in any point (x, y), as it was the case for the consumer. More Only the simplest case Lenoir considered (in which there is no fix capital) will be exposed here. 39 This illustrates the fact that during the early twentieth century, the basic concepts of microeconomics were not standardized (see Wulwick 1992 and 1995). 38

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light on this is afforded by the following explanation and its associated figure (figure 6.11): The producer that we consider being in A (x, y), the indifference direction in this point is defined as in the general case. The individual only tends to increase his production x of dx if he increases at the same time of at least dy the amount of money, y, and he only tends to reduce x of dx if this reduces y of less than dy. His indifference price p, in this point A, is

dy . dx

In A, our producer considers that he only has an advantage to produce dx if he can get at least dy in exchange; dy is, according to his estimation, the production cost of the last unit produced or to be produced, and the indifference price price.

dy is the marginal cost dx

(Lenoir 1913: 44 tr)

Figure 6.11 “Indifference directions” of the producer. For instance from A the producer increases output of dx if it generates at least an increase dy in receipts. Source: Lenoir (1913: 44).

Then, cost curves – coined “the indifference curves of the producer” – were obtained, although the explanation was rather terse: The beginning of production has no particular feature. The individual, who begins the production, only needs to make sure that he gets an infinitely small remuneration dy0 to produce an

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infinitely small quantity dx0. Moreover, his production is necessarily limited; whatever the labor furnished, he can never produce more than a certain quantity X. We can thus admit for the indifference curve C the shape given [in figure 6.12] (…). The curve D, defined as previously,40 (…) is [in the figure] the dotted curve. It gives the points where production stops, if all the quantity produced is sold at a same price, the indifference price of the last unit produced. This curve D, tangent to C in O, is entirely located below C, in the action zone of the individual, in the production zone. (Lenoir 1913: 44–5 tr)

Figure 6.12 The “indifference curves” of the producer. C is the average variable cost curve, D is the marginal cost curve. Source: Lenoir (1913: 45).

Actually, the curve C is the average variable cost curve, and the curve D is the marginal cost curve. From this visual analysis, Lenoir could deduce a supply curve Ƅ in (x, p) (figure 6.13).

This refers to the case of the consumer, analyzed in the previous section of Lenoir’s book. 40

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Figure 6.13 An individual supply curve Ƅ. Source: Lenoir (1913: 45).

The final step was the construction of an aggregate supply curve. Once more, the demonstration relies on several assumptions. Lenoir supposed the existence of N producers, each of them having the same maximum production X (figure 6.14). He also assumed that between O and X, the Ƅ curves are parallel straight lines, and that the producers are distributed uniformly. Lenoir could obtain the aggregate supply curve, in his own words the “indifference production of the group” (figure 6.15).

Figure 6.14 The distribution of individual supply curves ưi pi (which are supposed linear). Source: Lenoir (1913: 48).

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Figure 6.15 The aggregate supply curve. Source: Lenoir (1913: 49).

This was precisely the aggregate curve from which a statistical analysis of real markets could be achieved, and here Lenoir follows the same lines as in the case of the aggregate demand curve. He explained that such a curve could be useful to analyze the complex real world, although it results from a world that should not be considered the real world: “Here again we cannot expect from observation the precise determination of the shape of the supply curve. We can only expect from it some information on the shape of such a curve around one point” (1913: 50 tr). Let us take stock. The previous developments reveal the nature of Lenoir’s explanatory framework: given his worldview – the real economy, he believed, was too difficult to access and too complex to be just observed and understood – he reasons in an environment largely independent from observation, an environment under

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control, ceteris paribus41 – his explanatory frame is an artificial world, which depicts a simplified, idealized economy. Yet, he thought that knowledge about the real world could be provided by the model: the latter affords some mechanisms from which the real world could be read. In the second part of the Etudes, Lenoir precisely tried to understand some features of real markets on that basis: his agenda was the statistical estimation of the aggregate relationships previously obtained in the artificial world. 6.2. F ROM THE ARTIFICIAL WORLD TO THE RE AL WORLD: T HE E MPIRICAL E STIMATION OF DE MAN D AN D SUPPLY CURVE S The originality of Lenoir’s Etudes is to be found in the fact that the statistical analysis of the behavior of prices and quantities should be based on results afforded by the artificial world constructed by the economist. We thus have to examine the instruments he used in that perspective as well as the applied results he obtained. 6.2.1. Lenoir’s statistical instruments: The rising autonomy of correlation The most part of the statistical instruments Lenoir used comes from March’s toolbox: graphs and correlation. Yet, Lenoir put more emphasis on British mathematical statistics than on graphs. This difference between Lenoir and March illustrates the rising autonomy of correlation vis-à-vis historical time that occurred during the early twentieth century.42 The use of graphs The applied part of the Etudes is specifically devoted to “the examination and the comparison of certain series of numbers relative to certain series of years” (1913: 63 tr), and Lenoir saw graphs as

41 These curves result from a theoretical investigation, practiced inside the model. At the difference of what could be found in the work of Cournot and Briaune, who also determined relationships between price and quantity, observation and statistics are not used at this stage. 42 See Morgan (1997) for an analysis of that autonomy in the case of British statistical economics.

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useful instruments in that perspective.43 It is extremely difficult, even for a trained observer, to extract from the examination of a series of numbers nothing but a confusing general impression. A graph, by contrast, at first glance, generates a far more precise feeling, far more exact also. The advantage of graphs is even more obvious for the comparison of two series of numbers. The simple juxtaposition of two columns of numbers affords little information. We can compare two numbers, two pairs of numbers, but if the series becomes a little bit longer, we need to content ourselves with fragmentary remarks, whose relative importance can be badly perceived, and from which it is really difficult to draw a precise conclusion. The superimposition of two diagrams, appropriately constructed, makes it possible to rapidly formulate a somewhat exact opinion about the resemblance of the movements of the two phenomena compared. (Lenoir 1913: 63–4 tr) In addition, and following March (1905), Lenoir stressed the need for precise rules and conventions in the construction and the presentation of graphs. As such, this is a supplementary confirmation of the important role graphs were playing in statistical economics and in econometrics at the turn of the century (Morgan 1997 and Klein 1997). Graphs, mathematical statistics, and causality: An undisciplined disciple However, and in spite of the importance they play in the exposition of Lenoir’s theoretical developments, graphs play a relatively minor role in Lenoir’s applied work. In March’s work, graphs and correlation were controlling each other.44 By contrast, in Lenoir’s applied work – at least in the Etudes – a clear hierarchy exists: the confection of graphs is not the aim of applied research, as for instance March’s barometer was, it is rather the prolegomenon to further quantitative research. Graphs can be instruments of discovery; but the aim here is rather the determination of coefficients This also applies to other pieces of applied work Lenoir achieved (e.g. Lenoir 1919). 44 See sections 5.2 and 5.3.1. 43

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of correlation and regressions, which both offer a greater precision through quantification: It is however necessary to precise this judgment [i.e. the visual judgment]; it is convenient to synthesize it in a number that will measure the resemblance – this number is the coefficient of correlation or of covariation. (Lenoir 1913: 64 tr) This greater importance of correlation finds an easy explanation. Correlation, remember, negates historical time,45 and in comparison with March, historical time plays a relatively minor role in the Etudes. Lenoir’s aim was not to visualize historical movements; rather it was to try to get rid of complexity and to give more importance to ahistorical patterns. Long developments of the Etudes were precisely devoted to the exposition of correlation. Lenoir claimed that various measures of the “resemblance” of two curves exist, but to him the important point was to operate a conventional choice.46 Once more, we see that French econometricians of the early twentieth century were particularly careful in the definition of such conventions that would work for objectivity47 and that illustrate the definition of common rules in a rising scientific community. Lenoir exposed this need for conventions on the basis of an analogy with the measurement of temperature afforded by a conventional instrument, the thermometer: [i]n order to extract from the use of the coefficient of correlation all the information that we can expect, all you have to do is to use uniformly, as far as possible, the same system in the same group of studies. And then, once we have examined couples of graphs, which have known coefficients of correlation, we acquire a rather precise feeling about the degree of resemblance that such or such coefficient expresses. It is by this way that, when we look at the thermometer before going out, we imagine the sensation of heat or coldness that we shall See section 5.3.1. In addition, a true measure of an association was seen as impossible. 47 See section 5.4.2. 45 46

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feel. But for that, we have to be familiar with the gradation of the thermometer. (Lenoir 1913: 69 tr) It is in that perspective that Lenoir referred to and used Karl Pearson’s coefficient,48 that he considered an appropriate convention. He also presented partial correlation analysis; to my knowledge, this is the first time this approach was exposed by a French author. Lenoir’s analysis of correlation owes much to March. In particular, he follows March’s dissociation of correlation and causality: If the coefficient [of correlation] is very close to 1, if the resemblance is very high, does it demonstrate a causal relationship? It can suggest the existence of such a relationship, or it can confirm it, but it cannot prove it. Which phenomenon would be the cause, which one [would be] the effect? To determine this, a certain lag in the agreement of variations through time has to show us one as a constant antecedent. Moreover, many other links can exist between two phenomena, other than the relation of cause to effect, even if we admit that the constancy of the resemblance of the curves relative to both phenomena prevents us from rejecting the simple hypothesis of fortuitous coincidences. (Lenoir 1913: 75 tr) However, here once more, Lenoir is a rather undisciplined disciple. For March, causality was dissociated from correlation for philosophical reasons: the real world would be too complex to see causality in correlation, and more generally, March’s work was an indictment of causality.49 By contrast, causality was an important concept for Lenoir. Of course, from correlation we cannot deduce automatically causality. But causality played a major role in the 48 Lenoir also mentioned Fechner’s indices, exposed in section 5.2.1. They would be “simple, direct, almost intuitive” (1913: 69 tr), but were considered imprecise. At the difference of March, Lenoir thus paid little attention to them. 49 See section 5.3.1.

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model, which was actually devoted to the search for a kind of causal structure, at least some causal relationships. And if correlation is used within a frame in which causal relationships are founded and explained,50 then correlation could be used to verify these relationships. This is the idea behind Lenoir’s use of correlation. With correlation, the econometrician can check the relevance of the relationships obtained within the explanatory frame of the artificial world: the latter orientates and supports empirical investigations, and it offers the frame from which empirical results (and observed correlations) get a precise meaning and can be interpreted. This is another strong illustration of the new role economic theory plays in econometrics. Lenoir on time-series analysis The final component of Lenoir’s toolbox is a method of time-series decomposition influenced by March (1905) and Hooker (1901 and 1905). In every curve that represents an economic phenomena, Lenoir noticed that a “slow and continuous general movement” as well as “more abrupt oscillations, sometimes completely irregular, sometimes showing a certain regularity, around the general secular movement,” could be identified (1913: 65 tr). This refers to the distinction of long-term and short-term movements already operated by March in his 1905 paper, and which could also be found in the work of natural econometricians. Lenoir explains as follows the separation of these movements: It is natural to think that these two movements (…) can be related to different phenomena or groups of phenomena. It will thus be convenient to separate them and to decompose the initial curve in a continuous courbe interpolatrice, free from abrupt variations, and a curve made up of successive oscillations. This leads to decompose each numerical element x in a sum, x = x0 + Ʀ, where x0, which is the ordinate of the courbe 50 In this respect, Lenoir shares much with Henry Ludwell Moore, although their methodological and philosophical views strongly differ. For Moore, correlation and causality were associated because his framework and worldview (the world seen as a causal and deterministic machine) were affording an explanatory causal frame (see Le Gall 1999 and 2002a).

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interpolatrice, varies through time in a slow and continuous way, and where Ʀ is a small quantity, sometimes positive, sometimes negative. (Lenoir 1913: 65 tr) In the field of time-series decomposition, Lenoir is introducing a supplementary sophistication in comparison with the authors previously scrutinized. He split each time series in two components: a courbe interpolatrice – a trending factor – and a courbe oscillante – a cyclical factor, defined as a deviation from the trend. Although he claimed that such a decomposition could be graphically realized, he mainly focused on a mathematical scheme. In the general case, each data was split in such a way that xn = x n + Ʀn, where x n is the trending factor and Ʀn the cyclical factor. x n was defined as a moving average51 of nine-year length, and the cyclical factor was defined as the difference between xn and x n . Lenoir also explained how it was possible to consider “the relative deviation in percentage of the element from the average” (1913: 67 tr) such as rn = Ʀn/ x n and xn = x n (1 + rn). Why is x n defined as a moving average of nine-year length? Let us first follow the arguments Lenoir gave: In all our studies, the number chosen is 9.52 [This is also the choice made by R.H. Hooker: Correlation of the Marriage-Rate with Trade (Journal of the royal statistical Society. September 1901); G. Udny Yule: On the changes in the Marriage-and Birth-Rates in England and Wales during the Past Half Century with an Inquiry as to their Probable Causes (Journal of the R.S.S. March 1906) and Henri Bunle: Relation entre les variations des indices économiques et le mouvement des mariages (Journal de la société de statistique de Paris, March 1911).] We have thus mean values quite close to decennial averages, which we usually consider. Moreover, this choice, a little bit arbitrary, can find a more rational justification Lenoir only used the word “average.” According to Judy Klein (private correspondence), one of the earliest references to the term “moving average” is in King (1912). 52 The following sentence between brackets reproduces a footnote of the Etudes. 51

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for the elements whose oscillations present a certain regularity. Indeed it appears that, in this case, the period of these oscillations, which is the one of economic cycles, is close to 9 years (varying from 7 to 11 years). For the phenomena whose variations seem very capricious (agricultural productions for instance), our unique guide is the more or less important regularity of the mean curve. In order to be sure of the uniformity of the comparisons operated between the different phenomena, we always used averages of 9 years. But it is also sometimes interesting to examine curves constructed with averages relative to shorter intervals of time, such as quinquennial averages. (Lenoir 1913: 66–7 tr) This quote beautifully reveals, once more, a feature of early twentieth century econometrics. Of course, Lenoir relies – though in a broad sense – on observation to accept this length of the moving average. But most importantly, we also find here the idea of a conventional choice. Lenoir took for granted the choice made by British scholars as well as one of his colleagues of the Statistique Générale de la France. This is a supplementary illustration of the “unity of orchestration” rising at the time. 6.2.2. The statistical estimation of demand and supply curves Lenoir used these statistical instruments to estimate supply and demand curves for various commodities. It is at this stage that the model offers keys from which the real markets could be read and, at least partly, understood. As we wrote in the introduction to this chapter, the very correspondence between the relationships given by the model and the applied work remains loose, at least retrospectively. For instance, the model affords no “ready for estimation” relationships, with clear parameters to estimate, but rather some rational foundations to the aggregate relationships between price and quantity that Lenoir wants to estimate. The first market Lenoir investigated is that of coal. He split the crude data into the short-term and the long-term components (moving averages of nine-year length). First, he focused on the behavior of the composantes oscillantes. From a graphical analysis (see figure 6.16), he noticed a “remarkable concordance of both

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movements” (1913: 95 tr) when consumption is considered with a one-year lag53 and also the existence of three homogenous subperiods: from 1817–18 to 1846–47, from 1846–47 to 1878–79, and from 1878–79 to 1904–05. For these three sub-periods, correlations are respectively +0.10, +0.56, and +0.59. He found here a confirmation of his previous visual analysis: The values of the coefficient of correlation confirm what appeared first: independence of both phenomena during the first half of the nineteenth century; then variations in the same direction, with a rather close relation. (Lenoir 1913: 95 tr) This illustrates the way graphs are for Lenoir tools of discovery: his estimations of relationships between price and quantity are relative to historical homogenous sub-periods, and sometimes include lags determined from a visual inspection. However, we also see here the way graphs are not Lenoir’s ultimate goal: it is rather the determination of correlations (and regressions as well). Then, using the least squares, he turned precisely to an estimation of relationships between the short-term components of price (ƅp) and of consumption (ƅc) for two sub-periods: ƅp = 0.38ƅc + 0fr.16 (1847–1876) ƅp = 0.42ƅc – 0fr.05 (1876–1905) However, the relation is quite different in the long term. Discussing the relationship between the moving averages of the price of coal54 and an international index of the production of coal in four countries,55 he found that they varied negatively: “the movements are opposite. This suggests the idea that the movement in the mean price, during long periods, is in inverse relation to the acceleration in production” (1913: 101 tr).

This one-year lag is integrated to the construction of that graph. This index is relative to France, United Kingdom, Belgium, and Prussia. 55 United Kingdom, France, Belgium, and Germany. 53 54

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Figure 6.16 The short-term components in consumption (black curve) and price (dotted curve) of coal. Source: Lenoir (1913: 94).

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Let us briefly present the results Lenoir obtained for two other markets, and begin with that of cotton. He related the price of cotton (p) to coal consumption (h) – considered an index of general economic activity – and the production of cotton (P) for the 1875– 1906 period,56 and he found: ƅp = –0.43ƅP + 1.07ƅh, ƅp, ƅP, ƅh denoting the short-term components in the price of cotton, the cotton production, and coal consumption. In the case of the coffee market, consumption (c) was related to time (t ) and the price of coffee (p). Lenoir found an inverse relation between c and p (the composantes oscillantes of both variables) for the two sub-periods he considered (1847–1869 and 1873–1896) and he also determined here partial correlations: c = 833 + 43.5(t – 1858) – 1.44(p –227) (cp.t ) = –0.54 c = 1649 + 32.7(t – 1884.5) – 2.73(p –347) (cp.t ) = –0.85 At this stage57, a final question remained unanswered: How More precisely, h is the consumption of coal in France, p the price of cotton in France, and P the American production of cotton. Indeed, “even from the point of view of Europe, the American production can be considered a sufficient index of supply” (1913: 130 tr). 57 It can be noted that Lenoir also analyzed the iron market, and this was for him an opportunity to discuss the quantity theory (analyzed on pp.84–8 of the Etudes). He focused on a variable that could exert “an influence” on “the average movement in all the prices: the production of metallic money” (1913: 102 tr). His aim was here “to try to relate the mean price of iron to the acceleration of its production and to the production of precious metals” (1913: 102 tr). Considering (from 1845 to 1904) the “trending factors” of the price of iron (p), the production of iron (h), time (t ), the production of gold and silver (m), and the production of gold taken separately (µ), he determined the following partial correlations: (ph.mt ) = –0.42; (ph.µt ) = – 0.34; (pm.ht ) = +0.73; (pµ.ht ) = +0.82. From these results, he concluded that: “These coefficients indicate with precision a direct and very general 56

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could these empirical relationships be interpreted? In his definition of the econometric work, remember, Lenoir claimed that: When observation has verified some agreements of numerical series, it is again theory that helps to analyze them, that provides guidance in the search for the sequence of causes that these agreements can detect. (Lenoir 1913: 3 tr) Not surprisingly, then, Lenoir moved back to his explanatory framework. 6.2.3. The identification issue58 The issue at stake here is the way to interpret the previous estimated relationships: Are they estimations of demand or of supply curves? To answer that question, Lenoir wondered about the respective influence of supply and demand factors in a dynamic perspective. He extended his initial explanatory framework – the initial model was static, whereas the estimated relationships were obtained with the help of data produced by circumstances that vary through time – and he considered the various factors that could induce shifts in aggregate demand and supply curves. Here we reach a well-known part of the Etudes: the discovery of the identification problem,59 whose exposition was included in the theoretical part of the Etudes and which was considered by Lenoir an extension of his initial explanatory framework. Lenoir exposed this identification problem in two steps. First, he moved from a static to a dynamic analysis of demand and supply curves, as the following excerpt shows: covariation between price and production of metallic money, a very marked inverse covariation between price and the acceleration of iron production” (1913: 103 tr). It can be noted that Lenoir used here the same words than March. 58 All the translations from p.56 to p.62 of Lenoir’s Etudes used in this section are from Mary Morgan, Jean-François Richard and David Hendry, in Hendry and Morgan (1995: Chapter 17). 59 Lenoir never used the term “identification.” An accurate analysis of Lenoir’s treatment of identification can be found in Morgan (1990), Hendry and Morgan (1995), Zylberberg (1990), Chaigneau and Le Gall (1998).

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From what we have just seen,60 for a commodity which exchanges freely in a given market, between a group of producers and a group of consumers, if each individual always remains free at each instant to fix his own price, and to increase or decrease his production or consumption, there will finally be convergence, in the market, towards a certain equilibrium price p, for a certain quantity x of goods produced and consumed, p and x being well determined by the curves, say, ǐ and C. In fact, for a large numbers of goods, these conditions are roughly realized, and one can accept that the price which establishes itself in reality is nearly the theoretical equilibrium price. This [equilibrium] price depends: on the general economic condition (always supposed constant, in all of this study), on supply and on demand. Now these three elements never stop varying, and, during the course of time, the price follows their variations. In the second part of this study an attempt is made to distinguish by observation between these complicated influences. But we are able to predict here the direction of the variation which will tend to produce a change in each of the two last factors, supply and demand. We shall say that supply increases when the indifference curve Ƅ of the producers passes from Ƅ2 to Ƅ Ȩ2 [see figure 6.17]; then, to the same indifference price there corresponds a greater quantity produced, and to the same indifference production corresponds a lower price. Demand increases whenever the indifference curve Ƅ of the consumers passes from Ƅ1 to Ƅ Ȩ1; to the same indifference price there corresponds a greater quantity consumed, and to the same indifference consumption there corresponds a higher price. One now sees that, supply being constant, to any growth of demand there corresponds an increase in production– consumption and a rise in price. The representative point in p, x passes from A to B or from D to C. The price and the consumption vary in the same direction. If demand is constant, a growth of supply corresponds to an increase in production– consumption, and a fall in price. The representative point Lenoir refers here to his previous theoretical analysis of demand and supply (see section 6.1). 60

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passes from A to D or from B to C. Price and consumption then vary in opposite directions. If supply and demand simultaneously increase (from A to C), production– consumption will increase, but the price could vary in one or the other direction or remain constant. If supply grows, while demand diminishes (from B to D) the price will fall, and the production–consumption could vary or remain constant. (Lenoir 1913: 56–7)

Figure 6.17 Identification. Lenoir visualizes the shifts in demand and supply curves. Source: Lenoir (1913: 58).

Then, in a second step, he explained that the shifts in demand and supply curves depend on the kind of markets considered. He separated agricultural from industrial markets. For agricultural markets, the shifts in the supply curve dominate in the short term:

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For certain goods the influence of one of the two factors seems to be dominant. For an item of food in common use, produced by cultivation, such as wheat, one can accept that, in a given country, the demand curve varies only very slowly and remains nearly the same for several years. In contrast, the supply curve depending on the state of the harvests varies from one year to another. The representative point then moves along the same demand curve, and the price varies inversely to the supply, rising when the harvest is abundant, dropping when it is poor61 – not withstanding the influence which can be exerted by the general economic condition. (Lenoir 1913: 57) By contrast, for industrial markets, the shifts in the demand curve dominate in the short term: If we consider, instead, a good, such as coal, or cast iron, produced by industry, consumed, at least for the most part by industry, it seems that it is the demand which varies faster. The supply curve only varies here in response to a transformation of the means of production, a transformation which only takes place under the pressure of demand, rather slowly, and always or nearly always, in the same direction, tending to increase supply. Demand, in contrast, is more capricious, and its influence, in short time periods, is predominant. Price and production–consumption will then change in the same direction. (Lenoir 1913: 57–8) For instance, when industrial activity induces a rise in demand – the means of production remaining the same – one passes from A to B. Price and production increase, as well as the profit of producers, but the production of some of them reaches its maximum. Then producers change their means of production in order to “increase This is a mistake, as Morgan (1990: 165) noticed: Lenoir should have written that “The representative point then moves along the same demand curve, and the price varies inversely to the supply, rising when the harvest is poor, dropping when it is abundant.”

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their profits if the price maintains itself” (1913: 58) and other firms are created: the supply curve passes from Ƅ2 to Ƅ Ȩ2. If the demand curve had remained constant (Ƅ Ȩ1), one would pass to C; “there would be a fall in price at the same time as an increase in production–consumption” (1913: 59). But if demand still increases and its indifference curve passes to Ƅ ȨȨ1 when supply is Ƅ Ȩ2, one passes from B to E; the price still increases. In sum, any variation in price or in quantity produced and consumed of a good indicates a shift of the indifference curves which determine these elements. With the meaning which has been given to the words supply and demand, one can say that price is always determined by supply and demand, and always varies under the sole influence of relative variations in supply and demand. If price varies in the same direction as production– consumption, the variation in demand is predominant; if price varies in the opposite direction, it is the variation in supply which prevails. It is only upon this point that the comparative statistics62 on price and consumption will inform us, if one makes no additional assumptions. (Lenoir 1913: 60) However, the changes “which provoke these shifts in indifference curves can be very varied”: they result from the “psychological state of the producers or of the consumers, or [from] the techniques of production, or [from] the general state of the economic environment” (1913: 60). Here time had to be introduced into the analysis to be able to understand the respective influence of demand and supply on real markets. We are brought back to Lenoir’s time-series decomposition. Over short periods of time, one can consider as being negligible, at least to a first approximation, all the influences other than those of the variations in harvests for the production of agriculture, and of the variation of need for the consumption of industry. (Lenoir 1913: 60)

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In the sense of observed data.

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For long periods, the discrimination of causes is far more difficult. The scope for hypotheses is wider; the verification troublesome. The relative importance of the links which ensure cohesion of the economic world do not clearly appear. If the fluctuations in agricultural production, and industrial requirements – and we shall verify them – reveal themselves as characteristic phenomena tied to fluctuations of the indifference curves, then it is impossible to neglect, in a long time period (beside the combined movement of the harvest of an agricultural product, or the combined movement of the intensity of industrial need for a good), the changes which happen in the tastes of consumers, in the techniques of production, or in the situation of individuals as regards other goods – in particular as regards money. (Lenoir 1913: 61) It is from this analysis that Lenoir could interpret the empirical results previously exposed. Consider the case of coal. Lenoir could explain that his relationships between the composantes oscillantes were estimations of aggregate supply curves: This indicates that it is the dominating variation in the demand curve that determines the variation in price – with a lag caused by stocks – and this is one verification of the influence of the fluctuations in industrial demands on the formation of economic cycles. (Lenoir 1913: 97 tr) Otherwise stated, during short periods of time, price and consumption vary positively: supply remains constant whereas demand varies. However, during long periods of time, price and quantity vary inversely: demand remains constant whereas supply varies. From this study of the coal market, Lenoir could conclude that: In sum, three kinds of links appeared in the course of this study: In short periods, the price of coal varies as the quantities

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consumed, the oscillations in price follow the oscillations in demand, delineate economic cycles. In a long period, the secular movement in price seems subject to two influences: it varies as the production of metallic money, and in a direction inverse to the acceleration of production, following the variation in supply. (Lenoir 1913: 104 tr) Similar interpretations were given to the various relationships estimated for the other markets investigated. Lenoir’s conclusion was rather modest: From the statistical studies achieved, (…) two lessons appear. On the one hand, for each commodity we have recognized the existence and measured the strength of some permanent links between price and other elements (…). On the other hand, we have seen the general influences that seem to govern the movements in price (…). Probably, these are not novelties. The existence of economic laws, the generality of cycles, the influence of crops, the quantity theory, all this can be guessed from a careful examination of facts. However, a precise verification is not useless. This is what we have attempted, and the success perhaps justified the dryness of our methods. (Lenoir 1913: 161 tr) However, one may think that a major “novelty” is to be found here: Lenoir founded the econometric applied work on the construction of an explanatory frame that took the shape of a model, depicting an artificial world that could however enrich knowledge about the complex real world supposedly difficult to access. The model offers results that are, of course, dependent on an isolated environment, and in it the most part of the reasoning was operated by orthogonal detours from the real world. Yet, the model was offering a kind of orderly, simple, causal, and explanatory structure that could shed light on “stylized facts” and from which possible explanations of real phenomena could be afforded.

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CON CLUSION Lenoir’s Etudes represent two major breaks in the history of econometrics in France. First, in the continuity of March, Lenoir breaks with the worldview of natural econometricians. He thought that the social world was complex and he got rid of the belief in a simple, orderly, and deterministic economic world ruled by a divine natural order. The second break is relative to the way the econometrician deals with complexity. Of course, Lenoir has in common with March statistical instruments. But whereas March privileged a route dominated by the measurement of a complex economy, Lenoir developed a predilection for the construction of a model based on economic theory.63 It is in the construction of this artificial world and in the way it orientates the statistical work that Lenoir’s historical originality is to be found.64 If we use Trygve Haavelmo’s language, Lenoir believed that the econometrician could not access Nature’s “enormous laboratory” (Haavelmo 1944: 14), but that he could devise artificial “small worlds” that he controls and that could afford a possible reading and a possible explanation of the real world. Historians own a poisonous privilege: they know what the future has in store. What we can precisely see here is the emergence of some aspects of the kind of modeling that developed from the early 1930s with, in France, the work elaborated by Georges Guillaume and Edouard Guillaume and Bernard Chait,65 but also, at the international level, the methodology followed by Ragnar Frisch, Jan Tinbergen, and some of the Another face of the “unity of orchestration” unity appears with Lenoir: this new early twentieth century practice saw the rise of a connection between econometricians and theoreticians of economics. For instance, between 1907 and 1914, at least four authors became involved in the measurement and the statistical analysis of results afforded by theoreticians of demand: Rodolfo Benini, Corrado Gini, John Maurice Clark, and Henry Moore referred to the Walrasian approach or to the Marshallian approach to estimate demand curves. This means that, although Moore was a harsh opponent of Marshall (Le Gall 1999, Mirowski 1990, Wulwick 1995), these authors based their applied work on concepts and relationships defined by theoreticians. 64 Although in his review of the Etudes, Jean Lescure harshly wrote that Lenoir “could have suppressed Part one of his work (…)” (Lescure 1914: 114 tr). 65 See Guillaume and Guillaume (1932) and Chait (1938). 63

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developments realized in the Cowles Commission during the 1930s and the 1940s.66 In particular, the Cowles men’s search for structural relations, and Haavelmo’s search for autonomous relations,67 were based on mathematical models hypotheses about them as a way of interrogating the data, i.e. as instruments because the world is hard to grasp. On historical grounds, however, we should not overemphasize similarities between Lenoir and the Cowles men: in the Etudes, we find neither formal analysis of correspondence problems nor formal treatment of random,68 and for instance the importance of graphical reasoning in the book suggests that it cannot be separated from the context of the 1910s. However, Lenoir’s most important break in the history of econometric ideas in France lies in his belief that the econometric applied work should be based on economic theory – an idea that was also central in Ragnar Frisch’s definition of econometrics (see Frisch 1933a) – and on economic models. His own general conception of models can be directly compared with Haavelmo’s: Theoretical models are necessary tools in our attempts to understand and “explain” events in real life. In fact, even a simple description and classification of real phenomena would probably not be possible or feasible without viewing reality through the framework of some scheme conceived a priori. (Haavelmo 1944: 1) With Lenoir, econometricians mainly began to become active architects of these artificial worlds, and they were no more the discoverers and the observers of the divine “system of the world.” This illustrates a change of scale in the history of econometric ideas; here “the scale By contrast, March’s version of econometrics is, retrospectively, more consistent with Wesley Clair Mitchell’s work of the 1940s. 67 Actually, it can be noted that Haavelmo’s search for an autonomous structure governing the economy can be compared with the agenda of natural econometricians (and in both cases, we can find an underlying naturalism). I thank Mary Morgan for help on this question. Nancy Cartwright’s analysis of Haavelmo illuminates that point; see for instance Cartwright (1989). 68 In addition, in Lenoir’s Etudes we can find no connection between the model and policy advice and, more generally, no real analysis of economic policy. 66

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(…) is of humans, not of God,” if we refer once more to the words of Deirdre McCloskey69 (2002: 334).

69

See also, of course, Foucault ([1966] 1994).

7. Conclusion: From nature to models Change (…) consists in the realization or actualization of some of these potentialities. These realizations in their turn consist again of dispositions or potentialities – potentialities, though, that differ from those whose realizations they are. – Karl Popper, Quantum Theory and the Schism in Physics

Two questions are given answers in this book. The first question is: Is econometrics a twentieth century phenomenon? Following the canonical history that accompanied the development of the Econometric Society and the Cowles Commission, but also, in the case of France, the canonical histories in which twentieth century engineers sometimes self-promote,1 many histories superimposed the level of ideas and practice and the institutional level, and took for granted that econometric ideas only rose during the 1920s and the 1930s, at the time when the Econometric Society was constituted and when the label “econometrics” was coined. An important part of the historical dynamics of econometric ideas is then neglected: our book shows that, in the case of France, econometric ideas rose and developed from the 1830s to the 1920s, in close symbiosis with instruments, scientific practices, and philosophical views that prevailed during the period. However, this mode of analysis long The foundations of this biased history find an illustration in François Divisia’s motto (or postulate?): engineers “do economics while others talk about it” (Caquot 1939, in Divisia 1951: x tr). There are certainly good reasons for believing that engineers deeply contributed to econometrics in France during the twentieth century. For instance, econometrics was largely discussed at X-Crise, the Centre Polytechnicien d’Etudes Economiques, which was constituted in 1931 (see X-Crise 1982); François Divisia, Bernard Chait, and Jan Tinbergen gave conferences there. Engineers such as René Roy and Maurice Allais also played a major role during the early years of the Centre National de la Recherche Scientifique (see Bungener and Joel 1989), not to mention the role played by Edmond Malinvaud (see Fourquet 1980). However, such a story also conveys an alleged lag of universities, which should be analyzed more carefully. 1

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remained on the fringe of the field of dominant economics: in that respect, our authors – at least natural econometricians – were not fully “in the truth” (Foucault 1971: 36 tr).2 The second question is: Is econometrics (just) a useful toolbox for economists? Since more than twenty years, some economists and econometricians denounce, sometimes harshly, a lack of foundations of current econometrics, and wonder about the usefulness and rigor of the approach3 – Deirdre McCloskey claims, sharply enough, that “all the econometric work since the 1940s has to be done over again” (2000: 200).4 A frequent argument is that econometricians simulate well, but contribute little to explain the real world. What is especially denounced here is a certain pragmatism in the practice of econometrics and more specifically an autonomy of applied econometrics vis-à-vis explanatory frames such as economic theory5 or philosophical views.6 However, our sampling of authors illuminates the way econometric ideas are carried by careful analyses of economic phenomena, of the nature of the economic world, of “A proposition has to respect complex and severe requirements to belong to a discipline; before it can be considered right or wrong, it has to be ‘in the truth’, as M. Canguilhem would say” (Foucault 1971: 35–6 tr). 3 See (although their arguments strongly differ) Hendry (1993), Leamer (1983), McCloskey and Ziliak (2004), Spanos (1989), and Summers (1991). 4 This is probably why she also explains that she has “recently become a nuisance at historical conference [on cliometrics] and in referee reports about statistical significance” (2000: 194). 5 An explanation can be found in a significant trend at work from the 1940s, namely the progressive split of econometrics (at the scientific and the institutional levels) into applied econometrics, econometric theory, and theoretical economics. 6 A nice example is given by the posterity of Haavelmo’s 1944 thesis. Although Haavelmo offered a very careful philosophical justification of his probability approach (see Le Gall 2002a and 2002c; Morgan 1998; and Spanos 1989), attention was mainly paid to his technical innovations in subsequent developments of econometrics. For instance, in the famous Cowles Commission Monograph 10, Marschak (1950) legitimates probabilistic instruments independently from philosophical views, whether deterministic or probabilistic: probability would just be an efficient tool for econometricians. In the case of France, a nice example of interweaving of philosophy and econometrics during the twentieth century can be found in the work of Henri Guitton. See for instance Guitton (1978) and, on Guitton’s methodology, Schmidt (1994). 2

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science, and also, in some cases, of the whole world. In that respect, the econometric ideas our sample of authors developed are grounded on well-shaped explanatory frames and worldviews from which they get their meaning, and this is why they could generate knowledge about the real world. It is however necessary to dig a little bit deeper in both directions. First, on historical grounds, from this book natural econometrics may appear as a kind of “French exception.” Although more research should be achieved in that direction, this style of econometric ideas also rose in other countries: in several respects, our identification of natural econometrics may be an encompassing process. Second, from the 1830s to the 1920s, the analysis of our authors’ work shows the way instruments were used to serve worldviews that determine the knowledge econometrics could offer. 7.1. N ATURAL E CON OMETRICS: AN EN COMPASSIN G STORY? In the French political economy landscape, natural econometrics appears as a logical step between François Quesnay’s Tableau Economique and the early twentieth century econometrics. But more importantly here, it can contribute to unify some work that developed in various countries from the mid-nineteenth century until the early twentieth century. Three illustrations will be briefly discussed here: Richard Babson’s economic barometer, William Stanley Jevons’s “mechanical economics,” and the shape taken by Henry Ludwell Moore’s econometrics. 7.1.1. The rise of barometers and unification Although it is sometimes emphasized that barometers belong to “measurement without theory,” to use the words of Koopmans (1947), they can be far from a kind of statistical alchemy and they can rely on sound explanatory foundations and worldviews – as March’s work in that direction shows. In a series of studies, Eric Chancellier7 shows the way several early barometers find their roots in a worldview in which determinism and unification (and sometimes mechanism) play a key role. Consider Roger Babson’s famous

7

See Chancellier (2004, 2006a, 2006b).

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barometer (1925).8 Babson used a single index of economic activity and visualized the economic movement through time by a set of straight lines that would represent the normal course of business (figure 7.1).

Figure 7.1 Babson’s barometer. The X–Y broken line is obtained from Newton’s third law (action equals reaction) for successive sets of years. Source: Babson (1925: 108).

One feature of this barometer deserves particular attention. The determination of a straight line consists in postulating that it has to pass between the global index in such a way that the surface represented by the area above the line equals the surface of the area below the line, over a rather long period. The system may seem flimsy, but as Chancellier (2006b) explains, it relies on a direct reference made by Babson to Newton’s third law. From this law, Babson could claim that any element that undergoes an action in a particular direction will undergo an equivalent reaction in the opposite direction. Babson did not use that law by accident: his use of the method was based on a unified worldview. Indeed, for him, the whole world was obeying a set of similar rules and laws, of a mechanical and deterministic nature. The following long excerpt from Babson’s Business Barometers for Anticipating Conditions illustrates 8

See also Babson (1913).

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beautifully this worldview and its associated methodology: As soon as Sir Isaac Newton published these facts, a scientific reason existed for the ordinary balance scales and scores of other instruments which were then in use and which have since been developed. This law is the basis of the steam engine, the electric dynamo, water-power machinery, and every other power machine. All calculation of forces and all formulas relating to them derived their conception from this Law of Action and Reaction. If there is one thing which science teaches, it is that this Law of Action and Reaction cannot be eliminated. We may dread it and attempt to ignore it, but it is always in operation in thousands of diversified ways. Whether making a balloon ascension or raising our feet in walking, we are working in accordance with the Law of Action and Reaction. The study of hygiene is comparatively in the same stage in which that of mechanics was a couple of centuries ago. As a matter of history, it has been only in recent years that fundamental laws have been scientifically applied to the study of the human body. Instead of grasping the fact that the same laws apply to men as to commodities, physicians used to doctor with different methods and various drugs, hoping to hit something, by hook or by crook, that would perform a cure. Recently, however, there has been a great change, and they have learned that men are simply machines, and that to do good work they themselves must be good mechanics. This means that instead of bleeding a patient and filling him up with drugs, as they did years ago, physicians now look upon their patients as machines and realize that the machine needs to be kept clean, well oiled and supplied with fresh power. The great heart specialists are now simply utilizing Newton’s Law of Action and Reaction as applicable to the pump, while other specialists are realizing that other organs of the body are nothing but individual sewerage systems, power plants, and various other mechanical contrivances. Moreover, physicians recognize Newton’s Law of Action and Reaction in its relation to sleep, breathing, eating, exercise, etc. For instance, every man has a certain normal line of sleep; that is, he requires a certain amount of sleep, which varies with

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different individuals at different ages, but which for a given individual at a given age, is a constant factor. Furthermore, for all a man varies from this normal line of required sleep in one direction he must compensate by varying a corresponding amount the other side of the line. This can be illustrated by considering the X–Y Line of our regular Babsonchart as representing the normal amount of work which a given man can average, the outline of the black areas representing the amount of work that he actually does. Whenever the man performs an abnormal amount of labor, causing him to lose sleep, a black area is formed above the X–Y Line. It then becomes necessary for him to rest a corresponding amount, and this causes the black area to go below the X–Y Line. When any man attempts to ignore the Law of Action and Reaction and remain above his normal X–Y Line too long, he suddenly becomes ill, and is forced to go to bed and make up his required amount of rest. This Law of Action and Reaction applies in the same way to man’s breathing, food and exercise. Our bodies are like the spring rifle, we get out of them only what we put into them. Not only are certain physicians making great progress today through the use of Newton’s Law of Action and Reaction, but psychologists as well are employing it in their experiments. It is a fact well known to students of Newton’s investigations that the great scientist found this law to apply not only to mechanical and astronomical phenomena, but also believed it to apply to affairs more remotely removed from such sciences. (Babson 1925: 106–8) Of course, there is no econometrics here. But Babson’s work is a piece of statistical economics which is fully dependent on a worldview that shares much with the one that permitted natural econometrics and that determined the instruments used as well as the results obtained.9

Note that from what he considered a universal law, Babson could infer the possibility of forecasting.

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7.1.2. Jevons’s “mechanical reasoning” A second example, stronger in many respects, is given by William Stanley Jevons’s work. It is now well known that the core of his economic work, in particular of his theory of exchange, was permitted by analogies with mechanics (Schabas 1990). More recently, Harro Maas showed the way the theoretical and empirical work that Jevons achieved in the field of economics (on labor, economic cycles, or exchange) but also in the field of the natural sciences (mainly meteorology) is rooted in a “mechanical reasoning.” Maas (2005) explains this “mechanical reasoning” as follows: Jevons’s recourse to machines as engines of discovery in science challenged the boundaries between the moral and physical sciences that were cherished by John Stuart Mill, and challenged as well the sort of evidence that economists could take recourse to in support of their theoretical views. Using mechanical analogies, Jevons aimed at finding mathematical expressions for his quantitative data, attempting to explain their general form. In the Principles, Jevons explicitly argued that this was the format for all of the sciences. There was no one way from theory to data, nor did the opposite hold; statistical data might suggest the range of functions that came into consideration to explain the phenomena, while theory might dictate the admissible form of the functions from its side. Granted there are no boundaries between the sciences, it is hard arguing against the use of the tools and the instruments of the natural sciences in the moral ones. The complexity of the subject, the multifarious causes that produce a single social fact, may make inconceivable how such instruments are to be applied in the mental and social realms, but this is no longer a matter of principle. What could be done in astronomy or meteorology could be done in economics as well. (Maas 2005: 286) But there is much, as we can see in this quote. Indeed, Jevons also “pioneered the use of both mathematics and statistics in his work” (Morgan 1990: 4). Although he explained that “the difficulties of this union [the deductive science of Economy and the purely inductive science of Statistics] are immensely great” (Jevons 1871, in Morgan

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1990: 5), he practiced it and, given his worldview dominated by a “mechanical reasoning,” his econometric methodology shares much with the one developed by our French natural econometricians. In Chapter 2,10 we suggested the way Cournot’s idea of a possible inference of the mathematical “law of sales” from observations was close to one part of Jevons’s work: the extraction of a mathematical function relating prices and quantities from statistical data and their visualization on graphs.11 Maas summarizes that perspective as follows: With modern eyes, we may be inclined to take Jevons’s drawing as a very rudimentary fitting of a curve to the data. However, in Jevons’s use of the graphical method, the goal was not to fit the graph to the data, but to obtain an idea of the class of functions to which the “rational function” belonged – that is, to obtain an idea of the causal explanation of the phenomena behind the observed data. (Maas 2005: 235–6) In addition, Maas shows the way Jevons’s “mechanical reasoning” exerted a direct influence on the form of the mathematical expression of such curves. This work achieved by Jevons illustrates a central feature of natural econometrics: from observation and an appropriate statistical inquiry, mathematical laws ruling the real world could be revealed. In sum, in Jevons’s work a union of mathematics and statistics spread within the frame of a worldview in which determinism, mechanism, unification, and even natural order play a key role,12 and, from Maas’s analysis of Jevons, there is some ground to believe that the British polymath could easily be portrayed as a

See section 2.1.3. See figure 2.2 in section 2.1.3. 12 An illustration is given by Jevons’s work on commercial cycles. Although it is often derided, his sunspot hypothesis can be positively understood at the light of his “mechanical reasoning”: Jevons referred to the “well-known principle of mechanics that the effects of a periodically varying cause are themselves periodic, and usually go through their phases in periods of time equal to those of the cause” (Jevons 1884, in Maas 2005: 247). Given his unified worldview, he searched for a causal mechanism that could relate credit cycles to solar variations, although the search was not fully successful. 10 11

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natural econometrician.13 7.1.3. On Moore’s star system The final example, and the most spectacular in many respects, is given by Henry Ludwell Moore. Once at Columbia University, Moore largely contributed to the emergence of econometrics in the United States, and he advocated in 1908 “the statistical complement of pure economics”.14 Moore was certainly influenced by local circumstances: the specialization of Columbia in the application of statistics to the social sciences (Camic and Xie 1994). However, other factors played a major role in Moore’s development of Two differences with natural econometrics can however be noted. First, Jevons recurrently used experimental frames to investigate issues such as the formation of clouds or the measurement of muscular force. Second, he directly (and rather zealously) analyzed individual behavior. On these aspects of Jevons’s work, see Maas (2005). 14 This association was fully practiced from his first book on economic cycles (Moore 1914). For Moore, although economic theory had attained a high degree of mathematical formalization by 1900, it largely ignored or even rejected statistics. The result – a copy “of the severe beauty of the mathematico-physical sciences,” “a disguised form of the classical cæteris paribus, the method of the static state” (1914: 85–6) – could hardly be considered the philosopher’s stone: “It was assumed gratuitously that economics was to be modeled on the simpler mathematical, physical sciences, and this assumption created a prejudice at the outset both in selecting the data to be investigated and in conceiving of the types of laws that were to be the objects of research. Economics was to be a ‘calculus of pleasure and pain’, a ‘mechanics of utility’, a ‘social mechanics’, a ‘physique sociale’. The biased point of view implied in these descriptions led to an undue stressing of those aspects of the science which seemed to bear out the pretentious metaphors” (1914: 85–6). By contrast, he proclaimed the necessity for economists to draw their inspiration from the evolution of various statistical elements in science, namely the correlation and regression conceptions of the biometricians (1914: 87–8), the statistical mechanics tradition in physics (1908: 28), and the search for regularities based on accurate collection of observations in the field of astronomy (1923a: x). Thus, he claimed that economic theory required “an inductive statistical complement” (1908: 2), that “the method to be followed is the method which makes progress from the data to generalization by a progressive synthesis – the method of statistics” (1914: 86); in short, to him, “theoretical and statistical work should go hand in hand” (1914: 82). 13

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econometrics. Moore traveled to Europe to round out his education15 (Mirowski 1990), and there he discovered an author who exerted a strong influence on his subsequent work: Cournot.16 “With regards to the methodology of the social sciences, the writings of Cournot are always helpful,” Moore wrote (1914: 86, footnote 1). And precisely, Moore got from Cournot some of the major principles that guided his lifework: at the methodological level, the joint use of statistics and mathematics, and the extraction of laws from statistics; at the philosophical level, the idea that the whole “system of the world” was governed by a deterministic and natural order.17 For Moore, the aim of science was thus the identification of deterministic causal chains, of “natural laws” (Moore 1923a: 35). Four illustrations can briefly be given here. First, Moore’s deterministic framework explains his definition of cycles: a cycle is “mathematically defined with definite period, amplitude, and phase” (1923a: 5), and economic cycles would be as regular and exact as astronomical cycles. Second, Moore’s work is characterized by a methodological unification, rooted in the belief that the social and the natural phenomena obey similar rules: economists should then use the tools of natural scientists, as his own use of the periodogram shows.18 Third, from the use of periodogram analysis and correlation, Moore inferred the existence of an 8-year cycle in rainfall, agriculture, and industry, and he devoted one book, Generating Economic Cycles (1923a), to the identification of an exogenous cause that could explain these 8-year cycles: Venus.19

There, he was in contact with British statisticians (e.g. Karl Pearson) and with pioneers of mathematical economics (Edgeworth, Pareto and Walras). 16 Moore wrote several papers on Cournot (Moore 1905a and 1905b). Interestingly, he also often referred to the work of Quesnay and the Physiocrats (see for instance Moore 1914: 2–3). 17 This applies to the work he achieved prior to Synthetic Economics (1929). 18 See Cargill (1974), Morgan (1990), and Le Gall (1999). 19 See Le Gall (1999) on Moore’s demonstration. To him, the influence of Venus would be universal: it would explain not only the terrestrial weather, but also, just as precisely, the size of the rings of trees (1923a: 76), the barometric pressure (1923a: 84–8), magnetic storms (1923a: 109), the distortion in the tails of comets (1923a: 126), the aurora borealis (1923a: 132), and even economic phenomena. The law was simple, just like those built up by the natural scientists to whom he referred and who believed that 15

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Moore thus ended up with a “social astronomy,” which depicts an economy ruled by a regular natural order.20 Fourth, and finally, the methodology he practiced for estimating relationships between price and quantity is close to Cournot’s: as Mirowski (1990) and Wulwick (1992 and 1995) have shown, Moore’s “laws of demand” are mathematical regularities extracted from data, and they have to be considered driving belts connecting quantity to price and which contributed to explain the propagation of the 8-year cycle in the economic world (Le Gall 1999). As a whole, Moore is in many respects a typical figure of natural econometrics – and also, it seems, its last hero. Although a full analysis remains to be done in that direction, the development of natural econometrics in France during the nineteenth century may be part of a more general historical process, and it may contribute to enlighten the development of econometrics and statistical economics in other countries.21 After all, this should not be a surprise: French natural econometricians slipped into scientific paradigms that largely transcended national boundaries. 7.2. T HE CHAN GIN G SHAPE OF E CON OME TRICS The second conclusion of the book is that in the work of our authors, econometric ideas are fully permitted by worldviews. But from the 1830s to the 1920s, the nature of these foundations deeply changed, and different styles of econometric ideas developed. Of course, from Cournot to Lenoir, apparent continuities are existing – witness the focus on time-series decomposition or (with the exception of March) the identification of kinds of causal structures. Yet, the way instruments are used and, more fundamentally, the foundations and the aim of these styles of econometric ideas are in many respects orthogonal, incommensurable in a Kuhnian perspective.22 Nature was simple: a precision clock which is regular, orderly and highly predictable – a perfect machine driven by a perpetual motion. 20 In his books on economic cycles, Moore referred to Jevons but not to Briaune, although he often quoted French authors. 21 In addition, from our story it is possible to apprehend positively these pieces of work, which are often neglected or derided in a retrospective perspective. 22 See Kuhn (1962).

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7.2.1. Modeling, observing, and confessing First, although our authors based their economic work on a combination of mathematics23 and statistics, the reasons for using them – and the way they are combined – strongly differ. Consider a common agenda of Cournot, Briaune, and Lenoir: the elaboration of relationships between price and quantity. Although the works of Cournot and Briaune in that direction differ, statistics plays an active role in them: Cournot believed that his “law of sales” could be inferred from observation, and Briaune’s “law of proportionality” largely depends on statistics (in particular the mean price). By contrast, the relationships Lenoir statistically estimated are rather dependent on a preliminary analysis operated in his model. For natural econometricians, mathematics is the very language in which phenomena are written, the language in which Nature is written and confesses. This explains why natural econometricians – although Cournot can offer here a slightly different perspective – do not use mathematics as a demonstration device: rather, they obtained mathematical relationships from statistics, observation, and the economic translation of existing scientific laws. But there is no weakness here: the demonstration was permitted by the philosophical views to which these authors adhered and in which the mathematical relationships they found are rooted – in sum, there is here a strong coherence between their methodology and their philosophical views. With March and mainly Lenoir, another justification of the use of mathematics rose. The case of Lenoir is illuminating: he never explained that mathematics was Nature’s language; rather, mathematics was considered a useful and efficient tool in the construction of the model – the econometrician uses mathematics as a tool that ensures the logical steps leading to the conclusions of the model. But once more, the argument, we believe, can be turned very positively: there is a strong coherence between the methodology used and the philosophical views – the belief in a complex and out of reach real world, which led him to think that it was useful to reason in the simplified frame of an artificial world, in which possible explanations could be devised. Of course, the raison d’être of statistics also strongly differs in these various styles of econometric ideas. For Cournot, Briaune and 23

With the exception of March, who was rather reluctant to its use.

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Regnault, statistics is a methodological path from which one can make Nature talk: it is from observation and statistical instruments that economic mathematical laws could be unveiled. For March, statistics remains an active part of the agenda, in the sense that his whole approach is oriented toward the measurement of socioeconomic phenomena. For Lenoir, statistics plays a more minor role: as such, there is no room for statistics in the construction of the artificial world, and statistics is only used to read the real world at the light of the conclusions given by the model. In other words, statistics is no more a discovery device and it plays a more minor role. For Lenoir, the econometrician is neither a confessor of Nature nor an observer of the social world: he is a deviser of models, of malleable artificial models, and it is here that the power of the econometrician is to be found. 7.2.2. Which part of truth? The development of econometric ideas in France can thus be understood as the product of different conditions of “possibility,” in Canguilhem’s words ([1965] 1992: 47 tr), of different postulates and worldviews that changed historically and that contributed to the definition of different ways to reach different truths. Natural econometrics cannot be separated from finitude. For Cournot, Briaune, and Regnault, the association of statistics and mathematics was a means of penetrating the structure of a world in which historical time and uncertainties are tamed, a world converging toward an “end of history.” This idea originates in the set of postulates that form their worldview: determinism, mechanism, order, unification, and the belief in the principle of divine design. The whole set of postulates leads them to search for a natural order, mathematical in substance. The econometrician behaves here as the discoverer, the measurer and the observer of God’s design. The contrast with the “econometrician-in-the-lab” is sharp. In Lenoir’s econometrics, the image of the economy and of economic mechanisms becomes free from these “constraints.” The economy is understood in the frame of a model based on assumptions, and the only yardstick is this narrow and artificial world. Ontological unification, ontological determinism, religion, and of course natural order do not matter anymore here. The econometrician is no more the observer of the whole “system of the world,” rather he becomes the active architect of reduced-scale constructions that can contribute,

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however, to shed light on the real world. From our archaeology, the history of econometric ideas in France thus appears as being made up of continuities but also of abandonments, emergences, shifts, and breaks – it appears as the succession of incommensurable styles. Cournot, Briaune, Regnault, March, and Lenoir devised different stories about the economic world, and each of them offered his own “part of truth.” Each of them was able to mobilize, in a given scientific and philosophical context, instruments to serve his own quest, and to elaborate a scientific strategy for solving economic issues. It is, of course, this alchemy of econometric ideas and philosophical views that was powerful in their hands.

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Index Accidental causes, 30, 50, 78, 106, 116, 123, 124, 128, 142, 143, 145, 148, 153 Aftalion, A., 15, 204, 209 Allais, M., 255 American Association for the Advancement of Science, 201 Analogy, 8, 11, 16, 28, 46, 49, 50, 51, 71, 72, 120, 123, See Briaune, J.E. and analogies; Cournot, A.A. and analogies; Reductionism; Regnault, J. and analogies; Unity of phenomena; Unity of sciences with mechanics, 16, 36, 41, 50, 51, 59, 118, 119, 120, 152, 258, 259, 260, 261, 267, See Commercial machinery; Mechanical organization of the world; Mechanical reasoning; Cournot, A.A. and analogies with mechanics Andersen, P., 209 Anthropology, 201 Armatte, M., 7, 14, 39, 78, 125, 164, 182 Artificial world See Model Artus, P., 3 Asselain, J.C., 72 Astronomy, 8, 56, 123, 261, 263 Attraction, 11, 13, 67, 80, 108, 109, 120, 128, 152, See Regnault, J. and ‘attraction centers’; Regnault, J. and the law of attraction Auspitz, R., 214 Average, 7, 10, 11, 19, 22, 23, 27, 28, 31, 33, 38, 39, 40, 43, 60, 65, 69, 70, 71, 76, 78, 80, 96, 101, 104, 106, 109, 122, 123, 124, 125, 142, 145, 146, 149, 157, 179, 205, See Briaune, J.E. and averages; Cournot, A.A. and averages;

March, L. and averages; Regnault, J. and averages and time-series decomposition, 22, 78, 123 Moving average See moving average Average variable cost curve, 232 Babson, R., 257, 258, 259, 260 Bachelier, L., 19, 108, 109, 128, 130, 136 Banzhaf, H.S., 8, 9, 183 Beauty in science, 13, 28, 45, 46, 47 Benini, R., 252 Bernoulli, J., 112 Besomi, D., 73 Beveridge, W., 68 Bicquilley, C.F., 7 Biometrics, 163, 164, 179, 263 Bliss point, 220, 221 Boas, F., 201 Bohr, N., 211 Bompaire, F., 58 Bottinelli, E.P., 25 Boumans, M., 17, 78, 167, 183, 210, 211 Bowley, A., 14, 201, 202, 203, 208 Bravais, A., 163 Breton, Y., 4, 5, 7, 14, 163, 165, 167, 202, 208, 209 Briaune, J.E., 8, 10, 19, 21, 22, 23, 24, 26, 56, 65, 69, 110, 116, 118, 122, 147, 155, 157, 158, 195, 235, 265, 266, 267, 268 and analogies, 71, 72, 80 and averages, 69, 70, 71, 75, 76, 78, 80, 82, 96, 100, 101, 104, 106, 123 and causality, 69, 70, 71, 72, 73, 74, 78, 96, 97, 106, 116 and economic crises, 69, 70, 71,

Index 72, 73, 76, 96 and economic cycles, 70, 71, 96, 97, 98, 99, 100, 101, 103, 104, 106, 185 and economic policy, 69, 71, 103, 104, 105 and God, 96, 97, 98, 105, 118 and historical time, 73, 95, 105 and mathematics, 11, 22, 23, 24, 69, 70, 76, 78, 79, 80, 82, 95, 106, 126 and natural laws, 9, 10, 95, 97 and natural order, 70, 71, 74, 78, 94, 96, 98, 100, 101, 103, 104, 105, 106 and smoothing processes, 101 and statistics, 11, 22, 23, 24, 70, 76, 77, 78, 95, 100, 101, 105, 106, 266 and the ‘social body’, 70, 71, 72, 73, 86, 95, 104 and the Bible, 98, 99, 105, 106 and the law of proportionality See Law of proportionality and the search for periodicities, 98, 99, 100, 101 Briaune, J.E., 13 British Association for the Advancement of Science, 148 British mathematical statistics, 14, 163, 164, 182, 201, 207, 235 Broder, A., 163 Brownian motion, 128 Bulletin de la Statistique Générale de la France, 169, 202, 208 Bungener, M., 3, 255 Bunle, H., 14, 15, 17, 203, 207, 208, 240 Business barometer, 72, 182, 183, 190, 200, 257, 258, 260, See March, L. business barometer Business cycles, 15, 158, 164, 175, 182, 183, 185, 197, 257, See Briaune, J.E. and the search for periodicities; Briaune, J.E. and economic cycles; Business barometer; Economic cycles Cabanis, P., 121

287 Callens, S., 53 Camic, C., 201, 263 Canard, N.F., 7, 72 Canguilhem, G., 3, 256, 267 Canonical history of econometrics, 2, 3, 255 Cargill, T.F., 14, 83, 264 Carol, A., 170 Cartwright, N., 16, 164, 253 Causal chains, 53, 54, 56, 62, 69, 71, 72, 73, 74, 95, 97, 98, 264 Causality See Accidental causes; Briaune, J.E. and causality; Causal chains; Constant causes; Correlation and causality; Cournot, A.A. and causality; Lenoir, M. and causality; March, L. and causality; Regnault, J. and causality Centre National de la Recherche Scientifique, 255 Ceteris paribus, 210, 216, 225, 235 Chait, B., 252, 255 Chance, 16, 48, 49, 50, 53, 54, 55, 56, 57, 62, 104, 111, 113, 114, 117, 145, 164, 195, 198, 199, 200 Chancellier, E., 16, 72, 182, 199, 257, 258 Charles, L., 9 Cheysson, E., 2, 19, 166, 167, 197, 202, 214 and the ‘courbe des débouchés’, 5, 229 Christ, C.F., 2, 201, 209 Clark, C.M., 8, 9, 61, 126 Clark, J.M., 252 Classical school, 4, 144 Clements, F.E., 68 Cohen, I.B., 8, 120 Colson, C., 214 Columbia University, 201, 263 Commercial machinery, 36, 41, 44, 50, 56, 60, 216 Compensation (principle of), 30, 31, 36, 39, 78, 100, 106, 124, 142, 146, 173 Complexity of the world, 17, 18, 19, 159, 160, 165, 166, 168, 171, 173, 182, 185, 186, 188, 194, 195, 198,

288 199, 205, 209, 212, 213, 214, 216, 229, 234, 237, 238, 251, 252, 266 Condorcet, J.A., 7 Conservatoire National des Arts et Métiers, 5 Constant causes, 30, 39, 50, 73, 74, 78, 98, 106, 116, 119, 121, 122, 123, 124, 143, 144, 145, 146, 148, 153 Continuity, 35, 36, 195, 217 Correlation, 14, 17, 19, 160, 163, 173, 174, 176, 181, 182, 188, 190, 191, 192, 193, 205, 235, 237, 239, 263, 264, See Lenoir, M. and correlation; March, L. and correlation adaptation to socio-economic data, 163, 176, 179, 180 and causality, 174, 193, 194, 238, 239 and historical time, 189, 190, 235, 237 hunting, 180, 207 partial correlation, 238, 244 spurious correlations, 182 Coumet, E., 53 Cournot, A.A., 2, 7, 8, 10, 19, 21, 22, 23, 24, 25, 26, 67, 70, 79, 104, 110, 116, 118, 123, 127, 157, 158, 160, 196, 212, 214, 217, 223, 235, 264, 265, 266, 267, 268 and analogies, 13, 28, 45, 49, 50, 51 and analogies with mechanics, 36, 41, 47, 50, 52, 59, 118 and astronomy, 56 and averages, 27, 28, 29, 31, 38, 39, 40, 43, 44, 56, 60, 65, 78 and causality, 39, 50, 53, 54, 55, 56, 62, 116 and chance, 53, 54, 55, 56, 57, 62 and continuity, 35, 36 and God, 61, 62, 63, 98, 118, 119 and historical time, 55 and individual behavior, 30, 31, 39, 56, 58, 59, 63 and mathematics, 11, 22, 23, 24, 25, 26, 27, 28, 29, 34, 35, 37, 38, 42, 44, 54, 60, 126

Index and mechanics, 25, 41, 50, 51, 52, 59, 60, 61, 65 and natural laws, 9, 10, 61 and natural order, 26, 27, 28, 35, 52, 61, 65 and philosophical probability, 13, 28, 44, 45, 46, 47, 49, 52, 63, 64, 65, 135, 196 and probability, 53 and Quételet, 39 and science, 25, 38, 46, 52, 60, 61, 64, 65 and simplicity, 45, 46, 47, 48 and social history, 31, 44, 49, 53, 56, 57, 59, 60, 61, 62, 65, 105, 195, 212, 216 and social physics, 27, 28, 59 and statistics, 11, 22, 23, 24, 26, 27, 28, 37, 38, 39, 42, 43, 44, 48, 60, 121, 266 and testing procedures See Cournot A.A., philosophical probability and the ‘advanced state’ of society, 27, 28, 32, 33, 49, 56, 58, 59, 60, 65, 117, See End of history and the definition of economics, 29, 30, 39 and the lack of data, 40, 43, 48, 49, 60, 65 and the law of sales See Law of sales and the society like a beehive, 27, 58 and truth, 63, 64 as a polymath, 26 conception of market, 31, 32, 33, 36, 39, 41, 47, 59 law of sales See Law of sales Courtois, A., 107 Cowles Commission, 2, 16, 199, 252, 255, 256 Crichton, M., 1 Daston, L., 16, 53, 164 Data (gathering of), 7, 22, 77, 163, 164, 169, 172, 173 Data (imperfection of), 22, 196

Index Davis, J.B., 10 de Foville, A., 72, 202, 203 De Marchi, N., 12 De Vroey, M., 211 Deleau, M., 3 Descartes, R., 126 Desrosières, A., 3, 203 Determinism, 8, 10, 11, 16, 18, 21, 53, 56, 65, 69, 70, 74, 95, 96, 97, 98, 101, 103, 104, 106, 110, 114, 115, 116, 117, 142, 155, 195, 196, 206, 212, 216, 239, 257, 258, 262, 264, 267 erosion of, 15, 16, 17, 19, 159, 160, 163, 164, 198, 200, 205, 252, 267 Deviations, 22, 24, 78, 80, 96, 103, 122, 123, 147, 149, 151, 153, 154, 155, 180 reduction of, 24, 96, 103, 143, 153, 155 Dimand, R., 108 Divine organization of the world, 9, 10, 11, 18, 19, 21, 22, 23, 26, 61, 62, 70, 98, 100, 105, 110, 118, 119, 121, 126, 127, 157, 158, 161, 206, 212, 254, 267 Divisia, F., 4, 19, 255 Dormoy, E., 109 Dowell, M.E., 186 Ducrotoy, J.B., 68 Dufau, P.A., 7 Dugé de Bernonville, L., 15, 203 Dupuit, J., 5, 19, 127 Early applications of statistics and probability to economics, 7 Ecole des Mines, 5, 208 Ecole des Ponts et Chaussées, 5 Ecole Polytechnique, 5, 164, 208 Econo-engineers, 5, 7, 14, 127, 164, 255 Econometric Society, 2, 3, 4, 15, 255 Econometrica, 2, 4 Economic cycles, 8, 17, 68, 70, 72, 98, 100, 101, 183, 185, 188, 261, 264, See Briaune, J.E. and economic cycles; Briaune, J.E. and the search for periodicities;

289 Business barometer; Business cycles; Jevons, W.S. and sunspots; March, L. business barometer; Moore, H.L. and Venus movements; Social astronomy Economic policy (norms of), 12, 44, 69, 103, 105, 158, 253, See Briaune, J.E. and economic policy; Natural order (knowledge of) Edgeworth box diagram, 209, 225 Edgeworth, F.Y., 31, 202, 203, 214, 264 Ekelund, R.B., 2, 5, 29, 229 End of history, 24, 44, 57, 58, 65, 105, 110, 153, 155, 157, 189, 267 Epstein, R., 163 Errors, 22, 78, 95, 104, 111, 113, 122, 123, 155, 164, 173 of observation, 22, 172, 173 Etner, F., 5 Eugenics, 164, 170 Experimental farming, 69 Extrapolation See Forecasting Fama, E., 109, 128 Favreau, M., 79 Fechner indices, 175, 176, 238 Finitude, 24, 61, 157, 158, 198, 205, 206, 267, See End of history Fisher, I., 183, 201, 214 Forecasting, 48, 49, 56, 69, 100, 101, 111, 112, 116, 117, 118, 124, 142, 172, 185, 187, 188, 199, 200, 260 Foucault, M., 3, 5, 6, 61, 109, 158, 159, 254, 256 Fourquet, F., 255 French liberal school, 4, 7, 107 French Ministry of Agriculture, 22 French Revolution, 56 Friedman, M., 213 Frisch, R., 1, 4, 17, 164, 210, 211, 252, 253 Fry, C.L., 29 Function (mathematical), 34, 37, 54 Galton, F., 78, 125, 170, 198, 202 Gherardt, M., 109 Giddings, F., 201

290

Index

Gigenrenzer, G., 16, 164 Gini, C., 252 God See Briaune, J.E. and God; Cournot, A.A. and God; Divine organization of the world; Regnault, J. and God Granger, G.G., 105, 211 Graphical analysis, 5, 40, 101, 147, 149, 173, 175, 185, 190, 191, 200, 205, 210, 211, 212, 214, 235, 236, 241, 242, See Lenoir, M. and graphs; March, L. and graphs and correlation, 190, 191, 192, 194, 236, 242 Gravitation, 10, 11, 67, 80, 83, 96, 101, 104 Guillaume, E. and G., 202, 211, 252 Guitton, H., 29, 204, 256 Gusdorf, G., 106

and indifference curves Ingrao, B., 8, 51 Institut National de la Statistique et des Etudes Economiques (INSEE), 3 Institut Royal Agronomique, 69 Institut Supérieur de l’Université de Paris, 203 Institutionalization of econometrics, 1, 4, 15, 18, 161, 162, 166, 200, 201, 202, 205, 255, See Scientific community (rise of); Scientific conventions Instrumentalism, 16, 199, 213, 256 International Statistical Institute, 15, 173, 202, 203 Interpolation, 13 Israel, G., 2, 8, 9, 16, 17, 51, 126, 164, 199

Haavelmo, T., 164, 207, 210, 211, 252, 253, 256 Hacking, I., 16, 53, 159, 198 Hahn, R., 8 Hébert, R.F., 2, 5, 29, 229 Heidelberger, M., 16, 164 Hendry, D.F., 148, 209, 245, 256 Historical time, 24, 55, 56, 105, 182, 189, 190, 195, 215, 237, 267, See Correlation and historical time; Briaune, J.E. and historical time; Cournot, A.A. and historical time; Lenoir, M. and historical time; March, L. and historical time Hooker, R., 180, 182, 201, 207, 239, 240 Hoover, K., 186, 211 Huber, M., 15, 169, 202, 208 Hudson, R., 108 Hume, D., 111 Humphrey, T.M., 186

Jaffé, W., 29 Jevons, W.S., 2, 23, 31, 67, 148, 185, 214, 257, 261, 262, 263, 265 and sunspots, 68, 262 and the extraction of relationships from data, 40, 262 Joel, M.E., 3, 255 Journal de la Société de Statistique de Paris, 202 Journal des Economistes, 107 Journal of the Royal Statistical Society, 202 Jovanovic, F., 16, 107, 108, 109, 121, 126, 128, 130, 135, 136, 146, 200 Juglar, C., 72, 189 Julin, A., 72, 202

Identification, 209, 213, 245, 246, 247, 248, 249, 250 Ignorance, 22, 55, 73, 95, 104, 111, 114, 118, 153, 155 Index numbers, 173, 174, 182, 183, 185, 208 Indifference curves See Lenoir, M.

Kærgaard, N., 2, 209 Kater, H., 50 Kepler, J., 47 Keynes, J.M., 199 Kim, J., 12 King, W.I., 240 Klein, J.L., 7, 14, 68, 77, 101, 105, 123, 163, 179, 180, 182, 191, 207, 236, 240 Koopmans, T.C., 257 Koopmans-Vining controversy, 2

Index Krüger, L., 16, 164 Kuhn, T.S., 265 Kurita, K., 5 Lacroix, S.F., 7 Lags, 180, 181, 242 Laplace, P.S., 7, 8, 21, 47, 53, 55, 67, 96, 115, 116 Lardner, D., 50 Larrère, C., 9 Lassudrie-Duchêne, B., 4 Laurent, H., 14, 19, 109, 202, 208 Law of deviations, 125, 127, 130, 131, 132, 142, 152 test of, 135, 136 Law of error, 123, 125 Law of large numbers, 29 Law of proportionality, 22, 69, 70, 76, 78, 79, 80, 81, 82, 95, 96, 101, 104, 266 and averages, 82 double proportionality, 86, 87, 88, 89, 90 test of, 70, 71, 83, 84, 85, 90, 91, 93, 94, 95 Law of ruin See Regnault, J. and the law of ruin Law of sales, 8, 10, 22, 27, 28, 33, 34, 35, 39, 44, 48, 52, 54, 56, 58, 59, 60, 63, 65, 66, 73 and the maximization of wealth, 41, 42, 44, 50, 60 continuity, 36 contrasted readings, 28 extraction from statistics, 28, 29, 33, 38, 39, 40, 43, 44, 48, 49, 57, 60, 65, 262, 266 mathematics and statistics, 37, 38, 40, 42, 65 sales (definition of), 33 test of, 28, 44, 47, 48, 52 Le Corbeiller, Ph., 17 Le Play, F., 167, 197 Le Van-Lemesle, L., 4, 165 Leamer, E.E., 256 Least squares, 208, 242 Lefèvre, H., 108 Lehfeldt, R., 207 Lenoir, M., 14, 15, 17, 19, 35, 47,

291 160, 166, 196, 202, 203, 206, 208, 209, 265, 266, 267, 268 and aggregate demand curves, 209, 213, 217, 225, 226, 227, 228, 229, 250 and aggregate supply curves, 209, 213, 230, 233, 234, 250 and causality, 238, 239, 251 and correlation, 236, 237, 238, 239, 242, 244 and financial indices, 183 and graphs, 209, 211, 212, 214, 235, 236, 241, 242, 253 and historical time, 237 and indifference curves, 209, 217, 219, 220, 221, 222, 223, 224, 225, 226, 230, 231 and individual behavior, 212, 217, 218, 223, 224 and individual demand curves, 225 and individual supply curves, 230, 232 and mathematics, 209, 212, 214, 266 and models, 211, 212, 213, 214, 215, 216, 220, 222, 223, 225, 229, 230, 234, 235, 239, 241, 245, 251, 252, 253, 254, 266, 267 and statistics, 212, 213, 222, 229, 234, 241, 252, 267 and the estimation of relationships between price and quantity, 241, 242, 244, 250 and time-series decomposition, 239, 240, 241, 249 correlation and causality, 238, 239 economic theory as the basis of models, 209, 211, 213, 214, 215, 239, 245, 253 Lescure, J., 252 Lexis, W., 125, 173, 202, 203 Lieben, R., 214 Literary exposition of mathematics, 79, 82, 126, 133, 152 Logical time, 105 Lucas, R.E., 207, 210, 211

292 Luciani, J., 169 Lutfalla, M., 4, 163, 165 Maas, H., 2, 8, 23, 40, 41, 51, 68, 105, 191, 261, 262, 263 MacKenzie, D., 14, 78, 163, 164, 170 MacKenzie, G., 68, 101 Mackeprang, E., 209 Malgrange, P., 3 Malinvaud, E., 4, 255 Malthus, T., 106 Mandelbrot, B., 108, 128 March, L., 14, 15, 17, 19, 49, 160, 164, 203, 205, 208, 209, 211, 212, 213, 216, 222, 235, 236, 251, 252, 268 and averages, 186, 205 and causality, 168, 174, 185, 193, 194, 195, 238 and correlation, 17, 160, 173, 174, 176, 179, 181, 182, 185, 188, 189, 190, 191, 192, 193, 194, 202, 205 and eugenics, 164, 170 and graphs, 175, 185, 190, 191, 192, 194, 205, 236 and H.L. Moore, 190, 193, 197 and historical time, 165, 182, 185, 189, 190, 195, 237 and mathematics, 173, 198, 266 and monographs, 197, 198 and scientific conventions See Scientific conventions and statistics, 160, 164, 165, 166, 167, 168, 169, 170, 171, 172, 174, 186, 188, 189, 195, 196, 198, 199, 200, 203, 204 and the adaptation of correlation to socio-economic data, 179, 180 and the institutionalization of econometrics, 166, 201, 202, 203, 204, 206 and the measurement of the social world, 17, 19, 160, 165, 168, 188, 196, 197, 206, 252, 267 and the Normal law, 173, 174, 205

Index and the objectivity of statistics, 172, 173, 174 and the quantity theory of money, 186, 188 and the rejection of laws, 186, 187, 189, 195 and the relationship between financial indices, 176, 178 and the relationship between marriage and birth, 176, 177, 179, 180, 181 and the use of Fechner indices, 176, 178 and time-series decomposition, 180, 239, 240 business barometer, 182, 183, 190, 191, 200, 205, 236, 257 correlation and causality, 193, 194, 238 on correlation and causality, 174 Marchal, A., 204 Marginal cost curve, 232 Marginal rate of substitution, 218 Marietti, P.G., 164 Marschak, J., 256 Marshall, A., 29, 214, 252 Martin, T., 26, 35 Marvin, C.F., 68 Mathematical economics (rise of), 7, 127 Mathematical organization of the world, 9, 10, 11, 22, 23, 26, 27, 35, 60, 65, 70, 79, 80, 95, 126, 127, 157, 158, 198, 206, 266, 267 Mathematics See Briaune, J.E. and mathematics; Continuity; Cournot, A.A. and mathematics; Function (mathematical); Lenoir, M. and mathematics; Literary exposition of mathematics; March, L. and mathematics; Mathematical economics (rise of); Mathematical organization of the world; Regnault, J. and mathematics; Resistance to mathematical economics; Statistics as a means to unveil mathematical and natural laws McAllister, J.W., 47

Index McCloskey, D.N., 12, 17, 120, 254, 256 McKeen Cattell, J., 201 McKim, V.R., 16 Mechanical organization of the world, 22, 23, 27, 50, 51, 58, 60, 61, 65, 118, 120, 258 Mechanical reasoning, 23, 41, 68, 261, 262 Mechanics, 8, 25, 26, 41, 50, 51, 123, 152, 262, 263, See Analogy with mechanics; Commercial machinery; Cournot, A.A. and analogies with mechanics; Cournot, A.A. and mechanics; Mechanical organization of the world; Mechanical reasoning Median values, 130, 133, 146, 149 Ménard, C., 5, 7, 8, 15, 25, 26, 27, 28, 31, 35, 41, 50, 51, 56, 59, 60, 106, 120, 152, 167, 213 Mentré, F., 50, 55, 58, 59 Meteorology, 197, 261 Meyssonnier, S., 9 Mill, J.S., 169, 186, 261 Mirowski, P., 2, 8, 29, 39, 68, 252, 264, 265 Mitchell, W.C., 183, 201, 252 Model, 17, 18, 19, 160, 209, 210, 211, 212, 214, 216, 252, 253, 254, 266, 267, See Lenoir, M. and models and artificial world, 17, 19, 159, 160, 161, 196, 206, 209, 210, 212, 215, 216, 230, 235, 251, 252, 254, 266, 267 as experimental frame, 209, 210, 211, 216, 225 as thought experiment, 211, 220 rise of, 210, 252, 253, 254 Monographs See March, L. and monographs Moore, H.L., 2, 14, 67, 68, 83, 104, 164, 174, 185, 190, 193, 194, 197, 201, 202, 239, 252, 257, 263, 264, 265 and Cournot, 25, 45, 61, 264 and the laws of demand, 39, 265 and Venus movements, 68, 264,

293 265 Morgan, M.S., 2, 12, 14, 15, 16, 17, 40, 68, 69, 77, 105, 123, 147, 148, 163, 164, 167, 176, 179, 182, 186, 189, 190, 191, 207, 209, 210, 211, 216, 220, 222, 235, 236, 245, 248, 253, 256, 261, 264 Morrison, M., 14, 16, 47, 159, 164, 205, 211 Moving average, 240, 241, 242 N.B.E.R., 2, 206 Natural econometrics, 6, 10, 11, 12, 14, 15, 17, 18, 19, 21, 23, 24, 26, 28, 70, 105, 106, 110, 127, 152, 157, 158, 159, 160, 161, 165, 168, 186, 189, 195, 196, 199, 205, 206, 212, 214, 218, 222, 252, 253, 257, 260, 262, 263, 265, 266, 267 and the absence of institutionalization, 7, 18, 21, 24, 158, 161, 166, 200, 256 and the natural sciences, 8, 10, 11, 23 associated worldview, 7, 8, 9, 10, 11, 13, 18, 19, 21, 23, 26, 28, 52, 61, 63, 65, 66, 70, 98, 100, 104, 105, 106, 110, 114, 127, 157, 159 Natural laws, 9, 10, 24, 70, 97, 98, 104, 105, 108, 110, 173, 208, 264, See Briaune, J.E. and natural laws; Cournot, A.A. and natural laws; Natural order; Regnault, J. and natural laws Natural order, 6, 8, 9, 10, 12, 13, 18, 19, 22, 23, 24, 27, 28, 61, 65, 68, 70, 71, 72, 74, 78, 96, 98, 100, 101, 104, 105, 106, 110, 115, 119, 122, 145, 153, 155, 158, 159, 206, 210, 218, 252, 262, 264, 265, 267, See Briaune, J.E. and natural order; Cournot, A.A. and natural order; Natural order (knowledge of); Regnault, J. and natural order Natural order (knowledge of), 9, 11, 96, 105, 118, 153, 155, 157 Neumann-Spallart, F.X., 72 Newton, I., 8, 259

294 Newton’s third law, 258, 259, 260 Nikolow, S., 191 Normal law, 125, 173, 174, See March, L. and the Normal law Norton, J., 180, 201, 202 Objective probability, 53 Office du Travail, 169 Ontology, 10, 11, 16, 17, 18, 23, 79, 114, 212 decline of, 16, 17, 18, 160, 199, 212, 216, 223, 251, 267 Pareto, V., 202, 214, 264 Pareto’s distributions, 174 Paris Stock Exchange, 22, 107, 131 Pearson, K., 78, 171, 176, 193, 194, 202, 204, 238, 264 Peart, S., 186 Pénin, M., 208 Periodogram analysis, 14, 83, 264 Perrot, J.C., 2, 7, 9 Persons, K., 183 Philosophical probability See Cournot, A.A. Physical time, 101, 105, 189 Physiocracy, 2, 5, 8, 103, 264 and natural order, 9 Physiology, 71, 72 Picon, A., 5 Pirou, G., 204 Playfair, W., 191 Pleasure and pain, 31, 263 Poincaré, H., 36 Poisson, D., 7 Popper, K., 14, 15, 104, 163, 255 Porter, T.M., 7, 14, 22, 77, 78, 116, 122, 125, 163, 164, 165, 167, 171, 172, 193 Price offer curve, 225 Probabilistic revolution, 15, 16, 17, 159 Probability See Cournot, A.A. and philosophical probability; Cournot, A.A. and probability; Early applications of statistics and probability to economics; Objective probability; Probabilistic revolution;

Index Regnault, J. and probability; Subjective probability Psychology, 170, 201 Quantity theory of money, 186, 188 Quantum theory, 15 Quarterly Journal of Economics, 202 Quesnay, F., 9, 67, 72, 105, 155, 210, 257, 264 Quételet, A., 7, 21, 22, 39, 78, 107, 116, 121, 124, 125, 126, 136, 145, 148, 166 and social physics, 8, 77, 110, 121 Random shocks, 164 Random walk, 108, 109, 127, 128, 130 and mean values, 128, 152 and the construction of financial theory, 128 Raynaud, B., 9 Reductionism, 16, 23, 28, 68, 115, 127, See Unity of phenomena; Unity of sciences Regnault, J., 8, 10, 13, 19, 21, 22, 23, 24, 26, 55, 56, 62, 65, 67, 78, 79, 96, 104, 105, 107, 173, 267, 268 and ‘attraction centers’, 108, 151 and analogies, 118, 119, 120, 123, 136, 142, 151, 152 and averages, 78, 109, 122, 123, 124, 125, 128, 142, 145, 146, 148, 149, 151, 152 and brokerage fees, 127, 135, 138, 142 and causality, 111, 114, 115, 116, 117, 121, 123, 124, 128, 143, 144, 145, 148, 153, 154 and God, 98, 118, 119, 122, 142, 153, 155, 157 and individual behavior, 111, 117, 119, 122, 128, 142, 143, 144, 145, 153, 155, 157 and laws, 118 and mathematics, 11, 22, 23, 24, 79, 108, 109, 110, 112, 114, 119, 121, 125, 126, 127, 133, 137, 142, 152, 157 and natural laws, 9, 10, 108, 110,

Index 115, 116, 119, 124, 136, 142, 153, 155 and natural order, 110, 111, 114, 115, 118, 119, 122, 142, 145, 153, 155, 157 and probability, 112, 113, 114, 116, 117, 118, 122, 127, 128, 129, 130, 137, 139, 140 and social history, 130, 151, 156 and statistics, 11, 22, 23, 24, 108, 109, 110, 114, 117, 121, 122, 125, 127, 131, 132, 137, 142, 145, 146, 147, 148, 157, 267 and the law of attraction, 143, 151, 152, 153, 154 and the law of deviations See Law of deviations and the law of ruin, 108, 111, 114, 119, 127, 137, 138, 139, 140, 141, 142, 153, 154 and the random walk See Random walk and the ratio of instability, 130, 157 Regression, 14, 19, 242, 244, 263 Relationships between economic and social variables, 14, 181, 207 Relationships between price and quantity, 8, 14, 15, 158, 161, 163, 235, 265, 266, See Cheysson, E. and the ‘courbe des débouchés’; Jevons, W.S. and the extraction of relationships from data; Law of proportionality; Law of sales; Lenoir, M. and aggregate demand curves; Lenoir, M. and aggregate supply curves; Lenoir, M. and individual demand curves; Lenoir, M. and individual supply curves; Lenoir, M. and the estimation of relationships between price and quantity; Moore, H.L. and the laws of demand Resistance to mathematical economics, 5, 7 Resistance to statistics, 5, 7, 27, 167 Revue d’Economie Politique, 202, 208 Reynaud-Cressent, B., 170 Rhetoric, 2, 120

295 Ricardo, D., 69 Richard, J.F., 245 Rohrbasser, J.M., 9, 10, 61, 126 Roy, R., 2, 228, 255 Saint-Sernin, B., 55 Say, J.B., 5 Schabas, M., 8, 51, 261 Schmidt, C., 256 Schultz, H., 209, 221 and the law of sales, 29 Schumpeter, J., 2, 69 Schuster, A., 68 Scientific community (rise of), 1, 4, 14, 15, 18, 19, 161, 166, 202, 204, 208, 209, 237, 241, 252 Scientific conventions, 18, 19, 161, 165, 166, 172, 174, 182, 201, 204, 205, 236, 237, 238, 241 Seasonal effects, 148 Simiand, F., 208 Simonin, J.P., 5, 69 Simplicity, 13, 28, 45, 46, 47, 115, 163, 168, 171, 195, 206, 212, 216, 222, 223, 225, 251, 264, 265 Small worlds, 17, 54, 55, 56, 73, 160, 212, 216, 252 Smith, A., 32 Social astronomy, 68, 70, 71, 96, 97, 101, 104, 106, 185, 195, 265 Social history See Cournot, A.A. and social history; Cournot, A.A. and the ‘advanced state’ of society; End of history; Regnault, J. and social history Social meteorology See Social astronomy Social physics, 8, 27, 28, 52, 59, 77, 110, 118, 121, 263 Société de Statistique de Paris, 165, 202 Société Française d’Eugénique, 170 Sociology, 201 Spanos, A., 164, 256 Speculation (debates on), 107, 108, 111, 155 Statistics See Briaune, J.E. and statistics; Cournot, A.A. and statistics; Early applications of

296 statistics and probability to economics; Lenoir, M. and statistics; March, L. and statistics; March, L. and the measurement of the social world; March, L. and the objectivity of statistics; Regnault, J. and statistics; Resistance to statistics and models, 17, 18, 161, 212, 235, 239, 241, 251, 252, 267 as a means to unveil mathematical and natural laws, 10, 11, 19, 22, 23, 24, 27, 28, 76, 80, 105, 109, 121, 127, 142, 152, 157, 161, 198, 206, 212, 266, 267 as a substitute for the experimental method, 167, 189 Statistique Générale de la France, 3, 7, 15, 164, 169, 183, 203, 207, 208, 241 Steiner, Ph., 5, 8, 9 Stigler, G., 209 Stigler, S.M., 27 Subjective probability, 53, 116, 117, 118, 155 Summers, L.H., 256 Sunspot See Jevons, W.S. and sunspots SüƢmilch, J.P., 9 Taqqu, M.S., 107, 108 Testing procedures, 11, 12, 28, 44, 46, 48, 70, 77, 79, 83, 90, 95, 106, 109, 135, 147, 158, 186 comparison of theoretical values and observed data, 83, 84, 85, 90, 91, 93, 94, 135, 136, 147, 148 qualitative tests, 13, 28, 44, 46, 47, 51, 52, 135 Time See Historical time; Logical time; Physical time; Time-series decomposition Time-series decomposition, 11, 56,

Index 78, 116, 123, 124, 157, 158, 161, 180, 202, 239, 240, 241, 249, 265 Tinbergen, J., 164, 210, 211, 252, 255 Topalov, C., 163, 170, 204 Topp, N.H., 209 Turgot, A.R.J., 169 Turner, S.P., 16 Uncertainty, 17, 160, 165, 166, 188, 195, 205, 206 Unity of phenomena, 8, 10, 11, 13, 16, 18, 23, 49, 50, 51, 67, 68, 70, 71, 80, 96, 97, 101, 104, 106, 110, 113, 115, 118, 120, 121, 123, 127, 135, 151, 152, 154, 157, 161, 257, 258, 264, 266, 267 Unity of sciences, 8, 11, 16, 23, 37, 51, 67, 106, 110, 115, 120, 123, 127, 135, 157, 189, 264, 266 Utility, 31, 32, 218, 263 Van Der Pol, B., 16, 17, 97 Varian, H.R., 218 Vatin, F., 5, 8, 25 Ventelou, B., 158 Venus movements See Moore, H.L. and Venus movements Von Thunen, H., 169 Walras, L., 29, 127, 214, 264 Weather cycles, 69, 70, 71, 96, 97, 98, 106 Wulwick, N., 2, 230, 252, 265 X-Crise, 255 Xie, Y., 201, 263 Yule, G.U., 14, 201, 202, 203, 207, 240 Ziliak, S., 12, 256 Zouboulakis, M., 186 Zylberberg, A., 5, 208, 209, 228, 229, 245