The Economic Valuation of the Environment and Public Policy: A Hedonic Approach (New Horizons in Environmental Economics)

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The Economic Valuation of the Environment and Public Policy

NEW HORIZONS IN ENVIRONMENTAL ECONOMICS Series Editors: Wallace E. Oates, Professor of Economics, University of Maryland, USA and Henk Folmer, Professor of General Economics, Wageningen University and Professor of Environmental Economics, Tilburg University, The Netherlands This important series is designed to make a signiﬁcant contribution to the development of the principles and practices of environmental economics. It includes both theoretical and empirical work. International in scope, it addresses issues of current and future concern in both East and West and in developed and developing countries. The main purpose of the series is to create a forum for the publication of high quality work and to show how economic analysis can make a contribution to understanding and resolving the environmental problems confronting the world in the twenty-first century. Recent titles in the series include: Valuing Environmental and Natural Resources The Econometrics of Non-Market Valuation Timothy C. Haab and Kenneth E. McConnell Controlling Global Warming Perspectives from Economics, Game Theory and Public Choice Edited by Christoph Böhringer, Michael Finus and Carsten Vogt Environmental Regulation in a Federal System Framing Environmental Policy in the European Union Tim Jeppesen The International Yearbook of Environmental and Resource Economics 2002/2003 A Survey of Current Issues Edited by Tom Tietenberg and Henk Folmer International Climate Policy to Combat Global Warming An Analysis of the Ancillary Benefits of Reducing Carbon Emissions Dirk T.G. Rübbelke Pollution, Property and Prices An Essay in Policy-making & Economics J.H. Dales The Contingent Valuation of Natural Parks Assessing the Warmglow Propensity Factor Paulo A.L.D. Nunes Environmental Policy Making in Economics with Prior Tax Distortions Edited by Lawrence H. Goulder Recent Advances in Environmental Economics Edited by Aart de Zeeuw and John A. List Sustainability and Endogenous Growth Karen Pittel The Economic Valuation of the Environment and Public Policy A Hedonic Approach Noboru Hidano

The Economic Valuation of the Environment and Public Policy A Hedonic Approach

Noboru Hidano Professor, Department of Social Engineering, Tokyo Institute of Technology, Japan

NEW HORIZONS IN ENVIRONMENTAL ECONOMICS

Edward Elgar Cheltenham, UK • Northampton, MA, USA

© Noboru Hidano, 2002 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical or photocopying, recording, or otherwise without the prior permission of the publisher. Published by Edward Elgar Publishing Limited Glensanda House Montpellier Parade Cheltenham Glos GL50 1UA UK Edward Elgar Publishing, Inc. 136 West Street Suite 202 Northampton Massachusetts 01060 USA A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication Data Hidano, Noboru, 1949– The economic valuation of the environment and public policy : a hedonic approach / Noboru Hidano. p. cm. — (New horizons in environmental economics) Includes bibliographical references and index. 1. Environmental economics. 2. Hedonism. 3. Environmental policy. I. Title. II. Series. HD75.6. H53 2003 333.7—dc21

2002029827

ISBN 1 84376 168 8 Printed and bound in Great Britain by Biddles Ltd, www.biddles.co.uk

Contents ix xi xiii

List of figures List of tables Preface 1

Introduction

2

The hedonic approach Development of the hedonic conception Rosen’s method and work in the 1970s Econometrics after the 1980s Scotchmer’s crucial comments Reconsideration of capitalization theory

9 9 10 13 15 16

3

Theory of capitalization hypothesis Two types of capitalization Theory of cross-sectional capitalization Extension Conclusion

18 18 21 27 28

4

Hedonic measure as an approximation of benefit Introduction Examination of overestimation ratio Results An extension: CES functions

29 29 29 31 33

5

Empirical examination of the accuracy of the hedonic measure Large national project evaluation Introduction of accessibility and the model revised Parameter estimation method and data Results Conclusion

37 37 37 39 42 44

Comparison with contingent valuation method Meaning of comparison Air pollution

45 45 46

6

1

v

vi

Contents

Water Environment Conclusion 7

8

9

10

Estimation of hedonic price function Introduction Market segmentation and sample size for hedonic analysis Types of property data Explanatory characteristics of a property Making variables fit the reality Hedonic price function and unit and form of variables

47 49 51 51 51 52 61 63 68

Hedonic price method in estimating the value of environment and institutional regulation Introduction Changes in consumer preference on an upper-class housing estate in Tokyo, 1934 and 1985 Amenity value Environmental cost Value of institutional measures: The regulation on floor to land area ratio in the CBD Characteristics of the values of the environment and public services Concluding remark

96 101

Environmental cost–benefit analysis using the hedonic price method Introduction Basic principles of cost–benefit analysis Procedure A numerical example Conclusions

102 102 102 111 117 123

Concluding remarks

125

71 71 71 74 87 95

Appendix 1 Proof of time-series capitalization 127 Appendix 2 Proof of the overestimation theorem 130 Appendix 3 Proof of equality conditions 134 Appendix 4 Model and proof of the overestimation theorem in the case of heterogeneous consumers 139 Appendix 5 Short-run case 141 Appendix 6 Two-region general equilibrium model 144

Contents

vii

Appendix 7 Two-region two type of consumer general equilibrium model Appendix 8 Schedule of benefits and costs

147 150

Notation Bibliography Index

151 154 163

Figures 2.1 7.1 8.1 8.2 8.3 8.4 8.5 9.1 9.2

Hedonic price function and bid price function Land price map in Tokyo Metropolis Cost of flood risk Externality of neighbourhood amenity Marginal value of green environment Marginal negative value of façade Marginal cost of noise Equivalent and compensating variation, and equivalent and compensating surplus Barato River and Sapporo City, Japan

ix

11 56 76 80 86 86 90 106 118

Tables 1.1 4.1 4.2

4.3

4.4 4.5

5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 7.1 7.2 7.3 7.4 8.1 8.2 8.3 8.4

Comparison of selected valuation methods Overestimation ratios by size of the area and degree of improvement by the project Robustness of the results by the rate of substitution between an amenity and a composite good in utility Robustness of the results by the technical rate of substitution between an amenity and a worker in production Overestimation ratios by size of the area and degree of improvement by the project (CES functions) Overestimation ratios by size of the area and degree of improvement by the project with heterogeneous consumers A regional residential hedonic price function Utility function Production function Cost function Nationwide hedonic price functions Estimation of the willingness to pay function Regression results for a water environment Comparison of HPM and CVM Property (especially land) price data in Japan Attributes of residential land Characteristics observed on a lot of land Other variables for commercial and oﬃce land in Tokyo Regression results for Denenchofu, 1934, 1972 and 1985 Changes of elasticity in Denenchofu, 1934, 1972 and 1985 Regression results for riverside parks and flood risk in Setagaya Value of riverside park xi

5 31

32

32 34

35 41 41 41 42 43 48 49 49 57 62 63 64 73 74 75 75

xii

List of tables

8.5

Regression results for access to large parks and railway services 8.6 Regression results for view and noise in Setagaya 8.7 Distribution of major variables of a green environment in Setagaya 8.8 Regression results for a green environment and building façade 8.9 Elasticity of a green environment in Setagaya 8.10 Regression results for air pollution in Tokyo 8.11 Regression results for noise index and vibration in Setagaya 8.12 Distribution of major variables in Sapporo and Ishikari 8.13 Regression results for water quality in Sapporo and Ishikari 8.14 Regression results for effective floor to land ratio 8.15 Summary of value estimated amenities in Japan 9.1 Annual flows of benefits and costs A8.1 Schedule of benefits and costs

78 79 83 85 85 88 89 92 94 96 98 121 150

Preface Despite the fact that the importance of the hedonic approach in public policy evaluation and environmental value estimation is widely accepted among practitioners as well as researchers in economics, it is difficult to find either a good introductory text or a precise and comprehensive professional book in the field of study. This book is written to explain the hedonic approach not only from a fundamental conceptual viewpoint but also from rigorous theoretical perspectives. The book is especially designed to show the basic assumptions of the approach and the strengths and weaknesses of the method by careful treatment of the fundamental theorem on which the method is developed, that is, the crosssectional capitalization hypothesis. As to practical perspectives, the book examines the process of public policy or environmental valuation using understandable examples. In theoretical terms, the applicability of the method based upon the recent research findings is fully discussed. The book can be read without advanced knowledge of economics if the readers disregard the mathematical explanations (marked with an asterisk [*]). It can also be used by economics students, environmental science and technology specialists, and professionals in the public sector. The structure of the book is as follows. In the ‘Introduction’, we have an overview of the meaning of the hedonic approach and its characteristics. Chapter 2, ‘The hedonic approach’, starts with a brief research history of the approach, explaining the development of the hedonic conception, Rosen’s pioneering method and Ohta’s work in the early 1970s, the criticisms from Brown and Rosen in the 1980s and other econometric analyses, and finally discusses Scotchmer’s crucial comments on the hedonic approach. Readers should pay attention to the basic principle of the approach, namely the capitalization hypothesis in Chapter 3. The differences between ‘time-series and comparative static capitalization’ and ‘crosssectional capitalization’ are fully discussed. It should be noted that the hedonic approach must be based upon cross-sectional xiii

xiv

Preface

capitalization. This latter theorem is explained in the most comprehensive two-region general equilibrium framework of the study. After giving an explanation of the model using the simple Cobb–Douglas production and utilities case, we introduce the fascinating ‘overestimation theorem’ and equality condition proved by Kanemoto in 1988. Appendix 2, 3, 4 and 5 show the complete proof. In Chapter 4, we use numerical analysis to argue the applicability of the theorem in a Cobb–Douglas type of production and utility function case and in the case of more general CES functions. Chapter 5 discusses the applicability of the theorem by empirical examination in Japan. Chapters 2 to 5 are related to the theoretical side of the approach. In Chapter 6, the accuracy of the approach will be compared with the results of another valuation method, namely the contingent valuation method in the case of air and water pollution. In Chapter 7, the data, variables and functional form of the hedonic approach are fully discussed. Chapter 8 shows the results of the value estimation in environmental goods and public services in many types of public goods, especially in Japan. Chapter 9 explains some basic conceptions of cost–benefit analysis and shows the practical evaluation process for the environmental cost–benefit analysis of small and large projects. The crucial variables in the analysis, such as scenario, are discussed, and a case study gives as an example. Chapter 10 consists of concluding remarks. For my work on hedonic analysis, I am much indebted to Yoshiyasu Ono, and Yoshitsugu Kanemoto. I am also very grateful to David Pearce, P.-O. Johansson and Wallace Oates for their continuous encouragement during the writing of this book. I always received much stimulation from my laboratory colleagues at the Department of Social Engineering, Tokyo Institute of Technology; especially I owe thanks to Takumi Naito for his comments on part of my manuscript. The discussions in the seminars at the Department of Economics, University College London, the Department of Land Economy, Cambridge University, the Department of Government and Politics and the Department of Economics at the University of Maryland, the University of Humboldt and Stockholm School of Economics were also fruitful. My thanks to all friends and participants. I also thank the Tokyo Real Estate Association for permission to use part of its Tokyo Land Price Map (Tokyoto chika zu) for Figure 7.1. Finally I express my sincere gratitude to those who helped me to prepare this book: Cathy Taylor and

Preface

xv

Larry Lockhill for their editorial assistance, and Yukiko Ando for typing the manuscript. Noboru Hidano Tokyo, 2002

To a blue sky

1.

Introduction

The hedonic approach sounds strange to non-English-speaking people because the connotation of hedonic is not clear. The origin of the word comes from hedonism in Greek philosophy. The Epicures are one of the leading examples of this school of philosophy. Hedonism is a synonym of the word ‘pleasure’. More strictly we can refer to the Oxford English Dictionary (1999, second edition, CD-ROM version 2.0): Adj. Of or relating to pleasure. (In first quot. applied to the Cyrenaic school of philosophers.) In wider use, chiefly in Psychol.: of, pertaining to, or involving pleasurable or painful sensations or feelings, considered as aﬀects. Spec. hedonic tone, the degree of pleasantness or unpleasantness associated with an experience or state, esp. considered as a single quantity that can range from extreme pleasure to extreme pain.

We can find interesting examples, especially in psychology: 1901 F. Stout Man. Psychol. (ed. 2) i. i. 63 When we wish to say that pleasure or displeasure belongs to this or that mental process, we say that the process is pleasantly or unpleasantly toned. Hedonic-tone is a generic term for pleasure and the reverse, considered as attributes of this or that mental process. Anger has hedonic-tone, mostly of an unpleasant kind. Ibid. . . . 1932 G. Beebe-Center Psychol. Pleasantness & Unpleasantness i. 6 In the present volume . . . the general algebraic variable, whose positive values correspond to pleasantness and whose negative values correspond to unpleasantness, will be called hedonic-tone. 1940 Jrnl. Exper. Psychol. XXVI. 233 The oscillations of hedonic tone in his case are slight, and the tone rises continuously from the beginning, in spite of pain and fatigue, 227 While Ss worked Es took their tapping rate every minute . . . and in a number of cases called at stated intervals for a rating on a previously agreed hedonic scale. Ibid. 1

2

The economic valuation of the environment and public policy 1952 D.J. O’Connor John Locke 51 By pleasure and pain Locke . . . is referring to what the psychologists nowadays call the hedonic tone of our experiences which can be roughly measured on a scale ranging from very pleasant through mildly pleasant, neutral, mildly unpleasant to very unpleasant. 1961 P.T. Young Motivation & Emotion v. 153 The sign, intensity, and temporal changes of aﬀective processes can be represented upon the hedonic continuum.

The hedonic approach is a method of ascertaining the value of or the pleasure felt from attributes of a good. In contrast to conventional economic valuation, where the value of a good is calculated for the whole of the good, the hedonic approach regards a good as a set of attributes and considers the value of a good as a function of each attribute of that good. For example, value of a good(value of attribute 1) (quantity of attribute 1)(value of attribute 2) (quantity of attribute 2)

(1.1)

This value of an attribute is called an implicit price (a hedonic price) of the attribute, because it cannot be observed in a real market. We can estimate this price, however, by analysing the prices of a good that has diﬀerent quantities of each attribute in the market. The hedonic approach is defined as a method of finding out these implicit prices. The function, which determines the market price of a good by these attributes, is called the hedonic price function. The above formula is an example of the hedonic price function. Once the function is estimated, we can apply this method for three main purposes, namely, to construct the price index of a good, to evaluate the value of the attribute of a good, and to estimate the value of a good using the hedonic price function. The price index estimated by the hedonic approach is used, for example, for a computer, a car (Griliches, 1971), a telephone charge, housing prices (Bailey et al., 1963; Mills and Simenauer, 1996; Meese and Wallace, 1997 among others) and land prices (Hidano, 2000a). The most typical example is in the United States, where since 1986 the hedonic index has been used to estimate the deflator of a computer. As for the second

Introduction

3

purpose, many studies have been carried out to value an environment by analysing space values, such as land, housing prices or rent, and to value skilled labour by investigating wages. The third example can be seen in forecasting space values, that is, housing and property price estimation. The hedonic approach has very strong characteristics as an economic method. It is based upon revealed preferences of consumers and producers in actual markets. It also provides a simple procedure to achieve its purposes. As we shall explain in the text, the hedonic approach requires only the estimation of hedonic price function. The theoretical drawbacks of the method are that it assumes a perfect competition in the market with perfect information, and costless mobility of consumers and suppliers, that is, the openness of the market. But these assumptions are very common in most economic theories. It is sometimes claimed that the hedonic approach is only applicable in cases where policies produce a marginal impact on the market. This prevailing conception is not necessarily correct. We shall discuss this issue fully later in the book, since this idea is largely based upon a misunderstanding of the basic theory of the method. In addition to the hedonic approach, there are several other methods of identifying the value of environmental goods or benefits arising from the implementation of a public policy or project. Now we shall compare the characteristics of the hedonic approach from the viewpoint of evaluation. The evaluation methods can be classified according to who decides the value, that is, whether the method is based upon the preference of general consumers and producers, or is simply a reflection of a decision maker outside the market. Then the preferences can be divided into two types, that is revealed in the market or stated in a survey. Thus the methods can be classified as follows: 1.

Preference of a consumer and a producer a. Revealed preference i. Conventional demand and supply approach (consumer and producer surplus) ii. Production function approach Travel cost method (for local public goods) (TCM) Cost-avoidance approach (based upon households’ or firms’ behaviour) iii. Hedonic approach (hedonic price method (HPM))

4

The economic valuation of the environment and public policy

b.

2.

Stated preference i. Contingent valuation method (CVM) ii. Conjoint analysis or other choice methods Non-preference of a consumer or a producer a. Damage cost b. Countermeasure approach.

Table 1.1 compares selected valuation methods. In order to discuss the characteristics of the diﬀerent methods, we have to make clear what valuation is. Valuation, in this book, is the measurement of the value of environmental goods or the benefits of the projects and policies implemented. In the latter case, the value is clear that is, the increment of happiness (or utility) minus the increment of unhappiness due to the implementation of the public project or policy that is measurable by welfare measures such as equivalent valuation, or compensating valuation (see Chapters 3 and 9). The case of the value of environmental goods, however, is problematic. If we want to measure the value of a forest, which exists now, we have to decide in what situation we should value the forest. The approach taken in this book is to assume that the shadow project or policy is assumed hypothetically to produce a new forest under the condition that the forest should not exist. Alternatively the shadow project is assumed to destroy this forest. Then the welfare measures will be applicable to this forest evaluation as in the previous cases. This means that we can use the project or policy concept in estimating the environmental value of a good. We should also comment on the diﬀerences of the methods used in environmental valuation. It is well known that methods of valuing environmental goods should be based upon consumer preference. In this respect, the hedonic approach (called HPM in environmental project evaluation), the travel cost method (TCM) and the contingent valuation method (CVM) or other constructed market techniques (Carson, 1991) are preferable. Among them, CVM should depend on a stated preference. HPM and TCM are based upon revealed preference. HPM, however, is a more promising approach than TCM in terms of its simplicity, its theoretical soundness and the cost of the evaluation. Apart from this rather technical discussion, there is very strong criticism of the economic valuation of non-market goods. Schumacher, the author of Small is Beautiful (1973), is one of the leading proponents of the ‘non-economic’ view. He argues as follows:

5

Basic assumption

Respondent’s honest opinion

Respondent’s honest opinion

Single-purpose trip

Costless mobility

Contingent valuation method (CVM)

Conjoint analysis and choice methods

Travel cost method (TCM)

Hedonic approach (HPM)

Only real

Only real

Both

Both

Applicable goods, hypothetical or real

Comparison of selected valuation methods

Type of method

Table 1.1

Not necessarily small

Small

Basically small

Basically small

Degree of improvement by a project

Not necessarily small

Small

Any

Any

Region affected by a project

Considered

Usually not considered

Usually not considered

Usually not considered

Consideration of cost of a project

6

Data type, difficulty and accuracy

Survey data, cost of a survey, subjective response

Very complicated survey is required, cost of a survey, subjective and unreliable responses because of the difficulty of a questionnaire

Survey data, cost of a survey, rather objective response but still stated data of behaviour

Market data, data is available from public or private organizations, basically quite objective

Contingent valuation method (CVM)

Conjoint analysis and choice methods

Travel cost method (TCM)

Hedonic approach (HPM)

(continued)

Type of method

Table 1.1

The functional form, the missing variables, and multicollinearities among explanatory variables are as problematic as other econometric analyses But the hedonic price function is easy to estimate and the transparency of the analysis is high

If the ordinal demand function is applied, the formation of demand function tends to be subjective and unrobust due to many factors related to trips to the sites. If the choice models are applied, the formations of alternative choices of sites and behaviours are very subjective and the functional form of utility is problematic. Much subjectivity is included in the analysis

Many assumptions on distribution, and the functional form of the utility cause difficulty in interpreting the results, and unrobustness of the estimation

In the case of non-parametric estimation, the results are reliable because they are free from error distribution assumptions. But if the parametric estimations are applied, the results are highly dependent on model specifications

Ease, accuracy of the analysis

Introduction

7

It is hardly an exaggeration to say that, with increasing aﬄuence, economics has moved into the very center of public concern, and economic performance, economic growth, economic expansion, and so forth have become the abiding interest, if not the obsession, of all modern societies. In the current vocabulary of condemnation there are few words as final and conclusive as the word ‘uneconomic’. If an activity has been branded as uneconomic, its right to existence is not merely questioned but energetically denied. Anything that is found to be an impediment to economic growth is a shameful thing and if people cling to it, they are thought of as either saboteurs of fools. Call a thing immoral or ugly, soul destroying or a degradation of man, a peril to the peace of the world or to the well-being of future generations; as long as you have not really shown it to be ‘uneconomic’ you have not really questioned its right to exit, grow, and prosper. But what does it mean when we say something is uneconomic? I am not asking what most people mean when they say this; because that is clear enough they simply mean that it is like an illness: You are better oﬀ without it. The economist is supposed to be able to diagnose the illness and then, with luck and skill, remove it. Admittedly, economists often disagree among each other about the diagnosis and, even more frequently, about the cure; but that merely proves that the subject matter is uncommonly diﬃcult and economists, like other humans, are fallible. No, I am asking what it means, what sort of meaning the method of economics actually produces. And the answer to this question cannot be in doubt: something is uneconomic when it fails to earn an adequate profit in terms of money. (pp. 37–8)

Schumacher is mistaken here, however, because in economics any happiness or utility can be considered as economic goods and services. We shall discuss this point later. Schumacher continues: The method of economics does not, and cannot, produce any other meaning. Numerous attempts have been made to obscure this fact, and they have caused a very great deal of confusion, but the fact remains. Society, or a group or an individual within society, may decide to hang on to an activity or asset for non-economic reasons – social, aesthetic, moral, or political – but this does in no way alter its uneconomic character. The judgment of economics, in other words, is an extremely fragmentary judgment; out of the large number of aspects which in real life have to be seen and judged together before a decision can be taken, economics supplies only one – whether a thing yields a money profit to those who undertake it or not. Do not overlook the words ‘to those who undertake it’. It is a great error to assume, for instance, that the methodology of economics is normally applied to determine whether an activity carried on by a group within society yields a profit to society as a whole . . . However that may be, about the fragmentary nature of the judgments

8

The economic valuation of the environment and public policy of economics there can be no doubt whatever. Even within the narrow compass of the economic calculus, these judgments are necessarily and methodologically more weight to the short than the long term, because in the long term, as Keynes put it with cheerful brutality, we are all dead. And then, second, they are based upon a definition of cost which excludes all free goods; that is to say, the entire God-given environment, except for those parts of it that have been privately appropriated. This means that an activity can be economic although it plays hell with the environment, and that a competing activity, if at some cost it protects and conserves the environment, will be uneconomic. Economics, moreover, deals with goods in accordance with their market value and not in accordance with what they really are . . . (pp. 38–9)

Schumacher greatly criticized the concept of ‘market’ as a place of devils. What’s wrong with market value? If the market value should not reveal the real value, the problem is due to the lack of information of participants in the market or the lack of the power of enforcement on those who can enjoy services without paying appropriate costs, that is, free riders, or those who leave the market, such as polluters. But the market, itself, is not at odds with the former case. It is not a problem of market mechanism but a problem of how to utilize a market eﬃciently. We should emphasize the role of market to distinguish the quality of goods used by consumers. Thus the market is not a place of devils but a place of humans, since only humans can give a value of quality. However, Schumacher claims: In the market place, for practical reasons, innumerable qualitative distinctions which are of vital importance for man and society are suppressed; they are not allowed to surface. Thus the reign of quality celebrates its greatest triumphs in ‘The Market’. Everything is equated with everything else. To equate things means to give them a price and thus to make them exchangeable. To the extent that economic thinking is based on the market, it takes the sacredness out of life, because there can be nothing sacred in something that has a price. Not surprisingly, therefore, if economic thinking pervades the whole of society, even simple non-economic values like beauty, health, or cleanliness can survive only if they prove to be ‘economic’. (p. 41)

Is Schumacher’s opinion relevant to the case of valuation of local public goods? With local public goods, it is possible for consumers to have the choice between diﬀerent options. The hedonic approach, as we shall see, provides an answer to the question.

2.

The hedonic approach

DEVELOPMENT OF THE HEDONIC CONCEPTION There are several arguments over who first tackled the hedonic approach. Andrew Court proved by the hedonic method in 1939 that the price of an automobile after the Great Depression of 1929 declined greatly when compared with the prices before the depression, but Waugh, of Harvard University, had already done work in this area in 1927. According to Colwell and Dilmore (1999), G.C. Hass in 1922 and H.A. Wallace in 1926 might also be named as frontrunners in hedonic history. The history of the hedonic approach is also discussed by Goodman (1998). Waugh (1929) gathered data on the prices of agricultural products, such as asparagus, from Boston market during May and July 1927, and tried to explain the determinants of the price diﬀerences for the average prices of a bundle of asparagus, estimating the parameters of regression: composite pricef (attributes).

(2.1)

The actual equation he identified is: Price of bundle of asparagus i traded at t over the average price of bundle of asparagus at t 0.138 (length of green in inches) 1.534 (number of sticks of asparagus in a bundle as a proximity of diameter) 0.296 (variance of the diameter of pieces of asparagus)constant. (2.2) Then the determinant of the coeﬃcient (R2) is 0.58. He found that, in addition to the thickness and the variance of the thickness of the 9

10

The economic valuation of the environment and public policy

asparagus in a bundle, the length of green colour portion of the asparagus was important to Boston consumers. The results of the regression showed that the price of asparagus with eight inches of green portion was 38.5 cents higher than that with five inches. He concluded that Bostonians liked the green part. A.T. Court did the same analysis for automobile prices in 1939. He found that, though the average price of automobiles had increased during the period from 1925 to 1935, the actual price had fallen 55 per cent if we took into consideration the qualities of automobiles, such as power, weight and length. This fascinating result suggests to us that there is a great deal to understand about the prices in the real markets. Court is said to be the first person to attach the word ‘hedonic’ to this method, based on the fact that every attribute of the commodity provides us with hedonic pleasure.

ROSEN’S METHOD AND WORK IN THE 1970s Sherwin Rosen’s Breakthrough In the 1960s, Griliches (1971) developed the hedonic approach for measuring the price changes of commodities as a price index, just as Court did for automobile prices. Following Griliches, Sherwin Rosen (1974) comprehensively laid down a theoretical foundation for determining the bid prices, or implicit value of the attributes of a commodity for diﬀerent consumers. The bid price () is defined as the maximum amount of money which a consumer is willing to pay for a good under the condition that he or she retains a specific level of happiness or utility. He proposed to utilize the information from the tangent of the market price curve with which the consumers or producers share the same value of the equilibrium conditions. The methods used to identify the consumer’s bid price function and the producer’s oﬀer function () were fully discussed by him. The oﬀer function is defined as a function to determine the minimum value of price which a producer should accept to sell a good for a certain profit. The relationship among market price, bid price and oﬀer functions are shown in Figure 2.1. Rosen’s work is a breakthrough in that it enables us to understand the rigorous economic foundation of the empirical hedonic method. For those who are interested in the mathematical formulae, the

11

The hedonic approach

p(z),0,ϕ

p(z) o o o ϕ ϕ ϕ

0

z

p,ϕ

p(z) ϕ(z) ϕ(z',u) – ϕ(z,u)

0 Figure 2.1

z

z'

z

Hedonic price function and bid price function

process is as follows [*]. Consumers maximize their utilities under the budget constraints: max x,z u(x, z), subject to Ixp(z)

(2.3)

where u is a utility function, x is a composite good, z is a vector of attributes of a commodity, I is the income of a consumer, and p(z) is the market price function of a commodity. Producers seek to maximize their profit, selling the commodity under the cost of production technology constraints:

12

The economic valuation of the environment and public policy

max z,X p(z) XC(X, z)

(2.4)

and where is profit, X is the quantity of the commodity produced, and C(X, z) is a cost required for production z. In this situation, consumers will take the best combination of a composite good and the set of attributes of a commodity z, and obtain the greatest happiness or utility. The marginal value of an attribute of z in terms of monetary units is obtained at the rate of substitution of a composite good whose price is unity. The problem is that we cannot know the form of the utility function. There is, however, a hint of revealed utility. That is the tangent of bid price function which shows the marginal monetary value to pay for an additional increment of an attribute of commodity z. The proof of this is shown in note 1.1 And this tangent is the same as the tangent of the market price function of a commodity when a consumer takes a commodity at equilibrium or a consumer maximizes his or her happiness or utility. First the market price and the bid price should be the same at equilibrium. If the market price is higher than the bid price, a consumer cannot purchase a commodity. If the market price is lower than the bid price, a consumer can increase the happiness or utility by using the balance between the bid price and actual market price for buying another composite good. Thus, it is not equilibrium. We can see at equilibrium that the market price is the same as the bid price. Second, if the tangents of the bid price and the market price are not the same, there should be a point near this equilibrium point, at which the bid price curve exceeds the market price curve. But this can never happen for the reason stated above. Then we can see that the bid price curve is always an envelope curve of the market price curve. As for producers, the same principle would hold. If the market allows any new entry of producers, the market becomes perfectly competitive. The oﬀer curve is an envelope curve of the market price curve. If there is homogeneous consumer, then the market price function is identical to the bid price function of the consumer. Based upon this fact, Rosen found how to identify the bid price function and the oﬀer function that share the same tangent. His procedure is as follows: 1. 2.

estimate the market price function; calculate the value of the tangent of the market price function at all observed samples;

The hedonic approach

3.

4.

13

specify the bid price function which includes the level of attributes of a commodity (zi ) and socio-economic characteristics of the consumer ( y) and to specify the oﬀer function of the attributes of a commodity and the characteristics of producers; and estimate the parameters of these functions (first-derivative forms) using tangent data.

Thus we can estimate bid price function, which enables us to value the attributes of a commodity. It should be noted that the market price diﬀerential due to the increment of an attribute of a commodity would be larger than the bid price. Thus he concluded that the market price diﬀerences are always in the upper limit of the value of an attribute (Rosen’s inequality see Figure 2.1). Ohta’s Work Ohta (1975) had questioned Rosen’s assumption that producers are really competitive and the market is open and has free entry characteristics. In Rosen’s case, we can assume any form of market price functions. But Ohta assumed monopolistic or oligopolistic conditions in which producers have the power to determine the prices of the market. Under this condition, the market prices are: unit price(1)C(z),

(2.5)

where is a markup ratio which is determined by the producers’ minimum profit requirement, and C is the cost function of a firm. Ohta analysed the American boiler and turbogenerator market under this assumption.

ECONOMETRICS AFTER THE 1980s Criticisms from James Brown and Harvey Rosen Rosen’s elegant thesis was critically reviewed by Brown and Harvey Rosen (1982), who questioned whether we can identify marginal bid price function using simple linear functions as a derivative of bid function. They pointed out that Sherwin Rosen’s procedure was not necessarily able to identify bid price functions. An institutive

14

The economic valuation of the environment and public policy

explanation of this is that if the market price function has much richer information in it related to the level of an attribute of a commodity than bid price function has, that is, the implicit price should be exogenous to bidders, then we can estimate the latter function. More specifically, if the information of the slope of the market price function has even more information than the first derivatives of the bid price function, we can estimate the bid price function. But if not, the estimation is not possible or merely duplicates the parameter of the market price function. The simple example of second order in the z’s is as follows: p(z)a0 a1 za2 z2

(2.6)

(z, y)b0 b1 zyb2 z2 .

(2.7)

Then the first derivative is: p (z)a1 2a2 z.

(2.8)

And the first derivative of bid price function in terms of z is: (z, y)b1y2b2 z ,

(2.9)

then we regress this equation using the values of p (z) of every observation as data. In this case, 2b2 should equal 2a2, because the variance of p (z) data only depends on z. Thus this variance can be completely explained by z in equation 2.9. This regression just duplicates the same parameter. We cannot identify b2 from this procedure. Brown and Harvey Rosen proposed that in order to estimate a bid price function properly, the market price function has mth order or more in the z’s if the bid price function has m1th order or it is estimated from the data of more than two separate markets. This means that we should restrict the functional form of bid functions before we estimate these functions, or we should have multiple data sets for the estimation of the bid price functions. But in reality it is very diﬃcult to find multiple separate market data in which the consumer will have the same utility, as Sheppard (1999) discussed.

The hedonic approach

15

Other Econometric Analyses Many eﬀorts have been made to overcome the problem indicated by Brown and Harvey Rosen, especially the problems of identification between the hedonic price function and the bid price function (see recent survey by Sheppard, 1999). Although various econometric studies (Quigley, 1982; Kanemoto and Nakamura, 1986; Bartik, 1987a, 1987b; Epple, 1987; Horowitz, 1987; Kahn and Lang, 1988; among others) have been carried out since the Brown and Harvey Rosen paper was published, they are unfortunately far from identifying the robust individual preferences for practical cost–benefit analysis or decision making. Recently Cropper et al. (1993) compared the hedonic approach and the discrete choice logit model specification in a single market by simulating equilibrium.

SCOTCHMER’S CRUCIAL COMMENTS In 1985 and 1986, Scotchmer proved that it is not possible to distinguish the bid price function from the hedonic price function even in the case of the homogeneous consumer. She argued that a composite price on housing or land is a function of location and neighbourhood attributes and space: composite pricef (attributes, space).

(2.10)

But in the long-run the consumers can choose the attributes as well as the space. Suppose that homogeneous consumers face a situation in which the land with higher amenity value is too costly for them to aﬀord, then the land will inevitably be divided into smaller pieces, which they can purchase, or rent. A plot of land with a larger size should have the lower amenity and the smaller plot should have the higher amenity. Then the land size would be strongly correlated with the amenity. The land space can easily be explained by the level of amenity. In this case we can only identify the function of attributes and space (which is determined by its attributes). We cannot have enough variation data to estimate an actual preference for space: composite pricef (attributes, space (attributes)).

(2.11)

16

The economic valuation of the environment and public policy

Then, we need to estimate a unit price function to separate the influence of attributes on space: unit pricef (attributes).

(2.12)

Scotchmer formalized the consumer’s behaviour as follows [*]: max x,l,z u(x, l, z), subject to Ixp(z)l

(2.13)

where p(z) is unit land price and l is the area of a piece of land. It should be noted that housing characteristics such as structure, number of bedrooms and so on are all included in x, which we can choose. It is very important for Scotchmer to adopt this specification in order to avoid the complexity caused by the inclusion of housing structures. But she finally showed that in this unit price case we could identify more than two bid prices from this hedonic data even if there are homogeneous consumers in the market. This means that we cannot estimate the value of the amenity which we are interested in from the hedonic data, since in the long run and in the case of largescale projects, the lot size would be changed due to consumer preferences. It is necessary for us to know the form of bid or utility functions beforehand in order to estimate the benefits. If we have the complete information on the functions, we need not, of course, estimate the function.

RECONSIDERATION OF CAPITALIZATION THEORY This is the worst-case scenario of a hedonic approach. We have to come back to a basic theory that supports the hedonic approach, that is, a capitalization hypothesis. Many papers have been published on finding the environmental value or estimating the benefits of public policies and projects based upon the cross-sectional capitalization hypothesis. (It should be noted that the hedonic approach is not based upon capitalization in time-series or comparative statics). We shall discuss this theory in the next chapter. But the simple answer to Scotchmer’s crucial comments is that the cross-sectional capitalization theorem of Kanemoto (1985, 1988) can largely overcome the diﬃculty of the hedonic approach, and what we have to do in the hedonic approach is merely to estimate a sound hedonic price function.

The hedonic approach

17

Nevertheless, apart from the discussion of this historical overview, we can see the weaknesses of the method from a practical viewpoint. They are its data dependence, poor specification of the hedonic price functions, that is, the functional forms, missing variables and multicollinearity which produce a bias in the estimation of the parameters of the functions. These problems are of course very common in most econometric analyses. This book is, however, not designed to solve these issues fully by using econometrical techniques, but rather provides a practical process to decrease the intensity of these problems (see Chapter 7).

NOTE [*] 1. The indirect utility function for consumers is defined as utility expressed by prices and exogenous income and public goods: u (x, z)v [Ip(z), z]u. Rosen introduces a bid price function (z; I, u) that shows the maximum amount of money payable for a bundle of attributes z under the income constraint of I in order to keep the consumer’s utility level u. Thus the indirect utility function can be expressed using this bit price function: v [I (z; I, u)]u. The first derivative of this equation in terms of zi is:

x 0.

x zi zi It should be noted that the amount of x is defined as I x. Also, the first derivative of this x definition equation in terms of zi is:

x .

zi zi

Thus:

0.

x zi zi

The first derivative of in terms of zi is, i vz /vx. i

The right-hand side is the marginal rate of substitution of x (the composite good in terms of monetary unit) and attribute zi . Now we can see that the tangent of the bid price function is equivalent to the marginal monetary value of i attribute of z and is also the same tangent of the market price function (see the proof in the main text).

3.

Theory of capitalization hypothesis

TWO TYPES OF CAPITALIZATION As we discussed in the previous chapter, the hedonic approach assumes that the consumer’s preferences of the attributes of a good are reflected in the price diﬀerences of goods. In other words, the value of attributes for the consumer is incorporated into the value of the price of a good. Then the value diﬀerences should result in the diﬀerent prices of a good. This phenomenon is called capitalization. We can see many examples of capitalization in the market. In the stock market, the future profits of a company are capitalized into the stock price of the company. In a space market, such as a land or housing market, the future rent of a space is capitalized into the value of the space. In the labour market, the value of the skill of a worker should be capitalized into the wages of the worker. A cost should also be capitalized into the prices. For example, future property taxes should reduce the value of space (land, housing), that is, the tax is negatively capitalized into the value of space (land or housing). If the rate of the property tax is diﬀerent from city to city, then the space (land or housing) price diﬀerence among these cities should reflect the rate diﬀerence (on capitalization, see Oates, 1969; Starrett, 1981, 1988; among others). From this discussion, we can understand that there are two types of capitalization. One is time-series capitalization such as in the capitalization of future profits, and the other is cross-sectional capitalization such as in wage diﬀerences among workers at the same time. The latter shows the geographical or overall diﬀerences among goods at one specific time. It is easy to understand that the hedonic approach is based upon cross-sectional capitalization, because it discusses the price diﬀerentials of a good at the same time in the market. But we should know the diﬀerences between time-series and cross-sectional capitalization theories. 18

Theory of capitalization hypothesis

19

The hedonic method is applicable to many types of goods, as we saw in previous chapters. In this book, we are mainly interested in public policies and environmental valuations. So, in order to distinguish between the two capitalization theories, we shall discuss typical models, which deal with location-specific attributes that are very common in environmental and public policy evaluation. One model is based upon urban economics and the other on regional economics, or more specifically on regional finance analysis. 1.

2.

Urban economic model A conventional urban model developed by W. Alonso in the 1960s has one central business district (CBD) in the centre of a circular-shaped city, which is expanding to suburban areas that are occupied by residents who commute to the centre. In this type of model, the urban area is defined by the boundary in relation to agricultural land rent. The main advantages of the model are that it enables us to examine the characteristics of spatial phenomena in urban areas using distance to CBD as a proximity of spatial variables. There is a great deal of discussion on urban economics, in standard textbooks, such as Fujita (1989). Regional economic model The most traditional regional model is composed of two regions, which are assumed to be homogeneous within the region. Thus, the locational characteristics within the region are ignored. But this model is very strong in analytical discussion because of its simplicity. Examples can be found in Wildasin (1987).

Time-series and Comparative Statics Capitalization Now we can discuss capitalization theory in these models. Using comparative statics capitalization theory, Rosen (1979), Starrett (1981), Roback (1982), Hoehn et al. (1987) and Voith (1991), among others, have discussed how hedonic wage and rent capture the value of an amenity. Roback discussed the direction of the capitalization of an amenity into wage and rent in the sense of comparative statics assuming homogeneous consumers with the utility function: u (x, l h; z),

(3.1)

20

The economic valuation of the environment and public policy

where x is a composite good, l h is land, and z is an amenity. A consumer maximizes his or her utility to choose x and l h to satisfy a budget constraint: wsxr l h,

(3.2)

where w is wage, r is land rent and s is an endowment, that is, a sum of non-wage incomes which is equally distributed among consumers. Firms are assumed to maximize their profits under the production technology constraints of constant returns to scale, that is, Xf (n, l f; z),

(3.3)

where n is number of workers, and l f is a land input. The results of the analysis of the directions of capitalization are not clear since Roback adopted time-series capitalization on the grounds that wages and rents could both capture the amenity values. It is not clear what kind of model Roback had in mind. Perhaps she adopted a conventional urban model, that is, the Alonso-type model, in which urban area is defined by its boundary in relation to agricultural land rent. If urban rents are higher than non-urban ones, then the urban area expands. But at the same time the expansion of the urban land decreases the total area of agricultural land and total agricultural rent (if unit agricultural rent should be equal worldwide because of the constant price of agricultural products and the homogeneous production technology) and, thus, the total endowment. Following Roback’s interesting analysis, Hoehn et al. (1987), using this urban model, discussed the impact of commuters who live in a suburban area on the levels of capitalization. Then Voith (1991) introduced residential, commercial and mixed land use into the model to explain urban structure in a more realistic way. Or Roback may use a traditional two-regional model in which both regions are instead assumed to be homogeneous within the region. Roback did not mention how to calculate this endowment. In either case, the unclear treatment of the endowment will create a serious problem when we apply the model to evaluating large-scale projects or policies in a cost–benefit context. It is therefore important for us to distinguish between the time-series or comparative statics capitalization and cross-sectional capitalization. Time-series capitalization theory says that the benefits of the

Theory of capitalization hypothesis

21

improvement projects should be captured in land price or rent increment. We shall discuss this using the simple regional model. The timeseries measure equals the gross benefit: (r1* r1) H1 VC,

(3.4)

where r1* is the equilibrium price of land in Region 1 after the project improves the level of an amenity in Region 1 up to the level of Region 2; V is the net benefit and C is the cost of the project. The equality nearby holds only when area H1 is small, that is, the improvement does not change prices and endowments of society at large. The proof is given in Kanemoto (1992) (see Appendix 1). The simple interpretation of the condition is that, in comparative statics or time-series analysis, the project should be limited in its spatial direct influence. The partial equilibrium cases are included in this case. Cross-sectional Capitalization Cross-sectional capitalization claims that the benefits should be captured in the cross-sectional diﬀerences of land price or rent. The cross-sectional measure equals the gross benefit: (r2 r1) H1 VC.

(3.5)

This equality fortunately holds under more general conditions, unlike the case of time-series capitalization. As we discussed in the previous sections, studies that claim that the hedonic approach is only applicable to marginal cases are based upon a misunderstanding of the two diﬀerent types of capitalization.

THEORY OF CROSS-SECTIONAL CAPITALIZATION Cross-sectional capitalization cannot occur in a society where the same types of consumers live in the same locations at the same level of an amenity without mixing or moving to other locations even if the amenity level should change. The most basic assumption is costless mobility (that is, an open economy) with perfect information. Thus capitalization is not completely achieved under a closed

22

The economic valuation of the environment and public policy

economy or it may overestimate the benefits obtained when the consumers are heterogeneous (that is, having diﬀerent tastes or income). Most research takes openness for granted. It is sometimes claimed that the costless movement assumption is far from reality. But we should know that this assumption is not necessarily faulty, because there are always some people who would move and are able to move in most regions or countries in the world and for whom the costs of moving to optional destinations are generally not a problem once they have decided to move. In addition, in the long run, the cost of moving itself is less problematic than the total cost of living. We shall discuss the case of heterogeneity later in this chapter. It should be noted that the following discussion on a land market is obviously applicable to the value of space of housing or other properties when the supply of the space is parallel to land supply. The discussion is supported in the situation where a consumer chooses an area of vacant space based on the conditions of the neighbourhood and local amenities. The consumer then purchases the interior fittings such as central heating independently from the space as a part of composite good x. Thus, this discussion is not limited to land, such as open land in agricultural areas, but is valid for most of the cases in urban housing, business and commercial properties in intermediate terms. Now in order to explain this theory (after Kanemoto, 1988), we shall adopt a two-region general equilibrium framework because of its strength in theoretical analysis. The whole area is composed of two regions, l and 2, whose areas are H1, and H2, respectively, and homogeneous consumers (of number N) who maximize their utility [*]: maxx,l u(xi , l ih, zi)

(3.6)

wi sxi ri lih

(3.7)

s /N.

(3.8)

subject to

and

Homogeneous consumers can move from one region to the other costlessly if they change their place of residence. But they cannot

Theory of capitalization hypothesis

23

commute to the other region. The non-wage income (rents from lands and dividends from a firm’s profit) is distributed equally among consumers. The uniform national dividend scheme is applied. The price of x (a composite good) is unity for normalization. The firms maximize their profits under the constraints of a constant return to scale technology, which requires workers n and land for business l f [*]: maxn,l i Xi wi ni ri l if

(3.9)

Xi Xi (ni , l if, zi ).

(3.10)

subject to

Thus the number of the firms can be assumed to be unity for each region and profits are zero. (It should be noted that the amenity z aﬀects a firm’s productivity as local public goods.) The price of land for firms should be equal to that for residences because of the land owner’s intent to maximize his profits from the land. We can also introduce zoning and regulations on the use of land. In this case we use diﬀerent prices for business use and add them to an endowment as well as to the hedonic measure. The equilibrium and market-clearing conditions are: u1 u2

(3.11)

n1x1 n2x2 X1 X2

(3.12)

Nn1 n2

(3.13)

Hi ni lih l if

(3.14)

H H1 H2.

(3.15)

Then we introduce a project to improve the amenities in Region 1. The superscripts w and o mean with the project and without the project, respectively: z1 →z2; zw1 zo2 zw2 .

(3.16)

24

The economic valuation of the environment and public policy

The cost of the project is C and is collected by the government as a lump-sum tax. The project is completed by having a composite good as an input: s W /NC/N.

(3.17)

The commodity equilibrium condition with the project is: n1x1 n2x2 CX1 X2.

(3.18)

The hedonic measure is: B(r2 r1)H1.

(3.19)

Full capitalization means that the hedonic measure equals the gross benefit, thus: BCV,

(3.20)

VN EV.

(3.21)

where:

Equivalent variation (EV) is defined by the expenditure function E (see Chapter 9 and Johansson, 1993): EVE(1, ro2, zo2, uw)E(1, ro2, zo2, uo).

(3.22)

Solution of Cobb–Douglas Production and Utility The conditions of the full capitalization are not clear enough for us to determine how much of this theory is applicable in reality without specifying the form of the functions. Thus we assume the Cobb–Douglas type of function for the utility and production: ui xi (lih)zi

(3.23)

Xi nia(l if )1a zib.

(3.24)

Theory of capitalization hypothesis

25

First, we shall discuss two cases as follows: 1.

2.

The case of non-production If the wages are given to the consumers as endowments, are the benefits of the projects completely capitalized into land rent? Even in this simplest example, the equality cannot hold (see Appendix 2). The case of production only with worker input Constant returns to scale requires that a is unity and that there is no diﬀerence in wage rates between the two regions. The results are the same as above, that is, the hedonic measure generally does not equal the gross benefits.

Overestimation Theorem and Equality Condition (Kanemoto’s Theory) The above results are very interesting, but we cannot gain a clear image of how cross-sectional capitalization works under more general conditions. Kanemoto (1985, 1988) showed elegantly that the hedonic measure always overestimates or equals gross benefits within the general equilibrium framework. He assumed that the society is composed of two regions, 1 and 2, whose areas are H1 and H2, respectively, and that homogeneous consumers (of number N ) maximize their utility: u(x, l; z)

(3.25)

wsxrl,

(3.26)

under the budget constraint:

while firms maximize their profit: Xwn

(3.27)

under the technological constraint: XX(n)

(3.28)

where s(r1H1 r2H2 )/N. Kanemoto showed that when an amenity z in Region 1 (where the level of the amenities is less than

26

The economic valuation of the environment and public policy

that in Region 2) is increased up to the level of Region 2 by the project using composite goods (C ) and land in both regions, the hedonic measure: B(r2 r1)H1

(3.29)

is larger or equal to the sum of the cost of the project borne by all consumers (for the case when only residents in Region 1 pay for the cost1) and the net benefit, (N EV ). It should be noted that these rents (r1 and r2 ) are observable without the project. The overestimation theorem (proof given in Kanemoto, 1988, and in Appendix 2 for a simple case) is: B(r2 r1) H1 CN EVCV.

(3.30)

However, while the overestimation nature of the hedonic approach has been extensively discussed in hedonic literature, especially by Rosen (Rosen’s inequality) and his successors, who say that market equilibrium price diﬀerences between high- and low-amenity areas should be larger than or equal to the real willingness to pay or bid price diﬀerences, this theory diﬀers from theirs in two important aspects. The first is that, unlike the others, Kanemoto’s theory explicitly includes the costs of the project in the model, and thus the general equilibrium can be achieved. The second one is that the benefit measure in this theory is equivalent variation, while others adopt an ambiguous measure of willingness to pay, in terms of bid prices, which may not take price changes into account. The shortcomings of these existing studies are crucial when we apply the hedonic approach to a large-scale environmental project evaluation which requires a rigorous measure of welfare. Kanemoto showed the equality conditions as well. The equality holds when any of three conditions is satisfied as follows: 1. 2. 3.

the improvement is marginal (z2 z1 →0); the area of the region where the level of an amenity increases is small (H1 →0); and the production and utility functions do not permit substitutability among commodities (Leontief preferences and production).

Although the third condition would usually never be satisfied, the first and second conditions are very important. The first one means

Theory of capitalization hypothesis

27

that we can apply the hedonic approach in a spatially small project and the second enables us to use the method with small improvement projects. The proof of these equality conditions is in Kanemoto (1988) and in Appendix 3 for a simple case.

EXTENSION The Case of the Heterogeneous Consumer and Land-use Control for Production It should also be noted that the results stated above hold in all cases when: 1. 2. 3. 4.

the heterogeneous consumers live in both regions, or all types of heterogeneous consumers live in Region 2, or the firms require land as their production input whenever the land is for business use exclusively, or the land can be mixed land use.

When one or more types of consumer only live in Region 1, their preferences are not reflected in the price diﬀerences between the two regions. The hedonic measure overestimates the gross benefits (see Appendix 4). The Case of Short-run Evaluation In the short-run case, the land and housing lot size is not changed. The following two cases satisfy the overestimation theorem (see Appendix 5 and Kanemoto, 1992). 1.

2.

If the lot sizes are optimally chosen in Region 2 without the project, then the theorem holds by using the conditional expenditure function, with fixed lot sizes, rather than the ordinal expenditure function. If the lot sizes are the same in both regions without the project, then the theorem holds.

It should be noted, however, that the long-run theorems are relevant even in short-run cases, that is, open land is easily modified and

28

The economic valuation of the environment and public policy

housing structures can also be demolished in the short-run. Thus the regions in the outskirts of urban areas, in areas where wooden housing structures are dominant, such as in Japan, or in developing countries, can satisfy long-run cases.

CONCLUSION These results are quite important. We can measure the benefit of public policy and environmental projects by using the information of ex ante hedonic price diﬀerences among diﬀerent levels of an amenity without identifying the bid prices. But the problem is that we cannot know to what extent the theorem will be applicable and how much the hedonic measure exceeds the real gross benefits. This is fully discussed in the next chapter.

NOTE 1. Even when residents in Region 1 bear all the costs, the overestimation theorem holds (see Kanemoto, 1988).

4.

Hedonic measure as an approximation of benefit

INTRODUCTION As we discussed in the last chapter, the overestimation theorem is strong, especially with relation to the equality conditions of Kanemoto’s theorem. This suggests a broader applicability of the hedonic measure based upon cross-sectional capitalization. But unfortunately, even in the Cobb–Douglas specification, we cannot obtain clear results on the level of overestimation when we use the hedonic measure as an index of gross benefits of the projects. More precisely it is not clear to what extent we can apply the hedonic measure as an approximation of the real gross benefit when we evaluate the benefits of large-scale projects in space and in a degree of improvement. We shall examine this question by adopting the following measure: B/(CV ).

(4.1)

This ratio shows the approximation of the hedonic measure to estimate the exact gross benefit. If it is close to unity then capitalization is mostly achieved. As far as the practical cost–benefit analysis is concerned, a ratio of less than 1.2 or 1.3, though not unity, still makes sense, since benefit figures estimated in conventional environmental studies sometimes diﬀer by more than two or three times.

EXAMINATION OF OVERESTIMATION RATIO The existing literature shows that marginal improvements can be measured but fails to identify how large projects can be measured by these methods quantitatively. We introduced two criteria to measure 29

30

The economic valuation of the environment and public policy

the largeness of the projects to correspond to Kanemoto’s equality conditions, namely, the degree of improvement by the project and the size of Region 1. The former is measured in z1/z2, and H1:H2 indicates the size of the area aﬀected by the project directly. In order to minimize the subjectivity of the numerical analysis to examine the overestimation ratio, the parameters of Cobb–Douglas functions are given in systematic ways. The study adopts an objective method to test the overestimation theorem of capitalization as shown below. Utility function The sum of parameters (3.23) is set to be unity:

1,

(4.2)

and in order to separate the influence of the market inputs (workers and lands) and the amenity, we first set the ratio : and then

::

: 1:3, 1:1, 3:1

(4.3)

:3:1, 1:1, 1:3.

(4.4)

Production function In order to measure the level of overestimation in a more general context, we use the production function with worker, land and amenity inputs. In equation (3.24) a starts from 0 and increases in 0.25 intervals up to unity, and b is set under the same rule. Land and number of consumers and workers The total area is assumed to be unity, and the number of consumers and workers is identical and is normalized to unity. The largeness of the project We review the cases of z1 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 0.99. As to the size of the area directly aﬀected by the project, the ratios of H1 :H2 10:1, 5:1, 2:1, 1:1, 1:5, 1:10 are examined.

31

Hedonic measure as an approximation of benefit

RESULTS The Area Covered by the Project and the Overestimation Ratio The equilibrium values of the variables in the model developed in Chapter 3 for both without the project, and with the project, are calibrated by the Newton–Raphson method. Table 4.1 shows the result that the overestimation ratio calculated based upon these data is as small as 4 per cent, even when the area in which the project directly improves the level of the amenity encompasses ten-elevenths of the whole society. Table 4.1 Overestimation ratios by size of the area and degree of improvement by the project Size

H1:H2

(z1 0.9)

B/(C V ) 1.042 1.038 1.03

Degree of improvement z1

10:1

0.5

5:1

0.6

2:1

0.7

1:1

1:5

1:10

1.023 1.009 1.006 0.8

0.9

0.95

0.99

(H1:H2 1.1) B/(C V ) 1.091 1.077 1.061 1.042 1.023 1.013 1.005 Note: 0.25, 0.25, 0.5, a 0.5, b 0.5, C 1 per cent of total production without the project.

The Degree of Improvement by the Project The results of the degree of improvement by the projects are shown in Table 4.1. They indicate that in the case of a 20 per cent increase in the amenity level, the overestimation ratio is limited to less than 5 per cent. The Robustness of the Results for Diﬀerent Rates of Substitution Tables 4.2 and 4.3 show the robustness of the results under the conditions in which the rates of substitution in utility and production functions change. These results show that the overestimation ratios are very small in most cases across the space determined by the parameters. It is clear to us that, contrary to the conventional belief that a hedonic approach is only applicable to marginal cases, the hedonic measure B is very eﬀective in benefit estimation.

32

1.046

0.75 1.126

0.251 1.002

1.5 1.018

0.5

:1:1 1.070

0.167 1.000

0.752 1.005

0.25

:1:3

1.068

1.25 1.065

1 1.082

2

1.075

1

a:1–a 1:1 1.070

0.67

1.122

1

0.125, 0.125, 0.75, H1: H2 1:1, z1 0.9, C 1 per cent of total production without the project.

1.072

B/(C V )

Note:

3

(dz/z)/(dn/n) a/b

a:1– a 3:1

1.109

0.5

a:1–a 1:3

Table 4.3 Robustness of the results by the technical rate of substitution between an amenity and a worker in production

a 0.5, b 0.75, H1:H2 1:1, z1 0.9, C 1 per cent of total production without the project.

1.014

B/(C V )

Note:

2.252

:3:1

1.098

0.33

1.028

0.084

Robustness of the results by the rate of substitution between an amenity and a composite good in utility

(dz/z)/(dx/x) /

Table 4.2

Hedonic measure as an approximation of benefit

33

AN EXTENSION: CES FUNCTIONS Model and Results Based upon the model described in Chapter 3, we developed a more general type of two-region general equilibrium model as shown in Appendix 6, which allows for diﬀerent production technology in each region. In order to avoid the limitations of the Cobb–Douglas formation, we reformulate the model using CES functions as follows: ui [xi (lih) zi]1/

(4.5)

i b (l f ) i ]1/ i z i. Xi [ai n i i i i

(4.6)

Although the reformulations are attractive because we can examine the situation which is more in line with reality, the increased number of parameters due to the introduction of CES functions creates diﬃculties when we try to examine all parameter space. We adopt the following values to implement a numerical analysis as an example. Utility function:

0.3, 0.6, 2.0, 0.5, thus elasticity is 0.67. Production functions: a1 0.4, b1 0.6, 1 0.6, 1 0.8, a2 0.6, b2 0.4, 2 0.8, 2 0.6, thus elasticities of Regions 1 and 2 are 0.56 and 0.63, respectively. We assume that the production technology in Region 1 is more land intensive than that in Region 2. Total net benefit VN EV. The hedonic measure is B(r2 r1)H1, and the overestimation is measured by B/(CV). The model of this CES case is included in the model shown in Appendix 6. The results of the numerical analysis to calibrate equilibrium values of the variables by the Newton–Raphson method are shown in Table 4.4. Other values assigned are: total population, N is 38 million (number of households), area H is 120,000 km2 and annual cost of the project C is 10 billion yen: this

34

The economic valuation of the environment and public policy

Table 4.4 Overestimation ratios by size of the area and degree of improvement by the project (CES functions) Size

H1:H2

(z1 0.95)

1:0.1 1:0.25 1:0.5

1:1

1:2

1:4

1:10

B/(C V ) 1.410 1.142 1.101 1.087 1.074 1.063 1.040

Degree of improvement

z1

(H1:H2 1.1) B/(C V )

0.85

0.90

0.95

0.99

1.210 1.112 1.087 1.037

represents Japanese cases, but the results were not aﬀected by these values. It was no surprise that the benefits of the projects represented a 10 per cent improvement level in amenity, which may impact on more than 50 per cent of the whole area and can be estimated by the hedonic measure with a 1.11 overestimation ratio. It should be noted that in the case of the Leontief type of production and utility function (that is, elasticity is 0), the overestimation ratio is unity. The overestimation ratio in the case of Cobb–Douglas functions, in which the elasticity is unity, is found to be smaller than those in the case of CES functions. The reason is that we assume regionally diﬀerent production technology in the CES case which inevitably increases the overestimation ratio. The Case of Heterogeneous Consumers In this subsection, we introduce heterogeneous consumers whose endowments diﬀer, that is, the endowments are distributed to poor consumers and to rich consumers 1. The two-region, two-typeconsumer general equilibrium model is developed (see Appendix 7). We then assume that the cost of the project is financed by the tax on land price. The functions of utility for poor consumers (P) and rich consumers (R) and of production (X ) in each region are as follows: P x P x P)1/P uP(xip, l hip, zi )( PxiP P iP P iP

(4.7)

R x R x R)1/R uR(xiR, l hiR, zi )( RxiR R iR R iR

(4.8)

Xi (nip, niR, l if, zi )[ai (niP niR)i bi (l if )i]–1/i zi.

(4.9)

Hedonic measure as an approximation of benefit

35

The values we used in the analysis are as follows. Utility functions:

P 0.21, P0.19, P 0.60, P 0.12

R 0.12, R0.28, R 0.60, R 0.20. The elasticities of poor and rich consumers are 1.14 and 1.25, respectively. Production functions: a1 0.54, b1 0.46, 1 0.7, 1 0.05 a2 0.51, b2 0.49, 2 0.7, 2 0.05. The elasticity is 0.95. We assume that the production technology in Region 2 is more land intensive than that in Region 1. Other values are assigned as follows, each type of population NP is 46.4 million (number of households), NR is 11.6 million (number of households), total area H is 128,000 km2, and the annual cost of the project C is 150 billion yen. The results are shown in Table 4.5. They show that the overestimation ratio is higher than in the homogeneous cases, although the parameters assigned are diﬀerent. When we estimate the benefits by the hedonic measure of the project to improve the amenity by 15 per cent of the 20 per cent of the total area, the overestimation ratio goes up to 50 per cent. Table 4.5 Overestimation ratios by size of the area and degree of improvement by the project with heterogeneous consumers Size

H1:H2

1:0.25

1:0.5

1:1

1:2

1:4

B/(CV )

1.765

1.584

1.489

1.446

1.394

Degree of improvement

z1

0.85

0.90

0.95

0.99

(H1:H2 1.4)

B/(C V )

1.545

1.394

1.339

1.305

(z1 0.90)

It is important to note, however, that the distribution parameter is as high as 0.4, which means that only 40 per cent of the total endowment is distributed to 80 per cent of the total population. This is a very extreme case. Even so, the overestimation ratio is limited to less

36

The economic valuation of the environment and public policy

than 40 per cent for most cases we evaluated when H1 is less than 25 per cent of H2. Although our numerical analysis could not cover all spheres of parameters, the results are suﬃciently positive for us to use the hedonic measure in practical cost–benefit analyses. The equality conditions of the overestimation theorem are much less restrictive than we expected.

5.

Empirical examination of the accuracy of the hedonic measure

LARGE NATIONAL PROJECT EVALUATION In the last chapter, we demonstrated that the hedonic measure can be a very good estimate of the real gross benefits of the projects in the non-marginal cases using general equilibrium analysis. But we should be wary of the results because of the nature of numerical analysis, using hypothetical values of parameters. Thus, in this chapter, in order to validate the hedonic measure, we now apply it in the evaluation of a real project in Japan. The method we use is to compare the benefits of the project in terms of equivalent variation and the hedonic prices calibrated using a general equilibrium model and to test the diﬀerences between the EV value and the hedonic measure calculated using the nationwide estimated hedonic price function.

INTRODUCTION OF ACCESSIBILITY AND THE MODEL REVISED Accessibility The validity of the hedonic measure was assessed using the Hokuriku highway project, one of the main highway projects in Japan. The highway runs through five of the 47 prefectures (Japanese administrative jurisdictions), and will be the trunk road for the areas bordering the Sea of Japan. There should be spillover eﬀects of the project because of its large impact on the Japanese economy. We modify the model to include this eﬀect in both utility and production by the introduction of an accessibility measure (ACC ). This measure is defined as follows: ACCi

k

m 2 (DIDni ·DIDnk)/[minm (Pm ik Wt ik)]

37

1 2

(5.1)

38

The economic valuation of the environment and public policy

ACCi: Accessibility of region i DIDni : Population of the densely inhabited districts in region i Pm Transport costs (fares, petrol costs of private cars and ik: travel time cost) of transport mode m between i and region k W: Time value m t ik: Time of travel by mode m between i and k. This accessibility is interpreted as a potential transport amenity and defined as an inverse of the generalized cost weighted by the number of the population, which should reflect actual trips between the two regions. Model Revised The production and utility functions are specified using this measure, 1/ h h ui [ x i (l i ) (d i ) ACCi ]

(5.2)

Xi [ani b(l if ) c(d if )]1/ACCi

(5.3)

where d hi is the number of household trips and d if is the number of firms’ trips. The households maximize their utility subject to the budget constraint: wi sxi r hil hiPi d hi

(5.4)

where Pi is the unit transport fare. Public provision of transport service The government provides actual transport services and amenities. The production costs VC related to the services and maintenance of the stock are financed by the fares paid by users and the new investment is funded by the lump-sum tax T iT. The cost function is: VCi Ki Si

(5.5)

where K is the stock of infrastructure and is determined by the present stock and investment T, S is the supply of transport services

39

Empirical examination of the accuracy of the hedonic measure

and is a constant converter of monetary into physical stock. The market-clearing conditions are:

n x T VC X , i i

i

i

i

i

i

(5.6)

the governmental financial balance is:

P (n d d ) VC n T T i

i

h i i

i

f i

i

i

i

T i

(5.7) (5.8)

and the supply and demand of transport services should be equal. Si ni dih d if.

(5.9)

PARAMETER ESTIMATION METHOD AND DATA The parameters of utility, production and cost functions are basically estimated using 1985 data. In order to estimate the utility function in Japan, we have to convert it into the following transport demand functional form. This can be derived by the utility maximization under the budget constraints: ln[wi sPi dih)/dih ]1/(1)ln(/Pi )

1

1

+ln 1 1 (rih ) 1 .

(5.10)

Although most parameters can be estimated using this formula, the parameter of the amenity variable cannot because of the lack of a market. The study assumes 0.5, and the validity of the value is examined through sensitivity analysis (from 0.3 to 0.7). The Data All data used for the estimation of production and utility functions are at the regional (prefecture) level and are mainly from the 1985 cross-section regional statistics, except for rent data. Nationwide rent

40

The economic valuation of the environment and public policy

data are not available in Japan. The study converts the land data to rent data using a 5 per cent interest rate. Land price data are obtainable across the nation, but oﬃcially published average prices at the regional level are highly biased as they comprise merely the averages of assessed price and are not randomly distributed either spatially or socio-economically. In order to overcome this problem, there should be a suﬃcient number of samples in a region from the viewpoint of spatial distribution. The study adopts an alternative method of estimating normalized prices with the same attributes of land across the nation based upon the hedonic price functions estimated according to the region and land use, that is, residential, business or commercial use. The procedure for obtaining normalized prices of land is as follows: 1. 2.

3.

Select the capital or the largest city in all 47 regions. Estimate, by ordinal least square regression, 47 residential and 47 business or commercial land hedonic price functions based upon 1985 oﬃcially announced land prices in each city. Calculate 47 normalized regional land prices for each use of land assigning the same values for each attribute in the functions except for the distance from city centre, which is very diverse because of city size. We assume that 25 or 30 km from the centre is representative for Osaka and Tokyo, and 3 km in other cities.

An example of the results of the estimation of the regional hedonic functions in step (2) is shown in Table 5.1. Results of the Parameter Estimation Utility function The utility function can be estimated by using these data in the form of the transport demand function (see Table 5.2). Production function and transport production function The production function and the transport production cost function of the government can be estimated directly (see Tables 5.3 and 5.4). Transport data on 17 highways are obtained from the Japan Highway Corporation.

Empirical examination of the accuracy of the hedonic measure

Table 5.1 A regional residential hedonic price function (in Urawa city in Saitama Prefecture) Variable

Coefficient (t-statistics)

Sewage service Gas service Distance to CBD (km) Distance to railway station (km) Constant Sample size R2 MAPE Note:

23,800 (2.8) 29,000 (3.4) –25,200 (–2.1) –59,500 (– 4.8) 290,000 30 0.87 6.7

MAPE is mean absolute per cent error.

Table 5.2

Utility function

Parameter

Estimate (t-statistics)

Sample size R2 MAPE

0.251 (2.0) 0.273 (1.3) 0.811 (1.7) –0.11 (–2.0) 46 0.611 20.3

Note:

is assigned as 0.5.

Table 5.3

Production function

Parameter

Estimate (t-statistics)

a b c Sample size R2 MAPE

0.432 (4.0) 0.231 (2.3) 0.337 (2.2) 0.103 (3.2) –0.121 (–1.7) 46 0.622 24.7

41

42

The economic valuation of the environment and public policy

Table 5.4

Cost function

Parameter

Estimate (t-statistics)

Sample size R2 MAPE

–1.155 (–1.11) 0.034 (0.13) 1.666 (1.36) 17 0.711 25.1

RESULTS Comparison of the Hedonic Measure and the Gross Benefit The equilibrium values of the variables are calibrated by the Newton–Raphson method. Then the annual values are transformed into stock value with an interest rate i (5 per cent), B(ro2 ro1 )H1 /i.

(5.11)

In order to compare the hedonic measure and EV, we introduce the following formula to adjust the ACC improvement. The reason is that the project could not improve the ACC of the areas adjacent to the Hokuriku highway up to the ACC level in other regions even if the project were implemented. This is a linear adjustment of hedonic measure: B (r o2 ro1 )H1[(ACC w1 ACC o1 )/(ACC o2 ACC o1 )]/i.

(5.12)

From the calibration, N EVC is 3,844.4 billion yen and the adjusted hedonic measure is 4,289 billion yen. Thus, 12 per cent is overestimated. We can see that the result is acceptable from the cost–benefit viewpoint. It should be noted that the results are not aﬀected by changes of the parameter (see Hidano, 1997). Comparison of the Hedonic Measure Estimated by the National Hedonic Price Functions and the Gross Benefit Finally we should examine the possibility of estimating the benefit by using the real hedonic function rather than the equilibrium land

Empirical examination of the accuracy of the hedonic measure

43

prices. It is necessary to estimate a national land price function in order to calculate the benefit of large-scale projects. Although it is not common to estimate nationwide hedonic functions, this study examines the possibility of estimating the functions and the applicability of the functions to a cost–benefit analysis. The estimations are made based upon the normalized residential, and business or commercial land prices developed above. The results are shown in Table 5.5. Table 5.5

Nationwide hedonic price functions

Variable Annual wages Snowy days dummy Sewage dummy Number of beds in hospitals ACC (accessibility) Constant Sample size R2 MAPE Note:

Residential

Business and commercial

0.00068 (2.3) –0.0722 (–1.9) – 0.00000271 (2.0) 0.000138 (2.1) 4.25 47 0.68 23.1

0.00067 (1.9) – 0.182 (2.1) 0.0000116 (3.0) 0.000135 (2.0) 6.46 47 0.72 28.4

The dependent land price data are transformed into natural logarithmic value.

Using these functions we can estimate the benefit of this project. The hedonic measure using the hedonic functions can be obtained from the following formula: [LPh(ACC w1 )LP h(ACC o1 )]H h1+ [LP f(ACC w1 )LP f(ACC o1 )]H f1 (5.13) where LPh and LP f stand for residential and business land prices, respectively. In this formula, we assume that a fixed land area is designated for housing and business or commercial use, in contrast to the mixed land-use assumption in the original model. But this is validated by the fact that the areal size of each land use was scarcely changed as a result of the implementation of the project using the general equilibrium analysis above. The value is 3,955.5 billion yen, which exceeds the real one by only 3 per cent.

44

The economic valuation of the environment and public policy

CONCLUSION In this and the previous chapter, we have discussed the overestimation ratios of the hedonic measure for the evaluation of large-scale projects compared with the gross benefits using a general equilibrium analysis. The results are at odds with the prevailing idea that the hedonic approach is applicable only to small neighbourhood environmental valuations. Both numerical analysis and the empirical study indicate that the overestimation of the hedonic measure is less than 10 per cent for most cases that we usually have to evaluate. Even in those cases when we should consider the heterogeneity of the consumer, the numerical study shows that the discrepancy of the hedonic measures is still small. In most cases where we have to obtain the mean value of benefits rather than the distributional eﬀects of the projects, we need only to estimate the cross-sectional hedonic price function without the project, that is, ex ante situation, to obtain an estimation of the value of environmental and public services.

6.

Comparison with contingent valuation method

MEANING OF COMPARISON In this chapter, we compare the value estimated by the hedonic price method and the values estimated by another method. As we discussed in the previous chapters, hedonic price measures should give us accurate information from theoretical and empirical viewpoints. However, it is diﬃcult to ascertain the real values using only one method because each method has its shortcomings. We shall explain these cases by comparing the values of environmental goods obtained using the hedonic and the contingent valuation method. There has been little previous research on such a comparison. The most notable example is Brookshire et al.’s (1982) air pollution work, and there are other examples concerning earthquake risk in California, in the United States. We carried out a comparison study using an example of water environment in Japan (Hiramatsu and Hidano, 1989). The hedonic approach has already been accepted by major economists as a powerful tool for evaluating local public goods. Comparisons between the diﬀerent valuation methods have, in the past, mainly been carried out in an attempt to justify the stated preference approach, rather than to justify the hedonic approach. The CVM value may include biases, which have been fully discussed by many authors, including Mitchell and Carson (1989), Hanley and Spash (1993), Garrod and Willis (1999), Hidano (1999), and Bateman and Willis (1999) and we should therefore take care when discussing the CVM results. A careful comparison of the hedonic with the CVM results should employ the ranges of the hedonic value in the scale of values of diﬀerent estimating methods. This would enable us to utilize the HPM in real decision making, which requires reasonableness in the values as well as a theoretical soundness of method. 45

46

The economic valuation of the environment and public policy

AIR POLLUTION Brookshire et al. (1982) examined the validity of the CVM value using the hedonic approach. They compiled a price list of 634 singlefamily house sales between 1977 and 1978 and interviewed 290 residents in 12 census tracts of Los Angeles, in the United States, in 1978. The respondents were asked how much they were willing to pay for an improvement to reduce the level of air pollution in the area. Brookshire et al. attempted to show the validity of the CVM by proving Sherwen Rosen’s inequality, that is, the market hedonic price diﬀerential is larger than that of the bid price diﬀerential related to changes in the amenity level, with air pollution as an example. The results supported the hypothesis that the CVM could satisfy the condition of Rosen’s inequality. But the reported value estimate of the hedonic approach is more than twice that of the CVM. The discrepancy between the two values is less marked if the values are converged into certain ranges. Brookshire et al. discussed the reason for this discrepancy, with reference to the work of Bishop and Heberline (1979). Bishop and Heberline showed that the survey’s estimated value was only 45 per cent of the actual payment in the case of hunting permits while the value estimated by the travel cost method was 67 per cent of the real value. Thus the real willingness to pay maybe twice as much as the value obtained in the survey. Brookshire et al. claimed that the twice as high price of the survey estimates of eight out of the nine census tracts was still less than the hedonic price diﬀerential, that is, the real value of willingness to pay. There are some problems with this argument because, in the case of Bishop and Heberline, hunting permits were limited in number and there was no moral satisfaction in paying for them. The strategic behaviour of stating a lower value for the price of the permits would be possible to drive the price down. But in Brookshire et al.’s case, the direction of the bias was unclear for several reasons. On the one hand, the respondents might give a lower price for the same reason as for the hunting permits. On the other hand, they might feel moral satisfaction in paying or stating the amount of money they would be willing to pay for a better environment (called the ‘warm glow’ eﬀect) if the payments could be made by donation, utility bill addition, or even a tax increment. Although, it has been widely discussed that tax payments do not produce a warm glow (see Mitchell and Carson

Comparison with contingent valuation method

47

(1989), this is not necessarily true (see Hidano and Kato, 1999). Unfortunately, the payment mechanism was not clear in Brookshire et al.’s paper. The existing value, that is, the non-use value, should also be included in the amount of money that the respondents were willing to pay.

WATER ENVIRONMENT Hiramatsu and Hidano (1989) conducted an analysis to compare the hedonic value and the stated value in the case of the urban water environment. Price data on 153 plots of land were obtained from the land price map published by the Tokyo Real Estate Association in 1987, and 53 residents living within a distance of three hundred metres from a river in two areas in Tokyo, that is, the River No and the River Ichinoe Sakai, were interviewed. In order to minimize the bias of the CVM estimate, the study was designed to ask the respondents where they would choose to live between two optional parcels of land. One was valued at two million yen per 3.3 m2 with polluted river water located a minute’s walk away (80 m), and the other had a better water environment at the same distance but cost more. At several price diﬀerentials shown, the respondents chose one of two parcels of land. This method would reduce the ‘payment for moral satisfaction’ issue, and could also avoid the strategic behaviour of respondents because of the nature of land selection that already exists. The respondent’s willingness to pay for polluted land is normalized as the actual price of the land, that is, two million yen per 3.3 m2. The willingness to pay functions are shown in Table 6.1. The willingness to pay (WTP) for a better environment is used to estimate the WTP function, which includes the respondent’s socioeconomic characteristics and the quality of the water environment. The parameters estimated by the hedonic price functions are given in Table 6.2, and the means and standard deviations of the WTP of each area are shown in Table 6.3. The values based on CVM are evaluated on the interviewed respondent’s characteristics and those of hedonic price are evaluated on plots of land used for estimating the hedonic price function. Although the standard hypothesis testing technique can not be applied, every mean of the CVM is less than the hedonic value, to which they are also very similar. The discrepancies are less than 30 per

48

The economic valuation of the environment and public policy

Table 6.1

Estimation of the willingness to pay function

Variable (xk)

River No

1. Water quality (dummy)

0.040 (3.4)

0.011 (4.9)

2. Waterside Park (dummy)

0.027 (2.3)

0.019 (8.2)

3. Self-employed (dummy) 4. Household with elderly people (older than 65)

River Ichinoe Sakai

– 0.012 (1.1)

– 0.0002 (–1.1)

0.030 (2.3)

0.003 (1.3)

5. Willingness to move from present residence (definite3, probably2, no 1)

– 0.016 (2.1)

–

6. Frequency of walking to the river (frequent1, sometimes2, hardly ever3, never4)

– 0.011 (2.1)

–

7. Household income (million yen)

0.015 (1.5)

8. Land price (yen per 3.3 Constant Sample size R2

m2)

0.009 (2.1)

– 0.042 (0.9)

– 0.006 (– 0.3)

5.33

5.31

81

78

0.63

0.86

Notes: 1. ln (yen per 3.3 m2) 6k1 ak xk 8k7 ak ln xk constant. 2. t-statistics are in parentheses.

cent except in one case, that is, the water-quality improvement in the River Ichinoe Sakai, where the samples of hedonic land price are chosen to cover a much wider area than that where the respondents lived. The respondents in this case lived in a worse water environment and would be expected to have a lower willingness to pay for a better environment. Despite the limited number of samples analysed, this study gave some hints on the diﬀerences between the CVM value and the hedonic value in a surrogate market of the environment. The discrepancy between the values estimated using the two methods is surprisingly small. This fact suggests there is some validity in utilizing these methods in practice.

49

Comparison with contingent valuation method

Table 6.2

Regression results for a water environment

Variable (xk)

River No

River Ichinoe Sakai

1. Water quality (dummy)

0.045 (1.09)

0.08 (1.12)

2. Waterside Park (dummy)

0.031 (0.98)

0.048 (0.80)

3. Park (dummy)

0.12 (3.74)

0.21 (2.80)

4. Sewage service (dummy)

0.020 (0.50)

–

5. Distance to the railway station (km)

– 0.17 (–5.36)

6. Distance to a major road (km)

– 0.011 (– 0.92)

–

7. Time distance to CBD (minutes)

– 0.20 (–2.71)

–

8. Width of road (m)

0.080 (2.78)

– 0.23 (–3.36)

0.040 (1.22)

Constant

5.7

Sample size

90

63

0.75

0.63

R2

4.5

Notes: 1. ln (land price (10,000 yen per 3.3 m2)) 4k1 ak xk 8k5 ak ln xk constant. 2. t-statistics are in parentheses.

Table 6.3

Comparison of HPM and CVM HPM

CVM

Water-quality improvement River No (Nogawa) River Ichinoe Sakai

2.8 (1.9) 2.6 (2.1)

2.5 (0.7) 0.7 (0.1)

Waterside park River No (Nogawa) River Ichinoe Sakai

1.9 (1.9) 1.5 (1.9)

1.9 (0.8) 1.1 (0.1)

Note:

Price unit is 10,000 yen per 3.3m2 and standard deviations are in parentheses.

CONCLUSION In this chapter we compared the results of the hedonic price method with those of the contingent price method. The results demonstrated that theoretical requirements were satisfied in both studies. The

50

The economic valuation of the environment and public policy

discrepancy between the two methods found by Brookshire et al. was rather large, but that of our study was basically less than 30 per cent. The reason for these diﬀerences can be explained by the diﬀerent vehicle of payment adopted in each study. Brookshire et al. used public payments, such as taxes and public charges as a vehicle, which can include ‘warm glow’ biases. The choice of alternative land or housing was free from the payment for moral satisfaction issue. This is a much more promising vehicle to elicit a willingness to pay for environmental goods or public services (see Smith and Desvousges, 1986, among others). When we use this vehicle, the discrepancy is acceptable for practical decision making, in spite of the diﬃculty in estimating the value of non-market goods.

7.

Estimation of hedonic price function

INTRODUCTION We have discussed the importance of hedonic price functions in the previous chapters since we need an accurate hedonic price function in order to determine sound environmental and public project benefits based upon the limited nature of the discrepancy of the hedonic measures from the true values. The next stage is to concentrate on finding a method of estimating good hedonic price functions. But as we discussed in Chapter 2, the estimation of the functions is heavily dependent on the data. Thus the problem of the estimation can be reduced to the problem of sound data availability. In this chapter we shall take the property market as an example, although the discussions are applicable to other commodities as well.

MARKET SEGMENTATION AND SAMPLE SIZE FOR HEDONIC ANALYSIS The first question to ask in a practical hedonic analysis is ‘what market segment should we analyse?’ Clearly it depends on what we want to gain from the analysis. As far as the theory is concerned, the capitalization theorem in the previous chapters suggests that we should obtain the data from a market in which samples can be chosen from an area at the level of an amenity (or the level of public services), without a project (or a policy), and from an area at the level which would be achieved with the project that we have to evaluate. We must take into account the diﬀerent types of groups of consumers of an amenity, that is, those with diﬀerent tastes and income, or any other characteristics of consumers which may aﬀect their behaviour or the producers’ responses to the level of an amenity. In this case, some 51

52

The economic valuation of the environment and public policy

people from each group should live in or be located in areas with a higher level of amenity than is achieved by the project. This is required to avoid an overestimation of the hedonic evaluation. If like Rosen we wish to estimate the bid price functions or any other utilityrelated functions such as indirect utility functions rather than the hedonic price functions, either we have to consider multiple separate markets in space or in time which the same type of consumers inhabit, or we have to decide the functional forms of a utility as suggested by Brown and Rosen (1982). However, we are reluctant to estimate bid price functions because of the practical diﬃculties involved, as discussed in Chapter 2. From a practical viewpoint, in order to estimate the robust environmental value or the benefit of a public policy using hedonic price functions, we have to take into consideration data from all market segments in the area where we wish to evaluate the project. The problem of how to transfer the value from one market to another is often discussed in hedonic texts, but our experience in Japan shows that the beneﬁt transfer of an amenity is highly dependent on the context (see the discussion in the next chapter). To make a valid estimation, it is more reliable to study all areas rather than just some of them. Next, the problem of sample size cannot be solved easily because it is aﬀected by the structure of the data set, and the structure of the data is subject to the socio-cultural, institutional and political conditions of society itself. It should be noted, however, that our experience suggests that taking more than a hundred samples for the evaluation of a relatively minor feature in the environment, such as a green environment in a Japanese neighbourhood, will give stable results. It should also be noted that a study with a smaller number of samples, say 30, may be valid if we pay attention to the estimated parameter stability as far as the Japanese data are concerned (see more general discussions in a standard text of econometrics, such as Greene, 2000).

TYPES OF PROPERTY DATA The hedonic approach requires knowledge of the market price data of the commodity which we are interested in. If we are dealing with the real estate market, then we need data on rent prices, and the stock value of houses, oﬃces, commercial buildings, industrial estates and land. Property stock values and rent prices are the most basic data. If

Estimation of hedonic price function

53

we are interested in the human labour market, then data on wages across geographical regions and types of occupations are required. As such, any analysis of the hedonic approach should have access to the market data of the commodity. In the following discussion using hedonic analysis, we concentrate our attention on the real estate property market in order to avoid complex explanations of data issues in other markets. There are strong perceptions among people that property markets are not completely competitive. Most of the real estate market, for example, is to some extent controlled by government intervention, except in North America. But it should be noted that we can use the price data of a market in which there are institutional interventions by the government, other public bodies, or even social norms, such as a long tradition to prohibit specific use of land in some areas, as long as price control is not so stringent that it ignores public opinion. We can apply the hedonic method even in these markets, using the institutional variables in the hedonic price estimation. These property data are classified as market transaction price, sales price and assessed price. The market transaction price is the real value in the market. The sales prices are defined in this book as sellers’ oﬀering prices in the real estate market. The assessed prices are values estimated not by individual participants in a market, but by specialists such as surveyors, real estate agents and assessors. Naturally, the names diﬀer from country to country for those who assign a price to a specific property, taking into account the real market conditions. The provision of these data, or access to them, very much reflects the institutional setting of each nation. In the United States, for example, the federal government has no strong incentive to collect property data across the country, but many real estate firms are keen to sell this information to customers who are interested in finding property. Also, it is a legal requirement in many US states that a sales transaction requires a precise statement of the transaction price of the property in order to obtain proper insurance against loss by fire or other natural disasters. This is required in order to obtain a mortgage from a financial institution. So the actual transaction prices are shown in these documents and are usually accessible by a third party. Real estate market data in the United States can be said to be very transparent, although it may be expensive to obtain. In addition to the private sector in the United States, local governments, which may charge a property tax on a house or other real

54

The economic valuation of the environment and public policy

estate property, know the approximate value of a property for taxation purposes. In contrast to the United States, in Japan, the central government has had a long history of a strong interest in the price of land for taxation purposes. After the land price speculation in the 1970s, it had to be kept up to date with the changes in land prices all over the country. The present system of monitoring of land prices was established at that time in order to guide the appropriate land price levels. Every year, the central government, with the support of 47 regional (prefectural) governments, collects real estate transaction data in order to announce oﬃcially determined prices (oﬃcially announced price, OAP) of more than 30,000 land lots in Japan. This is so that people can ensure that they are paying reasonable prices for their real estate, and to show the price of land when the government or public sector needs to acquire it for public purposes such as the construction of infrastructure or to compensate people following the compulsory purchase of land. In order to publish these prices throughout Japan, regional governments ask assessors to collect the data for two or three actual transactions prices for each site to be assessed every year. The assessors usually collect such data but the regional governments also provide information on transactions, which has been obtained by the branch registry oﬃces of the Ministry of Justice. This information mainly comes from the registration of deeds to protect newly acquired property rights through purchase or inheritance. The price of the property is not included but the names of the owners or other parties who have any lawful right to the property are shown. These documents are available to the public. This transaction information is also sent to the branch oﬃces of the national tax department of the Ministry of Finance, to the tax oﬃces of regional governments, which collect a property transaction tax (a regional tax) from the party who acquires the property, and also to community or local governments which collect the property tax from the legal owner. Some of these transactions are recorded in the transaction record format by assessors, including the price of the land and buildings, if any, the details of the transaction, the specification and type of land, and its exact location. These data are usually kept by assessor’s regional associations, regional governments and the central government as well. The assessors estimate the OAP on the basis of these data. The land prices oﬃcially determined on New Year’s Day are published in March. The regional government also announces such

Estimation of hedonic price function

55

land prices on 1 July, following a similar procedure. Some of the data relating to the land assessed by the regional governments overlap with those from the central government survey. But unfortunately these real transaction data have not yet been made available to the public, though they are collected and kept. Other examples of oﬃcially published land price data are two sets of prices of land situated alongside a road, which are called the ‘line price’ of land. One is published annually by the branches of the national tax oﬃces of the Ministry of Finance for inheritance tax purposes, and the other one consists of the line price as well as the standard land price, announced every three years by the community or local governments for property tax purposes. The latter data have been made available to the public since the 1990s. All these data are assessed values produced through the estimation procedure. The former set of data is estimated by assessors at the level of 80 per cent of OAP, based upon the individual OAP data and some data collected by the national tax oﬃce. This oﬃce always sends a questionnaire asking for the real price of a property and the source of the funds used to purchase it. This is sent to all new purchasers in order to examine whether they should pay an appropriate amount of corporate or income tax. The latter prices are calculated at 70 per cent of the OAP using individual OAP data, and the community government’s own data by a regression analysis carried out by surveyor consultants in large municipalities (several hundred cities among about three thousand local municipalities) and authorized by each local property taxation committee. If the prices are not calculated by a community government because of a lack of either data or valuation expertise, then they are estimated using the line price announced by the national tax oﬃce. Quasi-public assessed price data are collected by the regional organization of real estate associations and are published in Tokyo Metropolis and Fukuoka Prefecture annually. The sample size is as large as 25,000 in Tokyo, as shown on Figure 7.1. The assessment process is diﬀerent from that for the OAP and is undertaken by the association’s specialists using transaction data collected by local real estate agents. The transaction price collected by individual real estate agents and stored by real estate associations for their business purposes. The market real estate transaction data are not publicly accessible, but are available from real estate agents individually for academic purposes.

56

The economic valuation of the environment and public policy

Source: Land Price Map in Tokyo 1998, Tokyo Real Estate Association.

Figure 7.1

Land price map in Tokyo Metropolis

The data are summarized in Table 7.1. But it should be noted again that an individual registration document does not include the price information at a registration oﬃce. All information on aggregated data is excluded in this table. The data in Japan are not as transparent as in the United States but the nationwide data are easy to obtain. In European countries1 the situation may be diﬀerent. The government of the United Kingdom does not provide any disaggregated data which can be pinpointed to an exact location. But data are kept by local governments, individual real estate agents, large real estate firms and surveyors who are responsible for assessing property values. As for land prices, there is not as much reliable data available because

Estimation of hedonic price function

Table 7.1

57

Property (especially land) price data in Japan 1. Public data

a. Line (street) land price data for inheritance tax provided by the central government (but value assessed by government officials and based on the OAP); published annually (for example, 430,000 locations in 1997). b. Line (street) land price data for property tax by a local government (but value assessed by government officials and based on the OAP); published every three years (for example, 403,646 locations in 1990). c. Officially announced land price OAP published by the national land department of the central government. The data are site specific assessed land prices for 30,300 (1997) plots, including some non-urban use agricultural land which may be used for building in the future. Officially announced land prices published by the regional government (ROAP) about 30,000 (1997) plots including forest. 2. Quasi-public data a. Several regional associations of real estate associations provide assessed value of land prices. In Tokyo, the prices of 25,625 plots of land are announced by the Tokyo Real Estate Association annually (RA). b. Nihon Fudosan Kenkyujo (Japan Real Estate Research Institute) publishes commercial site-specific assessed land prices for 223 cities at the end of March and September each year; (it also announces agricultural and forest land rents monthly at prefecture level). 3. Market data a. LAINS: The Ministry of National Land and Transport advises the real estate agencies to report and share information on offers and final prices of housing and land by computer in order to achieve greater market efficiency. But data for transactions completed within a few days are exempted. And also we do not necessarily find final prices in the documents. These data are not available to the public. b. Limited access to land price, housing rent and commercial or office rent data collected by estate firms or associations (personal connections). c. No access to individual transaction land price data collected by real estate assessors or surveyors for regional and central governments for publication (see above, 1c). d. No access to the land price data collected by real estate assessors and surveyors. However, they could be asked to assess various transaction prices.

58

The economic valuation of the environment and public policy

Table 7.1

(continued) 3. Market data (cont.)

e Offer prices and sales prices are published weekly in a private information journal such as Shukan Jutaku Joho in large urban regions in Japan. Housing and rent data are also available. Of course, the actual prices should be lower than these prices. f. Some access to final price data collected by certain associations of large real estate firms or other large firms (personal connection), especially the prices of flats. Some office and commercial rent prices are available. g. Every agricultural committee (quasi-governmental committees in rural areas) has access to agricultural land-use transaction price data. This is a legal requirement in Japan so that the transactions can be approved, but basically the data are not available to the public.

the number of transactions is not necessarily large, and because of the planning permission system in England. The prices are usually option prices and are aﬀected by the contents of the trade contracts, which usually include a termination clause in case permission is not granted, and also by the conditions placed on the development by the local government in terms of providing public services such as schools, road systems and so on. Individual transactions are identifiable at the registration oﬃces. Housing prices can sometimes be accessed at the registration oﬃces but they do not include housing attributes such as the number of bedrooms and so on. Access to real market data is subject to conditions but can be obtained from real estate agents. Most of the studies utilize oﬀer prices rather than transaction prices (Cheshire and Sheppard, 1995). In Scotland, the data were available to the public for more than two hundred years, but now such data are no longer collected. In France, there are no oﬃcial land transactions and prices equivalent to the OAP in Japan because the government is not willing to publish information on individual transactions gathered by the real estate surveyors. However, in some regions, surveyors’ associations or urban planning agencies collect transaction prices though they are not allowed to publish information on individual sales (only average figures in diﬀerent zones). The oldest serial data are those of the Toulouse metropolitan area (going back to 1981) collected by the Agence d’Urbanisme le la Région de Toulouse (AUAT). There are

59

Estimation of hedonic price function

reliable and comprehensive data on Paris, too, provided by the Chambre des Notaires (Association of Surveyors), for land and real estate transactions (beginning in the 1990s). There is another type of data concerning land and real estate delivered by the General Tax Department [DGI (Direction Générale des Impôts)]. These are national data starting from the 1970s but are not as reliable as the former data, because they are not based on transactions, but formulated by professional appraisers. There is much oﬃcial data on housing (Ministry of Transport and Construction), that is, house prices and rents, but none on commercial property. As for disaggregated data which the hedonic price method requires, this should be collected from real estate agents, private information sources (Jones Lang Wooton, for example), or from information obtained by local agences d’urbanisme (town-planning agencies). Bias of Assessed Prices Although market price data are important for estimating hedonic price functions, often only assessed values are available in a region or a country. It is meaningful to know the characteristics of assessed price data and compare them with the actual transaction data. Assessed price data are usually obtained from a typical lot of land or housing in an area because they are used as a benchmark of prices in the area. Thus the attributes of an assessed parcel of land tend to be the most common examples of value or of quality in the area. We examined the tendency of convergence of the assessed prices (x) in March 1989 by regression to the transaction prices (y) during July 1988 and January 1989, located near the assessed sample points at Setagaya ward in Tokyo. The result from 64 samples is: transaction price1.21 assessed price95

R0.89.

(7.1)

Also, the regression without a constant is: transaction price1.02 assessed price

R0.76.

(7.2)

This means that the average of both prices is the same, but the transaction price of the land with high assessed prices is higher than was expected by the assessed value. Thus, it is very possible that if we estimate the hedonic price functions using assessed prices we might

60

The economic valuation of the environment and public policy

underestimate the implicit price of a site-specific attribute which is normalized in assessed data, such as the width of the roads or the view from the property. In addition to this, we should recall that the time-series data of assessed prices may include a serious bias because of inertia in the time horizon. We have already demonstrated that the start of the bubble in the land market in Tokyo was misreported by the assessed price index and that in fact it started in 1984 rather than 1986 (see Hidano and Yamamura, 2001; Hidano, 2000a; and Hidano et al., 1995). Possible Bias in Transaction Data Transaction prices can sometimes have biases if land is traded under special conditions. Thus it should be noted that if we use transaction data, we might have to check the characteristics of individual transactions to identify unusual cases, such as whether a buyer is the land owner of adjacent land, or belongs to the same group of companies as the seller, or represents the public sector. In those cases, the prices may have some bias. We must also be very careful in using transaction price data of land, which are sometimes estimated as the total property price minus the estimated building value on the lot. In this case, the estimation of the value of the building by individual assessors may aﬀect the land price dramatically. We should use the total property price data or omit them altogether. An individual assessor’s subjective judgement may cause a bias in the hedonic analysis. Housing Price Transformation into Land Price As we discussed vis-à-vis Scotchmer’s comments in Chapter 2, we can glean much viable information from land price data as opposed to house price data, especially in cases where we wish to analyse the value of the environment and the benefits of public projects. It is possible to convert house prices into land prices. One of the methods is to estimate land price by subtracting all values related to housing from the total property value: Land pricetotal property price – assessed housing (business or commercial facilities) prices.

(7.3)

In order to estimate house values, we have to carry out a consistent procedure, utilizing assessors’ or real estate agents’ handbooks to esti-

Estimation of hedonic price function

61

mate the hedonic value of each attribute of housing. These manuals are available in most developed countries. An example of this adjustment procedure was partly implemented in the data on noise analysis in flats in Tokyo in the next chapter.

EXPLANATORY CHARACTERISTICS OF A PROPERTY The variables of the hedonic approach are dependent on a commodity in which we are interested. However, there are common categories of the explanatory variables, one being the set of attributes of a commodity. Another category of variables is the time of observation when the price and the attributes of the commodity should be determined. As we discussed in the previous chapters, the hedonic approach must be based upon cross-sectional data. But in reality we face a situation in which we cannot find enough samples at the same time. Time adjustment with diﬀerent times will be discussed later for pooling samples. The attributes of a commodity are divided into three types: the first is a set of characteristics of the commodity itself, such as the size, the shape and the aspect of the land, or the number of rooms, type of facilities, heating system and so on for housing; the second is the set of attributes of the commodity which aﬀect the quality of housing or land from the outside, such as the width of a road or street, the quality level of adjacent housing, the quality and quantity of open spaces in the neighbourhood, the view from the property, the level of noise and so on; and the third is the general environment, including access to transport facilities, such as a railway station (which is so important in large urban areas in Japan), access to the interchange of major roads, or to shopping centres, and the risk of flooding or other natural disasters and so on. These variables, of course, diﬀer from culture to culture, country to country. We should study carefully the characteristics of real estate property from the viewpoint of consumer utility or production technology in the market we observe. Variables for a Residential Land Price Function Attributes of residential land in large urban areas in Japan and the sources of data are shown in Tables 7.2 and 7.3. It should be noted that

62

The economic valuation of the environment and public policy

Table 7.2

Attributes of residential land

Attribute

Unit

Source

Plot size

Square metre

Transaction record

Width of road

Metre

Transaction record or observation

Floor to land ratio

Percentage

Transaction record or map

Gas service

Dummy (yes 1)

Transaction record

Sewage service

Dummy (yes1)

Transaction record

Distance from nearest railway station

Metre

Transaction record or map

Time distance from railway station to CBD

Minute

Measured by timetable

Distance to large shopping centre

Metre

Measured by map

Upper-level housing area

Dummy (yes1)

Observation

Fronting a main street

Dummy (yes1)

Measured by map

Density of retail activity

Square metre

Chiikikeizaisoran (regional statistics)

No. of consumers within catchment area of retail centre

Number

Estimated

these variables are not necessarily obtainable from existing sources of data and we should observe major variables by visiting the land in person. We should emphasize the importance of this on-site observation which is not usually recognized in existing hedonic studies. Variables for Commercial or Oﬃce Land Use in Japan In every country or region, the institutional constraints for commercial and oﬃce land use are diﬀerent but it is useful to know the general variables which determine the price of land for commerce and oﬃces. Tables 7.3 and 7.4 indicate the variables in oﬃce and commercial land use in Tokyo. These data can be obtained by making an on-site survey

Estimation of hedonic price function

Table 7.3

63

Characteristics observed on a lot of land

Characteristics

Measurement and criteria

Inclination of the land

Observation

Direction of the land

South or other directions

Width of pavement

Direct measure 50 cm unit

Street plants

Including small plants

Grade of road

Major street or back street

Shopping area

More than 4 plots occupied by shops among 6 adjacent to the land

Open space

Existence of front yard of buildings for public use, well-maintained parks or open spaces

Elevated roads or railways

Existence of unattractive sights

Harmony of height of buildings

More than 8 buildings among 10 adjacent to the plot

Landmarks

Historic and symbolic structures with 50 metres or clearly visible

View of landscape

Distant view of large parks, rivers, impressive buildings

Electricity and telegraph poles

Installation of underground facilities

of the characteristics of each lot, taking photographs and measuring landscapes, observing the actual socio-economic geographical conditions, and by using precise maps and Geographic Information System (GIS).

MAKING VARIABLES FIT THE REALITY Since the explanatory variables in a hedonic function should reflect consumer preferences, we have to develop more realistic variables than just observed ones.

64

The economic valuation of the environment and public policy

Table 7.4

Other variables for commercial and office land in Tokyo

Variable

Unit

Source

Width of road

Metre

Transaction record or observation

Lot size

Square metre

Transaction record

Length of lot fronting the main road

Metre

Transaction record or observation

Shape of lot

Dummy (square shape 1)

Transaction record or map

Corner of road

Dummy (corner 1)

Transaction record or map

Distance to nearest railway station

Metre

Transaction record or map

Land-use control

Dummy

Transaction record or map

Distance from Marunouchi business district

Metre

Map

Distance from Kasumigaseki

Metre

Map

Density of small buildings

Dummy

Map

Density of workers

Person per hectare (spatial unit: chome (block))

Jigyoshotokei (Management and Coordination Agency)

Density of retail outlets and services

Person per hectare (spatial unit: chome (block))

Jigyoshotokei (Management and Coordination Agency)

Retail sales per area

Ten thousand yen per square metre (spatial unit: chome)

Tokyo no shogyoshuseki-chiiki (Tokyo Metropolitan Government)

Estimation of hedonic price function

65

Institutional Restrictions We shall now explain how to formulate these variables, taking Japan as the example. Although zoning and land-use controls are not necessarily eﬀective in Japan, the potential use of land in the CBD is greatly restricted by the regulation of the maximum floor to land area ratio (FL ratio) under the building codes. This ratio is oﬃcially assigned to every lot in city areas. In addition to this, the FL ratio is further due to control over the vertical line of building façades and the incremental bonus to lots that have a 6 to 12 metre wide road frontage within 70 metres of a road with a width of 15 metres or more. A modification of the oﬃcial FL ratio is necessary to measure the potential use of the land. We calculated the eﬀective FL ratio of each lot, taking these regulations into consideration (see Chapter 8, and Hidano, 1997; Hidano et al., 1995). Reliable Distance Measure on Foot It is interesting to note the importance of accurately measuring the walking distance from a lot to significant places such as railway stations in megalopolises such as Tokyo, New York, London and Paris. We can often see the way that the distances are measured by GIS, but we should take account of the fact that walking routes are often diﬀerent from those chosen by GIS because digital maps may not consider footpaths. So we recommend using a cilbimeter on a detailed map to measure the distance. This method is also important for measuring distance by car in cases where the hedonic approach applies to areas with one-way restrictions in traﬃc. Introduction of Accessibility Measure In addition to walking distance, we have to introduce multimodal distance when applying the hedonic approach in a region where several types of transport may be used such as a car, a bicycle or public transport which may include a bus, a rapid transit vehicle, or a train. In a national or international context, we may need to consider air transport, inter- or intra-national high-speed rail transport and highways. Under these conditions, we have to consider the price of a trip, for example, public transport fares, fuel or other expenses for private vehicles, and duration of travel, all at the same time. A generalized

66

The economic valuation of the environment and public policy

cost concept is, thus, introduced as a distance measure of mode m between i and k, that is q m ik, defined: m m qm ik P ik Wt ik

(7.4)

Where: Pm ik: W: tm ik:

Transport cost (fare and so on) of transport mode m between i and k Time value Time of travel by mode m between i and k.

We usually adopt the minimum value of this generalized cost of available modes of travel as a distance. This distance is good for analysis in a small town or city, or a region where only one centre exists, but cannot describe the multicentre situation in an area. For this, it is necessary to introduce accessibility measures in hedonic analysis, especially in large urban areas. For example, Tokyo metropolitan region has more than 40 million residents and at least five centres, namely Tokyo, Yokohama, Kawasaki, Chiba and Urawa-Oomiya within the region. In Tokyo district, CBDs are located in diﬀerent areas, such as Marunouchi, Kasumigaseki, Ginza, Nihonbashi in Chiyoda and Chuo wards, Aoyama, Roppongi (Minato Ward), Shibuya, Shinjuku and Ikebukuro, among others. The city is far from being monocentric. The conventional measure of the distance to the CBD is hardly applicable to Tokyo. We thus introduce an accessibility measure to identify the location proximity to urban activities. The functional form is changeable, especially the description of distance q’s impact on the magnitude of relationships between the two points as follows: Gravity form

1/q

Exponential form exp (q) Then one typical accessibility expression of land i is: ACCi activity at 1/q i1 …activity at j/q ij

(7.5)

But partly because of the need for normalization of the index by an area AI in which land i is located, and partly because of consider-

67

Estimation of hedonic price function

ations of available labour, the demand for shopping facilities, and firms’ agglomeration eﬀect due to the complexity of urban activities, we can define the accessibility of commercial and business land in large urban regions as the sum of commuting accessibility, accessibility of demand of commerce and accessibility to other production activity, taking into account the share of an area I as follows, ACCi wcACCic wpACCip wtACC if ACC ic 1/AI ACC ip 1/AI

ACCif 1/AI

j

j

j

(Tj /q2ji )[(SI /q2ji )/

(S /q

(Nj /q2ji )[(ZI /q2ji )/ (Sj /q2ji )[(SI /q2ji )/

k

2 )] jk

k

(S /q k

k

2 )] jk

k

(Z /q k

(7.6)

2 )] jk

(7.7)

(7.8)

(7.9)

where ACCic is accessibility of land i for commuters, ACCip is accessibility of land i for shopping and other personal activities, ACCif is accessibility of land i for firm activities, wc, wp, wf are weights of each activity calibrated by the best-fit criteria or exogenous values such as the share of trips, AI is the area of zone I which includes land i, Tj is the number of secondary and tertiary sectoral workers living in zone j, Sj is the number of secondary and tertiary sectoral workers working in zone j, Nj is the figure for population in zone j, Zj is the number of retail and service workers working in zone j and qji is the minimum generalized cost from land i and zone j of rail or car mode defined as travel cost plus travel times multiplied by time value. These values are calculated using the data at the exact transaction time. It should be noted that even the minimum generalized costs should be obtained by transport network search procedures at the time of the transaction in order to estimate the accessibilities accurately. Assignment of Site-specific Value We should consider the problem of assigning the site-specific values to attributes of land in order to estimate implicit prices of an amenity (or a disamenity) accurately in cases where the level of the environment diﬀers considerably from lot to lot. The environment could be described in terms of noise, air pollution, view of a beautiful landscape

68

The economic valuation of the environment and public policy

and so on. In some hedonic studies, because of the diﬃculties of data collection, average values for an area or a neighbourhood rather than site-specific actual observation values are adopted and assigned to the value of an attribute of land. This, however, usually introduces a serious bias into the estimation of the implicit prices. This can be illustrated in the readily understood examples of a lot adjoining a main road, where the level of air pollution would be high, and one only ten metres away from the road where the level of air pollution would be considerably less if it is surrounded by relatively tall buildings in central Tokyo. It should be emphasized that using the estimated amenity value without actual observations of a particular lot, will not produce an accurate environmental valuation.

HEDONIC PRICE FUNCTION AND UNIT AND FORM OF VARIABLES Unit of Dependent Variable In the estimation of the hedonic price functions, the choice of a unit of price data is not a simple question but is rooted in basic and very important problems of the hedonic approach from both the theoretical and practical viewpoints. Most hedonic housing price studies adopt a composite price of a property as a whole, as do some hedonic land price analyses. As Scotchmer discussed in her excellent papers (1985, 1986), and we argued in Chapter 2, a consumer can choose a housing size and a set of attributes of amenities in the long-run. This leads to the problem of multicollinearity among explanatory variables because of the lack of suﬃcient variation in data, to separate the eﬀects of land or housing size and an amenity in a hedonic price function. It is therefore recommended that a unit price should be used as a dependent variable. But if we are interested in short-run cases where lot sizes and the levels of amenities are given exogenously to the consumer of housing or land, we may use composite prices under the condition that we can collect data samples whose lot sizes are the same and whose amenity levels are diﬀerent (see Chapter 3). Adjustment of Real Estate Price Multiperiod Data When we have to use property prices from multiperiods, we should convert the nominal value into real value at a fixed time using defla-

Estimation of hedonic price function

69

tors. However, it is very diﬃcult to find an appropriate deflator for housing and land prices because it is usually developed for national statistics, which cannot adjust the prices at the regional or city level. Thus the use of dummy variables is generally recommended to depict the time. Functional and Variables’ Form and Estimation It is always claimed that the results of the hedonic approach are highly dependent on the form of the hedonic price function and the set of variables used in the function. This may be true if the value of the environmental amenity outside the range of the data collected is estimated. But the careful selection of form and variables for a hedonic price function usually gives us a good estimate of the value whenever we estimate the value within the range of the level of an amenity which we observe from reality. There are several functional forms commonly used for a hedonic function: Linear: Semi-log: Double log (log-linear):

ya0 a1x1 . . .aj xj

(7.10)

ln ya0 a1x1 . . .aj xj

(7.11)

ln ya0 a1 ln x1 . . .aj ln xj .

(7.12)

Box–Cox ( yb 1)/ba0 a1 (x b11 1)/ transformation: b1 . . .aj (x jbj 1)/bj

(7.13)

when b, bi is not zero; if b is zero, then ( yb 1)/b is ln y; if bi is zero, then (xibi 1)/bi is ln xi. Parameters are estimated by the ordinary least squares (OLS) regression or the maximum likelihood estimation. The functional forms and a set of variables are selected using fitness criteria such as adjusted R2, and the maximum likelihood ratio, and by the distribution of errors such as mean absolute per cent error (MAPE). Individual variables are examined using t-statistics and the sign test of the coeﬃcients of a variable. Although the Box– Cox transformation form is said to be one of the most flexible functional forms and

70

The economic valuation of the environment and public policy

usually recommended for finding appropriate functional forms, the other three forms are often adopted because there is little diﬀerence from the Box–Cox results, if we consider the criteria mentioned above. Of course, there are other types of complicated functions which can incorporate non-separable preferences, such as quadratic form, generalized Leontief functions and so on (see Deaton and Muellbauer, 1983; Greene, 2000). These, however, are not used in hedonic estimations except in methodological developments of the estimation techniques, because they can handle only three, or at most four, variables in the functions. They are far from having a practical use for hedonic function estimations in environment and public policy evaluations. Even the Box–Cox transformation sometimes suﬀers from a serious problem of unrobust estimation of coeﬃcients since the method seeks the highest fitness, which may not necessarily give us the most stable parameters when some data are added or deleted. In addition, when we use this method in the exploration estimation, the values tend to be out of range. So the most important point for the estimation is not to cling to Box–Cox transformations, but to find an appropriate form for the explanatory variable x, usually amenity variables, that we are interested in.

NOTE 1. I am indebted to Christine Whitehead for the UK information, and to Vincent Renard and Natacha Aveline for that on France.

8.

Hedonic price method in estimating the value of environment and institutional regulation

INTRODUCTION In this chapter, we examine several cases concerning the estimation of environmental values and the value of institutional measures using the hedonic price method. One of the strengths of the hedonic approach is that it enables us to depict the preferences of past consumers by a simple procedure using market price data. We can see the changes in consumer preference and the dynamics of a society from these analyses. After giving an example of this, we go on to present various estimations of implicit prices of environment and institutional regulation.

CHANGES IN CONSUMER PREFERENCE ON AN UPPER-CLASS HOUSING ESTATE IN TOKYO, 1934 AND 1985 In any large urban areas in the world, there are several prestigious, exclusive or upper-class housing estates. Denenchofu, which developed in the 1920s, and literally means garden suburb in Chofu, is a good example in Tokyo. We shall examine the preference changes of the people on this housing estate during 1934 and 1985 (Yamaguchi and Hidano, 1988, cited in Hidano, 1997). We collected the sales price data in 1934 for the estate from a real estate agent’s brochure because we did not have any oﬃcial detailed site-specific data for that year. In order to understand the changes in preferences, we use assessed land prices from a map of 1972 and of 1985 published by the Tokyo Real 71

72

The economic valuation of the environment and public policy

Estate Association, shown in Figure 7.1. The map shows site-specific land prices in almost every block in Tokyo. The results of the OLS regression of linear hedonic price functions are shown in Table 8.1. The main explanatory variables are the width of the road, the existence of a pavement, the existence of trees in the street, the distance to the local park and the distance to the railway station. We can ascertain the preference changes by examining the changes of elasticity of these amenities (Table 8.2). The 1934 results are interesting compared with our present-day perspective. The sign of the coeﬃcient of the width of a road is negative and that of the distance to the local park is positive. This means that the price of a lot decreased when the width of the road in front of the lot increased and the distance to the park decreased. But we can identify the reasons: at the time the roads were not paved and on windy days sand was blown into the houses; and the local park had no facilities and was not considered a suitable place to visit due to juvenile delinquency. The most important reason, however, why a consumer did not give much weight to access to the park was that his land was large enough to do most things in his own garden and he did not need to walk to the park. The results estimated are understandable in the light of the content analysis of the community journal Ichou (Ginkgo trees) at the time. But the situation had changed by 1972, when people enjoyed the most rapid economic growth in Japan. The elasticity of the distance to the railway station was very high at the time. Access to transport services was very important for businessmen to be able to commute to their oﬃces during the rush hour. The decline of the elasticity of trees in the street can be interpreted in terms of the value shifts towards economic eﬃciency. In 1985, again, preference changes became obvious in several respects, that is, the importance of road width, access to the park, and the existence of street trees increased compared with the earlier period. This might be a reflection of the fact that land speculation after the Second World War had inevitably forced a number of residents to subdivide their lands in order to pay the high inheritance tax when they inherited the land from their forefathers. Lot size in 1985 had declined; there were no more large gardens and few plants. There were scarcely any open spaces where residents in Denenchofu could enjoy the sunshine on their own property. Rather than being used for traﬃc, the front roads had become a priceless open space for residents. As to street trees, some of the cherry trees there were cut down in 1981, destroying the pleasant view as described in the journal.

73 0.878

R2

t-statistics are in parentheses.

50

38

Sample size

Note:

39.77 (18.04)

33.69 (4.60)

Constant

0.544

0.66 (0.37)

7.40 (1.97)

A pavement (dummy)

0.833

58

248.6 (23.87)

0.42 (0.05)

46.05 (5.89)

0.013 (1.12)

1.74 (0.72)

0.004 (1.28)

– 10.85 (2.42)

Distance to water supply facility

6.20 (0.52) 0.041 (1.92)

0.002 (0.47)

6.20 (0.52)

–

9.82 (1.86)

0.92 (1.64)

0.01 (3.54)

A street tree (dummy)

0.02 (1.42)

3.44 (1.49)

0.69 (0.17)

Commercial zone (dummy) 0.01 (2.29)

1.19 (1.12

4.61 (1.84)

A corner (dummy)

Distance to shops

1.19 (1.11)

4.49 (1.80)

A slope (dummy)

Distance to symbolic facilites

0.03 (0.1)

0.02 (0.06)

Width of road

0.071 (4.54)

0.028 (1.18)

0.004 (1.11)

0.007 (1.54)

0.005 (0.81) 0.008 (0.97)

Distance to local park

1985

1972

1934

Regression results for Denenchofu, 1934, 1972 and 1985

Distance to railway station

Variable

Table 8.1

74

The economic valuation of the environment and public policy

Table 8.2

Change of elasticity1 in Denenchofu, 1934, 1972 and 1985 1934

1972

1985

A street tree

0.27

0.05

0.22

Distance to the park2

0.004

0.023

0.068

Distance to the railway station3 Width of

road4

0.013 0.004

0.22 0.0069

0.15 0.035

Notes: 1 Measured at mean value of land price. 2 Measured at 0.2 km. 3 Measured at 1.1 km. 4 Measured at 8 km.

AMENITY VALUE Value of a Riverside Park and Flood-risk Value Among residential amenities, the existence of trees, and of a road as an open space, and access to modest parks seemed important at the time of the previous analysis. Do consumers have a special preference for a particular type of park? Let us consider these aspects. A river landscape always provides some stimulus because of the running water. The landscape may differ upstream, midstream, downstream or at the mouth of the river. But rivers in Japan have changed considerably during the past 50 years since they have been contained within wall-like banks in order to prevent flooding. These artificial banks destroyed the amenity areas alongside the rivers and streams; they now look very ugly, and prevent access to the rivers. But recently there have been some rehabilitation projects, which have tried to reproduce the former landscape by developing small riverside parks. However, there is still flooding from heavy rain, and the area has to be protected with high banks due to the inadequacy of the pumping and drainage system. The risk of flooding is currently still quite high. In order to evaluate both this risk and the benefit of the riverside parks, a hedonic analysis was carried out (Yokomori et al., 1992, cited in Hidano, 1997). We collected data on 121 land transactions in Setagaya ward in Tokyo during January 1988 and June 1989. The value of a riverside park was measured by access to the park and the risk of flooding was

75

Hedonic price method

accessed by a compound index of the time of flooding and the distance from the flooded areas. The final risk measure is: Risk indexk (year of flooding k–1977) (10 – distance in metres from the flooding k area/10).

(8.1)

It should be noted that both the time and distance items of the index are set as non-negative values. The results of the regression are shown in Table 8.3. It is interesting to note that access to parks in general, rather than riverside parks in particular, may not be valued positively by residents. Conventional parks seem to lose their attractiveness in large urban areas. The changes of value of the riverside parks and the costs of flood risk are shown in Table 8.4 and Figure 8.1. Table 8.3 Regression results for riverside parks and flood risk in Setagaya Variable (xk )

Coeﬃcient (t-statistics)

1. Sewage service area (dummy)

21.15 (2.4)

2. Restricted zone for residential environment (dummy)

44.51 (2.7)

3. Time of transaction – 1989

20.69 (3.1)

4. Width of road (m)

7.40 (6.6)

5. Distance to railway station (m)

52.60 (7.4)

6. Distance to riverside parks (m)

15.78 (2.2)

7. Distance to conventional parks (m)

27.78 (7.1)

8. Risk index

6.99 (1.8)

Constant

375.71

Sample size

121.01

Coeﬃcient of determinant

110.62

Note: Unit land price (10,000 yen/m2) a0 a1x1 ... a5lnx5 a6lnx6 a7lnx7 a8lnx80.2.

Table 8.4

Value of riverside park

Distance (m)

100

200

300

400

500

600

1000

Benefit (10,000 yen/m2)

36.3

25.4

19.0

14.5

10.9

8.1

0

76

The economic valuation of the environment and public policy

70,000 60,000

1 year after flooding 3 years after flooding 5 years after flooding 7 years after flooding 9 years after flooding

yen/m2

50,000 40,000 30,000 20,000 10,000 0 0

10 20 30 40 50 60 70 80 90 Distance from flooding area (m)

Figure 8.1

Cost of flood risk

Value of Access to a Large Park and the Value of Railway Services It was suggested in the previous study that conventional parks in large urban areas may become less-desired urban facilities. But it is questionable whether all parks are seen in this light. Thus we shall examine the value of well-designed, medium to large-sized parks in Tokyo (Hidano and Takebayashi, 1992, cited in Hidano, 1997). The parks in the study are 10 ha or more in area. In addition, we shall evaluate the services of a rapid transit system, or a railway system in large urban areas, in view of the importance of reducing automobile traﬃc, which causes severe air pollution through excessive NOx and COx emissions. The study involved collecting the price details of a sample of 193 land transactions in west Tokyo in 1988. A detailed on-site survey of individual lots was also carried out to evaluate the height of housing adjacent to a lot, the layout of the land, the view from a lot as seen from the adjacent road, and the density of the neighbourhood environment. Accessibilities are measured from both the commuter’s and the consumer’s viewpoint. They are defined as the inverse distance weighted by the actual number of trips, as follows: ACC pimjOD pIjm /(qijm)ap

(8.2)

Hedonic price method

77

where ACC pi is the accessibility of trip purpose p to land i, p is commuting or shopping, m is the mode of transport (train or car), ODpIjm is the actual number of trips of p purpose by mode m between I and j where I is an area that includes land i, and ap is 0.7 for commuting and 0.2 for shopping. The regression equation is as follows: ln (unit land price, per m2) 0.5 0.5 a0 a1x 0.1 1 a2 x 2 a3x 3 0.1 0.2 a4x4 . . .a7x 7 a8x8 . . .a11x 11 a1210x12/200 a13x13.

(8.3)

The results of the regression are shown in Table 8.5. The positive value of a medium to large-sized well-designed park is evident in this analysis. It should also be noted that the neighbourhood landscape (adjacent housing quality), and view from a lot should have a high value among the amenities. Value of a View of a Symbolic Landscape: The Case of Flats in Tokyo It is well known that looking at beautiful landscapes such as lakes (Blomquist, 1988), forests, the sea, mountains and countryside always has a positive value as discussed in the previous section. We shall show the amenity value of a view in urban areas (Shimizu et al., 1988). The study involved collecting the price details of more than one hundred flats that had been sold in Setagaya ward in Tokyo between 1983 and 1985. As to a view, two measures were observed onsite: one was the extent of the view, judged according to photographs taken from the flat, and the other was a list of what could be seen from the windows as set out in a questionnaire to residents. In this study, in order to exclude the impacts of attributes of a flat on the transaction price, the prices were normalized to the price of a standard flat with elevators and modest maintenance, using an assessors’ valuation list of the structure and maintenance of a flat. We also measured traﬃc noise using an L50 measure in front of the actual entrance door, or corridor of an individual property. A linear regression for the unit price of a flat in terms of 10,000 yen (1985 year price) per square metre was carried out with 57 samples where we could observe the environmental and structural variables. The results are shown in Table 8.6.

78

The economic valuation of the environment and public policy

Table 8.5 Regression results for access to large parks and railway services Variable (xk)

Coeﬃcient

1. Accessibility of commuting facilities

4.95 (3.8)

2. Accessibility of shopping facilities

1.74 (3.2)

3. Adjacent housing quality (good3, fair2, poor 1)

0.218 (3.0)

4. South-facing direction (dummy)

0.049 (1.5)

5. View from land (dummy)

0.056 (1.9)

6. Use of adjacent lands (housing1)

0.060 (2.2)

7. Width of road (m)

1.51 (4.1)

8. Corner (dummy)

0.057 (1.9)

9. Unsuitably shaped land (dummy)

0.129 (4.1)

10. Housing zone (dummy)

0.189 (3.3)

11. Distance from waste-treatment plants, elementary schools and manufacturing plants

0.103 (4.1)

12. Distance to large parks (m)

0.262 (2.6)

13. Chuo railway line area (dummy)

0.108 (3.0)

Constant

1.609

Sample size Coeﬃcient of determinant Note:

193 0.687

t-statistics are in parentheses.

It is interesting that the value of a view of large parks and a river was more than 27,000 yen and the cost of noise of 1 dBA was 1,500 yen. These are 6.3 and 0.35 per cent of the average price of a flat, respectively. Value of a Green Residential Environment and Negative Value of the Building Façade Although the view of a beautiful landscape is highly preferred by consumers, greenery in the neighbourhood should also be evaluated as a benefit. The study was thus to design and examine the values of the

79

Hedonic price method

Table 8.6

Regression results for view and noise in Setagaya

Variable Distance to a railway station (km) Exclusive housing zone (dummy) Commercial zone (dummy) Corner (dummy) Good neighbourhood environment (dummy)

Coeﬃcient 5.41 (5.55) 3.12 (1.50) 3.07 (2.54) 2.84 (2.35) 4.88 (4.60)

Floor area (square metre)

0.03 (0.85)

Noise (dBA at L50)

0.15 (2.35)

Scale of open view (good1, fair (70%)0, poor (50%)1) View of large parks and the river (dummy)

1.33 (1.85) 2.73 (1.79)

Constant

47.31

Sample size

57

Coeﬃcient of determinant Note:

0.709

t-statistics are in parentheses.

characteristics of a local green environment (Hidano and Kameda, 1997). Figure 8.2 depicts the schematic expression of externality of attributes of a visual neighbourhood amenity. The characteristics of ‘green’ space can be classified as any greenery in a garden, plants on garden walls, tall trees in a garden, or trees in the street. A building façade may have a positive or negative impact on the environment according to its level of beauty and whether it is in harmony with the environment. The low-quality level of use of neighbourhood land, such as an ugly parking lot, causes negative externality towards the adjacent land. Poor quality or unattractive walls of a lot can create a negative influence. We shall discuss the value of these attributes in detail. The price data for 102 land transactions were collected in Setagaya ward in 1995. We conducted an onsite survey in November 1996. Measurement of the visual environment Most studies undertaken using the hedonic analyses of a local green environment have utilized a subjective judgement of the quality and

The economic valuation of the environment and public policy

Building Openness of space created by the setback of a building

Building

80

Beautiful building Greenery in garden Tall trees

Block walls

Medium- or high-rise flats

Land under observation

Parking lot

Lack of sunshine positive externality negative externality

Figure 8.2

Externality of neighbourhood amenity

quantity of the green environment that cannot distinguish the value of each attribute and which may not be comparable with the results of other studies. This study adopted the method of analysing objective visual data taken by a video camera. We filmed a scene in front of a 40 m lot at angles of 0, 20, 40 and 60 degrees, scenes of a street where a lot faces two different directions, and scenes of adjacent 5 m lots next to the land taken from the opposite side of the street. The scenes were digitalized by counting the actual space occupied by greenery or trees; the façade of a structure including buildings, garages and walls; sky; and others including the road surface, parking areas, or any areas of bare earth. These spaces are four types of objects that are perceived visually and evaluated as a percentage of the whole scene as observed by the digital data. We then converted these pecentages into a human response index based upon the findings of existing literature of green environment studies. They are also converted to a green index, weighted according to the road frontage, as follows: Green index 1k exp [0.15 (green share of kth angle – 30)] Green index 2 exp [0.15 (green mean share of 2, 3, 4th angle – 30)]

Hedonic price method

81

Green index 3 ln (green mean share of 2, 3, 4th angle 1) Green index 4 k exp [0.15 (green share of kth angle – 30)] ln (length of a lot) Green index 5 exp [0.15 (green mean share of 2, 3, 4th angle – 30)] ln (length of a lot) Green index 6 ln (green mean share of 2, 3, 4th angle 1) ln (length of a lot) Façade index 1 [ln (façade share)] / (mean distance from the buildings oppositewidth of a front road) Façade index 2 [ln (façade share)] / (mean distance from the buildings opposite 1) Façade index 3 exp (façade share /2). (8.4) The quality of the green environment and wall structures within 40 metres opposite the lots and on a road that borders adjacent lots are also considered, according to the height and species of trees, and the materials used for walls. The indexes of these qualities are constructed as a sum of a dummy variable: Quality index 1a high treea wall with vegetation Quality index 2a high tree – a wall with vegetation Quality index 3a high treea deciduous tree a tree canopy over a road Quality index 4a high treea tree canopy over a road– a wall with vegetation – a block wall Quality index 5a high treea tree canopy over a road – a deciduous tree – a wall with vegetation– a block wall. (8.5) Other variables In addition to the visual neighbourhood environment, we introduce several variables to describe the site, the neighbourhood and district characteristics. The sunlight conditions are assessed using a surrogate index, that is, the existence of medium or high-rise flats in a fourstoreyed or higher building within 50 metres in a southerly direction. Accessibility measures are defined as the sum of commuting and

82

The economic valuation of the environment and public policy

shopping accessibility because the area is basically a residential area. Each accessibility index is the inverse minimum generalized cost of rail and car between i and j weighted by the share of j destination from I zone which includes lot i. ACCi ACC icACC is

(8.6)

(1/q )[(S /q )/(S /q )]} ACC { (1/q )[(Z /q )/ (Z /q )]}, ACCic { s i

ij

j

j

ij

j

j

ij

ij

k

k

k

k

ik

ik

(8.7) (8.8)

where subscripts c and s stand for commuting and shopping respectively. It should be noted that these accessibilities are defined as an accessibility from residential land i which are different from the access defined in the previous chapter. Characteristics of the data and the regression results Finally, we give the distributions of the values of the variables of 94 samples for which the complete information is available and summarized in Table 8.7. The results of linear regression by OLS are shown in Table 8.8. The correlation among selected variables is less than 0.3. The selected elasticity evaluated at the mean price of land is shown in Table 8.9. It is clear that the elasticity of environmental amenity should not be higher than the transport ACC. But we must bear in mind that the elasticity is evaluated at the mean value of variables in this table. If the impacts of these variables are of a non-linear nature, the results might differ from those shown in the table. Environmental green value and value of setback The marginal values of a green environment and the negative value of a façade due to a 5 per cent increase in the share of each variable are, thus, shown in Figures 8.3 and 8.4. These figures are very meaningful in terms of understanding the present environmental situations in which the share of green vegetation space is so small and the building share is so large from the viewpoint of environmental externality. The external values of tall trees and trees covering a road are 43,000 yen/m2 or 6.9 per cent of the average land price. Although the marginal values are high in the better environment, the reality is that this situation could never be achieved. This is a typical example of the failure of the market mechanism, which cannot internalize the

83 10.9 12.8

Distance to the building to the south

Length of a lot fronting the road 5.9

0.106

Medium and high-rise building

Mean of the distance from a road to each building

1 43.5

4.31 10.1

0.138

Wall with plants

4.0

21.9

0.043

Length of parking lot

0.31

0.287

Block wall

15.0

0.347

0.203

0.455

88.2

1

1

1

1

1

1

1

Tree canopy

0.468

0.319

0.499

0.447

67.7

Deciduous tree

Sky share (%)

83.3

0

0

0

0

0

0

0

0

0

0

12.8

4.8

0.4

22.45

120.25 55.9

Min

Max

Tall Tree

11.6

43.7

Façade share (%)

12.8 14.6

17.1 37.6

Green share (%)

15.6

62.5

Unit land price (10,000 yen, 1995 price)

S.D.

Mean

Distribution of major variables of a green environment in Setagaya

Variable

Table 8.7

84

(continued)

Note:

S.D. is standard deviation.

Accessibility (ACC) 0.000352

0.000042

369

Distance to a large hospital

441

0.368

0.296

460

0.16

Slope facing in a southerly direction

821

0.095

Proximity to schools (within one block)

0.246

1,050

0.064

Risk of flooding (50 m from a river or in the area along Tama river)

0.358

Distance to a medium-sized or large park

0.148

Facing a road in southerly direction

0.264

2.28

899

0.074

Distance to a railway station

2.17

A lot facing only a private road

46

128

Depth to length ratio

206

241

2.98

S.D.

Lot size

5.52

Mean

Oﬃcial floor to land ratio

Width of road

Variable

Table 8.7

66

1,463

0.000483

2,160

1900

0.000275

13

0

0 40

2210

0

0

0

0

0.47

1

1

1

1

1

15

80

3

30 300

Min

Max

85

Hedonic price method

Table 8.8 Regression results for a green environment and building façade Variable Green index 2 Façade index 1

(t-statistics)

0.15

(1.99)

10.9 114,000

ACC Lot size

Coeﬃcient

(m2)

Facing a road in a southerly direction Risk of flooding Denenchofu, Seijyo (2, 5, 6 chome (Block)) dummy

0.015

(2.47) (5.13) (3.34)

12.2

(4.73)

20.3

(5.34)

15.0

(3.55)

Proximity to schools

8.61

(2.77)

Depth to length ratio (%)

2.93

(7.36)

Distance to a large hospital (m) Medium or high-rise buildings in southerly direction (dummy) Quality index 5

0.00499 9.15

(3.15)

4.32

(3.22)

Constant

31.3

Sample size

94

Coeﬃcient of determinant

(2.34)

(3.93)

0.713

Note: Dependent land price variable is measured in 10,000 yen (1995 price).

Table 8.9

Elasticity of a green environment in Setagaya

Variable

Value

Share of green (%)

0.0089

Share of building (%)

0.0153

ACC

0.642

Quality index 5

0.0162

86

The economic valuation of the environment and public policy

40,000

yen/m2

30,000

20,000

10,000

0

0

5

10

15

20

25

30

35

40

45

50

Percentage of green space

Figure 8.3 Marginal value of green environment (5 per cent increase in share)

yen/m2

15,000

10,000

5,000

0

0

10

15

20

25

30

35

40

45

50

55

Percentage of façade space

Figure 8.4 Maringal negative value of façade (5 per cent increase in share)

Hedonic price method

87

externality in the market. We recommend that we should find some social optimum level of a green environment using these values (see our proposal to internalize these externalities in residential areas, Hidano and Kameda, 1997, 1998).

ENVIRONMENTAL COST Value of Air Quality The cost of air pollution has been evaluated in many hedonic studies (Brookshire et al., 1982; Kanemoto et al., 1989; Nelson, 1978 among others; and a meta analysis by Smith and Huang, 1995). Kanemoto et al. analysed the cost of NOx and SOx in Tokyo using oﬃcially announced assessed prices of land. The results are shown in Table 8.10. They adopted several variables as Box–Cox transformation values. But some parameters of second-order variables of air pollution are not so significant. Thus the marginal values they calculated are ambiguous and problematic, that is, the negative benefit of a marginal improvement at a site of mean values of characteristics. The missing variables and correlation between explanatory variables should be considered. Cost of Noise Noise problems have been a basic nuisance issue in most countries for many years. Aircraft noise was one of the central political issues of the 1960s. The location of the third international airport in London was a notable example of this, where the political decision was made by considering the trade-off between transport accessibility to the airport and the negative value of the noise of aircraft for residents (see Pearce, 1982). There are many hedonic papers on transport noise, for example, Nelson (1982). Hidano et al. (1996), presented a method of measuring the value of the cost of traﬃc noise using land price data in urban areas in Japan. We collected the transaction price data for 191 land sales in 1993 in a residential area of Setagaya ward and carried out an on-site survey of noise and vibration levels caused by road traﬃc and railway services, and of other site-specific attributes in 1995.

88

The economic valuation of the environment and public policy

Table 8.10

Regression results for air pollution in Tokyo

Variable (xk )

Coeﬃcient

(t-statistics)

1. Distance to railway station (km) 2. Time from nearest railway station to the terminus (minutes) 3. NO2 (ppb) 4. NO2 (ppb) 5. SO2 (ppb) 6. SO2 (ppb) 7. Sewage service (dummy) 8. Chuo line (dummy) 9. Denentoshi line (dummy) 10. Joban line (dummy) 11. Keihintohoku line (dummy) 12. Soubu line (dummy) 13. Tobu line (dummy) 14. Toyoko line (dummy) 15. Exclusive housing zone I (dummy) 16. Exclusive housing zone II (dummy) Constant Sample size Coeﬃcient of determinant

0.000917 0.245

(0.93) (8.83)

0.00337 0.251 0.00247 0.112 0.0716 0.671 0.941 0.177 0.803 0.199 0.39 1.05 0.0633 0.0326 3.27 297 0.821

(1.54) (2.20) (0.26) (0.63) (1.57) (7.49) (9.51) (1.79) (7.85) (1.61) (3.62) (10.9) (1.10) (0.60) (2.22)

Note: ln (a unit price of land (100 yen/m2)) a0 a1(x12.09 1)/2.09 a2(x20.27 1) /0.27 a3x32 a4x4 a5x52 a6x6 . . .

Measurement, index of noise, and other variables The noise and vibration levels were measured in dBA in front of lots that were being traded. The noise levels during the day, evening and at night were transposed into an equivalent level of noise for a whole day as follows: Leq10 log (13*10 L1 /10 4 * 10L2 /10 7 * 10L3 /10)– 10 log 24. (8.9) Then an index of noise for human perception on disutility was calculated based upon noise research:

89

Hedonic price method

Noise indexexp [0.16 (Leq – 50)].

(8.10)

Among other variables, the residential accessibility was constructed by using actual travel behavioural data available from a person trip survey in the Tokyo region as an inverse generalized cost weighted by a share of trips from zone I which includes land i, ACCi ACC ci ACC is

(8.11)

purpose commuting, shopping mode car, rail ap j [(1/q ijmp )/(ODIj mp /p m j ODIpmj)]

(8.12)

Results of regression The results of the OLS regression are shown in Table 8.11. The marginal negative value of noise of 1 dBA is 5,300 yen/m2 evaluated at the level of 60 dBA of a lot costing 750,000 yen/m2 (see Table 8.11 Regression results for noise index and vibration in Setagaya Variables

Coeﬃcient

Noise index

0.00833 (2.32)

Vibration (L10) (dB)

0.00443 (1.62)

Width of road (m)

0.01969 (2.04)

Exclusive housing zone I (dummy)

0.134 (2.34)

Floor to land ratio (%)

0.002229 (4.19)

Distance to major roads (m)

0.00022 (2.66)

Quality level of a block (good2, fair 1, bad 0)

0.03787 (1.69)

Toyoko line (dummy)

0.149 (4.60)

Accessibility

4.779 (7.81)

Constant Sample size Coeﬃcient of determinant

6.307 191 0.575

Notes: 1. ln (a unit land price (1000 yen (1993 price)/m2) a0 k ak xk. 2. t-statistics are in parentheses.

90

The economic valuation of the environment and public policy

10,000

yen/m2

8,000 6,000 4,000 2,000 0

30

35

40

45

50 Noise

Figure 8.5

55

60

65

70 dBA

Marginal cost of noise

Figure 8.5). The marginal value of vibration of 1 dB is 3,300 yen/m2. The non-linear nature of the marginal cost of noise is clearly shown in Figure 8.5. Value of Water Quality We now turn to consider the cost of water pollution. It is well recognized that the rivers in large urban centres throughout the world have deteriorated considerably, due to pollutants from households, industries and agricultural farms, and also because of the lack of clean, fresh water from tributaries. We shall examine the quality of the water environment in Sapporo City and Ishikari City, Hokkaido in terms of economic value. In this area, the rivers are of two types: one is a group of large rivers, which the residents in Sapporo and Ishikari all recognize as major rivers of the region, that is, Ishikari River, Toyohira River and Barato River. The other is a group of small and medium-sized rivers, which are only perceived as rivers by the residents living near them. The level of the perception of these two types of rivers seems to differ. Thus we tried to identify the influences on the river environments separately.

Hedonic price method

91

The estimation of hedonic price function We collected transaction price data for 1,003 plots of land for housing use that had been traded from 1997 to 1999 by interviewing the real estate agents in Sapporo City across the whole region. None of the plots sold had any buildings. Thus, there is no need to consider the value of buildings. In order to measure the level of river water quality as accurately as possible, in October 1999 the water-quality data including the biochemical oxygen demand (BOD) measure at 209 points along all rivers in the region were collected. The values observed were converted to annual average values using the river authority’s equation. The adjusted BOD ranged from 0.6 to 26.3 mg/l. We then interpolated the observed values to all unobserved areas along the rivers in the study region to give a complete list of measurements. In order to identify the appropriate index to show the real perception of a river environment, we introduced the following accessibility measures to the river environment. We took the three nearest rivers among those perceived as rivers within 1 km distance of the residence. The index of these neighbourhood rivers is defined as: Index of water quality of neighbourhood rivers (IWQN) at i neighbourhood BOD ). 3j1exp (qijneighbourhood/laneighbourhood ) (lwq j

(8.13)

The index of the three major rivers, that is, the Ishikari, the Toyohira and the Barato, is also defined as: Index of water quality of three major rivers (IWQM) at i major BOD ). 3j1exp (qijmajor/lamajor) (lwq j

(8.14)

where q is physical distance, la is a distance decay parameter, lwq is perceptional threshold of quality over which people perceive the water environment as a desirable good. The distribution of major variables is summarized in Table 8.12. The parameters of water-quality indexes and transport accessibility are adopted by the highest fitness. The results of the regression are shown in Table 8.13. The values of BOD reduction by 1 mg/l of one of the neighbourhood rivers are estimated at 320 yen/m2 at the riverside and those of major rivers are 2,900 yen/m2 at the riverside and 1,000 yen/m2 at the land 10,000 m from one of the rivers.

92

0.046

Land use for small shops

633.4

489.8

Distance to elementary and secondary schools (m)

370.5

102.7

0.153

0.034

598.6

Land for flats 133.8

0.024

Length of lot to area ratio (m/m2)

0.150 4.26

Distance to a small hospital (m)

0.074

Width of road (m)

0.776

72.5

0.209

0.494

0.282

151.4

2.68

S.D.

Distance to a small park (m)

0.977 9.28

Lot fronting a public road

0.651

Direction index of roads fronting a lot (south 2, SE, SW1)

126.2

0.423

Non-square-shaped plot

Floor to land area ratio (%)

0.087

235.5

Legal category of a lot (field)

Lot size

7.55

Unit land price (10,000 yen, 1999 price)

(m2)

Mean

Distribution of major variables in Sapporo and Ishikari

Variable

Table 8.12

2,880

20

0 10

790

0

0.0043

3.64

0

0

40

0

0

0

45.5

1.20

Min

8,480

1

0.296

50

1

2

300

1

1

1

3,623

30.24

Max

93

1446.9

Distance from recycling, waste disposal and other facilities (m)

Note :

S.D. is standard deviation.

3.86

4.08 0.692

IWQN (la 1,000, lwq 0)

IWQM (la 10,000, lwq 3) 1.61

15.80

41.1

Public transport time distance to CBD (minutes; tram and bus doubly weighted)

558.0

596.3

Distance to large supermarket (m) 646.60

131.8

160.9

Access to major roads (m)

1.52

0

134

3,600

6.21

27.6

9

20

0 10

940 8,170

94

The economic valuation of the environment and public policy

Table 8.13 Regression results for water quality in Sapporo and Ishikari Variable Transaction 1997 first half Transaction 1997 second half Transaction 1998 first half Transaction 1998 second half Transaction 1999 first half Lot size (m)2 Legal category of a lot (field) Non-square-shaped plot Land use for small shops Floor to land area ratio (%) Direction index of roads fronting a lot (south 2, SE, SW 1) Lot fronting a public road Width of road (m) Length of lot to area ratio (m/m2) Land for flats Distance to a small park (m) Distance to a small hospital (m) Distance to elementary and secondary schools (m) Access to major roads (m) Distance to large supermarket (m) Distance from recycling, waste disposal and other facilities (m) Public transport time distance to CBD (minutes; tram and bus doubly weighted) IWQN (la 1,000, lwq 0) IWQM (la 10,000, lwq 3) Constant Sample size Adjusted coeﬃcient of determinant Note:

t-statistics are in parentheses.

Coeﬃcients 0.535 (0.99) 1.006 (4.28) 0.749 (3.20) 0.404 (1.79) 0.257 (1.11) 0.000976 (2.69) 0.456 (2.40) 0.439 (3.93) 0.702 (2.42) 0.00711 (7.31) 0.215 (3.09) 1.285 (3.63) 0.0537 (4.19) 9.97 (6.21) 2.321 (5.86) 0.00140 (2.50) 0.000367 (2.94) 0.000397 (2.13) 0.000568 (1.34) 0.000158 (1.11) 0.000181 (2.13) 0.0734 (16.44) 0.0319 (2.19) 0.292 (8.39) 7.724 (15.16) 1,003 0.624

Hedonic price method

95

VALUE OF INSTITUTIONAL MEASURES: THE REGULATION ON FLOOR TO LAND AREA RATIO IN THE CBD In previous sections we have shown some implicit economic values of regulations such as zoning, and restrictions on floor to land ratio. The regulations that we are now discussing can include any controls which restrict the degree of people’s use of any services or goods geographically, including, of course, accessibility. These institutional measures in fact have a strong influence on society. It is reasonable to examine the economic values of these measures using the hedonic approach if the regulations satisfy the conditions discussed in the theoretical part of this book, especially if they are local public goods. We shall now discuss more fully the value of floor to land area ratio as a typical example of institutional measures (Hidano et al., 1995). The floor to land ratio is a regulation which is intended to restrict the value of maximum floor area constructed and is used in relation to the area of a plot of land. This is a common measure in city planning in countries like the United States, Japan, East Asian countries, France and Germany. In Japan, all land in most urbanized areas within city planning regions is assigned this value oﬃcially. It is called an oﬃcial floor to land ratio. But in reality, especially in densely populated areas, the ratio is not an effective measure because other institutional measures in the building code laws are more restrictive. However, sometimes the law allows the building area to be larger for lots which locate near wide roads. The former restriction is designed to keep an open sky in densely built areas, and limits the space in which a building can be constructed to that measured from the opposite side of a road with a tangent of 1.5 over 1 towards the lot. Although the owner of the land has the right to use the space, it cannot be utilized by buildings. The concession for lots near wide roads, on the other hand, is to increase the floor to land ratio in order to give extra capacity for construction on a lot, according to the width of the front road, between 6 and 12 meters and to the distance from large roads, 70 metres and less. Thus the actual floor to land area ratio varies from lot to lot. These regulations are, in this study, translated into quantitative values. The most effective value is chosen as an effective floor to land ratio. We also examined the validity of the effective FL ratio at individual lots comparing with the actual floor area data from the registry office and got positive results.

96

The economic valuation of the environment and public policy

The study collected transaction price data for 60 lots of land for commercial and business use in Tokyo’s CBD, namely Chiyoda, Chuo and Minato wards, in the second half of 1987. The other variables are adopted from common variables discussed in Chapter 7. An on-site survey was conducted to measure the site-specific and neighbourhood attributes. The results of the regression are shown in Table 8.14. Table 8.14

Regression results for eﬀective floor to land ratio

Variables Month of transaction Annual retail sales in a high-density commercial zone (10,000 yen/floor m2) Distance to central government oﬃce area

Coeﬃcient 0.0448 (0.8) 0.001161 (2.7) 0.385 (2.6)

Number of employees in the retail and service sectors (person per ha)

0.103 (1.1)

Eﬀective floor to land ratio (%)

0.838 (9.3)

Accessibility ACC

0.151 (1.5)

Constant

13.6 (8.7)

Sample size

60

Coeﬃcient of determinant

0.76

Notes: 1. ln (yen/m2)a0 k ak lnxk. 2. t-statistics are in parentheses.

It is clearly shown in the table that the effective floor to land ratio is very influential and has a statistically significant value. Its elasticity is 0.84, which means that the value of land is very responsive to changes in institutional measures.

CHARACTERISTICS OF THE VALUES OF THE ENVIRONMENT AND PUBLIC SERVICES We shall review the results of these studies and discuss the robustness and characteristics of the values estimated in the hedonic analyses. The amenities that we are interested in are as follows:

Hedonic price method

1. 2.

3. 4.

97

Environmental amenities green environment (trees); view of landscape; noise; water quality. Urban facilities access to parks; open road space; sewage service; gas service; less-desired urban facilities; transport accessibility; access to railway service. Risk flooding. Institutional measures zoning; floor to land ratio.

In the following discussion, the values of environment or services (dy) are measured and compared to the share of the value over the property prices (y:10,000 yen/m2), that is dy/y. The type of property data, and the time and place when the data were collected are also shown. The study is referred to by number. The results are summarized in Table 8.15. We discuss the stability of the value and the percentage of the value to the total price when we compare the values among the different studies. Environmental amenities With respect to a view, the value of a good view is about 6 per cent of the total price. We can also find that the value of 1 dBA noise reduction is about 0.7 per cent of the whole value of land. The results of the study on flats had half of that, probably because it is easy to prevent outside noise with an improvement in the structure of the buildings. Urban facilities The openness of the road frontage has almost the same value, that is, 4 per cent of the total price when it increases from 8 to 10 m in width. The results from Setagaya, 1988, may be biased by the investors’ preferences, that is, the speculation in the bubble period in which investors sought to buy land on which multistoreyed flats could be built (see the discussion on the institutional measures above). Kunitachi is also not a typical case because of its famous wide streets, developed in the 1920s. The negative value of less-desired urban facilities such as elementary or secondary schools, because of their noise, and treatment plants, is nearly 12 to 14 per cent of the total value. The values of sewage and gas services are approximately 7 to 9 per cent of the total prices except in Sendai, Morioka and Akita, which are local

98

6.52 2.55 0.78 0.39 4.84 14.85 3.0

2.80 62.2 Worse than 10–2 mg/l 0.032 7.0 1 mg/l

4.5 0.46

5.8 1.7 4.1 1.3 4.3 9.9 4.0

0.15 0.35 0.53

112 150 19 30 112 150 75

43 50.0 75.0

0.2–0.1 km 0.5–0.4 km 8–10 m 8–10 m 8–10 m 8–10 m 8–10 m

1dBA 1dBA 60–61

0–1 –1–1 0–1

0.35 0.7 0.71

112 43 43

6.5 2.6 2.7

50–55 15–10 0–1

dx

5.8 6.0 6.3

62.5 62.5 62.5

y

3.37 0.88 4.3

dy

5.4 1.4 6.9

dy/y

Summary of value estimated amenities in Japan

1. Environmental amenities Share of green vegetation Share of façade Tall tree View of landscape Open view Open view Greenery and river Noise 1dBA 1dBA 1dBA Water quality 1 mg/l 1 mg/l 2. Urban facilities Access to parks Large Waterside Open road space

Table 8.15 Type of data*

Setagaya Trans Setagaya Trans Setagaya Trans

Place

88 88–89 84 86 88 88–89 93

87 99

Suginami Trans Setagaya Trans Yamato OAP (Kanagawa P.) Kunitachi Tokyo RA (Tokyo) Suginami Trans Setagaya Trans Setagaya Trans

Nogawa Tokyo RA (Setagaya) Sapporo Trans

82–85 Setagaya Flat Trans 89 Kawasaki ROAP 93 Setagaya Trans

88 Suginami Trans 82–85 Setagaya Flat Trans 82–85 Setagaya Flat Trans

95 95 95

Year

(2) (7) (9) (9) (2) (7) (5)

(6) (10)

(3) (9) (5)

(2) (3) (3)

(1) (1) (1)

Source

99

Gas service

1.0 1.26 1.0 1.9 0.4 1.0

0.25 25.0 0.54 43 0.32 32.0 0.69 36.4 0.03 6.9 1.22 120.0 1.1–1 km 1.1–1 km 1.1–1 km 1.1–1 km 1.1–1 km 1.1–1 km

1.1–1 km 1.1–1 km 1.1–1 km

1.36 1.29 0.17 21.2 19.0 12.0

Valet train 0.5–0.2 km 1% 1%

0–1 0–1 0.2–0.3 km 0–1 0–1

0–1 0–1 0–1 0–1 0–1

0–1

0.35 6.9 3.36 112 0.40 62.5

1.73 19.0 1.01 13.0 2.8 112 2.57 21.2 8.61 62.5

12.0

9.1 7.8 Less-desired urban facilities 2.5 12.1 13.8 Transport accessibility Interurban 5.1 ACC 3.0 ACC 0.64 0.10 ACC (CBD) Access to railway service 6.4 6.8 1.4

0.92

1.14 13.0 1.85 7 8.9 120 1.10 12.0 0.89 12.0

7.7

8.8 26.4 7.4 9.2 7.4

Sewage service

Sendai, Akita, Morioka, OAP Suginami Trans Setagaya Trans Tokyo CBD Trans

Northeast OAP (Tokyo Metropolitan Region) Misato OAP (Saitama P.) Sendai, Akita, Morioka, OAP Tokyo OAP Gifu ROAP Northeast OAP (Tokyo Metropolitan Region) Yamato OAP Misato OAP (Saitama P.) Suginami Trans Hachioji Tokyo RA Setagaya Trans

Hachioji Tokyo RA Yamato OAP Northeast OAP (Tokyo Metropolitan Region) 84 Adachi OAP 82–85 Setagaya Flat Trans 85 Kobe OAP 85 Nerima Tokyo RA 85 Sendai OAP 87 Tokyo OAP

82 84 84

85 88 95 87

84 84 88 82 95

84 85 87 88 84

84

(9) (9) (3) (9) (9) (9) (4)

(9) (9)

(9) (2) (1) (8)

(9) (9) (9) (2) (9) (1)

(9) (9) (9) (4) (9)

100

(continued)

dy/y

dy

Type of data*

Tsurumi River OAP Setagaya Trans Sapporo OAP, ROAP Setagaya Trans Tokyo Suginami Trans Setagaya Trans Setagaya Trans Tokyo CBD Trans

81 88 90 95 87 88 93 93 87

0–1 0–1 99% 0–1 0–1 0–1 0–1 1% 1%

120 112 75 75

Tokyo OAP Tokyo Region OAP Osaka OAP Sapporo OAP, ROAP

10.0 150.0 22.4 62.5

87 90 90 90

60–50 mi 60–50 mi 60–50 mi 60–50 mi

Suginami Trans Tokyo Region OAP Osaka OAP

Place

120.0 80.0 50.0 22.4

88 90 90

Year

1.2–1.1 km 1.1–1 km 1.1–1 km

dx

112.0 80.0 50.0

y

(5) (9)

(4) (2) (5)

(9) (7) (9) (1)

(4) (9) (9) (9)

(2) (9) (9)

Source

Note: *See Chapter 7, Table 7.1. Sources: (1) Hidano and Kameda (1997); (2) Hidano and Takebayashi (1992), cited in Hidano (1997); (3) Shimizu et al. (1988); (4) Kanemoto et al. (1989); (5) Hidano et al. (1996); (6) Hiramatsu and Hidano (1989); (7) Yokomori et al. (1992), cited in Hidano (1997); (8) Hidano et al. (1995); (9) Hidano (1997); (10) See Tables 8.12 and 8.13.

Access to railway service (continued) 0.9 1.00 3.4 2.72 3.8 1.90 Access to terminus (minutes) 14.1 16.89 11.2 8.96 2.6 1.30 4.0 0.90 3. Flood risk 4.5 0.45 8.3 12.5 1.1 0.25 32.48 20.3 4. Institutional measures Exclusive housing (zoning) 6.53 7.84 20.8 23.3 14.3 10.75 Floor to land ratio Official FL 0.22 0.17 Effective FL 0.84

Table 8.15

Hedonic price method

101

cities situated away from a metropolis where the cost of surrogate facilities is more than the 7 per cent of the land prices there. Access to the nearest railway station is about 1 per cent of the total value when it is measured by the value of 100 m at a lot located 1100m from the nearest railway station in Tokyo wards. Outside the metropolitan areas in Japan, the major transport mode is a car, so the value is not applicable to these areas.

CONCLUDING REMARK The results of the hedonic value estimation seem in general very consistent and the deviations of the values are quite small, with some exceptions, even in those cases where the reasons were obvious. But the benefit transfer of the values estimated in these studies is found to be limited to the cases that satisfy the conditions that the areas have similar physical environmental characteristics and the consumers of the land have the same tastes in the type of land, as discussed in Garrod and Wills (1999).

9.

Environmental cost–benefit analysis using the hedonic price method

INTRODUCTION As discussed in previous chapters, we can utilize stable and understandable values of the environment and public projects using the hedonic price method. In this chapter we explain how to proceed with cost–benefit analysis based upon the values estimated by the hedonic price method. It should be noted here that the process of cost–benefit analysis is basically the same as with ordinal cases but it requires special attention in handling the values because of the nature of the hedonic method, which is not necessarily taken into account by a standard textbook of cost–benefit analysis. Thus we shall explain the whole procedure of cost–benefit analysis with special emphasis on the hedonic price method.

BASIC PRINCIPLES OF COST–BENEFIT ANALYSIS Theoretical Considerations Measurement of benefit for individuals Cost–benefit analysis in this book means analysis that is used to examine the usefulness of a project or a policy-related environment or the provision of public services, from the viewpoint of society at large, rather than that of individuals, firms or organizations. It is thus different from firms’ accounting valuation or quasi-public organizational justifications of their spending. The questions are ‘what is society?’ or ‘who comprises the society?’. The former question is diﬃcult to answer but we shall discuss the social welfare func102

Environmental cost–benefit analysis using the hedonic price method

103

tions. Society is composed of households seeking to maximize their utility under constraints, private firms whose goals are to maximize their net profits, and public institutions who work for households and firms. This is a simplified explanation found in standard texts on economics. The social values are, thus, a function of the welfare of these three subjects. In the short run, the implementation of a marginal project gives the impact of marginal changes in prices, income and production. Its values can be examined in a partial equilibrium analysis of the specified market that we are interested in. In this case, the benefits are kept by the three subjects. But in the case of the long run in a non-marginal project, the benefits to firms or public organizations should not be kept by them. Rather, they should be transferred to the benefit of households because the profits of a firm should be capitalized into the value of the stock of the firm and realized by stockholders, that is, households and other firms, or because the profits of public organizations, if any, should be distributed to households through reductions in tax or public service charges. In this case, the value of a project can be measured by the welfare changes of households and should be evaluated in the general equilibrium analysis in which all prices and production of a commodity should change. As far as the welfare of firms is concerned, it is simple to estimate the amount of profit in terms of money and there are no problems even in large-scale projects, since money is money. But the measurement of the welfare of a household is another story because it is a utility. So monetary measurement of a utility is required. Note that the motivation of transforming utility into monetary value in cost–benefit analysis is based upon the fact that we like to compare utilities among different individuals implicitly. We shall discuss this issue later. In the cost–benefit context there are two ideas concerning monetary measurement: one is that an individual utility can be transformed into a cardinal value (that is, additive value) which is usually measured by exactly the same money scale used in previous chapters: equivalent variation (EV) and compensating variation (CV). This idea is a general conception of neoclassical economists. The other is that utility is not measurable and, thus, the monetary measures used in the cost–benefit analysis are not the measurement of the utility but are simply money. Since it is money, we can use CV for measurement purposes (see Mishan, 1988). In both cases, the results are the same as far as individual utility is concerned.

104

The economic valuation of the environment and public policy

But we should pay attention to this argument, which is not necessarily based upon the existing findings of welfare and public economics where only ordinal preferences, that is, ranked in order in accordance with our individual preferences for them, are used for rigorous discussion. It should be noted that the money used in the analysis can represent only special cases of preference theories (see a standard microeconomics text such as Mas-Colell et al., 1995, among others and Chapters 1, 2, 5 and Part 2 in Deaton and Muellbauer, 1983). This is one of the critical problems from the viewpoint of cost–benefit analysis. Although it is very diﬃcult to find a consistent scale to measure utility for all purposes of economic studies, it is worthwhile explaining here such monetary measures as EV, as developed by John Hicks. In practice, there are only two cases in which monetary value of welfare, such as EV and CV, is a proper measurement of utility, consistent with a utilitarian social welfare function discussed later, that is, quasi-linear or identical homothetic utility functions.1 There is a great deal of literature on cost–benefit studies, which explains these concepts using the partial equilibrium framework (see Hanley and Spash, 1993, for environmental valuation, among others). We prefer here to discuss these concepts in a general equilibrium framework. Equivalent and compensating variations are defined by the expenditure functions. An expenditure function is generally defined as a function that shows the minimum monetary value that the consumer expends on commodities to maintain the given utility level u under the given prices of commodities p and the public good z [*]. E( p, z, u)minx1,x2 . . . [p1x1 p2x2 . . . ; u(x1, x2 ,…, z)u].

(9.1)

Since this is a monotone transformation of utility u, E itself can be claimed as one of the utility functions. Then equivalent variation is defined using the price system without the project po as: EVE( po, uw) E( po, uo).

(9.2)

Then we can identify the utility changes due to the projects implementation. This measure was originally designed to show the utility changes related to price changes. Since minimum expenditure without the project, that is, E( po, uo), equals that with the project E( pw, uw). Thus:

Environmental cost–benefit analysis using the hedonic price method

EVE( po, uw) E( pw, uw).

105

(9.3)

Compensating variation is defined using the prices with the project pw: CVE( pw, uw)E( pw, uo)

(9.4)

CVE( po, uo) E( pw, uo).

(9.5)

and:

These conceptions can be extended to the public goods (z). In this case, there is no price for public goods but the level of public goods is given exogenously. Then equivalent surplus (ES) is defined as the differences between two values of expenditure function, that is, the value which is required to achieve the level of utility uw under the level of public good zo and that at uo under zo: ESE(zo, uw) E(zo, uo)

(9.6)

ESE(zo, uw) E(zw, uw),

(9.7)

and compensating surplus (CS) is: CSE(zw, uw) E(zw, uo)

(9.8)

CSE(zo, uo) E(zw, uo).

(9.9)

Figure 9.1 shows a graphic explanation of the concepts. The strengths and weaknesses of these monetary measures, as far as individual preferences are concerned, are summarized as follows. Compensating variation or surplus is easily measurable when we ask people about their valuation of an amenity using stated preference methods such as the contingent valuation method (discussed in Chapter 1) using a questionnaire survey. But CV has to use prices with the project. To estimate these prices is rather diﬃcult in the ex ante analysis because of the complexity of a general equilibrium analysis. In addition to this, if there are three projects to be evaluated, we have to use three different price systems, which creates a serious problem of how to integrate the three price systems as a common set of benchmark prices. Equivalent variation and surplus do not

106

The economic valuation of the environment and public policy

uw uw

uo uo CV EV pw

po EV

CV

pw

po

z

z Price decrease

Price increase

uw

uo

uo

CS

uw

ES

ES

zw

zo

Environmental deterioration

CS

z

zo

zw

z

Environmental improvement

Figure 9.1 Equivalent and compensating variation, and equivalent and compensating surplus

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confront this problem because they are always based upon the prices without the project (see Johansson, 1993, among others). But in the case of stated preference methods, it is not easy to depict the equivalent surplus value by asking people in a questionnaire survey because of the diﬃculty that respondents have of imagining a situation in which they are compensated as a result of sacrificing a better environment. In the hedonic approach, equivalent variation and surplus may be better measurements because we do not need to use a questionnaire to ascertain consumer preference. Measurement of opportunity cost In cost–benefit analysis, we measure the positive impacts on our utility as a benefit and negative ones as a cost. So costs just mean negative benefits. But in reality, the costs of a project or an environmental policy and the provision of public services are not only the disutility of a household but also the input of ordinary goods, services and resources. To maintain the wetlands or tropical rainforests for environmental purposes, for example, labour and material inputs are required for project implementation. In any case, the question is what prices of inputs of a project should we use for a cost–benefit analysis. The costs of resources should be values at the real cost, that is the benefit which we have to give up by not using the resources for alternative uses. This benefit is called the opportunity cost of resources. In neoclassical economic theory, it is always assumed that there is a stable and harmonized fully employed market. The market prices show the exact prices of inputs of a project (in this argument, we exclude externality or asymmetrical information or other distortions). But in the case of unemployment, the prices do not reflect the real opportunity costs. If unemployment is severe, then the opportunity costs of labour should be nearly zero. We should understand this fact in the real calculation of costs and benefits. From individual value to social value Although we discussed the diﬃculty of measuring individual utility in monetary terms, it is again not so easy to define the social value of a project. In order to determine the value of two or more than two people, that is, society, we need to decide several key factors. The first is to determine whether or not there is an extra value over and above the sum of the individual value of two people. This means that society itself is considered as an independent subject which has its own value

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that is determined not by an individual but by a collective. But this is usually not accepted by standard economics. Thus social value or social welfare is determined by a function of an individual utility of these two people, that is, a social welfare function. Second, is individual utility affected by the utility of the other person? Again, usually not. Thus the social welfare function is determined by an individual utility independent from another individual’s utility. Third, what criteria should we use to evaluate the utility of these two people? The eﬃciency and equity criteria are adopted, among other ethical ones. If we only consider the eﬃciency of resource allocation, the social welfare function is called the utilitarian welfare function (or Bentham-type welfare function) giving equal weight to each person’s utility. If we think two people are not equal, then we should weigh each one according to some equality criteria. If we think that individual utility should have the characteristics of decreasing the marginal utility of money (if we define the utility of individuals in monetary terms), then individual value may be weighted by the inverse of marginal utility. This type of social welfare function is called the nonutilitarian social welfare function. The extreme case is to consider only the utility of the person who has the least utility in the society. This is called the Rawlsian social welfare function. But the last two types are problematic, for example, why we should use the inverse of marginal utility of money to adjust the level of utilities among different people is not clear at all. Although Rawls (1971) claimed that we are all living in a society and have the possibility of being a member of the lowest utility, the Rawls criterion is not necessarily unique among many other distributive criteria. Thus in cost–benefit analysis, we usually adopt the utilitarian social welfare function to evaluate the projects from the viewpoint of eﬃcient allocation of resources. This function implicitly assumes that each person’s change of utility due to the implementation of a project can be transferable to the other. This is called the compensation principle. It means that one person’s decrease of utility can be potentially compensated in reality even though it will never be actualized. Thus potential Pareto improvements can be made possible by this transformation if the project produces positive social value from the viewpoint of an eﬃciency criterion. It should be noted that there are no consistent compensation tests by which potential Pareto improvement can be examined for all cases (see cost–benefit texts on this point, such as Johansson, 1993; Pearce, 1982; or Brent, 1996).

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Practical Considerations With and without a project In the process of a practical cost–benefit analysis, it is very important to describe the impact of a project correctly. In order to do so, we always have to estimate two hypothetical situations, namely without the project and with the project. Estimations should be carried out for all variables related to the benefits and costs during all time periods when we are to evaluate the impact of the project. In some cases, the estimations are made not by objective methods but by scenarios determined by analysts or decision makers. Even in these cases, the recognition of the situations with and without the projects should be so important as to depict clearly the impact of the project. It should be noted that descriptions after the evaluation periods, with and without the project, are required to calculate salvage values. Price adjustment The price systems in reality differ from time to time and from place to place. But in order to estimate the impact of a project and the costs of inputs for project implementation, sometimes data from different times and places have to be adopted. In this case, we must use real prices transposed from nominal prices by deflators. In a cost–benefit analysis, it is necessary to state the time and the place of prices which the analysis is based upon. Discount rate for present value In most cost–benefit analyses, the timing of utilities, which we can enjoy, or inputs of resources, which we have to bear, is not unique. We have to consider the rate of substitution among these goods and services at different times, just as we have to among goods and services at the same time. The rate of substitution at different times is called a discount rate. As discussed, we are interested in the sum of the individual utilities in the society as a social welfare function. We should adopt the discount rate of the utility. Then the present value of the utility value at t is: Present value of ut ut / (1iu)t

(9.10)

where ut is the value at time t and iu is a discount rate of utility.2 This discount rate is evaluated by consumers. There is another definition

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of the discount rate from the viewpoint of producers, that is, the interest rate of capital or the opportunity cost of capital. The values of the consumer’s discount rate and the producer’s interest rate become unitary when the market is under the conditions of neoclassical equilibrium. The choice of the discount rate is a problematic area in cost–benefit analysis. Many welfare economists claim that the discount rate should be zero (for example, A. Pigou) or that it is not applicable in the situation when we have to consider the next generations (Mishan), or that it should be determined by paternalistic methods. A summary of recent discussions on discount rate, especially in global warming issues, can be found in ‘Economic and Social Dimensions of Climate Change’ by the third working group of the Intergovernmental Panel on Climate Change (1995). In this book we use real interest rates of long-term national bonds from a practical viewpoint because normative discussions may not have converged so far. Net present value criterion As we discussed in the cost–benefit analysis, since benefits and costs are transferable among the members of a society, the net benefits due to the implementation of the project are defined as the benefits minus the costs. Thus the net benefits are defined by: The net present value (NPV)present value of benefits (B) present value of costs (C)B0 B1/(1im). . .Bt / (1im)t . . . (C0 C1/(1im ). . .Ct / (1im)t . . .). (9.11) If the net present value is non-negative, then the project should be implemented. This is the cost–benefit criterion for judging the social value of the project. But it should be noted that the results of this judgement are not necessarily consistent if we use different monetary measures, that is, EV (equivalent variation) or CV (compensating variation). In addition to what we have discussed in individual utility measurement and social value, we should consider the meaning of these measures in a two- or more-than-two-person society. In this society, compensation principle (or the potential Pareto improvement) is a basic principle for accepting the project, that is anyone’s disutility should be compensated for by the utility increase in a society. From this standpoint, the disutility should be evaluated in terms of compensating variation or surplus because a person who

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suffers this disutility has a right not to bear this situation. This is claimed by Mishan, who thinks that only compensating measures satisfy the Pareto criterion. But again this is a problem of social welfare functions in which we should decide who has a right to what goods and services in a specific situation. As Ronald Coase insisted, even a firm that produces a pollutant may have the right to pollute a society. In this book, we do not intend to discuss the problem of property rights, although this is the most fundamental issue we are facing in the field of cost–benefit analysis. (For this, see Mitchell and Carson, 1989, among others.) There are other criteria employed in cost–benefit analysis for deciding whether a project should be accepted or not. One is the cost–benefit ratio, which is defined as the present value of benefits over the present value of costs (B/C). The other is the internal rate of return (IRR) which is defined as a value (iirr) that satisfies the equation: Tt0(Bt Ct)/(1iirr)t 0

(9.12)

where T is when the evaluation ceases. The major problems of B/C are that (i) it cannot have a unique value when the distinction between benefits and costs is not clear, for example, a decrease in traﬃc noise can be classified as an increase of a benefit as well as a decrease in cost; (ii) the values of the net benefits cannot be compared among projects. This inevitably creates serious problems, as we cannot select optimal sets of projects under the budget constraint. The internal rate of return has several shortcomings; (i) the same problem that the shortcoming of (ii) of the benefit–cost ratio (B/C ) is applied; (ii) the values of the solution of the above equation are not unique; and (iii) it is not clear how to decide the acceptable value of the internal rate of return. Thus the net present value is the only sound criterion in cost–benefit analysis.

PROCEDURE Stock Value and Annual Flow of Benefits and Costs In this section, we show the practical procedure of cost–benefit analysis with special emphasis on the hedonic price method. If we use

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property values such as land price, or housing price, we have to convert these stock values into an annual flow of benefits or costs. If the price is for land whose title does not restrict its owner’s right to use the land, then we can estimate an annual flow of benefits as the stock price multiplied by the discount rate which we adopted in the calculation of the net present value. If it is housing or other property which is composed of buildings and land, and also, if we are interested in the attributes which are attached to the building structures, we should consider the depreciation of the structures using the assessor’s evaluation or on-site observation. Housing data usually include the history of its construction and rehabilitation or other major changes. Then we can obtain the average rate of depreciation which is used instead of the discount rate in the case of land. This average rate of depreciation is used for the evaluation of an amenity, such as the view from windows of a high-rise building, which will no longer apply when the buildings and structures themselves go out of use. Most of the cases we are interested in, however, are the evaluation of an amenity given exogenously by the public sector or the environment and whose characteristics are of local public goods. The values of these amenities belong not to the structures or buildings, but to the land. Thus we can apply the same discount rate used for land prices. Short-run Evaluation It is very important for the application of a hedonic approach in a cost–benefit analysis to consider the speed of the changes in market conditions, that is, land use, the density and the lot size in the case of the land market and, in the case of the housing market, the use and types of buildings and houses, the population density of residents, and the physical structures such as buildings and houses. When we are interested in the evaluation of a project whose lifetime is shorter than the changes in these properties, then we have to assume the lot size of a property and the use of land and housing as being the same as in the situation without the project in order to estimate the hedonic value correctly. The results, in the short-run case of the capitalization theorem in Chapter 3, are applied in those cases. Then we have to estimate a hedonic price function using a lot or area size as one of the explanatory variables in order to examine the influences on land and housing prices. And we should also check the characteristics of the data, which should include samples of land whose lot size is the same

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but whose amenity level is different enough to cover the increments by the implementation of a project. If we cannot find data which satisfy these conditions, we shall know that there still remain separation problems, that is, to distinguish between the implicit price of space and that of environment. Long-run Evaluation Small project Any project we have to evaluate makes an impact on society. Any impact, even a small one, should inevitably change all prices within that society from the viewpoint of general equilibrium analysis. But the actual practice of a cost–benefit analysis requires minimizing the cost of the analysis itself. We cannot apply a general equilibrium approach to all project evaluations. Thus in the case of a small project, that is, small changes in or improvements to the amenity which only make an independent impact on the consumer’s utility and on the producer’s production technology, or which have a marginal impact on a small area directly influenced by a project. We can analyse the markets for the residential, business, commercial and industrial use of land independently. After estimating the hedonic price functions and setting up the scenario of the impact of a project, we analyse the cost and benefit in the following process: Step 1 Identify the area which we should consider in the cost–benefit analysis. Step 2 Identify evaluation lots of land (i ) represented in zonal socio-economic characteristics. It should be noted that within a zone the socio-economic characteristics and the degree of influence of a project can be considered as constant. Step 3 Identify the net land area usable in each zone (Hi ). It should be noted that the area cannot include any space which is unusable, such as roads or rivers, or areas for public facilities and utilities. Step 4 Identify the impact of a project of every evaluation lot in terms of changes of variables in the hedonic price function in all periods of the analysis by assigning the values with the project and without the project. Step 5 Identify all values of exogenous variables of every evaluation lot, except the amenity variable, in which we are interested in all periods.

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Step 6 Calculate the hedonic value with the project and that value without the project using the hedonic price function and variables set during the analysis period. Step 7 Convert stock values into an annual benefit flow. Step 8 Identify the net value (Bti ) by subtracting the values with the project from the values without the project. Step 9 Estimate all the annual benefits (Bt ) by multiplying Bti by the area of Hi and calculating the total for the whole area. Step 10 Calculate the present value of the annual flow using equation 9.11 and the discount rate and add them together to find the total present value (B). Step 11 Calculate the total present value of the cost (C ). Step 12 Find the net present value of the project (NPVBC ). If there are changes in the area of zone i for exogenous reasons, the zonal area should be changed and therefore we use Hti instead of Hi . But in this case, the reason for these changes should be clearly stated in the scenario of the analysis. If these changes are an outcome of the project, we should consider their cost as well. Large project In the case of large-scale projects, we should consider the impact on the interactions between consumers and producers. Both are usually interrelated, as we discussed in Chapters 3, 4 and 5. For example, the increase of an amenity in some zones in the study area should increase the number of residents and thus also increase the supply of labour, thereby reducing the scarcity of labour that decreases the wages of firms in these zones. This means that even a project which directly affects only the utility of the consumer may also affect the land prices for industrial and business enterprises, because a decrease in wages should lead to an increase in the land rent for firms. The benefits of the projects are captured not only by residential but also by industrial property. We should evaluate both land uses at the same time. In these cases, we have to estimate hedonic price functions for residential, business or commercial, and industrial property, which include the variables that depict these interactions. The accessibility measures is one of the methods for including these interactions. Thus we have to include the amenity which the project should improve as a factor of the ACC. It should be noted

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that if we allow mixed land use or the changes of land use in the longrun, we have to estimate the unified hedonic price function applicable to all land use in order to evaluate the impact accurately. These modifications are not diﬃcult. The procedures for the large-scale project are the same as for the small one, except for the hedonic price functions we use. It should be noted that the scale of projects which can be evaluated using the hedonic price method is suﬃciently large for nearly all projects that we can imagine, as shown in the previous chapters, but it can never extend to the evaluation of pure public goods. It would be advisable to adopt a general equilibrium analysis for such projects or for policy evaluations such as policies related to global warming, or biodiversity. Cases of Fares and Charges Imposed on Users So far, we have discussed mainly cases of the evaluation of the environment and public services with local public good characteristics. Charges and fares are not required for residents or users to enjoy these services. However, if the project has an effect across a jurisdictional boundary, we have to consider the local tax differentials among different jurisdictions explicitly. Moreover there are many public services, such as transport, water and sewage services among others, for which users have to pay. Of course, if they are private goods without any distortion in the market, we need not utilize a cost–benefit analysis to value the benefits of a project. Most of the charges related to public services are controlled, however. In these cases, the benefits of the project are partly captured by land prices as well as user charges. Only the net increment of user utility is capitalized into land prices, due to the project implementation that the change in fares and charges (including a local tax) is subtracted from the total utility increase. Part of consumers’ ‘willingness to pay’ is levied as a fare, a charge, or a local tax. So it is necessary to estimate the hedonic price function, including the level of the services and charges. In order to estimate the benefits of the project, we have to calculate the total utility gained by the provision of the services both with and without the project. The total utility with the project is the sum of the hedonic price of the service level with the project and the total charges for a user of the project, and without the project it is the sum of the hedonic price of the service and the charges at the level without the project. If the charges are subject to the services consumed by a user,

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then we have to estimate the demand for the service in response to the charging system, and it is also necessary to estimate the cost of the provision of services to accomodate the demand. Thus the process of cost–benefit analysis becomes very complicated. But in cases where the charges and the cost-per area of providing services are fixed despite the level of consumption, then we do not need to estimate actual demand by the users. When there is any surplus, in terms of social value of the provider of the service caused by the implementation of the project, we have to add it to the net benefit. It is very diﬃcult to generalize about the process of cost–benefit analysis, because it is highly dependent on the nature of the provider, the tax and the financing system in a country. However the typical procedure is as follows: 1.

2.

Case A: Fixed unit charge per area and unit cost of the provision of services per area The modifications of the previous steps are: Step 4 Identify the impact, including service variables and charge variable. After Step 11, we have to consider the social surplus of the provider of the service. w ) (‘real’, indicates Step 1p Identify all real cost flows (C pt adjusted prices at fixed year) in terms of opportunity costs for a w ) with the project (one provider and all real revenue flows (Rpt authority across the area is assumed). Step 2p Identify all real cost flows (C pto ) in terms of opportunity costs for a provider and all real revenue flows (R pto ) without the project. Step 3p Calculate present net value of profits for a provider (Bp ). Step 12 is modified to calculate NPVBBp – C. Case B: Variable demand and cost of the provision of services In this case, we have to estimate the demand for each provider of the services. We can do this by (i) ordinal econometric estimation using as variables the number of residents and the amount of production of private firms, among others or by (ii) estimating a reduced form of the hedonic price functions and revenue functions of providers just using amenity and charge variables and the assuming providers’ production functions of the service only related to amenity and service variables given exogenously. In the former case, we estimate the hedonic price functions and other

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equations simultaneously. Then we simulate to find the number of residents, production, demand for services and other factors in each zone at a time through steps 4 to 8. And we can calculate the providers’ net profits through steps 1p to 3p. Then we can come back to step 12. In the latter case, we calculate the variable needed for steps 1p to 3p using these estimated revenue functions and assumed production functions. Ex Ante and Ex Post Evaluation In ex ante analysis, many variables are unknown because of the uncertainty of the future. So we have to use robust hedonic price functions which should be calculated using more than one time period and may be checked according to the stability of the parameters using different time data sets. The problem is not the estimation of the hedonic function, but the forecasting. It is very common for the forecast of future variables to be completely unreliable and highly biased by institutional reasoning, that is, the strong willingness to manipulate the values of the future to maximize institutional profits, and hence we should minimize the complexity of the forecast procedure as much as possible. Information about the scenario and the variables should be made available to the public. On the other hand, ex post analysis enables us to utilize past data to estimate sound hedonic functions not only on a one-time basis but also several times within the timeframe of the analysis. It should be noted that even in the ex post analysis, we have to create at least two variable sets, with and without the project.

A NUMERICAL EXAMPLE Finally, we explain the procedure using an example based upon actual hedonic price estimation. This numerical example is the case of water-quality improvement in Sapporo City in Hokkaido, Japan. The northern part of Sapporo City is situated by the River Barato, which flows into the River Ishikari, the third longest river in Japan. The Barato River has an ancient shape, which bends in the flood plain, like rivers in tropical forest regions, and has now developed an oxbow lake. This shows the dynamics of the river and how the forces of nature can change the topography of a region over long time periods

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Figure 9.2

Barato River and Sapporo City, Japan

(Figure 9.2). The water quality, in terms of biochemical oxygen demand (BOD) differs from place to place, ranging from more than 10 ppm (mg/l) to less than 2 ppm (mg/l). But in most areas of the river, the BOD level is worse than the standard set by the water pollution law (that is, 3 ppm (mg/l)). We evaluate a hypothetical project that will improve the water quality in all parts of the river to satisfy the environmental standard. The measures needed to achieve this goal include dredging out the

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waste products in the river, introducing fresh, clean water from other rivers, improving the quality of sewage water, and introducing agricultural wastewater treatment plants. We assume completion of the hypothetical project to implement these measures within 10 years. The impact on river water quality is also assumed during the time period of the project, that is, 50 years, from 2001 to 2050. The scenario is as follows: Every measure in the project is divided into two 5-year terms. The implementation of the project will improve the water quality by 50 per cent after completion of the first part of the project, that is, by 2005, and the environmental standard will be achieved by the end of the second term, that is, by 2010. The dredging of wastes in the river basin will be carried out intensively during the first 10 years in order to remove all waste. The introduction of fresh and clean water from other rivers will involve capital investment over the whole 10 years. The agricultural wastewater treatment plants are small-scale decentralized systems and should be replaced every 10 years. The sewage system improvement in this project is to develop reserve ponds to store polluted water for a short time when the existing system cannot function because of heavy rainfall. A population increase in the whole region is not assumed because the population of Japan is expected to decline after 2006. This improvement project is intended to increase the household utility of the residents, particularly those who live near the Barato River, but not affect the production environment of the firms and oﬃces in the central business districts of Sapporo city, or even the industries in the Sapporo region. Because there are already strong regulations concerning water-quality discharge from industries, the industries should satisfy this requirement, whether the project be implemented or not. Thus we can identify this improvement project as a small project case. We utilize the hedonic price function estimated in Chapter 8. Step 1 Identification of the study area. We limit our study area to an area of Sapporo City jurisdiction and that of Ishikari City, which is located just north of Sapporo and is situated near the River Barato. Step 2 Identification of zones and zonal representative land. The whole area is divided into zones in which the impact of the project should be assumed to be uniform across the area in every zone that corresponds to an administrative jurisdiction, in order to collect

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administrative socio-economic data. Next we should select a representative sample point in every zone, but in this study we utilize the same land lots that we shall use to estimate the hedonic price function. In this case, we should bear in mind the heteroscedasticity of the data, so it is important to check the distribution of sample data. If there are more than two samples in a zone, we shall choose the most representative sample point for the study in terms of the average characteristics of the attributes of land and the level of impact given by the project. The distribution of the evaluation sample points can be examined by the zonal data if they are available from external sources. Step 3 Identification of the net land area usable at each zone (Hi ). The usable area is limited by institutional regulations. In this area, we consider land for housing or other urban use, not agricultural farmland, that is, land for urbanization promotion areas determined by the land-use regulations. In addition, any space which is unusable, such as roads, rivers, and areas for public facilities (excluding housing), is excluded by using administrative statistics and by subtracting specific public facilities individually. Even a small project may sometimes result in changes in institutional land-use control on some parts of the land. If it is considered part of the project, the size of usable land should be adjusted. In this example, it is assumed that the existing regulations remain unchanged. Step 4 Identifying the impact of a project on every evaluation lot in terms of changes of variables in the hedonic price function in all time periods of the analysis by assigning values with the project and without the project. Step 5 Calculating all values of the exogenous variables of every evaluation lot that we are interested in during all time periods, except amenity variables. Step 6 Estimating the hedonic value with the project and the value without the project using the hedonic price function and variables set at every time period during the analysis. Step 7 Converting stock values into an annual benefit flow. Four per cent is used for the social discount rate in this example. Step 8 Calculating the net value (Bti ) by subtracting the values with the project from the values without the project. Step 9 Estimating the total annual benefits (Bt ) by multiplying Bti by the area of Hi and calculating the total for the whole area.

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Table 9.1 Annual flows of benefits and costs (unit: 100 million yen, 2001 price) Year

Period

Benefit

Present value of benefit

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

0 0 0 0 0 173 173 173 173 173 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384 384

0 0 0 0 0 142.193 136.724 131.466 126.409 121.548 259.417 249.439 239.845 230.620 221.750 213.222 205.021 197.135 189.553 182.263 175.253 168.512 162.031 155.799 149.807 144.045 138.505 133.178 128.055 123.130 118.394 113.841 109.462 105.252 101.204 97.312 93.569

Cost Present value of cost 560 560 560 560 560 615 615 615 615 615 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110

560 538.462 517.751 497.838 478.690 505.485 486.043 467.349 449.374 432.091 74.312 71.454 68.706 66.063 63.522 61.079 58.730 56.471 54.299 52.211 50.203 48.272 46.415 44.630 42.913 41.263 39.676 38.150 36.683 35.272 33.915 32.611 31.356 30.150 28.991 27.876 26.804

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Table 9.1 (continued) Year

Period

Benefit

2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050

37 38 39 40 41 42 43 44 45 46 47 48 49

384 384 384 384 384 384 384 384 384 384 384 384 384

50

4,000

Total Salvage value Grand total Net present value

Present value of benefit 89.970 86.510 83.182 79.983 76.907 73.949 71.105 68.370 65.740 63.212 60.781 58.443 56.195 5,998.301 562.850 6,561.151 98.389

Cost Present value of cost 110 110 110 110 110 110 110 110 110 110 110 110 110

25.773 24.781 23.828 22.912 22.031 21.183 20.369 19.585 18.832 18.108 17.411 16.741 16.098 6,462.762 6,462.762

The results of Steps 4 to 12 and the cost flows of the project are summarized in Table 9.1. (See also Appendix 8.) The results show that the project is evaluated as being socially acceptable (that is, net present value is positive: (9.8 billion yen). But of course they are completely dependent upon the scenario, the values estimated by the hedonic approach, and the value of the discount rate among other variables involved in the analysis. It is strongly recommended that in actual decision making, great care is taken to examine the results by a sensitive analysis using another value of the discount rate, the costs of the projects, the delay of project implementations and the hedonic values estimated.

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CONCLUSIONS We have discussed the most basic principles of cost–benefit analysis and the procedure of the hedonic price method for the analysis. The process of the HPM in the cost–benefit analysis is not as diﬃcult as other methods, such as the consumer surplus estimation or the travel cost method, which require accurate estimation of demand functions, and the contingent valuation method, which needs a large survey sample. As far as the evaluation of environment and the provision of public services that have the characteristics of local public goods are concerned, the hedonic price method seems to be rather promising. We should like to emphasize the following: ● ● ● ●

HPM can be applicable in non-marginal cases. HPM requires only the estimation of hedonic price functions. Market transaction price data of a property is preferable in HPM. HPM strongly requires accurate measurements of environment and public services.

Finally, it should be noted that a cost–benefit analysis is not easy, but careful application of the hedonic approach should show some of the reality of a complex world.

NOTES [*] 1. An indirect utility function is defined as follows: max u(x) subject to pxm, where m is monetary income. If the optimal utility which we can get is u, then u[x(p, m)] u, thus it can be expressed by p and m, ( p, m)u. ( p, m) is an indirect utility function. A quasi-linear utility function is expressed as ( p, m)g1( p)h1( p)m in terms of an indirect utility function. A homothetic utility function can be converted into an indirect utility function, that is, ( p, m)g2( p)h2(m) (h2 (m) > 0). Since we can identify a function which can convert an original utility function into a utility function that is homogeneous of degree one, h2(m) can be written just m in this case. Thus any homothetic utility function can be converted to g3(p)m. In both quasi-linear and homothetic utility functions we can assume that marginal utility of money can be constant. 2. If we use the monetary unit, that is, money, then the present value of utility xt in terms of money at time t is: Present value of xt xt /(1im)t. The definition of im is problematic. As we discussed in the main text and in note 1, cost–benefit analysis generally assumes a utility function where the marginal utility

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The economic valuation of the environment and public policy of money is constant. Thus im equals iu . But if we adopt another utility function which includes money as a factor of a utility function, then it becomes: im iu m m/m, m is the elasticity of marginal money which is defined as u(m) m / u (m), m is changes of money in terms of time and m is the amount of money. Neoclassical models usually exclude this value of money, that is, liquidity. Alternative rigorous discussion on discount rate in a macro-dynamic analysis which incorporates the value of liquidity can be seen in Ono (1994).

10.

Concluding remarks

This book attempts to explain the hedonic approach in the context of environmental and public policy evaluation from both theoretical and practical viewpoints, and to extend the role of the hedonic approach from marginal cases to large-scale public projects and environmental changes mainly based upon theoretical and empirical perspectives. The strength of this study, on the theoretical side, is being able to consider explicitly the price changes within the general equilibrium framework and the cost of public and environmental policies. Although it is claimed in the studies discussed from the viewpoint of time-series or comparative statics that the benefits of the projects should be incorporated into wages, it is shown, in our book, that the hedonic measure based upon cross-sectional capitalization theory can also correctly approximate the benefits in large-scale cases. We hope this book is instrumental in changing the prevailing conception of the limitations of the hedonic approach for benefit estimation, especially with respect to large-scale policies or environmental changes, although the results may have some limitations because of the parameters examined. Thus, we advocate that future evaluation of large-scale environmental projects and public policies should have a local public goods nature (that is, people are able to choose a good) using the hedonic price functions based upon land, housing, commercial, and business market price data. We also emphasize the importance of using comparative studies of hedonic and other benefit estimation methods in different circumstances, which will enable us to support the findings of this study. These studies will contribute considerably to the testing of the validity and applicability of the method. From a practical viewpoint, this book lists the estimated values of various environmental goods and public utilities. The most important contribution of this book, in this respect, is to demonstrate the necessity for the accurate measurement of physical characteristics of environmental goods in order to obtain a reasonable estimate of the 125

126

The economic valuation of the environment and public policy

economic value of the environment, which is not necessarily common in existing studies. It also emphasizes the importance of the transparency of the market transaction price data in order to utilize fully the hedonic method. Together with these real transaction data and the accurate measurements of the environment, the robustness of the hedonic price method is found to be high in many environmental and public services, using Japanese cases as examples. These results encourage us to use the method in a wider perspective. Finally we also provide detailed procedures of benefit estimation by cost–benefit analysis using the hedonic approach. It enables us to apply the hedonic approach in real decision making by examining various public policies and environmental projects incorporating the cross-sectional capitalization theory discussed in the book. The hedonic approach is not necessarily perfect, but it may help us to reconsider our actions and avoid unrealistic decision making in the real world. Karl Popper said in The Poverty of Historicism (1957): The piecemeal engineer knows, like Socrates, how little he knows. He knows that we can learn only from our mistakes. Accordingly, he will make his way, step by step, carefully comparing the results expected with the results achieved, and always on the look-out for the unavoidable unwanted consequences of any reform (p. 67).

We do hope that this book may direct us, like a stepping-stone in a Japanese garden, to enlarge our understanding of our own mistakes.

Appendix 1 Proof of time-series capitalization [*] The time-series measure is: (r*1 r1)H1 R.

(A1.1)

The sum of rents from the land is distributed among consumers equally. This is called the uniform national dividend scheme (UNDS), which is a common assumption in a general equilibrium analysis since there are only homogeneous consumers in the society. Before the project implementation, the endowment is: s(r1H1 r2H2)/N.

(A1.2)

A consumer has a utility function u(x, l, z) where x is a composite good, l is area of land used and z is a level of amenity. A consumer maximizes the utility: max u(x, x,l

l, z)

under the income constraint of wage w, which is given exogenously, and endowment: pxrlws

(A1.3)

where p and r are the price of a composite good and the unit rent (price) of land, respectively. The expenditure function is defined as follows: E( p, r, z, u)min x,l [( pxrl ); u(x, l, z)u].

(A1.4)

From Shepard’s lemma, the demand for goods is obtained as follows: x E/ p E( p, r, z, u)/ pEp

(A1.5)

l E/ r E( p, r, z, u)/ rEr.

(A1.6)

In the two regions, the utility should be equal because of the openness of regions: uu1 u2. 127

(A1.7)

128

The economic valuation of the environment and public policy

And the expenditures of both regions are: E(1, r1, z1, u)E(1, r2, z2, u)ws.

(A1.8)

The total land demand of each region should be equal to the supply of land: H1 N1 · Er(1, r1, z1, u); H2 N2 · Er(1, r2, z2, u)

(A1.9)

where N1 and N2 are the number of consumers in each region: N1 N2 N.

(A1.10)

After the project implementation, which increases the amenity of Region 1 from level z1 to z2, with the cost of C collected equally from all consumers, then r*1 r*2 r* and the expenditure function is: E(1, r*, z2, u*)ws*

(A1.11)

s* r*(H1 H2)/NC/N

(A1.12)

H1 H2 N · Er(1, r*, z2, u*).

(A1.13)

and the endowment is:

The total area is H. Then the area of land for an individual consumer is: l* (H1 H2)/NH/N

(A1.14)

ws* x* r*l *

(A1.15)

x* wC/N.

(A1.16)

u(x*, l*, z2)u*.

(A1.17)

and

The utility is:

PROOF OF EQUALITY CONDITIONS FOR THE CASE OF A SMALL REGION The hedonic measure of cross-sectional price differential is: B(r2 r1)H1.

(A1.18)

Appendix 1

129

The price differential before and after the project is: (r*1 r1)H1 R.

(A1.19)

Since these measures are a function of area H1, if for example, H1 is small, then: R(H1 ) B(H1 ) * r1 – r1 (H1) [r2 (H1) r1 (H1)]r*1 – r2 (H1) H1 lim

H1→ 0

R(H1 ) B(H1 ) lim [r*1 – r2 (H1)] 0. H1 H1→ 0

(A1.20) (A.21)

Thus: R(H1)B(H1).

(A1.22)

BCV

(A1.23)

Since:

when H1 →0 (see Appendix 2), then: R – CV

(A1.24)

Q.E.D. It should be noted that V is a benefit of the project in terms of equivalent variation.

Appendix 2 Proof of the overestimation theorem [*] The overestimation theorem is: B(r2 – r1) H1 CN EVCV.

(A2.1)

(r2 – r1) H1 CV.

(A2.2)

B(r2 – r1) H1.

(A2.3)

Thus:

The hedonic measure is:

PROOF A consumer has a utility function u(x, l, z), where x is a composite good, l is the area of land of a consumer, and z is an amenity. A consumer maximizes the utility: max x,l

u(x, l, z)

under the income constraint of wage w and endowment: pxrlws.

(A2.4)

The sum of rents from the land is distributed among consumers equally. Thus the endowment is: s(r1H1 r2H2)/N

(A2.5)

where p and r are the price of a composite good and unit rent (price) of land, respectively. Expenditure function is defined as follows: E( p, r, z, u) min x,l [( pxrl ); u(x, l, z)u]. 130

(A2.6)

131

Appendix 2 From Shepard’s lemma,1 the demand for goods is obtained as follows: x E/ p E( p, r, z, u)/ pEp

(A2.7)

l E/ r E( p, r, z, u)/ rEr.

(A2.8)

Now we turn to examine the equilibrium conditions without a project. In two regions, the utility should be equal because of the openness of regions: uu1 u2.

(A2.9)

And the expenditures of the two regions are: E(1, r1, z1, u)E(1, r2, z2, u)ws.

(A2.10)

The total land demand of each region should be equal to the supply of land: H1 N1 Er(1, r1, z1, u); H2 N2 Er(1, r2, z2, u)

(A2.11)

where N1 and N2 are the number of consumers in each region: N1 N2 N.

(A2.12)

With the implementation of a project to increase the level of amenity in Region 1 from z1 to z2, then r*1 r*2 r* and the expenditure function is: E(1, r*, z2, u*)ws*

(A2.13)

The project is assumed to require the composite good input and this cost C is shared by all consumers: s* r*(H1 H2)/NC/N

(A2.14)

since there are no differences between land in the two regions: H1 H2 N Er(1, r*, z2, u*).

(A2.15)

The whole area of the society is H. An individual land is: l * (H1 H2)/NH/N.

(A2.16)

ws* x* r*l *

(A2.17)

The budget constraint is:

A composite good consumed is: x* wC/N.

(A2.18)

132

The economic valuation of the environment and public policy

The equilibrium utility is defined as: u(x*, l *, z2)u*.

(A2.19)

The expenditure function is defined as: * E(1, r2, z2, u*) min x,l [(xr2l ): u(x, l, z2)u ].

(A2.20)

Using this expenditure function, the equivalent variation is: EV[E(1, r2, z2, u*)E(1, r2, z2, u)].

(A2.21)

VNEVN [E(1, r2, z2, u*)E(1, r2, z2, u)].

(A2.22)

Then net benefit is:

Thus the overestimation theorem can be written as: (r2 r1)H1 CV.

(A2.23)

BCV.

(A2.24)

r1H1 r2H2 Ns r1H1 Nsr2H2 r1H1 N[E(1, r2, z2, u)w]r2H2

(A2.25)

B(r2 r1)H1,

(A2.26)

Then: Since:

and

then using r1H1, BC is written as: BCr2H1 N[E(1, r2, z2, u)w]r2H2 C w · NN · E(1, r2, z2, u)r2(H1 H2)C w· NN · E(1, r2, z2, u)r2HC.

(A2.27)

l * H/N,

(A2.28)

Using:

then: BCwNNE(1, r2, z2, u)r2Nl * C

Appendix 2

N wr2l *

133

C NE(1, r2, z2, u) N

N (x* r2l *)NE(1, r2, z2, u).

(A2.29)

* * x* r2l * min x,l [(xr2l ): u(x, l, z2)u ]E(1, r2, z2, u ),

(A2.30)

Since:

of course the utility u(x*, l *, z2) satisfies u u* but x* r2l * is not necessarily the smallest. Thus: BCN[E(1, r2, z2, u*)E(1, r2, z2, u)]V.

(A2.31)

Q.E.D.

NOTE [*] 1. Shepard’s lemma is as follows. Suppose the utility satisfies the certain level of utility, then the consumption of a good is x* under the price system p*. We can define the following function: g( p)E( p, u)px*.

(A2.32)

Since the expenditure function is the minimum value which satisfies the given utility: E( p, u)px*

(A2.33)

g(p) equals or is less than zero. The equity holds when: pp*.

(A2.34)

In this case the value of this function reaches the maximum. Thus:

g 0

pi

(A2.35)

pp*.

(A2.36)

when:

The partial derivative in terms of price of a good i is:

g( p*, u) E( p*, u) x*i 0, (i1, . . . , n).

pi

pi

(A2.37)

Thus under any price system p*, the following equation holds: x*i

E .

pi

(A2.38)

Appendix 3 Proof of equality conditions [*] PROOF OF THE EQUALITY CONDITIONS FOR THE SMALL DEGREE OF IMPROVEMENT CASE The small degree of improvement means that z2 z1 is small. And z2 is fixed and not changed due to the project. Thus we can assume that the benefit and cost of the project are a function of z1. From the overestimation theorem A2.29 Appendix 2, we get: B(z1)C(z1)N(x* r2l *)NE.

(A3.1)

And x*, l * can be expressed by the partial derivatives of the expenditure function using Shepard’s lemma. This left-hand side of the equation equals: N{Ep[1, r*(z1), z2, u*(z1)]r2(z1) Er[1, r*(z1), z2, u*(z1)]E[1, r2(z1), z2, u(z1)]}.

(A3.2)

The net benefit of the project in terms of the equivalent variation V is: V(z1)N{E [1, r2(z1), z2, u*(z1)] E [1, r2(z1), z2, u(z1)]}.

(A3.3)

We can examine the following situation in order to prove the equality condition: B(z1 ) C(z1 ) . z1→ z2 z2 z1

(A3.4)

lim [B(z1)C(z1)]0,

(A3.5)

lim

Since: z1→ z2

then using l’Hôpital’s theorem, lim

z1→ z2

B(z1 ) C(z1 ) B (z1 ) C (z1 ) lim lim B (z1)C (z1) z2 z1 z1→ z2 1 z1→ z2 134

(A3.6)

Appendix 3 V(z1 ) lim V (z1) z1→ z2 z2 z1 z1→ z2 lim

135 (A3.7)

B (z1 ) C (z1 ) Epr[1, r*(z1), z2, u*(z1)]r* (z1) N Epu[1, r*(z1), z2,

r*(z1), z2, u*(z1)]u* (z1) u*(z1)]r2(z1)· Err[1, r*(z1), z2, u*(z1)] r 2(z1) Er[1, * r (z1)r2(z1) Eru[1, r*(z1), z2, u*(z1)] u* (z1) Er[1, r2(z1), z2, u(z1)] r 2(z1)Eu[1, r2(z1), z2, u(z1)] u (z1) r* (z1)[Epr r2(z1) Err]u* (z1) [Epu r2(z1) Eru] u (z1) Eu[1, r2(z1), z2, u(z1)] (A3.8) r 2(z1) {Er[1, r2(z1), z2, u*(z1)]Er[1, r2(z1), z2, u(z1)]}. Since: E(1, r, z, u)xrl,

(A3.9)

E is a function of x, l and can be written as: EEp(1, r, z, u)rEr(1, z, r, u).

(A3.10)

The total derivative of this equation is: Er(1, r, z, u)Epr(1, r, z, u)rErr(1, r, z, u)Er(1, r, z, u), (A3.11) then: Epr(1, r, z, u)rErr(1, r, z, u)0.

(A3.12)

Thus, the left-hand side of (A3.8) r 2(z1) {Er[1, r2(z1), z2, u*(z1)]Er[1, r2(z1), z2, u(z1)]} u* (z1) Eu[1, r2(z1), z2, u*(z1)] u (z1) Eu[1, r2(z1), z2, u(z1)].

(A3.13)

In the case of z1 →z2: r*(z1)r2(z1) l *(z1)l2(z1) Eu(r2)Epu(r2)r2Eru(r2).

(A3.14)

EEp rEr,

(A3.15)

Since:

136

The economic valuation of the environment and public policy

the partial derivative of utility u becomes: lim {Epu[1, r*(z1), z2, u*(z1)]r2Eru[1, r*(z1), z2, u*(z1)]}

z1→ z2

lim {Epu[1, r2(z1), z2, u*(z1)]r2Eru[1, r2(z1), z2, u*(z1)]} z1→ z2

lim Eu[1, r2 (z1), z2, u*(z1)]

(A3.16)

lim Er[1, r*(z1), z2, u*(z1)] lim Er[1, r2(z1), z2, u*(z1)].

(A3.17)

z1→ z2

z1→ z2

z1→ z2

Thus: B (z1 ) C (z1 ) u* (z1) Eu[1, r2(z1), z2, u*(z1)] N r 2(z1) {Er[1, r2(z1), z2, u*(z1)]Er[1, r2(z1), z2, u(z1)]} u (z1) Eu[1, r2(z1), z2, u(z1)] u* (z1) Eu[1, r2(z1), z2, u*(z1)] u (z1) Eu[1, r2(z1), z2, u(z1)].

(A3.18)

On the other hand: V (z1 ) u* (z1) Eu[1, r2(z1), z2, u*(z1)] N u (z1) Eu[1, r2(z1), z2, u(z1)] lim [B (z1)C (z1)] lim V (z1) z1→ z2

z1→ z2

N[Eu[1, r2, z2, u] u (z1)Eu[1, r2, z2, u*] u* (z1)].

(A3.19)

We can prove the following equality if z1 is very close to z2: B – CV

(A3.20)

Q.E.D.

PROOF OF EQUALITY CONDITIONS FOR THE CASE OF A SMALL AREA As we discussed in the case of a small improvement in the previous section, we can assume that the cost of the project, the prices of the land, and the utility are functions of the area of Region 1. Since: B(r2 r1)H1,

(A3.21)

Appendix 3

137

we can prove the theorem in the same way as before: lim

H1→ 0

B(H1 ) C(H1 ) lim [B (H1)C (H1)] H1 H1→ 0

(A3.22)

V(H1 ) lim V (H1) H1 H1→ 0

(A3.23)

lim

H1→ 0

B (H1 ) C (H1 ) Epu[1, r*(H1), z2, u* (H1)]u* (H1) N r2(H1) Eru[1, r*(H1), z2, u*(H1)]u* (H1) Eu[1, r2(H1), z2, u(H1)]u (H1) {Er[1, r*(H1), z2, u*(H1)]Er[1, r2(H1), z2, u(H1)]} r 2(H1) * * {Epr[1, r (H1), z2, u (H1)]r2(H1)Err[1, r*(H1), z2, u*(H1)]} (A3.24) r* (H1). V (H1 ) N Eu[1, r2(H1), z2, u*(H1)]u* (H1) Eu[1, r2(H1), z2, u(H1)]u (H1) Er[1, r2(H1), z2, u*(H1)]r2 (H1) Er[1, r2(H1), z2, u(H1)]r2 (H1)

(A3.25)

B (H1 ) C (H1 ) N Eu[1, r2(H1), z2, u*(H1)]u* (H1) Eu[1, r2(H1), z2, u(H1)]u (H1) 0 · r2(H1)0 · r* (H1) Eu[1, r12(H1), z2, u*(H1)]u* (H1) Eu[1, r2(H1), z2, u(H1)]u (H1)

(A3.26)

V (H1 ) Eu[1, r2(H1), z2, u*(H1)]u* (H1) N Eu[1, r2(H1), z2, u(H1)]u (H1)0 Eu[1, r2(H1), z2, u*(H1)]u* (H1) Eu[1, r2(H1), z2, u(H1)]u (H1).

(A3.27)

138

The economic valuation of the environment and public policy

Then: lim [B (H1)C (H1)] lim V (H1)

H1→ 0

H1→ 0

N{Eu[1, r2(H1),z2, u*(H1)]u* (H1) Eu[1, r2(H1), z2, u(H1)]u (H1)}. Q.E.D. We can prove the theorem of equality.

(A3.28)

Appendix 4 Model and proof of the overestimation theorem in the case of heterogeneous consumers [*] We assume that there are two types of consumers who are identified by superscripts 1 and 2. Consumer 2 lives in both Regions 1 and 2. The regions are identified using subscripts. Consumer 1 only lives in Region 1. Then the hedonic measure may overestimate the real gross benefit. Without an amenity improvement project: E 2(1, r1, z1, u2)E 2(1, r2, z2, u2)w2 s2

(A4.1)

E 1(1, r1, z1, u1)w1 s1 E 1(1, r2, z2, u1)

(A4.2)

H1 N 1E 1r(1, r1, z1, u1)N 21E 2r(1, r1, z1, u2)

(A4.3)

H2 N 22E 2r(1, r2, z2, u2).

(A4.4)

The number of consumers i in Region j is N ji : N 21 N 22 N 2

(A4.5)

N 1s1 N 2s2 r1H1 r2H2.

(A4.6)

If we implement a project to increase the level of amenity in Region 1 from z1 to z2 at cost C: E 1(1, r*, z2, u1*)w1* s1*

(A4.7)

E 2(1, r*, z2, u2*)w2* s2*

(A4.8)

H1 H2 N 1E 1r(1, r*, z2, u1*)N 2E 2r (1, r*, z2, u2*)

(A4.9)

N 1s1* N 2s2* r*(H1 H2)C.

(A4.10)

In this heterogeneous case, the overestimation theorem is: BCVD0 139

(A4.11)

140

The economic valuation of the environment and public policy

where: D N1[E1(1, r2, z2, u1)E1(1, r1, z1, u1)].

(A4.12)

D (0) is positive because there is no consumer 1 living in Region 2. This means that the value of expenditure function of consumer 1 in Region 2 is higher than that in Region 1.

PROOF OF THE OVERESTIMATION THEOREM IN THE CASE OF HETEROGENEOUS CONSUMERS

since

BC(r2 r1)H1 Cr2H1 r1H1 C r2H1 (r1H1 r2H2)r2H2 C r2(H1 H2)(N 1s1 N 2s2)C r2(H1 H2) [N 1E1(1, r1, z1, u1)N 1w1 N 2E 2(1, r2, z2, u2)N 2w2] CN 1w1 N 2w2 r2(H1 H2)C [N 1E 1(1, r1, z1, u1)N 2E 2(1, r2, z2, u2)]

(A4.13)

N 1x1* N 2x2* N 1w1 N 2w2 C

(A4.14)

BCN 1x1* N 2x2* r2(H1 H2) [N 1E1(1, r1, z1, u1)N 2E 2(1, r2, z2, u2)] N 1[(x1* r2l 1*)E 1(1, r1, z1, u1)] N 2[(x2* r2l 2*)E 2(1, r2, z2, u2)]

(A4.15)

VN 1EV 1 N 2EV 2

Q.E.D.

N 1[E 1(1, r2, z2, u1*)E 1(1, r2, z2, u1)] N 2[E 2(1, r2, z2, u2*)E 2(1, r2, z2, u2)]

(A4.16)

BCVN 1[(x1* r2l1*)E 1(1, r2, z2, u1*)] N 1[E 1(1, r2, z2, u1)E 1(1, r1, z1, u1)] N 2[(x2* r2l2*)E 2(1, r2, z2, u2*)] N 1[E 1(1, r2, z2, u1)E 1(1, r1, z1, u1)]0.

(A4.17)

Appendix 5

Short-run case [*]

OVERESTIMATION THEOREM IN THE CASE WHEN CONSUMERS IN REGION 2 CHOOSE THEIR LAND AREA OPTIMALLY When we consider the short-term case, the land area for an individual consumer cannot be chosen optimally by the consumer because the lot size of land in both regions is fixed. But if the land area is chosen optimally by a consumer in Region 2 without the project, then the overestimation theorem holds. First we introduce a conditional expenditure function as follows: EC( p, r, z, u) min [( pxrl ); u(x, l, z)u].

(A5.1)

x

In the two regions, the utility should be equal because of the openness of the regions: u u1 u2.

(A5.2)

And the expenditures of both regions are: EC(1, r1, z1, u)E(1, r2, z2, u)ws

(A5.3)

s(r1H1 r2H2)/N

(A5.4)

because, in Region 2, the land area is chosen optimally by a consumer. The overestimation theorem is: B(r2 – r1) H1 CN EVCV

(A5.5)

(r2 – r1)H1 CV.

(A5.6)

Thus:

PROOF OF OVERESTIMATION THEOREM The hedonic measure is: (r2 – r1)H1 B. 141

(A5.7)

142

The economic valuation of the environment and public policy BCr2H1 N [E(1, r2, z2, u )w]r2H2 C wNNE(1, r2, z2, u)r2(H1 H2 )C wNNE(1, r2, z2, u)r2HC BCwNNE(1, r2, z2, u)r2(N1l1 N2l2)C

N1 wr2l1

C C N2 wr2l2 NE(1, r2, z2, u) N N

N1(x*1 r2l1)N2(x*2 r2l2)NE(1, r2, z2, u).

(A5.8)

BCV N1(x*1 r2l1)N2(x*2 r2l2) N[E(1, r2, z2, u)E(1, r2, z2, u*)E(1, r2, z2, u)],

(A5.9)

VNEVN[E(1, r2, z2, u*)E(1, r2, z2, u)].

(A5.10)

BCV N1[(x*1 r2l1 E(1, r2, z2, u*)] N2[(x*2 r2l2 E(1, r2, z2, u*)].

(A5.11)

Then:

since:

Thus:

Since: xi* r2li* min [(xr2l ): u(x, l, z2)u*] x,l

E(1, r2, z2, u*), and u(x*1, l1, z2)u(x*2, l2, z2)u*.

(A5.12)

BCV0.

(A5.13)

Thus:

Q.E.D. In the case of equal land area in both regions, even if the individual land area has not been chosen optimally, the equality condition holds.

143

Appendix 5

EQUALITY THEOREM IN THE CASE OF SAME LOT SIZE If l1 l2, then BCVC 0 where: VC N[EC(1, r2, h2, z2, u*)EC(1, r2, h2, z2, u)].

(A5.14)

BCV N1[x*1 r2l1 EC(1, r2, z2, u*)] N2[x*2 r2l2 EC(1, r2, z2, u*)].

(A5.15)

l1 l2

(A5.16)

x*1 x*2,

(A5.17)

Proof:

Since:

then:

and thus the right-hand side becomes zero: BCVC 0. Q.E.D.

(A5.18)

Appendix 6 Two-region general equilibrium model We assume that the society is composed of two regions i(i1, 2), homogeneous households have the utility function u(·) whose components are a composite good, land and environmental amenity, xi, l hi , zi. A household maximizes its utility [*]: u(xi , l ih, zi ) max h xi,li

under the constraints of: wi sxi r ih lih

(A6.1)

where wi, rih, s are wage in region i, housing land rent in region i, and endowment, respectively: s /N

(A6.2)

where is total profits of firms and land owners; and N is the number of households as well as workers in the society. From the first-order condition, ul u/ l, ux u/ x ux rih ul wi sxi ril lih,

(A6.3)

we can get following demand functions: xi xi(wi s, rih, zi )

(A6.4)

lih lih(wi s, rih, zi ).

(A6.5)

V(wi s, rih, zi ) u[xi(wi s, rih, zi ),lih(wi s, rih, zi ),zi].

(A6.6)

Thus the utility is:

There are two types of firm in the society. Each type of firm produces the same composite good by regional specific technology using the same 144

145

Appendix 6

resources of worker, firm’s land and amenity of environment, ni, l if, zi. They produce Xi. They maximize their profit [*]: Xi (wi ni ri l if ) max f

(A6.7)

ni,li

under the production technological constraints: Xi Xi(ni,l if, zi ).

(A6.8)

Demand functions of worker and land are: ni ni(wi, ri, zi, Xi ), l if l if(wi, ri, zi, Xi ).

(A6.9)

Since perfect competition and free entry requires a homogeneous degree of one technology with respect to worker and land inputs, we can assume that the number of firms in each region is unity: mi 1.

(A6.10)

Thus the profit is zero and the price of composite good is unity as well. Thus, the unit cost function of firms is: c(w1, r1, z1)c(w2, r2, z2)1 Xi cC.

(A6.11) (A6.12)

The land owners maximize their profit [*]: L max h f hi ,hi

(r l m n r l m ) h h

i i

i

f f

i i

i i

i

H1 l h1m1n1 l f1m1, H2 l2hm2n2 l 2fm2,

(A6.13) (A6.14)

and the first-order condition requires that the land rent price of land for housing and firm are the same, thus: r h1 r1f r1, r2h r2f r2.

(A6.15)

Market equilibrium conditions without the project are: l h1n1 l f1H1, l2hn2 l 2f H2

(A6.16)

Nn1 n2

(A6.17)

V(w1 s, r1, z1)V(w2 s, r2, z2)

(A6.18)

n1x1 n2x2 X1 X2.

(A6.19)

When we introduce a project to improve the amenity of Region 1 up to the level of Region 2 , the cost C T is assumed, which requires composite input.

146

The economic valuation of the environment and public policy

We use the following notation for without the project and with the project respectively, o,w. Thus: zw1 z2o z2w.

(A6.20)

We collect lump-sum tax for project implementation: T T C T/N.

(A6.21)

The equilibrium conditions with the project are as follows: Vw V(wiw sw T T, riw, ziw )

(A6.22)

n1x1 n2x2 CT X1 X2

(A6.23)

V(wio so EVi, rio, zio)V(wiw sw T T, riw, ziw).

(A6.24)

Net benefits of the project can be evaluated using expenditure function E(·), equivalent variation is: EVi E(rio, zio, Vw)E(rio, zio, Vo).

(A6.25)

We use the price system of Region 2: EVE(r2o, z2o, Vw)E(r2o, z2o, Vo).

(A6.26)

NEV.

(A6.27)

Total net benefit is:

Appendix 7 Two-region two type of consumer general equilibrium model We assume that there are two types of consumers who have the same utility function, that is, the same taste but different endowment. The total profits from firms and land owners are distributed to consumers R and P by the following rate : 1. In this appendix, i stands for region and j stands for two types of consumers. We should determine how to collect the cost of the project from these consumers. There are three methods, that is, lump-sum tax from endowment, tax proportional to land rent, and tax proportional to income. It is widely acknowledged that tax distortion exists in the last two tax systems. Since we are not interested in the bias of the tax system in general, we use tax proportional to land rent price which may directly affect the capitalization ratio. These consumers maximize their utilities [*]: maxh ui(xij , lij , zi ), wi sj xij r hij (1Tirh)l hij .

(A7.1)

xi j ,li j

T irh is a tax rate. The endowments are:

sp /NP

(A7.2)

sR (1) /NR

(A7.3)

m n r i

i

j

h h f f ij ij l ij ri l i

Vj [wi sj, rhij(1T irh) zi ] U [xij ( ), r hij ( ), zi ] [wi sj, r hij(1Tirh) zi ].

(A7.4) (A7.5) (A7.6)

From the maximization of land owners’ profits, we can get: r hij r hirifri .

(A7.7)

Firms maximize their profits [*], thus we can get the cost function as follows: c[wi, r hi, Xi; zi) min f [wi(niP niR)r if(1Tirf )l if] niP,niR,li

147

(A7.8)

148

The economic valuation of the environment and public policy Xi Xi (niP, niR,l if ,zi ).

(A7.9)

Tirf is a tax rate for firm land. In order to maximize the profits: i 1 · Xi ci

(A7.10)

i

c

c 1 i 0, i 1.

Xi

Xi

Xi

(A7.11)

mi 1.

(A7.12)

Thus:

Without the project Tirh, Tirf are zero. Market equilibrium conditions are:

n l

h f ij ij li Hi

j

(A7.13)

n1P n2P NP, n1R n2R NR

(A7.14)

n x X

(A7.15)

i

ij

j

ij

i

j

VP(w1 sP, r h1, z1)VP(w2 sP, r h2, z2 ) VR(w1 sR, r h1, z1)VR(w2 sR, r h2, z2 ).

(A7.16)

We introduce a project to improve the amenity level of Region 1 up to the level of Region 2, z1 →z2: zw1 z2w, zo1 !zw1 .

(A7.17)

Tirf Tirh,

(A7.18)

If we assume:

market equilibrium with the project is as follows:

n r T j

i

h ij ij

rhl h r fT rfl f ij i i i

i

CT

n x C X T

i

j

ij ij

i

i

rh h VP[w1 sP, r h1(1T rh 1 ), z1]VP[w2 sP, r 2(1T 2 ), z2]

(A7.19)

(A7.20)

Appendix 7 rh h VR[w1 sR, rh1(1T rh 1 ), z1]VR[w2 sR, r2(1T 2 ), z2].

149 (A7.21)

In our numerical analysis, we specify the functions as follows: P x P x P)1/P uP(xip, l hip, zi)( P xiP p iP p iP R R R 1/R uR(xiR, l hiR, zi)( Rx iR RxiR RxiR ) Xi(niP, niR, lif, zi)[ai(niP niR) bi(l if )i](1/i)Zi.

(A7.22)

Appendix 8 Schedule of benefits and costs Table A8.1 Schedule of benefits and costs (2001 price: unit 100 million yen) Cost Year Time Benefit Dredging

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

2049 2050

48 49

0 0 0 0 0 173 173 173 173 173 384 384 384 384 384 384 384 384 384 384 same 384 384

AgriFresh cultural Water Treatment

Sewage Total System Improvement

50 50 50 50 50 60 60 60 60 60 20 20 20 20 20 20 20 20 20 20

10 10 10 10 10 15 15 15 15 15 10 10 10 10 10 10 10 10 10 10

200 200 200 200 200 210 210 210 210 210 20 20 20 20 20 20 20 20 20 20

300 300 300 300 300 330 330 330 330 330 60 60 60 60 60 60 60 60 60 60

560 560 560 560 560 615 615 615 615 615 110 110 110 110 110 110 110 110 110 110

20 20

10 10

20 20

60 60

110 110

Value left at the end of project period 2051 50 0 0

2,000

2,000

150

Notation a parameter of the Cobb–Douglas production function or general parameters of any functions AI area of Region I ACCi accessibility of Region i b a parameter of production function or general parameters of any functions B benefit or hedonic measures c total cost of production c a parameter of production function and a cost function (or unit cost) in Appendices 6 and 7 C cost of a project T C cost of a project in Appendices 6 and 7 d hi number of household trips f di number of firm trips DIDni population of densely inhabited districts in Region i E expenditure function EV equivalent variation f general function f f(n, l , z) production function f firm h household or consumers H area of the region i interest rate or stands for a region K stock of infrastructure lf land input for firms lh residential land for the household Leq equivalent power level of noise a

151

152

The economic valuation of the environment and public policy

LPh, LPf m n N O Pik Pm ik q r r*i s S tm ik T TTi u V VC w W x X z, Z

, , , ,

residential and business land prices, respectively number of firms number of workers or consumers number of consumers or total number of workers or consumers offer function of producers unit transport fare transport cost (for example, fares) of transport mode m between i and k generalized cost, time, or physical distance land rent equilibrium rent of land in Region i after the project has been implemented an endowment, that is, a sum of non-wage incomes supply of transport services time of travel by mode m between i and k investment lump-sum tax a utility or utility function indirect utility function net benefit or indirect utility function government production costs for transport service wage, and weight time value a composite good composite goods produced an amenity as local public goods parameters of utility function a power of a variable or a parameter of distance decay function a constant converter of monetary into physical stock parameters of the transport cost function

Notation

,

153

non-wage income (rents from lands and dividends from firms’ profits) firms’ or land owners’ profits parameters of production function markup ratio bid price function

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Index accessibility (ACC) 37, 38, 42, 43, 66, 67, 76–8, 81, 82, 84, 85, 87, 89, 91, 95–7, 99, 114 air pollution 45, 46, 67, 68, 76, 87, 88 amenity 15, 19, 20–23, 25, 26, 28, 30–32, 34, 35, 38, 39, 46, 51, 52, 67–70, 72, 74, 77, 79, 80, 82, 96–8, 112–14, 116, 120, 127, 128, 130, 139, 144, 145, 148 asparagus 9, 10 assessed price 40, 53, 55, 59, 60, 71 assessor 53–5, 57, 60, 77, 112 attribute 2, 9–15, 17–19, 40, 59–62, 67, 68, 77, 79, 80, 87, 97, 112 Aveline, N. 70 Bartik, T. 15 Bateman, I. 45 beneﬁt gross 21, 24, 25, 27–9, 37, 42, 44, 139 net 21, 26, 110, 116, 132, 134, 146 transfer 52, 101 bid price 10, 12, 21, 26, 28 function 10–17, 52 marginal 13 biochemical oxygen demand (BOD) 91, 118 biodiversity 115 Bishop, R. 46 Blomquist, G. 77 Boston 9, 10 Box–Cox transformation 69, 70, 87 Brent, R. 108 Brookshire, D. 45–7, 50, 87 Brown, J. 13–15, 52

capitalization cross-sectional 16, 18, 20, 21, 25, 29, 125, 126 hypothesis 16, 18 time-series 18–20, 21, 127 Carson, T. 4, 45, 46, 111 central business district (CBD) 19, 41, 49, 62, 65, 66, 93–6, 99, 100, 119 CES 33, 34 charge 2, 113, 115, 116 Cheshire, P. 58 Coase, R. 111 Cobb–Douglas 24, 29, 30, 33, 34 commute 67, 72, 76–8, 81, 82 comparative statics 19–21, 125 see also time series capitalization compensating surplus (CS) 105, 106, 110 compensating valuation (CV) 4, 103–6, 110 compensation principle 108, 110 composite good 9, 11, 12, 17, 20, 23, 24, 26, 32, 127, 130, 131, 144, 145 composite price 9, 12, 15, 17, 68 conjoint analysis 4–6 constant return to scale 20, 23, 25 content analysis 72 contingent valuation method (CVM) 4–6, 45–9, 105, 123 consumer 3, 4, 8, 10–14, 17, 18, 20, 22–5, 30, 34, 35, 44, 51, 52, 61, 62, 68, 71, 74, 76, 78, 101, 104, 109, 110, 113–5, 128, 130, 139–41, 147 homogeneous 12, 15, 16, 19, 22, 25, 127

163

164

Index

consumer (cont.) heterogeneous 27, 34, 35, 139, 140 preference 4, 16, 18, 63, 71, 107 surplus 3, 4, 123 cost–beneﬁt 15, 20, 29, 36, 42, 43, 102–4, 107–13, 115, 116, 123, 126 ratio 111 cost function 13, 38–40, 42, 145, 147 cost of project 5, 21, 24, 26, 33–5, 122, 134, 136, 147 costless mobility 3, 5, 21 Court, A. 9, 10 Cropper, M. 15 Deaton, A. 104 deﬂator 2, 68, 109 degree of improvement 5, 29–31, 34, 35, 134 depreciation 112 Desvousges, W. 50 discount rate 109, 110, 112, 114, 122, 124 distributional eﬀect 44 elasticity 33–5, 72, 74, 82, 85, 96, 124 endowment 20, 21, 23, 25, 35, 127, 128, 130, 144, 147 envelop 12 environmental standard 118, 119 Epicures 1 Epple, D. 15 equivalent surplus (ES) 105–7 equivalent valuation (EV) 4, 23, 24, 26, 37, 103–7, 110, 129, 132, 134, 146 ex-ante 28, 44, 105, 117 ex-post 117 expenditure function 24, 27, 104, 127, 128, 130–34, 140, 141, 146 exploration 70 externality 79, 80, 82, 87, 107 façade 65, 78–83, 85, 86, 98 ﬂat 61, 77, 78, 80, 81, 92, 94, 97, 98

ﬂooding 61, 74–6, 84, 85, 97, 100 ﬂoor to land ratio (FL ratio) 62, 65, 84, 89, 92, 94, 95, 97, 100 eﬀective 65, 95, 96 ﬂow 111, 112, 121 beneﬁt 114, 120 cost 116, 122 forecasting 3, 117 forest 4, 57, 77, 117 France 58, 70, 95 free rider 8 Fujita, M. 19 functional form 1, 6, 17, 52, 66, 69, 70 Garrod, G. 45, 101 general equilibrium 22, 25, 26, 33, 34, 37, 43, 44, 103–5, 113, 115, 125, 127, 144, 147 generalized cost 38, 65–7, 82, 89 geographic information system (GIS) 63, 65 Germany 95 global warming 110, 115 Greene, W. 52, 70 green environment 2, 52, 79–83, 85–7, 97 Griliches, Z. 3, 10 Hanley, N. 45, 104 happiness 4, 7, 10, 12 Hass, G. 9 Heberline, T. 46 hedonic 1, 9, 10 measure 22–9, 31, 33, 34, 37, 42–4, 51, 59, 91, 113–15, 128, 130, 139, 141 pleasure 10 price function 2, 3, 11, 15–17, 37, 40–44, 47, 51, 52, 59, 63, 68, 69, 72, 91, 112–17, 119, 120, 123, 125 price method (HPM) 3, 6, 45, 49, 71, 102, 111, 123 Hoehn, P. 19, 20 homogeneous of degree one 123, 145

Index Horowitz, J. 15 household 33, 35, 38, 48, 90, 103, 119, 144 housing price 2, 3, 58, 60, 61 Huang, J. 87 human response index 80 hunting permit 46 implicit price 2, 13, 60, 67, 68, 71, 113 see also hedonic price function inheritance tax 55, 57, 72 institutional measures 71, 95–7, 100 regulation 71, 120 interest rate 40, 42, 110 internal rate of return (IRR) 111 investment 38, 119 Johansson, P.-O. 24, 107, 108 Kahn, S. 15 Kanemoto, Y. 5, 15, 16, 21, 22, 25–30, 87, 100 land mark 63 land owner 23, 60, 144, 145, 147 land price 2, 3, 21, 34, 40, 43, 49, 54, 55, 60, 72, 74, 75, 77, 82, 83, 85, 101, 112, 114, 115 land price map 46, 56 land use control 27, 64, 65, 120 landscape 63, 67, 74, 77, 78, 97, 98 Lang, K. 15 large-scale project 16, 20, 26, 29, 43, 44, 103, 114, 115, 125 Leontief 26, 34, 70 l’Hopital’s theorem 134 line price 55, 57 liquidity 124 local tax 115 logit model 5, 15 long-run 15, 16, 22, 27, 28, 68, 103, 113, 115 lot size 16, 27, 64, 68, 72, 84, 85, 92, 94, 112, 141, 143 lump-sum tax 24, 38, 146, 147

165

market price 10, 12, 13, 52 price function 11–14, 17 see also hedonic price function segment 51, 52 separate 14, 52 markup ratio 13 Mas-Coell, A. 104 maximum likelihood estimation 69 Mishan, E. 103, 110, 111, 113 Mitchell, R. 45, 46, 111 mixed land use 20, 27, 43, 115 monetary measure 103, 105 monopolistic 13 moral satisfaction 46, 47, 50 Muellbauer, J. 104 multicollinearity 6, 17, 68 multiperiod 68 Nakamura, R. 15 Nelson, J. 87 net present value (NPV) 110, 114, 122 Newton-Raphson 31, 33, 42 noise 61, 67, 77–9, 87–90, 97, 98 noise index 89 non-market good 50 non-use value 47 numerical analysis 30, 33, 36, 37, 44 Oats, W. 18 oﬀer function 10, 13 oﬀer price 53, 58 oﬃcially announced land price (OAP) 40, 54, 55, 57, 58, 87, 98–100 Ohta, M. 13 oligopolistic 13 on-site 62, 76, 77, 79, 87, 96, 112 Ono, Y. 124 open space 61, 63, 72, 74 openness 3, 22, 80, 97, 127, 131, 141 opportunity cost 107, 116 option price 58 ordinal least square regression (OLS) 40, 69, 72, 82, 89 overestimation 22, 26, 29, 33, 44 ratio 29–31, 34, 35, 44

166

Index

overestimation theorem 25–7, 29, 30, 36, 130, 132, 134, 139–41 equality condition of 25–7, 29, 30, 36, 128, 134, 136, 142 parametric estimation 6 non-parametric estimation 6 park 48, 49, 72–9, 84, 92, 94, 97, 98 Pearce, D. 87, 108 perfect competition 3, 145 perfect information 3, 21 Pigou, A. 110 pleasure 1, 2 pooling sample 61 Popper, K. 126 potential Pareto improvement 108, 110 preference revealed 3 stated 4, 45, 105, 107 present value 109, 114, 121–3 price index 2, 10, 60 producer 3, 4, 10–13, 51, 110, 113, 114 production function 3, 30, 31, 33–5, 38–41, 116, 117 technology 11, 20, 33, 35, 61, 113 property price 3, 60, 68, 97 property right 111 property tax 18, 53–5 public good 17, 104, 105, 115, 125 local 2, 8, 23, 45, 95, 112, 115, 123 public policy 3, 4, 16, 19, 28, 52, 70, 125 questionnaire 6, 55, 77, 105, 107 Quigley, J. 15 railway service 76, 78, 97, 99 rate of substitution 12, 17, 31, 32, 109 Rawls, J. 108 Rawlsian social welfare function 108 real price 109 regional economic model 19

Renard, V. 70 residential land 61, 62 revenue 116, 117 risk 61, 74–6, 85, 97, 100 river 47–9, 74, 79, 90, 91, 98, 113, 117–20 Roback, J. 19, 20 robustness 31, 32, 96, 126 Rosen, H. 13–15, 52 Rosen, S. 10, 13, 17, 19, 26, 46, 52 Rosen’s inequality 13, 26, 46 salvage value 109, 122 Sapporo 90–92, 94, 117–19 scenario 16, 109, 113, 114, 117, 119, 122 Schumacher, E. 4, 7, 8 Scotchmer, S. 15, 16, 60, 68 sensitivity analysis 39, 122 setback 80 sewage 41, 43, 49, 62, 75, 88, 97, 99, 115, 119, 150 shadow project 4 Sheppard, S. 13–15, 58, 133 Shepard’s lemma 127, 131, 133, 134 shopping 61–3, 67, 77, 78, 82 short-run 27, 28, 68, 103, 112, 141 site-speciﬁc 60, 67, 68, 71, 72, 87, 96 size of area aﬀected by project 30, 31, 34, 35 small project 27, 113, 119, 120 Smith, K. 50, 87 social optimum 87 social welfare function 102, 104, 108, 109, 111 Spash, C. 45, 104 speculation 54, 72, 97 spillover eﬀect 37 Starrett, D. 18, 19 stock 38, 39, 42, 52, 111, 112, 114, 120 strategic behavior 46, 47 sun-shine 72, 80 surveyor 53, 55–9 time value 38, 66, 67 Tokyo 47, 55–7, 59, 60, 62, 64–6, 71, 74, 76, 77, 87, 88, 96, 99–101

Index transaction price 53–5, 57–60, 77, 87, 91, 95, 123, 126 travel cost method (TCM) 3, 46, 123 trip 5, 6, 38, 65, 66, 76, 77, 89 UK 56, 70 unemployment 107 uniform national dividend scheme 23, 127 unit price 13, 16, 68, 77, 88, 89, 127, 130 urban economic model 19 urban facility 76, 97–9 US 2, 45, 46, 53, 54, 56, 95 utilitarian 104, 108 utility function 11, 12, 16, 17, 19, 30, 31, 33–5, 38–41, 104, 127, 130, 144, 147 homothetic 104, 123 indirect 17, 52, 123 quasi-linear 104, 123 view 60, 61, 63, 67, 72, 76–9, 97, 98, 112 Voith, R. 19, 20

167

wage 18–20, 23, 25, 43, 53, 114, 125, 127, 130, 144 walking distance 65 Wallace, H. 9 water environment 45, 47, 49, 90 quality 48, 49, 90, 91, 94, 97, 98, 117–19 warm glow 46, 50 Waugh, F. 9 Whitehead, C. 70 width of road 49, 60–62, 64, 72–5, 78, 84, 89, 92, 94 Wildasin, D. 19 willingness to pay 10, 26, 46, 47, 50, 115 function 47, 48 Willis, K. 45, 101 with and without project 23, 51, 109, 113, 117, 120, 146 worker 20, 23, 25, 30–32, 67, 144, 145 zoning 23, 65, 95, 97, 100

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