International Encyclopedia of the SOCIAL SCIENCES
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International Encyclopedia of the SOCIAL SCIENCES
[ C O N T I N U E D ]
THOMAS, W. I. William Isaac Thomas (1863-1947), American sociologist and social psychologist, was born in Virginia. Little is known about his early years, but he entered the University of Tennessee at the age of 17 and graduated in 1884. He remained at the university for the next four years as an instructor in modern and classical languages, thereby acquiring a linguistic facility that was to prove invaluable in his later work. After marrying Harriet Park in 1888, he spent a year studying in Germany and then joined the faculty of Oberlin College, where he taught English. In 1893, while on leave from Oberlin, he began graduate work in sociology at the University of Chicago and received his doctorate in 1896. Between 1896 and 1910, when he attained his professorship at the University of Chicago, Thomas published a series of papers on the social psychology of sex (1907) and prepared the Source Book for Social Origins (1909). These early writings reveal an orderly and scholarly mind, a lucid, unpretentious prose style, a grasp of varied but relevant literature, and a flair for interpreting human phenomena. They also contain, in embryonic form, several ideas more fully developed in later works, e.g., the role of attitudes, the "four wishes," the importance of social science, and the interplay of biological and sociocultural factors in human behavior. (These are reviewed in detail in Young 1963.) Between 1908 and 1918 Thomas traveled extensively in Europe, with the support of the Helen Culver Fund for Race Psychology, and began to collect materials on Polish society and the migration of the peasants to America. In 1914 he began
his collaboration with Florian Znaniecki, which culminated in the monumental The Polish Peasant in Europe and America (1918-1920). This was not merely a monograph on a particular cultural and political group but a work that contained important theoretical and methodological insights. Included in it were the "Methodological Note"; a lengthy, intensive life history; theories of personality development and of social change; a typology of personalities; an analysis of the salient features of social organization; and the central attitudevalue schema. Nearly twenty years later it was selected as one of the most significant volumes in social science and was subjected to a searching reappraisal (see Blumer 1939). During this period Thomas also kept abreast of ideas in a variety of fields, from the newer biology of Jacques Loeb, H. S. Jennings, C. M. Child, and A. J. Carlson to the psychology of Pavlov and J. B. Watson and the psychiatry of Freud, Adolf Meyer, and Harry Stack Sullivan. This intense curiosity about ideas provided a rich intellectual background against which his own creativity could flourish. In 1918, as a result of a newspaper scandal, Thomas' appointment at the University of Chicago was terminated, and thereafter his only academic appointments were at the New School for Social Research, from 1923 to 1928, and at Harvard University, in 1936/1937. His later career was maintained through independent research and writing that was often supported by interested individuals, private foundations, or other agencies. With the assistance of Mrs. W. F. Dummer, a Chicago philanthropist, he completed The Unadjusted Girl (1923) and organized an important symposium, later published as The Unconscious (1928). He was in fact the author of Old World 1
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Traits Transplanted (1921), a volume in the Americanization Studies series, supported by the Carnegie Corporation. The Laura Spelman Rockefeller Memorial supported his work, with Dorothy S. Thomas, on approaches to the behavior problems of children, in The Child in America (1928). As president of the American Sociological Society in 1927, he delivered the address "The Behavior Pattern and the Situation" (1927). In succeeding years he was on the staff of the Social Science Research Council, preparing a lengthy memorandum on research problems in the field of culture and personality (published for the first time in 1951, part 4). In connection with this work he again traveled extensively in Scandinavia and elsewhere in Europe, reviewing research on crime, personality formation, and population trends. His first marriage ended in divorce in 1934. His second wife, Dorothy S. Thomas, whom he married in 1935, is an eminent sociologist in her own right and in 1952 was also president of the American Sociological Society. Thomas' last book, Primitive Behavior: An Introduction to the Social Sciences, was published in 1937, and a year later he took part in a symposium that reviewed the significance of The Polish Peasant (see Blumer 1939). After spending a few years in New Haven, Connecticut, he moved to Berkeley, California, where he died at the age of 84. In private life Thomas was an urbane, genial, and witty cosmopolitan. He savored good food, good wine, and good companionship. He had a zest for life, an enormous curiosity about all human experience^ and a generous capacity for warmth and friendship. Few men have worn the mantle of "gentleman and scholar" so gracefully. During the more than forty years of his active career, Thomas was author, coauthor, or editor of 7 books and 38 articles, all marked by erudition, imagination, and seminal ideas. Yet he had no formal doctrine or sociological system, nor did he found a school of sociology. Rather, he directed his attention to a variety of empirical areas— including sex differences, migration, delinquency, and social organization—and fashioned methods and concepts that seemed appropriate to the subject at hand. Nevertheless, certain central themes appear and reappear in a number of his works, and together they constitute his essential contributions to the development of social science. Social behavior. Thomas' interest in human behavior began with his first publications on the sources and consequences of sex differences. Exploring such subjects as modesty, feminine character, and the sex division of labor, he utilized
both biological and sociocultural data, a technique he was to use often. Although he viewed the behavioral differences between the sexes as a function of both internal (organic) and external (sociocultural) conditions, he followed the practice of his time by giving some primacy to the organic factors. That is, he had some tendency toward "reductionism," but he was not consistent, as the development of the "four wishes" and the situational approach to behavior indicates. The four wishes were first presented in the paper "The Persistence of Primary-group Norms" (1917). Thomas described them as "interests," connected with the "desires" for new experience, for mastery, for recognition, and for safety or security. While he did not indicate clearly the precise place of these wishes in the spectrum of motivation, he derived them from "original emotional reactions," such as fear, rage, and love. Further, he suggested the primacy of biology by the statement that all forms of behavior can ultimately be reduced to two fundamental appetites, food hunger and sex hunger. In The Polish Peasant, the wishes became in effect synonymous with attitudes and were defined as partly biological and partly social in character. Two of them—the desires for mastery and security —are linked respectively with the "instincts" of hate and fear, but the desires for new experience and for recognition are free of such organic anchorage. Further, Thomas altered the theoretical significance of the wishes: their rationale now is social control rather than reductionism. Society, through suitable appeals to the wishes as well as by punishments and rewards relating to their expression, can achieve effective social control because it is the essence of the wishes that they must be satisfied socially. The final formulation of the wishes appeared in The Unadjusted Girl, in which Thomas used them to analyze and interpret various forms of female delinquency. Now, however, he dropped the wish for "mastery," replacing it by the wish for "response," which is based on the instinct of love. In this version, the wishes for new experience and for security are linked respectively to the instincts of anger and fear; only the wish for recognition appears to be derived completely from social experience. In this work Thomas referred to the wishes as being "forces which impel to action" and as corresponding in general to the "nervous mechanism." The wishes, in one form or another, became extremely popular in American sociology; their very simplicity and versatility made them attrac-
THOMAS, W. I. This was Thomas' vision in "The Persistence of Primary-group Norms" (1917) and in the famous "Methodological Note" of The Polish Peasant (1918-1920). Clearly, Thomas' view was similar to the one developed by Emile Durkheim some twenty years earlier, for Durkheim was also concerned with problems of social integration and the development of a sociological science. The "social facts" which were the subject matter of Durkheim's social science did not, however, include individual consciousness or subjective states, "facts" that Thomas considered to be of great importance. Thus, in The Polish Peasant, the "attitude-value" schema was introduced precisely for the purpose of studying the relationship between objective and subjective factors. The concept of a "value" in the schema is very similar to Durkheim's concept of a "social fact" in that it is an objective datum. It is also similar to Thomas' earlier concept of "control" in the sense that it is an object of activity. An "attitude" is a motivational element in individual consciousness, such as one of the postulated four wishes. Thus, Thomas regarded social theory and social science as primarily concerned with the interactions and combinations of social values with individual attitudes, because the "cause" of a social or individual phenomenon is never one of these alone but always a joint product. The intent here was to limit, at least abstractly, the number and kind of phenomena with which social science must deal, in order to increase the possibility of formulating a limited number of sociological laws. Indeed, the laws of "social becoming" can be discovered only by studying the interaction of values and attitudes as it has occurred through time in various societies. The schema implied an endless series of empirical studies because the number of possible social values and individual attitudes is almost infinite; but such research would presumably result in a limited number of highly abstract laws, a conception that was clearly based upon the model of the more successful physical sciences of the time. In addition, since the greatest strides in these sciences had been made by men who were moved more by theoretical concerns than by the practical problems of the moment, such theoretical concerns should be primary for social scientists. In Thomas' view, the major weakness of social science was that it lacked theory rooted firmly in systematic data: there was too much aimless empiricism on the one hand and grand conceptualizing on the other, with little relationship between them. Social scientists had to develop methods of investigation compara-
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ble to those of the natural sciences, linking concepts and hypotheses with measurable systematic observations and eliminating their reference to a particular social "problem." The attitude-value schema is now generally regarded as being oversimplified. Nevertheless, it was important at the time as an illustration of what is involved in theory building and of what social science might become—not only a theoretical science, but also one that in due course might find practical application. In all his writings Thomas never deviated from his insistence that rigorous method lies at the heart of successful science. But some of his related views on social science were not so consistent. For example, in his later years he began to doubt that social science can discover "laws" in the same sense as physics and chemistry, for these sciences deal with relatively few variables; the properties of their phenomena do not change; and they can operate within closed systems. In social science, on the other hand, the variables are many; the properties of its phenomena (people) do change; and the systems of personality, society, and culture are open-ended. Thus he came to speak of probabilities and inferences rather than laws and at one point remarked that he did not believe in comparisons between physics and sociology. (For the evolution of Thomas' ideas regarding science and method, see 1951, part 1.) In his later works Thomas emphasized the advantages to social science that might result from taking a situational approach to behavior: "Individuals differentiated in what ways placed in what situations react in what patterns of behavior, and what behavioral changes follow what changes in situation?" (1951, p. 18). The task of the scientist is to describe the situation as accurately as possible in either experimental or field studies and then to observe the behavior in the situation of persons with specified characteristics. In this way systematic inferences can be drawn regarding the crucial variables intervening between stimulus and response. The use of control groups in research will also be facilitated. Many of these ideas regarding social science and social research are now so firmly held and practiced that they are commonplace. But in the years between the two great wars, they required a spokesman, an advocate, and a demonstrator— roles that Thomas filled with distinction. In several ways Thomas was one of the most influential social scientists of the century. During his years at the University of Chicago he helped
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by habit, but from time to time crises arise in social life, either in the form of completely new situations or of old situations on a different scale. Attention is then directed to alternative patterns and new solutions. Extraordinary individuals, building on existing techniques, become especially important in this process of change through adaptation. During his study of the Polish peasant, Thomas became interested in the different rates of change manifested in different societies and the consequences thereof. In nonliterate and peasant societies, the slowness of the rate of change permits the incorporation of new elements into the existing cultural fabric, thereby preventing any widespread demoralization among the people. In modern society, however, change seems so rapid and complex that traditional social controls are steadily being weakened. Group solidarity is being fragmented, and behavior is becoming individualized. The primary group is being replaced by a differentiated mass society with different and conflicting definitions of situations. To deal with these phenomena, Thomas and Znaniecki presented a new model of social change in The Polish Peasant. As a base line, there is an ideal type of "social organization" in which norms and behavior are generally congruent. In every group there are some deviations, either innovative or destructive, from the norms, but as long as these remain few and scattered, the validity of the norms themselves is not questioned; the group can handle the challenge of deviation through a process of "social reorganization," which is essentially any collective response that reaffirms and reinforces existing norms and values. However, when deviations become frequent and widespread, even reaching the point of rebellion or revolt, the normal process of reorganization is inadequate; "social disorganization" has set in, either through the general acceptance of new norms and values by younger generations or through lack of consensus among adults or through combinations of both. This condition, which reflects a decrease in the influence of social norms, is characteristic of modern complex societies and requires nothing less than "social reconstruction," or the creation of new codes and institutions better adapted to the changed conditions of life. In this process, creative individuals are once again assigned major leadership roles, to be guided perhaps by the fruits of successful social research. Since change appeared to sociologists of Thomas' generation to have gone beyond the point at which such concepts as social organization and reorgan-
ization could be effectively applied and since blueprints for a program of social reconstruction did not exist, sociological attention was focused on social disorganization. The phenomena of divorce, crime, delinquency, and mental illness were all studied intensively, and courses in social disorganization became standard offerings in most American colleges and universities. All too often, however, attention was concentrated on the phenotypic elements, and the underlying genotypic processes of change were ignored. As a result, little progress has been made in recent decades toward more comprehensive theories of deviance or of social disorganization as a phase of massive social change. Thomas' legacy, then, lies in formulating macro concepts of a distinctively sociological theory of change that may still warrant research which leads to more specific indicators and hypotheses. Toward a social science. At the beginning of the twentieth century, the idea of a social science was weak and uncertain. Anthropology was largely dominated by concepts borrowed from biology and archeology; psychology was in its infancy; sociology was largely concerned with amelioration of social "problems" or the creation of vast intellectual systems; social psychology was just beginning to be talked about; and psychiatry was preoccupied with nosology and organic approaches to "insanity." The principal science that seemed to offer any clues to understanding man and his behavior was biology and, understandably enough, many persons found it convenient to "reduce" social phenomena to biological terms. Only a few—Marx, Weber, Durkheim, Sumner, and, to some extent, Spencer—had managed to rise above the major presuppositions of the time. It is against such a background that Thomas' contributions to the development of a truly social social science must be viewed. As has been indicated, Thomas thought that the modern world was undergoing such rapid and farflung change that it was becoming disorganized socially. The mutual dependence of the individual and the group that fostered stability in the primary groups of the past was being shattered by forces and pressures that seemed incomprehensible. "Common sense" explanations of the causes and trends of events were proving inadequate, as was the social control technique of "ordering and forbidding." Thus, the great need was for a social science that would study, systematically and empirically, large classes of social events, with the intent of achieving explanatory principles that could then be applied to rational social control.
THOMAS, W. I. This was Thomas' vision in "The Persistence of Primary-group Norms" (1917) and in the famous "Methodological Note" of The Polish Peasant (1918-1920). Clearly, Thomas' view was similar to the one developed by Emile Durkheim some twenty years earlier, for Durkheim was also concerned with problems of social integration and the development of a sociological science. The "social facts" which were the subject matter of Durkheim's social science did not, however, include individual consciousness or subjective states, "facts" that Thomas considered to be of great importance. Thus, in The Polish Peasant, the "attitude-value" schema was introduced precisely for the purpose of studying the relationship between objective and subjective factors. The concept of a "value" in the schema is very similar to Durkheim's concept of a "social fact" in that it is an objective datum. It is also similar to Thomas' earlier concept of "control" in the sense that it is an object of activity. An "attitude" is a motivational element in individual consciousness, such as one of the postulated four wishes. Thus, Thomas regarded social theory and social science as primarily concerned with the interactions and combinations of social values with individual attitudes, because the "cause" of a social or individual phenomenon is never one of these alone but always a joint product. The intent here was to limit, at least abstractly, the number and kind of phenomena with which social science must deal, in order to increase the possibility of formulating a limited number of sociological laws. Indeed, the laws of "social becoming" can be discovered only by studying the interaction of values and attitudes as it has occurred through time in various societies. The schema implied an endless series of empirical studies because the number of possible social values and individual attitudes is almost infinite; but such research would presumably result in a limited number of highly abstract laws, a conception that was clearly based upon the model of the more successful physical sciences of the time. In addition, since the greatest strides in these sciences had been made by men who were moved more by theoretical concerns than by the practical problems of the moment, such theoretical concerns should be primary for social scientists. In Thomas' view, the major weakness of social science was that it lacked theory rooted firmly in systematic data: there was too much aimless empiricism on the one hand and grand conceptualizing on the other, with little relationship between them. Social scientists had to develop methods of investigation compara-
ble to those of the natural sciences, linking concepts and hypotheses with measurable systematic observations and eliminating their reference to a particular social "problem." The attitude-value schema is now generally regarded as being oversimplified. Nevertheless, it was important at the time as an illustration of what is involved in theory building and of what social science might become—not only a theoretical science, but also one that in due course might find practical application. In all his writings Thomas never deviated from his insistence that rigorous method lies at the heart of successful science. But some of his related views on social science were not so consistent. For example, in his later years he began to doubt that social science can discover "laws" in the same sense as physics and chemistry, for these sciences deal with relatively few variables; the properties of their phenomena do not change; and they can operate within closed systems. In social science, on the other hand, the variables are many; the properties of its phenomena (people) do change; and the systems of personality, society, and culture are open-ended. Thus he came to speak of probabilities and inferences rather than laws and at one point remarked that he did not believe in comparisons between physics and sociology. (For the evolution of Thomas' ideas regarding science and method, see 1951, part 1.) In his later works Thomas emphasized the advantages to social science that might result from taking a situational approach to behavior: "Individuals differentiated in what ways placed in what situations react in what patterns of behavior, and what behavioral changes follow what changes in situation?" (1951, p. 18). The task of the scientist is to describe the situation as accurately as possible in either experimental or field studies and then to observe the behavior in the situation of persons with specified characteristics. In this way systematic inferences can be drawn regarding the crucial variables intervening between stimulus and response. The use of control groups in research will also be facilitated. Many of these ideas regarding social science and social research are now so firmly held and practiced that they are commonplace. But in the years between the two great wars, they required a spokesman, an advocate, and a demonstrator— roles that Thomas filled with distinction. In several ways Thomas was one of the most influential social scientists of the century. During his years at the University of Chicago he helped
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to train a. number of young sociologists and social psychologists who, in turn, occupied faculty positions in many universities. Together with his colleagues at Chicago he formed a graduate department which, in terms of quantity and quality of graduate students and scholarly production, dominated American sociology for several decades. He helped to lead sociologists out of the armchair and into the field and the laboratory by establishing the tradition of empirical research for doctoral degrees in sociology. The many concepts he fashioned found their way into textbook after textbook and into the classrooms, thereby influencing generations of younger sociologists. His pioneering memorandum on research in culture and personality influenced the later course of the Social Science Research Council and the work of other scholars in the field. Moreover, he placed social science in the context of modern times, giving due weight to theory and fundamental research but also insisting that the ultimate test of a science must lie in its fruitful application to practical problems. His own keen insights led to a wealth of concepts that not only illuminated specific areas but also possessed more generalized theoretical power. He anticipated and contributed to the formation of a number of current issues in theory and research. His contributions have become a respected part of the culture of modern social science, and we are all, in one way or another, intellectually indebted to him.
(1923) 1964 The Unadjusted Girl: With Cases and Standpoint for Behavior Analysis. Boston: Little. 1927 The Behavior Pattern and the Situation. American Sociological Society, Publications 22:1-13. 1928 The Configurations of Personality. Pages 143-177 in The Unconscious: A Symposium, by C. M. Child et al. New York: Knopf. 1928 THOMAS, W. I.; and THOMAS, DOROTHY S. The Child in America: Behavior Problems and Programs. New York: Knopf. 1937 Primitive Behavior: An Introduction to the Social Sciences. New York: McGraw-Hill. 1951 Social Behavior and Personality: Contributions of W. I. Thomas to Theory and Social Research. Edited by Edmund H. Volkart. New York: Social Science Research Council. On Social Organization and Social Personality: Selected Papers. Edited and with an introduction by Morris Janowitz. Univ. of Chicago Press, 1966. SUPPLEMENTARY BIBLIOGRAPHY
BLUMER, HERBERT 1939 An Appraisal of Thomas and Znaniecki's The Polish Peasant in Europe and America. New York: Social Science Research Council. HINKLE, GISELA J. 1952 The "Four Wishes" in Thomas' Theory of Social Change. Social Research 19:464-484. JANOWITZ, MORRIS 1966 Introduction. In W. I. Thomas, W. I. Thomas on Social Organization and Social Personality. Univ. of Chicago Press. VOLKART, E. H. 1953 Aspects of the Theories of W. I. Thomas. Social Research 20:345-357. YOUNG, KIMBALL 1963 The Contribution of William Isaac Thomas to Sociology. Unpublished manuscript. -> Distributed by Student Book Exchange, 1737 Sherman Ave., Evanston, 111.
THOMAS AQUINAS, SAINT See AQUINAS, THOMAS.
E. H. VOLKART [For the historical context of Thomas' work, see the biographies of COOLEY; DURKHEIM; PARK; SUMNER; ZNANIECKI. For discussion of the subsequent development of his ideas, see CREATIVITY, article on SOCIAL ASPECTS; DEVIANT BEHAVIOR; OBSERVATION;
VALUES.] WORKS BY THOMAS 1907
Sex and Society: Studies in the Social Psychology of Sex. Univ. of Chicago Press. (1909) 1920 Source Book for Social Origins: Ethnological Materials, Psychological Standpoint, Classified and Annotated Bibliographies for the Interpretation of Savage Society. 6th ed. Boston: Badger. 1917 The Persistence of Primary-group Norms in Presentday Society and Their Influence in Our Educational System. Pages 159-197 in Suggestions of Modern Science Concerning Education, by Herbert S. Jennings et al. New York: Macmillan. (1918-1920) 1958 THOMAS, W. I.; and ZNANIECKI, FLORIAN The Polish Peasant in Europe and America. 2 vols. 2d ed. New York: Dover. 1921 Old World Traits Transplanted, by Robert E. Park and Herbert A. Miller. New York: Harper. -> Circumstances made it impossible for this work to be published under Thomas' name.
THOMPSON, WILLIAM William Thompson (1775-1833), a British socialist, was born in Cork, Ireland, but exercised his greatest political influence in England, where industrial development was raising new economic and social problems. The most powerful influence on his early writings was Bentham, from whom he derived his underlying utilitarian philosophy. Bentham, he wrote, "had done more for moral science than Bacon did for physical science" by exposing the fallacies of traditional social and political arguments and by relating the actions of both individuals and governments to the principle of "the greatest happiness of the greatest number" ([1824] 1963, p. x). The influence of Bentham shaped Thompson's earliest, biggest, and most important book, An Inquiry Into the Principles of the Distribution of Wealth (1824). Thompson's view of economics, however, diverged sharply from that of Bentham even at this early stage. Thompson was
THOMPSON, WILLIAM preoccupied with the problem of distribution. He drew a contrast between unequal distribution, under a system of competitive capitalist production, and fair distribution according to labor performed, under a system of cooperative production. He coined many interesting phrases (such as "misery in the midst of all the means of happiness") and touched on a number of original questions of theory (for example, diminishing utility). He saw the problems of economics as the problems of a "system" and incorporated in his analysis an account not only of "social motives" and incentives but of the relationship between cooperative distribution and production. A second influence on the Inquiry was Robert Owen, who in turn greatly admired Thompson's work. In the later 1820s, indeed, Thompson became the most powerful Owenite theoretician, drawing Owen himself into socialist argument and workingclass politics. Labour Rewarded (1827), a reply to Thomas Hodgskin's Labour Defended (1825), is specifically Owenite in tone, strongly advocating the creation both of cooperative societies and trade unions. Thompson distrusted the coercive power of the state, fully accepted Owen's program of community living, and in 1830 published detailed plans with the title Practical Directions for the Establishment of Communities. Yet Thompson's analysis had more depth than Owen's, for it passed from the mechanics of community building to a survey of broad trends in social history, an evaluation of rival contemporary philosophies, including utilitarianism and socialism, and a prediction of the shape of the future. He emphasized the facts of "exploitation," and he anticipated Marx by his use of the term "surplus value" and by his "realistic" approach to problems of class. He held, following James Mill, that public opinion in the past was "the opinion of the influential classes of society." The rich, "like all other classes in every community," must "obey the influence of the peculiar circumstances in which they are placed" ([1824] 1963, p. 211). "The Industrious Classes," however, were "learning their own importance" and would "soon speak out" (1827, pp. 40-41). This was a fair statement of the position in Britain at that time, and Thompson did much to stimulate working-class initiative. He was present at the Co-operative congresses of 1831 and 1832, advocated the appointment of "Cooperative missionaries" on Saint-Simonian and (later) Chartist lines to spread the gospel, and bequeathed his Irish estate to the Co-operative movement. He recognized the importance of agitation
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and propaganda among productive laborers as well as "mental labourers, literati and men of science." He accused Hodgskin of paying too much attention to the latter and quarreled with Owen in 1832 about the paternalist and autocratic elements in Owen's own plans. In his opposition to Owen he was supported by a majority of Co-operative delegates at the third congress of 1832 (see Co-operative Congress 1832). Although legal difficulties eventually prevented the Co-operators from securing his estate, his intellectual legacy was greatly treasured. The revival of interest in early socialist doctrines in the late nineteenth century led H. S. Foxwell and Anton Menger to proclaim Thompson as "the most eminent founder of scientific Socialism" from whom "the later socialists, the Saint-Simonians, Proudhon, and above all, Marx and Rodbertus, have directly or indirectly drawn their opinions" (Menger [1886] 1962, p. 51). One other aspect of Thompson's thought which has historical interest is his passionate championing of the rights of women. His Appeal of One Half the Human Race (1825) has an important place in the literature of female emancipation. ASA BRIGGS [For the historical context of Thompson's work, see the biographies of BENTHAM and OWEN; for discussion of the subsequent development of his ideas, sec ECONOMIC THOUGHT, article on SOCIALIST THOUGHT; and the biographies of MARX; PROUDHON; RODBERTUS.] WORKS BY THOMPSON (1824) 1963 An Inquiry Into the Principles of the Distribution of Wealth Most Conducive to Human Happiness. New York: Kelley. 1825 Appeal of One Half the Human Race, Women, Against the Pretensions of the Other Half, Men, to Retain Them in Political and Thence in Civil and Domestic Slavery. London: Longmans. 1827 Labour Rewarded: The Claims of Labour and Capital Conciliated; Or, How to Secure to Labour the Whole Products of Its Exertions. London: Hunt & Clarke. 1830 Practical Directions for the Establishment of Communities. London: Strange. SUPPLEMENTARY BIBLIOGRAPHY CO-OPERATIVE CONGRESS, THIRD, LONDON, 1832 1832 Proceedings. London: Strange. HODGSKIN, THOMAS (1825) 1922 Labour Defended Against the Claims of Capital. London: Labour Pub. MENGER, ANTON (1886) 1962 Right to the Whole Produce of Labour: The Origin and Development of the Theory of Labour's Claim to the Whole Product of Industry. New York: Kelley. -> First published as Das Recht auf den vollen Arbeitsertrag. PANKHURST, RICHARD K. P. 1954 William Thompson: Britain's Pioneer Socialist, Feminist, and Co-operator. London: Watts.
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THORNDIKE, EDWARD L. THORNDIKE, EDWARD L.
Edward Lee Thorndike (1874-1949) has been rightly called America's most productive psychologist. He was an indefatigable researcher with wide interests. As important as his capacity for work was his responsiveness to the intellectual and social currents generated by contemporary scientific and technological developments. He once described his career as "a conglomerate amassed under the pressure of varied opportunities and demands," and he doubted whether being faithful to one's own plans made science as rich as did following the world's plans for the scientist. Showing great imaginative and creative powers while living this credo, Thorndike so much determined the character of the whole of modern American psychology that his contribution is largely taken for granted. Historical background. "It is certain that man should try to match his understanding of masses, atoms, and cells by understanding of himself," Thorndike wrote in Human Nature and the Social Order (1940, p. 97). These words express the sentiment that had ordered not only his career but those of his fellow builders of a science of man since the dawn of the Darwinian age. Just as Bacon, Locke, and Newton had invigorated and redirected the physical sciences, so empiricism and theory building in the biological and social sciences flourished after the publication of Darwin's Origin of Species in 1859. The doctrine of evolution made man an objective, physical fact in a natural world. The interplay of organism and environment became something to be examined. The biological and psychological processes of the lower animals became relevant to the understanding of man. Interest in the differences between species and in the theory of natural selection generated a curiosity about intraspecies variation; the study and measurement of individual differences grew into a major enterprise of the "new psychology," especially in the United States. In sum, psychology became "genetic." It was feared by some that in the process of becoming genetic, the various social sciences would threaten the existing social order. Others, however, heralded the new sciences of man, modeled as they were upon the spirit and methods of the physical sciences, as basic to a future "social engineering." They hoped the new sciences would make social problems amenable to solution and would enrich social life, just as the older physical sciences had produced technological and material progress. To become scientific, however, psychology had to do more than view human nature and institutions as part of a continuum connecting all organic
life; it had to renounce armchair theorizing and introspection, develop a new methodology, and imitate the rigor and precision of the established sciences in gathering and interpreting data. The important features of the new approach were experimentation and quantification. Psychological experimentation received early direction from the German psychophysicists, especially Fechner and Helmholtz. Next, Wilhelm Wundt founded the first psychological laboratory, at Leipzig in 1879. By 1900 such laboratories were common as centers for research and training, especially in the United States. Although they were at first preoccupied with such psychophysical phenomena as sense perception and reaction time, many laboratories later turned to investigations of memory, learning, and problem solving. The methodological prototypes of contemporary American psychological investigation and data gathering were soon evident: G. Stanley Hall's questionnaires, Thorndike's problem boxes and paper-and-pencil tests, Charles Judd's instruments. By 1900 the "new psychology" was committed to the use of quantification: in the collection of empirical data through counting and measuring, as a statistical method of testing hypotheses, and as the universal language of scientific reporting. Public record keeping was improving rapidly, furnishing a potentially invaluable source of social science data. Still more important were early refinements in statistical methods of manipulating data. Galton developed the correlation coefficient for biology and applied it to psychology; he also used certain conceptual tools of astronomy. Pearson, Spearman, and Cattell contributed early improvements, and Thorndike popularized the statistical treatment of social science data, writing the first influential handbook in the field, An Introduction to the Theory of Mental and Social Measurements (1904). Thorndike's statement, "Whatever exists, exists in some amount and can be measured," epitomizes his devotion to quantification. There was yet another component in the intellectual legacy available to Thorndike. American pragmatism was evolving as an articulated philosophical system, and although Thorndike was not an exponent of philosophical pragmatism, he approached science from a pragmatic standpoint. He rejected traditionalism, sentimentalism, and a priori postulates. His theories of value and social action were firmly guided by appraisals of consequences. Furthermore, he helped to give American psychology its behavioristic and functional cast; behavior was to give the social sciences their data, and behavior was to test their theories.
THORNDIKE, EDWARD L. The formative years. Thorndike was born in Williamsburg, Massachusetts, the second of four children. His father, Edward Roberts Thorndike, was first a lawyer, then a Methodist clergyman. The religious environment of the home has been described as rather austere, and the children were active in church activities. As an adult Thorndike helped support the local Methodist church financially but did not attend or require attendance of his children. He believed churches had certain benefits for some people and could perform useful philanthropic tasks; however, he sought to guide his own life by ethical and not religious precepts. Intellectual pursuits were important in his childhood home-, his mother, Abigail Thorndike, described as highly intelligent, may well have encouraged them, and they were certainly stimulated by contact with the several intellectual, sophisticated congregations in the Boston-Cambridge area to which his father ministered. The children had good academic records and won scholarships and other aid, permitting them all to complete college despite the family's modest finances. The eldest son, Ashley, became a professor of English; Lynn, the third son, a historian; and Mildred, the youngest child, a high school English teacher. At one time or another, all three Thorndike brothers were professors at Columbia University. During Thorndike's boyhood the family moved frequently, propelled by the regulation that a. Methodist minister must change congregations every few years. Thorndike attended elementary schools in several Massachusetts towns, and high schools in Lowell, Boston, and Providence, R. I. Although his schooling did not suffer because of these frequent moves, the discontinuity in social contacts may have contributed to a certain reticence, extreme self-reliance, and lack of easy sociability apparent in the mature Thorndike. He came to prefer a small circle of cherished friends and disliked routine gatherings, whether they were faculty meetings or national scientific conventions. His work consumed his time and attention, wherever he was, and he found personal contention, competition, and the effort to influence others distasteful, viewing such activities as distractions from the research to which he had devoted himself. Thorndike entered Wesleyan University in Connecticut in 1891 without having chosen a career. As a boy he had had no interest in science; rather, his early bent had been toward English, a field to which he indirectly returned much later via word counts, semantic and phonetic studies, the authorship of dictionaries, and a theory of speech origins. He pursued the standard classical curriculum at
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Wesleyan, graduating in 1895 with honors, including membership in Phi Beta Kappa, but still without a commitment to any field. However, he had read William James's The Principles of Psychology and found its ideas and erudition extremely impressive. A scholarship to Harvard University permitted him to sample several disciplines, and after study under James, Thorndike decided upon psychology. He earned another bachelor's degree in 1896 and an M.A. in 1897. Although he had no intention of specializing in comparative psychology, Thorndike began experimental studies of animal learning, convinced that the existing research was impoverished and unsound. A substantial fellowship at Columbia University took him to New York City in 1897 to complete his doctoral study. Columbia offered additional training in biology and statistics, and James McKeen Cattell provided him with laboratory space. The next year Thorndike published his doctoral dissertation, Animal Intelligence (1898-1901). Rarely has a doctoral thesis earned the appellation "classic"; yet Thorndike's study was just that—a classic in comparative psychology, in learning theory, and in psychological methodology. Academic career. In 1898 Thorndike began teaching at the college for women at Western Reserve University in Cleveland, Ohio. On the recommendation of William James he returned to New York City in 1899 for a one-year trial as instructor in psychology and child study at Teachers College, Columbia University; thus began a forty-year association with that school. In 1901 he became adjunct professor and, in 1904, professor of educational psychology. He took on additional duties in 1922 as director of the division of psychology at the new Institute of Educational Research connected with Teachers College. He retired in 1940 but continued writing and published Selected Writings From a Connectionist's Psychology in 1949. He died in the early morning of August 9, 1949, at Montrose, New York, a few days short of his 75th birthday. He was survived by his wife, Elizabeth Moulton, whom he had married in 1900, and their four children: Elizabeth Frances, born in 1902, a mathematician; Edward Moulton, born in 1905, and Alan, 1918, both physicists; and Robert Ladd, 1910, a psychologist. Thorndike was awarded numerous honors during his lifetime: the presidencies of several scientific societies and honorary degrees from American and foreign universities. He was a member of the National Academy of Sciences, the American Philosophical Society, and the American Academy of Arts and Sciences. Foreign recognition brought him
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honorary membership in the British Psychological Society, the Comenius Educational Association of Czechoslovakia, and the Leningrad Scientific-Medical Pedological Society. In 1925, for his contributions to psychological measurement and its applications to education, Columbia University awarded Thorndike the Butler medal in gold, granted once every five years for the most distinguished contribution made anywhere in the world to philosophy or to educational theory, practice, or administration. He served on various committees and commissions and was head of the comparative psychology department at the marine biology laboratory at Woods Hole, Massachusetts, from 1900 to 1902. A theory of learning. For Thorndike's generation of experimental psychologists, the study of mental processes had the greatest attraction. In Animal Intelligence Thorndike set down what proved to be a lasting framework for his theory of mind and the laws of learning. He brought into the twentieth century the British tradition of "associationism"; his own learning theory came to be called "connectionism," or sometimes "stimulusresponse theory." The experiment that provided him with the empirical basis of his theory was the following: Observing the behavior of kittens as they tried to escape from simple boxes he had built, Thorndike concluded that it was random trial-and-error behavior that led to the animals' striking the latch that would open the cage. The desirable consequence was then gradually associated with the one correct movement that would bring it about, and the unrewarded errors were eliminated. According to Thorndike, mind has no separate identity as such, being merely a collective name for the brain cells, nerve cells, and chemicoelectric operations by which man reacts to internal and external stimulation. Thorndike had an unremitting bias in favor of physiological and biological explanations. In 1940 he reiterated this prejudice when he wrote that doctrines about processes such as learning, instinct, and suggestion—processes that can be translated into terms of conductivity, connection, facilitation, and other "known" neural actions—are "preferable to doctrines which rely upon fields of force, tensions, equilibria, valences, barriers, libido, specialized energies," all yet undemonstrated in the neurons (1940, p. 189). Mind, said Thorndike, is man's "connection system," forming a bond between some stimulus— Thorndike preferred the word "situation," recognizing the complexity of many stimuli—and some response made to it by the learner. All that a man knows, feels, "wants," or does is dependent upon
his having formed a connection between some situation and some response. The term "habit" is equally useful in accounting for a routine motor act or for a lofty abstraction; there are no qualitative differences between simple learning and the so-called higher mental processes. Thorndike's "laws of learning" explain the connection processes. His "law of exercise" recalls the principle of "frequency," or "use," found in nineteenth-century association theory: a response made is likely to be made again, merely as a result of having been made before. The "law of effect" states that the consequences (satisfying or not satisfying) of a response will increase or decrease the probability that the connection was formed and that the response will be repeated. Vaguely implied in the writings of Alexander Bain and the British animal psychologist C. Lloyd Morgan, the law of effect was made an articulate and heuristic principle of learning by Thorndike. Although the law confirmed common-sense observations, Thorndike's proposition that consequences can work back upon a stimulus-response connection neurologically has provoked considerable debate and experimentation. Thorndike's work on the amount and explanation of the transfer of training, beginning with the landmark Thorndike-Woodworth experiments published as "The Influence of Improvement in One Mental Function Upon the Efficiency of Other Functions" (Thorndike & Woodworth 1901), also sparked controversy. His research showed that learning any one skill has little effect upon the rate or ease of learning another, even for quite similar tasks. Furthermore, the small amount of transfer that does occur, he maintained, can be credited to the presence of "identical elements" in the two tasks or situations; it is not the result of insight or reason or conscious application of principles. Since educators argued that school subjects as disparate as the classical languages, mathematics, and manual training should all be included in the curriculum because of their "formal discipline" powers—their ability to train the memory, sharpen perceptions, and improve attention—considerable opposition was aroused. On the other hand, those educators who pleaded for a curriculum embodying content and activities that were highly specific, practical, and obviously relevant to daily life were encouraged by Thorndike's results. Determinants of human abilities. Thorndike believed that intellectual and achievement differences between people are quantitative, not qualitative. Individuals differ in the number and complexity of the connections that they possess and, beyond that, in their capacity to form connections. He held
THORNDIKE, EDWARD L. heredity to be primarily responsible for human equality. He scorned environmental explanations and was interested in eugenics as a means of improving human beings and society, thus perpetuating the views of Galton, for one. Furthermore, Thorndike supported an established American belief: expressed in common-sense terms, it asserted the triumph of character over circumstances, the faith that the ingredients of success are in a man and not around him. The cultural ethos had emphasized character, perseverance, intuition, and good judgment; Thorndike added a high order of intelligence as a basic ingredient in the American success story. With refinements in measures of individual variation and their more extensive use, the heredityenvironment debate became more heated.The validity of political, educational, welfare, and religious policies was at stake, and social science research was called upon to justify opposing views. All through the years when environmental theories were dominant—owing partly to social reform movements and partly to the cogency of Pavlovian conditioning theories and of Watson's brand of behaviorism—Thorndike held his ground. While his later writings acknowledged the importance of chance factors, such as opportunity, in determining whether innate potentialities would be realized, he consistently believed that heredity was prepotent and that the egalitarian vision of a true parity— whether attempted through education or a welfare state—was indeed just a dream. Practical applications. In 1917-1918 Thorndike served on the Committee on Classification of Personnel for the United States Army, traveling between Washington, D.C., and his teaching duties in New York. The committee was responsible for the "Army Alpha" project, which was the first mass testing of intelligence, and which subsequently stimulated testing in schools, colleges, and industry. (The ultimate result of his and others' efforts was the Army General Classification Test used in World War n.) Large numbers of people were trained in test construction and administration. The terms "intelligence quotient" (IQ) and "mental age" entered popular language. Furthermore, public attention was called to the great and inborn physical, intellectual, and educational differences found in the population and to the inequalities resulting from regional isolation and inadequate local schooling, which failed to develop the natural abilities of thousands of people. Adult education programs were invigorated when Thorndike's investigations of adult learning in the 1920s showed that innate and individual factors and not age are the determinants
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of the amount and quality of achievement and the ability to continue learning. Thorndike contributed both directly and indirectly to the development of efficient, scientifically based schooling, the desire for which had begun late in the nineteenth century. He was influential as a teacher of psychology to teachers: early books like Notes on Child Study (1901), The Principles of Teaching Based on Psychology (1906), and Education: A First Book (1912) turned teachers toward a concern for human nature and the learning process and enlisted their support for the scientific movement in education. Thorndike's numerous articles reporting studies using schoolchildren, school subjects, and various testing approaches were published between 1900 and 1925. The 1907 Annual Report of the U.S. Bureau of Education disclosed the statistics on pupils leaving school before graduation, dramatizing the inadequacies of existing programs and the extent of school retardation and thus giving aid to reformers of curriculum and teaching methods. Thorndike contributed much to the growing awareness of individual differences and to plans for educating the whole range of American children. The main divisions of modern educational psychology—measurement, learning, and individual differences—correspond to Thorndike's own major interests. Thorndike was active in the preparation of school materials and tools; various achievement scales, especially for handwriting and drawing, were one result. The psychology of school subjects became a preoccupation of some educational psychologists, and the Thorndike arithmetic and algebra texts were in widespread use. He also prepared college entrance examinations, a test for selecting students for the Columbia School of Law, and one of the best regarded of intelligence tests, the CAVD scale. (The acronym stands for sentence completion, arithmetical reasoning, vocabulary, and the ability to follow directions.) His counts of word usage established the basic vocabulary now used in virtually all school reading books, spellers, and spelling lists, and on achievement tests. The Teachers College program of training in statistics and measurement as applied to education inspired other attempts to create a scientific approach to curriculum selection and to school administration. Experimental schools multiplied and research on city schools increased. Thorndike would have taken great exception to the poor controls, naivete, and pretentious pseudoscientism that often prevailed; nevertheless, the sponsors of these activities looked to Thorndike and to his institution for stimulation.
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Theoretical work. There is much evidence to confirm the psychologist Irving Lorge's description of Thorndike, his teacher and close friend, as a great eclectic. This can partly be attributed to Thorndike's responsiveness to opportunities and requests to conduct studies. It is also related to the fact that the direction of Thorndike's interests was determined not exclusively by the logic of inquiry but also by the nature of the criticisms that were made of his work: when his work was challenged, he sought new evidence to support his theories, and this search for new evidence often led him in unexpected directions. It was a challenge to the "law of effect" that led to Thorndike's discovery of the "spread," or "scatter," phenomenon. He devised numerous experiments: for example, subjects were asked to supply missing words in a long series of statements, the experimenter rewarding certain answers by saying "right" and punishing others by saying "wrong," according to a predetermined key. Each series was repeated two or three times in succession. Predictably, the studies revealed that words that were rewarded were repeated—the connection was strengthened; they were "learned." Surprisingly, however, some words called "wrong" were also repeated, the more so the nearer in distance they were to the "right" words; words in the series just before and just after the rewarded words received the maximum scatter effect from the reward's power in strengthening responses, while those four or five words removed from the rewarded word were barely affected. Such findings tended to corroborate Thorndike's contention that the law of effect operates irrespective of reason, in a mechanical or automatic fashion. The repetition of an action called "right" can be considered evidence that reason guides learning. But repetition of erroneous responses as a result of symbolic rewards, and irrespective of the subject's understanding or insight, seriously challenges the cognitive psychologist's basic thesis. Thorndike regarded this as his most important contribution to scientific advancement. Further evidence of Thorndike's continued growth was his reversal of his early views on reward and punishment in learning. He first believed these to be simple opposites within the law of effect. Later investigation showed that reward is the more effective and stable "confirming" agent; punishment may sometimes strengthen a connection rather than consistently weaken it. He also showed that belief in a simple hedonism was unwarranted; small satisfactions usually work as well as large rewards. The implications of his findings about reward and punishment were neglected, Thorndike complained, by
educational, governmental, and penal institutions and by welfare agencies. In 1929 Thorndike surprised the Ninth International Congress of Psychology, meeting at Yale University, by announcing that he had long erred in maintaining that "exercise" and "effect" were companion laws of equal potency. He had come to believe instead that exercise—mere repetition of a response—was of minor importance in explaining the formation and strengthening of connections. As a result of this new conviction, he began a massive experimental program. A series of books published in the 1930s, Human Learning (1931), The Fundamentals of Learning (1932), and The Psychology of Wants, Interests, and Attitudes (1935), reveal a theory trying to come to terms with data. As Leo Postman has observed, Thorndike clearly did not consider connectionism a finished product (Postman 1962, pp. 340, 349). It was in the 1920s and 1930s that psychology became most highly fragmented into conflicting schools, each differing in its research methods, problems studied, and in its experimental results. New principles—like "belongingness," an explanation of the way certain things are connected by the learner because they "seem to go together"—were used by Thorndike merely to account for variations in the operations of his basic and still mechanistic principles of learning. Similarly, he considered "mental set"—the observed tendency to respond to some things in an environment of possible stimuli and to disregard other things—to be the residue of established stimulus-response bonds still operating to condition the making of new connections. He continued to concede little to gestaltist criticism and what he called the "possibly sound elements of Freudianism" (1940, pp. 336 ff.). His theoretical pre-eminence in the 1930s was unquestioned; as Edward C. Tolman observed: The psychology of animal learning—not to mention that of child learning—has been and still is primarily a matter of agreeing or disagreeing with Thorndike, or trying in minor ways to improve upon him. Gestalt psychologists, conditioned-reflex psychologists, signgestalt psychologists—all of us here in America seem to have taken Thorndike, overtly or covertly, as our starting point. And we have felt very smart and pleased with ourselves if we could show that we have, even in some very minor way, developed new little wrinkles of our own. (1938, p. 11) Interest in other social sciences. The economic and social conditions of the 1930s stimulated the social sciences. The Carnegie Corporation, for example, offered Thorndike a large grant, which enabled him to apply his methods and theories to a
THORNDIKE, EDWARD L. study of various social problems. While he was not interested in direct political activity, he had strong conservative and individualistic views, which emerged clearly in his writings of this period. At this time he was no longer primarily concerned with psychological theory. For instance, using census data and other statistics, he tried to analyze cities as he had earlier studied individuals. In Your City (1939) he presented the results and concluded that "good" cities are the result of good people whom they attract; good cities do not create good people. This was yet another expression of his hereditarian position; it had no discernible influence upon urban sociology. His massive Human Nature and the Social Order (1940) was a compendium of information about human abilities, behavior, and wants, general psychological principles, and the facts of individuality. He contended that the social sciences require such knowledge of how humans behave, what people can be and do, and what they want to be and do, and he suggested applications of this knowledge to many fields: economics, government, philanthropy, religion, law, ethics. In 1943 he wrote Man and His Works, which was similar in conception but on a far smaller scale. Thorndike's direct influence upon the social sciences other than psychology was probably small. However, the rapid growth of psychology may have indirectly favored development of the other behavioral fields. Some social psychologists now use Hullian principles, a synthesis of Thorndike and Pavlov; but they often take learning theory largely for granted. Thorndike himself always made motivation secondary to learning: men act the way they do because such behavior has previously been reinforced. Thorndike's influence on later work with attitude scales is doubtful. Statistical training has only lately become a common part of the sociologist's education. And anthropologists and sociologists have studied intelligence testing primarily for what it reveals about cultural bias. Major differences in points of departure between the several social sciences and the kind of psychology that interested Thorndike help explain this independent development. According to Thorndike, individual behavior, with all its variations, takes precedence over language, customs, and laws as a determinant of social action. This view of man contrasts with that of the sociologists, namely, that men are members of social groups and that although all men are not basically the same, their similarities are more crucial than their differences. Another important distinction between psychology and the other social sciences is the differential
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emphasis given to environmental factors. Many social scientists have concluded, as a result of comparative cultural studies, that psychologists have exaggerated the importance of inherited qualities. The hereditarian Thorndike, however, continually saw all environments as the product of the genetic equipment of their inhabitants. On one issue—the future possibilities of social science—there was common, widespread agreement among social scientists; it is reflected in Thorndike's reiteration in 1940 of his lifelong certainty that "the welfare of mankind now depends upon the sciences of man . . ." (1940, preface). GERALDINE JONCICH [For the historical context and subsequent development of Thorndike's ideas, see INTELLIGENCE AND INTELLIGENCE TESTING; LEARNING; and the biographies of many of the psychologists mentioned in the text.] WORKS BY THORNDIKE
(1898-1901) 1911 Animal Intelligence: Experimental Studies. New York: Macmillan. (1901) 1903 Notes on Child Study. 2d ed. New York: Macmillan. 1901 THORNDIKE, EDWARD L.; and WOODWORTH, ROBERT S. The Influence of Improvement in One Mental Function Upon the Efficiency of Other Functions. Psychological Review 8:247-261, 384-395, 553-564. (1904) 1913 An Introduction to the Theory of Mental and Social Measurements. 2d ed. New York: Columbia Univ., Teachers College. 1906 The Principles of Teaching Based on Psychology. New York: Seller. 1912 Education: A First Book. New York: Macmillan. (1913-1914) 1921 Educational Psychology. 3 vols. New York: Columbia Univ., Teachers College. -> Volume 1: The Original Nature of Man. Volume 2: The Psychology of Learning. Volume 3: Mental Work and Fatigue and Individual Differences and Their Causes. Part 2 of Volume 3 first appeared in 1903 as Educational Psychology. 1931 Human Learning. New York: Appleton. 1932 The Fundamentals of Learning. New York: Columbia Univ., Teachers College. 1933 An Experimental Study of Rewards. Teachers College Contributions to Education, No. 580. New York: Columbia Univ., Teachers College. 1935 The Psychology of Wants, Interests, and Attitudes. New York: Appleton. 1936 Autobiography. Volume 3, pages 263-270 in A History of Psychology in Autobiography. Edited by Carl Murchison. Worcester, Mass.: Clark Univ. Press. 1939 Your City. New York: Harcourt. 1940 Human Nature and the Social Order. New York: Macmillan. 1943 Man and His Works. Cambridge, Mass.: Harvard Univ. Press. Psychology and the Science of Education: Selected Writings. Edited by Geraldine M. Joncich. New York: Columbia Univ., Teachers College, 1962. ->• Published posthumously. Contains writings first published between 1901 and 1939.
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Selected Writings From a Connectionist's Psychology. New York: Appleton, 1949. -» Contains writings first published between 1913 and 1946. WORKS ABOUT
THORNDIKE
CURTI, MERLE E. (1935) 1959 Edward Lee Thorndike, Scientist: 1874-1949. Pages 459-498 in Merle E. Curti, The Social Ideas of American Educators. New ed., rev. Paterson, N.J.: Littlefield. Edward L. Thorndike: 1874-1949. 1949 Teachers College Record 51:26-45. -> See especially pages 42-45 for a bibliography of Thorndike's publications from 1940-1949. GARRETT, HENRY E. (1930) 1951 Great Experiments in Psychology. 3d ed. New York: Appleton. -> See especially "Thorndike's Law of Learning," pages 40-62. GOODENOUGH, FLORENCE L. 1950 Edward Lee Thorndike. American Journal of Psychology 63:291-301. HULLFISH, H. GORDON 1926 Aspects of Thorndike's Psychology in Their Relation to Educational Theory and Practice. Columbus: Ohio State Univ. Press. In Honor of Edward Lee Thorndike. 1926 Teachers College Record 27:457-586. -> An annotated, chronological bibliography of Thorndike's publications appears on pages 466-515. In Honor of E. L. Thorndike. 1940 Teachers College Record 41:695-788. H> See especially pages 699-725 for a bibliography of Thorndike's publications from 1898-1940. WOODWORTH, ROBERT S. 1952 Edward Lee Thorndike, 1874-1949. Volume 27, pages 209-237 in National Academy of Sciences, Washington, B.C., Biographical Memoirs. Washington: The Academy. SUPPLEMENTARY BIBLIOGRAPHY
BORING, EDWIN G. (1929) 1950 A History of Experimental Psychology. 2d ed. New York: Appleton. HILGARD, ERNEST R.; and BOWER, GORDON H. (1948) 1966 Theories of Learning. 3d ed. New York: Appleton. GRATA, PEDRO T. 1928 The Theory of Identical Elements. Columbus: Ohio State Univ. Press. POSTMAN, LEO 1962 Rewards and Punishments in Human Learning. Pages 331-401 in Leo Postman (editor), Psychology in the Making: Histories of Selected Research Problems. New York: Knopf. TOLMAN, EDWARD C. 1938 The Determiners of Behavior at a Choice Point. Psychological Review 45:1—41.
THORNTON, HENRY Henry Thornton (1760-1815), banker, philanthropist, and member of Parliament, is celebrated among economists as the author of An Enquiry Into the Nature and Effects of the Paper Credit of Great Britain, published in 1802, one of the most important and original contributions to monetary theory ever written. He was born at Clapham of a pious and prosperous city family which had moved from Yorkshire earlier in the century. Both his father and grandfather had been in the Russian trade and had been directors of the Bank of Eng-
land. After a schooling of which he himself was subsequently very critical, Thornton duly became a banker, joining the house of Down, Thornton, and Frere in 1784. Two years previously he had been elected member of Parliament for Southwark, and he retained the seat for the rest of his life. In 1792 he bought a house at Battersea Rise on Clapham Common, which, after his marriage in 1796, he populated with nine children. Before that, he had shared his house with William Wilberforce, the antislavery leader, his second cousin and very close friend, and around them there grew up what came to be known as the Clapham sect, an austerely evangelical wing of the Church of England. The group included John Venn, Hannah More, James Stephen, and Zachary Macaulay, father of the historian (none of them except Thornton stayed in Clapham for very long). Thornton himself was the author of a collection of family prayers, published in 1834, and it is said of him that before his marriage he devoted six-sevenths of his income to charity; after it, one-third. He served as president of the Sunday School Society and treasurer of the Religious Tract Society, the Church Missionary Society, and the British and Foreign Bible Society, all of which were founded by the Clapham sect. These societies left their mark not only in nineteenth-century Britain but also in other parts of the world. In Parliament Thornton rejected any party connection but tended to side with the Whigs. He supported parliamentary reform, Catholic emancipation, and the progressive income tax. But it was in dealing with problems of currency and banking that he made his great reputation, first in 1797 with his lucid and expert evidence to the committees of the House of Commons and the House of Lords inquiring into the suspension of cash payments by the Bank of England. He was a member of the committee on the Irish currency in 1804, and in 1810 he was a leading member of, and apparently part author of the famous report by, the "Bullion Committee, appointed to inquire into the cause of the high price of Gold Bullion, and to take into consideration the state of the Circulating Medium, and of the Exchanges between Great Britain and Foreign Parts." Thornton was also a member of the committee which inquired into the corn trade in 1813, and one of his last parliamentary speeches was in the important debate on the corn laws in the following year. Monetary theory. His contributions to monetary theory are contained mainly in his Enquiry on paper credit, although they are also to be found in his evidence to the committees of 1797 on the sus-
THORNTON, HENRY pension of cash payments and in his parliamentary speeches of 1811 on the bullion report. In the introduction to the Enquiry Thornton stated that his original intention had been "merely to expose some popular errors" regarding the suspension of cash payments in 1797, the policy of the Bank of England, and the effects of paper currency on prices. But there existed at the time little in the way of an accepted corpus of doctrine on monetary theory and policy on which he could build; Thornton does refer to the previous writings of Smith, Hume, Steuart, Locke, and Montesquieu, which must have constituted all, or nearly all, that existed in the way of monetary theory. Moreover, banking institutions and practices had been changing and developing considerably in the closing decades of the eighteenth century, particularly with regard to the rapid growth of country banking. In order to support and elucidate his diagnosis of the current problem, therefore—which he presented in masterly fashion—Thornton not only had to elucidate the basic concepts and hypotheses of a theory of money, but also had to explain the recent developments and workings of the British banking system. Perhaps the comprehensive character of his task, which no doubt did not emerge until his work was under way, made for a certain lack of clear-cut, systematic arrangement. His contribution to monetary theory has to be extricated from its setting amid the topical diagnosis and the expert institutional description. In part, Thornton's Enquiry seems to have been intended as a defense of the Bank of England against the attack by Walter Boyd in his pamphlet of 1801 ("A Letter to the Right Honourable William Pitt, on the Influence of Stoppage of Issues of Specie at the Bank of England; on the Prices of Provisions and Other Commodities"), the most prominent of a number of pamphlets attacking the Bank of England on the ground that its excessive issue of paper money had been responsible for a general rise in prices. In Chapter 4 of the Enquiry, Thornton stressed the bank's freedom from governmental "dictation" and its devotion to "the support of commercial as well as of public credit in general" (Enquiry, p. 109). Against the charge of over-issue Thornton was particularly concerned to emphasize that it is "merely theoretic" to suppose that it is always "a paramount duty of the Bank of England to diminish its notes, in some sort of regular proportion to that diminution which it experiences in its gold" (p. 116). He stressed the danger that sudden deflationary measures could lead to falling production and unemployment (or "an intermission in manufacturing labour"). Thornton insisted that "it
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may be hoped, however, that at least one point has now been fully and completely established, namely, that there may be an error on the side of too much diminishing bank notes, as well as on the side of too much increasing them" (p. 124). Although Thornton was, in 1802, prepared to defend the Bank of England's position with regard to the suspension of cash payments in 1797 and the slight degree of inflation in the ensuing five years, by 1810, as a member of the Bullion Committee, he had become thoroughly critical of the bank and in favor of a contraction of the note issue. Thornton's contributions to monetary theory may be summarized under four main heads: money; rapidity of circulation; interest, prices, and employment; international economic relations. Money. He elucidated the concept of money and the range of types of money, near money, and money substitutes. He emphasized that although legally the distinction between what is "legal tender" and what is not is, of course, clear-cut, in fact, each type of money or near money is certainly a close and easy (if not a perfect) substitute for its nextdoor neighbor in the spectrum, so that if the supply of one type were tightened or cut off, other types could and would be resorted to: . . . if bank paper were abolished, a substitute for it would be likely to be found, to a certain degree, in bills of exchange. . . . But further; if bills and bank notes were extinguished, other substitutes than gold would unquestionably be found. Recourse would be had to devices of various kinds. . . . Merely by the transfer of the debts of one merchant to another, in the books of the banker, a large portion of what are termed cash payments is effected at this time without the use of any bank paper, and a much larger sum would be thus transferred, if guineas were the only circulating medium of the country. Credit would still exist. . . . (Enquiry, pp. 100-101) In fact Thornton saw that although the different means of payment may differ in legal respects, they may, as Schumpeter said, "on a certain level of abstraction be treated as essentially alike" ([1954] 1960, p. 719). Rapidity of circulation. Thornton analyzed "the rapidity of circulation" and its variations and how these depend on the state of confidence and business conditions. A "high state of confidence" quickens the circulation of bank notes. [It] contributes to make men provide less amply against contingencies. At such a time, they trust, that if the demand upon them for a payment, which is now doubtful and contingent, should actually be made, they shall be able to provide for it at the moment. . . . When, on the contrary, a season of distrust arises, prudence suggests, that the loss of interest arising
16
THORNTON, HENRY
from a detention of notes for a few additional days should not be regarded. (Enquiry, pp. 96-97) Later Thornton referred to the fact that Bank of England paper bears no interest and emphasized the "loss sustained by keeping it" (p. 234). Here, without being aware of it, Thornton was developing ideas about "the rapidity of circulation" to be found earlier in Cantillon, while, of course, also pointing forward to the Keynesian analysis of liquidity preference. Interest, prices, and employment. Thornton made three very important theoretical contributions to the understanding of the relationships between money, interest, and the level of prices and employment. (1) In the first of his parliamentary speeches of 1811 on the Bullion Report, Thornton analyzed the distinction between the "real" and the "nominal" rates of interest, namely, the distinction between the actual "nominal" rate and this rate corrected into "real" terms for changes in the value of money —a distinction subsequently developed by Irving Fisher (in his Appreciation and Interest, 1896) and by Marshall. He showed the significance of this distinction in a period in which rising prices are more or less anticipated by borrowers, pointing out how the unexpected gains from previous borrowings will provide "so much additional temptation to borrow" (pp. 335-336). (2) More important than this analysis was Thornton's anticipation of Wicksell's distinction between the "natural" and the market rates of interest, that is, between the (expected) rate of return on investment and the market rate at which funds may be borrowed. When developing this distinction Thornton had been concerned to refute the argument that the canons of sound banking practice—with regard to lending only on good security, or discounting only "real" commercial bills—are sufficient to contain or prevent inflationary rises in prices. (He pointed out, also, how a rate of interest of 5 per cent, then the highest the Bank of England was, under the usury laws, even in time of war, statutorily permitted to charge, might be quite insufficient when the expected rate of return on borrowing might be much higher.) He showed that it is pointless to argue that "a liberal extension of loans would soon satisfy all demands" in conditions where the generally expected rate of profit on investment exceeds the market rate of interest: In order to ascertain how far the desire of obtaining loans at the bank may be expected at any time to be carried, we must enquire into the subject of the quantum of profit likely to be derived from borrowing there under the existing circumstances. This is to be judged
of by considering two points: the amount, first of interest to be paid on the sum borrowed; and, secondly, of the mercantile or other gain to be obtained by the employment of the borrowed capital, (p. 253) (3) Thornton analyzed the effects of credit expansion on the level of output, employment, and savings. He certainly made no general assumption of full employment, arguing that if there are "antecedently idle persons," an increase in "new capital" will first bring these into employment, but as it continues "it will set to work labourers, of whom a part will be drawn from other, and, perhaps, no less useful occupations" (p. 236). Thus, "although additional industry will be one effect of an extraordinary emission of paper, a rise in the cost of articles will be another" (p. 237). Thornton then showed how, if the rise in prices proceeds, with money wages remaining the same, "some augmentation of stock will be the consequence; for the labourer, according to this supposition, may be forced by his necessity to consume fewer articles" (p. 239). This is the process explained almost simultaneously by Bentham as "forced frugality" and by subsequent writers as "forced saving." It is interesting to note that Ricardo, in his comments on Bentham, holding firmly to the Turgot-Smith "saving is investing" doctrine, completely rejected this analysis with the question: "Why should the mere increase of money have any other effect than to lower its value? How would it cause any increase in the production of commodities? . . . Money cannot call forth goods—but goods can call forth money" (see Ricardo [1811] 1951, pp. 298, 301). International economic relations. Thornton contributed some important ideas about the monetary aspects of international economic relations. He anticipated what later came to be known as the purchasing power parity theory by showing how gold will tend to move between countries toward equilibrium, a distribution in which no profits will be possible from any further gold transfers. He went on to trace out, on the lines of Hume and others, how the mechanism of adjustment works through changes in relative prices to restore equilibrium, for example if equilibrium were disturbed by a bad harvest and were followed by an expansion of imports. Thornton's ideas were influential in his day; a brilliant review article by Francis Homer in the first number of the Edinburgh Review (1802) enhanced that influence. But his subtler insights came to be overshadowed by the simpler (and perhaps cruder) formulas of Ricardo, and over the decades the influence of his book receded. J. S. Mill in his Principles of Political Economy of 1848
THUNEN, JOHANN HEINRICH VON hailed Thornton's work as the clearest exposition of its subject, and some of Mill's contributions to the theory of international trade may show the influence of Thornton. But after Mill, Thornton's name almost disappeared until scholars in this century, notably Jacob H. Hollander and Jacob Viner, rediscovered his work. With the development of modern monetary theory from Wicksell to Keynes it came to be realized how much had been anticipated by Thornton, and Hayek's valuable 1939 edition of Thornton's work restored to him the eminent place in the history of monetary theory which is his due. T. W. HUTCHISON [For discussion of the subsequent development of Thornton's ideas, see BANKING, CENTRAL; INCOME AND EMPLOYMENT
THEORY;
INTEREST;
LIQUIDITY
PREFERENCE; MONEY; and the biographies of FISHER, IRVING; MARSHALL; WICKSELL.] WORKS BY THORNTON An Enquiry Into the Nature and Effects of the Paper Credit of Great Britain (1802); Evidence Given Before the Committees of Secrecy of the Two Houses of Parliament on the Bank of England, March and April 1797; Some Manuscript Notes; and Speeches on the Bullion Report, May 1811. Edited with an introducton by F. A. von Hayek. New York: Farrar & Rinehart; London: Allen & Unwin, 1939. SUPPLEMENTARY BIBLIOGRAPHY
FORSTER, E. M. 1956 Marianne Thornton: A Domestic Biography: 1797-1887. New York: Harcourt. HORNER, FRANCIS (1802) 1957 [A Book Review of] An Enquiry Into the Nature and Effects of the Paper Credit of Great Britain, by Henry Thornton. Pages 28-56 in Francis Horner, The Economic Writings of Francis Horner in The Edinburgh Review, 1802-1806. Edited with an introduction by Frank Whitson Fetter. London School of Economics and Political Science. MEACHAM, STANDISH 1964 Henry Thornton of Clapham: 1760-1815. Cambridge, Mass.: Harvard Univ. Press. -» Contains a bibliography of Thornton's works on pages 163-168. RICARDO, DAVID (1811) 1951 Notes on Bentham's "Sur les Prix," 1810-1811. Pages 259-341 in David Ricardo, Works and Correspondence. Volume 3: Pamphlets and Papers, 1809-1811. Cambridge Univ. Press. SCHUMPETER, JOSEPH A. (1954) 1960 History of Economic Analysis. Edited by E. B. Schumpeter. New York: Oxford Univ. Press. -> See especially pages 688-750, "Money, Credit and Cycles."
THUNEN, JOHANN HEINRICH VON Johann Heinrich von Thiinen (1783-1850) was a German economist of great originality who contributed highly significant concepts and techniques to economic theory. He was the first to develop an
17
exact definition of marginal productivity in the modern sense (although he did not use the term) and to apply the principle generally in the theory of production and distribution. He was a founder of mathematical economics and of econometrics, combining systematic empirical research with a genius for abstract reasoning and generalization. Most of his economic theory is based upon models of general static equilibrium, often expressed in terms of systems of equations, but he also contributed to the theory of capital formation and economic growth. Other areas in which he pioneered include theories of economic location, rent, and enterprise profit and some of the more practical aspects of agricultural economics. He emphasized far more than did his English contemporaries the central economic problem of allocating scarce resources so as to maximize the achievement of defined goals. Von Thiinen was born on his father's estate in the Grand Duchy of Oldenburg. His education included training in practical agriculture as well as in the academic disciplines, particularly mathematics. He attended the Agricultural College at Gross-Flottbeck near Hamburg and spent two semesters at the University of Gottingen. In 1810 he purchased Tellow, an estate in Mecklenburg, where he carried on the extensive experiments and systematic data-gathering that became the empirical basis for his great work, Der isolierte Staat. Von Thiinen's book won him considerable recognition during his lifetime. According to Schumacher (1868), Rodbertus credited von Thiinen with bringing to economics the rare combination of a most exact method and a humane heart, and the British Parliament used von Thiinen's calculations of the grain production of the European continent in its deliberations on the corn laws. But the voluminous proportions of the work, its seemingly formidable mathematics, and its unusual originality appear to have prevented it from being either widely read or understood until the rediscovery of marginal analysis and the introduction of mathematical formulation into the mainstream of economic theory more than twenty years after von Thiinen's death. Alfred Marshall acknowledged a major debt to von Thiinen. Rent, profit, and the "isolated state." For theoretical purposes, von Thiinen set up a model economy which he called the "isolated state," consisting of a single city in the center of a large plain of uniformly fertile land. The inhabitants of the city exchange manufactured goods for the agricultural products of the plain, with the wagon as the sole means of transportation. Various agricultural prod-
18
THUNEN, JOHANN HEINRICH VON
ucts are grown in concentric circles around the city. The location at which each crop is grown is determined by the cost of transportation to the city, in accordance with what we would call the principle of "opportunity cost." Land use ranges from the growing of garden vegetables nearest the city to grazing in the most distant circle, with the land beyond that occupied by forest which can be cleared if the economy expands. Von Thiinen changed the conditions of the model from time to time, to facilitate comparison and to illustrate various principles, always in full awareness of its abstract character. Von Thiinen's theory of land rent is based upon the same fundamental principles as that of Ricardo. In the "isolated state" the rent of each unit of land is determined exclusively by the difference between the cost of transporting the crop of that unit to the market city and the cost of transporting there an equal quantity of produce from the most distant land in use that yields no rent. Estate revenue consists of interest on the transferable capital invested in improvements, which must be paid at the current rate if the improvements are to be maintained, and payment for the land itself, which is the only true rent. If total estate revenue falls below the interest on transferable capital, payment for the land may for a time be negative, but under these circumstances the estate will sooner or later be abandoned. Von Thiinen's distinction between enterprise profit and interest on capital is modern, and it contrasts with the then prevailing concept of "profit" as both enterprise profit and interest. The entrepreneur's profit consists only of that part of revenue which remains after he has deducted interest on his capital, an insurance premium against all insurable risks, and his own salary for management. This profit remains to the entrepreneur despite competition, because there is no insurance against such uncertainties as adverse price movements. Although the chances of gain are often as great as the chances of loss, the former do not compensate wholly for the latter, since the entrepreneur's pleasure from doubling his fortune is less intense than his suffering from its complete loss. Wages, interest, and marginal analysis. Von Thiinen's application of marginal analysis to the theories of wages, interest, and resource allocation —the most important of his contributions to economic theory—appears in Volume 2 of Der isolierte Staat and was worked out during the period 1826 to 1848. He used a number of mutually corroborating approaches to the problem, with verbal, nu-
merical, and algebraic modes of expression. A few brief examples follow. Using his model of the "isolated state," he assumed free, homogeneous, mobile laborers, who receive wages in excess of minimum subsistence and who are capable of producing products either for current consumption or for capital formation. In his analysis of capital formation essentially independent of the capitalist-laborer relationship, the workers either accumulate the excess of their wages over subsistence until they can devote a year's labor to capital formation while living on their accumulated stocks, or they form groups of workers, some of which produce capital while the rest simultaneously produce subsistence for the entire group, all members then sharing equally in the ownership of the new capital. Von Thiinen demonstrated that in competitive equilibrium the interest per unit of capital equals the increment of product value resulting from an increment of capital, all other inputs remaining constant. The same principle is then applied to labor. Both labor and capital are shown to be subject to diminishing incremental returns, but the marginal product of labor increases as the quantity of capital per worker increases. Von Thiinen emphasized the importance of using infinitesimal increments in the formal analysis. He also pointed out that the natural rates of wages and interest prevail only under conditions of ideal competition and resource mobility that unfortunately do not prevail in the real world. He demonstrated by verbal and algebraic statement and by numerous examples the principles of cost minimization (Marshall's "principle of substitution") and net revenue maximization, with emphatic assertions of their general applicability and their fundamental economic importance. Productive agents can be substituted for one another, and an optimum is reached when the ratio of their respective marginal products equals the ratio of their respective unit costs. Net revenue is maximized when the value-product of the last added unit of each agent just equals its cost. An appreciation of von Thiinen's method of analysis and an understanding of his interesting blunders can be achieved only by sampling his mathematical reasoning. Let a + y be the annual wage, in commodity units, of a working family, where a is one family's annual subsistence and y is surplus over subsistence available for capital accumulation. Let q be the average quantity of capital per working family, measured in units equal to the annual wage of one working family, a + y; p be the average annual product of one working
THUNEN, JOHANN HEINRICH VON family when assisted by q units of capital; and z be the rate of interest in percentage per annum. Then on no-rent land at the boundary of the isolated state, a + y + q(a + y}z = p, and with perfect competition and free mobility of labor and capital the rate of interest throughout the state is z = [p — (a + y}]/q(a + y). VonThiinen assumed that each working family converts its annual surplus, y, into capital and that each wishes to maximize the annual revenue on that capital, expressed as zy = y[p — (a + y~)]/q(a + y*), which is maximized when
dy\ q(a + y) Solving this equation for the "natural wage," he obtained a + y = \/~ap. Von Thiinen applied the marginal productivity principle as follows. One worker with q units of capital produces p units of product, and with q + l/n units of capital he produces p + /3 units of product, where n is some large number. Then l/n units of capital yield an annual revenue of f3 units of product, and one unit of capital yields n(3 or a units. The annual wage is then p — aq, and the value of the capital used by one worker is q(p — aq). The interest rate is then given by z = aq/q(p — aq) — a/(p — aq), a worker's annual surplus by y — p — aq — a, and the revenue by zy = a(p — aq — a)/(p — aq). Since o: = f ( q ) , von Thiinen differentiated this expression for zy with respect to a to find the value for q which maximizes zy, thus: _d / a ( p ~ aq — da\ p — aq
= 0,
and solved for the wage p — aq = V a p . Here the wage is determined as the remainder of the product p after interest (determined as the marginal product of capital) has been paid. To determine the wage on the basis of the marginal product of labor, he assumed an enterprise hiring n workers at a wage A and using nq units of capital. Revenue is n(p — A). With one less worker, each remaining worker uses nq/(n — 1) units of capital and produces p + v units of product. Total product is now (n — 1) (p + v), the wage bill is (n — 1)A, and the revenue of the enterprise is (n — 1) (p + i>) — (n — 1)A. If in equilibrium the wage equals the marginal product of labor, the discharge of a worker should leave the revenue unchanged, or np — nA - (n — I) (p + v) - (n — I )A. Solving for the wage, A = p— (n — l)i>. If n is very large, this expression approximates p ~ nv, and the cap-
19
ital per worker approximates q + q/n. Thus, each remaining worker has additional capital of q/n and produces additional product of v. By the previous example, when a worker has additional capital of l/n units, his product increases by ft. Therefore, v — (3q, and since n(3 = a, nv ~ aq. Substituting in the expression for the wage, A = p — nv = p — aq, which agrees with previous results and in equilibrium equals \/ap. Although von Thiinen was so impressed with his "natural wage" as the geometric mean of a worker's subsistence and the average product of labor that he had "\/ ap" engraved upon his tombstone, it is today no more than an intellectual curiosity. Neither a nor p can be analytically defined. There is no reason to suppose that a rational worker would want to maximize the annual interest on one year's savings. Measurement of a unit of capital by its wage cost alone is inconsistent with the assumption that each worker must use q units of capital, interest on which is part of the cost of the unit of capital. The importance of the work lies in its method of analysis and in the kinds of problems to which that method is applied.
ARTHUR H. LEIGH [See also RENT and SPATIAL ECONOMICS. Other relevant material may be found in the biographies of BOHM-BAWERK;
LAUNHARDT;
MARSHALL;
MOORE,
HENRY L.] WORKS BY THUNEN
Der isolierte Staat in Beziehung auf Landwirthschaft und Nationalokonomie. 3 vols. Jena (Germany): Fischer, 1930. -> Volume 1: Untersuchungen uber den Einfiuss, den die Getreidepreise, der Reichtum des Bodens und die Abgaben auf den Ackerbau ausiiben (1826). Volume 2: Der naturgemdsse Arbeitslohn und dessen Verhdltnis zum Zinsfuss und zur Landrente (18501863). Volume 3: Grundsdtze zur Bestimmung der Bodenrente, der vorteilhaftesten Umtriebszeit und des Wertes der Holzbestdnde von verschiedenem Alter fur Kieferwaldungen (1863). A partial translation of Volume 2 as "The Natural Wage and Its Relation to the Rate of Interest and to Economic Rent" is included in B. W. Dempsey, The Frontier Wage: The Economic Organization of Free Agents, published by the Loyola University Press, Chicago, 1960. SUPPLEMENTARY BIBLIOGRAPHY
ACKERMANN, KONRAD P. 1954 Der ethisch-okonomische Erkldrungsdualismus in der Lehre vom naturgemdssen Arbeitslohn und Kapitalzins bei Joh. H. v. Thiinen unter Berucksichtigung des Grenzproduktivitdtsgedankens: Mit einem Anhang uber das Thiinen-Archiv und die neuere Thunen-Forschung. Winterthur (Switzerland): Keller. BOHM-BAWERK, EUGEN VON (1884-1912) 1959 Capital and Interest. 3 vols. South Holland, 111.: Libertarian Press. -» First published as Kapital und Kapitalzins.
20
THURNWALD, RICHARD
BULOW, FRIEDRICH 1950 Thiinen als Raumdenker. Weltwirtschaftliches Archiv 65:1-24. BULOW, FRIEDRICH 1958 Johann Heinrich von Thiinen als forstwirtschaftlicher Denker. Weltwirtschaftlich.es Archiv 80:183-234. CLARK, JOHN B. (1899) 1902 The Distribution of Wealth: A Theory of Wages, Interest and Profits. New York and London: Macmillan. -> Reprinted by Kelley in the "Reprints of Economic Classics." ENGELHARDT, WERNER 1953 Die Theorien der Produktion, des Preises und der Verteilung bei J. H. v. Thiinen: Analyse seines Werkes unter verandertem Blickpunkt. Schmollers Jahrbuch fur Gesetzgebung, Verwaltung und Volkswirtschaft im Deutschen Reiche 73:1-33. HOFFMAN, FRIEDRICH 1950 J. H. v. Thiinen im Blickfeld des deutschen Kameralismus. Weltwirtschaftliches Archiv 65:25-40. Johann Heinrich von Thiinen. 1958 Zeitschrift fur Agrargeschichte und Agrarsoziologie 6 (Special Issue). -> The entire issue is devoted to von Thiinen. KRZYMOWSK, RICHARD 1928 Graphical Presentation of Thiinen's Theory of Intensity. Journal of Farm Economics 10:461-482. LEIGH, ARTHUR H. 1946 Von Thiinen's Theory of Distribution and the Advent of Marginal Analysis. Journal of Political Economy 54:481-502. MARSHALL, ALFRED (1925) 1956 Memorials of Alfred Marshall. New York and London: Macmillan. -» Reprinted by Kelley in the "Reprints of Economic Classics." MELAMID, ALEXANDER 1955 Some Applications of Thiinen's Model in Regional Analysis of Economic Growth. Regional Science Association, Proceedings 1:L1—L5. MOORE, HENRY L. 1895 Von Thiinen's Theory of Natural Wages. Quarterly Journal of Economics 9:291304, 388-408. OHLIN, BERTIL G. 1935 Some Aspects of the Theory of Rent: Von Thiinen vs. Ricardo. Pages 171-183 in Economics, Sociology and the Modern World: Essays in Honor of T. N. Carver. Edited by Norman E. Himes. Cambridge, Mass.: Harvard Univ. Press. PETERSEN, ASMUS 1944 Thiinens isolierter Staat: Die Landwirtschaft als died der Volkswirtschaft. Berlin: Parey. PETERSEN, ASMUS 1959 Johann Heinrich v. Thiinen, Volume 10, pages 386-392 in Handworterbuch der Sozialwissenschaften. Stuttgart (Germany): Fischer. SCHNEIDER, ERICH 1934 Johann Heinrich von Thiinen. Econometrica 2:1-12. SCHUMACHER, H. 1868 Johann Heinrich von Thiinen: Ein Forscherleben. Rostock (Germany): Leopold. WICKSELL, KNUT (1901) 1951 Lectures on Political Economy. Volume 1: General Theory. London: Routledge. -» Translated from the third Swedish edition. See especially pages 216-217 on von Thiinen's theory of capital accumulation.
THURNWALD, RICHARD Richard Thurnwald (1869-1954), sociologist and anthropologist, was born in Vienna, the only son of a Viennese industrialist who came from a well-to-do farmer's family. After finishing the classical course at the Gymnasium and his required
military service, Thurnwald attended the University of Vienna. In the late nineteenth century, aspects of the social sciences were taught only in the faculty of law, so Thurnwald studied law, receiving his law degree and his state lawyer's certificate in 1894. Concurrently with his legal studies, he learned Turkish, Arabic, Russian, and Serbian. Also, he became acquainted with scholars in a variety of academic disciplines, among them the economic historian Max Schwiedland, the physical anthropologists R. Poch and A. Plotz, and several psychiatrists of the Zurich school. Perhaps most important for his scientific development were his contacts with the psychologist Karl Stumpf and with J. Kohler, a representative of the school of comparative law. While in Berlin from 1901 to 1905, he studied Egyptian under A. Erman and Assyrian under Fr. Delitzsch. Thurnwald's first and last field studies were conducted in Europe: the first in Bosnia in 1896, and the last in Berlin in 1946-1947. In between, he worked in Micronesia and the Solomon Islands, 1906-1909; New Guinea, 1912-1915; east Africa, 1930; and again in the Solomon Islands in 1932. From 1924 on, he held a position at the University of Berlin, mainly in anthropology and sociology, but he also taught at various American universities: the University of California, 1915-1917; Yale and Harvard, 1931-1932; and Syracuse University, 1949. He was the founder and editor of the Zeitschrift fur Volkerpsychologie und Soziologie (later Sociologus^) from 1925 on; one of the editors of the Archiv fur Anthropologie; and coeditor of the Zeitschrift fur vergleichende Rechtswissenschaft. Thurnwald's wide range of training and experience, combined with a lifelong interest in the natural sciences, made him critical of Wundt's Volkerpsychologie, the dominant anthropological theory in the first two decades of the twentieth century. In the late 1920s, he also became critical of Levy-Bruhl. Both these authors, he felt, lacked experience with non-Western societies, and their approach was nothing more than speculative. The French school of sociology, represented by Durkheim, suffered from the same fault, especially in their theories of the function of religion. In spite of his profound interest in comparative psychology, Thurnwald became a follower neither of Freud nor of Jung; and in spite of his commitment to comparative sociology, he rejected the Marxian school that was important in Berlin in the 1920s. In both cases, the paucity of supporting factual data made the theories unacceptable: Thurnwald regarded these unilinear schemes of development as a priori speculation. His line of
thinking did not fit, therefore, into the main stream of theory-oriented German social anthropology, and this explains the failure of the University of Berlin to create a regular chair for him despite his many years of successful teaching there. His own theories were based on the intimate knowledge of different societies that he gained on his many and long field trips. He may best be regarded as a functionalist who was fairly close to the British school of Malinowski, with the important difference that he never became antihistorical and that he always paid more attention to individual psychology than did the British school. His main functionalist ideas were formulated before those of the British school, but the British school appears to have developed the same ideas independently. Thurnwald did not develop a complete system or general theory of human development. He encouraged the comparison of social institutions in different societies; the differences that emerged would contribute to the understanding of the varying functions of a particular institution. He also compared the functional structure of societies, in order ultimately to establish historical developmental sequences. In explicit opposition to Max Weber's concept of "ideal types," which he regarded as purely speculative, Thurnwald tried in "Reprasentative Lebensbilder" (1931-1935, vol. 1) to identify specific societies as representative of types of societies. He complemented this "static" approach with the study of the dynamics of sociopsychological "situations," again trying to establish typical solutions to specific social problems, and typical sequences of situations. The individual's solution to a specific situation remained for Thurnwald the principal source of all social change. But although he was preoccupied with change, the idea of an equilibrium does lie behind his idea of a "typical society." Thurnwald regarded the prevailing level of technology as the main determinant of societal type. Technological change is a process involving the accumulation of objects and ideas, an irreversible process with respect to mankind, but not with respect to an individual social group. Technology and social structure are interdependent, yet the correlation between them is only one determinant of social development: the same technology can be used in different types of societies, and a new technology does not always change a society immediately, nor does it necessarily change different societies in the same way. The effect of technology on the type of economy is more nearly determinate;
indeed, a given technology largely determines the contemporaneous economy. Furthermore, the economic system has a high degree of influence on social organization. But since the economic system is also influenced by the social structure and since economic behavior is not entirely rational, the beginnings of social change, according to Thurnwald, lie primarily in the economic attitudes (Wirtschaftsgeist) of individuals rather than in the economic system. Thurnwald's idea of "superstratification" was a fruitful contribution to the field of political sociology. Processes of superstratification are typically different from those of stratification, for while stratification may be caused either by factors inside a society or by the conquest (military or other) of one society by another, superstratification results either from conquest or from the immigration into a stratified society of a new group which then occupies the lowest status positions (Unterwanderung'). The study of processes of superstratification led Thurnwald to examine the feudal system as well as states, cities, and kingship in their early stages of development. Another instance of superstratification is the colonial expansion of the West in the eighteenth and nineteenth centuries, and Thurnwald was the first German sociologist and one of the first in Europe to make special studies of processes of acculturation and adjustment in Africa. These studies, which he made with his wife, Hilde Thurnwald, avoided the "colonial ethnological" approach that influenced British anthropological thinking for some time. WOLFRAM EBERHARD [See
ANTHROPOLOGY, article on THE COMPARATIVE
METHOD IN ANTHROPOLOGY; ECONOMIC ANTHROPOLOGY; and the biography of MALINOWSKI.] WORKS BY THURNWALD
1916
Bdnaro Society: Social Organization and Kinship System of a Tribe in the Interior of New Guinea. American Anthropological Association, Memoirs, Vol. 3, No. 4. Lancaster, Pa.: New Era. 1931-1935 Die menschliche Gesellschaft in ihren ethnosoziologischen Grundlagen. 5 vols. Berlin and Leipzig: de Gruyter. 1932& THURNWALD, RICHARD (editor) Soziologie von heute: Ein Symposion der Zeitschrift fur Volkerpsychologie und Soziologie. Leipzig: Hirschfeld. 1932& Economics in Primitive Communities. London: Oxford Univ. Press. 1935 Black and White in East Africa; The Fabric of a New Civilization: A Study of Social Contact and Adaptation of Life in East Africa. With a chapter on women by Hilde Thurnwald. London: Routledge. 1948 Aufbau und Sinn der Volkerwissenschaft. Berlin: Akademie Verlag. Grundfragen menschlicher Gesellung: Ausgewdhlte Schriften. Berlin: Duncker & Humblot, 1957.
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THURSTONE, L. L. SUPPLEMENTARY BIBLIOGRAPHY
Beitrdge zur Gesellungs- und Volkerwissenschaft: Professor Dr. Richard Thurnwald zu seinem achtzigsten Geburtstag. 1950 Berlin: Mann. -» Contains a bibliography on pages 469-477. LOWIE, ROBERT H. 1937 The History of Ethnological Theory. New York: Farrar & Rinehart. -> See especially pages 242-249 on "Thurnwald." LOWIE, ROBERT H. 1954 Richard Thurnwald: 18691954. American Anthropologist New Series 56:863867.
THURSTONE, L. L. Louis Leon Thurstone (1887-1955), American psychometrician and psychologist, was born in Chicago. Both of his parents had been born in Sweden, and for a period Thurstone himself attended school in Stockholm. At Cornell University, which he entered in 1908, he first studied civil engineering but changed to electrical engineering. Even before graduating from college he patented a model motion-picture projector; it attracted the attention of Thomas A. Edison, who offered him an assistantship in his laboratory in East Orange, New Jersey. However, Thurstone did not remain long in Edison's laboratory, leaving in the fall of 1912 to teach descriptive geometry and drafting in the College of Engineering at the University of Minnesota. Thurstone's interest shifted to the experimental study of learning, and in the summer of 1914 he enrolled for graduate study in psychology at the University of Chicago. While still a graduate student he accepted an assistantship in Walter V. Bingham's newly established division of applied psychology at the Carnegie Institute of Technology. Thurstone continued at Carnegie after receiving his doctorate from Chicago, eventually becoming professor and chairman of the department of psychology. Early in 1923 Thurstone left Carnegie for Washington, to work for the foundation-supported Institute for Government Research and specifically to prepare instructional manuals and specimen materials that would assist civil-service agencies in using objective examinations. With the assistance of Thelma Gwinn, who became his wife in 1924, he prepared a psychological test for selecting or classifying college students; he and his wife were responsible for 24 successive annual editions of the American Council on Education Psychological Examinations. Thurstone returned to the University of Chicago in 1924, as associate professor of psychology, and taught courses in descriptive statistics and mentaltest theory. Three years later he became a full pro-
fessor, and in 1938 he was named Charles F. Grey distinguished service professor. He established the Psychometric Laboratory at Chicago, and after his retirement in 1952 he re-established his laboratory at the University of North Carolina, where he went as a research professor of psychology and as director of this laboratory. Although Thurstone credited others with the founding of the Psychometric Society and of its journal, Psychometrika, he was close to the nucleus of 10 or 12 persons who brought these into being in 1936 in order to foster the development of psychology as a quantitative rational science. Only a few of the many honors that Thurstone received can be mentioned here. He served as president of the American Psychological Association in 1932 and was the first president of the Psychometric Society (in 1936). He was elected honorary fellow of the British Psychological Society, the Spanish Psychological Society, and the Swedish Psychological Society. The University of Gb'teborg awarded him an honorary doctorate in 1954. Contributions to psychology Throughout his career in psychology, Thurstone was primarily concerned with the problem of measurement. He sought to establish valid principles of measurement in such areas as mental abilities, intelligence, attitudes, social judgment, psychophysics, and personality. Intelligence. Thurstone advanced the thesis that "Intelligence, considered as a mental trait, is the capacity to make impulses focal at their early, unfinished stage of formation" (1924, p. 159); that is, intelligence is "the capacity to live a trialand-error existence with alternatives that are as yet only incomplete conduct" (ibid., p. xv). In his early approaches, he regarded intelligence as an ability to abstract that involves the inhibition of immediate impulsive behavior and that opens up a number of alternate paths toward impulse satisfaction (need reduction or goal attainment). When abstraction does not occur, when awareness of impulse-driven behavior is limited, the organism is more likely to engage in behavior that is inappropriate to real impulse satisfaction (ibid., especially pp. 123-169). The area of mental abilities continued to absorb Thurstone. He took issue with the mental-age concept that had become so important to psychologists and educators. In 1926 he pointed out incisively that two different definitions of mental age were being used: one that infers mental age from the chronological age for which a specified test performance is average; and a second that infers
THURSTONE, L. L. mental age from the average chronological age of persons performing at a specific level. Thurstone demonstrated the inadequacy of both definitions for dealing with adult intelligence and suggested that test performance of children as well as of adults should be represented in terms of either percentile ranks or standard scores. Thurstone's later work on factor analysis (discussed below) bears directly on the study of mental abilities. In the late 1920s he began an analysis of the correlations between various types of aptitude tests. This area had already been investigated by both C. E. Spearman and E. L. Thorndike, who had come to quite different conclusions. Spearman claimed, as a result of his method of factor analysis, that there is a general factor "g" that characterizes all mental functioning, even though there are many additional specific, unique abilities (Spearman 1904; 1927). Thorndike took issue with Spearman's position and argued that intelligence is composed of a large number of separate factors or elements and that there is no general intelligence. Thurstone, using improved statistical techniques, arrived at a position somewhere between these two extremes. He claimed that performance on tests of cognitive abilities results from several factors rather than from one common general factor. After making several factor analyses, he identified a number of factors that he referred to as "primary mental abilities": spatial visualization, perceptual ability, verbal comprehension, numerical ability, memory, word fluency, and reasoning. He saw that some of these could be separated into two or more factors, depending upon the number of tests of the original factors introduced in new analyses and the nature of the specific variations incorporated in the tests. Thus when a number of tests of, for example, the spatial factor, first identified as a primary factor, are included in an analysis, additional or partitioned factors in the realm of space may be identified, as Thurstone was well aware. Noting that the primary factors are positively correlated, Thurstone suggested that a factor analysis of these correlations might reveal a "second-order factor," similar to Spearman's "g" (1948). Measurement theory and psychophysics. Various psychological scales then in use seemed to Thurstone to imply that distributions of scores for various age groups differ only with respect to the mean, and his first paper on measurement theory presented a scaling method that permits both the mean and the dispersion to vary (1925a). Thurstone approached the area of measurement vigorously. In one year, 1927, he published several
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articles dealing with various problems of subjective measurement, introducing the concept of discriminal dispersion and the law of comparative judgment, and relating the law of comparative judgment to the classical psychophysics of Weber and Fechner (see 1927; Measurement of Values, pp. 19-81). He also issued a lithoprinted work, "The Reliability and Validity of Tests" (1931a). Further papers, first published between 1928 and 1932, dealt with the inconsistency of the phigamma hypothesis with Weber's law (Measurement of Values, pp. 82-91), the limitations of the method of equal-appearing intervals (ibid., pp. 9299), the method of rank order as a substitute for paired comparisons (ibid., pp. 100-111), and the numerical evaluation of the dispersions of stimuli presented by the constant method (ibid., pp. 112122). In 1931 Thurstone wrote an article that was based upon the postulate that motivation toward accumulation of a commodity is inversely proportional to the amount already possessed (ibid., pp. 123-144). At the University of North Carolina, where he went in 1952, he worked with Lyle V. Jones, with whom he had collaborated earlier, on the experimental determination of the zero point on a scale of utility; they demonstrated that subjective values are additive (ibid., pp. 195-210). In a 1945 paper, Thurstone had shown that the dispersion of affective values, as well as the average affective value of a proposal, is significant in the measurement of the social attitudes of a group (ibid., pp. 145-160). Even in the last years of his life Thurstone continued to investigate approaches to the measurement of subjective attributes. He developed a new scaling method that avoided the assumption of the normality of the subjective distribution for each stimulus. He also explored the less restrictive assumption that repeated judgments by the same individual will be normally distributed on the subjective continuum. A 1954 paper, "The Measurement of Values," reviewed fundamental concepts of subjective measurement (ibid., pp. 182-194). The measurement of attitudes. Perhaps the most popular application of Thurstone's work in subjective measurement is his contribution to the scaling of social attitudes. Although he recognized the inadequacy of methods of attitude measurement current in the 1920s, he held that, in principle, attitudes were subject to measurement. Thurstone had earlier, in 1928, advanced the notion of equal-appearing intervals for subjective measurement, and later he extended it to development of an attitude scale. "The scale is so constructed that
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THURSTONE, L. L.
two opinions separated by a unit distance on the base line seem to differ as much in the attitude variable involved as any other two opinions . . . also separated by a unit distance" (Thurstone & Chave 1929, pp. xi-xii). Thurstone and Chave presented a series of 130 opinions about the church to 300 "judges" who were asked to arrange them in 11 piles ranging from extremely unfavorable to extremely favorable. An analysis of these judges' arrangements produced a final set of 45 items that had been rated relatively unambiguously and consistently and, most important, that represented a more or less uniformly graduated series of scale values. Subsequently, individual responses to this final opinion scale could be converted into meaningful scores and could be treated mathematically. The scale had internal reliability. Furthermore, on the basis of its ability to discriminate particular groups whose attitudes toward the church were assumed to be different, its validity was demonstrated. The uniqueness and importance of Thurstone's contribution to attitude scaling are still appreciated, as others continue to extend psychophysical methods to social phenomena that lack the simple scalable dimensions of physical stimuli. Multiple-factor analysis. Despite widespread interest in the application of attitude-measurement techniques to all sorts of issues and groups, Thurstone abandoned this field in the early 1930s to work on the development of multiple-factor analysis. Although later psychologists may place more emphasis upon Thurstone's contributions to psychophysics, his contemporaries probably paid more attention to his work in factor analysis. Thurstone was impatient with the debate on the merit of Spearman's single-factor method, the universality of a general factor, and the role of group factors. Instead of asking whether correlation coefficients support a general factor, he wondered how many factors must be postulated in order to account for observed correlations. The power of this approach lay in its ability to establish in the case of any particular study whether or not one factor should be regarded as general. Thurstone's excursions into multiple-factor analysis also embraced the concepts of communalities, rotation of the reference frame, oblique reference axes, and factorial invariance. The concept of simple structure—his solution to the problem presented by the infinite number of positions of reference axes—may well be his most noteworthy contribution to factor analysis. He was also concerned with second-order factors and with the effects of selection upon factorial structure.
Multiple-factor analysis was the subject of Thurstone's 1933 presidential address to the American Psychological Association, "The Vectors of Mind" (1934); he also wrote two major books on the subject (1935; 1947). He continued his work on factor analysis after he moved to North Carolina, and at about the same time that others began to work on this problem, he devised an analytical method of rotating the reference axes (1954). He also developed a new method of factor analysis designed to avoid the communality problem (1955). At the same time that he was refining the methodology of factor analysis, he was making important applications of the approach. His first large study entailed 57 tests of cognitive functions, administered to 240 subjects (1938). This research was followed by other studies, several of which were completed in his laboratory as student dissertations. An experimental battery of tests of primary mental abilities for use in schools was made available in 1938. In these and many other efforts, Thurstone was fortunate in having the collaboration of his wife. The study of personality. A recurrent interest of Thurstone's was the elusive realm of personality. He and his wife at one time developed a personality schedule patterned after Woodworth's questionnaire (1930). Returning to this earlier interest after World War n, he identified the psychological hypotheses implicit in such tests as the Rorschach and assembled more than sixty tests representing hypotheses concerning the manifestation of personality traits in performance on objective tests. A fairly short temperament schedule for use with normal persons resulted from factorial studies of personality questionnaires (1951). Although he himself did not pursue work in this field to its limits, Thurstone regarded objective laboratory tests of temperament as one of the most challenging areas of research. Thurstone not only contributed abundantly to the development of psychology but also exhibited a rare ability to capture the imagination of university colleagues and administrators, students, military leaders, industrialists, and the representatives of foundations. He had infinite skill in imparting ideas to others and inspiring them, too, to creative accomplishmen t. DOROTHY C. ADKINS [For the historical context of Thurstone's work, see the biographies of SPEARMAN; THORNDIKE; for discussion of the subsequent development of Thurstone's ideas, see APTITUDE TESTING; FACTOR ANALYSIS;
TIME: Psychological Aspects INTELLIGENCE AND INTELLIGENCE TESTING; PSYCHOMETRICS; PSYCHOPHYSICS; SCALING; and the biography of KELLEY.] WORKS BY THURSTONE The Nature of Intelligence. London: Routledge; New York: Harcourt. -» A paperback edition was published in 1960 by Littlefield. 1925a A Method of Scaling Psychological and Educational Tests. Journal of Educational Psychology 16: 433-451. (1925b) 1930 The Fundamentals of Statistics. New York: Macmillan. 1926 The Mental Age Concept. Psychological Review 33: 268-278. 1927 The Unit of Measurement in Educational Scales. Journal of Educational Psychology 18:505-524. 1928 The Absolute Zero in Intelligence Measurement. Psychological Review 35:175-197. (1929) 1937 THURSTONE, L. L.; and CHAVE, E. J. The Measurement of Attitude: A Psychophysical Method and Some Experiments With a Scale for Measuring Attitude Toward the Church. Univ. of Chicago Press. 1930 THURSTONE, L. L.; and THURSTONE, T. G. A Neurotic Inventory. Journal of Social Psychology 1:3—30. 1931a The Reliability and Validity of Tests. Unpublished manuscript, Ann Arbor, Mich. 1931b Multiple Factor Analysis. Psychological Review 38: 406-427. 1931c A Multiple Factor Study of Vocational Interests. Personnel Journal 10:198-205. 1934 The Vectors of Mind. Psychological Review 41:1-32. 1935 The Vectors of Mind: Multiple-factor Analysis for the Isolation of Primary Traits. Univ. of Chicago Press. 1938 Primary Mental Abilities. Psychomatic Monographs, No. 1. Univ. of Chicago Press. 1947 Multiple-factor Analysis: A Development and Expansion of The Vectors of Mind. Univ. of Chicago Press. 1948 Psychological Implications of Factor Analysis. American Psychologist 3:402-408. 1951 The Dimensions of Temperament. Psychometrika 16:11-20. 1954 An Analytical Method for Simple Structure. Psychometrika 19:173-182. 1955 A Method of Factoring Without Communalities. Pages 59-62 in Invitational Conference on Testing Problems, 1954, Proceedings. Princeton, N.J.: Educational Testing Service. The Measurement of Values. Univ. of Chicago Press, 1959. -» All the papers but one were first published between 1927 and 1955; the remaining one was completed by Lyle V. Jones and first published in this volume.
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TIME i. PSYCHOLOGICAL ASPECTS n. SOCIAL ORGANIZATION
Paul Fraisse Jack Goody
1924
SUPPLEMENTARY BIBLIOGRAPHY ADKINS, DOROTHY C. 1964 Louis Leon Thurstone: Creative Thinker, Dedicated Teacher, Eminent Psychologist. Pages 1—39 in Norman Frederiksen and Harold Gulliksen (editors), Contributions to Mathematical Psychology. New York: Holt. SPEARMAN, C. E. 1904 "General Intelligence" Objectively Determined and Measured. American Journal of Psychology 15:201-293. SPEARMAN, C. E. 1927 The Abilities of Man: Their Nature and Measurement. London: Macmillan.
PSYCHOLOGICAL ASPECTS
Time is a dimension of our experience and our activity, but this dimension does not correspond to a simple physical reality. The concept of time is imposed on us by our experience of changes: the physicist and the biologist must introduce a parameter t to account for the evolution of natural phenomena. Analysis of our experience and the requirements of science show that two fundamental aspects must be distinguished in the concept of time: (a) the sequence, and more precisely, the order of the changes; (b) the duration of the changes or of the period between them. The interlocking of order and duration defines the process of the change. We experience a great number of series of changes that are apparently autonomous—time of the seasons, time of day and night, time of human life, time of activities, and so forth. History of the psychology of time. The psychology of time begins with Kant. Prior to him, the reality of time had not been questioned, even though philosophers disputed its nature. Kant declared that our notion of time is not imposed by a noumenal reality but by the activity of the mind: it is one of the forms of our sensibility. In the nineteenth century, in a departure from Kant's essentially rationalistic approach, men became concerned with the actual study of the sense of time and with perception of time, and no longer merely with the time of phenomena. A psychophysics of time was developed by comparing estimates of duration with the measurements given by chronometers. Henri Pieron, in 1923, was the first to define the psychology of time in a behaviorist framework, through the objective study of human behavior in relation to time. This point of view was developed by Pierre Janet (1928), who raised the question of our adaptation to time. Jean Piaget (1946) studied the development of the notion of time in the infant. Paul Fraisse (1957) provided a general analysis of temporal behavior. Temporal behavior. The psychology of time is defined by studying temporal behavior, i.e., by our adaptations, at first to the sequence and duration of changes and later to the multiplicity of changing series in which we live. These adaptations take place on two levels. The
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TIME: Psychological Aspects
first is common to animals and man; through learning, activities become synchronous with series of changes. The second is peculiar to man, who is able to make symbols correspond to the various aspects of the changes. Society teaches these symbols to man, who uses them to represent the changes to himself, to orient himself within them, and also to control them. Adaptation to sequence and order Adaptation to sequence in conditioning. From the moment of their birth, organisms are subject to changes, and in particular, to their own internal changes. Stimuli precede the recurrence of needs and the means for satisfying them, which are reinforced by their reduction. Those stimuli that regularly precede need reduction become conditioned "signals." The organism then adapts to the sequence. The signals orient his activity toward the future. The infant smiles at the bottle at first, then at his mother preparing the bottle, and so forth. Some months later, he will cooperate in getting dressed, his movement anticipating the subsequent action. This Pavlovian type of conditioning is accompanied by an instrumental type of conditioning. The newborn child cries at annoyances in his first days, but he soon learns to make use of his crying to call for and evoke the action of others: he anticipates. At the age of about one year, the child adds to this behavior the act of designating what he wants by means of gestures and then by words. [See LEARNING, articles on CLASSICAL CONDITIONING and INSTRUMENTAL LEARNING.] Perception of sequence. To the physical sequence there corresponds a perceived sequence. The process of learning language reveals that the child is very soon able to repeat longer and longer ordered series of phonemes. This perception of an ordered sequence is spontaneous; it does not correspond to any superimposed contruction. Thus, it is always harder to repeat a series of digits in reversed order or in any order other than the one in which it was perceived. [See LANGUAGE, article on LANGUAGE DEVELOPMENT.]
The natural organization of the sequence is facilitated if the stimuli are of the same nature. For example, if we are presented visually with three digits in succession and if at the same time we are presented audibly with three other digits, we can only reproduce these stimuli by first repeating the visual series and then the auditory one, or vice versa (Broadbent 1958). [See GESTALT THEORY.]
The lower limit for the perception of sequence depends on the inertia of the sensory receptors: it is 10 ms. for hearing and touch and 100 ms. for sight, if the stimulations occur at the same site (Pieron 1945). Trained subjects can perceive two sensations of the same or different natures (sound and light, for example) as a sequence when they are separated by an interval of only 20 ms. (Hirsh & Sherrick 1961); an interval of 60 ms. is necessary for untrained subjects (Hirsh & Fraisse 1964). [See HEARING; SENSES; SKIN SENSES AND KINESTHESIS; VISION.]
The upper limit of the perception of sequence in the case of two stimuli has been determined by using rhythmic forms. This limit is about two seconds (Fraisse 1956). Beyond that, the sequence is no more perceived but is constructed. Between these limits lies an optimum for the perception of sequence: an interval of about 600 ms. to 800 ms. This interval corresponds to that for spontaneous motor activity, to that for word association (Wundt [1873-1874] 1886, p. 322), to the spacing of the conditioned and unconditioned stimuli for optimal learning, to the time for which a series of two stimuli appears most natural, i.e., not too slow or too fast (Frischeisen-Kohler 1933), and to the time for which counting permits the most precise evaluation of the duration (Davis 1962). Complex sequences. Perception of sequence is easy when the stimuli belong to a single series of changes. It is no longer so when two orders of succession have to be discriminated. For example, if two runners stop successively but the one that stops first in time is the one that goes the shortest distance spatially, a child of five will confuse the spatial order and the temporal order of the stops (Piaget 1946, p. 90). Likewise, a child of five cannot organize two series of sequences experienced simultaneously, as for example the successive levels of liquid in a vase that is being emptied and the successive levels in another vase that is being filled at the same time (Piaget 1946, p. 7). The coordination of complex sequences implies logical constructions and operations, to use Piaget's vocabulary, that are possible for children only from age seven, approximately. [See DEVELOPMENTAL PSYCHOLOGY, especially the article on A THEORY OF DEVELOPMENT; INFANCY.]
Estimating duration Delayed conditioning. If a time interval separates the conditioned stimulus from the uncondi-
TIME: Psychological Aspects tioned stimulus, the conditioned reaction tends gradually to take place after an interval that is nearly equal to the interval between the two stimuli, as Pavlov showed as early as 1907. The conditioned reaction adapts to the duration, which acts as a second conditioned stimulus. The activity of the animal can also take duration into account in operant conditioning. A rat that is reinforced at regular intervals only begins to respond toward the end of the interval (Skinner 1938). He can even be trained to space two responses at a given interval (Sidman 1956). It should be emphasized, however, that delayed conditioning of a defensive reaction is hard to obtain, no doubt because the animal cannot control his reaction spontaneously except in the case of double avoidance (Ruch 1931). The relative length of a confinement in the first branch of a T maze can also be a signal for taking the left or the right path (Cowles & Finan 1941). Perception and estimation of duration. Man is able to estimate directly the duration of an event, with a precision that can be checked either by comparing two intervals or by reproducing the period. If perception is an immediate discrimination reaction to a present stimulus, it may be asked whether it is possible to speak of perception of a duration. The answer is positive. Within the limits of the psychological present (Fraisse 1957), we may assume that the duration of an event is "present" for several seconds. Within these limits there is an interval of indifference of 700 ms., corresponding to the optimum sequence. Shorter intervals are overestimated, longer intervals underestimated. Beyond a few seconds it is better to speak of estimation of time rather than of perception of it, since more complex processes, of which not too much is known, then enter into the picture. While there are certainly physiological recordings, e.g., from delayed conditionings, it is out of the question that the frequency of the heartbeat or the respiration should be direct factors, since no author has been able to find a correlation between these variables and the estimated duration. Undoubtedly, a central process is involved. This biological estimation depends on the general level of biological activity. Thus, in experiments with sensory deprivation, duration is greatly underestimated (Vernon & McGill 1963). Michel Siffre (1963), who lived in a completely dark cave, isolated from the world and without any timepiece, estimated his stay of 58 days as having lasted 33 days. Recent research on animals and human subjects
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(Fraisse 1963) shows that in general, stimulants (mescaline, thyroxine, caffeine, amphetamine) cause an overestimation of time, and inhibitors (quinine, barbiturates) an underestimation. On this point, however, our knowledge is still rudimentary. Thus, many psychological variables alter the estimation of time. For durations of less than two seconds, the variability of reproduction is of the order of 10 per cent; for periods of several minutes, it rises to 20 to 30 per cent. Using the method of absolute judgments of duration, it is hardly possible to discriminate more than three stimuli, and the amount of information transmitted is less than two bits (Hawkes 1961). Psychological factors in estimating time. We know that we can make major errors in estimating durations. Two sets of variables have been studied in particular. The nature of the activity. Convergent results (Fraisse 1963) show that the more complex an activity is and the more it requires the attention of the subject, the shorter the time seems to be. Thus, copying a text or taking it down from dictation seems shorter than reading or listening (for equal objective durations of the activities). In the limiting case, during periods of inactivity duration seems very long. A complex activity appears to be short because in the course of it we note fewer changes than during a simpler activity. Again, a more complex activity is generally more interesting, and this brings up the influence of motivation. The influence of motivation. Whatever interests us seems to have a short duration, while what bores us seems interminable. Everybody has observed this law, which many experiments have confirmed. The best explanation of the phenomenon has been proposed by Katz (1906), who suggested that whenever attention is paid to the passage of time, the time seems to get longer. When we are bored, or waiting, or in a great hurry, time seems to go very slowly, because our attention is fixed on a number of changes, whereas an interesting activity absorbs us and puts us in a way "outside of time." [See ATTENTION.] Quantification and measurement of duration. The quantification, and, more precisely, the measurement of duration, must be distinguished from the over-all estimation of it. The units of these measurements are regular and "calibrated" changes —the ticks of a clock or metronome, the rotation of the earth, atomic clocks, and so forth. But man also makes use of the duration of changes whose
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TIME: Psychological Aspects
durations are less regular and less precise—the length of the distance covered, the number of pieces produced, and so forth. Employing these units is not possible for the child until he has become able to perform intellectual operations, and not until adolescence is the duration of unit changes understood as independent of the concrete nature of the changes (Piaget 1946). Orientation in time Nychthemeral rhythm. We experience many changes simultaneously, some of them being periodic. The latter serve as points of reference, by means of which the others can be located. The nychthemeral rhythm is the most important for living organisms. It is a remarkable fact that this originally exogenous rhythm becomes endogenous. The entire rhythm of the organism—the rhythms of alimentary activity, of sleep, of the body temperature, and of all physiological functioning—has a cycle of 24 hours that persists for several weeks even if the animal or the man's ecological conditions change. We need only recall how tired we are made by an airplane trip that takes us across several time zones. This rhythmic activity turns our organism into a regular clock and gives us points of reference by which we can orient ourselves to the time of day. Thus Siffre, who lived 58 days in a cavern, had 57 periods of sleep and waking during that period, whereas he estimated the duration at 33 days. His physiological clock had been more accurate than his estimates. This transformation of exogenous rhythms into endogenous rhythms is an established fact, and Pavlovian conditioning provides an explanation of it. If a dog is fed every 30 minutes, it gradually reaches the point of starting to salivate only at the end of the 30-minute period (Feokritova 1912). Temporal orientation of man. Man spontaneously makes use of the temporal points of reference provided by his organism. We are conditioned to the rhythm of meals, sleep, and so forth. Even a mental defective is able to demand his meal at a set hour (James 1890, vol. 1, p. 623). But in addition, the infant and then the adult learn to orient themselves to other periodic changes, the most important of which are the changes of nature (the solar day, the year). Man also learns to employ more conventional points of reference, such as clocks, calendars, and so forth. The principle is always the same: to make
the experienced moment correspond to the phase of a periodic change that serves as the system of reference. The temporal horizon The temporal horizon of action. Merely as the result of conditioning due to the repetition of cycles of activity, present signals make reference to a future action. The present stimulus has a previously acquired significance, and it triggers an activity that anticipates some aspect of the future. These cycles are present in animals as well as in man, but because of second-order and higher-order conditioning their period is longer the higher the place that the organism occupies in the phylogenetic scale. The temporal horizon of man. Man too is conditioned by the cycles of his activity, and his temporal horizon always depends on them. The horizon of the day laborer is one thing, that of the professor is another. But, in addition, man is able to distinguish the present moment from what has been (the past) and what will be (the future). This ability is manifest from the youngest age at which the child is able to make adequate use of the adverbs of time (yesterday, tomorrow, and so forth) and the verb forms that refer to the past and the future. Thus we see the child's temporal horizon develop: from the age of 18 months on, he is situated between a recent past and a very immediate future. Little by little this horizon expands, as can be seen from the adequate use of adverbs of time and the localization of memories in the past and projects in the future. From the age of seven or eight on, this horizon extends beyond personal experiences. The child becomes interested in the background of his parents and in his country's history, and he becomes able to imagine future events that have not formed a part of previous cycles of his activity (his own marriage, for example). This development is to a very great extent a function of intelligence, which makes possible, in particular, better organization of the past and better anticipation of the future (Kastenbaum 1961). Temporal horizon and society. Past and future are made more precise by the learning of the society's language. Along with language, society transmits its representations of the past and the future. Some of these representations, linked to the great philosophies, are of great generality. Among the Greeks, for example, a circular representation of time predominated. The Christians
TIME: Psychological Aspects formed a continuous representation, starting from a creation ex nihilo down to the end of time. All men, in different degrees, use cyclical conceptions with respect to years, generations, civilization, or economic plans. More specifically, each social framework (family, profession, church, nation, and so forth) has its own way of seeing time, and, with Gurvitch (1958), we may speak of the multiplicity of social times. Certain societies, such as the Hopi Indians, hardly have a temporal horizon, if we are able to judge by their language, for their verbs have no tenses and they are said to be content with distinguishing "the earlier from the later" (Whorf 1950). In a given society, the temporal horizon appears to be fairly closely bound up with the cycle of experienced expectations and satisfactions. Every man has the capacity to evoke very distant pasts or futures, but in practice the horizon that has solidity and reality for him is narrowly linked to his way of life. The time of the peasant is one thing, and the time of the city dweller another. For example, it has been found that workers' children make up stories covering a shorter period of time than middle-class children (Leshan 1952). Finally, it should be kept in mind that every man belonging to several social groups has multiple temporal perspectives. He has to pass from one to the other—from family time to office time, for example—and try to bring them into accord (Halbwachs 1947). Thus, every man, depending on his temperament, his intelligence, and the forms of socialization that formed him, comes to have his own temporal horizon, defined in its extent and polarity, assigning value to either the past or the future, or even just the present (Fraisse 1957, p. 174). Individual differences in temporal horizons, of which little is as yet known, are clearly present in mental pathology and have been emphasized in studies of juvenile delinquents (Barndt & Johnson 1955). Mastery of time Tolerance of delay. It is possible to set up delayed conditioning in animals when the unconditioned stimulus provides positive reinforcement. It seems impossible to obtain this result in rats when the reinforcement is negative (avoiding an electric shock); but it does seem possible to obtain conditioning to time in dogs to whom an electric stimulus on the paw is given every five minutes [see Dmitriev & Kochigina 1955; see also LEARNING, article on AVOIDANCE LEARNING].
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Children are greatly put out by the frustrations arising from the postponement of satisfaction. They are noticeably better able to stand delays as they grow older (Orsini & Fraisse 1957) and thus become able to prefer a reward that is greater, but delayed, to one that is smaller but immediate (Mischel & Metzner 1962). This progress appears to be linked on the one hand to development, education, and intelligence, and on the other, to emotional stability (Fraisse & Orsini 1955). Adolescents with emotional troubles react more impulsively to the stresses of the environment (Levine & Spivack 1959). Culture and the socioeconomic level (for the two are often linked) lead to the development of an appreciation of distant but valuable objectives and thereby of plans for organizing the future (Doob 1960). Maturity and culture make it possible to break free of the domination of the pleasure principle and to adjust better to the reality of time. The notion of time. Even when man is able to tolerate delays, he is enraged by irreversible changes. He finds relative security in conforming to the demands of society, whose pressure increases in proportion to the complexity of the network of social relations ("La pression temporelle" 1953); this is why the city dweller uses a watch more often than a farmer does. However, men seek to escape from the irreversibility of time by developing a notion of time that enables them to put the past and the future into the present. Cultivated men and societies like to set up memorials of their past in the forms of museums and archives and seek to survive their deaths by work that is as imperishable as possible. PAUL FRAISSE [See also DEVELOPMENTAL PSYCHOLOGY, article on A THEORY OF DEVELOPMENT; SLEEP. Other relevant material may be found in LANGUAGE, article on LANGUAGE DEVELOPMENT; PERCEPTION; PsYCHOPHYSICS;
SENSORY AND MOTOR DEVELOPMENT.] BIBLIOGRAPHY ASCHOFF, JURGEN 1965 Circadian Rhythms in Man. Science 148:1427-1432. BARNDT, ROBERT J.; and JOHNSON, DONALD M. 1955 Time Orientation in Delinquents. Journal of Abnormal and Social Psychology 51:343-345. BROADBENT, DONALD E. 1958 Perception and Communication. Oxford: Pergamon. COWLES, J. T.; and FIN AN, J. L. 1941 An Improved Method for Establishing Temporal Discrimination in White Rats. Journal of Psychology 11:335-342. DAVIS, R. 1962 Time Uncertainty and the Estimation of Time-intervals. Nature 195:311-312.
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DMITRIEV, A. S.; and KOCHIGINA, A. M. (1955) 1959 The Importance of Time as a Stimulus of Conditioned Reflex Activity. Psychological Bulletin 56:106-132. -> First published in Russian. DOOB, LEONARD W. 1960 Becoming More Civilized: A Psychological Exploration. New Haven: Yale Univ. Press. FEOKRITOVA, IULIIA P. 1912 Vremia kak uslovnyi vozbuditel' sliunnoi zhelezy (Time as a Conditioned Stimulus to the Salivary Gland). St. Petersburg: Tipografiia Shtaba Otdiel'nago Korpusa Zhandarmov. FRAISSE, PAUL, 1956 Les structures rhythmiques: Etude psychologique. Brussels: Erasmus; Univ. of Louvain. FRAISSE, PAUL (1957) 1963 The Psychology of Time. New York: Harper. -» First published in French. FRAISSE, PAUL 1963 Perception et estimation du temps. Pages 59-95 in Paul Fraisse (editor), Traite de psychologie experimental. Volume 6: La perception. Paris: Presses Universitaires de France. FRAISSE, PAUL; and ORSINI, FRANCINE 1955 Etude experimentale des conduites temporelles. I: L'attente. Annee psychologique 55:27-39. FRANKENHAEUSER, MARIANNE 1959 Estimation of Time: An Experimental Study. Stockholm: Almqvist & Wiksell. FRISCHEISEN-KOHLER, I. 1933 Feststellung des weder langsamen noch schnellen (mittelmassigen) Tempos. Psychologische Forschung 18:291-298. GURVITCH, GEORGES 1958 Structures sociales et multiplicite des temps. Societe Francaise de Philosophie, Bulletin 52:99-142. -» Includes 26 pages of discussion and comments. HALBWACHS, MAURICE 1947 La memoire collective et le temps. Cahiers internationaux de sociologie 2:3-31. -» Published posthumously. HAWKES, GLENN R. 1961 Information Transmitted Via Electrical Cutaneous Stimulus Duration. Journal of Psychology 51:293-298. HIRSH, I.; and FRAISSE, PAUL 1964 Simultaneite et succession de stimuli heterogenes. Annee psychologique 64:1-19. HIRSH, IRA J.; and SHERRICK, CARL E., JR. 1961 Perceived Order in Different Sense Modalities. Journal of Experimental Psychology 62:423-432. JAMES, WILLIAM (1890) 1962 The Principles of Psychology. 2 vols. New York: Smith. JANET, PIERRE 1928 L'evolution de la memoire et la notion du temps. Paris: Chahine. KASTENBAUM, ROBERT 1961 The Dimensions of Future Time Perspective: An Experimental Analysis. Journal of General Psychology 65:203-218. KATZ, DAVID 1906 Experimentelle Beitrage zur Psychologie des Vergleichs im Gebiete des Zeitsinns. Zeitschrift filr Psychologic und Physiologie der Sinnesorgane. 1. Abteilung. Zeitschrift fur Psychologic 42: 302-340; 414-450. LESHAN, LAWRENCE L. 1952 Time Orientation and Social Class. Journal of Abnormal and Social Psychology 47:589-592. LEVINE, MURRAY,- and SPIVACK, GEORGE 1959 Incentive, Time Conception and Self Control in a Group of Emotionally Disturbed Boys. Journal of Clinical Psychology 15:110-113. MISCHEL, WALTER; and METZNER, RALPH 1962 Preference for Delayed Reward as a Function of Age, Intelligence, and Length of Delay Interval. Journal of Abnormal and Social Psychology 64:425-431.
ORSINI, FRANCINE; and FRAISSE, PAUL 1957 Etudes des conduites temporelles. II: Etude genetique de 1'attente. Annee psychologique 57:359-365. PIAGET, JEAN 1946 Le developpement de la notion de temps chez I'enfant. Paris: Presses Universitaires de France. PIERON, HENRI 1923 Les problemes psychophysiologiques de la perception du temps. Annee psychologique 24:1-25. PIERON, HENRI (1945) 1952 The Sensations: Their Functions, Processes, and Mechanisms. New Haven: Yale Univ. Press; London: Miiller. -» First published as Aux sources de la connaissance: La sensation, guide de vie. La pression temporelle. 1953 Sondages 15, no. 3:1123. RUCH, FLOYD L. 1931 L'appreciation du temps chez le rat blanc. Annee psychologique 32:118-130. SIDMAN, MURRAY 1956 Time Discrimination and Behavioral Interaction in a Free Operant Situation. Journal of Comparative and Physiological Psychology 49:469473. SIFFRE, MICHEL 1963 Ears du temps. Paris: Juillard. SKINNER, B. F. 1938 The Behavior of Organisms: An Experimental Analysis. New York: Appleton. VERNON, JACK A.; and McGiLL, THOMAS E. 1963 Time Estimations During Sensory Deprivation. Journal of General Psychology 69:11-18. WALLACE, M.; and RABIN, A. I. 1960 Temporal Experience. Psychological Bulletin 57:213-236. WHORF, BENJAMIN L. 1950 An American Indian Model of the Universe. International Journal of American Linguistics 16:67-72. WUNDT, WILHELM (1873-1874)1886 Elements de psychologic physiologique. 2 vols. Paris: Alcan. -> First published in German as Grundziige der physiologischen Psychologic. Volume 1 was translated into English in 1905 as Principles of Physiological Psychology. II SOCIAL ORGANIZATION
Since all human activities occur in time, the existence of a social system necessitates some or ganization of time. Such organization entails : (1) systems of time measurement, based upor cosmic and human cycles; (2) the allocation and scheduling of time fr individuals; and (3) a set of attitudes toward time past, tirrn present, and time future. While many thinkers have been interested i] the basic categories of the understanding—time space, and so on—it was Durkheim's discussio: of this subject (1912) that laid the basis for moc ern social scientific treatments. Durkheim arguec developing Kant's view that the basic categorie of the understanding exist in the mind, that thes categories are not given a priori but are soci; constructs. It was Durkheim's observations th; encouraged other social scientists to study the w£
TIME: Social Organization in which cultural variations in concepts such as time and space are related to other aspects of social life (see, for example, Granet on China [1934]; Mauss on the Eskimo [1906]; EvansPritchard on the Nuer [1940]) as well as to the way children acquire concepts about time (see, for example, Piaget 1946). Not all societies have the equivalent of the category "time." Writing of the Nuer of the southern Sudan, Evans-Pritchard pointed out that for them the notion that we call "time" is not a separate idea but an integral part of social activities and of ecological and meteorological phenomena ([1940] 1963, pp. 104-108). Similarly, Bohannan has written of the Tiv of northern Nigeria: "Time is implicit in Tiv thought and speech, but it is not a category of it" (1953, p. 262). But if time is not necessarily an explicit category, it is always an aspect of experience, implicit in thought and speech. The experience of time takes two major forms—sequence and duration. From the standpoint of sequence, events are seen as located in a particular order along a moving continuum. The experience of duration derives from the relative span of events and of the intervals between them. The experience of time as a continuum is often compared metaphorically to the movement of water, sometimes the linear flow of a river, sometimes the cyclical ebb and flow of the ocean; indeed, the English word "time" has the same root as "tide." Although all societies have some system of time reckoning, some idea of sequence and duration, the mode of reckoning clearly varies with the economy, ecology, and technical equipment; with the ritual system; and with the political organization. A peasant system has little need of elaborate scheduling, nor does it always possess the mechanical devices that permit accurate measurement. In nonindustrial societies the repetitive patterns of human life and the world of nature provide the basic measures of time reckoning, the counters for verbalizing the experience of duration. These measures can be thought of in terms of two main cycles, the human and the cosmic. In each cycle the main points of significant change are marked by rites of passage. Sequence and duration, cyclical and linear patterns, and systems of reckoning occur in all human societies, but the emphases differ. The measurement of long periods of time (the chronology °f the historian) could hardly begin before the urban revolution, which brought with it writing a nd the possibility of elaborate calculations concerning the movement of the heavens. Strict chro-
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nology began, according to Cumont (1912), with the establishment by the Chaldeans of a fixed era, the Era of Nabonassar, in 747 B.C. The introduction of such a base point for the calculation of years was essential to the prediction (and to some extent the recording) of long-term periodic phenomena, such as eclipses. The use of a base point represents a partial disengagement from cyclical concepts: years now pass irretrievably, never to return; time accumulates and no longer just ebbs and flows. This idea of irreversible time, much stressed in Judaeo-Christian thought, is central to the development of science and history alike. But such general changes in ideas as the shift from "the myth of the eternal recurrence" to the concept of linear, irreversible time are matters of degree rather than kind. Sacred (or liturgical) time, as distinct from profane time, continues to be largely dependent upon cyclical concepts; even the apocalypse, a thoroughly linear belief, is followed by rebirth into a timeless universe. We experience the events of our lives and the succession of the natural seasons in terms of both concepts; indeed, the attempt to erect long-term cycles continues to be a feature of the work of historians such as Spengler and Toynbee (although they tend to confuse the persistence of certain mechanisms with the repetition of specific events). The same is true of the concepts of sequence and duration: they do not change radically. In simple societies the beginning of a ceremony is often determined by a natural event, or, as in the Tallensi ritual chain, it follows the performance of a similar ceremony by a neighboring group (Fortes 1936). Time indications tend to give way to time measurement with the invention of new mechanical devices; but even modern man, reviewing his own experience, often thinks in terms of the sequence of events rather than attempting to locate them in an absolute chronology. The subjective time of the "inner dialogue" (what Meyerhoff calls "human time"), which forms one of the great concerns of Proust, Joyce, Mann, and Virginia Woolf, stands in contrast to the more rigid time reckoning required either by the social intercourse of urban society or by scientific endeavor; in the latter, I include the establishment of a chronology for historical reconstruction, as distinct from the personal recollection of past experience. Since concepts of time and its social organization are basic to the development of modern science and technology, which, in turn, underlies the rise of modern industrial society, to what extent do the variations in these concepts account
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for differences in technological and industrial development? From the Chinese evidence, Needham has concluded (1965, p. 52) that differences in development cannot be attributed to concepts of time. These concepts vary only in degree and are not in themselves capable of preventing technological advance. Thus, in addition to the discrete cycles, the discontinuous "packaged" time of their general world outlook (Granet 1934), the Chinese also used the linear reckoning appropriate for historical narrative; both models were potentially available. It would appear that major changes in the concepts and organization of time follow rather than precede technological innovations. Measurement of time—the cosmic cycle The passage of time is calculated by reference to a series of repetitive units that are measured with varying degrees of precision. Certain of these units are based upon the movements of nature—the daily rotation of the earth, the regular phases of the moon, and the annual movement of the earth around the sun. The reckoning of days, months, and years occurs universally. But such units are not necessarily organized into an interlocking series, with one unit representing a specific fraction (or multiple) of another; instead, they may constitute a set of discontinuous time-indications. Night and day. Time reckoning begins with the recurrent division into night and day that commonly regulates activity levels in most forms of animal life. The division of human life into light and dark, movement and rest, and waking and sleeping often provides a symbolic framework for many other social activities. Night is generally seen as linked with evil, with witchcraft, and with illicit behavior of all kinds. It is the time for supernatural agencies to reveal themselves in dreams and for spirits of varied shapes and sizes to roam the earth. Night is also the time for sleep and sex, for dreaming and for thievery. To daytime belong the productive activities. In all societies, some division of the day is made according to the position of the sun in the sky; hence, concepts of dawn, forenoon, afternoon, and sunset, and the reckoning of time by the movement of light and shadow appear universally. Frequently, the periods of dawn and dusk, the times that call for a reorientation of activities from those of night to those of day, are further subdivided, and the terminology is refined. With the use of the sundial, the variation in the position of shadows can be formalized. Time reckoning thus moves in the direction of regular divisions of the night and the day into seconds, minutes, and hours, a
systematization that runs counter to the experience of the inhabitants of lands where there are seasonal differences in the length of daylight. Only with the development of mechanical devices can one divide night and day into equal units calculated against the rotation of the earth rather than on the basis of the length of sunlight. The precise divisions made by the clock are, of course, essential to any elaborate scheduling of the kind demanded by large-scale organizations like factories, offices, or communication systems. But the desire for more accurate time measurement long antedates the industrial revolution and relates to economic, ritual, military, and political needs. The sundial (or gnomon), the sandglass, and the clepsydra (or dripping water clock) were invented in Babylonia and Egypt, from whence they spread throughout the Old World. The oldest Egyptian water clock, graduated to show the lengths of hours at different seasons, dated from about 1500 B.C., and such instruments were further developed in Alexandria, in the Arabic world, and in Europe. The duties of the keeper of the clock are frequently mentioned in the rule books of monastic orders such as the Cistercians and included nightly adjustments according to observations of the stars. From the Fertile Crescent, sundials and watei clocks also spread to China. Lacking Euclidear deductive geometry, the Chinese never achievec the complexity of Arabic and western gnomonics But the water clock evolved much further into i complex hydromechanical instrument, and by 721: the Chinese had succeeded in controlling the rota tion of the water wheel by means of an "escape ment" of linkwork, which operated a kind of gate "Steady motion was thus secured by intersectin the progress of a powered machine into interval of equal duration—an invention of genius" (Neec ham 1965, p. 18). Whether or not this invention was the forerui ner of the purely mechanical clock is uncertaii But by the mid-fourteenth century the techniciar of western Europe had produced a weight-drive chronometer that depended upon a verge-and-foli< escapement to regulate its movement. From tf time of Archimedes, men had constructed m chanical models of the planetary orbits, and mo of the first clocks were "less chronometers tht exhibitions of the pattern of the cosmos"; the origin lay "in a complex realm of monument planetaria, equatoria, and geared astrolabe (White 1962, pp. 122-123). Indeed, the clock h been described as a machine to emulate the rotati of the earth.
TIME: Social Organization Coincident with the invention of such a clock, the temporary, or variable, hour, which had been favored for liturgical purposes, finally gave way to the system of equal hours. The division of the day into 12 hours, based upon the duodecimal system of the zodiac, was established in ancient Greece. About the middle of the fourteenth century it became usual to divide the hour into 60 minutes and the minute into 60 seconds. The measurement of time was now removed from the context of events; its divisions were given an abstract framework, and its reckoning became increasingly dissociated from immediate human experiences, shifting from the sun or tides to the formal divisions engraved on the face of a mechanical device. The next century saw the adaptation and use of the spring mechanism in clocks and later in watches. The new instrument was quickly taken up by the rich, particularly by the merchants, who had discovered, as Benjamin Franklin later said, that "time is money." "To become 'as regular as clockwork' was the bourgeois ideal, and to own a watch was for long a definite symbol of success" (Mumford 1934, p. 16). About the middle of the nineteenth century, the production of the cheap standardized watch, first in Geneva and then in America, made possible the wide use by individuals of devices for accurate, precise, and continuous time scheduling, as distinct from the communal (and less flexible) timekeeping of the muezzin's call, the village drum, the church bell, and the town-hall clock. In itself the clock is a technological achievement, but it also underlies four major aspects of modern life. First, it has made possible the precise measurement of time, which is perhaps the most fundamental operation in modern physics. Second, its manufacture has helped to train the craftsmen needed for further scientific endeavor, pure and applied. Third, it has provided a mechanical model for the operation of the universe. Fourth, it has permitted the detailed organization of time that an industrial system requires. In these ways, it has changed man's attitudes and his categories of time, and, therefore, it has been called the key machine of the modern world, surpassing in importance the steam engine itself. While accurate time measurement is a prerequisite of the complex social systems that mark industrial economies and of the scientific research on which they are based, earlier methods of timekeeping seem to have been stimulated by magical and religious concern as much as by pragmatic interests. Knowledge of the movements of the stars, although used for predicting seasonal changes and
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for determining direction, was often required for divinatory purposes. The Chaldean-derived horoscope consisted of observations of the configuration of the planets at a certain moment; the chosen time for the calculation was usually the moment of birth, which was believed to shape the individual's whole destiny. Astrology represents the most elaborate form of divinatory technique; it exists only in conjunction with writing, but it is based also upon a widespread belief, apparent in the giving of day-names and similar practices, that men's character and destiny are determined by the date of their birth. The measurement of hours, by sundial and by sand, by candle and by clock, was an ecclesiastical demand, and so too were ideas of punctuality. Members of the "regular" clergy of the medieval monastery were enjoined to organize their lives "by rule," that is, by a specific allocation of time for work, for sleep, and for worship. The ringing of the prayer bell seven times a day established time by recourse to instruments that divided the day into regular intervals. It was this rigid organization of time, combined with the intense devotion to work, that has led scholars to include the Benedictine order among the founders of modern capitalism. Other world religions developed their own diurnal ordering of time. Followers of Islam, for example, are required to offer the five canonical prayers (saldt) at fixed times during the course of the day. In practice, working people tend to restrict their devotions, leaving the full observances to clerics and to the retired, who are able to give their whole lives to the accumulation of religious grace. The working population concentrates upon the evening prayer, which carries the greatest weight; as in Judaism, it is the setting rather than the rising of the sun that initiates the daily cycle. The week. The week lacks any definite basis in the external environment. It is an entirely social construct, varying in length from society to society: seven days in the Judaeo-Christian world and three, four, five, or six days in certain parts of west Africa, southeast Asia, and Central America. In early Rome it was eight days; in China it was ten. However, the weekly cycle always consists of a relatively small number of days (usually named) and is used to regulate short-term, recurrent activities, especially those of the market place. In Mesopotamia the seven-day period was linked to the five planets, together with the sun and the moon, in a planetary or astrological week. The seven-day week spread through Europe, north Africa, India, and the Malay Peninsula and is used
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more or less universally today; present names continue to indicate the pre-Christian origin. The LoDagaa, a primarily agricultural society of northern Ghana, designate the six days of the week by the name of the village where a market takes place on the day in question. The very terms for "day" and "market" are the same (daa), and the weekly cycle is simply daar, "a plurality of markets," so that the names of the days not only record the pattern of market gatherings but also serve as a measuring rod for other short-range activities. The importance of market time is again illustrated in early medieval England, where each neighboring town held its market, or cheaping (hence "cheap"), on a different day of the week. The inhabitants of outlying districts would come in for the local trade and also for the opportunity of meeting together, so that disputes could be settled, marriages arranged, and leisure enjoyed. Thus, in many peasant societies the market week is a way of organizing social time as well as economic exchange. The weekly cycle of markets differentiates one day from another and serves to break up the continuity of agricultural activities by providing some change of pace—substituting rest for work, exchange for production. In the Judaeo-Christian tradition, there is also a weekly shift from the profane to the sacred, for a special day is allocated for religious activity. In Islam this day is Friday, in Judaism Saturday, and in Christianity Sunday. These calendrical differences reflect distinctions of theology and organization. In Islam, Friday is the day for worship at the town's main mosque, often with elaborate processions, but it is not a rest day in the full sense of the word; indeed, there is a maxim to the effect that it is blameworthy to abstain from work on Friday in imitation of the sabbath practices of Christians and Jews (Trimingham 1959, p. 73). The polytheistic religions of west Africa also have their day of rest, which sometimes coincides with the market day. Thomas suggested (1924, p. 199) that in west Africa, while the basis of the week is economic, the rest day is religious in origin; the days are usually named after markets, but sometimes after the gods worshiped on those days. Among the LoDagaa, one day each week is set aside as a "day of not using the hoe," when iron implements are forbidden. It is on this day that important sacrifices are made to the Earth shrine, under whose aegis all major uses of the soil, housebuilding, farming, burial, and ironwork are undertaken. Although modern industrial systems place a
great premium upon the continuous use of industrial facilities, the day of rest is found even in those societies where its role as a day of worship has been abandoned. In the Soviet Union a continuous workweek was introduced in 1929, and each worker was given one day off in five. The result was considerable chaos, in the home as well as at work. Two years later a six-day week with a common day of rest was instituted on the grounds that the shifting five-day schedule encouraged irresponsibility with respect to jobs and employment (Moore 1963, p. 122). In 1940 the seven-day week was restored, with Sunday as the day of rest. The double functions of the week of providing discontinuity in work and time for leisure seem to be even more necessary in an industrialized society than in a purely agricultural one, where seasonal changes impress their rhythms on the productive process. Moreover, there are strong pressures for the weekly break to be held in common: since individuals spend the bulk of their day in specialized work groups, family and neighborhood groups would be of only peripheral importance if they did not have the week end as a focus for joint activities. In the absence of effective crosscutting ties, overwhelming stress would be placed upon the monolithic economic institutions, and this could result in both emotional and cultural impoverishment. The month and the year. While itself consisting of a specified number of days, the week is rarely a subdivision of larger units of time measurement. The next unit in size, and one which is given universal recognition in some form or other, is the month, based upon the lunar cycle of 29.5 days. In nonliterate societies the month is calculated by direct reference to the waxing and waning of the moon, and special attention is paid to the three days of its death and rebirth, which are often seen as having a profound meaning for human life, being linked to ideas of immortality, death, and resurrection. Unlike weeks, months are usually thought of as organized segments of a seasonal cycle, although some societies use names only for certain of the lunar divisions. Nevertheless, all societies recognize some kind of yearly cycle, since this is required by both agriculture and hunting. Agriculture in particular demands an annual scheduling that determines the allocation of work and of food as well as the setting aside of seed at harvest time to be preserved until the next planting season. No society can avoid some long-term budgeting of this kind; the tropical paradise where wild fruits offer a natural superabundance of food and drink is a figment of the imagination of urban Europeans.
TIME: Social Organization Nobody, in fact, just passes the time, although it often seems so to those dependent upon more demanding schedules. There are, of course, outstanding differences in the degree of accuracy required by different schedules. While the weekly markets of medieval England catered to the local trade, there also existed the yearly fairs, or gearmarkets, to which traders came from far afield. The tolls for these fairs were often allocated to various eccelesiastical foundations, and the specific day on which the market took place was sometimes the saint's day of the religious house, so that the fair doubled as a fete and the traders as pilgrims. An activity of this kind that brings people together from widely separated places at a specific time of the year clearly requires a more accurate calculus than is provided by a simple count of moons, loosely linked to a seasonal cycle. It demands a calendar (or natural occurrence) that is accurate, regular, and widely known, so that precise coordination on an annual basis is possible. One difficulty in constructing such a system is that no sum of lunar months adds up to a yearly cycle. Intercalation is necessary in order to reconcile the year of 12 lunar months with the solar year on which the growth of crops depends. In the usual practice, no fixed number of days is assigned to the lunar month (in Islamic practice, for example, it begins when the new moon is seen), and likewise the year is considered to begin when the appropriate season comes round, the length of the months being adjusted accordingly. Thus, the harvest moon comes when the harvest is ready, and the planting moon is set by some biological clock, some natural phenomena, or what Linnaeus called the Horologe or "Watch of Flora." The abandonment of the lunar cycle results in a nonlunar month, or mense, under which term can be included any unit greater than ten days and less than a year (Thomas 1924, p. 188). For example, the Ashanti have the adae, a period of 42 days that is formed by the intersection of a six-day and seven-day weekly cycle, the first of local origin, the second probably of Muslim derivation. Both the great adae, which occurs after 18 days, and the little adae, which takes place after a further 24 days, were occasions for important sacrifices to the royal ancestors. As with the lunar reckoning of Islam, the adae (although unnamed) provides a continuous-chain type of calendar, divorced from the seasonal cycle but linked to a complex series of politico—religious festivals. The necessity for a closer "fit" between lunar months and solar years came only with the introduction of written calendars, which eventually
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led to the abandonment of the lunar month, as in the Julian calendar, or to the relinquishing of the solar year, as in the Islamic system established by Muhammad (where the year of 12 lunar months is ten days shorter than the solar year). Historically, the first breakthrough toward the Western system appears to have been made in Egypt, which established a year of 12 nonlunar months, each with 30 days. Writing permitted a further important formalization of the calendar. In nonliterate societies the accumulation of years takes place, if at all, against a background of regular ceremonies, which may occur every three, seven, or ten years (or occasionally more, as in the case of the 60-year cycle of the Dogon festivals). In early literate societies there was sometimes a set of names for the years, for example, the Year of the Mouse (China) and the Year of Moses (Islam). In ancient Greece, with its annual transfer of power, the years were known by the name of the particular archon. But monarchic systems often reckoned years from the beginning of a reign, and such regnal counts could also be made by the cutting of tallies, the counting of pebbles, or the tying of knots. In Sumeria (as elsewhere), the regnal system of reckoning years was associated with the idea that a new ruler brings with him a new dispensation, a theme of renewal that serves, like regular elections, to reconcile individuals to the gap between expectation and actuality. Similarly, the revolutionary regimes of eighteenth-century France and fascist Italy reckoned the beginning of a new era from the date of their coming to power. Time itself is seen as making a fresh start, the social order as being reborn. The idea of an era depends upon the introduction of a fixed point at which numbering may start. Large-scale time is then no longer reckoned only by cycles or by recurrent series of occurrences; it acquires a more linear character. The fixed point used by the Chaldeans was arbitrary, but later such fixed points were calculated with reference to a unique event—the creation of the world or the birth of the prophet. Time is no longer experienced as largely repetitive (Gluckman 1963) but is seen as flowing in a single line (called variously "progress," "evolution," or "change") and, at the beginning of this shift in viewpoint, often in a chiliastic direction, toward an earthly millennium, the coming of a messiah; thus, certain years of the era, such as 1000, are invested with mystical properties. The early formalization and elaboration of written calendars took place under a variety of pressures: the demands of agricultural planning.
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particularly in complex irrigation societies; the organization of trade, especially long-distance trade; and the coordination of the military and administrative activities of centralized polities. But as in nonliterate societies, magico-religious factors continued to be of prime importance in the arrangement and elaboration of the calendar, which mapped out the liturgical year as well as the economic year. Writing also made possible the recording of star positions and the development of mathematics, which were essential for the development of the horoscope as a means of forecasting future events and ascertaining divine will. Astrological and astronomical calculation always had much in common, and the mapping of the heavenly universe was important not only for divination but also for the development of chronometers and for navigation. One factor that inhibited navigation was the existence of purely local systems of time reckoning, and the development of a world-wide network of communications has inevitably led to the adoption of a unified calculus. Sun time, which varies by one minute every eight miles, had to give way to conventional time belts, which were established in the United States around 1880 at the instigation of the transcontinental railroads. Some years later a world congress completed the standardization of time that had begun with the founding of the Greenwich observatory two hundred years before and that led to the coordination of ships' chronometers with Greenwich mean time. Human action could now be synchronized on a world-wide scale. Systems of time reckoning have developed from concrete time indications of a discontinuous kind to increasingly abstract, numerical, and regular divisions linked to a continuous calendar based primarily on diurnal and annual movements. Through the means of writing, astronomy, and mechanics, there occurs an increasing dissociation of time measurement from commonplace events —the movement of animals, the growth of crops, and the human activities to which they are directly linked. Thus, there emerges a formal framework of objective divisions that are as applicable in Delhi as they are in Dallas. But the development of more abstract time scales tends to supplement rather than replace more concrete ideas of time, which often continue to be the measure for much subjective experience. Rites of passage in the cosmic cycle. For many social purposes, time is reckoned not by regular units of measurement but by the major festivals that break up the continuity of its passage ("Only 42 more shopping days to Christmas"). Such hol-
idays and festivals may be linked to any of the major time divisions—to days, weeks, months, or years. In England, the week revolves around its "holy day" and has its regular days for pay, sport, and rest. These regular days dominate patterns of food consumption (the Sunday roast) and of family interaction, as well as the whole industrial system; however, I am here concerned with the annual festivals that have a marked influence on the longrange planning of human activities. In agricultural communities, where productive activity is periodic, the major festivals of local religions tend to mark the beginning and end of the productive season. At the time of planting a rogation ceremony is often performed to obtain supernatural blessing for the growing crops; at harvest time a thanksgiving festival is held to acknowledge divine intervention in the productive process. In northern climes, where agriculture is much affected by the changing length of days and is influenced more by variations in sunshine than by the coming of the rains, ceremonies often cluster around the times of solstice and equinox, the major turning points of the solar year. Annual festivals, although mainly religious in orientation, have other consequences, intended and unintended. In tribal societies annual gatherings, such as the Australian corroboree, are important for the initiation of adolescents, the re-enactment of myths, and the restatement of cultural values. In addition, they provide a meeting point for persons of neighboring social groups, who not only participate in communal rituals but also use the occasion for settling disputes, getting brides, repaying debts, and generally regulating their affairs. Such events are often marked by a limited expression of tensions between groups, although the likelihood of overt conflict is inhibited by ritual peace, supported by special sanctions against the outbreak of violence (Fortes 1936). In Islamic countries the month of the pilgrimage (Dhu 'l-hijja) is sandwiched between two months during which raiding is prohibited, thus encouraging a ritual peace for the business and religious activities of the pilgrims. In state systems, festivals such as the Ashanti Odwira, the Hausa Gani, or the damba of northern Ghana are used to affirm political allegiance; on these occasions subordinate chiefs come to the capital to do public obeisance to their liege lords. Again, these occasions may also allow for the limited expression of conflict in rituals of rebellion directed against those in authority (Gluckman 1954). As religious festivals, these ceremonies are ob
TIME: Social Organization viously affected by changes in the beliefs of the participants. But often new cults that arise are forced to incorporate features from earlier rituals into their own because of the powerful hold of the traditional rites; indeed, the early Christians adopted Roman rituals to such an extent that Faustus, the Manichaean bishop, tried to convince the young Augustine that they were nothing better than idolaters. Whereas the major ceremonies of local religions usually celebrate the birth and death of the year (sometimes represented by the life cycle of a god), the main rituals of the prophetic religions enact the life and death of their founder, whose life cycle is encapsulated in the yearly calendar. The freedom from particular seasonal rhythms makes such calendars more appropriate for the world religions, whose adherents span many environments, and more appropriate also for urban communities, whose way of life is not governed by climatic changes. Such a liturgical calendar represents a further step in the dissociation of objective time reckoning from immediate human activities. Increasing secularism has meant that the political value of regular festivals has been openly acknowledged; the anniversaries of a nation's birth are celebrated with the same pomp and circumstance found in public demonstrations of loyalty to leader, state, and party. But while most ceremonies have a particular religious or national significance, the increased interaction between nations is producing a basic standardization of ceremonial time, a universal ritual calendar. The seven-day week is now world-wide, and, with the exception of a few Arab states of the Middle East, so too is the Sunday break; the post-Independence changes in Ceylon, which introduced a shifting weekly holiday (poya*) based upon the lunar calculation of the Buddhists, were inspired by political motives and seem unlikely to last. The most widespread public holiday is the first of January, the beginning of the Gregorian year, closely followed in popularity by Christmas and May Day. Despite the predominantly secularized character of the modern festival, a few groups reject the celebration of Christmas on religious grounds, but gift giving is often shifted to a nearby occasion—to Hanukkah among Jewish minorities and to New Year's Day in the European communist states. In some countries the first of May, the day on which the labor movement traditionally shows its strength, is celebrated as a holiday, but under certain right-wing regimes, as in Spain, all public manifestations of the holiday are banned, although this very denial has added to its value as a day
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of protest. In most of the new nations the day is celebrated as one of solidarity and exhortation to increased national effort. In this case, the element of protest has been transferred from inside the social system to external targets, especially to the "neocolonial" activities of the major European powers. The number of bank holidays provides a rough scale of the degree of national "puritanism": Roman Catholic countries have the most, Protestant ones fewer, and the communist states fewest of all; Brazil has 18, Britain 6, and Bulgaria 5. New nations display an eclectic choice that reflects their political situation, ideological tenets, and religious composition: Ceylon, for example, recognizes Christian, Muslim, and Buddhist festivals, together with May Day, Independence Day, and a few other holidays, making a total of 15. Measurement of time—the human cycle Objectively, the passage of time in both the cosmic and human cycles is measured by the units already described—days, weeks, months, and years. But just as the year is divided into seasons that broadly characterize its main phases, so too the life span of human beings is divided into such categories as infancy, adolescence, and adulthood. The movement of an individual from one age grade to another is often celebrated by a rite of passage. In some societies these stages of growth form the basis of social groups of coevals, and in others a continuing series of such groups (age sets) is linked in an over-all age organization, which may serve important political and military functions. In modern nation-states, age-determined groups are the basis of educational organization, of informal associations of adolescents, and often of military recruitment, but they are of little importance in later phases of the life cycle. The position of an individual in the life cycle not only influences the role he plays and the groups to which he belongs but also has a number of less obvious effects on his behavior. The composition of the unit around which his domestic life revolves inevitably changes radically over time. One consequence of this fact for sociologists is that the "average family" can never be directly derived from a synchronic census but must be seen in dynamic perspective, that is, in terms of the developmental cycle (Fortes 1958). This approach not only illuminates residential patterns and divorce statistics but also is important in analyzing changing attitudes and beliefs. Durkheim, for example, demonstrated the inverse correlation between suicide rates and family integration, while Argyle (1958)
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showed the link between age and religious commitment, the latter being highest at 18, dropping to a nadir at 30, and gradually increasing in strength the nearer the prospect of death. Clearly, an individual's perception of the social universe changes as his relationships with the living shift: the child defers to his elders, while the adult is deferred to. Rites of passage in the human cycle. The major changes in an individual's life are marked by rites of passage which announce and enact the acquisition of a new role, of new rights and duties. Thus, birth is usually followed by baptism, marriage rites celebrate the establishment of an enduring sexual union, and death is accompanied by elaborate funeral ceremonies that serve to dissociate an individual from his network of mundane relations and dispatch him to the world of the dead. In preindustrial societies funerals are usually the most important of the life-cycle ceremonies, since they have to accomplish the transfer of a man's rights and duties, especially over property, women, and office, to other members of the community; this process is necessarily gradual and hence often marked by a double funeral, the first stage of which is a burial service and the second a kind of memorial (Hertz 1907; Goody 1962). Ceremonies accompanying such distributions are particularly important in agricultural societies, where the volume of fixed and enduring property transmitted by kinship succession is high and where the ceremonies themselves often have integrative and cathartic functions for the local group. In urban industrial communities, where neighborhood and kinship ties are weak, where property inheritance is of more limited significance (since most people cannot bequeath the means of production), such ceremonies tend to become more perfunctory, especially as literacy permits the witnessing function of these rites to be accomplished by the issuing of licenses. But marriage, which involves the expression of intent by the participants, is still a significant public display in many industrial communities; birth continues to be the focus of important ceremonies among people of property; and the funeral complex (including published obituaries) often takes a highly elaborate form in the case of those who have done the state some service. The burial of great men performs an integrative function on a national level, restating the values the society holds dear and recalling the specific contributions made by other former citizens. The allocation of time Members of all societies have to make some allocation of the time to be spent on any one activ-
ity as against any other. In simple economies the basic allocation is closely linked to nature, being dominated by diurnal and seasonal rhythms. More accurate and more complex scheduling goes hand in hand with an increasing complexity of organization. It is made possible first by the development of writing, then by the invention of mechanical time keeping, and finally by the democratization of literacy through paper and the printing press. Time allocation, like other bureaucratic operations, can be removed from the uncertain sphere of memory and attached to objects in the outside world—"Make a note of that," "Put that in writing." But it is above all the watch that dominates the organization of time in modern societies. While radio signals, the factory siren, and the town-hall clock establish public time, the increasingly complex schedules of contemporary life are made possible by the mass-produced watch, a personal time keeper that individuals consult with the obsessive regularity of the White Rabbit in Alice in Wonderland. The coordination of joint activities, whether over large distances or within complex organizations, requires that each individual make precise measurements: army orders for the movement of troops may end with the synchronization of watches, and civilians display the same concern about being "on time." The watch is often a man's first major gift to his adolescent son, a stimulus to adopt the adult virtue of punctuality, an emblem of approaching responsibilities. Since many of the operations of industrial life occur at regular intervals, people are able to routinize their behavior and so reduce the strain of organizing schedules and making decisions. In the commuter's life (the epitome of routinized time allocation), the pattern is largely imposed from the outside, by factory, train, and office. However, elaborate scheduling also spills over into leisure hours; many individuals have regular times for washing the car, for going on walks, and for entertaining guests, and in this way themselves impose an order on these potentially less structured situations. As Mumford has pointed out, such regimentation was both essential to and the product of the rise of capitalism: "The new bourgeoisie, in counting house and shop, reduced life to a careful, uninterrupted routine: so long for business: so long for dinner: so long for pleasure—all carefully measured out, as methodical as the sexual intercourse of Tristram Shandy's father, which coincided, symbolically, with the monthly winding of the clock. Timed payments: timed contracts: timed
TIME: Social Organization work: timed meals: from this period on nothing was quite free from the stamp of the calendar or the clock. Waste of time became for protestant religious preachers, like Richard Baxter, one of the most heinous sins" ([1934] 1964, p. 42). Mechanical devices (like writing) can make for easier manipulation of time categories; when schedules are linked with natural events such as the budding of trees, they are less easy to adapt to innovations such as new crops. At the same time, these devices enabled man to accelerate the pace of life to fit more activities into the day. A major development in late medieval technology was the control of power, and increasing power quickened the tempo of social life. Production and transport were speeded up, and in this century the concern with speed has even affected sport; the stop watch became the tool of the athletic coach as well as of the time-motion study experts. Because the diversity of an individual's roles is so often tied to particular places, such as shop, clinic, or office, it demands very specific allotments of time. A man or woman at work has to meet a more exacting schedule than does a housewife, whose routine turns upon the husband's employment and the children's school. Economic and domestic roles are segregated in time and space; and to take on any additional ("voluntary") roles, such as that of local councilor, party chairman, or committee member, means a further careful allocation of this scarce commodity, since each one necessitates a whole set of timed appearances. In societies that lack a complex division of labor, the role structure is more homogeneous in that during their lives most people fill most roles and in that the activities themselves rarely involve so great a separation in space and time. The more elaborate the division of labor and the less ascriptive the recruitment to roles, the greater are the number of possible role opportunities open to the individual. Selection among these alternatives is a matter of allocating time over the whole span of a person's life, and adults speak feelingly of "the wasted years" or of "having their time over again," sentiments likely to be less important in undifferentiated communities, where a new life would tend to be much like the old. In Hindu society, which, although differentiated, is still based on the ascription of roles, movement through the role structure is left to future incarnations and depends upon an individual's performance in his existing status. Such an eschatology provides the possibility of future mobility as a compensation for the unchangeable present. "Career scheduling" involves choices on the part
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of both the senior and junior generations that often entail consideration of comparative rewards over the long term. Lengthy career training means the postponement of gratification in money, sex, and independence. The ability to carry out such a program derives from professional interest, the attraction of greater rewards, and the pressures of parents and peers; it is also supported by moral factors, such as the commitment to the Protestant ethic. The higher the desired status and the more complex the economy, the longer the time perspective needed to attain one's ends. On a national scale, there is a parallel problem concerning the restriction of immediate spending in the interests of investment. The running of any economy, whether socialist, capitalist, or mixed, requires a deliberate consideration of present action in the light of future needs. Attitudes toward time The past. In nonliterate cultures ideas and attitudes concerning the past tend to reflect present concerns. To some extent this happens in all societies, especially in those situations where we rely upon memory. But where the transmission of culture is entirely dependent upon oral communication, upon an interlocking series of conversations, the past is inevitably swallowed up in the present (Goody & Watt 1963). In the strictest sense, history begins with writing. Before (and partly after) the widespread use of writing, the past is a backward projection of the present, going straight back to the mythical age that saw the emergence of humanity and its present way of life. While stories of migration and genealogies contain much in the way of historical fact, they often constitute collective representations of contemporary relationships and act as the "charters" of existing institutions. For example, the variations in the average depth of genealogies are to be related not to intrinsic differences in short-term and long-term memories of the people concerned but to differences in the social groups that these genealogies help to tie together. However, in many centralized societies, accounts of dynastic events are often passed down by various mnemonic devices that partly shield their contents from the transmuting effects of oral tradition. It is only when writing gives a material embodiment to speech that the distant past can represent more than a backward extension of the present. Although each age still rewrites its own history, the past begins to acquire an independent existence of its own. Today an individual's cultural equipment is no longer limited to what is handed
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down orally from one generation to the next but includes, potentially at least, the entire contents of the libraries, the written records of the past ages and dead societies, and the thoughts of distant scholars. The cultural heritage is vastly extended and with it the whole conceptualization of space and time. Change and duration become a more concrete part of one's existence. With the extension of writing into the personal and the ephemeral, by means of letters, newspapers, and diaries, even one's own past can achieve a modicum of objectivity, providing memory with an individual check list. Recording the speech of people over time and over space widens human experience and increases the likelihood of further change by making skepticism and disagreement articulate and therefore cumulative; literate traditions of dissent open up vistas of alternative forms of human organization. With the articulated calendar, the passage of time takes on a measured regularity. Old men can no longer look back unchallenged upon a past of 200 summers; with the registration of births and deaths, the specification of exact age becomes an intrinsic part of life and death. The reckoning of annual birthdays, whether for customary celebration or for astrological calculation, is a literate device. The Akan of west Africa named their children according to the weekday of birth (for example, Kwame is Saturday's child), which was seen as determining a child's character and sometimes functioned as a self-fulfilling prophecy; however, the system specified only the name of the day, not the day of the month or the year. The recognition of age differences and age order is a feature of all societies, but people in Western societies are preoccupied with specific age. An adult's first question to a child, after hearing his name, is about his age, and age will be the first entry in a man's obituary and the main feature on his tombstone. Numerical age rather than physical condition determines adult status; the patterned ages of 7, 14, and 21, so important in medieval law, have been largely replaced by new numbers that define an individual's ability to marry, to fight, and even to work, for bureaucratic organizations increasingly enforce compulsory retirement by age rather than by capacity. But characteristically this restriction applies to the employee more than to the director, to civil servants more than to politicians. The present. Literacy influences attitudes not only to the past but to the present and future as well. The permanency of written records makes a radical difference in the accumulation and storage
of knowledge and opinions and thus creates the possibility of more rapid change. But literacy brings with it an often troublesome inability to forget the past, so that the present has to engage in a deliberate struggle with older modes of thought and action. Individuals, groups, and governments strive to repeal laws which in nonliterate societies would have quite simply been forgotten or else would have undergone imperceptible changes to bring them into line with the new conditions. Unlike statutes, the Bible, the Koran, and other books of God cannot be amended, but their contents are reinterpreted over time and what was once intended literally is later seen as allegory and symbol, as metaphor and myth. But above all, attitudes toward time present focus upon the alternative uses of time that are offered by an elaborate division of labor, the minute scheduling that this division of labor entails, and the continual presence of a watch upon the wrist, which makes man ever conscious of the fleeting moment. In most literary traditions, writers express their regret at the passing of pleasure and the shortness of human life, but it is the perpetual concern with the passage of time that is characteristic of industrial man. Made aware that time is his scarcest resource, he learns to "spend" and "save" it like money. The ideology that stands at the center of industrial society stresses the full and productive use of time, a commodity that requires the most careful husbanding. This concern is as characteristic of socialist systems as of capitalist systems; during the industrialization of the Soviet Union an association was formed to encourage the carrying of watches and to expound the benefits of punctuality. Managers often find that the behavior of newly industrialized workers in developing countries deviates sharply from these enunciated values. The peasant is not used to "watching the clock" or to the demanding (and desiccating) routine of much of factory life. "Slaves?" I was once asked by an African visitor when he first saw rows of women working on an assembly line, their exits and entrances timed by "the clock," their every move organized by time and motion studies. For the peasant, time has been nature's time, and the organization of his activities largely his own affair. The future. The factors that bear upon attitudes toward the present are also relevant to attitudes toward the future; indeed, the difference simply turns on the question of scheduling over the longer term, as compared to the shorter term. In peasant communities the scheduling of production operates on an annual basis, but it is largely
TIME: Social Organization repetitive and future activity is mainly a continuation of the present. With the development of centralized political systems planning became more elaborate and included the storage of grain against famine, the construction of capital works, the build-up of supplies for military campaigns, and the organization of long-distance trade. But while the future may be visualized in terms of the success or failure of such undertakings, which are recognized as responsive to human foresight and control, deliberate social change is at first organizational rather than structural; even changes in the political order are a matter of rebellion rather than revolution, of replacing the officeholder rather than changing the over-all distribution of power. The possibility of long-range planning is vastly increased by the existence of writing. Literacy not only makes it technically possible to follow a complex plan but also to project and publicize a variety of alternative worlds (and the programs for their attainment) that vary along a continuum ranging from the pragmatic to the Utopian. And by the process of "ideological feedback," these programs often influence, and sometimes dominate, the direction of change. Plans, the projected organization of future time, are as much a requisite of the personal sphere as of the national and industrial domains. The maintenance of a yearly balance between production and consumption is not in itself enough: in most professional and managerial groups there is the necessity of planning for a surplus throughout a man's total career, a surplus that is required for heavy expenses such as house purchases and educational fees; and since the dominant attitudes favor providing for individual security rather than familial dependence, there is the problem of making provision for old age. A man's total perspective of time future extends beyond the end of this life to an afterlife. Beliefs in the continuity of some element of the human personality after death characterize all cultures, with the possible exception of communist societies and minority groups in secularized Western states. In most societies the distant past and future tend to be of peripheral interest. However, the idea of an earlier golden age, a Garden of Eden, is not an uncommon way of dealing with the universal "problem of evil," of explaining the actual imperfections and potential perfectibility of man. And when a culture of the less complex kind is hard pressed, typically by contact with European society, there is a tendency to seek comfort in ritual designed to bend time backward to an earlier paradise or to leapfrog time and hurry on the advent
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of the Messiah, the coming of the millennium [Worsley 1957; Thrupp 1962; see also MILLENARISM]. By and large, the "other world" of agricultural societies is visualized as a continuation of this world, although there is usually some distribution of rewards and punishments for behavior on earth, so that those who have escaped from mundane punishments get their due in the afterlife. Societies with elaborate status hierarchies may redress the balance of this world by a reversal of status in the next; it is the rich rather than the poor who are told that it is difficult to enter the Christian heaven. The afterlife may be seen either as the final destination of humanity or as a stage in the continuous flow of life which leads back again into this world by some process of reincarnation or transmigration. Here again, the element of status reversal may be present; the relative lack of social mobility in Hindu society is partially offset by the fact that the worthy fulfillment of a man's present role may qualify him for a higher status in his next incarnation. The increasing pace of social change and individual mobility in industrial societies, combined with an increasing skepticism and secularization, makes such eschatologies of decreasing importance to society. Millennial dreams are replaced by political Utopias, the idea of a fixed destiny by a concern with educational mobility, and the belief in immortality by a concept of social progress and continuity. Nevertheless, few men, as they advance in age, do not feel the urge to extend the limits of their tenure, by church attendance, public activities, the written word, or identification with their progeny. It is difficult, if not impossible, for men to envisage a final end to time, on either a cosmic or an individual level, and the continuous chain of familial living helps to mitigate the prospect of complete finality. JACK GOODY [See also PERIODIZATION.] BIBLIOGRAPHY
ARGYLE, MICHAEL 1958 Religious Behaviour. London: Routledge. BAILLIE, G. H. 1929 Watches: Their History, Decoration and Mechanism. London: Methuen. BICKERMAN, ELIAS (1933) 1963 Chronologic. 2d ed. Leipzig: Teubner. BOHANNAN, PAUL J. 1953 Concepts of Time Among the Tiv of Nigeria. Southwestern Journal of Anthropology 9:251-262. BOLTON, LYNDON 1924 Time Measurement. Princeton, N.J.: Van Nostrand. CIPOLLA, CARLO M. 1967 Clocks and Culture: 13001700. London: Collins.
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CUMONT, FRANZ 1912 Astrology and Religion Among the Greeks and Romans. New York: Putnam. -> A paperback edition was published in 1960 by Dover. DE GRAZIA, SEBASTIAN 1962 Of Time, Work and Leisure. New York: Twentieth Century Fund. DURKHEIM, EMILE (1912) 1954 The Elementary Forms of the Religious Life. London: Allen & Unwin; New York: Macmillan. -»• First published as Les formes elementaires de la vie religieuse, le systems totemique en Australie. A paperback edition was published in 1961 by Collier. EVANS-PRITCHARD, E. E. (1940) 1963 The Nuer: A Description of the Modes of Livelihood and Political Institutions of a Nilotic People. Oxford: Clarendon. FORTES, MEYER 1936 Ritual Festivals and Social Cohesion in the Hinterland of the Gold Coast. American Anthropologist New Series 38:590-604. FORTES, MEYER (1949)1963 Time and Social Structure: An Ashanti Case Study. Pages 54-84 in Meyer Fortes (editor), Social Structure: Studies Presented to A. R. Radcliffe-Brown. New York: Russell. FORTES, MEYER 1958 Introduction. Pages 1-14 in Jack Goody (editor), The Developmental Cycle in Domestic Groups. Cambridge Papers in Social Anthropology, No. 1. Cambridge Univ. Press. GENNEP, ARNOLD VAN (1909) 1960 The Rites of Passage. London: Routledge; Univ. of Chicago Press. -> First published in French. GLUCKMAN, MAX 1954 Rituals of Rebellion in South-east Africa. Manchester Univ. Press. GLUCKMAN, MAX 1963 Order and Rebellion in Tribal Africa. New York: Free Press. GOODY, JACK 1962 Death, Property and the Ancestors: A Study of the Mortuary Customs of the LoDagaa of West Africa. Stanford Univ. Press. GOODY, JACK; and WATT, IAN 1963 The Consequences of Literacy. Comparative Studies in Society and History 5:304-345. GRANET, MARCEL (1934) 1950 La pensee chinoise. Paris: Michel. HALBWACHS, MAURICE 1925 Les cadres sociaux de la memoire. Paris: Alcan. HALLOWELL, A. IRVING 1937 Temporal Orientation in Western Civilization and in a Preliterate Society. American Anthropologist New Series 39:647-670. HERTZ, R. 1907 Contribution a une etude sur la representation collective de la mort. Annee sociologique 10:48-137. MAUSS, MARCEL (1906) 1960 Essai sur les variations saisonnieres des societes eskimos: Etude de morphologie sociale. Pages 389-477 in Marcel Mauss, Sociologie et anthropologie. 2d ed. Paris: Presses Universitaires de France. -» Written in collaboration with H. Beuchat; first published in Volume 9 of Annee sociologique. MEYERHOFF, HANS 1955 Time in Literature. Berkeley: Univ. of California Press. MILHAM, WILLIS L. (1923) 1945 Time and Timekeepers. New York: Macmillan. MOORE, WILBERT E. 1963 Man, Time and Society. New York: Wiley. MORGAN GUARANTY TRUST COMPANY OF NEW YORK 1965 Bank and Public Holidays Throughout the World. New York: The Company. MUMFORD, LEWIS (1934) 1964 Technics and Civilization. New York: Harcourt.
NEEDHAM, JOSEPH 1965 Time and Eastern Man. Royal Anthropological Institute of Great Britain and Ireland, Occasional Paper No. 21. London: The Institute. NEEDHAM, JOSEPH; LING, WANG; and PRICE, DEREK J. DE SOLLA 1960 Heavenly Clockwork: The Great Astronomical Clocks of Medieval China. Cambridge Univ. Press. NILSSON, MARTIN P. 1920 Primitive Time-reckoning. Oxford Univ. Press. PIAGET, JEAN 1946 Le developpement de la notion de temps chez I'enfant. Paris: Presses Universitaires de France. THOMAS, NORTHCOTE W. 1924 The Week in West Africa. Journal of the Royal Anthropological Institute of Great Britain and Ireland 54:183-209. THRUPP, SYLVIA L. (editor) 1962 Millennial Dreams in Action: Essays in Comparative Study. Comparative Studies in Society and History, Supplement No. 2. The Hague: Mouton. TOULMIN, STEPHEN; and GOODFIELD, JUNE 1965 The Discovery of Time. New York: Harper. TRIMINGHAM, JOHN S. 1959 Islam in West Africa. Oxford: Clarendon. USHER, A. P. (1929) 1954 A History of Mechanical Inventions. Rev. ed. Cambridge, Mass.: Harvard Univ. Press. -» A paperback edition was published in 1959 by Beacon. WHITE, LYNN 1962 Medieval Technology and Social Change. Oxford: Clarendon. WORSLEY, PETER 1957 The Trumpet Shall Sound: A Study of "Cargo" Cults in Melanesia. London: MacGibbon & Kee.
TIME BUDGETS A time budget is a log or diary of the sequence and duration of activities engaged in by an individual over a specified period, most typically the 24hour day. Time-budget research involves the collection of numerous such protocols from members of a population to analyze main trends and subgroup differences in the allocation of time. While many social inquiries are concerned with the amount of time spent on a particular kind of activity (the journey to work or time given to television watching), the term "time budget" is generally reserved for an exhaustive accounting of a slice of time in individual experience, whatever the component activities happen to be. Such time budgets naturally yield information on the time consumed by any of the wide range of activities in which man engages. Yet at the same stroke, this information is given a context, since the protocols pose the question of, for example, what else it is that people who spend little time on television do with the time thereby saved or of where the time comes from for those who devote enormous quantities to it. One of the special assets of time-budget research is the immutable fact that no human
TIME BUDGETS being, however rich, poor, wise, or foolish, can dispose of more time than any other within the same period. Hence, variations in time allocations from person to person must depend on "trading off" time from some activities toward others. Indeed, the phrase "time budget" has arisen because time, like money, is a resource that is continually being allocated by the individual, although with varying degrees of consciousness and shortterm discretion. Like money, time is thought of as being spent, saved, invested, or wasted. It is presumed that analysis of the structure of time allocation gives behavioral evidence of a peculiarly "hard" kind concerning individual preferences and values, especially in the more optional forms of time use. The time budget as a research tool has been employed in such areas as the study of life styles, the sociology of leisure, and research on aging and other aspects of the life cycle. Collection of systematic time-budget data is a relatively recent activity. Such data also provide material for curiosity concerning long-term secular trends in the "quality of life," such as the division of time between work and play (de Grazia 1962) and the role of systemlevel work inputs in economic development. The history of time-budget research The systematic collection of family financial budgets represents one of the earliest forms of empirical research at a microsociological level, with examples dating back to seventeenth-century Europe and coming to flower in the celebrated work of Frederic Le Play in the nineteenth century. The extension of the paradigm to time expenditure arrived somewhat more slowly, however. Friedrich Engels' The Situation of the Working Class in England, first published in 1845, contains a wide variety of information on the daily round of industrial workers, with some quantitative estimates of time expenditures. Perhaps the first careful and exhaustive time budgets covering at least the period of work were represented in the time-andmotion studies of Frederick Taylor in his attempt, around the turn of the century, to institute "scientific management." The first large-scale study of exhaustive 24-hour time budgets was carried out in 1924 on Moscow workers by Stanislav G. Strumilin, as part of the postrevolutionary drive toward more rational economic planning [see LEISURE]. In the West, most comparable work during the same period was focused on leisure, ignoring the portions of the day that were defined in some sense as nonleisure.
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However, near the end of the 1920s the Bureau of Home Economics of the U.S. Department of Agriculture conducted five studies of time use among farm women that involved full time budgets in the now customary sense of the phrase. By the 1930s more studies were beginning to appear. Lundberg and his associates (1934) based their intensive examination of suburban life in Westchester County in part on nearly 5,000 time budgets drawn from about 2,500 respondents. Sorokin and Berger's Time-budgets of Human Behavior (1939) attempted to use such materials to investigate the structure of human motives and in so doing provided one of the more germinal surveys of the possibilities of the time budget as a research tool. Along with the rapid expansion of survey research after World War n, the generation of timebudget data has shown an enormous increase, although this trend is less prominent in the United States than in most other industrialized nations. Part of the impetus for this research has come from commercial and governmental enterprises concerned with the timing of activities in their mass populations. Perhaps the largest single timebudget survey, involving a sample of 170,000 persons, was carried out in Japan in 1960-1961 to aid in the scheduling of radio and television programming (Nakanishi 1963). One of the few nationwide time-budget surveys in the United States was conducted in 1954 for similar reasons by the Mutual Broadcasting Company, and comparable, although smaller, surveys for the mass media have been done in most countries of western Europe. Another impetus to such work has come from the economic-planning needs of governments. After a period in which social research of all kinds was neglected, the tradition of time-budget surveys established by Strumilin in the Soviet Union was resumed on a massive scale in the late 1950s. In addition to thorough methodological work, the monitoring of time budgets has become sufficiently institutionalized in the Soviet Union for national scientific conferences to have been held for the purpose of establishing uniform codes and standards, and several hundred thousand man-days' worth of time-budget material has been accumulated (Szalai 1966). In a similar vein, time-budget data were gathered in Hungary in 1963 by the Central Statistical Office, as part of the official microcensus. Quite generally speaking, timebudget work represents one of the most vigorous traditions of social research in eastern Europe. Western social scientists have used the technique
44
TIME BUDGETS
much more sparingly, although often with an eye toward broadening its utility. The most ambitious effort at a rigorously comparative cross-national time-budget study was launched in 1964 under the sponsorship of UNESCO and the International Social Science Council. Directed by Alexander Szalai, research institutes in Bulgaria, Belgium, Czechoslovakia, France, East and West Germany, Hungary, Peru, Poland, the Soviet Union, the United States, and Yugoslavia had by 1966 successfully collected timebudget information on probability samples of urban populations in their respective countries, following standardized methods of interviewing and coding. Extensions of the study design to Greece, Cuba, and Canada were also projected (United Nations . . . 1966). Time-budget methodology The first decision to be faced by the student of time use has to do with choice of time scale for his budget collection. Some time budgets are organized to cover time spent at the workplace; others span only "leisure hours." At the opposite extreme, it is possible to imagine time budgets covering an individual's life cycle, yielding information of totally different significance, although nothing but the most sketchy efforts of this kind exist at present [see LIFE CYCLE]. There are grounds for arguing that estimates of productive work time should be based on time budgets covering annual cycles, thereby including vacations and a reasonable sampling of illnesses. In point of fact, however, the vast majority of time-budget research is geared to the 24 hours of a single day in the life of a respondent. By the gathering of enough time diaries, dispersed over weekdays and weekends as well as across the seasons of a year, from various individuals of differing ages, a synthetic picture of weekly, annual, and life-cycle variations can be organized from single-day protocols. In those rare instances where individuals have kept diaries for much longer than a single day or two, results have been reassuring. For example, Lundberg and his associates (1934, appendix) reported, among other things, that time diaries showed high stability in activity allocations for respondents maintaining them for longer periods. At first glance, the collection of 24-hour time budgets would seem to be a relatively simple and straightforward task. Indeed, the time continuum itself offers a quantitative variable of a purity and precision rarely found in social research, and one readily understood by almost any respondent in
industrialized societies. Yet closer familiarity makes clear that the gathering of even day-length time-budget information poses an oppressive array of complexities. The method shares all of the common problems of reliable population sampling and data elicitation and adds many unique burdens as well. Though time may be a "clean" and "hard" variable, activity units are not. How finely should we slice in establishing an array of activities? Chronicles of "a day's activities" might be so grossly characterized as to show but six or seven activities; or again, they might reflect such a fine grain of movement and action as to number two hundred or more for the same day. Some activities, such as sleeping, are rather clearly demarcated. Others are punctuated by major spatial displacements ("drove to the drugstore"). For many activities, however, lines of demarcation blur, and the common guideposts become deceptive. Is "work at the office" simply to be left as an undifferentiated block of time, or is it to be thinly subdivided? "Shopping" often involves a sequence of spatial displacements. Is it one activity by itself or one for each shop visited, each purchase made, or what? And more pressing still, how is the researcher to handle simultaneous activities, such as cooking dinner while listening to the radio and keeping an eye on the children? Increasingly, investigators have tried to depend on the respondent himself to define what an activity is by the way he chooses to record the events of his day. Thus, one method of data collection— asking the subject to check activities from a predesignated list of possibilities—tends to be avoided as imposing too much outside structure on spontaneous perceptions. Nevertheless, when "raw," or volunteered, descriptions are accepted, some of the burden returns to the investigator in the form of decisions as to how the concrete acts are to be coded into more general classes. And whether the respondent is asked to "precede" or the coding is accomplished later, there is an intrusion on reality which can affect results in vital ways. There are undoubtedly real differences in activity levels between persons, from the bedridden invalid to the harassed professional, so that the sheer number of activities per day should in fact vary. But some of the recorded interpersonal variation can be due to different perceptions of the task instructions, and the whole texture of findings can be displaced by nearly arbitrary decisions on the part of the investigator in providing task instructions or in fixing the frequency with which activities should be recorded (for instance, should it be
TIME BUDGETS every five minutes, every hour, or four times a day?). In general, the more activities are recorded or coded in gross fashion, the more alike people of different social statuses appear to be. In order to keep the time chronicle totaling a tidy 24 hours, researchers have often decided to discard the "less important" of any activities carried on simultaneously, although any such decisions lead immediately to new problems concerning the definition of importance. More recently, however, secondary and tertiary activities are being maintained as separate parts of the record, and intriguing work on the incidence and structure of such simultaneous activities is under way (Guilbert et al. 1965). Similarly, while some analytic grouping (that is, coding) of activities is always required, the trend is toward increasingly detailed activity codes that hew more closely to concrete reality, at least in the first stage of analysis. Subsequently, such codes permit greater flexibility in regrouping elements for differing analytic purposes. The standardized code for time-budget research in the Soviet Union involves 99 categories; the UNESCO multination project proceeds at the same level of detail. Broadly speaking, there are three main methods of eliciting 24-hour time budgets from respondents. In the diary method, the respondent simply writes down his own log of activities and their durations, more or less synchronously, on the basis of instructions and forms provided. Drawbacks of such a straightforward approach include the fact that subjects show considerable variation in the diligence and care with which such diaries are maintained, and the protocols are thus very uneven in quality. Moreover, functionally illiterate persons can be frightened by such a task, and a distressingly large proportion of them refuse to cooperate. A second method, the "yesterday interview," requires the subject to reconstruct his previous day's sequence of activities orally, under probing from an interviewer, and to estimate times spent on each until the full period of 24 hours has been accounted for. The limitations of this approach are obvious: people forget. Experimental evidence as to differences between perceived time and physical time abound, and many details are completely lost to memory at only a day's remove. A third method involves observation and recording of the individual's activities by a second party. However, such an approach tends to have low feasibility for both cost and privacy reasons, and it has become apparent that the outside observer has much more difficulty deducing meaningful "activity units" than does the actor himself.
45
While most research in the past has depended on the unsupported diary method, the current trend is toward overcoming the liabilities of each method by a combined approach. Thus, for example, a subject may be asked to maintain a diary for 24 hours in the standard manner, but the log itself may be used as merely a refresher or initial skeleton for more detailed discussion in a "yesterday interview." Even a sketchy diary will put stringent limits on the respondent's imagination as far as time durations are concerned, yet the interviewing can serve to bring the account of activities on the part of a poorly educated subject to a level of detail that a well-educated subject may be able to capture by himself. Whenever a diary or an outside observer is involved, a burden is placed on the respondent which considerably exceeds that of a standard samplesurvey interview. Therefore, refusal rates mount from the normal insignificant levels to heights that daunt the most experienced researcher. An embarrassing proportion of the time-budget literature from the past has been generated from captive audiences like schoolchildren, or suffers refusal rates so high as to call the data into question at the outset, or has paid no attention whatever to representative sampling. One of the time-budget studies which is most challenging at a conceptual level (Sorokin & Berger 1939) is based on about 5 per cent returns of diary forms distributed to workers on relief and white-collar unemployed in the Boston area during the depression of the 1930s. More generally, it is obvious that potential respondents who refuse to participate because they are "too busy" strike to the very heart of the purposes of the study. Although it has been shown possible in recent years to approach a probability sample of a cross-section population with the 24-hour timebudget task and keep refusals within tolerable limits (20 per cent, for example), such success depends on elaborately planned approaches and inducements. The variety of complexities in time-budget methodology acts in turn to reduce the cumulative value of such data collections. In principle, some of the most exciting questions that such research can help to answer have to do with long-term, secular trends in time use. Yet while studies have been done in many national contexts for several decades, the comparability across most of these investigations is limited or, worse still, unknown. Activity codes are incompatible from study to study; precise interviewing and coding instructions that affect the data are lost; samples are haphazard and unrepresentative. The best that can be
46
TIME BUDGETS
said is that there has been rapid methodological improvement, although good time-budget work remains complicated and expensive. Uses and limitations of time-budget data Assuming that they are reliably executed, time budgets by themselves provide extensive but not intensive information: the data are broad but shallow. Their breadth is reflected in the astonishing variety of researchers who can find in them titillating bits of information relevant to their specialties, or useful, if simple, parameter estimates. At the same time, most specialists are dismayed that the relevant information goes no further than it does. Hence, much of recent timebudget work has been moving toward a more multidimensional treatment of the activity itself; it may even involve use of the time budget as a backdrop, or frame of reference, for more intensive inquiry into some theoretically interesting subset of the day's activities. Before going further, however, it should be noted that the simple time budget can itself be manipulated in a striking number of ways, each of which has value in one or another specific context. Many studies begin and end with examination of the summary duration of time allotted to the various activities in the code, expressed as an average across respondents. However, it is often useful to modify this information with indications of the prevalence of an activity. Thus, for example, the average duration of working time outside the home is greater in the Soviet Union than in the United States. However, most of the increment is due to a much higher proportion of working women, rather than to long work hours for individuals. Thus both the collective fact and the individual fact are of social significance. For other inquiries, the timing of activities across the 24 hours of the day is of prime importance. This is true of programmers for the mass media, who need to know when in the day various portions of the populations will be at home and ready to turn on their television or radio sets. Similarly, regional planners and traffic experts collect and use data on the time of day that commuting and other travel take place as well as data on the duration of the journey to work. Studies of shift work by time budgets show the great differences in offwork activity that occur when a person's work schedule is out of phase with the modal rhythm in the society. Or again, time budgets can be analyzed from the point of view of patterns in the sequence of activities, quite apart from their duration or timing. Finally, people with similar patterns of
activity duration may also differ markedly in the frequency with which the same activities are repeated in a day's time: some organize their days into relatively large blocks, while others pick up activities and drop them often, either by design or through interruptions from the environment. Despite the numerous ways in which unadorned time-budget data can be viewed, there is an increasing tendency toward expansion of the information about the activities themselves. It is becoming commonplace, for example, to collect information on where and with whom each activity took place. The locus of activities and their sequence are again of interest in regional planning and have led to conceptualization of the "household activity system" as a part of urban ecology (Chapin & Hightower 1966). Time-budget data designating the "partners" for various activities can be used to test hypotheses concerning variations in interpersonal contacts (Reiss 1959). Nelson Foote and Rolf Meyersohn have experimented with the collection of further information concerning the affect felt toward each activity reported, the desire for more or less time for it, whether it is seen as work or play, routine or unusual, and whether the activity was initiated by the subject or by others acting toward him. Similarly, they have collected time budgets reflecting more of the nexus of social behavior, by pairing diaries for husbands and wives covering the same day (Foote 1961, p. 171). Somewhat similar analyses attempt to draw in all of the significant social microcosm of the individual—family, neighborhood, and co-workers (Chombart de Lauwe 1956). While such expansions are helping to enrich time-budget studies, the fact remains that a wide gulf still exists between the manifest activity as it is recorded and the latent functions of the activity for the individual which give it ultimate meaning or significance. The act of repairing an appliance in one's home may reflect a desire to convert free time into money saved to piece out one's income, or an inability to secure sufficiently rapid service from outside, or a hobby of tinkering, or some combination of the three. More theoretically satisfying ways of grouping detailed activities into broader classes are often avoided because of just such difficulties. Where ingenious activity groupings are made, there lurks the inevitable suspicion that were the truth known, the same activities might fall in quite different classes for various subjects and that the substantive results may be artifacts of such "forcings" of the data. It is for reasons of this sort that time budgets seem to have been found less useful for investiga-
TIME SERIES: General tions of life style than might be expected on the surface. Activity designations tend to be more incisive about the forms of activities than about their contents. The fact of watching television or having a conversation with a neighbor is recorded, but the types of programs watched or the subjects of informal discourse are rarely catalogued. And variations in what is called "life style" seem thoroughly muted in the process, although some differences do linger on in the forms themselves. Thus, at one level time-budget data convey an unusual range of implications for practical policy planning and also hold at least some interest for social theory. At the same time they are costly to collect in reliable ways, and without considerable expansion of the texture of information gathered, they often seem disappointingly primitive. PHILIP E. CONVERSE [See also INDUSTRIAL RELATIONS, articles on INDUSTRIAL AND BUSINESS PSYCHOLOGY and THE SOCIOLOGY OF WORK; LEISURE; PLANNING, SOCIAL, article on
47
lihood Time of the Japanese. Tokyo: NHK Radio & TV Culture Research Institute. REISS, ALBERT J. JR. 1959 Rural-Urban and Status Differences in Interpersonal Contacts. American Journal of Sociology 65:182-195. SOROKIN, PITIRIM A.; and BERGER, CLARENCE Q. 1939 Time-budgets of Human Behavior. Harvard Sociological Studies, Vol. 2. Cambridge, Mass.: Harvard Univ. Press. SZALAI, ALEXANDER 1966 Trends in Comparative Timebudget Research. American Behavioral Scientist 9, no. 9:3-8. UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION 1966 The Multinational Comparative Time Budget Research Project. Report for the Sixth World Congress of Sociology, Evian, France. Vienna: European Coordination Center for Research and Documentation in Social Sciences.
TIME SERIES i. GENERAL n. ADVANCED PROBLEMS in. CYCLES iv. SEASONAL ADJUSTMENT
Gerhard Tintner P. Whittle Herman Wold Julius Shiskin
REGIONAL AND URBAN PLANNING; TlME, article OU
SOCIAL ORGANIZATION; and the biography of LUNDBERG.] BIBLIOGRAPHY 1961 Work and Leisure. New York:
ANDERSON, NELS Free Press. CHAPIN, F. STUART JR.; and HIGHTOWER, HENRY C. 1966 Household Activity Systems: A Pilot Investigation. Urban Studies Research Monograph. Chapel Hill: Univ. of North Carolina, Institute for Research in Social Science, Center for Urban and Regional Studies. CHOMBART DE LAUWE, PAUL H. 1956 La vie quotidienne des families ouvrieres: Recherches sur les comportements sociaux de consommation. Paris: Centre National de la Recherche Scientifique. DE GRAZIA, SEBASTIAN 1962 Of Time, Work and Leisure. New York: Twentieth Century Fund. FOOTE, NELSON N. 1961 Methods for Study of Meaning in Use of Time. Pages 155-176 in Robert W. Kleemeier (editor), Aging and Leisure: A Research Perspective Into the Meaningful Use of Time. New York: Oxford Univ. Press. GUILBERT, MADELINE; LOWIT, NICOLE; and CREUSEN, JOSEPH 1965 Problemes de methode pour une enquete de budgets-temps: Les cumuls d'occupations. Revue francaise de sociologie 6:325-335. KLEEMEIER, ROBERT W. (editor) 1961 Aging and Leisure: A Research Perspective Into the Meaningful Use of Time. New York: Oxford Univ. Press. LARRABEE, ERIC; and MEYERSOHN, ROLF (editors) (1958) 1960 Mass Leisure. Glencoe, 111.: Free Press. LUNDBERG, GEORGE A. et al. 1934 Leisure: A Suburban Study. New York: Columbia Univ. Press. MEIER, RICHARD L. 1959 Human Time-allocation: A Basis for Social Accounts. Journal of the American Institute of Planners 25:27-33. NAKANISHI, NAOMICHI 1963 A Report on the How-DoPeople-Spend-Their-Time Survey: An Analysis of Live-
GENERAL
A time series is a set of data ordered in time, typically with observations made at regular intervals, for example, each census year, annually, quarterly, or monthly. This article focuses on the analysis of time series of economic data. The analytical methods used are also applied in other fields, for example, in psychological encephalography, in the analysis of sociological series from panel studies, and in the analysis of voting series in political science. Although data from sampling surveys have been used increasingly in recent years, most of the observations utilized in econometric studies still come from economic time series. This is especially true of econometric studies dealing with problems that are important from the point of view of economic policy, such as the nature of business cycles and the determinants of economic development. An area of growing theoretical and empirical interest is the pooling of time series and cross-section data [see CROSS-SECTION ANALYSIS]. Time series have provided an indispensable source of information for econometric analyses, but peculiar features of such data warrant special caution in their use. The difficulties that beset the use of time series in econometric studies have four different causes. The first is the simultaneity of economic relations. Observed values of economic variables are usually generated by a system of economic relations. It is now well known that it may be impos-
48
TIME SERIES: General
sible to estimate some of these relations; that is, some relations may be underidentified. Classical least squares estimation of a single relation, ignoring the others, is in general inconsistent. Since the pioneering efforts of Trygve Haavelmo, a substantial portion of the work of econometricians has been devoted to the development of consistent estimation methods for simultaneous economic relations [see SIMULTANEOUS EQUATION ESTIMATION]. The second cause of difficulty is errors in variables or errors in observations. Reported values of some economic variables are often subject to error resulting from techniques of collection or are only approximations to unobservable variables specified in the theoretical relation to be estimated. Methods have been advanced to deal with errors in variables in particular situations (see Johnston 1963, pp. 148-176), but there remains much to be done in this important area. Multicollinearity is the third cause of difficulty. Many economic time series are highly correlated with one another (are multicollinear), owing to common factors that influence all economic activity. Prior to estimating a particular economic relation, we are often led to specify a regression model containing a number of explanatory variables, and we are interested in isolating the independent influence of each of these variables on the variable to be explained. If the explanatory variables are multicollinear, it will be impossible, using the usual least squares regression procedure, to determine with any confidence the influence of each of them. Thus, multicollinearity of economic time series often impedes empirical testing of alternative hypotheses. The fourth cause of difficulty is autocorrelation. It is evident from our general knowledge of the economic system that the consecutive items of an economic time series will seldom be independent. The simplest case of this lack of independence is termed autocorrelation; it creates great problems in econometric studies, since the modern theory of statistical estimation and inference, as developed by R. A. Fisher, J. Neyman, A. Wald, and their disciples, is frequently designed for analysis of data that constitute random samples, i.e., where the assumption that items in the sample are statistically independent is justified or where the dependence has a simple character. Economic data, like the data of astronomy and meteorology, do not come from carefully designed experiments but are the result of complex and evolving empirical relationships. Autocorrelation typically increases with the decrease of the time interval of observations. Hence, if we could obtain daily instead of yearly observations (which is frequently impossible with
economic data), we would perhaps not increase the available number of degrees of freedom very substantially. Much effort has been expended in the development of methods for dealing with autocorrelation (more generally, lack of independence), but because of the great mathematical difficulties involved and the lack of simple, realistic theoretical models, the results have been less than spectacular. In practice, all four problems occur simultaneously. However, since it is so difficult to deal with all of them at once, much work focuses on only one problem and assumes that the others do not exist. Since this approach may be unrealistic when working with actual data, interpretations of empirical analyses are often most difficult, thus diminishing the value of such analyses for practical applications to economic policy. The traditional analysis of time series has dealt primarily with isolating the trend, the irregularcycle, the fairly regular periodic seasonal, and the random components of the series (Kuznets 1934). It is assumed that each component is independent of the others and can be analyzed separately, that each component is generated by a particular underlying process or model, and that the series is simply the sum of the components. This procedure is now considered somewhat obsolete, although it still provides a useful point of departure. It would be preferable to avoid these perhaps unrealistic assumptions, instead employing a procedure based upon the premise that a series is generated by a single model capable of producing trends and fluctuations and incorporating random elements. The mathematical model of a time series is a stochastic process (Bartlett 1955). A family of jointly distributed random variables linearly arranged according to a numerical index (often corresponding to time) is called a stochastic process. As it stands, this characterization is so inclusive as to be of little value; useful results can be obtained only by starting with restrictive assumptions on the random variables of the family. The theory of stochastic processes has been studied by many excellent mathematicians, and great progress has been made in recent years. Unfortunately, the study of statistical methods for observable stochastic processes is not nearly so well developed as studies of a more purely probabilistic nature. In part this stems from mathematical difficulties, but another factor is also important. Many of the outstanding and important applications of stochastic processes arise in physics, chemistry, and communications theory, where the samples involved are so large that purely statistical problems, involving statistical inference from the sample to the population, are perhaps not very important.
TIME SERIES: General Even where statistical results exist, as in the statistical treatment of stationary time series (Grenander & Rosenblatt 1957), i.e., time series that lack a trend and whose variances and higher moments are independent of time, the results are usually valid only for large samples. (Of course, the same is true for other branches of statistics as well.) Although development of a small-sample theory of stochastic processes faces formidable mathematical difficulties, it is just such a theory that is needed for the analysis of the relatively short economic time series commonly available. The mathematical problems can be made more tractable if we make highly unrealistic assumptions, for example, the so-called circular assumption—that samples are taken from the repetitive population Xj, X 2 , • • • , X^, X ± , X 2 , • • • . But lacking a small-sample theory, we are often forced to use large-sample methods as crude approximations to valid methods. It should also be remarked that many results in this field are still confined to tests of hypotheses; very few deal with the perhaps more important problems of estimation. Trend The trend is one of the most intractable features of economic time series. By "trend" we mean the long-term secular movement of a series, that is, the mathematical expectation of Xt, EXt, a function of time. It is, of course, difficult to distinguish the trend from cycles of long duration. Parametric tests for trend. One general procedure for estimating and testing for trend in a time series involves assuming a specific form for the trend function, estimating the function, and testing the significance of the estimated relation. Among the most commonly used functional forms are the polynomial and the logistic. Orthogonal polynomials. Suppose we have a set of observations, X ± , X 2 , • • • , Xt, • • •, XN, on the variable X for the equidistant points in time 1,2, • • • , N. We might assume that this series was generated by the polynomial function ut,
t=l,2, • • • , N,
where the a's are parameters to be estimated and Ut is a random error term that is normally distributed with constant variance. Also, the u's are independent. Rather than fit this ordinary polynomial, it is simpler to estimate the orthogonal polynomial i=l
t + ut,
where £it is an zth-degree polynomial in t such that ZXf < t = 0 for all i and Z?=1 £ « £ , « = 0 for all i
49
and j, i ^ j. Making use of orthogonal polynomials, we can easily estimate a polynomial of degree p, having once estimated a polynomial of degree p — 1. Application of the method of least squares yields
bt =
£
One method for determining the degree of the polynomial that best fits the data has been developed by R. A. Fisher (1925). Let Sp denote the sum of the squared residuals from an estimated polynomial of degree p. We fit polynomials of degree 1,2, • • • , until Sp+l — Sp is not statistically significant. This may be determined by an F-test, assuming the w's are normally distributed and independent. A recent method put forward by T. W. Anderson (1962) may turn out to have major advantages over Fisher's. However, application of Anderson's method requires that we decide a priori the highest degree of the polynomial that might possibly be used. The tests proposed by Anderson then enable us to decide whether we might adequately fit a polynomial of lower order. Although polynomial trends fitted by the method of orthogonal polynomials are often accurate representations of the past history of many time series, it is very dangerous to employ them for extrapolating these series, since polynomials tend to infinity with advancing time. The logistic function. The study of economic development focuses particular attention on long economic time series that can be used to characterize the nature of economic development. While the true form of long-term secular change is uncertain, the logistic function (Davis 1941, p. 247) recommends itself by its success, albeit limited, in animal and human population studies. Also, the logistic function, unlike the polynomial, has an upper asymptote—a desirable property. If we suppose once again that we have a time series Xt, t = 1, • • • , N, the stochastic form of the logistic function that we assume generated these observations can be written as
k 1 + be at
ut,
where k, a, and b are parameters to be estimated and ut is a random error term. Estimation of the parameters is difficult, since they enter the function in a nonlinear fashion. Hotelling (1927) proposed a method for fitting the logistic that sur-
50
TIME SERIES: General
mounts this difficulty. Working with the logistic in its nonstochastic form, he utilizes the time derivative of \ogKXt and forms the differential equation d(log e X,) dt
dXt dt
1
We can now obtain least squares or maximum likelihood estimators of a and a/k, and from these an estimator of k; b can then be estimated, using a method suggested by Rhodes (1940). Retelling's method has the disadvantage of requiring a discrete approximation to the derivative dXt/dt, since economic data are typically available only for discrete time intervals. Hence, it seems preferable to utilize an estimation procedure that relies on a difference equation rather than on a differential equation. Such a procedure has been developed by Tintner (1960, p. 273). Utilizing the transformation zt = l/Xt, a difference equation for zt can be derived from the logistic, namely, 1 -e-
+ e-azt
Application of least squares estimation methods, which are also maximum likelihood methods if the errors are normally distributed, will yield estimators of ( 1 — e~a}/k and e~a, from which estimators of a and k can be obtained; b may again be estimated by Rhodes's formula. Moving averages. In fitting polynomials or logistics to an economic time series in order to isolate trend, it is assumed that a simple function will accurately capture the trend throughout the series. An alternative method, which does not involve such a strong assumption, is the method of moving averages. Moving averages can most effectively be applied to time series containing seasonal or cyclical components of relatively constant period. Given a time series X t , t=l,---,N, the trend value of the series at t — m + 1 is found by taking an average of the first 2m + 1 elements of the series, where m is chosen so that 2m + 1 corresponds to the period of the seasonal or cyclical component. (The fact that the period of business cycles is irregular creates difficulties in the application of this method.) Similarly, the trend value at t — m + 2 is found by averaging the observations X,, • • • , X.2m+.,. In general, the trend value at t is an average of X,_ m , • • • , Xt+m. An immediately evident shortcoming of this procedure is that no trend values are obtained for the first and last m time periods covered by the original series unless special methods are adopted. The weights attached to the elements to be averaged in each set of 2m + 1 consecutive observa-
tions may be chosen in a variety of ways. Weighting each element by the constant l/(2m + 1 ) (taking a simple mean of the elements) is equivalent to fitting a linear relation to each set; more complex weighting schemes can be used, so that the procedure is equivalent to fitting a polynomial of any given degree to each set. The degree of the polynomial to be fitted may be found by the variate difference method proposed by Tintner (1940, p. 100). The method of moving averages is thus seen to be similar to the fitting of polynomial functions to time series, but rather than fitting one polynomial to the entire series, a polynomial is fitted to subsets of 2m + 1 consecutive observations. Caution must be exercised in the use of moving averages, since the application of such averages will introduce autocorrelation into even a pure random series and modify any existing autocorrelation. (Of course, the fitting of linear or polynomial trends may have similar effects.) Also, the use of moving averages will diminish the amplitude of existing periodic movements (Tintner 1952, pp. 203-207; see also Slutsky 1927). For example, if we use moving averages to eliminate the seasonal component, this will diminish the amplitude of other cyclical fluctuations in the series. Nonparametric tests for trend. The methods for estimating the trend component of a time series discussed thus far all rely on our having some a priori knowledge of the form of the trend function. As is frequently the case in economics, we may feel very uncertain about the form of the function and would like a statistical test for trend that does not depend on such knowledge, i.e., a nonparametric test. Such a test has been devised by Mann (1945) on the basis of earlier work by Kendall (1938). Given the series X,, t = 1, • • • , N, we assign ranks pl, • • • , pN to each of the observations. For example, if X, is the fourth largest item in the series, then pl ~ 4. We then compute a coefficient of disarray, T
2S N(N-l)'
where S, called the total score, is defined as S = 2 P - i N ( N - 1). Here P, the positive score, is the sum ICfr^rii, where n^ is the number of elements X i+1 , • • • , XA* with ranks larger than Pi. The coefficient T may take on values from — 1 to +1, large negative values indicating a downward trend in the series and large positive values an upward trend. If there is no trend, r should be in the neighborhood of zero. The significance of T may be determined by a sig-
TIME SERIES: General nificance test for S, for which tables have been provided by Kendall (1948) for small N. For larger values of N, S can be considered normally distributed, with mean zero and variance equal to N(N — 1)(2N + 5)/18. [Further discussions of nonparametric methods in trend analysis may be found in Foster & Stuart (1954) and Hemelrijk (1958). See also NONPARAMETRIC STATISTICS, article On RANKING METHODS.] Oscillatory and periodic movements The study of oscillatory and periodic movements in economic time series deals with seasonal fluctuations, the business cycle, and related matters. The procedures to be described have been developed to analyze series without trends or series from which trends have been eliminated. The primary concerns are discovering the statistical models that appear to have generated the oscillatory time series frequently observed and estimating the parameters of these models. (Useful methods for such analysis are to be found in Bruckmann & Pfanzagl 1960 and Hannan 1963.) Practically all economic time series display fluctuations of one sort or another. Before we embark on analysis of a particular series, it is desirable to determine whether the observed fluctuations represent anything beyond a purely random process. A nonparametric test for this purpose has been constructed by Walk's and Moore (1941). The test involves determining whether the number of completed runs of length 1, 2, and greater than 2 differs significantly from the expected number of such runs in a series of independent random observations. (A run is defined as the occurrence of consecutive first differences having the same sign.) The statistic comparing the actual with the expected number of such runs is used in an approximate x2 test, for which tables are provided by Wallis and Moore. They have also established a test employing the total number of completed runs as the test statistic, a statistic that is normally distributed in large samples. [See NONPARAMETRIC STATISTICS, article on RUNS.] Periodogram analysis. Periodogram analysis is based on the idea that a strictly periodic time series can be expressed as the sum of a number of harmonic waves, each represented by a sine or cosine term. Suppose the variable Y is a function of time, say, Y, = f ( t ) . If f(t + T) = f ( t ) for all values of t, then Yt can be expressed as a Fourier series, namely, tAJ
Y,
360jt , 360;A B, cos —~r— 1 > E'/ A, sin. —~r—ID
51
where T is referred to as the period of oscillation and Ao , AJ , and B, are constants. It can be shown that where R, is the amplitude (maximum value of Y) corresponding to the harmonic term with period of length T/j (Schuster 1906). In practical work we wish to determine the principal harmonic components of the time series X t , t = I , • • • , N. We assume that Xt is generated by a Fourier series plus a normally distributed nonautocorrelated random error term with zero mean and constant variance. We attempt to find the harmonic components corresponding to particular periods that are significant in explaining Xt . To accomplish this we compute the Fourier coefficients, ,
v
. 360nt f sln N
Bn =
COS
3QOnt N
corresponding to the harmonic component with period of length N/n. We can then compute the squared amplitude,
R 2n — ~
4 2 i DD2 n ^ n-
A
The graph of Rn against N/n for different values of n is called the periodogram of Xt. To determine whether the harmonic component with period N/n is significant, we test the significance of R2n. Three tests are available—Schuster's test, Walker's test, and Fisher's test. A complete discussion of these tests and tables for the test statistics are provided by Davis (1941). Although periodogram analysis has been used in the past, the results of empirical applications hardly justify much hope for its success in the future. The model on which it is based contains two unrealistic assumptions. First, it is assumed that apart from random disturbances, peaks and troughs occur with strict regularity in economic time series. Second, a random disturbance at a given date is assumed to have no effect on the future course of the time series. Spectral analysis. Many of the shortcomings of periodogram analysis can be overcome by employing a more general method known as spectral analysis. Spectral analysis has wider applicability, since it allows for random disturbances in the amplitudes, periods, and phase angles of the harmonic terms in the Fourier series representation of an economic time series. Both the periodogram and the spectrum of a time
52
TIME SERIES: General
series may be thought of as decompositions of the variance of the series at different frequencies (the frequency of a harmonic term is the reciprocal of the length of the period), but the periodogram is based on the assumption of strict periodicity. The periodogram of a series that is not strictly periodic is not a consistent estimator of the spectrum at given frequencies, although it is an unbiased estimator. Since most economic time series are not strictly periodic, statistical estimation of the spectrum is generally preferable to periodogram analysis. Rather than decompose the variance of the series into components at given frequencies ( as in periodogram analysis), we decompose the variance into components in the neighborhood of various frequencies, in order to obtain statistically consistent results. (Various methods have been proposed to estimate the theoretical spectral function, discussions of which may be found in Bartlett 1955; Blackman & Tukey 1958; Grenander & Rosenblatt 1957; Wilks 1962. For additional information on spectral analysis, see Hannan I960; 1963; Jenkins & Priestley 1957; Nerlove 1964; Parzen 1961; Symposium on Time Series Analysis 1963; Takacs I960; Whittle 1963.) Interdependence of observations The interdependence of successive observations, or autocorrelation, is the one outstanding feature that fundamentally distinguishes the methods appropriate for econometric analysis from statistical methods useful in fields where observations are independent. Tests for autocorrelation. Autocorrelation (sometimes called serial correlation) refers to correlation between Xs and Xt in a time series, where s ^ t. Correlation between Xt and Xt+l is often called firstorder autocorrelation. Autocorrelation may arise through different mechanisms and in different circumstances; hence, a variety of statistical tests for autocorrelation have been developed. The simpler procedures test for autocorrelation between Xt and X f _ ; - for a given value of ;". A very general test of this type is the nonparametric test suggested by Wald and Wolfowitz (1943). It is meant to test for correlation between Xt and X m , using the circular test statistic
test may be misleading for time series with strong trends, since R will then be too strongly influenced by the economically meaningless term X A -X T . A widely used parametric test for correlation between Xt and X,+1 involves the so-called von Neumann ratio as the test statistic and assumes joint normality of the observations of the sample. The ratio is defined as the mean square of first differences divided by the variance of the observations. Its distribution was established by von Neumann (1941), and tables for significance tests in small samples are given by Hart (1942). A parametric test, again based on a normal population, to determine whether X, is significantly correlated with Xt-} for any j is also available. The test statistic for j = L is the Lth noncircular autocorrelation coefficient computed from the sample, denoted by rL, that is, the simple correlation coefficient between the series X,, X,, • • • , X.V_L and the series XL+1, X L+2 , • • • , X y . Here rL is noncircular, since we do not identify XA>1 with X l , X v+2 with X 2 , etc. The Lth circular autocorrelation coefficient computed from the sample, r*L, is the simple correlation coefficient between the series Xl, X2, • • • , XN-i, XN a n d X L + 1 ,X L + 2 , - - ^ X ^ X ^ • • • , X L _ l 5 X L . T h e distribution of rL is not known, but the exact smallsample distribution of r*L has been derived by R. L. Anderson (1942) and can be used for an approximate test of the null hypothesis that X* and X,_ L are not correlated in the population. As a justification for approximating the distribution of rL with that of r*L, it can be argued that for large samples the influence of the circular terms becomes negligible. The relationship between the first autocorrelation coefficient and the von Neumann ratio (the von Neumann ratio equals 2N[1 — r*]/[N — 1]) has been investigated by T. W. Anderson (1948). More refined investigation of autocorrelation requires more refined statistical models. It was noted earlier that the general model of an economic time series is a stochastic process. An example of a stochastic process that is particularly useful in analyzing autocorrelation is the stochastic difference equation, or linear autoregressive process. The observed time series Xt,t=l, • • • , N, may have been generated by the pth-order linear autoregressive process: (1)
which for large N is normally distributed, with mean and variance as given by Wald and Wolfowitz. The null hypothesis tested is that the items of the series are independent. Unfortunately, the
Xt = a0
et,
the cii being constants and the et being nonautocorrelated random disturbances with zero mean and constant variance. Here Xt is seen to depend, in a complicated way, on its values for the previous p periods. Estimates of the parameters of (1) pro-
TIME SERIES: General vide information on the form of autocorrelation in the population from which the sample was obtained. Since (1) does define a stochastic process, the joint probability distribution of X t , • • • ,XM for any M can be found. If the joint probability distributions of X t , • • • , XM and Xt+i, • • • , XM+J are identical for all ; and for all choices of M, the process is said to be stationary. The values of the constants, at, i = 0, • • • , p, will determine whether or not (1) defines a stationary stochastic process. Should the process be stationary, maximum likelihood estimation of the parameters of (1) is equivalent to direct application of least squares to the equation. The estimators of the coefficients are consistent and normally distributed for large samples, but they are biased for small samples (Hurwicz 1950). The concept of weak stationarity is often useful when one is dealing primarily with first and second moments. If the variance of Xt exists for all t, the process Xt is said to be weakly stationary when (z) EXt does not depend on t and («) the covariance of Xt and Xs depends only on t - s. It follows from (ii) that for a weakly stationary process the variance of Xt does not depend on t. In practice the order of the stochastic difference equation to be fitted is unknown. However, Quenouille (1947) has provided a large-sample test for the goodness of fit of a linear autoregressive scheme. After the fitting of a pth-order difference equation, the Quenouille test determines whether a difference equation of higher order will better fit the sample. Correlation between autocorrelated series. Testing for correlation between two variables is often desired, but well-known tests for this purpose are generally based on the assumption that neither variable is autocorrelated. Since economic time series typically are autocorrelated, it is very important to have a test for correlation between two autocorrelated series. Orcutt and James (1948) have suggested a test based upon the idea that a set of N observations of two autocorrelated series is, in a certain sense, equivalent to a smaller number, n', of independent observations. Drawing upon earlier work by Bartlett (1935), they compute an approximation, valid in large samples, to the variance, V, of the sample correlation coefficient, r, between two autocorrelated series. If V < £, they show that n' is approximately equal to (V + 1)/V and that r approximately follows the t-distribution with n' — 2 degrees of freedom. The significance of r can then be tested, using this distribution. (For further discussion of and references to tests
53
for correlation between autocorrelated series, see Tintner 1952, pp. 247-250.) Autocorrelated residuals in regression. A special problem that frequently arises in regression studies of economic time series is the possibility of autocorrelation in the error term of a regression model. Once the regression function has been estimated by methods appropriate for a nonautocorrelated error term, it is desirable to test the residuals from the regression to determine whether or not the null hypothesis that there is in fact no autocorrelation in the disturbances can be accepted. The autocorrelation of residuals from fitted regression equations has been considered asymptotically by Moran (1948). Suppose the regression model relating variable X, to variable X2 is Xlt = a0
et ,
where a0 and az are constants and et represents the random disturbances at time t. We obtain estimates d0 and a., of a0 and a,, and we wish to use the residuals,
to test for autocorrelation of the et . We compute the first circular autocorrelation coefficient of the residuals : tf-i RI = E etet+i + $i$y. t=i
The significance of R: may be determined for large samples by a test involving the first two circular autocorrelation coefficients of X2 . In this case using the circular definition of R^ is probably not too damaging, since the residuals may well be homogeneous in time. But the autocorrelation coefficients for X2 are likely to be much influenced by the circular terms. The Durbin-Watson ratio (Durbin & Watson 1950-1951),
where zt is the residual at time t from a least squares regression with any number of independent variables, has been suggested as a test statistic for positive autocorrelation between zt and zt-\ . This ratio is related to the von Neumann ratio. Durbin and Watson have not established exact significance levels for d, but they do provide lower and upper bounds for various sample sizes and numbers of estimated parameters in the regression equation. If d exceeds the upper bound, the hypoth-
54
TIME SERIES: General
esis of positive autocorrelation in the disturbances must be accepted, whereas if d is less than the lower bound, this hypothesis must be rejected. Should d lie between the bounds, the test is inconclusive. An alternative approximate test for d has been suggested by Theil and Nagar (1961). R. L. Anderson and T. W. Anderson (1950) have established a test for autocorrelation of residuals from fitted Fourier series. [For additional information on autocorrelation, see MARKOV CHAINS; see also T. W. Anderson 1948; Cochrane & Orcutt 1949; Durbin I960; Parzen 1961; Quenouille 1947; Sargan 1961.]
series with very pronounced seasonal fluctuations. In addition, it is evident that this transformation is not appropriate for time series generated by stochastic difference-equation processes. The main objects of the variate difference method are to determine the difference series that best eliminates Mt and to estimate the variance of et . To accomplish the former, we compute the variance of the difference series of order k. Denote this variance as V fc . If Mt is nearly eliminated in the difference series of order kn , it can be shown that the following equalities should hold approximately :
Transformation of observations Since methods to deal with the class of stochastic processes that arise in economic time series are frequently not available, we are often forced to try to transform our observations in such a way that classical statistical procedures can legitimately be used. (Analogous transformations were mentioned above in the discussion of the logistic function.) Unfortunately, choosing the correct transformation requires knowledge of the underlying stochastic process. However, it is possible to indicate the transformations that are appropriate for various possible underlying stochastic processes, leaving it to the researcher to decide which type of stochastic process most likely generated his observations. Variate difference method. The variate difference method is a procedure for eliminating the systematic component from a time series composed of a systematic component and a random element. It does this by differencing the observations. The method has not been very popular in recent econometric applications, primarily because of its rather limited applicability, to be noted below. The method utilizes a somewhat primitive fundamental model of an economic time series. The series X t , t = 1, • • • , N, is assumed to be composed of two additive parts, namely, a "smooth" systematic part, Mt, and a random element, et. It is also assumed, perhaps unrealistically, that the mean value of et is zero, its variance is constant, and the et are not autocorrelated. If Mt is a polynomial function of time, then it can be eliminated from Xt by taking differences of the Xt of a sufficiently high order. If Mt is a sufficiently smooth function of time, it might be approximated by a polynomial in a finite interval, and taking differences of the Xt might reduce Mt sufficiently. The transformation of differencing the observations will not eliminate Mt to any marked degree if Mt is not sufficiently smooth. For example, the method is not applicable to certain monthly time
Thus, to determine whether the feth-order difference series eliminates Mt , we require a test for the equality of V7l. and V/m . Several tests have been suggested. O. Anderson (1929) and R. Zaycoff (1937) have given expressions for the standard error of V/£+1 — V7c . Thus, we might use the ratio of this difference to its standard error as the test statistic, a statistic that is normally distributed for large samples. Tintner (1940) indicated a quite inefficient small-sample test based upon systematic selection of items in the difference series in such a way that the items selected are independent. The exact distribution of V7v based upon a circular definition of the population has been established by Tintner (1955), providing an exact test (Rao & Tintner 1962). In practical applications we might use the exact distribution of the difference between the circularly defined variances as an approximation to the distribution of the difference between the noncircular variances, which in large samples will not differ significantly from that between the circular variances. Suppose we find that the fe,,th-order difference series does eliminate Mt ; then we may use as an estimator of the variance of et the variance of this series, namely, V fco . (For an alternative procedure, see Rao & Tintner 1963. For more information on the variate difference method, consult Durbin 1962; Grenander & Rosenblatt 1957; Wilks 1962, p. 526.) Transformations in multiple regression. One of the worst difficulties that plague empirical econometric research is autocorrelation of the residuals in regression studies of economic time series. Although the regression coefficients may be estimated without bias even if the residuals are autocorrelated, the standard errors of the coefficients obtained using classical least squares methods will not be valid. Suppose we estimate by least squares the regression function X l t = k0 + Wat + €t
TIME SERIES: General and find significant autocorrelation in the residuals, where Xu = kn + LX 2( . Then it can be shown that a valid estimator of the standard error of k2 is given by the classical estimator multiplied by the adjustment factor [1 + 2(r 1 R 1 + r,R2 + • • • ) ] * • In this formulation r, is the autocorrelation coefficient of et and et-i and R, is the autocorrelation coefficient of X.^ and X 2 .,-, : . Thus, this procedure requires knowledge of the correlograms of et and X 2f . If we were to assume that both of these variables were generated by a first-order linear autoregressive process (a simple Markov scheme), then we could use as estimators of the correlograms the first autocorrelation coefficients computed from the sample, say, rl and #1 . This would lead to the adjustment factor
55
However, it should be noted that eliminating trends in variables or introducing time as a separate variable in regression studies is really a confession of ignorance that is sometimes unavoidable. The relation that is being estimated must somehow have shifted over time, but rather than seek an explanation for this shifting, we simply eliminate it and estimate a relation that is stable over the period being considered. Autoregressive transformations. Cochrane and Orcutt (1949) have shown that autocorrelation in residuals can be eliminated by a simple transformation of variables if the residuals follow a simple Markov scheme. Assume that we want to fit, by the method of least squares, the relation (2)
,, = k0 + k2X2t + • • • +
+ ut
The ut are not independent but are known to follow the simple Markov scheme u, = Aut-i + vt,
An alternative to adjusting the standard errors in this manner is to transform the observations in such a way that autocorrelation in the residuals is removed, so that classical least squares estimation can legitimately be applied. Elimination of trends. Autocorrelation of residuals is frequently due to trends in the variables included in time series regression studies. Hence, econometricians often transform their observations by taking deviations from trends. This would generally necessitate fitting trend functions to each of the variables, although that can be avoided in some instances. For example, the variate difference method might be used to find a difference series for each variable that sufficiently eliminates the systematic trend components. First differences would be called for if each variable had a linear trend as its systematic component (an exponential trend, if we are working with logarithms of the variables). An important theorem, due to Frisch and Waugh (1933), also establishes a rather simple procedure for handling trends in variables. Suppose that all variables in the regression follow linear trends. Then it can be shown that the regression results obtained after transforming the variables into deviations from trends are the same as those obtained by using the original variables but including time itself as an independent variable in the regression. This theorem has been generalized by Tintner (1952, p. 301 ) to cases in which all variables have trends that are orthogonal polynomials of time or generally orthogonal functions of time, thus extending the applicability of the method.
where A is a constant, |A| < 1, and the vt have mean value zero, have finite and constant variance, and are not autocorrelated. If we make the transformations Yit = Xit — AXi.t-i, then least squares can legitimately be applied to the linear relationship for the transformed variables : (3) Y l f = fe 0 (l - A ) +fe 2 Y 2 ,+ • • • +kpYpt + vt. It should be noted that this transformation reduces to taking first differences of the observations when A is very close to unity, thus establishing a link between the autoregressive transformation and the variate difference method. A difficulty in applying this method is that it requires knowledge of the constant A, which characterizes the stochastic process generating ut . This difficulty can be surmounted in the following manner (Johnston 1963, pp. 192-195) : We first fit (2) by the method of least squares and compute the residuals ut = Xlt — Xlt. We then estimate A by applying least squares to ut =
vt.
Using A, the estimator of A, to transform the observations, we fit (3) by least squares and test the residuals vt = Yit — Ylt for autocorrelation. If the autocorrelation of these residuals is not significant, we have found a reasonably good estimator of A, and our task is completed. If the autocorrelation is significant, we use the residuals vt to obtain a new estimator of A by fitting
56
TIME SERIES: General
and repeat the above steps. We continue this process until the residuals computed from our estimator of (3) are not significantly autocorrelated. Stochastic processes in econometrics The most promising approach to the satisfactory analysis of economic time series is the explicit use of stochastic processes in econometric research. Although some headway has been made along these lines, the results achieved thus far are not very satisfactory. In statistical analysis of time series, we wish to use our observations to estimate the parameters of the underlying stochastic process that generated the time series. But in order to use a small sample to make statistical inferences concerning the values of population parameters, we must know the small-sample distributions of the estimators employed. Unfortunately, considerable mathematical difficulty is encountered in determining the small-sample distributions of parameter estimators of many types of stochastic processes. Stochastic processes have found wide and diverse applications in economic time series analysis. Dynamic economic problems are frequently analyzed with the aid of dynamic models that can be characterized as stochastic processes (see, for example, Adelman & Adelman 1959; de Cani 1961; F. M. Fisher 1962; Granger & Hatanaka 1964; Morgenstern 1961; Tinbergen 1939). Stochastic processes have been employed to analyze the formation of commodity and stock prices (Cootner 1964; Kendall 1953; Quenouille 1957). Much effort has been directed toward finding an explanation of the income distribution in terms of stochastic processes, as it is a distribution that is very skew and fits badly into the traditional analysis of statistical income distributions [see SIZE DISTRIBUTIONS IN ECONOMICS]. Labor mobility problems have been investigated with the aid of Markov processes (Blumen et al. 1955). Prais and Houthakker (1955) employed stochastic processes involving the lognormal distribution in analyzing household budgets. Stochastic processes have also been used quite successfully in operations research, and it is hoped that the same or related methods will be useful in analyses of economic time series (Bharucha-Reid I960; Takacs 1960). Estimation of parameters. To illustrate the application of maximum likelihood estimation to stochastic processes, consider the Poisson process [Fisz (1954) 1963, p. 488; see also QUEUES]. Let N(£) be the number of events occurring during the time period from 0 to t, where N(£) can take on values 0, 1, 2, • • • . We assume that N(£) has inde-
pendent and homogeneous increments, i.e., that N(£ 2 ) — N(£ a ) is independent of, and has the same distribution as, N(£ 2 + fe) — N(£ t + /z) for all choices of £, and £ 2 , £2 > £1, and for all choices of h greater than zero. The probability of the occurrence of more than one event in the time interval (t, t + A£) tends sufficiently fast to zero as A£ -> 0. The transition probability, Pa(tl, £ 2 ), is the probability that N(£,) = i if N(£,) = j and can be written = exp[-L(t 2 -*, where L, the parameter to be estimated, is the average number of events occurring per unit of time. Suppose we have observations on N ( £ ) for £ = £ 1; t, , • • - , £ „ and denote N(£ f c ) = j k , k = 1, • • • , n. The likelihood function is then
Maximizing P with respect to L yields the maximum likelihood estimator, L = ;'„/£„ . Large-sample or asymptotic distributions of maximum likelihood estimators have been established for simple Markov processes (T. W. Anderson 1959). Consider a first-order stochastic difference equation, Xe = aXi_! + ut , where a is a constant to be estimated from the sample Xt , • — ,XS. Assume that the initial value, X0 , is a constant and that ut is a nonautocorrelated normally distributed random variable with zero mean and constant and finite variance. The maximum likelihood estimator of a is
EX? t=l If a I < 1 (in which case Xt is a stationary time series or a time series with no trend), the expression (a — a) V~N is, under wide conditions, asymptotically normally distributed with mean zero. Using this result, approximate confidence interval estimates of a could be made for very large samples. More interesting is the case in which a > I . Then X t is an evolutionary time series — the stochastic equivalent of an economic time series with exponential trend — and the expression a2- 1 has a Cauchy distribution, a distribution whose mean and higher moments do not exist. However,
TIME SERIES: General if in addition to the above assumptions it is assumed that X0 = 0 and ut is normally distributed, then a is a maximum likelihood estimator, and the expression (a-a)
is asymptotically normal and provides a basis for approximate confidence interval estimates for very large samples. Asymptotic distributions such as these could be used as rough approximations to small-sample distributions of this estimator, but it is to be hoped that exact small-sample distributions will be established, so that they would be immediately applicable to the analysis of short economic time series. Multiple stochastic processes. Multiple stochastic processes arise frequently in econometric research. For example, in dynamic business cycle models we often attempt to explain the cyclical behavior of consumption, investment, and income by a system of equations in which the current value of each of these endogenous variables is related to its own lagged values, to lagged values of other endogenous variables, to current and lagged exogenous variables, and to a random term. The interdependence of economic variables leads us to analyze a particular time series in the context of a system of equations that constitutes a multiple stochastic process. [See ECONOMETRIC MODELS, AGGREGATE.] Not enough is known about the estimation of multiple stochastic processes. In econometric work, lagged endogenous variables are frequently handled like given constants, a treatment which is plainly inadequate. Also, small-sample distributions have not yet been sufficiently explored. Quenouille ( 1957, p. 70) has investigated the problems of estimating a multiple Markov scheme. This is a relatively simple multiple stochastic process, composed of a system of first-order stochastic linear difference equations. As an example, we might wish to estimate the constants ai} and bij in the system a n X l f + av,X.,t + b-LiX-i.t-i + br
with the sets of observations X1X , • • • , X1A- and X2i , • • • , X2N . We assume that e, and e.2 are random variables with zero means and constant and finite variances and that they are independent over time. Under certain conditions, we can solve for Xu and X.,t , rewriting the system as follows: Xlt = UuXi.t-i + Ui2X2.t-, + v,,e,t + v^e,t , X2t = u2iXlit-\ + u.J2X2it-i + v.2]elt + v«2e.,t .
57
Defining the simple covariances as j t-\
and the lagged covariances as 1
*
'ij ~ TV - I / j
X X
" *,*-i»
the maximum likelihood estimators of the ui} are found by solving the system of equations C
11W11 +
C
12W21 ~
C
ll >
C 2 Ai + C 22 W 21 = C'21 ,
c
iA* + c12w22 = c; 2 ,
C
21^12
I ^22 W 22
=
C 22 '
It is also possible to obtain standard errors of the estimated w,- ; -, but it is not possible to obtain estimators of the a i; and bi}•, In order to accomplish this, further assumptions about the coefficients have to be made. (See, for example, F. M. Fisher 1965. For a further discussion of multiple stochastic processes, see Bartlett 1955. Works containing additional information on the statistical treatment of stochastic processes as well as useful references to the vast literature on this topic are Moran 1951; 1953; Rosenblatt 1962.) GERHARD TINTNER [See also LINEAR HYPOTHESES, article on REGRESSION.] BIBLIOGRAPHY
ADELMAN, IRMA; and ADELMAN, FRANK L. (1959) 1965 The Dynamic Properties of the Klein-Goldberger Model. Pages 278-306 in American Economic Association, Readings in Business Cycles. Homewood, 111.: Irwin. -» First published in Volume 27 of Econometrica. ANDERSON, OSKAR N. 1929 Die Korrelationsrechnung in der Konjunkturforschung: Ein Beitrag zur Analyse von Zeitreihen. Bonn: Schroeder.
ANDERSON, R. L. 1942 Distribution of the Serial Correlation Coefficient. Annals of Mathematical Statistics 13:1-13. ANDERSON, R. L. 1954 The Problems of Autocorrelation in Regression Analysis. Journal of the American Statistical Association 49:113-129. -> A correction was published in Volume 50, page 1331. ANDERSON, R. L.; and ANDERSON, T. W. 1950 Distribution of the Circular Serial Correlation Coefficient for Residuals From a Fitted Fourier Series. Annals of Mathematical Statistics 21:59-81. ANDERSON, T. W. 1948 On the Theory of Testing Serial Correlation. Skandinavisk aktuarietidskrift 31:88-116. ANDERSON, T. W. 1959 On Asymptotic Distributions of Estimates of Parameters of Stochastic Difference Equations. Annals of Mathematical Statistics 30:676-687. ANDERSON, T. W. 1962 The Choice of the Degree of a Polynomial Regression as a Multiple Decision Problem. Annals of Mathematical Statistics 33:255-265.
58
TIME SERIES: General
ANDERSON, T. W. 1964 Some Approaches to the Statistical Analysis of Time Series. Australian Journal of Statistics 6, no. 1:1-11. BARTLETT, M. S. 1935 Some Aspects of the Time-correlation Problem in Regard to Tests of Significance. Journal of the Royal Statistical Society 98:536-543. BARTLETT, M. S. (1955) 1962 An Introduction to Stochastic Processes, With Special Reference to Methods and Applications. Cambridge Univ. Press. BHARUCHA-REID, ALBERT T. 1960 Elements of the Theory of Markov Processes and Their Applications. New York: McGraw-Hill. BLACKMAN, R. B.; and TUKEY, J. W. (1958) 1959 The Measurement of Power Spectra, From the Point of View of Communications Engineering. New York: Dover. -» First published in the Bell System Technical Journal. BLUMEN, ISADORE; KOGAN, MARVIN; and MCCARTHY, PHILIP 1955 The Industrial Mobility of Labor as a Probability Process. Cornell Studies in Industrial and Labor Relations, Vol. 6. Ithaca, N.Y.: Cornell Univ. Press. BRUCKMANN, G.; and PFANZAGL, J. 1960 Literaturbericht iiber die Zerlegung saisonabhangiger Zeitreihen. Deutsche Gesellschaft fur Versicherungsmathematik, Blatter 4:301-309. COCHRANE, DONALD; and ORCUTT, G. H. 1949 Application of Least Squares Regression to Relationships Containing Auto-correlated Error Terms. Journal of the American Statistical Association 44:32-61. COOTNER, PAUL H. (editor) 1964 The Random Character of Stock Market Prices. Cambridge, Mass.: M.I.T. Press. COWLES COMMISSION FOR RESEARCH IN ECONOMICS 1953 Studies in Econometric Method. Edited by William C. Hood and Tjalling C. Koopmans. New York: Wiley. DAVIS, HAROLD T. 1941 The Analysis of Economic Time Series. Cowles Commission for Research in Economics, Monograph No. 6. Bloomington, Ind.: Principia. DE CANI, JOHN S. 1961 On the Construction of Stochastic Models of Population Growth and Migration. Journal of Regional Science 3, no. 2:1-13. DURBIN, J. R. 1960 Estimation of Parameters in Timeseries Regression Models. Journal of the Royal Statistical Society Series B 22:139-153. DURBIN, J. R. 1962 Trend Elimination by Moving-average and Variate-difference Filters. Institut International de Statistique, Bulletin 39:131-141. DURBIN, J. R.; and WATSON, G. S. 1950-1951 Testing for Serial Correlation in Least Squares Regression. Parts 1-2. Biometrika 37:409-428; 38:159-178. FISHER, FRANKLIN M. 1962 A Priori Information and Time Series Analysis: Essays in Economic Theory and Measurement. Amsterdam: North-Holland Publishing. FISHER, FRANKLIN M. 1965 Dynamic Structure and Estimation in Economy-wide Econometric Models. Pages 589-635 in James S. Duesenberry et al., The Brookings Quarterly Econometric Model of the United States. Chicago: Rand McNally. FISHER, R. A. (1925) 1958 Statistical Methods for Research Workers. 13th ed. New York: Hafner. -» Previous editions were also published by Oliver and Boyd. Fisz, MAREKA (1954) 1963 Probability Theory and Mathematical Statistics. 3d ed. New York: Wiley. -> First published as Rachunek prawdopodobienstwa i statystyka matematyczna. FOSTER, F. G.; and STUART, ALAN 1954 Distributionfree Tests in Time-series Based on the Breaking of
Records. Journal of the Royal Statistical Society Series B 16:1-22. FRISCH, RAGNAR; and WAUGH, FREDERICK V. 1933 Partial Time Regressions as Compared With Individual Trends. Econometrica 1:387-401. GRANGER, CLIVE W. J.; and HATANAKA, M. 1964 Spectral Analysis of Economic Time Series. Princeton Univ. Press. GRENANDER, ULF 1957 Modern Trends in Time Series Analysis. Sankhya. 18:149-158. GRENANDER, ULF; and ROSENBLATT, MURRAY 1957 Statistical Analysis of Stationary Time Series. New York: Wiley. HANNAN, EDWARD J. (1960) 1962 Time Series Analysis. New York: Wiley. HANNAN, EDWARD J. 1963 The Estimation of Seasonal Variations in Economic Time Series. Journal of the American Statistical Association 58:31-44. HART, B. I. 1942 Tabulation of the Probabilities for the Ratio of the Mean Square Successive Difference to the Variance. Annals of Mathematical Statistics 13:207214. HEMELRIJK, JAN 1958 Distribution-free Tests Against Trend and Maximum Likelihood Estimates of Ordered Parameters. Institut International de Statistique, Bulletin 36:15-25. HOTELLING, HAROLD 1927 Differential Equations Subject to Error, and Population Estimates. Journal of the American Statistical Association 22:283-314. HURWICZ, LEONARD 1950 Least-squares Bias in Time Series. Pages 365-383 in Tjalling C. Koopmans (editor), Statistical Inference in Dynamic Economic Models. New York: Wiley. JENKINS, G. M.; and PRIESTLEY, M. B. 1957 The Spectral Analysis of Time-series. Journal of the Royal Statistical Society Series B 19:1-12. JOHNSTON, JOHN 1963 Econometric Methods. New York: McGraw-Hill. KENDALL, M. G. 1938 A New Measure of Rank Correlation. Biometrika 30:81-93. -» This introduces the T coefficient. Its use in testing for trend is discussed in Kendall 1948. KENDALL, M. G. (1948) 1963 Rank Correlation Methods. 3d ed., rev. & enl. New York: Hafner. KENDALL, M. G. 1953 The Analysis of Economic Timeseries. Part 1: Prices. Journal of the Royal Statistical Society Series A 116:11-25. KENDALL, M. G.; and STUART, ALAN (1946) 1961 The Advanced Theory of Statistics. Volume 2: Inference and Relationship. New ed. New York: Hafner; London: Griffin. -> The first edition was written by Kendall alone. KOOPMANS, TJALLING C. (editor) 1950 Statistical Inference in Dynamic Economic Models. New York: Wiley. KUZNETS, SIMON 1934 Time Series. Volume 14, pages 629-636 in Encyclopaedia of the Social Sciences. New York: Macmillan. MALINVAUD, EDMOND (1964) 1966 Statistical Methods in Econometrics. Chicago: Rand McNally. -» First published in French. MANN, HENRY B. 1945 Nonparametric Tests Against Trend. Econometrica 13:245-259. MANN, HENRY B.; and WALD, A. 1943 On the Statistical Treatment of Linear Stochastic Difference Equations. Econometrica 11:173-220. MORAN, P. A. P. 1948 Some Theorems on Time Series. Part 2: The Significance of the Serial Correlation Coefficient. Biometrika 35:255-260.
TIME SERIES: Advanced Problems MORAN, P. A. P. 1951 Estimation Methods for Evolutive Processes. Journal of the Royal Statistical Society Series B 13:141-146. MORAN, P. A. P. 1953 The Estimation of the Parameters of a Birth-and-death Process. Journal of the Royal Statistical Society Series B 15:241-245. MORGENSTERN, OSKAR 1961 A New Look at Economic Time Series Analysis. Pages 261-272 in Hugo Hegeland (editor), Money, Growth, and Methodology, and Other Essays in Economics. Lund (Sweden): Gleerup. NERLOVE, MARC 1964 Spectral Analysis of Seasonal Adjustment Procedures. Econometrica 32:241-286. ORCUTT, G. H.; and JAMES, S. F. 1948 Testing the Significance of Correlation Between Time Series. Biometrika 35:397-413. PARZEN, EMANUEL (1961) 1965 Stochastic Processes. San Francisco: Holden-Day. PHILLIPS, A. W. 1959 The Estimation of Parameters in Systems of Stochastic Differential Equations. Biometrika 46:67-76. PRAIS, S. J.; and HOUTHAKKER, H. S. 1955 The Analysis of Family Budgets With an Application to Two British Surveys Conducted in 1937-1939 and Their Detailed Results. Cambridge Univ. Press. QUENOUILLE, M. H. 1947 A Large Sample Test for the Goodness of Fit of Autoregressive Schemes. Journal of the Royal Statistical Society Series A 110:123-129. QUENOUILLE, M. H. 1957 The Analysis of Multiple Timeseries. New York: Hafner. RAO, J. N. K.; and TINTNER, GERHARD 1962 The Distribution of the Ratio of the Variances of Variate Differences in the Circular Case. Sankhyd 24A: 385-394. RAO, J. N. K.; and TINTNER, GERHARD 1963 On the Variate Difference Method. Australian Journal of Statistics 5:106-116. RHODES, E. C. 1940 Population Mathematics III. Journal of the Royal Statistical Society Series A 103:362-387. ROSENBLATT, MURRAY 1962 Random Processes. New York: Oxford Univ. Press. SARGAN, J. D. 1961 The Maximum Likelihood Estimation of Economic Relationships With Autoregressive Residuals. Econometrica 29:414-426. SCHUSTER, ARTHUR 1906 On the Periodicities of Sunspots. Royal Society of London, Philosophical Transactions Series A 206:69-100. SLUTSKY, EUGEN E. (1927) 1937 The Summation of Random Causes as the Source of Cyclic Processes. Econometrica 5:105-146. -> First published in Russian. Reprinted in 1960 in Slutsky's Izbrannye trudy. Symposium on Spectral Approach to Time Series. 1957 Journal of the Royal Statistical Society Series B 19: 1-63. Symposium on Stochastic Processes. 1949 Journal of the Royal Statistical Society Series B 11:150-282. SYMPOSIUM ON TIME SERIES ANALYSIS, BROWN UNIVERSITY, 1962 1963 Proceedings. Edited by Murray Rosenblatt. New York: Wiley. TAKACS, LAJOS 1960 Stochastic Processes: Problems and Solutions. New York: Wiley. THEIL, H.; and NAGAR, A. L. 1961 Testing the Independence of Regression Disturbances. Journal of the American Statistical Association 56:793-806. TINBERGEN, JAN 1939 Statistical Testing of Businesscycle Theories. Volume 2: Business Cycles in the United States of America: 1919-1932. Geneva: League of Nations, Economic Intelligence Service. TINTNER, GERHARD 1940 The Variate Difference Method. Bloomington, Ind.: Principia.
59
TINTNER, GERHARD 1952 Econometrics. New York: Wiley. TINTNER, GERHARD 1955 The Distribution of the Variances of Variate Differences in the Circular Case. Metron 17, no. 3/4:43-52. TINTNER, GERHARD 1960 Handbuch der Okonometrie. Berlin: Springer. VON NEUMANN, JOHN 1941 Distribution of the Ratio of the Mean Square Successive Difference to the Variance. Annals of Mathematical Statistics 12:367-395. WALD, A.; and WOLFOWITZ, J. 1943 An Exact Test for Randomness in the Non-parametric Case Based on Serial Correlation. Annals of Mathematical Statistics 14:378-388. WALLIS, W. ALLEN; and MOORE, GEOFFREY H. 1941 A Significance Test for Time Series Analysis. Journal of the American Statistical Association 36:401-409. WHITTLE, P. 1951 Hypothesis Testing in Time Series Analysis. Uppsala (Sweden): Almqvist & Wiksell. WHITTLE, P. 1963 Prediction and Regulation by Linear Least-square Methods. London: English Universities Press. WILKS, S. S. 1962 Mathematical Statistics. New York: Wiley. WOLD, HERMAN (1938) 1954 A Study in the Analysis of Stationary Time Series. 2d ed. Stockholm: Almqvist & Wiksell. ZAYCOFF, RASHKO 1936 V'rkhu razlaganeto na statisticheski redove po vreme na tri slagaemi (Uber die Zerlegung statistischer Zeitreihen in drei Komponenten). Sofia, Universitet, Statisticheski Institut za Stopanski Prouchvaniia Trudove [1936] no. 4:1-22. ZAYCOFF, RASHKO 1937 V'rkhu izkliuchvaneto na sluchainata slagaema posr"dstvom' metoda "Variatedifference" (Uber die Ausschaltung der zufalligen Komponente nach der "Variate-difference"-Methode). Sofia, Universitet, Statisticheski Institut za Stopanski Prouchvaniia Trudove [1937] no. 1:1-46. II ADVANCED PROBLEMS
Numerical data often occur in the form of a time series, that is, a sequence of observations on a variable taken either continuously or at regular intervals of time. As examples consider records of economic variables (prices, interest rates, sales, unemployment), meteorological records, electroencephalograms, and population and public health records. In contrast to much experimental data, the consecutive observations of a time series are not in general independent, and the fascination of time series analysis lies in the utilization of observed dependence to deduce the way the value of a variable (say, steel production) can be shown to be in part determined by the past values of the same variable, or of other variables (say, demand for automobiles). In the so-called discrete time case, observations are taken at regular intervals of time. The common interval of time can be taken as the unit, so that the value of a variable x at time t can be denoted by xt, where t takes the values • • • , —2, — 1, 0, 1, 2, • • • .
60
TIME SERIES: Advanced Problems
Of course, in practice one observes only a finite set of values, say xl, x2, • • • , xn, but it is useful to imagine that the series can in principle extend indefinitely far back and forward in time. For this reason t is allowed to run to infinity in both directions. (Of course, sometimes one observes a phenomenon continuously, so that x is measured for all t rather than just at intervals—such a process is referred to as continuous. However, since the discrete case is by far the more frequent in the social sciences, this discussion will be limited to that case.) Suppose that one has a model which explains how the xt series should develop. The model is termed a process and is denoted by {xt}; if some of the rules it specifies are probabilistic ones, it is called a stochastic process. Definition of a stationary process One class of stochastic processes is of particular importance, both in practice and in theory: this is the class of stationary processes. A stationary process is one that is in a state of statistical equilibrium, so that its statistical pattern of behavior does not change with time. Formally, the requirement is that for any set of instants of time, t a , t2, • • • , tn, and any time lag, s, the joint distribution of xtl,xt2, • • • , x t > l must be the same as that of xtl+s, xtz+a, • • • , xt>i+s. Thus, xl and x5 must have the same univariate distribution, ( x { , x 2 ) and (x-,, x 6 ) must have the same bivariate distribution, and so on. The assumption of stationarity is a strong one, but when it can be made it greatly simplifies understanding and analysis of a process. An intuitive reason for the simplification is that a stationary process provides a kind of hidden replication, a structure that does not deviate too far from the still more special assumptions of independence and identical distribution, assumptions that are ubiquitous in statistical theory. Whether the stationarity assumption is realistic for a particular process depends on how near the process is indeed to statistical equilibrium. For example, because most economies are evolving, economic series can seldom be regarded as stationary, but sometimes a transformation of the variable produces a more nearly stationary series (see the section on "smoothing" a series, below). Stationarity implies that if xt has an expectation, then this expectation must be independent of £, so that
(1)
£(*.)=/*>
say, for all t. Furthermore, if xt and xt.g have a
covariance, then this covariance can depend only on the relative time lag, s, so that (2)
COV(xt,
The important function Ta is known as the autocovariance function. Processes subject only to the restrictions (1) and (2), and not to any other of the restrictions that stationarity implies, are known as wide-sense stationary processes. They are important theoretically, but the idea of wide-sense stationarity is important also because in practice one is often content to work with first-order and second-order moments alone, if for no other reason than to keep computation manageable. This survey will be restricted to stationary processes in the strict sense, unless otherwise indicated. Note that t need not necessarily mean time. One might, for example, be considering variations in thickness along a thread or in vehicle density along a highway; then t would be a spatial coordinate. Some particular processes. One of the simplest processes of all is a sequence of independent random variables, {et}. If the et have a common distribution, then the process is strictly stationary— this is the kind of sequence often postulated for the "residuals" of a regression or of a model in experimental design. If one requires of {e(} merely that its elements have constant mean and variance, ra and o-2, and be uncorrelated, then the process is a widesense stationary process. From now on {et} will denote a process of just this latter type. Often such a process of "residuals" is presumed to have zero mean (that is, m — 0); however, this will not always be assumed here. What is of interest in most series is just that the observations are not independent or even uncorrelated. A model such as (3)
xt = atXt-i +
(a first-order autoregression^) takes one by a very natural first step from an uncorrelated sequence, {e^}, to an autocorrelated sequence, { x t } . Here a is a numerical constant whose value may or may not be known, and the term axt-i introduces a dependence between observations. Such a model is physically plausible in many situations; it might, for example, crudely represent the level of a lake year by year, axf..i representing the amount of water retained from the previous year and ef a random inflow. A common type of econometric model is a vector version of (3), in which xt,et are vectors and a is a matrix. If observations begin at time T, then the series
TIME SERIES: Advanced Problems starts with XT , xT+1 is axT + e r+ i, xT+2 is a?xT + acT+i + £ r+2 , and in general, for t ^ T, t-r-i
(4)
=Z fc=0
past disturbances. The sequence bk is the transient response of the system to a single unit disturbance. The relation between the coefficients ak and bk can be expressed neatly in generating function form:
If a; <1 and the model has been operative from the indefinitely distant past, then one can let T tend to —oo in (4) and obtain a solution for xt in terms of the "disturbing variables" et : (5)
The condition a\
does not converge in mean square as T tends to -oo; that is, there does not exist a random variable £ such that E(%T - £ ) 2 ^ 0.) The series [xt] generated by (5) is stationary, and one verifies that
m I -a
(6) f V\ I i //
N T~* — T"1 — /-»r\Tr ('V -v 1 e — 1-s — CUV Ix Jit . Jif-s 1 — I-i
tr'cr _
o '
a2
where m and
expressing xt in terms of its own immediate past and a stationary residual, et. When p= 1, (8) and (3) are the same except for trivia of notation: a0 and a, in (8) correspond to 1 and —a in (3). When p > 1, a process of type (8) can generate the quasi-periodic variations so often seen in time series. Of course, this is not the only model that can generate such quasi-periodic oscillations (one might, for example, consider a nonlinear process or a Markov chain), but it is probably the simplest type of model that does so. Corresponding to the passage from (3) to (5), process (8) can be given the moving-average representation
CO - \ ~ /
xt = Z
Je=o
which represents xf as a linear superposition of
1
-1
i—A
~«~
A/ \ -*1 \ ^ /
fc=0
p V»
A, akzK
r.
fc=0
For example, if z is set equal to 0, then b0 = if the functions are differentiated once and z is again set equal to 0, then £>, = —aja\. (Discussions of time series sooner or later require some knowledge of complex variables. An introduction to the subject is given in MacRobert 1917.) The necessary and sufficient condition for series (9) to converge to a proper random variable and for the resulting {xt} series to be stationary is that A(z), considered as a function of a complex variable z, have all its zeros outside the unit circle; this is again a stability condition on the relation (8). If, however, the stability condition is not fulfilled, relations such as (8) can still provide realistic models for some of the nonstationary series encountered in practice. A relation such as (9) is said to express {xt} as a moving average of {et}- There are, of course, many other important types of process, particularly the general Markov process [see MARKOV CHAINS] and the point processes (see Bartlett 1963), but the simple linear processes described in this section are typical of those that are useful for many time series analyses. Autocovariance function The autocovariance function, F s , defined in (2) gives a qualitative idea of the decay of statistical dependence in the process with increasing time lag; a more detailed examination of it can tell a good deal about the structure of the process. A key result is the following: Suppose that {xt} is a moving average of a process [yt],
xt = Z
(H)
k
where the summation is not necessarily restricted to nonnegative values of k, although in most physical applications it will be. Denote the autocovariances of the two processes by r(sx) r ( / } . Then
(12)
<*> = y
S
— t-J i
(9)
61
j l c
j-fc+
*
so that
(13)
= (Z V) (Z
62
TIME SERIES: Advanced Problems
a generating function relation that will be written in the form
If relation (11) defines a stationary process of finite variance, then (14) is valid for z| = 1 at least. A deduction from (14) and (10) is that for the autoregression (8) the autocovariance generating function is a-'
(15)
A(z)A(z-')
By calculating the coefficient of zs in the expansion of this function on the circle \z = 1 one obtains P., ; for process (3) one obtains the result (7) as before; for the second-order process with a0 = 1 one obtains
waters, a problem for which it was natural to consider a model of the type
(19)
xt = 1C A; sin cos
a «+l
08+1
2s ) ^
0,
s
_ o- 2 {sin[(s+l)0]- P 4 sin[(s- 1)0]} 1- > 2 1 -22cos20 + 4sin<9
The autocovariance, Ts , has a peak near a lag, s, of approximately 27T/0, indicating strong positive correlation between values of xt and xt-s for this value of lag. The nearer the damping factor, p, lies to unity, the stronger the correlation. This is an indication of what one might call a quasiperiodicity in the xt series, of "period" 27T/0, the kind of irregular periodicity that produces the "trade cycles" of economic series. Such disturbed periodicities are no less real for not being strict. Either from (15) or from the fact that CQV(Xt-i, € t ) =
n
The approximation lies in the use of rr
where or1, /3-1 are the zeros of A(z). If these zeros are complex, say, a, ft = p exp (±z#), then (16) has the oscillatory form ;
ts
\
= -r---j^-j -^- ( -z=- — ./ (1 — a/3 ) ( a — /3 ) \ 1 — a2 1 — (32 /
v
+ et .
2 v-A =— \ n
— x /
+ ]CC sin
That is, the series is represented as the sum of a number of harmonic components and an uncorrelated residual. If the frequencies, toy (corresponding to lunar and diurnal variations and so forth), are known, so that the A, and ay are to be estimated, then on the basis of an observed series x1}x2, • • • , xn the least square estimators of the coefficients By and Cy are approximately
(16) 0-2
+ ctj ) + e(
y pa ^ 2L >
h *- 2
E PA s o, t=\ where Pt and Qt are any two of the functions of time cos (w/t), sin (wyt) (;' = 1, 2, • • • ) . In this approximation, terms of relative order n~J are neglected. The squared amplitude, A2} = B 2 + C2., is thus estimated approximately by
(20)
—-^y^ y^ xsxt cos [o>y(s —t)]. /i . ' w „ *=1
t=l
This can also be written in the form
0,
it can be shown that for the autoregression (8)
(18)
0,
0.
These are the Yule-Walker relations, which provide a convenient way of calculating the Ys from the coefficients, ak. This procedure will be reversed below, and (18) will be used to estimate the ak from estimates of the autocovariances. Spectral theory Some of the first attempts at time series analysis concerned the prediction of tidal variation of coastal
which is mathematically (although not computationally) convenient. The importance of K] is that it measures the decrease in residual sum of squares (that is, the improvement in fit of model (19)) obtained by fitting terms in cos(co ; t) and sin(co,t). The larger this quantity, the greater the contribution that the harmonic component of frequency, coy, makes to the variation of xt. For this reason, if the coy are unknown, one can search for periodicities (see below) by calculating a quantity analogous to (20) for variable &>: the periodogram
TIME SERIES: Advanced Problems (24)
(21)
x x cos [&>(s — -TT / ^ / j s t
8=1
t=l
=— n
An unusually large value of f n (to) at a particular frequency suggests the presence of a harmonic component at that frequency. It is an empirical fact that few series are of the type (19): in general, one achieves much greater success by fitting structural models such as an autoregressive one. Even for the autoregressive model, however, or, indeed, for any stationary process, an analogue of representation (19) called the spectral representation holds. Here the sum is replaced by an integral. This integral gives an analysis of xt into different frequency components; for stationary series the amplitudes of different components are uncorrelated. In recent work the spectral representation turns out to be of central importance: the amplitudes of frequency components have simple statistical properties and transform in a particularly simple fashion if the process is subjected to a moving-average transformation (see eq. (26)); the frequency components themselves are often of physical significance. So even in the general case the periodogram fn(o)) provides an empirical measure of the amount of variation in the series around frequency w. Its expected value for large rz, the spectral density function (s.d.f.),
=lim
l --
n
j exp (-za>s)E (
= 2 E(xtxt-s ) exp ( — IMS ) , S = -00
provides the corresponding theoretical measure for a given process. If the xt have been reduced to zero mean (which, in fact, affects 0(o>) oiuy f°r w = 0). then the spectral density function becomes
(23) a
=flf[exp(-io>)].
There is a relation reciprocal to (23), the spectral representation of the autocovariance,
exp (—£
N
63
) = 1L r s exp(— icos),
nd, as can be seen from (13) and (14), this is °nly a trivial modification of the autocovariance generating function, #(z), already encountered. In fact,
(25)
r, =
277
exp (IMS
In more general cases $(ey) maY fail to exist for certain values, and $(w)do) must be replaced by dF(at') in (25), where F(w) is the nondecreasing spectral distribution function. An important property of spectral representations is the simplicity of their transformation under moving-average transformations of the process; relation (14) can be rewritten (26)
<J>,(°0 = B[exp(iw)]B[exp(-iG>)]),
showing that the effect of the moving-average operation (11) is to scale each frequency component up or down individually, by a factor |B[exp(zw)]| 2 . So, if for the autoregression with spectral density function determined by (15) the polynomial A(z) has zeros at p-1 exp (±0), and p is near unity, then <^((w) will have peaks near o> = ±9, indicating a quasiperiodicity of "period" 2-77/0. Note that for an uncorrelated series $(o)) is constant—all frequencies are equally represented on the average. For an autoregressive series $(&>) is variable but finite—this is an example of a process with continuous spectrum. A process of type (19) has a constant background term in (f> owing to the "noise," et, but also has infinite peaks at the values (o = ±a)j, these constituting a line spectrum component. For a discrete series one need only consider frequencies in the range —77 < a) ^TT, since with observations at unit intervals of time the frequencies 277S + a) (s integral) cannot be distinguished one from the other. This is the aliasing effect, which can occasionally confuse an analysis. If, however, the series has little variation of frequency greater than 77 (that is, of period less than two time units), then the effect is not serious, for the higher frequencies that could cause confusion hardly occur. Effect of "smoothing" a series—a caution. In order to isolate the "trend" in a series, {xt}, it has sometimes been common to derive a smoothed series, {xt}, by an averaging operation such as
(27)
2m + 1
Xt-Tc ,
although more elaborate and more desirable types of average are often used. In terms of frequency, the effect of the operation
64
TIME SERIES: Advanced Problems
1.00
GAIN FUNCTION
(l) b \
(2)
(3)'
FREQUENCY o)
Figure 1 — The gain functions for three linear operations on a time series a. Curve (2) represents the gain function for the ideal filter passing periods greater than five time units (frequencies less than 2ir/5). b. Curve (1) represents the gain function for a five-term uniform average (formula (27) with m = 2). c. Curve (3) represents the gain function for a finite moving average approximating the ideal filter (the average with weights given by (30) using u0 = 2ir/5, but truncated at fe = ± 10).
(27) is to multiply the spectral density function by a factor B[exp(z<w)]B[exp( —ito)], where (28)
sinjYra LV (2m
This function is graphed as the dotted curve (1) in Figure 1 and is known as the gain function of the transformation (27). Now, if the purpose of "trend extraction" is to eliminate the high frequencies from a series—that is, to act as a "low-pass filter"—then the ideal gain factor would correspond to the square-shouldered solid curve (2) in Figure 1. (A gain factor is sometimes referred to as a "window.") The function (28) obviously departs considerably from this ideal. To obtain a moving-average transformation (29)
— z-i
which acts as a perfect low-pass filter for the range —
The fact that these coefficients decrease rather slowly means that appreciable truncation of the
sum will be necessary (probably at a fe-value equal to a multiple of 27r/w 0 ), but the resultant operation will still be a considerable improvement over (27). The gain function of a truncated smoothing operator is illustrated as the dashed curve (3) in Figure 1. As was first pointed out by Slutsky (1927), injudicious smoothing procedures can actually have the effect of introducing periodicities — just because the gain function of the averaging operation has a peak at a frequency where it should not. One should always be quite clear about the effect of one's "smoothing" operations, and the way to do this is to graph the corresponding gain factor as a function of frequency. Attempts are sometimes made to "eliminate" trend in a series by the method of variate difference — that is, by calculating series such as
y' t X
This measure can have a rough success, in that it largely eliminates deviations from stationarity, although a more fundamental approach would be to fit a model which would actually generate the observed nonstationarity, such as an unstable autoregression. In any case, in evaluating the series obtained after differencing, one must remember
TIME SERIES: Advanced Problems that the application of a p-fold difference, Ap, has the effect of multiplying the spectral density function of a stationary series by (2sin-|co)2p. Sample analogues Consider now the problem of inference from a sample of nconsecutive observations, x1,x2, • • • ,xn. Autocovariance function. Define the uncorrected lagged product-sum,
(31) t=3+l
If E(%0 =0, then
(32)
C; =
n —s
certainly provides an unbiased estimate of Fs and, under wide conditions, also a consistent one. However, in general the mean will be nonzero and unknown. The sample autocovariance is in such cases naturally measured by
(33)
n —s
n —s
_ *=«+!
and EJC is estimated by
(34)
65
If the series has already been corrected for the mean (so that one works with xt — x rather than Xt'), then (36) will become (37)
f B (o>) =
/ J
C«cos (cos).
n
Whether one uses formula (36) or formula (37) is not of great consequence. A constant nonzero mean can be regarded as a harmonic component of zero frequency, so the two functions (36) and (37) will differ only near the origin. The sampling variability of f n (co) does not decrease with increasing n, and f n (co) is not a consistent estimator of c/>(co). The problem of finding a consistent estimator will be discussed below. Fitting and testing autoregressive models The autoregressive model (8) is a useful trial model, since it usually explains much of the variation and often has some physical foundation. Furthermore, its test theory is typical of a much more general case. The first problem is that of the actual fitting, the estimation of the parameters ak and cr2; the second problem is that of testing the fit of the model. If the et and xt have means 0 and /JL, respectively, then the model (8) must be modified slightly to
*=(38)
ak(Xt
— yU,) = €t .
Minor modifications of (33) will be found in the literature. Expression (33) will in general provide a biased but consistent estimate of Fs with a sampling variance of the order of (n — s)-1. For a given n the variability of Cs thus increases with s; fortunately, the earlier autocovariances generally contain most of the information. In order to eliminate problems of scale, investigators sometimes work with the autocorrelation coefficient
One usually assumes the et normally distributed— not such a restrictive assumption as it appears. To a first approximation the means and variances of autocorrelations are unaffected by nonnormality (see Whittle 1954, p. 210), and estimates of parameters such as the autoregressive coefficients, a fc , should be similarly robust. For normal processes the log-likelihood of the sample X-L, x2, • • • , xn is, for large n,
f\OO Q c r J\
(39)
n /n rI g — — v_;g/v_y0
rather than with C s , but this is not essential. Spectral density function. The sample analogue of spectral density function (the periodogram, formula (21) ) was introduced before the spectral density function itself. Note from (21) that one can write
n
L = const. — -^logcr2 —
Maximizing this expression with respect to obtains the estimator
EE (40)
*
7;
one
1
—
n / J
cos (cos) (36)
n
The second approximate equality follows if one neglects the difference between the various averages (1/n) Zli^-fc (fe = 0, 1, 2, • • • , p), that is, if,
66
TIME SERIES: Advanced Problems
as is often done, an end effect is neglected. Thus, the maximum likelihood estimator of JJL is approximately the usual sample arithmetic mean, despite the dependence between observations. Inserting this estimator in (39), one finds
(41) n I 1 L =s const. —-=r\ log cr2 H 5-
cr- / •* / A
2 \
so that the maximum likelihood estimators of the remaining parameters are determined approximately by the relations
as a x2 variable with q df. In both cases large values of the test statistic are critical. Fitting and testing more general models The approximate expression (41) for the loglikelihood (maximized with respect to the mean) can be generalized to any process for which the reciprocal of the spectral density function can be expanded in a Fourier series, CO
(47)
(ft(o))^ 1 = cr~2 E y* exp (iws). 8=-<x>
The generalized expression is
(42)
= 0,
j = 1, 2, • • • , p,
(48) (43)
= iv n Note the analogue between (42) and (43) and the Yule-Walker relations (18). To test prescribed values of the ak one can use the fact that the estimators dk are asymptotically normally distributed with means ak (respectively) and a covariance matrix
( Here [ajk] denotes a p x p matrix with typical element ajK, j , k — 1, 2, • • • , p.) This result holds if the et are independently and identically distributed, with a finite fourth moment. (See Whittle 1954, p. 214.) However, a more satisfactory and more versatile approach to the testing problem is provided by use of the Wilks X-ratio. This will be described in a more general setting below; for the present, note the following uses. To test whether a given set of coefficients a l 9 a2 , • • • , ap are zero, treat
as a x2 variable with p degrees of freedom (cZf). Here erf, has been used to denote the estimator (43), emphasizing the order p assumed for the autoregression. To test whether an autoregression of order p gives essentially as good a fit as one of order p + q, treat (46)
= (n — p — g)log
2 rp+q
OA—~m s=-oo
(49)
dco.
+
4?r
In general it will be easier to calculate the sum over autocovariances in (48) than to calculate the integral over the periodogram in (49), but sometimes the second approach is taken. If the model depends on a number of parameters, O-L, 02, • • • , Op (of which cr2 will usually be one), then 0(w) will also depend on these, and the maximum likelihood estimators, # ; , are obtained approximately by maximizing either of the expressions (48) and (49). The covariance matrix of the estimators is given asymptotically by
(50) [cov
= (n - p) log
\ \
where cr2 is the "prediction variance," the conditional variance of xt given the values of xt-i, xt-.,, • • • . (See Whittle 1954.) The sum in (48) cannot really be taken as infinite; in most practical cases the coefficients ys converge reasonably fast to zero as s increases, and the sum can be truncated. Another way of writing (48) is
L ==; const. —
(44)
(45)
4-J
, _ J_
n
I
n/
L ~ const. --=- log0-2 + —
dlog< 277-
d6k
dO
(See Whittle 1954.) Thus, for the moving-average process (51)
xt = et - Pet-i ,
with |/3 < 1, one finds that -i 1 (52) E
/3|S|CS
The maximum likelihood estimator of (3 is obtained by minimizing (52), and expression (52) with /3
TIME SERIES: Advanced Problems substituted for ft provides the maximum likelihood estimator of a2 = var(e). One finds from (50) that the two estimators are asymptotically uncorrelated, with 4 var(
(53)
n
Practical techniques for the calculation of the maximum likelihood estimators in more general cases have been worked out by Durbin (1959) and Walker (1962). Tests of fit can be based upon the X-ratio criterion. Let cr2 denote the maximum likelihood estimator of o-2 when parameters 0i, 0 2 , • • • , 9,, (one of these being cr2 itself) are fitted and the values of parameters 9p+l, 9p+2, • • • , 0P+q are prescribed. Thus, cr2+(j will be the maximum likelihood estimator of
i//2=(rc-p-
og
cr
as a x2 variable with g df. Multivariate processes In few realistic analyses is one concerned with a single variable; in general, one has several, so that xt must be considered a vector of m jointly stationary variables, (xlt, x2t, • • • , xmt). There is a generalization (Whittle 1954) of expression (49) for the log-likelihood in such cases, but the only case considered here is that of a multivariate autoregression, (55)
E ak(xt-k — u) = £«,
where the nk are m x m matrices with n0 = ', and £ ( £ « ) = 0, (56)
s = t, s ^ t.
This last assumption states that the vector residuals are mutually uncorrelated but that the covariance matrix of a single vector residual is V. As before, the maximum likelihood estimator of the mean vector, u., is approximately x, and with this inserted the following generalization of (41) results: (57)
^ n ~ l^/l i V V trtv ^««'V-l** f1 M L = const. — -^-[log |V| +2-, 2-« \nj* ak^j^)i'
Here Cs is the m x m matrix whose (jk)ih element is the sample covariance of xjt and xkit_s, that is, the (jfe)th element of C, is
67
(58)
(r .Yv V I
/ ^ Jv j $
\t=S + l
II
/^J
/ \ t=1
^Itt
\
)
n —s n —s and tr A denotes the sum of the diagonal elements of a matrix A. The maximum likelihood estimators are given by (59)
E fc=0
(60) For the important case p = 1, which can be written (61)
Xt = OLXt-i + £t,
these become (62) (63)
« = C1CS1, f — •-' f V— — '-'
Estimator (62) will, of course, be modified if certain elements of a are known and need not be estimated. Tests of fit can be based on the X-ratio criterion as before, with expression (57) used for the log-likelihood. In econometric work, models of type (61) are particularly important. One minor complication is that exogenous variables may also occur in the right-hand side (see (73), below); exogenous variables are variables which are regarded as external to the system and which need not be explained—for example, in a model of a national economy, variables such as overseas prices and technical progress might be regarded as exogenous. A much more severe complication is that of simultaneity: that xt may be represented as a regression upon some of its own elements as well as upon xt-i and exogenous variables. This latter difficulty has led to an extensive literature, which will not be discussed here (for a general reference, see Johnston 1963). Regression. An important special type of multivariate process is the regression (64)
Xt = E
+
where xt (now assumed to be scalar) is regarded as linearly dependent upon a number of variables, ujt, with a stationary residual, 7]t (in general autocorrelated). The processes [ujt] may be other stationary processes, even lagged versions of the {xt} process itself, or deterministic sequences such as t" or sin (cut). Simple and unbiased estimators of the /3j are the least square estimators, b j , obtained by minimizing £"=1i?2 and determined by the linear equations
68
TIME SERIES: Advanced Problems
(65)
E bk(ujt, M fct ) = (xt, Ujt},
7=1,2, ---.r,
where the notation (66)
(xt,yt) = E xtyt
has been used for the simple product-sum. The covariance matrix of these estimators is (67) r n n
vb = [(ujt, MM)]-1 EE*
fc=0
where [ajk] indicates an r x r matrix with typical element ajk and Ts the autocovariance function of {r)t}. If the processes {ujt} are jointly stationary, then one can write
n
(68)
exp
and (67) can be rewritten
(69)
n
where M(co) = [M;/,(w)], M = M(TT) - M(-TT), and 0(oj) is the spectral density function of {T^}. This principle can be extended even to mildly nonstationary processes, such as polynomials in t (Grenander & Rosenblatt 1957). The maximum likelihood estimators, /3;, will in general have smaller variances; these estimators are obtained by minimizing the log-likelihood, (70)
L ^ const. —
log cr2 +
They obey the equation system
(71) 7 = 1,2, - - - . r . Their covariance matrix is (72)
If the residual spectral density function, <£(eo), involves unknown parameters, then expression (70) must be maximized with respect to these as well as to the (3j. This maximization can be complicated, and a simpler way of allowing for some autocorrelation in {^t} is to fit, instead of (64), a model with some autoregression and with uncorrelated residuals, p (73) E + €, =E
27T
n
If 0(cu) has the same value at all co's for which any of the M; 7 ;(ft)) change value, then the variances of the least square estimators will be asymptotically equal to those of the maximum likelihood estimators, and, indeed, the two sets of estimators may themselves be asymptotically equal. For example, (40) above shows that the maximum likelihood estimator of a mean, /*, reduces asymptotically to the least square estimator x, a great simplification.
The p* of (73) cannot be identified with the p, of (64), but they do indicate to what extent the ujt can explain xt variation. Spectral (periodogram) analysis In fitting a parametric model one obtains an estimate of the spectral density function, Dut one often wishes to obtain a direct estimate without the assumptions implied in a model, just as one uses Cg to estimate the autocovariance function, Ts . The periodogram ordinate, f n ()-), one has also, for normal processes, (75) This variance does not tend to zero with increasing n, and f n (&>) is not a consistent estimator of <£(w). That explains the very irregular appearance of the periodogram when it is graphed and the reason one
E (3jUjt, Xf-
s
—
conceives the idea of estimating $(co) by smoothing the periodogram. What one can say concerning distributions is that the quantities (76)
I,= ' / e i - ' - x
are approximately independent standard exponential variables for 7 = 1,2, • • • , N, where N < n/2. That is, the I; have approximately a joint probability density function exp(— E^i^-)Suppose now that one attempts to estimate $(«) at w = X. by an estimator of the form
(77)
E
cos (CDS),
TIME SERIES: Advanced Problems
then for a bivariate stationary process {xt, y t } the idea of a spectral density function is replaced by that of a spectral density matrix
where K(o>) is a symmetric function of period represented by a Fourier series, (78)
K(o>)=£fe,exp(za>s). 8
(86)
From (76) it follows that -
(79)
(80)
var<5(X) ~ — / TiTT J
M
s
m
ks =
m,
si > m,
0,
(82)
'
To test whether a strong peak in the periodogram indicates the presence of a harmonic component (when a delta-function would be superimposed on the spectral density function), one can use the statistic
(83)
9=
max I,
SI,
for which (84)
p(g>u) =
J!
The sum in (84) is taken for all values of j not greater than 1/u. In constructing the I; one can use a formula of type (77) to estimate
=E
tyijx
(87)
The Fourier series K(w) will be chosen as a function with a peak at the origin; as this peak grows sharper, the bias of $(A) (determined from (79) ) decreases, but the variance (determined by (80)) increases. The best choice will be a compromise between these two considerations. The question of the optimal choice of weight function has been much studied. The choice is partly a matter of convenience, depending upon whether or not one works from the periodogram, that is, upon which of the two formulas (77) is used. If one is calculating digitally, then a simple and useful smoothing formula is Bartlett's, for which
(81)
[
Suppose one wishes to investigate the dependence of {yt} upon { x t } . As an alternative to low-lag linear models such as
K(\ -
2-7T
69
-* + et
one can apply multivariate techniques to the Fourier components of the processes, at individual values of a). Thus, $ OT/ (OJ) is the variance of the Fourier component of {yt} at frequency co; one can take a linear regression of this component onto the corresponding Fourier component of { x t } and find a "residual variance," (88)
The quantity C r , y (w) is the type of correlation coefficient known as the coherency; if it approaches unity in magnitude, then the frequency components at a) of the two series are closely related. It may well happen, for example, that low frequency components of two series keep well in step, although the short-term variation corresponding to high frequency components may be almost uncorrelated between the two series. Note that (88) is the spectral density function of the process 00
I1?*} = {yt- k E= -oo bbXt-k}, where the b's are chosen to minimize var(i7). In practice the elements of the spectral density matrix must be estimated by formulas analogous to (77). A sometimes illuminating alternative to a periodogram analysis is to decompose a series into components corresponding to different frequency bands by using a number of band-pass operators of type (29) and to examine these components individually.
P. WHITTLE [See also LINEAR HYPOTHESES, article on REGRESSION; MARKOV CHAINS.] BIBLIOGRAPHY There are no completely satisfactory texts, principally because virtually nobody has a satisfactorily broad grasp of both the theory and the application of time series analysis. A person with a mathematical background may do best
70
TIME SERIES: Cycles
to read the first four chapters of Grenander & Rosenblatt 1957 and to follow this with a study of Hannan 1960. For someone with less mathematics, chapters 29 and 30 of Kendall & Stuart 1966 provide an introduction which, although not deep, is nevertheless sound and well illustrated. Jenkins 1965 surveys some of the more recent work on spectral analysis. BARTLETT, M. S. 1963 The Spectral Analysis of Point Processes. Journal of the Royal Statistical Society Series B 25:264-296. DURBIN, J. 1959 Efficient Estimation of Parameters in Moving-average Models. Biometrika 46:306-316. GRANGER, CLIVE W. J.; and HATANAKA, M. 1964 Spectral Analysis of Economic Time Series. Princeton Univ. Press. GRENANDER, ULF; and ROSENBLATT, MURRAY 1957 Statistical Analysis of Stationary Time Series. New York: Wiley. HANNAN, EDWARD J. (1960) 1962 Time Series Analysis. London: Methuen. INTERNATIONAL STATISTICAL INSTITUTE 1965 Bibliography on Time Series and Stochastic Processes. Edited by Herman Wold. Edinburgh: Oliver & Boyd. JENKINS, G. M. 1965 A Survey of Spectral Analysis. Applied Statistics 14:2-32. JOHNSTON, JOHN 1963 Econometric Methods. New York: McGraw-Hill. KENDALL, MAURICE G.; and STUART, ALAN 1966 The Advanced Theory of Statistics. Volume 3: Design and Analysis, and Time Series. New York: Hafner; London: Griffin. MACROBERT, THOMAS M. (1917) 1947 Functions of a Complex Variable. 3d ed. New York: Macmillan. SLUTSKY, EUGEN E. (1927) 1937 The Summation of Random Causes as the Source of Cyclic Processes. Econometrica 5:105-146. -> First published in Russian. Reprinted in 1960 in Slutsky's Izbrannye trudy. SYMPOSIUM ON TIME SERIES ANALYSIS, BROWN UNIVERSITY, 1962 1963 Proceedings. Edited by Murray Rosenblatt. New York: Wiley. WALKER, A. M. 1962 Large-sample Estimation of Parameters for Autoregressive Processes With Movingaverage Residuals. Biometrika 49:117-131. WHITTLE, P. 1953 The Analysis of Multiple Stationary Time Series. Journal of the Royal Statistical Society Series B 15:125-139. WHITTLE, P. 1954 Appendix. In Herman Wold, A Study in the Analysis of Stationary Time Series. 2d ed. Stockholm: Almqvist & Wiksell. WHITTLE, P. 1963 Prediction and Regulation by Linear Least-square Methods. London: English Universities Press. WOLD, HERMAN (1938) 1954 A Study in the Analysis of Stationary Time Series. 2d ed. With an Appendix by P. Whittle. Stockholm: Almqvist & Wiksell. Ill CYCLES
Cycles, waves, pulsations, rhythmic phenomena, regularity in return, periodicity—these notions reflect a broad category of natural, human, and social phenomena where cycles are the dominating feature. The daily and yearly cycles in sunlight, temperature, and other geophysical phenomena are among the simplest and most obvious instances.
Regular periodicity provides a basis for prediction and for extracting other useful information about the observed phenomena. Nautical almanacs with their tidal forecasts are a typical example. Medical examples are pulse rate as an indicator of cardiovascular status and the electrocardiograph as a basis for analysis of the condition of the heart. The study of cyclic phenomena dates from prehistoric times, and so does the experience that the area has dangerous pitfalls. From the dawn of Chinese history comes the story that the astronomers Hi and Ho lost their heads because they failed to forecast a solar eclipse (perhaps 2137 B.C.). In 1929, after some twelve years of promising existence, the Harvard Business Barometer (or Business Index) disappeared because it failed to predict the precipitous drop in the New York stock market. Cyclic phenomena are recorded in terms of time series. A key aspect of cycles is the degree of predictability they give to the time series generated. Three basic situations should be distinguished: (a) The cycles are fixed, so that the series is predictable over the indefinite future. (b) The cycles are partly random, so that the series is predictable only over a limited future. (c) The cycles are spurious—that is, there are no real cycles—and the series is not predictable. For the purposes of this article the term "cycle" is used in a somewhat broader sense than the strict cyclic periodicity of case (a). Limited and unlimited predictability The fundamental difference between situations (a) and (b) can be illustrated by two simple cases. The scheme of "hidden periodicities." Suppose that an observed time series is generated by two components. The first is strictly periodic, with period length p, so that its value at time t + p is equal to its value at time t. The second component, superimposed upon the first, is a sequence of random (independent, identically distributed) elements. Thus, each term of the observed series can be represented as the sum of a periodic term and a random one. Tidal water is a cyclic phenomenon where this model applies quite well (see Figure 1). Here the observed series is the measured water level at Dover, the strictly periodic component represents the lunar cycle, 12 hours and 50 minutes in length (two maxima in one lunar day), and the random elements are the irregular deviations caused by storms, random variations in air pressure, earthquakes, etc. The periodic component provides a prediction—
TIME SERIES: Cycles
71
Predicted by model Observed
figure 1 — Level of tidal water at Dover, 6 daysi * Hypothetical data.
an unbiased predicted value for a future time with expectation equal to that future value of the periodic component, and with prediction error equal to the random element. The difficulty is that the periodic component is not known and must be estimated empirically. A simple and obvious method is that of Buys Ballot's table; each point on the periodic component is estimated by the average of several points on the observed series, separated in time by the length of the period, p, where p either is known or is assessed by trial and error. The larger is the residual as compared to the cyclic component, the longer is the series needed to estimate with confidence the cyclic component. The approach of hidden periodicities may be extended, with two or more periodic components being considered. Tidal water again provides a typical illustration. In addition to the dominating lunar component, a closer fit to the data is obtained by considering a solar component with period 183 days. In view of its simplicity and its many important applications, it is only natural that the approach involving strictly periodic components is of long standing. A distinction must be made, however, between formal representation of a series (which is always possible), on the one hand, and prediction, on the other. Under general conditions, any series, even a completely random one, can be represented by a sum of periodic components plus a
residual, and if the number of periodic components is increased indefinitely, the residual can be made as small as desired. In particular, if each of the periodic components is a sine or a cosine curve (a sinusoid), then the representation of the observed series is called a spectral representation. Such a representation, it is well to note, may be of only limited use for prediction outside the observed range, because if the observed range is widened, the terms of the representation may change appreciably. In the extreme case when the observations are all stochastically independent, the spectral representation of the series is an infinite sum of sinusoids; in this case neither the spectral representation nor alternative forecasting devices provide any predictive information. Irregular cycles. Until rather recently (about 1930), the analysis of oscillatory time series was almost equivalent to the assessment of periodicities. For a long time, however, it had been clear that important phenomena existed that refused to adhere to the forecasts based on the scheme of hidden periodicities. The most obvious and challenging of these was the sequence of some twenty business cycles, each of duration five to ten years, between 1800 and 1914. Phenomena with irregular cycles require radically different methods of analysis. The scheme of "disturbed periodicity." The breakthrough in the area of limited predictability came with Yule's model (1927) for the irregular
72
TIME SERIES: Cycles
Disturbances plotted as de from the observed series
Figure 2 — Sunspof intensity Source: Adapted from Yule 1927.
11-year cycle of sunspot intensity (see Figure 2). Yule interpreted the sunspot cycle as similar to the movement of a damped pendulum that is kept in motion by an unending stream of random shocks. [See the biography of YULE.] The sharp contrast between the scheme of hidden periodicities and the scheme of disturbed periodicity can now be seen. In the hidden periodicities model the random elements are superimposed upon the cyclic component(s) without affecting or disturbing their strict periodicity. In Yule's model the
series may be regarded as generated by the random elements, and there is no room for strict periodicity. (Of course, the two types can be combined, as will be seen.) The deep difference between the two types of model is reflected in their forecasting properties (see Figure 3). The time scales for the two forecasts have here been adjusted so as to give the same period. In the hidden-periodicities model the forecast over the future time span has the form of an undamped sinusoid, thus permitting an effec-
Disturbed periodicity model Hidden periodicity model
Figure 3 — Forecasting the future on the basis of the past
TIME SERIES: Cycles tive forecast over indefinitely long spans when the model is correct. In Yule's model the forecast is a damped sinusoid, which provides effective information over limited spans, but beyond that it gives only the trivial forecast that the value of the series is expected to equal the unconditional over-all mean of the series. Generalizations. The distinction between limited and unlimited predictability of an observed times series goes to the core of the probability structure of the series. In the modern development of time series analysis on the basis of the theory of stochastic processes, the notions of predictability are brought to full significance. It can be shown that the series yt under very general conditions allows a unique representation, (1)
yt
known as predictive decomposition, where (a) the two components are uncorrelated, (Z?) <&t is deterministic and ^t is nondeterministic, and (c) the nondeterministic component allows a representation of the Yule type. In Yule's model no O« component is present. In the hidden-periodicities model <£>i is a sum of sinusoids, while tyt is the random residual. Generally, however, <$>t, although deterministic in the prediction sense, is random. The statistical treatment of mixed models like (1) involves a variety of important and challenging problems. Speaking broadly, the valid assessment of the structure requires observations that extend over a substantial number of cycles, and even then the task is difficult. A basic problem is to test for and estimate a periodic component on the supplementary hypothesis that the ensuing
20.0
73
residual allows a nondeterministic representation, or, more generally, to perform a simultaneous estimation of the two components. A general method for dealing with these problems has been provided by Whittle (1954); for a related approach, see Allais (1962). Other problems with a background in this decomposition occur in the analysis of seasonal variation [see TIME SERIES, article on SEASONAL ADJUSTMENT]. Other stochastic models. Since a tendency to cyclic variation is a conspicuous feature of many phenomena, stochastic models for their analysis have used a variety of mechanisms for generating apparent or genuine cyclicity. Brief reference will be made to the dynamic models for (a) predatorprey populations and (£>) epidemic diseases. In both cases the pioneering approaches were deterministic, the models having the form of differential equation systems. The stochastic models developed at a later stage are more general, and they cover features of irregularity that cannot be explained by deterministic methods. What is of special interest in the present context is that the cycles produced in the simplest deterministic models are strictly periodic, whereas the stochastic models produce irregular cycles that allow prediction only over a limited future. Figure 4 refers to a stochastic model given by M. S. Bartlett (1957) for the dynamic balance between the populations of a predator—for example, the lynx—and its prey—for example, the hare. The data of the graph are artificial, being constructed from the model by a Monte Carlo experiment. The classic models of A. J. Lotka and V. Volterra are deterministic, and the ensuing cycles take the form
24.0
Figure 4 — Predator-prey populations according to a stochastic model Source: Bartlett 1957, p. 37.
74
TIME SERIES: Cycles
NUMBER OF CASES
4,000
1910
Figure 5 — Paralytic cases of poliomyelitis, Sweden 1905—1962 Source: Unpublished data.
of sinusoids. The cyclic tendency is quite pronounced in Figure 4, but at the same time the development is affected by random features. After three peaks in both populations, the prey remains at a rather low level that turns out to be critical for the predator, and the predator population dies out. The peaks in Figure 5 mark the severe spells of poliomyelitis in Sweden from 1905 onward. The cyclic tendency is explained, on the one hand, by the contagious nature of the disease and, on the other, by the fact that slight infections provide immunity, so that after a nationwide epidemic it takes some time before a new group of susceptibles emerges. The foundations for a mathematical theory of the dynamics of epidemic diseases were laid by Kermack and McKendrick (1927), who used a deterministic approach in terms of differential equations. Their famous threshold theorem states that only if the infection rate, p, is above a certain critical value, p 0 , will the disease flare up in epidemics. Bartlett (1957) and others have developed the theory in terms of stochastic models; a stochastic counterpart to the threshold theorem has been provided by Whittle (1955). Bartlett's predator-prey model provides an example of how a cyclic deterministic model may become evolutive (nonstationary) when stochasticized, while Whittle's epidemic model shows how
an evolutive deterministic model may become stationary. Both of the stochastic models are completely nondeterministic; note that the predictive decomposition (1) extends to nonstationary processes. The above examples have been selected so as to emphasize that there is no sharp demarcation between cycles with limited predictability and the spurious periodicity of phenomena ruled by randomness, where by pure chance the variation may take wavelike forms, but which provides no basis even for limited predictions. Thus, if a recurrent phenomenon has a low rate of incidence, say A per year, and the incidences are mutually independent (perhaps a rare epidemic disease that has no aftereffect of immunity), the record of observations might evoke the idea that the recurrences have some degree of periodicity. It is true that in such cases there is an average period of length 1/X between the recurrences, but the distance from one recurrence to the next is a random variable that cannot be forecast, since it is independent of past observations. A related situation occurs in the summation of mutually independent variables. Figure 6 shows a case in point as observed in a Monte Carlo experiment with summation of independent variables (Wold 1965). The similarity between the three waves, each representing the consecutive additions
TIME SERIES: Cycles
75
—1,500 -
-2,000 1800
1850
1900
Figure 6 — Spurious cycles and Kondratieff waves Sources: Consecutive sums, Wold 1965, p. 25; wholesale prices, Piatier 1961.
of some 100,000 variables, is rather striking. Is it really due to pure chance? Or is the computer simulation of the "randomness" marred by some slip that has opened the door to a cyclic tendency in the ensuing sums? (For an amusing discussion of related cases, see Cole's "Biological Clock in the Unicorn" 1957.) Figure 6 also gives, in the series of wholesale prices in Great Britain, an example of "Kondratieff waves"—the much discussed interpretation of economic phenomena as moving slowly up and down in spells of some fifty years. Do the waves embody genuine tendencies to long cycles, or are they of a spurious nature? The question is easy to pose but difficult or impossible to answer on the basis of available data. The argument that the "Kondratieff waves" are to a large extent parallel in the main industrialized countries carries little weight, in view of international economic connections. The two graphs have been combined in Figure 6 in order to emphasize that with regard to waves of long duration it is always difficult to sift the wheat of genuine cycles from the chaff of spurious periodicity. [See the biography of KONDRATIEFF.] Genuine versus spurious cycles Hypothesis testing. Cycles are a specific feature in many scientific models, and their statistical assessment usually includes (a) parameter estimation for purposes of quantitative specification of the model, and (£>) hypothesis testing for purposes of establishing the validity of the model and thereby of the cycles. In modern statistics it is often (sometimes tacitly) specified that any method under (a) should be supplemented by an appropriate device under (b). Now, this principle is easy to state, but
it is sometimes difficult to fulfill, particularly with regard to cycles and related problems of time series analysis. The argument behind this view may be summed up as follows, although not everyone would take the same position: (i) Most of the available methods for hypothesis testing are designed for use in controlled experiments—the supreme tool of scientific model building—whereas the assessment of cycles typically refers to nonexperimental situations. (ii) The standard methods for both estimation and hypothesis testing are based on the assumption of independent replications. Independence is on the whole a realistic and appropriate assumption in experimental situations, but usually not for nonexperimental data. (iii) Problems of point estimation often require less stringent assumptions than those of interval estimation and hypothesis testing. This is frequently overlooked by the methods designed for experimental applications, because the assumption of independence is usually introduced jointly for point estimation, where it is not always needed, and for hypothesis testing, where it is always consequential. (if) It is therefore a frequent situation in the analysis of nonexperimental data that adequate methods are available for estimation, but further assumptions must be introduced to conduct tests of hypotheses. It is even a question whether such tests can be performed at all in a manner corresponding to the standard methods in experimental analysis, because of the danger of specification errors that mar the analysis of nonexperimental data. (f) Standard methods of hypothesis testing in
76
TIME SERIES: Cycles
controlled experiments are thus of limited scope in nonexperimental situations. Here other approaches come to the fore. It will be sufficient to mention predictive testing—the model at issue is taken as a basis for forecasts, and in due course the forecasts are compared with the actual developments. Reporting of nonexperimental models should always include a predictive test. The following example is on the cranky side, but it does illustrate that the builder of a nonexperimental model should have le courage de son modele to report a predictive test, albeit in this case the quality of the model does not come up to the model builder's courage. The paper (Lewin 1958) refers to two remarkable events—the first permanent American settlement at Jamestown, Virginia, in 1607 and the Declaration of Independence in 1776 —and takes the 169 years in between as the basic "cycle." After another 84y2 years (% of the basic cycle) there is the remarkable event of the Civil War, in 1861; after 56 more years (y3 of the cycle) there is the beginning of the era of world wars in 1917; after 28 more years (y6 of the cycle) there is the atomic era with the first bomb exploded in 1945. The paper, published in 1958, ends with the following predictive statement: "The above relation to the basic 169 year cycle of yl5 y2, y3, % is a definite decreasing arithmetic progression where the sum of all previous denominators becomes the denominator of the next fraction. To continue this pattern and project, we have the 6th cycle—1959, next U.S. Epochal Event—14 year lapse—y12 of 169 years" (Lewin 1958, pp. 11-12). The 1959 event should have been some major catastrophe like an atomic war, if I have correctly understood what the author intimates between the lines in the first part of his article. It is well to note that this paper, singled out here as an example, is far from unique. Cycles have an intrinsic fascination for the human mind. A cursory scanning of the literature, particularly Cycles, the journal of the Foundation for the Study of Cycles, will suffice to show that in addition to the strictly scientific contributions, there is a colorful subvegetation where in quality and motivation the papers and books display all shades of quasiscientific and pseudoscientific method, down to number mysticism and other forms of dilettantism and crankiness, and where the search for truth is sometimes superseded by drives of self-realization and self-suggestion, not to speak of unscrupulous money-making. The crucial distinction here is not between professional scientists and amateurs. It is all to the good if the search for truth is strengthened by many modes of motivation. The sole valid
criterion is given by the general standards of scientific method. Professionals are not immune to selfsuggestion and other human weaknesses, and the devoted work of amateurs guided by an uncompromising search for truth is as valuable here as in any other scientific area. Further remarks Cycles are of key relevance in the theory and application of time series analysis; their difficulty is clear from the fact that it is only recently that scientific tools appropriate for dealing with cycles and their problems have been developed. The fundamental distinction between the hidden-periodicity model, with its strict periodicity and unlimited predictability, and Yule's model, with its disturbed periodicity and limited predictability, could be brought to full significance only after 1933, by the powerful methods of the modern theory of stochastic processes. On the applied side, the difficulty of the problems has been revealed in significant shifts in the very way of viewing and posing the problems. Thus, up to the failure of the Harvard Business Barometer the analysis of business cycles was essentially a unirelational approach, the cycle being interpreted as generated by a leading series by way of a system of lagged relationships with other series. The pioneering works of Jan Tinbergen in the late 1930s broke away from the unirelational approach. The models of Tinbergen and his followers are multirelational, the business cycles being seen as the resultant of a complex system of economic relationships. [See BUSINESS CYCLES; DISTRIBUTED LAGS.] The term "cycle," when used without further specification, primarily refers to periodicities in time series, and that is how the term is taken in this article. The notion of "life cycle" as the path from birth to death of living organisms is outside the scope of this presentation. So are the historical theories of Spengler and Toynbee that make a grandiose combination of time series and life cycle concepts, seeing human history as a succession of cultures that are born, flourish, and die. Even the shortest treatment of these broad issues would carry us far beyond the realm of time series analysis; this omission, however, must not be construed as a criticism. [For a discussion of these issues, see PERIODIZATION.] Cycles vs. innovations. The history of human knowledge suggests that belief in cycles has been a stumbling block in the evolution of science. The philosophy of the cosmic cycle was part of Stoic and Epicurean philosophy: every occurrence is a recurrence; history repeats itself in cycles, cosmic
TIME SERIES: Cycles cycles; all things, persons, and phenomena return exactly as before in cycle after cycle. What is it in this strange theory that is of such appeal that it should have been incorporated into the foundations of leading philosophical schools and should occur in less extreme forms again and again in philosophical thinking through the centuries, at least up to Herbert Spencer, although it later lost its vogue? Part of the answer seems to be that philosophy has had difficulties with the notion of innovation, having, as it were, a horror innovationum. If our philosophy leaves no room for innovations, we must conclude that every occurrence is a recurrence, and from there it is psychologically a short step to the cosmic cycle. This argument being a blind alley, the way out has led to the notions of innovation and limited predictability and to other key concepts in modern theories of cyclic phenomena. Thus, in Yule's model (Figure 2) the random shocks are innovations that reduce the regularity of the sunspot cycles so as to make them predictable only over a limited future. More generally, in the predictive decomposition (1) the nondeterministic component is generated by random elements, innovations, and the component is therefore only of limited predictability. Here there is a close affinity to certain aspects of the general theory of knowledge. We note that prediction always has its cognitive basis in regularities observed in the past, cyclic or not, and that innovations set a ceiling to prediction by scientific methods. [See TIME SERIES, article on ADVANCED PROBLEMS.]
77
— X cos (tit + fji sin cot,
(4) while
(5) is a sequence of random variables, independent of one another and of xt, and identically distributed with zero mean, E(e) = 0, and standard deviation o-(e). For any X and ft the sinusoid (4) is periodic, xt+p — xt, with period p = 2-Tr/co, and satisfies the difference equation (6)
— *2,pXt-i + Xt-z — 0,
where p = cos co. The sinusoid xt makes a forecast of yt+if over any prediction span k (of course, for real prediction the values of X, //., and p must be known or assumed), (7)
fe = 1, 2,
pred yt+k = xt+k ,
giving the prediction error A(t, fe) = yt+k
= €t+1c.
Hence the forecast (7) is unbiased and has the same mean-square deviation for all t and k,
(8a)
E(A) = 0,
Further light can be cast on the rationale of the forecast (7) by considering the coefficients X, p as limiting regression coefficients of yt on cos tot and sin cot :
X = lim — > yy t cos cot; T
Mathematical analysis The verbal exposition will now, in all brevity, be linked up with the theory of stochastic processes. The focus will be on (a) the comparison between the schemes of "hidden periodicities" and "disturbed harmonics" and (b) spectral representation versus predictive decomposition. Write the observed series
(2)
'~,yt-i,yt,yt*, • • - ,
taking the observations as deviations from the mean and letting the distance between two consecutive observations serve as time unit. Unless otherwise specified, the series (2) is assumed to be of finite length, ranging from t = 1 to t = n. Hidden periodicities. With reference to Figure 1, consider first the case of one hidden periodicity. The observed series yt is assumed to be generated by the model (3)
yt -xt
= 0,±l, ±2,
Where xt, the "hidden periodicity," is a sinusoid,
n^
n £-j
jj, — lim — N yt sin cot. n->oo fl
<
Disturbed periodicity. trated in Figure 2 is (9)
A
Yule's model as illus-
0 < y < 1,
yt -
where the notation makes for easy comparison with model (3): (a) In (3) the disturbances, et, are superimposed on the periodic component, xt, while yt in (9) is entirely generated by current and past disturbances, (10a)
yt = €t + a^t-i + a2€t-2 + • ' • ,
where «i = 2p (a0 — 1) and (lOfo)
ak = 2pak-i - y 2 a fc _ 2 ,
k = 2, 3, • • • .
Hence in (3) the correlation coefficient (11)
r(e t + f c , ? / 0 = 0
78
TIME SERIES: Cycles
Model (9)
Figure 7 — The standard deviation, a(A), of the prediction error as a function of the range, k, spanned by the forecast
for all k •£ 0 and t, while (9) gives (11) for all k > 0 and t. (b) (See Figure 3.) If the future disturbances, et+jc, were absent, yt+k in (3) would reduce to xt+k and thus make an undamped sinusoid (4), while yt+k in (9), say, y*t+k, would satisfy the difference equation
(12)
=o with initial values y* = yt,y]_^ = yt_lt giving ( 13a)
(13b)
z/;+fc = ak€t + a^e^ + ••• , fe)
k)].
Hence, y*t+k would make a damped sinusoid with damping factor 7, frequency to given by cos o> = p/y, and period 2?r/aj, and where the two initial values yt, yt-i determine the parameters X*, ft*. Since the difference equations in (lOfo) and (12) are the same except for the initial values, the form (13fo) of a damped sinusoid extends to ak, except that X*, /x* will be different. (c) In (3) the undamped sinusoid, xt, provides a forecast of yt+k that is unbiased in the sense of (8a). In (9) the damped sinusoid, y*t+k, provides a forecast of yt+k,
(14) where
(d) Figure 7 illustrates that in model (3) the prediction error has constant mean square deviation for all spans k. In (9) it has mean square deviation (16)
and thus is increasing with k. Formulas (8Z?) and (16) show that in (3) the disturbances, et, do not interfere with the sinusoid component, xt, while in (9) they build up the entire process, yt. (e) The fundamental difference between models (3) and (9) is further reflected in the correlogram of yt,
In (3) the correlogram is an undamped sinusoid (4), in (9) a damped sinusoid (13b). Hence, the two correlograms are curves of the same types as those shown in Figure 3. The graph actually shows the two correlograms, not any two forecasts. Generalizations. The scheme (3) extends to several hidden periodicities,
(17)
v — — Z-i V •it
cos co;t +
sin coj
giving the same prediction formulas (7)-(8). Yule's model (9) extends to the general scheme of autor egression,
(18)
showing that the forecast (14) is unbiased in the sense of the conditional expectation of yt+i< as conditioned by the current and past observations
[E(A 2 )]* = (1 + a\ + •• • + al Jo^e)
yt
giving expansions of type (10a) and (13a) and a prediction like (15a). Note that formula (17) is a composite undamped swinging. The difference equations (6) and (12) extend from order 2 to order 2h. The extension of (13b) gives y*uk as a composite damped swinging.
TIME SERIES: Cycles Stationary stochastic processes. The above models are fundamental cases of stationary stochastic processes. The observed series (2) is seen as a realization of the process. Station arity means that for any fixed n the random variables r]t+i , • • • , i?*+n that generate the observed values yt+i , • • • , yt+n have a joint probability distribution that is independent of t. In this interpretation a realization corresponds to a sampling point in an ?z-dimensional distribution, and the parameters X, JJL in model (3) are random variables that vary from one realization (2) of the process to another. Two general representation theorems for stationary stochastic processes will be quoted briefly. Spectral representation. The basic reference for spectral representation is Cramer (1940). Any real-valued stationary process 7jt allows the representation (19)
2 r =— /
where X ( « ) , / A ( W ) are real processes with zero means and zero intercorrelations, with increments dX(w), dft(w) which have zero means and zero intercorrelations, and with variances
where V(w) is the cumulative spectrum of the process. Conversely, X(«) and /*(w) can be represented in terms of 771 , Sin
tot
and correspondingly for ^t(w). (Here l.i.m. signifies limit in the mean; l.i.m. may exist even if the ordinary limit does not.) Applying the representation (19) to model (17), the spectrum V(«) has discontinuities at the points &> = a>i , while the component et corresponds to the continuous part of the spectrum. As applied to models (9) and (18), the representation (19) gives a spectrum V(w) that is everywhere continuous. Broadly speaking, the spectral representation (19) is useful for analyzing the cyclical properties of the series (2) inside the range of observations, while it is of operative use for prediction outside the observation range only in the case when V(w) presents one or more discontinuities. Predictive decomposition. The basic reference for predictive decomposition is Wold (1938). Any stationary process 771 with finite variance allows the
79
decomposition (1). The deterministic component, Oi, can be linearly predicted to any prescribed accuracy over any given span k on the basis of the past observations yt-i, yt-2, '' • • The nondeterministic component, ^, allows a representation of type (10a) with ]C«f < °°, correlation properties in accordance with (11) for all k > 0 and t, and hence a prediction of type (13a). The ensuing prediction for rjt+k, pred r)t+k = ®t+k + pred yt+*, has least square properties in accordance with (16), and if all joint probability distributions are normal (or have linear regressions), the prediction will be unbiased in the sense of (15b ). In models (3) and (17), xt is the deterministic component and et the nondeterministic component. Models (9) and (18) are completely nondeterministic. Levels D, M, N in Figure 7 refer to models that are completely deterministic, mixed, and completely nondeterministic, respectively, each level indicating the standard deviation of the prediction error for indefinitely large spans k. Making use of the analytical methods of spectral analysis, Kolmogorov (1941) and Wiener (1942) have developed the theory of the decomposition (1) and the nondeterministic expansion (10). This article aims at a brief orientation to the portrayal of cycles as a broad topic in transition. Up to the 1930s the cyclical aspects of time series were dealt with by a variety of approaches, in which nonscientific and prescientific views were interspersed with the sound methods of some few forerunners and pioneers. The mathematical foundations of probability theory as laid by Kolmogorov in 1933 gave rise to forceful developments in time series analysis and stochastic processes, bringing the problems about cycles within the reach of rigorous treatment. In the course of the transition, interest in cycles has been superseded by other aspects of time series analysis, notably prediction and hypothesis testing. For that reason, and also because cyclical features appear in time series of very different probability structures, it is only natural that cycles have not (or not as yet) been taken as a subject for a monograph. HERMAN WOLD [See also BUSINESS CYCLES and PREDICTION AND FORECASTING, ECONOMIC.] BIBLIOGRAPHY
ALLAIS, MAURICE 1962 Test de periodicite: Generalisation du test de Schuster au cas de series temporelles autocorrelees dans Fhypothese d'un processus de per-
80
TIME SERIES: Seasonal Adjustment
turbations aleatoires d'un systeme stable. Institut International de Statistique, Bulletin 39, no. 2:143193. BARTLETT, M. S. 1957 On Theoretical Models for Competitive and Predatory Biological Systems. Biometrika 44:27-42. BURKHARDT, H. 1904 Trigonometrische Interpolation: Mathematische Behandlung periodischer Naturerscheinungen mit Einschluss ihrer Anwendungen. Volume 2, pages 643-693 in Enzyklopddie der mathematischen Wissenschaften. Leipzig: Teubner. -> The encyclopedia was also published in French. BUYS BALLOT, CHRISTOPHER H. D. 1847 Les changemens periodiques de temperature dependants de la nature du soleil et de la lune mis en rapport avec le prognostic du temps deduits d'observations Neerlandaises de 1729 a 1846. Utrecht (Netherlands): Kemink. COLE, LAMONT C. 1957 Biological Clock in the Unicorn. Science 125:874-876. CRAMER, HARALD 1940 On the Theory of Stationary Random Processes. Annals of Mathematics 2d Series 41:215-230. Cycles. -» Published since 1950 by the Foundation for the Study of Cycles. See especially Volume 15. KERMACK, W. O.; and MCKENDRICK, A. G. 1927 A Contribution to the Mathematical Theory of Epidemics. Royal Society of London, Proceedings Series A 113: 700-721. KERMACK, W. O.; and MCKENDRICK, A. G. 1932 Contributions to the Mathematical Theory of Epidemics. Part 2: The Problem of Endemicity. Royal Society of London, Proceedings Series A 138:55-83. KERMACK, W. O.; and MCKENDRICK, A. G. 1933 Contributions to the Mathematical Theory of Epidemics. Part 3: Further Studies of the Problem of Endemicity. Royal Society of London, Proceedings Series A 141: 94-122. KEYSER, CASSIUS J. (1922) 1956 The Group Concept. Volume 3, pages 1538-1557 in James R. Newman, The World of Mathematics: A Small Library of the Literature of Mathematics From A'h-Mose the Scribe to Albert Einstein. New York: Simon & Schuster. -» A paperback edition was published in 1962. KOLMOGOROV, A. N. (1941) 1953 Sucesiones estacionarias en espacios de Hilbert (Stationary Sequences in Hilbert Space). Trabajos de estadistica 4:55-73, 243-270. -> First published in Russian in Volume 2 of the Biulleten Moskovskogo Universiteta. LEWIN, EDWARD A. 1958 1959 and a Cyclical Theory of History. Cycles 9:11-12. MITCHELL, WESLEY C. 1913 Business Cycles. Berkeley: Univ. of California Press. -> Part 3 was reprinted by University of California Press in 1959 as Business Cycles and Their Causes. PIATIER, ANDRE 1961 Statistique et observation economique. Volume 2. Paris: Presses Universitaires de France. SCHUMPETER, JOSEPH A. 1939 Business Cycles: A Theoretical, Historical, and Statistical Analysis of the Capitalist Process. 2 vols. New York and London: McGraw-Hill. -> An abridged version was published in 1964. SCHUSTER, ARTHUR 1898 On the Investigation of Hidden Periodicities With Application to a Supposed 26 Day Period of Meteorological Phenomena. Terrestrial Magnetism 3:13-41.
TINBERGEN, J. 1940 Econometric Business Cycle Research. Review of Economic Studies 7:73-90. WHITTAKER, E. T.; and ROBINSON, G. (1924) 1944 The Calculus of Observations: A Treatise on Numerical Mathematics. 4th ed. Princeton, N.J.: Van Nostrand. WHITTLE, P. 1954 The Simultaneous Estimation of a Time Series: Harmonic Components and Covariance Structure. Trabajos de estadistica 3:43-57. WHITTLE, P. 1955 The Outcome of a Stochastic Epidemic—A Note on Bailey's Paper. Biometrika 42: 116-122. WIENER, NORBERT (1942) 1964 Extrapolation, Interpolation and Smoothing of a Stationary Time Series, With Engineering Applications. Cambridge, Mass.: Technology Press of M.I.T. -» First published during World War n as a classified report to Section D2, National Defense Research Committee. A paperback edition was published in 1964. WOLD, HERMAN (1938) 1954 A Study in the Analysis of Stationary Time Series. 2d ed. Stockholm: Almqvist & Wiksell. WOLD, HERMAN 1965 A Graphic Introduction to Stochastic Processes. Pages 7-76 in International Statistical Institute, Bibliography on Time Series and Stochastic Processes. Edited by Herman Wold. Edinburgh: Oliver & Boyd. WOLD, HERMAN 1967 Time as the Realm of Forecasting. Pages 525-560 in New York Academy of Sciences, Interdisciplinary Perspectives on Time. New York: The Academy. YULE, G. UDNY 1927 On a Method of Investigating Periodicities in Disturbed Series, With Special Reference to Wolfer's Sunspot Numbers. Royal Society, Philosophical Transactions Series A 226:267-298. IV
SEASONAL ADJUSTMENT
The objective of economic time series analysis is to separate underlying systematic movements in such series from irregular fluctuations. The systematic movements in the economy—the signals— reveal seasonal patterns, cyclical movements, and long-term trends. The irregular fluctuations—the noise—are a composite of erratic real world occurrences and measurement errors. There are definite advantages in breaking down these two major factors into their respective components. Separation of the systematic components provides a better basis for studying causal factors and forecasting changes in economic activity. Separation of the irregular components provides a basis for balancing the costs of reducing statistical errors against the resultant gains in accuracy. This article is concerned with one of the systematic components, seasonal variations, especially how to measure and eliminate it from economic time series. The relationships between seasonal variations and the other components are also described, with special reference to economic time series in the United States. Characteristics of seasonal variations in different countries, regions, and industries are not discussed.
TIME SERIES: Seasonal Adjustment The seasonal factor. The seasonal factor is the composite effect of climatic and institutional factors and captures fluctuations that are repeated more or less regularly each year. For example, the aggregate income of farmers in the United States displays a definite seasonal pattern, rising steadily each year from early spring until fall, then dropping sharply. Most economic series contain significant seasonal fluctuations, but some (stock prices, for example) contain virtually none. Changing weather conditions from one season to another significantly affect activities in such industries as construction and agriculture. Movements in a series resulting from this factor are referred to as climatic variations. Differences from year to year in the intensity of weather conditions during each season introduce an irregular element in the pattern of these movements. For example, a very cold winter will have a greater effect on some industries than a winter with average temperature and precipitation. Intermingled with the effects of variations in climatic conditions are the effects of institutional factors. Thus, the scheduling of the school year from September to June influences the seasonal pattern of industries associated with education, and the designation of tax dates by federal and state authorities affects retail sales and interest rates. Holidays also help to shape the pattern of activities over 12-month periods. The effects of Christmas and Easter upon the volume of business are widespread, but most direct and largest upon retail sales. Other holidays, such as July 4, Memorial Day, and Labor Day, have a like but generally lesser effect. The number of shopping days between Thanksgiving and Christmas may have some effect upon the volume of Christmas shopping. The effects of certain of these holidays (Easter, Labor Day, and Thanksgiving Day) upon the activities of certain months is uneven, because they do not fall on the same day of the month each year; the dates upon which they fall affect the distribution of activity between two months. The movements resulting from this factor are referred to as holiday variations (and are illustrated by curve 2 of Figure 1, below). The use of the Gregorian calendar, which provides for months of different lengths and calendar composition, has a special effect upon monthly fluctuations. This effect is due mainly to differences in the character and volume of business activity on Saturdays and Sundays and the variations in the number of these days in the same month in different years. From this point of view there are more than 12 types of months; for example, there are
81
seven different types of months with 31 days, one starting with each different day of the week. The movements resulting from this factor are referred to as calendar, or trading day, variations (and are illustrated by curve 3 of Figure 1, below). Another type of variation that occurs regularly each year arises from the introduction of new models, particularly in the automobile industry. Although new models are introduced at about the same time each year, the exact date is not predetermined and is separately decided upon by the various companies in the industry. To some extent, these decisions are based upon economic conditions rather than climatic and institutional factors. The movements resulting from this factor are referred to as model year variations. This complex of factors yields an annual cycle in many economic series, a cycle that is recurrent and periodic. The pattern varies over time, partly because calendar variations are not the same from year to year, but mainly because of changes in the relative importance of firms, industries, and geographic areas. Thus, the seasonal pattern of construction in the United States has been changing as a result of the increasing importance of the south as compared with the north. The annual cycle is not divisible into shorter periods, because any period less than a year will not contain all the factors that determine the annual cycle; for example, holidays are spaced unevenly over the full 12 months, the school schedule spans most of the year, and the tax collection program has a different impact in the various quarters. Unlike business cycle fluctuations, the timing and pattern of seasonal movements in various economic processes, such as production, investment, and financial markets, are not highly correlated. The role of the seasonal factor. The pattern and amplitude of the seasonal factor are of considerable interest to economists and businessmen. Reducing the waste of resources that are left idle during seasonal low months is one of the targets of economists concerned with accelerating economic growth. Knowledge of the seasonal pattern in the sales of their products (as well as in the materials they purchase) is helpful to companies in determining the level of production that is most efficient in the light of storage facilities, insurance costs, and the risks of forced selling. It can be used to reduce overordering, overproduction, and overstocking. Some companies forecast only their annual total sales. Then, on the basis of this single forecast, they plan their production schedules, determine their inventory and price policies, and establish quotas for their salesmen. For the companies in
82
TIME SERIES: Seasonal Adjustment
this group that also experience large seasonal fluctuations, a good first approximation of the monthly pattern of sales can be obtained by prorating the estimated annual total over the months according to the pattern shown by the seasonal factors. A more refined method involves forecasting the cyclical and trend movements for each of the 12 months ahead and applying the seasonal factors to the forecasts. The seasonal factors can be of further value in making shorter-term forecasts as the year progresses. To keep the forecasts current, the original estimates of the cyclical and trend movements can be revised each month in the light of experience to date, and the seasonal factors can be applied to the revised forecasts. But the principal interest in economic time series is usually the longer-term cyclical and trend movements. The cycle consists of cumulative and reversible movements characterized by alternating periods of expansion and contraction. It lasts three to four years, on the average. The trend reflects the still longer-run movements, lasting many years. The nature of the interest in these longer-term movements can be illustrated by the situation in the spring of 1961. About a year earlier a recession had begun in the United States. Although the March and April 1961 data for most economic time series were below the levels reached in March and April 1960, they were higher than in the immediately preceding months. The question was whether the recent improvements were larger or smaller than normal seasonal changes. In forecasting the pattern in the months ahead, it was crucial to know whether the economy had entered a new cyclical phase— whether the economy had been rising or declining to the levels of March and April 1961. An accurate answer to this question was required to determine the economic programs appropriate at the time. If the underlying movements of the economy were continuing downward, anti-recession measures were in order. But if a reversal had taken place, a different policy was needed. A mistaken reading of statistical trends at such a critical juncture could be costly to the economy; one kind of error could lead to increased unemployment; the other, to eventual inflation. Cyclical movements are shown more accurately and stand out more clearly in data that are seasonally adjusted. Seasonally adjusted data not only avoid some of the biases to which the widely used same-month-year-ago comparisons are subject but also reveal cyclical changes several months earlier than such comparisons do. Seasonally adjusted series, therefore, help the economic statistician to make more accurate and more prompt diagnoses of current cyclical trends.
Figure 1, computed by the ratio-to-moving-average method (discussed below) by the Bureau of the Census computer program, illustrates various fluctuations discussed above and the resulting seasonally adjusted series. In addition, the figure shows the months for cyclical dominance (MCD) curve. This MCD measure provides an estimate of the appropriate time span over which to observe cyclical movements in a monthly series. In deriving MCD, the average (without regard to sign) percentage change in the irregular component and cyclical component are computed for one-month spans (January-February, February-March, etc.), two-month spans (January-March, February-April, etc.), up to five-month spans. Then MCD is the shortest span for which the average change (without regard to sign) in the cyclical component is larger than the average change (without regard to sign) in the irregular component. That is, it indicates the point at which fluctuations begin to be more attributable to cyclical than to irregular movements, and the MCD curve is a moving average of this many months. (This procedure is explained in full detail in Shiskin 19570.) Seasonal adjustment methods. There are many different methods of adjusting time series for seasonal variations. All are, however, based on the fundamental idea that seasonal fluctuations can be measured and separated from the trend, cyclical, and irregular fluctuations. The task is to estimate the seasonal factor and to eliminate it from the original observations by either subtraction or division, or some combination of the two. All familiar methods of seasonal adjustment, including the well-known link-relative and ratio-tomoving-average methods, follow this simple logic. The link-relative method was introduced in 1919 by Warren M. Persons (1919a; 1919b) of Harvard University. The ratio-to-moving-average method was developed in 1922 by Frederick R. Macaulay (1931) of the National Bureau of Economic Research in a study done at the request of the Federal Reserve Board. The ratio-to-moving-average method has the advantages of more precise measurement of the components and greater flexibility. In addition, it permits analysis of each of the successive stages in the seasonal adjustment process. For these reasons, it was adopted by almost all groups engaged in large-scale seasonal adjustment work, despite the fact that it is relatively laborious. The ratio-to-moving-average method. The first step in the ratio-to-moving-average method is to obtain an estimate of the trend and cyclical factors by the use of a simple moving average that combines 12 successive monthly figures, thereby eliminating the seasonal fluctuations. Such a moving
TIME SERIES: Seasonal Adjustment
83
Billions of dollars T32
- 28
- 24
5. Seasonally adjusted series
-1 14 1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
Figure I — Sysfemaf/c and irregular components of total retail sales, United States 1953—1965 Source: U.S. Bureau of the Census 1966, p. 33.
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average is known as a "trend-cycle curve" (see curve 6 of Figure 1), since it contains virtually all the trend and cycle movements and few or none of the seasonal and irregular movements in the data. Division of the raw data by the moving average yields a series of "seasonal-irregular" ratios. An estimate of the seasonal adjustment factor for a given month is then secured by averaging the seasonal-irregular ratios for that month over a number of years (see curve 4 of Figure 1). It is assumed that the irregular factor will be canceled out in the averaging process. Finally, the original observations are seasonally adjusted by dividing each monthly observation by the seasonal adjustment factor for the corresponding month (see curve 8 of Figure 1). This method yields a multiplicative seasonal adjustment; an additive adjustment can be made by an analogous procedure. At present there is no way of making a simultaneous additive and multiplicative adjustment by this method. The ratio-to-moving-average method has been programmed for electronic computers and is in widespread use throughout the world. The first seasonal adjustment computer program was developed at the U.S. Bureau of the Census in the summer of 1954. Shortly thereafter, it was used extensively for national series for the United States, Canada, the Organization for Economic Cooperation and Development countries, Japan, and other countries. It has also been utilized by many private concerns to adjust their own data. The U.S. Bureau of Labor Statistics adopted a similar method in 1960, and other adaptations were introduced at about the same time in several other countries. These programs take advantage of the electronic computer's high-speed, low-cost computations by utilizing more powerful and refined techniques than clerical methods had used in the past. Thus, weighted moving averages are used to represent the trend-cycle factor and to measure changing seasonal patterns. As a result, the computer programs are likely to produce satisfactory results more frequently. They also produce more information about each series—for example, estimates of the trend-cycle and irregular components and of the relations between them. This information can be used for checking the adequacy of the results, for forecasting seasonal and other movements, and for studying the relations among different types of economic fluctuations. For example, for the data graphed in Figure 1 the Bureau of the Census program also gives an indication of the relative importance of the components of the retail sales series by calculating the per cent of the total variation that is contributed by these components over one-
Tcrb/e 7 — Per cenf of total variation contributed by components of total retail sales, United States, 1953-1965 COMPONENT
PER CENT OF VARIATION Monfh-to-monfh
Holiday Trading day Seasonal Irregular Trend-cycle Tofa/
Twelve-month spans
0.5
0.5 7.1 0.0 2.4 90.0
100.0
100.0
0.4
33.1 64.8 1.2
Source: U.S. Bureau of the Census 1966, p. 33.
month and longer spans. These data are shown in Table 1. The Bureau of the Census method was designed to analyze a large variety of series equally well. To this end, alternative routines to handle different kinds of series were built into the program, along with techniques for automatically selecting the most appropriate routine for each series. The completeness, versatility, and economy of this method have stimulated broad interest in economic time series analysis in recent years. This program adjusts for changes in average climatic conditions and institutional arrangements during the year. Adjustments for variations in the number of trading days are also made for some series—for example, new building permits. Further adjustments for variable holidays, such as Easter, are made for certain series, such as retail sales of apparel. Similar adjustments for Labor Day and Thanksgiving Day help bring out the underlying trends. Studies of the effects of unusual weather upon some series have also been started. It is important to note, however, that conventional methods adjust for average weather conditions, and not for the dispersion about this average. For this reason many seasonally adjusted series, such as housing starts, will tend to be low in months when the weather is unusually bad and high in months when the weather is unusually good. The variants of the ratio-to-moving-average method all give about the same results, and there is considerable evidence that this method adjusts a large proportion of historical series very well. There are, however, some series that cannot be satisfactorily adjusted in this way—for example, those with abrupt changes in seasonal patterns or with constant patterns of varying amplitudes, or those which are highly irregular. Another problem concerns the appropriate seasonal adjustment of an aggregate that can be broken down into different sets of components, each with a different seasonal pattern. However, the principal problem remaining
TIME SERIES: Seasonal Adjustment now appears to be obtaining satisfactory seasonal adjustment factors for the current year and the year ahead. These are less accurate than those for previous years, but they play a more important role in the analysis of current economic trends and prospects. Regression methods. Attempts to use regression methods to analyze time series have been intensified since electronic computers have become available. The basic principle is to represent each of the systematic components by explicit mathematical expressions, usually in the functional form of a linear model. This can be accomplished in a simple form, for example, by regressing the difference between the unadjusted series and the trend-cycle component for each month on the trend-cycle values for that month. The constant term in the regression equation is the additive part of the seasonal component, and the product of the regression coefficient and the trend-cycle value is the multiplicative part of the seasonal component. Thus, this approach has the advantage over the ratio-to-moving-average method that it is not committed to a single type of relationship (e.g., additive or multiplicative) among the seasonal, cyclical, and irregular components of the series. Another advantage is that the different types of fluctuations can be related to the forces causing them by representing these forces as appropriate variables in the mathematical expressions. Thus, in measuring the seasonal factor, direct allowance can be made, say, for the level of the series or for temperature and precipitation. In certain series, special factors could be taken into account; for example, in measuring the seasonal factor in unemployment, allowance could be made for the number of students in the labor force, or in the case of automobile sales, the level of automobile dealers' inventories could be taken into account. Finally, the mathematical expressions for the estimates of the systematic components provide the basis for deriving measures of variance and significance tests to evaluate the reliability of the estimates; this applies, for example, to estimates of the seasonally adjusted series and to the seasonal component, or to the differences in either series over time. The principal doubt about the regression approach is whether fairly simple functional forms can adequately measure the implicit economic patterns. Or, to consider the matter from another point of view, do the complex mathematical forms required to represent the systematic movements of historical series constitute a plausible theory of economic fluctuations? A related question is whether either fairly simple functional forms, which only
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crudely measure historical patterns, or the more complex forms, which fit the past more closely, can provide the basis for accurate forecasts of future patterns. Thus far, regression methods have been applied to only a small number of series, and their powers to decompose series into the various systematic components and to forecast seasonal factors for future years have not yet been fully tested. While the ratio-to-moving-average method does not have the advantages provided by the mathematical properties of the regression method, extensive tests have demonstrated that it gives good results in practice. Tests completed at the Bureau of the Census show that regression methods yield historical seasonal factors very similar to those yielded by the ratioto-moving-average method, but that the regression "year-ahead" factors and the trend-cycle curves are less accurate. Criteria for judging a seasonal adjustment. Although it is not now possible to draw a set of hardand-fast rules for judging the success of a seasonal adjustment, five guidelines have proved useful. (a) Any repetitive intrayear pattern present in a series before seasonal adjustment should be eliminated and thus should not appear in the seasonally adjusted series, in the trend-cycle component, or in the irregular component. This implies that the seasonal factors are not correlated with the seasonally adjusted series, or with the trend-cycle or irregular components. (The correlations should be computed year by year, because residual seasonality sometimes shows up with inverse patterns in different years.) (b) The underlying cyclical movements should not be distorted. Seasonally adjusted series that in unadjusted form had a large seasonal factor should be consistent in terms of cyclical amplitude, pattern, and timing with other related economic series that either had no seasonal factor at all or had a small seasonal factor compared with the cyclical factor. Similarly, changes in a seasonally adjusted series such as new orders for machinery and equipment should be followed by like changes in a corresponding series such as sales. (c) The irregular fluctuations should behave like a random series when autocorrelations of lags of about 12 months are considered. Autocorrelations of smaller lags need not necessarily behave like the similar autocorrelations of a random series because some irregular influences, such as a long strike, spread their effects over several months. A seasonally adjusted artificial series containing a random component should produce a random series as the irregular component.
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( d ) The sum of the seasonally adjusted series should be equal to the sum of the unadjusted series. For most series, sums are meaningful in economic terms, and the preservation of sums meets the common-sense requirement that the number of units produced, traded, or exported in a year should not be altered by the seasonal adjustment. (e) Revisions in the seasonal factors that take place when data for additional years become available should be relatively small. Tests of seasonal adjustments. With the massive increase in the number of series seasonally adjusted in recent years, due largely to the increasing use of electronic computers for this purpose, the need for routine objective tests of the quality of the adjustments has grown. A general type of test involves examining the results of applying a seasonal adjustment procedure to artificial series. One method of constructing suitable artificial series is to combine the irregular, cyclical, and seasonal factors from different real economic series into artificial aggregates; that is, the seasonal factor from one economic series, the trend-cycle factor from another, and the irregular factor from a third are multiplied together to form a new series. A test of the Bureau of the Census method, using 15 different types of such artificial series, revealed that in most instances the "estimated" components trace a course similar to that of the "true" components (Shiskin 1958). Although some limitations were evident, this test showed that the Census method has considerable power to rediscover the different types of fluctuations that were built into the series and does not generate arbitrary fluctuations that have no relationship to the original observations. A statistical test for the presence of a stable seasonal adjustment component may be made by using the analysis of variance and the associated F-test. This is a test of the null hypothesis that monthly means are equal. Here, the variance estimated from the sum of squares of the differences between the average for each month and the average for all months (between-months variance) is compared with the variance estimated from the sum of squares over all months of the differences between the values for each month and the average for that month (within-months variance). If the betweenmonths variance of the "seasonal-irregular" ratios (computed by dividing the original observations by an estimate of the trend-cycle component) is significantly greater than the within-months variance, it can usually be assumed that there is a true seasonal factor in the series. If the between-months
variance is not significantly greater than the withinmonths variance of the irregular series (computed by dividing the seasonally adjusted series by an estimate of the trend-cycle component), then it can usually be assumed that a complete seasonal adjustment has been made. This test must, however, be used cautiously because differences between months can also appear as a result of differences in the behavior of the irregular component from month to month, because differences between months may be hidden when changes in seasonality in one month are offset by changes in another month, and because the assumptions of the test may not be well satisfied. Nevertheless, the F-test has proved to be a useful test of stable seasonality in practice. [See LINEAR HYPOTHESES, article on ANALYSIS OF VARIANCE.]
Experience in applying spectral analysis to physical science data has encouraged researchers to explore its use in economics, and this technique is now being used to test for seasonality. Spectral analysis distributes the total variance of a series according to the proportion that is accounted for by each of the cycles of all possible periodicities, in intervals for 2-month and longer cycles. If there is a seasonal pattern in a series, a large proportion of the variance will be accounted for by the 12-month cycle and its harmonics (cycles of 6, 4, 3, 2.4, and 2 months). A significant proportion of the total variance of a seasonally adjusted economic series should be accounted for by a cycle of 45 to 50 months, the average duration of the business cycle, but not by the 12-month cycle or its harmonics. A random series would not be expected to show a significant cycle at any periodicity. While quantitative statistical methods based on suitable assumptions for economic time series have not yet been developed for determining from a spectrum whether seasonality exists, such judgments can often be made from inspection of charts of the spectra. A question sometimes raised about spectral analysis is whether it is appropriate to consider an economic time series from the viewpoint of the frequency domain, as spectral analysis does, rather than the time domain, as most other methods do. This question comes up mainly because economic series are available for relatively short periods and economic cycles, other than the seasonal, are irregular in length and amplitude. However, the prospect that mathematical representation of a time series in this way may reveal relationships not otherwise apparent would appear to make this alternative view worth further exploration. These tests do not provide enough information
TIME SERIES: Seasonal Adjustment to determine whether all the criteria listed above are satisfied. To this end, comparisons of the sums of seasonally adjusted and unadjusted data are also made, often for all fiscal years in addition to calendar years. The magnitude of revisions resulting from different methods of seasonal adjustment is usually appraised by seasonally adjusting series which cover periods successively longer by one year (e.g., 1948-1954, 1948-1955, 1948-1956, and so forth) and comparing the seasonal factors for the terminal years with the "ultimate" seasonal factors. Relations of seasonal to other fluctuations. An analysis has been made of the cyclical, seasonal, and irregular amplitudes of a sample of about 150 series considered broadly representative of the different activities of the U.S. economy. This study revealed that, for the post-World War n period, seasonal movements dominate other kinds of monthto-month movements in most current economic series. Seasonal movements are almost always larger than either the irregular or the cyclical movements, and they are often larger than both of the other types combined. More specifically, the average monthly amplitude of the seasonal fluctuations exceeds that of the cyclical factor in 78 per cent of the series, exceeds the irregular factor in 65 per cent of the series, and exceeds the cycle-trend and irregular factors in combination in 45 per cent of the series. Furthermore, where the seasonal factor is larger, it is often much larger. The seasonal factor is three or more times as large as the cyclical factor in 45 per cent of the series, three or more times as large as the irregular factor in 16 per cent of the series, and three or more times as large as the cyclical and irregular fluctuations together in 11 per cent of the series. (See Shiskin 1958.) These results apply to observations of change over intervals of one month; over longer spans the relative importance of the several components would, of course, be different. Table 1 shows how seasonal and trading day fluctuations, which dominate the short-term movements, give way in relative importance to the trend-cycle factor when comparisons are made over longer periods. These findings emphasize the advantages of seasonally adjusted series over those not so adjusted for studying cyclical movements. Where the seasonal fluctuations are large, a difference in the unadjusted data for two months may be due largely or solely to normal seasonal fluctuations; if the data are seasonally adjusted, the difference can be assumed to be caused chiefly by cyclical or irregular factors. JULIUS SHISKIN
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BIBLIOGRAPHY
Much of the material in this article is discussed in greater detail in Shiskin 1957a; 1958; and the Shiskin paper in Organization for European Economic Cooperation 1961. References that deal with the problem of seasonal adjustment as it relates to current economic conditions are Organization for European Economic Cooperation 1961 and Shiskin 1957a; 1957b. Early works on seasonality and seasonal adjustment methods are Barton 1941; Burns & Mitchell 1946; Hotelling & Hotelling 1931; Kuznets 1933; Macaulay 1931; and Persons 1919a; 1919b. Works dealing with the history of the Bureau of the Census method and its variants are Organization for European Economic Cooperation 1961; Shiskin & Eisenpress 1957; Shiskin et al. 1965; and Young 1965. Alternative methods are described in Hannan 1963; Rosenblatt 1963; and U.S. Bureau of Labor Statistics 1964. Tests of seasonal adjustment methods are discussed in Burns & Mitchell 1946; Granger & Hatanaka 1964; Hannan 1963; Kuznets 1933; Rosenblatt 1963; and Shiskin 1957b. BARTON, H. C. JR. 1941 Adjustment for Seasonal Variation. Federal Reserve Bulletin 27:518-528. BURNS, ARTHUR F.; and MITCHELL, WESLEY C. 1946 Measuring Business Cycles. National Bureau of Economic Research, Studies in Business Cycles, No. 2. New York: The Bureau. H> See especially pages 43-55, "Treatment of Seasonal Variations" and "Notes on the Elimination of Seasonal Variations." GRANGER, CLIVE W. J.; and HATANAKA, M. 1964 Spectral Analysis of Economic Time Series. Princeton Univ. Press. -> See also "Review" by H. O. Wold in Annals of Mathematical Statistics, February 1967, pages 288-293. HANNAN, E. J. 1963 The Estimation of Seasonal Variations in Economic Time Series. Journal of the American Statistical Association 58:31-44. HOTELLING, HAROLD; and HOTELLING, FLOY 1931 Causes of Birth Rate Fluctuations. Journal of the American Statistical Association 26:135-149. KUZNETS, SIMON 1933 Seasonal Variations in Industry and Trade. New York: National Bureau of Economic Research. MACAULAY, FREDERICK R. 1931 The Smoothing of Time Series. New York: National Bureau of Economic Research. ORGANIZATION FOR EUROPEAN ECONOMIC COOPERATION 1961 Seasonal Adjustment on Electronic Computers. Report and proceedings of an international conference held in November 1960. Paris: Organization for Economic Cooperation and Development. PERSONS, WARREN M. 1919a Indices of Business Conditions. Review of Economics and Statistics 1:5-107. PERSONS, WARREN M. 1919£> An Index of General Business Conditions. Review of Economics and Statistics 1:111-205. ROSENBLATT, HARRY M. (1963) 1965 Spectral Analysis and Parametric Methods for Seasonal Adjustment of Economic Time Series. U.S. Bureau of the Census, Working Paper No. 23. Washington: Government Printing Office. -> First published in American Statistical Association, Business and Economics Section, Proceedings, pages 94-133. SHISKIN, JULIUS 1957a Electronic Computers and Business Indicators. National Bureau of Economic Research, Occasional Paper No. 57. New York: The Bureau. -> First published in Volume 30 of the Journal of Business.
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SHISKIN, JULIUS 1957b Seasonal Adjustments of Economic Indicators: A Progress Report. Pages 39-63 in American Statistical Association, Business and Economics Section, Proceedings. Washington: The Association. SHISKIN, JULIUS 1958 Decomposition of Economic Time Series. Science 128:1539-1546. SHISKIN, JULIUS; and EISENPRKSS, HARRY (1957) 1958 Seasonal Adjustments by Electronic Computer Methods. National Bureau of Economic Research, Technical Paper No. 12. New York: The Bureau. -> First published in Volume 52 of the Journal of the American Statistical Association. SHISKIN, JULIUS et al. 1965 The X-ll Variant of the Census Method. II: Seasonal Adjustment Program. U.S. Bureau of the Census, Technical Paper No. 15. Washington: The Bureau. U.S. BUREAU OF LABOR STATISTICS 1964 The BLS Seasonal Factor Method (1964). Washington: The Bureau. U.S. BUREAU OF THE CENSUS Monthly Retail Trade Report [1966]: August. YOUNG, ALLAN H. 1965 Estimating Trading-day Variation in Monthly Economic Time Series. U.S. Bureau of the Census, Technical Paper No. 12. Washington: The Bureau.
TITCHENER, EDWARD B. Edward Bradford Titchener (1867-1927), a psychologist, was born in England, reared in the German (Wundtian) tradition, and spent his adult, professional years in America. He spent his early years in Chichester, an ancient Roman city about seventy miles south of London, as the elder of two children and the only son of John and Alice Field (Habin) Titchener. He died in Ithaca, New York, from a cerebral tumor. Titchener was a precocious and studious lad, and it was well for him that he was, because his father's early death meant that there was no financial assistance forthcoming for his education. After his elementary training at the prebendal school in Chichester, of which his grandfather was at one time headmaster, he had to rely for his further education upon scholarships and other academic awards won by his own efforts. In 1881, when he was 14 years old, Titchener went to Malvern College in Worcestershire on such a scholarship. He did well there, for, as the story goes, James Russell Lowell, who one year distributed the prizes at the school, remarked, after he had presented the youthful Titchener with several prizes and saw the lad advance for still another, "I am tired of seeing you, Mr. Titchener." After Malvern, Titchener went in 1885 to Brasenose College, Oxford, on a senior scholarship in classics and philosophy and as Hulman "exhibitioner"—a supplementary scholarship awarded
on the basis of need as well as excellence. Near the end of his classical training, he elected a course in physiology under John Scott Burdon-Sanderson, regius professor of medicine at Oxford, and became so absorbed in that subject that he delayed his graduation one year, until 1890, to devote himself to it. During this time he translated into English the third edition of Wundt's huge two-volume Grundzuge der physiologischen Psychologic (18731874). He was attracted by Wundt's combination of philosophy and psychology and by his promise of a new experimental science of psychology; in the fall of 1890 he went to study in Wundt's laboratory in Leipzig. Titchener received his PH.D. degree after only two years' study at Leipzig. In that short period he assimilated Wundt's system and completed two experimental researches: his doctoral dissertation on the binocular effects of monocular stimulation and a study on the chronometry of cognition. At Leipzig he was also permanently influenced by the positivism of Ernst Mach and Avenarius. At that time, psychology was not recognized as a science in England, and although Titchener would have preferred to remain in his homeland, he had to go elsewhere to obtain a position in psychology and a laboratory. In the fall of 1892 he accepted an assistant professorship at Cornell and became head of the newly established laboratory of psychology there. His advancement at Cornell was rapid: in 1895, when he was only 28 years old, he was promoted to the Sage professorship of psychology, and in 1910, when he was offered the chairmanship of the department of psychology at Clark University, Cornell made him a professor in the graduate school, thus relieving him from undergraduate teaching. (After a short time, he missed the contacts with the undergraduates, and after receiving an additional appointment in the arts college, he resumed his popular undergraduate lectures and his direction of the undergraduate laboratories.) Titchener represented the Wundtian point of view in America. He insisted that psychology is a science and that as a science it is concerned with description, not with use or application. He stood throughout his life for the scientific study of the generalized, normal, adult human mind. In 1898, in an article called "The Postulates of a Structural Psychology," he accepted James's differentiation between the structural and functional points of view of mind, and thereafter he was known as the leader of the "structural school," which stood in opposition to the more popular "functional school" led by Dewey, James, and Angell. When behavior-
TITCHENER, EDWARD B. ism superseded functional psychology in America, Titchener opposed it on the grounds that behaviorism is biology, not psychology, and that it ignores the very problems that are the proper concern of psychology: the study of experience as dependent on an experiencing individual, that is, on a nervous system. He was deeply interested in the experimental results of gestalt psychology and readily accepted them, but not their interpretation. He maintained that the gestalt approach was too narrow, being concerned only with "perception" and with only one aspect of it, that is, "form." Titchener saw it as one of his first tasks in America to make the "new" German psychology available in English. He published translations of three successive editions of Kiilpe's Outlines of Psychology; with his colleague J. E. Creighton, he translated three editions of Wundt's Lectures on Human and Animal Psychology, and with his colleague J. H. Gulliver, he translated two editions of Wundt's Ethics. Also, with his student W. B. Pillsbury, he translated Kiilpe's Introduction to Philosophy. Titchener's translations of Wundt's Physiologische Psychologic could never quite keep up with Wundt's new editions of the work. The first book that Titchener wrote, An Outline of Psychology (1896), was patterned after Kiilpe's Outlines and thus also served to introduce German psychology into American universities. It went through many printings and three editions, as did his second book, A Primer of Psychology (1898Z?). In a further effort to make the teaching of psychology comparable to that of other scientific subjects, Titchener put together his famous twovolume work Experimental Psychology: A Manual of Laboratory Practice. It was patterned after manuals used in chemistry: one volume (1901) dealt with qualitative experiments and one (1905) with quantitative ones, and each of these volumes was further divided into two parts—a Student's Manual and an Instructors Manual. In the Student's Manual, Titchener presented a number of classical experiments that had "disciplinary value to the undergraduate student"; the Instructors Manual gave the instructors a wealth of background information about the selected experiments. The publication of Quantitative Experiments was delayed by the appearance in 1904 of G. E. Miiller's Gesichtspunkte und Tatsachen der psychologischen Methodik, which covered much the same subject matter. Titchener was sorely tempted, as he explained in the Preface to the Instructor's Manual, "to leave my text as it stood and to take account of Miiller's book simply in footnote references . . . but the better counsel prevailed" (1901-
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1905, vol. 2, part 2, p. iii). He embodied Miiller's new results in his exposition. Titchener then turned to problems of attention, feeling, and thought. In 1908 he published Lectures on the Elementary Psychology of Feeling and Attention. He sought to give the concept of feeling an independent, elementary status and to enhance the scientific validity of the concept of attention by relating it to specific aspects of the sensory experience. From among the various terms that had historically been used to describe change in the attentive consciousness, Titchener chose "clearness." It was an unfortunate choice because of the word's many connotations. Later he changed the term to "vividness" and still later to "attensity," but the confusion persisted, and his concept of attention, although widely discussed, was not widely accepted. The following year, Titchener published Lectures on the Experimental Psychology of the Thought-processes (1909a). This work constituted an attack on the theory of Kiilpe and the Wiirzburg school that thought is "imageless." Kulpe and his students were unable to analyze the thought processes and therefore concluded that thought is a separate, conscious element, comparable to sensations. Titchener repeated Kulpe's experiments at Cornell, corroborating most of the results but drawing very different conclusions from them. He asserted that these results did not warrant the abandonment of the view that thought is imaginal and sensory, and he provided a theory to explain the apparently imageless character of "imageless thought." Accepting N. Ach's concept of the determining tendency and the premise of the Wiirzburg school that thought may be unconscious, he offered the context theory of meaning, according to which "meaning is the conscious sensory or imaginal context that accrues (associatively, it would seem) to the initial sensory core of a perception or the initial imaginal core of an idea" (Boring [1929] 1950, p. 415). This theory sought to account for the lack of analyzable content in the results of the Wiirzburg experiments on thought. Titchener wrote two more textbooks. A Textbook of Psychology (1909&) was too systematic and too sophisticated for elementary courses in psychology. In 1915 he published A Beginner's Psychology, which was more suitable as an introductory text. Since he was never able to complete a projected three-volume work on systematic psychology, his textbooks are the only systematic accounts of his psychology that he left. Titchener was elected a charter member of the American Psychological Association but soon with-
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drew: he resented the association's failure to take action against a member who had plagiarized his translation of Wundt. Since, however, he missed the contacts with his colleagues that the annual meetings provided, he invited the heads of ten of the most prominent laboratories in the country to attend a conference on experimental psychology at Cornell in the spring of 1904. The group, unofficially known as "The Experimentalists," thereafter met annually; after Titchener's death, it became a more formal organization, the Society of Experimental Psychologists. The list of Titchener's honors is long, including honorary degrees from Oxford, Wisconsin, Harvard, and Clark, and memberships in the American Philosophical Society and the Royal Society of Medicine in England. He was coeditor of the American Journal of Psychology from 1895 to 1920 and sole editor from 1921 to 1925. From 1894 to 1920 he was also the American editor of Mind. His own list of publications was long (216); many other works (176) came from his students in the Cornell laboratory. Clearly, he was one of the most respected and influential figures in the development of the discipline of psychology in America. KARL M. DALLENBACH
BORING, EDWIN G. (1929) 1950 A History of Experimental Psychology. 2d ed. New York: Appleton. DALLENBACH, KARL M. 1928 Bibliography of the Writings of Edward Bradford Titchener: 1917-1927. Journal of Psychology 40:121-125. FOSTER, WILLIAM S. 1917 A Bibliography of the Published Writings of Edward Bradford Titchener: 18891917. Pages 323-337 in Studies in Psychology. Worcester, Mass.: Wilson. KULPE, OSWALD (1893) 1909 Outlines of Psychology, Based Upon the Results of Experimental Investigation. 2d ed. Translated by Edward Bradford Titchener. London: Sonnenschein; New York: Macmillan -» First published as Grundriss der Psychologic, auf experimenteller Grundlage dargestellt. Titchener was also the translator of the 1895 and 1901 English editions. PILLSBURY, W. B. 1928 The Psychology of Edward Bradford Titchener. Philosophical Review 37:95-108. Studies in Psychology. 1917 Worcester, Mass.: Wilson. -> A volume presented to Titchener by his colleagues and former students in recognition of the 25th anniversary of his doctorate. WARREN, HOWARD C. 1927 Edward Bradford Titchener. Science 66:208-209. WUNDT, WILHELM (1873) 1905 Principles of Physiological Psychology. Translated by Edward Bradford Titchener and J. E. Creighton. London: Sonnenschein; New York: Macmillan. -* First published as Volume 1 of Wilhelm Wundt's Grundziige der physiologischen Psychologic. Titchener and Creighton were also the translators of the 1894, 1896, and 1901 editions.
[For the historical context of Titchener's work, see the biographies of JAMES; KULPE; MULLER, GEORG ELIAS; WUNDT ; for discussion of the subsequent development of his ideas, see ATTENTION; PSYCHOPHYSICS; SENSES.]
TOCQUEVILLE, ALEXIS DE
WORKS BY TITCHENER (1896) 1902 An Outline of Psychology. New ed., enl. New York: Macmillan. 1898a The Postulates of a Structural Psychology. Philosophical Review 7:449-465. (1898k) 1925 A Primer of Psychology. Rev. ed. New York: Macmillan. 1901-1905 Experimental Psychology: A Manual of Laboratory Practice. 2 vols. New York and London: Macmillan. -» Volume 1: Qualitative Experiments, 2 parts. Volume 2: Quantitative Experiments, 2 parts. 1908 Lectures on the Elementary Psychology of Feeling and Attention. New York: Macmillan. 1909a Lectures on the Experimental Psychology of the Thought-processes. New York: Macmillan. (19096) 1910 A Textbook of Psychology. New York: Macmillan. 1910 The Past Decade in Experimental Psychology. American Journal of Psychology 21:404—421. 1915 A Beginner's Psychology. New York: Macmillan. 1929 Systematic Psychology: Prolegomena. New York: Macmillan. SUPPLEMENTARY BIBLIOGRAPHY
ANGELL, FRANK 1928 Titchener at Leipzig. Journal of General Psychology 1:195-198. BORING, EDWIN G. 1927 Edward Bradford Titchener. Journal of General Psychology 38:489-506.
Alexis de Tocqueville (1805-1859) lived at the time of two revolutions, the democratic and the industrial; their impact upon the traditional order furnished him with the major themes of his scholarly work. Tension between traditional and modern values dominated Tocqueville's life and writings. Convinced of the irreversibility of democracy and contemptuous of reactionaries who thought they could block this historical movement, he was nevertheless obsessed by the erosion of those traditional contexts and values—aristocracy, honor, localism, religion, cultural variety—on which European liberty had depended for so many centuries. In his personal life this conflict of values proved almost too great to contain, and in his final years he succumbed to melancholy, despairing of the future of liberty and culture in Europe. It was this same tension, however, that provided the underlying creative impulse behind the extraordinarily dispassionate analyses of modern society contained in his two major works, Democracy in America (1835) and The Old Regime and the French Revolution (1856). In these, Tocqueville formulated analytical perspectives that were to prove fruitful both for the continued study of Western society and for the study of the non-Western
TOCQUEVILLE, ALEXIS DE societies which in the twentieth century are undergoing a modernization strikingly akin to what fascinated Tocqueville in the "first new nation," the United States. Behind Tocqueville's analytical perspectives, and giving them coherence, is a unified philosophy of history that rests on what he called "the principle of equality." What class struggle was for Marx, Gesellschaft for Tonnies, and rationalization for Max Weber, equalitarianism was for Tocqueville. Each of these men endowed a single dynamic aspect of the social order with decisive developmental significance. In Tocqueville's eyes, the master principle of European history was the relentless leveling of social ranks that, he believed, had been going on since the end of the Middle Ages—a leveling as inexorable as it was universal in Europe, one that touched literally every sphere of society and culture. It is this principle of social development that gives meaning to the major areas of fact and insight into which his sociological work falls. There are four such areas: power, stratification, industrialism, and mass culture. Power. Tocqueville was fascinated by the problem of power, particularly the power of the modern democratic state. The impact of centralized, massbased sovereignty upon the traditional authorities of family, local community, social class, and morality is a theme in his work second only to that of equalitarianism. The two themes are, indeed, inseparable. Tocqueville was not the first to emphasize the affinity between social equality and political centralization, but his Democracy in America is certainly the first systematic treatment of the subject, just as his Old Regime and the French Revolution is the first scholarly demonstration of the roots of the French Revolution in the history of European administrative centralization. From the vantage point of contemporary sociology, three aspects of his consideration of power are noteworthy: the affinity between mass equality and bureaucracy, the role of public opinion, and the relation between political power and "secondary" or "intermediate" social authorities. In the history of European polity, Tocqueville wrote (anticipating Weber), "the substitution of paid for unpaid functionaries is of itself . . . sufficient to constitute a real revolution" ([1835] 1945, vol. 1, p. 208). Democracy inevitably has an accelerative influence upon bureaucracy, for unpaid political service can be performed only by the rich and privileged, whose very existence frustrates the objectives of democracy. Hence it is possible, he wrote, to measure the progress of democracy in a nation by the rate of increase of paid functionaries.
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Tocqueville saw the relation between bureaucratic centralization and social equalitarianism not only as historical but also as functional. All that erodes social hierarchy, regionalism, and localism is bound to intensify centralization in the state. Conversely, all that furthers the development of political centralization—war, dynastic ambition, and revolution—is bound to accelerate social leveling. While the major cause of modern bureaucracy is the democratization of power, Tocqueville identified four factors which account for its variable intensity from nation to nation: revolution, the role of the lower classes, level of literacy, and war. When revolution ushers in democracy, as in France, it makes for a higher degree of initial centralization than is the case when democracy evolves gradually, as in the United States. When the lower classes hold the balance of power, administration tends to be centralized, for this is the only means whereby the lower classes can wrest power from local aristocracy. The lower the level of literacy in a population, the greater and more inevitable the tendency to concentrate administration in an educated, governing elite. Finally, "All men of military genius are fond of centralization . . . and all men of centralizing genius are fond of war" (ibid., vol. 2, p. 300). The relation between Tocqueville's "administrative centralization" and what Weber was to call "rationalization" is, of course, very close. Both saw conflict between bureaucracy and the democratic impulses that had helped produce it. Tocqueville's depiction of the sort of despotism democratic nations have to fear is almost indistinguishable in tenor from that found two generations later in Weber's melancholy ruminations on administrative rationalization. For both men, any future despotism would emerge not primarily from individuals or groups but from the bureaucratic system per se. Tocqueville's dominating interest in public opinion followed from his view that the locus of democratic power is in mass majorities. What he called "the tyranny of the majority"—at bottom the sway of public opinion—may be more stifling to individuality, as it was in America, than even the medieval Inquisition had been. Despite his profound interest in public opinion, he had no clear awareness of its sources. It does not seem to have occurred to him that public opinion is something that can be manufactured by minority pressure groups. He conceived of it as a more or less direct emanation from the political masses. But if he did not explore its sources and variable expressions, he nevertheless correctly identified it as a new and powerful force in the modern state, one henceforth
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crucial to the legitimacy of governments. Equally important, Tocqueville, in contrast to most political conservatives of his day, feared not the instability but the stability of public opinion in democracy, a stability so great, in his view, that not only political revolution but even intellectual innovation would become increasingly unlikely. The role of "secondary" or "intermediate" authorities in democracy was a prime concern of Tocqueville's. Liberty, in his view, has little to do with the breadth of political power or the extent of mass participation in it. Liberty can exist only where there are countervailing authorities which stand as buffers between the individual and the central government. Traditional secondary authorities—aristocracy, guild, commune—had been eroded by the impact of equalitarian democracy. Tocqueville asked what authorities, if any, had succeeded these. In Europe he found almost none; hence his growing pessimism about the future of liberty there. In America, however, the great profusion of voluntary associations, the power and independence of local communities, the professions (especially the legal profession), and the whole system of division of powers within the political government seemed to him the effective basis of a pluralism that might restrain the powers of both majority opinion and administrative centralization. A distinction between authority and power is fundamental in Tocqueville, authority being the inner nature of association, rooted in function and allegiance, while power is coercion, generally with the implication of force externally applied. It is in terms of this distinction that his treatment of family, local community, master-servant, professional, and other social relationships can most readily be understood. Each of these, for Tocqueville, is a pattern of constraints as well as of activities, and its internal strength is a function of its relative immunity from political power. Stratification. Tocqueville's theory of social stratification follows from his conception of power. He is at the opposite extreme from Marx, who found in the capitalist class essentially the same union of power, wealth, and status that had characterized the feudal nobility. According to Tocqueville, the dominant tendency of modern history is toward the disengagement of these three elements from one another. Social class, in the sense of selfconscious and culturally distinct classes, is precluded in modern society by exactly the same forces that destroyed feudal aristocracy: political centralization, the greater importance of money, and civil equality. There are levels of wealth and privilege, but the nature of democracy and of a money-based economy prevents these levels from
hardening into real classes. Tocqueville was by no means blind to the power of manufacturing interests and their remoteness from workers. Indeed, he speculated on how "an aristocracy may be created by manufactures/' But however dangerous the power of manufacturers may be to the politics of democracy, manufacturers do not and cannot constitute a genuine social class. For while the category is fixed by industrialism, the content is ever-changing; incessant mobility prevents the crystallizing of attitudes and culture, the sinking of roots, and the socially recognized eminence that social class requires. What struck Tocqueville was the immense middle class in the United States. This class was neither rich nor poor; its position made it, in his view, a vast arena for status aspiration. Tocqueville's theory of stratification, in short, rests on status mobility rather than class. The decline of traditional class, far from lessening the desire for elevation of status, only intensifies it. When it is birth alone that ranks men in society, Tocqueville observed, everyone knows exactly what his own position is in the social scale. "He does not seek to rise, he does not fear to sink." But when equalitarianism prevails and money becomes the basis of rank in society, the desire to rise is matched by the fear of sinking in the social scale. The principle of equality is accompanied not by love of equality but by obsession with social status. "When inequality of conditions is the common law of society, the most marked inequalities do not strike the eye; when everything is nearly on the same level, the slightest [inequalities] are marked enough to hurt it. Hence the desire of equality always becomes more insatiable in proportion as equality is more complete" (ibid., vol. 2, p. 138). It is preoccupation with status that above all else explains why "Americans are so restless in the midst of their prosperity": a restlessness making for unhappiness on a wide scale. In France, Tocqueville wrote, this status anxiety produces high rates of suicide; in America, high rates of insanity. Tocqueville provided two classic paradigms of social status in modern democracy, each the subject of a long chapter. The first is the masterservant relation. Tension is the very essence of this relation, Tocqueville observed, given a setting in which civil equality is dogma as well as law. An "imperfect phantom of equality" haunts the mind of servant and master alike, making obedience as confused and reluctant a sentiment in the first as unwonted command is in the second. The same problem of context has dislocated the historic notion of honor. The social roots of this value, Tocqueville showed, are feudal, and all that has weakened
TOCQUEVILLE, ALEXIS DE the hierarchical arid personal character of European society has weakened the structural possibility of honor as a cementing value. Yet honor, like status, is, he noted, a verbal obsession of Americans. The subtlety and perception of Tocqueville's sociological treatment of these two values remained unmatched until Weber's and Simmel's work. In one sphere only did Tocqueville see the outline and substance of genuine social class in America: the Negro-white relationship. In the South, where slavery made a caste of the Negro, issues of status and mobility were nonexistent, but if Negroes "are once raised to the level of freemen, they will soon revolt at being deprived of almost all their civil rights; and as they cannot become the equals of the whites, they will speedily show themselves as enemies" (ibid., vol. 1, p. 378). Equally perceptive are Tocqueville's observations on the status of the Negro in the North, where, though legally free, the Negro encountered a different type of segregation. "I have remarked that the white inhabitants of the North avoid the Negroes with increasing care in proportion as the legal barriers of separation are removed by the legislature" (ibid., vol. 1, p. 375). It was visibility that made real assimilation between the two races a distant and dim prospect in Tocqueville's eyes. Recalling the long ages required in Europe for the erasure of social distinction between noble and commoner, he wrote: "I despair of seeing an aristocracy disappear which is founded upon visible and indelible signs" (ibid,, vol. 1, p. 358). The only real possibility of extreme social conflict, even revolution, that Tocqueville could foresee in America was that between Negro and white. One final element of Tocqueville's picture of stratification must be mentioned: intellectual and political elites. Here the social scene he was describing was not America but France, in the age just prior to the French Revolution. It was at this time, according to Tocqueville, that writers and philosophers became, for the first time, a significant political force, one that replaced traditional aristocracy. Intensely rationalist in temper, drawn to the uses of political power, and scornful of tradition, this group, which included all of the philosophes, became "a power in the country and ended up as its political leaders." Burke preceded Tocqueville in identifying the political role of the literary elite in eighteenth-century France, but Tocqueville showed that such elites are as inevitable an emergent of modern society as any of the other types or groups. Industrialism. Despite the overw