Irreversibility of Consumer Behavior in Terms of Numerical Preference Fields - Tsujimura, Kotaro; Sato, Tamotsu (The Review of Economics and Statistics, 1964)
T a given rate of growth in the general A level of personal income, which kind of expenditure will increase its share and which will decrease and, further, what will be the extent of these changes? requirement for this kind of knowledge has increased in recent years in relation to the theory of economic development as well as for purposes of short-run projection. Prior to the latter half of the 1940's, it had been thought that the above questions might be readily answered by the straightforword application of the generalized Engel's Law. Professors Allen and Bowley I gave the theoretical explanation with a specified form of preference function which was found to be consistent with the empirical cross-section regressions. Thus, it was suggested that if we could assume the invariability of the consumers' preferences both among income groups and over time, it would be possible to predict the consumption of various categories of goods and services and future savings, given income and prices and with the knowledge of the numerical values of the preference parameters. This line of approach had been tried from the time of Professors I. Fisher and R. Frisch.2 It is well known, however, that the validity of the analogy between the cross-section and the time series came to be doubted with the discovery of the long-run stability of the savings ratio in the aggregate time series by Professor Kuznets. Several new theories of consumption appeared with the common target of explaining with a unified theory all of these three kinds of empirical observations: the long-run time series, the short-run time series, and the cross-sectional relations. About ten years ago, the present authors began to try to estimate the consumers' preference functions in a numerical form, making use of continuous time series of the family budget data which were available, at that time, for interwar years in Japan. We undertook this task partly because of pure curiosity and partly because of the practical desire to improve the analysis of index-number problems,3 as well as to make predictions on the simultaneous determination of family expenditures. Starting from the classical model of Professors Allen, Bowley, and A. Wald,4 and after making some tentative computations, we came to see the necessity of introducing some shift elements into the structural equations which were used. First, we tried to adopt Professor Tobin's 5 liquid asset hypothesis in a generalized form which took not only the liquid assets, but also the asset holdings for every individual category of family expenditure into account. results of the empirical tests, however, did not show a logical consistency with our interpretation of Tobin's hypothesis. This forced us to examine the applicability of Professor Duesenberry's theory of interdependent preferences.6 * work on this paper was done as part of the Keio Economic Research Project financially supported by the Institute of Industry & Labor Studies, Keio University. final, considerably revised, version was prepared at Professor W. W. Leontief's Research Seminar during Tsujimura's stay at Harvard as a Fulbright Research Scholar, 1961 to 1962. We are also heavily indebted to Professors J. S. Duesenberry and H. S. Houthakker for valuable suggestions. They, of course, are not responsible for any remaining errors. 'R. G. D. Allen and A. L. Bowley, Family Expenditure: A Study of Its Variation (London, 1935), especially appendix. 2 Ragnar Frisch, New Methods of Measuring Marginal Utility (Tubingen, 1932). It is interesting to see that Frisch's analogy of the spring balance on the dynamic feature of consumer's taste appears to be very close to our present specification of Duesenberry's theory of habit formation. 'H. S. Houthakker, The Influence of Prices and Incomes on Household Expenditures, Bulletin of the International Statistical Institute (Bruxelles, 1960); W. W. Leontief, Composite Commodities and the Problem of Index Numbers, Econometrica, iv (1936); and P. A. Samuelson, Foundations of Economic Analysis (Harvard, 1945). 'A. Wald, The Approximate Determination of Indifference Surfaces by Means of Engel Curves, Econometrica, viii (April 1940). 'James Tobin, Relative Income, Absolute Income, and in, Money Trade, and Economic Growth (Macmillan: New York, 1951). 6 J. S. Duesenberry, Income, Saving, and the Theory of Consumer Behavior (Harvard, 1949).