In this paper we explore two issues in empirical demand analysis-the estimation of complete systems of demand equations using household budget data (Section I), and the incorporation of demographic characteristics into such systems (Section II). Although there are numerous studies which use time-series data to estimate complete demand systems, and many which estimate Engel curves from household budget data, there are virtually none which combine budget data from different periods to estimate complete systems. Since each budget study corresponds to a single price situation, one might conjecture that estimation of complete systems would not be possible unless budget studies were available from a large number of periods. This is incorrect. In Section I we argue that interesting complete demand systems can be estimated from a small number of budget studies, despite the limited price variability represented in such data. To demonstrate this, we use budget study data for two periods to estimate a pair of related demand systems: the familiar linear expenditure system (LES) and a quadratic expenditure system (QES), a generalization of LES in which the demand equations are quadratic in total expenditure.' The inclusion of demographic variables in the analysis of household consumption patterns is desirable because there are likely to be systematic differences in the consumption behavior of households with different demographic characteristics. But the effects of demographic characteristics have seldom been studied within the framework of complete demand systems. In Section II we propose "translating" as a general method for incorporating demographic variables into complete systems of demand equations. This method has not previously been discussed as a general technique for bringing demographic variables into demand systems, although it has been employed in several studies. To improve the estimates of the LES and the QES presented in Section I, we reestimate these two systems using translating to incorporate family size.

https://www.jstor.org/stable/info/1805266

Estimation of Complete Demand Systems from Household Budget Data: The Linear and Quadratic Expenditure Systems

Numerous studies have confirmed the importance of habit formation, as represented by a lagged dependent variable, in demand analysis. Although all work to date has been based on aggregate time series data, this study uses household level BLS Interview Panel data to test the habit hypothesis. An interrelated demand system for seventeen goods is estimated from cross-section data and compared with a similar system based on time series data. The results show that the habit component is significantly different between the two data sets and much smaller in the cross-section data. Habit effects, while not as large in cross-section data as time series, are still highly significant. Several explanations are offered concerning why the two sets of estimates differ. Copyright 1991 by MIT Press.

A Test of the Habit Formation Hypothesis Using Household Data

Frisch (1959) proposed the adoption of direct additive utility functions to facilitate empirical demand analysis. Double-log demand functions resulting therefrom are composed of the real income effect and the relative price effect. I show that the income elasticities and the own-price elasticities of demand are (approximately) constant (an assumption almost invariably made in applications) when the utility function is a generalized CES type. The income elasticity of marginal utility is the overall elasticity of substitution with no cardinal implications that Frisch stressed upon. The paper examines how approximate the constancy assumption is. A comparison is made with the linear expenditure system that is a special case. I suggest that the implied similarity of utility functions among countries provides the missing basis for international comparisons of purchasing power parities.

https://www.jstor.org/stable/info/1830134

Additive Utility Functions with Double-Log Consumer Demand Functions

In this study the neoclassical consumer behavior theory and its relation to empirical research in demand are presented in a unified framework. The goal is to make a contribution towards "bridging the gap" between empirical and theoretical demand analysis by generalizing and specializing the theory and extending its applicability to estimation of demand parameters. The neoclassical theory of consumer behavior and its extension to separable utility functions are treated first. Consumer budgeting as a behavioral justification for separability is then investigated and the concept of stagewise utility maximization is explored in the context of the above neoclassical theory. Based ori this framework, estimation procedures for demand parameters are devised which greatly reduce the amount of empirical information needed to obtain results. An empirical example is provided as an illustration of these procedures.

Empirical Analysis of Demand Under Consumer Budgeting

A dynamic analysis of expenditure patterns in rural India

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? The 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. The 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 * The 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. The 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, The 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 Saving," in, Money Trade, and Economic Growth (Macmillan: New York, 1951). 6 J. S. Duesenberry, Income, Saving, and the Theory of Consumer Behavior (Harvard, 1949).

Tamotsu Sato

Papers

Irreversibility of consumer behavior in terms of numerical preference fields