Macro Models Based on Aggregation of Micro Behavior Using Models of Changes in the Distribution of Individuals

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A great deal of applied econometric analysis uses aggregated data (from Census, the Bureau of Labor Statistics and so on) to test and apply theories about the behavior of individuals in the economy. For instance, studies estimating systems of demand equations for many types of consumer goods are based on the microeconomic theory describing individual optimizing behavior, but use consumer expenditure data of the entire country, thereby implicitly treating the aggregated data as if they were generated by a single person. In a similar circumstance the output of a firm is theoretically derived based on the principle of profit maximization. Estimation of production functions of firms, however, is often done using data based on an entire industry or country. The assumption of a single consumer or firm being a representative of the entire economy is a convenient one, in that it allows application and testing of microeconomic theories with available aggregate data, and it avoids intractable problems of aggregation and collective choice. Unfortunately, there is no reason deriving from economic theory to assume that national aggregate data, which is the result of adding the economic activities of millions of diverse individuals, will resemble the economic activity of a single firm or consumer. The researcher must thus assume some general parameters for the aggregated data in order to uncover the underlying optimizing behavior. Past theoretical work has shown that very little structure need be assumed on the aggregated data to infer the existence of aggregate demand or supply functions, and that those restrictions need be placed only on the statistical distribution of the aggregate data. Thus one can validly restrict the distribution of consumer expenditures to remain unchanged through time or to change in general specified ways. Such distributional assumptions can also be applied to production. Professor Lewbel derives aggregate demand equations for the economy by considering the restrictions on the changes over time in the distribution of total expenditures in the population, and combining them with specific individual demand behavior. These aggregate demand equations satisfy all the conditions of utility maximization on which individual demand equations are based. Technically, he constructs nonlinear models of macroeconomic data based on explicit models of both heterogeneous microeconomic behavior and of the evolution over time of the distribution of individual agents in the economy. This allows for the construction of models of shifts in the distributions through time that are compatible with aggregation theory. Professor Lewbel tests the theoretical validity of aggregate models by estimation using cross sectional or panel data, and by studying the distribution data in several time periods. These methods are applied to various national data sets like the National Income and Product Accounts, the Consumer Expenditure Survey, and the U. S. Current Population Reports.