Heterogeneity in Economics and Aggregation

Abstract

Heterogeneity is all around us. People differ substantially with respect to their tastes, expectations, and available resources, and firms are heterogeneous in technologies and the quantity or nature of input factors. Since macroeconomics deals, amongst others, with relationships between aggregates over heterogeneous populations of economic agents, sound macroeconomic models should not neglect nor implausibly restrict the variety of agents. In models without behavioral heterogeneity there is no room for distributional considerations, trade, asymmetric information or coordination of individuals. Finally, the presence of heterogeneity is crucial to guarantee the uniqueness and stability of equilibrium.<br /> Yet, many macroeconomic models treat heterogeneity in a very simplistic and often trivial way. They are based on the notion of the representative agent (RA) who solves an explicitly stated optimization problem and whose choices coincide with the aggregate choices of the heterogeneous individuals or firms. The traditional aggregate consumption function and aggregate production function are best examples of this modeling approach. However, the logical consistency of these models, that is, the compatibility with microeconomic theories of behavior, requires very restrictive and implausible assumptions on the heterogeneity of the population and on the model of individual behavior. The straightforward conclusion is that traditional aggregate consumption and production functions, in general, do not exist. This negative theoretical result is far from being new, as its earliest version goes back to Antonelli (1886). <br /> Surprisingly, despite these theoretical shortcomings, RA models are still common practice in the literature. It is surprising, since there exists a well developed statistical aggregation theory. This theory can be used to build aggregationally consistent macroeconomic models, which are flexible enough to include very general types of heterogeneity and analyze its effect on macroeconomic outcomes. In this context, Hildenbrand and Kneip (1999, 2005) proposed an approach, which concentrates directly on modeling economic aggregates in terms of entire distributions of individual variables. Its main advantage is that the parametric specification of the individual model of behavior and the pattern of heterogeneity in the population is not needed. The cornerstone of their model are distributional assumptions of the structural stability type, which are supported by empirical studies. Chapters 1 and 2 of this thesis are closely related to their work. In particular, in Chapter 1 a growth model for an economy consisting of firms which are heterogeneous in technologies and input demands is proposed. Aggregation over these firms is carried out according to the distributional approach established in Hildenbrand and Kneip (2005). It is shown that the growth rate in this economy depends not only on changes in the aggregate level of capital and labor, but also on changes in the allocation of these inputs across firms. As the latter effects are neglected in conventional growth models, they are misleadingly captured by the residual TFP measure. In contrast, one is able to quantify the influence of these components in our study. An empirical analysis, which is based on structural estimation from firm-level data, reveals that changes in allocation of capital and labor have pronounced effects on GDP-growth for most European countries. Further, cross-country differences in the distributional effects are taken into account to improve conventional growth accounting exercises. In particular, it is found that they explain a sizable part of growth differences across countries.<br /> Chapter 2 analyzes the property of structural stability of the joint distribution of households' income and wealth, which is required to build an aggregatively consistent model for aggregate consumption of a heterogeneous population. Empirical analysis based on the U.K. Family Resources Survey data from the period 1996-2001 examines whether the sequence of these distribution is structurally stable in the sense related to Malinvaud (1993). Hence, the main objective of this chapter is to look for the local time-invariance of a distribution derived by applying simple transformations like scaling or standardizing to the original distribution. This analysis makes use of kernel density estimation to identify the changes in shapes of the aforementioned distributions and to perform a nonparametric density time-invariance test as proposed by Li (1996). The main result is that accounting only for the changes in the vector of means of the original distribution is not sufficient to obtain the desired local time-invariance. In fact, this can be achieved by accounting for changes in the vector of means and dispersion parameters of the original distribution.<br /> Finally, Chapter 3 deals with different concepts of income elasticities of demand for a heterogeneous population and the relationship between individual and aggregate elasticities is analyzed. In particular, it allows to compare the income elasticity of demand of the representative agent with the distribution of individual income elasticities. It is shown that, in general, the aggregate elasticity is not equal to the mean of individual elasticities. The difference depends on the heterogeneity of the population and is quantified by a covariance term. Sign and magnitude of this term are determined by an empirical analysis based on the U.K. Family Expenditure Survey. It is shown that the relevant quantities can be identified from cross-section data and, without imposing restrictive structural assumptions, can be estimated by nonparametric techniques. It turns out that the aggregate elasticity significantly overestimates the mean of individual elasticities for many commodity groups.