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Aggregation, Efficiency, and Cross-Section Regression

Thomas M. Stoker

Abstract

In this paper several results are established which provide for the consistent estimation of macroeconomic effects using cross-section data, for general assumptions on the movement of the population distribution over time. We show that macroeconomic effects are always consistently estimated by linear instrumental variables coefficients, where the instruments are determined by the form of distribution movement. This leads to a natural way to assess the biases in OLS coefficients as estimators of macroeconomic effects, provides a nonparametric macroeconomic interpretation of linear instrumental variables coefficients when the true microeconomic behavioral model is unknown, and gives a nonparametric interpretation of standard regression decomposition statistics such as R^2 relative to the information costs of nonlinearities in aggregation. All of the results are valid without imposing any testable restrictions on the cross-section data.