The Use of Cross-Section Data to Characterize Macro Functions

Abstract

Abstract This article investigates the use of individual cross-section data to describe macro functions. Necessary and sufficient conditions (denoted by AS) are found for ordinary least squares (OLS) slope coefficients from a cross section to consistently estimate the first derivatives of the macro function. AS embodies both sets of aggregation assumptions known; linear aggregation and sufficient statistics, and thus represents generalized aggregation conditions. A methodology is given for estimating second-order derivatives of the macro function from cross-section data for distributions of the exponential family, which extends to higher-order derivatives. Finally, a general test of linear aggregation schemes is presented. Key Words: Cross-section least squares regressionAggregation theoryAsymptotic sufficiencyLinear aggregationSufficient statisticsExponential family