Alfred P . Sloan School of Management

This paper investigates the use of individual cross section data to describe macro functions. Necessary and sufficient conditions (denoted AS) are found for 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 described.