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Completeness, Distribution Restrictions, and the Form of Aggregate Functions

Thomas M. Stoker

Abstract

This paper presents the problem of aggregation over individual agents as a basic identification problem inherent to interpreting relationships between averaged economic variables. The concept of a complete aggregation structure is introduced, which embodies the correct condition for identification. Several examples of complete aggregation structures are provided by previous work on the aggregation problem in economics. Examples are also provided by work on complete distribution families in statistics, which in turn provide the correct conceptual framework for developing a theory of parameter estimation and tests of specific aggregation assumptions. The potential lack of correspondence between microeconomic behavior and estimated relations between averaged data is illustrated by distribution families obeying linear probability movement, which induce an extreme failure of the completeness property. Certain topics regarding empirical applications of aggregation results are reviewed.