Completeness, Distribution Restrictions, and the Form of Aggregate Functions
提出将个体聚合视为识别问题，引入完备聚合结构概念，通过统计中的完备分布族说明微观行为与平均数据估计关系可能不一致，并回顾聚合结果的经验应用。
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.