Aggregation in Economic Research

I. Introduction.- I. Introduction.- II. On Theory.- 1. Aggregation without side conditions.- 1.1. Introduction.- 1.2. Examples of consistent aggregation.- 1.3. Nataf's result on consistent aggregation.- 1.4. Some remarks on consistent multi-stage aggregation.- 1.5. Some further results on consistent aggregation.- 1.6. Consequences for empirical work.- Appendix A: Differences between some aggregates.- Appendix B: Proof of some lemmas.- 2. Aggregation of production functions under optimum conditions.- 2.1. Introduction.- 2.2. The production frontier and some properties of production functions.- 2.3. Aggregation on the frontier.- 2.4. Some consequences of the foregoing results.- 3. Aggregation and individual preferences.- 3.1. Introduction.- 3.2. Aggregation of utility (functions).- 3.3. Collective preference schemes based on individual schemes; Arrow's conditions.- 3.4. Some examples of aggregation of individual preferences; contingencies of the occurrence of inconsistencies.- 3.5. Proof of Arrow's "Possibility Theorem".- 3.6. Aggregation of individual demand functions; the representative consumer.- Appendix: Proof of some theorems.- 4. Aggregation and the distribution of individual characteristics.- 4.1. Introduction.- 4.2. Consistent aggregation in continuous analysis.- 4.3. Inconsistent aggregation: the analogy procedure.- 4.4. The distribution approach to the problem of deriving an industry's short-run production function.- 4.5. The distribution approach to the problem of aggregation over markets.- 5. Linear aggregation and estimation.- 5.1. Introduction.- 5.2. Aggregation bias.- 5.3. Aggregation gain.- Appendix: Proof of two lemmas.- 6. Aggregation over arguments of a function.- 6.1. Introduction.- 6.2. Aggregation over commodities.- 6.3. An example.- III. Some Applications.- 7. Aggregation and consumer behaviour.- 7.1. Introduction.- 7.2. Money illusion and aggregation bias.- 7.3. A quadratic Engel curve demand for per capita data.- 7.4. An alternative aggregate