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 demand system.- 7.5. Demand for leisure: a simulation example.- Appendix: the correlation-coefficient matrices used in 7.5.- 8. Collective choice and macro-economic policy.- 8.1. Introduction.- 8.2. Objective functions.- 8.3. The valuation of a compromise.- 8.4. Aggregation of results of actual interviewing (Canada).- 8.5. Some Dutch evidence.- IV. Epilogue: Optimal aggregation.- IV. Epilogue: Optimal aggregation.- References.- Author Index.

Our interest in problems of aggregation originates from about seven years ago when we became involved in research in the field of applied microeconomics. To our astonishment a vast majority of researchers in this area took it for granted that their, mostly thoroughly derived, micro models could meaningfully be confronted with per capita data. Nany of them did not even realize - at least they gave no utterance to it - that applying macro data in micro models raises considerable problems. Those who did mention the difficulty, almost always belittled its importance. Fortunately, there are noteworthy exceptions. Thinking about aggregation raises at least two questions: "Why or why not aggregate?" and "How to aggregate and, in particular, to what degree?" General answers to these questions can only be given in uninformative wording (as many assertions in economics): one aggregates for the sake of tractability, because of the lack of (individual) data, to avoid or to reduce multicollineartiy, to save degrees of freedom; one abstains from aggregation to avoid loss of information, to avoid aggregation biases and one aggregates such and to such degree as to bypass or reduce the drawbacks mentioned above.