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Evaluating the aggregation biases in a production economy : a stochastic approach Fortin, Nicole M.


This dissertation presents a theoretical framework to analyze and evaluate aggregation biases. These biases measure the information lost when macro relations evaluated in terms of aggregates do not capture all of the distributional properties of micro relations. The framework is developed in the context of producer theory, but it may be used to determine the biasedness of any representative agent model and to study general relationships between exact-aggregation macro parameters and their microfoundations. The model is based on a stochastic interpretation of the production characteristics which encompasses that of previous stochastic aggregation models (Houthakker, 1955; Hildenbrand, 1981; Stoker, 1984; Lewbel, 1986a). It admits the construction of "true" aggregate relations which can be compared to pre-specifed macro relations. Many of Theil's (1954, 1971) statistical results concerning the relations between micro and macro parameters then can be formalized at the population level and generalized to non-linear functions. A moments decomposition of the "true" aggregate relation makes it possible to identify the sources and causes of potential aggregation biases. Thus, the functional-form restrictions of exact-aggregation models (Gorman, 1968a; Blackorby and Schworm, 1984, 1988) are found to be neither necessary nor sufficient conditions for consistent aggregation, if the aggregates are taken to be the usual totals or averages. Traditionally, similarity among firms, either as a maintained hypothesis or as the long-run outcome of perfect competition, has proved to ensure exact aggregation. Here, economic diversification may also provide an alternative set of circumstances under which the aggregation biases may be minimized. In the case of an average-representative firm, the output aggregation bias is explicitly derived. Empirical analyses confirm that the magnitude of the bias increases as higher moment terms in the production characteristics increase in importance. Conditions under which exact-aggregation macro parameters possess stable microdefinitions are obtained; they explain Fisher's (1971) simulation results. Empirical results show that such macro parameters are relatively stable (within the estimated confidence intervals) when based on periods of relative economic stability. Finally, theoretical implications for macroeconometric modeling and policy evaluation are explored.

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