Theoretically Valid Aggregates in the Absence of Homothetic Preferences, Separable Utility, and Complete Price Data
Van Eenoo, Jr., Edward Charles
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The improper aggregation of commodities can have important consequences when estimating a system of group demand equations. Generally, aggregates are created under the assumptions that intra-group preferences are homothetic and the consumer's utility function is weakly separable over some partition. These assumptions place severe restrictions on the model that can significantly impact parameter and elasticity estimates. An alternative to imposing weak separability is to employ the Generalized Composite Commodity Theorem, which requires the relative intra-group commodity prices to be independent of the group price index. This study compares the results of estimating a demand system for composite beef, pork, and poultry products under the assumptions of weak separability and the Generalized Composite Commodity Theorem. Another important issue related to aggregation is the specification of an appropriate group price index. Price indices consistent with linear homogeneous preferences (a subset of the homothetic class of preferences) and non-homothetic intra-group preferences are identified and it is shown that several of the commonly employed indices are biased in the absence of complete price data.
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