SFB 303 Discussion Paper No. A-429

Author: Jerison, David, and Michael Jerison
Title: Commodity Aggregation and Slutysky Asymmetry
Abstract: Consumer expenditure data often violate the revealed preference axioms. The observed revealed preference inconsistencies must be measured in order to judge the extent to which optimizing models misrepresent demand behavior. This paper considers the "sizes" of violations of the Ville axiom, a differential revealed preference axiom that is equivalent to Slutsky symmetry. We study the effect to commodity aggregation is justified in the sense that it generates a well-defined aggregated demand function. Using a natural measure of Slutsky asymmetry and Ville axiom violation, we show that commodity aggregation can either expand or eliminate the revealed preference inconsistency. We obtain an upper bound on the increase in the maximal sizes of Ville axiom violations duee to commodity aggregation. The Slutsky asummetry norm of the aggregated demand can be larger than that of the original demand function by a factor that is not greater than the squareroot of nm/N, where N is the number of goods in the original demand system, m is the number of goods that are aggregated, and n=N-m+1 is the number of goods in the aggregated system.
Keywords:Slutsky symmetry, Ville axiom, revealed preference, commodity aggregation
JEL-Classification-Number: D11
Creation-Date: January 1994
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