Demand Dispersion, Metonymy and Ideal Panel Data
In a generic competitive economy with constant returns production and "increasing dispersion," market demand satisfies the weak axiom of revealed preference and equilibrium is unique. Increasing dispersion requires, roughly, that when the households' incomes rise slightly their demand vectors move apart. We show how to test for it using panel data with fixed relative prices under a "structural stability" hypothesis due to Hildenbrand and Kneip (1999). We also show how to test for it using cross section data if the households' demand functions and incomes are independently distributed, or under a much weaker condition called "dispersion metonymy." We show that this weaker condition is untestable---even with ideal panel data that allow a direct test of increasing dispersion. Thus, cross section tests of increasing dispersion rely on an assumption that is not potentially falsifiable.
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