Beyond the Mean: Testing Consumer Rationality through Higher Moments of Demand

Sebastiaan Maes and Raghav Malhotra
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Sebastiaan Maes: University of Antwerp
Raghav Malhotra: University of Leicester

CRETA Online Discussion Paper Series from Centre for Research in Economic Theory and its Applications CRETA

Abstract: We study a setting where an analyst has access to purely aggregate information about the consumption choices of a heterogenous population of individuals. We show that observing the statistical moments of market demand allows the analyst to test aggregate data for rationality. Interestingly, just the mean and variance of demand carry observable restrictions. This is in stark contrast to impossibility result of the Sonnenschein-Mantel-Debreu theorem, which shows that aggregate demand carries no observable restrictions at all. We leverage our approach to deliver a characterization of rationality in terms of moments for the common twogood case. We illustrate the usefulness of moment-based restrictions through two applications: (i) improving the precision of demand and welfare estimates; and (ii) testing for the existence of a welfare-relevant representative consumer.

Keywords: consumer demand; moments of demand; stochastic rationalizability JEL codes: C14; C31; D11; D12; D63 (search for similar items in EconPapers)
Date: 2024
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