The Empirical Content of Revealed Preference in High Dimensions

We examine how the empirical content of revealed preference theory depends on the dimensionality of the choice environment. While higher-dimensional choice problems may appear more demanding, we show that revealed preference restrictions become less informative. Using Selten's Area measure, we establish that for any fixed number of observations, the empirical content of GARP converges to zero exponentially fast in the number of goods. We provide complementary proofs based on revealed preference graphs and the Afriat inequalities, and show in simulations calibrated to scanner data that the effect is quantitatively large. We also evaluate potential responses in observational and experimental settings and find that, while these can slow the rate, they do not eliminate this loss of empirical content.