Stochastic Revealed Preferences with Measurement Error : Testing for Exponential Discounting in Survey Data

Measurement error causes a loss of distributional information, preventing the researcher from applying the deterministic revealed-preference tools at the individual level. This paper proposes a new statistical revealed-preference framework that is applicable to such cases. We use our framework to establish a nonparametric test of the standard exponential-discounting, time-separable consumer model in environments with measurement error in consumption. The proposed testing procedure is asymptotically consistent, though it may be conservative. We provide Monte Carlo evidence showing that measurement error in the standard deterministic revealed-preference tests may lead to mistakenly judging an otherwise time-consistent consumer to be time-inconsistent. In contrast, our methodology does not reject the exponential-discounting model in such cases. We find support for exponential-discounting behavior in a consumption panel survey for single-individual households, while rejecting the model for the case of couples' households