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 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 for consumer models that can be characterized by their first-order conditions in environments with measurement error in consumption. The proposed testing procedure is asymptotically consistent. We provide Monte Carlo evidence showing that measurement error in the standard deterministic revealed-preference tests may lead to mistakenly judging an otherwise model-consistent consumer to be model-inconsistent. In contrast, our methodology does not reject model consistency in such cases. In the application we develop, we find support in a consumption panel survey for exponential discounting behavior in single-individual households but not in couples' households. The first finding stands in contrast with the conclusions drawn from applying the deterministic revealed-preference test of Browning (1989) to the same sample