Stochastic Revealed Preferences with Measurement Error

TL;DR

This paper introduces a new nonparametric statistical framework for testing the utility maximization theory using consumer panel data, accounting for measurement error, and provides evidence supporting or rejecting UMT in different datasets.

Contribution

It develops a novel RP testing method that handles measurement error and heterogeneity, improving upon traditional deterministic tests.

Findings

Support for dynamic and time-consistent UMT in survey data with nonclassical measurement error.

Failure to reject static UMT in experimental data with price misperception.

Contrasts with previous deterministic RP test conclusions.

Abstract

A long-standing question about consumer behavior is whether individuals' observed purchase decisions satisfy the revealed preference (RP) axioms of the utility maximization theory (UMT). Researchers using survey or experimental panel data sets on prices and consumption to answer this question face the well-known problem of measurement error. We show that ignoring measurement error in the RP approach may lead to overrejection of the UMT. To solve this problem, we propose a new statistical RP framework for consumption panel data sets that allows for testing the UMT in the presence of measurement error. Our test is applicable to all consumer models that can be characterized by their first-order conditions. Our approach is nonparametric, allows for unrestricted heterogeneity in preferences, and requires only a centering condition on measurement error. We develop two applications that provide new evidence about the UMT. First, we find support in a survey data set for the dynamic and time-consistent UMT in single-individual households, in the presence of \emph{nonclassical} measurement error in consumption. In the second application, we cannot reject the static UMT in a widely used experimental data set in which measurement error in prices is assumed to be the result of price misperception due to the experimental design. The first finding stands in contrast to the conclusions drawn from the deterministic RP test of Browning (1989). The second finding reverses the conclusions drawn from the deterministic RP test of Afriat (1967) and Varian (1982).