Stochastic Revealed Preferences with Measurement Error

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 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).

Measurement systems

“…Sometimes the outcome variable   varies discontinuously with the explanatory variables (    *  ), making the identification problem more challenging, due to the resulting strong nonlinearity. A typical example comes from revealed preferences models (among many others, McFadden (2005), Aguiar and Kashaev (2020), Afriat (1973), Varian (1982)), where the outcome variable is the good being selected, while the good's characteristics and/or the individual preferences are only partially observed. Here again the identification analysis benefits from the availability of multiple outcomes where, say, unobserved preferences  *  are known to remain constant because the same individual is being observed, while the available goods' characteristics   may differ.…”

“…The ELVIS framework has also been used by Aguiar and Kashaev (2020) to devise more realistic tests of the fundamental exponential discounting model within a revealed preferences framework. The idea is that the consumers' exponentially discounting behavior can be masked if there is heterogeneity in their discount factors as well as measurement errors in prices and/or quantities.…”

Nonparametric Analysis of Dynamic Random Utility Models

“…This unification is advantageous because it (i) provides more informative bounds on counterfactual choice due to the richer variation in the panel of choices; (ii) provides a theoretical justification for slicing choices and using the RUM framework; and (iii) clarifies the role of the constant preferences across time assumption in the Afriat's framework that allows to test rationality using only time-series of choices. Fortunately, our primitive with a longitudinal level of variation is readily available in many consumption surveys, household scanner datasets, and experimental dataset as documented in Aguiar and Kashaev (2021).…”

“…The DRUM framework is rich and extends well beyond the Afriat's and McFadden-Richter world. We cover as special cases: (i) consumption models of errors in the evaluation of utility (Kurtz-David et al, 2019); (ii) dynamic random expected utility (defined in Frick, Iijima and Strzalecki (2019)) for choices over portfolios of securities as in Polisson, Quah and Renou (2020);(iii) static utility maximization in a population (without measurement error) (Aguiar and Kashaev, 2021); (iv) dynamic utility maximization in a population 2 (Browning, 1989, Gauthier, 2018, Aguiar and Kashaev, 2021; (v) changing utility or multiple-selves models (Cherchye et al, 2017); and changing-taste modeled with a constant utility in time with an additive shock (Adams, Blundell, Browning and Crawford, 2015).…”

Testable Implications of Models of Intertemporal Choice: Exponential Discounting and Its Generalizations

“…Adams et al (2014) work with the Spanish dataset and test EDU within a model of collective decision making at the household level. Aguiar and Kashaev (2018) provide a stochastic revealed-preference approach that is applicable to consumer survey data with measurement error.…”