Nonparametric Analysis of Dynamic Random Utility Models

TL;DR

This paper introduces the Dynamic Random Utility Model (DRUM), a framework for analyzing consumer choices over time with stochastic utility, providing a revealed preference characterization that unifies static and dynamic models for statistical testing.

Contribution

It develops a new dynamic model of consumer behavior with stochastic utility and offers a revealed preference characterization suitable for empirical testing.

Findings

Provides a unified framework for static and dynamic random utility models.

Offers a revealed preference test for DRUM using panel choice data.

Extends Afriat's theorem to dynamic stochastic utility settings.

Abstract

We study a dynamic generalization of stochastic rationality in consumer behavior, the Dynamic Random Utility Model (DRUM). Under DRUM, a consumer draws a utility function from a stochastic utility process and maximizes this utility subject to her budget constraint in each time period. Utility is random, with unrestricted correlation across time periods and unrestricted heterogeneity in a cross-section. We provide a revealed preference characterization of DRUM when we observe a panel of choices from budgets. This characterization is amenable to statistical testing. Our result unifies Afriat's (1967) theorem that works with time-series data and the static random utility framework of McFadden-Richter (1990) that works with cross-sections of choice.