Marginal homogeneity tests with panel data

TL;DR

This paper develops and compares several statistical tests for assessing marginal homogeneity in panel data, focusing on their asymptotic properties and finite-sample validity under different conditions.

Contribution

It introduces new tests for marginal homogeneity in panel data and analyzes their theoretical properties, including asymptotic correctness and finite-sample validity.

Findings

Asymptotic tests are asymptotically exact using bootstrap and asymptotic approximations.

Permutation tests are asymptotically valid for T=2, but vary for T>2 depending on studentization.

Under time-exchangeability, permutation tests are exact in finite samples.

Abstract

A panel dataset satisfies marginal homogeneity if the time-specific marginal distributions are homogeneous or time-invariant. Marginal homogeneity is relevant in many economic settings, including dynamic discrete games, difference-in-differences models, and finance. In this paper, we propose several tests for the hypothesis of marginal homogeneity and investigate their properties. We consider an asymptotic framework in which the number of individuals n in the panel diverges, while the number of periods T is fixed. We implement our tests by comparing a studentized or non-studentized T-sample version of the Cramer-von Mises statistic with a suitable critical value. We propose three methods for constructing the critical value: asymptotic approximations, the bootstrap, and time permutations. We show that the first two methods result in asymptotically exact hypothesis tests. The permutation test based on a non-studentized statistic is asymptotically exact when T=2, but is asymptotically invalid when T>2. In contrast, the permutation test based on a studentized statistic is always asymptotically exact. Finally, under a time-exchangeability assumption, the permutation test is exact in finite samples, both with and without studentization.