Robust GMM Tests for Structural Breaks

Abstract

We propose a class of new robust GMM tests for endogenous structural breaks. The tests are based on supremum, average and exponential functionals derived from robust GMM estimators with bounded influence function. We study the theoretical local robustness properties of the new tests and show that they imply a uniformly bounded asymptotic sensitivity of size and power under general local deviations from a reference model. We then analyze the finite sample performance of the new robust tests in some Monte Carlo simulations, and compare it with that of classical GMM tests for structural breaks. In large samples, we find that the performance of classical asymptotic GMM tests can be quite unstable already under slight departures from some given reference distribution. In particular, the loss in power can be substantial in some models. Robust asymptotic tests for structural breaks yield important power improvements already under slight local departures from the reference model. This holds both in exactly identified and overidentified model settings. In small samples, bootstrapped versions of both the classical and the robust GMM tests provide a very accurate and very stable empirical size also for quite small sample sizes. However, bootstrapped robust GMM tests are found to provide again a higher finite sample efficiency.

Keywords: Robust Tests, Generalized Method of Moment, Structural Breaks, Monte Carlo, Bootstrap

JEL Classification: C10, C12, C13, C15