Robust GMM tests for structural breaks

Abstract

We propose a class of new robust Generalized Method of Moments (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 via 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 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 both in exactly identified and overidentified model settings. In small samples, bootstrapped versions of the classical and the robust GMM tests provide accurate and stable empirical levels also for quite small sample sizes. However, bootstrapped robust GMM tests are found to provide again a higher finite sample efficiency.