Robust GMM Tests for Structural Breaks

We propose a class of new robust GMM tests for endogenous structural breaks. The tests are based on supremum and average statistics derived from robust GMM estimators with a bounded influence function. They imply a bounded linearized asymptotic bias of size and power under local model misspecifications. We illustrate the trade-o. between robustness and e.ciency of the new robust tests in some Monte Carlo simulation where we find that the performance of classical GMM tests is highly unstable under local model misspecifications. In particular, the loss in power can be very substantial in some models. Similarly, the size of the classical tests can be very unstable, especially in models based on nonlinear orthogonality functions. Robust testing procedures yield important power improvements under a misspecified model while under an exact reference model they yield a performance comparable to the one of classical tests. Moreover, robust procedures stabilize the size under a model misspecification for those models where important size instabilities of the classical tests have been observed. Finally, classical testing procedures based on the supremum functional seem to be less stable than those based on the average, implying larger power improvements of robust procedures in this case when compared with the case of an average statistic.