Structural Stability Testing in Models Estimated by Generalized Method of Moments

This article proposes a new methodology for testing structural stability in models estimated via generalized method of moments. Like most previous studies of this general problem, attention is focused on the case in which some aspect of the model potentially changes at a single point in the sample, known as the “breakpoint.” Unlike this earlier work, however, our approach is based on a decomposition of the null hypothesis into two components involving parameter constancy and the validity of the overidentifying restrictions both before and after the suspected breakpoint. Using this framework, we propose a testing strategy that offers the potential to discriminate between parameter variation and more general forms of instability. Statistics are presented for testing our null hypotheses in both the known and unknown breakpoint cases. The tests are applied to the conditional capital asset pricing model used by Harvey to explain the international variation in stock index returns. Harvey reported that data from five of the G7 countries satisfy the full-sample overidentifying restrictions of the model; our results indicate that all five of these models exhibit structural instability and so are misspecified.