Using OLS to estimate and test for structural changes in models with endogenous regressors

Abstract

We consider the problem of estimating and testing for multiple breaks in a single-equation framework with regressors that are endogenous, i.e. correlated with the errors. We show that even in the presence of endogenous regressors it is still preferable, in most cases, to simply estimate the break dates and test for structural change using the usual ordinary least squares (OLS) framework. Except for some knife-edge cases, it delivers estimates of the break dates with higher precision and tests with higher power compared to those obtained using an instrumental variable (IV) method. Also, the OLS method avoids potential weak identification problems caused by weak instruments. To illustrate the relevance of our theoretical results, we consider the stability of the New Keynesian hybrid Phillips curve. IV-based methods only provide weak evidence of instability. On the other hand, OLS-based ones strongly indicate a change in 1991:Q1 and that after this date the model loses all explanatory power.