Predictability Tests Robust against Parameter Instability

Abstract: We consider Wald type statistics designed for joint predictability and structural break testing based on the instrumentation method of Phillips and Magdalinos (2009). We show that under the assumption of nonstationary predictors: (i) the tests based on the OLS estimators converge to a nonstandard limiting distribution which depends on the nuisance coefficient of persistence; and (ii) the tests based on the IVX estimators can filter out the persistence under certain parameter restrictions due to the supremum functional. These results contribute to the literature of joint predictability and parameter instability testing by providing analytical tractable asymptotic theory when taking into account nonstationary regressors. We compare the finite-sample size and power performance of the Wald tests under both estimators via extensive Monte Carlo experiments. Critical values are computed using standard bootstrap inference methodologies. We illustrate the usefulness of the proposed framework to test for predictability under the presence of parameter instability by examining the stock market predictability puzzle for the US equity premium.