Instrumental variable and variable addition based inference in predictive regressions

Valid inference in predictive regressions depends in a crucial manner on the degree of persistence of the predictor variables. The paper studies test procedures that are robust in the sense that their asymptotic null distributions are invariant to the persistence of the predictor, that is, the limiting distribution is the same irrespective of whether the regressors are stationary or (nearly) integrated. Existing procedures are often conservative (e.g. tests based on Bonferroni bounds), are based on highly restrictive assumptions (such as homoskedasticity or assuming an AR(1) process for the regressor) or fail to have power against alternatives in a 1T neighborhood of the null hypothesis. We first propose a refinement of the variable addition method with improved asymptotic power approaching the optimal rate. Second, inference based on instrumental variables may further improve the (local) power of the test and even achieve local power under the optimal 1T rate. We give high-level conditions under which the suggested variable addition and instrumental variable procedures are valid no matter whether the predictor is stationary, near-integrated or integrated, or exhibits time-varying volatility. All test statistics possess a standard limiting distribution. Monte Carlo experiments suggest that tests based on simple combinations of instruments perform most promising relative to existing tests. An application to quarterly US stock returns illustrates the need for robust inference.