A Dimensionality-Robust Test in Multiple Predictive Regression

Abstract

We consider inference of predictive regression with multiple predictors. Extant tests for predictability, including those constructed with robustness to unknown persistence and endogeneity of predictors, may perform unsatisfactorily and tend to discover spurious predictability as the number of predictors increases. We propose a battery of new instrumental-variables based tests which involve enforcement or partial enforcement of the null hypothesis in variance estimation and analyze their asymptotic properties. A test based on the parsimonious system approach is recommended. Empirical Monte Carlos demonstrate the remarkable finite-sample performance regardless of numerosity of predictors. Empirical application to equity premium predictability is also provided.

Keywords: curse of dimensionality; Lagrange-multipliers test; persistence; predictive regression; return predictability

JEL Classification: C32; C53; C58; G12