Gaussian Inference in Predictive Regressions for Stock Returns

Predictive regressions are an important tool in empirical finance. Under persistent predictors and so-called predictive regression endogeneity, OLS-based estimators and tests exhibit nonnormal limiting distributions. M estimators in such predictive regressions inherit these traits. The limiting distributions of different M estimators and M estimation-based tests of predictability depend on the same non-standard component. We exploit this to eliminate the nonstandard component and obtain standard normal test statistics of no predictability by building suitable linear combinations of two different M-based t ratios. This further enables us to set up a fixed-regressors bootstrap procedure to avoid the multiple-testing problem when applying the new test in rolling subsamples. Examining the predictability of U.S. stock returns, we find evidence for stock return predictability in volatile business cycle periods, such as World War II, Oil Crisis and Great Recession.