Bagging Weak Predictors

Relations between economic variables are often not exploited for forecasting, suggesting that predictors are weak in the sense that the estimation uncertainty is larger than the bias from ignoring the relation. In this paper, we propose a novel bagging estimator designed for such predictors. Based on a test for finite-sample predictive ability, our estimator shrinks the OLS estimate not to zero, but towards the null of the test which equates squared bias with estimation variance, and we apply bagging to further reduce the estimation variance. We derive the asymptotic distribution and show that our estimator can substantially lower the MSE compared to the standard ,t-test bagging. An asymptotic shrinkage representation for the estimator that simplifies computation is provided. Monte Carlo simulations show that the predictor works well in small samples. In an empirical application, we find that our proposed estimators works well for inflation forecasting using unemployment or industrial production as predictors.