Bagging weak predictors

Often, relations between economic variables cannot be 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 ordinary least squares estimate—not to zero, but towards the null of the test that equates squared bias with estimation variance. We apply bagging to reduce the estimation variance further. We derive the asymptotic distribution and show that our estimator substantially lowers the mean-squared error compared to standard t-test bagging. An asymptotic shrinkage representation for the estimator that simplifies the computation is provided. Monte Carlo simulations showed that the predictor works well with small samples. Empirically, we found that our proposed estimator worked well for inflation forecasting when using unemployment or industrial production as predictors. In an application for predicting equity premiums, the combination of our estimator and a positive constraint on forecasts delivered statistically significant gains relative to the historical average using a wide range of predictors.