Nickell Meets Stambaugh: A Tale of Two Biases in Panel Predictive Regressions

Abstract: In panel predictive regressions with persistent covariates, coexistence of the Nickell bias and the Stambaugh bias imposes challenges for hypothesis testing. This paper introduces a new estimator, the IVX-X-Jackknife (IVXJ), which effectively removes this composite bias and reinstates standard inferential procedures. The IVXJ estimator is inspired by the IVX technique in time series. In panel data where the cross section is of the same order as the time dimension, the bias of the baseline panel IVX estimator can be corrected via an analytical formula by leveraging an innovative X-Jackknife scheme that divides the time dimension into the odd and even indices. IVXJ is the first procedure that achieves unified inference across a wide range of modes of persistence in panel predictive regressions, whereas such unified inference is unattainable for the popular within-group estimator. Extended to accommodate long-horizon predictions with multiple regressions, IVXJ is used to examine the impact of debt levels on financial crises by panel local projection. Our empirics provide comparable results across different categories of debt.