The Stambaugh bias in panel predictive regressions

Abstract

This paper analyzes predictive regressions in a panel data setting. The standard …xed e¤ects estimator su¤ers from a small sample bias, which is the analogue of the Stambaugh bias in time-series predictive regressions. Monte Carlo evidence shows that the bias and resulting size distortions can be severe. A new bias-corrected estimator is proposed, which is shown to work well in …nite samples and to lead to approximately normally distributed t-statistics. Overall, the results show that the econometric issues associated with predictive regressions when using time-series data to a large extent also carry over to the panel case. The results are illustrated with an application to predictability in international stock indices.JEL classi…cation: C22, C23, G1.

Predictable Financial Crises

“…15 Stambaugh (1999) bias arises in finite samples when the regression residuals are uncorrelated with current and past values of the predictors but may be correlated with future values of the predictors. This estimation bias is familiar from pure time-series settings, but a similar bias can arise in panel forecasting regressions (Hjalmarsson (2008)). Our setting involves estimating multivariate forecasting regressions in a panel setting with overlapping observations.…”

“…Our setting involves estimating multivariate forecasting regressions in a panel setting with overlapping observations. While there are analytical approaches to correcting for Stambaugh (1999) bias in panel settings (Hjalmarsson (2008)), when estimating multivariate regressions (Amihud, Hurvich, and Wang (2009)), and when using overlapping regressions (Boudoukh, Israel, and Richardson (2020)), we are not aware of an analytical approach that is appropriate in a setting like ours that combines these three elements. Accordingly, we use a nonparametric bootstrapping procedure to assess the finite-sample bias of our forecasting regressions.…”

The role of stickiness, extrapolation and past consensus forecasts in macroeconomic expectations

“…Thus, forecasters do not seem to use a qualitatively different forecasting rule in a more stable economic environment. Also, in Appendix B.3, we discuss that our results, here and in the following sections, are robust with respect to excluding small samples which potentially cause biases under fixed effects (Nickell, 1981;Hjalmarsson, 2008).…”

“…This is a relevant issue for the fixed effect estimates which may potentially be subject to small sample biases. These small sample biases are well understood in the context of dynamic panel models (Nickell, 1981) and predictive panel regressions (Hjalmarsson, 2008).…”