Bootstrapping Factor-Augmented Regression Models

• Activity Number: 273
• Type: Invited
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Silvia Goncalves*+ and Perron Benoit
• Companies: Universite de Montreal and Universite de Montreal
• Keywords: factor model ; bootstrap ; asymptotic bias

Abstract

The main contribution of this paper is to propose and theoretically justify bootstrap methods for factor-augmented regressions where some of the regressors are factors estimated from a large panel of data. We derive our results under the assumption that vT/N ? c, where 0 = c < 8, thus allowing for the possibility that factors estimation error enters the limiting distribution of the OLS estimator. Our main results can be summarized as follows. When c = 0, as in Bai and Ng (2006), the crucial condition for bootstrap validity is the ability of the bootstrap regression scores to mimic the serial dependence of the original regression scores. Mimicking the cross sectional and/or serial dependence of the idiosyncratic errors in the panel model is asymptotically irrelevant when c = 0 since the limiting distribution of the original OLS estimator does not depend on these dependencies. Instead, when c > 0, a two-step residual-based bootstrap is required to capture the factors estimation uncertainty, which shows up as an asymptotic bias term.