Bootstrap methods for inference in the Parks model

This paper shows how to bootstrap hypothesis tests in the context of the Parks's (1967) Feasible Generalized Least Squares estimator. It then demonstrates that the bootstrap outperforms FGLS(Parks)'s top competitor. The FGLS(Parks) estimator has been a workhorse for the analysis of panel data and seemingly unrelated regression equation systems because it allows the incorporation of cross-sectional correlation together with heteroskedasticity and serial correlation. Unfortunately, the associated, asymptotic standard error estimates are biased downward, often severely. To address this problem, Beck and Katz (1995) developed an approach that uses the Prais-Winsten estimator together with 'panel corrected standard errors' (PCSE). While PCSE produces standard error estimates that are less biased than FGLS(Parks), it forces the user to sacrifice efficiency for accuracy in hypothesis testing. The PCSE approach has been, and continues to be, widely used. This paper develops an alternative: a nonparametric bootstrapping procedure to be used in conjunction with the FGLS(Parks) estimator. We demonstrate its effectiveness using an experimental approach that creates artificial panel datasets modelled after actual panel datasets. Our approach provides a superior alternative to existing estimation options by allowing researchers to retain the efficiency of the FGLS(Parks) estimator while producing more accurate hypothesis test results than the PCSE.