Abstract
Abstract 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.
Highlights
Parks (1967) Feasible Generalized Least Squares (FGLS) estimator was designed as an efficient estimator for systems of equations with both serially and contemporaneously correlated disturbances.1 Such models include the SUR model and associated restricted forms, such as time-series, cross-section/panel data models
This paper demonstrates that the combined use of the FGLS(Parks) estimator with bootstrapping constitutes an approach that is superior to the panel-corrected standard errors” (PCSE) approach in both estimator efficiency and inference accuracy
For a comparative evaluation of the performance of the FGLS(Parks) and PCSE estimators with some alternatives, see Moundigbaye et al (2018). 8The bootstrapping approach that we propose is not limited to linear hypotheses
Summary
Parks (1967) Feasible Generalized Least Squares (FGLS) estimator was designed as an efficient estimator for systems of equations with both serially and contemporaneously correlated disturbances. Such models include the SUR model and associated restricted forms, such as time-series, cross-section/panel data models. Parks (1967) Feasible Generalized Least Squares (FGLS) estimator was designed as an efficient estimator for systems of equations with both serially and contemporaneously correlated disturbances.1 Such models include the SUR model and associated restricted forms, such as time-series, cross-section/panel data models. Beck and Katz (1995) documented that the estimated standard errors for the FGLS(Parks) estimator have severe downward bias when the time dimension is small relative to the number of cross-sections.. Beck and Katz (1995) documented that the estimated standard errors for the FGLS(Parks) estimator have severe downward bias when the time dimension is small relative to the number of cross-sections.3 To address this deficiency, they recommend using a Prais-Winsten estimator with corresponding “panel-corrected standard errors” (PCSE)
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