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This paper shows how to bootstrap hypothesis tests in the context of the Parks (Efficient estimation of a system of regression equations when disturbances are both serially and contemporaneously correlated 1967) estimator. It then demonstrates that the bootstrap outperforms Parks's top competitor. The 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 (What to do (and not to do) with time series cross-section data 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 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 Parks estimator. We demonstrate its effectiveness using an innovative experimental approach that creates artificial panel datasets modelled after actual panel datasets. Our approach provides a Pareto-improving option by allowing researchers to retain the efficiency of the Parks estimator while producing more accurate hypothesis test results than the PCSE.