Bootstrap Standard Error Estimates for Linear Regression

Standard errors of parameter estimates are widely used in empirical work. The bootstrap often can provide a convenient means of estimating standard errors. The conditions under which bootstrap standard error estimates are theoretically justified have not received much attention, however. This article establishes conditions for the consistency of the moving blocks bootstrap estimators of the variance of the least squares estimator in linear dynamic models with dependent data. We discuss several applications of this result, in particular, the use of bootstrap standard error estimates for bootstrapping Studentized statistics. A simulation study shows that inference based on bootstrap standard error estimates may be considerably more accurate in small samples than inference based on closed-form asymptotic estimates.

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