Let's Fix It: Fixed-b Asymptotics versus Small-b Asymptotics in Heteroscedasticity and Autocorrelation Robust Inference

Yixiao Sun

University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego

Abstract: In the presence of heteroscedasticity and autocorrelation of unknown forms, the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter. Depending on whether this lag truncation parameter is specified to grow at a slower rate than or the same rate as the sample size, we obtain two types of asymptotic approximations: the small-b asymptotics and the fixed-b asymptotics. Using techniques for probability distribution approximation and high order expansions, this paper shows that the fixed-b asymptotic approximation provides a higher order refinement to the first order small-b asymptotics. This result provides a theoretical justification on the use of the fixed-b asymptotics in empirical applications. On the basis of the fixed-b asymptotics and higher order small-b asymptotics, the paper introduces a new and easy-to-use asymptotic F test that employs a finite sample corrected Wald statistic and uses an F-distribution as the reference distribution. Finally, the paper develops a bandwidth selection rule that is testing-optimal in that the bandwidth minimizes the type II error of the asymptotic F test while controlling for its type I error. Monte Carlo simulations show that the asymptotic F test with the testing-optimal bandwidth works very well in finite samples.

Keywords: Physical Sciences and Mathematics; Social and Behavioral Sciences; Asymptotic expansion; F-distribution; Heteroskedasticity and Autocorrelation Robust; long-run variance; robust standard error; testing-optimal smoothing parameter choice; type I and type II errors. (search for similar items in EconPapers)
Date: 2013-05-01
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Let’s fix it: Fixed-b asymptotics versus small-b asymptotics in heteroskedasticity and autocorrelation robust inference (2014)
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