Inference in regression models with many regressors

Stanislav Anatolyev

Journal of Econometrics, 2012, vol. 170, issue 2, 368-382

Abstract: We investigate the behavior of various standard and modified F, likelihood ratio (LR), and Lagrange multiplier (LM) tests in linear homoskedastic regressions, adapting an alternative asymptotic framework in which the number of regressors and possibly restrictions grows proportionately to the sample size. When the restrictions are not numerous, the rescaled classical test statistics are asymptotically chi-squared, irrespective of whether there are many or few regressors. However, when the restrictions are numerous, standard asymptotic versions of classical tests are invalid. We propose and analyze asymptotically valid versions of the classical tests, including those that are robust to the numerosity of regressors and restrictions. The local power of all asymptotically valid tests under consideration turns out to be equal. The “exact” F test that appeals to critical values of the F distribution is also asymptotically valid and robust to the numerosity of regressors and restrictions.

Keywords: Alternative asymptotic theory; Linear regression; Test size; Test power; F test; Wald test; Likelihood ratio test; Lagrange multiplier test (search for similar items in EconPapers)
JEL-codes: C12 C21 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (29)

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Related works:
Working Paper: Inference in Regression Models with Many Regressors (2009)
Working Paper: Inference in Regression Models with Many Regressors (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:170:y:2012:i:2:p:368-382

DOI: 10.1016/j.jeconom.2012.05.011

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