Inference in Regression Models with Many Regressors

Stanislav Anatolyev

No w0125, Working Papers from New Economic School (NES)

Abstract: We investigate the behavior of various standard and modified F, LR and LM tests in linear homoskedastic regressions, adapting an alternative asymptotic framework where the number of regressors and possibly restrictions grows proportionately to the sample size. When restrictions are not numerous, the rescaled classical test statistics are asymptotically chi-squared irrespective of whether there are many or few regressors. However, when 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)
Pages: 41 pages
Date: 2009-07
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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https://www.nes.ru/files/Preprints-resh/WP125.pdf (application/pdf)

Related works:
Journal Article: Inference in regression models with many regressors (2012)
Working Paper: Inference in Regression Models with Many Regressors (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:abo:neswpt:w0125

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