Inference in Regression Models with Many Regressors

40 Pages Posted: 16 Aug 2009

Date Written: June 29, 2009

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

JEL Classification: C12, C21

Suggested Citation

Anatolyev, Stanislav, Inference in Regression Models with Many Regressors (June 29, 2009). Available at SSRN: https://ssrn.com/abstract=1452672 or http://dx.doi.org/10.2139/ssrn.1452672

Stanislav Anatolyev (Contact Author)

New Economic School ( email )

Skolkovskoe shosse, 45
Moscow, 121353
Russia

CERGE-EI ( email )

P.O. Box 882
7 Politickych veznu
Prague 1, 111 21
Czech Republic

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