Anatolyev, Stanislav (2012) "Inference in regression models with many regressors", Journal of Econometrics, vol. 170, no. 2, pp. 368-382
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.
Link to paper online:
Paper in accepted version:
London School of Economics, London, United Kingdom, March 6, 2008
2008 North American Winter Meeting of Econometric Society, New Orleans, USA, January 4–6, 2008
CIREQ Conference on GMM, Montreal, Canada, November 16-17, 2007