Hypothesis testing in linear regression when k/n is large
AbstractThis paper derives the asymptotic distribution of the F-test for the significance of linear regression coefficients as both the number of regressors, k, and the number of observations, n, increase together so that their ratio remains positive in the limit. The conventional critical values for this test statistic are too small, and the standard version of the F-test is invalid under this asymptotic theory. This paper provides a correction to the F statistic that gives correctly-sized tests both under this paper’s limit theory and also under conventional asymptotic theory that keeps k finite. This paper also presents simulations that indicate the new statistic can perform better in small samples than the conventional test. The statistic is then used to reexamine Olivei and Tenreyro’s results from [Olivei, G., Tenreyro, S., 2007. The timing of monetary policy shocks. The American Economic Review 97, 636–663] and Sala-i-Martin’s results from [Sala-i-Martin, X.X., 1997. I just ran two million regressions. The American Economic Review 87 (2), 178–183].
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 165 (2011)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/locate/jeconom
Dimension asymptotics; F-test; Ordinary least squares;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
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- Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2012. "Alternative Asymptotics and the Partially Linear Model with Many Regressors," CREATES Research Papers 2012-02, School of Economics and Management, University of Aarhus.
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