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 under both 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 "The Timing of Monetary Policy Shocks" (2007, AER) and Sala-i-Martin's results from "I Just Ran Two Million Regressions" (1997, AER).
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Bibliographic InfoPaper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 32216.
Date of creation: 20 Dec 2010
Date of revision:
Publication status: Published in Journal of Econometrics, December 2011, vol. 165 no. 2, pp. 163-174
Contact details of provider:
Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
Web page: http://www.econ.iastate.edu
More information through EDIRC
Dimension Asymptotics; F-Test; Ordinary Least Squares;
Other versions of this item:
- Calhoun, Gray, 2011. "Hypothesis testing in linear regression when k/n is large," Journal of Econometrics, Elsevier, vol. 165(2), pages 163-174.
- 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
This paper has been announced in the following NEP Reports:
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- Yoonseok Lee & Ryo Okui, 2009. "A Specification Test for Instrumental Variables Regression with Many Instruments," Cowles Foundation Discussion Papers 1741, Cowles Foundation for Research in Economics, Yale University.
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