Hypothesis Testing in Linear Regression when K/N is Large

Gray Calhoun

Staff General Research Papers Archive from Iowa State University, Department of Economics

Abstract: This 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).

Keywords: Dimension Asymptotics; F-Test; Ordinary Least Squares (search for similar items in EconPapers)
JEL-codes: C12 C20 (search for similar items in EconPapers)
Date: 2010-12-20
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (3)

Published in Journal of Econometrics, December 2011, vol. 165 no. 2, pp. 163-174

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Journal Article: Hypothesis testing in linear regression when k/n is large (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:isu:genres:32216

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