Working Paper Number
WP #10041, December 2010
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).
Published in Journal of Econometrics, Vol. 165 no. 2 (December 2011): 163-174.
Latest revision: July 18, 2011 (Original version: December 2010)
Calhoun, Gray, "Hypothesis testing in linear regression when k/n is large" (2011). Economics Working Papers (2002–2016). 93.