Hypothesis Testing in Linear Regression when K/N isLarge

This paper derives the asymptotic distribution of the F-test for the significance oflinear regression coefficients as both the number of regressors, k, and the number ofobservations, n, increase together so that their ratio remains positive in the limit. Theconventional critical values for this test statistic are too small, and the standard versionof the F-test is invalid under this asymptotic theory. This paper provides a correction tothe F statistic that gives correctly-sized tests both under this paper’s limit theory andalso under conventional asymptotic theory that keeps k finite. This paper also presentssimulations that indicate the new statistic can perform better in small samples than theconventional test. The statistic is then used to reexamine Olivei and Tenreyro’s resultsfrom “The Timing of Monetary Policy Shocks” (2007, AER) and Sala-i-Martin’s resultsfrom “I Just Ran Two Million Regressions” (1997, AER).[...]