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Hypothesis testing in linear regression when k/nk/n is large

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  • Calhoun, Gray

Abstract

This paper derives the asymptotic distribution of the FF-test for the significance of linear regression coefficients as both the number of regressors, kk, and the number of observations, nn, 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 FF-test is invalid under this asymptotic theory. This paper provides a correction to the FF statistic that gives correctly-sized tests both under this paper’s limit theory and also under conventional asymptotic theory that keeps kk 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.

Suggested Citation

  • Calhoun, Gray, 2011. "Hypothesis testing in linear regression when k/nk/n is large," ISU General Staff Papers 201101010800001117, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genstf:201101010800001117
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