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Hypothesis testing in linear regression when k/n is large

  • Calhoun, Gray

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 both under 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 [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. The American Economic Review 87 (2), 178–183].

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 165 (2011)
Issue (Month): 2 ()
Pages: 163-174

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Handle: RePEc:eee:econom:v:165:y:2011:i:2:p:163-174
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  1. Chris D. Orme & Takashi Yamagata, 2006. "The asymptotic distribution of the F-test statistic for individual effects," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 404-422, November.
  2. Anatolyev, Stanislav, 2012. "Inference in regression models with many regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 368-382.
  3. Giovanni P. Olivei & Silvana Tenreyro, 2004. "The timing of monetary policy shocks," Working Papers 04-1, Federal Reserve Bank of Boston.
  4. Hausman & Newey & Woutersen & Chao & Swanson, 2009. "Instrumental Variable Estimation with Heteroskedasticity and Many Instruments," Economics Working Paper Archive 566, The Johns Hopkins University,Department of Economics.
  5. Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
  6. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.
  7. Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
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