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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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File URL: http://www.sciencedirect.com/science/article/pii/S0304407611001448
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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, 07.
  2. C Orme & Y Yamagata, 2006. "The Asymptotic Distribution of the F-Test Statistic for Individual Effects," The School of Economics Discussion Paper Series 0610, Economics, The University of Manchester.
  3. Giovanni Olivei & Silvana Tenreyro, 2006. "The Timing of Monetary Policy Shocks," CEP Discussion Papers dp0725, Centre for Economic Performance, LSE.
  4. Gernot Doppelhofer & Ronald I. Miller & Xavier Sala-i-Martin, 2000. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (Bace) Approach," OECD Economics Department Working Papers 266, OECD Publishing.
  5. Stanislav Anatolyev, 2009. "Inference in Regression Models with Many Regressors," Working Papers w0125, Center for Economic and Financial Research (CEFIR).
  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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