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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 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).

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File URL: http://www.econ.iastate.edu/sites/default/files/publications/papers/p12216-2010-12-20.pdf
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Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 32216.

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Date of creation: 20 Dec 2010
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Publication status: Published in Journal of Econometrics, December 2011, vol. 165 no. 2, pp. 163-174
Handle: RePEc:isu:genres:32216
Contact details of provider: Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
Web page: http://www.econ.iastate.edu
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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. Stanislav Anatolyev, 2009. "Inference in Regression Models with Many Regressors," Working Papers w0125, Center for Economic and Financial Research (CEFIR).
  3. Giovanni Olivei & Silvana Tenreyro, 2006. "The Timing of Monetary Policy Shocks," CEP Discussion Papers dp0725, Centre for Economic Performance, LSE.
  4. Jerry Hausman & Whitney Newey & Tiemen Woutersen & John Chao & Norman Swanson, 2007. "Instrumental variable estimation with heteroskedasticity and many instruments," CeMMAP working papers CWP22/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
  6. 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.
  7. 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.
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