Hypothesis testing in linear regression when k/n is large
AbstractThis 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 165 (2011)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/locate/jeconom
Dimension asymptotics; F-test; Ordinary least squares;
Other versions of this item:
- Calhoun, Gray, 2010. "Hypothesis Testing in Linear Regression when K/N is Large," Staff General Research Papers 32216, Iowa State University, Department of Economics.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Giovanni Olivei & Silvana Tenreyro, 2006.
"The Timing of Monetary Policy Shocks,"
CEP Discussion Papers
dp0725, Centre for Economic Performance, LSE.
- Giovanni Olivei & Silvana Tenreyro, 2006. "The timing of monetary policy shocks," LSE Research Online Documents on Economics 3742, London School of Economics and Political Science, LSE Library.
- Giovanni Olivei & Silvana Tenreyro, 2004. "The timing of monetary policy shocks," Working Papers 04-1, Federal Reserve Bank of Boston.
- Olivei, Giovanni & Tenreyro, Silvana, 2006. "The Timing of Monetary Policy Shocks," CEPR Discussion Papers 5716, C.E.P.R. Discussion Papers.
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"Instrumental Variable Estimation with Heteroskedasticity and Many Instruments,"
Departmental Working Papers
201111, Rutgers University, Department of Economics.
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- 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.
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The School of Economics Discussion Paper Series
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- Anatolyev, Stanislav, 2012.
"Inference in regression models with many regressors,"
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- Stanislav Anatolyev, 2009. "Inference in Regression Models with Many Regressors," Working Papers w0125, Center for Economic and Financial Research (CEFIR).
- Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2012. "Alternative Asymptotics and the Partially Linear Model with Many Regressors," CREATES Research Papers 2012-02, School of Economics and Management, University of Aarhus.
- Calhoun, Gray, 2014. "Out-Of-Sample Comparisons of Overfit Models," Staff General Research Papers 32462, Iowa State University, Department of Economics.
- Yoonseok Lee & Ryo Okui, 2009. "A Specification Test for Instrumental Variables Regression with Many Instruments," Cowles Foundation Discussion Papers 1741, Cowles Foundation for Research in Economics, Yale University.
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