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].
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 165 (2011)
Issue (Month): 2 ()
Contact details of provider:
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.:
- 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.
- 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.
- Gernot Doppelhofer & Ronald I. Miller & Xavier Sala-i-Martin, 2000. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," NBER Working Papers 7750, National Bureau of Economic Research, Inc.
- 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.
- Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
- Chris D. Orme & Takashi Yamagata, 2006.
"The asymptotic distribution of the F-test statistic for individual effects,"
Royal Economic Society, vol. 9(3), pages 404-422, November.
- 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.
- 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.
- 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.
- Norman R. Swanson & John C. Chao & Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen, 2011. "Instrumental Variable Estimation with Heteroskedasticity and Many Instruments," Departmental Working Papers 201111, Rutgers University, Department of Economics.
- 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.
- Stanislav Anatolyev, 2009.
"Inference in Regression Models with Many Regressors,"
w0125, Center for Economic and Financial Research (CEFIR).
- Anatolyev, Stanislav, 2012. "Inference in regression models with many regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 368-382.
- 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.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.