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Inference in Regression Models with Many Regressors

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Author Info
Stanislav Anatolyev () (New Economic School)

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Abstract

We investigate the behavior of various standard and modi?ed F, LR and LM tests in linear homoskedastic regressions, adapting an alternative asymptotic framework where the number of regressors and possibly restrictions grows proportionately to the sample size. When restrictions are not numerous, the rescaled classical test statistics are asymptotically chi-squared irrespective of whether there are many or few regressors. However, when restrictions are numerous, standard asymptotic versions of classical tests are invalid. We propose and analyze asymptotically valid versions of the classical tests, including those that are robust to the numerosity of regressors and restrictions. The local power of all asymptotically valid tests under consideration turns out to be equal. The ?exact? F test that appeals to critical values of the F distribution is also asymptotically valid and robust to the numerosity of regressors and restrictions.

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Publisher Info
Paper provided by Center for Economic and Financial Research (CEFIR) in its series Working Papers with number w0125.

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Length: 41 pages
Date of creation: Jul 2009
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Handle: RePEc:cfr:cefirw:w0125

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Related research
Keywords: Alternative asymptotic theory; linear regression; test size; test power; F test; Wald test; Likelihood Ratio test; Lagrange Multiplier test;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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References listed on IDEAS
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  1. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935 Elsevier. [Downloadable!] (restricted)
  2. Berndt, Ernst R & Savin, N Eugene, 1977. "Conflict among Criteria for Testing Hypotheses in the Multivariate Linear Regression Model," Econometrica, Econometric Society, vol. 45(5), pages 1263-77, July. [Downloadable!] (restricted)
  3. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
  5. Peter Sandholt Jensen & Allan H. Würtz, 2006. "On determining the importance of a regressor with small and undersized samples," Economics Working Papers 2006-08, School of Economics and Management, University of Aarhus. [Downloadable!]
  6. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February. [Downloadable!] (restricted)
  7. John Galbraith & Victoria Zinde-Walsh, 2006. "Reduced-Dimension Control Regression," Departmental Working Papers 2006-17, McGill University, Department of Economics. [Downloadable!]
  8. Burnside, Craig & Eichenbaum, Martin S, 1996. "Small-Sample Properties of GMM-Based Wald Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 294-308, July.
  9. Rothernberg, Thomas J, 1984. "Hypothesis Testing in Linear Models When the Error Covariance Matrix Is Nonscalar," Econometrica, Econometric Society, vol. 52(4), pages 827-42, July. [Downloadable!] (restricted)
  10. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May. [Downloadable!] (restricted)
  11. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November. [Downloadable!] (restricted)
  12. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September. [Downloadable!] (restricted)
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