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Testing for partial exogeneity with weak identification

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  • Doko Tchatoka, Firmin

Abstract

We consider the following problem. A structural equation of interest contains two sets of explanatory variables which economic theory predicts may be endogenous. The researcher is interesting in testing the exogeneity of only one of them. Standard exogeneity tests are in general unreliable from the view point of size control to assess such a problem. We develop four alternative tests to address this issue in a convenient way. We provide a characterization of their distributions under both the null hypothesis (level) and the alternative hypothesis (power), with or without identification. We show that the usual chi-squares critical values are still applicable even when identification is weak. So, all proposed tests can be described as robust to weak instruments. We also show that test consistency may still hold even if the overall identification fails, provided partial identification is satisfied. We present a Monte Carlo experiment which confirms our theory. We illustrate our theory with the widely considered returns to education example. The results underscore: (1) how the use of standard tests to assess partial exogeneity hypotheses may be misleading, and (2) the relevance of using our procedures when checking for partial exogeneity.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 39504.

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Date of creation: 16 Apr 2011
Date of revision: Mar 2012
Handle: RePEc:pra:mprapa:39504

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Keywords: Subset of endogenous regressors; Generated structural equation; Robustness to weak identification; Consistency;

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  1. Nelson, C. & Startz, R., 1988. "The Distribution Of The Instrumental Variables Estimator And Its T-Ratio When The Instrument Is A Poor One," Discussion Papers in Economics at the University of Washington 88-07, Department of Economics at the University of Washington.
  2. Jean-Marie Dufour & Mohamed Taamouti, 2003. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," CIRANO Working Papers 2003s-39, CIRANO.
  3. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(04), pages 667-709, August.
  4. Jean-Marie Dufour, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," CIRANO Working Papers 2003s-49, CIRANO.
  5. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July.
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  7. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  8. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 10-2003, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  9. Choi, In & Phillips, Peter C. B., 1992. "Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 113-150.
  10. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1988.
  11. Frank Kleibergen, 2001. "Testing Parameters in GMM without Assuming that they are identified," Tinbergen Institute Discussion Papers 01-067/4, Tinbergen Institute.
  12. Doko Tchatoka, Firmin, 2010. "Subset hypotheses testing and instrument exclusion in the linear IV regression," MPRA Paper 29611, University Library of Munich, Germany, revised 02 Feb 2012.
  13. Kiviet, Jan F. & Niemczyk, Jerzy, 2007. "The asymptotic and finite sample distributions of OLS and simple IV in simultaneous equations," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3296-3318, April.
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  18. Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Working Papers 88-06, University of Washington, Department of Economics.
  19. J. A. Hausman, 1976. "Specification Tests in Econometrics," Working papers 185, Massachusetts Institute of Technology (MIT), Department of Economics.
  20. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  21. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
  22. Wu, De-Min, 1974. "Alternative Tests of Independence between Stochastic Regressors and Disturbances: Finite Sample Results," Econometrica, Econometric Society, vol. 42(3), pages 529-46, May.
  23. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  24. Revankar, Nagesh S & Hartley, Michael J, 1973. "An Independence Test and Conditional Unbiased Predictions in the Context of Simultaneous Equation Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 625-31, October.
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