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SUBSET HYPOTHESES TESTING AND INSTRUMENT EXCLUSION IN THE LINEAR IV REGRESSION

Published online by Cambridge University Press:  17 November 2014

Firmin Doko Tchatoka
Firmin Doko Tchatoka*
Affiliation:
University of Tasmania
*
*Address correspondence to Firmin Doko Tchatoka, School of Economics, The University of Adelaide, Australia; e-mail: firmin.dokotchatoka@adelaide.edu.au.
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Abstract

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This paper explores the sensitivity of plug-in subset tests to instrument exclusion in structural models. Identification-robust statistics based on the plug-in principle have been developed for testing hypotheses specified on subsets of the structural parameters. However, their robustness to instrument exclusion has not been investigated. This paper proposes an analysis of the asymptotic distributions of the limited information maximum likelihood (LIML) estimator and plug-in statistics when potential instruments are omitted. Our results provide several new insights and extensions of earlier studies. We show that the exclusion of instruments can eliminate the first-stage, thus weakening identification and invalidating the plug-in subset inference. However, when instrument omission does not affect LIML consistency, it preserves the plug-in subset test validity, although LIML is no longer asymptotically efficient. Unlike the instrumental variable (IV) estimator, the LIML estimator of the identified linear combination of the nuisance parameter is not asymptotically a Gaussian mixture, even without instrument exclusion.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 6 , December 2015, pp. 1192 - 1228
Copyright
Copyright © Cambridge University Press 2014 

References

REFERENCES

Anderson, T.W. & Rubin, H. (1949) Estimation of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics 20, 46–63.CrossRefGoogle Scholar
Andrews, D.W.K. & Stock, J.H. (2007) Inference with weak instruments. In Blundell, R., Newey, W., & Pearson, T. (eds.), Advances in Economics and Econometrics, Theory and Applications, 9th Congress of the Econometric Society, Vol. 3, Chap. 6. Cambridge University Press.Google Scholar
Antoine, B. & Renault, E. (2012) Efficient minimum distance estimation with multiple rates of convergence. Journal of Econometrics 170(2), 350–367.CrossRefGoogle Scholar
Bean, C.R. (1994) European unemployment: A survey. The Journal of Economic Literature 32(2), 573–619.Google Scholar
Berkowitz, D., Caner, M., & Fang, Y. (2008) Are nearly exogenous instruments reliable? Economics Letters 101, 20–23.CrossRefGoogle Scholar
Berkowitz, D., Caner, M., & Fang, Y. (2012) The validity of instruments revisited. Journal of Econometrics 166, 255–266.CrossRefGoogle Scholar
Chaudhuri, S. & Zivot, E. (2010) A New Method of Projection Based Inference in GMM with Weakly Identified Nuisance Parameters. Technical report, Department of Economics, New York University, N.Y.CrossRefGoogle Scholar
Choi, I. & Phillips, P.C.B. (1992) Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations. Journal of Econometrics 51, 113–150.CrossRefGoogle Scholar
Doko Tchatoka, F. & Dufour, J.-M. (2008) Instrument endogeneity and identification-robust tests: Some analytical results. Journal of Statistical Planning and Inference 138(9), 2649–2661.CrossRefGoogle Scholar
Doko Tchatoka, F. & Dufour, J.-M. (2014) Identification-robust inference for endogeneity parameters in linear structural models. The Econometrics Journal 17(1), 165–187.CrossRefGoogle Scholar
Dufour, J.-M. (1997) Some impossibility theorems in econometrics, with applications to structural and dynamic models. Econometrica 65, 1365–1389.CrossRefGoogle Scholar
Dufour, J.-M. (2003) Identification, weak instruments and statistical inference in econometrics. Canadian Journal of Economics 36(4), 767–808.CrossRefGoogle Scholar
Dufour, J.-M. (2009) Comments on “ Weak instrument robust tests in GMM and the new Keynesian Phillips curve” by F. Kleibergen and S. Mavroeidis. Journal of Business and Economic Statistics 27, 318–321.CrossRefGoogle Scholar
Dufour, J.-M. & Jasiak, J. (2001) Finite sample limited information inference methods for structural equations and models with generated regressors. International Economic Review 42, 815–843.CrossRefGoogle Scholar
Dufour, J.-M., Khalaf, L., & Beaulieu, M.-C. (2010) Multivariate residual-based finite-sample tests for serial dependence and GARCH with applications to asset pricing models. Journal of Applied Econometrics 25, 263–285.CrossRefGoogle Scholar
Dufour, J.-M., Khalaf, L., & Kichian, M. (2006) Inflation dynamics and the new Keynesian Phillips curve: An identification robust econometric analysis. Journal of Economic Dynamics and Control 30(9–10), 1707–1727.CrossRefGoogle Scholar
Dufour, J.-M., Khalaf, L., & Kichian, M. (2013) Identification-robust analysis of DSGE and structural macroeconomic models. Journal of Monetary Economics 60, 340–350.CrossRefGoogle Scholar
Dufour, J.-M. & Taamouti, M. (2005) Projection-based statistical inference in linear structural models with possibly weak instruments. Econometrica 73(4), 1351–1365.CrossRefGoogle Scholar
Dufour, J.-M. & Taamouti, M. (2007) Further results on projection-based inference in IV regressions with weak, collinear or missing instruments. Journal of Econometrics 139(1), 133–153.CrossRefGoogle Scholar
Fleishman, A. (1978) A method for simulating nonnormal distributions. Psychometrika 43, 521–532.CrossRefGoogle Scholar
Guggenberger, P. (2010) The impact of a Hausman pretest on the size of the hypothesis tests. Econometric Theory 156, 337–343.Google Scholar
Guggenberger, P. (2012) On the asymptotic size distortion of tests when instruments locally violate the exogeneity assumption. Econometric Theory 18, 387–421 .CrossRefGoogle Scholar
Guggenberger, P. & Chen, L. (2011) On the Asymptotic Size of Subvector Tests in the Linear Instrumental Variables Model. Technical report, Department of Economics, UCSD.CrossRefGoogle Scholar
Guggenberger, P., Kleibergen, F., Mavroeidis, S., & Chen, L. (2012) On the asymptotic sizes of subset Anderson-Rubin and Lagrange multiplier tests in linear instrumental variables regression. Econometrica 80(6), 2649–2666.Google Scholar
Guggenberger, P. & Smith, R. (2005) Generalized empirical likelihood estimators and tests under partial, weak and strong identification. Econometric Theory 21, 667–709.CrossRefGoogle Scholar
Habib, A.M. & Ljungqvist, A.P. (2001) Interpricing and entrepreneurial wealth losses in IPOs: Theory and evidence. Review of Financial Studies 14(2), 433–458.CrossRefGoogle Scholar
Hansen, C., Hausman, J., & Newey, W. (2008) Estimation with many instrumental variables. Journal of Business and Economic Statistics 26(4), 398–422.CrossRefGoogle Scholar
Hansen, L.P., Heaton, J., & Yaron, A. (1996) Finite sample properties of some alternative GMM estimators. Journal of Business and Economic Statistics 14, 262–280.Google Scholar
Kiviet, J.F. & Niemczyk, J. (2007) The asymptotic and finite-sample distributions of OLS and simple IV in simultaneous equations. Computational Statistics and Data Analysis 51, 3296–3318.CrossRefGoogle Scholar
Kiviet, J.F. & Niemczyk, J. (2012) Comparing the asymptotic and empirical (un)conditional distributions of OLS and IV in a linear static simultaneous equation. Computational Statistics and Data Analysis 56, 3567–3586.CrossRefGoogle Scholar
Kleibergen, F. (2002) Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70(5), 1781–1803.CrossRefGoogle Scholar
Kleibergen, F. (2004) Testing subsets of structural coefficients in the IV regression model. Review of Economics and Statistics 86, 418–423.CrossRefGoogle Scholar
Kleibergen, F. (2005) Testing parameters in GMM without assuming that they are identified. Econometrica 73, 1103–1124.CrossRefGoogle Scholar
Kleibergen, F. (2008) Subset Statistics in the Linear IV Regression Model. Technical report, Department of Economics, Brown University, Providence, Rhode Island.Google Scholar
Kleibergen, F. (2009) Tests of risk premia in linear factor models. Journal of Econometrics 149, 149–173.CrossRefGoogle Scholar
Kleibergen, F. & Mavroeidis, S. (2008) Weak instrument robust tests in GMM and the new Keynesian Phillips curve. Technical report, Department of Economics, Brown University, Providence, Rhode Island.CrossRefGoogle Scholar
Kleibergen, F. & Mavroeidis, S. (2011) Inference on Subsets of Parameters in GMM without Assuming Identification. Technical report, Department of Economics, Brown University, Providence, Rhode Island.Google Scholar
Kocherlakota, N. (1990) On tests of representative consumer asset pricing models. Journal of Monetary Economics 26, 285–304.CrossRefGoogle Scholar
Kotz, S., Balakrishnan, N., & Johnson, N. (2000) Continuous Multivariate Distributions, 2nd ed. Wiley.CrossRefGoogle Scholar
Loughran, T. & Ritter, J. (2004) Why has IPO underpricing changed over time? Financial Management 33(3), 5–37.Google Scholar
Malcomson, J. & Mavroeidis, S. (2006) Matching Frictions, Efficiency Wages, and Unemployment in the USA and the UK. Technical report, Department of Economics, Brown University, Providence, Rhode Island.Google Scholar
Mavroeidis, S. (2004) Weak identification of forward-looking models in monetary economics. Oxford Bulletin of Economics and Statistics 66, 609–635.CrossRefGoogle Scholar
Mavroeidis, S. (2005) Identification issues in forward-looking models estimated by GMM with an application to the Phillips curve. Journal of Money, Credit and Banking 66(3), 421–449.CrossRefGoogle Scholar
Mikusheva, A. (2010) Robust confidence sets in the presence of weak instruments. Journal of Econometrics 157, 236–247.CrossRefGoogle Scholar
Moreira, M.J. (2003) A conditional likelihood ratio test for structural models. Econometrica 71(4), 1027–1048.CrossRefGoogle Scholar
Phillips, P.C.B. (1989) Partially identified econometric models. Econometric Theory 5, 181–240.CrossRefGoogle Scholar
Staiger, D. & Stock, J.H. (1997) Instrumental variables regression with weak instruments. Econometrica 65(3), 557–586.CrossRefGoogle Scholar
Startz, R., Nelson, C.R.N., & Zivot, E. (2006) Improved inference in weakly identified instrumental variables regression. In Corbae, D., Durlauf, S.N., & Hansen, B.E. (eds.), Econometric Theory and Practice: Frontiers of Analysis and Applied Research, Chap. 5. Cambridge University Press.Google Scholar
Stock, J.H. & Wright, J.H. (2000) GMM with weak identification. Econometrica 68, 1055–1096.CrossRefGoogle Scholar
Stock, J.H., Wright, J.H., & Yogo, M. (2002) A survey of weak instruments and weak identification in generalized method of moments. Journal of Business and Economic Statistics 20(4), 518–529.CrossRefGoogle Scholar