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TESTING UNDER WEAK IDENTIFICATION WITH CONDITIONAL MOMENT RESTRICTIONS

Published online by Cambridge University Press:  21 May 2012

Sung Jae Jun  and
Joris Pinkse
Sung Jae Jun*
Affiliation:
The Pennsylvania State University
Joris Pinkse
Affiliation:
The Pennsylvania State University
*
*Address correspondence to Sung Jae Jun, 619 Kern Bldg, Department of Economics, The University of Pennsylvania, University Palrk, PA 16802, USA; e-mail: sjun@psu.edu.
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Abstract

We propose a semiparametric test for the value of coefficients in models with conditional moment restrictions that has correct size regardless of identification strength. The test is in essence an Anderson-Rubin (AR) test using nonparametrically estimated instruments to which we apply a standard error correction. We show that the test is (1) always size-correct, (2) consistent when identification is not too weak, and (3) asymptotically equivalent to an infeasible AR test when identification is sufficiently strong. We moreover prove that under homoskedasticity and strong identification our test has a limiting noncentral chi-square distribution under a sequence of local alternatives, where the noncentrality parameter is given by a quadratic form of the inverse of the semiparametric efficiency bound.

Type
Articles
Information
Econometric Theory , Volume 28 , Issue 6 , December 2012 , pp. 1229 - 1282
Copyright
Copyright © Cambridge University Press 2012 

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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., Moreira, M.J., & Stock, J.H. (2004) Optimal Invariant Similar Tests for Instrumental Variables Regression. Discussion paper, Cowles Foundation.Google Scholar
Andrews, D.W., Moreira, M.J., & Stock, J.H. (2006) Optimal two–sided invariant similar tests for instrumental variables regression. Econometrica 74, 715–752.Google Scholar
Bekker, P.A. (1994) Alternative approximations to the distribution of instrumental variables estimators. Econometrica 62, 657–681.CrossRefGoogle Scholar
Chao, J.C. & Swanson, N.R. (2005) Consistent estimation with weak instruments. Econometrica 73, 1673–1692.CrossRefGoogle Scholar
Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.CrossRefGoogle Scholar
de la Peña, V.H. (1999) A general class of exponential inequalities for martingales and ratios. Annals of Probability 27, 537–564.CrossRefGoogle Scholar
Domínguez, M. & Lobato, I. (2004) Consistent estimation of models defined by conditional moment restrictions. Econometrica 72(5), 1601–1615.CrossRefGoogle Scholar
Dufour, J.-M. (1997) Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65, 1365–1387.CrossRefGoogle Scholar
Han, C. & Phillips, P.C. (2006) GMM with many moment conditions. Econometrica 74, 147–192.CrossRefGoogle Scholar
Hausman, J.A., Newey, W.K., Woutersen, T., & Chao, J.C. (2007) Instrumental Variable Estimation with Heterskedasticity and Many Instruments. Discussion paper, MIT.Google Scholar
Heckman, J.J. (1978) Dummy endogenous variables in a simultaneous equations system. Econometrica 46, 931–959.CrossRefGoogle Scholar
Jun, S.J. & Pinkse, J. (2009) Semiparametric tests of conditional moment restrictions under weak or partial identification. Journal of Econometrics 152, 3–18.CrossRefGoogle Scholar
Kleibergen, F. (2002) Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70, 1781–1804.CrossRefGoogle Scholar
Kleibergen, F. (2005) Testing parameters in GMM without assuming that they are identified. Econometrica 73, 1103–1123.CrossRefGoogle Scholar
Moreira, M.J. (2003) A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048.Google Scholar
Newey, W.K. (1990) Efficient instrumental variables estimation of nonlinear models. Econometrica 58, 809–837.CrossRefGoogle Scholar
Newey, W.K. (1993) Efficient Estimation of Models with Conditional Moment Restrictions, pp. 419–454. North Holland.Google Scholar
Newey, W.K. (2004) Many Weak Moment Asymptotics for the Continuously Updated GMM Estimator. Discussion paper, MIT.Google Scholar
Newey, W.K. & Windmeijer, F. (2009) GMM with many weak moment conditions. Econometrica 77, 687–719.Google Scholar
Phillips, P. (1989) Partially identified econometric models. Econometric Theory 5(02), 181–240.CrossRefGoogle Scholar
Robinson, P.M. (1987) Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 55, 875–891.CrossRefGoogle Scholar
Staiger, D. & Stock, J.H. (1997) Instrumental variables regression with weak instruments. Econometrica 65, 557–586.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, 518–529.CrossRefGoogle Scholar
Stock, J.H. & Yogo, M. (2005) Asymptotic distributions of instrumental variables statistics with many instruments. In Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg, pp. 109–120. Cambridge University Press.CrossRefGoogle Scholar
Stone, C.J. (1977) Consistent nonparametric regression. Annals of Statistics 5, 595–620.CrossRefGoogle Scholar
van der Vaart, A.W. (1998) Asymptotic Statistics. Cambridge University Press.CrossRefGoogle Scholar