Hostname: page-component-7dd5485656-hw7sx Total loading time: 0 Render date: 2025-10-31T03:37:23.677Z Has data issue: false hasContentIssue false
  • English
  • Français

GMM ESTIMATION AND UNIFORM SUBVECTOR INFERENCE WITH POSSIBLE IDENTIFICATION FAILURE

Published online by Cambridge University Press:  29 November 2013

Donald W.K. Andrews  and
Xu Cheng
Donald W.K. Andrews
Affiliation:
Cowles Foundation for Research in Economics, Yale University
Xu Cheng*
Affiliation:
University of Pennsylvania
*
*Address correspondence to Xu Cheng, Department of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA, 19104. e-mail: xucheng@econ.upenn.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CSs) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CSs are established.

The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t, and quasi-likelihood ratio tests and CSs whose critical values are designed to yield robustness to identification problems.

The results of the paper are applied to a nonlinear regression model with endogeneity and a probit model with endogeneity and possibly weak instrumental variables.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 2 , April 2014 , pp. 287 - 333
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Amemiya, T. (1974) Multivariate regression and simultaneous-equation models when the dependent variables are truncated normal. Econometrica 42, 999–1012.Google Scholar
Andrews, D.W.K. (2002) Generalized method of moments estimation when a parameter is on a boundary. Journal of Business & Economic Statistics 20, 530–544.Google Scholar
Andrews, D.W.K. & Cheng, X. (2012a) Estimation and inference with weak, semi-strong, and strong identification. Econometrica 80, 2153–2211.Google Scholar
Andrews, D.W.K. & Cheng, X. ( 2012b ) Supplemental material for “Estimation and inference with weak, semi-strong, and strong identification.” Econometric Society website, http://www.econometricsociety.org/ecta/Supmat/9456_miscellaneous.pdf.Google Scholar
Andrews, D.W.K. & Cheng, X. (2013a) Maximum likelihood estimation and uniform inference with sporadic identification failure. Journal of Econometrics 173, 36–56.Google Scholar
Andrews, D.W.K. & Cheng, X. (2013b) Supplementary material for “Generalized method of moments estimation and uniform subvector inference with possible identification failure.” Google Scholar
Andrews, D.W.K., Cheng, X., & Guggenberger, P. (2009) Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests. Cowles Foundation Discussion Paper Number 1813,Yale University.Google Scholar
Andrews, D.W.K. & Guggenberger, P. (2009) Validity of subsampling and “plug-in asymptotic” inference for parameters defined by moment inequalities. Econometric Theory 25, 669–709.Google Scholar
Andrews, D.W.K. & Guggenberger, P. (2010) Asymptotic size and a problem with subsampling and with the m out of n bootstrap. Econometric Theory 26, 426–468.Google Scholar
Andrews, I. & Mikusheva, A. (2011) Maximum Likelihood Inference in Weakly Identified DSGE Models. Manuscript, Department of Economics, MIT.Google Scholar
Andrews, I. & Mikusheva, A. (2012) A Geometric Approach to Weakly Identified Econometric Models. Manuscript, Department of Economics, MIT.Google Scholar
Antoine, B. & Renault, E. (2009) Efficient GMM with nearly weak instruments. Econometrics Journal 12, S135–S171.Google Scholar
Antoine, B. & Renault, E. (2010) Efficient inference with poor instruments, a general framework. In Giles, D. & Ullah, A. (eds.), Handbook of Empirical Economics and Finance, Chap. 2, pp. 29–70. Taylor and Francis.Google Scholar
Areosa, W.D., McAleer, M., & Medeiros, M.C. (2011) Moment-based estimation of smooth transition regression models with endogenous variables. Journal of Econometrics 165, 100–111.Google Scholar
Armstrong, T.B., Hong, H., & Nekipelov, D. (2012) How Strong Must Identification Be for Conventional Asymptotics in Nonlinear Models? Manuscript, Cowles Foundation, Yale University.Google Scholar
Caner, M. (2010) Testing, estimation in GMM and CUE with nearly weak identification. Econometric Reviews 29, 330–363.Google Scholar
Cheng, X. (2008) Robust Confidence Intervals in Nonlinear Regression under Weak Identification. Working Paper, Department of Economics, Yale University.Google 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
Davies, R.B. (1977) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64, 247–254.Google Scholar
Dufour, J.-M. (1997) Impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65, 1365–1387.Google 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, 2649–2666.Google Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimation. Econometrica 50, 1029–1054.Google Scholar
Heckman, J.J. (1978) Dummy endogenous variables in a simultaneous equation system. Econometrica 46, 931–959.CrossRefGoogle Scholar
Kleibergen, F. (2002) Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70, 1781–1803.Google Scholar
Kleibergen, F. (2005) Testing parameters in GMM without assuming that they are identified. Econometrica 73, 1103–1123.Google Scholar
Lee, L.F. (1981) Simultaneous equations models with discrete endogenous variables. In Manski, C.F. & McFadden, D. (eds.), Structural Analysis of Discrete Data and Econometric Applications, Chap. 9, pp. 346–364. MIT Press.Google Scholar
Lee, L.-F. & Chesher, A. (1986) Specification testing when score test statistics are identically zero. Journal of Econometrics 31, 121–149.Google Scholar
Ma, J. & Nelson, C.R. (2008) Valid Inference for a Class of Models where Standard Inference Performs Poorly; Including Nonlinear Regression, ARMA, GARCH, and Unobserved Components. Manuscript, Department of Economics, University of Washington.Google Scholar
Moreira, M.J. (2003) A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048.Google Scholar
Nelson, C.R. & Startz, R. (1990) Some further results on the exact small sample properties of the instrumental variables estimator. Econometrica 58, 967–976.Google Scholar
Nelson, C.R. & Startz, R. (2007) The zero-information-limit condition and spurious inference in weakly identified models. Journal of Econometrics 138, 47–62.Google Scholar
Nelson, F. & Olson, L. (1978) Specification and estimation of a simultaneous-equation model with limited dependent variables. International Economic Review 19, 695–709.Google Scholar
Pakes, A. & Pollard, D. (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1057.CrossRefGoogle Scholar
Park, J.Y. & Phillips, P.C.B. (1988) Statistical inference in regressions with integrated processes: Part 1. Econometric Theory 4, 468–497.Google Scholar
Phillips, P.C.B. (1989) Partially identified econometric models. Econometric Theory 5, 181–240.Google Scholar
Qu, Z. (2011) Inference and Specification Testing in DSGE Models with Possible Weak Identification. Working paper, Department of Economics, Boston University.Google Scholar
Rivers, D. & Vuong, Q.H. (1988) Limited information estimators and exogeneity tests for simultaneous probit models. Journal of Econometrics 39, 347–366.Google Scholar
Rotnitzky, A., Cox, D.R., Bottai, M., & Robins, J. (2000) Likelihood-based inference with singular information matrix. Bernoulli 6, 243–284.Google Scholar
Sargan, J.D. (1983) Identification and lack of identification. Econometrica 51, 1605–1633.CrossRefGoogle Scholar
Schorfheide, F. (2011) Estimation and Evaluation of DSGE Models: Progress and Challenges. NBER Working paper 16781.Google Scholar
Shi, X. & Phillips, P.C.B. (2011) Nonlinear cointegrating regression under weak identification. Econometric Theory 28, 1–39.Google Scholar
Smith, R.J. & Blundell, R.W. (1986) An exogeneity test for a simultaneous equation tobit model with an application to labor supply. Econometrica 54, 679–685.Google 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 instruments. Econometrica 68, 1055–1096.Google Scholar
Stock, J.H. & Yogo, M. (2005) Testing for weak instruments in linear IV regression. In Andrews, D.W.K. & Stock, J.H. (eds.), Identification and Inference for Econometric Models: A Festschrift in Honor of Thomas J. Rothenberg, Chap. 5, pp. 80–108. Cambridge University Press.Google Scholar
Wright, J.H. (2003) Detecting lack of identification in GMM. Econometric Theory 19, 322–330.Google Scholar
Supplementary material: PDF

Andrews and Cheng Supplementary Material

Supplementary Material

Download Andrews and Cheng Supplementary Material(PDF)
PDF 1.7 MB