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Generalized Method of Moments Estimation When a Parameter Is on a Boundary

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  • Andrews, Donald W K

Abstract

This article establishes the asymptotic distributions of generalized method of moments (GMM) estimators when the true parameter lies on the boundary of the parameter space. The conditions allow the estimator objective function to be nonsmooth and to depend on preliminary estimators. The boundary of the parameter space may be curved and/or kinked. The article discusses three examples: (1) instrumental variables (IV) estimation of a regression model with nonlinear equality and/or inequality restrictions on the parameters; (2) method of simulated moments estimation of a multinomial discrete response model with some random coefficient variances equal to 0, some random effect variances equal to 0, or some measurement error variances equal to 0; and (3) semiparametric least squares estimation of a partially linear regression model with nonlinear equality and/or inequality restrictions on the parameters.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 20 (2002)
Issue (Month): 4 (October)
Pages: 530-44

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Handle: RePEc:bes:jnlbes:v:20:y:2002:i:4:p:530-44

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Cited by:
  1. Riccardo Colacito & Mariano M. Croce, 2011. "Risks for the Long Run and the Real Exchange Rate," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 153 - 181.
  2. Jeremy T. Fox & Kyoo il Kim, 2011. "A Simple Nonparametric Approach to Estimating the Distribution of Random Coefficients in Structural Models," NBER Working Papers 17283, National Bureau of Economic Research, Inc.
  3. Chen, Song Xi & Cui, Hengjian, 2007. "On the second-order properties of empirical likelihood with moment restrictions," Journal of Econometrics, Elsevier, vol. 141(2), pages 492-516, December.
  4. Aretz, Kevin & Bartram, Söhnke M. & Pope, Peter F., 2011. "Asymmetric loss functions and the rationality of expected stock returns," International Journal of Forecasting, Elsevier, vol. 27(2), pages 413-437.
  5. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, 09.
  6. Le-Yu Chen & Jerzy Szroeter, 2009. "Hypothesis testing of multiple inequalities: the method of constraint chaining," CeMMAP working papers CWP13/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Donald W.K. Andrews & Xu Cheng, 2011. "GMM Estimation and Uniform Subvector Inference with Possible Identification Failure," Cowles Foundation Discussion Papers 1828, Cowles Foundation for Research in Economics, Yale University, revised Jan 2013.
  8. Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  9. Donald W.K. Andrews & Xu Cheng & Patrik Guggenberger, 2011. "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests," Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.

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