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CONSISTENCY OF PLUG-IN ESTIMATORS OF UPPER CONTOUR AND LEVEL SETS

Published online by Cambridge University Press:  03 August 2011

Neşe Yildiz
Neşe Yildiz*
Affiliation:
University of Rochester
*
*Address Correspondence to Neşe Yildiz, University of Rochester, Department of Economics, 231 Harkness Hall, Rochester, NY 14627, USA; e-mail: [email protected].
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Abstract

This paper studies the problem of estimating the set of finite-dimensional parameter values defined by a finite number of moment inequality or equality conditions and gives conditions under which the estimator defined by the set of parameter values that satisfy the estimated versions of these conditions is consistent in Hausdorff metric. This paper also suggests extremum estimators that with probability approaching 1 agree with the set consisting of parameter values that satisfy the sample versions of the moment conditions. In particular, it is shown that the set of minimizers of the sample generalized method of moments (GMM) objective function is consistent for the set of minimizers of the population GMM objective function in Hausdorff metric.

Type
ARTICLES
Information
Econometric Theory , Volume 28 , Issue 2 , April 2012 , pp. 309 - 327
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Andrews, D.W.K., Berry, S.T., & Jia, P. (2004) Confidence Regions for Parameters in Discrete Games with Multiple Equilibria, with an Application to Discount Chain Store Location. Working paper, Yale University.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Andrews, D.W.K. & Soares, G. (2007) Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection. Cowles Foundation Working Paper CFDP 1631.Google Scholar
Bugni, F. (2010) Bootstrap inference in partially identified models defined by moment inequalities: Coverage of the identified set. Econometrica 78, 735–753.Google Scholar
Chernozhukov, V. & Fernandez-Val, I. (2005) Subsampling inference on quantile regression processes. Sankhyã 67, 253–276.Google Scholar
Chernozhukov, V., Hong, H., & Tamer, E. (2002) Parameter Set Inference in a Class of Econometric Models. Working paper, MIT.Google Scholar
Chernozhukov, V., Hong, H., & Tamer, E. (2007) Estimation and confidence regions for parameter sets in econometric models. Econometrica 75, 1243–1284.CrossRefGoogle Scholar
Hansen, L.P. & Singleton, K. (1982) Generalized instrumental variables estimation of nonlinear rational expectations models. Econometrica 50, 1269–1286.CrossRefGoogle Scholar
Imbens, G. & Manski, C.F. (2004) Confidence intervals for partially identified parameters. Econometrica 72, 1845–1872.CrossRefGoogle Scholar
Luenberger, D.G. (1969) Optimization by Vector Space Methods, paperback ed. Wiley.Google Scholar
Manski, C.F. & Tamer, E. (2002) Inference on regressions with interval data on a regressor or outcome. Econometrica 70, 519–546.CrossRefGoogle Scholar
Marsden, J.E. & Hoffman, M.J. (1993) Elementary Classical Analysis, 2nd ed.Freeman, W.H..Google Scholar
Mas-Colell, A., Whinston, M.D., & Green, J.R. (1995) Microeconomic Theory. Oxford University Press.Google Scholar
Newey, W. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engle, R. & McFadden, D. (eds.), Handbook of Econometrics, vol. IV, pp. 2111–2245. North Holland.Google Scholar
Romano, J. & Shaikh, A.M. (2008) Inference for identifiable parameters in partially identified econometric models. Journal of Statistical Planning and Inference: Special Issue in Honor of T. W. Anderson, Jr. on the Occasion of His 90th Birthday 138, 2786–2807.CrossRefGoogle Scholar
Romano, J. & Shaikh, A.M. (2010) Inference for the identifed set in partially identifed econometric models. Econometrica 78, 169–211.Google Scholar
Yildiz, N. (2008) Inference in Partially Identified Nonparametric Instrumental Variables Models. Unpublished manuscript, University of Rochester.Google Scholar