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Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions

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Chunrong Ai
Xiaohong Chen

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Abstract

We propose an estimation method for models of conditional moment restrictions, which contain finite dimensional unknown parameters (theta) and infinite dimensional unknown functions (h). Our proposal is to approximate h with a sieve and to estimate theta and the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator of h is consistent with a rate faster than n-super--1/4 under certain metric; (ii) the estimator of theta is root-n consistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of the theta estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of theta attains the semiparametric efficiency bound. We illustrate our results with two examples: a partially linear regression with an endogenous nonparametric part, and a partially additive IV regression with a link function. Copyright The Econometric Society 2003.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 71 (2003)
Issue (Month): 6 (November)
Pages: 1795-1843
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Handle: RePEc:ecm:emetrp:v:71:y:2003:i:6:p:1795-1843

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  1. Patrick Gagliardini & C. Gourieroux & E. Renault, 2005. "Efficient Derivative Pricing by Extended Method of Moments," University of St. Gallen Department of Economics working paper series 2005 2005-05, Department of Economics, University of St. Gallen. [Downloadable!]
  2. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  3. Christelle Viauroux, G.L. Gayle, 2004. "Root-N Consistent Semiparametric Eestimators of a Dynamic Panel Sample Selection Model," University of Cincinnati, Economics Working Papers Series 2004-05, University of Cincinnati, Department of Economics. [Downloadable!]
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  4. Hidehiko Ichimura, 2006. "Characterization of the Asymptotic Distribution of Semiparametric M-Estimators," CIRJE F-Series CIRJE-F-426, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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  5. Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2002. "Efficient Estimation of Semiparametric Multivariate Copula Models," Working Papers 0420, Department of Economics, Vanderbilt University, revised Sep 2004. [Downloadable!]
  6. Daniel McFadden, 2001. "Economic Choices," American Economic Review, American Economic Association, vol. 91(3), pages 351-378, June. [Downloadable!] (restricted)
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  8. DUBOIS, Pierre & JULLIEN, Bruno & MAGNAC, Thierry, 2005. "Formal and Informal Risk Sharing in LDCs: Theory and Empirical Evidence," IDEI Working Papers 351, Institut d'Économie Industrielle (IDEI), Toulouse, revised Dec 2007. [Downloadable!]
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  9. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric Identification of Regression Models Containing a Misclassified Dichotomous Regressor Without Instruments," Boston College Working Papers in Economics 675, Boston College Department of Economics. [Downloadable!]
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  10. Xiaohong Chen & Markus Reiss, 2007. "On Rate Optimality for Ill-posed Inverse Problems in Econometrics," Cowles Foundation Discussion Papers 1626, Cowles Foundation, Yale University. [Downloadable!]
  11. Yingyao Hu & Arthur Lewbel, 2008. "Identifying the returns to lying when the truth is unobserved," CeMMAP working papers CWP06/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  12. Kyoo il Kim, 2006. "Semiparametric Estimation of Signaling Games," Working Papers 19-2006, Singapore Management University, School of Economics. [Downloadable!]
  13. Hatipoglu, Ozan, 2008. "An Empirical Analysis of the Relationship Between Inequality and Innovation in a Schumpeterian Framework," MPRA Paper 7856, University Library of Munich, Germany. [Downloadable!]
  14. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation, Yale University. [Downloadable!]
  15. Hélène Bonnal & Éric Renault, 2004. "On the Efficient Use of the Informational Content of Estimating Equations: Implied Probabilities and Euclidean Empirical Likelihood," CIRANO Working Papers 2004s-18, CIRANO. [Downloadable!]
  16. Bas Donkers & Marcia M Schafgans, 2005. "A method of moments estimator for semiparametric index models," STICERD - Econometrics Paper Series /2005/493, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  17. Thomas A. Severini & Gautam Tripathi, 2005. "Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors," Working papers 2005-12, University of Connecticut, Department of Economics. [Downloadable!]
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  18. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Moments," Cowles Foundation Discussion Papers 1650, Cowles Foundation, Yale University. [Downloadable!]
  19. Subbotin, Viktor, 2007. "Asymptotic and bootstrap properties of rank regressions," MPRA Paper 9030, University Library of Munich, Germany, revised 20 Mar 2008. [Downloadable!]
  20. Arthur Lewbel, 2003. "Using Heteroskedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Boston College Working Papers in Economics 587, Boston College Department of Economics, revised 13 Jun 2007. [Downloadable!]
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