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Generalization Of Gmm To A Continuum Of Moment Conditions

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Author Info
Carrasco, Marine
Florens, Jean-Pierre

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Abstract

This paper proposes a version of the generalized method of moments procedure that handles both the case where the number of moment conditions is finite and the case where there is a continuum of moment conditions. Typically, the moment conditions are indexed by an index parameter that takes its values in an interval. The objective function to minimize is then the norm of the moment conditions in a Hilbert space. The estimator is shown to be consistent and asymptotically normal. The optimal estimator is obtained by minimizing the norm of the moment conditions in the reproducing kernel Hilbert space associated with the covariance. We show an easy way to calculate this estimator. Finally, we study properties of a specification test using overidentifying restrictions. Results of this paper are useful in many instances where a continuum of moment conditions arises. Examples include efficient estimation of continuous time regression models, cross-sectional models that satisfy conditional moment restrictions, and scalar diffusion processes.

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File URL: http://journals.cambridge.org/abstract_S0266466600166010
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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 16 (2000)
Issue (Month): 06 (December)
Pages: 797-834
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Handle: RePEc:cup:etheor:v:16:y:2000:i:06:p:797-834_16

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  1. GARCIA, RenŽ & RENAULT, Eric & VEREDAS, David, 2006. "Estimation of stable distributions by indirect inference," CORE Discussion Papers 2006112, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  2. Juan Carlos Escanciano, 2005. "A Consistent Diagnostic Test for Regression Models Using Projections," Faculty Working Papers 09/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
    Other versions:
  3. Marine Carrasco, 2004. "Chi-square Tests for Parameter Stability," RCER Working Papers 508, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
  4. Jean-Pierre Florens & Marine Carrasco, 2004. "On the Asymptotic Efficiency of GMM," Econometric Society 2004 North American Winter Meetings 436, Econometric Society. [Downloadable!]
    Other versions:
  5. Chunrong Ai & Xiaohong Chen, 2009. "Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions," Cowles Foundation Discussion Papers 1731, Cowles Foundation, Yale University. [Downloadable!]
  6. Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  7. Manuel Vega-Gordillo & José Luis Álvarez-Arce, 2005. "Heterogeneity In Economic Freedom: Free Clusters Or Free Countries," Faculty Working Papers 08/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  8. Robert Elliott & Carlton-James Osakwe, 2006. "Option Pricing for Pure Jump Processes with Markov Switching Compensators," Finance and Stochastics, Springer, vol. 10(2), pages 250-275, April. [Downloadable!] (restricted)
  9. Manuel A. Domínguez & Ignacio N. Lobato, 2006. "A Consistent Specification Test For Models Defined By Conditional Moment Restrictions," Economics Working Papers we064111, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  10. Yingyong Dong & Arthur Lewbel, 2009. "Nonparametric identification of a binary random factor in cross section data," CeMMAP working papers CWP16/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  11. Marine H. Carrasco & Jean-Pierre Florens, 2000. "Estimation of a Mixture via the Empirical Characteristic Function," Econometric Society World Congress 2000 Contributed Papers 0514, Econometric Society. [Downloadable!]
  12. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2003. "There is a Risk-Return Tradeoff After All," University of California at Los Angeles, Anderson Graduate School of Management 1155, Anderson Graduate School of Management, UCLA. [Downloadable!]
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  13. Darolles, Serge & Florens, Jean-Pierre & Renault, Eric, 2003. "Non Parametric Instrumental Regression," IDEI Working Papers 228, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
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  14. Carrasco, Marine & Chernov, Mikhaël & Florens, Jean-Pierre & Ghysels, Eric, 2000. "Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions," IDEI Working Papers 116, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2002. [Downloadable!]
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  15. Andrew Chesher, 2008. "Instrumental variable models for discrete outcomes," CeMMAP working papers CWP30/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  16. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "The MIDAS Touch: Mixed Data Sampling Regression Models," CIRANO Working Papers 2004s-20, CIRANO. [Downloadable!]
  17. Anne Vanhems & Jean-Michel Loubes, 2004. "Saturation spaces for regularization methods in inverse problems," Econometric Society 2004 North American Summer Meetings 380, Econometric Society. [Downloadable!]
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