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Generalized empirical likelihood for a continuum of moment conditions

  • Pierre Chaussé

    (Department of Economics, University of Waterloo)

This paper extends the generalized empirical likelihood method to the case in which the moment conditions are defined on a continuum (CGEL). We show, for the iid case, that CGEL is asymptotically equivalent at the first order to the generalized method of moments for a continuum (CGMM) developed by Carrasco and Florens (2000). Because the system of equations that we need to solve becomes singular when the number of moment conditions converges to infinity, we treat CGEL as a nonlinear ill-posed problem and obtain the solution using the regularized Gauss-Newton method. This numerical algorithm is a fast and relatively easy way to compute the regularized Tikhonov solution to nonlinear ill-posed problems in function spaces. In order to compare the properties of CGEL and CGMM, we then perform a numerical study in which we estimate the parameters of a stable distribution using moment conditions based on the characteristic function. The results show that CGEL outperforms CGMM in most cases according to the root mean squared error criterion.

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File URL: http://economics.uwaterloo.ca/documents/11-004PC.pdf
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Paper provided by University of Waterloo, Department of Economics in its series Working Papers with number 1104.

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Length: 44 pages
Date of creation: Oct 2011
Date of revision: Oct 2011
Handle: RePEc:wat:wpaper:1104
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  1. Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
  2. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
  3. 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.
  4. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
  5. Marine Carrasco & Rachidi Kotchoni, 2013. "Efficient Estimation Using the Characteristic Function," Working Papers hal-00867850, HAL.
  6. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
  7. Stanislav Anatolyev & Nikolay Gospodinov, 2008. "Specification Testing in Models with Many Instruments," Working Papers w0124, Center for Economic and Financial Research (CEFIR).
  8. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
  9. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
  10. Berkowitz, Jeremy, 2001. "Generalized spectral estimation of the consumption-based asset pricing model," Journal of Econometrics, Elsevier, vol. 104(2), pages 269-288, September.
  11. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
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