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Indirect Likelihood Inference (revised)

  • Michael Creel

    ()

  • Dennis Kristensen

Standard indirect Inference (II) estimators take a given finite-dimensional statistic, Z_{n} , and then estimate the parameters by matching the sample statistic with the model-implied population moment. We here propose a novel estimation method that utilizes all available information contained in the distribution of Z_{n} , not just its first moment. This is done by computing the likelihood of Z_{n}, and then estimating the parameters by either maximizing the likelihood or computing the posterior mean for a given prior of the parameters. These are referred to as the maximum indirect likelihood (MIL) and Bayesian Indirect Likelihood (BIL) estimators, respectively. We show that the IL estimators are first-order equivalent to the corresponding moment-based II estimator that employs the optimal weighting matrix. However, due to higher-order features of Z_{n} , the IL estimators are higher order efficient relative to the standard II estimator. The likelihood of Z_{n} will in general be unknown and so simulated versions of IL estimators are developed. Monte Carlo results for a structural auction model and a DSGE model show that the proposed estimators indeed have attractive finite sample properties.

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Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 931.13.

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Length: 32
Date of creation: 12 Jun 2013
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Handle: RePEc:aub:autbar:931.13
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  1. Dennis Kristensen & Yongseok Shin, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-58, Department of Economics and Business Economics, Aarhus University.
  2. RUGE-MURCIA, Francisco J., 2003. "Methods to Estimate Dynamic Stochastic General Equilibrium Models," Cahiers de recherche 2003-23, Universite de Montreal, Departement de sciences economiques.
  3. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
  4. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing Solution Methods for Dynamic Equilibrium Economies," PIER Working Paper Archive 04-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. Christian Gourieroux & Peter C. B. Phillips & Jun Yu, 2006. "Indirect Inference for Dynamic Panel Models," Cowles Foundation Discussion Papers 1550, Cowles Foundation for Research in Economics, Yale University.
  6. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S63-84, Suppl. De.
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  8. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, 06.
  9. Fermanian, Jean-David & Salani , Bernard, 2004. "A Nonparametric Simulated Maximum Likelihood Estimation Method," Econometric Theory, Cambridge University Press, vol. 20(04), pages 701-734, August.
  10. Darrell Duffie & Kenneth J. Singleton, 1990. "Simulated Moments Estimation of Markov Models of Asset Prices," NBER Technical Working Papers 0087, National Bureau of Economic Research, Inc.
  11. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
  12. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
  13. Smets, Frank & Wouters, Raf, 2007. "Shocks and frictions in US business cycles: a Bayesian DSGE approach," Working Paper Series 0722, European Central Bank.
  14. Michael Creel & Dennis Kristensen, 2011. "Indirect likelihood inference," UFAE and IAE Working Papers 874.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  15. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  16. Pfanzagl, J. & Wefelmeyer, W., 1978. "A third-order optimum property of the maximum likelihood estimator," Journal of Multivariate Analysis, Elsevier, vol. 8(1), pages 1-29, March.
  17. Michael Creel & Dennis Kristensen, 2009. "Estimation of Dynamic Latent Variable Models Using Simulated Nonparametric Moments," UFAE and IAE Working Papers 792.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  18. Ruge-Murcia, Francisco, 2012. "Estimating nonlinear DSGE models by the simulated method of moments: With an application to business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 36(6), pages 914-938.
  19. Adjemian, Stéphane & Bastani, Houtan & Karamé, Fréderic & Juillard, Michel & Maih, Junior & Mihoubi, Ferhat & Perendia, George & Pfeifer, Johannes & Ratto, Marco & Villemot, Sébastien, 2011. "Dynare: Reference Manual Version 4," Dynare Working Papers 1, CEPREMAP, revised Jul 2014.
  20. Dennis Kristensen, 2008. "Uniform Convergence Rates of Kernel Estimators with Heterogenous, Dependent Data," CREATES Research Papers 2008-37, Department of Economics and Business Economics, Aarhus University.
  21. repec:dau:papers:123456789/5724 is not listed on IDEAS
  22. Li, Tong, 2010. "Indirect inference in structural econometric models," Journal of Econometrics, Elsevier, vol. 157(1), pages 120-128, July.
  23. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  24. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355, 06-2016.
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