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Convergence Properties of the Likelihood of Computed Dynamic Models

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Author Info
Jesús Fernández-Villaverde
Juan F. Rubio-Ramírez
Manuel S. Santos

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Abstract

This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function rather than the exact likelihood implied by the exact policy function. What are the consequences for inference of the use of approximated likelihoods? First, we find conditions under which, as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we show that second order approximation errors in the policy function, which almost always are ignored by researchers, have first order effects on the likelihood function. Third, we discuss convergence of Bayesian and classical estimates. Finally, we propose to use a likelihood ratio test as a diagnostic device for problems derived from the use of approximated likelihoods. Copyright The Econometric Society 2006.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2006.00650.x
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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 74 (2006)
Issue (Month): 1 (01)
Pages: 93-119
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Handle: RePEc:ecm:emetrp:v:74:y:2006:i:1:p:93-119

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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2006. "Estimating Macroeconomic Models: A Likelihood Approach," NBER Technical Working Papers 0321, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Victor Aguirregabiria & Pedro mira, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers tecipa-297, University of Toronto, Department of Economics. [Downloadable!]
    Other versions:
  3. Thomas Flury & Neil Shephard, 2008. "Bayesian inference based only on simulated likelihood: particle filter analysis of dynamic economic models," Economics Series Working Papers 413, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  4. Manuel Santos, . "Consistency Properties of a Simulation-Based Estimator for Dynamic Processes," Working Papers 0705, University of Miami, Department of Economics. [Downloadable!]
  5. Burriel, Pablo & Fernández-Villaverde, Jesús & Rubio-Ramirez, Juan Francisco, 2009. "MEDEA: A DSGE Model for the Spanish Economy," CEPR Discussion Papers 7297, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  6. Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2006. "The Research Agenda: Jesus Fernandez-Villaverde and Juan F. Rubio-Ramirez on Estimating DSGE Models," EconomicDynamics Newsletter, Review of Economic Dynamics, vol. 8(1), November. [Downloadable!]
  7. Cuong Le Van & John Stachurski, 2007. "Parametric continuity of stationary distributions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00101157_v1, HAL. [Downloadable!]
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  8. Taeyoung Doh, 2009. "Yield curve in an estimated nonlinear macro model," Research Working Paper RWP 09-04, Federal Reserve Bank of Kansas City. [Downloadable!]
  9. Fernández-Villaverde, Jesús, 2009. "The Econometrics of DSGE Models," CEPR Discussion Papers 7157, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  10. Tovar, Camilo Ernesto, 2008. "DSGE Models and Central Banks," Economics Discussion Papers 2008-30, Kiel Institute for the World Economy. [Downloadable!]
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  11. Gianni Amisano & Oreste Tristani, 2007. "Euro area inflation persistence in an estimated nonlinear DSGE model," Working Paper Series 754, European Central Bank. [Downloadable!]
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  12. Juan F. Rubio-Ramirez & Jesus Fernández-Villaverde, 2005. "Estimating dynamic equilibrium economies: linear versus nonlinear likelihood," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 891-910. [Downloadable!]
    Other versions:
  13. Jesús Fernández-Villaverde & Juan F Rubio-Ramírez, 2007. "How Structural Are Structural Parameters?," Levine's Bibliography 843644000000000057, UCLA Department of Economics. [Downloadable!]
    Other versions:
  14. Gianni Amisano & Oreste Tristani, 2006. "Euro area inflation persistence in an estimated nonlinear," Computing in Economics and Finance 2006 347, Society for Computational Economics. [Downloadable!]
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