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Convergence Properties of the Likelihood of Computed Dynamic Models

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Author Info
Jesus Fernandez-Villaverde () (Department of Economics, University of Pennsylvania)
Juan F. Rubio-Ramirez () (Federal Reserve Bank of Atlanta)
Manuel Santos () (College of Business, Arizona State University)

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Abstract

This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, economists approximate the policy functions of the agents in the model with numerical methods. But this implies that, instead of the exact likelihood function, the researcher can evaluate only an approximated likelihood associated with the approximated policy function. What are the consequences for inference of the use of approximated likelihoods? First, we show that as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we prove that the approximated likelihood converges at the same rate as the approximated policy function. Third, we find that the error in the approximated likelihood gets compounded with the size of the sample. Fourth, we discuss convergence of Bayesian and classical estimates. We complete the paper with three applications to document the quantitative importance of our results.

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Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 04-034.

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Length: 56 pages
Date of creation: 31 Aug 2004
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Handle: RePEc:pen:papers:04-034

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Related research
Keywords: computed dynamic models; likelihood inference; asymptotic properties;

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
E1 - Macroeconomics and Monetary Economics - - General Aggregative Models

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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!]
    Other versions:
  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)
    Other versions:
  10. Tovar, Camilo Ernesto, 2008. "DSGE Models and Central Banks," Economics Discussion Papers 2008-30, Kiel Institute for the World Economy. [Downloadable!]
    Other versions:
  11. Gianni Amisano & Oreste Tristani, 2007. "Euro area inflation persistence in an estimated nonlinear DSGE model," Working Paper Series 754, European Central Bank. [Downloadable!]
    Other versions:
  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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