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Estimating Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood

  • Jesus Fernandez-Villaverde


    (Department of Economics, University of Pennsylvania)

  • Juan F. Rubio-Ramirez


    (Federal Reserve Bank of Atlanta)

This paper compares two methods for undertaking likelihood-based inference in dynamic equilibrium economies: a Sequential Monte Carlo filter proposed by Fernández-Villaverde and Rubio-Ramírez (2004) and the Kalman filter. The Sequential Monte Carlo filter exploits the nonlinear structure of the economy and evaluates the likelihood function of the model by simulation methods. The Kalman filter estimates a linearization of the economy around the steady state. We report two main results. First, both for simulated and for real data, the Sequential Monte Carlo filter delivers a substantially better fit of the model to the data as measured by the marginal likelihood. This is true even for a nearly linear case. Second, the differences in terms of point estimates, even if relatively small in absolute values, have important effects on the moments of the model. We conclude that the nonlinear filter is a superior procedure for taking models to the data.

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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 04-005.

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Length: 37 pages
Date of creation: 20 Jan 2004
Date of revision:
Handle: RePEc:pen:papers:04-005
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  1. Geweke, John, 1994. "Priors for Macroeconomic Time Series and Their Application," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 609-632, August.
  2. Jesus Fernandez-Villaverde & Juan Rubio & Manuel Santos, 2005. "Convergence Properties of the Likelihood of Computed Dynamic Models," NBER Technical Working Papers 0315, National Bureau of Economic Research, Inc.
  3. Jinill Kim & Sunghyun Kim & Ernst Schaumburg & Christopher A. Sims, 2003. "Calculating and using second order accurate solutions of discrete time dynamic equilibrium models," Finance and Economics Discussion Series 2003-61, Board of Governors of the Federal Reserve System (U.S.).
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  12. Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252 Elsevier.
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