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Convergence Properties of the Likelihood of Computed Dynamic Models

  • 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)

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
Date of revision:
Handle: RePEc:pen:papers:04-034
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  1. Jesus Fernandez-Villaverde & Juan Francisco Rubio-Ramírez, 2003. "Some results on the solution of the neoclassical growth model," FRB Atlanta Working Paper No. 2003-34, Federal Reserve Bank of Atlanta.
  2. Foley, Duncan K & Hellwig, Martin F, 1975. "Asset Management with Trading Uncertainty," Review of Economic Studies, Wiley Blackwell, vol. 42(3), pages 327-46, July.
  3. P. D., 1988. "Introduction," Journal of Post Keynesian Economics, M.E. Sharpe, Inc., vol. 10(4), pages 527, July.
  4. Peter N. Ireland, 2002. "Technology Shocks in the New Keynesian Model," Boston College Working Papers in Economics 536, Boston College Department of Economics.
  5. Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood," PIER Working Paper Archive 04-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  6. Ariel Pakes & Michael Ostrovsky & Steve Berry, 2004. "Simple Estimators for the Parameters of Discrete Dynamic Games (with Entry/Exit Samples)," NBER Working Papers 10506, National Bureau of Economic Research, Inc.
  7. Keane, Michael P & Wolpin, Kenneth I, 1997. "The Career Decisions of Young Men," Journal of Political Economy, University of Chicago Press, vol. 105(3), pages 473-522, June.
  8. M. Keane & R. Moffitt, . "A structural model of multiple welfare program participation and labor supply," Institute for Research on Poverty Discussion Papers 1080-96, University of Wisconsin Institute for Research on Poverty.
  9. Ellison, Glenn & Fudenberg, Drew, 1992. "Rules of Thumb for Social Learning," IDEI Working Papers 17, Institut d'Économie Industrielle (IDEI), Toulouse.
  10. Donna B. Gilleskie, 1998. "A Dynamic Stochastic Model of Medical Care Use and Work Absence," Econometrica, Econometric Society, vol. 66(1), pages 1-46, January.
  11. Boldrin, Michele & Woodford, Michael, 1990. "Equilibrium models displaying endogenous fluctuations and chaos : A survey," Journal of Monetary Economics, Elsevier, vol. 25(2), pages 189-222, March.
  12. Sargent, Thomas J, 1989. "Two Models of Measurements and the Investment Accelerator," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 251-87, April.
  13. Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report 232, Federal Reserve Bank of Minneapolis.
  14. Christopher Otrok, 2000. "On Measuring the Welfare Cost of Business Cycles," Econometric Society World Congress 2000 Contributed Papers 1094, Econometric Society.
  15. Schenk-Hoppe, Klaus Reiner & Schmalfu[ss], Bjorn, 2001. "Random fixed points in a stochastic Solow growth model," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 19-30, September.
  16. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-53, March.
  17. Manuel S. Santos & Adrian Peralta-Alva, 2003. "Accuracy Of Simulations For Stochastic Dynamic Models," Economics Working Papers we034615, Universidad Carlos III, Departamento de Economía.
  18. Fernandez-Villaverde, Jesus & Francisco Rubio-Ramirez, Juan, 2004. "Comparing dynamic equilibrium models to data: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 123(1), pages 153-187, November.
  19. repec:cup:cbooks:9780521265140 is not listed on IDEAS
  20. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  21. Keane, Michael P & Wolpin, Kenneth I, 1994. "The Solution and Estimation of Discrete Choice Dynamic Programming Models by Simulation and Interpolation: Monte Carlo Evidence," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 648-72, November.
  22. Jesús Fernández-Villaverde & Juan Francisco Rubio-Ramírez, 2004. "Estimating nonlinear dynamic equilibrium economies: a likelihood approach," FRB Atlanta Working Paper No. 2004-1, Federal Reserve Bank of Atlanta.
  23. John Rust & Christopher Phelan, 1997. "How Social Security and Medicare Affect Retirement Behavior in a World of Incomplete Markets," Econometrica, Econometric Society, vol. 65(4), pages 781-832, July.
  24. repec:cup:cbooks:9780521388702 is not listed on IDEAS
  25. Lubik, Thomas A. & Schorfheide, Frank, 2007. "Do central banks respond to exchange rate movements? A structural investigation," Journal of Monetary Economics, Elsevier, vol. 54(4), pages 1069-1087, May.
  26. Rosenzweig, Mark R & Wolpin, Kenneth I, 1993. "Credit Market Constraints, Consumption Smoothing, and the Accumulation of Durable Production Assets in Low-Income Countries: Investment in Bullocks in India," Journal of Political Economy, University of Chicago Press, vol. 101(2), pages 223-44, April.
  27. Ali Dib, 2003. "An estimated Canadian DSGE model with nominal and real rigidities," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 949-972, November.
  28. Smets, Frank & Wouters, Rafael, 2004. "Comparing Shocks and Frictions in US and Euro Area Business Cycles: A Bayesian DSGE Approach," CEPR Discussion Papers 4750, C.E.P.R. Discussion Papers.
  29. Daula, Thomas & Moffitt, Robert, 1995. "Estimating Dynamic Models of Quit Behavior: The Case of Military Reenlistment," Journal of Labor Economics, University of Chicago Press, vol. 13(3), pages 499-523, July.
  30. Mireia Jofre-Bonet & Martin Pesendorfer, 2001. "Estimation of a Dynamic Auction Game," NBER Working Papers 8626, National Bureau of Economic Research, Inc.
  31. Thomas Lubik & Frank Schorfheide, 2002. "Testing for Indeterminacy:An Application to U.S. Monetary Policy," Economics Working Paper Archive 480, The Johns Hopkins University,Department of Economics, revised Jun 2003.
  32. Manuel S. Santos, 2003. "Simulation-Based Estimation Of Dynamic Models With Continuous Equilibrium Solutions," Economics Working Papers we034716, Universidad Carlos III, Departamento de Economía.
  33. DeJong, David N. & Ingram, Beth F. & Whiteman, Charles H., 2000. "A Bayesian approach to dynamic macroeconomics," Journal of Econometrics, Elsevier, vol. 98(2), pages 203-223, October.
  34. Victor Aguirregabiria & Pedro Mira, 2004. "Sequential Estimation Of Dynamic Discrete Games," Working Papers wp2004_0413, CEMFI.
  35. Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-120, December.
  36. Rabanal, Pau & Rubio-Ramirez, Juan F., 2005. "Comparing New Keynesian models of the business cycle: A Bayesian approach," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1151-1166, September.
  37. Frank Smets & Raf Wouters, 2002. "An estimated dynamic stochastic general equilibrium model of the euro area," Working Paper Research 35, National Bank of Belgium.
  38. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  39. Stephen Ryan & Patrick Bajari & Han Hong, 2005. "Identification and Estimation of Discrete Games of Complete Information," Computing in Economics and Finance 2005 53, Society for Computational Economics.
  40. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  41. James J. Heckman & Christopher J. Flinn, 1982. "New Methods for Analyzing Structural Models of Labor Force Dynamics," NBER Working Papers 0856, National Bureau of Economic Research, Inc.
  42. 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.
  43. Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
  44. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
  45. Frank Schorfheide, 2000. "Loss function-based evaluation of DSGE models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 645-670.
  46. Gregory S. Crawford & Matthew Shum, 2005. "Uncertainty and Learning in Pharmaceutical Demand," Econometrica, Econometric Society, vol. 73(4), pages 1137-1173, 07.
  47. Ferrall, Christopher, 1997. "Unemployment Insurance Eligibility and the School-to-Work Transition in Canada and the United States," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(2), pages 115-29, April.
  48. Ariel Pakes, 1984. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," NBER Working Papers 1340, National Bureau of Economic Research, Inc.
  49. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  50. Ellen McGrattan & Richard Rogerson & Randall Wright, 1995. "An equilibrium model of the business cycle with household production and fiscal policy," Staff Report 191, Federal Reserve Bank of Minneapolis.
  51. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
  52. Wolpin, Kenneth I, 1984. "An Estimable Dynamic Stochastic Model of Fertility and Child Mortality," Journal of Political Economy, University of Chicago Press, vol. 92(5), pages 852-74, October.
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