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Convergence Properties of the Likelihood of Computed Dynamic Models

Listed author(s):
  • Jesús Fernández-Villaverde
  • Juan F. Rubio-Ramírez
  • Manuel S. Santos

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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  1. M. Keane & R. Moffitt, "undated". "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.
  2. Timothy J. Kehoe & David K. Levine, 1982. "Comparitive Statics and Perfect Foresight in Infinite Horizon Economies," UCLA Economics Working Papers 259, UCLA Department of Economics.
  3. Jesús Fernández-Villaverde & Juan Francisco Rubio-Ramírez, 2004. "Estimating dynamic equilibrium economies: linear versus nonlinear likelihood," FRB Atlanta Working Paper 2004-3, Federal Reserve Bank of Atlanta.
  4. Frank Smets & Raf Wouters, 2002. "An estimated dynamic stochastic general equilibrium model of the euro area," Working Paper Research 35, National Bank of Belgium.
  5. repec:cmf:wpaper:wp2004_0413 is not listed on IDEAS
  6. Mireia Jofre-Bonet & Martin Pesendorfer, 2001. "Estimation of a Dynamic Auction Game," NBER Working Papers 8626, National Bureau of Economic Research, Inc.
  7. Ali Dib, 2001. "An Estimated Canadian DSGE Model with Nominal and Real Rigidities," Staff Working Papers 01-26, Bank of Canada.
  8. Klaus Reiner Schenk-Hopp� & Bj�rn Schmalfuss, "undated". "Random Fixed Points in a Stochastic Solow Growth Model," IEW - Working Papers 065, Institute for Empirical Research in Economics - University of Zurich.
  9. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
  10. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-784, July.
  11. 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 852-874, October.
  12. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
  13. D. K. Foley & M. F. Hellwig, 1973. "Asset Management with Trading Uncertainty," Working papers 108, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. 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.
  15. 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.
  16. 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.
  17. Frank Schorfheide, 2000. "Loss function-based evaluation of DSGE models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 645-670.
  18. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-643, August.
  19. Santos, Manuel S., 2003. "Simulation-based estimation of dynamic models with continuous equilibrium solutions," UC3M Working papers. Economics we034716, Universidad Carlos III de Madrid. Departamento de Economía.
  20. Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report 232, Federal Reserve Bank of Minneapolis.
  21. 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.
  22. Raf Wouters & Frank Smets, 2005. "Comparing shocks and frictions in US and euro area business cycles: a Bayesian DSGE Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(2), pages 161-183.
  23. Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating Nonlinear Dynamic Equilibrium economies: A Likelihood Approach," PIER Working Paper Archive 04-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  24. 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.
  25. 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 648-672, November.
  26. Victor Aguirregabiria & Pedro Mira, 2004. "Sequential Estimation of Dynamic Discrete Games," Industrial Organization 0406006, EconWPA.
  27. 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.
  28. Thomas A. Lubik & Frank Schorfheide, 2004. "Testing for Indeterminacy: An Application to U.S. Monetary Policy," American Economic Review, American Economic Association, vol. 94(1), pages 190-217, March.
  29. P. D., 1988. "Introduction," Journal of Post Keynesian Economics, M.E. Sharpe, Inc., vol. 10(4), pages 527-527, July.
  30. 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.
  31. Flinn, C. & Heckman, J., 1982. "New methods for analyzing structural models of labor force dynamics," Journal of Econometrics, Elsevier, vol. 18(1), pages 115-168, January.
  32. 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.
  33. Michele Boldrin & Michael Woodford, 1988. "Equilibruim Models Displaying Endogenous Fluctuations and Chaos: A Survey," UCLA Economics Working Papers 530, UCLA Department of Economics.
  34. 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.
  35. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  36. Peter N. Ireland, 2004. "Technology Shocks in the New Keynesian Model," NBER Working Papers 10309, National Bureau of Economic Research, Inc.
  37. 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.
  38. John F. Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  39. Mas-Colell,Andreu, 1985. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521265140, December.
  40. McGrattan, Ellen R & Rogerson, Richard & Wright, Randall, 1997. "An Equilibrium Model of the Business Cycle with Household Production and Fiscal Policy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 267-290, May.
  41. Sargent, Thomas J, 1989. "Two Models of Measurements and the Investment Accelerator," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 251-287, April.
  42. Chris Otrok, 1999. "On Measuring the Welfare Cost of Business Cycles," Virginia Economics Online Papers 318, University of Virginia, Department of Economics.
  43. 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.
  44. Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
  45. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
  46. Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-1120, December.
  47. Gregory S. Crawford & Matthew Shum, 2005. "Uncertainty and Learning in Pharmaceutical Demand," Econometrica, Econometric Society, vol. 73(4), pages 1137-1173, 07.
  48. Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Some Results on the Solution of the Neoclassical Growth Model," PIER Working Paper Archive 04-002, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  49. 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 115-129, April.
  50. 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.
  51. Rosenzweig, Mark R. & Wolpin, Kenneth I., 1989. "Credit Market Constraints, Consumption Smoothing and the Accumulation of Durable Production Assets in Low-Income Countries: Investments in Bullocks in India," Bulletins 7487, University of Minnesota, Economic Development Center.
  52. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
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