IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Convergence properties of the likelihood of computed dynamic models

  • Jesús Fernández-Villaverde
  • Juan Francisco Rubio-Ramírez
  • Manuel Santos

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.frbatlanta.org/filelegacydocs/wp0427.pdf
Download Restriction: no

Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2004-27.

as
in new window

Length:
Date of creation: 2004
Date of revision:
Handle: RePEc:fip:fedawp:2004-27
Contact details of provider: Postal: 1000 Peachtree St., N.E., Atlanta, Georgia 30309
Phone: 404-521-8500
Web page: http://www.frbatlanta.org/Email:


More information through EDIRC

Order Information: Email:


References listed on IDEAS
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.:

as in new window
  1. Frank Smets & Raf Wouters, 2004. "Comparing shocks and frictions in US and euro area business cycles: a Bayesian DSGE approach," Working Paper Research 61, National Bank of Belgium.
  2. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  3. 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.
  4. John Rust & Christopher Phelan, 1994. "How Social Security and Medicare Affect Retirement Behavior in a World of Incomplete Markets," Public Economics 9406005, EconWPA, revised 06 Jul 1994.
  5. Mireia Jofre-Bonet & Martin Pesendorfer, 2001. "Estimation of a Dynamic Auction Game," NBER Working Papers 8626, National Bureau of Economic Research, Inc.
  6. Jesus Fernandez-Villaverde & Juan Francisco Rubio-Ramírez, 2003. "Some results on the solution of the neoclassical growth model," Working Paper 2003-34, Federal Reserve Bank of Atlanta.
  7. 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.
  8. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
  9. Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-120, December.
  10. Ariel Pakes, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," NBER Working Papers 1340, National Bureau of Economic Research, Inc.
  11. 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.
  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. Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. Peter N. Ireland, 2004. "Technology Shocks in the New Keynesian Model," NBER Working Papers 10309, National Bureau of Economic Research, Inc.
  20. 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.
  21. D. K. Foley & M. F. Hellwig, 1973. "Asset Management with Trading Uncertainty," Working papers 108, Massachusetts Institute of Technology (MIT), Department of Economics.
  22. Otrok, Christopher, 2001. "On measuring the welfare cost of business cycles," Journal of Monetary Economics, Elsevier, vol. 47(1), pages 61-92, February.
  23. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
  24. Manuel S. Santos, 2003. "Simulation-Based Estimation Of Dynamic Models With Continuous Equilibrium Solutions," Economics Working Papers we034716, Universidad Carlos III, Departamento de Economía.
  25. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, 06.
  26. Frank Smets & Raf Wouters, 2002. "An estimated dynamic stochastic general equilibrium model of the euro area," Working Paper Research 35, National Bank of Belgium.
  27. 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.
  28. 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.
  29. T. J. Kehoe & D. K. Levine, 1982. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Working papers 312, Massachusetts Institute of Technology (MIT), Department of Economics.
  30. 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.
  31. Frank Schorfheide, 2000. "Loss function-based evaluation of DSGE models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 645-670.
  32. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  33. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
  34. Thomas Lubik & Frank Schorfheide, 2003. "Do Central Banks Respond to Exchange Rate Movements? A Structural Investigation," Economics Working Paper Archive 505, The Johns Hopkins University,Department of Economics.
  35. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, 01.
  36. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-43, August.
  37. 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.
  38. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July.
  39. 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.
  40. P. D., 1988. "Introduction," Journal of Post Keynesian Economics, M.E. Sharpe, Inc., vol. 10(4), pages 527, July.
  41. Michele Boldrin & Michael Woodford, 1988. "Equilibruim Models Displaying Endogenous Fluctuations and Chaos: A Survey," UCLA Economics Working Papers 530, UCLA Department of Economics.
  42. 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.
  43. Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report 232, Federal Reserve Bank of Minneapolis.
  44. 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.
  45. 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.
  46. 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.
  47. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  48. Gregory S. Crawford & Matthew Shum, 2005. "Uncertainty and Learning in Pharmaceutical Demand," Econometrica, Econometric Society, vol. 73(4), pages 1137-1173, 07.
  49. 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.
  50. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:fip:fedawp:2004-27. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Meredith Rector)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.