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

  • Jesus Fernandez-Villaverde
  • Juan Rubio
  • Manuel 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.

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.nber.org/papers/t0315.pdf
Download Restriction: no

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0315.

as
in new window

Length:
Date of creation: Oct 2005
Date of revision:
Publication status: published as Fernández-Villaverde, Jesus, Juan F. Rubio-Ramírez, and Manuel S. Santos. "Convergence Properties of the Likelihood of Computed Dynamic Models." Econometrica 74, 1 (2006): 93-119.
Handle: RePEc:nbr:nberte:0315
Note: TWP
Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
Phone: 617-868-3900
Web page: http://www.nber.org
Email:


More information through EDIRC

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. 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.
  2. 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.
  3. Peter N. Ireland, 2004. "Technology Shocks in the New Keynesian Model," NBER Working Papers 10309, National Bureau of Economic Research, Inc.
  4. 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.
  5. 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.
  6. Christopher Otrok, 2000. "On Measuring the Welfare Cost of Business Cycles," Econometric Society World Congress 2000 Contributed Papers 1094, Econometric Society.
  7. Ali Dib, 2001. "An Estimated Canadian DSGE Model with Nominal and Real Rigidities," Working Papers 01-26, Bank of Canada.
  8. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  9. 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.
  10. 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.
  11. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  12. Jesús Fernández-Villaverde & Juan Francisco Rubio-Ramírez, 2004. "Estimating nonlinear dynamic equilibrium economies: a likelihood approach," Working Paper 2004-1, Federal Reserve Bank of Atlanta.
  13. 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.
  14. Michael P. Keane & Kenneth I. Wolpin, 1994. "The solution and estimation of discrete choice dynamic programming models by simulation and interpolation: Monte Carlo evidence," Staff Report 181, Federal Reserve Bank of Minneapolis.
  15. Victor Aguirregabiria & Pedro Mira, 2004. "Sequential Estimation of Dynamic Discrete Games," Industrial Organization 0406006, EconWPA.
  16. Gregory S. Crawford & Matthew Shum, 2005. "Uncertainty and Learning in Pharmaceutical Demand," Econometrica, Econometric Society, vol. 73(4), pages 1137-1173, 07.
  17. 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.
  18. M. Keane & R. Mofitt, 1995. "A Structural Model of Multiple Welfare Program Participation and Labor Supply," Working Papers 95-4, Brown University, Department of Economics.
  19. Mireia Jofre-Bonet & Martin Pesendorfer, 2003. "Estimation of a Dynamic Auction Game," Econometrica, Econometric Society, vol. 71(5), pages 1443-1489, 09.
  20. 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 267-90, May.
  21. 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.
  22. 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.
  23. 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.
  24. Michael P. Keane & Kenneth I. Wolpin, 1995. "The career decisions of young men," Working Papers 559, Federal Reserve Bank of Minneapolis.
  25. 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.
  26. Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
  27. 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.
  28. 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.
  29. 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.
  30. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
  31. 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.
  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. Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-120, December.
  34. 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.
  35. 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.
  36. 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.
  37. Stachurski, J., 2001. "Stochastic Optimal Growth with Unbounded Shock," Department of Economics - Working Papers Series 777, The University of Melbourne.
  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. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, 09.
  40. Manuel S. Santos & Adrian Peralta-Alva, 2003. "Accuracy of Simulations for Stochastic Dynamic Models," Levine's Bibliography 666156000000000264, UCLA Department of Economics.
  41. 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.
  42. 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.
  43. 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.
  44. 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.
  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. Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report 232, Federal Reserve Bank of Minneapolis.
  47. 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.
  48. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  49. 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.
  50. P. D., 1988. "Introduction," Journal of Post Keynesian Economics, M.E. Sharpe, Inc., vol. 10(4), pages 527, July.
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:nbr:nberte:0315. 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: ()

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.