Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/fip/fedawp/2004-27.html
   My bibliography  Save this paper

Convergence properties of the likelihood of computed dynamic models

Author

Listed:
  • Jesús Fernández-Villaverde
  • Juan F. Rubio-Ramirez
  • Manuel S. Santos
Abstract
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.

Suggested Citation

  • Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez & Manuel S. Santos, 2004. "Convergence properties of the likelihood of computed dynamic models," FRB Atlanta Working Paper 2004-27, Federal Reserve Bank of Atlanta.
    • Handle: RePEc:fip:fedawp:2004-27
    as

    Download full text from publisher

    File URL: https://www.frbatlanta.org/-/media/documents/research/publications/wp/2004/wp0427.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    4. 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 223-244, April.
    5. Keane, Michael & Moffitt, Robert, 1998. "A Structural Model of Multiple Welfare Program Participation and Labor Supply," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 553-589, August.
    6. Mireia Jofre-Bonet & Martin Pesendorfer, 2003. "Estimation of a Dynamic Auction Game," Econometrica, Econometric Society, vol. 71(5), pages 1443-1489, September.
    7. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-453, March.
    8. 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.
    9. Ali Dib, 2003. "An estimated Canadian DSGE model with nominal and real rigidities," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 949-972, November.
    10. 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.
    11. Frank Smets & Raf Wouters, 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.
    12. Frank Schorfheide, 2000. "Loss function-based evaluation of DSGE models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 645-670.
    13. 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.
    14. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
    15. Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-1120, December.
    16. 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.
    17. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, September.
    18. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    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. Juan F. Rubio-Ramirez & Jesus Fernández-Villaverde, 2005. "Estimating dynamic equilibrium economies: linear versus nonlinear likelihood," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 891-910.
    21. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, October.
    27. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    28. Gregory S. Crawford & Matthew Shum, 2005. "Uncertainty and Learning in Pharmaceutical Demand," Econometrica, Econometric Society, vol. 73(4), pages 1137-1173, July.
    29. Otrok, Christopher, 2001. "On measuring the welfare cost of business cycles," Journal of Monetary Economics, Elsevier, vol. 47(1), pages 61-92, February.
    30. Duncan K. Foley & Martin F. Hellwig, 1975. "Asset Management with Trading Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 327-346.
    31. 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.
    32. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
    33. 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.
    34. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    35. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
    36. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    37. Peter N. Ireland, 2004. "Technology Shocks in the New Keynesian Model," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 923-936, November.
    38. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    39. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
    40. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    41. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating nonlinear dynamic equilibrium economies: a likelihood approach," FRB Atlanta Working Paper 2004-1, Federal Reserve Bank of Atlanta.
    42. 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.
    43. 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.
    44. 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.
    45. 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, June.
    46. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448, Elsevier.
    47. 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.
    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. 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.
    50. Ellen R. McGrattan, 1998. "Application of weighted residual methods to dynamic economic models," Staff Report 232, Federal Reserve Bank of Minneapolis.
    51. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    52. 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.
    53. 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.
    54. 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, September.
    55. 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.
    56. Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juan F. Rubio-Ramirez & Jesus Fernández-Villaverde, 2005. "Estimating dynamic equilibrium economies: linear versus nonlinear likelihood," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 891-910.
    2. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1059-1087.
    3. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    4. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    5. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    6. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating nonlinear dynamic equilibrium economies: a likelihood approach," FRB Atlanta Working Paper 2004-1, Federal Reserve Bank of Atlanta.
    7. Marc P. Giannoni & Jean Boivin, 2005. "DSGE Models in a Data-Rich Environment," Computing in Economics and Finance 2005 431, Society for Computational Economics.
    8. Özer Karagedikli & Troy Matheson & Christie Smith & Shaun P. Vahey, 2010. "RBCs AND DSGEs: THE COMPUTATIONAL APPROACH TO BUSINESS CYCLE THEORY AND EVIDENCE," Journal of Economic Surveys, Wiley Blackwell, vol. 24(1), pages 113-136, February.
    9. Keane, Michael P. & Todd, Petra E. & Wolpin, Kenneth I., 2011. "The Structural Estimation of Behavioral Models: Discrete Choice Dynamic Programming Methods and Applications," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 4, pages 331-461, Elsevier.
    10. Kalouptsidi, Myrto & Scott, Paul & Souza-Rodrigues, Edouardo, 2015. "Identification of Counterfactuals and Payoffs in Dynamic Discrete Choice with an Application to Land Use," TSE Working Papers 15-596, Toulouse School of Economics (TSE).
    11. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2008. "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, Elsevier, vol. 146(1), pages 92-106, September.
    12. Pablo A. Guerrón-Quintana & James M. Nason, 2013. "Bayesian estimation of DSGE models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 21, pages 486-512, Edward Elgar Publishing.
    13. Santos, Manuel S., 2004. "Simulation-based estimation of dynamic models with continuous equilibrium solutions," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 465-491, June.
    14. Myrto Kalouptsidi & Paul T. Scott & Eduardo Souza-Rodrigues, 2015. "Identification of Counterfactuals in Dynamic Discrete Choice Models," NBER Working Papers 21527, National Bureau of Economic Research, Inc.
    15. Milani, Fabio, 2007. "Expectations, learning and macroeconomic persistence," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2065-2082, October.
    16. Peter Arcidiacono & Robert A. Miller, 2011. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 79(6), pages 1823-1867, November.
    17. Peter Arcidiacono & Holger Sieg & Frank Sloan, 2007. "Living Rationally Under The Volcano? An Empirical Analysis Of Heavy Drinking And Smoking," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(1), pages 37-65, February.
    18. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2008. "How Structural Are Structural Parameters?," NBER Chapters, in: NBER Macroeconomics Annual 2007, Volume 22, pages 83-137, National Bureau of Economic Research, Inc.
    19. Daniel Ackerberg, 2009. "A new use of importance sampling to reduce computational burden in simulation estimation," Quantitative Marketing and Economics (QME), Springer, vol. 7(4), pages 343-376, December.
    20. Peter Arcidiacono & Paul B. Ellickson, 2011. "Practical Methods for Estimation of Dynamic Discrete Choice Models," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 363-394, September.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. 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.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Rob Sarwark (email available below). General contact details of provider: https://edirc.repec.org/data/frbatus.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.