IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/9130.html
   My bibliography  Save this paper

Estimating Dynamic Equilibrium Models with Stochastic Volatility

Author

Listed:
  • Rubio-Ramírez, Juan Francisco
  • Fernández-Villaverde, Jesús
  • Guerron-Quintana, Pablo A.

Abstract

We propose a novel method to estimate dynamic equilibrium models with stochastic volatility. First, we characterize the properties of the solution to this class of models. Second, we take advantage of the results about the structure of the solution to build a sequential Monte Carlo algorithm to evaluate the likelihood function of the model. The approach, which exploits the profusion of shocks in stochastic volatility models, is versatile and computationally tractable even in large-scale models, such as those often employed by policy-making institutions. As an application, we use our algorithm and Bayesian methods to estimate a business cycle model of the U.S. economy with both stochastic volatility and parameter drifting in monetary policy. Our application shows the importance of stochastic volatility in accounting for the dynamics of the data.

Suggested Citation

  • Rubio-Ramírez, Juan Francisco & Fernández-Villaverde, Jesús & Guerron-Quintana, Pablo A., 2012. "Estimating Dynamic Equilibrium Models with Stochastic Volatility," CEPR Discussion Papers 9130, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:9130
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP9130
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. van Binsbergen, Jules H. & Fernández-Villaverde, Jesús & Koijen, Ralph S.J. & Rubio-Ramírez, Juan, 2012. "The term structure of interest rates in a DSGE model with recursive preferences," Journal of Monetary Economics, Elsevier, vol. 59(7), pages 634-648.
    2. Neil Shephard & Siddhartha Chib & Olin School of Business & Washington University & Michael K. Pitt & Department of Economics & University of Warwick, 2004. "Likelihood based inference for diffusion driven models," Economics Series Working Papers 2004-FE-17, University of Oxford, Department of Economics.
    3. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 115(1), pages 147-180.
    4. Nason James M. & Smith Gregor W, 2008. "Great Moderation(s) and US Interest Rates: Unconditional Evidence," The B.E. Journal of Macroeconomics, De Gruyter, vol. 8(1), pages 1-33, November.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    6. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramirez & Martin Uribe, 2011. "Risk Matters: The Real Effects of Volatility Shocks," American Economic Review, American Economic Association, vol. 101(6), pages 2530-2561, October.
    7. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    8. Jonas D. M. Fisher, 2006. "The Dynamic Effects of Neutral and Investment-Specific Technology Shocks," Journal of Political Economy, University of Chicago Press, vol. 114(3), pages 413-451, June.
    9. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, May.
    10. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230, National Bureau of Economic Research, Inc.
    11. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.
    12. Neil Shephard & Torben G. Andersen, 2008. "Stochastic Volatility: Origins and Overview," Economics Series Working Papers 389, University of Oxford, Department of Economics.
    13. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    14. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    15. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
    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. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    18. Osnat Stramer & Matthew Bognar & Paul Schneider, 2010. "Bayesian Inference for Discretely Sampled Markov Processes with Closed-Form Likelihood Expansions," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(4), pages 450-480, Fall.
    19. 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.
    20. Stacey L. Schreft, 1990. "Credit controls: 1980," Economic Review, Federal Reserve Bank of Richmond, vol. 76(Nov), pages 25-55.
    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. Siddhartha Chib & Michael K Pitt & Neil Shephard, 2004. "Likelihood based inference for diffusion driven models," OFRC Working Papers Series 2004fe17, Oxford Financial Research Centre.
    23. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    24. Dario Caldara & Jesus Fernandez-Villaverde & Juan Rubio-Ramirez & Wen Yao, 2012. "Computing DSGE Models with Recursive Preferences and Stochastic Volatility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 188-206, April.
    25. Olaf Posch & Juan F. Rubio-Ramírez & Jesús Fernández-Villaverde, 2011. "Solving the new Keynesian model in continuous time," 2011 Meeting Papers 829, Society for Economic Dynamics.
    26. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
    27. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    28. Judd, Kenneth L. & Guu, Sy-Ming, 1997. "Asymptotic methods for aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1025-1042, June.
    29. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    30. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2009. "Understanding Markov-switching rational expectations models," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1849-1867, September.
    31. Flury, Thomas & Shephard, Neil, 2011. "Bayesian Inference Based Only On Simulated Likelihood: Particle Filter Analysis Of Dynamic Economic Models," Econometric Theory, Cambridge University Press, vol. 27(5), pages 933-956, October.
    32. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pablo A. Guerron-Quintana & Tomohiro Hirano & Ryo Jinnai, 2019. "Recurrent Bubbles and Economic Growth," CARF F-Series CARF-F-457, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Tao Zha & Juan F. Rubio-Ramirez & Daniel F. Waggoner & Andrew T. Foerster, 2010. "Perturbation Methods for Markov-Switching Models," 2010 Meeting Papers 239, Society for Economic Dynamics.
    3. Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, July.
    4. Christopher Otrok & Andrew Foerster & Alessandro Rebucci & Gianluca Benigno, 2017. "Estimating Macroeconomic Models of Financial Crises: An Endogenous Regime Switching Approach," 2017 Meeting Papers 572, Society for Economic Dynamics.
    5. Andrew Binning & Junior Maih, 2015. "Sigma point filters for dynamic nonlinear regime switching models," Working Paper 2015/10, Norges Bank.
    6. Kristoffer P. Nimark, 2014. "Man-Bites-Dog Business Cycles," American Economic Review, American Economic Association, vol. 104(8), pages 2320-2367, August.
    7. Jump, Robert Calvert & Levine, Paul, 2019. "Behavioural New Keynesian models," Journal of Macroeconomics, Elsevier, vol. 59(C), pages 59-77.
    8. Ciccarone, Giuseppe & Giuli, Francesco & Marchetti, Enrico & Tancioni, Massimiliano, 2020. "Leaning against the bubble. Can theoretical models match the empirical evidence?," MPRA Paper 105004, University Library of Munich, Germany.
    9. Pablo Cuba‐Borda & Luca Guerrieri & Matteo Iacoviello & Molin Zhong, 2019. "Likelihood evaluation of models with occasionally binding constraints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(7), pages 1073-1085, November.
    10. Pablo A. Guerron-Quintana & Tomohiro Hirano & Ryo Jinnai, 2021. "Bubbles, Crashes, Ups and Downs in Economic Growth Theory and Evidence," CIGS Working Paper Series 21-006E, The Canon Institute for Global Studies.
    11. Nigar Hashimzade & Oleg Kirsanov & Tatiana Kirsanova & Junior Maih, 2024. "On Bayesian Filtering for Markov Regime Switching Models," CESifo Working Paper Series 10941, CESifo.
    12. Dietrich, Alexander M., 2023. "Consumption categories, household attention, and inflation expectations: Implications for optimal monetary policy," University of Tübingen Working Papers in Business and Economics 157, University of Tuebingen, Faculty of Economics and Social Sciences, School of Business and Economics.
    13. Giraitis, Liudas & Kapetanios, George & Theodoridis, Konstantinos & Yates, Tony, 2014. "Estimating time-varying DSGE models using minimum distance methods," Bank of England working papers 507, Bank of England.
    14. Patella, Valeria & Tancioni, Massimiliano, 2021. "Confidence Swings and Sovereign Risk Dynamics," Structural Change and Economic Dynamics, Elsevier, vol. 56(C), pages 195-206.
    15. Le Thanh Ha & To Trung Thanh & Doan Ngoc Thang, 2021. "Welfare costs of monetary policy uncertainty in the economy with shifting trend inflation," Scottish Journal of Political Economy, Scottish Economic Society, vol. 68(1), pages 126-154, February.
    16. Giraitis, Liudas & Kapetanios, George & Theodoridis, Konstantinos & Yates, Tony, 2014. "Estimating time-varying DSGE models using minimum distance methods," Bank of England working papers 507, Bank of England.

    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. 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.
    2. Jesús Fernández-Villaverde, 2010. "The econometrics of DSGE models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 1(1), pages 3-49, March.
    3. Juan Rubio-Ramirez & Jesus Fernandez-Villaverde & Pablo A. Guerron-Quintana, 2010. "Fortune or Virtue: Time Variant Volatilities versus Parameter Drifting in U.S. Data," 2010 Meeting Papers 270, Society for Economic Dynamics.
    4. Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, July.
    5. Jesús Fernández-Villaverde & Pablo Guerrón-Quintana & Juan F. Rubio-Ramirez, 2010. "Reading the recent monetary history of the U.S., 1959-2007," Working Papers 10-15, Federal Reserve Bank of Philadelphia.
    6. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana, 2020. "Uncertainty Shocks and Business Cycle Research," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 118-166, August.
    7. Ralph S.J. Koijen & Jules H. van Binsbergen & Juan F. Rubio-Ramírez & Jesus Fernandez-Villaverde, 2008. "Likelihood Estimation of DSGE Models with Epstein-Zin Preferences," 2008 Meeting Papers 1099, Society for Economic Dynamics.
    8. 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.
    9. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1059-1087.
    10. Hong Lan & Alexander Meyer-Gohde, 2013. "Decomposing Risk in Dynamic Stochastic General Equilibrium," SFB 649 Discussion Papers SFB649DP2013-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
    12. Lorenzo Bretscher & Alex Hsu & Andrea Tamoni, 2019. "Response of the Macroeconomy to Uncertainty Shocks:the Risk Premium Channel," 2019 Meeting Papers 1567, Society for Economic Dynamics.
    13. Alexander Meyer-Gohde, 2014. "Risky Linear Approximations," SFB 649 Discussion Papers SFB649DP2014-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Jesus Fernandez-Villaverde & Pablo Guerron-Quintana & Juan F. Rubio-Ramirez & Martin Uribe, 2011. "Risk Matters: The Real Effects of Volatility Shocks," American Economic Review, American Economic Association, vol. 101(6), pages 2530-2561, October.
    15. Bianchi, Francesco, 2016. "Methods for measuring expectations and uncertainty in Markov-switching models," Journal of Econometrics, Elsevier, vol. 190(1), pages 79-99.
    16. Marcelo Ferman, 2011. "Switching Monetary Policy Regimes and the Nominal Term Structure," FMG Discussion Papers dp678, Financial Markets Group.
    17. Canova, Fabio & Ferroni, Filippo, 2012. "The dynamics of US inflation: Can monetary policy explain the changes?," Journal of Econometrics, Elsevier, vol. 167(1), pages 47-60.
    18. Serguei Maliar & John Taylor & Lilia Maliar, 2016. "The Impact of Alternative Transitions to Normalized Monetary Policy," 2016 Meeting Papers 794, Society for Economic Dynamics.
    19. Richard Higgins, C., 2020. "Financial frictions and changing macroeconomic volatility," Journal of Macroeconomics, Elsevier, vol. 64(C).
    20. Martin Andreasen, 2012. "On the Effects of Rare Disasters and Uncertainty Shocks for Risk Premia in Non-Linear DSGE Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 295-316, July.

    More about this item

    Keywords

    Bayesian methods; Dynamic equilibrium models; Parameter drifting; stochastic volatility;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)

    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:cpr:ceprdp:9130. 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: the person in charge (email available below). General contact details of provider: https://www.cepr.org .

    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.