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How to Maximize the Likelihood Function for a DSGE Model

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  • Martin Andreasen

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Abstract

This paper extends two optimization routines to deal with objective functions for DSGE models. The optimization routines are i) a version of Simulated Annealing developed by Corana, Marchesi & Ridella (1987), and ii) the evolutionary algorithm CMA-ES developed by Hansen, Müller & Koumoutsakos (2003). Following these extensions, we examine the ability of the two routines to maximize the likelihood function for a sequence of test economies. Our results show that the CMA-ES routine clearly outperforms Simulated Annealing in its ability to find the global optimum and in efficiency. With 10 unknown structural parameters in the likelihood function, the CMA-ES routine finds the global optimum in 95% of our test economies compared to 89% for Simulated Annealing. When the number of unknown structural parameters in the likelihood function increases to 20 and 35, then the CMA-ES routine finds the global optimum in 85% and 71% of our test economies, respectively. The corresponding numbers for Simulated Annealing are 70% and 0%.
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Suggested Citation

  • Martin Andreasen, 2010. "How to Maximize the Likelihood Function for a DSGE Model," Computational Economics, Springer;Society for Computational Economics, vol. 35(2), pages 127-154, February.
  • Handle: RePEc:kap:compec:v:35:y:2010:i:2:p:127-154
    DOI: 10.1007/s10614-009-9182-6
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    References listed on IDEAS

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    1. 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.
    2. David Altig & Lawrence Christiano & Martin Eichenbaum & Jesper Linde, 2011. "Firm-Specific Capital, Nominal Rigidities and the Business Cycle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(2), pages 225-247, April.
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    4. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
    5. 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.
    6. 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.
    7. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    8. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    9. Martin Møller Andreasen, 2008. "Ensuring the Validity of the Micro Foundation in DSGE Models," CREATES Research Papers 2008-26, Department of Economics and Business Economics, Aarhus University.
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    Cited by:

    1. Giovanni Angelini & Luca Fanelli, 2016. "Misspecification and Expectations Correction in New Keynesian DSGE Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(5), pages 623-649, October.
    2. Boris Blagov, 2013. "Financial crises and time- varying risk premia in a small open economy: a Markov-Switching DSGE model for Estonia," Bank of Estonia Working Papers wp2013-8, Bank of Estonia, revised 09 Dec 2013.
    3. Stephen Morris, 2014. "The Statistical Implications of Common Identifying Restrictions for DSGE Models," 2014 Meeting Papers 738, Society for Economic Dynamics.
    4. Bernd Hayo & Britta Niehof, 2014. "Monetary and Fiscal Policy in Times of Crises: A New Keynesian Perspective in Continuous Time," MAGKS Papers on Economics 201455, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    5. Born, Benjamin & Pfeifer, Johannes, 2014. "Policy risk and the business cycle," Journal of Monetary Economics, Elsevier, vol. 68(C), pages 68-85.
    6. Andreasen, Martin, 2011. "An estimated DSGE model: explaining variation in term premia," Bank of England working papers 441, Bank of England.
    7. Solomon, Bernard Daniel, 2010. "Firm leverage, household leverage and the business cycle," MPRA Paper 26504, University Library of Munich, Germany.
    8. Morrisy, Stephen D., 2017. "Efficient estimation of macroeconomic equations with unobservable states," Economic Modelling, Elsevier, vol. 60(C), pages 408-423.
    9. Tae Bong Kim & Hangyu Lee, 2016. "Macroeconomic Shocks and Dynamics of Labor Markets in Korea," Korean Economic Review, Korean Economic Association, vol. 32, pages 101-136.
    10. Liran Einav & Amy Finkelstein & Paul Schrimpf, 2013. "The Response of Drug Expenditures to Non-Linear Contract Design: Evidence from Medicare Part D," NBER Working Papers 19393, National Bureau of Economic Research, Inc.
    11. 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.
    12. Mickelsson, Glenn, 2015. "Estimation of DSGE models: Maximum Likelihood vs. Bayesian methods," Working Paper Series 2015:6, Uppsala University, Department of Economics.
    13. Marcin Bielecki & Michał Brzoza-Brzezina & Marcin Kolasa & Krzysztof Makarski, 2017. "Could the boom-bust in the eurozone periphery have been prevented?," GRAPE Working Papers 17, GRAPE Group for Research in Applied Economics.
    14. Martin Møller Andreasen, 2008. "Explaining Macroeconomic and Term Structure Dynamics Jointly in a Non-linear DSGE Model," CREATES Research Papers 2008-43, Department of Economics and Business Economics, Aarhus University.
    15. Burgess, Stephen & Fernandez-Corugedo, Emilio & Groth, Charlotta & Harrison, Richard & Monti, Francesca & Theodoridis, Konstantinos & Waldron, Matt, 2013. "The Bank of England's forecasting platform: COMPASS, MAPS, EASE and the suite of models," Bank of England working papers 471, Bank of England.
    16. Martin Møller Andreasen, 2008. "Non-linear DSGE Models, The Central Difference Kalman Filter, and The Mean Shifted Particle Filter," CREATES Research Papers 2008-33, Department of Economics and Business Economics, Aarhus University.
    17. Blagov, Boris & Funke, Michael, 2013. "The regime-dependent evolution of credibility : A fresh look at Hong Kong s linked exchange rate system," BOFIT Discussion Papers 24/2013, Bank of Finland, Institute for Economies in Transition.
    18. Morris, Stephen D., 2017. "DSGE pileups," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 56-86.
    19. Born, Benjamin & Pfeifer, Johannes, 2014. "Policy risk and the business cycle," Journal of Monetary Economics, Elsevier, vol. 68(C), pages 68-85.
    20. Tae Bong Kim, 2013. "Monetary Policy in Korea through the lense of Taylor Rule in DSGE model," 2013 Meeting Papers 746, Society for Economic Dynamics.
    21. Dario Caldara & Richard Harrison & Anna Lipinska, 2012. "Practical tools for policy analysis in DSGE models with missing channels," Finance and Economics Discussion Series 2012-72, Board of Governors of the Federal Reserve System (U.S.).

    More about this item

    Keywords

    CMA-ES optimization routine; Multimodel objective function; Nelder–Mead simplex routine; Non-convex search space; Resampling; Simulated Annealing; C61; C88; E30;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)

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