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Merging Simulation and Projection Approaches to Solve High-Dimensional Problems

Author

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  • Kenneth L. Judd
  • Lilia Maliar
  • Serguei Maliar

Abstract

We introduce an algorithm for solving dynamic economic models that merges stochastic simulation and projection approaches: we use simulation to approximate the ergodic measure of the solution, we construct a fixed grid covering the support of the constructed ergodic measure, and we use projection techniques to accurately solve the model on that grid. The grid construction is the key novel piece of our analysis: we select an ε-distinguishable subset of simulated points that covers the support of the ergodic measure roughly uniformly. The proposed algorithm is tractable in problems with high dimensionality (hundreds of state variables) on a desktop computer. As an illustration, we solve one- and multicountry neoclassical growth models and a large-scale new Keynesian model with a zero lower bound on nominal interest rates.

Suggested Citation

  • Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2012. "Merging Simulation and Projection Approaches to Solve High-Dimensional Problems," NBER Working Papers 18501, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:18501 Note: EFG PE TWP
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    References listed on IDEAS

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    1. Lawrence Christiano & Martin Eichenbaum & Sergio Rebelo, 2011. "When Is the Government Spending Multiplier Large?," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 78-121.
    2. Del Negro, Marco & Schorfheide, Frank & Smets, Frank & Wouters, Rafael, 2007. "On the Fit of New Keynesian Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 123-143, April.
    3. 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.
    4. 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.
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    Cited by:

    1. Maliar, Lilia & Maliar, Serguei, 2013. "Envelope condition method versus endogenous grid method for solving dynamic programming problems," Economics Letters, Elsevier, vol. 120(2), pages 262-266.
    2. Arellano, Cristina & Maliar, Lilia & Maliar, Serguei & Tsyrennikov, Viktor, 2016. "Envelope condition method with an application to default risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 436-459.
    3. S. Borağan Aruoba & Pablo Cuba-Borda & Frank Schorfheide, 2012. "Macroeconomic Dynamics Near the ZLB: A Tale of Two Countries," PIER Working Paper Archive 14-035, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 19 Jun 2014.
    4. Julien Albertini & Hong Lan, 2016. "The importance of time-varying parameters in new Keynesian models with zero lower bound," SFB 649 Discussion Papers SFB649DP2016-013, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Fernández-Villaverde, Jesús & Gordon, Grey & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Nonlinear adventures at the zero lower bound," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 182-204.
    6. Holden, Tom D., 2016. "Computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 144569, ZBW - German National Library of Economics.
    7. Michael Reiter, 2015. "Solving OLG Models with Asset Choice," 2015 Meeting Papers 1509, Society for Economic Dynamics.
    8. Rabitsch, Katrin & Stepanchuk, Serhiy & Tsyrennikov, Viktor, 2015. "International portfolios: A comparison of solution methods," Journal of International Economics, Elsevier, vol. 97(2), pages 404-422.
    9. Vadym Lepetyuk & Lilia Maliar & Serguei Maliar, 2017. "Should Central Banks Worry About Nonlinearities of their Large-Scale Macroeconomic Models?," Staff Working Papers 17-21, Bank of Canada.
    10. Julien Albertini & Arthur Poirier, 2015. "Unemployment Benefit Extension at the Zero Lower Bound," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(4), pages 733-751, October.
    11. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
    12. Holden, Tom D., 2016. "Existence, uniqueness and computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 127430, ZBW - German National Library of Economics.
    13. Andrew Binning & Junior Maih, 2017. "Modelling Occasionally Binding Constraints Using Regime-Switching," Working Paper 2017/23, Norges Bank.
    14. Guerrieri, Luca & Iacoviello, Matteo, 2015. "OccBin: A toolkit for solving dynamic models with occasionally binding constraints easily," Journal of Monetary Economics, Elsevier, vol. 70(C), pages 22-38.
    15. Filip Rozsypal, 2015. "Schumpeterian business cycles," 2015 Meeting Papers 320, Society for Economic Dynamics.
    16. Mennuni, Alessandro, 2013. "Labor Force Composition and Aggregate Fluctuations," Discussion Paper Series In Economics And Econometrics 1302, Economics Division, School of Social Sciences, University of Southampton.
    17. Hommes, C.H. & Massaro, D. & Salle, I., 2015. "Monetary and Fiscal Policy Design at the Zero Lower Bound - Evidence from the Lab," CeNDEF Working Papers 15-11, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    18. Karel R. S. M. Mertens & Morten O. Ravn, 2014. "Fiscal Policy in an Expectations-Driven Liquidity Trap," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1637-1667.
    19. repec:kap:compec:v:51:y:2018:i:1:d:10.1007_s10614-017-9670-z is not listed on IDEAS
    20. Nick Draper & André Nibbelink & Johannes Uhde, 2013. "An Assessment of Alternatives for the Dutch First Pension Pillar, The Design of Pension Schemes," CPB Discussion Paper 259, CPB Netherlands Bureau for Economic Policy Analysis.
    21. Reiter, Michael, 2015. "Solving OLG Models with Many Cohorts, Asset Choice and Large Shocks," Economics Series 320, Institute for Advanced Studies.
    22. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2014. "Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-06, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    23. Nick Draper & André Nibbelink & Johannes Uhde, 2015. "An Assessment of Alternatives for the Dutch First Pension Pillar System," De Economist, Springer, vol. 163(3), pages 281-302, September.
    24. Julien Albertini & Arthur Poirier, 2014. "Unemployment benefits extensions at the zero lower bound on nominal interest rate," SFB 649 Discussion Papers SFB649DP2014-019, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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