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Merging Simulation and Projection Approaches to Solve High-Dimensional Problems

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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
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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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    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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