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Numerically Stable Stochastic Simulation Approaches for Solving Dynamic Economic Models

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  • Serguei Maliar

    (Hoover Institution at Stanford University and University of Alicante)

  • Lilia Maliar

    (Hoover Institution at Stanford University and University of Alicante)

  • Kenneth Judd

    (Hoover Institution at Stanford University)

Abstract

We develop numerically stable stochastic simulation approaches for solving dynamic economic models. We rely on standard simulation procedures to simultaneously compute an ergodic distribution of state variables, its support and the associated decision rules. We differ from existing methods, however, in how we use simulation data to approximate decision rules. Instead of the usual least-squares methods, we examine a variety of alternatives, including the least-squares method using SVD, Tikhonov regularization, least-absolute deviation methods, principal components regression method, all of which are numerically stable and can handle ill-conditioned problems. These new methods enable us to compute high-order polynomial approximations without encountering numerical problems. Our approaches are especially well suitable for high-dimensional applications in which other methods are infeasible.

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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2010 Meeting Papers with number 280.

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Date of creation: 2010
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Handle: RePEc:red:sed010:280

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Postal: Society for Economic Dynamics Christian Zimmermann Economic Research Federal Reserve Bank of St. Louis PO Box 442 St. Louis MO 63166-0442 USA
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Web page: http://www.EconomicDynamics.org/society.htm
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  1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, April.
  2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  3. Lilia Maliar & Serguei Maliar, 2003. "The Representative Consumer in the Neoclassical Growth Model with Idiosyncratic Shocks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(2), pages 368-380, April.
  4. Aiyagari, S Rao, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, MIT Press, vol. 109(3), pages 659-84, August.
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  6. Ray C. Fair & John B. Taylor, 1980. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear RationalExpectations Models," NBER Technical Working Papers 0005, National Bureau of Economic Research, Inc.
  7. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  8. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer, vol. 1(3), pages 211-218, September.
  9. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 45-75, January.
  10. Santos, Manuel S., 1999. "Numerical solution of dynamic economic models," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 5, pages 311-386 Elsevier.
  11. Krueger, Dirk & Kubler, Felix, 2004. "Computing equilibrium in OLG models with stochastic production," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1411-1436, April.
  12. Lawrence J. Christiano & Jonas D. M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Staff Report 171, Federal Reserve Bank of Minneapolis.
  13. den Haan, Wouter J & Marcet, Albert, 1990. "Solving the Stochastic Growth Model by Parameterizing Expectations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 31-34, January.
  14. Per Krusell & Anthony A. Smith, Jr., . "Income and Wealth Heterogeneity in the Macroeconomy," GSIA Working Papers 1997-37, Carnegie Mellon University, Tepper School of Business.
  15. Lilia Maliar & Serguei Maliar, 2001. "Parametrized Expectations Algorithm And The Moving Bounds," Working Papers. Serie AD 2001-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  16. Albert Marcet & Guido Lorenzoni, 1998. "The Parameterized Expectations Approach: Some Practical Issues," QM&RBC Codes 128, Quantitative Macroeconomics & Real Business Cycles.
  17. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979, Octomber.
  18. Michael Creel, 2008. "Using Parallelization to Solve a Macroeconomic Model: A Parallel Parameterized Expectations Algorithm," Computational Economics, Society for Computational Economics, vol. 32(4), pages 343-352, November.
  19. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
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  21. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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Cited by:
  1. Laurence Kotlikoff, 2013. "The US Fiscal Cliff – When Economists Recklessly Endanger the Economy," CESifo Forum, Ifo Institute for Economic Research at the University of Munich, vol. 14(2), pages 03-08, 08.
  2. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2010. "A Cluster-Grid Projection Method: Solving Problems with High Dimensionality," NBER Working Papers 15965, National Bureau of Economic Research, Inc.
  3. Alexandre Dmitriev & Ivan Roberts, 2013. "International Business Cycles with Complete Markets," RBA Research Discussion Papers rdp2013-08, Reserve Bank of Australia.
  4. 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.
  5. 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.
  6. Thomas Mertens, 2012. "Solving General Incomplete Market Models with Substantial Heterogeneity," 2012 Meeting Papers 1173, Society for Economic Dynamics.
  7. Jasmina Hasanhodzic & Laurence J. Kotlikoff, 2013. "Generational Risk–Is It a Big Deal?: Simulating an 80-Period OLG Model with Aggregate Shocks," BYU Macroeconomics and Computational Laboratory Working Paper Series 2013-01, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
  8. Dmitriev, Alexandre & Roberts, Ivan, 2013. "The cost of adjustment: On comovement between the trade balance and the terms of trade," Economic Modelling, Elsevier, vol. 35(C), pages 689-700.

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