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Approximating and Simulating the Stochastic Growth Model: Parameterized Expectations, Neural Networks, and the Genetic Algorithm

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  • Paul McNelis

    (Georgetown University)

  • John Duffy

Abstract

This paper compares alternative methods for approximating and solving the stochastic growth model with parameterized expectations. We compare polynomial and neural netowork specifications for expectations, and we employ both genetic algorithm and gradient-descent methods for solving the alternative models of parameterized expectations. Many of the statistics generated by the neural network specification in combination with the genetic algorithm and gradient descent optimization methods approach the statistics generated by the exact solution with risk aversion coefficients close to unity and full depreciation of the capital stock. For the alternative specification, with no depreciation of capital, the neural network results approach those generated by computationally-intense methods. Our results suggest that the neural network specification and genetic algorithm solution methods should at least complement parameterized expectation solutions based on polynomial approximation and pure gradient-descent optimization.

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Bibliographic Info

Paper provided by EconWPA in its series GE, Growth, Math methods with number 9804004.

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Length: 34 pages
Date of creation: 30 Apr 1998
Date of revision: 04 May 1998
Handle: RePEc:wpa:wuwpge:9804004

Note: Type of Document - MS Word 97; prepared on IBM PC; to print on HP; pages: 34 ; figures: included
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Web page: http://128.118.178.162

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  8. Wouter J. den Haan & Albert Marcet, 1993. "Accuracy in simulations," Economics Working Papers 42, Department of Economics and Business, Universitat Pompeu Fabra.
  9. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
  10. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
  11. Tauchen, George, 1990. "Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 49-51, January.
  12. Beaumont, Paul M & Bradshaw, Patrick T, 1995. "A Distributed Parallel Genetic Algorithm for Solving Optimal Growth Models," Computational Economics, Society for Computational Economics, vol. 8(3), pages 159-79, August.
  13. 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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Cited by:
  1. Richard Dennis, 2008. "The Frequency Of Price Adjustment And New Keynesian Business Cycle Dynamics," CAMA Working Papers 2008-19, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  2. Javier J. Pérez, 2004. "A Log-Linear Homotopy Approach to Initialize the Parameterized Expectations Algorithm," Computational Economics, Society for Computational Economics, vol. 24(1), pages 59-75, 08.
  3. Paul D. McNelis & Guay Lim, 2006. "Inflation Targeting, Learning and Q Volatility in Small Open Economies," Computing in Economics and Finance 2006 104, Society for Computational Economics.
  4. G.C. Lim & P.D. McNelis, 2002. "Central Bank Learning, Terms of Trade Shocks & Currency Risks: Should Only Inflation Matter for Monetary Policy?," Computing in Economics and Finance 2002 68, Society for Computational Economics.
  5. S. Sirakaya & Stephen Turnovsky & M. Alemdar, 2006. "Feedback Approximation of the Stochastic Growth Model by Genetic Neural Networks," Computational Economics, Society for Computational Economics, vol. 27(2), pages 185-206, May.
  6. Richard Dennis, 2004. "Specifying and estimating New Keynesian models with instrument rules and optimal monetary policies," Working Paper Series 2004-17, Federal Reserve Bank of San Francisco.
  7. Lim, G.C. & McNelis, Paul D., 2007. "Central bank learning, terms of trade shocks and currency risk: Should only inflation matter for monetary policy?," Journal of International Money and Finance, Elsevier, vol. 26(6), pages 865-886, October.
  8. G.C. Lim & Paul D. McNelis, 2001. "Central Bank Learning, Terms of Trade Shocks & Currency Risk: Should Exchange Rate Volatility Matter for Monetary Policy?," Boston College Working Papers in Economics 509, Boston College Department of Economics.
  9. Heer, Burkhard & Maußner, Alfred, 2008. "Computation Of Business Cycle Models: A Comparison Of Numerical Methods," Macroeconomic Dynamics, Cambridge University Press, vol. 12(05), pages 641-663, November.
  10. McAdam, Peter & McNelis, Paul, 2005. "Forecasting inflation with thick models and neural networks," Economic Modelling, Elsevier, vol. 22(5), pages 848-867, September.
  11. G. Lim & Paul Mcnelis, 2006. "Central Bank Learning and Taylor Rules with Sticky Import Prices," Computational Economics, Society for Computational Economics, vol. 28(2), pages 155-175, September.
  12. Floortje Alkemade & Han Poutré & Hans Amman, 2006. "Robust Evolutionary Algorithm Design for Socio-economic Simulation," Computational Economics, Society for Computational Economics, vol. 28(4), pages 355-370, November.
  13. Hull, Isaiah, 2013. "Approximate dynamic programming with postdecision states as a solution method for dynamic economic models," Working Paper Series 276, Sveriges Riksbank (Central Bank of Sweden).
  14. Lim, G. C. & McNelis, Paul D., 2004. "Learning and the monetary policy strategy of the European Central Bank," Journal of International Money and Finance, Elsevier, vol. 23(7-8), pages 997-1010.
  15. Roumasset, James A. & Wada, Christopher A., 2012. "Ordering the extraction of renewable resources: The case of multiple aquifers," Resource and Energy Economics, Elsevier, vol. 34(1), pages 112-128.

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