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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.

Suggested Citation

  • Paul McNelis & John Duffy, 1998. "Approximating and Simulating the Stochastic Growth Model: Parameterized Expectations, Neural Networks, and the Genetic Algorithm," GE, Growth, Math methods 9804004, EconWPA, revised 14 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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    1. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    2. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
    3. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
    4. 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.
    5. 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.
    6. Cooley, Thomas F & Hansen, Gary D, 1989. "The Inflation Tax in a Real Business Cycle Model," American Economic Review, American Economic Association, vol. 79(4), pages 733-748, September.
    7. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    8. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 3-17.
    9. Bullard, James & Duffy, John, 2001. "Learning And Excess Volatility," Macroeconomic Dynamics, Cambridge University Press, vol. 5(02), pages 272-302, April.
    10. 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.
    11. Albert Marcet, 1991. "Simulation analysis of dynamic stochastic models: Applications to theory and estimation," Economics Working Papers 6, Department of Economics and Business, Universitat Pompeu Fabra.
    12. Beaumont, Paul M & Bradshaw, Patrick T, 1995. "A Distributed Parallel Genetic Algorithm for Solving Optimal Growth Models," Computational Economics, Springer;Society for Computational Economics, vol. 8(3), pages 159-179, August.
    13. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    14. Schmertmann, Carl P, 1996. "Functional Search in Economics Using Genetic Programming," Computational Economics, Springer;Society for Computational Economics, vol. 9(4), pages 275-298, November.
    15. Dorsey, Robert E & Mayer, Walter J, 1995. "Genetic Algorithms for Estimation Problems with Multiple Optima, Nondifferentiability, and Other Irregular Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 53-66, January.
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    Cited by:

    1. 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.
    2. Floortje Alkemade & Han Poutré & Hans Amman, 2006. "Robust Evolutionary Algorithm Design for Socio-economic Simulation," Computational Economics, Springer;Society for Computational Economics, vol. 28(4), pages 355-370, November.
    3. S. Sirakaya & Stephen Turnovsky & M. Alemdar, 2006. "Feedback Approximation of the Stochastic Growth Model by Genetic Neural Networks," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 185-206, May.
    4. 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.
    5. G. C. LIM & PAUL D. McNELIS, 2002. "Central Bank Learning, Terms Of Trade Shocks & Currency Risks: Should Only Inflation Matter For Monetary Policy?," Department of Economics - Working Papers Series 831, The University of Melbourne.
    6. McAdam, Peter & McNelis, Paul, 2005. "Forecasting inflation with thick models and neural networks," Economic Modelling, Elsevier, vol. 22(5), pages 848-867, September.
    7. 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.
    8. 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.
    9. JOSEPH Charles & DEWANDARU Janu & GUNADI Iman, "undated". "Playing Hard or Soft? : A Simulation of Indonesian Monetary Policy in Targeting Low Inflation Using a Dynamic General Equilibrium Model," EcoMod2003 330700074, EcoMod.
    10. Shaw, Philip, 2014. "A nonparametric approach to solving a simple one-sector stochastic growth model," Economics Letters, Elsevier, vol. 125(3), pages 447-450.
    11. Lim, G.C. & McNelis, Paul D., 2007. "Inflation targeting, learning and Q volatility in small open economies," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3699-3722, November.
    12. Richard Dennis, 2006. "The frequency of price adjustment and New Keynesian business cycle dynamics," Working Paper Series 2006-22, Federal Reserve Bank of San Francisco.
    13. 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.
    14. G. Lim & Paul Mcnelis, 2006. "Central Bank Learning and Taylor Rules with Sticky Import Prices," Computational Economics, Springer;Society for Computational Economics, vol. 28(2), pages 155-175, September.
    15. Javier J. Pérez, 2004. "A Log-Linear Homotopy Approach to Initialize the Parameterized Expectations Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 24(1), pages 59-75, August.
    16. Hull, Isaiah, 2015. "Approximate dynamic programming with post-decision states as a solution method for dynamic economic models," Journal of Economic Dynamics and Control, Elsevier, vol. 55(C), pages 57-70.
    17. 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.

    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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