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

  • Paul McNelis

    (Georgetown University)

  • John Duffy

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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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
Contact details of provider: Web page: http://128.118.178.162

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  1. 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.
  2. Cooley, T.F. & Hansen, G.D., 1988. "The Inflation Tax In A Real Business Cycle Model," Papers 88-05, Rochester, Business - General.
  3. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper 9711, Federal Reserve Bank of Cleveland.
  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. Schmertmann, Carl P, 1996. "Functional Search in Economics Using Genetic Programming," Computational Economics, Society for Computational Economics, vol. 9(4), pages 275-98, November.
  6. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  7. Wouter J. den Haan & Albert Marcet, 1993. "Accuracy in simulations," Economics Working Papers 42, Department of Economics and Business, Universitat Pompeu Fabra.
  8. John B. Taylor & Harald Uhlig, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," NBER Working Papers 3117, National Bureau of Economic Research, Inc.
  9. 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.
  10. repec:dgr:kubcen:199597 is not listed on IDEAS
  11. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  12. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
  13. Bullard, James & Duffy, John, 2001. "Learning And Excess Volatility," Macroeconomic Dynamics, Cambridge University Press, vol. 5(02), pages 272-302, April.
  14. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
  15. 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.
  16. 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.
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