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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://econwpa.repec.org

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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. Wouter J. den Haan & Albert Marcet, 1993. "Accuracy in simulations," Economics Working Papers 42, Department of Economics and Business, Universitat Pompeu Fabra.
  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. Schmertmann, Carl P, 1996. "Functional Search in Economics Using Genetic Programming," Computational Economics, Society for Computational Economics, vol. 9(4), pages 275-98, November.
  5. Lawrence J. Christiano & Jonas D.M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Working Paper Series, Macroeconomic Issues 94-6, Federal Reserve Bank of Chicago.
  6. Thomas F. Cooley & Gary D. Hansen, 1987. "The Inflation Tax in a Real Business Cycle Model," UCLA Economics Working Papers 496, UCLA Department of Economics.
  7. 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.
  8. 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.
  9. James Bullard & John Duffy, 1999. "Learning and Excess Volatility," Computing in Economics and Finance 1999 224, Society for Computational Economics.
  10. 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.
  11. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  12. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  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. 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.
  15. 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.
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