IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v25y2001i9p1273-1303.html
   My bibliography  Save this article

Approximating and simulating the stochastic growth model: Parameterized expectations, neural networks, and the genetic algorithm

Author

Listed:
  • Duffy, John
  • McNelis, Paul D.

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Duffy, John & McNelis, Paul D., 2001. "Approximating and simulating the stochastic growth model: Parameterized expectations, neural networks, and the genetic algorithm," Journal of Economic Dynamics and Control, Elsevier, vol. 25(9), pages 1273-1303, September.
    • Handle: RePEc:eee:dyncon:v:25:y:2001:i:9:p:1273-1303
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(99)00077-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    6. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
    7. Harald Uhlig, 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper / Institute for Empirical Macroeconomics 101, Federal Reserve Bank of Minneapolis.
    8. 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.
    9. Bullard, James & Duffy, John, 2001. "Learning And Excess Volatility," Macroeconomic Dynamics, Cambridge University Press, vol. 5(02), pages 272-302, April.
    10. 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.
    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. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
    14. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    15. 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.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Maliar, Lilia & Maliar, Serguei, 2022. "Deep learning classification: Modeling discrete labor choice," Journal of Economic Dynamics and Control, Elsevier, vol. 135(C).
    2. Fernández-Villaverde, Jesús & Ebrahimi Kahou, Mahdi & Perla, Jesse & Sood, Arnav, 2021. "Exploiting Symmetry in High-Dimensional Dynamic Programming," CEPR Discussion Papers 16285, C.E.P.R. Discussion Papers.
    3. 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.
    4. 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.
    5. Pedro Afonso Fernandes, 2024. "Forecasting with Neuro-Dynamic Programming," Papers 2404.03737, arXiv.org.
    6. 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.
    7. 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.
    8. 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.
    9. McAdam, Peter & McNelis, Paul, 2005. "Forecasting inflation with thick models and neural networks," Economic Modelling, Elsevier, vol. 22(5), pages 848-867, September.
    10. 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.
    11. Marlon Azinovic & Luca Gaegauf & Simon Scheidegger, 2022. "Deep Equilibrium Nets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1471-1525, November.
    12. 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.
    13. JOSEPH Charles & DEWANDARU Janu & GUNADI Iman, 2010. "Playing Hard or Soft? : A Simulation of Indonesian Monetary Policy in Targeting Low Inflation Using a Dynamic General Equilibrium Model," EcoMod2003 330700074, EcoMod.
    14. Shaw, Philip, 2014. "A nonparametric approach to solving a simple one-sector stochastic growth model," Economics Letters, Elsevier, vol. 125(3), pages 447-450.
    15. 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.
    16. Lepetyuk, Vadym & Maliar, Lilia & Maliar, Serguei, 2020. "When the U.S. catches a cold, Canada sneezes: A lower-bound tale told by deep learning," Journal of Economic Dynamics and Control, Elsevier, vol. 117(C).
    17. 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.
    18. Heer, Burkhard & Maußner, Alfred, 2008. "Computation Of Business Cycle Models: A Comparison Of Numerical Methods," Macroeconomic Dynamics, Cambridge University Press, vol. 12(5), pages 641-663, November.
    19. 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.
    20. 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.
    21. Maliar, Lilia & Maliar, Serguei & Winant, Pablo, 2021. "Deep learning for solving dynamic economic models," Journal of Monetary Economics, Elsevier, vol. 122(C), pages 76-101.
    22. 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.
    23. Adalbert Mayer, 2022. "An Agent-Based Macroeconomic Model with Endogenous Intertemporal Decision Rules," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 48(4), pages 548-579, October.
    24. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2014. "Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-06, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    2. 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.
    3. John Duffy & Paul D. McNelis, "undated". "Approximating and Simulating the Real Business Cycle: Linear Quadratic Methods, Parameterized Expectations and Genetic Algorithms," Computing in Economics and Finance 1997 63, Society for Computational Economics.
    4. Peter Woehrmann & Willi Semmler & Martin Lettau, "undated". "Nonparametric Estimation of the Time-varying Sharpe Ratio in Dynamic Asset Pricing Models," IEW - Working Papers 225, Institute for Empirical Research in Economics - University of Zurich.
    5. Alfonso Novales & Javier J. PÈrez, 2004. "Is It Worth Refining Linear Approximations to Non-Linear Rational Expectations Models?," Computational Economics, Springer;Society for Computational Economics, vol. 23(4), pages 343-377, June.
    6. Kenneth Judd & Lilia Maliar & Serguei Maliar, 2009. "Numerically Stable Stochastic Simulation Approaches for Solving Dynamic Economic Models," NBER Working Papers 15296, National Bureau of Economic Research, Inc.
    7. 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.
    8. Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
    9. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    10. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    11. 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.
    12. Serguei Maliar & John Taylor & Lilia Maliar, 2016. "The Impact of Alternative Transitions to Normalized Monetary Policy," 2016 Meeting Papers 794, Society for Economic Dynamics.
    13. José Cao-Alvira, 2010. "Finite Elements in the Presence of Occasionally Binding Constraints," Computational Economics, Springer;Society for Computational Economics, vol. 35(4), pages 355-370, April.
    14. Maliar, Serguei & Maliar, Lilia & Judd, Kenneth, 2011. "Solving the multi-country real business cycle model using ergodic set methods," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 207-228, February.
    15. Ayşe Kabukçuoğlu & Enrique Martínez-García, 2021. "A Generalized Time Iteration Method for Solving Dynamic Optimization Problems with Occasionally Binding Constraints," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 435-460, August.
    16. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 2002. "An approximation algorithm for optimal consumption/investment problems," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 11(2), pages 55-69, April.
    17. Paul Pichler, 2005. "Evaluating Approximate Equilibria of Dynamic Economic Models," Vienna Economics Papers 0510, University of Vienna, Department of Economics.
    18. José Cao-Alvira, 2012. "Velocity Volatility Assessment of Monetary Shocks on Cash-in-Advance Economies," Computational Economics, Springer;Society for Computational Economics, vol. 40(3), pages 293-311, October.
    19. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    20. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585, Elsevier.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:25:y:2001:i:9:p:1273-1303. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.