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Solving nonlinear rational expectations models by parameterized expectations: Convergence to stationary solutions

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  • Albert Marcet
  • David A. Marshall

Abstract

This paper develops the Parameterized Expectations Approach (PEA) for solving nonlinear dynamic stochastic models with rational expectations. The method can be applied to a variety of models, including models with strong nonlinearities, sub-optimal equilibria, and many continuous state variables. In this approach, the conditional expectations in the equilibrium conditions are approximated by finite-dimensional classes of functional forms. The approach is highly efficient computationally because it incorporates endogenous oversampling and Monte-Carlo integration, and it does not impost a discrete grid on the state variables or the stochastic shocks. We prove that PEA can approximate the correct solution with arbitrary accuracy on the ergodic set by increasing the size of the Monte-Carlo simulations and the dimensionality of the approximating family of functions.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Albert Marcet & David A. Marshall, 1994. "Solving nonlinear rational expectations models by parameterized expectations: Convergence to stationary solutions," Economics Working Papers 76, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:76
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    Cited by:

    1. Burnside, Craig, 1998. "Solving asset pricing models with Gaussian shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 329-340, March.
    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. Alexandre Dmitriev, 2006. "Technological Transfers, Limited Commitment and Growth," Computing in Economics and Finance 2006 248, Society for Computational Economics.
    4. Tarik Ocaktan & Michel Juillard, 2008. "Méthodes de simulation des modèles stochastiques d'équilibre général," Économie et Prévision, Programme National Persée, vol. 183(2), pages 115-126.
    5. Gorostiaga, Arantza, 2003. "Should fiscal policy be different in a non-competitive framework?," Journal of Monetary Economics, Elsevier, vol. 50(6), pages 1311-1331, September.
    6. Michael Creel, 2008. "Using Parallelization to Solve a Macroeconomic Model: A Parallel Parameterized Expectations Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 32(4), pages 343-352, November.
    7. Maldonado, Wilfredo L. & Svaiter, B.F., 2007. "Holder continuity of the policy function approximation in the value function approximation," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 629-639, June.
    8. Monique C. Ebell, 2000. "Why Are Asset Returns more Volatile During Recessions? A Theoretical Examination," Econometric Society World Congress 2000 Contributed Papers 1554, Econometric Society.
    9. repec:eee:macchp:v2-527 is not listed on IDEAS
    10. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, Elsevier.
    11. Ilaski Barañano, 2001. "Endogenous growth and economic fluctuations," Investigaciones Economicas, Fundación SEPI, vol. 25(3), pages 515-541, September.
    12. 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.
    13. Marcet, Albert & Singleton, Kenneth J., 1999. "Equilibrium Asset Prices And Savings Of Heterogeneous Agents In The Presence Of Incomplete Markets And Portfolio Constraints," Macroeconomic Dynamics, Cambridge University Press, vol. 3(02), pages 243-277, June.
    14. Teresa Garcia-Milà & Albert Marcet & Eva Ventura, 2010. "Supply Side Interventions and Redistribution," Economic Journal, Royal Economic Society, vol. 120(543), pages 105-130, March.
    15. Young, Eric R., 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm and non-stochastic simulations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 36-41, January.
    16. Flam, Sjur Didrik & Mirman, Leonard J., 1998. "Groping for optimal growth," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 191-207, September.
    17. 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.
    18. 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.
    19. Palm, Franz C. & Pfann, Gerard A., 1998. "Sources of asymmetry in production factor dynamics," Journal of Econometrics, Elsevier, vol. 82(2), pages 361-392, February.
    20. S. Rao Aiyagari & Albert Marcet & Thomas J. Sargent & Juha Seppala, 2002. "Optimal Taxation without State-Contingent Debt," Journal of Political Economy, University of Chicago Press, vol. 110(6), pages 1220-1254, December.
    21. Pérez, Javier J. & Sánchez, A. Jesús, 2009. "Alternatives to initialize the Parameterized Expectations Algorithm," Economics Letters, Elsevier, vol. 102(2), pages 116-118, February.
    22. Wilfredo Leiva Maldonado & Benar Fux Svaiter, 2001. "On the accuracy of the estimated policy function using the Bellman contraction method," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-8.

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