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

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Author Info
Albert Marcet
David A. Marshall

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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.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Discussion Paper / Institute for Empirical Macroeconomics with number 91.

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Date of creation: 1994
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Handle: RePEc:fip:fedmem:91

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Keywords: Rational expectations (Economic theory) ; Econometric models;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Marcet, Albert & Marimon, Ramon, 1992. "Communication, commitment, and growth," Journal of Economic Theory, Elsevier, vol. 58(2), pages 219-249, December. [Downloadable!] (restricted)
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  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  3. Marshall, David A, 1992. " Inflation and Asset Returns in a Monetary Economy," Journal of Finance, American Finance Association, vol. 47(4), pages 1315-42, September. [Downloadable!] (restricted)
  4. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July. [Downloadable!] (restricted)
  5. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September. [Downloadable!] (restricted)
  6. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November. [Downloadable!] (restricted)
  7. Townsend, Robert M, 1983. "Forecasting the Forecasts of Others," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 546-88, August. [Downloadable!] (restricted)
  8. Marimon, Ramon, 1989. "Stochastic turnpike property and stationary equilibrium," Journal of Economic Theory, Elsevier, vol. 47(2), pages 282-306, April. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. José V. Rodríguez Mora, 1995. "Shared Knowledge," Economics Working Papers 144, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  2. Alexandre Dmitriev, 2008. "Technological Transfers, Limited Commitment and Growth," Discussion Papers 2008-05, School of Economics, The University of New South Wales. [Downloadable!]
    Other versions:
  3. Wilfredo Leiva Maldonado & Benar Fux Svaiter, 2001. "On the accuracy of the estimated policy function using the Bellman contraction method," Economics Bulletin, Economics Bulletin, vol. 3, pages 1-8. [Downloadable!]
    Other versions:
  4. Alfonso Novales & Javier J. Pérez, 2002. "Is it Worth Refining Linear Approximations to Non-Linear Rational Expectations Models?," Economic Working Papers at Centro de Estudios Andaluces E2002/15, Centro de Estudios Andaluces. [Downloadable!]
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  5. 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. [Downloadable!]
    Other versions:
  6. Javier J. Pérez, 2001. "A Log-linear Homotopy Approach to Initialize the Parameterized Expectations Algorithm," Economic Working Papers at Centro de Estudios Andaluces E2001/02, Centro de Estudios Andaluces. [Downloadable!]
    Other versions:
  7. Albert Marcet & Kenneth J. Singleton, 1990. "Equilibrium Asset Prices and Savings of Heterogeneous Agents in the Presence of Incomplete Markets and Portfolio Constraints," Economics Working Papers 319, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 1998. [Downloadable!]
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  8. Teresa Garcia-Milà & Albert Marcet & Eva Ventura, 1995. "Supply Side Interventions and Redistribution," Economics Working Papers 115, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  9. Ilaski Barañano, 2001. "Endogenous growth and economic fluctuations," Investigaciones Economicas, Fundación SEPI, vol. 25(3), pages 515-541, September. [Downloadable!]
  10. Albert Marcet & Thomas J. Sargent & Juha Seppala, 1996. "Optimal Taxation without State-Contingent Debt," Economics Working Papers 170, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2001. [Downloadable!]
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  11. Arantza Gorostiaga, 2003. "Should Fiscal Policy be different in a Non-Competitive Framework?," DFAEII Working Papers 200228, University of the Basque Country - Department of Foundations of Economic Analysis II. [Downloadable!]
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  12. 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. [Downloadable!]
  13. Michael Creel, 2008. "Using Parallelization to Solve a Macroeconomic Model: A Parallel Parameterized Expectations Algorithm," Computational Economics, Springer, vol. 32(4), pages 343-352, November. [Downloadable!] (restricted)
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