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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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  1. 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!]
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  2. Lawrence J. Christiano & Jonas D. M. Fisher, 1994. "Algorithms for solving dynamic models with occasionally binding constraints," Staff Report 171, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  3. 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!]
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  4. 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!]
  5. 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!]
  6. Alexandre Dmitriev, 2008. "Technological Transfers, Limited Commitment and Growth," Discussion Papers 2008-05, School of Economics, The University of New South Wales. [Downloadable!]
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  7. 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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  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, revised Jul 2008. [Downloadable!]
  9. Ilaski Barañano, 2001. "Endogenous growth and economic fluctuations," Investigaciones Economicas, Fundación SEPI, vol. 25(3), pages 515-541, September. [Downloadable!]
  10. 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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