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

  • Albert Marcet
  • David A. Marshall

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 Chicago in its series Working Paper Series, Macroeconomic Issues with number 94-20.

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Date of creation: 1994
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Handle: RePEc:fip:fedhma:94-20
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  1. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September.
  2. Marimon, Ramon, 1989. "Stochastic turnpike property and stationary equilibrium," Journal of Economic Theory, Elsevier, vol. 47(2), pages 282-306, April.
  3. Nicholas Ricketts & Thomas H. McCurdy, 1995. "An International Economy with Country-Specific Money and Productivity Growth Processes," Canadian Journal of Economics, Canadian Economics Association, vol. 28(s1), pages 141-162, November.
  4. 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.
  5. Marcet, Albert & Marimon, Ramon, 1992. "Communication, commitment, and growth," Journal of Economic Theory, Elsevier, vol. 58(2), pages 219-249, December.
  6. Bansal, Ravi & Gallant, A. Ronald & Hussey, Robert & Tauchen, George, 1995. "Nonparametric estimation of structural models for high-frequency currency market data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 251-287.
  7. 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.
  8. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  9. Townsend, Robert M, 1983. "Forecasting the Forecasts of Others," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 546-88, August.
  10. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
  11. Ingram, Beth Fisher, 1990. "Equilibrium Modeling of Asset Prices: Rationality versus Rules of Thumb," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 115-25, January.
  12. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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