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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 Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 76.

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Date of creation: Mar 1994
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Handle: RePEc:upf:upfgen:76
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  1. Nicholas Ricketts & Thomas H. McCurdy, 1991. "An International Economy with Country-Specific Money and Productivity Growth Processes," Working Papers 846, Queen's University, Department of Economics.
  2. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  3. Darrell Duffie & Kenneth J. Singleton, 1990. "Simulated Moments Estimation of Markov Models of Asset Prices," NBER Technical Working Papers 0087, National Bureau of Economic Research, Inc.
  4. 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.
  5. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
  6. Albert Marcet & Ramon Marimon, 1991. "Communication, commitment and growth," Economics Working Papers 1, Department of Economics and Business, Universitat Pompeu Fabra.
  7. 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.
  8. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September.
  9. Marimon, Ramon, 1989. "Stochastic turnpike property and stationary equilibrium," Journal of Economic Theory, Elsevier, vol. 47(2), pages 282-306, April.
  10. Townsend, Robert M, 1983. "Forecasting the Forecasts of Others," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 546-88, August.
  11. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  12. 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.
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