Computational Economics

, Volume 15, Issue 1–2, pp 25–57 | Cite as

Solution of Nonlinear Rational Expectations Models with Applications toFinite-Horizon Life-Cycle Models of Consumption

  • Michael Binder
  • M. Hashem Pesaran
  • S. Hossein Samiei


This paper considers the solution of nonlinear rationalexpectations models resulting from the optimality conditions of afinite-horizon intertemporal optimization problem satisfying Bellman'sprinciple of optimality (and possibly involving inequality constraints). Abackward recursive procedure is used to characterize and solve thetime-varying optimal decision rules generally associated with these models.At each stage of these backward recursions, either an analytical ornumerical solution of the optimality conditions is required. When ananalytical solution is not possible, a minimum weighted residual approach isused. The solution technique is illustrated using a life-cycle model ofconsumption under labor income and interest rate uncertainties (and possiblyinvolving liquidity constraints). Approximate numerical solutions areprovided and compared with certainty-equivalent solutions and, whenpossible, with exact solutions.

nonlinear rational expectations models intertemporal consumer choice minimum weighted residual method exact and certainty-equivalent solutions 


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  1. Aoki, M. (1989). Optimization of Stochastic Systems. 2nd Edition, Academic Press, San Diego.Google Scholar
  2. Caballero, R.J. (1990). Consumption puzzles and precautionary saving. Journal of Monetary Economics, 25, 113-136.Google Scholar
  3. Caballero, R.J. (1991). Earnings uncertainty and aggregate wealth. American Economic Review, 81, 859-871.Google Scholar
  4. Chow, G.C. (1975). Analysis and Control of Dynamic Economic Systems. John Wiley, New York.Google Scholar
  5. Christiano, L.J. and Fisher, J.D.M. (1994). Algorithms for solving dynamic models with occasionally binding constraints. Mimeo. Northwestern University and University of Western Ontario.Google Scholar
  6. Deaton, A. and Laroque, G. (1992). On the behavior of commodity prices, Review of Economic Studies, 57, 677-688.Google Scholar
  7. Fair, R.C. and Taylor, J.B. (1983). Solution and maximum likelihood estimation of dynamic nonlinear rational expectations models. Econometrica, 51, 1169-1185.Google Scholar
  8. Fair, R.C. and Taylor, J.B. (1990). Full information estimation and stochastic simulation of models with rational expectations. Journal of Applied Econometrics, 5, 381-392.Google Scholar
  9. Fuhrer, J.C. and Bleakley, C.H. (1996). Computationally efficient solution and maximum likelihood estimation of nonlinear rational expectations models. Mimeo. Federal Reserve Bank of Boston.Google Scholar
  10. Gourinchas, P.-O. and Parker, J.A. (1996). Consumption over the lifecycle. Mimeo. MIT and CERAS.Google Scholar
  11. Hall, R.E. (1978). Stochastic implications of the life cycle-permanent income hypothesis: Theory and evidence. Journal of Political Economy, 96, 971-987.Google Scholar
  12. Helgason, T. and Wallace, S.W. (1991). Approximate scenario solutions in the progressive hedging algorithm, Annals of Operations Research, 31, 425-444.Google Scholar
  13. Jeffrey, A. (1995). Handbook of Mathematical Formulas and Integrals. Academic Press, San Diego.Google Scholar
  14. Judd, K.L. (1992). Projection methods for solving aggregate growth models. Journal of Economic Theory, 58, 410-452.Google Scholar
  15. Judd, K.L. (1996). Approximation, perturbation, and projection methods in economic analysis. In H.M. Amman, D.M. Kendrick and J. Rust (eds.), Handbook of Computational Economics, Vol. I, 509-585. North-Holland, Amsterdam.Google Scholar
  16. Kall, P. and Wallace, S.W. (1994). Stochastic Programming. John Wiley, New York.Google Scholar
  17. Kimball, M.S. and Mankiw, N.G. (1989). Precautionary savings and the timing of taxes. Journal of Political Economy, 97, 863-879.Google Scholar
  18. Marcet, A. and Marshall, D.A. (1994). Solving nonlinear rational expectations models by parameterized expectations: Convergence to stationary solutions. Mimeo. Universitat Pompeu Fabra and Northwestern University.Google Scholar
  19. Marcet, A. and Singleton, K.J. (1991). Equilibrium asset prices and savings of heterogeneous agents in the presence of incomplete markets and portfolio constraints. Mimeo. Carnegie Mellon University and Stanford University.Google Scholar
  20. McGrattan, E.R. (1996). Solving the stochastic growth model with a finite element method. Journal of Economic Dynamics and Control, 20, 19-42.Google Scholar
  21. Miranda, M.J. and Rui, X. (1997). Maximum likelihood estimation of the nonlinear rational expectations asset pricing model. Journal of Economic Dynamics and Control, 21, 1493-1510.Google Scholar
  22. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992). Numerical Recipes in FORTRAN. 2nd Edition, Cambridge University Press, Cambridge.Google Scholar
  23. Rockafellar, R.T. and Wets, R.J.-B. (1991). Scenarios and policy aggregation in optimization under uncertainty. Mathematics of Operations Research, 16, 119-147.Google Scholar
  24. Rosa, C. and Ruszczynski, A. (1994). On augmented Lagrangian decomposition methods for multistage stochastic programs. Mimeo. International Institute for Applied Systems Analysis, Laxenburg.Google Scholar
  25. Rust, J. (1996). Numerical dynamic programming in economics. In H.M. Amman, D.M. Kendrick and J. Rust (eds.), Handbook of Computational Economics, Vol. I, 619-729. North-Holland, Amsterdam.Google Scholar
  26. Simon, H.A. (1956). Dynamic programming under uncertainty with a quadratic criterion function. Econometrica, 24, 74-81.Google Scholar
  27. Talmain, G. (1995). Exact and approximate solutions to the problem of precautionary savings. Mimeo. University of British Columbia.Google Scholar
  28. Tauchen, G. and Hussey, R.C. (1991). Quadrature-based methods for obtaining approximate solutions to nonlinear asset pricing models. Econometrica, 59, 371-396.Google Scholar
  29. Theil, H. (1958). Economic Forecasts and Policy. North Holland, Amsterdam.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Michael Binder
    • 1
  • M. Hashem Pesaran
    • 2
  • S. Hossein Samiei
    • 3
  1. 1.Department of EconomicsUniversity of Maryland, Tydings Hall, CollegeParkU.S.A.
  2. 2.Faculty of Economics and PoliticsUniversity of CambridgeCambridgeU.K.
  3. 3.International Monetary FundWashingtonU.S.A.

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