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Computationally Efficient Solution and Maximum Likelihood Estimation of Nonlinear Rational Expectations Models

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  • Jeffrey C. Fuhrer
  • C. Hoyt Bleakley

    (Federal Reserve Bank of Boston)

Abstract

This paper presents new, computationally efficient algorithms for solution and estimation of nonlinear dynamic rational expectations models. The innovations in the algorithms are as follows: (1) The entire solution path is obtained simultaneously by taking a small number of Newton steps, using analytic derivatives, over the entire path; (2) The terminal conditions for the solution path are derived from the uniqueness and stability conditions from the linearization of the model around the terminus of the solution path; (3) Unit roots are allowed in the model; (4) Very general models with expectational identities and singularities of the type handled by the King-Watson (1995a,b) linear algorithms are also allowed; and (5) Rank-deficient covariance matrices that arise owing to the presence of expectational identities are admissible. Reasonably complex models are solved in less than a second on a Sun Sparc20. This speed improvement makes derivative-based estimation methods feasible. Algorithms for maximum likelihood estimation and sample estimation problems are presented.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1997 with number 35.

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Handle: RePEc:sce:scecf7:35

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Postal: CEF97, Stanford University, Department of Economics, Stanford CA USA
Web page: http://bucky.stanford.edu/cef97/
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References

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  1. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
  2. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  3. Amemiya, Takeshi, 1983. "Non-linear regression models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 6, pages 333-389 Elsevier.
  4. Ray C. Fair & John B. Taylor, 1980. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear RationalExpectations Models," NBER Technical Working Papers 0005, National Bureau of Economic Research, Inc.
  5. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
  6. Armstrong, John & Black, Richard & Laxton, Douglas & Rose, David, 1998. "A robust method for simulating forward-looking models," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 489-501, April.
  7. Ellen R. McGrattan, 1993. "Solving the stochastic growth model with a finite element method," Staff Report 164, Federal Reserve Bank of Minneapolis.
  8. Gagnon, Joseph E, 1990. "Solving the Stochastic Growth Model by Deterministic Extended Path," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 35-36, January.
  9. Sargent, Thomas J, 1978. "Estimation of Dynamic Labor Demand Schedules under Rational Expectations," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 1009-44, December.
  10. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.
  11. Bennett T. McCallum, 1990. "Real Business Cycle Models," NBER Working Papers 2480, National Bureau of Economic Research, Inc.
  12. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  13. Christiano, Lawrence J, 1990. "Solving the Stochastic Growth Model by Linear-Quadratic Approximation and by Value-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 23-26, January.
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Cited by:
  1. A Garratt & K Lee & M H Pesaran & Yongcheol Shin, 1999. "A structural cointegrating VAR approach to macroeconometric modelling," ESE Discussion Papers 8, Edinburgh School of Economics, University of Edinburgh.
  2. Giovanni Olivei & Silvana Tenreyro, 2007. "The Timing of Monetary Policy Shocks," American Economic Review, American Economic Association, vol. 97(3), pages 636-663, June.
  3. Paolo Zagaglia, 2005. "Solving Rational-Expectations Models through the Anderson-Moore Algorithm: An Introduction to the Matlab Implementation," Computational Economics, Society for Computational Economics, vol. 26(1), pages 91-106, August.

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