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A toolkit for analyzing nonlinear dynamic stochastic models easily

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Author Info
Uhlig, H. (Tilburg University, Center for Economic Research)

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Abstract

Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the method of undetermined coefficients. This paper contains nothing substantially new. Instead, the paper simplifies and unifies existing approaches to make them accessible for a wide audience, showing how to log-linearizing the nonlinear equations without the need for explicit differentiation, how to use the method of undetermined coefficients for models with a vector of endogenous state variables, to provide a general solution by characterizing the solution with a matrix quadratic equation and solving it, and to provide frequency-domain techniques to calculate the second Since the method is an Euler-equation based approach rather than an approach based on solving a social planners problem, models with externalities or distortionary taxation do not pose additional problems. MATLAB programs to carry out the calculations in this paper are made available. This paper should be useful for researchers and Ph.D. students alike.

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Publisher Info
Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 97.

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Date of creation: 1995
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Handle: RePEc:dgr:kubcen:199597

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Keywords: Stochastic Models

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This paper has been announced in the following NEP Reports: This item is featured on the following reading lists:
  1. Quantitative Macroeconomics and Real Business Cycles (QM&RBC)
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. John Y. Campbell & John H. Cochrane, 1994. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," CRSP working papers 412, Center for Research in Security Prices, Graduate School of Business, University of Chicago. [Downloadable!]
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  2. 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.
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  3. Gary D. Hansen & Edward C. Prescott, 1992. "Recursive methods for computing equilibria of business cycle models," Discussion Paper / Institute for Empirical Macroeconomics 36, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  4. Binder,M. & Pesaran,H.M., 1995. "Multivariate Rational Expectations Models and Macroeconomic Modelling: A Review and Some New Results," Cambridge Working Papers in Economics 9415, Faculty of Economics, University of Cambridge.
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  5. Uhlig, H. & Xu, Y., 1996. "Effort and the cycle : Cyclical implications of efficiency wages," Discussion Paper 49, Tilburg University, Center for Economic Research. [Downloadable!]
  6. Roger E.A. Farmer & Jang Ting Guo, 1992. "Real Business Cycles and the Animal Spirits Hypothesis," UCLA Economics Working Papers 680, UCLA Department of Economics. [Downloadable!]
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  7. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November. [Downloadable!] (restricted)
  8. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231. [Downloadable!] (restricted)
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  9. Kydland, Finn E & Prescott, Edward C, 1991. " The Econometrics of the General Equilibrium Approach to Business Cycles," Scandinavian Journal of Economics, Blackwell Publishing, vol. 93(2), pages 161-78.
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  10. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November. [Downloadable!] (restricted)
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  11. Campbell, John Y., 1994. "Inspecting the mechanism: An analytical approach to the stochastic growth model," Journal of Monetary Economics, Elsevier, vol. 33(3), pages 463-506, June. [Downloadable!] (restricted)
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  12. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June. [Downloadable!] (restricted)
  13. Danthine, J.P. & Donaldson, J.B., 1993. "Computing Equilibria of Non-Optimal Economies," Papers 93-01a, Columbia - Graduate School of Business.
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  14. 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. [Downloadable!] (restricted)
  15. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November. [Downloadable!] (restricted)
  16. Lars Peter Hansen & Ellen R. McGrattan & Thomas J. Sargent, 1994. "Mechanics of forming and estimating dynamic linear economies," Staff Report 182, Federal Reserve Bank of Minneapolis. [Downloadable!]
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