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A toolkit for analyzing nonlinear dynamic stochastic models easily

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  • Uhlig, H.

    (Tilburg University, Center for Economic Research)

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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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1995-97.

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

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  1. John B. Taylor & Harald Uhlig, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," NBER Working Papers 3117, National Bureau of Economic Research, Inc.
  2. John Y. Campbell, 1992. "Inspecting the Mechanism: An Analytical Approach to the Stochastic Growth Model," NBER Working Papers 4188, National Bureau of Economic Research, Inc.
  3. Jean-Pierre DANTHINE & John B. DONALDSON, 1993. "Computing Equilibria of Non-Optimal Economies," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 9306, Université de Lausanne, Faculté des HEC, DEEP.
  4. Kenneth L. Judd, 1991. "Minimum weighted residual methods for solving aggregate growth models," Discussion Paper / Institute for Empirical Macroeconomics 49, Federal Reserve Bank of Minneapolis.
  5. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
  6. Farmer Roger E. A. & Guo Jang-Ting, 1994. "Real Business Cycles and the Animal Spirits Hypothesis," Journal of Economic Theory, Elsevier, vol. 63(1), pages 42-72, June.
  7. 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.
  8. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  9. King, R.G. & Rebelo, S.T., 1989. "Low Frequency Filtering And Real Business Cycles," RCER Working Papers 205, University of Rochester - Center for Economic Research (RCER).
  10. John Y. Campbell & John H. Cochrane, 1995. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," NBER Working Papers 4995, National Bureau of Economic Research, Inc.
  11. 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.
  12. Uhlig, H.F.H.V.S. & Xu, Y., 1996. "Effort and the Cycle: Cyclical Implications of Efficiency Wages," Discussion Paper 1996-49, Tilburg University, Center for Economic Research.
  13. 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.
  14. Maurice Obstfeld & Kenneth S. Rogoff, 1996. "Foundations of International Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262150476, December.
  15. Finn E. Kydland & Edward C. Prescott, 1990. "The econometrics of the general equilibrium approach to business cycles," Staff Report 130, Federal Reserve Bank of Minneapolis.
  16. Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252 Elsevier.
  17. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  18. 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.
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  1. Blogs review: A guide to survive Math Camp
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  1. > Schools of Economic Thought, Epistemology of Economics > Economic Methodology > Dynamic Stochastic General Equilibrium > Solution Methods for DSGE models
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