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Anticipated Shocks in Continuous-time Optimization Models: Theoretical Investigation and Numerical Solution

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  • Trimborn, Timo

Abstract

We derive the well-known continuity principle for adjoint variables for preannounced or anticipated changes in parameters for continuous-time, infinite-horizon, perfect foresight optimization models. For easy and intuitive numerical computation of the resulting multi point boundary value problem we suggested to simulate the resulting differential algebraic system representing the first order conditions. By ensuring that the state variables and the adjoint variables are continuous, potential jumps in the control variables are calculated automatically. This can be easily conducted with the relaxation algorithm as proposed by Trimborn et al. (2007). We solve a Ramsey model extended by an elementary Government sector numerically. Simulations of a preannounced increase in the consumption tax show a qualitative different pattern depending on the intertemporal elasticity of substitution.

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File URL: http://diskussionspapiere.wiwi.uni-hannover.de/pdf_bib/dp-363.pdf
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Bibliographic Info

Paper provided by Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät in its series Hannover Economic Papers (HEP) with number dp-363.

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Length: 20 pages
Date of creation: Apr 2007
Date of revision:
Handle: RePEc:han:dpaper:dp-363

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Keywords: anticipated shocks; continuous-time optimization; numerical solution;

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References

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  1. Willem H. Buiter, 1984. "Saddlepoint Problems in Contifuous Time Rational Expectations Models: A General Method and Some Macroeconomic Ehamples," NBER Technical Working Papers 0020, National Bureau of Economic Research, Inc.
  2. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 737-753, May.
  3. Robert J. Barro & Paul M. Romer, 1991. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr91-1, May.
    • Robert J. Barro & Paul Romer, 1993. "Economic Growth," NBER Books, National Bureau of Economic Research, Inc, number barr93-1, May.
  4. Timo Trimborn & Karl-Josef Koch & Thomas Steger, 2006. "Multi-Dimensional Transitional Dynamics: A Simple Numberical Procedure," CESifo Working Paper Series 1745, CESifo Group Munich.
  5. Judd, Kenneth L, 1985. "Short-run Analysis of Fiscal Policy in a Simple Perfect Foresight Model," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 298-319, April.
  6. Casey B. Mulligan & Xavier Sala-i-Martin, 1991. "A Note on the Time-Elimination Method For Solving Recursive Dynamic Economic Models," NBER Technical Working Papers 0116, National Bureau of Economic Research, Inc.
  7. Howitt, Peter & Sinn, Hans-Werner, 1989. "Gradual Reforms of Capital Income Taxation," Munich Reprints in Economics 19370, University of Munich, Department of Economics.
  8. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
  9. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
  10. Auernheimer, Leonardo & Lozada, Gabriel A, 1990. "On the Treatment of Anticipated Shocks in Models of Optimal Control with Rational Expectations: An Economic Interpretation," American Economic Review, American Economic Association, vol. 80(1), pages 157-69, March.
  11. Mercenier, Jean & Michel, Philippe, 1994. "Discrete-Time Finite Horizon Appromixation of Infinite Horizon Optimization Problems with Steady-State Invariance," Econometrica, Econometric Society, vol. 62(3), pages 635-56, May.
  12. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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Cited by:
  1. Mário Amorim Lopes & Fernando A. C. C. Fontes & Dalila A. C. C. Fontes, 2013. "Optimal Control of Infinite-Horizon Growth Models — A direct approach," FEP Working Papers 506, Universidade do Porto, Faculdade de Economia do Porto.

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