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

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Trimborn, Timo

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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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Paper provided by Universität Hannover, Wirtschaftswissenschaftliche Fakultät in its series Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Universität Hannover with number dp-363.

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

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Related research
Keywords: anticipated shocks continuous-time optimization numerical solution

Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
O40 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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  1. 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. [Downloadable!] (restricted)
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  2. 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. [Downloadable!] (restricted)
  3. Howitt, Peter & Sinn, Hans-Werner, 1989. "Gradual Reforms of Capital Income Taxation," American Economic Review, American Economic Association, vol. 79(1), pages 106-24, March. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation, Yale University. [Downloadable!]
  6. 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. [Downloadable!] (restricted)
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  7. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July. [Downloadable!] (restricted)
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