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

  • Trimborn, Timo

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 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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  1. 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.
  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. Buiter, Willem H, 1984. "Saddlepoint Problems in Continuous Time Rational Expectations Models: A General Method and Some Macroeconomic Examples," Econometrica, Econometric Society, vol. 52(3), pages 665-80, May.
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  6. Trimborn, Timo & Koch, Karl-Josef & Steger, Thomas M., 2008. "Multidimensional Transitional Dynamics: A Simple Numerical Procedure," Macroeconomic Dynamics, Cambridge University Press, vol. 12(03), pages 301-319, June.
  7. 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.
  8. 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.
  9. Howitt, Peter & Sinn, Hans-Werner, 1989. "Gradual Reforms of Capital Income Taxation," Munich Reprints in Economics 19370, University of Munich, Department of Economics.
  10. 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.
  11. 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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  13. 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.
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