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Optimal and Time-Consistent Polices in Continuous Time Rational Expectations Models

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  • Willem H. Buiter

Abstract

In this note the method of Hamiltonian dynamics is used to characterize the time-consistent solution to the optimal control problem in a deterministic continuous time rational expectations model. A linear quadratic example based on the work of Miller and Salmon is used for simplicity. To derive the time-consistent rational expectations (or subgame-perfect) solution we first characterize the optimal solution made familiar e.g. through the work of Calvo. The time-consistent solution is then obtained by modifying the optimal solution through the requirement that the co-state variables (shadow prices) of the non-predetermined variables be zero at each instant. Existing solution methods and computational algorithms can be used to obtain the behaviour of the system under optimal policy and under time-consistent policy.

Suggested Citation

  • Willem H. Buiter, 1983. "Optimal and Time-Consistent Polices in Continuous Time Rational Expectations Models," NBER Technical Working Papers 0029, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0029
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    References listed on IDEAS

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    1. Calvo, Guillermo A, 1978. "On the Time Consistency of Optimal Policy in a Monetary Economy," Econometrica, Econometric Society, vol. 46(6), pages 1411-1428, November.
    2. Miller, Marcus & Salmon, Mark, 1985. "Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies," Economic Journal, Royal Economic Society, vol. 95(380a), pages 124-137, Supplemen.
    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 665-680, May.
    4. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
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    Cited by:

    1. Reinhard Neck, 1986. "Kann Stabilisierungspolitik unter Unsicherheit und Risiko "optimal" sein?," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 122(III), pages 509-534, September.
    2. Gilles Oudiz & Jeffrey Sachs, 1984. "International Policy Coordination in Dynamic Macroeconomic Models," NBER Working Papers 1417, National Bureau of Economic Research, Inc.
    3. Amitrajeet Batabyal, 1996. "Consistency and optimality in a dynamic game of pollution control II: Monopoly," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 8(3), pages 315-330, October.
    4. Levine, Paul & Currie, David, 1985. "Optimal feedback rules in an open economy macromodel with rational expectations," European Economic Review, Elsevier, vol. 27(2), pages 141-163, March.
    5. Willem H. Buiter & Marcus H. Miller, 1983. "Costs and Benefits of an Anti-Inflationary Policy: Questions and Issues," NBER Working Papers 1252, National Bureau of Economic Research, Inc.
    6. Willem H. Buiter, 1984. "Policy evaluation and design for continuous time linear rational expectations models: some recent development," NBER Technical Working Papers 0034, National Bureau of Economic Research, Inc.
    7. William Roberds, 1986. "Solution of linear-quadratic- Gaussian dynamic games using variational methods," Staff Report 105, Federal Reserve Bank of Minneapolis.
    8. Miller, Marcus H, 1985. "Monetary Stabilization Policy in an Open Economy," Scottish Journal of Political Economy, Scottish Economic Society, vol. 32(3), pages 220-233, November.

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