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


  • Willem H. Buiter


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 Note: ITI IFM

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    References listed on IDEAS

    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. 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.
    3. Gilles Oudiz & Jeffrey Sachs, 1984. "International Policy Coordination in Dynamic Macroeconomic Models," NBER Working Papers 1417, National Bureau of Economic Research, Inc.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. William Roberds, 1986. "Solution of linear-quadratic- Gaussian dynamic games using variational methods," Staff Report 105, Federal Reserve Bank of Minneapolis.

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