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How Should Control Theory be Used by a Time-Consistent Government?

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  • Cohen, Daniel
  • Michel, Philippe

Abstract

It has been recognized that the optimal strategy of a government is generally time-inconsistent: optimality requires that the government take into account expectations effects in the formulation of its policy and to ignore these effects when applying the policy. In order to analyse the problem, we study different solutions to a simple one-dimensional linear quadratic game. The optimal but time-inconsistent solution appears to be paradoxical: in the long term, the government plays against its objective function, in order to induce the private sector to take early corrective measures. The time-consistent solution, by contrast, is defined as a solution to the Hamilton-Jacobi-Bellman equation, i.e. as a policy where the government has no-precommitment capability. We demonstrate that this solution can be obtained by imposing the assumption that the government does not take into account the private sector's first order conditions but instead takes as given an equilibrium feedback rule. This solution is compared to a policy where the government has an "instantaneous" precommitment, to a Cournot-Nash equilibrium and to an optimal policy rule. In each case, we show how control theory should or should not be applied to calculate the equilibrium.

Suggested Citation

  • Cohen, Daniel & Michel, Philippe, 1986. "How Should Control Theory be Used by a Time-Consistent Government?," CEPR Discussion Papers 141, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:141
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    References listed on IDEAS

    as
    1. Abel, Andrew B., 1980. "Empirical investment equations : An integrative framework," Carnegie-Rochester Conference Series on Public Policy, Elsevier, pages 39-91.
    2. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    3. Cuddington, John T. & Vinals, Jose M., 1986. "Budget deficits and the current account : An Intertemporal Disequilibrium Approach," Journal of International Economics, Elsevier, pages 1-24.
    4. Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, vol. 50(1), pages 213-224, January.
    5. Jeffrey Sachs & Charles Wyplosz, 1984. "Real Exchange Rate Effects of Fiscal Policy," NBER Working Papers 1255, National Bureau of Economic Research, Inc.
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    8. William H. Branson & Willem H. Buiter, 1982. "Monetary and Fiscal Policy with Flexible Exchange Rates," NBER Working Papers 0901, National Bureau of Economic Research, Inc.
    9. Jacob A. Frenkel & Carlos A. Rodriguez, 1982. "Exchange Rate Dynamics and the Overshooting Hypothesis," NBER Working Papers 0832, National Bureau of Economic Research, Inc.
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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. Philippe Michel & Daniel Cohen, 1987. "Théorie et pratique du chômage en France," Revue Économique, Programme National Persée, vol. 38(3), pages 661-676.

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