How Should Control Theory be Used by a Time-Consistent Government?
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.Download Info
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Bibliographic Info
Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 141.Length:
Date of creation: Dec 1986
Date of revision:
Handle: RePEc:cpr:ceprdp:141
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Keywords: Control Theory; Differential Games; Government Policy; Nash Equilibrium; Optimal Control; Time Consistency;References
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Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- 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.
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