Working Paper: CEPR ID: DP141
Authors: Daniel Cohen; Philippe Michel
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.
Keywords: optimal policy; control theory; precommitment; time consistency
JEL Codes: 022; 323
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Optimal government policy (H21) | time inconsistency (D15) |
| Government policy decisions (D78) | private sector expectations and responses (E69) |
| Time-consistent policy (D15) | adherence to Bellman's dynamic programming principle (C61) |
| Government ignoring private sector's first-order conditions (P19) | stable equilibrium (C62) |
| Government actions (H11) | private sector responses (L39) |
| Feedback mechanism (D91) | convergence towards equilibrium (D50) |
| Suboptimal outcomes (I14) | incorrect management of government policy (H12) |