Implementing the Commitment Solution via Discretionary Policy-Making

In a large class of linear-quadratic models with rational expectations, the commitment solution can be implemented by a policy-maker who acts purely under discretion. To show this, we construct discretionary equilibria with payoff-irrelevant state variables. These additional state variables are constructed in a way such that the policy-maker finds it impossible to renege on past promises. On the equilibrium path, the state variables are identical to the Lagrange multipliers associated with the constraints for the non-predetermined variables in the corresponding commitment problem. We illustrate our approach with the help of the canonical new Keynesian model