Time consistent policymaking: the infinite horizon linear-quadratic case

This paper is concerned with the calculation of time consistent macroeconomic policies. We provide a taxonomy for four different infinite horizon time consistent equilibria, combining Nash and Stackelberg behaviour on the part of the policymaker with either open loop or feedback strategies. We argue that policy design exercises on estimated, usually nonlinear, models necessarily restrict attention to the open loop equilibria, which have not been studied before in this detail nor compared to the feedback equilibria. We therefore describe how such equilibria should be calculated and examine their properties. All the different time consistent equilibria are illustrated using a small stylised model of the output-inflation trade-off. We note that the open loop equilibria may not always be well defined when the instrument of the private sector, in this case the price level, is itself a target of policy.