Recursive methods for computing equilibria of general equilibrium dynamic Stackelberg games

We extend the Hansen and Prescott approximation method for the numerical solution of dynamic business cycle models to models of two agents who play a dynamic Stackelberg game. Such models have application to the analysis of issues of optimal policy with the government as the leader and a representative private agent as the follower. We show in detail how to derive time-consistent policy rules. We discuss the details of the numerical algorithm and its convergence, and we consider an application of the algorithm to a model of optimal fiscal policy.