Computing Time-Consistent Equilibria: A Perturbation Approach

Time-consistency is a key feature of many important policy problems, such as those relating to optimal fiscal policy and optimal monetary policy. It is also important for private-sector decision-making through mechanisms such as quasi-hyperbolic discounting. These problems are generally solved using some form of projection method. The difficultly with projection methods is that their computational complexity increases rapidly with the number of state variables, limiting the sophistication of the models that can be solved. This paper develops a perturbation method for solving models with time-inconsistency that enables larger models to be more readily solved and analyzed. The method operates on a model's (generalized) Euler equations; it does not require forming a quadratic approximation to household welfare and it does not require that the model's steady state be efficient. We apply the method to several models featuring time-inconsistency and show that it exhibits good accuracy.