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, optimal monetary policy, macro-prudential policy, and sovereign lending. It is also important for private-sector decision-making through mechanisms such as quasi-geometric discounting. These problems are generally solved using some form of projection method. The difficulty 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. 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 illustrate the method and its applicability to different environments by applying it to a range of models featuring time-inconsistency.