Abstract
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.
Highlights
Time-consistency features importantly in many areas of macroeconomics: fiscal policy, monetary policy, banking regulation, and sovereign lending, to name just a few
Time-consistency is a key feature of many important policy problems, such as those relating to optimal fiscal policy and optimal monetary policy
This paper has developed and illustrated a procedure for solving dynamic stochastic models containing generalized-Euler equations—models exhibiting time-inconsistency—using perturbation methods
Summary
Time-consistency features importantly in many areas of macroeconomics: fiscal policy, monetary policy, banking regulation, and sovereign lending, to name just a few. This paper presents a perturbation method to solve optimization-based dynamic macroeconomic models for first-order accurate time-consistent equilibria. Our procedure inherits the scalability of perturbation methods, allowing it to be applied to medium- to large-scale models, ones that cannot reasonably be solved accurately using projection methods, even using sparse grid technology Because it is based on (generalized) Euler equations, our method does not require second-order welfare approximations and nor does it ask that the perturbation point be the model’s efficient steady state. Oped here is described in Krusell, Kuruscu, and Smith (2002) Like ourselves, they express the problem to be solved in terms of a system containing a generalized Euler equation and solve simultaneously for the model’s steady state and equilibrium dynamics. An appendix identifies and discusses special cases where LQ approximations can be employed to solve for time-consistent equilibria and shows why LQ methods cannot be applied generally
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