The VFI Toolkit can now solve general equilibrium transition paths for Bewley-Huggett-Aiyagari models (general equilibrium heterogeneous agents models with idiosyncratic shocks but no aggregate shocks). This is done using the command TransitionPath_Case1 (and corresponding Case2).

The command can compute transition paths for a unannounced parameter change, a pre-announced parameter change, or any finite series of pre-announced parameter changes.

Other than arguments that are already required by the commands for computing the general equilibrium of a Bewley-Huggett-Aiyagari model the additional inputs are easy. In addition to the parameter path for which you wish to compute the transition you pass an initial agent distribution, and initial guess for the price path, and the final value function (which can be easily found using existing VFI Toolkit commands). Note that the final value function (as well as the final price in the guess for the price path) must be equal to the general equilibrium relating to the final parameter values; in principle the initial agents distribution need not be related to the general equilibrium of the initial parameter values.

An example, finding the general equilibrium transition path for a change in the value of the capital share parameter in the Cobb-Douglas production in the model of Aiyagari (1994) is provided.

For more details on the use of the command, it’s inputs, outputs, and internal options see the VFI Toolkit Documentation.

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Some related theory and algorithm findings can be found in working paper: Transition paths for Bewley-Huggett-Aiyagari models: Comparison of some solution algorithms (VUW-SEF Working Paper 1-2017)