Transition paths for Bewley-Huggett-Aiyagari models: Comparison of some solution algorithms

We analyse general equilibrium transition paths for Bewley-Huggett-Aiyagari models: general equilibrium models with heterogeneous agents, incomplete markets, and idiosyncratic but no aggregate uncertainty. We first provide precise definitions of the theoretical problem to be solved. We then consider a variety of algorithms for computation of the finite horizon general equilibrium transition paths. These algorithms can solve for unannounced one-off changes, pre-announced one-off changes, or even any finite series of one-off changes (such as announcing today a series of tax increases to be rolled out over the next few years). The algorithms are all based on shooting-algorithms but differ in how they update the price paths during convergence. Evaluation of the algorithms in terms of both robustness and runtime is performed by applying them to looking at capital tax reforms in the model of Aiyagari (1994) and its extension to endogenous labour. Simulation results show that the literature standard of simply using a fixed factor to update the entire path performs both fast and robustly; and that a weight of 0.9 on the old path is typically the best by these criterion.