By Grey Gordon
Theoretical formulations of dynamic heterogeneous-agent economies typically include a distribution as an aggregate state variable. This paper introduces a method for computing equilibrium of these models by including a distribution directly as a state variable if it is finite-dimensional or a fine approximation of it if infinite-dimensional. The method accurately computes equilibrium in an extreme calibration of Huffman’s (1987) overlapping-generations economy where quasi-aggregation, the accurate forecasting of prices using a small state space, fails to obtain. The method also accurately solves for equilibrium in a version of Krusell and Smith’s (1998) economy wherein quasi-aggregation obtains but households face occasionally binding constraints. The method is demonstrated to be not only accurate but also feasible with equilibria for both economies being computed in under ten minutes in Matlab. Feasibility is achieved by using Smolyak’s (1963) sparse-grid interpolation algorithm to limit the necessary number of grid points by many orders of magnitude relative to linear interpolation. Accuracy is achieved by using Smolyak’s algorithm, which relies on smoothness, only for representing the distribution and not for other state variables such as individual asset holdings.
This is an interesting method that should extend significantly the class of heterogeneous models with aggregate shocks that can be solved with reasonable accuracy and within reasonable computing time. The relevant computer code is also available, which should boost its usage.