Market Clearing and Krusell-Smith Algorithm in an Economy with Multiple Assets

Abstract

This paper proposes a novel method to compute the Krusell and Smith (1997, 1998) algorithm, used for solving heterogeneous-agents models with aggregate risk and incomplete markets when households can save in more than one asset. When used to solve a model with more than one asset, the standard algorithm has to impose equilibria for each additional asset (find the market-clearing price) in each period simulated. This procedure entails root-finding in each period, which is computationally expensive. I show that it is possible to avoid root-finding at this level by not imposing equilibria each period, but instead temporarily suspending market clearing. The proposed method then updates the law of motion for asset prices by using the information on the excess demand for assets via a Newton-like method. Since the method avoids the root-finding for each time period simulated, it leads to a significant reduction in computation time. In the example model with two assets, the proposed version of the algorithm leads to an 80% decrease in computational time, even when measured conservatively. This method is potentially useful in computing general equilibrium asset-pricing models with risky and safe assets, featuring both aggregate and uninsurable idiosyncratic risk, since methods that use linearisation in the neighborhood of the aggregate steady state are considered to be less accurate than global solution methods for such models.