Solving Models with Incomplete Markets and Aggregate Uncertainty Using the Krusell-Smith Algorithm: A Note on the Number and the Placement of Grid Points

By Michal Horvath

http://d.repec.org/n?u=RePEc:san:cdmawp:1105&r=dge

This paper shows that numerical solutions to models with incomplete markets and aggregate uncertainty obtained using the Krusell and Smith (1998) algorithm are sensitive to the parameterization of the grid in the aggregate asset holdings direction. Higher moments of the cross-sectional distribution of asset holdings can be particularly affected, which is important for welfare analysis. Using grids that are denser around the mean of the ergodic distribution of individual asset holdings can enhance the consistency of the results across parameterizations. The accuracy of the approximation to individual decision functions can be much improved this way.

Solving heterogeneous agent models with aggregate shocks is very difficult. The Krusell-Smith method has considerably simplified this for some models, but it is not without pitfalls as this paper shows. The choice of grid points can matter and the solution id unfortunately to use more well placed points.

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2 Responses to Solving Models with Incomplete Markets and Aggregate Uncertainty Using the Krusell-Smith Algorithm: A Note on the Number and the Placement of Grid Points

  1. Jabbadoo says:

    Nothing to see here — the “point” of the paper is to note that putting grid points where they are not needed and not where they are is a bad idea.

  2. mhorvath says:

    The paper is a comment written in the context of a JEDC special issue. The “point” of the paper, as you kindly say, is nothing new in general, and I agree. It is the context that should matter here.

    One way to read the note is that the accuracy of the solution in the case of one of the papers in the JEDC special issue can be significantly improved upon. Given that it was a horse race, and the people involved usually care a lot about the tiniest differences, this should be an interesting point for them.

    However, my preferred message from the note is that if someone uses that particular solution algorithm to conduct policy experiments, for example, he/she should not forget about this point, because the welfare analysis may be significantly affected.

    This is all this note is meant to say. Chris Carroll is keen on converting this sort of a model into a workhorse for economists, and he refers a lot to Maliar et al. (2010), so I thought some people would find this useful in their work.

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