Solving heterogeneous-agent models with parameterized cross-sectional distributions

Abstract

A new algorithm is developed to solve models with heterogeneous agents and aggregate uncertainty that avoids some disadvantages of the prevailing algorithm that strongly relies on simulation techniques and is easier to implement than existing algorithms. A key aspect of the algorithm is a new procedure that parameterizes the cross-sectional distribution, which makes it possible to avoid Monte Carlo integration.The paper also develops a new simulation procedure that not only avoids cross-sectional sampling variation but is also more than ten times faster than the standard procedure of simulating an economy with a large but finite number of agents. This procedure can help to improve the efficiency of the most popular algorithm in which simulation procedures play a key role.

Solving the incomplete markets model with aggregate uncertainty using the Krusell–Smith algorithm and non-stochastic simulations

“…This method has three advantages. One, it does not introduce additional sampling error that must be removed for the households' aggregate behavior to be consistent with the law of large numbers; as noted in Algan et al (2007), sampling error may be significant for certain conditional moments, so avoiding Monte Carlo approaches for the cross-section can be important. Two, it can be applied to economies in which the mean of the idiosyncratic shock depends on individual decisions and is thus not known in advance, such as a search model of unemployment; imposing the law of large numbers would not be feasible without knowledge of the mean.…”

Solving the incomplete markets model with aggregate uncertainty by backward induction

“…In many applications it may be appropriate to use a smooth representation of the cross-sectional density (for example, an exponential of polynomials as in Algan et al, 2008). Here I use a non-smooth approximation, namely a histogram.…”

Solving the incomplete markets model with aggregate uncertainty using parameterized cross-sectional distributions

“…The procedure to solve for the policy rules uses standard projection techniques without a simulation step. Algan et al (2008) (AAD hereafter) propose a new procedure to simulate cross-sections with a continuum of agents. The most common procedure to simulate models with a continuum of agents consists of using a finite number of agents and a random number generator to draw the idiosyncratic shocks.…”