Solving the incomplete markets model with aggregate uncertainty by backward induction

Comparison of solutions to the incomplete markets model with aggregate uncertainty

“…Those are the backward induction procedure, referred to as BInduc throughout this paper, developed in Reiter (2009b), the parameterized distribution procedure, referred to as Param, of Algan et al (2009), and the explicit aggregation algorithm, referred to as Xpa, developed in den Haan and Rendahl (2009). These algorithms are summarized in the subsections on projection methods.…”

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

“…The algorithm iterates on this procedure until the information provided by the simulation is consistent with the assumptions made about the shape of the cross-sectional distribution. The philosophy that underlies our algorithm is similar to the one in Reiter (2009). The differences are mainly in terms of implementation, which is less cumbersome for our algorithm.…”

Solving the incomplete markets model with aggregate uncertainty using explicit aggregation

“…First, it illustrates the simplicity of our algorithm and brings to light the advantages relative to alternative algorithms. Second, we want to make clear why our algorithm can solve models with heterogeneous agents without generating a complete cross-sectional distribution by simulating a panel as is done by Krusell and Smith (1998) and without parameterizing the distribution as is done by Algan et al (2008Algan et al ( , 2009) and Reiter (2009).…”

“…The individual policy rules describe optimal behavior conditional on the aggregate laws of motions and the aggregate laws of motion provide a close fit for the behavior of the aggregates in a simulated panel that is generated using the individual policy rules. Algan et al (2008Algan et al ( , 2009) and Reiter (2009) parameterize the cross-sectional distribution, which is used to calculate next period's aggregate moments by numerically integrating over the individual choices. These algorithms have in common that (i) an additional function related to an aggregate variable, like a moment or the distribution, is separately parameterized and (ii) information about the crosssectional distribution-obtained by simulating a panel or by parameterizing the distribution-is used to establish a link between the individual and aggregate behavior.…”