An interior point algorithm for computing equilibria in economies with incomplete asset markets

Computing equilibria in general equilibria models with incomplete asset (GEI) markets is technically difficult. The standard numerical methods for computing these equilibria are based on homotopy methods. Despite recent advances in computational economics, much more can be done to enlarge the catalogue of techniques for computing GEI equilibria. This paper presents an interior-point algorithm that exploits the special structure of GEI markets. We prove that the algorithm converges globally at a quadratic rate, rendering it particularly effective in solving large-scale GEI economies. To illustrate its performance, we solve relevant examples of GEI market

AN INTERIOR POINT ALGORITHM FOR COMPUTING EQUILIBRIA IN ECONOMIES WITH INCOMPLETE ASSET MARKETS

Computing equilibria in general equilibria models with incomplete asset (GEI) markets is technically difficult. The standard numerical methods for computing these equilibria are based on homotopy methods. Despite recent advances in computational economics, much more can be done to enlarge the catalogue of techniques for computing GEI equilibria. This paper presents an interior-point algorithm that exploits the special structure of GEI markets. We prove that the algorithm converges globally at a quadratic rate, rendering it particularly effective in solving large-scale GEI economies. To illustrate its performance, we solve relevant examples of GEI markets.

An interior-point algorithm for computing equilibria in economies with incomplete asset markets

Computing equilibria in general equilibria models with incomplete asset (GEI) markets is technically difficult. The standard numerical methods for computing these equilibria are based on homotopy methods. Despite recent advances in computational economics, much more can be done to enlarge the catalog of techniques for computing GEI equilibria. This paper presents an interior-point algorithm that exploits the special structure of GEI markets. It is proved that, under mild conditions, the algorithm converges globally at a quadratic rate, rendering it particularly effective in solving large-scale GEI economies. To illustrate its performance, relevant examples of GEI markets are solvedPublicad

Solving incomplete markets models by derivative aggregation

This article presents a novel computational approach to solving models with both uninsurable idiosyncratic and aggregate risk that uses projection methods, simulation and perturbation. The approach is shown to be both as efficient and as accurate as existing methods on a model based on Krusell and Smith (1998), for which prior solutions exist. The approach has the advantage of extending straightforwardly, and with reasonable computational cost, to models with a greater range of diversity between agents, which is demonstrated by solving both a model with heterogeneity in discount-rates and a lifecycle model with incomplete markets

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

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.Incomplete Markets, Aggregate Uncertainty, Heterogeneous agents, Simulations, Numerical Solutions.

Patience, Persistence and Properties of Two-Country Incomplete Market Models

No abstract.

Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm

This paper studies the properties of the solution to the heterogeneous agents model in Den Haan, Judd and Juillard (2008). To solve for the individual policy rules, we use an Euler-equation method iterating on a grid of prespecified points. To compute the aggregate law of motion, we use the stochastic-simulation approach of Krusell and Smith (1998). We also compare the stochastic- and non-stochastic-simulation versions of the Krusell-Smith algorithm, and we find that the two versions are similar in terms of their speed and accuracy.

Incomplete Markets, Heterogeneity and Macroeconomic Dynamics

This paper solves a real business cycle model with heterogeneous agents and uninsurable income risk using perturbation methods. A second order accurate characterization of agent's optimal decision rules is given, which renders the implications of aggregation for macroeconomic dynamics transparent. The role of cross-sectional holdings of capital in determining equilibrium dynamics can be directly assessed. Analysis discloses that an individual's optimal saving decisions are almost linear in their own capital stock giving rise to permanent income consumption behavior. This provides an explanation for the approximate aggregation properties of this model documented by Krusell and Smith (1998): the distribution of capital does not affect aggregate dynamics. While the variance-covariance properties of endogenous variables are almost entirely determined by first order dynamics, the second order dynamics, which capture properties of the wealth distribution, are nonetheless important for an individual's mean consumption and saving decisions and therefore the mean equilibrium capital stock. Policy evaluation exercises therefore need to take account of these higher order terms.