Computation of equilibria in heterogeneous agent models

This paper essentially puts together procedures that are used in the computation of equilibria in models with a very large number of heterogeneous agents. It is not a complete description of all procedures used in the literature. It describes procedures that deal with infinitely lived agent versions of the growth model with and without aggregate uncertainty, overlapping generations models, and dynamic political economy models.Econometric models

Improving Tatonnement Methods of Solving Heterogeneous Agent Models

This paper modifies standard block Gauss-Seidel iterations used by tatonnement methods for solving large scale deterministic heterogeneous agent models. The composite method between first- and second-order tatonnement methods is shown to considerably improve convergence both in terms of speed as well as robustness relative to conventional first-order tatonnement methods. In addition, the relative advantage of the modified algorithm increases in the size and complexity of the economic model. Therefore, the algorithm allows significant reductions in computational time when solving large models. The algorithm is particularly attractive since it is easy to implement – it only augments conventional and intuitive tatonnement iterations with standard numerical methods.

Improving Tatonnement Methods for Solving Heterogeneous Agent Models

This paper modifies standard block Gauss-Seidel iterations used by tatonnement methods for solving large scale deterministic heterogeneous agent models. The composite method between first- and second-order tatonnement methods is shown to considerably improve convergence both in terms of speed as well as robustness relative to conventional first-order tatonnement methods. In addition, the relative advantage of the modified algorithm increases in the size and complexity of the economic model. Therefore, the algorithm allows significant reductions in computational time when solving large models. The algorithm is particularly attractive since it is easy to implement - it only augments conventional and intuitive tatonnement iterations with standard numerical methods.

"Causes of Financial Instability: Don’t Forget Finance"

Given the economy's complex behavior and sudden transitions as evidenced in the 2007–08 crisis, agent-based models are widely considered a promising alternative to current macroeconomic practice dominated by DSGE models. Their failure is commonly interpreted as a failure to incorporate heterogeneous interacting agents. This paper explains that complex behavior and sudden transitions also arise from the economy's financial structure as reflected in its balance sheets, not just from heterogeneous interacting agents. It introduces "flow-of-funds" and "accounting" models, which were preeminent in successful anticipations of the recent crisis. In illustration, a simple balance-sheet model of the economy is developed to demonstrate that nonlinear behavior and sudden transition may arise from the economy’s balance-sheet structure, even without any microfoundations. The paper concludes by discussing one recent example of combining flow-of-funds and agent-based models. This appears a promising avenue for future research.Credit Crisis; Finance; Complex Systems; DSGE; Agent-based Models; Stock-flow Consistent Models

Labor-Market Heterogeneity, Aggregation, and the Policy-(In)variance of DSGE Model Parameters

Data from a heterogeneous-agents economy with incomplete asset markets and indivisible labor supply are simulated under various fiscal policy regimes and an approximating representative-agent model is estimated. Preference and technology parameter estimates of the representative-agent model are not invariant to policy changes and the bias in the representative-agent model’s policy predictions is large compared to predictive intervals that reflect parameter uncertainty. Since it is not always feasible to account for heterogeneity explicitly, it is important to recognize the possibility that the parameters of a highly aggregated model may not be invariant with respect to policy changes.Aggregation, DSGE Models, Fiscal Policy, Heterogeneous-Agents Economy, Policy Predictions, Representative-Agent Models

Labor-Market Heterogeneity, Aggregation, and the Lucas Critique

This paper assesses biases in policy predictions due to the lack of invariance of "structural" parameters in representative-agent models. We simulate data under various fiscal policy regimes from a heterogeneous-agents economy with incomplete asset markets and indivisible labor supply. Imperfect aggregation manifests itself through preference shocks in the estimated representative-agent model. Preference and technology parameter estimates are not invariant with respect to policy changes. As a result, the bias in the representative-agent model's policy predictions is large compared to the length of predictive intervals that reflect parameter uncertainty.Aggregation; Fiscal Policy; Heterogeneous Agents Economy; Lucas Critique; Representative Agent Models.

Equilibrium Heterogeneous-Agent Models as Measurement Tools: some Monte Carlo Evidence

This paper discusses a series of Monte Carlo experiments designed to evaluate the empirical properties of heterogeneous-agent macroeconomic models in the presence of sampling variability. The calibration procedure leads to the welfare analysis being conducted with the wrong parameters. The ability of the calibrated model to correctly predict the long-run welfare changes induced by a set of policy experiments is assessed. The results show that, for the policy reforms with sizable welfare effects (i.e., more than 0.2%), the model always predict the right sign of the welfare effects. However, the welfare effects can be evaluated with the wrong sign, when they are small and when the sample size is fairly limited. Quantitatively, the maximum errors made in evaluating a policy change are very small for some reforms (in the order of 0.02 percentage points), but bigger for others (in the order of 0.6 p.p.). Finally, having access to better data, in terms of larger samples, does lead to substantial increases in the precision of the welfare effects estimates, though the rate of convergence can be slow.Ex-ante Policy Evaluation, Incomplete Markets, Heterogeneous Agents, Monte Carlo, Welfare

Scaling limits for continuous opinion dynamics systems

Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their current value and that of another observed agent. It is shown that, in the limit of large agent population size, the empirical opinion density concentrates, at an exponential probability rate, around the solution of a probability-measure-valued ordinary differential equation describing the system's mean-field dynamics. Properties of the associated initial value problem are studied. The asymptotic behavior of the solution is analyzed for bounded-confidence opinion dynamics, and in the presence of an heterogeneous influential environment.Comment: Published at http://dx.doi.org/10.1214/10-AAP739 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org