Asset Market Dynamics in Equilibrium Models with Heterogeneous Agents: Analytical Results

P M Beaumont,A N Kercheval,A J Culham

doi:10.13189/aeb.2013.010202

Abstract

We examine market dynamics in a discrete- time, Lucas-style asset-pricing model with heteroge- neous, utility-optimizing agents. Finitely many agents trade a single asset paying a stochastic dividend. All agents know the probability distribution of the dividend but not the private information such as wealth and asset holdings of other agents. The market clearing price is determined endogenously in each period such that sup- ply always equals demand. Our aim is to determine whether and how the pricing function evolves toward equilibrium. In the special case where all agents have logarithmic utility, but possibly different holdings and discount factors, we completely describe the market dynamics, including the evolution of the pricing and demand functions, and asset holdings of the agents. The market converges to a stable equilibrium state where only the most patient agents remain, and the equilibrium pricing function is the same as the one arising in the simple homogeneous setting.

Highlights

In a general equilibrium asset pricing model, the existence of a rational expectations equilibrium (REE) implies that each trader solves a utility-optimization problem that incorporates all current information about the market
Using the terminology from [1], we will say that the market is at a “correct expectations equilibrium” (CEE), if all agents are using the same pricing function Pm(·) to solve for optimal demand, and this pricing function is correct in the sense that the actual resulting market clearing price is Pm(D) in every period
We will find that there is a unique CEE pricing function given by agents with discount factor equal to β. This result is consistent with the long-known principle (e.g. [3]) for REE equilibria that the most patient agent eventually holds all the wealth. Our work confirms this principle in the CEE boundedly rational context typical of agent-based computational economic (ACE) and we provide a formal proof of convergence to the familiar pricing function well-known in the homogeneous case

Summary

Introduction

In a general equilibrium asset pricing model, the existence of a rational expectations equilibrium (REE) implies that each trader solves a utility-optimization problem that incorporates all current information about the market. This allows us to model the economy both at and away from equilibrium To compute their optimal asset demand and consumption functions each agent must solve an expectation involving future market-clearing prices. Using the terminology from [1], we will say that the market is at a “correct expectations equilibrium” (CEE), if all agents are using the same pricing function Pm(·) to solve for optimal demand, and this pricing function is correct in the sense that the actual resulting market clearing price is Pm(D) in every period This framework has the advantage that agent behavior is well-defined whether or not the market is at equilibrium. [3]) for REE equilibria that the most patient agent eventually holds all the wealth Our work confirms this principle in the CEE boundedly rational context typical of ACE and we provide a formal proof of convergence to the familiar pricing function well-known in the homogeneous case. Our work contributes to this literature by adding a formal mathematical analysis of the dynamical behavior of asset markets in a general equilibrium model with heterogeneous agents

Model framework

The log utility case

Proof of Theorem 1

An Illustration with Two Agents

Conclusions