Asset pricing equilibria for heterogeneous, limited-information agents

The standard general equilibrium asset pricing models typically make two simplifying assumptions: homogeneous agents and the existence of a rational expectations equilibrium. This context sometimes yields outcomes that are inconsistent with the empirical findings. We hypothesize that allowing agent heterogeneity could assist in replicating the empirical results. However, the inclusion of heterogeneity in models where agents are fully rational proves impossible to solve without severe simplifying assumptions. The reason for this difficulty is that heterogeneous agent models generate an endogenously complicated distribution of wealth across the agents. The state space for each agent's optimization problem includes the complex dynamics of the wealth distribution. There is no general way to characterize the interaction between the distribution of wealth and the macroeconomic aggregates. To address this issue, we implement an agent-based model where the agents have bounded rationality. In our model, we have a complete markets economy with two agents and two assets. The agents are heterogeneous and utility maximizing with constant coefficient of relative risk aversion [CRRA] preferences. How the agents address the stochastic behaviour of the evolution of the wealth distribution is central to our task since aggregate prices depend on this behaviour. An important component of this dissertation involves dealing with the computational difficulty of dynamic heterogeneous-agent models. That is, in order to predict prices, agents need a way to keep track of the evolution of the wealth distribution. We do this by allowing each agent to assume that a price-equivalent representative agent exists and that the representative agent has a constant coefficient of relative risk aversion. In so doing, the agents are able to formulate predictive pricing and demand functions which allow them to predict aggregate prices and make consumption and investment decisions each period. However, the agents' predictions are only approximately correct. Therefore, we introduce a learning mechanism to maintain the required level of accuracy in the agents' price predictions. From this setup, we find that the model, with learning, will converge over time to an approximate expectations equilibrium, provided that the the initial conditions are close enough to the rational expectations equilibrium prices. Two main contributions in our work are:;begin{enumerate} item to formulate a new concept of approximate equilibria, and item to show how equilibria can be approximated numerically, despite the fact that the true state space at any point in time is mathematically complex. end{enumerate}.;These contributions offer the possibility of characterizing a new class of asset pricing models where agents are heterogeneous and only just slightly limited in their rationality. That is, the partially informed agents in our model are able to forecast and utility-maximize only just as well as economists who face problems of estimating aggregate variables. By using an exogenously assigned adaptive learning rule, we analyse this implementation in a Lucas-type heterogeneous agent model. We focus on the sensitivity of the risk parameter and the convergence of the model to an approximate expectations equilibrium. Also, we study the extent to which adaptive learning is able to explain the empirical findings in an asset pricing model with heterogeneous agents.