Diverse Beliefs, Survival and the Market Price of Risk

Abstract

We study prices and allocations in a complete-markets, pure-exchange economy in which there are two types of agents with different priors over infinite sequences of the aggregate endowment. Aggregate consumption growth evolves exogenously according to a two-state Markov process. The economy has two types of agents, one that learns about transition probabilities and another that knows them. We examine allocations, the market price of risk and the rate at which asset prices converge to values that would be computed under the assumption that all agents know the transition probabilities. Cogley and Sargent (2008) showed that market prices of risk would be high in an economy with a risk-neutral Bayesian representative agent who learns about the parameters of a transition matrix for aggregate consumption growth starting with a pessimistic prior in 1933.1 This article studies the robustness of that finding to a per turbation that adds a small fraction of agents who know the parameters of the trans ition matrix. Traders participate in a Walrasian equilibrium in which they do not infer information from prices (Grossman, 1981).23 Under what we assume to be the true data-generating mechanism, the survival-of-the-fittest force analysed by Blume and Easley (2006) causes the more knowledgeable agents' influence on equilibrium prices to grow over time along with their wealth. We study how quickly that dissipates the effects of the initial pessimism of the less informed agents on equilibrium prices.4 To give the survival mechanism a large scope to moderate the effects of initial pessim ism, we assume complete markets that allow agents to make trades of claims to wealth that are motivated solely by the different subjective probabilities they put on future states. That gives the agents many opportunities to place bets that over time stochastically increase the share of wealth of the traders who know transition probabilities. We solve a Pareto problem to compute competitive equilibrium prices and alloca tions, thereby implicitly defining an initial allocation of wealth. We study how the market price of risk evolves as a function of the relative Pareto weight on the better informed agent. Among other things, we want to know how large the Pareto weight on