Heterogeneity and learning with complete markets

We study an endowment economy with complete markets and heterogeneous agents who do not have rational expectations, but form their beliefs using adaptive learning algorithms that may differ from one individual to another. We show that market completeness allows agents to smooth consumption across states of nature, but not across time, and that the initial wealth distribution is not enough to pin down the long-run equilibrium. Consequently, initial differences in beliefs create persistent consumption imbalances that are not grounded in fundamentals. In some cases these imbalances are eventually unsustainable: the debt of one of the agents would grow without bounds, and binding borrowing limits are necessary to prevent Ponzi schemes. Finally, we find that our slight departure from rational expectations affects efficiency properties of the competitive equilibrium: if the social welfare function attaches fixed Pareto weights to the different individuals, there are configurations of individual expectations under which society is better off with financial autarky than with complete markets. The first best can be restored by introducing a distortionary tax on borrowing, which transfers consumption from the more optimistic agent to the other.