This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibria when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and significant fluctuations in individual portfolios may be correct but it needs some qualifications. We consider an infinite horizon stochastic endowment economy populated by many Bayesian agents with heterogeneous priors over the stochastic process of the states of nature. Our approach hinges on studying the portfolios that decentralize Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents believe that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed generate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the true process consists of i.i.d. draws from a common distribution and the support of every agent's prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d.Keywords: heterogeneous beliefs, asset trading, dynamically complete markets. * We thank Rody Manuelli and Juan Dubra for detailed comments. We are also very grateful to one of the referees for very detailed comments that greatly improved the paper and the proof of Proposition 16. All the remaining errors are ours.
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AbstractIn his seminal paper of 1928, Ramsey conjectured that if agents discounted the future differently, in the long run all agents except the most patient would live at the subsistence level. The validity of this conjecture was investigated in different environments. In particular, it has been confirmed in the neoclassical growth model with dynamically complete markets. This paper studies this conjecture in a version of this model that includes private information and heterogeneous agents. A version of Bayesian Implementation is introduced and a recursive formulation of the original allocation problem is established. Efficient allocations are renegotiation-proof and the expected utility of any agent cannot go to zero with positive probability if the economy does not collapse. If the economy collapses all agents will get zero consumption forever. Thus, including any degree of private information in the neoclassical growth model will deny Ramsey's conjecture, if efficient allocations are considered.
Private information may limit insurance possibilities when two agents get together to pool idiosyncratic risk. However, if there is capital accumulation, bilateral insurance possibilities may improve because misreporting distorts investment. We show that if one of the Pareto weights is sufficiently large, that agent does not have incentives to misreport. This implies that, under some conditions, the full information allocation is incentive compatible when agents have equal Pareto weights. In the long run, either one of the agents goes to immiseration, or both agents' lifetime utilities are approximately equal. The second case is only possible with capital accumulation.
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