Dimensionality and Disagreement : Asymptotic Belief Divergence in Response to Common Information

When information is of lower dimension than the model generating the data, Bayesian updating of marginal probabilities need not converge to the truth. Because the information is of lower dimension than the model, agents face an identification problem, affecting the role of data in inference. We provide conditions under which learning is asymptotically inconsistent with positive probability, and sometimes almost surely. Robustly, two agents with differing priors who observe identical, unambiguous data may disagree forever, with stronger disagreement the more data is observed. Agents use common observations to differentially update marginal beliefs about different parameters