Dynamic Inconsistency and Inefficiency of Equilibrium under Knightian Uncertainty∗ Patrick Beissnery Michael Zierhutz March 14, 2019 Abstract This paper extends the theory of general equilibrium with Knightian uncertainty to economies with more than two dates. Agents have incomplete preferences with multiple priors `ala Bewley. These priors are updated in light of new informa- tion. Contrary to the two-date model, the market outcome varies with choice of updating rule. We document two phenomena: First, agents may find it optimal to deviate from their initial trading plans. This dynamic inconsistency may result in Pareto inefficiency, even if the market is dynamically complete. Second, ambiguous probability mass may spread; new information may create new uncertainty. Ei- ther phenomenon is avoided under certain updating rules: Full Bayesian updating guarantees dynamic consistency and Pareto efficiency, while maximum-likelihood updating prevents ambiguity spillovers. We ask whether it is possible to design updating rules that combine both properties. The answer is negative: No such rule exists. JEL Classification: D52; D53; D81 Keywords: Knightian uncertainty, Dynamic consistency, General equilibrium, In- complete markets ∗The authors thank Pablo Beker, Federico Echenique, Georgios Gerasimou, Christian Kellner, Fabio Maccheroni, Filipe Martins-da-Rocha, Frank Riedel, Ronald Stauber, Georg Weizs¨acker, and Jan Werner, as well as participants in the 2018 North American Summer Meeting of the Econometric Society and the workshop on Mathematics of Behavioral Economics and Knightian Uncertainty in Financial Markets at ZiF Bielefeld for helpful comments. M. Zierhut gratefully acknowledges financial support by the German Research Foundation (DFG) under project ZI 1673/1-1. yResearch School of Economics, ANU, 26012 Canberra, Australia,
[email protected] zInstitute of Financial Economics, Humboldt University, 10099 Berlin, Germany, michael.zierhut@hu- berlin.de.