TY - JOUR
AU - Acemoglu, Daron
AU - Chernozhukov, Victor
AU - Yildiz, Muhamet
TI - Learning and Disagreement in an Uncertain World
JF - National Bureau of Economic Research Working Paper Series
VL - No. 12648
PY - 2006
Y2 - October 2006
DO - 10.3386/w12648
UR - http://www.nber.org/papers/w12648
L1 - http://www.nber.org/papers/w12648.pdf
N1 - Author contact info:
Daron Acemoglu
Department of Economics
MIT
50 Memorial Drive
Cambridge, MA 02142-1347
Tel: 617/253-1927
Fax: 617/253-1330
E-Mail: daron@mit.edu
Victor Chernozhukov
Department of Economics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, Mass. 02139
E-Mail: vchern@mit.edu
Muhamet Yildiz
Department of Economics
E52-515
MIT
77 Massachusetts Avenue
Cambridge, MA 02139
E-Mail: myildiz@mit.edu
AB - Most economic analyses presume that there are limited differences in the prior beliefs of individuals, as assumption most often justified by the argument that sufficient common experiences and observations will eliminate disagreements. We investigate this claim using a simple model of Bayesian learning. Two individuals with different priors observe the same infinite sequence of signals about some underlying parameter. Existing results in the literature establish that when individuals are certain about the interpretation of signals, under very mild conditions there will be asymptotic agreement---their assessments will eventually agree. In contrast, we look at an environment in which individuals are uncertain about the interpretation of signals, meaning that they have non-degenerate probability distributions over the conditional distribution of signals given the underlying parameter. When priors on the parameter and the conditional distribution of signals have full support, we prove the following results: (1) Individuals will never agree, even after observing the same infinite sequence of signals. (2) Before observing the signals, they believe with probability 1 that their posteriors about the underlying parameter will fail to converge. (3) Observing the same sequence of signals may lead to a divergence of opinion rather than the typically presumed convergence. We then characterize the conditions for asymptotic agreement under "approximate certainty"---i.e., as we look at the limit where uncertainty about the interpretation of the signals disappears. When the family of probability distributions of signals given the parameter has "rapidly-varying tails" (such as the normal or exponential distributions), approximate certainty restores asymptotic agreement. However, when the family of probability distributions has "regularly-varying tails" (such as the Pareto, the log-normal, and the t-distributions), asymptotic agreement does not obtain even in the limit as the amount of uncertainty disappears. Lack of common priors has important implications for economic behavior in a range of circumstances. We illustrate how the type of learning outlined in this paper interacts with economic behavior in various different situations, including games of common interest, coordination, asset trading and bargaining.
ER -