Fragility of Asymptotic Agreement Under Bayesian Learning

44 Pages Posted: 27 Mar 2008 Last revised: 28 Aug 2008

Daron Acemoglu

Massachusetts Institute of Technology (MIT) - Department of Economics; Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER)

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics; New Economic School

Muhamet Yildiz

Massachusetts Institute of Technology (MIT) - Department of Economics

Date Written: March 15, 2008

Abstract

Under the assumption that individuals know the conditional distributions of signals given the payoff-relevant parameters, existing results conclude that as individuals observe infinitely many signals, their beliefs about the parameters will eventually merge. We first show that these results are fragile when individuals are uncertain about the signal distributions: given any such model, a vanishingly small individual uncertainty about the signal distributions can lead to a substantial (non-vanishing) amount of differences between the asymptotic beliefs. We then characterize the conditions under which a small amount of uncertainty leads only to a small amount of asymptotic disagreement. According to our characterization, this is the case if the uncertainty about the signal distributions is generated by a family with "rapidly-varying tails" (such as the normal or the exponential distributions). However, when this family has "regularly-varying tails" (such as the Pareto, the log-normal, and the t-distributions), a small amount of uncertainty leads to a substantial amount of asymptotic disagreement.

Keywords: asymptotic disagreement, Bayesian learning, merging of opinions

JEL Classification: C11, C72, D83

Suggested Citation

Acemoglu, Daron and Chernozhukov, Victor and Yildiz, Muhamet, Fragility of Asymptotic Agreement Under Bayesian Learning (March 15, 2008). MIT Department of Economics Working Paper No. 08-09. Available at SSRN: https://ssrn.com/abstract=1112855 or http://dx.doi.org/10.2139/ssrn.1112855

Daron Acemoglu (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-380b
Cambridge, MA 02142
United States
617-253-1927 (Phone)
617-253-1330 (Fax)

Centre for Economic Policy Research (CEPR)

77 Bastwick Street
London, EC1V 3PZ
United Kingdom

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-262f
Cambridge, MA 02142
United States
617-253-4767 (Phone)
617-253-1330 (Fax)

HOME PAGE: http://www.mit.edu/~vchern/

New Economic School

47 Nakhimovsky Prospekt
Moscow, 117418
Russia

Muhamet Yildiz

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-522
Cambridge, MA 02142
United States
617-253-5331 (Phone)
617-253-6915 (Fax)

Paper statistics

Downloads
263
Rank
93,157
Abstract Views
2,617