The More We Know, the Less We Agree: Public Announcements and Higher-Order Expectations

Abstract

The stylized fact that public announcements in financial markets are followed by intense trading, high trading volume and volatile prices, is widely perceived as the sign of increasing disagreement due to the announcement. However, it is common to argue that this would be inconsistent with Bayesian-learning and common priors. In this paper, we not only show that -with certain information structures -increasing disagreement is possible in a Bayesian model, but we also argue that with the assumption that traders trade for resale -so they try to second guess future traders' guesses -there are information structures which are simple, intuitive and plausible and result in increasing disagreement even in a standard, multi-period Grossman-Stiglitz model.

Optimal Degree of Public Information Dissemination

“…Our results show, however, that imprecise signals should not be released to a general audience. Kondor (2004) provides examples showing that public announcements may increase disagreement in higher-order beliefs, if the correlation between private information sets of different groups of traders is low but all information sets are correlated with the public announcement. Lindner (2006) shows that complementary information may induce private beliefs instead of common knowledge.…”

When are signals complements or substitutes?

“…There are two further cases: we first consider the case in which β provides the strongest individual evidence for b: q β (b) ≥ qβ(b). In this case, conditions (12) and (13) become:…”

“…Lord et al interpret their findings as evidence for biased information processing. In contrast, Kondor [12] and Andreoni and Mylovanov [1] have recently described information structures where increased polarization following the public disclosure of additional evidence is consistent with Bayesian updating. 17 In these authors' models agents hold opposing private information about how to interpret the public signal.…”

“…The intuition for this finding is that an additive method for aggregating votes does not allow a vote to reverse meaning, which is required for efficient information aggregation if signals are complements, and hence sometimes reverse meaning. 14 12 The example in this subsection is based on Lemma 1 in [8]. We thank Kata Bognar for allowing us to describe her result here.…”

“…We are interested in how their disagreement evolves after signal 2 is released. We discuss the notions of disagreement proposed by Kondor [12] and Andreoni and Mylovanov [1]. Kondor offers the following notion of disagreement: (ii) Signals exhibit belief swap with respect to s 2 ∈ {α,β} if observing s 2 swaps the order of beliefs: q β,s 2 (a) > q α,s 2 (a).…”