Working Paper: NBER ID: w19114
Authors: Roland G. Fryer Jr.; Philipp Harms; Matthew O. Jackson
Abstract: We introduce and analyze a model in which agents observe sequences of signals about the state of the world, some of which are ambiguous and open to interpretation. Instead of using Bayes' rule on the whole sequence, our decision makers use Bayes' rule in an iterative way: first to interpret each signal and then to form a posterior on the whole sequence of interpreted signals. This technique is computationally efficient, but loses some information since only the interpretation of the signals is retained and not the full signal. We show that such rules are optimal if agents sufficiently discount the future; while if they are very patient then a time-varying random interpretation rule becomes optimal. One of our main contributions is showing that the model provides a formal foundation for why agents who observe exactly the same stream of information can end up becoming increasingly polarized in their posteriors.
Keywords: belief updating; polarization; Bayesian inference; ambiguity
JEL Codes: D03; J01
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| agents with different priors (D80) | differing posteriors (H73) |
| differing posteriors (H73) | belief polarization (D72) |
| interpretation of ambiguous signals (D80) | belief polarization (D72) |
| iterative use of Bayes' rule (C11) | divergent beliefs (Z12) |
| ambiguous signals (D80) | belief updating (D83) |