Abstract
A great deal of attention has recently been focused on communication in economic contexts. While some models of credible announcements have been based on reputational forces or penalties imposed by third parties, as in Sobel [21] and Cothren [4], several recent papers have addressed the possibility of communication through talk, that is, talk in situations with no explicit penalties for deception. Perhaps the most prominent application of cheap talk in the literature is the recent model of Federal Reserve announcements by Stein [22].' This paper will show that cheap talk equilibria of the sort modeled by Stein and others often depend in a fundamental way on implausible discontinuities in public responses to government announcements. That is, cheap talk equilibria are frequently only possible if certain infinitesimally small changes in government announcements are capable of causing large, discontinuous changes in public expectations and behavior. Intuitively, if public expectations are a continuous function of government announcements, then the government can tune these expectations. The government will therefore often be tempted to deviate from the cheap talk equilibrium announcements in order to manipulate expectations. This causes the equilibrium to unravel. Discontinuous public reactions sometimes prevent these equilibria from unraveling because they convert continuous choice problems, which allow manipulative fine tuning, into discrete choice problems, where such fine tuning is impossible. These discontinuities are implausible, however, and this may often rule out cheap talk as a realistic model of governmental policy announcements.2
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