Herd Behavior and Investment: Reply
回应Ottaviani和Sorensen的评论，澄清关于声誉羊群模型中预测误差相关性必要性的分歧，指出不同定义导致不同结论，并论证严格定义更适用于分析经济效应。
In our 1990 paper, we showed that managers concerned with their reputations might choose to mimic the behavior of other managers and ignore their own information. We presented a model in which “smart” managers receive correlated, informative signals, whereas “dumb” managers receive independent, uninformative signals. Managers have an incentive to follow the herd to indicate to the labor market that they have received the same signal as others, and hence are likely to be smart. This model of reputational herding has subsequently found empirical support in a number of recent papers, including Judith A. Chevalier and Glenn D. Ellison’s (1999) study of mutual fund managers and Harrison G. Hong et al.’s (2000) study of equity analysts. We argued in our 1990 paper that reputational herding “requires smart managers’ prediction errors to be at least partially correlated with each other” (page 468). In their Comment, Marco Ottaviani and Peter Sorensen (hereafter, OS) take issue with this claim. They write: “correlation is not necessary for herding, other than in degenerate cases.” It turns out that the apparent disagreement hinges on how strict a definition of herding one adopts. In particular, we had defined a herding equilibrium as one in which agent B always ignores his own information and follows agent A. (See, e.g., our Propositions 1 and 2.) In contrast, OS say that there is herding when agent B sometimes ignores his own information and follows agent A. The OS conclusion is clearly correct given their weaker definition of herding. At the same time, however, it also seems that for the stricter definition that we adopted in our original paper, correlated errors on the part of smart managers are indeed necessary for a herding outcome—even when one considers the expanded parameter space that OS do. We will try to give some intuition for why the different definitions of herding lead to different conclusions about the necessity of correlated prediction errors. Along the way, we hope to convince the reader that our stricter definition is more appropriate for isolating the economic effects at work in the reputational herding model. An example is helpful in illustrating what is going on. Consider a simple case where the parameter values are as follows: p 5 3⁄4; q 5 1⁄4; z 5 1⁄2, and u 5 1⁄2. In our 1990 paper, we also imposed the constraint that z 5 ap 1 (1 2 a)q, which further implies that a 5 1⁄2. The heart of the OS Comment is the idea that this constraint should be disposed of—i.e., we should look at other values of a. Without loss of generality, we will consider values of a above 1⁄2, and distinguish two cases.