Financial crises as herds: overturning the critiques

Financial crises are widely argued to be due to herd behavior. Yet recently developed models of herd behavior have been subjected to two critiques which seem to make them inapplicable to financial crises. Herds disappear from these models if two of their unappealing assumptions are modified: if their zero-one investment decisions are made continuous and if their investors are allowed to trade assets with market-determined prices. However, both critiques are overturned–herds reappear in these models–once another of their unappealing assumptions is modified: if, instead of moving in a prespecified order, investors can move whenever they choose. We thank Susan Athey, Abhijit Banerjee, Sushil Bikhchandani, Harold Cole, David Levine, George Mailath, Enrique Mendoza, Stephen Morris, Andrew Postlewaite, Hyun Shin, and an anonymous referee for useful comments. We thank Kathy Rolfe for editorial assistance. We thank the National Science Foundation for financial support. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. Capital flows to emerging markets are notoriously volatile. Many researchers have argued that a substantial fraction of this volatility is due to herd behavior. In discussing financial crises in developing countries, for example, Calvo and Mendoza [5] say that “ ‘the fall from grace’ in world capital markets . . . may be driven by herding behavior not necessarily linked to fundamentals.” Similar views can be found in other recent work, including that of Chari and Kehoe [8], Cole and Kehoe [9], and Sachs, Tornell, and Velasco [16]. More generally, the belief that herd behavior is widespread in financial markets is held by both market participants and economists (Devenow and Welch [10, p. 603]). Recently, models of herd behavior in which agents rationally mimic the behavior of other agents have been developed (by, for example, Banerjee [3] and Bikhchandani, Hirshleifer, and Welch [4]). In these models, herds occur because information becomes trapped; agents’ actions do not reveal their underlying signals. While these models, at first glance, seem appealing for understanding financial crises in emerging markets, a closer look reveals a problem: In order to generate herds, the models include two stark simplifying assumptions which make applying the models to financial crises di cult. The two stark assumptions are that investment decisions are discrete, zero-one decisions and that there are no traded assets with market-determined prices. Researchers have shown that if the assumptions are relaxed, then the models no longer generate herds. Lee [14] shows that if investment decisions are continuous instead of discrete, then herds disappear from the models. Avery and Zemsky [2] and Glosten and Milgrom [11] show that once the models allow for trade in financial markets, prices reveal information, and herds disappear. With the more natural assumptions, these models do not generate herds because investors can use the continuous variable, either investment or prices, to infer private signals; hence, no information gets trapped. We label these critiques the continuous investment critique and the price critique. In modeling financial crises it seems undesirable to abstract from continuous investment or prices. The scale of investments in financial markets can often be easily changed so that discrete investment assumptions seem unappealing. Moreover, prices are central to the operation of financial markets so that abstracting from prices seems particularly unappealing. Taken together, the critiques suggest that the early models of herd behavior, at least as they stand, are not applicable to financial crises. Yet, as we will show, both critiques can be overturned by replacing another stark simplifying assumption of the early herd models with an assumption that is more natural for applied situations. The stark assumption is that of exogenous timing, namely, that investors move in a prespecified order. We show that when this assumption is replaced by the assumption of endogenous timing–when investors can move whenever they choose–the two critiques are overturned; herds reappear in both the model with continuous investment and the model with prices. In our continuous investment model, investors must choose how to divide their assets between a risky project and a safe one. The returns in the risky project are determined by whether the economy’s underlying state is high or low. Information about that state arrives slowly in the economy, in the form of a signal in each period. This signal is received privately by one of the investors. Other investors attempt to infer this signal from observed levels of investment. In each period, investors face a trade-o between investing and waiting to invest: waiting is potentially beneficial because it lets investors gain information, but it is costly because of discounting. In this model, a small number of high signals leads all investors to invest in the risky project while a small number of low signals leads all investors to not invest in the risky project. The model generates herd-like behavior because, at some point, the benefits from waiting for more information are outweighed by the costs from waiting due to discounting, and investors choose not to wait for future signals. The information contained in future signals is never revealed to the market, and in this sense, information becomes trapped. We call these outcomes herds because they satisfy two criteria: investors make the same decisions regardless of their private signals, so that the outcomes are a cascade, and the outcomes are ine cient relative to those that emerge from solving a mechanism design problem. The outcomes in our continuous investment model are ine cient because of an information externality that leads the private return to waiting to be lower than the social