Journal of Socio-Economics 32 (2003) 661–673 Herd behavior and the quality of opinions Shinji Teraji Department of Economics, Yamaguchi University, 1677-1 Yoshida, Yamaguchi 753-8514, Japan Accepted 14 October 2003 Abstract This paper analyzes a decentralized decision model by adding some inertia in the social leaning process. Before making a decision, an agent can observe the group opinion in a society. Social learning can result in a variety of equilibrium behavioral patterns. For insufficient ranges of quality (precision) of opinions, the chosen stationary state is unique and globally accessible, in which all agents adopt the superior action. Sufficient quality of opinions gives rise to multiple stationary states. One of them will be characterized by inefficient herding. The confidence in the majority opinion then has serious welfare consequences. © 2003 Elsevier Inc. All rights reserved. JEL classification: D83 Keywords: Herd behavior; Social learning; Opinions; Equilibrium selection 1. Introduction Missing information is ubiquitous in our society. Product alternatives at the store, in catalogs, and on the Internet are seldom fully described, and detailed specifications are often hidden in manuals that are not easily accessible. In fact, which product a person decides to buy will depend on the experience of other purchasers. Learning from others is a central feature of most cognitive and choice activities, through which a group of interacting agents deals with environmental uncertainty. The effect of observing the consumption of others is described as the socialization effect. The pieces of information are processed by agents to update their assessments. Here people may change their preferences as a result of E-mail address: [email protected] (S. Teraji). 1053-5357/$ – see front matter © 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.socec.2003.10.004 662 S. Teraji / Journal of Socio-Economics 32 (2003) 661–673 interpersonal contact. Then information externalities arise that drive towards the emergence of some patterns of influences among individuals.1 Recently there has been increasing interest in economic models in the presence of in- formation externalities, which put a great emphasis on the notion of social learning. In social and economic situations, we are often influenced in our decision making by what others around us are doing.2 Mimetic contagion was thought of as an irrational behavior that is responsible for pathological dynamics such as financial bubbles. Some studies have been seen as a way to formulate rigorously a number of challenges to standard economic doctrine.3 Individual behavior may be governed by herd externality. What everyone else is doing is rational because their decisions may reflect information that they have and we do not. Everyone may do what everyone else is doing, even when his or her private information suggests doing something different. The sort of herding behavior corresponds to human be- havior reported by Becker (1991). When faced with two apparently very similar restaurants on either side of a street, a large majority chose one rather than the other, even though this involved waiting in line. The consequences will indeed be different due to the behavior of other agents in a society.4 An individual’s choice will then depend on his or her degree of confidence in the majority view concerning the state of the world. It is important to observe the self-reinforcing nature of confidence in the group opinion in a society. In this paper, the quality (precision) of opinions, which reflects the confidence in the majority opinion, is a central parameter. Several questions arise regarding the relationship between the quality of opinions and herd externality. Specifically, by comparing situations where each person’s decision is more or less responsive to the majority view, this paper considers how the quality of opinions has an impact on the efficiency of the long-run outcome in the social learning. The social learning model of Banerjee (1992) and Bikhchandani et al. (1992) describes the decision problem faced by a sequence of exogenously ordered individuals each acting under the state of the world.5 An agent conditions the decision in a Bayes-rational fashion on both one’s privately observed information and the ordered history of all predecessors’ decisions. The rest of the population is then allowed to choose sequentially, with each agent observing the choices made by all the predecessors. An information cascade occurs when agents ignore their own information completely and simply take the same action as predecessors have taken. The aggregate information that is available in the population is not correctly revealed by the sequence of decisions. This may eventually lead the whole 1 This terminology may be a close parallel to what Leibenstein (1950) called the “bandwagon effect” and “snob effect” in his classic study on the static market demand curve. By the bandwagon (snob) effect he referred to the extent to which the demand for a commodity is increased (decreased) because others are consuming the same commodity. 2 Note that the decision may not be optimal from the social point of view since the individual does not take account of the effect of his or her decision on the information of others. 3 See, for example, the analysis of ‘rumours’ in Banerjee (1993) and ‘fashions’ in Karni and Schmeidler (1990). 4 See also Kirman (1993) for an explanation of asymmetric aggregate behavior arising from the interaction between identical individuals. 5 Anderson and Holt (1997) induce the emergence of information cascades in a laboratory setting. Their re- sults seem to support the hypothesis that agents tend to decide by combining their private information with the information conveyed by the previous choices made by other agents, in conformity with Bayesian updating of beliefs. S. Teraji / Journal of Socio-Economics 32 (2003) 661–673 663 population to take the wrong decision, and therefore to a socially inefficient outcome. However, the formation of a cascade is strongly influenced by the initial decisions. Orléan (1995) considers the dynamics of imitative decision processes in non-sequential contexts where agents are interacting simultaneously and modifying their decisions at each period in time. Such a framework is better suited for the modeling of herd behavior. In many circumstances, agents are always present and they revise their opinions in a continuous mode, not one for all. In this setting, opinions are modified endogenously as a result of interaction between agents. He describes the herd behavior as corresponding to the stationary distribution of a stochastic process rather than to switching between multiple equilibria. In this paper, to offer a clear justification for possible equilibrium patterns, I provide an explanation for switches from one to the other in the social learning dynamics.6 It is worth to offer an equilibrium selection criterion of how a particular equilibrium will emerge collectively in a non-sequential context. In this paper, I consider a choice between two competing alternatives with unequal pay- offs, and show how individuals are likely to herd onto a single choice. I specify a sim- ple model for boundedly rational choice given the information conveyed by the majority opinion. I consider the society consisting of a continuum of agents each of whom are Bayesian optimizers. They must make a short-run commitment to the action they chose. Opportunities to switch actions arrive at random, which are identical and independent across agents.7 This friction reflects uncertainty that leads to inertia. Following this in- terpretation, no agent can change his or her choice at every point in time because of the inability to make an assessment of the current configuration of opinions continuously. It seems to capture a certain aspect of boundedly rational behavior. The social dynam- ics generate equilibrium paths of behavioral patterns in the presence of herd externality. In some situation, the stability properties of stationary states depend not on the initial decisions, but rather on the degree of quality of opinions defined below. What may be surprising is that the two stationary states, corresponding to the two long-run configu- rations of opinions, possess different stability properties when we change the quality of opinions. I show that sufficient quality of opinions tends to yield inefficient herding in the long-run. A key element is the multiplicity of equilibrium paths of behavioral patterns.8 Then one has to determine which equilibrium actually gets established. The emphasis on the quality of opinions also distinguishes my work from other explanations of equilibrium selection in economic problems (e.g. Keynesian macroeconomics in Cooper and John, 1988 and 6 Akerlof (1980) says that there are multiple equilibria in the sense that different customs, once established, could be followed in equilibrium. In one of these equilibria a custom is obeyed, and the values underlying the custom are widely subscribed to by members of the community. In the other equilibrium, the custom has disappeared, no one believes in the values underlying it, and it is not obeyed. 7 The equilibrium dynamics of this kind is used in Matsuyama (1992). However, the interpretation attached to this dynamics here is quite different. 8 The fundamental argument in the path dependency literature (David, 1985; Arthur, 1989) is that the free market typically generates sub-optimal equilibrium solutions to a variety of economic problems and the probability of sub-optimal equilibrium outcomes increases where increasing returns prevail. It is even possible for efficient and inefficient (sub-optimal) solutions to prevail simultaneously in the world of path dependency. For this reason, one cannot expect the free market to force the economy to converge to unique equilibrium. 664 S. Teraji / Journal of Socio-Economics 32 (2003) 661–673 economic development in Murphy et al., 1989; Matsuyama, 1992).9 The literature offers very few formal approaches to the process through which interacting agents’ beliefs are formed.