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Article Excerpt
Summary. We consider a set-up in which firms sequentially adopt a technology. The technology is a public good. Late movers, upon observing the early movers adopting the old technology, (partly) infer that the new technology does not exist. This hampers their incentives to innovate. Early movers anticipate this and rather exert effort to try to invent the new technology. Hence, in our model herding reduces free-rider problems and may--in the presence of switching costs--even increase efficiency.
Keywords and Phrases: Free-rider problem, Public good, Information externality, Herd behaviour, Social learning.
JEL Classification Numbers: D83, D82, D62.
1 Introduction
People often infer information from the actions of others. For example, consumers often choose the most popular brand because they believe that its popularity indicates a better price/quality ratio (1). People do not go and eat in an empty restaurant, because they believe that the food quality is low.
In two well-known papers, Banerjee [2] and Bikhchandani, Hirshleifer and Welch [3] (henceforth BHW) showed how these information externalities cause herding: a behaviour where one person after observing the action(s) of his/her predecessor(s), and after updating his/her prior beliefs, has more incentives to imitate his/her predecessor(s). More interestingly, both papers argued that herding may cause a "bad outcome", i.e. an outcome where all (or the vast majority) of players adopt an action which ex post turns out to be suboptimal. Other economists have argued that herding may also cause short-run price bubbles (Avery and Zemsky [1]), slow learning (Vives [11]), inefficient trade in markets with sequential bids (Neeman and Orosel [8]), inefficient drilling decisions in the oil exploration industry (Hendricks and Kovenock [7]), inefficient investment decisions (Chamley and Gale [6], Chamley [5]),.... In this paper we add a public good in a variant of the standard herding models and we argue that herding, by reducing free-rider problems, also possesses some efficiency-increasing properties.
We study the following set-up. A fixed number of firms enter sequentially in an emerging market. Upon entrance, their managers must adopt a technology. Each manager can adopt an "old" technology without exerting effort. Managers can also choose to exert effort to try to invent a new (and more profitable) technology. Following Banerjee [2] and BHW [3] we work under an "exogenous queue" assumption: managers only choose their effort level at their time of entry. The new technology is a public good: if a manager invents it, all his predecessors and subsequent movers can freely copy it and enjoy a higher payoff. Managers act strategically in the sense that they all may exert no effort and adopt the old technology in the hope to free-ride on the effort of another manager who will invent the new technology. If a manager switches from the old to the new technology, he incurs a switching cost. Hence, to save on switching costs, efficiency requires the first manager to exert effort. The problem is that manager one knows that many other managers (= future free-ride opportunities) will enter the market after him. Hence, intuition suggests that in equilibrium manager one will probably not exert effort.
We first show that this intuition is correct if all players observe their predecessors' effort levels and technologies (2). However, we next show that this intuition fails to go through if all managers only observe their predecessors' technologies (and not their effort levels). To understand this result, consider the following two-manager example. Assume manager two observes manager one adopting the old technology. Depending on manager two's beliefs (concerning manager one's effort level), he may infer the nonexistence of the new technology out of the first manager's action. This hampers manager two's incentives to innovate (i.e. manager two herds on manager one's technology (3)). Manager one correctly anticipates that manager two is going to "blindly imitate" his technology, and, thus, that he will not be able to free-ride on manager two's effort level. Therefore, it's optimal for him to exert effort which implies that the new technology may be invented at time one (which is the most efficient outcome).
The central result of this paper can be divided in two "sub-insights": (i) herding induces early effort provision and (ii) this may increase efficiency. We next explain why no paper in the herding literature contains both sub-insights.
In Hendricks and Kovenock [7] two oil firms possess a private imperfect signal concerning the profitability of drilling an exploratory oil well. If one firm drills, then the other firm costlessly observes whether there is oil or not and (in case of success) makes a riskless investment decision in the next period. Their paper is closely related to ours in the sense that their model also features: (i) strategic waiting (firms do not drill at time one in the hope that the other firm will do so), (ii) information externalities (if Firm One does not drill at time one, this negatively influences Firm Two's time-two posterior) and (iii) a public good (if Firm One drills, Firm Two also observes whether there is oil or not). The authors characterise the set of Bayesian equilibria and explain why information externalities may induce both firms to let their leases expire without drilling any wells. In their model, players do not care about each others' second-period posteriors because--by assumption--players cannot free-ride on time-two drilling decisions. Hence, their model does not possess the insight that future herding (or the downward revision of time-two posteriors) positively influences time-one incentives to drill.
Chamley (4) [5] analyses a set-up in which players can invest in two periods. Prior to the second-period investment decision, everyone observes how many players invested at time one. Chamley shows that his waiting game may be characterised by the following equilibrium: assume everyone anticipates that all players (optimists as well as pessimists) invest at time one. By definition, this represents an informational cascade: all players--irrespective of their types--undertake the same action at time one. Given this anticipation, no player wants to delay her investment action because by doing so she only faces a discounting cost without receiving any informational gain. Therefore, if players anticipate an informational cascade, this adversely affects their gain of waiting and increases their incentives to invest at time one. This "incentive-mechanism" is similar to the one operating in this paper: future herding reduces a manager's gain of not exerting effort, thereby increasing his incentives to exert effort. A similar mechanism is also at work in Zhang [12]. Both papers thus contain sub-insight (i). However, in the next paragraph we explain why those papers do not contain sub-insight (ii).
We proved the main insight of our paper by comparing equilibrium outcomes in the herding and the non-herding environment with the efficiency benchmark. Hence, to check whether sub-insight (ii) is present in Chamley [5] and Zhang [12], we must provide an answer to the following questions: "What is the non-herding environment in Chamley [5] and Zhang [12]?", "Which equilibrium outcome do we then get?" and "How does this equilibrium outcome compare (in terms of efficiency) to the one originally described in Chamley [5] and Zhang [12]?" In Chamley [5] and Zhang [12] the non-herding environment corresponds to the observable actions and observable signals case. This is intuitive: in the observable signals case, all players would assign the same probability to the event that the state of the world is good (say, probability p). In that case, whether player i invests or not does not affect posterior beliefs. Hence, this environment is void of any information externality. In the observable signals case, it is optimal to invest at time one if p is bigger than the investment cost (5). Note that this is also the ex ante most efficient outcome! Thus in our model the equilibrium outcome in the herding environment may be better (for efficiency) than the one in the non-herding environment, while this is not the case in Chamley [5] and Zhang [12]. Hence, sub-insight (ii) is not present in the latter papers. The reason therefore is that the non-herding environment in Chamley [5] and Zhang [12] is not plagued by a public good problem.
This paper is organised as follows. The basic assumptions of our model are explained in Section 2. In Section 3 we introduce a social planner in our model and compute the most efficient strategy profile. We then analyse the workings of our model under the assumption of observable effort levels and observable technologies (Sect. 4). In Section 5 we work under the assumption that players do not observe one another's effort levels. First we illustrate how herding may increase efficiency by focusing on a simple equilibrium in which...
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