Policy Advice with Imperfectly Informed Experts
Advances in Theoretical Economics
We study policy advice by several experts with noisy private information and biased preferences. We highlight a trade-off between the truthfulness of the information revealed by each expert and the number of signals from different experts that can be aggregated to reduce noise. Contrary to models with perfectly informed experts, because of this trade-off, full revelation of information is never possible. However, almost fully efficient information extraction can be obtained in two cases. First,
... n two cases. First, there is an equilibrium in which the outcome converges to the first best benchmark with no asymmetric information as we increase the precision the experts' signals. Second, the inefficiency in communication also converges to zero as the number of experts increases, even when the residual noise in the experts' private signals is large and all the experts have significant and similar (but not necessarily identical) biases. JEL Classification: D72, D78, D82. . These results are also insightful to understand the optimal organization of jurisdictions in committees or other organizations: in the equilibrium that achieves full information revelation (as the number of experts increases), experts necessarily report on overlapping jurisdictions. This feature is well documented in the empirical literature on legislative organizations. Besides this, there is another reason why it is important to study noisy communication. When there are many experts and they all observe the same signal, there may be situations in which the posterior beliefs of the policy maker are not defined: for example, in a fully revealing equilibrium, it would be impossible that two experts report two different observations. This leaves some arbitrariness in the construction of the equilibria because some of them can be constructed with ad hoc out-of-equilibrium beliefs. Battaglini  and Krehbiel  have recently criticized these constructions on the grounds of the "plausibility" of out-of-equilibrium beliefs. In our model with imperfect signals, out-of-equilibrium beliefs never arise and therefore equilibria are robust to this criticism. The paper is organized as follows. In Section 2 we present the model. Section 3 proves that it is impossible to achieve full revelation in equilibrium, for any finite number of experts and with any dimensionality of the environment. In Section 4.1 we explore the case in which only two experts can be consulted and we show that as the experts' residual noise is decreased, the inefficiency in communication converges to zero. In Section 4.2, we consider the case with n > 2 experts. Section 4.3 discusses when it is optimal to delegate the policy choice and the robustness of the equilibria to beliefs specification. Section 5 concludes. In the remainder of this section we discuss some related literature. Related literature A vast literature has recently built on the seminal paper by Crawford and Sobel  to study how communication by privately informed agents can affect policy making. 1 Gilligan and Krehbiel  study a model in which privately informed committees report in front of the floor before a decision is taken by majority rule and study the effect on information transmission of different institutional arrangements: in particular they compare a "closed rule" in which the floor delegates the decision to a committee to an "open rule" in which the committees can only make a report. This model has started a literature characterized by two assumptions: first, the policy space is unidimensional; secondly the experts are perfectly informed on the state of the world. Krishna and Morgan  have recently completed the analysis of this framework providing a careful characterization of the possible equilibria. 2 Austen -Smith [1990a] is the first to study the case of imperfectly informed experts. This approach is used in Austen-Smith [1990b , 1993b to analyze the case of multiple referrals under an open rule decision procedure, comparing the informative properties of the equilibria with either joint or sequential referrals. As in previous literature, these papers continue to assume a unidimensional environment. Different from our work, however, these papers do not focus on the size of the inefficiency and do not present results under which the policy maker can achieve full information extraction. Wolinsky  considers a related problem in which there are more than two biased experts with noisy signals. He is interested in the optimal organization of communication procedures. In a model with binary information and binary policy space, he shows that allowing partial communication among the experts might induce more information revelation. An alternative model with imperfectly informed experts is developed by Ottaviani and Sorensen . Contrary to our approach and from the papers cited above, they study the case in which the state can be verified ex post, and therefore they focus on situations in which experts' compensation does not depend on the policy choice but, because of reputation effects or particular incentive schemes, only on the accuracy of their signals. All of these papers, therefore, do not consider the trade-off between information aggregation and information extraction that we wish to highlight and study in this work. 3 The study of multidimensional models of cheap talk is introduced by Austen-Smith [1993a] and Battaglini . The first paper attempts to combine noisy signals with a multidimensional environment in a model in which experts receive a finite number of imperfect signals. The author extends the model introduced by Austen-Smith [1990a] to the case in which the policy space is two dimensional. In this environment, he provides conditions that guarantee some information transmission and studies the experts' incentives to acquire information.