Informational Herding and Optimal Experimentation

We explore the constrained efficient observational learning model — as when individuals care about successors, or are so induced by an informationallyconstrained social planner. We find that when the herding externality is correctly internalized in this fashion, incorrect herds still obtain. To describe behaviour in this model, we exhibit a set of indices that capture the privately estimated social value of every action. The optimal decision rule is simply: Choose the action with the highest index. While they have the flavour of Gittins indices, they also incorporate the potential to signal to successors. We then apply these indices to establish a key comparative static, that the set of stationary ‘cascade’ beliefs strictly shrinks as the planner grows more patient. We also show how these indices yield a set of history-dependent transfer payments that decentralize the constrained social optimum. The lead inspiration for the paper is our proof that informational herding is but a special case of myopic single person experimentation. In other words, the incorrect herding outcome is not a new phenomenon, but rather just the familiar failure of complete learning in an optimal experimentation problem. ∗A briefer paper without the index rules and associated results appeared under the title “Informational Herding as Experimentation Déjà Vu.” Still earlier, the proposed mapping appeared in July 1995 as a later section in our companion paper, “Pathological Outcomes of Observational Learning.” We thank Abhijit Banerjee, Meg Meyer, Christopher Wallace, and seminar participants at the MIT theory lunch, the Stockholm School of Economics, the Stony Brook Summer Festival on Game Theory (1996), Copenhagen University, and the 1997 European Winter Meeting of the Econometric Society (Lisbon) for comments on various versions. Smith gratefully acknowledges financial support for this work from NSF grants SBR9422988 and SBR-9711885, and Sørensen equally thanks the Danish Social Sciences Research Council. †e-mail address: [email protected] ‡e-mail address: [email protected]