This paper is an adaptation of the Chamley-Gale endogenous-timing information-revelation model of investment (Econometrica 1994). It models a game with pure informational externality where agents can learn by observing others' actions. The social learning can result in herding and possibly in an inefficient cascade. While Chamley and Gale characterize the equilibrium of such a game, this paper permits the derivation of comparative static results of the likelihood of inefficient cascades. This is useful for two reasons: First, the derivation of comparative static results in a model with endogenous timing provides a framework that may be useful in the analysis of a wide variety of applied issues. It is often argued that information cascades may help to explain a wide variety of economic issues including business cycles, bank runs, speculative attacks and IPO underpricing among others. However, it has proven difficult to move beyond the demonstration that herding may help explain these phenomena to analyze the welfare implications and policy tools available to decrease the likelihood of inefficient herding in these markets. This paper develops a framework that may be useful in providing a first pass in the analysis of these issues. Secondly, the analysis allows a deeper understanding of the relationship between exogenous and endogenous timing herding models. With endogenous timing the discount rate plays an important role in the determination of the probability of an inefficient cascade. This paper shows that as agents become more patient the probability of an inefficient negative cascade goes up. The relevant time for this discounting is the time to react to the decisions of others. Hence financial markets where agents can react quickly to the observed actions of others are likely to have relatively more inefficient negative cascades (inefficient collapses) than in real investment markets where agents observe and react to the actions of others with a longer delay
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