Wald Revisited: The Optimal Level of Experimentation

This paper revisits Wald's (1947) sequential experimentation paradigm, now assuming that an impatient decision maker can run variable-size experiments each period at some increasing and strictly convex cost before finally choosing an irreversible action. We translate this natural discrete time experimentation story into a tractable control of variance for a continuous time diffusion. Here we robustly characterize the optimal experimentation level: It is rising in the confidence about the project outcome, and for not very convex cost functions, the random process of experimentation levels has a positive drift over time. We also explore several parametric shifts unique to our framework. Among them, we discover what is arguably an 'anti-folk' result: Where the experimentation level is positive, it is often higher for a more impatient decision maker. This paper more generally suggests that a long-sought economic paradigm that delivers a sensible law of demand for information is our dynamic one namely, allowing the decision maker an eternal repurchase (resample) option.