Learning to Wait: A Laboratory Investigation

Abstract

An irreversible investment opportunity has value V governed by Brownian motion with upward drift and random expiration. Human subjects choose in continuous time when to invest. If she invests before expiration, the subject receives V C: the final value V less a given avoidable cost C. The optimal policy is to invest when V first crosses a threshold V = (1 w )C , where the option premium w is a specific function of the Brownian parameters representing drift, volatility and discount (or expiration hazard) rate. We ran 80 periods each for 69 subjects. Subjects in the Low w treatment on average invested at values quite close to optimum. Subjects in the two Medium and the High w treatments invested at values below optimum, but with the predicted ordering, and values approached the optimum by the last block of 20 periods. Behavior was most heterogeneous in the High treatment. Subjects underrespond to differences in both the volatility and expiration hazard parameters. A directional learning model suggests that subjects react reliably to ex-post losses due to early investment, but react more strongly to missed investment opportunities. Simulations show that this unbalanced learning process converges on a nearly optimal steady state.