The Virtues of Hesitation‡

In many economic, political and social situations, circumstances change at random points in time, reacting is costly, and changes appropriate to present circumstances may be inappropriate after later changes, requiring further costly change. Waiting is informative if the hazard rate for the arrival of the next change is non-constant. In a broad range of contexts we show that hesitation or delayed reaction is often optimal when the hazard rate is decreasing, and that it might be optimal never to change at times when the hazard rate is increasing. The first result corresponds to having waited long enough to know that future changes in circumstances are comfortably in the future, the second corresponds to the counsel of patience in unsettled circumstances. These results provide a new set of motivations for building delay into legislative and other decision systems. These results in non-stationary dynamic optimization arise from extensions to semi-Markovian decision theory.