Control, cost, and confidence: Perseverance and procrastination in the face of failure

We study effort provision and the development of the belief that effort matters over time: a student is uncertain whether she has control over success through her effort or whether success is determined by her innate ability, which she also does not know. In each period, what she can learn about her control and her ability depends on the level of effort she exerts. The student's optimal effort policy in this two-dimensional bandit problem takes the form of a linear belief cutoff rule and typically features repeated switching of the effort level. Moreover, we define perseverance and procrastination as indices for the student's behavior over time and analyze how they are affected by control, cost, and confidence. Finally, we relate our results to findings in educational psychology and discuss policies to foster perseverance and to lower procrastination.