Optimal Job Design and Career Dynamics in the Presence of Uncertainty

This paper investigates a learning model in which information about a worker's ability, unobserved to both the worker and the firm, can be acquired in any period by both parties by observing the worker's performance at a given task. Tasks are differentially informative about productivity: more profitable tasks generate noisier signals of a worker's ability. We characterize the (essentially unique) optimal retention, task assignment and promotion policy for the class of sequential equilibria of this game, by showing that the equilibria of interest are strategically equivalent to the solution of an experimentation problem, a discounted multi-armed bandit with independent and dependent arms. These equilibria are all ex ante efficient but involve ex post inefficient task allocation and separation. In particular, a firm benefits from assigning jobs at which a worker has a comparative disadvantage early in his career, in order to improve on the accuracy of the inference process about ability. While eventually a retained worker can only be assigned the most profitable task, the ex post inefficiency of separations persists even as the time horizon becomes arbitrarily large. In addition, when the ability endowment consists of multiple skills and ability is task specific, low performing promoted workers are fired rather than demoted, if a higher level job, compared to a lower level job, provides a less precise measure of the specific dimension of ability it requires. We then examine the strategic effects of the dynamics of learning on a worker's career profile. We prove that price competition among firms does not alter the ex ante efficiency of turnover and of each firm's assignment strategies, independently of the degree of transferability of human capital. Finally, we show that our results are consistent with stylized properties of hierarchies and promotion systems inside firms