Repeated moral hazard with effort persistence

Abstract

I study a problem of repeated moral hazard in which the effect of effort is persistent over time: each period's outcome distribution is a function of a geometrically distributed lag of past efforts. I show that when the utility of the agent is linear in effort, a simple rearrangement of terms in his lifetime utility translates this problem into a related standard repeated moral hazard. The solutions for consumption in the two problems are observationally equivalent, implying that the main properties of the optimal contract remain unchanged with persistence. To illustrate, I present the computed solution of an example.

Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach

“…The envelope condition (13) shows that everything except for the continuation utility and the marginal continuation utility is irrelevant for determining whether an allocation rule is incentive compatible. This suggests that everything else may be also irrelevant for the recursive formulation itself.…”

“…shocks, agents with high cur- 2 The first order approach employed in this paper has also been recently used in related dynamic environments. Werning [20] and Abraham and Pavoni [1] use it to study dynamic hidden savings problem while Jarque [13] uses it to analyze moral hazard environment with effort persistence.…”

“…13 Because the price of consumption is constant, the efficient modified allocation rule will be time independent. I will therefore drop the time subscript and denote next period with prime.…”

Optimal Capital Taxation for Time-Nonseparable Preferences

“…The present paper is also related to the dynamic contracting literature on effort persistence, which studies private information problems with a production technology that is timenonseparable; see Mukoyama and Sahin (2005), Kwon (2006), Jarque (2010), and Hopenhayn and Jarque (2010). In contrast to the present model, the Inverse Euler equation remains valid in that framework.…”

Only Time Will Tell: A Theory of Deferred Compensation

“…As is well known, in repeated-action settings the timing of pay may play an important role even when actions are immediately and perfectly observed (cf., Ray (2002)): In this literature, backloading of rewards to the agent has the benefit that it incentivizes both current as well as future actions. Work by Jarque (2010), Sannikov (2014), or Zhu (2017 combines the effects of repeated actions and persistence. The additional complexity, however, requires special assumptions on the signal process.…”