Only Time Will Tell: A Theory of Deferred Compensation

Abstract

This paper characterizes optimal compensation contracts in principal-agent settings where the consequences of the agent’s action are only observed over time. The optimal timing of pay trades-off the costs of deferred compensation arising from the agent’s relative impatience and potential consumption smoothing needs against the benefit of exploiting additional informative signals. By capturing this information benefit of deferral in terms of the likelihood ratio dynamics, our characterization covers general signal processes in a unified setting. With bilateral risk neutrality and agent limited liability, optimal contracts are high-powered and stipulate at most two payout dates. If the agent is additionally risk-averse, payouts are contingent on performance exceeding a hurdle that is increasing over time. We obtain clear-cut predictions on how the duration of optimal compensation depends on the nature of information arrival as well as agent characteristics and derive implications for the maturity structure of securities in financial contracting settings.

The Economics of Deferral and Clawback Requirements

“…Since (1) further implies that ∂ log S(t|a) ∂a is a strictly increasing function of t, histories involving a failure at some s < t also have a lower score than date-t survival. Hence, making incentive pay contingent on survival provides the strongest incentives per unit of expected pay at each given t. Having established that in our setting, the survival history has the highest score, the remaining parts of the proof simply adapt the key ideas of the proof of Theorem 1 in Hoffmann, Inderst, and Opp (2021) to our specific setting.…”

“…We next characterize the optimal timing of pay without the regulatory constraint (DEF). The proof is adapted from Hoffmann, Inderst, and Opp (2021) (see in particular the proof of their Theorem 1 as well as Theorem B.1 in their Internet Appendix). For notational convenience, we subsume the unconditional upfront payment w (which is equivalent to a survivalcontingent date-0 bonus since S(0|a) = 1) into the bonus process b t .…”

“…Without either of these ingredients, it would always be weakly optimal to wait until all information is revealed (the end of time). For tractability reasons, we favored the assumption of relative impatience, as introducing agent risk aversion in our setting would imply that optimal contracts stipulate payments for a larger set of states and times (see Propositions 2 and 3 in Hoffmann, Inderst, and Opp (2021)) rather than a single payout time and state (survival). However, this additional richness in optimal unconstrained contracts produces no new economic insights regarding the qualitative effects of deferral regulation on the equilibrium action choice, which is the focus of this paper.…”

“…Finally, our paper builds on recently developed technical tools that permit a tractable characterization of optimal compensation design in principal-agent models with persistent effects (see Hoffmann, Inderst, and Opp (2021)). The particular modeling of a (potentially rare) negative event is shared with Biais et al (2010) and notably Hartman-Glaser, Piskorski, and Tchistyi (2012) as well as Malamud, Rui, and Whinston (2013).…”

“…This is without loss of generality if (PC) is slack, in which case unregulated optimal contracts always feature a single payout date, while maximally two payout dates are optimal when (PC) binds (seeHoffmann, Inderst, and Opp (2021)). Importantly, Lemma 1 applies in all cases.18 See, for example,Innes (1990) and, for the formal argument in our setting, the proof of Lemma A.1.…”