Optimal Short-Termism

This paper develops a dynamic contracting (multitasking) model of a levered firm. In particular, the manager selects long-term and short-term efforts, and shareholders choose optimal debt and default policies. Excessive short-termism ex post is optimal for shareholders because debt has an asymmetric effect: shareholders receive all gains from short-term effort but share gains from long-term effort. We find that grim growth prospects and shareholder impatience imply higher optimal levels of short-termism. Also, an incentive cost effect and a real option effect create nontrivial patterns for the endogenous default threshold. Finally, we quantify agency costs of excessive short-termism, which underscore the economic significance of our results. This paper was accepted by Gustavo Manso, finance.

Dynamic contracting with limited commitment and the ratchet effect

We study dynamic contracting with adverse selection and limited commitment. A firm (the principal) and a worker (the agent) interact for potentially infinitely many periods. The worker is privately informed about his productivity and the firm can only commit to short‐term contracts. The ratchet effect is in place since the firm has the incentive to change the terms of trade and offer more demanding contracts when it learns that the worker is highly productive. As the parties become arbitrarily patient, the equilibrium outcome takes one of two forms. If the prior probability of the worker being productive is low, the firm offers a pooling contract and no information is ever revealed. In contrast, if this prior probability is high, the firm fires the unproductive worker at the beginning of the relationship.

Dynamic Contracting under Positive Commitment

We consider a firm that sells products that arrive over time to a buyer. We study this problem under a notion we call positive commitment, where the seller is allowed to make binding positive promises to the buyer about items arriving in the future, but is not allowed to commit not to make further offers to the buyer in the future. We model this problem as a dynamic game where the seller chooses a mechanism at each period subject to a sequential rationality constraint, and characterize the perfect Bayesian equilibrium of this dynamic game. We prove the equilibrium is efficient and that the seller’s revenue is a function of the buyer’s ex ante utility under a no commitment model. In particular, all goods are sold in advance to the buyer at what we call the positive commitment price.

Recursive Contracts

We obtain a recursive formulation for a general class of optimization problems with forward‐looking constraints which often arise in economic dynamic models, for example, in contracting problems with incentive constraints or in models of optimal policy. In this case, the solution does not satisfy the Bellman equation. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle‐point functional equation (analogous to a Bellman equation) that characterizes a recursive solution to the planner's problem. The recursive formulation is obtained after adding a co‐state variable μ t summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with μ t playing the role of weights in the objective function. Our approach is applicable to characterizing and computing solutions to a large class of dynamic contracting problems.

Optimal dynamic contracting: The first‐order approach and beyond

We explore the conditions under which the “first‐order approach” (FO approach) can be used to characterize profit maximizing contracts in dynamic principal–agent models. The FO approach works when the resulting FO‐optimal contract satisfies a particularly strong form of monotonicity in types, a condition that is satisfied in most of the solved examples studied in the literature. The main result of our paper is to show that except for nongeneric choices of the stochastic process governing the types' evolution, monotonicity and, more generally, incentive compatibility are necessarily violated by the FO‐optimal contract if the frequency of interactions is sufficiently high (or, equivalently, if the discount factor, time horizon, and persistence in types are sufficiently large). This suggests that the applicability of the FO approach is problematic in environments in which expected continuation values are important relative to per period payoffs. We also present conditions under which a class of incentive compatible contracts that can be easily characterized is approximately optimal.