Policy Commitments in Relational Contracts
with Dan Barron
Business relationships often rest upon parties' goodwill rather than the contracts they sign--fear of destroying future surplus can motivate individuals both to perform well and to reward strong performance by their partners. In the canonical relational-incentive contracting models that capture this intuition (Bull, 1987; MacLeod and Malcomson, 1988; Levin, 2003), the principal's only role is to promise and pay monetary compensation to her agents. She is otherwise entirely passive.
Yet in any real-world enterprise, managers make a host of decisions that affect how a group of individuals contribute to the firm's objectives. Supervisors assign tasks to team members. Supply-chain managers source from suppliers. Executives allocate capital to divisions. Human-resource managers hire and fire employees. These decisions make certain individuals more integral and others less integral to the firm. And these decisions are often made on the basis of past performance, even when doing so harms future prospects. Supervisors bias promotions, CFOs bias capital allocations, and supply-chain managers bias future business toward those who saw past success (Peter and Hull, 1969; Graham, Harvey, and Puri, 2013; Asanuma, 1989). If the firm can compensate employees with monetary bonuses, then in principle it should be able to reward past successes without inefficiently tainting future decisions. Why, then, are biased decisions such a widespread feature in organizations?
In this paper, we argue that backward-looking policies can arise in optimally managed relationships among a principal and her agents. To make this point, we develop a general framework that builds upon Levin (2003)'s repeated principal-agent model with moral hazard, transferable utility, and risk-neutral parties. We extend Levin's framework to accommodate persistent public states and multiple agents. In addition, the key feature of our model is that the principal can make a public decision in each period that influences how agents' choices affect the firm's output. A policy is a complete plan of such decisions. A policy is backward-looking if it does not maximize total continuation surplus at each history. At histories where total continuation surplus is not maximized, we say that the corresponding decision is biased.
We first show that backward-looking policies never arise if relationships are public--that is, if all players commonly observe the history of past play. In this setting, the agents can coordinate to jointly punish the principal if she does not uphold her promises. In effect, the future surplus produced by all of the agents is at stake in each relationship. Biased decisions decrease continuation surplus and weaken the principal's incentives to uphold her promises, and therefore have no place in an optimal relationship. The principal "settles up" with her agents at the end of each period, while future decisions are made to maximize continuation surplus.
In contrast, backward-looking policies arise naturally if relationships are bilateral--that is, if each agent cannot observe the actions of other agents. In this setting, players cannot coordinate punishments or rewards. A decision that makes an agent more integral to the principal ensures that the principal and that agent have more to lose if they do not uphold their promises to one another. Future decisions biased toward an individual therefore complement more generous reward schemes for that individual but also negatively affect the firm's overall future performance.
As an example of how backward-looking policies might optimally emerge, consider hiring decisions made by the owner of an up and coming business. Achieving early success requires sacrifice from early employees, and motivating this sacrifice requires the owner to promise rewards of either compensation or future goodwill. But these promises are only credible if maintaining relationships with early employees is important for the business. One way to ensure that early employees remain valued is for the owner to adopt a policy of being slow to hire following an increase in demand for the firm's products, which would make existing workers relatively more indispensable for the firm. Such a policy is not without costs, as orders may go unfulfilled, but these costs may be worth incurring in order to establish cooperative behavior early on. We explore this example in more detail in the next section.
To formally argue that backward-looking policies arise in optimal relational contracts, we have to define a self-enforcing relational contract in a game with imperfect private monitoring. We consider belief-free equilibrium (BFE) of the dynamic game. This solution concept provides a tractable approach that highlights why backward-looking policies arise.
We develop a set of straightforward necessary and sufficient conditions for a policy to be part of a self-enforcing relational contract. Using these conditions, we first consider a broad class of smooth repeated games and show that backward-looking policies are typically part of optimal relational contracts. Indeed, unless players are very patient or very impatient, decisions are biased with positive probability in nearly every period.
Finally, we explore several examples and show that backward-looking policies can arise in non-stationary, non-smooth environments. Revisiting the hiring example, we confirm that additional hiring may optimally lag an increase in demand. We also argue that a firm might delay employee-specific investments and bias those investments towards workers who performed well in the past. And we show that a firm might inefficiently stick with an employee after learning that he is worse than the alternatives. The inefficiencies that arise in these examples are of potential independent interest.