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Relative performance evaluation in a multi-plant firm.

Article Excerpt
Summary. We analyze optimal compensation schedules for the directors of two plants belonging to the same owner and producing the same good but serving geographically differentiated markets. Since the outcome of each director depends on his own effort and on a random variable representing market conditions, the problem takes the form of a principal multi-agent model. We first provide appropriate extensions of the MLR and CDF conditions that ensure the validity of the first-order approach in the single agent case. Then, we show that affiliation of the random variables is a necessary and sufficient condition for the compensation of one director to negatively and monotonically depend on the performance of the other.

Keywords and Phrases: Principal-agent problems, Relative performance evaluation, First-order approach, Monotone likelihood ratio, Affiliation.

JEL Classification Numbers: D23, D82.

1 Introduction

Relative performance evaluation (RPE) is a common practice in organizations. Comparisons among the performances of different agents who are assigned to similar tasks are sometimes explicitly contained in labor contracts. Sellers' compensations usually depend on the level of sales relative to the achievements of other sellers; CEOs compensations may contain a bonus based on a comparison with competitors' returns. In other cases, even in the absence of explicit contract clauses, compensations implicitly depend on the results of peers working in similar conditions. Informal comparisons among workers are crucial both when firms set internal performance standards and when hierarchical superiors evaluate their subordinates.

Agency theory (Holmstrom, 1982; Mookherjee, 1984) has provided a rationale for these practices in terms of their informational content. When agents' outcomes are subject to a common element of uncertainty, the output of each individual acts both as a signal of his own performance and as a signal of the realizations of the common uncertain parameter. As a consequence, comparisons of agents' performances are valuable because they bring additional pieces of information to the system. This has important consequences also for the design of both jobs and accounting systems. Duplication of tasks or job rotation may be of value to the firm as well as the definition of comparable profit/cost centers precisely because they allow relative evaluation.

Here we consider a firm producing a single good in two plants located in geographically different areas. Each plant faces identical costs but serves a different market whose stochastic demand is positively related to that of the other market. Such a positive relation might represent common macro factors that add to idiosyncratic demand components. These market conditions are reflected in stochastic and positively dependent returns to the (unobservable) effort of each plant's director. We investigate the form of the compensation schedules that the owner of the firm (the principal) should offer to directors (the agents) in order to motivate them to exert the optimal level of effort. Given that returns are stochastically dependent, we expect that optimal compensation schedules will be interdependent. In particular we want to investigate the sign of such interdependence and to determine conditions that ensure monotonically negative relation between the compensation of one director and the performance of his colleague.

Although the informational relevance of relative performance evaluation has been stressed in the literature (1), the model with one principal and many agents has not been completely characterized. First of all, the applicability of the first-order approach (i.e. of the procedure that substitutes incentive compatibility constraints with their first-order conditions) has not been investigated. Extensions of the monotone likelihood (MLR) and of the convexity of the distribution function (CDF) conditions that ensure the validity of the first-order approach in the single agent case (Mirrlees, 1979; Rogerson, 1985) have only been established for the general multi-signal case (Sinclair-Desgagne, 1994). Our multi-agent model can be considered part of the class of...

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