Discussion of "Optimal employmentcontracts and the retums to monitoring

in a principal-agent context"*

PETER CHENG Purdue University

IntroductionBaiman, May, and Mukherji [1990] (BMM) study a principal-agent model inwhich the agent is endowed with predecision private infonnation about the statespace. After learning the prevailing state of nature, the agent can quit beforetaking any productive action. The basic model is similar to Sappington (1983),Demski and Sappington (1984), and Demski, Sappington and Spiller (1988).An additional feature of the BMM model is that the principal has access toa costless perfect/imperfect monitoring system that confirms the agent's reporton his private infonnation with a probability 1 — z of making a type II error.The focus of BMM is the relationship of the optimal incentive contract withthe monitoring system, namely, what are the incremental benefits to both theprincipal and the agent as the parameters of the monitoring system vary?

There have been quite a few monitoring papers in the literature under variousinfonnation structures (for example, Holmstrom, 1979 and 1982; Townsend,1979) and applications in variance investigation models (for example, Baimanand Demski, 1980). Indeed, in the variance investigation models in which theoptimal contract and the monitoring system are both endogenously determined, amore difficult problem has been addressed. BMM retum to the basic monitoringmodel adding further insights to the existing results.

Economic implications of the modelThe agent's ability to quit after privately observing the random productive stateallows the model to include moral hazard and adverse selection in a nontrivialmanner even when the principal and the agent are both risk neutral. The agent'srisk neutrality greatly simplifies the mathematics and allows the authors to derivemeaningful comparative statics results. I believe that most of the results in thefirst part of the paper will still hold if the agent is risk averse. However, someof the comparative statics results may not be invariant to such an alteration.* The author would like to thank Bala Balachandran for helpful discussions on the paper.

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Discussion of Optimal Employment Contracts 805

From an economic and modeling viewpoint, the scenario in which the agentcan quit after observing predecision private information is equivalent, in al!respects, to one in which the agent obtains precontract private information. Theeconomic consequences of an agency model with precontract private infonna-tioa are quite different from those of a basic agency model, in which thereis no private information, or those of a model with predecision (postdecision)private (public) information, in which the agent observes private (public) infor-mation before (after) taking productive actions but is bound to remain in the firmregardless of the signal he receives. Some results in this paper, especially thoseio the comparative statics section, are valid only in the context of the cun'entmodel (one with precontract private information) and may not be true in general.

The first part of the paper establishes the fact that the principal's optimizationproblem satisfies the Kuhn-Tucker necessary and sufficiency conditions suchthat the optimal solution can be characterized by the first order conditions. Thecases of full information, z = 1, and no information, z ~ 0, are well knownin the literature. Rightly so, the paper concentrates on the case of an imperfectmonitoring system, that is, 0 < z < 1.

Various assumptions are imposed to establish the necessary and sufficientKahn-Tucker conditions. These assumptions are required for the entire paperbecause all comparative statics analysis are performed under the validity of theKuhn-TUcker conditions. Of these assumptions, (f) and (g) seem to be the mosttroublesome. These two assumptions are not commonly found in the agency liter-ature, and they greatly restrict the type of production functions the firm can haveand/or the conditional probability functions of the outcome given the agent'seffort, ^(y | a). The authors conjecture that these assumptions are satisfied fora large number of reasonable production functions, and offer the Cobb-Douglasproduction function as an example.

Using the Kuhn-Tucker conditions, the optimal solution is shown to haveonly three possible sets of binding constraints (proposition 1). There are twoimplications from proposition 1 that are quite interesting. First, in spite of animperfect monitor, a first-best solution can be obtained for certain parametervalues of the problem. Figujes 4 and 5 indicate that Case A is obtained evenwhen z is as low as 0.35. To get Case A (full information), one would expecta very high z (close to one). The second observation is the existence of Case Cin which the principal is able to design an incentive scheme to price out all theagent's rents from private information. It is well known that in an agency modelwith precontract private information (with no monitoring), the agent derivesstrictly positive information rent in the more productive states (Sappington,1983; Demski and Sappington, 1984). Here, with an imperfect monitor, theprincipal extracts all information rents for himself. The examples in Figures 2-5show that both Cases A and C are supported by a range of z values. It will beinteresting to see whether the set of production parameters that support thesetwo cases is of nonzero measure.

806 P. Cheng

In a similar setting with two agents, proposition 1 in Demski and Sappington(1984) shows that if the agents are both risk neutral, the principal can achievethe full information efficient solution, a result equivalent to Case A. Demski andSappington (1984) achieve the full information solution by utilizing both agents'outputs to decouple their private information. Their results rely on the fact thatthe agents' environments are positively but imperfectly correlated. In BMM,there is only one agent, but the monitoring system serves the same function asthe other agent's output.

Comparative statics resultsBecause the monitoring system is costless, an increase in z trivially relaxesconstraints 1.1 and 1.2 and it follows that the principal's expected utility ismonotonically increasing with respect to z.^ One of the main comparative staticsresults is that such a relationship is strict. Obviously, this and other comparativestatics results rely on the fact that the monitor is costless. As pointed out byBMM, it is useful to consider the choice of a costly monitoring system as partof the optimal contracting problem and the effects of the cost of the monitor onthe comparative statics results.

In discussing the above result, the authors identify two sources of distortions:shirking in the low state and excess returns to the agent in the high state. Suchobservation is valid only when the agent has precontract private informationand the productive state space is binary. When the agent observes a low state,QL, the binding rationality constraint forces him to produce yi, and he will notshirk. Hence, constraint 1.1 is not binding. When a high state, 0// is observed,the agent can shirk and produce yi as shown by the fact that constraint 1.2is binding. This implies that the principal is incurring agency costs to preventsuch behavior: the production effect. With constraint 1.2, the agent is induced toproduce y^. However, as mentioned earlier, in models with precontract privateinformation, he earns excess rents in the high state: the wealth effect. In otherprivate information settings, the agent's rationality constraint is always binding.Hence, the wealth redistribution effect applies to models with precontract privateinformation only.

The paper does not find a strict Pareto improvement as z increases in CaseB and contrasts this result with that of Holmstrom (1979). However, I findthat they are not comparable. The Holmstrom results are based on models withpure moral hazard and/or with predecision private information or postdecisionpublic information in which the agent's rationality constraint is always binding.Any improvement on the principal's expected utility cannot be obtained at theexpense of the agent. Actually, the monitor as modeled in the paper trivially sat-isfies the informative requirement of Holmstrom (1979). It is a sufficient statisticfor the unobservable agent's effort. With similar differentiability and continu-ity assumptions, I believe that a strict improvement on the principal's expected

1 A similar statement is made in an earlier version of the BMM paper.

Discussion of Optimal Employment Contracts 807

utility as z increases can also be derived in a more general agency setting. In amodel with precontract private information, the principal has more degrees offreedom to improve his expected utility with a monitoring system as some of theagent's rationality constraints are not binding. In fact, the relationship betweenthe principal's and the agent's expected utilities and the changes in z discussedin BMM is a distinct feature of a precontract private information model.

Because the agent's rationality constraint is always binding in the case of puremoral hazard and models with predecision or postdecision information, changesin z and other parameters have no impact on the agent's expected utility. Thecomparative statics on the agent's expected utility as z varies make sense onlyin the context of the current model.

The definition of the agent's expected utility (Appendix, p. 779)

A = #i(ri - h(yL, e j ) + ^Hirn ~ hiyH,eH)),

seems to be inconsistent with the economic events of the model. The agent neverreally faces any uncertainty. He agrees to the contract before he observes thestate of nature, but he is allowed to quit before taking any productive action. Heis immunized from any risk by both constraints 1.3 and 1.4. His only concernis his net utility under the two states.

AH =rH

Hence, comparative statics should be done on AH and AL separately. Clearly,this does not alter the resulting economic intuitions of the paper. However, inaddition to being more consistent with the model, this highlights its features.Because constraint 1.3 is binding, there is no change in the agent's utility undera low state, AL, as z changes. However, for Case B.

3 = hiydz dz

The impact on An is non-zero because constraint 1.4 is nonbinding as the agenteams excess returns in the more productive state.

ConclusioEBMM's study on the effects of costless monitoring in a principal-agent settingwith precontract private information has been successful in general. They areable to identify the appropriate assumptions under which the Kuhn-Tucker nec-essary and sufficient conditions hold. With risk neutrality on both the principaland the agent, this enables them to perform a series of comparative statics onthe problem. However, many of the comparative statics results are valid onlyunder these assumptions and an environment with precontiact private informa-tion. Nevertheless, agency with precontract private information is by itself an

808 P. Cheng

interesting economic environment that warrants better understanding. In that re-gard, the authors have accomplished their goal. One can only wish that theassumptions are less restrictive.

ReferencesBaiman, S., J.H. May, and A. Mukherji, "Optimal Employment Contracts and the

Returns to Monitoring in a Principal-Agent Context," Contemporary AccountingResearch (Spring, 1990) pp. 761-799.

Baiman, S. and J.S. Demski, "Economically Optimal Performance Evaluation andControl Systems," Supplement, Journal of Accounting Research (1980) pp. 184-220.

Demski, J.S. and D. Sappington, "Optimal Incentive Contracts with Multiple Agents,"Journal of Economic Theory (June 1984) pp. 152-171.

, and P.T. Spiller, "Incentive Schemes with Multiple Agents and BankruptcyConstraints," Journal of Economic Theory (February 1988) pp. 156-167.

Holmstrom, B., "Moral Hazard and Observability," The Bell Journal of Economics(Spring 1979) pp. 74-91.

, "Moral Hazard in Teams," The Bell Journal of Economics (Autumn 1982) pp.324-340.

Sappington, D., "Limited Liability Contracts Between Principal and Agent," Journal ofEconomic Theory (February 1983) pp. 1-21.