Subjective Performance Indicators and Discretionary Bonus ...

1 Subjective Performance Indicators and Discretionary Bonus Pools Madhav V. Rajan Stefan Reichelstein Graduate School of Business Stanford University November 2004 a Abstract This paper analyzes the effectiveness of Discretionary Bonus pools in utilizing Subjective information for contracting purposes. We characterize the efficiency of Bonus pools relative to the benchmark of optimal contracts that could have been written with objective and verifiable information. It is shown that ceteris paribus the principal prefers an increase in the number of managers participating in the Bonus pool due to improved risk sharing. In a more specialized LEN setting with both verifiable and unverifiable Performance Indicators , we characterize the relative weights to be placed on different information signals. We also demonstrate that correlation in measurement errors has a different impact on optimal incentive schemes depending on whether the Performance Indicators are verifiable or merely Subjective .

2 A We are grateful to Stan Baiman, Tim Baldenius, Jon Glover, Jack Hughes, and workshop participants at Carnegie Mellon University, Columbia University, University of Pittsburgh, Rice University, UCLA, and Washington University for many helpful suggestions. 1 Subjective Performance Indicators and Discretionary Bonus Pools I. INTRODUCTION Our prior Bonus plan established an annual variable Bonus pool based on the company s achievement of increased net sales and certain specified levels of economic value added.. In accordance with the prior Bonus plan, we distributed 25% of the total Bonus pool to all eligible executive officers pro rata according to their relative salary levels. The remaining 75% of the Bonus pool was distributed based on each executive s relative achievement of individual and group Performance goals, as well as based on other Subjective factors. (Fresh Brands, Inc.; Proxy Statement filed with the SEC, April 12, 2002) In many firms the provision of managerial incentives does not rely exclusively on verifiable and objective Performance Indicators , such as accounting numbers, productivity measure or the firm s stock price.

3 Incentives are also based on Subjective measures such as direct observations or informal reports from third parties. From a management control perspective, it is essential to understand the constraints imposed by the non-verifiability of some Performance Indicators . Much of the recent work on contracting with non-verifiable information has focused on the dynamic interactions between a principal and a single Our primary goal in this paper is to examine how a principal can use Subjective (and hence non-verifiable) information to create incentives for a team of agents. With multiple agents the effectiveness of Discretionary Bonus pools is of particular interest. The main feature of Bonus pools in practice is that the principal commits contractually to pay out a certain amount in total (which may vary with some underlying objective measure like overall corporate profit). However, the exact division of the total Bonus among the participating agents is not specified in the 1 For instance, the papers by Bull (1987), Baker el al.

4 (1994), Pearce and Stacchetti (1998) and Levin (2003) fall into this camp. 2 For a recent example, consider the following excerpt from Micron Technology s proxy statement, filed with the SEC on October 18, 2002: Cash bonuses to executive officers are intended to reward executive officers for the Company's financial Performance during each fiscal year. Accordingly, bonuses are determined based on Performance criteria established at the beginning of each fiscal year formulated primarily as a percentage of the Company's profits at the end of the fiscal year. Performance Bonus percentages are established according to a 2 For the purposes of our model we interpret a Bonus pool as an implicit contracting arrangement in which a principal ( , the compensation committee or a departmental manager) communicates to a group of agents how she will divide a total amount of money depending on the realization of certain information variables.

5 The agents choose their productive contribution anticipating that the principal will indeed allocate the pool as promised since ex-post she has no incentive to do In comparison to a benchmark setting in which the information variables available to the principal are verifiable for contracting purposes, the key restriction of Bonus pools is that the total payout must remain invariant to the observed outcomes. Our first question is whether one can find incentive schemes that perform better than Bonus pools if the principal can rely only on Subjective Performance Indicators . In a one-agent model, MacLeod (2003) has shown that it may be optimal to involve third parties. Under these schemes, the principal retains discretion as to whether a given amount of money is paid out entirely to the agent or partly diverted to a third party (such as a charitable organization) depending on the realization of some Subjective We demonstrate that with Subjective information only and two or more agents it is optimal for the principal to set up a Discretionary Bonus pool.

6 Thus, there is no need to divert compensation to third pools entail an additional agency cost relative to the hypothetical second-best benchmark in which the principal s information is verifiable and contractible. Agents must be burdened with additional risk due to the balancing requirement inherent in Bonus pools. The resulting Performance level may be viewed as third-best and our analysis seeks to capture the Subjective analysis of each executive officer's contribution to the Company according to the same criteria utilized to determine base salary. 3 In our one-period model, the principal is indifferent about carrying out the terms of the implicit contract. This indifference will be supplanted by reputation concerns in a multi-period model.

7 It would be desirable for future research on implicit contracts to capture the interactions between multiple agents and multiple time periods. 4 Given the monotone likelihood ratio property, MacLeod (2003) demonstrates that the optimal third party scheme is to pay the agent the entire amount unless the principal observes the lowest possible outcome. 5 If the agents observe signals that are correlated with the Subjective signals received by the principal, then it may benefit the principal to set up message sending games in which the agents payoffs are determined according to messages sent by the parties; see MacLeod (2003). We discuss the class of admissible mechanisms in more detail in Section II below. 3attendant cost to the principal. The primary motivation for studying this cost is to understand the constraints imposed by Subjective information. At the same time our results shed light on the agency costs associated with implicit rather than explicit contracts.

8 An alternative motivation for our study is that all information variables are fully contractible yet because of the costs of writing and enforcing multi-agent incentive contracts, the principal may opt for a simpler Bonus pool arrangement. Such arrangements are contractually incomplete beyond the principal s commitment for a fixed collective payout. While it has been difficult for the theory of contracts to capture the costs of contracting, our results do speak to the relative loss associated with implicit contracts, , Bonus understand the relative agency costs associated with Subjective Performance Indicators , we consider several specialized settings. When the signals available to the principal reflect the agents efforts perfectly, the first-best can, of course, be attained with verifiable signals. We find that with perfect observability Bonus pools also achieve the first-best.

9 Depending on the feasibility of sufficiently large punishments, the first-best can in fact be attained in dominant strategies. In the presence of limited liability constraints, the first-best will still be attainable as the unique strategy that emerges when agents sequentially eliminate any strictly dominated strategies. One would expect that ceteris paribus the balancing requirement associated with Bonus pools would be less severe for a larger group of agents. We demonstrate this effect for the case of -identical agents and stochastically independent signals. Intuitively, the balancing requirement of a Bonus pool implies that the variance associated with agent i s incentive scheme be spread among the remaining agents. As in a portfolio with independent securities, the effective risk imposed on each of the other n1 n1 n agents is then to the order of 211n of the variance of agents i s incentive compensation.

10 Formally, we demonstrate that the loss associated with Bonus pools, relative to the second-best benchmark, declines on a per-capita 6 Earlier literature has formalized alternative notions of costly contracting to explain delegation and delegated contracting. See Dye (1985), Melumad et al. (1997) and Laffont and Martimort (2001) on this point. 4basis for an increasing number of agents. In interpreting this result, it should be noted that we are holding the quality of the Subjective information signals fixed for each agent as the size of the team increases. Thus our model abstracts from any confounding span of control effects. A familiar result in the agency literature is that when multiple signals are informative about an agent s action, the signals should be aggregated according to their signal-to-noise ratios for contracting We revisit this finding for a setting in which the principal obtains an objective (verifiable) and a Subjective (unverifiable) signal for each agent.