Endogenous Precision of Performance Measures and Limited Managerial Attention

^‡Accepted by Christian Hofmann.

Abstract

In this paper, we model two drivers that underlie the economic trade-off that shareholders face in designing incentives for optimal effort allocation by managers. The first driver is the presence of a performance-reporting task, by which we mean managers may exert effort to improve the precision of their performance measures. The second is limited managerial attention, where performing one task may have an adverse effect on the cost efficiency of performing another. We show that the subtle interactions of the two drivers may alter the characteristics of incentive provision. First, the interaction may lead to a positive relation between the strength of the incentive and the variance of the performance measures. Second, the interaction may cause an informative performance signal to not be used in equilibrium incentive contracts. In particular, it is possible that the principal will not use a signal whose precision can be improved by the manager in order to discourage the manager from diverting attention to the performance-reporting task. Finally, we apply the model to a project-selection setting and show that, in order to induce the agent to choose higher risk, higher return projects, the principal may need to raise the bonus rate when the choice of project is unobservable.

Acknowledgements

We wish to thank Christian Hofmann (the editor), an anonymous referee, Mark Bagnoli, Jeremy Bertomeu, John Christensen, Ron Dye, Jon Glover, Bjorn Jorgensen, John O'Brien, Sri Sridhar, Susan Watts, Martin Wu, and other participants at the 2009 AAA Annual Meetings at New York City, the 2009 Carnegie Mellon University Accounting Conference, and seminars at Purdue University and Tsinghua University for their helpful comments.

Notes

^‡ Accepted by Christian Hofmann.

¹See, for example, Tucker and Zarowin (2006), Subramanyam (1996), Hunt et al. (2000), and Francis et al. (2005).

²In particular,

management should evaluate the design of the controls to determine whether they adequately address the risk that a material misstatement in the financial statements would not be prevented or detected in a timely manner. … that the evaluation of evidence about the operation of controls should be based on assessments of the controls’ associated risk. (KPMG, 2007)

³In a testimony on Capital Hill in April 2005, SEC Chairman Donaldson (2005) commented that complying with SOX Section 404 has been time-consuming and expensive for most companies, as confirmed by surveys (see Stovall, 2008). Sayther (2003) claims that compliance demands steal CFOs' focus and leave less time and fewer resources for strategic thinking; Stone (2005) reports comments by industry insiders that SOX is siphoning away CEO creativity and forces CEOs to worry more about compliance and losing their jobs than figuring out how to invest in growth for the future.

⁴The value of additional signals has also been a focus of agency work since its early years. Holmstrom (1979) pioneered this inquiry and established the early standard result called the Informativeness Criterion. In accounting, this work is followed by Antle and Demski (1988), Demski (1994), Feltham and Xie (1994), Feltham and Wu (2000), Arya et al. (2007), and Christensen et al. (2010), among others.

⁵Hughes (1982), Danielsson et al. (2002), Baker and Jorgensen (2005), and Bertomeu (2008) also consider the agent's ability to change the risk profile of the firm output, and thus the agent's performance measure. In all of these papers, limited managerial attention is not a key research issue.

⁶We focus on the single-agent setting in the model. However, the key assumption is that the agent's unobservable managerial efforts contain these two dimensions. Even if the principal assigns the two tasks to two agents separately, one agent may still choose to execute both tasks because the efforts are unobservable and the agent still has an incentive to improve the precision of the performance measures as well as improving production (see related work on teams in Huddart and Liang, 2005, and in Liang et al., 2008).We also explicitly examined a setting in which the performance-reporting effort is assigned to a CFO, while the CEO can exert both productive effort and performance-reporting effort. We are able to show that inducing no performance-reporting effort from the CEO is not optimal. A detailed analysis of this setting is included in the appendix. This result may suggest that, empirically, when reporting effort is unobservable and the CEO's and CFO's reporting efforts are substitutes, perfect task specialization between the CEO and CFO is unlikely. This job-design question may be of potential interest for future studies.

⁷Dye and Sridhar (2007) and Stocken and Verrecchia (2004) also look at the case in which the precision of a disclosed estimate or that of a firm's accounting-reporting system is a choice variable. In Dye and Sridhar's study, a risk-averse initial owner discloses an estimate of the mean future cash flow to risk-neutral investors. Their study shows that whether the initial owner's precision choice is private or public and whether her disclosure is voluntary or mandatory lead to different equilibria of risk allocation between the owner and the investors. Their paper focuses on the allocational effects, while our paper focuses on the interaction between the agent's productive effort and precision choice. Stocken and Verrecchia's study examines the interaction between the manager's choice of the precision of a firm's accounting-reporting system and the manager's disclosure management decision. It shows that the manager may not choose the most precise reporting system when he has the option to manipulate the financial report. Again, their study does not consider the effect of precision on the choice of productive effort.

⁸In our paper, we focus on the agent's effort to improve the precision of performance measures. Notice that we assume the performance-reporting effort (e₂) only reduces noise associated with the performance measure (σ_y ); it does not affect either the expectation or the variance (i.e. risk) of the underlying cash flow (x). In Section 5, we introduce a third managerial choice, which determines the risk-return profile of the cash flow (i.e. project selection). With this assumption, we rule out cases in which effort designed to reduce measured risk (such as e₂) in our model may also affect the real variables (such as E[x] and Var[x]). Arguably, all performance-reporting tasks may affect real variables in practice. Incorporating these effects will undoubtedly complicate the model, but doing so may unveil some additional interactions. For example, adding a real effect to e₂ would add to the model an element of goal congruence. That is, because both e₁ and e₂ affect the expected output, an added tension would emerge concerning the optimal combination of these two efforts in both first- and second-best cases (see Feltham and Xie, 1994). As to how goal congruence would affect the tension between productive vs. performance-reporting tasks, adding a productive aspect to e₂ may make inducing more e₂ slightly more attractive (compared with cases in which e₂ does not have a positive/productive real effect). This attraction may make our main result (that the risk–incentive relation may be positive) less or more likely to survive, depending on how the spillover between e₁ and e₂ responds to the level of e₂ productivity on output. If the spillover is very high but e₂′s real effect is also high, the principal might not redirect attention away from e₂ (unlike the case we show in Section 3), making the positive relation less likely to emerge.

Alternatively, if we allow the agent to garble the performance measures in this model through (i.e. higher increases, rather than decreases, the performance variance), the results of analyzing incentive–risk relation and additional signals may still remain or may be even strengthened. In the relation between incentive and risk, as the performance-reporting effort brings less benefit (potential garbling in addition to inducing a higher marginal cost of productive effort), the principal would be more strongly motivated to induce less performance-reporting effort and more productive effort, which may lead to the positive relation between the variance and incentive. When considering an additional signal, potential garbling through may make the principal more likely to ignore the signal whose precision can be manipulated.

⁹Notice that when the manager exerts zero performance-reporting effort, the performance-measure variance is which is not necessarily Here, only represents an exogenous determinant of the performance-measure variance, not the variance with zero performance-reporting effort.

¹⁰Peng and Roell (2008) record a recent example of limited managerial attention, that

in the real world, the time constraint is one of the most important constraints faced by managers. And they do complain of the significant amount of time and attention they are forced to devote to public relations and reassuring the stock market (in Europe, prominent business leaders have pointed out that the threat of a takeover, now that corporate control is more contestable than it used to be, is having the unfortunate side effect of distracting management from running the underlying business). This time cost comes out clearly in the London Stock Exchange's A Practical Guide to Listing (2002): ‘Both the flotation process itself and the continuing obligations – particularly the vital investor relations activities … – use up significant amounts of management time which might otherwise be directed to running the business … It is vital that you maintain your company's profile, and stimulate interest in its shares on a continuing basis. Many listed companies, even relatively small ones, employ specialist financial public relations and investor relations advisors on a retainer basis to keep the business on the financial pages and in the minds of investors. … However, you cannot leave press or investor relations to your advisers. Top executives will commonly devote at least a couple of days a month to developing and nurturing such contacts. … This must be regarded as time well-spent. … As a publicly-quoted company, it is a core element of running your business properly and responsibly.’ (London Stock Exchange, 2002, pp. 11, 47–48)

¹¹Formally, we assume is continuous and differentiable over , where and . In some examples, we may consider a specific cost function to illustrate economic intuition using closed-form solutions. In these examples, we consider where In this case, condition reflects the limited managerial attention. In the example for separable costs, we consider which has the property Finally, we assume to satisfy the second-order condition.

¹²To ensure that the two first-order conditions (FOCs) characterize the maximum, we compute and verify that the Hessian is indeed negative-definite, given that . In the specific examples we use later in the paper, second-order conditions are satisfied with details given in the appendix.

¹³Formally, for any given positive bonus weight , a manager choosing is not optimal because at , the marginal benefit is proportional to and the marginal cost is . By continuity, the manager can always find an to equate the marginal benefit and the marginal costs.

¹⁴We thank an anonymous referee for bringing this point to our attention.

¹⁵This is because the principal can always adjust the fixed wage , without affecting any incentive constraints, to make sure the agent takes the contract by setting .

¹⁶Specifically, substituting the agent's FOCs (Equations (1) and (2)) into Equation (4) and differentiating Equation (4) with respect to again, we have

To ensure the FOC characterizes a global maximum, we assume

This condition is verified for specific examples we use later in the paper.

¹⁷Furthermore, it is easily verified that the optimal supplied by the agent at the solution to (PP) is identical to the solution of a slightly modified problem (PP′) where is supplied by the principal (at the same cost, separate from the cost of ). In other words, without spillover costs, there is no conflict of interest with respect to the provision of

¹⁸This intuition can be shown to hold even if is a function of (and thus ), making Equation (6) implicit in . In the standard LEN model, the cost of effort is usually quadratic, making a constant and making Equation (6) explicit in .

¹⁹We thank an anonymous referee for suggestions on simplifying the math of our analysis. This assumption is not the driving assumption for our results, but helps simplify the mathematical complexity in our analysis of incentive–variance relation. All results in Section 3 hold without this assumption. In addition, Sections 4 and 5 are not restricted by this assumption. The more general analysis without this simplifying assumption was in an earlier version of our paper and is available upon request.

²⁰More specifically, where is the second-order condition discussed in Footnote 16. Since the second-order condition for must be negative and the principal must decrease the bonus rate as increases. Therefore, the incentive–risk relationship remains negative.

²¹In practice, the manager's effort may become less effective when facing high risk in business. When addressing the risk management in industries that rely on R&D and innovations, Elsum (2008) comments that ‘one size does not fit all – distinctly different management frameworks are required for success in research, development and/or innovation with high compared with low uncertainty. Most organizations find this difficult to cope with’.

²²We can show that an explicit sufficient condition for is A detailed analysis is presented in the proof in the appendix.

²³An alternative specification would be to assume that the additional signal (z) is informative about e₂ (e.g. z = e₂+ϵ_z ). Reporting effort (e₂) is arguably even harder to measure in reality than productive effort (e₁); however, for completeness of our analysis, we examined this setting. Doing so, we find that if the incentive on signal z cannot be negative, the principal will not use signal z when e₂ is not effective enough in reducing the performance variance. However, if we allow the incentive on signal z to be negative, the principal will use signal z and impose a negative incentive on z to lower e₂.

We thank an anonymous reviewer for bringing this point to our attention. A detailed analysis is available upon request.

²⁴We assume for simplicity, but any fixed variance V is valid for our analysis.

²⁵In this paper we only consider non-negative bonus rates on signals about e₁, since e₁ is productive effort. This can be regarded as an implicit constraint . If we incorporate this constraint in the program and examine the Kuhn–Tucker conditions, we see that this condition is not binding in most cases. However, when , the FOC with respect to is not zero, and its Kuhn–Tucker multiplier is zero, while the condition is binding with its Kuhn–Tucker multiplier being positive. Thus, must be zero and cannot deviate from zero.

Given we only need to check the second-order condition with respect to The second-order derivative of the principal's objective function with respect to is Therefore, the second-order condition is satisfied, and is indeed the global maximum when

²⁶To elaborate, in standard agency settings, the marginal benefit is positive when the bonus weight is close to zero, while the marginal cost approaches zero because both the risk premium and the manager's personal cost of efforts are quadratic. In the separable costs case with no spillover, the marginal cost of increasing the incentive on signal z approaches zero as the bonus weight approaches zero due to the quadratic form of personal effort cost, but the total marginal cost does not go to zero because of the term due to the covariance between the signals (see Equation (15) in the appendix). However, the total marginal cost is always outweighed by the marginal benefit, and it is still efficient to include signal y in the contract. When the spillover occurs between effort choices, not only does the total marginal cost of increasing not approach zero as approaches zero, but it can also outweigh the marginal benefit (see Equation (A24) in the appendix).

²⁷The explicit condition for is See the proof in the appendix.

²⁸Our result does not change if

²⁹The assumptions and are only made to simplify our calculation and do not affect our results. We focus on the comparison between in the observable setting and in the unobservable setting. Whether is equivalent to in the observable setting does not influence our analysis.

³⁰When we have and, thus, which can be rewritten as Therefore, we have