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Article Excerpt
1. Introduction
According to a new Hewitt (1) global study, 2006 will mark an "increased activity in the area of variable pay, as companies rely more on bonuses as a primary means of attracting, motivating, and retaining key talent" (Business Wire 2005). For example, the Bank of America offers performance-based contracts to all employees because "incentive pay makes people work harder," just as Alpharma Inc. puts more money into incentive compensation because they "have seen a connection between company performance and employee incentive" (Wall Street Journal 2004, p. D1). (2)
Bonus pay is typically tied to corporate profitability, either in an egalitarian structure, or a "meritocracy" that differentiates employees based on their quarterly or annual performance. According to Hewitt, "companies are putting more focus on the notion of performance, and they're willing to spend [...] more on bonus pay when the results justify it." To determine performance, firms look at a wide array of measures, ranging from objective sales targets, to customer satisfaction ratings, all the way to subjective assessment of interpersonal effectiveness.
Recognizing the value of top performing employees, firms are "making special efforts to [...] keep them engaged in their work and the company, as well as appropriately rewarded," Hewitt reports. In the effort to better understand and manage the firm's human resources, this research proposes to investigate, from a rational agent perspective, the drivers of managerial motivation, defined as the "willingness to exert effort to achieve the organization's goals" (Coulter and Robbins 1999). Specifically, we focus on the optimized decisions of a manager, so-called agent, whose motivation is measured by the level of effort expended into his work activity, when the firm offers a particular performance-based contract. We analyze what intrinsic and extrinsic factors influence the managers' effort, and what properties of the agent's preferences and reward structure lead to specific motivational patterns.
The managerial compensation literature has studied these issues primarily in the context of a principal-agent framework. (3) Agency models focus on designing optimal compensation from the firm's profit perspective, with the agent's motivational drivers as a by-product. In contrast, this paper focuses on the agent's response problem: we zoom on the individual manager and describe his optimal behavior under a given (but general) contract.
Our investigation is relevant to organizations seeking to better understand how employees react to existing or proposed compensation plans, and how their motivation is affected by various factors (e.g., the agent's attitude toward risk, market factors, a projected change in compensation, etc.). For example, a firm may believe that by increasing salary or total compensation by five percent, it will motivate its managers to work harder. Our results ([section]4) show that the opposite may be true, and explain when this is the case. We do not prescribe, however, the optimal package to offer.
In reality, firms offer contracts that are not always optimal or responsive to the environment. This is in part because optimal contracts (as prescribed by agency theory) are overly complex, and need to adjust (optimally) in response to the myriad of factors affecting the firm's profits. While this is theoretically desirable, it is not always practical. Even if a firm offered optimal contracts, these would typically be set for extended periods (e.g., one year). Our model is particularly relevant during this time frame, when changes in the working environment, market factors, or interim performance affect the agent's motivation, but not his contract.
Surprisingly, little is known about the agent's effort response under given types of contracts. According to Ross (2004, p. 208): "Unfortunately, the effort to characterize [contract] optimality--often in highly specific and parametric models--has crowded out the study of the agent given specific contract forms of the sort that are commonly observed in practice."
This gap in the literature prompts the focus of our work on the agent's problem, within the classical principal-agent model. We analyze how the agent's preferences, the firm's policies, and market conditions affect effort and profits, under given contract structures. Focusing on the agent's problem allows for tractable analysis and strong comparative statics results under very general modeling assumptions on preferences, rewards, and the effort-output function. This leads to robust insights characterizing motivational patterns in response to given (but general) incentive structures.
Our results are different from the principal-agent literature, where the agent's behavior is studied in response to optimal compensation. In the agency framework, changes in a given factor affect the agent's effort level not only directly (as in our model), but also indirectly, by altering the agent's contract (optimally for the firm). Focusing on the agent's problem allows us to separate these effects and obtain new, interesting insights that hold under very general conditions. In contrast, we find that insights arising from existing (parametric) principal-agent models are not robust, hence should be applied with caution to specific needs of an organization.
A common myth in managerial, particularly sales-force, compensation is that motivation is related to the agent's degree of risk aversion. Indeed, previous results indicate that less risk averse agents exert more effort when the agent's risk aversion is wealth independent (Lal and Srinivasan 1993). We show that this relationship is not robust in the general case and can be reversed, for example, when agents have linear plus exponential utility. In general, no systematic effect of risk aversion on effort can be claimed. This may partially explain inconsistent results on the relationship between risk aversion and optimal reward structure found in empirical studies (e.g., Joseph and Kalwani 1995). Our results indicate that, all else equal, agents with higher marginal utility for wealth will work harder, but those with lower risk aversion may not. In particular, a comparison of marginal utilities can predict who will work harder.
Our analysis of how reward plans impact effort shows that a salary raise does not stimulate managers to work harder. This may explain why "companies are moving away from the traditional annual pay raise in favor of beefing up the amount of money earmarked for employee bonuses" (Wall Street Journal 2004, p. D1). Interestingly however, we find that increasing variable pay may not be a good motivator either, unless agents exhibit so-called aggressive preferences, i.e., their marginal utility is inelastic to changes in wealth. There are no benefits, however, in offering higher rewards to conservative agents (the terms aggressive and conservative are formalized in Definition 2). It is therefore important to elicit these properties of the agent's preferences before designing compensation plans. In general, firms can induce rational agents to work harder by offering lower but steeper compensation plans (these need not convexify the agent's value function). This condition is also necessary to induce motivation from a diverse workforce, when performance, also referred to as output, is unpredictable by the firm.
Factors that influence output have an indirect impact on effort; these include the agent's productivity and past performance, the firm's capabilities, as well as market factors, such as price or risk. In this context, we investigate which properties of the agent's (reward-induced) preferences for output (see Definition 1) are relevant triggers of motivational patterns. We find that agents with aggressive preferences for output are motivated by their own and the firm's productivity, contrary to conservative ones. Agents with risk-seeking preferences for output expend more effort in bigger markets, or when prices are lower (the opposite holds in the risk-averse case). An increase in market risk motivates agents with prudent output preferences and demotivates imprudent ones (see Definition 3). We also show that the corresponding trigger properties of the agent's preferences (risk seeking, aggressive, prudent) are also necessary to elicit a robust motivational pattern. Finally, we provide conditions on the compensation plan to induce such preferences for output.
The last part of this paper investigates how past performance and evaluation horizon affect the agent's effort level in a dynamic setting, where variable compensation is delivered based on cumulated output at the end of a multiperiod horizon (year, quarter). We identify the agent's induced risk aversion for output as the trigger property of consistent effort behavior. Specifically, managers with risk-averse output preferences (e.g., linear compensation plans) are unmotivated by past successes (i.e., expend less effort the better their achievements). Longer evaluation horizons are not motivating for such agents, who tend to procrastinate at the beginning of the evaluation period and undertake more effort closer to bonus time. Interestingly, these patterns can be reversed by changing the reward function in a way that induces risk seeking preferences for output.
1.1. Literature Review and Positioning
Our work is related to three main streams of literature in marketing (salesforce compensation), decision sciences (economic agent models), and finance (executive compensation). A seminal paper in the salesforce compensation literature is Basu et al. (1985), who characterize the optimal contract in a static principal-agent setting, with power utility and gamma/binomial sales. They provide comparative statics with respect to market uncertainty, salesforce effectiveness, and production cost under linear contracts. A wide range of variations and extensions have been subsequently proposed, but few are related to our work. (4) Lal and Srinivasan (1993) extend Basu et al. (1985) to a dynamic setting; their dynamic problem is elegantly reduced to a static one due to the exponential utility assumption. Dynamics are also considered by Tapiero and Farley (1975) in a multiproduct deterministic setting, and by Dearden and Lilien (1990) in a two-period production learning model. Reviews on salesforce compensation are due to Coughlan and Sen (1989) and Coughlan (1993). The insights from these parametric principal-agent models are contrasted with the robust, nonparametric results derived from our analysis of the agent's problem.
In the decision analysis literature, (5) a stream of work related to ours considers the problem of an agent who controls a risky distribution of losses by exerting effort. Dionne and Eeckhoudt (1985) show that the agent's risk aversion has an ambiguous effect on effort under a Binomial loss model. Jullien et al. (1999) provide sufficient conditions on the risk distribution for higher risk aversion to induce higher effort. Eeckhoudt and Gollier (2005) determine prudence as the key determinant of the agent's optimal effort behavior, in line with our results in [section]5. We provide a general, in-depth analysis of how the agent's preferences affect effort in [section]3.
Besides effort, another important aspect of the agent's output is risk. Optimal response to risk, under various compensation schemes, is investigated from an agent's perspective by Gaba and Kalra (1999) and Gaba et al. (2004), and, in a principal-agent model, by Godes (2004). The financial literature has extensively investigated the influence of nonlinear contracts (typically convex options) on the agent's risk-taking behavior. In particular, Ross (2004) focuses on the agent's problem to derive conditions on utility and reward plans to induce more or less risk-averse behavior.
1.2. Structure and Framing
The rest of this paper is organized as follows. The main static model is presented in [section]2. Section 3 investigates the impact of the agent's preferences on effort. The motivational impact of pay structures is the subject of [section]4. Section 5 investigates comparative statics with respect to factors affecting output, including the agent's and the firm's productivity, and market factors. Section 6 extends the problem to a dynamic setting and obtains insights with respect to the agent's past performance and time to evaluation. Section 7 concludes the paper.
Our model and results are applicable in contexts where the agent is subject to any form of performance pay, and effort is a strategic decision affecting the agent's performance or output. For simplicity, however, we focus the exposition of this...
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