Incentives and Behavior Prof. Dr. Heiner Schumacher KU Leuven 14. Multitasking/Crowding Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 1 / 20
Introduction In the last chapters, we discussed how we can solve problems of asymmetric information with monetary incentives. However, are monetary incentives always good for performance? In reality, employment contracts often specify …xed wages. Incentives within …rms frequently are muted. In this chapter, we discover two reasons why monetary incentives may harm performance: Multiple tasks and motivational crowding out. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 2 / 20
Introduction Overview Multitasking Motivational Crowding Out Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 3 / 20
Multitasking In most real-world work environments, an agent has not only one task, but many tasks. For example, the CEO of a company has to hire managers, search for new markets, communicate with investors and so on. In general, when there a multiple tasks, the contract design does not only in‡uence incentives and risk-allocation, but also the allocation of the agent’s attention among her duties. In the following, we study optimal incentives in a setting with multiple tasks. In particular, we consider a simpli…ed version of Holmström and Milgrom (1991). 1 1 Holmström, Bengt, and Paul Milgrom (1991): “Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design,” Journal of Law, Economics and Organization 7, 24 - 52. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 4 / 20
Multitasking Assumptions (1) A has to perform two independent tasks. The e¤ort levels are a 1 and a 2 , respectively. She has CARA preferences U ( w , a ) = � e � η [ w � ψ ( a 1 , a 2 )] , where η is her coe¢cient of absolute risk aversion. The cost function is ψ ( a 1 , a 2 ) = 1 2 ( c 1 a 2 1 + c 2 a 2 2 ) + δ a 1 a 2 , where 0 � δ � p c 1 c 2 . For δ = 0 the two e¤orts are technologically independent, for δ = p c 1 c 2 the two e¤orts are perfect substitutes. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 5 / 20
Multitasking Assumptions (2) P observes the outputs q 1 , q 2 from the two tasks. The production function of task i is given by q i = a i + ε i , where ε i is normally distributed with variance σ 2 i . The covariance between outputs of di¤erent tasks is 0. P o¤ers the following linear incentive contract to A : w = t + s 1 q 1 + s 2 q 2 . Hence, t is a …xed payment and s i the incentive pay for task i . P ’s …nal payo¤ is q 1 + q 2 � w . Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 6 / 20
Multitasking We derive the optimal incentive scheme. A ’s certainty equivalent from contract f t , s 1 , s 2 g can be calculated as t + s 1 a 1 + s 2 a 2 � η 2 ) � 1 2 ( s 1 σ 2 1 + s 2 σ 2 2 ( c 1 a 2 1 + c 2 a 2 2 ) � δ a 1 a 2 . (1) From this expression we can derive A ’s unique best-response to contract f t , s 1 , s 2 g : a 1 = s 1 c 2 � δ s 2 c 1 c 2 � δ 2 and a 2 = s 2 c 1 � δ s 1 c 2 c 1 � δ 2 . (2) P ’s objective is to maximize a 1 ( 1 � s 1 ) + a 2 ( 1 � s 2 ) � t subject to the constraints that the expression in (1) weakly exceeds the value of A ’s outside option (PC), and A ’s e¤ort is given by (2) (IC). Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 7 / 20
Multitasking The solution to the maximization problem (make sure that you can derive it) is given by 1 + ( c 2 � δ ) ησ 2 s � 2 = 2 ( c 1 c 2 � δ 2 ) , 1 1 + η c 2 σ 2 2 + η c 1 σ 2 1 + ησ 2 1 σ 2 1 + ( c 1 � δ ) ησ 2 s � 1 = 2 ( c 1 c 2 � δ 2 ) , 2 1 + η c 2 σ 2 2 + η c 1 σ 2 1 + ησ 2 1 σ 2 and t � is such that the (PC) holds with equality. In the following, we assume that an interior solution exists, i.e., s � i 2 ( 0 , 1 ) for i 2 f 1 , 2 g . Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 8 / 20
Multitasking We analyze what happens to incentives if σ 2 2 increases (i.e., it becomes more di¢cult to distinguish e¤ort from noise). Clearly, s � 2 decreases in σ 2 2 . The more noise there is in the production function, the more di¢cult it is to provide incentives. More surprisingly, s � 1 also decreases in σ 2 2 . We can calculate that � ∂ s � � � � = � sgn [ s � 1 δη ( ησ 2 sgn = sgn 1 ( δ � c 1 ) � 1 ) 2 ] ∂σ 2 2 and s � 2 is positive by assumption. Note that there is an e¤ort-substitution problem: When task i is highly incentivized, while the other task � i is not, A allocates too much of her e¤ort to task i . In order to reduce the e¤ort-substitution problem, both tasks are optimally less incentivized when the quality of the output measure for one task decreases. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 9 / 20
Multitasking When P cares about a task where it is very hard to relate output to input (a task i with σ 2 i = ∞ ), then it may be best to give no incentives at all (for this result Holmström and Milgrom assume that A provides some e¤ort in the absence of any incentives). This is a very important result. It shows that in many circumstances it is optimal to provide no incentives even if some dimensions of the job have very precise link between input and output. A good example are contracts for teachers (which typically have “low-powered” incentives). While some dimensions of their “output” are simple to measure (students’ test scores), others are not (creativity, oral communication skills). Linking pay to test scores would then bias teachers’ e¤ort to skills that are tested on standardized exams. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 10 / 20
Multitasking Exclusion from other tasks. When designing the optimal organizational design, P also has to consider what A can do outside his job (outside work). If the market starts valuing outside work more highly, P either has to increase incentive pay or exclude A from outside work. Allocating tasks among agents. If P can allocate tasks among several (identical) agents, it may be useful that some agents specialize in tasks that are hard to monitor (and get low-powered incentives), while others only engage in tasks that are easy to monitor (and get high-powered incentives). Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 11 / 20
Motivational Crowding Out In psychology, people di¤erentiate between two categories of motivation. Extrinsic Motivation occurs when people are compelled to do something or act a certain way because of external factors. For example, a manager works hard for his bonus, or a student studies hard in order to obtain a good grade. Intrinsic Motivation occurs when people are internally motivated to do something because it brings them pleasure, or they think that it is important, or they feel that what they are doing is signi…cant . For example, a manager may exert e¤ort even in the absence of monetary incentives if she is convinced that she is working or a good cause. Or a student studies hard, because she likes the subject. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 12 / 20
Motivational Crowding Out The crowding-out e¤ect suggests that raising monetary incentives crowds out intrinsic motivation and therefore may reduce supply (of e¤ort). In certain circumstances, it is therefore not advisable to use monetary incentives to elicit e¤ort, but intrinsic motivation. Now even economists admit that the crowding-out e¤ect may play an important role. Gibbons (1998) says: 2 “A more troubling possibility is that management practices based on economic models may dampen (or even destroy) non-economic realities such as intrinsic motivation and social relations.” 2 Gibbons, Robert (1998): “Incentives in Organizations,” Journal of Economic Perspectives 12(4), 115 - 132. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 13 / 20
Motivational Crowding Out The e¤ect of external rewards on intrinsic motivation has been attributed to two psychological processes: Impaired Self-Determination. When individuals perceive an external intervention as reducing their self-determination, intrinsic motivation is substituted by extrinsic control. Impaired Self-Esteem. When outside intervention carries the notion that the actor’s motivation is not acknowledged, his or her intrinsic motivation is e¤ectively rejected. An intrinsically motivated person is deprived of the chance of displaying his or her own interest and involvement in an activity when someone else o¤ers a reward. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 14. Multitasking/Crowding 14 / 20
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