GERMAN ECONOMIC ASSOCIATION OF BUSINESS ADMINISTRATION GEABA DISCUSSION PAPER SERIES IN ECONOMICS AND MANAGEMENT

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1 DISCUSSION PAPER SERIES IN ECONOMICS AND MANAGEMENT Recurring Tasks in Forward-Looking Incentive Contracts Frederike Hinz Discussion Paper No GERMAN ECONOMIC ASSOCIATION OF BUSINESS ADMINISTRATION GEABA

2 Recurring Tasks in Forward-Looking Incentive Contracts Frederike Hinz May 4, 017 Abstract Managers often focus on tasks with short-term consequences to the detriment of long-term rm protability. Forward-looking performance measures in compensation contracts can shift the managers' orientation away from the short run to the long run. This paper examines the optimal design of incentive systems with forward-looking performance measures in an environment with recurring shortsighted eort and a one-shot farsighted eort when renegotiation is possible. I show that it is not always benecial to motivate a recurring shortsighted eort. In particular, if the future shortsighted task is rather unproductive relative to the farsighted task, the rm might be better o by not motivating the future task. In addition, I derive recommendations for the optimal use of long-term performance measures in forward-looking incentive contracts. Keywords: Forward-Looking Performance Measures, Incentive Contracts, Renegotiation, Repeated Eort University of Frankfurt, f.hinz@econ.uni-frankfurt.de

3 1 Introduction A manager's area of responsibility usually consists of several tasks that have dierent eects on the rm's performance. Shortsighted tasks with short-term consequences, i.e., tasks that aect the rm's current outcome, include, for example, decisions on the produced quantity or price of a product. Farsighted tasks, i.e., tasks aect the rm's future outcome, have a long-term impact. Examples include decisions on investments in product development or employee training programs that cause costs in the current period but increase future demand and thereby the rm's future payo. Managerial myopia, the overvaluation of short-term rewards and undervaluation of longterm consequences (Laverty 004), aects the allocation of eort such that managers focus on shortsighted tasks while neglecting farsighted ones. This can result in economic losses, as seen for example from the nancial crisis where long-term eects of managerial actions were neglected. Managerial myopia arises from a higher individual preference for current than for future consumption. A possible reason might be that managers have a shorter employment or decision horizon than the rm owner because of retirement plans, job change, or pursuit of reputation in the labor market (e.g., Narayanan 1985, Holmström and Costa 1986, Campbell and Marino 1994). Several empirical studies (e.g., Bushee 1998, Marginson and McAulay 008) support this argument. Dechow and Sloan (1991), for example, investigate the investment behavior of managers in their nal years and nd that CEOs near retirement spend less on Research & Development (R&D), that is, they invest less in projects that have long-term consequences. In order to motivate both types of tasks, rms use short-term and long-term performance 1

4 measures in incentive contracts. As an example, Daimler has a compensation plan for CEOs that consists of a base salary, a short-term, and a long-term component. The short-term component depends on the individual performance of the CEO and the rm performance of the previous year. The long-term component evaluates the performance of the last three years considering the return on sales and the development of the share price. The combination of these components creates an incentive to secure the rm's long-term success. However, farsighted tasks are not suciently motivated by using a long-term and a shortterm component in the incentive contract. First, managerial myopia still leads to a focus on shortsighted tasks. As the manager is interested in a higher short-term utility, the incentive eect of the long-term performance measure decreases such that the farsighted task is less performed. Second, the realization of long-term performance measures is dicult to predict. Because of several unforeseeable events, the uncertainty of the long-term measure is high (Prelec and Loewenstein 1991). Following the optimization of the risk and incentive tradeo (Prendergast 00), a riskier performance measure is less emphasized in a compensation contract such that the manager's focus is still on the shortsighted task (Banker and Datar 1989). In order to shift the manager's attention away from the short run to the long run, the implementation of a forward-looking performance measure is useful as it creates an incentive in the current period for performing farsighted tasks. Prior literature, e.g., Banker and Datar (1989) and Feltham and Xie (1994), shows that an additional performance measure can compensate for the noise and goal incongruence of a nancial long-term performance measure. In fact, Ittner et al. (1997) nd that nonnancial measures are more emphasized in bonus contracts if the noise of nancial performance measures is higher. In order to motivate myopic managers to exert eort on tasks that aect

5 future payos, forward-looking performance measures are meaningful (Farrell et al. 008). Examples for such, frequently nonnancial, performance measures are product quality, customer and employee satisfaction, market share, and development. These measures reect a prediction for the rm's future protability. If a rm uses, for example, product quality as a performance measure in contract design, the manager will exert eort in the improvement of quality. Customers prefer higher quality such that the customer satisfaction and loyalty increases. Positive word to mouth from satised customers will also attract new customers. The resulting higher demand leads to an increase of the rm's future prot. Thus, an improvement of product quality today will aect the rm's future payo. 1 Evidence in practice also supports the use of incentives based on forward-looking performance measures. In particular, Rucci et al. (1998) present the business model at Sears which illustrates the successful implementation of an incentive contract with forward-looking components. Furthermore, Banker et al. (000) nd that the implementation of nonnancial measures of customer satisfaction in incentive contracts improves nancial performance. Other studies (e.g., Mat jka et al. 009 and Abernethy et al. 013) show that forward-looking performance measures result in a longer-term orientation such that managers with short employment horizons are motivated to perform farsighted task. As a manager usually is responsible for several tasks with dierent temporal impacts on the rm's outcome, this paper investigates the optimal incentive design in an environment with recurring shortsighted eort and one-shot farsighted eort. For this purpose, this paper presents a two-period LEN model, closely related to Dikolli (001), with a risk-neutral 1 See Anderson and Sullivan (1993), Rust et al. (1995), Ittner and Larcker (1998), Smith and Wright (004), Farrell et al. (008) for empirical evidence. 3

6 principal and a risk-averse agent. At the beginning of period 1, the agent exerts eort on two tasks: The shortsighted eort aects only rm prot in period 1 while farsighted eort aects the prot in period. At the beginning of period, the agent exerts a repeated shortsighted eort that aects the prot of this period. In practice, dierent types of eort can be selling a product as a shortsighted task because this action aects the current rm outcome. Farsighted eort might be investment decisions in R&D. Investments in R&D are crucial for the renement of existing products and the development of innovative products such that the demand for future products increases. Thus, current investments aect the rm's future outcome. The principal oers a contract that includes three performance measures. At the end of period 1, a short-term measure rewards shortsighted eort and a forwardlooking measure rewards farsighted eort. At the end of period, the rm's prot serves as a performance measure in order to evaluate farsighted eort and repeated shortsighted eort. In regard to the example, the short-term measure might be rm prot, the forwardlooking measure capital invested in R&D, and the second-period measure rm prot in the subsequent period. The agent's myopia is expressed by a future preference factor that discounts the agent's expected future utility. In addition, the agent has the possibility to renegotiate the contract after short-term and forward-looking performance measures are realized and before choosing the repeated shortsighted eort level in the second period. Fudenberg and Tirole (1990) claim that especially in situations with long time lags between the agent's action choice and its realized consequences on rm outcomes, full commitment is not a credible assumption. As exactly farsighted eort is confronted with this time lag, I consider renegotiation in the analysis. To my knowledge, theoretical research has not investigated the impact of recurring eort 4

7 on the design of a forward-looking incentive contract if renegotiation is possible. Sliwka (00) analyzes the eect of a forward-looking performance measure without regard to managerial myopia and nds that the implementation of this additional performance measure is always benecial for contracting purposes. Raith (01) comes to a similar result when he introduces a signal that can be interpreted as a forward-looking measure. However, the model assumes full commitment. Dutta and Reichelstein (003) examine the eect of a leading indicator variable on incentive design without considering a dierent discount factor for the agent. They nd that a leading indicator can be valuable, particularly in short-term contracts. Other studies (e.g., Hermalin and Katz 1991, abac 007, Christensen et al. 005) analyze several aspects in presence of renegotiation but the impact of managerial myopia in incentive contracts with forward-looking performance measures is not considered. The model contributes to the explanation of contract design with forward-looking performance measures. I extend Dikolli (001) by the introduction of a recurring shortsighted eort in period. The analysis shows that the optimal incentives for farsighted eort are aected by the additional repeated shortsighted eort and the accompanying possibility of renegotiation. More precisely, although both eorts have a productive impact on the rm's outcome, there exists no substitutive eect between them. Intuitively, because of renegotiation, the rm chooses a weight on the second-period performance measure in order to motivate the recurring eort. Farsighted eort also aects this measure such that the incentive to exert repeated shortsighted eort motivates the exertion of farsighted eort simultaneously. Consequently, eorts are complements. Hence, a lower productivity of shortsighted eort leads The motivation of a second-period eort leads to the possibility of renegotiation. In Dikolli (001) renegotiation does not make sense because there is no action choice in period. Then, no motivation of eort is necessary and the bonus payment equals zero. 5

8 to a lower emphasis of the second-period measure in incentive contract. As a consequence, shortsighted and farsighted eort levels fall. The results contribute to the explanation of the occurrence of underinvestments in long-term projects. Moreover, I derive recommendations for the optimal use of long-term performance measures in forward-looking incentive contracts and show that the motivation of an additional eort is not always benecial. In particular, the results indicate that the motivation of recurring shortsighted eort is not benecial if it is rather unproductive relative to the farsighted eort. This implies that a rm might be better o by not motivating a future task through a long-term performance measure depending of the relative eort productivity. The remainder of the paper is organized as follows. In the second section, I develop the basic analytical model. The third section provides the optimal contract design. The fourth section analyzes the contract oered to the agent and the fth section analyzes the eect of the motivation of the recurring shortsighted eort. The study ends with a conclusion. Basic Model.1 Output and Agent's Actions Consider a two-period model in which a risk-neutral principal (e.g., an owner) hires a riskand eort-averse agent (manager) at date t = 0. In each period t, t = 1,, the agent exerts eort a t on a shortsighted task that aects prot π t of the same period. Furthermore, he exerts farsighted eort b in period 1 which only aects second-period prot. As an example, shortsighted eort might be selling the product. This action has an impact on the rm's 6

9 current outcome. A farsighted eort might be decision making in R&D investments that contribute to the renement of existing products and to the development of new, innovative products that increase customer demand. The agent's personal costs of eort have the following structure: κ 1 (a 1, b) = 1 (a 1 + b ) in t = 1 (1a) and κ (a ) = 1 a in t =. (1b) From Expression (1a) and (1b), eort costs are additive and are not aected by any scale eects. The rm's prot in period t = 1 is given by π 1 = ga 1 + ε 1 () and the rm prot in period t = by π = ga + hb + ε (3) where the noise term ε t is normally distributed with ε t N(0, σt ), t = 1,. The factor g > 0 is the productivity of the shortsighted eorts and h > 0 is the productivity of farsighted eort. Productivity means the marginal contribution of eorts to realized prots. It is possible that shortsighted and farsighted eort have dierent productivities, i.e., g h. Then, the eort with higher productivity has a stronger impact on prot than the other eort. 7

10 . Incentive Contract, Agent's and Principal's Preferences As eorts are not observable, the principal uses rm prots for performance evaluation. The timing of the model is presented in Figure 1. First-period prot serves as short-term performance measure that evaluates the agent's shortsighted action in period 1. Secondperiod prot serves two roles: First, it serves as a short-term performance measure for evaluating the agent's shortsighted eort in period. Second, it is a long-term indicator for the agent's farsighted eort in period 1. At the end of period 1, a forward-looking performance measure is observable that measures the consequences of farsighted eort with an error: y = b + ε y (4) where the noise term ε y is normally distributed with ε y N(0, σ y). With regard to the example, the forward-looking measure can be capital invested in R&D. Other examples are indices for customer satisfaction or quality. At date t = 0, the principal oers the agent a single contract for both periods that consists of two parts. The agent's compensation in period 1 consists of a xed salary and a short-term and a forward-looking component: 3 w 1 = α 1 + v 1 π 1 + v y y. (5) The second-period compensation is paid at the end of period and is based on a xed salary 3 Linear contracts are common in practice (e.g., Bose et al. 011, Holmström and Milgrom 1987). Referring to Dikolli (001), I investigate the optimal structure of a compensation contract given the contract is linear. 8

11 Fixed Wage in Period 1 1 Shortsighted Effort a 1 Farsighted Effort b Profit Period 1 (Short-Term Measure) Forward-Looking Measure y 1 Wage in Period 1 w 1 Fixed Wage in Period Profit Period (Short-Term Measure for a ) (Long-Term Measure for b) Wage in Period w Shortsighted Effort a t = 0 t = 1 Possibility of Renegotiation t = Figure 1: Timing of the Model. plus an incentive based on the prot in period : w = α + v π. (6) The parameter α t represents the xed wage in each period t = 1, and the parameters v j are the incentive weights on the respective performance measures. If the agent accepts this contract, the principal and the agent commit to the employment relationship for both periods. However, they cannot commit to not renegotiate the contract after period 1. The renegotiated contract is oered by the principal in form of a take-it-or-leave-it oer. Both parties have to agree to the new contract for replacing the initial one. If the agent rejects the principal's oer, the initial contract is binding. If the agent accepts it, the initial contract is invalid and the new one is binding. 9

12 I assume that the agent has time-additive preferences. He has a negative-exponential utility function with an Arrow-Pratt measure of absolute risk aversion r: U A = e r(w 1 κ 1 ) δe r(w κ ). (7) The future preference factor δ (0, 1) represents the agent's myopia and is dened by δ = 1 1+i where i is the interest rate. Thus, a higher interest rate results in a lower future preference factor, that is, the agent has a lower preference for future utility. If this factor is close to zero, the agent has a low preference for future utility at date t = 0, so he acts more myopically. If the factor is close to one, the agent has a high preference for future utility and he acts more farsightedly. 4 According to the going concern principle, a rm aims for continuing the business such that it has a longer decision horizon than an employee. Thus, the principal has the same preference for current and future net payo and her future preference factor is normalized to 1. The principal's preferences are described by the linear utility function U P = π 1 + π w 1 w, (8) i.e., she maximizes the dierence between expected rm prots and wage payments to the agent in both periods. 4 See Dikolli (001) for further interpretations of δ. 10

13 3 Optimal Contract 3.1 Second-Period Contract Using backward induction, I start with the renegotiated contract in the second period. At date t = 1, eorts a 1 and b have already been exerted and performance measures y and π 1 have been realized. According to the framework of Holmström and Milgrom (1987), the agent's expected utility at t = 1 can be represented by the certainty equivalent CE (w â 1, ˆb, ŷ, ˆπ 1 ) = E[w ] κ (a ) r σ v (9) where the hat denotes the realized values from period 1. Thus, the agent optimizes his utility by maximizing his wage minus eort costs and risk premium. The risk premium compensates the agent for bearing the risk imposed by the performance measures. The principal's optimization problem in period is characterized by: max v NP (w â 1, ˆb, ŷ, ˆπ 1 ) =E[π â 1, ˆb, ŷ, ˆπ 1 ] E[w â 1, ˆb, ŷ, ˆπ 1 ] (10a) s. t. CE (w â 1, ˆb, ŷ, ˆπ 1 ) U I, (10b) a argmax a CE (w â 1, ˆb, ŷ, ˆπ 1 ). (10c) The principal maximizes her expected net payo in period, NP, subject to the agent's participation constraint given in Expression (10b) and the incentive compatibility constraint given in Expression (10c) in period. The participation constraint expresses that the agent accepts the renegotiated contract if it provides at least the utility that he would receive with 11

14 the initial contract denoted by U I. The agent's optimal eort choice derived according to (10c) is given by: a = gv. (11) Recurring shortsighted eort is motivated solely by the second-period prot. Although second-period prot is also aected by farsighted eort that is already exerted and based on the incentive from the forward-looking performance measure in the previous period, the motivation of shortsighted eort is independent of the forward-looking measure. The reason is that renegotiation takes place after farsighted eort has already been exerted. Therefore, the motivation of farsighted eort is not necessary anymore and the principal provides incentives only for shortsighted eort in period. Then, the principal selects the xed wage payment α such that the participation constraint (10b) is binding. The optimal shortsighted action (Expression (11)) and the xed wage are substituted into the principal's objective function (10a) which is dierentiated with respect to the incentive weight v. Solving the rst order condition yields the optimal incentive weight on the second-period prot: v = g. (1) g + rσ Due to renegotiation, the principal determines the incentive weight on second-period prot in order to motivate recurring shortsighted eort. Farsighted eort, that also aects the prot in period, has already been exerted at this point of time and is considered as a given parameter in the principal's optimization problem. However, in t = 0, the agent anticipates 1

15 renegotiation, so he can strategically choose his farsighted eort level in order to maximize his utility in both periods. 3. First-Period Contract Back to the rst period, the agent chooses shortsighted eort a 1, that aects rst-period prot, and farsighted eort b, that aects second-period prot, taking into account their impact on his compensation in both periods. As, at date t = 0, the agent anticipates the renegotiated contract, his expected utility is expressed by the certainty equivalent as follows: [ CE 1 = E[w 1 ] κ 1 (a 1, b) r ( )] σ 1v1 + σyv y + δ [E[w v, a ] κ (a ) r σ(v ) ]. (13) As described in Section., the factor δ (0, 1) discounts the agent's utility from period. The principal also anticipates renegotiation in period, so her optimization problem at t = 0 can be represented as follows: max NP 1 =E[π 1 ] + E[π v v 1,v y, a ] E[w 1 ] E[w v, a ] (14a) s. t. CE 1 0, (14b) a 1, b argmax a 1,b CE 1. (14c) The principal maximizes her expected net payo of both periods subject to the agent's participation constraint (14b) and the incentive compatibility constraint (14c). The participation constraint ensures that the agent accepts the compensation contract for both periods. The 13

16 agent maximizes his expected utility according to (14c) which leads to the optimal shortsighted eort level a 1 = gv 1 (15) and the optimal farsighted eort level b = v y + δhv. (16) From Expression (16), despite renegotiation at date t = 1, farsighted eort is motivated by both the forward-looking performance measure and the second-period prot because the agent anticipates renegotiation by accepting the contract. Considering the renegotiated contract in period, the principal selects the wage payment such that the participation constraint (14b) is binding. The wage payments and the optimal shortsighted (Expression (15)) and farsighted eort (Expression (16)) are substituted into the principal's objective function (14a). The optimization of the principal's unconstrained decision problem leads to the optimal incentive weight on the short-term performance measure v 1 = g g + rσ 1 (17) and the optimal incentive weight on the forward-looking performance measure v y = h(g (1 δ) + rσ ) (g + rσ )(1 + rσ y). (18) 14

17 The principal chooses an incentive weight on the forward-looking performance measure depending on her anticipation of the renegotiated contract. Rearranging (18) and using (1) yields: v y = h (1 δv 1 + rσ ). (19) y While the incentive weight on the second-period prot is independent of the provision of incentives in period 1 (i.e., v is independent of v y ), the incentive weight on the forwardlooking performance measure is reduced by the weight placed on the prot in period. This substitutive eect arises from the fact that farsighted eort is motivated by both performance measures at date t = 0. The intensity of this eect depends on the agent's future preference factor, δ. A high factor, reecting low myopia of the agent, leads to a stronger impact of the second-period incentive weight on the forward-looking weight which results in a lower incentive weight on the forward-looking performance measure. A low future preference factor leads to a weak impact of the incentive weight on the second-period prot. Thus, also if renegotiation is possible, the higher the agent's myopia the more the forward-looking performance measure is used in contract design in order to motivate farsighted eort. This result is summarized in the following Lemma. Lemma 1 While, due to renegotiation, the incentive weight on the second-period prot is independent of the provision of incentives in period 1, the incentive weight on the forwardlooking performance measure is negatively aected by the incentive weight on the prot in period depending on the degree of the agent's future preference factor. 15

18 The principal's optimal net payo is g 4 NP = (g + rσ ( 1) (g + rσ) ( g 4 (1 + rσy) + h (g (1 + δrσy) + rσ) ) ) δ g 4 h rσy +. (g + rσ) (1 + rσy) (0) All derivations of the results for the optimal contract are presented in Appendix A. 4 Performance Measure Choice and Eort Motivation In this section, I investigate the relationship between recurring shortsighted and farsighted eort as well as the impact of the agent's myopia, dierent eort productivities, and longterm risk on incentive design. Table 1 summarizes the comparative statics for the optimal incentive weights and the optimal eort levels. Part A of the table outlines the impact of several parameters on the optimal incentive weights, whereas Part B outlines the impact on the optimal eort choices. The calculation of all derivatives is presented in Appendix B. In the following, each of the impact factors is discussed. Impact of the Agent's Myopia The agent's myopia aects contract design as described in the rst row of Part A and B in Table 1. A larger future preference factor δ means that the agent is less myopic and thus has a higher interest in future returns at date t = 0. 5 In order to rise future returns, the agent exerts farsighted eort b that aects the second-period prot and, as a consequence, his 5 Note that the future preference factor is dened by δ = 1 1+i where i is the interest rate. A higher interest rate results in a lower future preference factor which means that the agent has a lower preference for future utility. 16

19 Part A: Optimal Incentive Weights Parameter j sgn[ v / j] sgn[ v y/ j] sgn[ ( v ) / j] v y δ 0 + g + + h 0 + σ + Part B: Optimal Eort Levels Parameter j sgn[ a / j] sgn[ b / j] sgn[ ( a b ) / j] δ 0 + g h 0 + σ Table 1: Comparative Statics of Optimal Incentive Weights and Optimal Eort Choices. second-period wage. Thus, the optimal level of b increases with δ ( b / δ > 0). As the agent is motivated to exert b through his farsighted attitude, the principal can correspondingly reduce the incentive weight on the forward-looking performance measure, y (v y/ δ < 0). The weight on the forward-looking performance measure and the agent's future preference factor are substitutes for providing incentives for the farsighted eort, b. A lower preference factor reects a higher myopia of the agent and thus less interest for future returns. Then, the agent's interest in second-period utility and wage payment at date t = 0 is low and he exerts less eort on the farsighted task. In order to motivate b, the principal emphasizes y. However, the optimal level of b decreases which implies that the forward-looking performance measure cannot fully substitute the agent's myopia for motivating farsighted eort. Because of renegotiation, v is not aected by δ. Myopia is relevant at date t = 0 when 17

20 the agent discounts expected future utility from period. At date t = 1, when renegotiation takes place, period is the present period. Thus, at this point in time, second-period utility is no longer discounted. As π then becomes a short-term performance measure for the repeated shortsighted eort, a is also not aected by δ. The following Corollary summarizes the result. Corollary 1 Due to the possibility of renegotiation, the agent's myopia has no impact on the provision of incentives for shortsighted eort in period. Impact of Eort Productivities The second and third row of Part A and B in Table 1 outline the eect of dierent eort productivities on the optimal contract design. First, the productivity of shortsighted eort, g, is analyzed. A higher g means that the shortsighted eort has a stronger impact on the second-period prot. Thus, the principal enhances the incentive for repeated shortsighted eort by emphasizing π ( v / g > 0) which results in a higher repeated shortsighted eort, a. As π also motivates farsighted eort, b, the principal can reduce the incentive weight on the forward-looking performance measure, y ( v y/ g < 0). Table 1 states that, ceteris paribus, a higher g leads to an increase of the optimal farsighted eort level despite of a decreasing v y ( b / g > 0). Figure illustrates the impact of shortsighted eort productivity on the optimal eort levels. The results suggest that a higher shortsighted eort productivity leads to a stronger incentive eect of π than of y for motivating b. This result is in line with Abernethy et al. (013) and leads to the following Corollary. Corollary If, ceteris paribus, the productivity of recurring shortsighted eort is higher, 18

21 the incentive eect of the second-period prot outweighs the incentive eect of the forwardlooking performance measure for motivating farsighted eort. In designing a compensation contract, it has to be considered that these performance measures are not perfect substitutes in incentivizing farsighted eort. The incentive eect of π is higher than the one of y for motivating b. This result justies the intensied use of long-term incentive contracts for rms with high productive shortsighted tasks in practice. Firms should consider changes in eort productivities such that they emphasize forwardlooking performance measures if the shortsighted task's productivity is lower. However, the implementation of a forward-looking performance measure improves the rm's payo as will be discussed in the next section. a,b 4 Agent's Optimal Effort Choices 3 Repeated Shortsighted Effort a Farsighted Effort b g Figure : Optimal Eort Levels as a Function of Shortsighted Eort Productivity with δ = 0.75, h = 3, r = 0.5, and σ 1 = σ = σ y = 1. Second, the productivity of the farsighted eort, h, is considered. A larger productivity of the farsighted eort only aects the incentive weight on y and thus the optimal level of farsighted eort. If b is more productive, the principal motivates the agent to exert a higher eort level by emphasizing y ( v y/ h > 0). The rising v y leads to an increase in the optimal level of farsighted eort ( b / h > 0). Because of renegotiation, the incentive weight on 19

22 π, and thereby the optimal shortsighted eort, are not aected by a change in productivity of farsighted eort. Figure 3 illustrates the impact of farsighted eort productivity on the optimal eort levels. a,b Agent's Optimal Effort Choices 3 Repeated Shortsighted Effort a Farsighted Effort b h Figure 3: Optimal Eort Levels as a Function of Farsighted Eort Productivity with δ = 0.75, g = 3, r = 0.5, and σ 1 = σ = σ y = 1. As farsighted eort is motivated by π and y, it increases in both productivities, whereas shortsighted eort is motivated only through π and therefore increases only in g. In addition, when shortsighted eort is more productive, shortsighted eort rises to a higher extent than farsighted eort ( ( a b )/ g > 0). Hence, the level of shortsighted eort exceeds the level of farsighted eort if the shortsighted task is suciently productive relative to the farsighted task or, looking at it the other way round, if the farsighted task is suciently unproductive relative to the shortsighted task. This situation can be described formally by the following condition for the productivity of farsighted eort: h < g 3 (1+rσ y ) g (1+δrσ y )+rσ. Graphically, this threshold is the point of intersection of the two functions in Figure 3. For all h left from this point (h < ), a exceeds b. Finally, I investigate the impact of both eort productivities, g and h. To summarize, the motivation of recurring shortsighted eort is independent of h, but a higher shortsighted 0

23 eort productivity, g, leads to an increase of v and a. As v and v y are substitutes for motivating b, v y decreases in g. However, a higher farsighted eort productivity leads to an increase of v y. If both productivities are higher, the eect of the shortsighted eort productivity outweighs the one of the farsighted eort productivity such that the forwardlooking performance measure is less emphasized ( v y g h < 0). Nevertheless, farsighted eort increases. This result also implies that the second-period prot is a stronger incentive for motivating farsighted eort than the forward-looking performance measure, as has been described in Corollary. Impact of Long-Term Risk The impact of the long-term risk σ on incentive design and on the agent's eort choice is summarized in the last row of Part A and B in Table 1. As both eorts are motivated through the second-period prot, the imposed risk aects the motivation of both eorts. A higher σ means that the prot in period is riskier and the principal has to compensate the agent for the higher risk in form of a risk premium. In order to reduce the risk premium, the principal lowers the incentive weight on π ( v / σ < 0). This leads to a lower shortsighted eort level, a ( a / σ < 0). The forward-looking performance measure, y, acts as a substitute for motivating b which is why it is more emphasized in the compensation contract ( v y/ σ > 0). In total, b decreases with a rising σ because the incentive eect of y is lower than that of π ( b / σ < 0). However, y motivates the farsighted eort such that the implementation of this measure leads to a lower decrease of b. The forward-looking performance measure creates an increase 1

24 of b equal to b = h(g (1 δ)+rσ ) (g +rσ )(1+rσ y ). The higher the long-term risk, the higher is b because of the higher emphasis of y and thereby the higher incentive for exerting b. Figure 4 visualizes the described relationship between the risk of the second-period prot and the agent's optimal eort choice. It shows that y leads, rst, to a higher level of b and, second, to a lower decrease in σ. The implementation of the forward-looking performance measure yields an increase of the principal's net payo of NP = h (g (1 δ)+rσ ) (g +rσ ) (1+rσ y ).6 As NP 0, the use of y is always benecial for the principal if it is available at suciently low or no costs. The expression shows that y becomes more valuable with a higher σ as it balances the lower emphasis of π for motivating b. Proposition 1 summarizes the importance of the forward-looking performance measure. Proposition 1 The implementation of a costless forward-looking performance measure is always benecial for a rm. In particular, it is useful for compensating long-term risk as the value of this measure increases with a higher risk. The results imply that rms should implement forward-looking performance measures, such as product quality or customer satisfaction, in incentive contracts in order to motivate farsighted tasks. In particular, if they face an uncertain future environment (e.g., startups), they should set a higher weight on forward-looking measures than on future returns as performance measures. In the following, I discuss the impact of a simultaneous change of eort productivities and long-term risk. If shortsighted eort productivity and long-term risk change simultaneously, the change in the provision of incentives is not obvious anymore, but depends on the relation 6 Expression NP is the dierence between the principal's net payo with and without the forwardlooking performance measure. The principal's optimal net payo is calculated according to Appendix A but without the forward-looking performance measure, y. The same approach is chosen for calculating b.

25 a,b Agent's Optimal Effort Choices Repeated Shortsighted Effort a Farsighted Effort b Farsighted Effort b without y σ Figure 4: Optimal Eort Levels as a Function of Risk with δ = 0.75, r = 0.5, g = h = 3, and σ 1 = σ y = 1. between risk and productivity. For g > rσ, the eect of g outweighs the eect of σ such that π is more emphasized ( v g σ > 0), whereas the weight on y decreases ( v y g σ < 0) if both parameters are higher. As the incentive eect of π is stronger than that of y, farsighted eort increases ( b g σ > 0). If g < rσ holds, the opposite eect is stronger, i.e., v y increases, whereas v and thus b decrease. If, in addition to the higher risk, also farsighted eort productivity is higher, π is less emphasized in the incentive contract as v decreases in σ and is independent of h. The incentive weight on the forward-looking measure increases for motivating b, that is more productive, and for compensating the lower weight on π. However, farsighted eort decreases ( b h σ < 0), so the incentive of π outweighs the one of y. By using the forward-looking performance measure in contract design, the optimal farsighted eort level is higher compared to the contract without y. The higher h and σ, the higher is the contribution of y to the motivation of b ( b h σ > 0). Overall, these results show that the optimal eort levels change in the same direction 3

26 (or shortsighted eort does not change) if the described parameters vary. This implies that eorts are not substitutes though both aect the rm's prot. The reason is that the secondperiod prot motivates both eorts. The forward-looking measure acts substitutive but it has a lower incentive eect such that the motivation of farsighted eort is predominantly determined by the second-period prot. Consequently, there exists a complementary eect between shortsighted and farsighted eort when productivity of shortsighted eort or longterm risk change. The following Proposition summarizes the main results of this section: Proposition Recurring shortsighted and farsighted eort are complements with respect to their impact on the rm's nal prot if ˆ the productivity of the recurring shortsighted eort is high or ˆ risk of the second-period prot is low. This means that a higher shortsighted eort productivity leads to an increase of the incentive weight on second-period prot with the result of rising eorts a and b. A lower long-term risk, σ, has the same eect as a less risky performance measure is more emphasized in the incentive contract. To summarize, the emphasis of the second-period prot in the incentive contract leads to the motivation of both eorts. Thus, if a manager's bonus depends on the rm's future prot, he will exert eort on tasks in the current and future period that aect the future prot. 4

27 5 The Impact of Repeated Shortsighted Eort In this section, I investigate the impact of recurring shortsighted eort on contract design. Without the motivation of repeated shortsighted eort, a, renegotiation would not be benecial for both parties, because renegotiation takes place when eorts are already compensated through the contractible short-term and forward-looking performance measure. The secondperiod prot is not needed anymore as there is no action to motivate the agent for in period. Thus, the agent does not participate in second-period prot and does not bear any risk. As a result, the principal pays no bonus in period and neither the principal nor the agent improves her/his situation through renegotiation. The motivation of repeated shortsighted eort leads to the possibility of renegotiation because the principal motivates an additional eort in period after eventual renegotiation. Here, I would like to answer the question whether it would be benecial for the principal not to motivate recurring shortsighted eort in period in order to reduce the welfare loss resulting from renegotiation. 7 For comparing both situations, the optimal contract without recurring shortsighted eort is derived in Appendix C. The setting without recurring shortsighted eort and without renegotiation is very similar to Dikolli (001). He investigates the incentive design that motivates only one-shot shortsighted and farsighted eort in period 1. There, the second-period prot serves only as a long-term performance measure for evaluating farsighted eort. The impact of recurring shortsighted eort depends particularly on the relation between eort productivities. In order to analyze the protability of motivating the additional ef- 7 Fudenberg and Tirole (1990) point out that the possibility of renegotiation leads to a dead weight loss. 5

28 fort, I dierentiate between three scenarios depending on thresholds for the farsighted eort productivity. First, the motivation of repeated shortsighted eort leads to an increase in farsighted eort if the following condition holds: Aσ h < δσy(c δg ) h 1, with A = g (1 + rσy) and C = g + rσ. This condition reects that the farsighted task, b, is less productive in relation to the shortsighted task, a. In order to motivate a, the performance measure π is more emphasized in the compensation contract. The incentive weight on the forward-looking performance measure, y, decreases in order to reduce the incentive for b. As π also motivates b and as its incentive eect is higher than that of y, the optimal level of b increases. In contrast, without repeated shortsighted eort a, the positive eect of a higher a does not aect contract design in period. This leads to a higher net payo when a is motivated. The results indicate that, if b is less productive relative to a, the motivation of a leads to an increase in b. Consequently, eorts are complements if the farsighted task is relatively unproductive. Second, the motivation of repeated shortsighted eort leads to a decrease in farsighted eort if h > h 1. Then, b is relatively more productive than a. Thus, the forward-looking performance measure, y, is more emphasized, whereas π is less emphasized in the compensation contract in order to lower the incentive for the rather unproductive repeated shortsighted effort. Because of the higher inventive eect of π, b decreases. Without a, b always increases in productivity because π only motivates this productive eort. The result is summarized 6

29 as follows: Lemma The motivation of repeated shortsighted eort leads to a lower optimal level of Aσ farsighted eort if h > holds, i.e., farsighted eort is rather productive in relation δσy(c δg ) to repeated shortsighted eort. Third, while the motivation of repeated shortsighted eort leads to a lower farsighted eort level if the latter is rather productive, it is not obvious whether the principal's net payo decreases or increases. The impact of a on the principal's net payo depends on a dierent threshold for farsighted eort productivity: A ( δg 4 + rσ C + C(C(δ g 4 + 4rσ (C δg )) + δ g 4 rσ ) ) h = δrσ y(c δg ) > h 1. In case h > h > h 1, b is relatively productive such that the motivation of a decreases the optimal b, but the principal's net payo increases. The reason is that the additional eort also contributes to second-period prot and balances the lower farsighted eort such that overall net payo increases when shortsighted eort is motivated in period. In case h > h > h 1, b is highly productive relative to a. This leads to a lower incentive through the second-period prot for exerting it. As already explained, this also yields a lower optimal level of b though it is highly productive. As the optimal level of repeated shortsighted eort is very low, the low farsighted eort cannot be balanced (unlike in case h > h > h 1 ). This results in a low net payo for the principal. In contrast, if shortsighted eort is not motivated in period, a high farsighted eort productivity always leads to a rising eort level and a rising net payo as the motivation of farsighted eort is independent of the incentive for shortsighted eort and thereby of its productivity. 7

30 The protability of the motivation of repeated shortsighted eort for the principal is illustrated in Figure 5 as a function of eort productivities. The blue area in this graph visualizes the rst case (h > h > h 1 ) where the implementation of repeated shortsighted eort results in a higher net payo for the principal. The second case (h > h > h 1 ) is illustrated by the orange area of the graph where the principal's net payo is lower when she motivates recurring shortsighted eort. Thus, the threshold h is the border between the two areas. Figure 5: Changes in the Principal's Expected Net Payo as a Function of Eort Productivities with δ = 0.75, r = 0.5, and σ 1 = σ = σ y = 1. The following proposition resumes the result: Proposition 3 For the principal, it is not benecial to motivate repeated shortsighted effort if h > ) A (δg 4 +rσ C(C(δ C+ g 4 +4rσ (C δg ))+δ g 4 rσ ) δrσ y (C δg ) productive relative to recurring shortsighted eort., i.e., farsighted eort is much more Proposition 3 implies that it is not always benecial to motivate an additional task. If the contribution to the rm's future prot of a farsighted task (e.g., investments in R&D) is much 8

31 higher than of a future shortsighted task (e.g., selling the product), it may be benecial to compensate the manager only for the undertaken investments. Then, it can be advantageous to reduce the manager's area of responsibility and delegate the future shortsighted task to a dierent manager. 6 Conclusion This paper studies the optimal design of incentive systems in an environment with recurring shortsighted eort and a one-shot farsighted eort. In particular, I investigate a forwardlooking compensation contract oered to a myopic manager. The analysis provides insights about the impact of recurring shortsighted eort on the incentive design if renegotiation is possible. The ndings indicate that the additional repeated shortsighted eort and the accompanying possibility of renegotiation aect the incentive for exerting farsighted eort. In fact, farsighted eort is motivated through both the forward-looking performance measure and the second-period prot. I nd that the weight placed on the prot has a stronger eect on the motivation of farsighted eort than the weight on the forward-looking measure. Due to renegotiation, the second-period prot is independent of the forward-looking incentive because it is placed in order to motivate the repeated shortsighted eort. However, the motivation of shortsighted eort in period motivates simultaneously farsighted eort in the rst period as the agent creates expectations about both periods. The complementary eect is intensied with a rising productivity of the repeated shortsighted eort and a decreasing risk of second-period prot. More precisely, if shortsighted eort becomes less produtive, also the motivation of farsighted eort decreases with that both eort levels fall. Referring 9

32 to practice, this contract design can be a possible reason for underinvestments in long-term projects. Thus, rms should consider that the forward-looking performance measure and future prots are not perfect substitutes in motivating farsighted tasks. The results suggest that the incentive eect of a performance measure like future rm prot is much higher independent of the manager's myopic attitude even so the implementation of a forward-looking measure improves the rm's overall performance, as it is found in the empirical study of Abernethy et al. (013). Moreover, I nd conditions under which the motivation of a recurring shortsighted eort is not benecial. If shortsighted eort is very unproductive relative to farsighted eort, then the motivation through the second-period prot decreases whereby both eort levels decrease despite the forward-looking incentive. Without the motivation of shortsighted eort in period, the high productive farsighted eort is motivated by both a higher second-period prot and a higher forward-looking performance measure. Thus, the repeated shortsighted task in period should not be motivated if it is rather unproductive relative to the farsighted task though both tasks contribute to the rm's prot. This means for practice that it is not always benecial to motivate an additional productive task. If the additional future task is rather unproductive in relation to the current task and both aect future rm outcome, then the future task should not be motivated at all. The rm might be better o when it employs a second manager for the shortsighted task or even neglect the task. 30

33 Appendix A. Derivation of the Optimal Contract. The optimal contract is determined by using backward induction. At date t = 1, the agency problem is: max v NP (w â 1, ˆb, ŷ, ˆπ 1 ) =E[π â 1, ˆb, ŷ, ˆπ 1 ] E[w â 1, ˆb, ŷ, ˆπ 1 ] (1a) s. t. CE (w â 1, ˆb, ŷ, ˆπ 1 ) U I, (1b) a argmax a CE (w â 1, ˆb, ŷ, ˆπ 1 ). (1c) The incentive compatibility constraint (1c) is: max a CE (w â 1, ˆb, ŷ, ˆπ 1 ) =E[w ] κ (a ) r σ v () =α + v (ga + hb) 1 a r σ v (3) Taking the rst derivative with respect to the agent's eort choice a yields: CE a = gv a a = gv. (4) Substituting the binding participation constraint (1b) and the optimal eort choice (4) into the objective function and take the rst derivative with respect to the incentive weight on the second-period prot yields: CE v = g v (g + rσ ) v = g. (5) g + rσ 31

34 Insert (5) into (4) leads to the optimal eort choice a = g 3. (6) g + rσ The optimization problem at date t = 0 is: max NP 1 =E[π 1 ] + E[π v v 1,v y, a ] E[w 1 ] E[w v, a ] s. t. CE 1 0, (PC1) a 1, b argmax a 1,b CE 1. (IC1) The incentive compatibility constraint at the beginning of period 1 (IC1) is: [ max CE 1 = E[w 1 ] κ 1 (a 1, b) r ( )] σ a 1,b 1v1 + σyv y + δ [E[w v, a ] κ (a ) r σ(v ) ] =α 1 + v 1 ga 1 + v y b 1 (a 1 + b ) r ( ) σ 1v1 + σyv y + δ [α + v (ga + hb) 1 (a ) r σ(v ) ] Taking the rst derivatives with respect to the eorts a 1 and b yields: CE 1 a 1 = gv 1 a 1 a 1 = gv 1 (7) and CE 1 b = δg h + (g + rσ)(v y b) b = v y + δg h. (8) g + rσ Using the optimal second-period contract resulting from (1a) to (1c) and substituting 3

35 the optimal eort levels (7) and (8), and the participation constraint (PC1) leads to the unconstrained optimization problem: 8 max NP 1 =g v 1 + ( ga + h ( v y + δg h )) v 1,v y g + rσ 1 ( (gv1 ) ( + vy + δg h ) ) g + rσ 1 (a ) r ( σ 1v 1 + σ yv y + σ (v ) ) (9) Solving the rst order conditions yields NP 1 v 1 = g + v 1 (g + rσ 1) v 1 = g g + rσ 1 (30) and NP 1 v y = h(g (1 δ) + rσ ) v y (g + rσ )(1 + rσ y) v y = h(g (1 δ) + rσ ) (g + rσ )(1 + rσ y). (31) Insert (30) into (7) and (31) into (8) leads to the optimal eort levels a 1 = g 3 g + rσ 1 (3) and b = h(g (1 + δrσ y) + rσ ) (g + rσ )(1 + rσ y). (33) The optimal prot levels are calculated by inserting the optimal eort levels from Expression 8 As the agent and the principal anticipate renegotiation, the second-period contract is already calculated via backward induction. Therefore, the binding participation constraint (1b), the optimal incentive weight v and the optimal recurring eort a are substituted into the objective function. Dikolli (001) uses a similar approach that is explained in Appendix C. 33