- Email: [email protected]
Multiple tasks and political organization
Economics Letters 128 (2015) 48–50
Contents lists available at ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
Multiple tasks and political organization Tom Hamami ∗ Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208, USA
highlights • • • •
Considers multiple-task effort distortion problem in restricted contract space. Agents may only be re-elected rather than compensated with some transfer. Finds that positive spillover effects may outweigh negative distortion problems. Implies highly desirable and highly undesirable tasks should be bundled together.
article
info
Article history: Received 2 October 2014 Received in revised form 12 December 2014 Accepted 9 January 2015 Available online 19 January 2015 JEL classification: H1 M5
abstract Consider an environment such as a political election where a principal requires the completion of multiple tasks, but an agent can only be rewarded with a hire/fire decision rather than an endogenously chosen monetary payment. When the principal hires a single agent to perform multiple tasks, the agent allocates effort between the tasks inefficiently. I demonstrate that, even though hiring multiple agents completely mitigates this effort distortion problem, the principal is still better off hiring a single agent if the (exogenous) rewards for the tasks are sufficiently different. In contrast to similar results in the multi-task literature, this finding is not driven by risk aversion or noise. Rather, it is a direct result of the restricted contract space inherent to the environment. © 2015 Elsevier B.V. All rights reserved.
Keywords: Multiple tasks Elections Job design Government structure
1. Introduction Literature in job design is replete with models that examine optimal organizational design in a variety of settings. In particular, scholars are interested in alleviating the so-called effort distortion problem wherein an agent who performs multiple tasks under imperfect monitoring does not allocate his effort efficiently. Nearly all such analyses, however, allow for affine contracts – contracts that include a fixed salary component and a component that varies linearly with output, both chosen by the principal – since Holmstrom and Milgrom (1987) showed such contracts are optimal. There exist environments, however, where the principal is unable to choose contract terms with such precision. In some such cases, the principal can only observe some performance measure and subsequently decide whether or not to retain the agent for
∗
Tel.: +1 410 818 8472. E-mail address: [email protected].
http://dx.doi.org/10.1016/j.econlet.2015.01.010 0165-1765/© 2015 Elsevier B.V. All rights reserved.
another period. Notably, elected political positions fit this description. The personal benefits accrued by elected officials are typically treated as exogenous (so-called ego rents). Such officials serve as agents of an electorate that decides whether or not to re-elect them. The purpose of this paper is to determine the optimal organizational structure when the contract space is restricted in this way. In particular, we consider an environment where the principal requires the completion of multiple tasks and must decide how many agents to hire to perform these tasks. Intuitively (and consistently with the traditional job design literature), we would expect that, when the effort distortion problem exists, hiring multiple agents yields better results than hiring a single agent. The main result of this paper is that hiring a single agent may actually be more effective if the ego rents of two tasks are sufficiently different. In particular, this result holds even without effort externalities or agent risk aversion—two factors that generally favor the single-agent structure. Instead, this finding is a direct result of the restricted contract space. When one task is not very rewarding to the agent, the single agent structure allows for a spillover effect wherein the agent exerts effort towards the less
T. Hamami / Economics Letters 128 (2015) 48–50
rewarding task to ensure he will be able to perform the more rewarding task again in the future. The main proposition and corollary of the model below thus provide a testable prediction: when the discrepancy in desirability between two tasks for the agent is large relative to the discrepancy in desirability for the principal, we are more likely to observe the tasks being bundled together in a single job. Related literature. This paper is closely related to a strand of literature on job design with multiple tasks spawned by the seminal work of Holmstrom and Milgrom (1991). The most relevant of their results is the finding that, when agents are risk averse and the contract space allows for affine contracts, it is always preferable to assign a single agent to each task. Of many subsequent articles, the most similar is Laux (2001), who also demonstrated that a restricted contract space can induce counterintuitive results. In his case, the principal was restricted by a limited liability constraint. Laux found that assigning a single agent to multiple tasks slackened this limited liability constraint and that this benefit can outweigh the harm caused by the effort distortion problem. Gersbach and Liessem (2008) also considered this multiple task issue in an electoral context. They found that the electoral mechanism alone is unable to induce the first-best outcome, but that combining the electoral mechanism with an incentive contract can alleviate the inefficiency. While that analysis was restricted to a single agent, the current article maintains the restricted contract space and examines the effect of hiring multiple agents. Concurrently and independently, Ashworth and Bueno de Mesquita (2014) have constructed a framework to address the same question as this paper. Their model is considerably more complex, though this allows for some richer analysis (for example, allowing heterogeneous competencies among agents). The marginal contribution of this paper over that one is to show the primary result – the comparative static regarding the tradeoff between total effort and allocational efficiency – can be obtained in an exceptionally simple framework. In particular, the current article captures this effect without any exogenous noise in the principal’s monitoring technology. 2. Model A principal must hire one or two agents to complete two tasks. In a political context, we may think of the principal as the collective interest of the electorate and the agents as elected officials. The key difference between this environment and the standard multi-task principal–agent setting is the inflexibility of the electoral mechanism. While the principal would ordinarily be able to motivate the agents by using a piece rate contract, here its choice is binary (either re-elect or do not). The agents exert effort toward each task, the benefit from which accrues directly to the principal. Specifically, the agents choose effort e ≡ (e1 , e2 ) ≥ 0, which provide benefit v(e) = e1 + e2 to the principal. However, the principal does not observe e or v(e) directly. Instead, it has access monitoring technology that produces signal g (e) = e1 + γ e2 where γ ≥ 1. The idea is that, while the principal values effort from each task equally, an agent who performs both tasks has incentive to choose e2 ‘‘too high’’ and e1 ‘‘too low’’.1 The value of γ captures the magnitude of this effect. The cost of exerting effort is quadratic and separable across tasks. Specifically, c (e) = 21 e21 + 21 e22 . An agent accrues personal benefit
49
(so-called ego rents) from performing task i equal to Ri > 0. Without loss of generality, we assume that R2 ≥ R1 . An agent has outside option with value normalized to 0. The goal of the principal is to induce as much total effort out of the agent(s) as possible. The timing is as follows: 1. The principal chooses whether to hire one or two agents as well as an electoral mechanism that maps from non-negative real numbers into {Y , N }, where Y means the agent will be re-elected and N means that he will not be re-elected. If the principal hires two agents, each agent works exclusively on a single task. This mechanism must satisfy each agent’s participation constraint and is common knowledge. 2. The agent(s) choose(s) e = (e1 , e2 ). The principal does not observe this choice. 3. The principal observes g (e) and the agent is either re-elected or not in accordance with the mechanism to which the principal committed in the first stage. 4. Payoffs are realized. We proceed by characterizing the optimal contract for each organizational structure. 2.1. Two agents When each agent only performs one task, there is no effort distortion issue. Either each agent exerts exactly enough effort to be re-elected or he exerts the zero effort.2 The best the principal can do with this organizational structure is to bind each agent’s participation constraint: Ri −
1 2
e2i = 0
⇐⇒
ei =
2Ri .
This yields social benefit:
v(e) =
√ 2
R1 +
R2
≡ V2 .
Note that this solution is completely independent of γ . If the principal were restricted to hiring exactly two agents, this would represent the best achievable outcome. It is for this reason that, if we were operating in a traditional job design setting with a rich contract space, the two-agent structure would be unambiguously superior. With no effort distortion problem, the principal could simply choose monetary incentives to induce the efficient level of effort from each agent. 2.2. One agent Since there is no noise in the signaling technology, it is immediate that the principal will use a forcing contract to induce the highest possible signal. Denote this signal level by g¯ (i.e. an agent is re-elected only if g (e) ≥ g¯ ). The optimal choice of g¯ will be the one that binds the agent’s participation constraint subject to satisfaction of his incentive compatibility constraint. This incentive compatibility constraint is characterized by the agent’s effort choices as a function of g¯ . Specifically, the agent solves:
min e
1 2
e21 +
1 2
e22
subject to e1 + γ e2 ≥ g¯ .
1 That the principal values each task equally is a normalization made for simplicity. What matters is that the weight with which the principal values task 2 relative to task 1 is weakly smaller than γ , thus inducing effort in tasks 1 and 2 that are weakly ‘‘too low’’ and ‘‘too high’’, respectively.
2 Technically, this induces a coordination game between the two agents. We focus on the equilibrium of this game where both agents exert positive effort.
50
T. Hamami / Economics Letters 128 (2015) 48–50
This constraint binds. Substitution and first-order conditions yield solution: e1 (¯g ) =
1 + γ2
γ g¯ . e2 (¯g ) = 1 + γ2 The principal will subsequently choose g¯ so that the agent’s participation constraint binds. That is, 1 2
e1 (¯g )2 −
g¯ =
⇐⇒
1 2
e2 (¯g )2 = 0
2(R1 + R2 )(1 + γ 2 ).
√
2
1+γ
1+γ
2
R1 + R2
≡ V1 (γ ).
The main purpose of this analysis is to compare expressions V1 and V2 under different parameter values. This leads to our main result: Proposition 1. For any values of R1 and R2 , there exists a value γ ∗ such that V1 ≥ V2 for all γ ∈ [1, γ ∗ ] and V2 > V1 for all γ > γ ∗ . If R1 ̸= R2 , then V1 > V2 for all γ ∈ [1, γ ∗ ). Proof. First, note that V1′ (γ ) =
√
2(R1 + R2 )
1−γ 3
(1+γ ) 2
< 0 for
all γ > 1. Thus, since V2 is independent of γ , if there exists a γ ∗ such that V1 (γ ∗ ) = V2 , we know that V1 > V2 if and only if γ < γ ∗ . Lastly, we show that such a γ ∗ exists and that it is equal to R2 . R1
V1
R2 R1
√ =
=
1+
2
√ =
√
1+
2
The principal tension in the single agent model is between harm caused by the effort distortion problem and the benefit of the spillover effect when R1 ̸= R2 . Our interest is when the latter outweighs the former. Proposition 1 states that, unless R1 = R2 , there always exists a value of γ small enough that the single agent structure yields better results. Since we assumed R2 ≥ R1 , the corollary states that, the greater the ratio of ego rents between the two tasks, the more likely it is that γ is small enough to make the single agent structure better.
The key finding of this paper is that conventional wisdom regarding multiple tasks and job design does not necessarily lead to the correct conclusion when the set of possible contracts is restricted in a particular way. Moreover, this type of restriction is quite common. Besides elected political officials, this result is relevant for project managers who must choose members of a team without control over the members’ compensation. The model suggests that using desirable tasks to induce high effort in undesirable tasks can be effective despite introducing other incentive problems. Moreover, the model generates a testable prediction. The greater the difference in desirability between two tasks (measured, perhaps, by the number of candidates who seek election), the more likely it should be that we see the tasks bundled together into a single job. The extent to which this effect is observable in available data is worthy of further investigation.
R 1 +R 2 √ R1
R1 + R2
R2 R1
√
R1 +
R2 . R1
References
R2 R1
R1 + R2 √ R1
2 √
√
3. Conclusion
And total social benefit is equal to:
v(e) =
R2 . R1
Proof. This result is immediate from the fact that γ ∗ =
g¯
R1 + R2 −
Corollary 1. γ ∗ is strictly increasing in
R1 + R2
R2
= V2 .
Ashworth, Scott, Bueno de Mesquita, Ethan, 2014. Multitask, accountability, and institutional design. Mimeo, Harris School of Public Policy Studies, University of Chicago. Gersbach, Hans, Liessem, Verena, 2008. Incentive contracts and elections for politicians with multi-task problems. J. Econ. Behav. Organ. 68, 401–411. Holmstrom, Bengt, Milgrom, Paul, 1987. Aggregation and linearity in the provision of intertemporal incentives. Econometrica 55 (2), 303–328. Holmstrom, Bengt, Milgrom, Paul, 1991. Multitask principal–agent analyses: incentive contracts, asset ownership, and job design. J. Law Econ. Organ. 7, 24–52. Laux, Christian, 2001. Limited-liability and incentive contracting with multiple projects. RAND J. Econ. 32 (3), 514–526.
Contents lists available at ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
Multiple tasks and political organization Tom Hamami ∗ Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208, USA
highlights • • • •
Considers multiple-task effort distortion problem in restricted contract space. Agents may only be re-elected rather than compensated with some transfer. Finds that positive spillover effects may outweigh negative distortion problems. Implies highly desirable and highly undesirable tasks should be bundled together.
article
info
Article history: Received 2 October 2014 Received in revised form 12 December 2014 Accepted 9 January 2015 Available online 19 January 2015 JEL classification: H1 M5
abstract Consider an environment such as a political election where a principal requires the completion of multiple tasks, but an agent can only be rewarded with a hire/fire decision rather than an endogenously chosen monetary payment. When the principal hires a single agent to perform multiple tasks, the agent allocates effort between the tasks inefficiently. I demonstrate that, even though hiring multiple agents completely mitigates this effort distortion problem, the principal is still better off hiring a single agent if the (exogenous) rewards for the tasks are sufficiently different. In contrast to similar results in the multi-task literature, this finding is not driven by risk aversion or noise. Rather, it is a direct result of the restricted contract space inherent to the environment. © 2015 Elsevier B.V. All rights reserved.
Keywords: Multiple tasks Elections Job design Government structure
1. Introduction Literature in job design is replete with models that examine optimal organizational design in a variety of settings. In particular, scholars are interested in alleviating the so-called effort distortion problem wherein an agent who performs multiple tasks under imperfect monitoring does not allocate his effort efficiently. Nearly all such analyses, however, allow for affine contracts – contracts that include a fixed salary component and a component that varies linearly with output, both chosen by the principal – since Holmstrom and Milgrom (1987) showed such contracts are optimal. There exist environments, however, where the principal is unable to choose contract terms with such precision. In some such cases, the principal can only observe some performance measure and subsequently decide whether or not to retain the agent for
∗
Tel.: +1 410 818 8472. E-mail address: [email protected].
http://dx.doi.org/10.1016/j.econlet.2015.01.010 0165-1765/© 2015 Elsevier B.V. All rights reserved.
another period. Notably, elected political positions fit this description. The personal benefits accrued by elected officials are typically treated as exogenous (so-called ego rents). Such officials serve as agents of an electorate that decides whether or not to re-elect them. The purpose of this paper is to determine the optimal organizational structure when the contract space is restricted in this way. In particular, we consider an environment where the principal requires the completion of multiple tasks and must decide how many agents to hire to perform these tasks. Intuitively (and consistently with the traditional job design literature), we would expect that, when the effort distortion problem exists, hiring multiple agents yields better results than hiring a single agent. The main result of this paper is that hiring a single agent may actually be more effective if the ego rents of two tasks are sufficiently different. In particular, this result holds even without effort externalities or agent risk aversion—two factors that generally favor the single-agent structure. Instead, this finding is a direct result of the restricted contract space. When one task is not very rewarding to the agent, the single agent structure allows for a spillover effect wherein the agent exerts effort towards the less
T. Hamami / Economics Letters 128 (2015) 48–50
rewarding task to ensure he will be able to perform the more rewarding task again in the future. The main proposition and corollary of the model below thus provide a testable prediction: when the discrepancy in desirability between two tasks for the agent is large relative to the discrepancy in desirability for the principal, we are more likely to observe the tasks being bundled together in a single job. Related literature. This paper is closely related to a strand of literature on job design with multiple tasks spawned by the seminal work of Holmstrom and Milgrom (1991). The most relevant of their results is the finding that, when agents are risk averse and the contract space allows for affine contracts, it is always preferable to assign a single agent to each task. Of many subsequent articles, the most similar is Laux (2001), who also demonstrated that a restricted contract space can induce counterintuitive results. In his case, the principal was restricted by a limited liability constraint. Laux found that assigning a single agent to multiple tasks slackened this limited liability constraint and that this benefit can outweigh the harm caused by the effort distortion problem. Gersbach and Liessem (2008) also considered this multiple task issue in an electoral context. They found that the electoral mechanism alone is unable to induce the first-best outcome, but that combining the electoral mechanism with an incentive contract can alleviate the inefficiency. While that analysis was restricted to a single agent, the current article maintains the restricted contract space and examines the effect of hiring multiple agents. Concurrently and independently, Ashworth and Bueno de Mesquita (2014) have constructed a framework to address the same question as this paper. Their model is considerably more complex, though this allows for some richer analysis (for example, allowing heterogeneous competencies among agents). The marginal contribution of this paper over that one is to show the primary result – the comparative static regarding the tradeoff between total effort and allocational efficiency – can be obtained in an exceptionally simple framework. In particular, the current article captures this effect without any exogenous noise in the principal’s monitoring technology. 2. Model A principal must hire one or two agents to complete two tasks. In a political context, we may think of the principal as the collective interest of the electorate and the agents as elected officials. The key difference between this environment and the standard multi-task principal–agent setting is the inflexibility of the electoral mechanism. While the principal would ordinarily be able to motivate the agents by using a piece rate contract, here its choice is binary (either re-elect or do not). The agents exert effort toward each task, the benefit from which accrues directly to the principal. Specifically, the agents choose effort e ≡ (e1 , e2 ) ≥ 0, which provide benefit v(e) = e1 + e2 to the principal. However, the principal does not observe e or v(e) directly. Instead, it has access monitoring technology that produces signal g (e) = e1 + γ e2 where γ ≥ 1. The idea is that, while the principal values effort from each task equally, an agent who performs both tasks has incentive to choose e2 ‘‘too high’’ and e1 ‘‘too low’’.1 The value of γ captures the magnitude of this effect. The cost of exerting effort is quadratic and separable across tasks. Specifically, c (e) = 21 e21 + 21 e22 . An agent accrues personal benefit
49
(so-called ego rents) from performing task i equal to Ri > 0. Without loss of generality, we assume that R2 ≥ R1 . An agent has outside option with value normalized to 0. The goal of the principal is to induce as much total effort out of the agent(s) as possible. The timing is as follows: 1. The principal chooses whether to hire one or two agents as well as an electoral mechanism that maps from non-negative real numbers into {Y , N }, where Y means the agent will be re-elected and N means that he will not be re-elected. If the principal hires two agents, each agent works exclusively on a single task. This mechanism must satisfy each agent’s participation constraint and is common knowledge. 2. The agent(s) choose(s) e = (e1 , e2 ). The principal does not observe this choice. 3. The principal observes g (e) and the agent is either re-elected or not in accordance with the mechanism to which the principal committed in the first stage. 4. Payoffs are realized. We proceed by characterizing the optimal contract for each organizational structure. 2.1. Two agents When each agent only performs one task, there is no effort distortion issue. Either each agent exerts exactly enough effort to be re-elected or he exerts the zero effort.2 The best the principal can do with this organizational structure is to bind each agent’s participation constraint: Ri −
1 2
e2i = 0
⇐⇒
ei =
2Ri .
This yields social benefit:
v(e) =
√ 2
R1 +
R2
≡ V2 .
Note that this solution is completely independent of γ . If the principal were restricted to hiring exactly two agents, this would represent the best achievable outcome. It is for this reason that, if we were operating in a traditional job design setting with a rich contract space, the two-agent structure would be unambiguously superior. With no effort distortion problem, the principal could simply choose monetary incentives to induce the efficient level of effort from each agent. 2.2. One agent Since there is no noise in the signaling technology, it is immediate that the principal will use a forcing contract to induce the highest possible signal. Denote this signal level by g¯ (i.e. an agent is re-elected only if g (e) ≥ g¯ ). The optimal choice of g¯ will be the one that binds the agent’s participation constraint subject to satisfaction of his incentive compatibility constraint. This incentive compatibility constraint is characterized by the agent’s effort choices as a function of g¯ . Specifically, the agent solves:
min e
1 2
e21 +
1 2
e22
subject to e1 + γ e2 ≥ g¯ .
1 That the principal values each task equally is a normalization made for simplicity. What matters is that the weight with which the principal values task 2 relative to task 1 is weakly smaller than γ , thus inducing effort in tasks 1 and 2 that are weakly ‘‘too low’’ and ‘‘too high’’, respectively.
2 Technically, this induces a coordination game between the two agents. We focus on the equilibrium of this game where both agents exert positive effort.
50
T. Hamami / Economics Letters 128 (2015) 48–50
This constraint binds. Substitution and first-order conditions yield solution: e1 (¯g ) =
1 + γ2
γ g¯ . e2 (¯g ) = 1 + γ2 The principal will subsequently choose g¯ so that the agent’s participation constraint binds. That is, 1 2
e1 (¯g )2 −
g¯ =
⇐⇒
1 2
e2 (¯g )2 = 0
2(R1 + R2 )(1 + γ 2 ).
√
2
1+γ
1+γ
2
R1 + R2
≡ V1 (γ ).
The main purpose of this analysis is to compare expressions V1 and V2 under different parameter values. This leads to our main result: Proposition 1. For any values of R1 and R2 , there exists a value γ ∗ such that V1 ≥ V2 for all γ ∈ [1, γ ∗ ] and V2 > V1 for all γ > γ ∗ . If R1 ̸= R2 , then V1 > V2 for all γ ∈ [1, γ ∗ ). Proof. First, note that V1′ (γ ) =
√
2(R1 + R2 )
1−γ 3
(1+γ ) 2
< 0 for
all γ > 1. Thus, since V2 is independent of γ , if there exists a γ ∗ such that V1 (γ ∗ ) = V2 , we know that V1 > V2 if and only if γ < γ ∗ . Lastly, we show that such a γ ∗ exists and that it is equal to R2 . R1
V1
R2 R1
√ =
=
1+
2
√ =
√
1+
2
The principal tension in the single agent model is between harm caused by the effort distortion problem and the benefit of the spillover effect when R1 ̸= R2 . Our interest is when the latter outweighs the former. Proposition 1 states that, unless R1 = R2 , there always exists a value of γ small enough that the single agent structure yields better results. Since we assumed R2 ≥ R1 , the corollary states that, the greater the ratio of ego rents between the two tasks, the more likely it is that γ is small enough to make the single agent structure better.
The key finding of this paper is that conventional wisdom regarding multiple tasks and job design does not necessarily lead to the correct conclusion when the set of possible contracts is restricted in a particular way. Moreover, this type of restriction is quite common. Besides elected political officials, this result is relevant for project managers who must choose members of a team without control over the members’ compensation. The model suggests that using desirable tasks to induce high effort in undesirable tasks can be effective despite introducing other incentive problems. Moreover, the model generates a testable prediction. The greater the difference in desirability between two tasks (measured, perhaps, by the number of candidates who seek election), the more likely it should be that we see the tasks bundled together into a single job. The extent to which this effect is observable in available data is worthy of further investigation.
R 1 +R 2 √ R1
R1 + R2
R2 R1
√
R1 +
R2 . R1
References
R2 R1
R1 + R2 √ R1
2 √
√
3. Conclusion
And total social benefit is equal to:
v(e) =
R2 . R1
Proof. This result is immediate from the fact that γ ∗ =
g¯
R1 + R2 −
Corollary 1. γ ∗ is strictly increasing in
R1 + R2
R2
= V2 .
Ashworth, Scott, Bueno de Mesquita, Ethan, 2014. Multitask, accountability, and institutional design. Mimeo, Harris School of Public Policy Studies, University of Chicago. Gersbach, Hans, Liessem, Verena, 2008. Incentive contracts and elections for politicians with multi-task problems. J. Econ. Behav. Organ. 68, 401–411. Holmstrom, Bengt, Milgrom, Paul, 1987. Aggregation and linearity in the provision of intertemporal incentives. Econometrica 55 (2), 303–328. Holmstrom, Bengt, Milgrom, Paul, 1991. Multitask principal–agent analyses: incentive contracts, asset ownership, and job design. J. Law Econ. Organ. 7, 24–52. Laux, Christian, 2001. Limited-liability and incentive contracting with multiple projects. RAND J. Econ. 32 (3), 514–526.