Monitoring Team Production by Design

Bono, Giovanni Working Paper Monitoring Team Production by Design Quaderni - Working Paper DSE, No. 540 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Bono, Giovanni (2005) : Monitoring Team Production by Design, Quaderni - Working Paper DSE, No. 540, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4750 This Version is available at: https://hdl.handle.net/10419/159381 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/3.0/ Monitoring Team Production by Design∗ Giovanni Bono Universit`a di Bologna – Dipartimento di Scienze Economiche e–mail: [email protected] web: http://www.dse.unibo.it/bono/ June 10, 2005 Abstract This work addresses the optimal design of the monitoring technology for a team when collective liability can not form. It shows that the principal’s optimal design choice is then to concentrate monitoring on the less productive agent in a team. By controlling the less productive agent she fully discipline the more productive. This result helps in studying the interplay between the institutional set-up and the technological capabilities of teams. Keywords: Team Production, Endogenous Information Structure, Individual Liability. Jel: L23, C72, . . . ∗ « Giovanni Bono, 2005. This document was produced on a GNU system (Debian GNU/Linux) using GNU Emacs (21.3) for the editing and L A T EX 2εfor the typesetting. Thanks to Debraj Ray. And to: Paolo Bertoletti, Alberto Bisin, Daniele Checchi, In´es Macho- Stadler, Pau Olivella, Howard Pethit. Last revision: June 28, 2004. 1 G. Bono, Monitoring Teams 2 Contents 1 Framework............................................................ 4 1.1 Assumptions.............................................................. 5 Monitoring – Contracting Stage 1.2 Model.................................................................... 6 Wage Rule – Agents Game 2 Optimal Monitoring Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Remarks .............................................................. 10 3.1 Model’s Building Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 From Two to n-Agents 3.2 RelatedLiterature......................................................... 13 Job Design – Renegotiation 3.3 Researchdirections ........................................................ 15 References................................................................ 16 G. Bono, Monitoring Teams 3 This work addresses the optimal design of the monitoring technology for a team when collective liability can not form. It shows that the principal’s optimal design choice is then to concentrate monitoring on the less productive agent in a team. By controlling the less productive agent she fully discipline the more productive. This result helps in studying the interplay between the institutional set-up and the technological capabilities of teams. This work studies the optimal design of team monitoring technologies. This is done using a team production model in the tradition of Alchian and Demsetz (Alchian and Demsetz, 1972:[1]) and Holmstrom (Holmstr¨om, 1982:[3]). That is a principal–multi agent game with hidden actions and production externalities. The standard framework is modified here in two respects. First, by adding a (non–degenerate) public monitoring technology. Agents actions are partially observable and the principal is in charge of monitoring design. Second, by changing the contracting technology available to the parties. Holmstrom’s landmark contribution (Holmstr¨om, 1982:[3]) displays a sharing rule conditional on output that achieves efficiency. This holds in the standard framework regardless of other verifiable signals. Then a weakening of the contractual mechanisms is in order to study the optimal design of monitoring signals. To this end here the contracting stage game is defined so as to exclude the formation of collective liability. On one side, this rules out contracts that rely on one agent being accountable for another agent deviation—like the sharing rule in (Holmstr¨om, 1982:[3]). On the other, it points to a simple and general institutional feature. Monitoring is modeled as a device that yelds informative signals only below certain treshold in the agents actions space. This reflects the inherent informational advantage of agents or a cost greater than the principal’s gain above that treshold, and negligible below. The monitoring technology is a collection of alternative tresholds. The principal designs monitoring by choosing one of them. As an example, consider a device that can take recordings of one agent at a time. In this case, the principal chooses for how long to target each one agent facing the trade-off with the lenght of the other recordings. In a two–agent model, the principal’s optimal design choice is to concentrate monitoring on the less productive agent.1This is by definition the one whose least undetectable deviation from efficiency induces the lower loss in output. Controlling the less productive fully disciplines the more productive. The result rests on the possibility of combining observed output and cross-monitoring to infer contractible lower bounds on agents actions. The principal’s best contracts are conditional on direct monitoring signals and on these indirect monitoring bounds. At least one agent is constrained by indirect more than by direct monitoring. Since indirect monitoring depends ex post on both agents actions, signing contracts puts agents in a game. For a given design, the agents strategic advantages are at the opposite ends because one’s deviation would cause a lower output loss. In the Nash equilibrium of the game direct monitoring is binding for this agent while indirect monitoring is binding for the other. By choosing the design the pricipal essentially picks the agent who will deviate from efficiency. The literature on principal many-agents problems explores mostly the stochastic properties of monitoring technologies. For example, in the cited seminal 1In a n-agents model the result holds with slight modifications. See the discussion in section 3.1.1. G. Bono, Monitoring Teams 4 contribution (Holmstr¨om, 1982:[3]) Holmstrom addresses the relation between these and incentives, concentrating on what makes information systems redundant. He shows that for a given set of observable signals the critical property is statistical sufficiency with respect to agent actions. This result is applied to the comparison of contracts that depend on an individual monitoring signal and contracts that depends on other agents signals as well, and the two are shown to be equivalent if agents outputs are independent. The characterization of classes of equivalence between (constrainedly) efficient and restricted mechanisms, in an analogous fashion, has been extensively pursued in the literature and is not reviewed here. This work focuses instead on a restriction of the mechanisms available to the principal that precludes the formation of collective liability. With the exceptions of (Ishiguro and Itoh, 2001:[5]) and (Marx and Squintani, 2003:[7]) in the context of hidden information, the effects of impediments to collective liability is to my knowledge a neglected area of research. However, there are practical contracting environment in which its formation is not a trivial matter.2For example labor contracts provide tipically for individual liability, even when they are collectively bargained. Conversely, when they contain collective liability this is almost always partial and bargained in a heavily institutionalized environment. With the proposed restriction in place it is possible to address the “physical” properties of monitoring as a simple allocation problem, leading to the corner solution which is the main claim of this work. This result agrees with a proposition advanced in an important contribution to the job–design literature (H¨olmstr¨om and Milgrom, 1991:[4]). Holmstrom and Milgrom show in (H¨olmstr¨om and Milgrom, 1991:[4]) that the optimal job design for two risk–averse agents implies the concentration of easy–to–monitor tasks on the one that bears the highest cost of effort. The asymmetry is induced by the strategic interaction between agents and regards the intensity of monitoring here, whereas is induced by their relative risk-preferences and regards its dispersion in (H¨olmstr¨om and Milgrom, 1991:[4]).3 1 Framework As in the standard team production model, agents—here denoted4I={1,2}— choose whether to sign a contract offered by the principal, who acts as a residual claimant and has all of the bargaining power. Both the principal and the agents utility indexes are linear in money, and production is represented by a smooth concave function. Agents actions—here denoted ∀i:xi∈[0,1]—are their private information unless in the scope of monitoring. Besides these, the information generated in production and monitoring is verifiable ex post by an enforcement authority trusted by the parties. Verification is based upon explicit 2See (Marx and Squintani, 2003:[7]) and for a discussion of these and other limits to collective liability 3Section 3.2.1 discusses the similarities and differences with their result. 4The notational conventions used here are: capital letters for sets, the corresponding small letters for elements, braces for unordered lists, and parentheses for ordered lists. An index preceded by “−” marks an element that is not the same as the one indexed without “−”. An indexed element enclosed in parentheses stands for the complete list. G. Bono, Monitoring Teams 5 contracts. 1.1 Assumptions. The two assumptions presented hereafter depart from the standard model. The first specifies monitoring. The second introduces a a contracting stage not amenable to the formation of collective liability. 1.1.1 Monitoring. Monitoring delivers a post-production signal: ∀i:˜ hi=xifor xi< hi hifor xi≥hi(1) that fully reveal agent i’s action below the treshold hiand become uninformative above. The design of monitoring is a complete list of such tresholds: (hi). The principal chooses the design from a given set H⊆[0,1]×[0,1]. The requirement placed on Hare that it contains a component by component upper bound: ∀i:∃hu i(∀hi:hi≤hu i) Note that Hincludes, as a degeneration, the standard case of unobservability of all agents actions. 1.1.2 Contracting Stage. Collective liability means that any agent bears responsability for one agent’s deviation. To be held collectively liable, agents have thus to enter into two kind of commitments. One is a promise to act as guarantors for each other. The other is a promise to the principal. As a consequence of the first each agent is individually liable to each other. Collective liability is then build upon this web of mutual guarantees by the second one. Pictorially: p         > > > > > > > 1 @@       2 ^^> > > > > > > from this pattern of commitment collective liability can not form: each agent exchanges promises only with the principal . . . p         > > > > > > > 1 @@       //2 oo ^^> > > > > > > . . . here exchange of promises take place also between agents and collective liability may form. In the standard team model the formation of collective liability is modeled as a rule of the stage game in wich agents sign contracts. At this stage, each agent has a veto power over production taking place: agents simultaneously sign a take it or leave it offer, and if one reject it the main game ends. The veto makes a contract conditional on any other contract being signed. That the principal is given all of the bargaining power means in this case that she chooses the agents mutual guarantees as well as their indiviual obligations to her. Without the veto acting as an automatic guarantee to others, collective liability can not emerge because of the multilateral threat of opportunistic behavior.5Then this 5Assuming that there is no alternative way of making contracts conditional on one another. G. Bono, Monitoring Teams 6 description of the contracting stage game excludes its formation: the principal choose whether to offer a contract to each agent and, if any is signed, production and monitoring take place. It is also assumed that a party who does not sign a contract get a reservation payoff normalized to zero. Note the strategy to build collective liability through renegotiation adopted by (Ishiguro and Itoh, 2001:[5]). Ishiguro and Itoh assume in (Ishiguro and Itoh, 2001:[5]) that the principal uses only individual-based contracts. The timing of their game contains a further contracting stage in which one agent makes a take it or leave offer to the other and this becomes, if signed, their renegotiation proposal to the principal. See a more complete review of Ishiguro and Itoh’s results in 3.2.2 and the picture of how collective liability takes form in their renegotiation stage here: p  > > > > > > > 1//2 oo ^^> > > > > > > also from this pattern collective liability may form, but just one agent exchange promises with the principal as in the second contracting stage in (Ishiguro and Itoh, 2001:[5]). 1.2 Model. Output is in money units: y=g((xi)) with ∀i:∂2g/∂x2 i≤0< ∂g/∂xi.g(1,1) is the efficien output. Denoting wages with w, utility indexes are: vp=y−Piwiand ∀i:vi=wi−xi 1.2.1 Wage Rule. The principal offers a wage rule: ∀i:wi=˜wiwhenever ˜ hi=hiand y≥g(1,˜ h−i) 0 otherwise (2) This provides two criteria that a party can submit to an external authority for verification. If one fails, the rule defaults to no money transfer. The first criterion relies on monitoring directly. Signing this clause makes agent icommit to xi≥hi. The second relies on cross-monitoring and on output. By signing this, agent iaccepts responsability if output falls short of a value computed using −i’s monitoring signal. Since an agent would not commit to an unverifiable action on part of the other agent, that in (2) is the highest contractible level of output. Note that in the linear utility context of this work the contracts: ∀i:wi=˜wiwhenever y≥g(1,1) 0 otherwise induce the efficient actions if collective liabilty may form. The second clause in (2) is computated inverting the production function at a point: y→˜xi=g−1(·, x−1) calculated in x−1=˜ h−1 and finding the level of output that maps to ˜xi= 1. The collective liabilty counterpart of this clause replaces the computation with: y→˜xi=g−1(·, x−1) calculated in x−1= 1 G. Bono, Monitoring Teams 7 in which an agent acts as a guarantor if the other is doing the same. Then both contracts need to include an analytical description of the production technology. This is a strong informational requirement, fulfilled in practice by contracts that link to blueprints, technical documentation, state of the art business practices, the organization past record and the like—or by enforcement authorities that use similar information in a predictable way. For the game presented here this requirement is of particular relevance, since it is not assumed that the monitoring design is revealed ex ante to agents. As a benchmark, consider the exchange that would take place on a spot market. This is by definition limited to the verifiable (hi). The efficiency gains above g(hi, h−i) are realized by contractual mechanisms thanks to the public character of technical knowledge in (2) or thanks to cross-guarantees when collective liability can emerge. 1.2.2 Agents Game. The optimal contracts ( ˜w∗ i) are drafted by the principal taking into account the agents strategic interaction. It is convenient to describe the game in the optimal context, assuming that agents had the contracts signed and fulfill the obligations, and to describe how monitoring constrains the optimal actions of agents. For a given (hi), agent irespects the indirect clause of the contract if he chooses his optimal action in a region delimited by a reaction function: x∗ i≥min{xi:g(xi, x∗ −i)≥g(1, h−i)}(3) By construction, this coincides with the set above and including the isoquant of g(·) passing through (1, h−i). At the same time, to meet the direct monitoring requirement: x∗ i≥hi(4) In the following the conditions in (3) and (4) are called the indirect and the direct monitoring constraints. Agent ichooses the minimal action that satisfy both and so −i. To find a Nash equilibrium of this game, assume that their indirect constraints are on different isoquants and hence can not cross. In this case, agent i’s indirect constraint intersects −i’s direct constraint at just one point, where i’s action reaches its maximal value. This point is an equilibrium if i’s indirect constraint is on an higher isoquant than that of −i. Otherwise the equilibrium is the analogous point on −i’s indirect constraint. The Nash equilibrium of this game is thus unique unless the indirect monitoring constraints coincide. When this is the case, there is a continuum of equilibria along the isoquant. In the unique equilibrium an agent is either on his direct or on his indirect monitoring constraint. Monitoring matters for just one agent and so the principal faces a choice between maximizing monitoring on one agent or on the other. The multiple equilibria case arises when she is indifferent between the two. Thus, the monitoring design for the unique equilibrium case is still optimal. Figure 1 illustrates the strategic situation in two diagrams. Both plot a monitoring technology set Hand some isoquants of a production function in the space of agents actions. In the example His perfectly symmetric—∀a∈(0,1) : (hi=a)∈H⇔(h−i=a)∈H—and g(·) is such that ∀a, b ∈(0,1) : a>b⇔ g(a, b)< g(b, a). G. Bono, Monitoring Teams 8 Figure 1: the agents game and the problem of the principal Nash equilibrium i (hi, h−i) −i H optimal monitoring design i hu i hu −i−i .the diagram on the left presents the agents game. Monitoring design is fixed at (hi, h−i). (3) and its analogous for agent −iare the dashed isoquants. The lower belongs to agent i. (4) and analogous are both satisfied in the shaded region—including the frame. At the Nash equilibrium of the game agents actions are (x∗ i=hi, x∗ −i= 1). Note also that (hi, h−i) is on the highest isoquant crossing H. That is, is the design the principal would choose had she only access to a spot market. .the diagram on the right presents the problem of the principal. The dashed isoquant corresponds to the optimal choice (h∗ i=hu i, h∗ −i= 0). The shaded regions highlight the components upper bounds of H. 2 Optimal Monitoring Design The principal solves the optimal design prolem looking for the higher g(hu i,1). Knowing that one agent is anyway playing x∗ i= 1, she maximizes monitoring on the other. Then, she maximizes monitoring on the agent that would cause the lower efficiency loss when he is on his direct monitoring constraint. In the following this potential loss is called productivity: gu i=g(1,1) −g(hu i,1) and a production function g(·) is called anonymous if gu i=gu −i. Anonymity depends on a single point in the domain of g(·) induced by the monitoring technology set upper-bounds. Thus for a given Han anonymous production function is non-generic.6The main claims of this work are then summarized: 6That is, is possible to find a function arbitrarily “close” to it but non-anonymous. For a work that uses genericity in the context of team production in a similiar altough more subtle way, and for the formal definitions, see (Battaglini, 2003:[2]). G. Bono, Monitoring Teams 15 serve a perfect but unverifiable signal that mutually reveals actions. The decentralized contracting stage described above in 1.1.2 follows this mutual monitoring signal. By assumption in the first contract stage the principal can not rely on unrestricted mechanisms. As shown for instance by Ma in (Ma, 1998:[6]), when agents actions are mutually observable there exists a mechanism that uniquely implement the first best action profile. Without the restriction in place, renegotiation would thus be pointless in (Ishiguro and Itoh, 2001:[5]) as much as monitoring is useless with collective liability contracts here. Ishiguro and Itoh’s main result is that renegotiation “reduces the cost of implementing any implementable action profile down to the first-best level”. This can be applied directly to (E) because they concentrate on initial constant-budget contracts as the one in (8).16 The interest of the application is in that it envisions a route for modeling the endogenous formation of collective liability. As Ishiguro and Itoh argue, the mechanism decentrated via renegotiation is relevant for addressing unionized production environments. 3.3 Research directions. The result presented by this work: (E)when collective liability can not form, the principal’s optimal design choice is to concentrate monitoring on the less productive agent in a team. is intended as an introductory step in the study of the relation between the institutional set-up and the technological capabilities of teams.17 The optimal choice is at a corner because the Nash equilibrium of the agents game—unique, except in a non-generic case—reduces the principal’s problem to a binary choice. The skewness in the optimal design holds for an arbitrary monitoring technology set. The game between agents is a direct consequence of the set of identical contracts offered by the principal, in turn determined by the exclusion of collective liability. There is thus a direct link between the ability to form collective liability and the properties of the monitoring technology. That this may be useful in the institutional study of the technological capabilities of teams is in a way obvious, as monitoring is itself a technological capability. More interestingly, monitoring collects and analyzes data on other technological capabilities. Since these data and analysis are relevant to contract enforcement one can expect them to be optimal, reliable and formal. Accordingly monitoring can be thought of as the output of an efficient research activity or as the ideal input for other research activities. In this vein, it generally lowers the cost of acquiring technological capabilities because it yelds research as a free by-product. Then the characteristics of the institutional set-up may induce different paths of technological learning in teams. (E) could imply, for example, specialization in the monitoring of low productivity jobs where the principal is not relying on collective liability and, by the external effect, the modularization of such jobs.18 I am pursuing an examination of this line of interpretation and an attempt at 16When the first-best is not attainable with a constant-budget contract, they observe, it may “. . . exists an initial contract outside the set of constant-budget contracts that attain the firstbest outcome via renegotiation”. This is indeed the case here, if one adds the renegotiation stage and a variable component to the wage rule. 17It may as well be applied to regulatory issues and to other contexts. 18See example 3. G. Bono, Monitoring Teams 16 endogenizing the emergence of collective liability elsewher, as both issues require an extension of the present framework. References [1] A. A. Alchian and H. Demsetz. Production, information costs, and economic organization. The American Economic Review, 62:777–795, 1972. [2] M. Battaglini. Moral hazard in teams with vector outputs. working paper, January 2003. http://www.princeton.edu/~mbattagl/teams.pdf. [3] B. Holmstr¨om. Moral hazard in teams. The Bell Journal of Economics, 13(2):324–340, 1982. [4] B. H¨olmstr¨om and P. Milgrom. Multitask principal-agent analysis: Incentive contracts, asset ownership, and job design. The Journal of Law, Economics & Organizations, VII Sp:24–52, 1991. [5] S. Ishiguro and H. Itoh. Moral hazard and renegotiation with multiple agents. Review of Economic Studies, 68:1–20, 2001. [6] C. Ma. Unique implementation of incentive contracts with many agents. The Review of Economic Studies, 55(4):555–571, 1998. [7] L. M. Marx and F. Squintani. Individual accountability in teams. working paper, University of Rochester, July 2003. http://www.econ.rochester.edu/Squintani/teams.pdf. [8] H. Matsushima. Multi-group incentives. CIRJE Discussion Paper F-201, The University of Tokyo, March 2003. http://www.e.u-tokyo.ac.jp/cirje/research/03research03dp.html. [9] R. Strausz. Moral hazard in sequential teams. Journal of Economic Theory, 85:140–156, December 1999.