The discussion so far focused on parties who want to contract on effort but may decide to contract on output. This is because they expect the advantage of observability and verifiability to outweigh the potential disadvantage of imperfect risk sharing348, due to the increased importance of the external factor. In fact, the above models of output monitoring and input monitoring serve to derive **optimal contracts stipulating contingencies upstream in the case of input monitoring and downstream in the case of output monitoring. In a next step the two optimal contracts can be compared.** In a situation where the optimal output monitoring contract dominates the optimal input monitoring contract, more

348 If the agent is relatively more risk-averse.

downstream performance measures will be chosen and vice versa. As a byproduct of the analysis, much is said about how to specify the resulting contract.

But, so far, one important problem was ignored: If the **principal switches to alternative measures of performance because total contribution cannot be contracted upon** (or only at prohibitive cost), there will not only be the potential problem of imperfect risk-sharing: There will also be a **tension between what the principal desires and what the agent is rewarded for.** This problem, called **distortion,** was highlighted by *Kerr,* when he described the "folly of rewarding A while hoping for B"349• The rational and opportunistic agent only has the incentive to perform the tasks he is rewarded for and therefore will not serve the best interest of the principal, or in Kerr's words: "What you measure is what you get". *Kerr* attributes this problem to the "fascination with objective performance measures". Therefore, "if you can't measure what you can, you end up wanting by what you can measure"350•

But, the discussion above showed that there is more to this problem than a simple **psychological trap,** easily avoided by cool-headed rational thinking. What is wanted just may not be contractible. If this problem is unattended to, many potential gains of trade cannot be realised because people will not trade. So, if a related alternative performance measure can be found that can be contracted upon, some of the gains can be realised by going for this **second best solution.** So far, imperfect risk sharing, residual loss due to shirking, and direct cost of the monitoring mechanism were mentioned. Now, another source of loss must be added: distortion. The following propositions will be derived:

349 Kerr ( I 97 5)

350 Gibbons (200 I), p. 4

## **4.2.2 The Model**

If **total contribution** y, or "everything the principal cares about except for wages"351 is not contractible, the agent's incentive will depend on an **alternative performance measure** p . "The essence of the incentive problem, is the **divergence** between the agent's incentive to increase p and the principal's desire to increase y"352• To clarify the effect, a model will be introduced.

If y = a + E and p = a + tj, , and the contract specifying compensation is w = s + bp, there will be no such distortion. The agent, by trying to increase his compensation also increases the principal's utility y. It can, however, be imagined that **two actions** ( or "tasks") are required in order to promote the principal's interest. Consider a client who might be interested in **cutting his cost**  in order to enhance his long-term profit perspectives. Thus, the tricky task for the consultant is to cut costs without decreasing the capability of the client to produce valuable products and services to his customers; it is normally straightforward to observe and verify cost cutting while less obvious to assess the implications on the company's capabilities, which will show much later, if at all. To formalize this situation, y is modelled to depend on two tasks y = a 1 + a2 + E (in the example a 1 would be cost cutting and a 2 the observance of the restriction that capabilities must be maintained). The performance measure will be p = a1 + tj, . It can easily be seen that the agent's incentive to perform one task or the other depends on the way a, and a 2affect the performance measure p and on the bonus rate b. Therefore the agent will promote a 1, but not a 2 •

Another case is where y = a 1+ E and p = a 1+ a 2+ tj, . The agent will have an incentive to perform both tasks a 1 and a 2 although a 2 creates no value at all for the principal. An example would be the problem of **"impression management".** Agents will sometimes devote considerable resources to improve the impression the principal gets from them instead of pushing forward with the real task. Even if the agent does not know by which criterion he is evaluated, he will overemphasize highly **visible tasks.** There are some performance criteria that are good indicators of performance as long as they are not used as incentives. In order to evaluate a teacher, students' performance on standardized tests may be a **good indicator.** As soon, however, as this is used as an incentive, teachers will try to **"teach to the test".** The principal (in this case the parents or the government) may fail to get the good education for their children they ultimately desire.

351 Gibbons (2001 ), p. *5*

352 Gibbons (200 I)

The extreme case, y == a1 + E and p == a 2+ ~, is where the agent only performs a 2 , not creating any value at all. The models dealing with these problems are called "multi-task models"353 • A tractable example will be presented in the following354 :

It is assumed that the **value** created to the principal is given by:

$$\mathbf{y} = \mathbf{f}\_1 \mathbf{a}\_1 + \mathbf{f}\_2 \mathbf{a}\_2 + ... \\ \mathbf{f}\_n \mathbf{a}\_n + \mathbf{e} = \mathbf{\tilde{f}} \mathbf{\tilde{a}} + \mathbf{e} \ . \tag{7.1}$$

And the **measured performance** is given by:

$$\mathbf{p} = \mathbf{g}\_1 \mathbf{a}\_1 + \mathbf{g}\_2 \mathbf{a}\_2 + ... \\ \mathbf{g}\_n \mathbf{a}\_n + \boldsymbol{\Phi} = \overrightarrow{\mathbf{g}} \overrightarrow{\mathbf{a}} + \boldsymbol{\Phi} \,. \tag{7.2}$$

The principal offers the agent **a linear contract** contingent on p ,

$$\mathbf{w} = \mathbf{b}\mathbf{p} + \mathbf{s} \,. \tag{7.3}$$

The agent accepts the contract if compensation is high enough to cover his **costs** which are assumed to be:

$$\mathbf{c}\left(\vec{\mathbf{a}}\right) = \mathbb{I}\left/2\vec{\mathbf{a}}^2\right. \tag{7.4}$$

He will choose his actions a unobserved by the principal. The principal determines p 355 and pays the compensation as specified by the contract. Even if the principal cannot observe a , given the terms of the contract he can perfectly predict the choice of the utility maximizing rational agent. Against this backdrop, he has to choose the contract terms maximizing his own utility. This is the **familiar agency model** where the principal maximizes his expected pay-off subject to an incentive and a participation constraint. For simplicity it is assumed that both principal and agent are risk neutral, so that both maximize expected value EP, EA. The maximization problem can therefore be set up as follows:

$$\max\_{\mathbf{b}, \mathbf{v}, \mathbf{t}^\*} \vec{\text{f}} \vec{\mathbf{a}} - \mathbf{b} \left(\vec{\text{g}} \vec{\mathbf{a}}\right) - \mathbf{s} \tag{7.5}$$

353 These models were originated by Holmstriim/Milgrom ( 1991)

354 The model presented is a slightly more general version than the model presented by Gibbons (2001). Gibbons refers to more elaborate models: see Feltham and Xie (1994), Kulp, Datar, and Lambert (1999), and Baker (2000).

355 Whether or not he observes y is irrelevant in the one-shot relationship.

$$\text{s.t. IC: } \overline{\text{a}}^{\bullet} \in \arg\max\_{\mathfrak{a}} \mathbf{b}\left(\overline{\text{g}}\overline{\text{a}}\right) + \text{s} - \frac{1}{2}\overline{\text{a}}^{2} \tag{7.6}$$

$$\text{PC: } \mathbf{b}\left(\overline{\mathbf{g}}\overline{\mathbf{a}}\right) + \mathbf{s} - \frac{1}{2}\overline{\mathbf{a}}^2 \ge \mathbf{0} \tag{7.7}$$

The incentive constraint is a maximization problem. Therefore, the **firstorder** condition must bold.

$$\text{Grad}\left(\mathcal{E}\_{\mathsf{A}}\right) = \mathbf{0} \Longleftrightarrow \mathbf{b}\vec{\mathbf{g}} - \vec{\mathbf{a}} = \mathbf{0} \tag{7.8}$$

Replacing the maximization problem of the incentive constraint by the firstorder condition requires it not only to be **necessary but also sufficient.** It can easily be seen that:

$$\frac{\partial \mathbf{E}\_{\mathbf{A}}^{2}}{\partial \mathbf{a}\_{i}^{2}} = -1 \text{ and } \frac{\partial \mathbf{E}\_{\mathbf{A}}^{2}}{\partial \mathbf{a}\_{i} \partial \mathbf{a}\_{i}} \text{ (i \neq j)} = 0 \tag{7.9}$$

Therefore, the quadratic form is negative definite and EA is concave. The first-order condition can therefore replace the maximization problem of the incentive constraint.

Inserting (7.8) and **restating** the maximization problem gives:

$$\max\_{\mathbf{b}, \mathbf{s}, \mathbf{t}} \overleftarrow{\sf f} \overleftarrow{\sf \mathbf{a}} - \mathbf{b} \left(\overrightarrow{\sf g} \overleftarrow{\sf \mathbf{a}}\right) - \mathbf{s} \tag{7.5}$$

$$\text{s.t. IC: } \mathbf{b}\vec{\mathbf{g}} - \vec{\mathbf{a}} = \mathbf{0} \Longleftrightarrow \vec{\mathbf{a}} = \mathbf{b}\vec{\mathbf{g}}\tag{7.6}$$

$$\text{PC: b} \left(\overline{\text{g}}\,\overline{\text{a}}\right) + \text{s} - \frac{1}{2}\,\overline{\text{a}}^2 = \text{0} \tag{7.7}$$

Solving (7.6)' for a and inserting into (7.7) gives:

$$\mathbf{b}^2 \overline{\mathbf{g}}^2 + \mathbf{s} - \frac{1}{2} \mathbf{b}^2 \overline{\mathbf{g}}^2 = \mathbf{0} \tag{7.7}$$

Solving (7.7)' for s yields:

$$\mathbf{s} = -\frac{1}{2}\mathbf{b}^2 \overline{\mathbf{g}}^2 \tag{7.7}$$

**Inserting** (7.7)" and (7.6)' into (7.5) gives:

$$\mathbf{b}\mathbf{\tilde{f}}\mathbf{\tilde{g}} - \mathbf{b}^2\mathbf{\tilde{g}}^2 + \frac{1}{2}\mathbf{b}^2\mathbf{\tilde{g}}^2 = \mathbf{b}\mathbf{\tilde{f}}\mathbf{\tilde{g}} - \frac{1}{2}\mathbf{b}^2\mathbf{\tilde{g}}^2\tag{7.5}$$

The **first-order** condition for an optimal b is therefore:

$$\overline{\text{f}}\overline{\text{g}} - \mathbf{b}^{\bullet}\overline{\text{g}}^{2} = \mathbf{0} \tag{7.10}$$

Solving for b• yields:

$$\mathbf{b}^\* = \frac{\overline{\mathbf{f}} \overline{\mathbf{g}}}{\overline{\mathbf{g}}^2} \tag{7.10}$$

As fg = !fl lgl cos *<p* and lgl = *.ff* ~g2 = lgl2 :

$$\mathbf{b}^\* = \frac{\left|\mathbf{f}\right| \left|\mathbf{g}\right|}{\left|\mathbf{g}\right|^2} \cos \boldsymbol{\upphi} = \frac{\left|\mathbf{f}\right|}{\left|\mathbf{g}\right|} \cos \boldsymbol{\upphi}\,,\tag{7.11}$$

where *<p* is the angle between the vectors f and g and lfJ , JgJ the length of the vectors.

It becomes clear from the model that the optimal bonus rate depends on two important factors: **scaling** and **alignment356 •**

If the weights357 g measuring the effect of the different actions on the performance measure p are **generally higher** than the weights f reflecting the contribution of these actions to the principal's value y, it means that pis relatively more sensitive to higher levels of action than y. One would therefore expect the bonus rate to be small. This is exactly what is expressed in the model.

*Proposition 25: I/the weights measuring the effect of the different actions on the performance measure are generally higher than the weights reflecting the contribution of these actions to the principal's value, the bonus rate will be small.*

356 Gibbons (200 l) p. 7

357 By analogy one could speak of marginal products

Besides the overall scale of the weights, a relevant feature is the extent to which the weights of y and p have a **similar pattern.** If the pattern is similar, the distortive effect by "rewarding A, while hoping for B" will be small. This is because there will not be many instances where a particular action has a strong effect on p but not on y . For intuitive illustration, consider the graphical interpretation of vectors f and g, representing the weights on y and p respectively. In fact, the **cosine of the angle between them summarizes the extent of pattern similarity.** If the angle between them is small ( and cosine will be high), they roughly point in the same direction. They are well "aligned". In these cases, one would expect the bonus rate to be rather high since **distortive effects are low.** This is exactly what is shown in the model: **The lower the angle, the higher** cos <p **and therefore the higher the bonus rate.**

*Proposition 26: If the incentives are well aligned with the ultimate goal, distortion will be low and the bonus rate will be high.*

### **4.2.3 Discussion**

Distortion arises if there is a tension between what the principal wants and what the agent is rewarded for. Often it is not possible to eliminate this tension. What the principal wants just might not be contractible. As was shown in this subsection, distortion can be divided into two components: scaling and alignment. scaling refers to the relative sensitivity of the two measures to changes in the drivers, and alignment to the similarity of driver patterns. If a university rewards a scientist (by promotion or resources) according to the number of articles published during a certain period of time ( driver), there will be a problem of alignment if the university cares about both quantity and quality. Indeed, the researcher would have the incentive to publish many articles in low quality journals. If no ranking of journals to account for quality is available, rewards should not depend too much on the number of published articles. Now, considering different departments it could be that a typical researcher in, say, marketing has 5 times as many publications than a typical researcher in, say, mathematics. If the basis for the bonus is the number of published articles, a scaling argument suggests the bonus rate for marketing researchers to be one-fifth of the bonus rate for mathematicians.

As will be elaborated later in more detail, it is obvious that there is a conflict with the risk-incentive trade-off. This model suggests that the bonus rate should be high if the observed variable is relatively undisturbed358 • This will be the case

358 see Proposition 4

for upstream parameters, but these will be the most distorted which suggests that the bonus rate should be low.

## **5 Dynamic Extensions**

## **5.1 Introduction**

Up to now, the analysis has been largely one period. Only in one instance did a dynamic idea sneak into the argument; namely, when it was argued that non-linear incentive schemes - in particular the step function scheme - create **pathdependant incentives359.** This was taken as a favourable feature of linear incentive schemes. Yet, there is a more general point to be made about dynamic extensions.

Many traditional models of contract theory are one period. The subject of this Chapter will be to analyse the effect of time on contracts. The starting point of this discussion is the often stated thesis that time can resolve incentive issues that arise in one-shot relationships costlessly, or at least can significantly reduce incentive costs360• Four models will be presented here to discuss this question. The first model deals with the advantage of long-term contracts over short-term contracts. Time allows lowering the cost of incentives by reducing imperfect risk sharing of output-based contracts (5.2). The second and third models deal with situations wherein relational contracts solve problems of enforcement. The theory of supergames will be used to argue that time may sustain contracts with otherwise desirable properties, which would not be feasible in a one-shot relationship. This is the case where contract parameters are observable but not verifiable (5.3). The fourth model introduces career concerns which induce the agent to exert effort, although choice of effort cannot be contracted on. It will be shown that an implicit contract links the agent's current choice of effort to future pay-off. (5.4). In conclusion, it will be argued that the thesis that time solves incentive issues costlessly cannot be generally upheld. Time merely alters and enriches the insights from one-period models: Conclusions from the one-period models are not necessarily valid in the multi-period settings.

359 see Sub-Section IV2.4.3

360 Fama (I 980)

## **5.2 Income smoothing**

## **5.2.1 Introduction**

Whenever parties are unable to contract on what they are really interested in, they are forced to switch to alternative perfonnance measures. Output monitoring was shown to be relatively cheap and undistorted, but input monitoring created less exposure to the external factor leading to better risk sharing.

The Mirrlees argument361 on the superiority of step functions over linear incentive schemes and the "shifting support" argument both attempted to combine the best of two worlds: Perfect risk sharing in the presence of output monitoring. These solutions were mainly attacked on practical grounds. It could be established that such schemes were an extreme case of fine tuning362 •

Time alters this argument. If many periods are observed, the law of large numbers filters out uncertainty and it becomes easier to distinguish shirking from bad luck. The intuition is simple: In a one-shot relationship, if the project fails and the agent is punished, there is a considerable risk that he is punished innocently. If a project fails repeatedly, the risk of this being due to bad luck decreases. Thus, the cost of imperfect risk sharing is lower than in the multi-period case363 • In practice, the principal can offer the principal a long term contract wherein the decision on bonus or punishment is made towards the end of the contract. Until then be is paid a low but regular income. If the principal can commit to such a scheme, the agent knows that ifhe is not shirking he will receive the bonus. In this Section, the following proposition will be illustrated:

27. Long term contracts can provide cheaper incentives than a sequence of short term contracts if the agent has saving and borrowing constraints.

### **5.2.2 The Model**

In order to further illustrate this argument, a simple model is constructed: It is assumed, that the agent can choose two levels of effort a, and ah representing the mean of a nonnal distribution ( Y, = a1 + E and Yh = ah + E, where E - N ( 0, a), ah > a 1 ). In the one-shot relationship the distribution of outcomes contingent on effort is therefore:

361 Mirrlees (1974)

362 Hart, Holmstrom ( 1987), S. 90/91

363 Radner (1981)

$$
\begin{array}{l}
\tilde{\mathbf{Y}}\_{\mathsf{l}} \sim \mathrm{N}(\mathbf{a}\_{\mathsf{l}}, \boldsymbol{\sigma}) \\
\tilde{\mathbf{Y}}\_{\mathsf{h}} \sim \mathrm{N}(\mathbf{a}\_{\mathsf{h}}, \boldsymbol{\sigma})
\end{array}
\tag{12.1}
$$

The n-period relationship is modelled as the sum of n identically distributed, independent random variables (actions are uncorrelated):

$$\begin{aligned} \tilde{\mathbf{Y}}\_{\text{l}}^{\prime} &= \mathbf{n} \tilde{\mathbf{Y}}\_{\text{l}} \\ \tilde{\mathbf{Y}}\_{\text{h}}^{\prime} &= \mathbf{n} \tilde{\mathbf{Y}}\_{\text{h}} \end{aligned} \tag{12.2}$$

Applying the law of large numbers, the distribution of Y/ and Yh' respectively can be calculated to be:

$$\begin{aligned} \tilde{\mathbf{Y}}\_{\mathsf{l}}' &\sim \mathbf{N}\left(\mathbf{na}\_{\mathsf{l}}, \sqrt{\mathbf{n}} \boldsymbol{\sigma}\_{\mathsf{l}}\right) \\ \tilde{\mathbf{Y}}\_{\mathsf{h}}' &\sim \mathbf{N}\left(\mathbf{na}\_{\mathsf{h}}, \sqrt{\mathbf{n}} \boldsymbol{\sigma}\_{\mathsf{h}}\right) \end{aligned} \tag{12.3}$$

Obviously, the distance of means increases proportionately, while the standard error increases less than proportionately with time. Thus, separation between the two distributions becomes better. This will be shown in *Exhibit 8,*  where the density functions of shirking vs. non-shirking in the one-shot and in the multi-period case are depicted:

In the area where the chance of punishing the honest agent is infinitesimal, harsh punishments can be inflicted without additional monitoring or review procedure. The portions where this is the case are called "actionable range" in *Exhibit 8.* It becomes clear that the shirking agent expects a probability of punishment of about 5% in the one-shot relationship under such a scheme, whereas he expects a probability of punishment of about 50% in the long-term relationship. 5% may be enough if punishment can be high enough, but bankruptcy constraints are likely to render such a scheme unfeasible. Therefore, either imperfect risk-sharing has to be accepted or ex post monitoring (in the form of a revision process) has to be introduced.

The cost of monitoring is determined by the monitoring technology and the probability that the monitoring process is triggered. It will be assumed for simplicity that ex post monitoring is accurate and comes at a given cost. So, the probability of revision taking place is the only cost driver. For concreteness, it is assumed that punishment can be made high enough to make the agent choose "not shirking" if the probability of detection is 66%. It becomes clear that the monitoring process is triggered in 50% of the cases (see area ABC) in the one-

shot relationship and in about 8% of the cases (see area DEF) in the multi-period relationship. The range of outcomes triggering the revision process is referred to in *Exhibit 8* as "control range".

**Exhibit 8: Shirking/Non-Shirking: One-shot vs. Long-term**

If it is assumed that in the one-shot relationship the actionable range will never be sufficiently wide to implement first best at realistic bankruptcy constraints, there will have to be an ex-post monitoring process. If there is a chance of error, punishment cannot be too high. The control range will have to be rather wide relative to the relevant support set (if "not shirking" is implemented, the relevant support set is that of "not shirking"). In the multi-period case, the "actionable range" may be wide enough to achieve first best at realistic punishment levels. If additional monitoring is needed to avoid imperfect risksharing, the control range will be small relative to the relevant support set. Therefore, in the multi-period case "punishment can be made harsher and the control range tighter"364•

## **5.2.3 Discussion**

Thus, shirking can be dealt with more cheaply in the multi-period relationship, because the principal can engage in income smoothing for the agent. This, however, will only be of value to the agent if he has saving and borrowing restrictions which is not necessarily the case365 • Still, information problems of an outside party suggest that the principal of the primary relationship will often be the privileged counterparty for such transactions. Therefore:

### *Proposition 27: Long term contracts can provide cheaper incentives than a sequence of short term contracts if the agent has saving and borrowing constraints.*

One should understand the nature of this transaction in order to preclude any misunderstanding. Saving and borrowing enables people to shift the present value of their business relationships in time. It is just the possibility for the agent to borrow if he knows that by bad luck he received less as he would normally receive and to save if he has a windfall profit higher than his effort would normally justify. This is no case of insurance. There is almost certainty about the present value, because in equilibrium the agent will not shirk, which will ultimately be seen by the principal366•

364Holmstrom, Hart (I 987)

365 Allen (1985)

366 Of course, if one allows for the agent to default then there might be a moral hazard if too much borrowing is permitted and the incentive scheme breaks down. This will also happen if insurance in its proper sense is possible for the agent. In this case, the agent will receive the same utility whatever the circumstances. In such a situation, there would be no incentives for the agents to exert effort. But normally, such insurance would never be offered. A well-known case where this might happen nevertheless is if the agent can securitize the present value of his claims from his business relationship and sell them. This happens when managers receiving stock options for incentive reasons sell these stock-options in the market in order to reduce Exposure, which is why there are normally restrictions to such sales in stock-option schemes.

## **5.3 Reputation Effects in Supergames**

### **5.3.1 Introduction**

In the last Section, time was built into an explicit long term contract and allowed to lower the cost of incentives by reducing imperfect risk sharing of output-based contracts. Output-based contracts were an answer to the uncontractability of input parameters.

It was already argued that contractibility presupposes the knowledge of the production function, observability and verifiability. An especially interesting case is where parties can observe a performance measure that will not be verifiable by a third party like a court. There are certain situations wherein a self-enforcing mechanism - also referred to as an implicit contract - exists, sustaining a contract based on such subjective performance measures. The fundamental reasoning for these mechanisms is that if one of the parties makes a promise, it must be able to commit to this promise. Otherwise, the promise is worthless and cannot create incentives. In other words, it must be clear that at the moment when the party will have to make good on its promise it must be in its interest to do so. Otherwise, it can hold up the other party. Thus, the centre of interest is the decision rule of the party361\_

Consider, for instance, a situation where effort is observable but cannot be objectively verified. The principal cannot commit to paying a bonus contingent on effort because it will always be in his interest to renege later. So, maybe he commits on something else that constrains his future action space in such a way that it will be in his interest to make good on his promise. The tournament mechanism368 is a case in point. The principal facing many agents commits based on the total amount of bonuses paid out. By taking away the option of saving money by reneging, he can also credibly commit to paying the bonus as promised if only an infinitesimal preference for honesty is assumed. In this Section, it is shown that long term relationships actually are able to create circumstances in which parties find it easier to commit.

The basic intuition is simple: If one party has experienced that the other party acted opportunistically, it will stop doing business with this party. However, if the other party values the ongoing trade relationship, it will, anticipating this decision, not let its business partner down in the first place. It is therefore argued

367 see Gibbons (200 I)

368 see Lazear(l 981)

that long term relationships can in some circumstances support contracts that may otherwise not be feasible by reputation effects created between the parties369•

In the following subsections, two models will be presented: The first model (5.3.2) deals with a situation where effort is observable but not objectively verifiable. It was argued that in such cases, parties will switch to output-based bonus contracts. Yet, reputation effects may make a flat fee contract based on observed effort feasible. This is because the agent will not engage in shirking because his reputation is at stake.

The second model (5.3.3) deals with a situation where effort is not observable. Parties therefore switch to output monitoring, but now it is assumed that it is output which cannot be objectively verified, although it is observable to both parties. In such a case, it can be argued that it was impossible to create incentives because the principal cannot commit on the bonus payment. Again, reputation effects can make such an arrangement feasible because the principal might refrain from reneging because of reputation concerns. The following propositions will be derived:

369 The classic reference is Bull ( 1987)

#### **5.3.2 Observable but Uncontractible Effort**

The basic idea of reputation effects is that present action influences not only payoff in the current period, but also in future periods370• Thus, in any period the agent has to take into account the payment of this period and of the following t > 't periods. It is assumed that the agent can decide whether to choose high or low effort (al, aH ), which stochastically determines output ( Yi = ai + Ei with i = L, H ). The disutility of effort is assumed to be a linear function of effort ( J3al , J3aH )37'. The principal will commit to paying a flat fee that will be between the expected cost to the agent (J3a 0 ) and the expected value of output ( a0 ). The exact distribution of the gains of trade will be determined by bargaining, and depend on the bargaining power372 ( *y* ):

$$
\beta \mathbf{a}^{\mathfrak{e}} < \gamma \mathbf{a}^{\mathfrak{e}} \le \mathbf{a}^{\mathfrak{e}} \Rightarrow \gamma \in (\mathfrak{k}, 1] \tag{12.4}
$$

Profit for the agent will therefore be:

$$
\gamma \mathbf{a}^\star - \beta \mathbf{a}\_i \,, \tag{12.5}
$$

which depends on the principal's expectations (a 0 ) and on the agent's choice of effort ( ai ). Independent of whether or not the principal agrees to a low or a high flat fee, the agent will profit from choosing low effort. Therefore, the principal will have low expectations ( a• =al). The profit for the agent will thus be aL (y-J3). Because al (y-J3) < aH (y-J3), profit would be higher for the agent if he could commit to choosing high effort ( aH ). This is impossible in the oneshot relationship.

However, if the parties are playing a repeated version of this one-shot game this might change. It is assumed that the principal plays a trigger strategy. He expects the agent to choose high effort until he observes that he is choosing low effort. In this case he will assume low effort forever after.

370 This model is inspired by a model of Bester in an unpublished script.

371 Disutility is usually modelled as a convex function in effort. In this model, there is another focus and a linear disutility function is assumed for ease of exposition.

372 There are some models (e.g. Rubinstein 1982, see Kreps 1990, 556n) where the outcome of bargaining depends on the process of bargaining. An alternative to a bargaining solution would be to assume that the market mechanism determines a market price. It is common e.g. to assume that many principals compete against each other, driving the profits down to zero. As it is intended to apply the models to the client-consultant relationship where services are normally very specific to the relationship, a bargaining approach is taken.

The agent's discount factor373 is assumed to be o and the growth rate of the expected gains of trade cj> • The growth rate is introduced to model the agent's expectation that the business relationship with the client will increase or decrease in value over time. Then the agent's pay-off for choosing high effort ( aJ in period , is:

$$\sum\_{\mathfrak{s}=0}^{\mathfrak{s}} \mathfrak{s}^{\mathfrak{t}} \mathfrak{s}^{\mathfrak{t} \star \mathfrak{r}} \left(\mathfrak{y} - \mathfrak{y}\right) \mathbf{a}\_{\mathfrak{A}} \tag{12.6}$$

Doing some algebra374 this can be written as:

$$
\phi' \xrightarrow[1 \to \delta\phi]{a\_y} \text{for } \delta\phi \neq 1 \tag{12.6}
$$

On the other hand, the pay-off from defecting will result in a higher pay-off in the first period but in lower pay-offs forever after:

$$\left(\boldsymbol{\Phi}^{\mathsf{r}}\left(\gamma\mathbf{a}\_{\mathsf{H}} - \beta\mathbf{a}\_{\mathsf{L}}\right) + \sum\_{\mathsf{t}=\mathsf{l}}^{\mathsf{a}} \boldsymbol{\delta}^{\mathsf{t}} \boldsymbol{\phi}^{\mathsf{t}\ast\mathsf{r}}\left(\boldsymbol{\eta} - \beta\right)\mathbf{a}\_{\mathsf{L}}\right.\tag{12.7}$$

Again, doing some algebra375 yields:

$$\phi'\left[\chi\left(a\_{\mu}-a\_{\iota}\right)+\frac{\left(\chi-\beta\right)a\_{\iota}}{1-\delta\phi}\right] \tag{12.7}$$

The agent will choose high effort if pay-off (12.6)' is bigger than pay-off (12.7)':

$$\phi' \frac{a\_{\mu} \left(\boldsymbol{\gamma} - \boldsymbol{\beta}\right)}{1 - \delta \phi} > \phi' \left[\boldsymbol{\gamma} \left(a\_{\mu} - a\_{\iota}\right) + \frac{\left(\boldsymbol{\gamma} - \boldsymbol{\beta}\right) a\_{\iota}}{1 - \delta \phi}\right] \tag{12.8}$$

This condition can be simplified376 to:

$$
\beta < \delta \phi \gamma \tag{12.8}
$$

373 The agent's reputation is at stake here.

374 See Mathematical Appendix at the end of this Paragraph.

375 See Mathematical Appendix at the end of this Paragraph.

376 See Mathematical Appendix at the end of this Paragraph.

*Proposition 28: It can be seen that the agent will be less likely to renege if gains of trade are high (low* ~ *), the agent's discount rate is low (high*  8 *), the agent's expected growth rate for the value of the trade relationship is high (high ~) and the bargaining power of the agent is high (high y ). If the growth rate is zero(~=* 1), *it can be seen that condition (12.8) 'always holds/or a discount rate approaching O (8* • 1) *if the agent gets at least a tiny fraction of the gains of trade, as was stipulated in the assumptions (ye* (~,l]J. *In this case, first best will always be feasible.*

*Mathematical Appendix*

Footnote 374:

$$\sum\_{\iota=0}^{\infty} \delta^{\iota} \phi^{\iota+\iota} \left(\gamma - \beta\right) a\_{\iota\iota} = \phi^{\iota} \sum\_{\iota=0}^{\infty} \delta^{\iota} \phi^{\iota} \left(\gamma - \beta\right) a\_{\iota\iota}$$

$$= a\_{\iota\iota} \left(\gamma - \beta\right) \phi^{\iota} \sum\_{\iota=0}^{\infty} \left(\delta \phi\right)^{\iota} = \phi^{\iota} \frac{a\_{\iota\iota} \left(\gamma - \beta\right)}{1 - \delta \phi}$$

Footnote 375:

$$\begin{split} &\phi^{\mathrm{r}}\left(\gamma a\_{\mathrm{H}}-\beta a\_{\mathrm{L}}\right)+\sum\_{\iota=1}^{\infty}\delta^{\iota}\phi^{\wedge\ast\operatorname{r}}\left(\gamma-\beta\right)a\_{\mathrm{L}}\\ &=\phi^{\mathrm{r}}\left(\gamma a\_{\mathrm{H}}-\beta a\_{\mathrm{L}}\right)+\phi^{\mathrm{r}}\left(\gamma-\beta\right)a\_{\mathrm{L}}\left[\frac{1}{1-\delta\phi}-1\right] \\ &=\phi^{\mathrm{r}}\left(\gamma a\_{\mathrm{H}}-\beta a\_{\mathrm{L}}-\gamma a\_{\mathrm{L}}+\beta a\_{\mathrm{L}}\right)+\phi^{\mathrm{r}}\frac{\left(\gamma-\beta\right)a\_{\mathrm{L}}}{1-\delta\phi} \\ &=\phi^{\mathrm{r}}\left[\gamma\left(a\_{\mathrm{H}}-a\_{\mathrm{L}}\right)+\frac{\left(\gamma-\beta\right)a\_{\mathrm{L}}}{1-\delta\phi}\right] \end{split}$$

Footnote 376:

$$\phi^{\epsilon^{\prime}} \frac{a\_{\varPi}(\varchi - \beta)}{1 - \delta \phi} > \phi^{\epsilon} \left[ \chi \left( a\_{\varPi} - a\_{\varPi} \right) + \frac{(\varchi - \beta) a\_{\varPi}}{1 - \delta \phi} \right],$$

$$\begin{aligned} 0 &> \phi \Big[\gamma \left(a\_H - a\_L\right) + \frac{(\gamma - \beta)\left(a\_L - a\_H\right)}{1 - \delta \phi} \Big] \\ 0 &> \phi \Big[\frac{\gamma \left(a\_H - a\_L\right)(1 - \delta \phi) - \gamma \left(a\_H - a\_L\right) + \beta \left(a\_H - a\_L\right)}{1 - \delta \phi} \Big] \\ 0 &> \phi \frac{-\delta \phi \gamma \left(a\_H - a\_L\right) + \beta \left(a\_H - a\_L\right)}{1 - \delta \phi} \\ 0 &> \frac{\phi \Big[\beta - \delta \phi \gamma\Big]}{1 - \delta \phi} \\ \beta - \delta \phi \gamma &< 0 \end{aligned}$$

#### **5.3.3 Observable but Uncontractible Output**

If effort is uncontractible, parties might switch to output-based compensation. However, output could be observable to the parties while not objectively verifiable. This raises the possibility that the principal reneges on the promised bonus. He might, however, decide not to renege for reputation concerns 377•

Two possible levels of outcomes are assumed: "low outcome (L)" and "high outcome (H)". Effort ( a e (0, l]) is interpreted as the probability of "high outcome **(H)".** Therefore, expected outcome is:

$$\mathbf{a}\mathbf{H} + \left(\mathbf{I} - \mathbf{a}\right)\mathbf{L} = \mathbf{L} + \mathbf{a}\left(\mathbf{H} - \mathbf{L}\right) \tag{12.9}$$

The efficient effort choice, maximizing joint utility and used as a benchmark is:

$$\max\_{\mathbf{a}} \mathbf{L} + \mathbf{a} \left( \mathbf{H} - \mathbf{L} \right) - \mathbf{c} \left( \mathbf{a} \right) \tag{12.10}$$

Taking derivatives, one can write:

$$\mathbf{b}^\* = \mathbf{c}'(\mathbf{a}) = \mathbf{H} - \mathbf{L} \tag{12.11}$$

377 see Bull ( 1987), Levin (2000), Gibbons (200 I)

The principal promises the agent to pay a base salary s plus a bonus b in the event that he observes high outcome ( H ). If the principal honours the contract when high outcome is observed, his pay-off will be:

$$\mathbf{H} - \mathbf{s} - \mathbf{b} \tag{12.12}$$

If he reneges his pay-off will be:

$$\mathbf{H} - \mathbf{s} \tag{12.13}$$

If the agent expects the principal to honour his promise his expected pay-off will be:

$$\mathbf{s} + \mathbf{a}\mathbf{b} - \mathbf{c}\mathbf{(a)}\tag{12.14}$$

If he expects the principal to renege:

$$\mathbf{s} - \mathbf{c}(\mathbf{a})\tag{12.15}$$

The disutility of effort for the agent is a strictly increasing convex function in a:

$$\mathbf{c}(\cdot) > 0, \ c'(\cdot) > 0, \ c''(\cdot) > 0 \lim\_{\mathbf{a} \to \mathbf{l}} \mathbf{c}(\mathbf{a}) = \text{"\infty"} \tag{12.16}$$

It is assumed that the agent is playing a trigger strategy: he expects the principal to honour his contract until he defects. In this case he assumes defecting forever after, but if the agent expects that he will not be paid a bonus, he will not exert effort ( a = 0) and outcome will be low in certainty. In this case the principal knows that his pay-off will be:

$$\mathbf{L} - \mathbf{s} \tag{12.17}$$

An additional assumption will be included here: The project will only be profitable in the event of high outcome:

$$\mathbf{L} - \mathbf{c}\begin{pmatrix} 0 \end{pmatrix} - \mathbf{w}\_\* < 0,\tag{12.18}$$

where w a is the agent's reservation utility. Consequently, the principal will not be willing to offer a contract s ~ c ( 0 )-w • . But, any other contract would violate the agent's participation constraint and would therefore not be accepted: No trade takes place and pay-off is zero for both parties.

Thus, if the principal defects in period • , he will have a higher pay-off in this period but zero pay-off for periods t > -r . If he does not renege, his expected pay-off for periods t > • will be L + a (H -L)-s - ab.

Therefore, reputation concerns will induce the principal not to renege, if the following condition holds:

$$\mathbf{r}(\mathbf{H} - \mathbf{s}) + \mathbf{0} \le (\mathbf{H} - \mathbf{s} - \mathbf{b}) + \frac{\mathbf{L} + \mathbf{a}\left(\mathbf{H} - \mathbf{L}\right) - \mathbf{s} - \mathbf{a}\mathbf{b}}{\mathbf{r}} \tag{12.19}$$

The agent's incentive constraint if he thinks that the principal will honour the contract is:

$$\mathbf{a} \in \arg\max\_{\mathbf{a}'} \mathbf{s} + \mathbf{a}'\mathbf{b} - \mathbf{c}\left(\mathbf{a}'\right) \tag{12.20}$$

Replacing the maximization problem by the first order condition (which can be shown to be necessary and sufficient) yields:

$$\mathbf{b} = \mathbf{c}'(\mathbf{a}) \implies \mathbf{a} = \mathbf{a}^\star(\mathbf{b}) \tag{12.21}$$

Using (12.21), agent's participation constraint is given by:

$$\mathbf{s} + \mathbf{a}^\*(\mathbf{b})\mathbf{b} - \mathbf{c}\left(\mathbf{a}^\*(\mathbf{b})\right) \succeq \mathbf{w}\_\mathbf{a} \tag{12.22}$$

Using (12.22) and rearranging, (12.19) can be written as

$$\mathbf{b} \le \frac{\mathbf{a^\*} \mathbf{b} \mathbf{b} \mathbf{c^\*} \mathbf{b}}{\mathbf{r}} \mathbf{b} \le \frac{\mathbf{r}}{\mathbf{r}} \mathbf{b} \tag{12.23}$$
  $\mathbf{b} \le \frac{\mathbf{b^\*} \mathbf{b} \mathbf{b}}{\mathbf{r}}$

*Exhibit 9* shows this relationship (for c( a)= -a/ a -1, and L- w = 0 ). The shaded area represents the contracts satisfying the reneging constraint condition (12.23) i.e. contracts that can be sustained by reputation concerns of the principal. The function b\* (a) represents the efficient bonus rate maximizing joint utility (see (12.11)).

**Exhibit 9: Reputation Effects: a) First best incentives b) Second best incentives** c) **No trade**

It can be seen that, for a given differential between high and low outcome ( ~ = H - L ), first best incentives are possible at a low discount rate *(Exhibit 9 (a)).* From condition (12.11), it follows that the efficient bonus rate b• equals the differential between high and low outcome ~ . If the principal is offering b • , the agent will perform the efficient effort a• . He anticipates that the principal will honour his promise because the reneging constraint is loose (point A is within the shaded area). In other words: As not honouring the contract would hurt his longterm interests, the principal can provide efficient incentives which are credible to the agent. As the discount rate increases, this may no longer be the case.

In *Exhibit 9 (b),* the principal cannot commit on the efficient bonus rate b•. If the principal was to offer b• the agent believes that he will renege on his promise (point A is outside the shaded area) and will therefore not exert any effort. The principal, anticipating that, will try to induce the highest effort level a' <a•, not violating the incentive constraint. At the given outcome differential *ti,* a' is constructed by moving from A parallel to the abscissa until reaching B, which is just within the shaded area, and then projecting down onto the axis to find a'. The second best bonus level is found by moving upward to C, which lies on b • (a) . Moving to the ordinate gives the bonus level b' < b • , which is needed to induce a'. Thus, second best incentives can be created. If the discount rate becomes very high, there may not be any bonus rate, which is small enough to satisfy the reneging constraint'78 • This is the case in *Exhibit 9 (c).* No trade will take place.

It can also be seen that if the discount rate is close to zero, first best incentives can always be provided at any output differential ~ ( even if there is a small value to the trading relationship); but if the discount rate increases, first best contracts may still be possible if there for very high~.

*Proposition 29: Reputation effects are more likely to sustain a bonus contract if the value of the trade relationship (* ~ = H - L) *is high and the principal's discount rate (r) is low.*

### **5.3.4 Reinterpretation of the Discount rate**

In both models, one assumption was infinite repetition of the basic one period game in order to create reputation effects. Assuming that the relationship ends after t periods, clearly in the last period t, the dominant strategy will be to defect; but then there will be no value to the trade relationship in the last period, meaning that also in period t-1 the optimal strategy will be to defect, etc. The game will thus unravel backwards and the argument breaks down. Indefinite repetition, however, seems to be a very strong assumption.

Fortunately, the models can be saved if it is assumed that the game is not infinitely repeated but instead concludes at an uncertain date379• In fact, the discount *factor* 8 in Section 5.3.2 and the discount *rate* r in Section 5.3.3 can be reinterpreted as a combination of the actual discount factor [rate] and the probability of the game ending after each period played. If the probability of ending is q , the probability of the game continuing in the next period is 1 - q . Thus, if the actual discount factor [rate] of the party whose reputation is at stake is µ [ s] , the present value of a regular pay-off V is given by:

378 In fact, for a· = 0, no contract will be offered. The intercept (D) is just the bonus that would minimize losses to the principal if he offered a contract.

379 Gibbons (200 I)

$$\sum\_{\mathbf{i}=\mathbf{0}}^{\bullet} \mu^{\mathfrak{r}} \left(\mathbf{l} - \mathbf{q}\right)^{\mathfrak{r}} \mathbf{V} = \frac{1}{1 - \mu\left(\mathbf{l} - \mathbf{q}\right)} \mathbf{V} \tag{12.24}$$

Thus, the discount factor 8 can be reinterpreted as follows:

$$\mathbf{\dot{s}} = \mu \begin{pmatrix} 1 - \mathbf{q} \end{pmatrix} \tag{12.25}$$

The relationship between the discount factor and the discount rate is given by:

$$\mathbf{S} = \frac{1}{\mathbf{l} + \mathbf{r}}, \mu = \frac{1}{\mathbf{l} + \mathbf{s}} \tag{12.26}$$

Inserting (12.26) into (12.25) yields:

$$\frac{1}{1+\mathbf{r}} = \frac{1}{1+\mathbf{s}}(1-\mathbf{q})\tag{12.27}$$

Solving for r and rearranging gives the reinterpretation for r 380:

$$\mathbf{r} = \frac{\mathbf{s} + \mathbf{q}}{1 - \mathbf{q}} \tag{12.27}$$

Therefore:

#### *Proposition 30: The strong assumption of indefinite repetition can be relaxed by assuming uncertainty with respect to the the game's conclusion.*

It seems plausible that this is very often the case in business relations, where parties can express their judgement of the relationship continuing rather in terms of probabilities than in terms of definite dates of conclusion381 •

380 e.g. see Gibbons (200 l ), p. 9 footnote

381 Still, experiments suggest that parties will often find some way of cooperating in games with finite repetition, contrary to the logic of the presented argument. Having mentioned this behavioural evidence for something like a "trust mechanism" it will be ignored in the following as this thesis stands firmly on the grounds of rational decision making and opportunistic behaviour in its formal part. Still, as the reinterpretation of the rational model for uncertain ending shows, ignoring behavioural ideas does not come at such high a price as is often suggested.

Another advantage of this reinterpretation is that it actually enriches the model with a further variable. It is not only the discount rate (sometimes very aptly called "patience" rate) of one party whose reputation is at stake, which is relevant, but also the probability of the relationship's continuity, which is a judgement involving the relationship and thus both parties.

### **5.3.5 A Multiparty Extension**

A common multiparty interpretation for the models presented is to assume that, in the relationship between an employer and his workers, workers live for one period but pass their experience on to fellow workers, who will in turn act in the following period as if the experience of their colleagues were their own382•

This can be easily extended to the case where the workers live more than one period, but are spreading the news to their fellow workers. This can be modelled by adding a growth rate in the spirit of Section 5.3.2., reinforcing the reputation effect.

This is only one step short of assuming that there is a market reputation effect. The only difference, indeed, is that it is implicitly assumed in the case of the workers that the spreading of news is in some way facilitated by the fact that they work within the same organization.

It can very well be imagined that e.g. in the consultant-client relationship, observed shirking or reneging can play a role beyond the original relationship. If the project is highly visible, public interest will make sure that judgements are spread, possibly by press coverage. If the client or the consultant is very well entrenched in business circles, they will also have plenty of opportunity to spread around their experience. The mechanisms in place require close scrutiny which is probably more a sociological task. From an economic perspective, it can be asked, what motivates parties to spread news. The threat to do so can help in contractual relationships, but the same threat can be used for blackmailing. Therefore, the credibility of such comments is questionable.

Yet, the point is an important one. Consulting companies insist that their business is done very much on recommendation. Therefore, the argument goes, concerns for reputation make bonus contracts redundant. It does not, however, seem plausible that this argument is true to the same extent for all cases. There

382 see e.g. Gibbons (2001), p. 9 footnote 6

clearly seems to be a difference if the client is a large multinational company or a small start-up, if the consultant is a small one person firm or a big international consultancy, if the project is highly visible or not.

## **5.3.6 Discussion**

First best can be achieved if utilities are not discounted in an infinitely repeated version of the basic one period model383 • The intuition behind this argument is that players start by cooperating, but if one party starts to defect, they will defect forever after. If this is accepted to be the strategy of the players, the dominant strategy is to cooperate. The immediate gain from defecting is always overcompensated by the loss in later periods.

The main criticism is that infinite repetition and no discounting are very unrealistic assumptions. This argument breaks down as soon as there is an end to the game. Then, the dominant strategy in the last period will be to defect. The game will unravel backwards. If games are finite, first best cannot be achieved because of backward unravelling.

If there is a discount rate and conclusion of the game is uncertain, first best can only be sustained in special cases. In some cases there will also be a secondbest solution. As a general rule, the reputation effects are more likely to sustain contracts if the discount rate of the party whose reputation is at stake is low, if the judgement of this party attributes a low probability to the scenario that the relationship is discontinued, and if the gains of relational trade are high and possibly expected to rise.

The two models discussed above can be seen as complementary: If effort is not contractible, but can be observed, reputation concerns of the agent can support flat fee contracts based on effort. If this is not possible, parties may switch to output-based bonus contracts; but these contracts may not be feasible if output is just observable and not contractible. Reputation concerns of the principal may solve this problem. This suggests a sequence of analysis: Only if agent reputation effects are too low or observability limited will bonus contracts be considered.

The reputation mechanism may work beyond the original bilateral relationship. A "news-spreading mechanism" has to be assumed in these cases. Often it is not explicitly modelled. The relevant variables will be project visibility and the parties' position and credibility within the relevant community.

383 see Radner ( 1981)

## **5.4 Career Concerns - Learning**

## **5.4.1 Introduction**

So far, two different kinds of arguments have been presented: First of all, it was shown that time can help to write explicit multi-period contracts which can reduce imperfect risk-sharing compared to one-period contracts.

Then, it was argued in the theory of supergames that reputation concerns might allow parties to contract on contingencies which are observable but not verifiable. Although an explicit contract would not be enforceable, an implicit contract ties observed effort to future pay-offs. Pay-offs will be lower if one party defects because the counterparty stops trusting, which reduces the future gains of trade. Thus, parties may be able to eschew switching to alternative perfonnance measures which induce imperfect risk-sharing or are more distorted.

Another such implicit contract which ties current effort to future pay-offs is described by the model of career concerns. The intuition, as fonnulated by Fama384, is that there is no need for explicit contracts, because the market can effectively police agents. This is because the agent's career will depend on his performance track record. The market monitors past perfonnance and only agents who achieve high performance levels will be promoted. So, they will exert effort in order to positively affect their career chances.

This intuition is fonnalized by Holmstrom385 • He shows that Fama's conclusion that career concerns can provide efficient incentives will only hold under very special assumptions. Major inefficiencies can arise both in the short and in the long run.

The model allows important insights into incentive effects in a setting where the market monitors the agent's output in order to learn about his productive capabilities. The following propositions will be derived:

31. It can be seen that incentives are high if the discount rate is low, if the precision of the production technology is high, and if the disutility of effort does not increase too fast.

384 Fama (1980)

385 Holmstrom (1982 reprinted in 1999) model will be presented in the following Section. His reasoning will be somewhat adjusted to make it easier for the non-technical reader to appreciate the argument. Minor errors of the article are corrected.

#### **5.4.2 The Basic Model**

It is assumed in the model of career concerns that the agent's output in each period y, depends on bis effort a,, his productive capability ri and a sequence of unrelated shocks *e,* representing the external factor:

$$\mathbf{y}\_t = \mathfrak{n} + \mathbf{a}\_t + \mathfrak{e}\_t \quad \mathbf{t} = 1, 2, \dots \tag{12.28}$$

where *e,* is normally distributed with O mean and a variance of cr; .

$$
\mathfrak{e}\_{\mathfrak{e}} \sim \mathbf{N}\left(\mathbf{0}, \sigma\_{\mathfrak{e}}^{2}\right) \tag{12.29}
$$

It is further assumed that both the agent and the principal do not know the agent's productive capability. They do, however, share the same prior beliefs. These beliefs are represented by an initial assessment m1 of the agent's capabilities and the assumed precision of these beliefs h, (which equals the inverse of the variance h, = 1 / cr; ). As time proceeds, these beliefs are updated on the basis of the agent's performance track record. In the models of signaling and screening it is assumed that the agents have private information on their own capability. In these cases it will be explored if it is possible to extract information from the agents. In the model of career concerns, however, it can be seen that information is assumed to be imperfect but symmetric: The agent and the market monitor the same normal learning process.

The focus here will be to show that, in the described setting, career concerns will create incentives in the absence of explicit incentive contracts. This is done by creating an indirect link between current effort and future compensation. The objective of this model set up by Holmstrom is to formalize the well-known argument of Fama, who went so far as to claim that career concerns will make explicit incentive contracts redundant by providing efficient incentives costlessly. It is therefore central to understand why the agent should believe that his current effort would positively effect his future compensation.

First, the agent's problem is considered. His pay-off in any period t equals his compensation c, minus his disutility of effort g1 ( a, ) , which is assumed to be an increasing and convex function in effort.

$$\mathbf{u}\_t = \mathbf{c}\_t - \mathbf{g}\_t(\mathbf{a}\_t) \tag{12.30}$$

where

$$\mathbf{g}\_t(\mathbf{a}\_t) > 0, \mathbf{g}\_t \nwarrow (\cdot) > 0, \mathbf{g}\_t \nwarrow (\cdot) > 0\tag{12.31}$$

The agent is not only concerned about his current pay-off, but tries to choose effort in order to maximize the present value of current and future payoffs. It is obvious that this present value does not only depend on the current choice of effort, but also on all choices of effort in the future; but future decisions cannot be made today, because the information on which they are based is future information and therefore not currently available. Therefore, the agent's problem is to solve for the optimal decision rule which prescribes in every period t which decision a, will be taken contingent on the basis of the information y1\_1 , which will then be available. This will automatically produce the optimal current choice of effort by setting in current information:

$$\mathbf{a}\_t = \mathbf{a}\_t(\mathbf{y}\_{t-1}) \tag{12.32}$$

The fact that future information is not available today also implies that the agent is faced with a decision under uncertainty. It is assumed that the agent is risk-neutral and therefore maximizing expected present value. The optimal decision rule is therefore the solution to the following maximization problem:

$$\mathbf{a}^\*(\cdot) \in \arg\max\_{\mathbf{a}'(\cdot)} \sum\_{\iota=\iota}^\infty \mathbb{B}^{\iota-1} \left[ \mathbf{E} \mathbf{c}\_{\iota} - \mathbf{E} \mathbf{g}\_{\iota} \left( \mathbf{a}\_{\iota}^{'} \left( \mathbf{y}\_{\iota-1} \right) \right) \right] \tag{12.33}$$

where ~ is the discount factor and a• ( •) is a vector representing the optimal decision rule.

It will now be analysed, what determines compensation. It is assumed that the agent faces a competitive risk-neutral market. This implies that his compensation equals expected marginal output'86:

$$\mathbf{c}\_{\mathbf{i}} = \mathbb{E}\left(\mathbf{y}\_{\mathbf{i}}\right) \tag{12.34}$$

It follows from the production function (12.28) that the market determines compensation by adding expected capability and expected choice of effort.

$$\mathbf{c}\_{\text{t}} = \mathbf{E}\_{\text{t}} \left( \boldsymbol{\eta} \right) + \mathbf{E} \left( \mathbf{a}\_{\text{t}} \right) \tag{12.35}$$

It is obvious from the production function that effort is a substitute for capability. Therefore, the whole game played by the agent is to choose effort in order to bias the learning process of the market in his favour. But this is anticipated by the market. One might think that, because his action cannot be observed, asymmetric information will develop over time, but this is not the case387 : His maximizing behaviour makes him perfectly predictable if his utility function is assumed to be common knowledge, in line with the usual assumptions of agency theory. His is trapped. He cannot fool the market, but ifhe did not show maximizing behaviour he would bias the learning process against him388 • Therefore, expected effort choice in (12.35) equals the agent's optimal decision rule:

$$\mathbf{E}\left(\mathbf{a}\_{\text{t}}\right) = \mathbf{a}\_{\text{t}}^{\text{\textquotedblleft}}\left(\mathbf{y}\_{\text{t}-\text{t}}\right) \tag{12.36}$$

386 Note that the assumption of competitive markets is a short-cut for saying that the agent faces a number of principals and that there is competition among these principals, driving their profits down to zero. This assumption is not as strong as it seems. Indeed, the market model could be replaced by a bargaining model, which would make the argument more complex but would not change its insights. So, the zero-profit hypothesis is just a way of holding one party's utility constant while maximizing the utility of the other party, which insures Pareto optimality. This is in the same spirit as setting agents' utility to their reservation level as was done in other instances.

387 see Gibbons (2001)

388 Holmstrom (1999) calls this situation a "rat race".

It was also mentioned that the market assesses capability on the basis of the agent's performance track record. So, assessment m, in period t is a function of the assessment at the beginning of the last period t -1, updated by the observed outcome at the end of the last period y1\_ 1 • As

$$\mathbf{y}\_{t-l} = \mathfrak{n} + \mathbf{a}\_{t-l} + \mathfrak{e}\_{t-l} \tag{12.37}$$

and a,\_1 can perfectly be anticipated ( at-1 =a:\_,), (12.37) can be written as

$$\mathbf{z}\_{t-1} = \mathbf{y}\_{t-1} - \mathbf{a}\_{t-1} = \boldsymbol{\eta} + \boldsymbol{\varepsilon}\_{t-1} \tag{12.38}$$

where z, is a sequence of the agent's capability disturbed by an error term. Updating the market's beliefs on the agent's capability then occurs by calculating the weighted average of the initial belief and the observation. The weights are the precision of the initial belief ht-1 and the precision of the observation h,, respectively.

$$\mathbf{E}\_{\rm t} \left( \eta \right) = \mathbf{m}\_{\rm t} = \frac{\mathbf{h}\_{\rm t-1} \mathbf{m}\_{\rm t-1} + \mathbf{h}\_{\rm s} \mathbf{z}\_{\rm t-1}}{\mathbf{h}\_{\rm t-1} + \mathbf{h}\_{\rm s}} = \frac{\mathbf{h}\_{\rm l} \mathbf{m}\_{\rm l} + \mathbf{h}\_{\rm s} \sum\_{s=1}^{\rm s-1} \mathbf{z}\_{\rm s}}{\mathbf{h}\_{\rm l} \left( 1 - \mathbf{t} \right) \mathbf{h}\_{\rm s}} \tag{12.39}$$

The market's assessment of the agent's capability becomes ever more precise as the learning process continues (precision is increasing int):

$$\mathbf{h}\_{\mathbf{t}} = \mathbf{h}\_{\mathbf{t}-\mathbf{t}} + \mathbf{h}\_{\mathbf{s}} = \mathbf{h}\_{\mathbf{t}} + \left(\mathbf{t} - \mathbf{1}\right)\mathbf{h}\_{\mathbf{s}}\tag{12.40}$$

As the agent's maximization problem for finding the optimal decision rule depends on compensation (see (12.33)) but compensation in turn depends on the optimal decision rule (see (12.35) and (12.36)), there is an interdependence between the two decision problems, which means that they have to be solved simultaneously. Rewriting (12.33) and inserting (12.39) and (12.36) into (12.35), this simultaneous decision problem can be stated as:

$$\mathbf{a}^\*\left(\cdot\right) \in \arg\max\_{\mathbf{a}^\*(\cdot)} \sum\_{t=1}^\bullet \mathbf{\mathcal{J}}^{t-1} \left[ \mathbf{E} \mathbf{c}\_t - \mathbf{E} \mathbf{g}\_t \left( \mathbf{a}\_t^{'} \left( \mathbf{y}\_{t-1} \right) \right) \right] \tag{12.33}$$

And:

$$\mathbf{c}\_{\mathbf{c}} = \frac{\mathbf{h}\_{\text{l}}\mathbf{m}\_{\text{l}} + \mathbf{h}\_{\text{e}}\sum\_{\mathbf{s}=\mathbf{l}}^{\text{l}-1}\mathbf{z}\_{\mathbf{s}}}{\mathbf{h}\_{\text{e}}} + \mathbf{a}\_{\text{e}}^{\text{\*}}\left(\mathbf{y}\_{\text{e}-\text{l}}\right) \tag{12.35}$$

This is solved by taking expectation of (12.35)'389

$$\mathbf{E}\mathbf{c}\_{\mathrm{t}} = \frac{\mathbf{h}\_{\mathrm{l}}\mathbf{m}\_{\mathrm{l}}}{\mathbf{h}\_{\mathrm{t}}} + \frac{\mathbf{h}\_{\mathrm{e}}}{\mathbf{h}\_{\mathrm{t}}} \sum\_{\mathrm{s}=\mathrm{l}}^{\mathrm{t}-\mathrm{l}} \left[\mathbf{m}\_{\mathrm{l}} + \mathbf{a}\_{\mathrm{s}} - \mathbf{E}\mathbf{a}\_{\mathrm{s}}^{\mathrm{\mathsf{T}}} \left(\mathbf{y}\_{\mathrm{s}-\mathrm{l}}\right)\right] + \mathbf{E}\mathbf{a}\_{\mathrm{t}} \,^{\mathrm{\mathsf{t}}} \left(\mathbf{y}\_{\mathrm{t}-\mathrm{l}}\right) \tag{12.35}$$

and inserting the resulting (12.35)" into (12.33). Then, the first order conditions y1 , t = 1,2, ... can be written as390 :

$$\gamma\_{\mathfrak{e}} \equiv \sum\_{\mathfrak{s} \simeq t \simeq 1}^{\mathfrak{o}} \mathfrak{J}^{\mathfrak{s}^{-t}} \frac{\mathbf{h}\_{\mathfrak{s}}}{\mathbf{h}\_{\mathfrak{s}}} = \mathfrak{g}'(\mathbf{a}\_{\mathfrak{e}}) . \tag{12.41}$$

*Proposition 31: It can be seen that incentives are high if the discount rate is low91, if the precision of the production technology is high392 and if the disutility of effort does not increase too fast*

Efficient incentives are characterized by a situation where marginal product equals marginal cost:

$$\mathbf{g'(a) = l} \tag{12.42}$$

In the model described so far, equilibrium will be very inefficient: In the long run ( t • oo ) it can be seen that there will be no incentives from career concerns ( y 1 • 0) as the assessment will become indefinitely precise ( h, • oo ). This is an intuitive result: The agent will only have incentives to exert effort from career concerns, as long as his capability is not fully known.

389 See Mathematical Appendix at the end of this Paragraph.

390See Mathematical Appendix at the end of this Paragraph.

#### *Mathematical Appendix:*

**Footnote 389:**

$$\begin{aligned} \mathbf{E}\mathbf{c}\_{\texttt{t}} &= \mathbf{E}\frac{\mathbf{h}\_{\texttt{l}}\mathbf{m}\_{\texttt{l}}}{\mathbf{h}\_{\texttt{l}}} + \mathbf{E}\left(\frac{\mathbf{h}\_{\texttt{e}}}{\mathbf{h}\_{\texttt{l}}}\sum\_{\texttt{s}=\texttt{l}}^{\texttt{t}-\texttt{l}} \mathbf{z}\_{\texttt{s}}\right) + \mathbf{E}\mathbf{a}\_{\texttt{t}}^{\star}\left(\mathbf{y}\_{\texttt{t}-\texttt{l}}\right) \\ &= \frac{\mathbf{h}\_{\texttt{l}}\mathbf{m}\_{\texttt{l}}}{\mathbf{h}\_{\texttt{l}}} + \frac{\mathbf{h}\_{\texttt{e}}}{\mathbf{h}\_{\texttt{e}}}\sum\_{\texttt{s}=\texttt{l}}^{\texttt{t}-\texttt{l}} \mathbf{E}\mathbf{z}\_{\texttt{s}} + \mathbf{E}\mathbf{a}\_{\texttt{t}}^{\star}\left(\mathbf{y}\_{\texttt{t}-\texttt{l}}\right) \end{aligned} \tag{4.1}$$

z, can be written as:

$$\mathbf{z}\_s = \mathbf{y}\_s - \mathbf{a}\_s = \eta + \mathbf{e}\_s - \mathbf{a}\_s + \mathbf{a}\_s = \eta + \mathbf{a}\_s + \mathbf{e}\_s - \mathbf{a}\_s \tag{9}$$

Inserting ( ~) into (a) gives:

$$\mathbf{E}\mathbf{c}\_{\mathrm{t}} = \frac{\mathbf{h}\_{\mathrm{t}}\mathbf{m}\_{\mathrm{l}}}{\mathbf{h}\_{\mathrm{t}}} + \frac{\mathbf{h}\_{\mathrm{e}}}{\mathbf{h}\_{\mathrm{e}}} \sum\_{s=1}^{\mathrm{l}-1} \left[ \mathbf{m}\_{\mathrm{l}} + \mathbf{a}\_{s} - \mathrm{E}\mathbf{a}\_{s}^{\star} \left( \mathbf{y}\_{s-\mathrm{l}} \right) \right] + \mathrm{E}\mathbf{a}\_{\mathrm{e}}^{\star} \left( \mathbf{y}\_{\mathrm{t-l}} \right),$$

**Footnote 390:**

"' h "' h = O+ *L ~s-i* \_.\_·1+0-g'(a,) = *L ~•-<* \_.\_\_g'(a,) = 0 s=t+l h, s=t+l h,

#### **5.4.3 Extension: Adding Innovation**

The situation changes if a plausible assumption is added to the basic model. This is by assuming that competence is not invariant over time but is modelled as an

autoregressive process. More specifically, it is assumed that this period's capability equals last period's capability plus a stochastic shock:

$$
\mathfrak{m}\_{\mathfrak{t}} = \mathfrak{m}\_{\mathfrak{t}-1} + \delta\_{\mathfrak{t}-1} \tag{12.43}
$$

where the sequence of stochastic shocks is driftless with variance cr; :

$$\delta\_{\mathfrak{s}\downarrow} \sim \mathbf{N}\left(\mathbf{0}, \sigma\_{\mathfrak{s}}^{2}\right) \tag{12.44}$$

The shocks can be interpreted as reflecting innovation. Innovation changes job characteristics. Therefore, someone who was well qualified to do the job in the past is not necessarily well qualified to do the job now or in the future.

Having motivated the noise term in the competence process, it will now be analysed which effects this assumption has on incentives. In fact, beliefs are still updated by calculating the weighted average of last period's initial beliefs and last period's observation, with the precision of the initial beliefs and the precision of the observation as weights, respectively:

$$\mathbf{m}\_{\rm t} = \boldsymbol{\mu}\_{\rm t-l} \mathbf{m}\_{\rm t-l} + \left(1 - \boldsymbol{\mu}\_{\rm t-l}\right) \mathbf{z}\_{\rm t-l} \tag{12.45}$$

where

$$\mathbf{h}\_{\text{t-l}} = \frac{\mathbf{h}\_{\text{t-l}}}{\mathbf{h}\_{\text{t-l}} + \mathbf{h}\_{\text{c}}} \tag{12.46}$$

What changes is the way the precision of the belief is assessed. By updating the initial belief it will be made more precise.

$$
\bar{\mathbf{h}} = \mathbf{h}\_{\text{t-l}} + \mathbf{h}\_{\text{e}} \tag{12.47}
$$

But the belief refers to last period's capability, which is irrelevant because last period's decisions have already been made before updating occurs. What is interesting is the current period's assessed capability. Contrary to the basic model, it is now assumed that last period's capability does not fully determine present capability. It is still the best estimate, which is why beliefs are updated in the same ,way. Yet, the precision of the present belief about capability will be lower than h because innovation adds uncertainty of whether someone who was capable in the past will also be capable at present and in the future.

$$\frac{1}{\mathbf{h}\_{\text{t}}} = \frac{1}{\mathbf{h}\_{\text{t}-l} + \mathbf{h}\_{\text{e}}} + \frac{1}{\mathbf{h}\_{\text{g}}} = \frac{\mathbf{h}\_{\text{g}} + \mathbf{h}\_{\text{t}-l} + \mathbf{h}\_{\text{e}}}{\left(\mathbf{h}\_{\text{t}-l} + \mathbf{h}\_{\text{s}}\right)\mathbf{h}\_{\text{g}}} \tag{12.48}$$

What happens is that first precision is increased by making another observation and then decreased by adding the noise ( cr; = 1 /ha) of the competence process. Obviously, one can try to solve for a stationary state which is defined as the state where decrease of noise due to learning is exactly offset by the increase of noise due to innovation. It will later be shown that the stationary state actually is a stable equilibrium.

For technical reasons, the stationary state is calculated in terms of µs, which are tied to hs by expression (12.46). It can be shown that'93 :

$$
\mu\_{\rm t} = \frac{1}{2 + \mathbf{r} - \mu\_{\rm t-1}} \tag{12.49}
$$

In the stationary state the precision does not change anymore from one period to the other:

$$\mathbf{h}^\* = \mathbf{h}\_t = \mathbf{h}\_{t-1} \implies \boldsymbol{\mu}^\* = \boldsymbol{\mu}\_t = \boldsymbol{\mu}\_{t-1} \tag{12.50}$$

Inserting (12.50) into (12.49) gives:

$$
\mu^\* = \frac{1}{2 + \mathbf{r} - \mu^\*} \Leftrightarrow -\mu^{\*2} + (2 + \mathbf{r})\mu^\* - 1 = 0 \tag{12.51}
$$

Solving the quadratic equation gives:

$$\left(\mu\_{\text{1}/2}\right)^{\*} = 1 + \frac{1}{2}\mathbf{r} \pm \sqrt{\frac{1}{4}\mathbf{r}^{2} + \mathbf{r}}\tag{12.52}$$

From (12.45) follows that µ• < 1. Therefore:

$$\mu^\* = 1 + \frac{1}{2}\mathbf{r} - \sqrt{\frac{1}{4}\mathbf{r}^2 + \mathbf{r}}\tag{12.53}$$

393 See Mathematical Appendix at the end of this Paragraph.

Taking account of the modified learning process:

$$\mathbf{m}\_{\mathbf{t}} = \mathbf{m}\_{\mathbf{t}} \prod\_{i=1}^{t-1} \boldsymbol{\mu}\_{\mathbf{i}} + \sum\_{s=1}^{t-1} \mathbf{z}\_{s} \left[ \prod\_{i=s+1}^{t-1} \boldsymbol{\mu}\_{\mathbf{i}} \right] \left( 1 - \boldsymbol{\mu}\_{s} \right) \tag{12.54}$$

the market's compensation rule can once again be inserted into the agent's maximization problem. The first order conditions *y,* can be written as394 :

$$\gamma\_{\iota} = \left(1 - \mu\_{\iota}\right) \sum\_{s=\iota+1}^{\bullet} \mathfrak{F}^{s-1} \prod\_{i=\iota+1}^{s-1} \mu\_{i} = \mathbf{g}'\left(\mathbf{a}\_{\iota}\right) \tag{12.55}$$

In the stationary state, first-order conditions can be further simplified395:

$$\gamma\_r = \frac{\left(1 - \mu^\bullet\right)\beta}{1 - \beta\mu^\bullet} = \mathbf{g}'(a\_r) \tag{12.56}$$

*Proposition 32: Interpreting the level of incentives in the stationary state, it can be said, that incentives will never be higher than the efficient level:*

$$\frac{\mathfrak{J}\left(1-\mu^{\star}\right)}{1-\mu^{\star}\mathfrak{J}}=\mathfrak{g}'\left(\mathfrak{a}^{\star}\right)\le 1\tag{12.57}$$

*They will always be efficient if the discount rate is zero* (13 = 1). *This was Fama's result The result requires that there is some noise in the competence process (however small).* µ • < l • r > 0 • cr~ > 0.

$$\frac{1-\mu^\*}{1-\mu^\*} = 1\tag{12.58}$$

*As soon as the discount rate is different from zero, incentives will be lower than the efficient level Incentives will be closer to efficiency if the discount rate is low, updating of beliefs is fast and utility of effort increases slowly.*

394 See Mathematical Appendix at the end of this Paragraph.

395 See Mathematical Appendix at the end of this Paragraph.

Updating is a very intuitive concept. It is the weight (1- µ • ) which is given to the most recent observation. Updating will be fast ifµ' is low, which happens if the precision of the production process is high relative to the precision of the competence process, or equivalently if the competence process is very disturbed relative to the production process. These results are recorded in *Exhibit 10.*

**Exhibit 10: Career Concerns: Incentives in Equilibrium**

The level of incentives is shown as a function of the speed of updating for different discount rates396• The surprising result is that Fama's prediction of efficient incentives becomes true for zero discount rate even at an infinitesimally small updating speed (if only a small amount of noise is added to the competence process), as was mentioned before.

396 In this Exhibit, r represents the discount rate (not to be confused with the r in the text which refers to relative precision of the output process compared to the competence process).

#### *Mathematical Appendix:*

#### **Footnote 393:**

$$
\mu\_{\iota} = \frac{h\_{\iota}}{h\_{\iota} + h\_{\iota}} = \left(1 + \frac{h\_{\iota}}{h\_{\iota}}\right)^{-1} \tag{6}
$$

Inserting (12.48) into (a) gives:

$$\begin{split} \mu\_{t} &= \left[ 1 + \frac{h\_{\varepsilon} \left( h\_{\delta} + h\_{\varepsilon - 1} + h\_{\varepsilon} \right)}{\left( h\_{\varepsilon - 1} + h\_{\varepsilon} \right) h\_{\delta}} \right]^{-1} = \left[ 1 + \frac{h\_{\varepsilon}}{h\_{\delta}} \left( \frac{h\_{\delta}}{h\_{\varepsilon - 1} + h\_{\varepsilon}} + 1 \right) \right]^{-1} \\ &= \left[ 1 + \frac{h\_{\varepsilon}}{h\_{\delta}} \left( \left( \frac{h\_{\varepsilon}}{h\_{\delta}} + \frac{h\_{\varepsilon - 1}}{h\_{\delta}} \right)^{-1} + 1 \right) \right]^{-1} \end{split} \tag{9}$$

Solving (12.46) for h,\_1 gives:

$$h\_{t-1} = \frac{h\_g \mu\_{t-1}}{1 - \mu\_{t-1}} \tag{4}$$

Inserting *(r)* into (P) gives:

$$\mu\_{\iota} = \left\{ 1 + \frac{h\_{\varepsilon}}{h\_{\delta}} \left[ \left( \frac{h\_{\varepsilon}}{h\_{\delta}} + \frac{h\_{\varepsilon}}{h\_{\delta}} \frac{\mu\_{\iota-1}}{1 - \mu\_{\iota-1}} \right)^{-1} + 1 \right] \right\}^{-1}$$

Setting *r* = *h,* / *h0* gives:

$$\begin{aligned} \mu\_i &= \left\{ 1 + r \left[ r^{-1} \left( 1 + \frac{\mu\_{\iota-1}}{1 - \mu\_{\iota-1}} \right)^{-1} + 1 \right] \right\}^{-1} = \left\{ 1 + 1 - \mu\_{\iota-1} + r \right\}^{-1} \\ \mu &= \frac{1}{2 + r - \mu\_{\iota-1}} \end{aligned}$$

195

**Footnote 394:**

$$\mathbf{E}\mathbf{c}\_{\mathfrak{t}} = \mathbf{m}\_{\mathfrak{l}} \prod\_{l=1}^{t-1} \mu\_{\mathfrak{t}} + \sum\_{\mathfrak{s}=\mathfrak{l}}^{t-l} \mathbf{E}\left(\mathbf{z}\_{\mathfrak{s}}\right) \prod\_{i=\mathfrak{s}+\mathfrak{l}}^{t-l} \mu\_{\mathfrak{t}} \left(1-\mu\_{\mathfrak{s}}\right) + \mathbf{E}\mathbf{a}\_{\mathfrak{t}}^{\mathfrak{t}}\left(\mu\_{\mathfrak{t}-\mathfrak{l}}\right),$$

Setting z. = TJ + a, + i:. - a. , it can be written:

$$\mathbf{E}\mathbf{c}\_{\mathrm{t}} = \mathbf{m}\_{\mathrm{t}}\prod\_{i=\mathrm{l}}^{\mathrm{t}-1}\boldsymbol{\mu}\_{\mathrm{i}} + \sum\_{\mathrm{s}=\mathrm{l}}^{\mathrm{t}-1} \left\{ \left(\mathbf{m}\_{\mathrm{l}} + \mathbf{a}\_{\mathrm{s}} - \mathbf{E}\mathbf{a}\_{\mathrm{s}}^{\star}\left(\mathbf{y}\_{\mathrm{s}-\mathrm{l}}\right)\right) \left[\prod\_{i=\mathrm{s}+\mathrm{l}}^{\mathrm{t}-1}\boldsymbol{\mu}\_{\mathrm{i}}\right] \left(\mathbf{1} - \boldsymbol{\mu}\_{\mathrm{s}}\right) \right\} + \mathbf{E}\mathbf{a}\_{\mathrm{t}}\,^{\star}\left(\mathbf{y}\_{\mathrm{s}-\mathrm{l}}\right),$$

Inserting in the agent's maximisation problem and taking the derivative gives:

$$\begin{split} & \frac{\partial}{\partial \mathbf{a}\_{t}} \sum\_{s=t}^{\infty} \mathfrak{B}^{s-t} \left[ \operatorname{Esc}\_{s} - \operatorname{Eg}\_{s} \left( \mathbf{a}\_{s} \left( \mathbf{y}\_{s-1} \right) \right) \right] \\ &= \left\{ \frac{\partial}{\partial \mathbf{a}\_{t}} \sum\_{s=t}^{\infty} \mathfrak{B}^{s-t} \operatorname{m}\_{t} \prod\_{i=1}^{s-1} \mu\_{i} \right\} + \left\{ \frac{\partial}{\partial \mathbf{a}\_{t}} \sum\_{s=t}^{\infty} \mathfrak{B}^{s-t} \prod\_{i=1}^{s-1} \left\{ \left( \operatorname{m}\_{t} + \mathbf{a}\_{i} - \operatorname{Ea}\_{i} \right) \left[ \prod\_{j=1}^{s-1} \mu\_{j} \right] \left( 1 - \mu\_{i} \right) \right\} \right\} \\ &+ \left\{ \frac{\partial}{\partial \mathbf{a}\_{t}} \sum\_{s=t}^{\infty} \mathfrak{B}^{s-t} \operatorname{Ea}\_{s} \right\} - \left\{ \frac{\partial}{\partial \mathbf{a}\_{t}} \sum\_{s=t}^{\infty} \mathfrak{B}^{s-t} \operatorname{Eg} \left( \mathbf{a}\_{s} \right) \right\} \\ &= 0 + \sum\_{s=t+1}^{\infty} \mathfrak{B}^{s-1} \cdot 1 \cdot \prod\_{j=t+1}^{s-1} \mu\_{j} \left( 1 - \mu\_{i} \right) + 0 - \mathrm{g}^{\prime} \left( \mathbf{a}\_{i} \right) \end{split}$$

Therefore, the first order condition y1 can be written as:

$$\gamma\_{\mathfrak{r}} = \left(1 - \mu\_{\mathfrak{r}}\right) \sum\_{\mathfrak{s} = \mathfrak{r} + 1}^{\infty} \mathfrak{B}^{\mathfrak{s}^{-1}} \prod\_{i=\mathfrak{s} + 1}^{\mathfrak{s} - 1} \mu\_{\mathfrak{i}} = \mathfrak{g}'\left(\mathbf{a}\_{\mathfrak{r}}\right)$$

(Readers comparing this result with the original Holmstrom article will note that there is a typing error in the original.)

**Footnote 395:**

Applying the formula of the sum of infinite geometric sequences to the right hand side gives:

$$\begin{aligned} \mathcal{Y}\_{\boldsymbol{\iota}} &= \left(1 - \boldsymbol{\mu}^{\star}\right) \sum\_{\iota=1}^{n} \mathcal{B}^{\prime} \boldsymbol{\mu}^{\star \star \iota} = \mathbf{g}^{\prime} \left(a\_{\iota}\right) \\ \mathcal{Y}\_{\boldsymbol{\iota}} &= \left(1 - \boldsymbol{\mu}^{\star}\right) \frac{1}{\boldsymbol{\mu}^{\star}} \left[\frac{1}{1 - \beta \boldsymbol{\mu}^{\star}} - 1\right] = \mathbf{g}^{\prime} \left(a\_{\iota}\right) = \left(1 - \boldsymbol{\mu}^{\star}\right) \frac{1}{\boldsymbol{\mu}^{\star}} \left(\frac{\beta \boldsymbol{\mu}^{\star}}{1 - \beta \boldsymbol{\mu}^{\star}}\right) = \mathbf{g}^{\prime} \left(a\_{\iota}\right) \\ \mathcal{Y}\_{\boldsymbol{\iota}} &= \frac{\left(1 - \boldsymbol{\mu}^{\star}\right) \beta}{1 - \beta \boldsymbol{\mu}^{\star}} = \mathbf{g}^{\prime} \left(a\_{\iota}\right) \end{aligned}$$

The trick is that, in the stationary state, *µ;'s* with i ~ *T* equal *µ* •. Also note the convention that

$$\prod\_{\ast}^{\sharp \mathsf{l}} \mu\_{\mathsf{i}} = 1.$$

#### **5.4.4 Disequilibrium - Transient Effects**

It is important to understand what happens before the stationary state is reached. This will be particularly relevant in situations where updating is slow and periods are very long. In such a situation, not many "learning loops" are possible in a given span of time, the observed signal is bad and competence is very stable over time. So, the market tends to stick with its prior beliefs. Here, the stationary state might never be reached in the considered period and disequilibrium might be the only relevant state.

The dynamics of incentives are studied by doing comparative statics in the first order conditions (12.55) of the agent's maximization problem. It can be seen that incentives increase in all periods if updating speed increases ( µ1 decreases )397 • The weight µ, is an increasing function of h, as can be seen in (12.46). Therefore, as precision of beliefs with respect to capability ( h,) increases, updating becomes slower and incentives decrease.

397 see Holmstrom ( 1999), p. 17 4 for the formal proof by induction

As µ1 is an increasing function of µ,\_ 1as can be seen in (12.49), and there is only one stationary state in the relevant interval ( 0, 1) , it can be seen from *Exhibit* 11398 that if last period's speed of updating was higher than in the stationary state ( µ1-1 < µ •) - which is equivalent to saying that the precision of last period's belief was lower than the precision of beliefs in the stationary state ( h1-1 < h • ), the speed of updating will decrease ( µ, > µ,\_ 1 ) or the precision of beliefs will increase ( h, > h1-1 ). This means that the sequence µ, will be approaching µ' from below.

**Exhibit 11: Career Concerns: Incentives in Disequilibrium**

It can therefore be said that

*Proposition 33: If precision of beliefs is initially lower than in the stationary state, speed of updating is high and therefore incentives are high. As they approach the stationary state over time precision increases, speed of updating decreases and incentives become lower. The opposite holds true if the precision of beliefs is initially higher than in the stationary state. In this case,*

398 Taken with small modification from Holmstrom (I 999), p. 175

*incentives are low in the beginning and become higher over time. There/ore, the system is stable.*

### **5.4.5 Discussion**

Holmstrom's formalization of Fama's argument shows that, in equilibrium, career concerns will provide efficient incentives only under very special conditions. The most notable assumption is a zero-discount rate. There also has to be some change of job characteristics due to innovation in order to prevent the market from eventually fully learning the agent's capability.

If the discount rate is not zero, incentives will never be efficient in equilibrium. They will, however, be close to efficiency if the discount rate is low, job characteristics change considerably due to innovation, and the external factor in the output process is unimportant. In absolute terms, incentives will also be higher if the dis utility of effort rises only slowly. A useful and intuitive concept in this context is the speed of updating. In fact, if the noise of the production function is low relative to the noise of the competence process, the speed of updating will be high, which in tum will make incentive increase since the agent knows that higher effort will have an impact. If, however, talent will be expected to last forever, once it has been proven and potential signals to the contrary are very unreliable, one will stick to the prior belief.

Therefore, if the discount rate is low and updating fast, there will be fairly high incentives to perform in equilibrium. The intuitive idea is that reputation is not worth so much, or high reputation has to be reproven very often. In this situation, career concerns solve the shirking problem. Conversely, if the discount rate is high (the agent does not care about the future) and updating is slow, there will be low incentives in the steady state.

In some situations, incentives in disequilibrium will be very important. This is especially true in cases where updating is slow and the frequency of observation is low (due to a long production process). Incentives will be initially high if the precision of the initial belief is thought to be higher in later periods. Incentives will be initially low if the precision of the initial belief is thought to be lower in later periods. The first case will be true in most cases. In the beginning, not much is known about the agent. Therefore, beliefs will be relatively imprecise.

In a situation where the noise of the production function is high relative to noise of the competence process, which is equivalent to a situation where there is little change of job characteristics due to innovations, and observation of output is only a very bad signal due to an important external factor, it was said that updating will be slow and incentives will be much too low in equilibrium. If there is low initial precision it was also said that incentives will be much too high in the beginning. This situation will persist for quite some time as the speed of updating is low. Therefore, an agent working in an industry where job characteristics are not expected to change much and the external factor is very important, as might be expected for many service industries, will get very inefficient incentives from career concerns.

## **V Conclusions**

## **1.1 Results**

It was shown in Section (IV2.l) that, if effort is not contractible, compensation shall be made contingent on output. It was also shown that, in this case, welfare levels can never be higher than in the case of observable effort. Barring the unrealistic cases of a deterministic production function and risk neutrality of both the principal and the agent, the optimal compensation scheme leads to a welfare loss due to imperfect risk sharing.

Section (IV2.2) derives a closed-form solution which negatively links the use of variable fee contracts to the agent's level of risk aversion, the level of project risk and the convexity of the disutility function. The weakness of this model is its lack of generality and its unrealistic assumptions as e.g. the constant absolute risk averseness of the agent's preferences. Especially the linear sharing rule seems to be completely arbitrary.

So far, it has been argued that variable fees may provide useful incentives in situations of hidden action, but also create imperfect risk sharing. Quite apart from any other consideration, Section (IV2.3) looks closer at the **mechanics of risk sharing:** In the traditional agency models, the principal is always assumed to be risk-neutral, while the agent is assumed to be risk-averse or risk-neutral. This need not be the case. The assumption that the principal is risk-neutral is often justified by the argument that he is the economically more potent party to the contract. This is largely inspired by the traditional story behind principal-agency models referring to the relationship between a company and its employees. There are several arguments why the economically more potent party should be less riskaverse: First, it is often plausible to assume that as a person becomes wealthier his absolute level of risk aversion decreases. Second, if the company is held by an entrepreneur he might be the less risk-averse type of person in the first place. In addition, employees usually only work for one company, while the owner might hold many different companies. So, he is probably better diversified. This last point is especially true for publicly held companies. However,ut in the case of a client and his consultant, things can be different. The small consultant partnership is clearly more risk-averse than its multinational client, but this changes if the big international consultancy firm provides services to a small start-up company through its incubator branch. Clearly, in the setting analysed so far - the case where, say, the principal is risk-averse and the agent risk-neutral - does not appear to be problematic as optimal incentive provision and optimal risk sharing are compatible. But what ifthere is a bilateral moral hazard problem? To answer this and other questions, one has to look at risk sharing in its own right. Two separate

sources of value creation by risk sharing are explored: **differences in risk attitudes** which might arise from predisposition or different levels of wealth, and **differences in diversification.** The result of this Section highlights the parties' level of risk tolerance (both absolute and relative to each other), the specific quality of the risk involved as determined by its correlation with existing risk exposure and the level of project risk as relevant factors of optimal risk sharing. If a risk-neutral party is involved it carries all the risk. The sharing rule is independent in each state of the probability assigned to that state. Finally, the risky part of each party's compensation is proportional to its own risk tolerance divided by the overall risk tolerance of society, if the parties' preferences over lotteries exhibit constant risk aversion (which can be assumed locally).

In Section (IV2.4), a control theory model is set up to determine the optimal sharing rule. It is possible to reprove some of the results of earlier sections. If effort is contractible, flat fee contracts will be used. If it is not contractible it will depend on output. However, contrary to earlier results, it is also possible to shed some light on the mechanics of the optimal sharing rule. Compensation depends on output through the likelihood ratio. There are two implications: The optimal sharing rule can be understood quite intuitively as rewarding the agent if the signal makes it likely that high effort was chosen, but it also explains why little general constraints can be derived for the shape of the optimal sharing rule: It is very sensitive to specifications of utility functions and distributional assumptions. Although the optimal contract can only be derived to be linear under awkwardly improbable assumptions, there are a number of reasons explaining the practical prominence of such contracts. First, there is the transaction cost argument. Setting up complex contracts is just too expensive. Second, linear contracts are argued to be relatively robust for a large number of settings. But also non-distributional assumptions like the number of different options available to the agent affects the optimal incentive scheme. So, paradoxically, there are reasons to believe that adding complexity makes contracts simpler. It is also shown that information is only valuable if it affects posterior assessment of the effort level chosen. It must therefore be related to effort choice, but it must also be impossible to perfectly infer the information - to the extent that it is relevant to this assessment - from information of variables already included into the contract.

A common assumption is that there is a **comparative cost advantage** of output monitoring compared to input monitoring. Why should this be the case? In order to implement input monitoring, the principal has to watch the agent while performing the required task. This causes **opportunity costs** to the principal. Still worse, if the principal does not know the production function of the agent he may well watch the agent while performing a task but will be **unable to interpret his actions** as to whether they are instrumental in achieving the required output.

These costs are amplified by the fact that usually the very motivation to hire an agent in the first place was that the principal either did not want or could not perform the task himself. So, either the principal has something else to do, which means that his opportunity costs are high, or the performance of the task requires specialized knowledge that the principal does not possess. The latter case does make it difficult for the principal to monitor the agent effectively. Alternatively, the principal could hire **other qualified agents** to do the monitoring for him, but then it may be difficult to prevent these monitoring agents from colluding with the operative agents. For all these reasons, input monitoring is likely to be very costly in many circumstances. On the other hand, **output monitoring should be very easy.** One only has to look to which extent the required result was achieved providing that it can be properly defined. So, if a client hires a consultant to perform a cost cutting project, it will be much easier for the client to evaluate how much cost was reduced than to interpret the wide variety of single measures the consultant takes to achieve his goal. Having clearly established the intuition for comparative cost advantage of output monitoring compared to input monitoring in a wide variety of situations, it may come as a surprise that **input monitoring can theoretically infinitely approximate first best.** This is because the agent, in his decision whether to cheat or not, will weigh the benefits of cheating (in the case of shirking reduced disutility of effort) against the expected value of punishment. Therefore, if **harsh enough punishments are announced,** the probability of detection and therefore the number and thoroughness of inspection can be infinitely reduced. In this case, there seems **no rationale for output monitoring.**  If it is not cheaper, it will only provide an additional drawback: imperfect risk sharing. The traditional argument is that **input monitoring always establishes the truth** while output monitoring is prone to error. This is a crucial point, because the **driving force behind imperfect risk sharing** in output monitoring is the possibility of error in judgement and the subsequent punishment of the innocent. If it can be shown that output monitoring can achieve perfect accuracy or input monitoring is prone to error as well, this distinction breaks down. In fact, both can be shown to be plausible assumptions in some circumstances: Output **monitoring will be perfectly accurate** in the case of deterministic production functions but also if there is **shifting support399.** Indeed the argument of Mirrlees on step-functions is in the same spirit. On the other hand, it seems implausible to assume that input monitoring will be able to prove cheating at I 00%. There will always be judgement, inferences, circumstantial evidence. Whatever the process, there is a chance of error. Therefore, the above assumption needs to be relaxed to allow for **error in input monitoring.** These arguments appear construed, and in fact they are. In general, input monitoring will be more costly and output

399 see next Section

monitoring more prone to error. Ignoring these arguments therefore seems to be a justified abstraction, but there still is some merit to taking them seriously. In brief, they say that regardless of whether one is looking at input monitoring or at output monitoring there are two relevant issues: **Error in judgement** and **cost of monitoring,** and that under some circumstances both schemes fare equally well or bad on these two dimensions. By acknowledging that there generally is a distinction between input monitoring and output monitoring, one is actually saying that these circumstances will rarely be present. Understanding why this is the case helps to identify other relevant situational variables which influence the problem of optimal contracting.

Chapter (IV3) discusses the role of the **bankruptcy constraints** and the **role of error** in the monitoring process. Section (IV3. l) shows that input monitoring can approximate first best even if it comes at a cost if there are no bankruptcy constraints and no possibility of error in judgement. If there is a bankruptcy constraint there will be welfare loss, because of direct monitoring cost and possibly efficiency wages or complete uncontractability (no trade). The phenomenon of efficiency wages can be understood by realizing that, for purposes of incentive, provision differentials in agent pay utility, and not absolute pay levels, are relevant. Therefore, in the absence of error in judgement, increasing agent risk averseness even helps to set up cheap incentive schemes. Yet, if error in judgement is permitted, problems of imperfect risk-sharing arise, requiring the simultaneous minimization of the cost arising from investment in the monitoring technology, the frequency of inspections and the risk-premium.

Just as input monitoring can have a problem of imperfect risk sharing due to pitfalls in the monitoring process, there are **situations where output monitoring is perfectly accurate** and can achieve first best beyond the obvious case of a deterministic production function. This will be the case for shifting support schemes, but Section (IV3.2) shows that such schemes are often unrealistic because of bankruptcy constraints (legal, moral, economic) and the problem of fine tuning. Another problem is **moral hazard with respect to risk** which arises in output monitoring schemes in the presence of bankruptcy constraints which make incentive schemes de facto asymmetrical, limiting the downside. The agent will have the incentive to choose very risky projects even if they have a lower expected value than alternative projects (this can be thought of as a call option).

Section (IV 4.1) mentions **direct transaction costs** which arise for input monitoring and for output monitoring, though it will often be plausible that they are **lower for output monitoring.** However, there are also **indirect transaction costs** which arise from provisions which designed to lower direct transaction costs. The goal is to **rationalize monitoring** or to **directly influence the agent's**  **disutility function.** This leads to inefficiencies because production technology is prescribed from top to bottom in a way that is known to be inefficient. In addition, innovation from bottom to top is stifled. This is a distortive effect.

Section (IV4.2) deals with distortion. **Distortion** arises if there is tension between what the principal wants and what the agent is rewarded for. Often it is not possible to eliminate this tension. What the principal wants just might not be contractible. As was shown in this subsection, distortion can be divided into two components: scaling and alignment. Scaling refers to the relative sensitivity of the two measures to changes in the drivers and alignment to the similarity of driver patterns. If a university rewards a scientist (by promotion, or resources) by the number of published articles during a certain period of time ( driver), there will be a problem of **alignment** if the university cares about both quantity and quality. Indeed, the researcher would have the incentive to publish many of articles in low quality journals. If no ranking of journals to account for quality is available, rewards should not depend too much on the number of published articles. Now, considering different departments it could be that a typical researcher in, say, marketing has *5* times as many publications than a typical researcher in, say, mathematics. If the basis for the bonus is the number of published articles, a **scaling** argument suggests the bonus rate for marketing researchers to be one-fifth of the bonus rate for mathematicians. It is obvious that there is a conflict with the risk-incentive trade-off. This model suggests that the bonus rate should be high if the observed variable is relatively undisturbed400• This will be the case for parameters close to the agent. These, however, will be the most distorted, suggesting that the bonus rate should be low. This is consistent with the observation that variable compensation is used more often for top managers than for middle managers. For top managers, undistorted incentives (the share price) happen to correspond with their direct responsibility for the whole company. For middle managers, however, incentives are either distorted if they depend on the individual performance of the department (failing to take into account that it is important to cooperate among departments for the benefit of the company as a whole), or too disturbed, as the share price depends on many factors beyond the reach of the middle manager.

The basic problem of contracting is to find the best contract parameters or the best mix of contract parameters. **Multi-period models do not solve the contracting problem costlessly** as is sometimes claimed, but rather add predictions as to which contract parameters should enter the contract given the situational setting. It could well be that parties have to decide whether they want

400 see Proposition 4

to contract on an input or an output parameter. They predict that using the input variable will lead to considerable monitoring costs, distortion and enforcement problems. They will therefore consider output contracting, but as the agent is very risk-averse they will abandon this alternative and ultimately decide to contract on the input variable. In multi-period settings this might change, as is discussed in Section (IV5.2), because the **law of large numbers** filters out uncertainty, reducing the problem of imperfect risk sharing. Therefore, multi-period contracting could become an attractive alternative. The model also stipulates situational conditions where this will work. First of all, there has to be a **possibility to conclude long-term contracts.** Therefore, the business relationship must be such that similar projects will repeatedly arise. In this case, long-term contracts will still be less flexible than a sequence of short-term contracts. Therefore, the question is how important flexibility is or how predictable the future will be. Moreover, it will be more expensive to write long-term contracts compared to short-term contracts. Therefore, increased transaction cost becomes an issue. Finally, parties will value long-term contracts only if there are **saving and borrowing constraints** for the agent outside the primary principal-agent relationship. This might plausibly be the case for informational reasons. Therefore, if time is built into an explicit long-term contract it is possible to reduce the cost of incentives by reducing imperfect risk sharing of output-based contracts.

It has already been argued that contractibility presupposes the knowledge of the production function, observability and verifiability. An especially interesting case is discussed in Section (IV5.3) where parties can observe a performance measure that will not be verifiable by a third party such as a court. There are certain situations where a self-enforcing mechanism, also referred to as an implicit contract, exists, sustaining a contract based on such **subjective performance measures.** The fundamental reasoning for these mechanisms is that if one of the parties makes a promise, it must be able to commit to this promise. Otherwise, the promise is worthless and cannot create incentives. In other words, it must be clear that at the moment when the party will have to make good on its promise it must be in its interest to do so. Otherwise, it can hold up the other party. Thus, the centre of interest is the decision rule of the party. Consider, for instance, a situation where effort is observable but cannot be objectively verified. The principal cannot commit to paying a bonus contingent on effort because it will always be in his interest to renege later. So, maybe he commits on something else that constrains his future action space in such a way that it will be in his interest to make good on his promise. The **tournament mechanism** is a case in point. The principal facing many agents commits on the total amount of bonuses paid out. By taking away the option of saving money by reneging, he can also credibly commit to paying the bonus as promised if only an infinitesimal preference for honesty is

assumed. Also, long-term relationships are actually able to create circumstances in which parties find it easier to commit. The basic intuition is simple: If one party has experienced that the other party acted opportunistically, it will stop doing business with this party. However, if the other party values the ongoing trade relationship, it will, anticipating this decision, not let its business partner down in the first place. It was therefore argued that long-term relationships can in some circumstances support contracts that may otherwise not be feasible by **reputation effects** created between the parties. This is the case in a situation where one would like to contract on an input parameter but effort is not contractible as it cannot be objectively verified. Or, alternatively, one would like to contract on an output parameter but the principal cannot commit on promised bonus because it is not verifiable. In these situations a reputation effect can sustain these contracts if the trade relationship is valuable and likely to increase in value, the time horizon of the parties will not be short-term (low discount rate), the expected probability of the relationship ending is low, and the bargaining power of the agent is not too low. Moreover, the project's visibility and the parties' entrenchment in business circles also will play a role.

In Section (IVS.4) a situation is considered where the input parameter is not observable, but one can act as if it were contractible because of an implicit contract. This is because the agent's **"career"** will depend on his performance track record. The market monitors past performance and only agents who achieve high performance levels will be promoted. So, they will exert effort in order to positively affect their career chances. In such a case one would not be forced to change to output contracting, which might be very expensive. If the discount rate is not zero, incentives will never be efficient in equilibrium. They will, however, be close to efficiency if the discount rate is low, job characteristics change considerably due to innovation, and the external factor in the output process is unimportant. In absolute terms, incentives will be also higher if the disutility of effort only rises slowly. A useful and intuitive concept in this context is the **speed of updating.** In fact, if the noise of the production function is low relative to the noise of the competence process, the speed of updating will be high, which in tum will make incentive increase, because the agent knows that higher effort will have an impact. If, however, talent will be expected to last forever, once it has been proven and potential signals to the contrary are very unreliable, one will stick to the prior belief. Therefore, if the discount rate is low and updating fast, there will be fairly high incentives to perform in equilibrium. The intuitive idea is that reputation is not worth so much, or high reputation has to be reproved very often. In this situation, career concerns solve the shirking problem. Conversely, if the discount rate is high (the agent does not care about the future) and updating is slow, there will be low incentives in the steady state. In some situations, **incentives in disequilibrium** will be very important. This is especially true in

cases where updating is slow and the frequency of observation is low ( due to a long production process). Incentives will be initially high if the precision of the initial belief is thought to be higher in later periods. Incentives will initially be low if the precision of the initial belief is thought to be lower in later periods. The first case will be true in most cases. In the beginning, not much is known about the agent. Therefore, beliefs will be relatively imprecise. In a situation where noise of the production function is high relative to the noise of the competence process, which is equivalent to a situation where there is little change of job characteristics due to innovations, and observation of output is only a very bad signal due to an important external factor, it was said that updating will be slow and incentives will be much too low in equilibrium. If there is low initial precision it was also said that incentives will be much too high in the beginning. This situation will persist for quite some time as the speed of updating is low. Therefore, an agent working in an industry where job characteristics are not expected to change much and the external factor is very important, as might be expected for many service industries, will get very inefficient incentives from career concerns. Situations relevant for the viability of such an implicit contract will therefore be the agent's time horizon, the role of the external factor in the production process, the amount of innovation in the relevant industry, the duration of projects, the precision of initial beliefs concerning the talent of the agent, the market's capability to monitor the agent's track record. The thesis that time can solve incentive problems costlessly cannot be generally upheld. It was shown that this will only be the case under very unrealistic circumstances like zero discount rate and infinite repetition. Yet, the important insight from Chapter (IV 5) is that the conclusions from the one-period models are not necessarily valid in the multiperiod settings. The optimal contract in the one-shot relationship will be different from the optimal contract in multi-period relationships.

## **1.2 Checklist**

Given the complexity of contract theoretic models, it would be tempting to develop tools which allow the practitioner to apply the insights of contract theory without bothering too much about the underlying models. There are, however, two obstacles to such an approach that were already mentioned. First, no recipe or scorecard to solve for the optimal contract can be given as the final step of application requires qualitative judgement close to the specific problem. Second, even if it is possible to give a checklist of factors which are relevant to the contracting problem, it is probably difficult to apply the checklist without having understood at least the general thrust of the models they are derived from. In the following, such a checklist of all the identified relevant factors shall nevertheless be given.

## **1.3 Outlook**

Traditionally, economists specializing in contract theory advise government regulation authorities or appear as expert witnesses in competition lawsuits if they have a practical interest at all. This is surely a very important field of application. The objective to help individuals, companies and lawyers to design better contracts and organizations in the course of their business is relatively less prominent.

There is a reason for that. It was already discussed that it is questionable whether contract theory can actually provide any added value in this field. It could be argued that most of what it has to say is already known by lawyers and practitioners of other fields. The underlying argument is that contracts and institutions are the product of evolution and that they survived because they proved to be successful in the past. Especially in very stable settings, it is difficult to imagine that something which was used and tested in a myriad of situations for decades or even centuries (like basic contract types of civil law) should be fundamentally flawed. Claiming such a thing would indeed be an example of the most naive form of rationalist hubris.

Still, it was argued that there is some scope for rational construction. The analytical approach provides the notions necessary to analyse complex phenomena. It helps to understand that what drives the success of established institutions, to classify and describe institutional phenomena and to teach and communicate about what happens in institutions; but beyond that it would not have much practical relevance in improving existing contracts. It may, however, be speculated that this argument does not apply in situations which are relatively new. Explicit knowledge is unimportant for doing routine business, but as soon as a new situation arises there is an advantage of turning implicit knowledge into explicit knowledge. This facilitates thinking about these new challenges and making use of past experience by means of recombination401 •

Moreover, even if some features of the underlying problem of contracting like information asymmetry and uncertainty will always be the same, the pace of institutional change has arguably increased at a time of rapid technological innovation and an increasingly deregulated and globalized economy. Deregulation allows for new kinds of labour contracts, financial innovation and increased global competition increasing the action space of individual agents. The revolution in communication technology led to innovations in transactions (peerto-peer online auctions, e-commerce). Global competition leads to an increased need for flexible and unorthodox transnational company alliances, but also cultural change affects contracting: The decline of moral institutions402, but also the break-up of cosy national clubs where a renegade agent could easily be punished by social sanctioning changes the way contracts can be enforced.

On a fundamental level, it could be questioned if adaptation to change should not be left to decentralized spontaneous order. In a provocative way one could ask if the rationalist who was ousted as the great central planner should have a comeback as an advisor of individual agents. In other words, even if evolution did not have a chance, it may still be better to proceed by trial-and-error than by trying to save time by taking a short-cut using analytical models. This is not the view of the author. Still, it has to be acknowledged that economic contract theory still has to undergo much more of a market test. It is the ability of such theories to explain existing institutions and the extent to which it is possible to convince practitioners of the value and the additional insight provided by this approach which validates these modes much more than any econometric test. It is in this respect that contract theory still has a long way to go.

Of course, some examples were mentioned in the text. The predictions of contract theory seem to fit quite well with certain institutional phenomena. Yet, it is far from playing a role as a framework for setting up real world contracts. Economists routinely complain about the fact that lawyers apparently do not care about what economists have to say, but the experience of the author suggests otherwise. Lawyers and managers are very interested in the promise of contract

401 This is actually the method of analysis-synthesis.

402 If everybody believed in divine justice this would be a very elegant way to solve the problem of moral hazard. But it is hard to believe that this mechanism ever worked effectively. Historically, it seems that it worked to some extent to suppress the lower classes, but even at the time failed to convince the estate manager to be honest towards the absentee noble landowner.

theory but soon get frustrated when they see what they think is considerable analytical complication for relatively meagre results. This is partly to blame on the mathematical illiteracy of most lawyers, or conversely the unwillingness of economists to "translate" their findings into common language, but there are still other problems: As was already mentioned in the introduction, there is the obsession of many economists with modeling single effects rather than dealing with concrete problems. Some effects are certainly more important than others, but in order to decide which effect is important and what can safely be ignored, one must see the whole picture. While there may be some importance in modeling small effects, there is certainly an imbalance between modeling such effects and summarizing, describing and applying them. It was also argued in the methodological part that analytical models can very fruitfully be used to derive qualitative results but that casuistic work should be used for the applications, leaving out the intractible middle ground; but the wrong conclusion for an economist would be to stop when analysis ends and informed judgement begins. This could be justified by citing separation of labour, saying that the development of applications can be done by others. The truth is, however, that nobody is waiting on the other side of this unilaterally defined interface. The fact that applications require judgement and are no longer analytically tractable or can be accessed by econometrics does not mean that they are any less "scientific". Indeed, they are a very important part of the argument.

The following research programme is therefore proposed: First the analytical contract theoretical models should be summarized and systematically arranged. This should be done in a way that makes it possible for readers to treat these models largely as black box models. Then, much of casuistic work should be done in order to apply the models, mindful of the act that this application is nothing mechanical but rather an integral part of problem solving. Such casuistic work would not only display best practice of problem solving and be a good way of communication and teaching, but also enrich the model by helping to understand phenomena which evolved over time. In addition, translation into specific contexts allows submitting contract theory to a market test which is arguably the best empirical corroboration available for contract theory. A particularly interesting avenue for future research would be not just to analyse codified civil law but also model-contract collections of law firms and organizational solutions within companies.

**Wilson,** R. (1968): The Theory of Syndicates; Econometrica 36: 119-32

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