Editing Principal–agent problem (section)

==Contract design==
Milgrom and Roberts (1992) identify four principles of contract design: When perfect information is not available, Holmström (1979)<ref>[https://www.gwern.net/docs/economics/1979-holmstrom.pdf "Moral Hazard and Observability"] {{Webarchive|url=https://web.archive.org/web/20210427014946/https://www.gwern.net/docs/economics/1979-holmstrom.pdf |date=April 27, 2021 }}, ''The Bell Journal of Economics'', Vol. 10, No. 1 (Spring, 1979), pp. 74-91</ref> developed the '''Informativeness Principle''' to solve this problem. This essentially states that any measure of performance that (on the margin) reveals information about the effort level chosen by the agent should be included in the compensation contract. This includes, for example, Relative Performance Evaluation—measurement relative to other, similar agents, so as to filter out some common background noise factors, such as fluctuations in demand. By removing some exogenous sources of randomness in the agent's income, a greater proportion of the fluctuation in the agent's income falls under their control, increasing their ability to bear risk. If taken advantage of, by greater use of piece rates, this should improve incentives. (In terms of the simple linear model below, this means that increasing ''x'' produces an increase in ''b''.)

However, setting incentives as intense as possible is not necessarily optimal from the point of view of the employer. The '''Incentive-Intensity Principle''' states that the optimal intensity of incentives depends on four factors: the incremental profits created by additional effort, the precision with which the desired activities are assessed, the agent's risk tolerance, and the agent's responsiveness to incentives. According to Prendergast (1999, 8), "the primary constraint on [performance-related pay] is that [its] provision imposes additional risk on workers ..." A typical result of the early principal–agent literature was that piece rates tend to 100% (of the compensation package) as the worker becomes more able to handle risk, as this ensures that workers fully internalize the consequences of their costly actions. In incentive terms, where we conceive of workers as self-interested rational individuals who provide costly effort (in the most general sense of the worker's input to the firm's production function), the more compensation varies with effort, the better the incentives for the worker to produce.

The third principle—the '''Monitoring Intensity Principle—'''is complementary to the second, in that situations in which the optimal intensity of incentives is high corresponds highly to situations in which the optimal level of monitoring is also high. Thus employers effectively choose from a "menu" of monitoring/incentive intensities. This is because monitoring is a costly means of reducing the variance of employee performance, which makes more difference to profits in the kinds of situations where it is also optimal to make incentives intense.

The fourth principle is the '''Equal Compensation Principle''', which essentially states that activities equally valued by the employer should be equally valuable (in terms of compensation, including non-financial aspects such as pleasantness of the workplace) to the employee. This relates to the problem that employees may be engaged in several activities, and if some of these are not monitored or are monitored less heavily, these will be neglected, as activities with higher marginal returns to the employee are favoured. This can be thought of as a kind of "[[disintermediation]]"—targeting certain measurable variables may cause others to suffer. For example, teachers being rewarded by test scores of their students are likely to tend more towards teaching 'for the test', and de-emphasise less relevant but perhaps equally or more important aspects of education; while [[AT&T Corporation|AT&T]]'s practice at one time of paying programmers by the number of lines of code written resulted in programs that were longer than necessary—i.e., program efficiency suffering (Prendergast 1999, 21). Following Holmström and Milgrom (1990) and Baker (1992), this has become known as "multi-tasking" (where a subset of relevant tasks is rewarded, non-rewarded tasks suffer relative neglect). Because of this, the more difficult it is to completely specify and measure the variables on which reward is to be conditioned, the less likely that performance-related pay will be used: "in essence, complex jobs will typically not be evaluated through explicit contracts." (Prendergast 1999, 9).

Where explicit measures are used, they are more likely to be some kind of aggregate measure, for example, baseball and [[American Football]] players are rarely rewarded on the many specific measures available (e.g., number of home runs), but frequently receive bonuses for aggregate performance measures such as Most Valuable Player. The alternative to objective measures is subjective performance evaluation, typically by supervisors. However, there is here a similar effect to "multi-tasking", as workers shift effort from that subset of tasks which they consider useful and constructive, to that subset which they think gives the greatest appearance of being useful and constructive, and more generally to try to curry personal favour with supervisors. (One can interpret this as a destruction of organizational [[social capital]]—workers identifying with, and actively working for the benefit of, the firm – in favour of the creation of personal social capital—the individual-level social relations which enable workers to get ahead ("networking").)

===Linear model===
The four principles can be summarized in terms of the simplest (linear) model of incentive compensation:

<math display="block">
w = a + b(e + x + gy) \,
</math>

where ''w'' (wage) is equal to ''a'' (the base salary) plus ''b'' (the intensity of incentives provided to the employee) times the sum of three terms: ''e'' (unobserved employee effort) plus ''x'' (unobserved exogenous effects on outcomes) plus the product of  ''g'' (the weight given to observed exogenous effects on outcomes) and ''y'' (observed exogenous effects on outcomes). ''b'' is the slope of the relationship between compensation and outcomes.

<math display="block">
\begin{align}
\text{wage} = {} & (\text{base salary}) 
+ (\text{incentives})
\cdot \Big(\text{(unobserved) effort} + \text{(unobserved) effects} \\[5pt]
& {} + (\text{weight }g) \cdot (\text{observed exogenous effects})\Big)
\end{align}
</math>

The above discussion on explicit measures assumed that contracts would create the linear incentive structures summarised in the model above. But while the combination of normal errors and the absence of income effects yields linear contracts, many observed contracts are nonlinear. To some extent this is due to income effects as workers rise up a tournament/hierarchy: "Quite simply, it may take more money to induce effort from the rich than from the less well off." (Prendergast 1999, 50).  Similarly, the threat of being fired creates a nonlinearity in wages earned versus performance. Moreover, many empirical studies illustrate inefficient behaviour arising from nonlinear objective performance measures, or measures over the course of a long period (e.g., a year), which create nonlinearities in time due to discounting behaviour. This inefficient behaviour arises because incentive structures are varying: for example, when a worker has already exceeded a quota or has no hope of reaching it, versus being close to reaching it—e.g., Healy (1985), Oyer (1997), Leventis (1997). Leventis shows that New York surgeons, penalised for exceeding a certain mortality rate, take less risky cases as they approach the threshold. Courty and Marshke (1997) provide evidence on incentive contracts offered to agencies, which receive bonuses on reaching a quota of graduated trainees within a year. This causes them to 'rush-graduate' trainees in order to make the quota.

===Options framework===
{{See|Business valuation#Option pricing approaches|Corporate finance#Corporate governance}}
In certain cases agency problems may be analysed by applying the techniques developed for [[option (finance)|financial options]], as applied via a [[real options]] framework.<ref>[[Aswath Damodaran]]:  [http://pages.stern.nyu.edu/~adamodar/New_Home_Page/lectures/opt.html Applications Of Option Pricing Theory To Equity Valuation] {{Webarchive|url=https://web.archive.org/web/20120427075914/http://pages.stern.nyu.edu/~adamodar/New_Home_Page/lectures/opt.html |date=April 27, 2012 }} and [http://people.stern.nyu.edu/adamodar/pdfiles/eqnotes/optequity.pdf Option Pricing Applications in Valuation] {{Webarchive|url=https://web.archive.org/web/20120916122726/http://people.stern.nyu.edu/adamodar/pdfiles/eqnotes/optequity.pdf |date=September 16, 2012 }}.</ref><ref>D. Mauer and S. Sarkar (2001).  [http://www1.american.edu/academic.depts/ksb/finance_realestate/mrobe/Seminar/Mauer.pdf Real Options, Agency Conflicts, and Financial Policy] {{Webarchive|url=https://web.archive.org/web/20160304050513/http://www1.american.edu/academic.depts/ksb/finance_realestate/mrobe/Seminar/Mauer.pdf |date=March 4, 2016 }}; G. Siller-Pagaza, G. Otalora, E. Cobas-Flores (2006). [http://realoptions.org/papers2006/Siller-Pagaza_RO2.pdf The Impact of Real Options in Agency Problems] {{Webarchive|url=https://web.archive.org/web/20160602221722/http://realoptions.org/papers2006/Siller-Pagaza_RO2.pdf |date=June 2, 2016 }}</ref> [[Stockholders]] and [[bondholders]] have different objective—for instance, stockholders have an incentive to take riskier projects than bondholders do, and to pay more out in [[dividends]] than bondholders would like. At the same time, since equity may be seen as a [[call option]] on the value of the firm, an increase in the [[variance]] in the firm value, other things remaining equal, will lead to an increase in the value of equity, and stockholders may therefore take risky projects with negative net present values, which while making them better off, may make the bondholders worse off. Nagel and Purnanandam (2017) notice that since bank assets are risky debt claims, bank equity resembles a subordinated debt and therefore the stock's payoff is truncated by the difference between the face values of the corporation debt and of the bank deposits.<ref>[S. Nagel and A. Purnanandam (2017).  [https://www.dropbox.com/s/t6r9xvihh6lrntr/BankCreditRisk.pdf?dl=0 Bank Risk Dynamics and Distance to Default] {{Webarchive|url=https://web.archive.org/web/20230423162432/https://www.dropbox.com/s/t6r9xvihh6lrntr/BankCreditRisk.pdf?dl=0 |date=April 23, 2023 }};</ref> Based on this observation, Peleg-Lazar and Raviv (2017) show that in contrast to the classical agent theory of Michael C. Jensen and William Meckling, an increase in variance would not lead to an increase in the value of equity if the bank's debtor is solvent.<ref>[S. Peleg-Lazar and A. Raviv (2017). [http://onlinelibrary.wiley.com/doi/10.1111/eufm.12102/abstract Bank Risk Dynamics Where Assets are Risky Debt Claims] {{Webarchive|url=https://web.archive.org/web/20170805105545/http://onlinelibrary.wiley.com/doi/10.1111/eufm.12102/abstract |date=August 5, 2017 }};</ref>