Editing Principal–agent problem (section)

===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.