The impact of bonus caps on excessive risk-taking
and effort levels: an experimental analysis
Reineke Davidsz August 2015 Master thesis 15 EC
MSc Business Economics, specialization in Organization Economics University of Amsterdam
Thesis supervisor: Thomas Buser
Abstract
By means of an experiment, this study investigates how bonus caps affect individuals’ excessive risk-taking behaviour and effort levels. Unfortunately, this analysis does not find statistically significant coefficients of interest. However, the results imply that bonus caps lead to increased client’s expected variable earnings, which result from managers’ risk-taking behaviour and effort levels. As predicted, the findings suggest that bonus caps have the desired effect of decreased excessive risk-taking because they ensure that agents do not personally gain from taking risk. But, in contrast to what was expected, there is no evidence for a negative side effect of decreased effort levels. If anything, the bonus cap seems to increase effort levels. Overall, the results indicate that bonus caps achieve their wanted effect of reducing careless treatment of stakeholders.
Table of contents
1 Introduction 3
2 Theoretical background 10
3 Experimental design 14
3.1 Groups and roles 14
3.2 Project parameterization 14
3.3 Tasks 16
3.4 Data description and comparison across groups 18
4 Results 22
4.1 Main empirical analysis 22
4.2 Decomposition of desired effect on risk-taking behaviour 26 4.3 Extended analysis of negative side effect on effort levels 29
4.4 Participants’ motivational factors 30
5 Discussion 32
5.1 Policy advice and future research 32
5.2 Methodological issues 34
6 Conclusion 35
Acknowledgements 36
Appendix A Experimental design 37
Appendix B Additional regression analyses 40
1 Introduction
Financial organizations and its remuneration structures provided executives with incentives for excessive risk-taking in the build-up to the financial crisis (Bebchuk & Spamann, 2010). This caused large public debate on the level of bonuses and the risk of careless treatment of stakeholders that it may cause. As Jensen and Murphy (1990) state, after the announcement of executives’ compensation political figures, union leaders, and consumer activists issue now-familiar denunciations of executive salaries and urge that directors curb top-level pay in the interests of social equity and statesmanship.
Taking excessive risk refers to taking actions that either increase or decrease the value for another party, but whose expected effect is negative (Bebchuk & Spamann, 2010). In the build-up to the financial crisis, agents were incentivized to take excessive risk because compensation arrangements shielded executives from a large fraction of possible losses. This limited liability on the agent’s side creates a conflict of interest between the agent and the other party, because they value projects differently (Baghestanian, Gortner & Massenot, 2015). Specifically, the expected effect of risk-taking is positive for the agent, whereas the expected effect is negative for the other party who is not shielded from potential losses. In that case, private actors have incentives to take risks that are socially excessive yet privately optimal.
In order to address the issue of perverse incentives in the financial sector, regulatory reforms are made. Remuneration policies are enforced which regulate the level of bonuses. A deal reached by European Parliament and Council in 2013 says that bankers’ bonuses should not normally exceed their fixed salary (Economic and monetary affairs, European Parliament, 2013). They introduced a basic salary-to-bonus ratio of one-to-one, which was created to make banks more resistant to crises and to curb excessive risk-taking.
In the Netherlands an even stricter remuneration policy1 was introduced in February 2015 (Rijksoverheid, 2015). Specifically, it states that bonuses cannot be higher than twenty per cent of fixed pay. The Government indeed decided to implement this law because perverse incentives, such as high rewards and bonuses, were globally seen as one of the main causes of the financial crisis in 2008, and the main rationale was that remuneration
1 The law is called ‘Wet beloningsbeleid financiële ondernemingen (Wbfo)’, which translates into ‘Law remuneration policies financial enterprises’.
components and structures can lead to the risk of careless treatment of consumers, clients or other stakeholders.
In response to public pressure and remuneration laws, many financial organizations have cut their bonus payments. According to Financial Times analysis, the UK’s five largest banks cut bonus pools by more than £1 billion in 2013 (Noonan, 2015). Overall, bonuses at Barclays, HSBC, Lloyds Banking Group, Royal Bank of Scotland and Standard Chartered fell from around £6.5 billion in 2013 to around £5.5 billion in 2014.
The desired effect of bonus caps is to foster financial stability and decrease excessive risk-taking (Baghestanian et al., 2015). They state that the reason for decreased risk-taking is that bonus caps reduce the potential gains of risk-taking for agents. It can occur that the expected effect of taking risk becomes negative; therefore it is not in the agent’s personal interest to take risk anymore. Hence, the incentive to take excessive risk is eliminated.
As a result of reduced excessive risk-taking, agents who have a bonus cap are expected to act more in the other party’s interest given that the other party prefers the agent to not take risk. Related to this, it is predicted that agents with a bonus cap take less risk on behalf of others. Here, risk-taking on behalf of someone else refers to the situation where an agent’s risk-taking behaviour affects another party’s expected payoff. This can occur in a situation where the agent does not receive any payoff and the other party does, but also when both the agent and another party’s payoff depend on the agent’s risk-taking behaviour.
In this study, the focus lies on the latter situation because the effect of a bonus cap on the manager’s risk-taking behaviour is researched. In the former situation, the bonus cap does not apply because the manager does not earn a payoff at all. On the other hand, the latter situation resembles reality since a manager’s risk-taking behaviour affects a client even if the manager personally receives a (restricted) variable pay.
A limited stream of literature on excessive risk-taking on behalf of others, however, investigates the former situation. Andersson, Holm, Tyran, and Wengström’s (2014) motivation for studying risk-taking on behalf of others was that actors in the financial sector were accused of excessive risk-taking on behalf of others prior to the recent financial crisis. The results on how feeling responsible for someone else affects individual decision-making are mixed ranging from increased risk aversion to increased risk seeking or null results (see e.g. Pahlke, Strasser & Vieider, 2012).
Eriksen and Kvaløy (2009) find that subjects take less risk with their client’s money than with their own, based on an experimental study. Additionally, Montinari and Rancan’s
(2013) experimental results show that on average, individuals exhibit less risk-taking when deciding on behalf of a friend rather than only for himself or a stranger. On the other hand, Andersson et al. (2014) provide experimental evidence and find that when choosing between risky prospects for which losses are ruled out by design, subjects make the same choices for themselves as for others. However, when losses are possible, they find that subjects who make choices for themselves take less risk than those who decide for others when losses loom.
Even though these studies research risk-taking on behalf of others, the approaches differ in various respects. To start, Eriksen and Kvaløy’s (2009) main question is whether people behave consistently with myopic loss aversion (MLA) on behalf of other people’s money. MLA assumes that people are myopic in evaluating outcomes over time, and are more sensitive to losses than to gains (Gneezy & Potters, 1997). On the other hand, Montinari and Rancan (2013) focus on two elements: the relevance of other regarding preferences and the effect of social distance, while Andersson et al. (2014) study risk taking on behalf of others both when choices involve losses and when they do not.
Consequently, the studies’ experimental tasks differ according to what is investigated. Eriksen and Kvaløy’s (2009) use Gneezy and Potter’s (1997) design which includes a lottery (betting game) where there was a probability of 2/3 of losing the amount bet and a probability of 1/3 of winning two and a half times the amount bet. They paired the subjects in ‘investment managers’ and ‘clients’ and manipulated both the investment managers’ and the clients’ evaluation rounds. Simarly, Montinari and Rancan (2013) use Gneezy and Potters’s (1997) design, but they introduce a small variation to the task such that their lottery had a negative expected value. On the other hand, in Andersson et al.’s (2014) study, participants chose between risky lotteries in a version of the well established multiple price list format.
In line with Eriksen and Kvaløy (2009), the current study incorporates the roles of managers and clients. However, in contrast to the other studies’ tasks, participants in this experiment were asked to choose between a safe and a risky project, and exert effort on a real-effort task. The safe project had a certain payoff both for the manager and client, whereas the risky project had a positive and negative expected variable payoff for the manager and client respectively. This simulates real-life where managers were incentivized to take excessive risk prior to the financial crisis.
Additionally, the studies differ in terms of treatments. In Eriksen and Kvaløy’s (2009) main experiment, subjects made investment decisions with other subjects’ money. In order to
test myopic loss aversion, they had treatments with frequent and infrequent evaluation rounds. In Montinari and Rancan’s (2013) within subjects design, every participant decided once for himself and twice on behalf of someone else: in one treatment the risky decision is made on behalf of an anonymous stranger, while in the other treatment it is made on behalf of a friend who comes to the laboratory together with the decision maker. Lastly, in Andersson et al.’s (2014) study there were four treatment conditions with and without losses: individual (payment to decision maker), hypothetical (no payment), both (payment to both decision maker and receiver) and other (payment only to receiver).
The main treatment in the current study is the bonus cap, where subjects’ bonuses in the treatment group were restricted to twenty per cent of their fixed pay. Moreover, the current experiment had situations similar to Andersson et al.’s (2014). However, the hypothetical treatment was excluded because there is no reason to expect an effect since no one receives a payment. Additionally, the main objective of Andersson et al.’s (2014) study was comparing Other with Individual, whereas in the current study the focus lies on comparing Individual and Both. The latter comparison is most relevant for concluding on the effect of bonus caps on risk-taking on behalf of others, since it addresses the effect of the risk exposure of the passive receiver while keeping the decisions maker’s individual (restricted) incentives constant.
Concluding, the most important difference between the previous experimental studies and the current research is the focus on bonus caps. The impact of bonus caps could also be empirically tested by means of field experiments or data resulting from a policy change, yet this type of research on this topic is limited. A potential reason is that there are no easily accessible databases with personnel data (Prendergast, 1999, p. 56). Additionally, remuneration policies are only recently implemented in response to the financial crisis in 2008. Hence, there are data limitations hindering empirical analyses of bonus caps.
The literature that comes closest to the current study is a working paper by Baghestanian et al. (2015). In an experimental setting they investigate how compensation schemes affect liquidity provision and asset prices. Instead of the roles of managers and clients, they designed a laboratory experiment in which investors can entrust money to traders who trade in an asset market. The setup allows comparing how different compensation schemes of traders affect liquidity provision and asset prices. They implemented four compensation treatments: unlimited liability (both investors and traders are liable for losses), limited liability (only investors are liable for losses), unlimited liability and
cap and limited liability and cap. Hence, similar to the current experiment they also study the effect of bonus caps, where the gains were capped at thirty per cent of the initial endowment. Their results show that bonus caps do not seem to have an impact on bubbles. If anything, they foster bubbles by increasing liquidity provision. These results stand in stark contrast to recently implemented remuneration policies that mainly focus on bonus caps. They find that asset prices are closer to the fundamental value when traders are liable for losses than under limited liability. This suggests that, as expected, traders take more risk when they are not liable for losses. Therefore, their work emphasized that making traders liable for losses seems more effective than bonus caps in reducing asset price bubbles; thereby fostering financial stability.
While Baghestanian et al. (2015) study the effect of bonus caps on liquidity provision and asset prices, the current study focuses on the desired effect of decreased risk-taking and another potential side effect, namely decreased effort levels. Even though caps can have the desired effect of reducing excessive risk-taking, a maximum bonus could at the same time result in lower effort levels. The reason is that agents may only be incentivized up to their bonus cap. This negative side effect of maximum bonus policies is closely linked to standard agency theory.
To begin, in agency theory the classic focus was on the trade-off between insurance and incentives. However, recent work on incentives in organizations has moved beyond this focus (e.g. see Gibbons, 1998 for a discussion of the classic model and four new strands in agency theory). Additionally, as Prendergast (1999) concludes from his overview of existing work on incentives, agency theory has provided an important framework for understanding compensation issues. One critical issue is how firms should shape compensation contracts to motivate agents to operate in the principal’s interest. Therefore, a vast agency literature on the design of optimal pay-for-performance schemes has developed. One of the main focuses of this literature is how responsive pay should be to performance (Sloof & Van Praag, 2010). It is argued that higher incentives, such as bonuses, lead to more effort and higher performance. This is an effect of monetary incentives, called the standard direct price effect (Gneezy, Meier & Rey-Biel, 2011). Indeed, the analysis of theoretical evidence by Prendergast (1999) indicates that agents respond to incentives. Also, according to Heinrich (2007) standard principal agent theory shows that high-powered incentives induce higher effort levels and therefore firm performance should also improve.
Proceeding from the standard direct price effect, maximum bonus policies are predicted to have a negative side effect on effort levels. The reason is that restricted bonuses imply that agents are only monetarily incentivized up to the bonus cap, which leads to less effort and lower performance. Correspondingly, Jensen (2003, p. 388) argues that managers who reach their maximum bonus have no incentives to exceed the maximum because they are not rewarded beyond that level. His argument, however, is merely intuitive and not based on empirical analysis.
In the end, the impact of bonus caps on excessive risk-taking and effort results in the client’s expected earnings. The desired effect of decreased risk-taking implies higher client’s expected variable earnings, whereas the negative side effect of decreased effort predicts lower client’s expected variable pay. Therefore, how these two effects offset each other determines the actual impact of bonus caps on client’s expected earnings. Hence, the interest lies in the difference between the expected earnings for clients with a manager whose bonus is restricted and clients with a manager whose bonus is unrestricted. Ultimately, it is wanted that client’s expected earnings increase as a result of bonus caps, given that the main rationale behind bonus caps is to limit careless treatment of stakeholders.
In this experimental study, the focus is to draw from previous literature on excessive risk-taking and agency theory, and add to it by providing empirical results specifically on the desired and side effects of maximum bonus policies. By means of an experiment, the effect of maximum bonus policies on individuals’ excessive risk-taking behaviour and effort levels is analysed. The research question is stated as follows: Do bonus caps have the desired effect of decreased excessive risk-taking behaviour by eliminating agents’ personal gain from taking risk? Moreover, do maximum bonuses have a negative side effect of lower effort levels? In the end, do they lead to higher expected earnings for clients?
A major advantage of experiments over naturally occurring data is the high level of control and the possibility to implement truly exogenous changes, implying a ceteris paribus setting. Subjects were randomly allocated to the treatment or the control group, where the former group’s bonus is restricted to twenty per cent of fixed salary and the latter group’s bonus is unrestricted. Additionally, every manager had a client who was another randomly matched participant of the experiment. The manager’s decisions could also affect their client’s bonus. In order to measure excessive risk-taking behaviour, participants had to choose between implementing a safe or a risky project. Moreover, in order to measure the
effect on effort levels, subjects were asked to perform a real-effort task, namely adding three two-digit numbers (e.g. Sloof & Van Praag, 2010).
Additionally, there were six rounds where the effort levels were set exogenously at a low level or an average level (based on a pilot study), and the implemented project either affected only their own bonus, both their and their clients’ bonuses or only their clients’ bonus (e.g. Andersson et al., 2012). Subsequently, subjects were asked whether they wanted to implement the safe or the risky project in every situation. These results are used to decompose the effect of a bonus cap on excessive risk-taking. Moreover, there were two rounds where the implemented project was set prior to the experiment. In these rounds, participants subsequently had to exert effort on the exogenously determined project. This allows further analysis of the effect of a maximum bonus on effort levels.
The results of this experimental study show that the main coefficients of interest are not statistically significant. The findings, however, suggest that as predicted a maximum bonus policy decreases individuals’ risk-taking behaviour because a bonus cap ensures that agents do not personally gain from taking excessive risk. Hence, managers are said to take less risk on behalf of others since the managers’ risk-taking affects the client’s payoff. Therefore, they act more in their client’s interest given that the client prefers his manager not to take risk. Additionally, there is no evidence that agents exert less effort when their bonus is capped, which is in contrast to the prediction following the standard direct price effect. If anything, the results indicate that agents with a bonus cap exert more effort.
All in all, the model estimated that the expected variable pay from the investment is €0.52 higher for a client with a manager whose bonus is capped than for a client with a manager whose bonus is unrestricted, holding everything else constant. However, this result approaches but fails to achieve a customary level of statistical significance. In spite of that, the positive sign suggests that bonus caps lead to less careless treatment of other parties, which is a wanted effect of maximum bonus policies.
This paper proceeds as follows. Section 2 presents a theoretical background and subsequent predictions. The experimental design is described in section 3 and the results are presented in section 4. Subsequently, in section 5 a discussion is provided and section 6 concludes.
2 Theoretical background
The classic agency model is described by Gibbons (1998) as follows: consider an agent who exerts effort a to produce output y. The production function might be linear, for example: 𝑦 = 𝑎 + 𝜀, where ε is a noise term. The principal owns the output but writes a contract to share it with the agent by paying a wage w dependent on output. The wage contract might be linear, for example: 𝑤 = 𝑠 + 𝑏𝑦, where the intercept s is the salary and the slope b is the bonus rate. The agent’s payoff is 𝑤 – 𝑐(𝑎), i.e. the realized wage minus the disutility of action c(a). The principal’s payoff is 𝑦 – 𝑤, i.e. the realized output minus wages.
In this research a comparable situation is considered in which a manager’s compensation contract is assumed to be linear in output. Moreover, it is assumed that there is zero noise, therefore 𝑦 = 𝑎. This implies that the compensation contract is linear in effort:
𝑤!!(𝑎) = 𝑠 + 𝑏 !!𝑎,
where superscript M stands for manager and subscript i indicates the safe (A) or risky (B) project. Effort level a is a non-negative integer determined by the subject’s effort level on a real-effort task. The manager’s total bonus is 𝑏!!𝑎. The client’s payoff is similar and also
depends on the manager’s effort level a:
𝑤!!(𝑎) = 𝑠 + 𝑏 !!𝑎,
where superscript C stands for client and subscript i indicates the safe (A) or risky (B) project. The client’s total bonus is simply his variable earnings from the investment, and equal to 𝑏!!𝑎. Hence, the client’s expected variable earnings depend on the manager’s
risk-taking behaviour and effort level. The firm’s problem of choosing the optimal compensation contract is not considered and the mentioned payment scheme is taken as given, which means that the principal plays a passive role.
Managers can implement two projects, which can affect their and their client’s bonus. One project is safe (i.e. i =A) and the other is risky (i.e. i = B), where the risky project has a fifty-fifty per cent chance that it will succeed or fail. A 50–50 gamble is used because it makes the procedure easy to understand for participants (Andersson et al, 2014).
The unrestricted variable payoffs are presented in Table 1. The variable pays for the manager and the client under the safe project are 𝑏!!𝑎 and 𝑏
!!𝑎 respectively, where 𝑏!! = 𝑏!!.
The manager’s and the client’s bonuses equal 𝑏!!𝑎 and 𝑏
!!𝑎 if the risky project succeeds,
where 𝑏!! = 𝑏
the client’s bonus equals – 𝑏!!𝑎. The maximum loss for the client equals the fixed salary s,
implying that clients cannot lose money in this experiment. Furthermore, it is assumed that 0 < 𝑏!! < ½ 𝑏
!!.
The manager’s expected bonus of the risky project is E[TotalBonus]! ! = 0.5 ∗
𝑏!!𝑎 + 0.5 ∗ 0a = ½ 𝑏
!!𝑎 , while his expected bonus of the safe project is
E[TotalBonus]!! = 𝑏
!!𝑎. Since it is assumed that 0 < 𝑏!! < ½ 𝑏!!, E[TotalBonus]! ! >
E[TotalBonus]!!. Hence, managers are incentivized to take risk.
On the other hand, the client’s expected bonus of the risky project is E[TotalBonus]! ! = 0.5 ∗ 𝑏
!!𝑎 + 0.5 ∗ −𝑏!!a = 0, while his expected bonus of the safe
project is E[TotalBonus]! ! = 𝑏
!!𝑎 . Therefore, for the client
E[TotalBonus]! ! < E[TotalBonus] !
! .2 This implies that it is in the client’s interest if his manager does not take risk.
Figure 1
Unrestricted variable payoffs per project
Manager’s bonus Client’s bonus
Safe project (A) 𝑏!!𝑎 𝑏
!!𝑎 Risky project (B) Success (50%) Failure (50%) 𝑏!!𝑎 0𝑎 (=0) 𝑏!!𝑎 -𝑏!!𝑎 (max. s)
Note: a is the manager’s effort level. s is the fixed salary. It is assumed that 0 < 𝑏!! <
½ 𝑏!!. Also, 𝑏
!! = 𝑏!! and 𝑏!! = 𝑏!!.
This set-up corresponds to remuneration structures of financial organizations prior to the financial crisis, which incentivized individuals to take excessive risk. To eliminate
2 Note that when 𝑎 > !
!!!!! !!!, the client’s expected total bonus is higher under the risky
project than under the safe project. This is because the maximum loss for the client is s when the project fails. Formally: E[TotalBonus]! ! > E[TotalBonus]
!
! = !!!!!!
! > 𝑏!
!𝑎. Solving
for a gives 𝑎 > ! !
!!!! !!!. In this case, it is actually in the client’s interest for the manager to take risk.
perverse incentives, maximum bonus policies were implemented aiming to reduce excessive risk-taking behaviour of agents (e.g. the Dutch law on remuneration policies). Therefore, in this study two groups are introduced: one where the manager’s total variable pay is restricted (treatment), i.e.0 ≤ 𝑏!!𝑎 ≤ 𝑧, and one where it is unrestricted (control), i.e. 𝑏
!! ≥ 0. Here
z is the maximum bonus.
The desired effect of bonus caps is decreased excessive risk-taking. The explored reason is that maximum bonuses eliminate the personal gain of excessive risk-taking for agents. For the control group it is always in the personal interest to take excessive risk since the expected payoff of the risky project is higher than the safe project. However, for the treatment group, if a certain effort level is assumed, which is equal for both the risky and the safe project, it is not in their personal interest to take excessive risk. The reason is that the expected payoff of the risky project is now lower than the safe project.
Formally this is shown as follows. The treatment group’s bonus is restricted to z, in other words 0 ≤ 𝑏!!𝑎 ≤ 𝑧. This implies for the risky project that 𝑏
!!𝑎 = 𝑧 when 𝑎 > !!
!!. Accordingly, E[TotalBonus]! ! = 0.5 ∗ 𝑏
!!𝑎 + 0.5 ∗ 0𝑎 = 0.5 ∗ z + 0.5 ∗ 0 = ½ z when
𝑎 > !!
!! . For the safe project, E[TotalBonus]!
! = 𝑏 !!𝑎 when !! !! < 𝑎 < ! !!! . Here, 𝑏!!𝑎 > ½ z assuming 0 < 𝑏 !! < ½ 𝑏!! . Furthermore, 𝑏!!𝑎 = 𝑧 when 𝑎 > !! !!. Hence, E[TotalBonus]!! = 𝑏
!!𝑎 = z which is larger than ½ z.
From these derivations it follows that E[TotalBonus]!! < E[TotalBonus] !
! when
𝑎 > !!
!!. In other words, a bonus cap ensures that managers do not personally gain from taking risk when 𝑎 > !!
!! is assumed; therefore agents are not incentivized to implement the risky project.
Because personal gain of excessive risk-taking for managers is eliminated, managers are expected to take less excessive risk. Since the manager’s risk-taking behaviour also affects the client’s variable earnings, risk-taking on behalf of others is expected to decrease. Therefore, the manager is predicted to act more in their client’s interest given that the client prefers the manager to implement the safe project (i.e. E[TotalBonus]! ! <
E[TotalBonus]! ! ).
Furthermore, in this study a negative side effect is explored, namely decreased effort levels. From the standard direct price effect it follows that bonus caps lower incentives for agents to exert effort. Formally, it is expected that when a manager’s bonus is capped at z, he
exerts effort until he reaches z. In other words, when 0 ≤ 𝑏!!𝑎 ≤ 𝑧, it is predicted that
0 ≤ 𝑎 ≤ !
!!!.
It is important to note that the assumed effort level to eliminate personal gain (i.e. 𝑎 > !!
!!) is higher than what the predicted effort level following the standard direct price effect for the risky project is (i.e. 0 ≤ 𝑎 ≤ !!
!!). This means that it is impossible that both predictions hold at the same time. However, in this experiment it is separately tested whether effort levels decrease as a result of a maximum bonus policy. Subsequently, it is assumed that individuals exert an average effort level despite a bonus cap, in order to ensure personal gain from taking risk is eliminated.
Ultimately, how much risk a manager takes and how much effort he exerts determines his client’s expected variable earnings from the investment. As explained above, a bonus cap is expected to affect both determinants of the client’s variable payoff. As a result of decreased excessive risk-taking, the client’s expected variable pay is predicted to increase. However, the client’s expected bonus is predicted to decrease as a consequence of decreased effort levels. The actual effect of bonus caps on excessive risk-taking and effort levels, therefore, determines the impact of bonus caps on the client’s expected variable earnings.
To summarize, the main expected consequences of bonus caps are:
Prediction 1 A bonus cap decreases individuals’ excessive risk-taking behaviour. This means
that agents whose bonus is restricted are less likely to implement the risky project than agents whose bonus is unrestricted. This is because bonus caps ensure that agents do not personally gain from taking excessive risk. Correspondingly, risk-taking on behalf of others is reduced and agents act more in their client’s interest.
Prediction 2 A bonus cap decreases individuals’ effort levels. The reason is that agents who
are within reach of their maximum bonus are not incentivized to exert more effort beyond that point.
3 Experimental design
3.1 Groups and roles
In this experiment the control group’s bonus was not restricted, whereas for the treatment group the variable pay was restricted to twenty per cent of fixed pay. Participants were randomly allocated to the control or the treatment group without being aware of these labels. This implies a between-subject design regarding the unrestricted and restricted bonus variations.
Participants were given a situation description informing them about the roles that were played in this experiment (see Appendix A1). They were informed that they had to make decisions and exert effort as a manager, which affected their and their client’s bonuses. It was specifically mentioned that they did not have to solve all equations, but that they could decide for themselves how much effort to exert.
Due to a limited number of participants and the importance of two roles being part of the experiment, everyone played two roles at the same time: a manager and a client. A manager and a client were randomly matched participants of a session and were not the same person. As a client there were no decisions to be made and the role was passive, whereas as a manager the participants had to decide between two projects and choose their effort levels affecting their and their client’s bonuses.
3.2 Project parameterization
Both clients and managers received a fixed payment (show-up fee) of €7.50. Additionally, they could receive a variable payment depending on the implemented project and the manager’s effort level on a real-effort task (see Table 2). The set-up is based on the financial structure of financial organizations and remuneration structures that provided executives with incentives for excessive risk-taking in the build-up to the financial crisis.
The safe project (project A) had a certain outcome for the manager and the client in the sense that the variable pay for both was equal to €0.25 times the number of correct calculations solved by the manager. However, the risky project resulted in either a success or a failure with equal probabilities determined by a coin flip at the end of the experiment. The manager’s variable payoff in case project B succeeded was €0.75 times the number of correct
calculations solved by the manager. In case it failed the manager’s bonus was €0 times of the number of correct calculations solved by the manager; therefore always leading to a payoff of zero. Including the fixed pay this still resulted in an overall payoff of €7.50 for the manager.
Similarly, in case project B succeeded, the client’s variable payoff was €0.75 times the number of correct calculations solved by the manager. However, if project B failed, it was -€0.75 times the number of correct calculations solved by the manager. The client’s maximum loss was €7.50 ensuring that including the fixed pay this resulted in an overall payoff of zero.
Thus, the manager’s expected bonus rate of project B is €0.375 (= 0.5*0.75 + 0.5*0), which is higher than the certain bonus rate of €0.25 for project A. On the other hand, the client’s expected bonus rate of project B is €0 (= 0.5*0.75 + 0.5*-0.75), which is lower than the certain bonus rate of €0.25 for project A. In other words, project B is in the economic interest of the managers but not of the clients, which incentivizes managers to take excessive risk. 3
Table 2
Project parameterization of unrestricted variable payoffs
Manager’s bonus Client’s bonus
Safe project (A) 0.25a 0.25a
Risky project (B) Success (50%) Failure (50%) 0.75a 0a (= 0) 0.75a -0.75a (maximum = 7.50) Note: a is the number of correct calculations solved by the manager. Fixed pay s equalled 7.50. Numbers are in Euros. 0 < 𝑏!! < ½ 𝑏
!!.
3 Note that for the client it is almost always better for the manager to implement the safe project. Only, E[TotalBonus]! ! > E[TotalBonus]
!
! when a > 30, given that the maximum
loss is 7.50 (= s). In that case, the client would actually benefit from the manager taking risk. However, such high effort levels are excluded from the experiment, since solving more than thirty equations in three minutes was unlikely.
In this experiment a maximum bonus policy implies that variable pay is capped at twenty per cent of fixed pay for the treatment group (see Appendix A2). Hence, their maximum bonus was equal to €1.50 (= 20%*€7.50). When a is an integer between zero and three, E[TotalBonus]!! ≥ E[TotalBonus]
!
!. When a is larger than or equal to four,
E[TotalBonus]!! < E[TotalBonus] !
!. In the latter case, it is not in the personal interest for
the manager to take excessive risk. As a result, the expected effect of a bonus cap on excessive risk-taking is negative.
Furthermore, following the standard direct price effect it is expected that agents exert effort up to the point where they reach their bonus cap. Therefore, the expected effect of a maximum bonus on effort levels is negative. The predicted effort levels, i.e. number of correct calculations, are 0 ≤ 𝑎 ≤ !.!"!.!" = 6 and 0 ≤ 𝑎 ≤ !.!"!.!" = 2 for the safe and risky project respectively.
3.3 Tasks
To measure the effect on excessive risk taking, participants decided between implementing the safe (project A) or the risky (project B) project. Additionally, to identify the effect on effort levels, participants exerted effort on a real-effort task. The real-effort task is arithmetic and consists of adding up three two-digit numbers (see e.g. Sloof & Van Praag, 2011) in three minutes. Subjects were not allowed to use a calculator to perform these calculations, but they were given scrap paper. In each round thirty equations were presented below each other on paper and students were asked to solve as many equations as they preferred in the presented order (see Appendix A4). All subjects received the same sequence of equations. Students did not receive feedback on the number of (correctly) solved equations during the experiment.
In the first part of the experiment, managers decided between implementing project A or B, and decided how much effort to exert on their chosen project. This round is analogue to real-life as managers simultaneously decide on how much risk to take and how much effort to exert, resulting in the client’s expected earnings. The results allow concluding on the effect of a bonus cap on the expected earnings for the client. Additionally, this allows testing whether there is a significant difference in choosing the risky project between the control and treatment groups. Significantly fewer participants choosing project B in the treatment group indicates that maximum bonuses lead to decreased excessive risk-taking. Moreover, it allows
testing whether individuals in the treatment condition only exert effort until they believe their maximum bonus is reached. Significantly lower effort levels in the treatment group indicates that bonus caps lead to decreased effort.
Before this round, there were two rounds where the implemented project was exogenously determined in a random order prior to the experiment, and the participants exerted effort on this ex-ante determined project. In other words, managers implemented either project A or project B in round one and the other project in round two. Exogenously implementing project A or B allows measuring the difference in effort levels between the two projects. According to standard agency theory, bonus rates affect agent’s effort; therefore it may be that effort levels differ across projects since the bonus rates are different per project. Part two of the experiment is conducted to decompose the desired effect of reducing excessive risk-taking. Participants decided between the safe (project A) and the risky (project B) project in six different situations (see Appendix A5 for an example). These six situations allow interpreting the effect of a bonus cap on risk-taking. A within-subject design is used, implying that all subjects experience all six situations in a randomly determined order.
To test the impact of eliminating personal gain, two different effort levels are assumed. Specifically, the assumed effort levels were two and ten. In the first condition, managers in the treatment and control groups are incentivized to take excessive risk, since their expected variable payoffs of project B are higher than of project A, i.e. E[TotalBonus]!! > E[TotalBonus]
! !. 4
In the second condition, effort level is exogenously set at an average effort level based on a pilot study. This pilot study included a sample of ten individuals who performed the same real-effort task as in one of the rounds of the actual experiment. However, due to a budget constraint they did not receive a payment; therefore they were not monetarily incentivized.
In this condition, for the treatment group, the expected value of project B is lower than project A. 5 This implies that they are not incentivized to take excessive risk. For the
4 The manager’s expected variable payoff in the treatment and control groups when the assumed effort level is two: E[TotalBonus]!! = 0.5*(0.75*2)+ 0.5*0 = 0.75 and
E[TotalBonus]!! = 0.25*2 = 0.50. So, E[TotalBonus] !
! > E[TotalBonus] ! !.
5 The manager’s expected variable payoff in the treatment group when the assumed effort level is ten: E[TotalBonus]!! = 0.5*(0.75*10)+ 0.5*0 = 3.75, but due to a bonus cap the
control group it is still in the personal interest to take excessive risk since the expected bonus of the risky project is higher than the safe project. 6
To measure how risk taking on behalf of others differs from taking risk for oneself, a set-up is used based on the experiment conducted by Andersson et al. (2012) on a large sample of the Danish population. Three situations were introduced: ‘individual’ (only manager is paid), ‘both’ (manager and client are paid) and ‘other’ (only client is paid). As described by Andersson et al. (2012), comparing ‘individual’ and ‘both’ shows the effect of the risk exposure of the passive receiver while keeping the decisions maker’s individual (restricted) incentives constant. This comparison is most interesting for interpreting the effect of a bonus cap on risk-taking on behalf of others.
All in all, there were six situations: individual and effort level is two (Ind2), individual and effort level is ten (Ind10), both and effort level is two (Both2), both and effort level is ten (Both10), other and effort level is two (Oth2), and other and effort level is ten (Oth10). These are compared in order to interpret the effect of bonus caps on risk-taking behaviour.
3.4 Data description and comparison across groups
An in-class pen-and-paper experiment was conducted in five classes at a high school in Amsterdam, The Netherlands, which totalled to 98 individuals. Eleven students were absent during class, two were late to class and one student did not participate in the experiment during class. Therefore, the sample size is 84 subjects. The number of students in sessions one through five was 28, 19, 19, 11 and 8 respectively.
Table 3 presents descriptive statistics. The average age was sixteen years old and sixty per cent were female. The average monthly income was €74.19. Participants were either in higher general secondary education or pre-university education and either in their fourth or fifth year.7 Approximately half of the students were in pre-university education and the E[TotalBonus]!! = 0.5*1.50+0.5*0 = 0.75. E[TotalBonus]
!
! = 0.25*10 = 2.50, but due to the
bonus cap it is restricted to 1.50. Thus, E[TotalBonus]!! < E[TotalBonus] ! !.
6 The manager’s expected variable payoff in the control group when the assumed effort level is ten: E[TotalBonus]!! = 0.5*(0.75*10)+ 0.5*0 = 3.75 and E[TotalBonus]
!
! = 0.25*10 =
2.50. Thus, E[TotalBonus]!! > E[TotalBonus] ! !.
7 In the Netherlands, secondary school entails three different levels of education: lower vocational education, higher general secondary education and pre-university education,
majority of the students were in their fourth year. Additionally, participants’ level of mathematics class was mathematics-A, mathematics-B or mathematics-C, and they followed one of the following study tracks: Culture and Society (C&M), Economics and Society (E&M), Nature and Health (N&G) and Nature and Technology (N&T). The percentage of students taking mathematics-A, mathematics-B and mathematics-C was 55.9%, 29.8% and 14.3% respectively. The percentage of students in the Culture and Society, Economics and Society, Nature and Health and Nature and Technology track was 20.2%, 47.6%, 7.2% and 25% respectively.
Table 3
Descriptive statistics
Obs. Mean Std. Dev. Min. Max.
Age 84 16.19 0.83 14 18 Female 84 0.60 0.49 0 1 Monthly income 84 74.19 102.28 0 500 5th year 84 0.13 0.34 0 1 Pre-university education 84 0.55 0.50 0 1 Math level 84 0.58 0.73 0 2 Study track 84 1.37 1.07 0 3
Note: Age is in years, female shows the percentage females, monthly income is in euros, 5th year shows the percentage of 5th year students, pre-university education shows the percentage of pre-university education students, math level equals 0 if Math-A; 1 if Math-B and 2 if Math-C, study track equals 0 if C&M; 1 if E&M; 2 if N&G; 3 if N&T.
To control for risk-aversion a survey question on the willingness to take risk is included because this may affect an individual’s preference for choosing the safe or risky ranging from practical to academic schooling respectively. These different levels take four, five and six years respectively. Furthermore, there are three levels of mathematics: mathematics-A, mathematics-B and mathematics-C. The order from a basic to advanced level is mathematics-C, mathematics-A to mathematics-B respectively. Students specialize in their senior years in one out of four fields of study, namely Culture and Society (Cultuur en Maatschappij), Economics and Society (Economie en Maatschappij), Nature and Health (Natuur en Gezondheid) and Nature and Technology (Natuur en Techniek). These differ in study programme, where the former two profiles offer alpha courses (such as geography and languages) and the latter two profiles focus on beta courses (such as physics and biology).
project. Dohmen et al.’s (2011) findings show that asking for a global assessment of willingness to take risks reflects a useful all-round measure of risk attitudes.8 Subjects were asked to answer on an 11-point scale, ranging from ‘not at all willing to take risks’ (equal to 0) to ‘very willing to take risks’ (equal to 10). Analogue to Dohmen et al. (2011), when individuals indicate a level smaller than five, they are assumed to be risk-averse.
Finally, the variables ‘enjoy’, ‘difficulty’ and ‘math skills’ are based on three statements, which were posed in order to subjectively measure participants’ mathematical ability and their motivation to solve equations.9 These were presented as statements where subjects were asked to respond on a 7-point Likert scale, ranging from ‘totally disagree’ (equal to 0) to ‘totally agree’ (equal to 6).
Comparing background characteristics across groups allows verifying that observed differences between the control and treatment groups are not due to subject pool effects. Table 4 shows that on all accounts except for ‘age’, the differences are not significant. Three different tests are conducted depending on the variable in question. The first test is the Wilcoxon rank-sum test, which is used for the continuous variables ‘age’ and ‘monthly income’. This is a non-parametric test similar to the independent samples t-test, which is used when it is not assumed that the variables are normally distributed. Secondly, a test of proportions is used for the binary variables ‘gender’, ‘school year’, and ‘school level’. This tests that the variables have the same proportions in the control and treatment groups. Lastly, a Fisher’s exact test is used to test whether there is a relationship between two categorical variables and when there are cells that have an expected frequency of five or less. In this case, this measures the relationship between being in the treatment or control group and categorical variables such as ‘math level’ and ‘study track’.
Since most characteristics are not significantly different, the observed differences in outcomes between the control and treatment groups cannot be attributed to differences in exogenous background characteristics. However, a potential problem is that age is significantly different at a five per cent level across the control and treatment groups. This
8 The question was “How do you see yourself: are you generally a person who is fully prepared to take risks or do you try to avoid taking risks?” In Dutch the wording of the question was: “Hoe zie jij jezelf: ben je in het algemeen een persoon die volop bereidt is om risico’s te nemen of probeer je risico’s te vermijden?”
9 The statements were: “I enjoy solving equations” (enjoy), “I find solving equations difficult” (difficulty), and “I am good at solving equations” (math skills). In Dutch the wording was: “Ik vind sommen oplossen leuk”, “Ik vind sommen oplossen moeilijk”, and “Ik ben goed in het oplossen van sommen”.
implies that the results might be caused by differences in age across groups; therefore conclusions have to be drawn cautiously.
Table 4
Background characteristics across groups
Note: ** significant at a 5% level. + tested with Wilcoxon-Mann-Whitney test; ++ tested with test of proportions and +++ tested with Fisher’s exact test. Age is in years, female shows the percentage females, monthly income is in euros, 5th year shows the percentage of 5th year
students, pre-university education shows the percentage of pre-university education students, math level equals 0 if Math-A; 1 if Math-B and 2 if Math-C, study track equals 0 if C&M; 1 if E&M; 2 if N&G; 3 if N&T, risk aversion is measured on a scale of 0 to 10 and enjoy, difficulty and math skills are measured on a scale of 0 to 6.
Due to a limited budget five randomly selected managers and their clients received their payoff for one randomly selected round, which was determined by a lottery after all sessions were completed. This implied an equal probability for all students to receive their payoff and induced all subjects to make decisions as if it affected their payoff, as it indeed may be. The participants received their payment in an envelope one week after the experiment was conducted. They earned an average of €7.60 with a minimum of zero and a maximum of €15, including a fixed pay of €7.50.
Control Treatment p-value
Age+ 15.98 16.40 0.0394** Female++ 56.10% 62.79% 0.5322 Monthly income+ 60.18 87.54 0.2382 5th year++ 7.31% 18.60% 0.1253 Pre-university education++ 51.35% 51.28% 0.8102 Math level+++ 0.54 0.63 0.488 Study track+++ 1.44 1.30 0.708 Risk aversion+++ 5.85 5.84 0.516 Enjoy+++ 3.44 3.44 0.478 Difficulty+++ 2.39 2.23 0.574 Math skills+++ 3.73 3.67 0.680 N 41 43
The data collection took place on two subsequent days in May 2015 to avoid students receiving information about the experiment from other classes. The collected data is empirically analysed using Stata 13. In the next section the empirical results are discussed.
4 Results
4.1 Main empirical analysis
In real-life, managers simultaneously decide on how much risk to take and how much effort to exert, resulting in clients’ expected variable earnings. Round three of part one is analogue to this situation since participants were asked to choose which project to implement and subsequently exert effort on the project of their choice. Therefore, the results of this round are firstly empirically analysed.
In order to measure the effect of a bonus cap and background characteristics on outcomes, regressions are performed to explain the client’s expected variable pay, manager’s risk-taking behaviour and manager’s effort levels (see Table 5). The background characteristics are age, female, monthly income, fifth year, pre-university education, math level and study track. Also, the regressions always include a constant. Enjoy, difficulty and math skills are converted to dummy variables, where the dummy equals one if the corresponding ordinal variable is above the median and zero otherwise. Risk is also converted to a 0/1-dummy, which equals one if the variable is below five and zero otherwise (i.e. similar to Dohmen et al., 2011). Robust standard errors, in other words heteroskedasticity consistent standard errors, are used.
First off, the results of OLS regression 1 show that the effect of a bonus cap on the client’s expected variable earnings is positive. Specifically, it is estimated that on average the expected bonus is €0.52 higher for a client with a manager whose bonus is capped than a client with a manager whose bonus is unrestricted, holding everything else constant. However, this result approaches but fails to achieve a customary level of statistical significance (p-value 0.151). Prior to the financial crisis, remuneration components and structures led to the risk of careless treatment of consumers, clients or other stakeholders. A wanted effect of bonus caps is to ensure agents act more in the interest of the other party. The
Table 5
Regressions of client’s expected bonus, manager’s risk-taking behaviour and manager’s effort level in part 1 round 3 on the bonus cap and background characteristics
Dependent variable: Client’s expected bonus (1) Manager’s risk-taking behaviour(2)+ Manager’s effort level (3) Bonus cap 0.5163 (0.3557) -0.6009 (0.6726) 0.8425 (1.0378) Risk aversion 0.6800* (0.3695) -3.9106*** (1.1921) -1.0487 (1.0029) High enjoy 0.2829 (0.4535) 0.3573 (0.7906) 0.7916 (1.0826) High difficulty -0.7583** (0.3508) 0.4470 (0.8029) -4.2344* (0.9750) High math 0.1083 (0.4744) -0.2820 (0.6584) -0.5537 (1.2990) Age -0.4786* (0.2495) 1.4110** (0.6495) 0.2062 (0.5324) Female 0.3156 (0.3698) 0.5136 (0.7119) 3.0791*** (1.0076) Monthly income -0.0029 (0.0019) 0.0096*** (0.0032) 0.0120*** (0.0045) 5th year 0.3711 (0.6566) -0.2024 (1.1276) -0.3017 (1.6296) Pre-university education 0.3366 (0.4149) -0.5265 (0.7296) 1.0045 (1.0609) Math-B -1.9302 (1.2783) 11.749*** (2.0562) -7.8602** (3.8957) Math-C 0.1920 (0.7838) -1.7815 (1.6093) -4.2493* (2.3809) E&M -0.0019 (0.7204) -0.8431 (1.5916) -3.8052** (1.6912) N&G 1.0388 (1.1426) -9.7903*** (2.7389) 4.0218 (3.8394) N&T 1.1203 (1.5754) -9.8255*** (3.2802) 5.1854 (4.3747) Constant 9.4262 (4.2175) -23.974** (11.524) 9.2297 (8.6640) R2 0.2975 0.3439++ 0.4056 N 84 84 84
Note: */**/*** significant at a 10%/5%/1% level. Robust standard errors are in parentheses.
+ Logit regression. ++ Pseudo R2. Bonus cap equals one if the subject was in the treatment
group, age is in years, female equals one if the subject is female, monthly income is in euros, 5th year equals one if the subject is a 5th year students, pre-university education equals one if
the subject is a pre-university education students, math level equals 0 if Math-A; 1 if Math-B and 2 if Math-C, study track equals 0 if C&M; 1 if E&M; 2 if N&G; 3 if N&T, risk-aversion equals one if the variable is below five and zero otherwise, High enjoy, high difficulty and high math equal one if the corresponding ordinal variable is above the median and zero otherwise.
positive effect suggests that a bonus cap policy is favourable to the client as it leads to higher expected variable earnings.
The significant negative coefficient of high difficulty shows that a client whose manager has high difficulty with solving calculations has lower expected variable earnings than a client who has a manager with low difficulty. This is sensible since expected earnings depend on the number of correct calculations solved by the manager. Also, being older has a significantly negative effect on the client’s expected bonus. Furthermore, the other significant coefficient shows that a client whose manager is risk-averse has a higher expected variable pay than a client with a manager who is not risk-averse. Again, this is not surprising since it is in the client’s interest if the manager does not take risk.
In line with the positive coefficient of a bonus cap in regression 1, the client’s mean (median) expected bonus was €1.71 (€2) and €2.13 (€2.25) for the control and treatment group respectively. This suggests that a bonus cap leads to a higher expected variable payoff for the client. However, a Wilcoxon rank-sum test again shows that this difference is not significant (p-value 0.4199).
The client’s expected bonus follows from the manager’s risk-taking behaviour and effort level. Therefore, the desired effect of bonus caps on excessive risk-taking behaviour in this round of the experiment is analysed. Logistic regression 2 shows that a bonus cap decreases the subject’s probability of taking risk, however the coefficient is not significant (p-value 0.372). In particular, the model says that, holding everything constant at a fixed value, the odds of taking risk for managers with a bonus cap (bonus cap = 1) over the odds of taking risk for managers without a bonus cap (bonus cap = 0) is 𝑒!.!""# = 0.5483.
Therefore, in terms of percentage change, the odds of taking risk for managers with a restricted bonus are 45.17% lower than the odds for managers with an unrestricted bonus, all else constant.
This result is in line with the first prediction, namely that bonus caps lead to decreased excessive risk-taking. Moreover, since both the manager and client’s bonuses are affected by the manager’s taking behaviour, this evidence suggests that bonus caps lead to less risk-taking on behalf of others. Given that clients prefer managers to not take risk, this finding indicates that managers act more in their clients’ interest. In turn, this leads to higher expected variable earnings for clients, which is in line with the previous result.
As expected, the significant negative coefficient of risk aversion shows that subjects who are risk-averse are less likely to take risk than the ones who are not risk-averse. Other
significant negative coefficients are N&G and N&T, which imply that the probability of subjects in the N&G and N&T track to take risk is lower than those in the C&M track. Furthermore, the significant positive coefficients of age and monthly income show that agents who are older and have higher monthly income are more likely to take risk. Additionally, subjects who take mathematics-B are more likely to take risk than those who take mathematics-A.
Corresponding to the negative coefficient of bonus caps on manager’s risk-taking, the mean percentage of risk-taking was 34.1% and 30.2% for the control and treatment group respectively. This indeed shows that fewer subjects with a restricted bonus take risk than subjects whose bonuses are unrestricted. However, a test of proportions where the null-hypothesis is that the proportion of risk-taking is lower in the treatment group than in the control group shows that the difference in risk-taking across groups is not significant (p-value 0.3505).
Next, the manager’s effort level in this round is discussed. The main measure of effort is the number of correct equations solved by individuals. Surprisingly, OLS regression 3 shows that the effect of a bonus cap on effort is positive, however not at a significant level (p-value 0.420). Particularly, the model predicts that managers with a bonus cap solve 0.84 more equations than managers without a bonus cap, holding everything else constant. This is in contrast to the prediction following the standard direct price effect, namely that restricted bonuses lead to less effort and lower performance. However, increased effort levels do explain higher client’s expected bonuses since the relation between these variables is positive.
Several background characteristics have a significant effect on effort in this round of the experiment. Having high difficulty with solving calculations has a significantly negative effect on the average number of correct calculations. Additionally, women perform more correct calculations and monthly income positively affects the number of correct calculations. The ones who take mathematics-B or mathematics-C perform significantly less correct calculations than the ones with mathematics-A. Moreover, the ones who are in the E&M track solve significantly less correct calculations than the ones in the C&M track.
Likewise, the mean (median) number of correct equations solved was 10.8 (11) and 11.7 (11) for the control and treatment group respectively. This indicates that subjects in the treatment group solve more equations than subjects in the control group. A Wilcoxon rank-sum test shows that this positive difference for the treatment group is insignificant (p-value
0.5654). Also, the results of a two-sample Kolmogorov-Smirnov test confirm this finding (p-value 0.914), which is a non-parametric test of continuous, one-dimensional probability distributions to compare two samples.
Additionally, regressions without background characteristics are performed to check the robustness of the models (see Appendix B1). The coefficients of interest have the same sign as in the complete model but are smaller for the client’s expected earnings and manager’s risk-taking behaviour, while it shows a larger effect on manager’s effort. Specifically, it shows that on average the expected bonus is €0.40 higher for a client with a manager whose bonus is capped than a client with a manager whose bonus is unrestricted, holding everything else constant. From regression 2 it follows that all else constant the odds of taking risk for managers with a restricted bonus are 6.99% lower than the odds for managers with an unrestricted bonus. Additionally, regression 3 predicts that managers with a bonus cap solve 0.92 more equations than a manager without a bonus cap, holding everything else constant. Furthermore, in the first regression, the coefficient of high difficulty is no longer statistically significant, whereas for the other two regressions the same coefficients remain significant as in the complete model.
All in all, the results of this part of the experiment are in line with the first prediction, but in contrast to the second prediction. Resulting from this, the effect of a bonus cap on the client’s expected earnings is positive. However, none of these coefficients appear to be significant; therefore we have to be cautious with drawing conclusions from these findings.
4.2 Decomposition of desired effect on risk-taking behaviour
Next, the effect of bonus caps when effort levels are fixed (i.e. part 2 of the experiment) is analysed. Tests of proportions are conducted on the observations in part two of the experiment (see Table 6). Subsequently, Wilcoxon signed rank-sum tests on the proportions of risk-taking across the different situations allow interpreting the effect of a bonus cap on risk-taking behaviour.
When the effort level is exogenously set at ten and risk taking is either on behalf of only the manager or on behalf of both the manager and the client, risk-taking behaviour of the treatment group is significantly lower at a 1% and 5% level respectively. At a 10% level the risk taking behaviour is also lower for the treatment group in the Oth2 situation. Surprisingly,
the treatment group takes more risk in the Ind2 and Oth10 situations, however not significantly.
Table 6
Average proportion of risk-taking behaviour (i.e. implementing project B) per situation across groups
Control Treatment Difference in pp. p-value Ind2 61.0% 74.4% 13.4% 0.9064 Ind10 61.0% 7.0% -54.0% 0.0000*** Both2 58.5% 51.2% -7.3% 0.2487 Both10 31.7% 14.0% -17.7% 0.0259** Oth2 53.7% 39.5% -14.2% 0.0972* Oth10 31.7% 32.6% 0.9% 0.5333 N 41 43
Note: */**/*** significant at a 10%/5%/1% level. Tests of proportions are conducted.
Wilcoxon signed rank-sum tests show that the difference-in-differences are in line with the expectation that agents with a maximum bonus take less excessive risk because a bonus cap ensures that agents do not personally gain from risk-taking. Comparisons between effort levels two and ten within Indivdual and Both show that eliminating personal gain for the treatment group induces them to take significantly less risk. Namely, the p-value equals 0.0000 between Ind2 and Ind10 and 0.0003 between Both2 and Both10. The control group, on the other hand, still personally gains from taking risk when the assumed effort level is ten. Indeed the proportion of risk-taking remains the same in the Ind10 as in the Ind2 situation (p-value 1.000). However, the control group also shows significantly lower risk-taking behaviour in the Both10 compared to the Both2 situation (p-value 0.0218). This cannot be explained by the elimination of personal gain since the control group’s expected payoff of the risky project is larger than of the safe project.
In order to conclude on risk-taking on behalf of the client, the focus lies on comparing the Individual and Both situations. These are most relevant for concluding on the effect of bonus caps on risk-taking on behalf of others, since it addresses the effect of the risk exposure of the passive receiver while keeping the decisions maker’s individual restricted
