BEEM127 - Experimental Methods

ASSIGNMENT PAPER

Self-Interest through Delegation: An

Additional Rationale for the Principal-Agent

Relationship

(John R. Hamman, George Lowenstein and Roberto A.

Weber)

Fall 2015

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In this research paper titled “Self-Interest through Delegation: An additional Rationale for the Principal-Agent Relationship” the authors analyse the principal-agent relationship, asking themselves whether it could used to carry out functions it is not usually meant to. Standard economic theory assumes that agents are hired by principals to take advantage of efficiencies delegation involves. Indeed agents either have special ability or require less effort. Authors instead suppose that delegation in some cases might be used to execute self interested or immoral actions.* This paper is of undoubtable practical importance because understanding what the principal-agent relationship is really used for provides insights into many real-world matters (frauds, business scandals, financial mismanagement etc. Remember the Enron scandal). Authors’ experimental hypothesis is that principals are significantly less generous towards a recipient when acting through an agent rather than directly. The hypothesis is derived from literature and authors’ own intuition. To test it they devise an experimental setup in the form a dictator game (a principal allocates money from an endowment to an anonymous recipient) and 3 different experiments which will be analysed are carried out. It is important to stress that this research is unique because there is no literature on settings where there are no strategic motives for delegating.**

EXPERIMENT 1

In experiment 1, allocations from 3 different treatments are compared.

*Authors intuition is that delegation may make principal more detached while agents may feel they are just carrying out orders making nobody take full responsibility for the actions. **In general, the principal-agent relationship has been extensively analysed in contexts such as psychology and politics. Economic literature on the topic is quite scarce.

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As the table above shows they are: - Baseline (standard dictator game) - Agent - Agent/Choice

In the agents treatments each principal selects an agent to make the allocation on his behalf. 12 subjects (Baseline - 6 principals, 6 recipients) or 15 subjects (Agent treatments - 6 principal, 6 recipients , 3 agents) participated in each session. Each having 12 rounds (for details see table). In each round, each principal (=dictator) received an allocation of 10$ to be divided in .10 increments between him and his randomly matched recipient. In the Baseline treatment, principals made the allocation by specifying an amount as in a standard dictator game. In the Agent, every decision was made by one of 3 agents. In the first round, each agent was matched with an equal number of principals. From round number 2 instead every principal selected an agent. The Agent/Choice was identical to the latter apart from the last 4 rounds where the principal had the option to either continuing to delegate the decision or make the choice on his own. Importantly agents’ payoff function was completely independent of the decisions made depending only on the number of principals selecting the agent. Each agent started the experiment with 5$.

Each participant regardless of his role received a 7$ show-up fee and one random round was selected for payment in the case of principals and recipients. For extra-clarity it is specified that participants were undergraduate and postgraduate students at Carnegie Mellon and the University of Pittsburg.

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Agent’s payoff function

EXPERIMENT 2

Experiments two consists of 2 treatments: - Baseline - Announce

The Baseline was identical to experiment 1 but was re-run because there was a one year lag between exp. 1 and exp. 2. The Announce condition was the same as Agent in exp. 1 with two relevant differences. Before the principals selected an agent, the agents sent them a message stating the amount they were willing to share*. The messages were “cheap talk” (non binding = whatever amount could be shared) but there was little incentive in using deception. The other difference was that selection of agents started from round 1, not round 2 differently from exp. 1. Experiment 2 was conducted to see whether results would have differed if agents had better information about agents’ sharing behaviour. Also, with messages, it should be more difficult for agents to claim “deniability” for agents’ actions. A total of 10 session was carried out (5/treatment), involving 135 subjects.

QUESTIONNARIE

Following each session and importantly before the round selected for payment was revealed, subjects in the two experiments completed a brief questionnaire measuring perceptions of fairness, responsibility and enjoyment in participating to the session (five responses ranging from (-2) strongly disagree to (+2) strongly agree).

EXPERIMENT 3

Experiment 3 involves one treatment only known as Fixed-Agent. It was carried out to eliminate competition between agents and see whether it had any effect in contribution amounts. In fact, in the Fixed-Agent treatment each principal was matched for the whole experiment with the same agent (6 principals, 6 recipients, 6 agents). Consequently competition between agents was completely eliminated. For every round, the agent sent to the assigned principal a message stating the amount he was willing to share. The principal could then decide to delegate the action to the agent or carry it out on his own.

*messages where not shown to recipients

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Each agent the action was delegated to received 0.50$. If it was not selected the 0.50$ were equally divide among the remaining 5 agents. Two sessions were conducted.

RESULTS

EXP. 1

This table shows the mean amount given to recipient by treatment. We can see how contribution in the first 4 rounds of the Agent treatments is not significantly lower than the Baseline. In rounds 5-11 instead contribution is importantly lower in the Agent conditions than the Baseline. It seems that principals needed some time to find the right agent. In the table a comparison between Baseline and the pooled agent conditions is made for the first eight rounds (the two agent conditions are identical in the first eight rounds). A statistical comparison (baseline-pooled agent conditions, baseline-agent, baseline-agent/choice) was then run using the Mann-Whitney rank-sum and the t-statistic obtaining higher statical significance for round 5-8 (pooled agent conditions) and 5-11 (agent and agent/choice). In my view, choosing a t-test was completely acceptable given that the sample size is relative little but at the same time not too small (>15). Was also a good idea, in order to obtain more support for the experimental hypothesis to run a non-parametric test

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such as the Mann-Whitney rank-sum. It is also common place in economic research to pair a t-test (parametric) with a Mann-Whitney (non-parametric - differently from the t-test it does not assume that the population variances are equal and that the difference between the samples is normally distributed. When t-test reliability might be uncertain a Mann-Whitney is often used). So, authors choice is completely accurate.*

In this graph we can see the cumulative percentage of total allocations and was a good intuition to include it to make it easier to understand for people not familiar with statical methods.

Beginning from round 2 in the Agent treatment, all principals had to choose an agent among three, including the opportunity to keep the same agent as in the preceding round. Data analysis confirms that principals pursued selfish outcomes in their switching choices. In fact, the frequency with which principals retained the same agent decreased dramatically with the amount shared.

*both test where used to see whether the two samples were statically different from each other

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The table above shows logistic regressions with subject fixed-effects outlining how the highly significant coefficient on the amount shared mean that the higher the amount the more likely is that the principal will switch agent. It was a good idea to use a logistic regression (binomial in this case: outcomes are switch/not switch) because it was the simplest and clearest analysis available for the case and OLS or a linear regression (does not restrict predicted values between 0 or 1 and it heteroscedastic) would have instead been inappropriate.*

Remember that in the last 4 rounds of the Agent/Choice, principals could decide to delegate the action or not. Approximately 40% decided to delegate, meaning that the remains 60% was comfortable with sharing a low amount (conversely the remaining 40% was too morally embarrassed to do so directly) or that during the session there had been some degree of desensitisation.

Moreover we can notice how in the last round of the Agent treatment sharing is high ($2.97) which could mean that psychological forces backfire at the end and that some cross-section heterogeneity was observed. In fact, 2 out of 7 agent sessions produced contributions fairly higher that the others.

*the log-likelihood was used to compare the goodness to fit of the two models. Remember that regression is used to estimate the relationship between a dependent and independent variable.

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EXP. 2

The table shows the mean amount given to recipients by treatment. It can be noticed how mean giving is always lower in Announce (apart from round 12 where a high contribution is recorded*) with high statistical significance in almost every round. Requiring agents to send a message stating the amount they were willing to share decreased contribution starting from round 1 compared to exp.1 in which contribution was initially high and decreased over a number of rounds. A statistical comparison Announce-Baseline was run using Mann-Whitney ranks sum and a t-test for the same reason it was run in experiment number 1 and the choice was in my view again correct (see exp. 1 for reasoning).

*remember that a high contribution in round 12 is also observed in the agent treatment in exp.1. Probably psychological forces backfire.

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The graph above shows the distribution of amount shared by condition outlining how principals preferred agents willing to share low amounts. It was a good idea to include such a graph to make understanding easier and intuitive.

A logistic regression was then run showing how the large positive coefficients on the amount shared mean that principals switched away from agents who shared significant amounts. In model 2, in can be shown, that unlikely in exp.1, round number had a relevant negative effect on the willingness to switch agent. This indicates that subjects settled with their preferred agent after a few rounds and stopped switching. Agents who built a reputation for reliability in sharing zero were incredibly successful in attracting principals.

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It was appropriate to run a logistic regression (binomial with outcomes: switch/not switch) to keep analysis easy and clear. Running an OLS or a linear regression (does not restrict predicted values between 0 or 1 and it heteroscedastic) would have instead been inappropriate.

QUESTIONNARIE ANALISYS

Given, that exp.1 and exp.2 structure is quite similar, questionnaire answers were analysed together.

The table displays mean responses ordered by role for different questions. It can be seen how principals felt less responsible when acting through agents rather than directly. However, agent conditions recipients reported less fair treatment than those in the baseline treatment. Also, recipients in the agent conditions perceived the behaviour of agents slightly more harshly than that of principals (this difference is not statically significant. If the experiment are considered separately, it is bigger fort exp.1 and smaller for exp 2. This is not surprising given that in the latter principals received a message from agents).

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The table above shows a number of ordered probit regressions* using questionnaire responses as dependent variables. Independent variables are instead average earnings across rounds and a binary variable for treatment (0 = Baseline; 1 = Agent, Agent/Choice, or Announce). It was appropriate to use an ordered probit because the outcomes are more than two.

EXPERIMENT 3

*it is a generalisation of the probit model in case of more than two outcomes

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In the graph above the mean amount shared by round can be observed noticing how contribution in the fixed agent is quite low. Consequently competition between agents has not a relevant effect and is not the reason why contribution goes low.* Round 12 is an exception (as happened in exp.1 - agent and exp. 2 - announce) seeing a considerable amount of contribution. This graph allows to immediately visualise the situation in a really simple way and was a good choice to include it.

CONCLUSIONS

In conclusion, sharing decreases dramatically when decisions are delegated and agents willing to transfer nothing attract most/all the business. A “vertical diffusion of responsibility” makes principals feel like they are behaving fairly. In other words this research suggest that the principal-agent relationship might be exploited to carry out functions beyond those usually attributed to it. In particular to pursue selfish or immoral outcomes. Recall that in the Agent treatment - exp. 1 in two sessions a high amount of contributions was observed. This could mean that reducing the number of agents available could reduce the likelihood of finding a selfish one (however agents in real world environments are hardly members of the population and may in-fact self select them into that role). A policy suggestion derived from this paper would be to introduce social pressure by requiring principal to certify or approve agents’ decisions (something similar was done in the USA with the Sarbanes-Oxley bill). A design suggestion would be the re-run the experiment introducing real-world contracts involving incentives between principals and agents. This however, would make data analysis more complicated. An educated guess would be that such a modification would push contribution even lower.

FINAL REMARKS

- It would have probably been useful to include some bar graphs showing sharing distribution (some readers could find them easier to understand than line graphs)

- It would interesting to conduct the experiment with an higher number of agents, keeping a low number of principals to see whether competition between agents has any effect

- Data analysis was overall clear and fairly easy to understand - Experimental design was accurate and simple making authors’ choice totally

accurate. Was also a good choice to have students as experimental subjects (easy to recruit, low opportunity cost and steep learning curve).

*in the fixed-agent condition the decision was delegated 66% of the time

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TERMINOLOGY:

Mann-Whitney rank-sum: It is a widely used non-parametric (distribution free ) alternative to the two-sample t-test. It is based one the orders the observations from the two samples fall only. Thanks to it we can check whether the population distributions are identical without assuming them to be normally distributed (N.B. The two samples being tested should be independent of each other).

T-test: it is the standard parametric test for checking that two populations means are equal. It is widely used when the variances of two normal distributions are unknown and when the sizes are small (but not too small).

Normal distribution: A symmetrical distribution (symmetry about the centre) with mean = median = mode

Cumulative percentage: it is a different way to express frequency distribution. It computes the percentage of the cumulative frequency within each interval.

Regression or Regression Analysis: In general, it is used to investigate the relationship between dependent and independent variables (e.g. linear regression)

Logistic regression: Also called logit model is used with dichotomous outcome variables. The dataset to be analysed can contain one or more independent variables which determine a dichotomous outcome in the dependent variable. It is a non-linear regression forcing the output to be 0 or 1.

Ordered Probit Regression: It is a probit (the probit is almost identical to the logit model*) generalisation when the outcomes of an ordinal outcome variable are more than two.

Heteroscedasticity: The standard deviation of a variable, over a certain time-frame, is non-constant.

*in the probit errors are assumed to follow the normal distribution instead in the logit they are assumed to follow the standard logistic distribution

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TERMINOLOGY BIBLIOGRAPHY:

- ResearchGate.net - medcalc.org - statcan.gc.ca - investopedia.com

N.B. ALL TABLES AND GRAPHS ARE TAKEN FROM THE MENTIONED RESEARCH PAPER

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