«IZA DP No. 4262 PAPER Gift Exchange and Workers’ Fairness Concerns: When Equality Is Unfair Johannes Abeler DISCUSSION Steffen Altmann Sebastian ...»
-1.5 Figure 4: Magnitude of eﬀort reactions. The average change in eﬀort from period t to period t + 1 is shown given that the agent experienced no norm violation, an advantageous violation or a disadvantageous norm violation in period t. The width of the bars corresponds to the number of observations.
(Mann-Whitney test on matching group shares: p = 0.03).
3.3.2 Simulation with Equity-Concerned Agents We demonstrated above that horizontal fairness concerns shape agents’ behavior under the two payment schemes. In combination with the frequent violations of the norm of equity in the EWT, this can explain the performance diﬀerences across treatments. In order to further illustrate how institutions and equity-concerns interact, we take our previous ﬁndings on agents’ period-to-period reactions and link them to the aggregate dynamics in the experiment. We do so with a simulation in which all agents are assumed to derive utility from money, but to also suﬀer whenever the equity principle is not met. When deciding about their eﬀort in a given period, the simulated agents compare their eﬀort and proﬁt in the previous period with the eﬀort and proﬁt of their co-worker in that period. According to the comparison along these two dimensions, four reactions can be distinguished for the simulated agents. (i) For an agent who had a higher eﬀort and a higher proﬁt, the norm of equity is fulﬁlled and the pecuniary comparison is also advantageous for him, so he keeps his eﬀort constant. (ii) For an agent who exerted a lower eﬀort and got a lower proﬁt, the norm is satisﬁed but proﬁt maximization is not, thus he partly adjusts his eﬀort in the direction of his co-worker’s eﬀort, i.e., he chooses an eﬀort (ei,t +ej,t )/2. (iii) An agent with higher eﬀort and lower proﬁt feels distressed as he suﬀers from a disadvantageous norm violation. He adjusts his eﬀort fully and chooses ei,t+1 = ej,t. (iv) Finally, for an agent with lower eﬀort and higher proﬁt the norm violation is advantageous, thus the resulting utility is higher than in case (iii). He chooses an eﬀort (ei,t + ej,t )/2. The reactions in cases (i) to (iv) are in line with the period-to-period reactions presented in Table 4 and Figure 4.
In the simulation, we use actual eﬀort data from the experiment only for the ﬁrst period. The subsequent eﬀort decisions are based on the simulated proﬁts and simulated eﬀorts of the previous period. The simulated principals pay the average wage for a given eﬀort (IWT) or the average wage sum for a given eﬀort sum (EWT) as calculated from the experimental data. Proﬁts are then calculated as wage minus cost of eﬀort exertion. We use the same matching protocol as in the experiment.
Figure 5 shows how eﬀort choices evolve over time in the experimental data and in the simulations. The simulations ‘EWT sim’ and ‘IWT sim’ trace the real data very well and are able to reproduce the large eﬀort diﬀerence between treatments. In the individual wage simulation, eﬀorts increase like the real eﬀorts although the slight downward trend in the second half of the experiment cannot be reproduced. Eﬀorts in the equal wage simulation constantly decrease down to an eﬀort level slightly above 3 in the ﬁnal period. This pattern is very similar to the dynamics in the real data.
Note that the pivotal agent is diﬀerent between the simulated treatments: in the equal wage simulation the norm of equity is violated when agents choose diﬀerent eﬀort levels. In these cases, the agent with the higher eﬀort will fully adjust his eﬀort in the direction of his co-worker’s eﬀort while the co-worker will increase his eﬀort level only to the average eﬀort of the last period. In the EWT simulation, the average eﬀort therefore converges to the lowest ﬁrst period eﬀort as agents are subsequently re-matched: the low-eﬀort providers are pivotal. By contrast, in the IWT the higheﬀort providers have the decisive impact on the overall outcome. The norm of equity is mostly fulﬁlled in the IWT. Thus, the agent with the higher eﬀort keeps his eﬀort constant while his co-worker adjusts his eﬀort. The average eﬀort therefore converges to the highest ﬁrst period eﬀort. We will analyze this point in more detail in the next section.
Result 6: Simulations based on agents who have preferences for money and equitable treatment are in line with the eﬀorts observed in the experiment and are able to reproduce the observed treatment eﬀect.
3.4 Dynamics of High- and Low-Eﬀort Providers As already seen in Figure 2, subjects exhibit a substantial degree of heterogeneity with respect to eﬀort provision. In the following, we analyze if the agents who are most or least willing to exert eﬀort are aﬀected diﬀerently by the two payment modes at hand.
A common informal argument claims that equal wages will be especially detrimental to the motivation of high performers but clean empirical evidence is scarce. Furthermore, it is unclear how weakly motivated agents react to equal or individual wages. We also address the question whether high and low performers impact the overall results diﬀerently in the two treatments. The simulations presented in the previous section suggest that this could indeed be the case: in the EWT simulation, the low-eﬀort providers are decisive for the ﬁnal outcome while it is the high-eﬀort providers in the IWT simulation.
To analyze these questions in the experimental data we classify agents according to their eﬀort decision in the ﬁrst period. We deﬁne the agent with the highest ﬁrst-period eﬀort in each matching group as “high-eﬀort provider” and the agent with the lowest eﬀort as “low-eﬀort provider”. This type deﬁnition is chosen because when agents decide on their eﬀort in the ﬁrst period, they do not have any information about the behavior of other subjects and all learning and coordination processes occur after this initial eﬀort choice. Thus ﬁrst-period eﬀort is likely to be a good proxy for the intrinsic willingness of a speciﬁc agent to exert eﬀort. If some of the subjects are intrinsically inclined to exert high eﬀorts they should show up in the group of high-eﬀort providers.
In contrast, if some of the subjects are intrinsically inclined to exert low eﬀorts they should show up in the group of low-eﬀort providers.
In Figure 6 we follow the high-eﬀort providers and low-eﬀort providers in both treatments and show their eﬀort decisions over time. In the ﬁrst period, the groups of high-eﬀort providers and the groups of low-eﬀort providers are close together across treatments.13 This changes completely over the course of the 12 periods. In the individual wage treatment, high-eﬀort providers continue to provide high eﬀort levels.
Low-eﬀort providers increase their eﬀorts dramatically up to the level of the higheﬀort providers and even higher in the last periods. In the equal wage treatment, the dynamics are reversed. Here, the low-eﬀort providers keep their eﬀort provision constant and the high-eﬀort providers reduce their eﬀorts to the level of the low-eﬀort providers. In the last six periods, eﬀort levels are not diﬀerent within treatments (Wilcoxon signed rank test: p = 0.67 (IWT), p = 0.78 (EWT)) while they diﬀer between treatments (Mann-Whitney test: p 0.01 (high-eﬀort providers), p 0.01 (low-eﬀort providers)). Put diﬀerently, the “good” agents push the “bad” agents up under individual wages while under equal wages the “bad” ones pull the “good” ones down.
These dynamics underline the importance of the diﬀerent non-monetary motives induced by the two wage setting institutions. Remember that agents face similar monetary incentives in both treatments, but wage equality often violates the norm of equity. Agents in this treatment who are in principle willing to exert high levels of First period’s eﬀort levels are not signiﬁcantly diﬀerent between treatments for high-eﬀort providers (Mann-Whitney test: p = 0.14) while they are close together but diﬀerent for the loweﬀort providers (Mann-Whitney test: p = 0.03). Within treatments, the high-eﬀort and low-eﬀort
providers choose statistically diﬀerent eﬀort levels in the ﬁrst period (Wilcoxon signed rank test:
p = 0.01 (IWT), p = 0.01 (EWT)).
eﬀort seem to get frustrated and lower their eﬀorts. On the contrary, under individual wages where the norm of equity is intact, good performance spreads. These results suggest that choosing a wage scheme also inﬂuences the social dynamics between the agents. In our experiment, individual wages lead to positive dynamics since agents orientate themselves by the most hard-working agents. In contrast, the equal wage scheme focuses agents’ attention on the least motivated agents.
Result 7: The pivotal agent is diﬀerent between treatments: in the IWT, agents who initially provide low eﬀort align with the high-eﬀort providers over time. In the EWT, agents who initially provide high eﬀort align with the loweﬀort providers over time.
3.5 The Role of Intentions So far, we interpret our results as supporting the notion that subjects care about the norm of equity. However, by design our treatments necessarily diﬀer in the number of instruments that a principal has at hand. In the EWT, principals only choose a single wage—whereas principals in the IWT decide on two wages and consequently can tailor reactions individually to agents’ preceding choices. Therefore, agents might attribute a diﬀerent degree of intentionality to principals’ decisions: in the EWT, the role of intentions is limited to the level of the wage. The IWT contains an additional element of intentionality because principals also decide on relative wages and consequently whether the equity norm is fulﬁlled or violated. In light of the literature that stresses the behavioral importance of intentions in situations of reciprocal interaction (e.g., Dufwenberg and Kirchsteiger 2004, Falk et al. 2008a), there is thus a potential alternative explanation for our treatment eﬀect. In other words, one might speculate that the diﬀerence is not caused by the diﬀerent frequency of norm fulﬁllment per se, but rather by the additional element of intentionality.14 To test this alternative explanation, we conducted an additional control treatment (wage level treatment or WLT) that clearly isolates the eﬀect of norm fulﬁllment on agents’ eﬀort choices. As in the EWT, principals in the WLT only choose a single wage. The other agent’s wage is then exogenously set by a computer program such that the equity norm is always fulﬁlled, i.e., agents who exerted a higher eﬀort than their co-worker automatically receive a higher payoﬀ. This is common knowledge.
Importantly, this implies that the fulﬁllment of the equity norm is not attributable to principals’ decisions. Except for this change of the wage-setting institution, the instructions and the experimental design were identical to the previous treatments.
The 72 subjects who participated in the four additional sessions had not previously taken part in the IWT or the EWT.
The speciﬁc equity norm implemented in the WLT experiments dictates proportionality between agents’ monetary payoﬀs and eﬀorts. We chose this “equity formula” as it is probably the most prominent formulation of the equity principle (see Section 2.2).
Given a principal’s decision for the low-eﬀort agent, the wage for the high-performing agent is exogenously ﬁxed such that both agents receive the same payoﬀ per unit of eﬀort provided, i.e., (πlow /elow ) = (πhigh /ehigh ) holds. For example, if the principal observes eﬀorts of 2 and 6 and sets the wage for the low-eﬀort provider to be 5, the payoﬀ of this agent is 5 − c(2) = 4 (compare Table 1). Following the equity formula, the payoﬀ of the high-eﬀort provider will then automatically be set to (4/2) · 6 = 12;
which implies a wage of 20 after taking the cost of providing 6 units of eﬀort into account.15 We thank the Editor, Patrick Bolton, and an anonymous referee for pointing this out.
The equity formula leads to counterintuitive implications whenever negative values for the inputs
The wage-setting institution in the WLT is not meant to be an analog of institutions found in actual labor markets, as it is the case for the IWT and the EWT. It exogenously implements the incentive structure that is endogenously created by principals in the IWT.16 If we observe similar eﬀorts in the WLT as in the IWT we can rule out intentions as an explanation for the diﬀerence between our two main treatments, IWT and EWT.
Figure 7 compares agents’ mean eﬀort choices over time for all three treatments.
As can be seen, the exogenous implementation of the equity norm suﬃces to elicit or outcomes are possible. Therefore, if in our experiment the eﬀorts diﬀer and the principal’s choice of wlow implies πlow ≤ 0, the other agent’s wage is instead set such that πhigh = πlow + 5. This guarantees that the norm of equity is fulﬁlled for all possible wage-eﬀort combinations. Nevertheless, the high-eﬀort agent still faces the risk of making losses whenever the low-eﬀort agent gets a negative payoﬀ.
As shown in Result 3, the monetary incentives in the IWT imply that proﬁt-maximizing agents should provide non-minimal eﬀort levels. As a consequence of exogenously implementing these implicit incentives in the WLT, new subgame-perfect Nash equilibria necessarily arise. Our focus of interest, however, rests on the comparison of the observed behavior across treatments rather than on comparing behavior to the game-theoretical equilibrium predictions. For a similar approach of “exogenizing” endogenous incentives to test for the impact of intentions, compare for example Blount (1995), Charness (2004), or Cox (2004).