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«IZA DP No. 4262 PAPER Gift Exchange and Workers’ Fairness Concerns: When Equality Is Unfair Johannes Abeler DISCUSSION Steffen Altmann Sebastian ...»

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-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.

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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)).

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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

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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).

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