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Table 3 reports the variation in group account contributions by treatment, this time pooling data from all three blocks. Results from the combined private and public inequality sessions (the far right column in Table 3) show that contributions were highest in the egalitarian treatment (3.01 versus 2.63 for symmetric and 2.61 for skewed). Like the previous table of results, the higher level of contributions under the egalitarian treatment is present only in the public inequality sessions and does not hold for the private inequality sessions. We tested for statistically significant differences in subject contributions by inequality treatment using a series of Wilcoxon signed rank tests for matched pairs. Contributions in the egalitarian treatment were significantly different (at the 95% level) from contributions in the two unequal (symmetric and skewed) treatments combined, but only in the public inequality sessions. In no case (public or private inequality) could we reject the null hypothesis that contributions in the egalitarian treatment were the same as contributions in either of the unequal treatments considered separately.
Table 3. Contribution means and standard deviations, by form of inequality and distribution
Distribution of payments
Private inequality
Public inequality
Both private and public inequalities
Egalitarian 2.85 (2.45), n = 240 3.17 (3.26), n = 240 3.01 (2.89), n = 480
Symmetric 3.04 (2.69), n = 240 2.22 (2.66), n = 240 2.63 (2.70), n = 480
Skewed 2.76 (2.43), n = 240 2.46 (3.24), n = 240 2.61 (2.86), n = 480
All 2.88 (2.52), n = 720 2.62 (3.09), n = 720 2.75 (2.82), n = 1440

Differences in mean contributions by treatment can reflect variation in factors other than inequality per se, such as the level of the fixed payment a subject received, the effect of repetition and the order of the treatments, and possibly subject traits. To identify the effect of inequality on group account contributions holding all else equal, we next conduct multivariate analyses of our data. Before examining the effects of inequality on contributions, we first estimate several variants of a basic model of contributions to demonstrate the effect of some of these other factors on subject decisions. In this model, the dependent variable is the number of tokens contributed to the group account by a subject in a given round of play, and the explanatory variables include the fixed payment received by the subject and controls for the round of play. To allow for unobserved subject-specific differences in group contributions, we estimate the model as a generalized least squares model (GLS) with random-subject-effects.19 In this specification, the error term is assumed to be distributed normally with mean zero, and composed of two parts, a random disturbance term for the individual subject and a disturbance term for the decision made by the subject in the given round. Table 4 reports the base model results first using the full data set and then using separate samples from the private inequality sessions and public inequality sessions. In most models, the coefficient of the fixed payment variable is positive but not statistically significant. This suggests that the absolute amount of the fixed payment does not explain the differences in contributions to the group account reported in Table 3, and that our fixed payments were sufficiently low as to avoid wealth effects.
Table 4. Random effects GLS models of contributions
Explanatory variable
All sessionsa
Private inequalityb
Public inequalityb
Public −0.267 (0.58)
Fixed payment 0.024 (1.01) −0.017 (0.62) 0.068* (1.74)
Round 2 0.729* (1.90) 1.019** (2.26) 0.440 (0.71)
Round 3 0.444 (1.16) 0.949** (2.11) −0.060 (0.10)
Round 4 0.000 (0.00) 0.352 (0.78) −0.352 (0.57)
Round 5 0.007 (0.02) 0.727 (1.62) −0.713 (1.16)
Round 6 −0.438 (1.14) 0.199 (0.44) −1.074* (1.74)
Round 7 −0.493 (1.28) 0.352 (0.78) −1.338** (2.17)
Round 8 −0.660* (1.72) 0.046 (0.10) −1.366** (2.22)
Round 9 −0.792** (2.06) −0.301 (0.67) −1.282** (2.08)
Round 10 −1.653*** (4.31) −0.968** (2.15) −2.338*** (3.79)
Second block −0.850*** (5.57) −1.407*** (7.87) −0.292 (1.19)
Third block −1.213*** (7.95) −1.648*** (9.22) −0.778*** (3.18)
Reset 1 0.704 (1.46) 0.907 (1.61) 0.500 (0.65)
Reset 2 0.942* (1.95) 1.481*** (2.62) 0.403 (0.52)
Hausman Test p-value 1.000 1.000 1.000
Note: Absolute values of t-statistics are shown in parentheses. Statistical significance is indicated by *** for the 0.01 level, ** for the 0.05 level and * for the 0.10 level.
a n = 1440.
b n = 720.

When we estimate the base model using data from all sessions, we use a dummy variable to capture the effect of the public manner of revealing the inequality in the subject fixed payments. We control for repeated play with round dummy variables as well as additional dummy variables to identify decisions made in the second and third blocks. To capture the two reset effects depicted in Fig. 1, we also include two dummy variables, one is equal to 1 for the first round of the second block and 0 otherwise, and the second is equal to 1 for the first round of the third block and 0 otherwise. In general, the estimated effects of the round, block, and reset variables have the expected signs. The full sample results show that repeated play had an initial positive and significant effect in round 2, no effect on contributions in the middle rounds, and negative and significant effects in rounds 8 though 10. In both the public and private session samples, contributions made in the second and third blocks were lower relative to the first round of play. Some differences exist in the coefficients of the control variables across the public and private session samples. For example, the estimated reset effects are positive and significant only in the private inequality sessions.
To summarize, we find that repeated play generally had the predicted negative effect observed in previous studies, that there are some differences in subject behavior according to the manner in which inequality was revealed, and that the level of the fixed payment had little independent effect on contributions to the group account. In addition, the results of Hausman tests reported in the bottom row of Table 4 support the use of a random-effects specification for our data.
We next test the effect of inequality on contributions to the group account by introducing additional explanatory variables to the base model, as shown in Table 5. We begin by adding only explanatory variables to account for the inequality in different model specifications; these are reported in columns (1) and (4). Each model includes the explanatory variables measuring inequality that are shown in the relevant rows, as well as controls for fixed payment and round of play. In each of the models shown, the results of Hausman tests support the use of random-effects estimation.
Table 5. Random and fixed effects GLS models of contributions
Private inequality
Public inequality
(1)
(2)
(3)
(4)
(5)
(6)
Model 1
Unequal distribution 0.054 (0.37) 0.054 (0.37) 0.054 (0.37) −0.827*** (4.16) −0.827*** (4.16) −0.827*** (4.16)

Model 2
Relative deprivation index 0.044 (0.09) 0.060 (0.13) 0.054 (0.11) −2.172*** (3.35) −2.156*** (3.32) −2.134*** (3.27)

Model 3
Relative deprivation index −0.277 (0.35) −0.234 (0.29) −0.253 (0.31) 0.044 (0.04) 0.110 (0.10) 0.214 (0.19)
Unequal distribution 0.123 (0.50) 0.113 (0.45) 0.118 (0.47) −0.838** (2.45) −0.855** (2.49) −0.881** (2.55)

Model 4
Maximum payment 0.419 (1.22) 0.410 (1.19) 0.483 (1.40) −0.323 (0.70) −0.303 (0.66) −0.331 (0.71)
Unequal distribution 0.368 (1.24) 0.361 (1.22) 0.417 (1.40) −1.069*** (2.68) −1.055*** (2.64) −1.075*** (2.67)

Model 5
Payment relative to max 0.587 (1.36) 0.579 (1.34) 0.596 (1.38) −0.660 (1.14) −0.661 (1.14) −0.687 (1.18)
Unequal distribution 0.311 (1.30) 0.307 (1.28) 0.315 (1.32) −1.116*** (3.46) −1.116*** (3.45) −1.128*** (3.49)

Control for race and gender, political ideology and major No Yes No No Yes No
Control for subject random effects Yes Yes No Yes Yes No
Control for subject fixed effects No No Yes No No Yes
Notes: Absolute values of t-statistics are shown in parentheses. All models control for the subject's fixed payment, the round of play, the order of the treatment and reset effects. The number of observations used in each model's estimation is 720. The subject traits added to some models are indicator variables measuring subject sex (female), race (non-White), academic major (economics or not) and political ideology (Democratic and neither party relative to Republican). Statistical significance is indicated by *** for the 0.01 level, ** for the 0.05 level and * for the 0.10 level.

Model 1 includes an indicator variable for an unequal distribution of fixed payments; the omitted category represents the egalitarian distribution in which all subjects received a fixed payment of US$ 7.50. The results suggest that the inequality treatment had no effect in the private sessions but depressed contributions in the public treatment by about 32% of the average contribution in the public sessions, or 0.827/2.62. The negative coefficient on the inequality variable is consistent with the model of Alesina et al. (1999), in which heterogeneity dampens the ability to provide public goods.20
In Model 2, we examine whether inequality affected all subjects in an identical manner, or whether the subject's relative payment within the distribution mattered. To do this, we add to the base model a subject-specific measure called the relative deprivation index, or RDI, following a definition provided in Deaton (2001).21 The index is calculated as:

(1)where xi is the fixed payment for individual i, (1 − F(xi)) is the proportion of the group with payments greater than xi, μ+(xi) is the mean of all payments to subjects with payments greater than xi and μr is the mean of all payments in the reference group. In the public sessions, the relative deprivation measure has a negative and significant influence on contributions. In Model 3, we control for both the relative deprivation index and the nature of the payment distribution. All else equal, when fixed payments are drawn from an unequal distribution, subjects in the public sessions reduced contributions to the group account, again by about 32%. After controlling for the presence of inequality, the subject's placement within the distribution (indicated by the RDI) does not have a significant effect.
Models 4 and 5 employ two alternate subject-specific measures of relative income; both models also control for inequality in the fixed payment distribution. One measure is a dummy equal to 1 if the subject received the maximum payment in the distribution; another measure is calculated by dividing the subject's payment by the maximum payment in the fixed payment distribution. Models 4 and 5 produce results that are qualitatively similar to Model 3, but generate larger point estimates for the inequality effect, here about 41–42% of the average contribution.
One persistent result across all specifications is that inequality substantially reduced contributions in the public sessions. We investigated the robustness of this finding by introducing additional controls to the model. We constructed measures of subjects’ race, gender, academic major and political ideology from a survey administered at the conclusion of the experiment. Columns (2) and (5) include controls for these variables, and in each case, our main result—that inequality dampens contributions to the group account in the public sessions—persists with the additional controls. In columns (3) and (6), we present the results of fixed-subject-effects models that adjust for unobservable, fixed, subject traits. These results also show that inequality was associated with reduced contributions to the group account in the public treatment. Notably, the inclusion of these additional control variables does not appreciably alter the magnitude of the inequality effect in the public sessions.
We conducted additional robustness checks that are not reported in Table 5. To all of the models, we added a variable capturing the level of contributions made by other members of the subject's group in the previous round. Focusing on the public session results, we found that the significant effects of the inequality measures persisted in 12 of the 15 models reported in Table 5. In another exercise, we estimated our models using only those observations from the first 10 rounds each subject played. These models generated a between-subjects analysis (in contrast to the within-subjects analysis reported in Table 5), and addressed the concern that subject experiences under one type of inequality treatment may have persistent effects on subject behavior under a new treatment. Our main result, that inequality dampens contributions to the group account by all members in the public sessions, was also observed in the 10-round sample.

จากคุณ	: J3w_brown
เขียนเมื่อ	: 15 ส.ค. 54 23:40:39