than in the BASE treatment. Firms, however, compensate workers for this loss by not cutting wages in recession as much as in the BASE treatment.
Finally, we know that wage cuts are smaller in the CasRP than in the BASE treatment.
Additionally however, out of recession wages are already smaller in the CasRP than in the BASE treatment. So are wages in recession higher in the CasRP than in the BASE treatment, as the non-parametric test (on the individual level) suggested? They are but only with marginal significance (testing for regression (3): Z = 1.71, two-sided p = 0.087).
Overall, the question that arises from these results is what drives the treatment differences.
3.4.2 Workers’ Behavior and Treatment Differences
In this section, I will analyze to what extent differences in workers’ behavior can explain differences in the firms’ wage-setting behavior, observed in the previous section. Table 3.4 provides a first average measure of workers’ behavior in different treatments. We see that in both treatments average effort is cut. For the BASE treatment, this cut is significant according to one-sided Wilcoxon signed rank tests (Session: p = 0.014, Individual: p = 0.010). For the CasRP treatment, statistical results whether effort is reduced or not are mixed (Direct effort cut Session: p = 0.014, Individual: p = 0.027; Indirect effort cut -Session: p = 0.124, Individual: p = 0.171). The effort cut in the CasRP is lower than in the BASE treatment, but this difference is only marginally significant according to one measure31 But even if there was a difference between treatments, this might of course just be a reflection of lower wages paid by firms in the BASE treatment.
Figure 3.3 gives a first impression why we might observe a treatment difference. This figure reports workers’ reaction, their effort change, to different wage changes of firms
31One-sided Wilcoxon rank sum test: Direct effort cut - Session: p = 0.075, Individual: p = 0.026;
Indirect effort cut - Session: p = 0.261, Individual: p = 0.225.
Figure 3.3: Workers’ Reaction to Wage Changes - CasRP
for the CasRP treatment (for which direct wage cut data is available).32 If firms e.g. do not change wages at all (wage change of zero), workers react by slightly increasing their effort by roughly 0.3. The overall picture of the graph seems to be that wage cuts are punished and stable (or increased) wages are rewarded. Figure 3.3 does, however, not control for the wage level. It would be possible that the whole pattern just reflects the positive relationship between effort and wage, typically observed in gift-exchange games.
Importantly, however, wage cuts seem on average to be punished strong enough to make them unprofitable, whereas stable (or increased) wages are rewarded strong enough to make them profitable. A wage cut of at most 5 is punished by an effort decrease by more than 0.5, whereas a wage increase is also rewarded by an effort increase by more than 0.5.
Hence on average, increasing a wage by at most 5 points increases firms’ payoff, whereas decreasing a wage by at most 5 points decreases firms payoffs. This punishment-reward pattern of workers’ behavior provides a first hint that a reference-point effect might matter in the CasRP treatment.
The regression analysis of Table 3.5 confirms this conjecture. Table 3.5 only uses data from the CasRP treatment and provides panel fixed effects (FE)33 regressions. This time, the dependent variable is effort. Regression (1) just explains effort by wages, a quadratic wage term, and a constant, controlling for a quadratic time trend. Regression (2) includes a recession dummy that is significant. Workers effort in the CasRP treatment is 0.29 points higher in recession than out of recession. So, although on average less effort is provided in recession as shown by Table 3.4, controlling for wages, workers provide slightly more effort.
32For the BASE treatment, direct wage data is by design not available and hence we cannot report results similar to Figure 3.3 for the BASE treatment.
33Because I do not want to include time-invariant variables in these regressions, no random effects (RE) regressions are provided. These regression, however, would only lead to results with even slightly higher levels of significance.
3.4. RESULTS 69 Table 3.5: Panel Regressions on Effort - CasRP
(1) (2) (3) (4)
FE FE FE FE
Wage 0.109∗∗ 0.113∗∗ 0.113∗∗
(0.0316) (0.0308) (0.0313)
Recession-dummy 0.285∗ 0.408∗∗ 0.379∗ (0.132) (0.150) (0.150)
Constant -2.532 -2.710∗∗ -2.695∗∗ 8.371∗∗∗
(0.875) (0.821) (0.830) (0.687)
Observations 827 827 827 827
R2 0.669 0.671 0.672 0.682
Notes: Panel fixed effects (FE) regressions on effort, only for the CasRP treatment. Standard errors are reported in parentheses, adjusted for clus-tering at the session level. ∗∗∗indicates significance at the 1 percent level,
∗∗ at the 5 percent level, and∗at the 10 percent level.
Regression (3) adds an additional dummy (Rec × Wage cut) that only has a value of one if a recession occurs and the firm cuts wages. In this specification, the recession dummy reflects about how much workers increase their effort when a recession occurs and wages are kept stable (or are even increased). Hence, if a recession occurs and wages are not cut, average effort is about 0.41 points higher than average effort out of recession. If wages, however, are instead cut, average effort is 0.26 points lower than if wages are at least kept stable, and this difference is significant at the 5%-level. Importantly, the effort increase for wage cuts (0.15 points) is statistically not different from zero (Z = 1.14, two-sided p = 0.256). Overall this means that, controlling for the wage level, workers only exert more effort in recession for stable (or increased) wages but punish wage cuts relative to wage increases by not increasing effort in recession. This suggests that subjects have established a reference point that leads them to relatively punish wage cuts beyond the pure effect of a lower wage level that is implied by a wage cut.
A potential concern could be that the wage-cut dummy does not really reflect a reference point but captures non-linearities in the wage-effort relationship. Wages that are cut are on average lower than stable (or increased) wages. In order to control for this problem, a quadratic wage term is included in the regressions (1)-(3). Regression (4) provides a different control by including wage-dummies for wage intervals with length of 5 instead of a quadratic wage term.34 Results change slightly but remain significant at least at the marginal level.35 Hence, overall, we have the following result:
34Overall, 14 wage-dummies are included: [30, 35], (35, 40], . . . , (95, 100].
35Additionally, Table B.1 (Appendix B.1) provides a similar analysis as Table 3.5 but focuses only on recession data. The reason also to use only recession data is that in these regressions wages, the quadratic wage term, and the wage dummies capture precisely the wage-effort relationship in recession and not the overall relationship in and out of recession, as in Table 3.5. Results of Table B.1 confirm those of Table
Table 3.6: Panel Regressions on Effort - BASE and CasRP
Rec x CasRP x No wage cut -0.228 -0.150 -0.220 -0.139
(0.176) (0.226) (0.172) (0.222)
Wage*CasRP -0.0501 -0.0494
(0.0465) (0.0462)
Wage2 X X X X X X
Wage*CasRP & Wage2*CasRP X X
Period & Period2 X X X X X X
Constant -3.281∗∗∗ -3.413∗∗∗ -3.401∗∗∗ -3.831∗∗∗ -3.169∗∗∗ -3.123∗∗∗
(0.685) (0.680) (0.690) (0.853) (0.732) (0.624)
Observations 1419 1419 1419 1419 1419 1419
R2 0.526 0.528 0.528 0.531 0.622 0.628
Notes: Panel random effects (RE) and fixed effects (FE) regressions on effort for the BASE and the CasRP treatment.
Standard errors are reported in parentheses, adjusted for clustering at the session level.∗∗∗indicates significance at the 1 percent level,∗∗at the 5 percent level, and∗at the 10 percent level.
Result 4: In the CasRP treatment, workers react differently to wage cuts