Appendix A: Learning effects
In each session, subjects played 18 times the two-stage game in Section 2. During the course of the experiment, they may have changed their behavior, for instance, because over time, they learned how to play the game. To make sure that our conclusions are not biased due to ignoring such learning effects, we consider in this appendix the data from the last nine and the final three periods separately as well. The focus is on investment levels (cf. Result 1 and Table 4) and on delay of agreement (cf. Result 3 and Table 7). Recall that, in the regressions reported in the main text that led to Results 2 and 4, we already control for potential learning effects.
The design of the experiment was such that the first and last nine periods included the same frequency of low, intermediate, and high levels of the worker's outside wage. Moreover, each value of w was represented exactly once in the final three periods. Tables 10 and 11 (investment levels and bargaining length, respectively) report the same statistics as in Tables 4 and 7, but now, also for the last nine and final three periods separately. The top panels of Tables 10 and 11 correspond exactly with the tables presented in the main text. The middle panels only consider the data from the second half of the experiment, while the bottom panels only use the data from the final three periods.
Table 10 reports average investment levels by treatment. Statistical tests are again based on the average investment levels of individual investors. The results in the middle and bottom panels almost exactly reproduce the results of the top panel. The single difference is that no significant differences are found anymore under the TP game when w=7,800. This holds despite the fact that the mean levels over all investors are fairly far apart. Comparing for this particular case (i.e., w=7,800 under the TP game) the average investment levels across the different panels of Table 10 by means of a Wilcoxon signed-rank test, we find no significant differences when the worker invests (the lowest p value is 0.304). For the case in which the employer invests, however, the top panel differs significantly from both the middle (p=0.047) and bottom panels (p=0.032). Over time, employers thus tend to invest less in this case, while workers do not change their investment behavior. Based on these learning effects, we still conclude that, under the TP game, workers invest more than employers do when the outside wage is high.Footnote 38
As an additional test of learning effects, we regressed, for each of the 12 treatments, the investment levels on a variable that measures the time that the investor was confronted with this particular value of the outside wage (besides a constant term). Only in two treatments did this time trend have a statistically significant (negative) coefficient: the case where w=1,800 under E-OO and the case where w=6,800 under W-OO. As can be seen from Table 10, however, the differences in overall mean investment levels for both these treatments in the three panels are small (and they display a nonmonotonic pattern). Taking all the above checks together, we conclude that Result 1 on investment behavior is not contaminated by learning effects.
Table 11 presents for each treatment the percentage of cases in which agreement is reached immediately and the average number of bargaining rounds before agreement is reached. Columns labeled “n” give the number of observations on which the latter averages are based; observations in which one of the parties opted out (OO game) or no agreement was reached are left out. Comparing the middle with the top panel, it is observed that average delay is typically shorter in the second half than in the first half of the experiment. This follows because in almost all treatments, the average number of bargaining rounds before agreement is reached decreases when we take only the last nine periods into account (the two exceptions occur when w=6,800 under E-OO and W-TP). Apparently, subjects learn to avoid costly delay when they play the game. Result 3 on delay of agreement is, however, not seriously affected by this. It is fully supported when we consider periods 10 to 18 only.Footnote 39 For the final three periods, the same types of differences are found, although not all of them are significant. Moreover, there, we observed that overall agreement is reached sooner under the OO game when the worker invests. In case of the TP game, there are no significant differences, although when w=1,800, the overall observed mean bargaining length before agreement is substantially larger when the employer invests than when the worker invests, in line with Result 3(b).