Do separation rules matter? An experimental study of commitment

Abstract

Coasian reasoning predicts that the conditions under which parties may terminate a partnership will affect bargaining between partners, but not the durability of partnerships. This paper endeavors to test both predictions in an experimental setting that allows agents to form and end partnerships endogenously and to bargain over resources. We find that separation rules have less effect on bargaining than predicted by theory, but larger effects on partnership stability. Perhaps surprisingly, agents who are weaker relative to their partners are more successful when either party can end a partnership unilaterally than when both must consent to a separation.

Keywords:

• separation rule
• commitment
• bargaining
• experiments

Acknowledgements

The authors are particularly grateful to the Department of Economics and Finance at the City University of Hong Kong for financial support and the Center for Experimental Business Research at the Hong Kong University of Science and Technology for laboratory facilities. The authors thank Gary Charness, David Dickinson, Werner Guth, David Masclet, Fabien Moizeau, Stephane Robin, Marie-Claire Villeval, Anthony Ziegelmeyer, seminar participants at the Max Planck Institute of Economics, City University of Hong Kong, Lingnan University, University of Lyon, University of Rennes, National Taiwan University, National Chengchi University, Academia Sinica, National Dong Hwa University, and Fudan University, participants at the 2006 and 2007 Economic Science Association Asia-Pacific Regional Meeting, and the 2007 Economic Science Association World Meeting for helpful comments. The paper was previously circulated under the title ‘An experimental study of commitment under different separation rules.’

Notes

1. The Coase theorem states that, in the absence of transaction costs, efficiency can be achieved through bargaining regardless of the initial allocation of property rights or legal entitlement.

2. Several other papers have studied if and how the ability to make contingent transfers or compensation promotes cooperation in prisoners’ dilemma games. See, for example, Andreoni and Varian (1999) and Charness et al. (2007).

3. See Davis and Holt (1993, pp. 255–262) for a summary of experiments on the Coase Theorem.

4. In addition to Johnson et al. (2002), see Davis and Holt (1993, pp. 102–109) for a summary of experiments on testing backward induction rationality.

5. The conversion rate was 25 francs to 1 USD or 3 francs to 1 HKD. The exchange rate in spring 2007 was about 1 USD = 7.80 HKD.

6. The bargaining phase lasted three minutes for at least the first three periods. After making sure that all subjects were comfortable with the decision environment and bargaining procedure, we then reduced the time to one minute.

7. One can think of the ‘penalty’ here as legal or emotional costs of failing to reach an agreement with one's partner. For simplicity, we assume the same penalty for both unilateral and mutual consent separation rules.

8. See, for example, Camerer and Weigelt (1993), Duffy and Ochs (1999, 2002), Noussair and Matheny (2000), and Lei and Noussair (2002).

9. The combination of a 10% probability of ending rule and having more than ten pairs of subjects in each session ensured that there were always enough unattached agents so that no one would be paired with the same counterpart for two consecutive periods. For example, in session UB1 there were 11 pairs. If only one pair chose to separate, we randomly chose one of the other ten pairs to end its match. For the pair that chose to separate, the 10% probability of ending rule still applied, except that in this case the experimenter's decision was not binding. If none or at least two pairs decided to end their matches, we then randomly picked two pairs out of eleven (2/11) and simultaneously terminated both matches with probability 55%. Hence, the probability that a match would be exogenously terminated was still (2/11) × 55% = 10%, and we always have zero or at least two pairs of agents to be rematched. In sessions with 12 or 13 pairs of subjects, the random ending rule was executed similarly.

10. If there was exactly one pair that decided to break off its match, we exercised the random ending rule using the same procedure as described in Note 9. But if no pair or more than one pair terminated their partnerships, we imposed the 10% random ending rule to terminate all partnerships simultaneously.

11. See the working paper version of this manuscript (Vesely, Lei & Drewianka, 2010) for a formal derivation.

12. We choose not to add an interaction term between the rule and the payoff dummy variables in our probit analysis. Instead, we report extra four probits that include treatment dummy variables in the lower panel of Table 4. See Ai and Norton (2003) for reasons why the coefficient calculated by standard software on the interaction effect in nonlinear models may have incorrect magnitude, sign, and statistical significance.

13. Since we ran sessions at two different universities, we have also experimented with including a dummy variable distinguishing between the two locations. The dummy variable was never statistically significant, and the estimated effects of the separation rules were virtually identical to those we report.

14. We have also run a variation on this model that includes person-specific multiplicative random effects (‘frailty’) that are gamma distributed with mean 1. The two specifications produced very similar results.

15. For example, if the match is entering its sixth period, the new explanatory variable is the absolute value of the total difference in the partners’ net earnings over the previous five periods, divided by five periods.

16. Considering that this new variable is endogenous and determined by the same bargaining process that produces the decision to continue or terminate the partnership, it would be improper to consider the coefficient on this variable as a causal effect. Nevertheless, such estimates could still be considered descriptive evidence about which matches end, so it would be proper to say that the hypothesized finding implied that couples who had larger differences in earnings were more likely to separate.

17. Although the table does not report their estimated coefficients, the specification also includes all the factors that were reported in Table 5.

18. Regression results showing statistically significant differences between actual and predicted transfers and also between actual transfers across treatments are available from the corresponding author upon request.