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Reference point effects in legislative bargaining: experimental evidence

Experimental Economics volume 22, pages 735–752 (2019)Cite this article

Abstract

Recent interest in reducing budget deficits raises questions regarding the impact on legislative bargaining of cuts versus increases in government spending. Using an experimental design where the outcomes are theoretically isomorphic results in significant differences in bargaining outcomes: There are longer delays in reaching agreement with cuts than with increases, along with which legislative types get their proposals passed. These results can be attributed to a change in agents’ reference point in conjunction with differential responses to gains versus losses.

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Fig. 1
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Notes

  1. See, for example, McKelvey (1991), Fréchette et al. (2005) and Diermeier and Morton (2005). See Palfrey (2016) for a review of the literature.

  2. See Fréchette et al. (2012), Christiansen et al. (2014), Christiansen (2015) and Agranov et al. (2016).

  3. See Plott and Zeiler (2005).

  4. Their emphasis is on using an eye-tracking technique to record information search to determine the extent to which agents use backward induction.

  5. We want to distinguish reference point effects from pure framing effects. The former combine both a different initial setting (e.g., different initial endowments) and a pure framing effect (e.g., going from gains to losses). In contrast, in a pure framing effect initial endowments are the same, only the frame is switched.

  6. If the game fails to terminate, a default decision (a policy location and split of the private goods) is implemented. It turns out that even if δ = 1 the default decision plays no role in the analysis when X > 0. See JM for details.

  7. See Baron–Ferejohn for a discussion of the properties of the SSPE.

  8. Instructions are at the web site: https://sites.trinity.edu/sites/sites.trinity.edu/files/instructions_gains_costs.pdf.

  9. Christiansen et al. (2017) investigate the BF model under gains and costs with modest discounting of payoffs when proposals are rejected.

  10. Using a Mann–Whitney test or proportions test with bargaining round as the unit of observation.

  11. An MWC is defined as a proposal in which only one other legislator votes for it. In this case 3% of the time T2s proposals passed unanimously.

  12. T1’s continuation value under the SSPE is 617 versus 622 under the EES. For T2 the continuation values are 550 and 555, respectively, and for T3 they are 298 and 332.

  13. Estimated differences between the EES and the SSPE were 6.5ECUs, 46.5ECUs and 78.4ECUs for T1, T2, and T3 respectively. Estimated differences from payoff maximizing proposals were − 26.6, − 11.9, and 0 for T1, T2, and T3 respectively. See ESM of Table A1, in the appendix, for predictions under the SSPE.

  14. A fairness norm makes it difficult for a T2 proposer to deviate from the behavioral equilibrium and lower T1’s payoff below the EES in order to take a higher payoff for herself.

  15. The software was designed to permit up to 15 stages of bargaining before the program moved onto a new bargaining round. All bargaining rounds ended well before 15 stages.

  16. This compares to 3 sessions, with 39 subjects in the Gains treatment in CGK. The additional session for the Costs treatment compensated for one of the earlier sessions that ended after 11 bargaining rounds as a result of computer problems (the data for this session is used up through the 11th round). This, along with higher turnouts in the experiment reported here, accounts for the higher participation rate than in the Gains treatment.

  17. There were three Baseline sessions with E = 600 totaling 42 subjects.

  18. The reader is referred to CGK for detailed analysis of the Baseline treatment relative to the Gains treatment.

  19. The movements in policy relative to the Baseline are statistically significant using a Mann–Whitney test with the outcomes in each bargaining round as the unit of observation (\(p < 0.01\)).

  20. Unless stated otherwise, statistical tests reported are Mann–Whitney, with results for each group in each bargaining round as the unit of observation.

  21. Another way to measure whether there is more difficulty in coming to agreement in Costs is to calculate the average number of stages until agreement is reached. The average rises from 1.3 stages in Gains to 1.5 stages in Costs (\(p = 0.10\)).

  22. This criteria is used to eliminate proposals that essentially had no chance of being accepted in both the Gains and Costs treatments. Only 6 T3 proposals in Gains and 6 in Costs did not meet this criteria.

  23. Note that because T3’s unit walking cost is so high, even a proposal that allocates all of the private goods to T1 and proposes a policy of 90 lowers T3’s payoff to 540.

  24. NEES proposals yield payoffs of R3 ∈ [540,610] and R1 ∈ [590,610] and include the EES as a special case.

  25. The results are similar if the data is restricted to EES proposals. The acceptance rates are 89 and 44% for Gains and Costs, respectively \((p\, < \,0.05\)).

  26. Clustering at the session level results in no changes in the statistical significance of the coefficients. See the Appendix for more session level analysis of the data.

  27. This restriction eliminates only 3 proposals in Gains and 1 in Costs where T1 has a payoff above the NEES. We do not include these in the probit because they provide higher payoffs to T1s than proposals at or below the NEES, resulting in a substantially higher probability of being accepted than the proposals included in the probit with payoffs to T1 at or below the NEES.

  28. This result is not driven by egalitarian T1s who might dislike the relatively low payoff for T2. Running the same probit over T1 voters who simultaneously propose own payoffs above 600, which guarantees at least one other player a much lower payoff than the proposer, yields similar results.

  29. See Kőszegi and Rabin (2006) for a formal description of the gain–loss function.

  30. CARA utility functions were chosen for ease of use, but later we discuss the implications of utility functions displaying increasing or decreasing risk aversion.

  31. Similar results would follow from satisficing assuming that small deviations from maximizing payoffs are more acceptable with Gains compared to Costs.

  32. This follows from Harrington (1990) who shows that risk aversion will result in voters accepting lower offers than with risk neutrality. Similarly, voters will require higher offers than with risk neutrality to vote in favor of a proposal if they are risk loving.

  33. To see why, note that for payoffs below 600 the level of local risk aversion is identical across treatments by the CARA assumption. However, for payoffs above 600, players in the Gains treatment are locally more risk averse than in Costs because they are above their endowment. Together this implies that players in Gains are globally more risk averse for any payoff distribution that includes the possibility of a payoff above 600. See Pratt (1964). With respect to other forms of utility, the same result will hold if individuals are more risk-loving over lower payoffs. In that case, players are locally more risk-loving in Costs for payoffs above 600 as before, and for payoffs below 600 since for any given payoff they are farther away from their endowment in Costs than in Gains.

  34. This calculation holds the empirical continuation value constant.

  35. If T3’s proposals in the Costs treatment were accepted at the same rate as in Gains, total average payoffs would have risen from 1473 to 1484.

  36. A “stable” party is one for which no member can form an agreement with another set of players and achieve a higher payoff. JM assume parties split the gains according to the Nash bargaining. T2 and T3 are indifferent between forming parties with one another and with T1. However, because of the proximity of their ideal points, there are more gains for T1 from forming a party with T2 than with T3.

  37. Using empirical continuation values from accepted stage 1 proposals adjusted to account for the varying frequency with which each type is selected the proposer, the benefit for T2 from partnering with T1 instead of T3 falls by more than half (12 ECUs in Gains to 5 ECUs in Costs). In short, a T2–T3 coalition is closer to being stable under Costs compared to Gains.

  38. The implications would be similar for pay-as-you-go or cut-as-you-go budget requirements which limit the amount of government spending by forcing the legislative body to pay for new spending by cutting spending elsewhere.

  39. See: http://www.washingtonpost.com/blogs/wonkblog/wp/2014/01/14/heres-a-breakdown-of-whats-in-congress-1-012-trillion-spending-bill/ and http://www.upi.com/Top_News/US/2014/01/13/Republicans-Democrats-reach-deal-on-11-trillion-spending-bill/UPI-24531389665791/?spt=hts&or=1.

  40. Baron (1991) solves a legislative bargaining model with benefits and taxes where players get net payoffs that can be either positive or negative. The advantage to using the BF model to bargain over taxes is that payoffs for all players would be exclusively in the loss frame.

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Acknowledgement

Funding was provided by National Science Foundation (Grant No. SES-1226460), (Grant No. SES-1630288).

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Authors and Affiliations

  1. Department of Economics, Trinity University, San Antonio, TX, USA

    Nels Christiansen

  2. Department of Economics, Ohio State University, Columbus, OH, USA

    John H. Kagel

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  1. Nels Christiansen
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  2. John H. Kagel
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Correspondence to John H. Kagel.

Additional information

This is a substantially revised version of an earlier paper entitled, “The Effects of Increasing versus Decreasing Private Goods on Legislative Bargaining: Experimental Evidence”. We are grateful for comments received at the 2014 Behavioral Models of Politics Conference at Duke University, the 2013 Political Economy meeting at Cal Tech, and the 2013 Public Choice Society Meetings. We received able research assistance from Xi Qu and Matt Jones. This research has been partially supported by National Science Foundation Grant SES-1226460 and SES-1630288. Opinions, findings, conclusions or recommendations offered here are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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Christiansen, N., Kagel, J.H. Reference point effects in legislative bargaining: experimental evidence. Exp Econ 22, 735–752 (2019). https://doi.org/10.1007/s10683-017-9559-7

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Keywords

  • Reference point effects
  • Legislative bargaining
  • Budget deficits versus budget surpluses
  • Experiment

JEL Classification

  • D72
  • C92
  • C52

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