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Inequality aversion and the house money effect

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Abstract

In this paper, we analyse if individual inequality aversion measured with simple experimental games depends on whether the monetary endowment in these games is either a windfall gain (“house money”) or a reward for a certain effort-related performance. We then examine whether the way of preference elicitation affects the explanatory power of inequality aversion in social dilemma situations. Our results indicate that individual inequality aversion measured by the model of Fehr and Schmidt (Quarterly Journal of Economics 114(3):817–868, 1999) is not generally robust to the way endowments emerge. The inequality aversion model has only low predictive power for individual behaviour. It performs best when the endowment is house money and relatively small.

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Notes

  1. Other examples of models of other-regarding preferences are Bolton and Ockenfels (2000), Charness and Rabin (2002), Dufwenberg and Kirchsteiger (2004), or Falk and Fischbacher (2006).

  2. The house money effect has also been investigated in other areas of research and with different experimental settings: for house money effects in public good games see e.g. Clark (2002), Harrison (2007), Cherry et al. (2005), Kroll et al. (2007), for house money effects in risky choices see e.g. Keeler et al. (1985), Thaler and Johnson (1990), Arkes et al. (1994), Keasey and Moon (1996), and Ackert et al. (2006).

  3. In the following, all conditions are stated for the case of two players. The generalisation to the n-player case is straightforward and can be found in Fehr and Schmidt (1999).

  4. This condition is employed by Fehr and Schmidt (1999) in order to facilitate the critical condition for cooperation in a voluntary contribution game (VCG). Proposition 4 of their proof (part C, p. 862) states that a player with β i >1−m, where m denotes the marginal per capita return of the public investment, chooses to cooperate in a VCG if the following condition is met: k/(n−1)≤(m+β i −1)/(α i +β i ) where k are players with β i <1−m. If α i ≥β i this is the sole condition that has to be fulfilled. If we abandon α i ≥β i a second condition might become binding, namely k/(n−1)≤m/2. As we will see in Sect. 3, for treatments with cooperation hypothesis this condition always holds in our experiment.

  5. We used z-tree for programming, see Fischbacher (2007), and ORSEE for recruitment of subjects, see Greiner (2003). For experimental instructions see the Appendix in Dannenberg et al. (2010).

  6. Namely, title and authors of the article, name, volume, and page number of the journal.

  7. They were informed about their relative performance, so subjects could infer to which group (rich or poor) they belong.

  8. Payoffs in games A and B were determined in experimental pre-tests to ensure that we obtained a sufficient number of observations for each decision.

  9. With respect to this aspect our design differs from previous experiments (see the introduction for an overview). However, since in real world decision situations inequity concerns often prevail in situations were both sides have to show effort in order to create the cake at stake we believe that our implementation is warrantable.

  10. The €1.00 was chosen as a minimum payoff in order to avoid the possibility of zero payoffs.

  11. While the direct-response method is often considered as the first-best solution, Brandts and Charness (2011) argue: “[The strategy method]… may lead subjects to make more thoughtful decisions and, through the analysis of a complete strategy, may lead to better insights into the motives and thought-processes underlying subjects’ decisions” (p. 377).

  12. Several authors, see e.g. Ockenfels and Weimann (1999), Ben-Ner et al. (2004), and Fischbacher and Gächter (2010), choose a similar way when they match subjects according to the behaviour in previous games without informing subjects in advance about this procedure.

  13. As the threshold values for F&S parameters, α i =0.1 and β i =0.4, also the value for the punishment costs, c=0.1, was derived from the F&S model. More precisely, the value c=0.1 was chosen in order to make for game D (the PD with punishment) punishment of a defector a credible threat for a subject with α i >0.1 (see Sect. 3.4).

  14. If not otherwise stated all statistical tests are two-sided throughout the paper.

  15. The chi-square test statistics are: No effort rich vs. Effort rich (chi-squared=12.7, df=3, p=0.005), No effort rich vs. Effort poor (chi-squared=14.2, df=3, p=0.003) and No effort rich vs. No effort poor (chi-squared=12.7, df=3, p=0.005).

  16. A linear-probability specification (OLS) leads to almost identical results with respect to the magnitude of effects and significance. The same holds for Tables 8 and 10.

  17. Nearly identical results are obtained when the logit regression for the PD is done with subsamples which are pooled across treatment variables (Effort, No Effort, Rich and Poor). In particular C-hypothesis is significant in No effort poor only.

  18. This conclusion is also supported when the logit regression for the PD is done with subsamples which are pooled across treatment variables (Effort, No Effort, Rich and Poor).

  19. Nearly identical results are obtained when the logit regression for the punishment decision is done with subsamples which are pooled across treatment variables (Effort, No Effort, Rich and Poor). In particular, P-hypothesis is significant in No Effort rich only.

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Acknowledgements

The authors would like to thank two anonymous referees and the editor for very useful comments and suggestions. Financial support from the German Science Foundation is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Centre for European Economic Research (ZEW), Mannheim, Germany

    Astrid Dannenberg & Bodo Sturm

  2. Faculty of Business Studies and Economics, University of Kaiserslautern, Kaiserslautern, Germany

    Thomas Riechmann

  3. Department of Business Administration, Leipzig University of Applied Sciences, Leipzig, Germany

    Bodo Sturm

  4. Department of Business Administration, Bochum University of Applied Sciences, Bochum, Germany

    Carsten Vogt

Authors
  1. Astrid Dannenberg
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  2. Thomas Riechmann
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  4. Carsten Vogt
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Corresponding author

Correspondence to Bodo Sturm.

Appendices

Appendix 1

Table 11 Socio-economic characteristics
Full size table
Table 12 Fraction of decisions in games A and B
Full size table
Table 13 Fraction of types
Full size table
Table 14 Punishment behaviour
Full size table

Appendix 2

In this appendix we derive the Nash equilibrium for game C (PD) and the subgame perfect equilibrium (SPE) for game D (PD-P).

PD game (C—cooperation, D—defection)

PD

j

Utility

C

D

i

C

8.4, 8.4

4.2−7.0α i , 11.2−7.0β j

D

11.2−7.0β i , 4.2−7.0α j

7.0, 7.0

Strategy combination {i,j}

i

j

{C,C}a

8.4>11.2−7.0β i ⇒β i >0.4

8.4 > 11.2 - 7.0β j ⇒β j >0.4

{D,D}a

7.0>4.2−7.0α i ⇒α i >−0.4

7.0>4.2−7.0α j ⇒α j >−0.4

{C,D}

4.2−7.0α i >7.0⇒α i <−0.4

11.2−7.0β j >8.4⇒β j <0.4

{D,C}

11.2−7.0β i >8.4⇒β i <0.4

4.2−7.0α j >7.0⇒α j <−0.4

  1. a{C,C} is a Nash equilibrium if β i >0.4 and β j >0.4. {D,D} is always a Nash equilibrium
  2. {C,C} is the Nash equilibrium for the following i−j−matchings FAIR-FAIR, FAIR-CARING, CARING-CARING. {D,D} is the Nash equilibrium for all other matchings

PD-P game (P—punishment, NP—no punishment)

PD-P: {C,C}

j

Utility

P

NP

i

P

4.0, 4.0

8.0−3.6β i , 4.4−3.6α j

NP

4.4−3.6α i , 8.0−3.6β j

8.4, 8.4

Strategy combination {i,j}

i

j

{NP,NP}a

8.4>8.0−3.6β i ⇒β i >−0.1

8.4>8.0−3.6β j ⇒β j >−0.1

{P,P}a

4.0>4.4−3.6α i ⇒α i >0.1

4.0>4.4−3.6α j ⇒α j >0.1

{NP,P}

4.4−3.6α i >4.0⇒α i <0.1

8.0−3.6β j >8.4⇒β j <−0.1

{P,NP}

8.0−3.6β i >8.4⇒β i <−0.1

4.4−3.6α j >4.0⇒α j <0.1

  1. a{NP,NP} is always a Nash equilibrium. {P,P} a Nash equilibrium if α i >0.1 and α j >0.1, however, it is Pareto dominated by {NP,NP}

PD-P: {C,D}

j

Utility

P

NP

i

P

−0.2−7.0α i , 6.8−7.0β j

3.8−3.4α i , 7.2−3.4β j

NP

0.2−10.6α i , 10.8−10.6β j

4.2−7.0α i , 11.2−7.0β j

Strategy combination {i,j}

i

j

{NP,NP}a

4.2−7.0α i >3.8−3.4α i ⇒α i <0.1

11.2−7.0β j >10.8−10.6β j ⇒β j >−0.1

{P,P}

−0.2−7.0α i >0.2−10.6α i ⇒α i >0.1

6.8−7.0β j >7.2−3.4β j ⇒β j <−0.1

{NP,P}

0.2−10.6α i >−0.2−7.0α i ⇒α i <0.1

10.8−10.6β j >11.2−7.0β j ⇒β j <−0.1

{P,NP}a

3.8−3.4α i >4.2−7.0α i ⇒α i >0.1

7.2−3.4β j >6.8−7.0β j ⇒β j >−0.1

  1. a{NP,NP} is a Nash equilibrium if α i <0.1. {P,NP} is a Nash equilibrium if α i >0.1

PD-P: {D,C}

j

Utility

P

NP

i

P

6.8−7.0β i , −0.2−7.0α j

10.8−10.6β i , 0.2−10.6α j

NP

7.2−3.4β i , 3.8−3.4α j

11.2−7.0β i , 4.2−7.0α j

Strategy combination {i,j}

i

j

{NP,NP}a

11.2−7.0β i >10.8−10.6β i ⇒β i >−0.1

4.2−7.0α j >3.8−3.4α j ⇒α j <0.1

{P,P}

6.8−7.0β i >7.2−3.4β i ⇒β i <−0.1

−0.2−7.0α j >0.2−10.6α j ⇒α j >0.1

{NP,P}a

7.2−3.4β i >6.8−7.0β i ⇒β i >−0.1

3.8−3.4α j >4.2−7.0α j ⇒α j >0.1

{P,NP}

10.8−10.6β i >11.2−7.0β i ⇒β i <−0.1

0.2−10.6α j >−0.2−7.0α j ⇒α j <0.1

  1. a{NP,NP} is a Nash equilibrium if α j <0.1. {NP,P} is a Nash equilibrium if α j >0.1

PD-P: {D,D}

j

Utility

P

NP

i

P

2.6, 2.6

6.6−3.6β i , 3.0−3.6α j

NP

3.0−3.6α i , 6.6−3.6β j

7.0, 7.0

Strategy combination {i,j}

i

j

{NP,NP}a

7.0>6.6−3.6β i ⇒β i >−0.1

7.0>6.6−3.6β j ⇒β j >−0.1

{P,P}a

2.6>3.0−3.6α i ⇒α i >0.1

2.6>3.0−3.6α j ⇒α j >0.1

{NP,P}

3.0−3.6α i >2.6⇒α i <0.1

6.6−3.6β j >7.0⇒β j <−0.1

{P,NP}

6.6−3.6β i >7.0⇒β i <−0.1

3.0−3.6α j >2.6⇒α j <0.1

  1. a{NP,NP} is always a Nash equilibrium. {P,P} a Nash equilibrium if α i >0.1 and α j >0.1, however, it is Pareto dominated by {NP,NP}

We analyse 10 possible i−j-matchings FAIR-FAIR, FAIR-CARING, CARING-CARING, FAIR-ENVIOUS, FAIR-EGO, ENVIOUS-ENVIOUS, CARING-ENVIOUS, CARING-EGO, ENVIOUS-EGO, EGO-EGO. Thereby, we substitute the Nash equilibrium of the punishment subgame into the payoff matrix of the contribution stage in the PD. Here we show only the matchings ENVIOUS-ENVIOUS and ENVIOUS-EGO. All other matchings can be analysed accordingly.

ENVIOUS-ENVIOUS

PD

j

Utility

C

D

i

C

8.4, 8.4

3.8−3.4α i , 7.2−3.4β j

D

7.2−3.4β i , 3.8−3.4α j

7.0, 7.0

  1. {{C,C} {NP,NP}} is the SPE

ENVIOUS-EGO

PD

j

Utility

C

D

i

C

8.4, 8.4

3.8−3.4α i , 7.2−3.4β j

D

11.2−7.0β i , 4.2−7.0α j

7.0, 7.0

  1. {{D,D} {NP,NP}} is the SPE

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Dannenberg, A., Riechmann, T., Sturm, B. et al. Inequality aversion and the house money effect. Exp Econ 15, 460–484 (2012). https://doi.org/10.1007/s10683-011-9308-2

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