A note on the modelling and interpretation of a public goods game experiment

ABSTRACT

This paper presents an alternative interpretation of an experimental public goods game dataset, particularly on the understanding of the observed antisocial behaviour phenomenon between subjects of a public goods experiment in different cities around the world. The anonymous nature of contributions and punishments in this experiment are taken into account to interpret results. This is done by analysing dynamic behaviour in terms of mean contributions across societies and their association with antisocial punishment. By taking into account the heterogeneity between the cities in which the public goods experiment has been performed, this analysis shows a contrasting interpretation. Instead of one trend across cities, two opposite trends are seen across different cities. In addition, we find that the presence of these trends to have an impact on the role of antisocial and pro-social behaviour in public goods games. When accounting for these trends, the antisocial and pro-social behaviour is found to have a significant role in Western societies.

KEYWORDS:

• Convergence
• experiments
• panel data
• public goods games
• pro-social and antisocial punishment

Acknowledgements

The authors would like to thanks Peter Phillips and Donggyu Sul for having shared the Aptech’s GAUSS code for convergence testing and discussed its usage with us and Benedikt Herrmann for having shared the dataset. We would like to thank the anonymous referees for their constructive comments and suggestions to significantly improve the quality of this paper. We also thank Donggyu Sul for his guidance regarding the approach applied and Chang Yee Kwan for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 See Table S1, page 6.

2 Further information is available on Hermann et al. [4].

3 In this paper, the terms ‘cluster’ and ‘club’ are used interchangeably.

4 Overall convergence refers to testing the convergence hypothesis across all states together.

5 GAUSS code for clustering algorithm is available online to download directly from Sul’s personal webpage: http://www.utdallas.edu/~dxs093000/papers/exm.pgm. R users may refer to Package ‘ConvergenceClubs’: https://cran.r-project.org/web/packages/ConvergenceClubs/ConvergenceClubs.pdf. Stata users may use ‘logtreg’ command: https://docs.google.com/viewer?a=v%26pid=sites%26srcid=ZGVmYXVsdGRvbWFpbnxrZXJyeWR1MjAxNnxneDozYWNlZGRkM2NiZjdlMmE4.

6 The estimate is taken from Hermann et al. [3].

7 This can also be interpreted as cross society mean contribution since the data have been collected in various societies.

8 We also report bootstrap statistics in Appendix 1. The bootstrap-based findings suggest that contribution with punishment within each club is divergent. This implies further investigation is required on the causes of this divergence. This require large data set, which unfortunately is not possible for us to obtain. Consequently, our results should be interpreted with caution.

9 The codes below are extracted and slightly modified from the original codes provided by Phillips and Sul [6]. The reader can refer to the link http://www.utdallas.edu/~dxs093000/papers/exm.pgm for detailed GAUSS codes.