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Estimating the causal effect of beliefs on contributions in repeated public good games

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Abstract

We use instrumental variables for estimating the causal effect of beliefs on contributions in repeated public good games. The effect is about half as large as suggested by ordinary least squares. Thus, we present evidence that beliefs have a causal effect on contributions, but also that beliefs are endogenous. We compare the causal, belief-based model of contributions to alternative models based on matching the previous contributions of others and responding to one’s deviation from the average in the previous round. The causal, belief-based model performs well, indicating that beliefs have a central role in determining contributions.

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Notes

  1. Croson (2007) has subjects play two ten round games, but the restart creates a structural break.

  2. There is a literature about belief elicitation. Croson (2000), and Gaechter and Renner (2010) study belief elicitation in public good games. Costa-Gomes and Weizsaecker (2008), Nyarko and Schotter (2002), and Rutstrom and Wilcox (2009) examine belief elicitation in other games. Our objective in this paper is to address the endogeneity associated with a common approach to eliciting beliefs. We do not claim to have found an ideal method of belief elicitation.

  3. Subjects reported their beliefs to the nearest 0.1 LD. Admittedly, incentives for accuracy were lost when guesses were not within 1 LD of the actual amounts. However, strictly incentive compatible mechanisms, such as the one used by Croson (2007), where payoffs are inversely related to the absolute differences between guesses and the actual amounts, also provide increasingly small rewards for accuracy as guesses diverge from the actual amounts. We favored a mechanism heavily rewarding accuracy within small margins of the actual amounts. Subjects received positive amounts 50 % of the time (634/1,280), so on average, they had a reasonable chance of receiving payoffs for their guesses.

  4. That is, subjects made contribution decisions and reported their beliefs on the same screen in z-Tree (Fischbacher 2007).

  5. Fischbacher and Gaechter (2010) do not specify the order in which subjects choose contributions and report beliefs.

  6. The results are very similar to those obtained using multiple other methods, including random effects and tobit models, as well as a model estimated by feasible generalized least squares, accounting for an autoregressive component in the error structure of the multiple observations from each subject.

  7. An F-test of equality of coefficients is not straightforward because the standard errors of the Arellano-Bond model are not computed in the usual way.

  8. A third potential source of bias is omitted variables. However, fixed effects (in the case of specification (2)) and differencing (in the case of specification (3)) account for time invariant omitted variables.

  9. Not shown, but available upon request.

  10. We are unaware of other experimental economics papers using lagged variables as instruments for endogenous regressors. However, using lagged variables as instruments is not new. In fact, the Arellano-Bond method uses lagged variables as instruments for the lagged dependent variable.

  11. Sargan and Basmann test statistics are not available following cluster-robust estimation. The p-values given are those calculated following 2SLS estimation with a variance/covariance matrix that is not cluster-robust. However, this only makes it more likely that the null hypothesis is rejected.

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Authors and Affiliations

  1. Department of Social Science and Policy Studies (SSPS), Worcester Polytechnic Institute (WPI), 100 Institute Road, Worcester, MA, 01609, USA

    Alexander Smith

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  1. Alexander Smith
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Correspondence to Alexander Smith.

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Financial support from Worcester Polytechnic Institute (WPI) is gratefully acknowledged.

The author thanks John Spraggon, Younghwan Song, two anonymous reviewers, Editor Jakob K. Goeree, seminar participants at Union College, and conference participants at the 2011 CEAs in Ottawa, the 2011 International ESAs in Chicago and the 2011 North American ESAs in Tucson for excellent comments and suggestions. Financial support from Worcester Polytechnic Institute (WPI) is gratefully acknowledged.

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Appendix

Appendix

Table 3 First stage of Instrumental Variables (IV) regression—Regression of beliefs on instruments
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Smith, A. Estimating the causal effect of beliefs on contributions in repeated public good games. Exp Econ 16, 414–425 (2013). https://doi.org/10.1007/s10683-012-9345-5

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