3.1 Contributions by endowment origin

In line with the existing literature, contributions in the public goods game do not differ significantly across treatments, i.e., effort levels. Of their equally high endowment, subjects contribute 55% in the Low and 48% in the High Effort treatment ( $p=.210$ , independent t testFootnote ¹³; $p=.230$ , Mann–Whitney U test, $n=116$ ; Fig. 1).

Fig. 1 Mean contributions by treatment group (sample size in parentheses)

3.2 Contributions by cognitive ability

For the analysis of contributions by cognitive ability, I divide the sample into individuals with high (40% of the sample) and low cognitive skills (60%). High CRT (Low CRT) individuals answered all three (two or less) questions correctly. Across treatments, contributions of individuals with a high CRT score are not significantly different to those of their low CRT counterparts, both contributing around 51% ( $p=.885$ , t test with unequal variances; $p=.826$ , Mann–Whitney U test, $n=154$ ; Fig. 2). This suggests that subjects with low and high cognitive ability do not differ in how much they contribute to a public good when the dominant strategy is to give nothing.

Fig. 2 Mean contributions by CRT scores (sample size in parentheses)

3.3 Contributions by endowment origin and cognitive ability

A breakdown of contributions by treatment and CRT results confirms the hypothesis derived in Sect. 1. As depicted in Fig. 3, I find that subjects’ contributions depend on the interaction of their cognitive abilities and their endowment source. On the one hand, individuals with a low CRT score contribute 62.9% in the Low Effort treatment and 43.9% in the High Effort treatment. An independent t test shows that this difference is significant ( $p=.008$ , t test; $p=.016$ , Mann–Whitney U test, $n=63$ ) and demonstrates that a low CRT score is associated with behaviour exhibiting the house money effect. On the other hand, contributions by individuals with a high CRT score do not differ significantly by endowment source, 48% in the Low versus 55% in the High Effort treatment ( $p=.496$ , t test; $p=.578$ , Mann–Whitney U test, $n=53$ ). This suggests that subjects with higher cognitive ability are less likely to exhibit the house money effect.

The endowment source determines whether subjects with a low CRT score appear to be more or less co-operative than subjects with a high CRT score. In the Low Effort treatment, contributions by subjects with low CRT scores are 14.8 percentage points higher than contributions by subjects with high scores, 62.9 versus 48.1% ( $p=.044$ , t test; $p=.053$ , Mann–Whitney U test, $n=65$ ). Thus, subjects with low CRT scores behave relatively more co-operatively when they had to exert less effort to obtain their endowment. Contrarily, in the High Effort treatment, their contributions are 10.8 percentage points lower than those of subjects with high scores (43.9 versus 54.7%). However, this difference is not statistically significant, possibly due to a too small sample size ( $p=.250$ , t test; $p=.295$ , Mann–Whitney U test, $n=51$ ).Footnote ¹⁴ Hence, while being more co-operative than subjects with high CRT scores in the Low Effort treatment, subjects with lower CRT scores behave similarly to the high CRT scorers and possibly less co-operative when using earned income. An independent t test shows that this interaction of treatment and CRT scores is statistically significant ( $p=.029$ ).

Fig. 3 Mean contributions by CRT score and treatment group. Error bars indicate 95% confidence intervals (sample size in parentheses)

3.4 Multivariate analysis

The interaction effect is also robust to controlling for gender, age, and session effects. Similar to Harrison (Reference Harrison2007), I resort to the Hurdle model (2) that accommodates the extensive and intensive margin of decisions in public goods games. As depicted by Fig. 4, a large fraction of subjects (11.0%) decides to contribute zero to the public good.

Fig. 4 Histogram of contributions

The Hurdle model therefore has two components. First, it estimates whether a subject contributes anything at all (3). Second, it fits a linear outcome model (4). It can be characterised by the following set of relations (see Botelho et al., Reference Botelho, Harrison, Pinto and Rutström2009, for a discussion of the Hurdle model)

(2) $\begin{array}{cc}{y}_i& =s_i{h}_i^{\ast },\end{array}$

(3) $\begin{array}{cc}\text{with}{s}_i& =\left(\begin{array}{c}1\text{if}{x}_i\gamma +{ϵ}_i>0\\ 0\text{otherwise,}\end{array}\right)\end{array}$

(4) $\begin{array}{cc}\text{and}{h}_i^{\ast }& =x_i\beta +{\nu }_i,\end{array}$

where $y_i$ is the estimated contribution. $s_i$ is the selection variable which is 1 if a subject is estimated to contribute a positive amount and 0 otherwise. $h_i^{\ast }$ , the latent variable, is a subject's expected contribution, conditional on the contribution being positive. $x_i$ is the vector of explanatory variables. I include the same variables in both the selection and the outcome model. Thus, $\gamma$ and $\beta$ are the corresponding vectors of coefficients, and ${ϵ}_i$ and ${\nu }_i$ are error terms.

Table 1 reports the estimation results using the dummy for CRT score. While none of the control variables has a significant effect on the contribution to the public good, the required effort to earn the original endowment significantly reduces contributions by subjects with low cognitive skills by $-21.5$ , given they decide to contribute. Due to the interaction effect, $\text{High Effort}\times \text{High CRT}$ of 30.6, this effect vanishes for subjects with high CRT scores. Surprisingly, none of the variables has a significant effect on the extensive margin. I am grouping the intensive and extensive margin in Appendix B, obtaining a qualitatively identical result.

Table 1 Maximum-likelihood estimates of the Hurdle model of contributions using the binary treatment variable (High Effort) and the binary CRT variable High CRT

	Contribution	Selection (Probit)
High Effort	− 21.474*	− 0.620
	(8.605)	(0.629)
High CRT	− 11.746	− 0.836
	(7.145)	(0.573)
High Effort $\times$ High CRT	30.617**	0.670
	(11.565)	(0.763)
Age	1.603	− 0.101
	(1.316)	(0.074)
Male	7.077	− 0.863
	(5.977)	(0.505)
Constant	30.724	4.859**
	(27.811)	(1.754)
Session Effects	Yes	Yes
N	116

Notes: The variable High Effort is a binary variable, which takes a value of one if the subject is assigned to the High Effort treatment and zero for the Low Effort treatment. Therefore, the regression is run on 116 observations of the Low and High Effort treatment, excluding those of the Medium Effort treatment. High CRT is equal to 1 if the subject has answered all CRT questions correctly and 0 otherwise. Male is equal to one for males and zero otherwise

Standard errors in parentheses; $\ast$ $p<0.05$ , $\ast \ast$ $p<0.01$ , $\ast \ast \ast$ $p<0.001$

Computing the predicted values based on the coefficients of both stages of the Hurdle model confirms the interaction effect and the differences within treatments observed in the non-parametric analysis (see Table 2). Individuals with low CRT scores contribute 22.1 percentage points less in the High than in the Low Effort treatment (combined marginal effect of the variable High Effort for Low CRT subjects, $p=.006$ ). For subjects with high CRT scores, the difference is positive (they contribute more), but not significant (7.9, combined marginal effect of the variable High Effort for High CRT subjects, $p=.443$ ). The difference between individuals with low and high CRT scores is 16.8 (combined marginal effect of the variable High CRT, $p=.023$ ) in the Low Effort treatment and $-$ 13.1 (combined marginal effect of the variable High CRT, $p=.144$ ) in the High Effort treatment.

Table 2 Contributions as estimated by the Hurdle model

	Low effort	High effort	p-value
Low CRT	64.6	42.6	0.006
High CRT	47.7	55.6	0.443
p-Value	0.023	0.144

To conclude, subjects with low CRT scores exhibit the house money effect, giving more in the Low than in the High Effort condition. By contrast, contributions by subjects with high CRT scores are statistically indistinguishable. Moreover, subjects with low CRT scores give more than their high CRT counterparts in the Low Effort treatment, but less in the High Effort treatment. As these differences partly cancel out, it seems that cognitive ability does not affect co-operative behaviour when pooling treatments.Footnote ¹⁵

3.5 Discussion

The results raise the question whether studies that find no significant effect of effort in public goods games but do not account for cognitive ability should at least find suggestive evidence for a house money effect.

In fact, Antinyan et al. (Reference Antinyan, Corazzini and Neururer2015) obtain a negative but insignificant effect of effort on contributions in their No Punishment treatment as well as in their Punishment treatment without controlling for an interaction of time and effort. Further, effort reduces the proportion of endowment contributed to the public good in Cherry et al. (Reference Cherry, Kroll and Shogren2005). Finally, Clark (Reference Clark2002) finds suggestive but insignificant evidence for a house money effect in the initial round of a repeated public goods game. Similarly, with an experimental design that addresses issues with the design of Clark (Reference Clark2002), Bailey et al. (Reference Bailey, Ramalingam and Stoddard2022) find no significant house money effect, but slightly higher contributions by subjects who received the endowment on the day of the experiment (their house money treatment) versus 3 weeks prior to the experiment (which subjects mostly viewed to be their own money by the time the public goods game was played).

Hence, the interaction between cognitive ability and the house money effect in my experiment, combined with previous studies showing similar but insignificant effects in the same direction, suggests that their insignificance results may be the consequence of homogenous subject pools (university students in all mentioned studies). A house money effect might be more prevalent in a cross-section of society. Also, my experiment was not designed to investigate the persistence of a house money effect. However, the revealed interplay between cognitive skills and endowment origin asks for further experiments investigating the house money effect over time across distinct cognitive types.

Despite the evidence of a house money effect among subjects with lower cognitive skills and the broad existence of a house money effect in dictator games (Cherry, Reference Cherry2001; Cherry et al., Reference Cherry, Frykblom and Shogren2002; Cherry & Shogren, Reference Cherry and Shogren2008; Reinstein & Riener, Reference Reinstein and Riener2012; Oxoby & Spraggon, Reference Oxoby and Spraggon2008; Carlsson et al., Reference Carlsson, He and Martinsson2013), it remains unclear whether the origin of the endowment indeed affects social preferences. Alternatively, unearned income or income that required little effort might just be more loosely handled without any pro-social motive. Identifying the exact psychological mechanism should be the purpose of future research.