4.1 Random-effects meta-analysis

Figure 2 shows a forest plot of the estimated gender gap for each of the 117 conditions in our sample; and the random effects results are also reported in Online Appendix Table A1. We show the results both separately for the standard DG and the charity DG, and pooled for both DG versions. Women give on average 4 percentage points more than men and the gender gap is statistically significant. The average donation in our data is 32% of the endowment (see Table 2) and women on average give 13% more than men (Cohen’s $d=0.16$ )Footnote ⁵. The standard deviation in the true effect size–the variation between studies over and above sampling variation–is slightly higher than the average effect size at $\hat{\tau }$ = 4.6 percentage points. To further assess heterogeneity in the gender gap, we estimate the gender gap in the standard DG and the charity DG respectively.

In the standard DG where the recipient is another participant, women on average donate 2.3 percentage points more than men, with a standard deviation in the true effect size of $\hat{\tau }$ = 3.3 percentage points. In the charity DG the gender gap is larger, with women on average giving 10.9 percentage points more than men with a standard deviation in the true effect size of $\hat{\tau }$ = 6.4 percentage points. A meta-regression in Table A2 confirms that there is a statistically significant difference in the gender gap between the standard DG and the charity DG. The gender gaps of 2.3 percentage units in the standard DG and 10.9 percentage units in the charity DG imply that women give 9% more than men in the standard DG (Cohen’s $d=0.10$ ) and 26% more than men in the charity DG (Cohen’s $d=0.35$ ).

Excluding the ‘all or nothing’ conditions reduces the gender gap found in the overall sample from 4 to 3.1 percentage points (Cohen’s $d=0.13$ ), but it remains statistically significant with heterogeneity in the true effect size of $\hat{\tau }$ = 3.8 percentage points. In the charity DG the gender gap is reduced from 10.9 to 8 percentage points (Cohen’s $d=0.27$ ), with heterogeneity $\hat{\tau }$ = 4.7 percentage points. The smaller gender gap in the charity DG decreases the meta-regression estimate of the difference in the gender gap between the standard DG and the charity DG from 8.7 to 5.9 percentage points.

Fig. 2

Random effects model (estimated with the Ipdmetan command in Stata). a Contains experiments with the standard DG and b contains experiments with the charity DG. The diamonds indicate the estimated effect size (and the CI) for each sub sample and the pooled (overall) effect size is at the bottom

4.2 Individual level regression analysis

In Table 3 we report the results of the individual level regression analysis. In column 1, where we only include a binary variable for the gender of the dictator, women give on average 4.8 percentage points more than men, which is similar to the gender gap of 5.8 percentage points reported in Engel (Reference Engel2011). Controlling for the charity DG in column 2 gives an overall gender gap of 4 percentage points, which is identical to the gender gap found with the random-effects meta-analysis.Footnote ⁶ In column 3-6 we add an interaction between the female variable and the charity DG. The gender gap is statistically significantly larger in the charity DG compared to the standard DG in all four specifications, with an interaction coefficient of between 9.3 and 9.8 percentage points. Women give on average around 2 percentage points more than men in the standard DG and 11–12 percentage points more in the charity DG. These gender gaps are statistically significant for both types of DG in all the four regression models, except for the standard DG in column 3 where there is suggestive evidence of a gender difference (p = 0.0058). If we exclude the ‘all or nothing’ conditions, the results are similar (see Table 4).

Table 3

OLS results of the estimated gender gap in the DG. Standard errors clustered on the condition level in parentheses

	(1)	(2)	(3)	(4)	(5)	(6)
	Share	Share	Share	Share	Share	Share
Female	0.048 ${}^{\ast \ast \ast }$	0.040 ${}^{\ast \ast \ast }$	0.020 ${}^{\ast }$	0.020 ${}^{\ast \ast \ast }$	0.023 ${}^{\ast \ast \ast }$	0.021 ${}^{\ast \ast \ast }$
	(0.010)	(0.008)	(0.007)	(0.006)	(0.006)	(0.006)
Charity DG		0.194 ${}^{\ast \ast \ast }$	0.144 ${}^{\ast \ast \ast }$	0.141 ${}^{\ast \ast \ast }$
		(0.029)	(0.029)	(0.035)
Charity DG * Female			0.094 ${}^{\ast \ast \ast }$	0.093 ${}^{\ast \ast \ast }$	0.097 ${}^{\ast \ast \ast }$	0.098 ${}^{\ast \ast \ast }$
			(0.018)	(0.017)	(0.016)	(0.016)
Constant	0.300 ${}^{\ast \ast \ast }$	0.263 ${}^{\ast \ast \ast }$	0.272 ${}^{\ast \ast \ast }$	0.463 ${}^{\ast \ast \ast }$	0.302 ${}^{\ast \ast \ast }$	0.362 ${}^{\ast \ast \ast }$
	(0.012)	(0.012)	(0.011)	(0.050)	(0.007)	(0.025)
Condition fixed effects	No	No	No	No	Yes	Yes
Individual controls ${}^a$	No	No	No	Yes	No	Yes
Treatment controls ${}^b$	No	No	No	Yes	No	No
Female +(Charity DG * Female)			0.113 ${}^{\ast \ast \ast }$	0.114 ${}^{\ast \ast \ast }$	0.120 ${}^{\ast \ast \ast }$	0.119 ${}^{\ast \ast \ast }$
			(0.016)	(0.015)	(0.015)	(0.014)
Observations	15,016	15,016	15,016	15,016	15,016	15,016
Number of conditions	117	117	117	117	117	117

^aIndividual controls: Student characteristics, age and region

^bTreatment controls: Double-blind, setting characteristics, random payment and partitioning of endowment

* $p<0.05$ , ** $p<0.005$ , *** $p<0.001$

Table 4

OLS results of the gender difference in the DG, excluding the “all or nothing” DG study. Standard errors clustered on the condition level in parentheses

	(1)	(2)	(3)	(4)	(5)	(6)
	Share	Share	Share	Share	Share	Share
Female	0.035 ${}^{\ast \ast \ast }$	0.028 ${}^{\ast \ast \ast }$	0.020 ${}^{\ast }$	0.021 ${}^{\ast \ast \ast }$	0.023 ${}^{\ast \ast \ast }$	0.021 ${}^{\ast \ast \ast }$
	(0.009)	(0.007)	(0.007)	(0.006)	(0.006)	(0.006)
Charity DG		0.184 ${}^{\ast \ast \ast }$	0.147 ${}^{\ast \ast \ast }$	0.137 ${}^{\ast \ast \ast }$
		(0.036)	(0.034)	(0.035)
Charity DG * Female			0.066 ${}^{\ast \ast }$	0.067 ${}^{\ast \ast }$	0.065 ${}^{\ast \ast \ast }$	0.066 ${}^{\ast \ast \ast }$
			(0.022)	(0.020)	(0.018)	(0.017)
Constant	0.289 ${}^{\ast \ast \ast }$	0.268 ${}^{\ast \ast \ast }$	0.272 ${}^{\ast \ast \ast }$	0.496 ${}^{\ast \ast \ast }$	0.317 ${}^{\ast \ast \ast }$	0.373 ${}^{\ast \ast \ast }$
	(0.012)	(0.011)	(0.011)	(0.046)	(0.007)	(0.026)
Condition fixed effects	No	No	No	No	Yes	Yes
Individual controls ${}^a$	No	No	No	Yes	No	Yes
Treatment controls ${}^b$	No	No	No	Yes	No	No
Female + (Charity DG * Female)			0.086 ${}^{\ast \ast \ast }$	0.087 ${}^{\ast \ast \ast }$	0.088 ${}^{\ast \ast \ast }$	0.087 ${}^{\ast \ast \ast }$
			(0.021)	(0.019)	(0.017)	(0.016)
Observations	13,614	13,614	13,614	13,614	13,614	13,614
Number of conditions	107	107	107	107	107	107

^aIndividual controls: Student characteristics, age and region

^bTreatment controls: Double-blind, setting characteristics, random payment and partitioning of endowment

* $p<0.05$ , ** $p<0.005$ , *** $p<0.001$

4.2.1 Robustness checks

In a robustness test, we estimate a mixed random effects model where we allow for both the intercept and the gender gap to have random effects on the condition level.Footnote ⁷ These results are reported in tables A3 and A4. We find very similar results in these estimations, although the pooled gender gap of 4.6 percentage points is slightly higher. The gender gap in the standard DG is around 2 percentage points and the gender gap in the charity DG is 11 percentage points and significantly higher than in the standard DG. The gender gap is statistically significant in both the standard DG and the charity DG, both with and without the ‘all or nothing’ conditions included.

In a second robustness test, we re-estimate our results using a tobit model. The action space is limited to a donation between 0 and 1 even though some subjects may possibly prefer to take from the recipient or give more than the endowment. In the tobit model we allow censoring to occur at both 0 and 1. We report these results in tables A5 and A6, and the coefficients in these tables should be interpreted as the gender gap with respect to the latent (that in theory can take on both negative values and values above 1) dependent variable. The tobit model yields higher estimates of the gender gap, with a gender gap of 6.6 percentage points in the pooled sample. The gender gap is around 4 percentage points in the standard DG and 17 percentage points in the charity DG, and this difference is statistically significant. The gender gap is statistically significant in both the standard DG and the charity DG, both with and without the ‘all or nothing’ conditions included. As can be seen from Fig. 1, men are more likely to donate zero in both the standard DG and the charity DG and women are more likely to donate the full endowment in the charity DG. These differences at the censoring points of 0 and 1 result in a higher estimated gender gap in the tobit model when these observations are interpreted as being censored.

So far we have measured the gender gap as the difference in the share of the endowment donated. As both men and women donate more in the charity DG it is possible that the gender gap is larger in percentage points but not in terms of percentage of the average donation. We test this in an additional robustness check where we instead use the measure from Eq. (2) below, where we divide the individual share donated in the DG $\left(s_{\mathrm{ij}}\right)$ by individual i that took part in condition j by the average donation in condition j,

(2) $\begin{array}{c}{\hat{s}}_{\mathrm{ij}}=\frac{s_{\mathrm{ij}}}{\overline{s_j}}.\end{array}$

Multiplying this measure with 100 allows us to interpret each observation in terms of percent of the average donation within the condition that the participant took part.

Our results are confirmed by this standardization when we include all the DG studies in Table A7. Women on average give around 9% more than men in the standard DG and 25% more in the charity DG; and this difference is statistically significant. In Table A8 we carry out this analysis excluding the “all or nothing” DG study. This reduces the gender gap in the charity DG by one fifth to around 20%, and the gender gap is not statistically significantly larger in the charity DG any more (but there is suggestive evidence for a larger gender gap in the charity DG in all models). When we measure donations in relative terms the evidence of a larger gender difference in the charity DG is thus less strong, as the donations are larger on average in the charity DG compared to the standard DG.

4.3 Gender in the title of the studies

Of the 53 (117) papers (conditions) included in our study 16 (31) have gender in the title of the paper, and we test if the gender difference differs between papers with and without gender in the title.Footnote ⁸ If we observe such a difference we cannot tell if this is due to that studies explicitly designed to study gender differences lead to different results, or if the difference is due to that studies with gender in the title were framed as studies of gender differences and published because they found a significant gender difference. We return to the issue of publication bias in Sect. 4.5.

A meta-regression in Table A9 provides no evidence that the gender gap differs between papers with gender in the title and the other DG studies. We also estimate Eq. (1) in an OLS model in Table A10, where we include a dummy for “gender in the title”, that is interacted with the female variable to test if the gender gap is significantly larger in papers with gender in the title. The null results from the meta-regression are confirmed in the OLS model. In Table A10 we also report the estimated gender difference among the subset of papers with gender in the title (it is the sum of the gender coefficient and the interaction coefficient) and it is between 3.8 and 3.9 percentage points when we include both types of DGs, and between 2.6 and 2.9 percentage points for the standard DG and between 10 and 10.8 percentage points for the charity DG. The gender difference is statistically significant in all models except in model 3 where there is suggestive evidence.

4.4 Statistical power

In Table A11 we summarize the statistical power to detect the gender gap found in this meta-analysis. The power estimates are based on estimating the mean difference between males and females using two-sided hypothesis testing, and they are based on the average standard deviation of the standard DG papers (STD = 0.233) and the charity DG papers (STD = 0.310). We use the random effects results of a gender difference of 2.3 percentage units in the standard DG and 10.9 percentage units in the charity DG to estimate power in each DG type; but we also report power for the overall gender difference of 4 percentage units for both types of DGs. We do the power calculations for tests at the 5% level, as that is most commonly used in the literature. But we also report results for the more stringent 0.5% threshold used in this paper.

We calculate the sample size as the total number of observations in a paper, which means that we sum over all conditions within the paper. The median sample size in the standard DG papers is 130 observations, which yields a statistical power of only 9% (16%) to detect an effect size of 2.3 (4) percentage points. To reach 80% power a paper would need around 3224 (1068) observations to detect an effect size of 2.3 (4) percentage points in the standard DG. The median sample size for the charity DG papers is 192 observations, yielding 68% (14%) power to detect an effect size of 10.9 (4) percentage points. All the above estimates are based on tests at the 5% level, and using the more stringent 0.5% threshold leads to even lower power (see Table A11).

Some of the included DG studies were not designed to study gender differences, which may explain the inadequate power. However, the power for studies that have gender in the title of the paper are only slightly higher. There are 13 papers in the standard DG and three papers in the charity DG that have gender in the title of the paper. The median sample size of the 13 standard DG studies is 191, which gives 10% (22%) statistical power to detect a 2.3 (4) percentage units gender difference. The median sample size of the three charity DG studies is 216, which gives 73% (16%) statistical power to detect a 10.9 (4) percentage units gender difference.

4.5 Publication bias

Figure A1 shows funnel plots for the full sample, the standard DG sample, and the charity DG sample with the estimated effect sizes on the x-axis and the corresponding standard errors on the y-axis. An asymmetric plot could be evidence of publication bias, where only significant studies are published. The outliers at the far right in Figure A1 (a) and A1 (c) are two of the ‘all or nothing’ conditions. The funnel plots in Figure A1 do not provide any clear visual evidence of publication bias. In Figure A2 we restrict the funnel plots to papers with gender in the paper’s title. There is no clear visual evidence of any asymmetry in these plots either.Footnote ⁹

To statistically test if there is evidence of publication bias we have employed Egger’s and Begg’s tests of publication bias in Table A12. We find no evidence of publication bias in either the pooled sample or when looking at each dictator game separately. We furthermore carry out these tests including only papers with gender in the title, but we do not find a statistically significant publication bias in these tests either.