4.1 Extensive-margin analysis

We now turn to the experimental results, focusing first on the extensive margin, as measured by the variable will donate. Results are shown in Table 3, where we use a logistic regression model with robust standard errors. We report average marginal effects for all logistic regressions.

Table 3

Effect of shortage and hygiene treatments on donation willingness at the extensive margin

	Dependent variable: will donate
	(1)	(2)	(3)	(4)	(5)
	All	All	All	Donors	Non-donors
Shortage	0.1044***	0.0935***	0.0989***	0.0463	0.1479***
	(0.0321)	(0.0310)	(0.0275)	(0.0348)	(0.0421)
Hygiene	− 0.0730**	− 0.0803**	− 0.0669**	− 0.0771**	− 0.0573
	(0.0327)	(0.0314)	(0.0280)	(0.0379)	(0.0412)
Baseline mean	0.6700	0.6700	0.6700	0.8270	0.5330
Adj. $R^2$ (McFadden)	0.0196	0.0995	0.2586	0.2285	0.2115
N	1207	1207	1207	552	655
Base controls	No	Yes	Yes	Yes	Yes
Additional controls	No	No	Yes	Yes	Yes

Average marginal effects from logistic regressions. Base controls are explained in Sect. 3.5. Missing variable indicators included for controls. Additional controls include (non-)donor reasons and happiness with last donation (see OA). Base category in all specifications: control. Robust standard errors are reported in parentheses. The symbols *, **, and *** represent significance levels of 10%, 5%, and 1%, respectively

Table 3, column 1 regresses the binary dependent variable will donate on the two treatment dummies without controls, pooling donors and non-donors together. Informing participants about the shortage increases the donation willingness by 10.4pp, on average. This is driven by non-donors becoming willing to donate, showing an increase of 14.8pp relative to the control group (column 5). The extensive-margin willingness of prior donors does not change in response to the treatment, on average.

Second, the hygiene treatment causes a reduction in donation willingness of -7.3pp, on average in (column 1), which was entirely driven by prior donors (-7.7pp, column 4). Hence, communication of the the COVID-19 donation regulations crowds out the motivation of prior donors. It is unlikely that the reduction in donation willingness is driven by sorting out of donors who have recently been infected with SARS-CoV-2, as they could intend to donate next month.

Together, these findings suggest that providing information about the supply shortage is useful to maintain or increase the blood supply, and that informing donors about hygiene requirements, despite attempting to reduce uncertainty about safety, potentially makes the costs of donation more salient. These costs could come from, e.g., mask-wearing, or increased salience of donation risks, which we address below.

4.2 Intensive-margin analysis

In the next specification, we tested if there was a change in the willingness to donate quickly in response to our treatments. The shortage treatment should have a stronger effect on immediate donations, as respondents are told that the shortage is occurring at present. Further, treatment effects of both conditions might be smaller if some donors are fearful of contracting SARS-CoV-2 while donating, who might postpone donation to after the COVID-19 lockdown has ended.

First, in the top-left panel of Fig. 1, we show the distributions of responses to donation intentions by treatment. These show a significant shift to the left (intention to donate faster) for the shortage condition (Mann–Whitney U test (“MW-U” hereafter): $p<0.0000$ ), and a marginally significant shift to the right for the hygiene treatment (MW-U: $p=0.1023$ ). The shortage condition shows significant intention to donate faster than the hygiene condition (MW-U: $p<0.0000$ ).Footnote ³

In the second from top panel in the left column of Figure 1, we focus on donors, who intend to donate more quickly in the shortage condition (MW-U: $p=0.0007$ ), but do not intend to donate less quickly in the hygiene condition (MW-U: $p=0.9108$ ). The variance of donors’ intentions in the hygiene condition is greater than in the control condition (Fligner–Killeen's test: $p=0.0121$ ), which we explore below. Non-donors, shown in the third from top panel of Figure 1, intend to donate more quickly in the shortage condition (MW-U: $p=0.0005$ ) and less quickly in the hygiene condition (MW-U: $p=0.0696$ ).

For all intensive-margin analyses, we ran ordered logistic regressions with next week taking the lowest category, next month taking the second-lowest, and so on. This means the coefficient sign should be interpreted opposite to above. These regressions deliver similar results (Table 4 shows a summary, see Tables A.4–A.7, OA, for full results). The shortage condition consistently shows a positive impact on the intention to donate quickly, while hygiene is less robust.

Fig. 1

Distribution of responses to donation intention by experimental condition. Left column (top 3 panels): all subjects ( $N=1077$ ), donors ( $N=422$ ), and non-donors ( $N=655$ ). Right column (top 3 panels): respondents belonging to ABO blood group O ( $N=227$ ), blood group A ( $N=208$ ) and blood groups B and AB ( $N=113$ ). Bottom two panels: respondents with high fear of contracting SARS-CoV-2 (scale items 4 and 5, $N=296$ ) and low fear (scale items 1–3, $N=777$ ). Bottom two panels include only non-missing fear observations

Table 4

Effect of shortage and hygiene treatments on donation intention at the intensive margin

	Dependent variable: donation intention
	(1)	(2)	(3)	(4)	(5)	(6)	(7)
	All	Donors	Non-donors	Blood type 0	Blood type A	Blood types B and AB	All
Shortage	− 0.6072***	− 0.6931***	− 0.6439***	− 0.4985*	− 0.9119***	− 0.1982	− 0.6276***
	(0.1372)	(0.2148)	(0.1830)	(0.2849)	(0.3207)	(0.4058)	(0.1612)
Hygiene	0.2264	− 0.0272	0.3307*	− 0.1162	0.3344	0.3460	0.0745
	(0.1384)	(0.2183)	(0.1829)	(0.3023)	(0.3083)	(0.4363)	(0.1652)
High fear							− 0.1841
							(0.2140)
High fear × shortage							0.1070
							(0.3075)
High fear × hygiene							0.5238*
							(0.3037)
N	1077	422	655	227	208	113	1073

This table shows log-odds from ordered logistic regressions of donation intention (see Table 2) on condition dummies, without controls. Next week takes the lowest category and not donate takes the highest category. The symbols *, **, and *** represent significance levels of 10%, 5%, and 1%, respectively

4.3 Heterogeneity analyses

We now conduct heterogeneity analyses. One test that might suggest donors are reacting to the supply shortage specifically, is an heterogeneity analysis by own blood group. The shortage treatment in both Tuebingen and Cologne highlighted that blood groups O and A are especially needed. Hence, one expects that respondents with these blood groups will intend to donate fastest. Responses by blood group are shown in the right column of Figure 1. We find that intentions to donate quickly increase in the shortage treatment for blood groups O (MW-U: $p=0.0735$ ) and A (MW-U: $p=0.0039$ ), but less so for blood groups B and AB (MW-U: $p=0.575$ , ties prevented exact calculation). This is robust when estimating ordered logistic regressions by blood group (Table 4, columns 3–6, and Table A.7, OA).

One might ask why the hygiene treatment backfired. This might depend on the increased risk of personal harm via infection risk, or increased donation cost due to waiting times. Survey evidence has found a baseline reduction in donations for individuals with high fear of SARS-CoV-2 infection risks (Chandler et al., Reference Chandler, Neumann-Böhme and Sabat2021), but not yet identified interactions with policies.

First, we explore whether there are effect differences along fear of contracting the SARS-CoV-2 virus. We split subjects into a high-fear group (reporting 4 or 5, $N=296$ ) and a low-fear group (1 to 3, $N=777$ ). Responses by fear group are shown in the bottom two panels of Figure 1. The hygiene treatment shows a significant reduction in donation intention speed for high-fear (MW-U: $p=0.0161$ ), but not for low-fear (MW-U: $p=0.6617$ ). Hence, one potential channel is the increased salience of contracting SARS-CoV-2 due to hygiene information. In column 7 of Table 4, we estimate interactions between treatments and fear in an ordered logistic regression. The significantly positive interaction effect of the hygiene treatment with high fear suggests that the hygiene treatment likely backfired by making donation risks more salient. The effect magnitude, but not significance, is robust to including interactions with risk, time, and base controls (Table A.5, OA).

Next, we focus on sensitivity to, e.g., scheduling appointments, as proxied by time preference (which we label patience here for readability). Spearman's $\rho$ (patience, fear) is 0.0782, indicating time is a separate dimension. We do not find significant or large differences in the hygiene treatment by below-median patience (Figure A.2, OA, $N=471$ , MW-U: $p=0.1625$ ) or above-or-equal-to-median patience (Figure A.2, OA, $N=598$ , MW-U: $p=0.4021$ ). Interaction effects from ordered logistic regressions are less than half the size of the fear interaction and insignificant (column 3 of Table A.5, OA).

We do not find differences in the hygiene treatment between below-or-equal-to-median risk tolerance ( $N=569$ ) and above-median risk tolerance ( $N=508$ ) individuals (Figure A.2, OA, MW-U risk-tolerant: $p=0.2322$ , MW-U risk-averse: $p=0.2455$ ). Interaction effects from ordered logistic regressions are small and insignificant (column 1, Table A.5, OA). Spearman's $\rho$ (risk, fear) is $-0.2622$ , indicating that fear and risk tolerance are somewhat related.

4.4 Social pressure

An important question raised by the literature on the welfare effects of giving is whether social pressure drives giving (DellaVigna et al., Reference DellaVigna, List and Malmendier2012). In our study, the Tuebingen shortage treatment may induce social pressure as the blood groups with low (high) storage levels show sad (happy) emojis (Figure A.1, OA). The Cologne treatment does not contain this framing. Both treatments indicate that blood groups with A and O are urgently needed. Hence, we test the social pressure effect of emojis by analyzing effect heterogeneity between Tuebingen and Cologne.

Figure A.2, OA, shows the distributions of responses for Tuebingen and Cologne. Both Tuebingen and Cologne respondents intend to donate more quickly in response to the shortage treatment (MW-U: $p<0.0000$ and $p=0.0678$ , respectively). We also estimate interaction effects between treatments and the Cologne dummy in an ordered logistic regression (Table A.6, OA). The odds-ratio (transformed from Table A.6) for the shortage group in Tuebingen (reference group) is 0.53 ( $p<0.0000$ ), and the odds-ratio of the interaction between shortage and Cologne is 1.11, and insignificant ( $p=0.7479$ ). This suggests our results are not entirely driven by social pressure or framing.