Risking Your Health to Help Others: The Effect of Pandemic Severity on Volunteering

The COVID-19 pandemic affected the provision of voluntary work across the globe. We study informal volunteers who buy and deliver groceries for people in a high-risk group or in quarantine. Using data from a volunteering grocery delivering app in Switzerland that coordinated these volunteers, we are able to track volunteering during the pandemic. Combined with public health data on cases and deaths, we test how the severity of the pandemic affects the provision of voluntary work in the form of neighborhood grocery deliveries. We find a positive effect of the number of deaths on voluntary deliveries. However, in contrast to the literature studying the effect of the severity of the pandemic on giving, this effect is concave. We suggest that this concave effect is due to the signal of risk of infection implied by rising death rates, which is at odds with the signal of need to help others.


Introduction
Catastrophes like earthquakes or pandemics can affect thousands of people, which can lead to a drastic increase in the demand for help.As catastrophes often occur unexpectedly, professional services might not be able to meet this demand for help (NHS, 2020), which often leads to volunteers joining the helping efforts.For example, survivors of an earthquake might join rescue efforts, and in the COVID-19 pandemic volunteers delivered groceries to people who had to self-isolate, as professional delivery services were not able to meet the demand (Meyersohn, 2020).While there are accounts showing that catastrophes lead to a wave of solidarity (Carlsen et al., 2020;Zaki, 2020), the jury is still out for how COVID-19 affected volunteering around the globe.While some spoke of a wave of solidarity that led to a surge in volunteering (UNRIC Brussels, n.d.), other studies found that the pandemic led to a decrease in formal volunteering (Dederichs, 2022).While the effect of catastrophes like COVID-19 on helping behavior is still disputed, we know even less about how the severity of a catastrophe affects helping behavior.There is some evidence from cross-sectional studies showing that earthquake severity correlates with volunteer turnout (Iizuka & Aldrich, 2022).However, to the best of our knowledge, there is no evidence on how the severity of a long-lasting catastrophe like the COVID-19 pandemic affects individual helping behavior in the form of informal volunteering.From a theory standpoint, it is not clear whether the evidence from these cross-sectional studies translates to a longitudinal setting.From a standpoint of practical relevance, lack of such evidence makes disaster management suboptimal, since officials cannot gauge how professional helping services are complemented by informal help as the catastrophe intensifies or diminishes.
This work aims to provide such evidence by answering how the severity of the COVID-19 pandemic (as measured by the case and death numbers) affects informal volunteering 1 (in the form of grocery food deliveries).To answer this research question, we use data on volunteer grocery food deliveries from a mobile application (app) that was designed to match people who need groceries delivered (i.e., because they had to self-isolate) with people who were willing to do so on a voluntary basis.The app launched in March 2020 as the first wave hit Switzerland and terminated its service in May 2021 as the need for this kind of help eventually subsided.Over this time period, almost 27,000 people registered to do deliveries.The platform registered a total of 78,961 orders and 72,379 successful deliveries.We use fixed effects regression models to test how the weekly case and death numbers relate to the number of weekly deliveries made by individuals.To identify the effect of the case and death numbers on deliveries, we control for the number of orders placed and the number of other volunteers that are registered in a volunteer's delivery area.
We find that the death numbers have a concave (i.e., significant positive linear and negative quadratic) effect on the number of deliveries made.The case numbers show no consistent effect across the models.Thus, consistent with previous studies on how the severity of a catastrophe affects volunteering, the severity of the COVID-19 pandemic (i.e., number of deaths) seems to have had a positive effect on informal volunteering.However, previous studies reported a linear and not a concave effect (Iizuka & Aldrich, 2022;Rotolo et al., 2015).We argue that the concavity of the effect is caused by the risk of getting infected when volunteers go out to deliver groceries.Our results are relevant both from a theoretical and from a practical point of view.First, we show that the evidence from cross-sectional studies translates only partially to a longitudinal setting.Second, we show that the risk that volunteering poses to one's health seems to have a negative effect on informal volunteering.Third, our results are valuable for practitioners, as it allows for better planning on how volunteer helping services will complement professional helping efforts.As most orders were also delivered, our results also show that platform mediated matching of volunteers with volunteering opportunities is an effective and efficient way of volunteer management and might be a viable solution to deal with the problem of an oversupply of volunteers (Simsa et al., 2019).The following section gives a short overview of volunteering during the COVID-19 pandemic and then introduces the limited literature that examines how the severity of a disaster affects prosocial behavior (e.g., volunteering and donating).The "Methods" section introduces the methods and data used, the "Results" section presents the results, and the "Discussion and Conclusion" section discusses how the study contributes to research on informal crisis volunteering.

Volunteering During the COVID-19 Pandemic
Only few studies provide insights regarding who engaged in (in)formal volunteering during the pandemic.Mak and Fancourt (2021) found that older people were more likely to participate in neighborhood volunteering than younger people.They also found that people who lived in urban areas were less likely to engage in neighborhood volunteering.Regarding psychosocial factors, they found that people with a larger social network and with higher levels of social support were more likely to participate in all types of voluntary work.People with a diagnosed disability or illness had lower odds of volunteering in neighborhood support (Mak & Fancourt, 2021).According to a review by Mao et al. (2021) local knowledge, social trust, and social networks were key dimensions associated with community organizing and volunteering.Volunteers were mostly women, middle-class, highly educated, and working-aged people.Similarly, Dederichs (2022) found that formal volunteering was more common among women, university graduates, elderly individuals, and those with high levels of selfrated health.These are characteristics that were also found to be positively related to volunteering before the pandemic (Wilson, 2012).Dederichs (2022) also investigated which socio-demographic characteristics are linked to formal volunteering in response to COVID-19.Being healthier, holding a university degree and being a woman was significantly positively associated with volunteering in response to COVID-19 (Dederichs, 2022).Already volunteering before the pandemic was the strongest predictor of volunteering in response to COVID-19 while age and whether children were present in the household had no significant effect.
Regarding the activities the volunteers engaged in, a review by Mao et al. (2021) suggests that especially during the early days of the pandemic, food shopping, and providing emotional support were the most common activities.In the later stages of the pandemic, there was a shift toward activities that address the wider impact of the pandemic on areas such as homelessness, mental health, and employment (Mao et al., 2021).Jones et al. (2020) report that neighborhood support, from giving food and medical prescription assistance to providing health information and raising morale through humor was common in the United Kingdom.Mao et al. (2021) report a shift from offline to online volunteering, as the circumstances imposed by COVID-19 made offline volunteering challenging.
Studies that looked at how the amount of volunteering provided changed during the pandemic found that formal volunteering declined (Dederichs, 2022) and informal volunteering remained at a stable level (Cnaan et al., 2022).Mak and Fancourt (2021) report that older adults, people with more social support and people with higher education were doing more voluntary work during the pandemic than before.On the other hand, people living in urban areas were less likely to have increased their volunteering.
Given this short overview of volunteering during the pandemic, we now move on to literature that studied how the severity of a catastrophe affects prosocial behavior.

Prosocial Behavior During Catastrophes
There is evidence showing an increase in volunteering following disasters, such as floods (Harris et al., 2017), hurricanes (Michel, 2007), terrorist attacks (Beyerlein & Sikkink, 2008), and foreclosures (Rotolo et al., 2015).This research also showed that the individuals who volunteered in response to these disasters displayed characteristics that are mostly similar to those of regular volunteers.However, Rotolo and Berg (2011) find that volunteers who volunteer for disaster relief tasks tend to be younger and less educated compared with volunteers who perform more general volunteering tasks.While there is evidence showing that disasters tend to lead to an increase in (disaster-related) volunteering, the literature on how the severity of a disaster/crisis relates to the amount of volunteering during/after the crisis is very limited.To study the link between the severity of a crisis and volunteer turnout, Rotolo et al. (2015) used data from 120 U.S. metropolitan areas to assess the association between the foreclosure crisis and volunteering.They found that areas that experienced an increase in foreclosures also experienced an increase in volunteering rates.Using the variance in the severity of 57 disasters in Japan, Iizuka and Aldrich (2022) found that the number of deaths and missing persons as well as the size of the population affected by the disaster correlate most strongly with volunteer turnout.
Because the literature on the effect of the severity of crises/disasters on people's willingness to help in the form of volunteering is limited, we also make us of the donation literature to gain more insights into this relationship.While we acknowledge that the motives of volunteering and donating money differ in some ways, much of the literature deals with the concept of altruism as a motivation for both volunteering and donating money (Bekkers & Wiepking, 2011;J. Carpenter & Myers, 2010).This also holds true for the COVID-19 pandemic: Dury et al. (2022) found that altruism was the predominant motive for providing help during the first lockdown in Belgium, as 86.4% of the motives for providing help were linked to altruism.Adena and Harke (2022) conducted an experiment to estimate the impact of COVID-19 severity on charitable donations using participants from England.They found that an additional 1% of cases resulted in an increase in donations by 2 to 11 pence.The authors suggest that increased awareness about COVID-19, due to higher local severity, was responsible for this effect.This interpretation was supported by a positive correlation between media coverage about the severity of COVID-19 and donations.Adding a COVID-19 reference to the donation request also increased donations.While Adena and Harke (2022) provide causal evidence that the severity of the COVID-19 pandemic positively affects donations, the study provides no insight into which psychological mechanism could be responsible for this effect.Because Adena and Harke (2022) attribute the effect to an increased awareness about COVID-19, empathy is a likely candidate.The increased awareness about COVID-19 and its negative effects on society could lead individuals to feel empathy with the victims of COVID-19, which would then lead to increased altruism reflected in the form of monetary donations or volunteering (a well-documented link according to the empathyaltruism hypothesis (Batson et al., 1991)).
This interpretation is in line with the reasoning of Zheng et al. (2021), who studied the effect of the severity of collective threats on people's donation intention.Zheng et al. (2021) studied whether collective threats, such as the COVID-19 pandemic, positively affect people's intention to donate.They used environmental pollution and the COVID-19 pandemic to examine this effect and found that the severity of a collective threat has a positive effect on people's intention to donate to others facing the same threat.They found that this effect is serially mediated by people's other-focused attention and empathy.These results generalize nicely to our setting, as the volunteers in our sample also helped people that face the same threat as them and because Swiss people tended to see the COVID-19 pandemic as a collective threat (Albrecht et al., 2021).
While volunteering is a form of prosocial behavior and is likely motivated at least partly by similar motives (J.Carpenter & Myers, 2010), there is an important difference between donating and volunteering: the risk of the act of helping.A donation can be placed from the safety of one's own home, while groceries cannot be delivered without getting into contact with others, which means subjecting oneself to the risk of getting infected with COVID-19.The risk of becoming infected is especially high if one is in an enclosed space with many other people (Noorimotlagh et al., 2021).This is the situation one encounters when going grocery shopping.The risk of becoming infected in situations such as this has been communicated and emphasized repeatedly by public health officials. 2Thus, in the case of voluntary grocery deliveries, the positive effect of the severity of the COVID-19 pandemic on prosocial behavior (i.e., voluntary grocery deliveries) stands in conflict with the effect of one's own risk of becoming infected.
There is ample evidence showing that volunteers were afraid of becoming infected due to their volunteering activities during the COVID-19 pandemic (Cervera-Gasch et al., 2020;Lazarus et al., 2021).This very likely had a negative effect on volunteering.Ding et al. (2021) showed that fear of getting infected negatively affected intentions to perform voluntary work, but only if it included social contact.This effect was mediated by the state anxiety people experienced during the pandemic.A study by Rosychuk et al. (2008) also shows that risk perception had a negative effect on the decision to volunteer during an influenza pandemic.This negative effect is amplified by the evidence that shows that COVID-19 risk perception and prosociality are correlated (Dryhurst et al., 2020).Thus, given that volunteering in our case involved social contact and that our sample is by definition made up of prosocial individuals (i.e., volunteers), the fear of getting infected likely had a negative effect on volunteering in our setting.Therefore, while the reviewed literature suggests that rising case and death numbers should lead to more deliveries, this effect might be diminished by the rising risk of making deliveries, especially for prosocial individuals.Given that in earlier pandemics, volunteers were willing to incur health risks for volunteering (Yonge et al., 2010), we do not think that this effect will completely offset the assumed positive effect of the severity of the pandemic.
Based on the reviewed literature that shows that the severity of disasters has a positive effect on prosocial behavior (i.e., volunteering), we hypothesize that the severity of the COVID-19 pandemic, as measured by the case and death numbers, had a positive effect on the amount of volunteering performed by individuals in our sample:

Hypotheses 1 (H1):
There is a positive effect of weekly case and death numbers on the number of deliveries made per week.
A death from COVID-19 is more severe than simply contracting COVID-19 (i.e., a case).Given the literature that shows that the severity of disasters has a positive effect on prosocial behavior, we would, therefore, expect an increase in the death numbers to have a larger positive effect on volunteering than an equal increase in case numbers: Hypotheses 2 (H2): The effect of the number of deaths on the number of deliveries made is larger than the effect of the number of cases on the number of deliveries made.
The reviewed literature also showed that the risk of getting infected with COVID-19 and the health impacts thereof negatively affect volunteering.We hypothesize that rising case and death numbers will be perceived as a signal of the risk of volunteering and will therefore dampen the positive effect of the severity of the pandemic on volunteering.This hypothesis draws on the appraisal-tendency framework (Lerner & Keltner, 2000, 2001), which states that fear amplifies risk estimates.In the context of COVID-19, Harper et al. (2021) also found that fear of COVID-19 and risk perception were correlated.Thus, fear of not getting optimal treatment if one contracts COVID-19 likely amplifies the perceived risk of contracting COVID-19.As this fear is arguably higher when case and death numbers are high and the health care system operates at or even over capacity, this amplification is stronger when case and death numbers are high.The positive effect of threat severity on protective behavior (e.g., staying at home) is also formalized in theories like the health belief model (Janz & Becker, 1984) and the protection motivation theory (Rogers, 1975).These theories posit that the likelihood and magnitude of potential outcomes (e.g., likelihood of contracting COVID-19, magnitude of adverse health outcomes) affect protective behavior (Brewer et al., 2007).The positive association between protective health behavior and both the perceived likelihood of contracting a disease and its expected severity was demonstrated by meta-analyses (Brewer et al., 2007;C. J. Carpenter, 2010;Floyd et al., 2000).Transferred to our setting, these theories suggest that protective behavior (e.g., staying at home) increases as rising case and death numbers lead to an increase in the likelihood and magnitude of adverse outcomes (i.e., potentially severe illness due to COVID-19).Based on these theories and evidence, we expect a concave effect of the case and death numbers on the number of deliveries made.

Hypotheses 3 (H3):
The effect of the case and death numbers on the number of deliveries made is concave.
Of course, the case and death numbers can only influence people's decision to volunteer if individuals are aware of those numbers.In a representative sample from Switzerland (collected in June 2020), half of the respondents knew the absolute number of COVID-19-related deaths, and a third of the respondents correctly stated the 7-day incidence rate (Albrecht et al., 2021).Combined with the broad covering of these numbers on the news, we are thus confident that this was the case.
In what follows, we present the data that allow us to test these hypotheses.

Methods
The "Amigos" Platform and Data Before describing the platform and data, we shortly provide some background about the Swiss context.According to the Swiss Volunteering Survey (Lamprecht et al., 2020), 39% of the population aged 15 and above engage in formal voluntary work through clubs and organizations, while 46% participate in informal voluntary work by serving as caretakers, assisting others, or supporting events and projects outside the scope of clubs and organizations.As Switzerland is a welfare state, individuals that suffered a loss of income due to the pandemic were supported by the government.Switzerland's federal insurance programs that address sickness, unemployment, accidents, and old age work effectively and provide generous levels of benefits (Armingeon et al., 2021).Trust in others and especially in neighbors is high in Switzerland (Ortiz-Ospina & Roser, 2016).
The Amigos platform was launched as a cross-sector collaboration between Switzerland's largest retailer (Migros) and Pro Senectute, Switzerland's largest nonprofit for elderly people.The purpose of Pro Senectute is to maintain and enhance the well-being of the elderly in Switzerland.It does this by providing services for elderly both through professionals and through volunteers.The Amigos platform allowed people who belonged to a risk group or who currently had to self-isolate to place grocery orders.These orders could then be delivered by volunteers who themselves signed up on the platform to do these deliveries.When volunteers signed up, they had to specify the geographical radius from which they wanted to be notified when an order was placed (Figure 1 left).Once the volunteers signed up, they saw a list of orders that were placed and are still open for delivery (Figure 1 right).Each item in the list shows the date and time window in which the order should be delivered and the zip code of the delivery address.It also shows how many items should be bought, how many shopping bags are (approximately) needed to carry the groceries, and the rating of the person who placed the order.
Deliveries happened on a voluntary basis, but the person who placed the order could tip the delivery person via the app or in person.The volunteers were thus able to receive some form of remuneration, but the platform capped the maximum tip.The cap was first set to five Swiss francs.However, the operators of the platform noticed that almost all deliveries were tipped to the full five Swiss francs.Because of this ceiling effect, they decided to raise the cap to first seven and then nine Swiss francs.This remuneration is much below the remuneration paid by for-profit actors for similar services (e.g., Uber Eats) and much below the opportunity cost of volunteering (Wallrodt & Thieme, 2022).Therefore, using the definition of volunteering by Cnaan et al. (1996), delivering groceries still qualifies as voluntary work.Migros provided us with an anonymized version of the data they collected.

Data
The data contain the date and status of each order (i.e., if the order has been successfully delivered and if yes by whom).For people who signed up to do deliveries, we have data on their age and sex.We also know the size of their delivery area (the zip codes they received notifications from when an order was placed).We augmented the Amigos data with COVID-19 case and death number data provided by the Swiss Federal Office of Public Health.We first calculated the 7-day rolling average for both death and case numbers for each day before taking the mean of the resulting averages for each week.To control for the number of orders placed in a person's delivery area, we summed all orders that were placed in the person's delivery area in a given week.We use the number of deliveries made in a given week by a person as the dependent variable (DV).This gives us an unbalanced panel data frame with a total of 26,960 individuals with up to 57 observations (i.e., weeks) per individual.A descriptive table of the data can be found in Table 1 and will be discussed in more detail in the "Results" section.

Regression Models
To identify the effect of the case and death numbers on the number of deliveries made by a volunteer, we need to control for the number of orders that were placed in a volunteer's delivery area.This is to control for the indirect paths of the case and death numbers on the number of deliveries made that is mediated by the number of orders in a volunteer's delivery area.The same applies to the number of other delivery persons that are in a volunteer's delivery area (see Figure 2).By doing this, we can estimate the direct effect of the case and death numbers on the number of deliveries made by a volunteer.There is one caveat to our identification strategy: raising case numbers also means that more volunteers will become infected, rendering them unable to make deliveries.We would mistake the reduction in deliveries caused by this as a reduction in the willingness to do these deliveries.It might thus be that we slightly underestimate the effect of case numbers on deliveries if it is positive or overestimate the effect if it is negative.However, we believe that this bias is small, as the proportion of people who were infected in a given week was still rather small.We use fixed effects regression models to estimate this direct effect by predicting the number of deliveries a volunteer made in a given week.The advantage of the fixed effects estimator is that it controls for unobserved heterogeneity on the level of volunteers that is constant over time (e.g., risk perception, trait empathy).As our DV is the number of deliveries a volunteer made in a given week, we assume that the DV follows a Poisson distribution and thus use Poisson regression models.The Poisson model assumes that the mean and variance are the same, an assumption that is often violated.We nevertheless adhere to the Poisson model because it is more robust than models that incorporate an additional parameter to allow for over-or underdispersion (i.e., the negative binomial model) (Blackburn, 2015).
For the reasons mentioned above, all regression models control for the number of orders placed in the person's delivery area, the number of other delivery persons in the person's delivery area, and the interaction between these two.We run three model specifications: the first model uses case and death numbers as independent variables, the second model only the death numbers, and the third model only the case numbers.We run each of these models once with case and death numbers that were aggregated over Switzerland and once with the local numbers.With local, we mean that we used the case and death numbers of a volunteer's delivery area.These numbers were available on a cantonal level.If a volunteer's delivery areas spanned multiple cantons, we used the weighted average (weighted by the number of delivery areas in each canton) of the canton's case and death numbers.The models with the local case and death numbers also allow us to use time fixed effects in addition to individual fixed effects.These time fixed effects control for time specific shocks that affected all individuals (e.g., lockdowns).All regression models use Driscoll and Kraay (1998) standard errors, which are robust to heteroscedasticity, serial correlation, and cross-sectional dependence.The lag of the Driscoll and Kraay (1998) standard errors is based on the work of Newey and West (1987).We use the coefficients from the linear effects of the case and death numbers from the fixed effects models to test Hypotheses 1 and 2, and the quadratic effects of these predictors to test Hypothesis 3.

Descriptive Results
Over the period the platform was in use, 26,960 volunteers signed up to deliver groceries.As seen in Figure 3a, most of those signups happened during the early pandemic, that is, while the first wave hit Switzerland.Figure 3a also shows that most of the volunteers who signed up did not end up delivering a single order.Only 7,569 volunteers who signed up also ended up making a delivery.These volunteers made a total of 72,379 deliveries.Figure 3b shows the weekly orders and deliveries.The figure reveals that most of the placed orders were also delivered.The largest relative mismatch between orders and deliveries could be observed in the summer, where both case and death numbers were relatively low.Figure 3c and 3d shows the average weekly case and death numbers, respectively.The pattern of the weekly average number of deaths corresponds better to the number of deliveries than the pattern of the weekly average number of cases.
Figure 4a shows the distribution of the total deliveries per person.Of those who made at least one delivery, most made no more than 10 deliveries in total.However, the upper part of Figure 4a shows that some people ended up making hundreds of deliveries.Figure 4b visualizes the total number of deliveries made by people who made a given number of deliveries.This makes people who made many deliveries more visible because their count is now scaled by the total number of deliveries made by the given group of people who made the same number of total deliveries.Figure 4b shows that there are some people who ended up making many deliveries.To ensure that our results are not driven by these people, we exclude volunteers who ended up making more than 34.3 deliveries (mean + 2 SD).This removed a total of 384 people from our data set (1.4%).While this is a small subgroup, it was  responsible for almost half of all deliveries (35,310 deliveries, 48.7%).We report all results where these outliers are included in the appendix (Tables A1, A3 & A4).Overall, the results are very similar for the models with and without outliers.A person who signed up on the platform ended up making 1.39 (median = 0, SD = 3.99) deliveries on average.The subgroup of people who made at least one delivery on average ended up making 5.16 deliveries (median = 2, SD = 6.29).
Table 1 lists summary statistics of the volunteer's individual characteristics, delivery characteristics and delivery area characteristics.The table is facetted by whether the volunteers ended up making at least one delivery or not.This allows us to see whether these two groups differ in substantial ways in any of the characteristics.The mean age of those who made at least one delivery was slightly lower than the mean age of those who did not make any deliveries.Although the difference is small, it is statistically significant.The distribution of sex was not significantly different between the group of people who made at least one delivery and those who did not.Those who ended up making at least one delivery on average received a tip of 5.44 Swiss Francs.Although most of the differences between the two groups are small in magnitude, they are still statistically significant due to the large N. Table A2 in the appendix reports the same results but grouped by outlier status.The nonoutlier group on average received a tip of 5.44 Swiss Francs, the outlier group received a slightly larger tip of 5.71 Swiss Francs on average.The two groups were also relatively similar with regard to the other characteristics reported in Table A2.However, two notable differences emerged.First, the outlier group on average had a larger number of delivery areas (16.20) than nonoutliers (8.56).Second, volunteers from the outlier group on average signed up earlier (3.39 weeks after platform launch) than volunteers from the nonoutlier group (7.38 weeks after platform launch).Both factors likely contributed to the larger number of deliveries made by the volunteers in the outlier group.

Regression Model Results
Table 2 reports the estimated regression models.Looking at the coefficients of the case and death numbers, we see that the effects of the death numbers are more consistent across the models than the effects of the case numbers.The case numbers have a significant negative effect in the models with the aggregated case and death numbers (models 1 and 3).But the significance of this effect vanishes once time fixed effects are introduced (model 4) or even turns significantly positive when the effect of the death numbers is not accounted for (model 6).A similar pattern holds for the effect of the squared case numbers that we used to check for the nonlinearity of the effect.The effect of the squared case numbers is positive (models 1 and 3) but again vanishes in the models with the local case and death numbers (models 4 and 6).In contrast to the number of cases, the effects of the number of deaths are consistent across all models.Across all models (models 1, 2, 4, and 5), the number of deaths has a positive effect on the number of deliveries made per week.The sign of the squared death numbers is negative across all models (models 1, 2, 4, and 5), indicating a concave effect.The fact that testing capacities increased over time (Federal Office of Public Health, 2022) could explain why the effect of the number of deaths is robust to the inclusion of time fixed effects, while the case numbers are not.In large part due to the increased testing capacity, case numbers were generally much higher in later stages of the pandemic than they were, for example, in the first wave (Wu et al., 2020).Only the models with the time fixed effects control for this.We thus think that the negative effect of the case numbers on the number of deliveries made in the models with the aggregated case and death numbers is an artifact of that.Because deaths are thus a more consistent measure of the severity of the pandemic, past research similar to ours opted to only use death numbers as a predictor (Fridman et al., 2022).However, for the sake of transparency, we opted to use both case and death numbers.
The effect of a one-unit increase in the death numbers on the rate of deliveries depends on the value of the death numbers because of the exponential form of the Poisson model and because of the quadratic term.We therefore calculate the ratio of the expected rates of delivery for two consecutive case-or death numbers.The formula to do this is the following: where β 1 represents the coefficient of the linear effect and β 2 .reflects the coefficient of the quadratic effect.Notice that this ratio still depends on the value of x because of the quadratic term.A one-unit increase in the local death numbers when going from one to two local deaths (values close to the median) changes the rate of delivery by a factor of ~1.07 when using the coefficients from model 5 in Table 2.The effect for the same model but with lagged values (Table 3) is slightly larger (~1.09).The values for the models where the case numbers are also included are very similar.Because of the quadratic effect of the death numbers, this factor gradually declines until an increase in the number of deaths leads to a decrease in the ratio of expected deliveries (see Figure 5).This happens at around 11 local deaths for the model with the lagged deaths and at around 13 deaths for the models without lag.
Looking at our hypotheses, we can only partially confirm hypothesis 1.Only the number of deaths, but not the number of cases, had a consistent positive effect on the number of deliveries made in all models.We can hence confirm Hypothesis 2, namely, that the number of deaths has a larger effect on the number of deliveries made than the number of cases.Because only the effect of the number of deaths is concave, we can partially confirm Hypothesis 3.
The models discussed so far used the case and death numbers of the week in which the deliveries were also made.However, it might be that the volunteers need some time to adapt their behavior to a change in case and death numbers.We therefore fitted the same models with case and death numbers lagged by 1 week.These models are presented in Table 3.
The fit statistics are better for the models with the lagged case and death numbers.This supports the conjecture that volunteers need some time to react to changes in case  (which is to be expected since the case and death numbers are autocorrelated), we will not repeat them here and refer the reader to Table 3.This also means that the conclusion regarding our hypotheses remains unchanged.Since gauging the nonlinearity of an effect from regression coefficients is difficult, we plotted the effect of the case and death numbers in Figure 5.We do this only for the models with the local case and death numbers since we believe that these models are more robust.We also only plot the coefficients from models where both the linear and the nonlinear terms were significant, this drops all case number coefficients.Plots for all regression models where both effects were significant are reported in the appendix for completeness (Figure A1). Figure 5 shows the concave effect of the number of deaths on the number of deliveries made that even turns slightly negative at the far end of the spectrum.However, as indicated by the boxplot on the top of the figure, the effect was positive for most of the time.
Finally, looking at the coefficients of the control variables, we see that across all models, the number of other delivery persons in a volunteer's delivery area is negatively associated with the number of deliveries made per week.This is expected, as more delivery persons in a delivery area mean that there are more people who can potentially claim an open delivery order.Unsurprisingly, the number of orders placed in a volunteer's delivery area is positively associated with the number of deliveries made per week across all models.The interaction between the last two reported variables is significantly negative across all models.Thus, the more other delivery persons there were in a volunteer's delivery area, the smaller the effect of an additional order.Overall, the signs of these control variables are all what one expects.

Discussion and Conclusion
In this work we tried to answer how the severity of the COVID-19 pandemic affected the provision of voluntary labor in the form of grocery food deliveries.Using fixed effects regression models, we found that the severity of the COVID-19 pandemic (i.e., the number of deaths) has a positive (but concave) effect on the amount of informal volunteer work provided by a given individual.The positive effect of the severity of the pandemic on the amount of volunteering is consistent with earlier, although cross-sectional, literature (e.g., Iizuka & Aldrich, 2022).However, past studies that investigated how the severity of the COVID-19 pandemic affected giving found a positive linear, and not concave, effect of COVID-19 severity on giving (Adena & Harke, 2022;Zheng et al., 2021).We assume that the rising risk of getting infected that is caused and signaled by rising case and death numbers is most likely to be responsible for the concavity of this effect.However, it is curious that we only find a concave effect for the death and not the case numbers, since cases and not deaths cause infections.It could be that higher death numbers signaled a higher risk of negative health events when contracting COVID-19.This would be in line with the introduced literature that shows that fear amplifies risk perception (Lerner & Keltner, 2000, 2001).Evidence from the Health Belief Model could also explain why only the death numbers had a concave effect.A meta-analysis found that that the perceived severity had a larger effect on protective health behaviors than the perceived susceptibility (C.J. Carpenter, 2010).It could be that rising death numbers and news about hospitals reaching capacity made the severity of contracting COVID-19 more salient.As rising case numbers likely only have an effect on perceived susceptibility, the positive effect of rising death numbers on protective health behaviors would be higher than the one of rising case numbers.
A reason why we find different results for case and death numbers might be that people were more motivated to volunteer at the beginning of the pandemic.Indeed, most deliveries were made in the early parts of the pandemic.During that time, the death-to-case ratio was considerably higher than in the second period with many deliveries (winter 2020/2021).The models with the time fixed effects control for this, and the fact that the negative effect of the case numbers vanishes in these models is in line with this conjecture.
There are also other mechanisms that could lead to the observed concave effect, for example, compassion fade (Butts et al., 2019), and our data again do not allow us to rule out one or the other.However, the widespread media coverage about the risks of COVID-19 (Silini, 2020), the correlation between prosociality and risk perception (Dryhurst et al., 2020), and the fact that risk perception negatively influenced the decision to volunteer in past pandemics (Rosychuk et al., 2008) all point to risk perception being the most plausible explanation.The fact that studies that looked at how the severity of the pandemic affected giving did not find a nonlinear effect (e.g., Adena & Harke, 2022) also speaks for risk perception, as compassion fade should affect both giving and volunteering in the same way.This interpretation is also in line with the finding of Mak and Fancourt (2021) that people with a diagnosed disability or illness had lower odds of volunteering in neighborhood support during the COVID-19 pandemic (preexisting conditions are a risk factor for severe COVID-19 outcomes, Jordan et al., 2020).Finally, risk perception has been found to play a role in an earlier survey study conducted on a sample of the population studied here.Trautwein et al. (2020) studied under which conditions volunteers were satisfied with their COVID-19 volunteering mediated by platforms, such as Amigos.They found that the perceived susceptibility to a COVID-19 infection moderated the relationship between the evaluation of the crisis-policy measures implemented by the platform and satisfaction with the volunteering experience.
Regarding the implications for practice, our study provides evidence that online platforms, such as Amigos are an effective and efficient way of matching spontaneous volunteers with people who need help, as more than 90% of the orders that were placed were also delivered.Thus, such platforms prove to be an effective way to address some of the challenges associated with informal volunteering in emergencies and disasters (Daddoust et al., 2021;Whittaker et al., 2015).For example, such platforms might be a viable solution to deal with the problem of an oversupply of volunteers (Simsa et al., 2019).By taking care of the matching before volunteers arrive on site, oversupply is by design not possible.This reduces disappointment on the side of the volunteers and at the same time strengthens confidence in asking for help by beneficiaries.While matching in our case was quite easy because the type of activity was quite simple, it is easy to imagine the use of such platforms in other cases.For example, after a flooding, a platform might match people whose homes have been demolished with people who are willing to help with cleanup/rebuilding.The people affected could list the activities to be performed, the expected duration and the number of volunteers needed, and the platform could facilitate matching based on these criteria.Schmidt and Albert (2022) provide proof of the feasibility of such a paradigm where volunteers self-assign to tasks from an ordered list of recommendations.Betke (2018) lays out in detail how such a platform might work and how it could be successfully integrated into existing structures.In a very recent event, Swiss citizens signed up on online platforms that matched Ukrainian refugees with people who were willing to temporarily host these refugees in their homes (von der Brelie, 2022).By providing low-barrier access to helping opportunities, platforms like Amigos could also be an effective tool to counteract the decline in formal volunteering seen in the early stages of the pandemic (Dederichs, 2022).While it might have been true in the past that spontaneous volunteers cannot be actively "harvested" (Koolen-Maas et al., 2022), our results show that app-mediated active harvesting (i.e., recruiting) of spontaneous volunteers can be done with great success.Such apps can thus be a valuable tool to manage the different types of volunteer resources (Koolen-Maas et al., 2022).
To mitigate the negative effect of the risk of volunteering, such platforms should provide volunteers with information on how to minimize the risk caused by volunteering (e.g., wearing masks).Indeed, in an earlier study conducted on a sample of individuals that used the Amigos platform to volunteer, Trautwein et al. (2020) found that the evaluation of the platforms' crisis-policy measures (e.g., supply of health information) had a positive impact on COVID-19 volunteering satisfaction.This is in line with the findings of Rosychuk et al. (2008).
Given the nature of our data set covering only one task and one country might limit the generalizability of our findings.However, delivering groceries was the most frequent informal volunteering task during the pandemic in other countries (e.g., Mao et al., 2021), and there is no reason to expect that our proposed underlying mechanism that drives our results should radically differ across countries.As our research concerns behavior during a pandemic/crisis, it is not clear whether or how these findings generalize to normal times.Generally, our study supports existing studies that emphasize the use of technology to improve volunteer matching in normal times (Chui & Chan, 2019).The fact that the demographic profile of COVID-19 volunteers resembled that of people who volunteer during normal times (Mak & Fancourt, 2021) promises at least cautious transferability.This also alleviates concerns regarding a selection bias of our sample.However, we acknowledge that there could still be selection bias, as we do not know how the group of people who signed up on the platform compares to the group of people who did not.It is possible that the group who signed up could have been more prosocial and/or less risk averse than the group of people who did not sign up.While not ruling out selection, the fact that the platform was designed and advertised by two of the most wellknown organizations in Switzerland should have ensured that the platform was known by many people.Finally, we did not consider the amount of media coverage of the service, which could have influenced the number of volunteers that signed up on the platform and the number of deliveries made by these volunteers.)

Figure 1 .
Figure 1.Left: When Signing Up, Volunteers Had To Specify the Radius From Which They Wanted To Receive Order Notifications.Right: After Signing Up, Volunteers See a List of Open Orders That They Can Choose To Deliver.

Figure 2 .
Figure 2. Depiction of the Assumed Causal Relationship Between the Variables.Dotted Lines Represent Indirect Effects of the Case and Death Numbers on the Number of Deliveries Made by a Volunteer.Solid Lines Represent the Direct Effects That We Isolate With the Regression Models.

Figure 3 .
Figure 3. (a) Number of Volunteer Signups per Week.The Color Represents Whether the Volunteers Who Signed up Ended up Delivering at Least One Order or not.(b) Number of Orders and Deliveries per Week.(c) Number of COVID-19 Cases per Week.(d) Number of COVID-19 Deaths per Week.

Figure 4 .
Figure 4. (a) Histogram of the Total Number of Deliveries Made Per Person.Because Some Volunteers Made a Lot of Deliveries, We Zoomed Into the Distribution in the Lower Part of the Figure as Indicated by the Gray Shading in the Upper Part of the Figure.(b) Distribution of the Total Number of Deliveries Made by Bins That Represent Volunteers Who Made a Given Number of Total Deliveries.
standard errors in parentheses Signif.codes: ***.001, **.01, *.05.and death numbers.Because the results are very similar to those reported in Table 2

Figure 5 .
Figure 5. Plot of the Combined Linear and Nonlinear Effects of the Local Death Numbers on the Number of Deliveries Made as Reported in Tables 2 and 3.The Box Plot on the Top of the Figure Visualizes the Distribution of the Weekly Local Death Numbers.The y-Axis Has No Numbered Scale Because the Fixed Effects Models Do Not Have an Intercept.

Figure A1 .
Figure A1.Plot of the Combined Linear and Nonlinear Effects of the Aggregated Death and Case Numbers on the Number of Deliveries Made as Reported in Tables 2 and 3.Only Models Where Both the Linear and Nonlinear Effects are Significant are Shown.The Box Plot on the Top of the Figure Visualizes the Distribution of the Weekly Death and Case Numbers.The y-Axis Has No Numbered Scale Because the Fixed Effects Models Do Not Have an Intercept.

Table 3 .
Regression Models With Lag of 1 Week.

Table A3 .
Regression Table With Outliers.

Table A4 .
Regression Table With Outliers and Lag of 1 Week.