Experimental Economics
https://doi.org/10.1007/s10683-021-09732-9
ORIGINAL PAPER
Subsidizing unit donations: matches, rebates,
and discounts compared
Johannes Diederich1 · Catherine C. Eckel2
Timo Goeschl1 · Philip J. Grossman4
· Raphael Epperson3
·
Received: 7 October 2020 / Revised: 8 September 2021 / Accepted: 9 September 2021
© The Author(s) 2021
Abstract
An influential result in the literature on charitable giving is that matching subsidies dominate rebate subsidies in raising funds. We investigate whether this result
extends to “unit donation” schemes, a popular alternative form of soliciting donations. There, the donors’ choices are over the number of units of a charitable good
to fund at a given unit price, rather than the amount of money to give. Comparing
matches and rebates as well as simple discounts on the unit price, we find no evidence of dominance in our online experiment: the three subsidy types are equally
effective overall. At a more disaggregated level, rebates lead to a higher likelihood
of giving, while matching and discount subsidies lead to larger donations by donors.
This suggests that charities using a unit donation scheme enjoy additional degrees
of freedom in choosing a subsidy type. Rebates merit additional consideration if the
primary goal is to attract donors.
Keywords Charitable giving · Unit donation · Subsidies · Online field experiment ·
Framing
JEL Classification C93 · D12 · D64 · H24 · H41 · L31
1 Introduction
Subsidies are a common way of incentivizing charitable giving. They typically take
the shape of rebates, in which a third party (e.g., the government) refunds a fraction
r of the gift back to the donor; or the shape of matches, in which a third party (e.g., a
generous donor) supplements each donation at a rate m, such that the charity
receives a total of (1 + m) times the original donation. Both rebates and matches
* Johannes Diederich
johannes.diederich@awi.uni-heidelberg.de
Extended author information available on the last page of the article
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have been extensively studied and several key findings have emerged in the literature
(see Vesterlund 2016; Epperson and Reif 2019, for comprehensive reviews). Probably the most notable result is that although rebates and matches imply the same price
m
of giving if the corresponding subsidy rates r and m satisfy r = m+1
, overall donations received by the charity are higher under matches than under equivalent rebates
(Eckel and Grossman 2003, 2006a, b, 2008b, 2017; Davis et al. 2005; Lukas et al.
2010; Bekkers 2015; Gandullia and Lezzi 2018; Gandullia 2019).1 Another finding
is that matching subsidies often significantly increase private contributions net of
the subsidy compared to a no subsidy condition without a lead donor (Eckel et al.
2007; Karlan and List 2007; Gneezy et al. 2014; Huck et al. 2015; Eckel and Grossman 2017).2
The literature has established these findings in a setting in which individuals are
asked to decide how much money to give to a charity, arguably the most common
scheme for soliciting donations. We refer to this as a money donation scheme. Yet
another frequently applied strategy is to frame the donor’s choice variable not in
terms of money, but in terms of physical units of a charitable good awaiting funding.
A prominent example that has attracted donors from all over the world is ShareTheMeal, a smartphone app and initiative of the UN World Food Programme, which
is used to provide food to children in need. Donors for ShareTheMeal do not simply
choose an amount of money to give. Instead, they are informed that feeding one
child for a day costs $0.80 and are then asked to indicate the number of feeding days
(“meals”) that they would like to fund.3 We refer to this alternative scheme as a unit
donation scheme.
Do the key findings about the effects of matches and rebates in money donations
generalize to the alternative unit donation scheme? In this paper, we examine the
effect of subsidies on unit donations by conducting an online field experiment. We
asked 558 subjects how many units of a charitable good they would like to provide
to a predetermined charity, funded out of their reward for answering an unrelated
online survey. The decision variable was framed in quantities of nutritional packages provided for malnourished children in South Sudan. The charity we worked
with, Sign of Hope, provided this service for $0.50 per nutritional ration. This cost
served as the unsubsidized unit price in our donation experiment. In the baseline,
no subsidy was offered. The main treatments differed across three subsidy types and
two subsidy rates. The first type, the rebate, was offered at a rate of either 33% or
1
In this literature, rebates are realized without any delay. If a delay is involved (as is the case for tax
deductions), time preferences need to be considered. Furthermore, we are aware of only one paper that
finds the same level of charity receipts between rebates and matches, but it does so under a choice architecture that does not resemble a typical donation decision: In Davis (2006), subjects do not decide how
much to donate (checkbook giving) but how much the charity receives (charity receipts). This choice
architecture, motivated by an investigation of the causal mechanism that underpins the standard result of
non-equivalence, makes it difficult to compare his results with ours.
2
There are counterexamples to this finding, however (e.g., Karlan et al. 2011; McCarty et al. 2018).
3
Similar food provision campaigns are the “100 Thousand Meals” appeal of the Salvation Army Australia or the “Help with €2” campaign of Misereor, the German Catholic Bishops’ Organisation for
Development Cooperation.
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Subsidizing unit donations: matches, rebates, and discounts…
50% such that a third party refunded to the subject about one third or one half of the
reward she spent on nutritional packages. The second type, the match, was offered
at a rate of 0.5 (1:2) or 1 (1:1) such that a third party added a nutritional package for
either every two or each package donated. The third subsidy type is novel for the
study of charitable giving and took the form of a per unit price discount of either
33% or 50% (with a third party covering the remaining cost). In other words, the unit
was offered to subjects for either $0.33 or $0.25, instead of $0.50. This subsidy type
is without a direct parallel in money donations.
The contribution of this paper is threefold. First, we define unit donations as a
separate class of charitable donations distinct from money donations. Second, we
investigate how rebates and matches perform in a setting of unit donations and compare the results to the established literature on money donations. Based on betweensubjects evidence, our core result is that matches and rebates are equally effective in
incentivizing private net donations and in generating total charity receipts. In other
words, we do not replicate the superiority of matching subsidies observed in the case
of money donations. Third, we check whether, in a setting of unit donations, the discount subsidy offers an attractive alternative to these subsidy types. We find that discounts are equally effective as matches and rebates when considering net donations
or charity receipts. This may well be good news for charities: In a world in which
subsidy types perform equally well, charities enjoy additional degrees of freedom in
campaign design. At the same time, the different subsidy types perform differently
when disaggregated into the extensive and the intensive margin of giving: Rebates
are more effective than matches in attracting donors, but matches result in larger
donations. Under discounts, the likelihood of giving is lower than under rebates, and
on both margins, behavior corresponds to that under matches. We conclude that if
attracting donors is a secondary objective of a fundraising campaign that uses unit
donations, rebates merit additional consideration. New donors offer the possibility
of an ongoing income stream for charities, since previous donors are more likely to
give in the future (Eckel and Grossman 2008b; Landry et al. 2010).
The remainder of the paper is organized as follows. In a background section
(Sect. 2), we contrast money and unit donations, explain the mechanics of subsidizing the latter, and review the relevant literature. Section 3 describes our experimental design, followed by a presentation of our main results in Sect. 4, and a discussion
of potential explanations in Sect. 5. Section 6 concludes.
2 Background
2.1 Unit versus money donations
For our purposes, we define a money donation scheme as a solicitation scheme in
which potential donors are asked to decide how much money to give to a charity.
It is arguably the most common scheme for solicting donations. Academic papers
in the lineage of the now classic donation models (Bergstrom et al. 1986; Andreoni
1988, 1989) capture its main features by generally assuming a linear production
technology for the charitable public good and normalizing the per-unit price of both
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J. Diederich et al.
the private and the public good to one. In such models, the prospective donor i’s
choice is to divide her endowment wi (in dollars) between private consumption xi (in
dollars) and giving gi (in dollars) to the charitable good, G. Under a money donation
scheme, therefore, the donor’s choice variable gi is denominated in terms of monetary expenditures.
By contrast, we define a unit donation scheme as a solicitation scheme that frames
the donor’s choice variable in terms of physical units of a charitable good awaiting funding. Unit donation schemes have a popularity that extends beyond the food
programs mentioned above. Development aid agencies, for example, promote child
sponsorships by fixing the monthly donation for the sponsorship—usually around
$35—and prospective donors choose the number of child-months to sponsor rather
than the amount of money to donate. Similarly, fundraising drives for biodiversity
conservation or reforestation programs let donors indicate the number of acres or
trees to fund.4 In unit donation schemes, the price of a unit of the charitable good G
is no longer implicit. Instead, the fundraiser states an explicit price p and asks how
many discrete units gi the potential donor would like to fund. In this respect, the setting resembles early models of the private provision of public goods that are explicit
about units and prices (e.g., Warr 1983). Under a unit donation scheme, therefore,
the donor’s choice variable gi is denominated in terms of the quantity of the charitable good funded.
Although donors eventually provide money under both schemes, there are important differences between unit and money donations. First, donors’ choice sets differ. Under a unit donation scheme, the units of the charitable good to be provided
are typically indivisible, which introduces an element of discreteness that is largely
absent in the virtually continuous money donations. Second, the information provided to prospective donors differs. By stating the per-unit price of the charitable
good, unit donation schemes make statements about the charity’s marginal cost of
production, whereas money donation schemes frequently provide little information
on the cost structure of producing the charitable good. While information on the
share of fundraising and overhead costs is increasingly available to donors (Ribar
and Wilhelm 2002; Meer 2014), information on the impact of a contribution (or the
absence thereof) can substantially affect donations (Bekkers and Wiepking 2011;
Lewis and Small 2019). Third, the framing of the choice differs. By asking for the
number of physical units of the charitable good, unit donation schemes emphasize
how a donation generates specific outcomes for recipients. As a result, the motive of
giving to create an impact (Duncan 2004) might become more relevant for the donation decision.
Diederich et al. (2021) compare the two donation schemes in an experimental
study and show that the choice of the donation scheme significantly affects the likelihood of receiving donations. The direction of the effect depends on the size of
a physical unit: A unit donation scheme attracts more donors than the equivalent
4
For instance, in the Monarch Butterfly Habitat Exchange program of the Environmental Defense Fund,
donors sponsor acres of milkweed habitat for $35 per acre. In the Plant A Tree program of the Jewish
National Fund, donors choose the number of trees to be planted at $18 a tree.
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Subsidizing unit donations: matches, rebates, and discounts…
money donation scheme if the unit size is small (daily nutritional rations at a price of
$0.50) but fewer donors if the unit size is large (weekly rations at a price of $3.50).
The difference at the large unit size is driven primarily by the restricted choice set
under the unit donation scheme.
2.2 Subsidizing unit donations
Subsidizing unit donations involves some small but important differences compared
to subsidizing money donations. In unit donations, rebates can be applied by refunding a fraction of the donor’s provision costs back to the donor. If, for example, a unit
of the charitable good costs $0.50 and a 50% rebate is offered, the donor receives
$0.25 back for each unit funded. Matches can be applied to unit donations by providing supplementary units of the charitable good. If, for example, a 1:1 match
is offered for tree plantings, the third party funds one additional tree for each tree
funded by the donor. Due to the indivisibility of units, matching payments by the
third party are restricted to complete units of the charitable good. This introduces
some discontinuity in the matching payment if the matching rate is not an integer:
For example, at a matching rate of 0.5 (1:2) every second tree funded by the donor
induces one tree funded by the third party. However, for a donation of only one tree,
there is no additional funding by the third party. This is in contrast to the continuous
choice in money donations, in which the matching rate typically applies to any arbitrary amount in the same way (i.e., at a matching rate of 0.5, a donation of any dollar
amount induces a matching payment of 0.5 times this amount).
The transferability of results from money to unit donations is therefore not only a
matter of framing effects: When matches consist of supplementary units and rebates
are refunded costs, rebates and matches are also no longer theoretically equivalent.
This is particularly evident at the extensive margin of becoming a donor: The smallest positive donation is to fund one unit of the charitable good. Given a unit price p,
this implies a minimum expense of p required under matches. In contrast, rebates
provide a refund on the donation given and, at subsidy rate r, the cost of becoming
a donor is p(1 − r) < p. As a result, rebates are potentially more effective in attracting donors. An additional difference comes into play when subsidy rates take noninteger values: The change in the matching payment due to a one unit increase in
the donation depends on the donation level. In contrast, under rebates any increase
in the donation proportionally increases the subsidy payment, as is the case for both
subsidy types under money donations. In sum, there are not only structural differences between money and unit donations; there are also reasons to expect that subsidies perform differently under the two schemes.
In a way, unit donation schemes resemble the shopping experience for private
goods. For example, WorldVision provides a comprehensive gift catalog where
donors can choose the number of units of various gifts that are associated with
explicit prices.5 In this regard, a matching subsidy is similar to bonus packs or “buy
5
https://donate.worldvision.org/giftcatalog (accessed on March 31, 2021).
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J. Diederich et al.
one get two” offers, whereas a rebate is comparable to coupons that provide an
instant refund at checkout or cash-back programs (although the latter usually involve
a time delay between the payment and the refund). However, with a well-defined
good and an explicit price, there is a third option available, which is a direct price
discount. Similar to stores that advertise price reductions, a charity can announce the
discounted price of a gift and reveal that the gap to the original price is provided by
a large donor or a governmental grant. Hence, if a unit of the charitable good costs
$0.50 and a 50% discount is offered, the donor can fund one unit at a price of $0.25
while being informed that the remaining $0.25 are funded by an external party.
A discount at rate d is theoretically equivalent to a rebate at rate r when d = r .
However, two small differences exist that could cause different behavior.6 First,
rebate subsidies are paid to the donor whereas discount subsidies are paid to the
charity. Second, in comparison to rebates (and matches), discounts obviate the need
for donors to calculate the effective price of giving. In an online charity gift shop
like the one by WorldVision, the rebate would take effect as an instant refund upon
checkout whereas the discount is applied to the advertised prices during “shopping.”
Furthermore, evidence for private goods shows that consumers may indeed respond
different to rebates and direct price discounts (Davis and Millner 2005), which
makes it crucial to distinguish between both subsidy types in our research.
2.3 Related literature
We are not aware of any previous study that conducts a clean comparison between
subsidy types under a pure unit donation scheme. At the same time, there are parallels with a number of papers studying charitable giving. Like our study, Meier
(2007) and Gneezy et al. (2014), for example, feature discrete choice sets. However,
both frame donations in money, rather than physical quantities, and focus on matches
only, yielding results that align with the wider money donation literature. A different
parallel is with Lewis and Small (2019) who also provide subjects with information
about the cost of a unit of impact and test different framings of the information. They
find that a cheaper unit price leads to lower donations, an effect that is eliminated or
reversed if the price is framed in units-per-dollar rather than dollars-per-unit. Yet,
donations in their study are again framed in terms of money, rather than physical
quantities, and the authors do not compare different subsidy types. Also relevant is
a literature in marketing that experimentally compares product promotion strategies
such as bonus packs (which are similar to matching subsidies) and price promotions
(which are similar to our discount subsidy if they explicitly state the effective price).
The papers in this literature provide mixed evidence (see, e.g., Sinha and Smith
2000; Mishra and Mishra 2011; Chen et al. 2012), with bonus packs either being
6
If rebates are realized with a delay, a third difference comes into play: The expenses at the time of the
donation are larger under a rebate than under a discount. In this paper, rebates are realized without delay
as it allows us to compare our rebate to its money donation counterpart in the experimental literature
that brought about the seminal result of matches outperforming rebates (e.g., Eckel and Grossman 2003,
2006b; Davis et al. 2005).
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Subsidizing unit donations: matches, rebates, and discounts…
superior, equivalent, or inferior to price promotions. More in line with the money
donations literature is Davis and Millner (2005), who find that matches outperform
rebates also for private goods and that direct price discounts have an intermediate
effect. While our focus on charitable giving sets our paper apart from this literature,
its setting of unit donations offers the opportunity to study price discounts, a tool
from private product promotion, in the context of charitable donations.
The paper probably closest to the focus of ours is Kesternich et al. (2016). The
authors compare the effectiveness of rebate and matching subsidies in the context of
carbon offsetting: When buying their ticket(s) online, clients of a long distance bus
operator decide whether to offset the carbon emissions from their travel at a given
price per kilogram of emissions. Rebates are found to increase the likelihood of a
decision to offset emissions while matches do so only to a lesser extent and only
for certain matching rates. However, the overall contributions net of the subsidy are
higher under matches. Key differences to our study are the binary decision format
and the use of an impure public good for which the size of giving is tied to the private good. Both limit the comparability of our study and Kesternich et al. (2016). A
few other studies implicitly employ an experimental design soliciting unit donations
to an environmental public good (Löschel et al. 2013; Diederich and Goeschl 2014,
2017, 2018), but they do not compare subsidy types.7
3 Experimental design
3.1 Donation appeal
We adapt the real-donation dictator game introduced by Eckel and Grossman (1996)
and subsequently applied to compare subsidy types (Eckel and Grossman 2003;
Davis and Millner 2005; Davis 2006; Eckel and Grossman 2006a, b). In the standard
version of the game, subjects decide how much of a money endowment to hold and
how much to pass to a charity. In our variant of the game, subjects decide how many
units of the charitable good to fund at a given nominal price.
Our variant of the game requires a charitable good or service that is easily quantifiable. We approached a relief organization, Sign of Hope e.V., which frequently
uses various forms of unit donation schemes in their fundraising campaigns. Among
their activities, we chose the treatment of malnourished children in a certain area of
South Sudan as this service offered practical units and prices for our experiment.
At the time of the experiment, children were treated in two “bush clinics” operated
by the relief organization. Treating one child for one month using a special nutritional paste and high energy cookies required a donation of US$15. We divided this
7
Weakly related to a unit donation scheme are so called “buy-one give-one” business models (see, e.g.,
Marquis and Park 2014; Hamby 2016) where for each product purchased the selling company donates a
similar product. However, in these models, the donation is tied to the consumption of a private good. We
are not aware of any paper introducing or comparing subsidies in that context.
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J. Diederich et al.
Table 1 Treatment conditions
Subsidy type
Subsidy
Nominal
Effective
rate
unit price
unit price
N
No subsidy
–
$0.50
$0.50
83
Rebate
33%
$0.50
$0.33
71
Match
1:2
$0.50
$0.33
85
Discount
33%
$0.33
$0.33
90
Rebate
50%
$0.50
$0.25
58
Match
1:1
$0.50
$0.25
80
Discount
50%
$0.25
$0.25
91
number into practical units of nutritional packages per child and day, which implied
a “price” of $0.50 per package.
The donation appeal was part of an online survey and participants used their
reward for completing the survey ($2) to make any donations. The donation appeal
introduced the charity, the charitable good, and the marginal cost of providing the
charitable good. We also provided a link to the charity’s web page and informed
subjects about a transparency award the charity had won to increase trust in the charity (Adena et al. 2019). The final part of the donation appeal was treatment specific.
Table 1 shows the seven treatment conditions. In the control condition, no subsidy
was applied and subjects chose how many packages to fund at a price of $0.50. The
remaining six treatment conditions follow a 3 × 2 factorial design with one factor
being the subsidy type (rebate, match, or discount) and the other factor being the
effective price ($0.33 or $0.25) implied by the subsidy level. In the instructions, we
framed the rebate conditions as 33% (50%) rebate and stated that while providing
packages would cost the subject $0.50 apiece, a rebate of $0.17 ($0.25) per package
would be added to the subject’s final reward at the end of the experiment. For the
matching conditions, instructions stated that for every two packages (each package)
that the subject provided at a nominal cost of $0.50 apiece, one package would be
matched at no additional cost to the subject. As a result, the charity would receive
the combined number of packages. For the discount conditions, instructions stated
that the subject would be able to provide packages for $0.33 ($0.25) instead of $0.50
apiece. Hence, the nominal price corresponded to the effective price. For all subsidy types, instructions noted that the subsidy, i.e., the rebate, the matched units,
or the money needed to reduce the nominal price, was provided by “a third party.”
This was a truthful yet indefinite reference to the research budget involved. Subjects
chose the desired number of packages from a drop-down menu. The exact wording
of each treatment can be found in Table 2.8
8
Figure C1 in Online Appendix C shows a screenshot of the complete donation appeal.
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Subsidizing unit donations: matches, rebates, and discounts…
Table 2 Final part of donation appeal wording by treatment
Treatment
Wording
No subsidy
In this survey, you may use all, part, or none of your reward of $2.00 for this HIT to
provide these nutrition packages. Thus, you may choose any number between 0 and 4
packages. $0.50 per package will be subtracted from your reward
33% rebate
[Same text as in no subsidy condition]
Upon completion of the survey, a third party has agreed to fund a 33% rebate for each
package you provide. The rebate ($0.17 per package provided) will be added to your
reward
1:2 match
[Same text as in no subsidy condition]
A third party has agreed to match every two packages you provide, at no additional cost
to you. So, for example, if you choose to provide 2 packages, Sign of Hope will receive 3
33% discount
50% rebate
In this survey, you will be able to provide these nutritional packages for $0.33 apiece (a
third party will fund the remaining $0.17). You may use all, part, or none of your reward
of $2.00 for this HIT to provide packages. Thus, you may choose any number between 0
and 6 packages. $0.33 per package will be subtracted from your reward
[Same text as in no subsidy condition]
Upon completion of the survey, a third party has agreed to fund a 50% rebate for each
package you provide. The rebate ($0.25 per package provided) will be added to your
reward
1:1 match
[Same text as in no subsidy condition]
A third party has agreed to match each package you provide, at no additional cost to
you. So, for example, if you choose to provide 2 packages, Sign of Hope will receive 4
50% discount
In this survey, you will be able to provide these nutritional packages for $0.25 apiece (a
third party will fund the remaining $0.25). You may use all, part, or none of your reward
of $2.00 for this HIT to provide packages. Thus, you may choose any number between 0
and 8 packages. $0.25 per package will be subtracted from your reward
A Human Intelligence Task (HIT) is how Amazon Mechanical Turk calls a “self-contained, virtual task
that a Worker can work on, submit an answer, and collect a reward for completing” (Retrieved July 23,
2021, from https://www.mturk.com/worker/help)
3.2 Experimental protocol
We conducted the experiment online recruiting U.S. residents from the online labor
market Amazon Mechanical Turk (AMT).9 In the case of money donations, online
field experiments based on AMT (Gandullia and Lezzi 2018; Gandullia 2019) and
not based on AMT (Bekkers 2015) have been successfully used to replicate the
superiority of matches over rebates. Gandullia and Lezzi (2018) and Gandullia
9
AMT provides several benefits to researchers, among them fast and easy access to subjects, a diverse
subject pool, and low costs (Paolacci et al. 2010; Mason and Suri 2012). Several papers have examined
the suitability of AMT for experimental research and have found encouraging results (Paolacci et al.
2010; Ross et al. 2010; Mason and Suri 2012; Rand 2012). Results in these papers highlight a high internal consistency of self-reported demographics, an incentive-compatibility of earnings, and a “spammer”free workforce from the built-in reputation system. They also present and review results from successful
replications of standard experimental games in AMT (e.g., Paolacci et al. 2010; Rand 2012). In implementing our experiment, we followed the suggestions for researchers in that literature and the Guidelines
for Academic Requesters on AMT (WeAreDynamo 2014).
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J. Diederich et al.
(2019) use the same endowment level and subsidy rates as we do. Our task was
posted five times on the AMT task queue between July and October 2015, resulting
in five online sessions. Interested workers were informed that they would earn $2
for answering a 20-minute academic survey on several topics. The payment is rather
high when compared to the average hourly wage of about $3.1 to $3.5 per worker on
AMT (Hara et al. 2018). Each worker was able to participate only once. Donations
were mentioned as one of the topics, but the real-donation dictator game was not
particularly salient compared to other survey elements. As a result, it is unlikely that
subjects considered the donation task as the main subject of investigation. Interested
workers followed a link which directed them to the survey containing the experiment on Qualtrics. Having followed the link to the survey platform, interested workers read and confirmed an informed consent page about the research study.
The experimental survey consisted of four parts: (1) the donation appeal, (2)
a questionnaire on various topics, (3) a low-stake version of the Eckel-Grossman
Risk Task (Eckel and Grossman 2002, 2008a),10 and (4) a 5-item manipulation
check questionnaire comparable to Eckel and Grossman (2003, 2006b) and Davis
and Millner (2005). Parts (1) and (2) were presented in random order. Hence, a
subject encountered the donation appeal either before or after the questionnaire.
One of the treatment conditions was drawn at random and presented to the subject
(between-subjects design).11 The questionnaire of part (2) consisted of questions on
sociodemographics, employment, and religious beliefs, as well as current ambient
environmental conditions and the Ten Item Personality Inventory (TIPI), which is
a standard one-minute version of more extensive multi-item instruments to assess
the Big Five personality dimensions (Gosling et al. 2003; Ehrhart et al. 2009). After
completion of all survey parts, a unique code was shown that the subject had to enter
into the survey task window on AMT to receive payment.
In total, we have 613 observations of participants starting the survey and 599
completed records. Incomplete records were dropped from the analysis.12 The obvious concern that some subjects may fraudulently use multiple accounts to participate
10
We opt for the Eckel-Grossman Risk Task because of its simplicity and brevity. A sample of AMT
workers is likely to exhibit larger heterogeneity in numeracy than a standard laboratory sample of students. The Eckel-Grossman task has been shown to produce better results with people with low mathematical skills (Dave et al. 2010). Stakes in the Risk Task started out at $0.28 for the sure option and end
up at $0.02 and $0.70 for the most risky gamble.
11
A different sample of 113 subjects received the treatment conditions in a within-subjects (WS) design
to investigate how the results differ if individuals are forced to directly compare different subsidy types.
Unlike in the between-subjects design, matches and discounts are more effective in providing the charitable good than rebates, including a significant crowding-in of net donations for those two subsidy types.
Our analysis suggests that those different results for the WS sample are mostly an artifact of the WS
design, which we consider less externally valid: When confronted with all possible subsidies, subjects
seem to make a single decision at the extensive margin of giving across all subsidy types with a similar
rate and then respond to the subsidy type mostly at the intensive margin. We provide more details about
the WS design and the associated results in Online Appendix D.
12
Among the complete observations, three subjects had restarted the survey and hence created an
incomplete duplicate record. We kept the complete observations of these three subjects after making sure
that they had not encountered a treatment condition in their first attempt and gave the same answers in
the survey.
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Subsidizing unit donations: matches, rebates, and discounts…
more than once is generally seen as a minor problem in online experiments (Horton
et al. 2011; Paolacci et al. 2010).13 We nevertheless follow the common approach
to exclude 40 subjects with duplicate Internet Protocol addresses from the analysis
(Reips 2000; Birnbaum 2004). Including them does not change the results. We also
dropped one subject who indicated an age below 18 in the questionnaire, despite
having confirmed an age above 18 when agreeing to the informed consent statement.
This leaves us with a sample of 558 subjects (see Table 1 for the allocation of subjects across treatments). Average payouts were $1.80 (net of donations and including
an average of $0.33 additional payment for the risk task). Subjects took on average
8.26 minutes to complete the experiment.
4 Results
Variables elicited in the questionnaire suggest a diverse sample of subjects (see
Table B2 in Online Appendix B): Slightly less than half of subjects are female, and
slightly less than half graduated from college. About one-third of subjects are married, and about the same share has children under age 16 living in the household.
Both age and income are well spread, with the median age in category 26–34 and
the median yearly income in category US$40,000–49,999. Separate F-tests suggest
that the characteristics are well-balanced across our treatment groups. Only one out
of 35 comparisons is significant at the five percent level, and only three additional
ones with p-values of 0.08, 0.10, and 0.11 could be seen as borderline significant.
Answers to the manipulation check questions indicate that on average, subjects
clearly understood instructions and procedures, felt that their anonymity was preserved, trusted the experimenters and the charity, and found the recipients of the
donations worth supporting (Table B2 in Online Appendix B). With the exception
of the last item, the answers to the manipulation check questions do not significantly
differ across treatments.
Table 3 presents descriptive results of donation decisions observed in the experimental treatments. Panel A reports mean values and standard deviations. Column 1
shows the average number of nutritional packages that subjects chose to donate in
their version of the donation appeal. Hence, column 1 represents the units purchased
before any rebate or matching subsidy while accounting for subsidized nominal
prices in the discount conditions. If multiplied by the nominal price, column 1 would
correspond to out-of-pocket expenses that are frequently denoted as “checkbook giving” in standard money donation experiments. Column 2 reports individual net donations in dollars after accounting for all subsidies. That is, column 2 is column 1 evaluated at the (discounted) nominal price minus any rebates. Column 3 lists the mean
number of nutritional packages the charity “receives,” based on subjects’ choices,
that is, column 1 plus any matched packages. If we multiplied column 3 by $0.50 for
all treatments, we would obtain gross charity receipts in dollars, a common focus in
13
In the case of AMT, having multiple accounts is forbidden by Amazon’s Terms of Service (Mason
and Suri 2012) and creating an account requires a unique credit card number (Paolacci et al. 2010).
13
J. Diederich et al.
Table 3 Descriptive results
Treatments
Condition
Donation variable
Nominal
unit
price
($)
Effective
unit
price
($)
Individual
choice
(units)
Net
donation
($)
Charity
receipt,
uncond.
(units)
Charity
receipt,
cond.
(units)
Prob.
of
donation
(1)
(2)
(3)
(4)
(5)
1.169
0.584
1.169
2.256
0.518
A. Mean values (S.D.)
No subsidy
33% rebate
1:2 match
33% discount
50% rebate
1:1 match
50% discount
0.50
0.50
0.50
0.33
0.50
0.50
0.25
0.50
0.33
0.33
0.33
0.25
0.25
0.25
(1.413) (0.706) (1.413)
(1.177) (0.503)
1.690
2.400
0.558
1.690
0.704
(1.545) (0.510) (1.545)
(1.294) (0.460)
1.059
3.048
0.529
1.506
0.494
(1.339) (0.670) (2.021)
(1.886) (0.503)
1.478
2.771
0.533
(1.973) (0.651) (1.973)
0.488
1.927
(0.502)
1.931
2.732
0.707
0.483
1.478
1.931
(1.705) (0.426) (1.705)
(1.379) (0.459)
1.113
3.787
0.556
2.225
0.588
(1.253) (0.626) (2.506)
(2.176) (0.495)
2.143
3.545
0.536
2.143
0.604
(2.831) (0.708) (2.831)
(2.879) (0.492)
33% rebate vs. 1:2 match
0.01
0.76
0.52
0.06
0.01
33% rebate vs. 33% discount
0.44
0.44
0.44
0.27
0.03
1:2 match vs. 33% discount
0.10
0.68
0.93
0.49
0.60
50% rebate vs. 1:1 match
0.00
0.41
0.41
0.01
0.15
50% rebate vs. 50% discount
0.57
0.57
0.57
0.07
0.20
1:1 match vs. 50% discount
0.00
0.84
0.84
0.63
0.82
50% vs. 33% rebate
0.41
0.36
0.41
0.24
0.97
1:1 vs. 1:2 match
0.79
0.79
0.05
0.09
0.23
50% vs. 33% discount
0.07
0.64
0.07
0.11
0.34
33% rebate vs. no subsidy
0.03
0.79
0.03
0.58
0.02
1:2 match vs. no subsidy
0.61
0.61
0.21
0.02
0.76
33% discount vs. no subsidy
0.24
0.35
0.24
0.12
0.84
B. Tests of subsidy types: p-values
B1. At effective price of $0.33
B2. At effective price of $0.25
C. Tests of subsidized prices: p-values
D. Tests of subsidized vs. unsubsidized prices: p-values
D1. Low subsidy rate
13
Subsidizing unit donations: matches, rebates, and discounts…
Table 3 (continued)
Treatments
Donation variable
Individual
choice
(units)
Net
donation
($)
Charity
receipt,
uncond.
(units)
Charity
receipt,
cond.
(units)
Prob.
of
donation
(1)
(2)
(3)
(4)
(5)
50% rebate vs. no subsidy
0.01
0.29
0.01
0.09
0.03
1:1 match vs. no subsidy
0.79
0.79
0.00
0.00
0.37
50% discount vs. no subsidy
0.00
0.65
0.00
0.00
0.25
Condition
Nominal
unit
price
($)
Effective
unit
price
($)
D2. High subsidy rate
Panel A shows mean values of the donation variables for each treatment (standard deviations in parentheses). Column 1 reports the number of packages that subjects selected to give at the nominal price.
Column 2 shows the net dollar contribution implied by subjects’ choices, i.e., column 1 evaluated at the
nominal price minus the rebate (if any). Column 3 reports the overall number of packages received by
the charity, i.e., column 1 plus matched units (if any). Column 4 reports the same measure as column
3 but conditional on giving (intensive margin). Column 5 reports the share of subjects who donated at
least one package (extensive margin). Panels B to D show pairwise tests between treatment conditions.
Panel B compares subsidy types conditional on the effective price. Panel C compares the two subsidized
prices, $0.25 and $0.33, conditional on subsidy type. Panel D compares the unsubsidized price with the
subsidized price arising from the low subsidy rate for each subsidy type. Columns 1 to 4 in panels B to D
report p-values of two-tailed t-tests with unequal variances. Column 5 report p-values of Pearson 𝜒 2 tests
for binary data
money donation experiments. Because of perfect collinearity of both receipts measures, we only use charity receipts expressed in units in the following analysis, with
the exception of Fig. 1 where we use charity receipts expressed in dollars to illustrate
its composition. Columns 4 and 5 show the intensive and the extensive margin of
giving, respectively. Column 4 reports mean charity receipts conditional on being a
1.25
1
$
.75
.5
.25
Net donation
50
%
di
sc
ou
nt
ch
at
1
re
1:
%
50
m
ba
t
e
nt
co
u
at
ch
di
s
m
%
33
1:
2
re
33
%
N
o
su
b
si
dy
ba
te
0
Subsidy payment
Fig. 1 Average charity receipts in dollars (divided into average net donations and corresponding subsidy
payments) by treatment. This corresponds to charity receipts in units (column 3 of Table 3) multiplied by
the (unsubsidized) unit price of $0.50
13
J. Diederich et al.
donor while column 5 reports the fraction of donors. For each variable, panels B to D
report p-values of pairwise comparison tests between treatments.
The remainder of this section presents the results of our analysis. We first focus on
rebates and matches (Sect. 4.1) and subsequently turn to the effectiveness of discount
subsidies (Sect. 4.2). We discuss potential explanations for our results in Sect. 5.
4.1 Rebates versus matches
Three main results follow from columns 1 to 3 of Table 3. First, column 3 in panel
A shows that the charity received about 1.7 units per subject in the 33% rebate condition and about 1.5 units per subject in the comparable 1:2 matching condition.
When the higher subsidy rate was used, the charity received 1.9 units per subject in
the 50% rebate condition and 2.2 units in the 1:1 match condition. At both effective
prices, the levels of charity receipts do not significantly differ between the two subsidy types ( p = 0.52 and p = 0.41, panels B1 and B2).
Result 1 (Charity receipts) Charity receipts do not significantly differ between
rebate and matching subsidies.
Second, column 3 also shows that charity receipts significantly increase in the
subsidy level, either from introducing a subsidy ( p < 0.05 for a 33% rebate, 50%
rebate, and 1:1 match, panel D) or from increasing the subsidy rate ( p = 0.05 in case
of the match, panel C).
Result 2 (Law of demand) Charity receipts significantly decrease in the price.
Third, column 2 in panel A indicates that net donations exhibit a roughly constant
share of around one quarter of the endowment across all treatment conditions. Thus, neither the introduction of a subsidy at any rate nor an increase in the subsidy rate results in
significant changes of subjects’ own contributions net of the subsidy ( p ≥ 0.29 for pairwise comparisons, panels C and D). Note that in order to achieve the same level of charity receipts and own net donations, subjects need to select more units to donate under a
rebate than under a match (since the match is paid on top of the units selected). This is
exactly what we observe in column 1: The average number of units selected is at least
0.5 units larger in panel A ( p ≤ 0.01 at both effective prices, panel B).
Result 3 (Net donations) There is no evidence for crowding-in or crowding-out of
net donations by rebate or matching subsidies of any level.
Result 3 has an important implication: It implies that the increase in charity receipts
(Result 2) is entirely driven by the additional money provided as subsidy payment by
the third party, instead of being driven by individuals actually giving more (see Fig. 1
for an illustration). This finding does not generally hold in the money donation literature. Several papers find that matches significantly increase net donations compared to
a no subsidy condition without lead donor (Eckel et al. 2007; Karlan and List 2007;
13
Subsidizing unit donations: matches, rebates, and discounts…
Gneezy et al. 2014; Huck et al. 2015; Eckel and Grossman 2017). However, there are
also some papers that do not find a significant effect on net donations (Lukas et al.
2010; Karlan et al. 2011; McCarty et al. 2018). Evidence for rebates is scarcer and
rather points in the opposite direction, i.e., that rebates crowd out net donations (Eckel
and Grossman 2003, 2008b; Gandullia and Lezzi 2018; Gandullia 2019).
The most substantial difference between our findings and those that are predominant in the money donation literature is the equality of rebates and matches regarding charity receipts (Result 1). The well-established finding in the context of money
donations is that charity receipts under matches exceed those under rebates (Eckel
and Grossman 2003, 2006a, b, 2008b, 2017; Davis et al. 2005; Lukas et al. 2010;
Bekkers 2015; Gandullia and Lezzi 2018; Gandullia 2019), while “checkbook giving,” which corresponds to column 1 in panel A of Table 3 multiplied by the nominal price, is often roughly the same under both subsidy types. We therefore now
examine whether our results are robust to controlling for available covariates. For
this purpose, we estimate an Ordered Probit Model with the individual choice as
dependent variable and use it to analyze the effect of the different subsidies on the
level of charity receipts. Online Appendix A presents details of the model.14
Columns 1 and 2 in panel A of Table 4 present the results in the form of the average marginal effects on charity receipts without and with controlling for covariates.
For example, offering a 33% rebate is estimated to increase average charity receipts
per individual by about 0.5 packages compared to not offering any subsidy (column
1, Rebate), whereas increasing the subsidy rate from 33% to 50% has no significant effect in the case of the rebate (column 1, Rebate × low price). Analogously to
Table 3, the predicted levels of charity receipts are compared pairwise across subsidy types in panel B, holding the effective price constant. The estimates confirm
Result 1 and Result 2. We repeat the same exercise for predicted levels of net donations. In line with Result 3, we neither find significant differences in net donations
between subsidy types at the same effective price nor any evidence for crowding-in
or crowding-out at any conventional significance level when changing the price of
giving due to a specific subsidy type.15
Having observed that charity receipts do not differ between rebates and matches,
we ask whether this result masks heterogeneities in the “conversion rates” of the
experimental donation call (the extensive margin of giving) and the conditional level
of charity receipts demanded by donors (the intensive margin of giving). As discussed in Sect. 1, rebates decrease the minimum net expense required to become a
donor, making them potentially more effective at the extensive margin than matches.
Indeed, switching back to the descriptive results shown in Table 3 confirms that
14
Whereas a common approach in the literature is to estimate a Tobit Model with the monetary value
that the individual has chosen to give, charity receipts, or their logarithmized value as dependent variable, the discrete nature of our donation decision makes it an unsuitable choice to model our data. This
is supported by conditional moment tests significantly rejecting the assumption of normally distributed
error terms for the Tobit Model with charity receipts or logarithmized charity receipts as dependent variable ( p < 0.01). We nevertheless run different Tobit specifications and OLS regressions as robustness
checks and find similar results (available from the authors upon request).
15
Results are available from the authors upon request.
13
J. Diederich et al.
Table 4 Estimation results
Charity receipts,
unconditional
(units)
Probability
of donation
(binary)
(1)
(3)
(2)
Charity receipts,
conditional
(units)
(4)
(5)
(6)
A. Marginal effects
Rebate
Match
Discount
Rebate × low price
Match × low price
Discount × low price
0.546**
0.533**
0.186**
0.220***
0.091
−0.039
(0.237)
(0.257)
(0.077)
(0.081)
(0.256)
(0.27)
0.324
0.248
−0.024
−0.011
0.799**
0.488
(0.261)
(0.291)
(0.077)
(0.086)
(0.359)
(0.392)
0.306
0.231
0.015
0.012
0.537
0.316
(0.247)
(0.272)
(0.076)
(0.084)
(0.332)
(0.357)
0.218
0.218
0.003
−0.018
0.326
0.342
(0.277)
(0.302)
(0.081)
(0.088)
(0.266)
(0.279)
0.888**
0.992**
0.093
0.104
0.783*
0.782*
(0.373)
(0.405)
(0.077)
(0.084)
(0.448)
(0.466)
0.585*
0.613*
0.071
0.057
0.571
0.807
(0.326)
(0.366)
(0.073)
(0.084)
(0.448)
(0.503)
B. Tests of subsidy types: p-values
B1. At effective price of $0.33
33% rebate vs. 1:2 match
0.43
0.35
0.01
0.00
0.05
0.17
33% rebate vs. 33% discount
0.37
0.30
0.02
0.01
0.17
0.31
1:2 match vs. 33% discount
0.95
0.96
0.60
0.79
0.53
0.69
B2. At effective price of $0.25
50% rebate vs. 1:1 match
0.23
0.22
0.14
0.21
0.00
0.01
50% rebate vs. 50% discount
0.71
0.81
0.19
0.13
0.09
0.08
0.78
1:1 match vs. 50% discount
0.43
0.37
0.82
0.77
0.33
Covariates a
No
Yes
No
Yes
No
Yes
Log likelihood
−801.28
−592.51
−372.07
−250.92
−427.37
−314.94
Observations
558
428
558
428
326
256
(1)–(2): Ordered Probit with the number of packages selected by the individual as dependent variable.
(3)–(4): Probit for whether or not a donation was made. (5)–(6): Ordered Probit conditional on being a
donor, with the number of packages selected by the individual as dependent variable. (1)–(2) and (5)–(6)
treat a single observation with 5 selected packages as if it were 6 selected packages
Panel A presents average marginal effects. Standard errors reported in parentheses, * p < 0.1,
**p < 0.05, ***p < 0.01. For (1)–(2) and (5)–(6), marginal effects refer to the average change in
expected charity receipts over all individuals or donors only, respectively. For each individual considered,
the change is calculated by taking the difference in expected charity receipts between receiving a particular subsidy at the low rate (rebate, match, discount) and not receiving any subsidy or between receiving
a particular subsidy at the high rate (rebate × low price, match × low price, discount × low price) and
receiving the same subsidy at the low rate
Panel B presents p-values for the pairwise comparison of treatment effects (subsidy treatment vs. no subsidy) between subsidy types, based on the average marginal effects
a
Covariates include gender, marital status, the Big Five personality dimensions, risk preferences, categorical variables for age, income, residential environment, and religion, and dummies for whether the
individual holds a college degree, whether children under the age of 16 live in the household, whether
13
Subsidizing unit donations: matches, rebates, and discounts…
Table 4 (continued)
the individual is a registered voter, whether the individual frequently attends religious services, whether
the individual works for a not-for-profit organization and task order. Likelihood ratio tests reject that their
coefficients in model (2), (4) and (6) are jointly zero ( p < 0.01, p < 0.01 and p < 0.05, respectively)
rebates attract a larger share of donors than matches. In particular, column 5 in
panel A reveals that the difference amounts to roughly 21 percentage points (70.4%
vs. 49.4%) in the case of the high effective price and to about 12 percentage points
(70.7% vs. 58.8%) in the case of the low effective price. Pairwise tests show that the
difference is significant at the high effective price ( p = 0.01, panel B1) but not at the
low effective price ( p = 0.15, panel B2).16 We take this as evidence that the equality
result for the level of charity receipts is partly driven by the fact that rebate subsidies
are more effective at the extensive margin.
Result 4 (Extensive margin) Rebates are more effective in attracting donors than
matches.
Turning to the intensive margin, column 4 of Table 3 shows that conditional charity receipts under both match conditions significantly exceed the corresponding values in the rebate conditions (3.0 vs. 2.4 units and 3.8 vs. 2.7 units, panel A; p = 0.06
and p = 0.01, panels B1 and B2).
Result 5 (Intensive margin) Charity receipts per donor are higher under matching
than under rebate subsidies.
Comparing matching and rebate treatments to the control treatment reinforces
the view that the channel through which rebates raise unconditional charity receipts
primarily is the extensive margin whereas matches unfold their impact through the
intensive margin. For the rebate, introducing the low subsidy rate increases the share
of donors in column 5 in panel A from 51.8% to 70.4% ( p = 0.02, panel D1) compared to the no subsidy condition, while the intensive margin in column 4 is not
significantly affected ( p = 0.58, panel D1). In contrast, for the match, introducing
the low subsidy rate increases mean conditional charity receipts in column 4, panel
A from 2.3 to 3.0 units ( p = 0.02, panel D1) compared to the no subsidy condition,
while the extensive margin in column 5 is unaffected ( p = 0.76, panel D1).
Again, we supplement the descriptive results by estimating appropriate parametric models. Columns 3 and 4 of Table 4 refer to a Probit without and with covariates, respectively, while columns 5 and 6 capture the intensive margin by estimating
an Ordered Probit Model for donors only. The latter is set up analogously to the
16
The fact that the difference in the extensive margin is more pronounced for the low subsidy rate is not
surprising, since for the 1:2 match the first unit donated does not result in a matching payment. Consequently, the minimum expense required to become a donor is larger than for the equivalent rebate while
the impact of the action is the same: a single nutritional package received by the charity. As a result, not
only the costs but also the effective prices at the margin of becoming a donor differ, further decreasing
the relative attractiveness of the match.
13
J. Diederich et al.
Ordered Probit Model used above.17 The parametric estimation in Table 4 confirms
results 4 and 5, with the exception that the difference between the 33% rebate and
the 1:2 match at the intensive margin becomes insignificant when covariates are
included (column 6, panel B).
One concern regarding the comparison of rebate and matching subsidies in our
experiment might be that differences in the budget constraints for charity receipts
could drive some of the results. Under a rebate, the highest possible number of packages received by the charity is always four, since the donor must fully fund each
selected unit at a nominal price of $0.5 before receiving the refund. In contrast, the
matching subsidy applies on top of the selected packages: If under a 1:1 match a
donor decides to spend her whole endowment of $2 to fund four packages, then the
charity receives eight packages.18 Similar differences apply to almost all laboratory
experiments comparing rebates and matches in the money donation literature, as
they also endow subjects with a limited amount of money. In the money donation
literature, it is shown that the higher effectiveness of matches observed in laboratory studies also holds in field experiments where subjects use their own income
(Eckel and Grossman 2008b, 2017). If the budget constraint mattered in our design,
the results could understate the effectiveness of rebates compared to matches for
situations in which the budget constraint is looser or non-binding. This implies that
rebates might be even more effective than matches in such situations.
To provide a robustness check on this matter, we revisit Result 1 and Result 5 by
recoding subjects’ choices in order to equalize budget constraints. In our data, a total
of 29.5% of subjects give the maximum amount under rebates, compared to 10.9%
in the matching conditions. For each condition, we set all charity receipts above four
packages to four packages (the maximum level of charity receipts under rebates).
Detailed results are presented in Table B4 in Online Appendix B. Although rebates
now provide the highest average number of packages received by the charity, the
difference to matches is not significant at the high subsidy rate ( p = 0.65) and only
marginally significant at the low subsidy rate ( p = 0.09). Hence, Result 1 survives
the robustness check. In contrast, the difference on the intensive margin (Result 5)
vanishes after censoring charity receipts at four packages. A possible explanation is
that matches create larger conditional donations only in settings where the budget
constraint is binding for a sufficiently large share of individuals.
4.2 Discount subsidies
Subsidies that consist of a simple nominal price reduction turn out to be as effective as rebate and matching subsidies that produce equivalent effective prices.
Charity receipts in column 3 and net donations in column 2 of Table 3 do not
significantly differ from those under the other two subsidy types ( p ≥ 0.44 for
17
If we assumed that after controlling for observable characteristics, the error terms between the decisions to donate and how much to donate are uncorrelated, we could interpret these two models jointly as
a Two-Part model.
18
See Table B3 in Online Appendix B for the detailed choice set by treatment.
13
Subsidizing unit donations: matches, rebates, and discounts…
each pairwise comparison in panel B). Hence, the increased salience of the effective price under discounts does not seem to affect demand, and this alternative
subsidy type does not lend itself to a more effective subsidy. Instead, the selected
number of units (column 1, panel A) under a discount is statistically indistinguishable from that selected under a rebate ( p = 0.44 and p = 0.57, panels B1
and B2) but by an amount higher than under the corresponding match ( p = 0.10
and p < 0.005, panels B1 and B2), which approximately makes up for the additional units provided as matching payment. In line with the law of demand, charity receipts in column 3 increase in the subsidy level by applying the 50% discount instead of the no subsidy condition ( p < 0.01, panel D2) or instead of the
33% discount ( p = 0.07, panel C). There is again no evidence for crowding-in
or -out. Our Ordered Probit estimates in Table 4, columns 1–2, confirm these
findings.
Result 6 (Discounts) The discount subsidy produces the same level of charity receipts and net donations as rebates and matches. Increasing the subsidy rate
increases charity receipts, without crowding-in or crowding-out net donations.
As in the previous section, we can differentiate the behavior into the extensive and the intensive margin. At the low subsidy rate, the likelihood of giving
under the discount is significantly lower than under the rebate ( p ≤ 0.03, column
5 in panel B1 of Table 3 and columns 3 and 4 in panel B1 of Table 4). Since we
would expect the responses to rebates and discounts to be similar at the extensive margin, this difference may hint towards a behavioral bias in the response
to an equivalent decrease in the cost of becoming a donor. At the intensive margin, there is only some marginally significant difference between discounts and
rebates at the high subsidy rate, shown in column 4 of Table 3 and columns 5–6
of Table 4. In comparison to the matching subsidies, significant differences arise
at neither the extensive nor the intensive margin.
5 Discussion
In our experiment, we find equivalence between matches and rebates as subsidybased incentives to donors and an equivalence with price discounts. This equivalence under a unit donation scheme contrasts with the existing literature that has
examined subsidy types under a money donation scheme and has generally found
matches outperforming rebates. This includes papers that also use an online
experimental methodology (Bekkers 2015; Gandullia and Lezzi 2018; Gandullia
2019), two of which recruit from a similar subject pool and use the same endowment level as we do (Gandullia and Lezzi 2018; Gandullia 2019). A closer parallel exists with experimental evidence comparing product promotions in the marketing literature. For private goods, matches (bonus packs) and price promotions
13
J. Diederich et al.
sometimes perform equally well (Sinha and Smith 2000; Hardesty and Bearden
2003; Chen et al. 2012). For charitable goods, however, our finding is unusual.
To guide our intuition about this result, note that as discussed in Sect. 2.2, rebates
and matches are no longer theoretically equivalent under a unit donation scheme.
When donors face the choice architecture of a unit donation scheme, the minimum
net expense required to become a donor is lower under rebates than under matches.
This does not hold for a money donation scheme. As a result, the behavior on the
extensive margin might be a crucial factor to explain why matches do not outperform
rebates in our setting. In line with this reasoning, our results on the extensive margin
differ from those obtained in the context of money donations schemes. While we find
that rebates attract more donors than matches, Bekkers (2015) finds the opposite by
using similar subsidy rates in a standard money donation choice architecture. Furthermore, Gandullia and Lezzi (2018) use the same online population, subsidy rates, and
endowment levels as we do but focus on a standard money donation scheme. In their
experiment, both rebates and matches increase the fraction of donors compared to a
no-subsidy condition and effect sizes between the different subsidy types are similar.
Additional evidence that the lower cost of becoming a donor under rebates might
drive the results comes from a simple recoding exercise. In our experiment, the minimum positive net donation under a match amounts to $0.50. Under a 33% (50%) rebate,
25% (22%) of donors give less than $0.50. Recoding those subjects as non-donors
eliminates any significant difference at the extensive margin, and matches now lead to
higher charity receipts than rebates (1.506 vs. 1.437 units at the low subsidy rate and
2.225 vs. 1.707 units at the high subsidy rate), yet differences between the two subsidy
types remain statistically insignificant ( p = 0.817 and p = 0.167). Hence, equalizing
the cost of becoming a donor ex post moves the subsidy comparison towards the standard result from money donations, namely that matches outperform rebates.
The importance of the extensive margin to explain our results is also in line
with findings by Diederich et al. (2021). The authors show that using unit instead
of money donation schemes affects the propensity to give, with the primary driver
being the discrete choice set under unit donation schemes. This characteristic is also
responsible for the different cost of becoming a donor between rebates and matches
in our experiment. While the discreteness thus appears to be an important factor to
explain our results, we cannot exclude the possibility that the other distinct characteristics of unit donation schemes discussed in Sect. 2.1—i.e., the additional
information on the effectiveness of a donation and the framing in terms of physical
units—may also play a role.19 Additional research is required to quantify the relative
effects of the different characteristics on the responsiveness to subsidies. One possible approach would be to introduce one characteristic at a time, similar to Diederich
et al. (2021), and investigate whether and how the effectiveness of certain subsidy
types changes.
19
As pointed out by an anonymous referee, a potential explanation for a different response to rebates
under a unit instead of a money donation scheme is fungibility: Due to the unit framing, the donation
is in terms of physical units whereas the rebate is in terms of money, which might abate the feeling that
money is taken away from the recipient.
13
Subsidizing unit donations: matches, rebates, and discounts…
Regarding the comparison of the rebate and discount subsidies, the equivalence
on the aggregate level accords with our prior expectations. However, our data offers
some evidence that rebates are more effective in attracting donors. Although we
should await future research to confirm the robustness of this finding, such a difference is surprising given that both subsidies imply the same price of becoming a
donor. One speculative explanation is that a donor has the feeling of providing the
whole unit of the charitable good herself under the rebate but only a fraction of the
unit under the discount. In this case, the donor might derive lower warm glow utility
from becoming a donor under the discount than under the rebate.
An interesting question for future research is how the effectiveness of the different
subsidy types under a unit donation scheme depends on the level of the unsubsidized
unit price. At a given subsidy rate, a larger unsubsidized price increases the absolute
difference in the minimum expense required to become a donor between rebates and
matches. As a result, the differences on the extensive margin might become more
pronounced, which in turn might be sufficient to make the rebate raise more money
than the match. In contrast, reducing the unit size might move results closer to what
has been found for money donation schemes.
Future research could also help verify the generalizability of our results, for
example, with respect to the absolute size of the earned endowment and the relative sizes of unit price and endowment. At $2, the earned endowment is small in
absolute terms, even though it is large in the context of the experimental population
we recruit. Gandullia and Lezzi (2018) and Gandullia (2019) use the same endowment level with a similar subject pool and replicate the standard finding of matches
outperforming rebates under a money donation scheme. These results hint at generalizability, but more research is needed for the specific case examined in the present
paper. At $0.50, the unsubsidized unit price of the charitable good is a quarter of
the earned endowment and therefore restricts the room for variation in the donation
decision, potentially limiting the scope for identifying differences. Although we still
find significant differences between the subsidy and no subsidy conditions as well as
between the subsidy types on the extensive and intensive margin, the equivalence of
rebates and matches regarding charity receipts merits further examination.
6 Conclusion
This paper defines a class of donations in which donors are asked to choose the
number of discrete units of the charitable good to fund instead of the amount of
money to give. We call the former a unit donation and the latter a money donation. We present empirical evidence from an online field experiment designed to
analyze how different subsidy types affect unit donations. In doing so, we focus on
the two prevalent subsidy types, rebates and matches, as well as a subsidy type that
is novel to charitable giving and framed as a simple price discount. The latter can be
applied since for unit donations, each physical unit has a well-defined price that can
be explicitly reduced.
The results remarkably differ from the well-established findings on the performance of subsidy types applied to money donations. Matching subsidies do not
13
J. Diederich et al.
outperform rebates but are equally effective in raising funds. Yet matching and
rebate subsidies create different responses at the extensive and intensive margin of
giving. While rebates significantly increase the fraction of donors, matches produce
larger donations. The significantly higher likelihood of giving under rebates compared to matches is in contrast to the money donation literature and appears to be
one reason why rebates catch up with matches in the unit donation setting of our
experiment. Price discounts raise similar levels of funds as rebates and matches.
None of the subsidy types significantly affects net donations.
Our results highlight the relevance of the decision environment when soliciting
donations and, thus, have important implications for practitioners. First, charities
that employ unit donations in their fundraising efforts cannot rely on the insights
from the existing literature on subsidizing money donations. Second, whether it is
useful to apply a certain type of subsidy to unit donations depends on a charity’s
objectives. Previous research has shown that individuals that donated once are more
likely to give in the future. If the charity desires to maximize the set of donors, our
evidence suggests that a rebate is preferable over a match. If the charity instead
seeks to maximize charity receipts, the choice of the subsidy type seems to be irrelevant, offering some additional degrees of freedom to charities in their campaign
design. Third, in cases where funds are not tied to being used as a subsidy, subsidizing unit donations is not necessarily beneficial as on the aggregate it may not crowd
in private giving.
Supplementary Information The online version contains supplementary material available at https://doi.
org/10.1007/s10683-021-09732-9.
Acknowledgements We wish to thank René Bekkers, Christian Conrad, Mark Ottoni-Wilhelm, Konrad
Stahl, the editor at Experimental Economics, and two anonymous referees for their helpful comments.
We also thank participants at the 5th Science of Philanthropy Initiative Conference, Indianapolis, the
24th Annual Conference of the European Association of Environmental and Resource Economists, Manchester, the 34th Annual Congress of the European Economic Association, Manchester, and the Annual
Conference of the German Economic Association, Leipzig, as well as seminar and workshop audiences
at Heidelberg University, the University of Bonn, the University of Mannheim, the Centre for European
Economic Research Mannheim, and the Karlsruhe Institute of Technology. We thank Sign of Hope
e.V. for cooperation and Woodrow Ahn for language assistance in developing the donation question.
Funding Open Access funding enabled and organized by Projekt DEAL.
Availability of data and materials Data for this article is available under https://doi.org/10.11588/data/
GANTNY
Code availability Code for this article is available under https://doi.org/10.11588/data/GANTNY
Conflict of interest The authors declare that they have no conflict of interest.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as
you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article
are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the
material. If material is not included in the article’s Creative Commons licence and your intended use is
not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission
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Subsidizing unit donations: matches, rebates, and discounts…
directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licen
ses/by/4.0/.
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Authors and Affiliations
Johannes Diederich1 · Catherine C. Eckel2
Timo Goeschl1 · Philip J. Grossman4
· Raphael Epperson3
·
Catherine C. Eckel
ceckel@tamu.edu
Raphael Epperson
raphael.epperson@uibk.ac.at
Timo Goeschl
goeschl@uni-heidelberg.de
Philip J. Grossman
Philip.Grossman@monash.edu
1
Department of Economics, Heidelberg University, Bergheimer Str. 20, Heidelberg, Germany
2
Department of Economics, Texas A&M University, College Station, TX 77843-4228, USA
3
Department of Public Finance, University of Innsbruck, Universitätsstraße 15, Innsbruck,
Austria
4
Department of Economics, Monash Business School, Monash University, Clayton, VIC 3800,
Australia
13