Discussion Paper No. 1004

GROUP SIZE AND CONFORMITYIN CHARITABLE GIVING:
EVIDENCE FROM A DONATION-BASEDCROWDFUNDING PLATFORM
IN JAPAN
Shusaku Sasaki

Revised May 2018
May 2017

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Group size and conformity in charitable giving: Evidence froma donation-based crowdfunding platform in Japan

Shusaku Sasaki*†
May 1st, 2018

Abstract
A charitable donor typically imitates the majority contribution of other donors. This study examines

the relationships between majority size and this so-called donor’s conformity behavior, by empiricallyinvestigating the impacts of multiple earlier donations on the donation of a subsequent donor to

JapanGiving, a donation-based crowdfunding platform in Japan. This analysis is possible because theplatform’s webpage displays the previous donation amounts in chronological order, thus allowing us

to examine the modal amount of more recent donations. By using data on 9,989 actual donations, our*Corresponding Author: Faculty of Economics, Keio University, Tokyo
E-mail: ssasaki.econ@gmail.com, Postal Address: 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan†
This paper is a direct descendant of my two un-published working papers (Sasaki, 2014, 2015).
I thank the Japan Society for the Promotion of Science for financial support (Grant Number 14J04581). This researchwould not have been possible without support from JapanGiving. I thank its founders, Daigo Sato and Takuya Kajikawa. I
thank Fumio Ohtake, Sarah Smith, Richard Steinberg, Mark Ottoni-Wilhelm, Sera Linardi, Rene Bekkers, Brenda Gainer,
Atta A. Ceesay, Takanori Ida, Takahiro Hoshino, Katsunori Yamada, Miki Kohara, Yoshiaki Nomura, Naoto Yamauchi, andRyo Okui for discussions, comments, and encouragement. I also thank participants at the 8th ISTR Asia Pacific Regional
Conference 2013, ARNOVA’s 42nd Annual Conference 2013, ABEF’s 7th Annual Conference 2013, the Japanese
Economic Association Fall Meeting 2014, the 9th Applied Econometrics Conference 2014, the Second SPI Annual
Conference 2014 and ABEF’s 8th Annual Conference 2014 as well as seminar participants at Osaka University and the
University of Chicago (Science of Philanthropy Initiative webinar).
This paper is awarded “Emerging Scholars Award” at ARNOVA (Association for Research on Nonprofit Organizations
and Voluntary Action) 42nd Annual Conference and “Encouragement Award” at ABEF (Association of Behavioral
Economics and Finance) 8th Annual Conference 2014. All errors in this paper are my own responsibility.

1dynamic panel analyses suggest that when the two most recent donations are identical, a subsequent

donor is likely to match the last donation. In other words, when the last donor imitates the donation of

the penultimate donor, the subsequent donor is also likely to imitate this amount. Additionally, thelikelihood increases when the number of most recent continuous modal donations increases. These

results support the notion that a donor’s conformity behavior is more likely to occur when a greater

proportion of the other donors give a similar amount. Furthermore, the effects of continuous modal

donations are strongly observed for low monetary ranges. We discuss that individuals would obtain an

excuse for less cooperation due to others’ behaviors or initiating further cooperation among a large

number of less cooperative others would become harder. Our findings connect economic studies ofcharity and social psychology studies of conformity and could help improve the effectiveness offundraising by charities.

Keywords: Charitable giving, Conformity, Free-ride, Dynamic panel model, Crowdfunding,Fundraising management
JEL Classification Codes: D64, H41, C99

2

1. Introduction
The literature shows that a charitable donor is often influenced by other donors and an influenced
donor imitates the others’ contributions. (Frey && Croson,2009). For example, Shang and Croson (2009) find that potential donors make larger donation amounts
on average when they know about another’s donation than when they do not. This so-called conformity
behavior by donors also matters in practice. Indeed, charities deliberately provide information about
previous donations (e.g., in their solicitation letters, brochures, and homepages) to solicit new
donations (The Behavioral Insights Team, 2013).

Then, when is a charitable donor more likely to conform to others’ contributions? This issue
in donors’ conformity behavior remains a subject of debate and analysis. Answering the question can
aid fundraising activities by charities. If we reveal a secret that aids in prompting donors’ conformity
behavior, it must enable charities to collect donations more effectively and achieve fundraising targets
at a faster pace.
One method 1 of investigation involves providing potential donors with information on
multiple donors making a similar donation amount. Seminal studies in social psychology revealed thatan individual’s conformity behavior is likely to appear when a large number of other people behave in
one individual imitates the choice ofanother, a third individual is likely to match their choice. Furthermore, the likelihood increases with
the number of others who have made a similar choice.

1

Previous studies have explored the issues in other ways. For instance, Shang et al. (2008) show that donor conformity
depends on similarities between donors in that when donors obtain information about another donor of the same sex, they
are more likely to be influenced by the other donor. Croson and Shang (2013) find that donor conformity depends on thecontribution level of the other donor. When donors see another’s extremely high contribution, they are less likely to be
influenced by it. Jones and Linardi (2014), among others, find that donor conformity depends on the visibility of his/her
contribution. That is, donors are more likely to be influenced by other donors when their own contribution is visible.
3

If that is the case with charitable giving, providing information regarding multiple donors
could influence potential donors more strongly if and when more of the multiple donors have donatedthe same amount as compared with other times when they may not donate the same amount in suchhigh numbers. That is, subsequent donors’ contribution could mirror the majority contributions ofmultiple donors. However, few study has found this “majority effect” in everyday situations, including
real charitable giving, to the best of our knowledge.
We study the causal impact of majority size on donors’ conformity behavior, by using a datasetof 9,989 actual donations on a donation-based crowdfunding platform, JapanGiving, and a dynamic
panel modeling approach. JapanGiving is the largest donation-based crowdfunding platform in Japan
as well as an affiliate of the world’s largest platform, JustGiving in the United Kingdom.2 As an online
fundraising intermediary, JapanGiving connects nonprofit organizations (NPOs) and fundraisers withpotential donors. The main feature of JapanGiving that can be exploited for the analysis in this study
is that its fundraising campaign webpage displays previous donation amounts in chronological order.
Potential donors would see the four or five most recent individual donations and combinations ofprevious donations when accessing the page and donating at different times.
In other words, to exploit causality from majority size on donors’ conformity behavior, weinvestigate the effects of informing subsequent donors regarding the monetary contributions thatmultiple previous donors already made to JapanGiving. Our empirical models include variables to
explain representative combinations of previous donations, and the main variables are the modal
amount among the five most recent donations and their appearance along the sequence. Using thesevariables, we examine the effect of the conformity behavior of previous donors on that of subsequent2

The platform’s name changed from JustGiving Japan to JapanGiving in January 2015.
4

donor. This implies that our model specifications include lagged dependent variables as independent
variables, and this modelling causes a downward bias in fixed effects estimates (Nickell, 1981). We
use a dynamic panel modelling approach, excluding the bias. We further introduce our model
specification and identification strategy in Section 4.
Our data, models, and empirical strategy are based on those propounded by Smith et al. (2015),
who use a large sample of data from JustGiving and Virgin Money Giving in the United Kingdom
whose webpages also display previous donations chronologically. Their analyses show that a new
donation amount responds affirmatively to large and small donations among previous donations,changes in their modal amount, and the mean amount of previous donations. Getting an idea from theliterature, we examine the significance of the number of people making donations of a similar size interms of the likelihood of people following previous donations.
Our empirical analyses provide findings that are consistent with those in laboratory studies insocial psychology. When the two most recent donations are identical, a subsequent donor is likely tomatch the last donation. In other words, when the last donor imitates the donation of the penultimate
donor, the subsequent donor is likely to match their amount. Furthermore, we find that the likelihood
increases when the number of the most recent continuous modal donations increases. These results
support the notion that a donor’s conformity behavior is more likely to occur when a greater proportionof other donors give a similar amount as compared with when they do not.
Our study, which applies the findings from social psychological studies of conformity to theeconomic analysis of charitable giving and adopts a dynamic panel modeling approach to test theempirical hypotheses, is the first to discover the effect of majority size on conformity behavior in realcharitable giving. The presented findings can assist fundraising activities by suggesting that charities
5alter the presented donation amounts accordingly to achieve their fundraising targets at a faster pace.

2. Literature review
In social psychology, Asch (1951, 1955) produces seminal works regarding majority size andindividuals’ conformity behavior. In his laboratory experiment, he presents two cards to experimental
subjects. He writes just one line on one card and multiple lines on the other card. He asks subjects toselect a line from the multiple lines on the latter card that equals the line on the former card. The main
finding is that when a subject knows that more of the group has selected the wrong choice, he/she ismore likely to match this wrong choice. The Asch’s conformity experiments have been replicated by
an extensive experimental literature (see Bond, 2005 Tanford & Penrod, 1984). Most results have beenfound in the laboratory setting

recent studies start to complement these conformity

experiments by using more natural observations and assessing conformity behavior in everyday
situations (Claidière et al.
To conduct a similar investigation in natural settings, including real charitable giving,
researchers need to inform potential donors about combinations of multiple donations. Hence, because
employing a field experiment for the analysis would require a large number of treatments, few relevant
studies of charitable contributions has been undertaken. In this strand of the research, Martin andRandal (2008) use a see-through donation box in an art gallery to investigate how compositions ofvisible bills and coins influence new donations. However, they do not track and record each individual
donation and cannot draw conclusions on how each donor reacted to the stimulus. In a laboratory
experiment, Samek and Sheremeta (2014) analyze the effects of recognizing (i) only the largest or
smallest donations and (ii) all multiple donations. However, their work does not shed light on how
6other combinations affect new donations.
Websites are ideal for displaying various information patterns (Blake et al., 2015
al.

et

& Reiley, 2014). Hence, researchers can track and record detailed data on website

visitors, such as when they visited, what information they saw, and which activity they undertook. By
using this information, they can then compute the effects of the treatment information on a visitor’s
activity. However, if treatment information on websites is not randomly assigned to visitors, aneconometric method is necessary to identify the causality from the treatment information to a visitor’s
activity.
Smith et al. (2015) apply a dynamic panel modeling approach, a method of causal inference,
to a large sample of micro panel data of real donations recorded on JustGiving and Virgin Money
Giving. 3 As noted in the Introduction, these crowdfunding platforms display previous donations
chronologically. The authors examine the effects of other donors by investigating how previous
donations affect subsequent donations on these platforms. They use the dynamic panel modelingapproach to exclude downward bias in the fixed effects estimates, finding that a £10 rise in thearithmetic mean of all previous donations increases a new donation amount by £2.50. Their study thus
establishes positive causality running from previous to new donations.

3. Study setting
Between its launch in March 2010 and December 2014, JapanGiving attracted 111,700 donations
totaling ¥121.4 million (US$1.5 million at the 2011 exchange rate)4 in contributions.5 NPOs and3

Bøg et al. (2012) use a small sample of cross-sectional data from JustGiving, finding a systematic positive correlation
between contributions in the early stage of a fundraising campaign and those in its later stage.
4
1 US dollar was equivalent to 79.8 Japanese yen in 2011.
5
Donors can also register with JapanGiving and can donate by credit card or through Internet banking.
7

fundraisers register with JapanGiving and create fundraising webpages for their causes. They firstsolicit friends, families, and colleagues for donations, who in turn are expected to share the URL of
the fundraising webpage and the solicitation message or their donations with their social andprofessional associates. Accordingly, most donors on a webpage are likely to belong to an NPO’s orfundraiser’s existing networks.
We use data from the 9,989 donations made via JapanGiving from February 2011 to December
2011.6 All sampled donors viewed the same webpage design during this period.7 JapanGiving records
the monetary amounts of donations, their dates and times, and the recipient organizations (see theexample in Figure 1). Information is displayed chronologically on one electronic page. A donor
therefore sees the last four or five donations prominently. First, we identify the order of donations
within a campaign webpage from the time and date data. Subsequently, we use the amounts donatedand their sequence to capture the information that each donor saw when he/she visited the webpage.
We identify donors by randomly assigned IDs and gather no personal information.
[Figure 1 is here]

4. Empirical strategy
4.1. Model specifications and variables
To examine the spread of conformity behaviors, we first investigate whether positive causality runs
from the conformity behavior of a previous donor to that of a new donor. In other words, when a

6

The total number of donations in this period was 67,595. Most pertained to the reconstruction process from the Great
East Japan Earthquake and Tsunami in 2011. We selected the sample for our analysis from the 67,595 donations byfollowing the procedure in Section 4.2 and obtained a plausibly homogeneous sample.
7
Although JapanGiving sometimes changes the website’s design, no changes were made in the period during which those
9,989 donations were made.
8

previous donor imitates the donation of another previous donor, to what extent is a subsequent donor
likely to match their amount. In the second model specification, we investigate whether a new donor’s
conformity behavior is more likely to occur when more previous donors conform.

4.1.1. Model specification (1)The first model specification is as follows:8

,

=

+

,

+

+

,

, ,

,

= 1, if

,

=

,

,

= 0, if

,

≠

,

(1)

Empirical Hypothesis 1: When the two most recent donations are identical, a new donor is likely tomatch the last donation.

where

,

refers to the amount of the

The dependent variable,

donation to campaign webpage .

is a dummy that takes 1 whenotherwise. In other words, we define that the
and

,

,

exactly equals

donor conforms to the−1,

are identical. Note that this dependent variable expresses the conformity behavior of thefirst lag of the dependent variable

8, and 0donor whendonor and does not alone identify why he/she conforms. The independent variable

to the,−2, . This variable expresses whether thedonor. Its parameter γ represents the effect of the

−1

−1

,

is thedonor conforms

donor’s conformity

To examine the existence of donor conformity, we estimated the following model: , = ++ , δ + , . The,
estimated results showed thatis small and insignificant. This result implies that a new donor does not respond only to achange in the last donation and this led us to examine combinations of multiple previous donations.
9behavior on that of thedonor.

Here, we test the hypothesis that when the last donor imitates the amount that the penultimate
donor made, a subsequent donor is likely to match their amount. We assume that a subsequent donor
looks particularly at the last donor’s behavior among previous donors. This assumption is plausible
because the most recent donation is displayed at the top of a list of previous donations on a JapanGiving
campaign webpage, making it more visible to the subsequent donor.
We define the dependent and independent variables in the above ways and use these variables
to test the first hypothesis, because it allows us to use a simple dynamic panel model, which provides
a solution for the problem of endogeneity. As we will explain details in Section 4.1.3, econometricians
have developed methods of causal inference for the dynamic panel model, and the methods have been
applied in several empirical studies. Conversely, if we define that theequals

,

,

,

, or

,

donor conforms when,

, using a dynamic panel model would be unsuitable. Therefore,

adapting the definitions of our variables and model specification is a simple and pragmatic strategy. If
γ > 0 holds, it confirms our first empirical hypothesis, suggesting positive causality running from theconformity behavior of a previous donor to that of a new donor.
Some might argue that the definition of the dependent variable is too strict because it judgesthat thedonor does not conform to the−1

donor even when

,

and

,

are almost,but not exactly, the same. This definition could thus underestimate the parameters in our model.
Nevertheless, we define this so for the following three reasons. First, if we find the directionality ofthe expected parameter from the underestimated results, this strongly supports our hypothesis. It canalso provide academic and practical implications. Second, many of social psychology studies examine
whether one individual’s choice exactly equals others’ choices, to the best of our knowledge. Third,
10this definition is based on the JapanGiving payment system, which provides nine options for donatedamounts. 9 Over 90 percent of all donations concur with the amounts presented in these options.
Donors could decide their contribution by choosing from the options, and they could make a binary
decision of whether they select the option that other previous donors selected.
The control variables,

include some of the information that thedonor sees on the

webpage, such as the number of previous donations and target completion rate.
duration from the inception of the webpage to the date of the,also includes the

donation. Furthermore, we use

monthly, weekday, and time zone dummies to accommodate common shocks among the time intervals.

4.1.2. Model specification (2)In the second model specification, we further explore a spread of conformity behaviors. Here, we
assume—in the same way as in the first model specification—that a subsequent donor looks at the last
donor’s behavior. However, we additionally assume that he/she considers the behaviors of the last fivedonors. The second model subdivides

,

=

+

,

+

! T2 ,+

into several cases to test the second empirical hypothesis:,

T3 , +

T4 , +

OT1 , +,

= 1, if

,

=

,

,

= 0, if,≠,& OT2 ,

+

,

+

, ,

(2)

Empirical Hypothesis 2: When the number of the most recent continuous modal donations increases,
a new donor is more likely to match the modal amount.

9

These are (proportion of donations consistent within the nine options): ¥500 (2.0 percent share), ¥1,000 (8.5 percent),¥2,000 (13.3 percent), ¥3,000 (12.2 percent), ¥5,000 (25.8 percent), ¥10,000 (25.4 percent), ¥30,000 (3.1 percent), ¥50,000(0.9 percent), and ¥100,000 (0.9 percent).
11

[Figure 2 is here]

As shown in Figure 2, the first lagged dependent variable
when

at least equals,,! . Next,

,

,

,

!,

,

,

, and

,

,

,

! , and,is a dummy that takes 1

T1 , , T2 , , T3 , , and T4 , are dummies that take 1

when only the two most recent donations ofrecent donations of

,

and

,

,

!

are identical, when the three mostare identical, when the four most recent donations ofare identical, and when all five of the most recent donations are

identical, respectively. In all these treatments,,

takes 1. T1 , explains the largest variation

among the five most recent donations, whereas T4 , explains the smallest variation. We define thedegree of conformity behaviors among the five most recent donors to be lowest in the former case,with the degree of conformity behaviors rising in the order of T2 , , T3 , , and T4 , .
exhibits the effect of treatment 1 on the

We interpret the parameters in the following way.
probability that the dependent variable,takes 1.

+

!,

+

, and

+

are the effects oftreatment 2, treatment 3, and treatment 4, respectively. The second model specification adds crossterms with the lagged dependent variable into the first model specification. This simple enhanced
version of the first model specification allows us to regard the second model specification as a dynamic
panel model.
We explain the degree of conformity behaviors among the last five donors by examining themost recent continuous modal donations. In particular, we consider the difference in the salience ofmodal donations between larger and smaller variations. For example, a subsequent donor could easily
recognize when the last and penultimate donations are identical, which may strengthen the pressure toconform by contrast, he/she might not do so when two donations of the modal amount appear at an
12interval. In addition, the pressure to conform might weaken in this case because a subsequent donor
could find more recent donors who did not conform. However, the latter case could also generate moreor less pressure to conform to the last donation, and ignoring this case leads to the underestimation of
the parameters, particularly

and! . We therefore construct a covariate of the other treatments 1

OT1 , to explain the case, and we add it into the second model specification.
Furthermore, we must deal with the case where modal donations appear among the other four
recent donations (i.e., all donations except the last). In this case, a subsequent donor might donate themodal

however, our dependent variable does not judge whether the subsequent donor

conforms because his/her donation amount is different from that of the last donation. If we do notconsider this case, it then causes the overestimation of the parameters of

,

!,

, and

. The

second model specification thus includes a covariate of the other treatments 2 OT2 , to explain thecase, controlling for its effect.

4.1.3. Bias corrections in dynamic panel models
In model specifications (1) and (2), the error term is decomposed as,= ' + ( , . ' is a constantpage-specific effect that captures the unobserved inter-(,

is a random error term. In view of the characteristics of the error term, the OLS estimates ofandare likely to be upward-biased because of unobserved correlations. To exclude this bias, we use
fixed effects linear probability models to estimate the above two equations. However, the fixed effects
estimates ofandare likely to be downward-biased (Nickell, 1981), since the two model

specifications are a dynamic panel model that includes lags of the dependent variable. A correlation
thus remains between the treatment variables and error term even after we eliminate the constant page13

specific effect by first differencing.
We address this downward bias by adopting the following two methodologies. The first is thegeneralized method of moments (GMM) for dynamic panel estimations, particularly Difference GMM(Arellano & Bond, 1991) and System GMM (Blundell & Bond, 1998). The second methodology is thehalf-panel jackknife fixed effects estimation developed by Dhaene and Jochmans (2015).
In Difference GMM, we use as instruments the several period lags of the dependent variable
that influence just the differenced independent variable after we eliminate the constant page-specificeffect by first differencing. System GMM adds the level moment condition to the moment conditionsof Difference GMM and estimates the equation. These methodologies have been applied in several
empirical studies, and Smith et al. (2015) also adopt Difference GMM for their estimations.
We use the second methodology to deal with the downward bias since GMM estimates are
not always stable because of the problems of weak instruments, too many instruments, and nonstationarity of the dependent variable (Bun et al., 2015 Roodman, 2009a). To avoid these problems,
econometricians have developed another methodology, by which they directly exclude the downward
bias in the fixed effects estimates and obtain reliable estimates (Bun & Carree, 2005
Jochmans, 2015 Hahn &ene &Kiviet, 1995). We adopt the half-panel jackknife fixed

effects estimation method developed by Dhaene and Jochmans (2015) has been applied in recent
empirical studies (Hospido, 2012, 2015). In this method, we first assume that the fixed effects estimator
includes downward bias ) and that ) decreases as the time * dimension increases. Next, weestimate the fixed effects estimates of +,-. by using the full+,-. includes downward

bias )*. We also divide the full panel into halves and estimate the fixed effects values of +,-., and+,-.,! by using the subsamples. +,-., and +,-.,! that include common downward bias 2)*. Finally,14

we obtain the half-panel jackknife estimator without the downward bias by substituting +,-. , +,-., ,
1

1

0
50
and +,-.,! for 2+,-. − 23,4 23,6. We check whether our main estimation results are stably observed!

when we use Difference GMM, System GMM, and the half-panel jackknife fixed effects estimation.

4.2. Preliminary identification analysis
Our identification strategy for the parameters of
attributes and characteristics do not depend on,

and T2 , − T4 , assumes that donors’

after controlling for a constant page-specific effectby using dynamic panel estimations. Ordinal regressions corroborate this assumption by directly
adding the variables of attributes and preferences into the equation: however, we gathered no personal
information for its protection. Subsequently, we justify the assumption by confirming that the
distribution of donated amounts on a webpage is stationary throughout the campaign. In that case, we
can judge that plausibly homogeneous donors visit the campaign webpage and donate there. This
subsection delineates examples to confirm this assumption.
First, we consider that the distributions of donated amounts, number of donors per webpage,and length of the campaign are skewed because of a few successful fundraisers10 and generous donors(Smith et al., 2015). We exclude from the analysis webpages that have single donations exceeding¥500,000 (US$6,266), webpages with fewer than 25 or more than 100 donations, and webpages withdonations made more than 50 days after their inception. Furthermore, we exclude some exceptional
donations, including continuous donations made by an identical donor and donations made by
JapanGiving founders before a campaign webpage opened to the public.
10

One of the most successful fundraisers is Dr. Shinya Yamanaka, a Japanese Nobel Prize-winning stem cell researcher.
He raised more than ¥¥1,000,000 (US$12,533).
15

Second, we exclude the first three donations on each webpage because their donors are more
likely to be the fundraiser’s friends, family, and colleagues, and tend to donate different amounts(Agrawal et al., 2015 Smith et al., 2015).11 The data indicate that the mean of the first three donations(¥17,467) significantly exceeds the mean of the remaining donations (¥8,568) with 1% statisticalsignificance. Therefore, we exclude them. Furthermore, we exclude the fourth and fifth donations
because our analysis focuses on the effects of the last five donations.
Finally, we verify that amounts without the initial five donations are sufficiently stationary
throughout the entire campaign. Then, we use the Kolmogorov–Smirnov test to compare the
distribution of monetary amounts donated in the first half and second half of the campaign. The null
hypothesis is that the two sample groups have identical distributions, and the test does not reject thisin 291 out of 359 campaign webpages (p > 0.100 ). Thus, the 9,989 data points across the 291
campaign webpages are plausibly homogeneous.
As shown in Table 1, the arithmetic mean donation is ¥8,823 (US$111). The mean number ofdonations per campaign webpage is approximately 47, 12 and the mean target price is ¥997,724(US$12,504). The number of campaigns with final target completion rates of 100 percent or more is
98. The arithmetic mean donation on JapanGiving might be higher than normal donations in Japan.
One possible explanation is that most samples donated for the reconstruction process from the Great
East Japan Earthquake and that such donations are likely to be higher. The Japan Fundraising

11

Agrawal et al. (2015) use data from a Canadian crowdfunding platform, showing that early donors have closer
relationships with fundraisers. Smith et al. (2015) report that the average amount of the first three donations isclude the initial three donations
from their analysis.
12
As we have explained, our analyses use the sample, which excludes the exceptional donations from the donations per
campaign webpage. Therefore, the number of our sample, 9,989, is inconsistent with the number, which is calculated out
by multiplying the number of donation per campaign webpage, 47, by the number of campaign webpage, 291. The numberof donation per campaign webpage in our sample is around 34.
16

Association (2012) reports that relief money or donations averaged around ¥10,000 nationally at thistime.
[Table 1 is here]

5. Basic analysis
This section first presents the estimation results of model specification (1), testing the first empiricalhypothesis that when the two most recent donations are identical, a new donor is likely to match thelast donation. Next, we present the estimation results of model specification (2), testing the second
empirical hypothesis that when the number of the most recent continuous modal donations increases,
a new donor is more likely to match the modal amount. We run the regressions, considering the control
variables’ effects, several fixed effects, and serial correlation effects.

5.1. First hypothesis test results
Table 2 presents the results of the OLS estimations, fixed effects model estimations, and dynamic panel
model estimations. In the Difference GMM and System GMM estimations, we use more than the twoperiod lags of the dependent variable and more than the three-period lags of the donation amount as
instrumental variables. In addition, we collapse these instrumental variables to deal with the problem
of excessive instrumental variables because too many instrumental variables could over-fit theendogenous variables as well as weaken the Hansen test of over-identifying restrictions. 13 ,14 The
Arellano–Bond test for serial correlation does not reject the null hypothesis of no second-order serial
13

The econometric software STATA provides a “collapse” option (Roodman, 2009b).
Several empirical studies in macroeconomics have reported plausible causal effects using GMM estimations, but theseresults suffered from problems associated with excessive instruments (Bazzi & Clemens, 2013). After collapsing the
instruments to address these problems, most analyses showed no evidence that supported causality.
17

14

correlation, implying that more than the two-period lags are valid as instruments. The Hansen test
indicates that the instrument set is plausible.15[Table 2 is here]
Our findings confirm the first empirical hypothesis. Table 2 shows that all the dynamic panel
estimates ofare positive and statistically significant at the 1 percent level. We find that when thelast two donations are identical, the likelihood that a new donor matches the last donation increases by
13.6–13.7 percent. This finding also supports the notion of positive causality running from theconformity behavior of the most recent donor to that of a new donor.16
As discussed in Section 4.1.1, the magnitudes can be underestimated because we define thatthe−1

donor conforms to the−2

donor whendefinition allows the control group to include the case where

and

,

,

and

,

,

!

are identical, and this!

are similar. The above

results show that even when employing this strict definition, the magnitudes exceed 13.6. This finding
implies that we cannot ignore the extent to which the conformity behavior of previous donors
influences that of a new donor.

5.2. Second hypothesis test results
The model specification (2) subdivides,

into five cases. We estimate this model, testing thatwhen the number of the most recent continuous modal donations increases, a new donor is more likely
to match the modal amount.
15
The estimated results are consistent with the theoretical predictions for biases. The fixed effects estimate is smaller thanthe OLS estimate, while the OLS estimate is biased upward. All the dynamic panel estimates oflie between the OLS
and fixed effects estimates. The fixed effects estimate is biased downward. However, the biases may not always generate
as the theoretical predictions in model specifications with covariates.
16
Even the fixed effects estimate with downward bias shows a positive and statistically significant effect. From the fixed
effects estimation results, our data show that the conformity behavior of the previous donor is causative of new donor
behavior.
18

Before presenting the estimation results, we reintroduce the parameters associated with the
key independent variables. First,

is the parameter of the first lagged dependent variable, whichtakes 1 when at least the last two donations are identical. Second,

!,

, and

are the parameters

for the three most recent continuous modal donations (treatment 2), the four most recent continuous
modal donations (treatment 3), and the five or more most recent continuous modal donations (treatment
4). The baseline is the two most recent continuous modal donations (treatment 1). Third, we interpretthe parameters in the following ways.
dependent variable,, , takes 1.

exhibits the effect of treatment 1 on the probability that the
+

!,

+

, and

+

are the effects of treatment 2,

treatment 3, and treatment 4, respectively.
[Table 3 is here][Figure 3 is here]
Our findings confirm the second empirical hypothesis. As shown in Table 3, all the dynamic
panel estimates of・ !・ ・are positive and statistically significant at least at the 10 percent

level.17 Our additional tests in Figure 3 show that the effects of treatments 2, 3, and 4 are 2.2 times,
3.4 times, and 6.2 times, respectively, larger than treatment 1.18 In other words, the effect rises in theorder of treatment 1, 2, 3, and 4. These results imply that as the number of the most recent continuous
modal donations increases among the last five donations, a new donor is more likely to match the last
donation. This finding confirms our second empirical hypothesis as well as supports our contention
that when more previous donors have contributed similarly in monetary terms, a new donor’s
conformity behavior is more likely to occur. The likelihood increases not strictly linearly but

17

Similarly, in model (1), the Arellano–Bond test and Hansen test imply that our instrumental variables are valid andplausible.
18
As an example, we use the Difference GMM estimations to conduct the additional tests and present the test results.
19continuously with the number of the most recent continuous modal donations.
The effect of treatment 1 is smaller than those of treatments 2–4 because a new donor mightrecognize that the two most recent continuous modal donations are not the majority among the last
five donations. That is, when facing those cases, a subsequent donor might not think that many previous
donors contribute the same amount as the last donation. On the contrary, the three or more most recent
donations are identical in treatments 2–4, and thus a new donor might recognize that the last donor
belongs to the majority.
The other treatments have parameters that are consistent with our expectations. OT1 ,explains the cases in which donations identical to the last donation appear at intervals. The results showthat these cases generate some pressure to match their donation amount. In addition, OT2 , explains
the cases where modal donations appear among the other four recent donations without the last
donation. This parameter shows a negative sign, indicating that a subsequent donor might match theamount of the modal donation. Therefore, we again recognize that we need to control for these twocases when identifying

・ !・ ・ .

6. Further analysis
6.1. Heterogeneity between monetary amount ranges
Section 5 showed that when the two most recent donations are identical, a subsequent donor is likely
to match the last donation. The likelihood further increases when the number of the most recent
continuous modal donations increases. This section conducts additional analysis, within the limitationsof data availability, to discuss why donors conform in this manner and thus deepen the interpretationof our findings.
20

In advance, we introduce the major following mechanisms to explain the relationship between
others’ behaviors and individual conformity (Zafar, 2011): (1) image-related

concern (Andreoni & Petrie, 2004 Bernheim, 1994 Rege & Telle, 2004) and (2) social learning(Banerjee, 1992 Bikhchandani et al., 1992). Social psychology calls the first mechanism normative
conformity and the second one informational conformity. In the first mechanism, people stick to asimilar choice because they want to be considered generous. People who care about their own
reputation tend to avoid their own choice inconsistent with others’ choices because departures fromsocial trends can impair their social status. In the second mechanism, people learn about the best choicefrom information about others’ choices and hence make the same choice. Although they might
determine their best choice independently, doing so can be costly or time-consuming. In addition,
Carpenter (2004) proposes another mechanism, namely (3) free-riding in providing a public good. In
the third mechanism, people would obtain an excuse for less cooperation from others’ free-riding
behavior, or initiating more cooperation among a large number of free-riders would become harder.
The other recent studies indicate that donors are often reluctant to give are looking for some excuses
to avoid donations (Exley & Petrie

Klinowski, 2016 Reyniers & Bhalla, 2013).

To explore which mechanism works better, we examine the heterogeneity in the effect ofcontinuous modal donations across monetary amount ranges. More concretely, we construct interaction
terms between the dummies for the ranges in the amounts donated and variables of continuous modal
donations. We then use the variables to investigate the extent to which the effect of continuous modal
donations differs across these ranges.
The effects should differ by mechanisms in the following ways. First, if an image-related
concern shapes donors’ conformity behavior in our sample, we find a more strongly positive effect of
21

continuous modal donations in higher monetary ranges. Recall that most of the donations in our sample
are for the reconstruction process from the Great East Japan Earthquake in 2011 therefore, there exists
a social norm that expects donors to give a higher amount. Second, if social learning explains our
results, the effect of continuous modal donations is the same across these ranges. Third, if free-riding
causes our results, we find a stronger positive effect of continuous modal donations in lower monetary
ranges.
[Table 4 is here]
Table 4 presents the results that support the third mechanism of free-riding. The effects of themost recent three or more continuous modal donations are positive and statistically significant in theranges of ¥1–¥29,999 in the half-panel jackknife estimation (at least at the 10 percent level). 19
However, the effect is largest in the lowest range of ¥1–¥1,999, and it reduces as the range elevates. In
addition, the effect loses statistically significance in the range of ¥30,000 or more. These results imply
that when the most recent three or more continuous modal donations are identical in lower monetary
ranges, a subsequent donor is more likely to match the modal amount, but the likelihood decreases inhigher ranges.
Our analysis also finds that donation amounts between ¥5,000 and ¥29,999 themselves havepositive and statistically significant effects. This result implies that when the last donor contributes¥5,000–¥29,999, a subsequent donor is likely to contribute a similar range even if he/she does not see
the most recent continuous modal donations in this range. In our samples, the average donation amount

19

Using Difference or System GMM for this model specification might be unsuitable because it includes a large numberof the interacted variables, generates too many instrumental variables, and could produce unstable estimation results. In
fact, Hansen tests indicate that the estimation results are weakened by the many instruments. Therefore, we mainly use forthe discussion the results of the half-panel jackknife estimation, which are not impeded by this problem. However, since,in our sample, the Difference and System GMM estimations present similar results to the half-panel jackknife estimation,
we report them for readers’ reference.
22

is ¥8,822, and more than 50 percent of the samples donate in these high ranges of ¥5,000–¥29,999, as
discussed in Section 4. These sample characteristics could cause the above effects.
In sum, when the most recent three or more continuous modal donations are identical in the
low range of ¥1–¥1,999, a subsequent donor is most likely to match the modal amount. If he/she did
not see the most recent continuous modal donations, he/she could contribute in the higher ranges of¥5,000–¥29,999. The information on previous modal donations in lower ranges would provide a
subsequent donor with an excuse, which allows him/her to behave in a less cooperative manner (i.e.,save money). An alternative explanation is that since a large number of previous donors make a lower
donation, it creates an unspoken rule that does not allow a subsequent donor to behave initially in amore cooperative manner.
These findings call fundraisers’ attention to the information on previous modal donations insuch lower amount ranges, which could encourage subsequent donors to stick to lower ranges when
deciding on their donation amount. Fundraisers must thus enhance subsequent contributions by newly
providing information on another single donation or multiple modal donations of higher amounts.
However, modal donations of too high amounts would not have conformity effects on a new donor.

6.2. Sample selection issues
Some might still argue that the most recent continuous modal donations hold positive effects because
information on modal donations attracts different groups of donors. For example, fundraisers might
ask their friends and colleagues to donate a lower monetary amount, say ¥1–¥1,999. If so, this does
not allow us to interpret our estimation results in the way of Section 6.1. This concern relates to sample
homogeneity. Although we recognize that our dynamic panel approach accommodates this problem,23

we take another approach to readdress this concern in this subsection. However, it is difficult to directly
test the existence of sample selection bias because we lack information on webpage traffic and donor
characteristics. Instead, we use information on the arrival rate of donations (i.e., the duration from the−1

donation to the

donation). Since the arrival of a different group of donors would coincidewith changes in arrival rates, we can investigate the existence of sample selection bias indirectly by
investigating continuous changes in modal donations and the arrival rate of subsequent donations. For
the analysis, we use the dependent variable that explains the duration from thethe−1

donation to

donation. If information on continuous modal donations attracts different cohorts of donors,

the continuous modal donations should exert statistically significant effects on the dependent variable.
[Table 5 is here]
The results in Table 5 assuage this concern. They show that continuous modal donations do
not display any statistically significant effects in the key ranges of monetary amounts. Again, we foundfrom Section 6.1 that when the most recent three or more continuous modal donations are identical in
the low range of ¥1–¥1,999, a subsequent donor is most likely to match the modal amount. Table 5shows that in this and some higher ranges, the continuous modal donations do not influence when asubsequent donor appears and gives.20
These findings do not support the possibility of sample selection bias. Fundraisers might ask
their friends and colleagues to make donations of a similar amount. If so, continuous modal donations
should have a statistically significantly positive impact in lower ranges. However, this is not the case.

20

Although the most recent at least two continuous modal donations exhibit a negative impact in the range of ¥10,000–¥29,999, its significance level is relatively weak (the 10 percent level). In addition, the most recent three or more continuous
modal donations have a strongly negative impact in the range of ¥30,000 or more. However, the treatment itself does nothave the effect which promotes donors’ conformity behavior. Also, the low frequency of the treatment could create thisresult. Therefore, these findings do not disturb our interpretations.
24

In addition, these findings do not support the other cases of sample selection. For example, a donor
might seek out a campaign webpage that displays the last continuous modal donations and donate there.
If so, his/her information should have statistically significant positive impacts. Again, this is not thecase. Conversely, a donor might rather avoid a campaign webpage that displays continuous modal
donations. If so, his/her information should have statistically significant negative impacts. However,once again, this is not the case.

25

7. Discussion and conclusion
In this study, we investigated how presenting the amounts of multiple previous charitable contributions
publicly (i.e., on the campaign webpage) affects subsequent donations. By using data from a donationbased crowdfunding platform in Japan, we found that when the number of the most recent continuous
modal donations increases among the last five donations, a subsequent donor is more likely to matchthe modal amount. This finding implies that a donor conforms to the majority’s behavior and that donor
conformity is strengthened when the size of the majority expands.
Our findings are consistent with those of social psychological studies of conformity. The
extensive experimental literature in this area finds that people mirror the majority’s behaviors andchoices. Hence, we contribute to raising the external validity of social psychological studies. Ourfindings imply that the laboratory experimental results in social psychology are similarly observed inreal charitable giving contexts, which is one of everyday occurrences. Although laboratory studies ofconformity started in the 1950s, relatively a few studies have established similar results in everyday
situations (Claidière et al.

).

Next, this finding contributes to economic studies of charity. Several economic studies haveshown that presenting a single donation influences a subsequent donor and demonstrated the likelihoodof matching the presented donation (Alpizar et al.

& Croson, 2009). Our findings showthat presenting multiple donations of a similar amount further strengthens the likelihood.
We found from further analysis that when the most recent three or more continuous donations
are identical in lower monetary ranges, a subsequent donor is more likely to match the modal amount,indicating that our sample’s donors conform by free-riding. Information on previous modal donations
in lower ranges could provide a subsequent donor with an excuse that may allow them to behave in a26

less cooperative manner (i.e., save their money). Alternatively, since a large number of previous
donors make lower donations, it could create an unspoken rule that does not allow a subsequent donor
to behave initially in a more cooperative manner.
These findings practically contribute to improving online peer-to-peer fundraising activities
by charities. Knowing previous modal donations of a lower amount could encourage subsequent
donors to stick to lower ranges. In these situations, charities should aim to enhance subsequent
contributions by newly providing information on higher donations. On the contrary, even if the effectsof the most recent three or more continuous donations weaken, they remain positive and statisticallysignificant in some higher ranges. These findings indicate that charities can control the amounts
contributed by subsequent donors by presenting multiple donations of a similar amount. Our study cancontribute to these multiple objectives because we connect economic studies of charity and social
psychological studies of conformity.

27

References
Agrawal, A.K., Catalini, C., & Goldfarb, A. (2015). Crowdfunding: Geography, social networks, andthe timing of investment decisions. Journal of Economics & Management Strategy, 24(2), 253274. (https://doi.org/10.1111/jems.12093)
Alpizar, F., Carlsson, F., & Johansson-Stenman, O. (2008). Anonymity, reciprocity, and conformity:
Evidence from voluntary contributions to a national park in Costa Rica. Journal of Public
Economics, 92(5), 1047–1060. (https://doi.org/10.1016/j.jpubeco.2007.11.004)
Andreoni, J., & Petrie, R. (2004). Public goods experiments without confidentiality: A glimpse into
fund-raising. Journal of Public Economics, 88(7), 1605–1623. (https://doi.org/10.1016/S00472727(03)00040-9)
Arellano, M., & Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence andan application to employment equations. The Review of Economic Studies, 58(2), 277–297.
(https://doi.org/10.2307/2297968)
Asch, S.E. (1951). Effects of group pressure upon the modification and distortion of judgments. In M.
Henle (Ed.), Documents of Gestalt Psychology (pp. 222–236). California: University ofCalifornia Press.
Asch,

S.E.

(1955).

Opinionsandsocialpressure.

Scientific

American,193,

31–35.

(http://dx.doi.org/10.1038/scientificamerican1155-31)
Banerjee, A.V. (1992). A simple model of herd behaviour. The Quarterly Journal of Economics, 107(3),797–817. (https://doi.org/10.2307/2118364)
Bazzi, S., & Clemens, M.A. (2013). Blunt instruments: Avoiding common pitfalls in identifying thecauses of economic growth. American Economic Journal: Macroeconomics, 5(2), 152–186.
28

(https://doi.org/10.1257/mac.5.2.152)
The Behavioral Insights Team (2013). Applying behavioural insights to charitable giving. [London]:Cabinet Office.
Bernheim, B.D. (1994). A theory of conformity. Journal of Political Economy, 102(5), 841–877.
(https://doi.org/10.1086/261957)
Bikhchandani, S., Hirshleifer, D., & Welch, I. (1992). A theory of fads, fashion, custom, and culturalchange as informational cascades. Journal of Political Economy, 100(5), 992–1026.
(http://www.jstor.org/stable/2138632)
Blake, T., Nosko, C., & Tadelis, S. (2015). Consumer heterogeneity and paid search effectiveness: A
large-scale

field

experiment.

Econometrica,

83(1),

155-174.

(https://doi.org/10.3982/ECTA12423)
Blundell, R., & Bond, S. (1998). Initial conditions and moment restrictions in dynamic panel data
models.

Journalof

Econometrics,

87(1),

115–143.

(https://doi.org/10.1016/S0304-

4076(98)00009-8)
Bøg, M., Harmgart, H., Huck, S., & Jeffers, A.M. (2012). Fundraising on the Internet. Kyklos, 65(1),18–30. (https://doi.org/10.1111/j.1467-6435.2011.00525.x)
Bond, R. (2005). Group size and conformity. Group Processes & Intergroup Relations, 8(4), 331–354.
(https://doi.org/10.1177/1368430205056464)
Bun, M.J.G., Sarafidis, V., & Baltagi, B.H. (2015). Dynamic panel data models. In B.H. Baltagi (Ed.),
The Oxford Handbook of Panel Data (pp. 76–110). Oxford: Oxford University Press.
Bun, M.J.G., & Carree, M.A. (2005). Bias-corrected estimation in dynamic panel data models. JournalofBusinessandEconomic
29

Statistics,

23(2),

200–210.

(https://doi.org/10.1198/073500104000000532)
Carpenter, J.P. (2004). When in Rome: Conformity and the provision of public goods. The Journal of
Socio-Economics, 33(4), 395–408. (https://doi.org/10.1016/j.socec.2004.04.009)
Claidière, N., Bowler, M., & Whiten, A. (2012). Evidence for weak or linear conformity but not for
hyper-conformity in an everyday social learning context. PloS One, 7(2), e30970.
(https://doi.org/10.1371/journal.pone.0030970)
Claidière, N., Bowler, M., Brookes, S., Brown, R., & Whiten, A. (2014). Frequency of behavior
witnessed and conformity in an everyday social context. PloS One, 9(6), e99874.
(https://doi.org/10.1371/journal.pone.0099874)
Croson, R., & Shang, J. (2013). Limits of the effect of social information on the voluntary provisionof public goods: Evidence from field experiments. Economic Inquiry, 51(1), 473–477.
(https://doi.org/10.1111/j.1465-7295.2012.00468.x)
Dhaene, G., & Jochmans, K. (2015). Split-panel jackknife estimation of fixed-effect models. The
Review of Economic Studies, 82(3), 991–1030. (https://doi.org/10.1093/restud/rdv007)
Exley, C.L., & Petrie, R. (2018). The Impact of a Surprise Donation Ask. Journal of Public Economics,
158, 152–167. (https://doi.org/10.1016/j.jpubeco.2017.12.015)
Frey, B.S., & Meier, S. (2004). Social comparisons and pro-social behavior: Testing ‘conditional
cooperation’ in a field experiment. The American Economic Review, 94(5), 1717–1722.
(https://doi.org/10.1257/0002828043052187)
Hahn, J., & Kuersteiner, G. (2002). Asymptotically unbiased inference for a dynamic panel model with
fixed effects when both n and T are large. Econometrica, 70(4), 1639–1657.
(https://doi.org/10.1111/1468-0262.00344)
30

Hardwick, P. (2014). Characteristics of a good year-end fundraising letter. Mississippi Business
Journal, Retrieved January 23, 2017 from http://msbusiness.com/2014/12/phil-hardwickcharacteristics-good-year-end-fundraising-letter/.
Hospido, L. (2012). Modelling heterogeneity and dynamics in the volatility of individual wages.
Journal of Applied Econometrics, 27(3), 386–414. (https://doi.org/10.1002/jae.1204)
Hospido, L. (2015). Wage dynamics in the presence of unobserved individual and job heterogeneity.
Labour Economics, 33, 81–93. (https://doi.org/10.1016/j.labeco.2015.03.012)
Japan Fundraising Association (2012). GivingJapan 2012. Tokyo: Keidanren Publishing.
JG MARKETING Co. Ltd. (2014). JapanGiving webpage. Retrieved June 24, 2014 fromhttp://www.justgiving.jp/c/7882.
Johnson, G.A., Lewis, R.A., & Reiley, D. (2014). Location, location, location: Repetition andproximity increase advertising effectiveness. Available at SSRN 2268215.
Jones, D., & Linardi, S. (2014). Wallflowers: Experimental evidence of an aversion to standing out.
Management Science, 60(7), 1757–1771. (https://doi.org/10.1287/mnsc.2013.1837)
Kameda, T., & Hastie, R. (2015). Herd Behavior. In R.A. Scott & S.M. Kosslyn (Ed.), Emerging Trends
in the Social and Behavioral Sciences: An Interdisciplinary, Searchable, and Linkable Resource.
John Wiley and Sons, Wiley Online Library.
Klinowski, D. (2016). Reluctant donors and their reactions to social information. Mimeo. (https://davsecon.github.io/KlinowskiReluctant.pdf)
Kiviet, J.F. (1995). On bias, inconsistency, and efficiency of various estimators in dynamic panel data
models. Journal of Econometrics, 68(1), 53–78. (https://doi.org/10.1016/0304-4076(94)01643E)
31

Lewis, R.A., & Reiley, D.H. (2014). Online ads and offline sales: Measuring the effect of retail
advertising via a controlled experiment on Yahoo! Quantitative Marketing and Economics,
12(3), 1–32. (https://doi.org/10.1007/s11129-014-9146-6)
Martin, R., & Randal, J. (2008). How is donation behavior affected by the donations of others? Journalof

Economic

Behaviorand

Organization,

67(1),

228–238.

(https://doi.org/10.1016/j.jebo.2007.08.001)
Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica, 49(6), 1417–1426.
(http://www.jstor.org/stable/1911408)
Prior, A. (2014). How charities can get more out of donors: What the latest research says about getting
people

to

give.

The

Wall

StreetJournal,Retrieved

January

23,

2017

from

http://www.wsj.com/articles/how-charities-can-get-more-out-of-donors-1418598068.
Rege, M., & Telle, K. (2004). The impact of social approval and framing on cooperation in public good
situations. Journal of Public Economics, 88(7), 1625–1644. (https://doi.org/10.1016/S00472727(03)00021-5)
Reyniers, D., & Bhalla, R. (2013). Reluctant altruism and peer pressure in charitable giving. Judgment
and Decision Making, 8(1), 7.
Roodman, D. (2009a). A note on the theme of too many instruments. Oxford Bulletin of Economics
and Statistics, 71(1), 135–158. (https://doi.org/10.1111/j.1468-0084.2008.00542.x)
Roodman, D. (2009b). How to do xtabond2: An introduction to difference and system GMM in Stata.
Stata Journal, 9(1), 86–136. (http://dx.doi.org/10.2139/ssrn.982943)
Samek, A.S., & Sheremeta, R.M. (2014). Recognizing contributors: An experiment on public goods.
Experimental Economics, 17(4), 673–690. (http://dx.doi.org/10.1007/s10683-013-9389-1)
32

Shang, J., & Croson, R. (2009). A field experiment in charitable contribution: The impact of social
information on the voluntary provision of public goods. The Economic Journal, 119(540), 1422–
1439. (https://doi.org/10.1111/j.1468-0297.2009.02267.x)
Shang, J., Reed, A., & Croson, R. (2008). Identity congruency effects on donations. Journal ofMarketing Research, 45(3), 351-361. (https://doi.org/10.1509/jmkr.45.3.351)
Sasaki, S. (2014). An Exact Conformity of Online Donors. Journal of Behavioral Economics andFinance,Vol.7,

Proceedings

of

the

8th

AnnualMeeting,

88-91.

(https://doi.org/10.11167/jbef.7.88)
Sasaki, S. (2015). Conformity in Charitable Giving: Evidence from Empirical Analysis of JapaneseOnline Donations. Science of Philanthropy Initiative (SPI) Working Paper, 139, 1-37.
(http://spihub.org/site/resource_files/publications/spi_wp_139_sasaki.pdf)
Smith, S., Windmeijer, F., & Wright, E. (2015). Peer effects in charitable giving: Evidence from the(running)field.

The

Economic

Journal,125(585),1053–1071.

(https://doi.org/10.1111/ecoj.12114)
Tanford, S., & Penrod, S. (1984). Social Influence Model: A formal integration of research on majority
andminority

influence

processes.

Psychological

Bulletin,95(2),

189–225.

(http://dx.doi.org/10.1037/0033-2909.95.2.189)
Zafar, B. (2011). An experimental investigation of why individuals conform. European Economic
Review, 55(6), 774–798. (https://doi.org/10.1016/j.euroecorev.2011.01.002)

33

34

Figure 2. Main independent dummy variables
,

T1 ,

T2 ,

T3 ,

T4 ,

,

,

First Lagged Dependent Variable:
At Least Two Continuous Modal Donations

1

Baseline

*

*

*

●

Treatment 1 (Baseline):
Two Continuous Modal Donations

1

Baseline000Treatment 2:
Three Continuous Modal Donations

1

Baseline

10Treatment 3:
Four Continuous Modal Donations

1

Baseline

0

Treatment 4:
Five Continuous Modal Donations

1

Baseline0

Main Independent Dummy Variables

!

,

,

,

●

*

*

*

●

●

X

Y

Z

0

●

●

●

Y

Z

1

0

●

●

●

●

Z

0

1

●

●

●

●

●

Notes: The circular marks explain donations of an identical amount. X, Y, and Z explain donations that are different from this amount. The asterisk marks imply that the donation amount is notconditional.

35

36

Table 1. Descriptive statistics
Mean

Std. Dev.

Min

Max

Donation Unit, N=9,989
Donation Amount (Japanese Yen)

8,822.585

19190.530

100

500,000

46.85619.091

25

100Campaign Webpage Unit, N=291
Number of Donations
Target Price (Japanese Yen)

997,723.800

1,621,552.000

77,777

10,000,000

Target Completion Rate

0.822

0.733

0.017

7.297

Over 100% (Dummy Variable)

0.337

0.473

0

1

Note: Our analyses use the sample, which excludes the exceptional donations from the donations per campaign webpage.
Therefore, the number of our sample, 9,989, is inconsistent with the number, which is calculated out by multiplying thenumber of donation per campaign webpage, 47, by the number of campaign webpage, 291. The number of donation per
campaign webpage in our sample is around 34.

37

Table 2. Basic analysis: Hypothesis 1 test results
Linear Probability Model
Model 1:
Lag1.dependent variable(t-1)th Donation Amount (Log-transformed)
Number of Previous Donations
Target Completion Rate
From Inception of the Webpage

Arellano–Bond test for AR(1), p-value
Arellano–Bond test for AR(2), p-value
Hansen test, p-value(over-ID restrictions)
FE Campaign Webpage
FE Monthly
FE Weekday
FE Time Zone

(1)

(2)

(3)

(4)

(5)

OLS

Fixed Effects

Difference GMM

System GMM

Half-Panel Jackknife

0.163***(0.016)0.104***(0.014)0.136***(0.015)0.137***(0.015)0.136***(0.015)-0.006(0.006)-0.000(0.000)-0.002(0.013)-0.001(0.001)-0.011**(0.004)-0.001*(0.000)-0.005(0.013)0.001(0.001)-0.057***(0.007)-0.001(0.003)-0.129(0.115)0.004(0.004)-0.054***(0.006)-0.002(0.002)-0.015(0.026)-0.001(0.002)-0.010**(0.004)-0.001-0.001-0.013-0.0370.002-0.002

-

-

0.000
0.922
0.374
(13)

0.000
0.914
0.452
(17)

-

NO
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

Notes:
1. The number of donations is 9,989 and the number of campaign webpages is 291.
2. Cluster robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1.
3. The dependent variable is a binary variable that takes 1 when the (t)th donation amount is equal to the (t-1)th donation amount.

38

Table 3. Basic analysis: Hypothesis 2 test results

Linear Probability Model

(1)

(2)

(3)

(4)

(5)

OLS

Fixed Effects

Difference GMM

System GMM

Half Panel Jackknife

0.051***(0.014)0.022(0.014)0.056***(0.015)0.058***(0.015)0.046***

Model 2: The Five Most Recent Donations
Lag1.Dependent Variable

t-1
●

t-2
●

t-3
*

t-4
*

t-5
*

T1 variable

●

●

X

Y

Z

Baseline

Baseline

Baseline

Baseline

Baseline

T2 variable

●

●

●

Y

Z

T3 variable

●

●

●

●

Z

T4 variable

●

●

●

●

●

0.121***(0.030)0.194***(0.036)
0.366***(0.038)0.070**(0.030)0.114***(0.034)0.246***(0.035)0.066*(0.034)0.137***(0.047)0.294***(0.045)0.072**(0.033)0.124***(0.045)0.292***(0.044)0.100***(0.032)0.153***(0.036)
0.306***(0.044)0.161***(0.014)-0.025**(0.012)0.120***(0.013)-0.081***(0.013)0.113***(0.017)-0.056***(0.020)0.109***(0.016)-0.058***(0.019)0.134***(0.014)-0.051***(0.013)-0.007*(0.005)-0.000(0.000)-0.001(0.009)-0.001(0.001)-0.011***(0.004)-0.001**(0.000)-0.006(0.013)0.001(0.001)-0.049***(0.006)-0.002(0.003)-0.132(0.132)0.005(0.004)-0.046***(0.005)-0.003*(0.001)-0.022(0.026)0.000(0.002)-0.010**(0.004)-0.001(0.001)-0.011(0.035)0.002(0.002)

-

-

0.000
0.346
0.224
(28)

0.000
0.414
0.387
(37)

-

NO
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

OT1 variable
OT2 variable(t-1)th Donation Amount (Log-transformed)
Number of Previous Donations
Target Completion Rate
From Inception of the Webpage

Arellano–Bond test for AR(1), p-value
Arellano–Bond test for AR(2), p-value
Hansen test, p-value(over-ID restrictions)
FE Campaign Webpage
FE Monthly
FE Weekday
FE Time Zone

(0.014)

Notes:
1. The number of donations is 9,989 and the number of campaign webpages is 291.
2. Cluster robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1.
3. The dependent variable is a binary variable that takes 1 when the (t)th donation amount is equal to the (t-1)th donation amount.
4. The circular marks explain donations of an identical amount. X, Y, and Z explain donations that are different from this amount. The asterisk marks imply that the donation amount is not conditional.

39

Table 4. Further analysis: Heterogeneity between monetary ranges
(1)

(2)

(3)

(4)

(5)

OLS

Fixed Effects

Difference GMM

System GMM

Half-Panel Jackknife

1 - 1,999 yen

Baseline

Baseline

Baseline

Baseline

Baseline

2,000 - 4,999 yen

0.024(0.016)0.103***(0.018)0.088***(0.018)-0.111***(0.014)0.016(0.016)
0.095***(0.018)0.081***(0.018)-0.117***(0.017)0.007(0.021)
0.094***(0.025)0.077***(0.024)-0.158***(0.027)0.011(0.020)0.094***(0.024)0.079***(0.024)-0.152***(0.026)0.016(0.016)
0.095***(0.018)0.084***(0.019)-0.113***(0.017)0.050(0.040)0.045*(0.023)0.030(0.024)0.048**(0.023)0.066(0.071)0.000(0.035)0.009(0.024)0.008(0.025)0.025(0.022)0.038(0.069)0.084*(0.048)0.068**(0.032)0.019(0.030)0.060**(0.028)0.092(0.074)0.089*(0.048)0.058*(0.030)0.024(0.029)0.061**(0.028)0.108*(0.063)0.028(0.036)0.042*(0.025)0.032(0.025)0.044*(0.023)0.052(0.070)Linear Probability Model(t-1)th Donation Amount Ranges

5,000 - 9,999 yen
10,000 - 29,999 yen
30,000 yen or more

Lag1. dependent variable × (t-1)th Donation Amount Ranges

1 - 1,999 yen
2,000 - 4,999 yen
5,000 - 9,999 yen
10,000 - 29,999 yen
30,000 yen or more

T1 variable
T2, T3, or T4 variable × (t-1)th Donation Amount Ranges

1 - 1,999 yen
2,000 - 4,999 yen
5,000 - 9,999 yen
10,000 - 29,999 yen
30,000 yen or more

Other Treatments
Number of Previous Donations
Target Completion Rate
From Inception of the Webpage
Arellano–Bond test for AR(1), p-value
Arellano–Bond test for AR(2), p-value
Hansen test, p-value(over-ID restrictions)
FE Campaign Webpage
FE Monthly
FE Weekday
FE Time Zone

Baseline

Baseline

Baseline

Baseline

Baseline

0.438***(0.095)0.132***(0.048)0.206***(0.037)0.180***(0.036)0.142(0.139)0.299***(0.091)
0.053(0.048)0.130***(0.034)0.100***(0.034)0.094(0.147)0.250***(0.093)0.138**(0.062)
0.093*(0.051)0.107**(0.043)0.306(0.530)0.300***(0.097)0.166***(0.063)0.088*(0.049)0.095**(0.043)0.324(0.490)0.371***(0.129)0.103**(0.049)0.166***(0.036)0.140***(0.037)0.193(0.219)

YES
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

-

-

0.000
0.464
0.024
(55)

0.000
0.557
0.057
(73)

-

NO
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

YES
YES
YES
YES

Notes:
1. The number of donations is 9,989 and the number of campaign webpages is 291.
2. Cluster robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1.
3. The dependent variable is a binary variable that takes 1 when the (t)th donation amount is equal to the (t-1)th donation amount.
4. The regression includes control variables and four types of fixed effects.

40

Table 5. Further analysis: Sample selection issues(1)Time until the next donation(in hour)Fixed Effects Model(t-1)th Donation Amount Ranges

1 - 1,999 yen

Baseline

2,000 - 4,999 yen-0.492(3.361)
0.534(3.344)1.435(3.488)-7.808(4.825)5,000 - 9,999 yen
10,000 - 29,999 yen
30,000 yen or more

1 - 1,999 yen

Lag1. dependent variable × (t-1)th Donation Amount Ranges

2,000 - 4,999 yen
5,000 - 9,999 yen
10,000 - 29,999 yen
30,000 yen or more

T1 variable-6.527(7.185)-2.108(4.038)-1.329(3.385)-6.806*(4.035)17.299(18.293)
Baseline

T2, T3, or T4 variable × (t-1)th Donation Amount Ranges

1 - 1,999 yen
2,000 - 4,999 yen
5,000 - 9,999 yen
10,000 - 29,999 yen
30,000 yen or more

8.021
(16.176)
9.175(9.946)1.955(6.426)
3.839(5.976)-112.044***(28.734)

Other Treatments
Number of Previous Donations
Target Completion Rate
From Inception of the Webpage

YES
YES
YES
YES

FE Campaign Webpage
FE Monthly
FE Weekday
FE Time Zone

YES
YES
YES
YES

Notes:
1. The number of donations is 9,878 and the number of campaign webpages is 290.
2. Cluster robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1.
3. The dependent variable explains the duration from the (t-1)th donation to the (t)th donation.
4. All regressions include control variables and four types of fixed effects.

41