Does Cumulative Advantage Increase Inequality in the Distribution ofSuccess? Evidence from a Crowdfunding Experiment ∗

Rembrand KoningStanford GSB

Jacob ModelStanford GSB

September 29, 2015

Abstract

The diffusion of online marketplaces has increased our access to “social informa-tion” – records of past behavior and opinions of consumers. One concern with thisdevelopment is that social information may create cumulative advantage dynamicsthat distort marketplaces by increasing inequality in the distribution of success. Criti-cally, this argument assumes that products that are likely to succeed disproportionatelybenefit from social information. We challenge this assumption and argue that cumu-lative advantage processes can aggregate to have nearly any effect on distribution ofsuccess, even decreasing the level of inequality in some cases. We assess these claimsusing archival data and a field experiment in a crowdfunding marketplace. Consistentwith prior work, randomized changes to social information generate cumulative advan-tage. However, our treatments did not change the distribution of success. Productsbenefited equally from our treatments regardless of their predicted likelihood of suc-cess. Our treatments still affected marketplace dynamics by weakening the relationshipbetween predicted and achieved success.

∗Both authors contributed equally, order is alphabetical. Special thanks to DonorsChoose for making thisresearch possible. This work has benefited from feedback provided by participants at CAOSS, AOM, andASA. Generous funding was provided by Stanford’s Center on Philanthropy and Civil Society and Centerfor Social Innovation.

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1 Introduction

One of the seminal insights of social science is that social information, past behav-

ior and opinions of others, powerfully shapes our attitudes, beliefs and actions. The

rise of online platforms has made social information in the form of popularity, ratings

and reviews increasingly accessible. However, concomitant with this profusion of so-

cial information, there is a growing controversy as to whether it facilitates or distorts

marketplaces (Zuckerman, 2012; Muchnik, Aral and Taylor, 2013). On the one hand,

such information may provide informative signals about difficult to observe aspects of

products and services (Zhang and Liu, 2012). On the other hand, the use of social infor-

mation is subject to many well-documented biases that may undermine or even pervert

its potential signaling value (Cialdini, 1993; Simonsohn and Ariely, 2008). Small and

arbitrary initial differences in social information may lead to large differences in success

due to self-reinforcing “cumulative advantage” dynamics (Banerjee, 1992; DiPrete and

Eirich, 2006). Indeed, a large body of archival (Simonsohn and Ariely, 2008; Chen,

Wang and Xie, 2011; Burtch, Ghose and Wattal, 2013) and experimental (Salganik,

Dodds and Watts, 2006; Tucker and Zhang, 2011; Muchnik, Aral and Taylor, 2013;

van de Rijt et al., 2014) research has found evidence that changes in social information

lead to cumulative advantage processes. Scholars have used this evidence to argue that

social information in marketplaces inherently magnifies inequality in the distribution

of success (Salganik, Dodds and Watts, 2006; Tucker and Zhang, 2011; Muchnik, Aral

and Taylor, 2013; van de Rijt et al., 2014).

Prior to any differences in social information, products in a marketplace already

differ in their expected success. For instance, we take for granted that some products

auctioned on eBay are more or less likely to reach their reserve price based on factors

such as appearance and the reputation of the seller. Past research has largely side-

stepped these incoming differences by employing sophisticated statistical controls or

using randomization to account for pre-existing differences (cf. Salganik, Dodds and

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Watts, 2006). However, in order to understand how social information changes the

distribution of success in marketplaces, we need to know how incoming differences in

expected success interact with changes in social information.

Consider the case of two new books being sold in an online marketplace such as

Amazon. One that is from a first-time author and one that is from a well-known

author. A positive change in social information to both books, such as a good review,

will create a wider gap in sales if the well-known author benefits more from the review.

Alternatively, the same good review may plausibly benefit the first-time author more

than a well-known author as the latter already has some established reputation and

audience (Kovacs and Sharkey, 2014). In this case, the change in social information will

reduce the gap in success between these two books. This example illustrates how the

direction of the effect of cumulative advantage on inequality is not obvious (Allison,

Long and Krauze, 1982). Without an understanding of how cumulative advantage

processes interact with a product’s expected success, we can say little about the effects

of social information on inequality of success in a marketplace.

In this paper, we investigate how changes to social information interact with a

product’s expected success and explore the implications of these interactions for the

distribution of success in online marketplaces. Specifically, we couple archival data

from a online fundraising marketplace with an field experiment to examine the in-

teraction between a product’s expected success and cumulative advantage processes.

The marketplace, DonorsChoose, is a two-sided marketplace that helps public school

teachers find donors willing to fund school supplies. DonorsChoose facilitates this

by enabling teachers to post fundraising appeals (called “projects”) and by providing

modern search tools to donors to find projects that appeal to them.

One significant challenge is that the expected success of a product is typically not

directly observable in field settings. We build on the approach taken in Salganik,

Dodds and Watts’s (2006) seminal study of online culture markets in which Salganik

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and colleagues created multiple online markets with the identical set of products. The

authors experimentally manipulated the presence or absence of social information (in

their context, popularity) and tracked the success of products in the marketplace. In

their design, the success of products in marketplaces without social information served

as a direct measure of expected success in the absence of social information.

Although we cannot observe the same DonorsChoose project in multiple condi-

tions, we take a conceptually similar approach to Salganik and colleagues by creating a

counterfactual measure of expected success for projects that received our experimental

treatments. We estimate expected success by generating predictions for each project

using a Random Forest algorithm trained on the characteristics and fundraising out-

comes of over 400 thousand past projects. With this measure of expected success,

we then randomly contributed $5 or $40 to 320 projects and tracked their progress to-

wards their fundraising goals. This randomization enables us to test whether exogenous

changes in social information lead to cumulative advantage dynamics. Critically, we

test whether these dynamics disproportionately benefit projects that were (un)likely to

succeed by interacting our randomized treatments with our measure of expected suc-

cess. This approach enables us to assess how arbitrary changes to social information

change the distribution of funding outcomes.

Consistent with prior work on social information in online marketplaces, we find

that our randomly assigned contributions result in cumulative advantages that in-

crease the probability that a project reaches its funding goal. Surprisingly, this effect

is remarkable homogeneous across projects with different levels of predicted success;

projects with characteristics that made them very likely to succeed benefited just as

much as projects with characteristics that made them unlikely to succeed. In this way,

our intervention introduced more noise into the fundraising process by reducing the

correlation between a project’s expected and realized success. The utility of this noise

depends on the goals of the marketplace. Increasing the unpredictability of success

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reduces the chance that projects with the most popular characteristics succeed. How-

ever, a little noise also creates greater opportunities for novel, innovative and risky

projects to reach their funding goals.

2 Social Influence, Cumulative Advantage and

Inequality

Cumulative advantage processes are considered a key driver of inequalities in society

and markets (DiPrete and Eirich, 2006). Initial advantages become magnified through

self-reinforcing dynamics resulting in a distribution of success that is highly unequal.

Scholars have suggested two mechanisms that produce cumulative advantage processes:

resource accumulation and information cascades. In the first case, small initial differ-

ences in the distribution of resources become magnified as those with initial resource

advantages can channel these into additional resources and skills (Merton, 1968). An

example of this is Merton’s pioneering work on cumulative advantage in academic re-

search. This work takes a broad view of resources to include status garnered through

awards. Award winners leverage their increased status to get additional funding for

their work and so attract more talented students and collaborators (Merton, 1968).

In this sense, Merton’s mechanism is one of resource accumulation —award winners

can use their initial advantage to improve the quality of their work. Even if the ini-

tial allocation of the award were arbitrary, the emergent performance differences are

merited.

An alternative mechanism is information cascades (Banerjee, 1992). In these mod-

els, the assumption is that the quality of a product or service is difficult to observe

directly. Consumers must rely on other observable signals such as social information

that have some correlation, however weak, with quality (Podolny, 2005). For products

and services, common examples of social information include information on popular-

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ity, endorsements or reviews. This information tends to be self-reinforcing; a marginal

increase in the popularity or number of endorsements a product receives makes it more

attractive to subsequent consumers and reviewers. The core difference between Mer-

ton’s cumulative advantage mechanism and the information cascade model is that in

the latter, success can become decoupled from a product’s underlying quality. The

primary concern regarding cumulative advantage in Merton’s example of resource ac-

cumulation is that arbitrary and negligible initial differences allow certain scientists

to receive a disproportionate amount of success. This resulting inequality reflects real

differences in quality. That said, the arbitrary processes that lead to the inequality

may be deemed unfair. The concern of information cascades scholars is quite different;

their concern is that the resulting inequality in success may be largely uncorrelated

with the underlying features and quality of a product or service.

The expanding role of social information in our everyday lives has increased concerns

over the decoupling of social information from underlying quality (Muchnik, Aral and

Taylor, 2013; Colombo, Franzoni and Rossi-Lamastra, 2014). For example, business

owners can manipulate their online reputations by purchasing and then reviewing their

own products, or more nefariously, by paying others to give perfect reviews. This is

a commonplace activity; one scholar estimated that upwards of one-third of online

reviews are fake.1 Even if they are eventually identified and removed, fake reviews or

ratings may influence other consumers, leading them to alter their ratings, reviewing

or purchasing behavior. Once a process of cumulative advantage begins, it may be

difficult to correct. Even beyond outright fraud, natural variation in marketplace

activity may generate cumulative advantage processes. For example, differences in the

timing of initial endorsements or purchases, which may be effectively random, could

lead to cumulative advantages. These sources of advantage may be even more difficult

to address than outright fraud. Ideally, outcomes in marketplaces would be relatively

1http://www.nytimes.com/2012/08/26/business/book-reviewers-for-hire-meet-a-demand-for-online-raves.html

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robust to these perturbations.

However, research suggests that some marketplaces may not be especially robust to

these effects. In their pioneering studies of online culture markets, Salganik and col-

leagues examined how such arbitrary differences in social information change a prod-

uct’s success in a simplified online marketplace created by the researchers (Salganik,

Dodds and Watts, 2006; Salganik and Watts, 2008). They randomly assigned partic-

ipants into marketplaces that either displayed the popularity of a product —in their

setting, the number of downloads of a song— or suppressed this information. Prod-

uct success, as measured by the number of downloads of a song, was more variable

in marketplaces with popularity information than those without it. In the popular-

ity conditions, the songs that arbitrarily received a few initial downloads achieved

greater market share than the same song in a marketplace without social information.

This study demonstrates that markets with social information create cumulative advan-

tages through endogenous processes that disproportionately benefit the most appealing

songs. In turn, this increases inequality within the marketplace.

In a follow-up study, Salganik and colleagues also show that these endogenous

processes are not destiny. In the same marketplace, they directly manipulated the

popularity of songs by reversing the endogenous ranking of songs (Salganik and Watts,

2008). The impact of this manipulation of social information varied across products

within the same marketplace, as measured by their success in marketplaces without

social information. It strongly benefited the songs with the lowest levels of expected

success. In contrast, songs with the highest levels of expected success did regain posi-

tion in the download rankings but only after hundreds of subsequent downloads. The

combination of these effects implies that in this second experiment, the social influence

manipulation (i.e., the ranking inversion) likely reduced the inequality in popularity.

In sum, the results of Salgnik and colleagues’ studies suggest that social information

can generate cumulative advantage processes that have the potential to magnify or

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reduce inequality in success, even within the same marketplace.

A flourishing body of research has extended this work by examining whether changes

to social information produce cumulative advantage effects in field settings. For exam-

ple, Zhang and Liu (2012) found evidence in an observational study of a peer-to-peer

lending platforms that changes in social information lead to cumulative advantage ef-

fects. However, it is difficult to casually identify social influence effects with observation

data. Changes to social information are usually endogenous to a product’s expected

success; people tend to consume, review or rate products that are likely to be appeal-

ing and succeed in the marketplace. The combination of the difficulty of measuring

a product’s appeal coupled with selection processes makes it extremely challenging to

determine how much success is due to changes in social information.

Several recent studies have adopted a field experiment approach and to address

these concerns by randomizing changes to social information. This research stream

has largely reached similar conclusions (cf. Burtch, Ghose and Wattal, 2013) with

studies finding that changes to social information through exogenous positive endorse-

ments or contributions leads to cumulative advantage in a wide variety of settings

including wedding services marketplaces (Tucker and Zhang, 2011), online social news

aggregators (Muchnik, Aral and Taylor, 2013), online petitions, online reviews, and

crowdfunding platforms (van de Rijt et al., 2014). Therefore, we expect as our baseline

hypothesis:

Hypothesis 1: Exogenous endorsements of or contributions to products produce cu-

mulative advantage effects

If changes to social information produce cumulative advantage, what are the impli-

cations for the distribution of success in markets? Scholars have tended to erroneously

equate evidence of cumulative advantage with evidence for increased inequality of suc-

cess (van de Rijt et al., 2014). However, the relationship is not deterministic because

changes in the inequality of success implies that success of products relative to one

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another—not just the absolute levels of success of a given product—change. The re-

search design of randomly assigning changes to social information in a market only

allows a researcher to estimate changes to absolute levels of success. It does not allow

a researcher to draw conclusions on how these effects shape the distribution of success

across products.

Consider the simplest case where the cumulative advantage effects are identical

across all products (e.g., a 10% increase in success rates). This produces a general

shift in absolute success rates but relative success is unchanged. However, when cu-

mulative advantage effects systematically vary across different types of products, the

implications are more complex. If products with high levels of expected success benefit

more from changes to social information than products with low levels of expected

success, this would increase the inequality of success. Conversely, inequality in the dis-

tribution of success may decrease if products with low levels of expected success benefit

more from changes to social information than products with high levels of expected

success. Of course more complex relationships are possible, such as products with high

and low levels of expected success benefiting more than those with average levels of

expected success. Overall, these cases illustrate how cumulative advantage effects may

aggregate to have nearly any effect—or no effect at all—on the level of inequality in

the distribution of success.

To illustrate this more concretely, imagine two musicians who are trying to raise

similar amounts of money to produce a new album. These musicians decide to list

their fundraising efforts on a crowdfunding platform, a popular type of online market-

place. These platforms aggregate individual contributions towards a publicly stated

fundraising goal. They also commonly feature social information, typically the number

and size of prior contributions. The first musician is an established one and is likely to

reach her fundraising goal because she can rely on her established fan base for support.

The second musician is an inexperienced musician and is less likely to reach his goal.

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Imagine that each one of them randomly receives an initial contribution of $50. The

question for scholars of cumulative advantage is which album benefits more from this

contribution?

One possibility suggested by the cumulative advantage literature is a “success-

breeds-success” dynamic where the experienced musician disproportionately benefits.

Potential contributors may prefer--perhaps because they are risk averse—to fund an

album that they perceive as very likely to succeed. In this case, the first contribution

will lead to stronger cumulative advantage effects for the established musician that, in

turn, will create a wider gap in fundraising success than one would expect without this

contribution. An alternative possibility suggested by the research on status and market

uncertainty is that the inexperienced musician may disproportionately benefit from the

contribution. The rationale is that it is likely that potential contributors have more

uncertainty regarding the success of the inexperienced musician relative to the estab-

lished musician (Podolny, 2005; Azoulay, Stuart and Wang, 2013). If the contribution

decreases the level of uncertainty regarding the quality of the inexperienced musician’s

fundraising appeal more than the experienced musician, then the contribution would

disproportionately help the inexperienced musician. This mechanism would suggest

that the first contribution would reduce the gap in realized success relative to expected

success.

These mechanisms are meant to be illustrative rather than exhaustive. Either one

or even a combination of each, is plausible. Moreover, the functional form of the

interaction of expected success and the $50 contribution may change the implications

for inequality as well. For instance, there could be ceiling or floor effects. If an

extremely well-known musician like Paul McCartney were to try to fundraise for an

album on a crowdfunding platform, an initial contribution would likely have little effect

on the distribution of success. Understanding these considerations is important, but

the focus of our study is not to quantify the size or form of these mechanisms. Instead,

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we are concerned with how the effects produced by changes in social information,

regardless of the mechanism, aggregate to affect the distribution of success.

While we shown that cumulative advantage may affect the distribution of success

in myriad of ways, prior work has suggested that cumulative advantage processes tend

to increase inequality in the distribution of success (Salganik, Dodds and Watts, 2006;

Tucker and Zhang, 2011; Muchnik, Aral and Taylor, 2013; van de Rijt et al., 2014).

Therefore, we expect:

Hypothesis 2: Exogenous endorsements of or contributions to products benefit prod-

ucts with high levels of expected success more than products with low levels of expected

success

We explicitly examine whether cumulative advantage leads to increased inequality

by testing if social information has differential benefits across products and services

with different levels of expected success. In order to map differential benefits from

cumulative advantage to changes in inequality in success, one needs a counterfactual

estimate of expected success. Following Salganik and colleagues, we propose that a

product’s expected level of success without an exogenous change to social informa-

tion provides a reasonable way to create a counterfactual (Salganik, Dodds and Watts,

2006). This counterfactual enables us overcome two measurement issues. First, it pro-

vides a basis for measuring cumulative advantage. Deviation from expected success

can be used to quantify cumulative advantage effects. Second, it enables one to locate

products on the distribution of expected success prior to being affected by social in-

formation. This placement enables us to draw conclusions on how a change in social

information may affect the shape of the distribution of success. In the following sec-

tion, we describe the philanthropic marketplace we use in order to demonstrate our

methodology.

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3 Study Context

Our study takes place on one of the largest and oldest crowdfunding platforms: www.donorschoose.org

(referred to as DonorsChoose henceforth). Since its founding in 2003, DonorsChoose

has raised over $300 million dollars for classrooms by acting as an online marketplace

that connects teachers in need of school supplies with donors interested in supporting

public education. Teachers list a project in the marketplace by completing a standard-

ized template which includes the supplies they want for their classroom, the total cost

of the supplies and a brief description of how the supplies will be used. The projects

range from basic classroom supplies such as textbooks to more novel requests such as

educational technology. The majority of funding requests range from a few hundred

up to one thousand dollars.

Potential donors can search through tens of thousands of projects using standard

internet searching features such as keywords and facets. The barriers to entry for

support are extremely low: one can contribute little as one dollar. Figure 1 presents a

screenshot taken at the time of our experiment of a randomly selected project’s website.

DonorsChoose provides very detailed information, most of which they verify through

third-party sources. This information includes time-invariant details like the shipping

costs, the level of poverty of the school and a text description of the project created by

a teacher. It also includes dynamically updated social information such as the number

of previous donations, the total amount raised so far and text messages of support

from prior donors. When making a donation, donors can either reveal their identity or

make an anonymous donation. They are also prompted to write a message for other

potential donors to view, though this step is optional. Immediately after a donation,

the project page is updated to reflect the donated amount, number of past donors and

any new messages of support written by the donor.

DonorsChoose operates in a similar manner to other prominent crowdfunding sites

such as Kickstarter or IndieGoGo. Projects are successful if they achieve their funding

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goal. When a project reaches its goal, DonorsChoose ships the supplies directly to

the school to be used. Projects cannot receive donations above their fundraising goal

and are immediately closed to donations once it reaches its goal. If the project fails to

meet its funding goal after five months of listing, DonorsChoose removes the project

from the website and donors are refunded the amount they donated to use towards

other projects in the marketplace. This marketplace, which over 200,000 teachers and

two million donors have participated in, is a prototypical example of a philanthropic

crowdfunding platform (Agrawal, Catalini and Goldfarb, 2011; Burtch, Ghose and

Wattal, 2013; Meer, 2014).

We selected a philanthropic crowdfunding platform for several reasons. First, there

are clear metrics of success on the platform: whether a product is funded and how

quickly it reaches its fundraising goal. Second, there is variation in outcomes and ex-

pected levels of success. Roughly two-thirds of projects are funded in the marketplace

and this varies greatly based on geography, subject matter and other project charac-

teristics. Third, social information is very prominent in this marketplace. Information

on the number of donors and a progress bar, which displays how much money has

already been contributed, is displayed at the top of a project’s website (see Figure 1).

Donors to a project also have the option of writing short messages that are listed on

the project page. Overall, the platform is designed to communicate social information

to inform the decisions of potential donors.

Fourth, philanthropic crowdfunding is a place where social information should mat-

ter because “quality” of charitable causes is often difficult to directly observe (Hans-

mann, 1987). In particular, on DonorsChoose the beneficiaries of the donations, the

teacher and the students, are typically distinct groups from the donors.2 This makes

it difficult to assess the potential use of the pedagogical resources in the classroom

2DonorsChoose tracks donations made by teachers who posted the projects These are rare events.Through our qualitative examination of donor comments and conversations with DonorsChoose, it is clearthat the majority of donors are direct beneficiaries

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and, once acquired, to monitor their use. The lack of direct observability creates the

necessary preconditions for social information to lead to cumulative advantage effects;

it is possible for social information to influence evaluations such that there is a decou-

pling of evaluations from a product’s underlying features. Indeed, a large literature in

behavioral economics on matching and seed donations show that initial or matching

contributions lead to increased rates of subsequent donations (e.g., List and Reiley,

2002; Karlan and List, 2012). Based on this work and research on crowdfunding plat-

forms (van de Rijt et al., 2014), we expect that cumulative advantage operates in this

setting. This is critical to our study because in order for social information to affect the

distribution of funding outcomes, it needs to be able to produce cumulative advantage

effects.

Beyond theoretical considerations, understanding cumulative advantage in the phil-

anthropic domain is important in its own right. Individual philanthropy is economi-

cally significant as individuals are estimated to have donated over $250B to charities

in 2014.3 According to Gallup surveys, the vast majority of Americans —over 80 %

overall and over 95 % of Americans with incomes above 75 thousand dollars— are esti-

mated to donate to charity in a given year.4 Online giving, in particular, is becoming

increasingly important. Online donations grew at an estimated 8.9% in 2014 compared

to the 2.1% increase of donations overall.5 As online donations and crowdfunding plat-

forms become an increasingly important way for charities to fundraise, it is critical to

understand how social information shapes these decisions and affects the fundraising

process.

In addition, our particular setting is well-suited for our approach. DonorsChoose

has collected extremely detailed data on all the donation activity on its website since its

inception. They have the exact time (up to the nearest second), amount and source for

3Giving USA 20154http://www.gallup.com/poll/166250/americans-practice-charitable-giving-volunteerism.aspx5Blackbaud Charitable Giving Report: How Nonprofit Fundraising Performed in 2014

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every donation on the website. This data enables us to construct a linked longitudinal

set of donations for every project and every donation on DonorsChoose. We leverage

this rich historical data to construct accurate predictions on the expected success of a

project based on its time-invariant features when it is first listed on the marketplace.

While attractive for theoretical reason and empirical reasons, there is a reasonable

concern that studying donation decisions may not be generalizable to choice decisions

in other marketplaces, such as consumer purchasing decisions. Scholars have suggested

that donations are motivated by factors such as social signaling (Benabou and Tirole,

2006; Karlan and McConnell, 2014) and the intrinsic utility or “warm glow” of the act

of donating rather than aspects of the cause (Andreoni, 1990). While these factors

certainly affect some donations on this platform, there are several reasons to believe

that a large subset of donors on DonorsChoose are basing their decisions on more

technical aspects of a project and are making decisions which are more analogous to

traditional models of choice. First, one of the main attractions of DonorsChoose as a

resource to donors is the ability to search and compare projects through keyword search

and faceting (hence the name of the platform). Donors also have many alternatives

to support public education such as school fundraisers, parent-teacher organizations,

scholarship funds and a plethora of education nonprofits. If a donor wanted to support

public eduction for warm glow or social signaling reasons, these are widely available

options that do not involve the costs of searching through the platform. Thus, we

would expect some degree of sorting amongst donors.

Second, empirical analyses of DonorsChoose suggest donors are sensitive to aspects

of the projects. For instance, Meer (2014) and our own analysis of DonorsChoose have

found that donors are less likely to fund projects that have high levels of so-called

“overhead costs” such as sales tax and shipping costs. In addition, Meer (2014) found

that projects with higher levels of competition from similar projects are less likely

to be funded, suggesting that donors are choosing between projects. These results

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are consistent with recent research on donations more generally, which suggests that

some donors are concerned with how their charitable dollars are being used (Gneezy,

Keenan and Gneezy, 2014). In sum, the empirical evidence suggests that donors on

DonorsChoose are making decisions using criteria, such as competition and price, that

we would expect would affect choice behavior in other marketplaces.

4 Data and Methods

Identifying the effect of cumulative advantage is difficult even with the detailed data

that DonorsChoose collects. Without some form of randomization, naturally occurring

or induced by a third-party, one cannot confidently separate social influence effects from

unobserved heterogeneity (Manski, 1993; Shalizi and Thomas, 2011). For example, one

project in our data very quickly attracted numerous donors from across the country

and was funded withing hours of being listed, far less time than a typical project.

It was a request for a set of books from the very popular book series, The Hunger

Games. The timing of the project also set it up for success as a popular movie based

on the book had been released shortly before the project was listed. As a result, fans

of this series from around the country were searching the marketplace for The Hunger

Games-related projects to support. Based on our reading of the messages left by the

donors, it is likely that most were making their decisions to support the project based

on their interest in the series and not based on the activities of prior donors. However,

this relationship would be difficult to discern statistically as the flurry of donations

would induce a correlation between early donations and eventual fundraising success.

This is certainly an extreme example, but it illustrates how difficult it is for an analyst

to differentiate social influence from difficult to observe aspects of products.

We follow recent studies of social influence and sidestep the problem of unobserved

heterogeneity by taking an experimental approach. Specifically, we donated $7,200

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in $5 and $40 increments to 320 randomly selected projects on DonorsChoose over

a 30-day period. We randomized which projects received our anonymous donations

to isolate the causal effects of an initial contribution on funding outcomes. We also

account for the fact that in this marketplace our donation simultaneously increases

the probability of a project being funded by reducing the amount a project needs to

reach its funding goal by either five or forty dollars. We control for this “mechanical”

reduction by using a non-parametric modeling strategy to isolate the social influence

effect.

Our experimental approach allows us to test if social influence leads to cumula-

tive advantages. This alone does not inform us on how cumulative advantage process

affect the inequality of outcomes. This is because we cannot say if projects with a

greater chance of being funded disproportionately benefit from changes to social infor-

mation. Randomization has washed away such differences. To overcome this hurdle,

we construct a counterfactual measure of a project’s expected success in the absence

of our randomized donation. The interaction between this predicted level of success

and the randomized contribution enables us to assess if the change in unpredictability

varies across projects in different parts of the distribution of success. If projects likely

to succeed disproportionately benefit then we have evidence for success-breeds-success

inequality dynamics.

We take advantage of the fine-grained historical data available on DonorsChoose

to build a measure of expected success. Specifically, we use data on the characteris-

tics and outcomes of hundreds of thousands of past projects to create an estimate of

the probability a project would be funded without our intervention. If our exogenous

changes to social information through randomized donations lead to success-breeds-

success dynamics, then projects with a higher predicted probability of success should

benefit more than other projects. Conversely, if projects with lower predicted probabil-

ities of success disproportionately benefit, then our randomized donations may actually

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be reducing inequality in outcomes.

The next section describes how we generate these estimates.

4.1 Predicting Success

We used data on all projects posted between January 1st, 2005 and August 21st,

2012 to train a prediction algorithm that estimates a newly posted project’s chance of

success. We excluded data from before 2005 as the website was significantly smaller

and the information concerning each project is much less detailed. This window leaves

us with 426,790 projects after excluding a handful of outlier projects that requested

either zero or more than ten-thousand dollars. These 426,790 projects comprise our

training set.

This data provides a large number of project characteristics with which we can

predict funding success. For each project, we know the timing of when a project

comes online, the sales tax amount, fulfillment costs, vendor shipping charges, number

of students who benefit, resource type, subject matter and if the project is eligible

for matching funds. For each teacher, we know the teacher’s salutation (a proxy for

gender), the grade-level they teach, if the teacher is part of Teach for America, and

if the teacher is a New York Teaching Fellow. For each school, we know the location

of the school, the school poverty level, if it is a charter school, a year-round school, a

magnet school, an New Leaders for New Schools school, and if the school is part of the

KIPP system.

Each of these variables may independently affect the probability that a project will

reach its funding goal. In addition, it is likely that complex functions and combinations

of these variables matter as well. For example, on average projects that request iPads

may be less successful than projects that request that request textbooks. However,

this difference may be even greater for low poverty schools than high-poverty schools.

Donors may see technology at wealthier schools as especially unappealing. One might

18

also imagine that teacher characteristics have important interactions. Perhaps gender

stereotypes matter and male teachers are more successful at fundraising for sports

equipment projects than their female counterparts. Overall, we want to use a prediction

method that is able to account for potentially complex interactions between the project,

teacher and school characteristics.

We account for these potential interactions in a computationally tractable man-

ner using a widely used machine learning algorithm, Random Forests (Breiman, 2001;

Friedman, Hastie and Tibshirani, 2008). Random Forests are an extension of Classifi-

cation and Regression Trees (CART). Unlike standard regression analysis, the CART

algorithm automatically determines which covariates to include and how to include

them. It does this by scanning over the set of variables and picking the single variable

that best predicts the outcome of interest when split into two groups. Within each of

these groups, the algorithm again selects the single variable that best subdivides these

groups when split. It iterates in this manner until it there are less than a pre-specified

number of observations in each group.

The tree allows for the modeling of complex interactions since each of the sub-

groups may split on different variables. For example, the tree may first split projects

into high-poverty schools that are likely to be funded and low-poverty schools that are

unlikely to be funded. Then the algorithm would try to split each of these groups.

For the low-poverty group, the split may be on the fundraising goal, indicating that

donors are price sensitive. For the high-poverty group, the next split may be on vendor

shipping charges, indicating that donors to this group are averse to funding overhead

costs.

Despite the theoretical and interpretative clarity of CARTs, they often have poor

predictive performance and are unstable. The Random Forests algorithm addresses this

issue by averaging the predictions of many CARTs trained on different bootstrapped

samples of the data and by considering a randomly selected set of variables at each

19

split in each tree. This second step decorrelates the trees, which results in less vari-

ability when making predictions using the entire forest of trees. Random Forests have

performed extremely well in benchmark tests of machine learning prediction techniques

(Friedman, Hastie and Tibshirani, 2008; James et al., 2013). We use the “randomFor-

est” package in R to build a predictive model of project success and treat the 426,790

projects described above as our training set.

In the training sample, 65.5% of projects reach their funding goal. Therefore,

a naive algorithm that always predicts every project ends up funded would yield a

classification error rate of 34.5%. We improve on this error rate by fitting a Random

Forest using 28 variables (see Figure 2 for the complete list). Instead of including

cities or zip codes for each school, we include the longitude and latitude of the school,

allowing the Random Forest to inductively partition geographical variation. After

an initial exploratory analysis, we found that building a forest with 250 trees and

considering five randomly selected variables at each split yielded the greatest predictive

performance. The performance of the model is evaluated using the out-of-bag error

rate, a procedure conceptually similar to cross-validation. The final error rate is 24.2%,

a 30% decrease from naively guessing that every project is funded. The model exhibits

few false negatives. The Random Forest incorrectly classifies projects that are funded

as unfunded only 8.7% of the time. In contrast, for projects that do not reach their

funding goal, the algorithm is only correct 53.6% of the time. In sum, the Random

Forest greatly improves upon the naive prediction and does an especially good job at

predicting which projects are likely to be winners.

We also assessed the performance of the algorithm against our qualitative under-

standing of what factors matter on the platform. We first examined which variables the

algorithm determined were most important when predicting whether a project would

be funded. Figure 2 shows the importance of each variable in fitting the Random For-

est, from most important at the top to least important at the bottom. Intuitively, this

20

graphs shows which variables lead to the greatest gains in classification accuracy. While

variable importance tends to be biased towards variables that are continuous or have

more categories, the plot nonetheless provides a way to check for which variables mat-

ters for project success. Consistent with our expectations, the amount requested is the

most important variable, followed by date posted, geography, and then the project’s

subject. This accords with other analyses of this platform (Meer, 2014) and more

generally, with analyses of descriptive statistics of crowdfunding platforms (Mollick,

2014).

To further unpack what the algorithm is doing, we randomly selected projects from

each decile of predicted funding probability and present the differences and similarities

in Table 1. A cursory glance at this table would suggest that larger projects are less

likely to get funded. But this relationship is not deterministic. For example, the

project in the 5th row only requests $194.02 but the predicted probability of funding is

27.6%. However, the project in the 20th row is the most likely to get funded (95.6%)

and requests an additional $201.84 for a total of $395.86. That said, reducing the

amount requested for the project in the 1st row from $816.54 to $250 would increase

the predicted probability of funding from 5.6% to 48.28%. Moving the date of posting

for the project in the 15th row from March to June reduces the funding probability

from 77.2% to 66.4%. This difference suggests that it may be harder to raise money

in the summer months when most schools are not in session. For the project in the

16th row, removing the secondary focus subject reduces the predicted probability of

funding from 97.6% to 66.8%, suggesting that having a secondary focus subject may

be beneficial. In contrast, for the project in the 18th row adding a secondary focus

subject lowers the predicted probability of funding from 88.8% to 82.4%. It may be

that secondary focus subject interacts with other project characteristics in ways that

would likely be difficult to capture without the aid of the Random Forest algorithm.

21

4.2 Experimental Design

Our experiment made contributions to 320 randomly selected DonorsChoose projects

as soon as they were listed in the marketplace: 160 five dollar donations and 160

forty dollar donations. These are the 10th percentile and 65th percentile of donation

amounts on the site, respectively. We worked with the Chief Technology Officer of

DonorsChoose to create a customized data feed for all newly listed projects in a given

day. We only include projects that have not received any prior contribution in the few

hours since they went live. Over 99% of projects were included in our feed. We also

restricted our sample to projects with a primary or secondary subject as “Literacy,”

“Literature & Writing,” or “ESL”. This second selection criterion reduces the natural

variation that occurs across categories and increases our statistical power (Gerber and

Green, 2012).

The selection procedure worked as follows. For each of the twenty days on which

we made contributions, we first generated a list of all projects that fit the criteria

described above. We avoid altering macro-level market dynamics by only donating to

a small number of the listed projects. Donating to a large number of projects in one day

might change the probability of funding for both the treated and untreated projects.

Therefore, we restrict the number of projects that we contribute to on any given day in

order to ensure that we can meet the stable unit treatment value assumption (SUTVA).

This assumption would be violated if we dramatically changed the dynamics of the

marketplace (Morgan and Winship, 2007). Specifically, we limit the number of projects

we donate to at most 16 on any given day, a small fraction of active projects.

We donated to projects on twenty days from August 22nd to September 18th, 2012.

To maintain strict comparability between our treatment and control groups, we only

analyze projects listed on days in which we made a donation. Figure 3 shows the

number of projects we donated to, and the total number of projects at risk at receiving

our treatment. Our donations were anonymous and all contributions appear visually

22

identical to potential donors to minimize potential donor identity effects (Karlan and

List, 2012). We worked with DonorsChoose to ensure that our initial donation did not

immediately alter the project’s search rank.6 (Ghose and Yang, 2009; Ghose, Ipeirotis

and Li, 2014).

We construct a control group out of the 2,651 projects that were at risk for being

selected into treatment but were randomly excluded. We cannot include the entire

sample of non-treated projects in our models because the number of projects and

funding probability vary greatly across days. From our prediction modeling, we know

that timing effects are important and thus including the entire sample may lead us to

bias our estimates by improperly weighting some days more than others. To address

this issue, one can include fixed effects for each day to control for inter-day variation in

funding probability or sample projects proportional to the number of projects treated

on each day. We chose to randomly sample projects in proportion to the number

treated on that day.7 Specifically, we sample 5 control projects per 1 treatment project

to maximize our power. We have to drop two days where there are too few potential

control projects to sample. This procedure leaves us with 144 projects that receive the

$5 treatment, 144 the $40 treatment, and 1,440 randomly selected projects serving as

our control group.

5 Results and Analysis

We begin our analysis by comparing our treatment and control groups. Table 2 presents

summary statistics for the control, $5 treatment, and $40 treatment groups. The vari-

6By the design of the search algorithm, the amount contributed does not alter the search rank until theproject is nearing its 5 month time frame for funding Even at this point, the primary characteristics used torank search are the school characteristics, time remaining and amount outstanding to raise. Checking thesearch order qualitatively during our experiment revealed no difference between our treatment and controlgroups. Finally, the effects observed from our treatments occur before the algorithm meaningfully alterssearch results.

7Results are qualitatively unchanged using the fixed-effect approach.

23

ables “Total Project Amount”, “Number of Students Reached”, and the “Random

Forest Predicted Probability of Funding” are time invariant and are measured prior

to our treatment donations. In Table 2 the italicized variables “Days to Funding”

and “Project is Funded” are measured after our treatment. Correlations between

these variables are presented in Table 3. The pre-treatment variables show no statis-

tically significant differences between groups and provide first-order evidence that our

randomization procedure was successful. More formally, Table 4 regresses the three

pre-treatment variables on our treatment conditions. If our randomizations are unre-

lated to project characteristics, then it should be the case that the coefficients on our

treatment variables should be very close to zero. Indeed, the coefficients are small, and

all insignificant. This gives us confidence that our procedure resulted in randomized

treatment assignments.

The effects of our intervention on the post-treatment variables are presented in

Table 2. We find that our randomized donations alter the time to funding and the

probability that a project is funded. Projects in the $40 treatment group have a

funding rate of 84%, 10% higher than the control group rate of 73%. They also reach

their funding goal on average 13 days faster than the 70 days it takes the control group.

Unexpectedly, projects in the $5 treatment arm appear to perform somewhat worse

than the control being funded at a 72% rate as compared to the control rate of 74%.

Moreover, projects that received the $5 donations take on average 9 days longer to be

funded than projects in the control group.

We examine the hazard of funding by fitting separate Kaplan-Meier survival curves

by experimental condition in order to better understand how our treatments altered

funding dynamics. This approach also enables us to account for the right-censoring that

occurs when DonorsChoose removes projects that have been on the site for 5 months

(approximately 150 days). Given enough time, some (or perhaps all) of these projects

would be fully funded. Analyzing funding rates allows us to account for this censoring.

24

Figure 4 plots the probability of funding by experimental condition. The x-axis is the

number of days since posting. Consistent with Table 2, the $40 treatment appears to

have a greater hazard rate of funding than the control group and this difference appears

to grow larger with time. This increase is consistent with models of social influence

leading to cumulative advantages. The funding probability for projects that received

the $5 treatment appears slightly lower, but this decrease does not appear to change

with time.

While the $40 Kaplan-Meier curve is suggestive of cumulative advantage, it does

not take into account that our donation reduces the amount of outstanding money a

teacher has to raise to reach their goal, which we refer to as the “amount outstanding”.

For instance, projects in the $40 treatment arm have $40 less to raise. Therefore, even

if donors were unaffected by our treatment, projects in the $40 treatment arm should

still be more successful at reaching their funding goals, ceteras paribus. We account

for the reduction in the amount outstanding by controlling for it in a non-parametric

way. Specifically, we fit Generalized Additive Models with coefficients for each of our

treatments and with a penalized regression spline in the amount outstanding. We set

the number and location of knots for the spline by minimizing the error rate using

cross-validation.

Table 5 present linear probability models of funding and Table 6 presents hazard

models of funding. Model 1 and Model 5 replicate the summary statistic and Kaplan-

Meier analysis presented above in regression form. The results are consistent with

the visual evidence in Figure 4. The probability of funding for the projects in the $40

treatment condition increases by 9.7 percent (SE = 0.038) and the hazard of funding by

0.29 (SE = 0.096). While the $5 treatment is negative, the coefficient size is small and

statistically insignificant. Model 2 and Model 6 control for the mechanical reduction

by incorporating a spline in the amount outstanding. Model 6, the Cox model, also

25

includes strata for each quintile of the amount outstanding.8

We find some evidence for cumulative advantage in Models 2 and 6. Once we

account for the mechanical reduction in the amount outstanding, the coefficient for

the $40 treatment drops from 0.097 to 0.069 and is only significant at the 10% level.

In Model 6, the hazard drops from 0.291 to 0.217 but remains significant at the 5%

level. Taking these results together, it appears that roughly one-third of our effect

occurs because of the mechanical reduction in the amount outstanding and the other

two-thirds by changing the hazard rate of future donations. The $5 donations do not

appear to have any meaningful effect on outcomes. Overall, Hypothesis 1 is largely

supported for our $40 treatment.

Next, we investigate Hypothesis 2 by testing whether these cumulative advantage

effects change the distribution of outcomes. We estimate these changes by interacting

our treatments with our measure of predicted success. We begin by first including

normalized predicted funding probability in Models 3 and 7 in Tables 5 and 6. The

predicted funding probability coefficient is highly significant in the linear probability

and Cox models. To get a sense of the effect size, it is useful to compare the coefficient

in our regression to the overall variability of our measure. A one standard deviation

increase corresponds to a 15% increase in predicted probability. In the linear proba-

bility model, the coefficient on our normalized measure is 14.5%. This implies that a

one standard deviation increase in the predicted probability of funding (15% higher)

leads to a 14.5% increase in the actual probability of funding in our data. This pro-

vides strong evidence that our predicted probability measure is capturing differences

in the likelihood of project success. Moreover, we increase our power by capturing a

substantial amount of project heterogeneity with the inclusion of the predicted funding

8One concern with fitting Cox models is meeting the proportional hazards assumption. In unreportedanalyses, we find that larger projects are less likely to get funded in the early days than projects that requesta smaller amount, though this difference dissipates over time. To account for this, we stratify models 6-8 onquintiles of project size. Testing the model with these strata reveals that we meet the proportional hazardsassumption.

26

probability variable in Models 3 and 7. The magnitude and statistical significance of

our $40 treatment increases in both models. This provides further evidence that our

$40 treatment leads to cumulative advantage.

Models 4 and 8 in Tables 5 and 6 interact our treatment indicators with the pre-

dicted probability of funding. We find little evidence that projects that have higher

predicted probabilities of funding benefit more from a randomized $40 treatment. The

coefficient on the interaction term is small and statistically insignificant in both mod-

els. The main effect of the $40 donation does not change in magnitude nor significance.

Thus, we find little evidence for cumulative advantage distorting the baseline chance of

funding success. All projects appear to benefit equally from arbitrary and exogenous

variation in social information.

A potential concern with our analysis is that the functional form of the interaction

effect may be non-linear. Our assumption of linearity may be masking underlying ef-

fects that at the tails of the distribution. We account for these possibilities by again

using Generalized Additive Models with a flexible spline specification. Specifically, we

fit models in which we interact our $40 treatment with a spline of predicted funding

probability. This allows us to see if our treatments have larger or small effects at differ-

ent points in the predicted funding probability distribution. Since the $5 treatment has

no effect thus far, we drop these observations from this analysis to ease interpretation.

As above, we determine the location and number of knots using cross-validation and

minimization of the the out-of-fold error rate.

Interpreting the implications of these non-linear interactions using coefficient esti-

mates directly is extremely difficult. In lieu of regression tables, we present the results

of these non-linear interactions by plotting the marginal effects in Figure 5. The x-

axis in both plots is the standardized predicted funding probability. The black lines

represent changes in funding probability for projects in the control group. The blue

line changes in the funding probability for the the projects in the $40 treatment group.

27

The light shaded areas are the 95 percent confidence intervals. While the spline in

the linear probability model is slightly non-linear at the tails, the Cox hazard model

is perfectly linear. For both groups and in both models, the realized funding proba-

bility increases linearly with the predicted funding probability. We find no evidence

for non-linear interaction effects. In short, we find no evidence for Hypothesis 2. Our

treatments are constant no matter a project’s expected level of success; the unlikely to

succeed and the very likely to succeed appear to equally benefit.

In summary, we find that our $40 treatment leads to cumulative advantage. How-

ever, we find little evidence that our treatment varies across projects with different

predicted levels of success. These results taken together suggest that cumulative ad-

vantage operates in our setting but that random variation in social information plays

no direct role creating wider differences in success than one would expect. Instead, it

seems that exogenous changes in social information induced by our treatments ben-

efits projects across the distribution of expected success in a relatively equally way.

This suggests that exogenous changes in social information may simply lead to more

unpredictable outcomes, even if the distribution of success in expectation is relatively

similar.

6 Discussion

Our study has shown that the existence of cumulative advantage induced by exoge-

nous changes does not necessarily increase inequality of success. This existence proof

is an important corrective to the assumption made by many scholars that cumulative

advantage, often created by social influence processes, inherently increases the inequal-

ity of success in marketplaces (Salganik, Dodds and Watts, 2006; Muchnik, Aral and

Taylor, 2013; van de Rijt et al., 2014). Rather than assume a direct mapping between

cumulative advantage and changes in the inequality of success, we provide a replicable

28

methodology for assessing the existence and strength of this link. Quantifying these

effects is necessary in order to design marketplaces that balance the benefits of social

information with the potential costs of the distortions such information may introduce.

Though we did not find evidence that exogenous changes to social information

produce differential cumulative advantage effects, there are other mechanisms through

which cumulative advantage processes may exacerbate inequalities. For example, prod-

ucts that have an innate appeal may be more likely to receive an initial review, en-

dorsement or contribution. Receiving earlier support could provide an initial advantage

for these products over comparable products. In addition, some products in certain

marketplaces may be more likely to receive large contributions, which prior research

(along with our results) suggests may be more likely to attract subsequent customers

(List and Reiley, 2002). Future research should investigate the role of these endogenous

processes. However, our analysis greatly reduces concerns that arbitrary and exoge-

nous early differences in social information deterministically lead to increases in the

inequality of success. In our setting, products that are unlikely to succeed and that are

likely to succeed equally benefit from changes to social information that is uncorrelated

with underlying features of a product.

By focusing on the inequality of success, our approach also sidesteps the contentious

debate over whether the “wisdom of crowds” exists when social information in a mar-

ketplace leads to potentially interdependent rather than independent judgments (Zhang

and Liu, 2012). This is an important debate to have, but it ignores the fact that mar-

ketplaces are often designed in ways that shepherd crowds towards particular goals. For

example, crowdfunding platforms like Kickstarter and IndieGoGo curate and promote

products that would otherwise be difficult to discover. DonorsChoose explicitly high-

lights projects that serve high-poverty public schools precisely because one of its goals

as a philanthropic marketplace is to help direct capital to needy students. In practice,

these platforms tend to reduce the inequality of success by promoting products that

29

are aligned with the goals of the marketplace designers.

An important limitation to our study is the generalizablilty of its context. While we

argue that the behavior of donors on DonorsChoose is similar to what we would expect

in other marketplaces, we cannot be certain without replication in other contexts. For

instance, it is possible that our interventions affect only aspects of evaluation that are

particular to a philanthropic context, such as social signaling or warm glow, rather

than more general perceptions of project’s features. Although we cannot rule out these

explanations with our current study, future research should attempt to study these

possibilities. Moreover, understanding both commercial and philanthropic motivations

is particularly timely as new products and services are increasingly combining the two

(Battilana and Lee, 2014). For example, consider the case of so-called “rewards-based”

crowdfunding platforms such as Kickstarter and IndieGoGo. While some contributors

use these platforms to buy a product or service (i.e., the contributor’s reward is the

actual product or service being developed), many contributors support the overall

endeavor and do not receive the actual products and services created. Instead, they

typically receive recognition or trinkets as their rewards, which is very similar to what

donors normally receive in exchange for charitable contributions.

7 Conclusion

One of the key findings of our study is that social information may increase unpre-

dictability of success in marketplaces. But when would unpredictability be desirable

and when might it be detrimental? Our view is that the value of unpredictability is

that it is one way to promote diversity of success in a marketplace. Diversity is not

always a good thing. For instance, unpredictability is especially harmful in market-

places where consumers have common goals, a consensus on what constitutes “quality”

and a consensus on how to measure it. One example of this type of marketplace would

30

be peer-to-peer lending. Lenders have similar goals; they are looking for the best risk

adjusted rate of return they can get. A situation in which social influence increases the

funding of poor performing loans is bad for the consumers of these marketplaces and,

in the long run, may jeopardize the viability of these platforms if lenders lose money.

It is also likely bad for people who are taking the loan, as failing to repay a loan may

hurt their credit rating or ability to get future loans.

Alternatively, many marketplaces have consumers with diverse motivations and

where assessments of quality are more varied (Zuckerman, 2012). These marketplaces

may benefit from unpredictability as it leads to diversity in the distribution of success.

The chance of an unpredicted success may encourage risk-taking, innovation, and ex-

ploratory strategies (March, 1991). The diversity of success may be an explicit goal

for marketplaces seeking to foster innovation, a goal of many crowdfunding platforms.

Concerns about decoupling success from the underlying appeal of a product may be

muted because the single ideal or metric of “quality” may not exist. In sum, the

greater levels of unpredictability created through social information may, on average,

help products with less inherently popular characteristics. But it may also enable less

appealing but more innovative products to succeed.

31

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8 Figures and Tables

Figure 1: Example of the DonorsChoose website at the time the experiment took place.

35

KIPP School

Promise School

NYTF Teacher

NLNS School

Magnet School

Year Round School

Charter School

TFA Teacher

Almost Home Match Eligible

School Poverty Level

Teacher Mr, Mrs, or Ms

Double Impact Match Eligible

Primary Focus Area

Fulfillment Costs

Grade Level

Resource Type

Secondary Focus Area

Year

Sales Tax

Day of Week

Number Students Reached

Vendor Shipping Charges

Primary Focus Subject

Secondary Focus Subject

School Latitude

School Longitude

Day in Year

Tota Project Amount

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

0 5000 10000 15000 20000

Variable Importance

MeanDecreaseGini

Figure 2: Random Forest variable importance. Variables at the top of the list are moreimportant in predicting a project’s probability of success than variables at the bottom of thelist.

36

Table 1: Two Randomly Selected Projects from each Decile of Predicted Funding Probability

PID P(Funding) Date Project Amt Primary Subject Secondary Subject Shipping StudentsProject Title

1 0.056 05-12 816.54 Literature & Writing Literacy 12 175A New Projector Would Make Presentations-Kids Brighter!

2 0.068 04-16 377.72 Literature & Writing Literacy 12 27Continuing To Expand Our Electronic Library

3 0.136 05-06 1, 899.96 Mathematics Other 158 24Teaching Through Technology

4 0.156 03-15 412.50 Mathematics ESL 31.29 100Becoming Mathematicians With Technology

5 0.276 02-18 194.02 Special Needs Mathematics 0 30Create And Learn

6 0.292 08-09 661.49 Environmental Science Applied Sciences 0 70Geologists In The Making

7 0.316 07-21 210.02 Literature & Writing 0 24Stay Gold, Ponyboy

8 0.320 03-30 379.85 Literature & Writing Mathematics 12 18Learning and Growing through Music

9 0.404 06-16 440.60 Literature & Writing Literacy 0 31Help Us Make Writing Wondrous!

10 0.452 03-14 252.47 Literacy Mathematics 12 21iCan Learn with iPods!

11 0.536 05-10 735.32 Music 0 120Keyboards to Keep Kids Learning Part 2!

12 0.572 06-15 434.45 Literacy Literature & Writing 0 30We Are Greatly in Need of General School Supplies

13 0.656 02-23 777.27 Literature & Writing 12 75New Technology for Our Classroom 2

14 0.696 06-12 142.32 Literacy Special Needs 0 21Keeping Our Classroom Colorful in the New School Year!

15 0.772 03-07 598.26 Special Needs 47.21 9Technology for Special Needs Students

16 0.796 02-19 296.83 Literacy Early Development 0 18Where Are the Books?

17 0.816 05-25 339.35 Music 0 10Help Us Learn Guitar!

18 0.888 03-11 612.59 Literacy 0 27Empowering First Graders

19 0.928 03-16 250.84 Special Needs Literacy 12 13Read and Explore

20 0.956 08-11 395.86 Literacy 0 26Fill Our bookshelves!

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Table 2: Summary Statistics by Experimental Condition

Variable N Mean St. Dev. Min Median Max

Training Set Projects

Control ProjectsTotal Project Amount 1,440 534.80 393.55 133.47 434.77 4,512.88Number Students Reached 1,440 68.1 111.4 5 30 999Predicted Probability 1,440 0.66 0.15 0.22 0.67 0.96Days to Funding 1,440 69.9 56.1 1 49 150Project is Funded 1,440 0.74 0.44 0 1 1

$5 Treated ProjectsTotal Project Amount 144 495.18 297.88 131.72 435.63 2,216.21Number Students Reached 144 61.8 96.8 7 30 999Predicted Probability 144 0.66 0.15 0.27 0.65 0.94Days to Funding 144 78.7 56.2 2 58 150Project is Funded 144 0.72 0.45 0 1 1

$40 Treated ProjectsTotal Project Amount 144 491.74 391.95 134.95 418.36 3,297.28Number Students Reached 144 74.5 145.1 12 29.5 999Predicted Probability 144 0.67 0.15 0.29 0.69 0.92Days to Funding 144 56.7 52.2 1 39 150Project is Funded 144 0.84 0.37 0 1 1

Italicized variables are measured post treament.

Table 3: Correlations

(1) (2) (3) (4) (5) (6) (7) (8)

(1) Total Project Amount(2) Number Students Reached 0.08(3) Predicted Probability -0.63 -0.07(4) Number of Natural Donors -0.09 -0.02 0.09(5) Days to Funding 0.18 -0.01 -0.32 -0.26(6) Reached Funding Goal -0.14 0.02 0.28 0.38 -0.78(7) Forty Dollar Treatment -0.03 0.02 0.02 -0.01 -0.07 0.06(8) Five Dollar Treatment -0.03 -0.02 -0.02 -0.02 0.05 -0.02 -0.09

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Table 4: Balance Tests

Dependent variable:

PFP Log(Project Amount) Log(Num Students Reached)

(1) (2) (3)

$5 Treatment −0.008 −0.046 0.004(0.013) (0.051) (0.075)

$40 Treatment 0.010 −0.088 0.013(0.013) (0.051) (0.075)

Constant 0.663∗∗ 6.098∗∗ 3.705∗∗

(0.004) (0.015) (0.023)

Observations 1,728 1,728 1,728Model D.F. 3 3 3Log Likelihood −843.173 −1,513.84 −2,195.23Adjusted R2 −0.001 0.001 −0.001

Note: ∗p<0.05; ∗∗p<0.01Linear Regression Models.

Predicted Funding Probability (PFP).

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Table 5: Linear Probability Models

Is the project funded?

(1) (2) (3) (4)

$5 Treatment −0.028 −0.033 −0.020 −0.019(0.038) (0.037) (0.036) (0.036)

$40 Treatment 0.097∗ 0.069 0.087∗ 0.084∗

(0.038) (0.037) (0.036) (0.037)

Predicted Funding Probability (PFP) 0.145∗∗ 0.141∗∗

(0.015) (0.015)

$5 Treatment × PFP 0.022(0.036)

$40 Treatment × PFP 0.027(0.036)

Constant 0.744∗∗ 0.746∗∗ 0.744∗∗ 0.744∗∗

(0.011) (0.011) (0.011) (0.011)

Project Amount Splines No Yes Yes Yes

Observations 1,728 1,728 1,728 1,728Estimated Model D.F. 3 6.87 6.17 8.12Log Likelihood −1,007.198 −974.833 −934.405 −935.990Adjusted R2 0.003 0.042 0.085 0.085

Note: ∗p<0.05; ∗∗p<0.01;Linear probability models with penalized splines.

All continuous variables standardized.Predicted Funding Probability (PFP).

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Table 6: Cox-Proportional Hazard Models

Days till project is funded

(5) (6) (7) (8)

$5 Treatment −0.138 −0.186 −0.145 −0.149(0.103) (0.103) (0.104) (0.105)

$40 Treatment 0.291∗∗ 0.217∗ 0.270∗ 0.239∗

(0.096) (0.097) (0.097) (0.102)

Predicted Funding Probability (PFP) 0.388∗∗ 0.374∗∗

(0.045) (0.047)

$5 Treatment × PFP 0.032(0.106)

$40 Treatment × PFP 0.160(0.107)

Project Amount Quintile Strata No Yes Yes YesProject Amount Splines No Yes Yes Yes

Observations 1,728 1,728 1,728 1,728Estimated Model D.F. 2 3.17 5.01 7.91Log Likelihood -8,936.613 -6,813.302 -6,773.990 -6,772.463

Note: ∗p<0.05; ∗∗p<0.01;Cox-proportional hazard models with penalized splines.

All continuous variables standardized.Predicted Funding Probability (PFP).

41

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Figure 3: Number of projects per day posted during experimental intervention period bycondition.

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0 50 100 150

Days since project posted

00.

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81

Exp Condition

Control$5$40

Figure 4: Kaplan-Meier Curves showing the probability after x days that a project is fullyfunded by condition.

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-3 -2 -1 0 1 2

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Linear Probability Model

Standardized Predicted Funding Probability

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Figure 5: Testing the Linearity of the Interaction Effect using Generalized Addative Models.

44