When FinTech Competes for Payment Flows

Christine A. Parlour
Haas School of Business, University of California-Berkeley, USA

Uday Rajan
Stephen M. Ross School of Business, University of Michigan, USA

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Haoxiang Zhu
MIT Sloan School of Management and NBER, USA

We study the impact of FinTech competition in payment services when a monopolist bank
uses payment data to learn about consumers’ credit quality. Competition from FinTech
payment providers disrupts this information spillover. The bank’s price for payment services
and its loan offers are affected. FinTech competition promotes financial inclusion, may hurt
consumers with a strong bank preference, and has an ambiguous effect on the loan market.
Both FinTech data sales and consumer data portability increase bank lending, but the effects
on consumer welfare are ambiguous. Under mild conditions, consumer welfare is higher
under data sales than with data portability. (JEL G21, G23, G28, D43)

Received April 1, 2020; editorial decision March 21, 2022 by Editor Itay Goldstein.

Banks have historically offered a bundle of services, including payment

processing and loans, to both businesses and individuals. Currently, in
the United States, technology giants, such as Apple, and more specialized
companies, such as PayPal and Venmo, compete in the payment processing
market. In China, mobile payments made through payment processors, such
as Alipay and WeChat Pay, account for over 16% of gross domestic product
(GDP) (see Bank for International Settlements 2019). In Kenya, M-Pesa is

We are grateful to the Editor Itay Goldstein, two anonymous referees, Gilles Chemla, Will Diamond, Jon Frost,
Paolo Fulghieri, Gary Gensler, Zhiguo He, Wenqian Huang, Christian Laux, Gregor Matvos, Mario Milone, Gans
Narayanamoorthy, Robert Oleschak, Cecilia Parlatore, Amiyatosh Purnanandam, Amit Seru, Antoinette Schoar,
Andrew Sutherland, Xavier Vives, Jialan Wang, Jiaheng Yu, and Yao Zeng, as well as seminar and conference
participants at the Bank of Canada, the Bank of Finland, the Bank for International Settlements, Baruch College,
the Cambridge Corporate Finance Theory Symposium, EPFL/University of Lausanne, the Finance Theory Group,
the Future of Financial Information Conference, Goethe University Frankfurt, GSU-RFS FinTech Conference,
HEC Paris, MIT Sloan, the NBER Household Finance Group, Search and Matching Virtual Seminar, SFS
Cavalcade, Swiss National Bank, Tulane University, University of Hong Kong, University of Amsterdam, UCLA,
University of Maryland, University of North Carolina, Vienna Graduate School of Finance, and the WFA.
Haoxiang Zhu’s work on this paper was completed prior to December 10, 2021. Send correspondence to Uday
Rajan, urajan@umich.edu

The Review of Financial Studies 35 (2022) 4985–5024

© The Author(s) 2022. Published by Oxford University Press on behalf of The Society for Financial Studies.
All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
https://doi.org/10.1093/rfs/hhac022 Advance Access publication April 27, 2022

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 The Review of Financial Studies / v 35 n 11 2022

used by about three-quarters of households (see Jack and Suri 2014). FinTech
competition in payment processing has been supported by regulations, such
as the Payment Services Directive 2 in Europe (which requires banks to
provide customers’ account information to third-party payment providers in
a standardized format) and the Open Banking initiative in the United Kingdom
and Canada. Many FinTech and Big Tech firms entered the financial space
by competing in payments and have since expanded their activities to include
lending and banking more broadly.
The rise of competition for stand-alone payments uniquely disrupts the
historical banking model because payment flows are informative about credit

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risk. For example, Black (1975) observes that the flows in an account allow a
bank to better understand a customer’s credit quality. An extensive empirical
literature on consumer and business credit confirms this intuition.1
In this paper, we construct a parsimonious model of a bank as a payment
processor and lender, and consider the effect of low-cost competition in
payments. We focus on payments for two reasons. First, payment service
is economically large and important. Second, competition in payments is
relatively new: prior to the rise of digital payments, the only competition across
bank-based payments was physical cash. By contrast, banks have always faced
competition in the loan market.2
In our model, the bank is a monopolist in lending, but competes with two
identical FinTech firms for payment processing. The bank and FinTech firms
have the same payment technology. The FinTech firms engage in Bertrand
competition and offer payment services at a price normalized to zero. The
bank strategically prices payment services to maximize its total profit, and
internalizes the benefit of access to payment data. Consumers differ in their
creditworthiness, which can be high or low. In addition, consumers have a
value for unmodeled bank services that we label “bank affinity.” Bank affinity
serves to generate horizontal differentiation between the bank and the FinTech
firms. A negative bank affinity means a cost to access banks. We allow the
distribution of bank affinity to depend on consumers’ creditworthiness.
Crucial to the model is that payment processing is valuable to the provider. A
payment processor can extract a signal about the credit quality of its customers

1 McKinsey (2019) states that “payments generate roughly 90 percent of banks’ useful customer data.” The
connection between transaction account flows and credit quality has been made by Puri, Rocholl, and Steffen
(2017) using German data on consumers, Mester, Nakamura, and Renault (2007) using Canadian data on small
businesses, and Hau et al. (2019) using data on loans made by Ant Financial to online vendors. Agarwal et
al. (2018) show that relationship customers in the United States are less likely to default on credit card debt.
Liberti, Sturgess, and Sutherland (2021) find that lenders who join a commercial credit bureau early (and hence
have access to the longer payment histories of borrowers), gain market share relative to lenders who join late.
Rajan, Seru, and Vig (2015) find that a loss of information in the loan-making process can lead to a consistent
misestimation of default probabilities on the loan portfolio.
2 We call incumbents in the payment space “banks;” in practice, this includes large banks, such as JP Morgan and
Citibank, as well as card networks, such as Visa and Mastercard. We call the entrants into the payment space
“FinTech;” entrants comprise a diverse set of businesses from startups to small online banks to “Big Tech” firms,
such as Alibaba, Tencent, Amazon, and Apple.

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 When FinTech Competes for Payment Flows

from information about their transactions. Thus, a bank that does not handle
the payments of a loan applicant has less precise information about their credit
quality. As a result, payments spill over onto the credit market. This spillover
has different welfare implications for consumers, banks, and regulators.
The notion of creditworthiness in our model is conditional on all other
(nonpayment) information available to the bank, including the borrower’s credit
score and financial statements. Thus, our model applies well to situations in
which the payment signal is particularly valuable, such as for borrowers who
have a limited financial history and those seeking unsecured loans.
Consumers know their own credit type and, as is standard in a screening

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model, the bank offers a menu of two contracts to each consumer and allows
them to choose. The contracts differ both in loan quantity and in interest rate.
The optimal screening menu has the feature that the participation constraint of
the less creditworthy consumer and the incentive compatibility constraint of
the more creditworthy consumer bind. Thus, the former obtains zero surplus
while the latter obtains an informational rent. The optimal menu also generates
a social inefficiency: the bank distorts the loan quantity that it offers to low
creditworthy consumers downward, whereas high creditworthy consumers are
offered an efficient loan quantity.
A consumer’s demand for bank payment services depends on their bank
affinity, the price of the bank’s payment service relative to nonbank options,
and their expected utility from a loan. A change in the price of payment services
by the bank has the expected direct effect on the bank’s profit. It also has an
indirect effect, as it changes the bank’s set of payment customers. This in turn
changes the bank’s information and thus its optimal screening contracts in the
loan market, which then alters consumers’ expected loan market surplus and
hence feeds back into the demand for bank payments.
Although standard intuition about competition may lead one to expect that
FinTech competition leads to a fall in the bank’s price for payment services,
we present conditions under which the price instead increases. Facing FinTech
entry, the bank’s choice is between a higher profit margin on a narrower set of
consumers versus a smaller profit margin on a broader set of consumers. The
bank may choose either response, depending on the bank affinity distribution
of consumers. The industrial organization literature has shown that increased
competition may lead to higher prices.3 Our model includes an additional effect,
in the novel feedback loop between consumers’ demand for bank services and
their expected surplus in the loan market.
The consequences of FinTech competition for loan market surpluses are
intricate. As mentioned earlier, the bank’s optimal menu of contracts depends

3 Chen and Riordan (2008) show in theoretical terms that when consumer valuations have a decreasing hazard rate,
the price of a good is higher under duopoly than monopoly. In a model with random consumer utilities, Gabaix
et al. (2016) show that firms’ markups increase in the number of firms if the distribution of consumer valuations
has “fat tails.” Empirically speaking, Sun (2021) shows that in response to the entry of low-cost Vanguard index
funds, funds sold with broker recommendations (i.e., likely with captive customers) increased their fees.

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on the information it has about each loan applicant. If the pool of borrowers it
faces has a concentration of high (low) credit type consumers, the bank designs
its menu of contracts to primarily extract surplus from high (low) types. Because
the bank affinities of high and low credit consumers have flexible distributions,
FinTech entry may leave the bank with a consumer pool tilted toward either
credit type. Therefore, the high credit consumers’ loan surplus can go up or
down with FinTech competition in payment. For a similar reason, high credit
consumers’ loan surplus is generally nonmonotone in the quality of the bank’s
signal extracted from payment data.
Despite the subtle and nuanced changes in loan market surplus, the impact of

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FinTech competition is unambiguous for some consumers. In particular, those
who were previously unbanked now use a FinTech firm to process payments,
and benefit from financial inclusion. In contrast, consumers with strong bank
affinity stay with the bank, unswayed by FinTech competition. Among such
consumers, the welfare of low credit types depends purely on the price of
payment services, which changes on FinTech entry. Our results therefore point
to cross-sectional trade-offs across different consumer segments.
Our baseline model assumes that once payment data are diverted from the
bank, they are inaccessible in the credit market. In reality, payment data are
frequently used as an input for lending through FinTech-bank partnerships. For
example, in 2012, a large bank in Kenya and the operator of M-Pesa mobile
money formed a partnership to launch M-Shwari, which provides credit to
borrowers, even if they have no banking or credit history. Bharadwaj, Jack, and
Suri (2019) find that such mobile money-enabled credit quickly gained market
share and increased household resilience. Using the Indian demonetization
event, Ghosh, Vallée, and Zeng (2021) find that firms adopting cashless payment
receive better outcomes in the credit market, consistent with their model in
which cashless payment is verifiable information but cash payment is not.4
The synergy between data and lending is also evident in partnerships, such
as those between Ant Group and its partner banks in China,5 between Atom
Bank and Plaid in the United Kingdom, and between TAB Bank and Mulesoft’s
Anypoint Platform in the United States. Such economic relationships allow the
FinTech company to transfer data to the lender.
Another possibility for data transfer is that consumers own their data and
port them when needed. Policy makers and practitioners have embraced this
idea. For example, the General Data Protection Regulation (GDPR) in Europe
suggests that consumers should have more direct control of their data. In July

4 The lender in their model is competitive and only makes loans, whereas the bank in our model has two business
lines, loans and payments.
5 In its prospectus ahead of its planned initial public offering (IPO) in Hong Kong (which Chinese regulators later
called off), the company says “[a]s of June 30, 2020, approximately 98% of credit balance originated through our
platform was underwritten by our partner financial institutions or securitized.” In September 2021, the Chinese
government proposed a plan to split up the payment and lending arms of Alipay and to turn over data to a joint
venture that would be partly state owned (see Reuters 2021).

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 When FinTech Competes for Payment Flows

2021, the Biden administration in the United States issued an executive order
to, among other things, allow consumer portability of their data.6 Industry
initiatives, such as the Financial Data Exchange, seek to standardize bank
payment data, to allow consumers to port their data.7
Motivated by these developments, we compare two methods by which
payment data find their way back to the lending market: FinTech firms selling
data to the bank and consumers owning their data and choosing whether to port
their data to the bank. In both regimes, the bank, as the sole lender, has access
to the signal about a consumer’s credit quality extracted from payments, even
if the consumer uses a FinTech firm to process payments. The difference is

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that in the case of FinTech data sales, competitive FinTech firms reimburse the
proceeds of data sales back to consumers in the form of subsidized payment
services. In contrast, when consumers port their own data, we show that a
form of unraveling effectively forces everyone to share data with the bank for
free. Put differently, while data porting is in principle voluntary, the fact that
others share data imposes a negative data externality on those who do not.
Thus, policies that aim to give consumers more direct, and potentially stricter,
control of their data may have the unintended, opposite effect. In anticipation
of such forced data sharing, the bank’s price for payment services worsens in
the regime with consumer data porting.
Importantly, in our model the bank remains a monopolist lender throughout,
whereas the FinTech firms act as Bertrand competitors in payments. More
broadly, our results should be interpreted as pointing out that whether data
sales or consumer ownership of data is more beneficial for consumers critically
depends on how surplus is shared between banks, FinTech firms, and consumers
in the former case and between banks and consumers in the latter case. The
surplus-sharing regime that emerges, of course, depends on the structure of
competition in the payment and loan markets.
A third way for payment data to be used in lending is to have the
FinTech firm lend directly. We exclude this possibility from our paper, in
part because oligopolistic competition in screening contracts is significantly
more complicated than monopolist screening. FinTech lending (or nonbank
lending more broadly) has been extensively examined in the literature. For
example, He, Huang, and Zhou (2021) provide a model of FinTech and bank
competition in lending with consumer data sharing. Their main result is that
under some circumstances open banking can make all consumers worse off,
with the intuition again being partly based on unraveling. In contrast, our focus
is FinTech competition in the payment market, and its effect for lending is
primarily through the endogenous self-selection of consumers and the screening
by the bank. These two approaches are, thus, complementary.

6 See, for example, https://www.whitehouse.gov/briefing-room/statements-releases/2021/07/09/fact-sheet-

executive-order-on-promoting-competition-in-the-american-economy/.
7 See https://financialdataexchange.org/.

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In recent work, Vives and Ye (2021) consider the effect of technological

advances on the lending market in the presence of competing banks. In
particular, technological improvement can lead to reduced welfare if it mitigates
the effect of distance on screening or monitoring costs. Vives (2019) provides
a detailed survey of digital disruption in banking, and Morse (2015) reviews
the P2P literature.8
To summarize, our analysis highlights two fundamental tensions when
FinTech competes for payment flows. The first tension is between financial
inclusion and disruption. For unbanked or underbanked consumers, not only
does FinTech competition provide access to more convenient electronic

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payment systems but also the data generated in the payment process become
“hard information” that leads to increased credit provision to this population.
In contrast, enhanced competition and data sharing could harm consumers
who are well off in the current system. If, for example, banks respond to
FinTech competition by raising their price for payment services, those who
stay with the bank may be worse off. Likewise, high credit consumers may
receive a lower surplus in the loan market if data sharing leads to more accurate
price discrimination by banks. The trade-off between these two effects is likely
country specific. It is perhaps unsurprising that FinTech payment competition
tends to be viewed as “inclusive” in developing economies and “disruptive” in
developed ones.
The second tension is between a bank regulator (such as the Federal Reserve
Board) and a competition regulator (such as the Federal Trade Commission).
The bank regulator cares about the stability of banks, and one way to achieve its
goal is to keep banks profitable. The competition regulator cares about consumer
welfare. The conflict here is unavoidable. In our model, the bank receives all
surplus from lending to low credit consumers, and under some conditions, data
generated in the payment process harms high credit consumers. Consumer data
ownership is supposed to give consumers an upper hand, but we show that this
policy may backfire. How to establish consumer sovereignty over their own
data while preventing a data externality and unraveling is, to the best of our
knowledge, an open problem.

1. Model
Consider an economy with two financial services: electronic payment services
and consumer loans.9 One strategic bank offers both loans and payment
services, while two identical and competitive FinTech firms are stand-alone

8 Recent empirical papers on P2P lending, crowdfunding, and online lenders include Iyer et al. (2016), Hildebrand,
Puri, and Rocholl (2017), Buchak et al. (2018), Fuster et al. (2018), Vallée and Zeng (2019), Tang (2019), and
de Roure, Pelizzon, and Thakor (2021), among others.
9 One can also interpret the model as the bank offering a different nonpayment (but credit-informative) service,
such as investment management along with loans.

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 When FinTech Competes for Payment Flows

payment processors.10 All parties are risk neutral. For simplicity, the risk-free
interest rate is normalized to be zero.
There is a unit mass of risk-neutral consumers, who may be thought of
as small firms or as households. With probability ψ, each consumer is hit
with a liquidity shock and requires a loan. A consumer has either a high or
low repayment probability on the loan. This probability is denoted as θj with
j ∈ {h,}, and we refer to it as the credit type of the consumer. A mass mh
of consumers have repayment probability θh , while a mass m = 1−mh have
repayment probability θ < θh . We emphasize that the credit types θ and masses
m are conditional on all available information other than payment data.11

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Each consumer receives utility v > 0 from access to an electronic payment
service. We assume that the quality of the payment service provided by the
bank and FinTech firms is the same.
Each consumer i with credit type θj also enjoys incremental utility bi from
using the bank’s payment service. This idiosyncratic utility generates horizontal
differentiation, and we call it bank affinity. The bank affinity bi has a probability
distribution conditional on credit type θ , denoted by F (· | θ) with density f (· | θ).
Conditional on credit type θ, bank affinity is i.i.d. and has support over the entire
real line. A negative bank affinity implies a cost to using the bank’s payment
services.
A consumer who uses neither the bank nor a FinTech firm for electronic
payment services conducts all transactions in cash, in which case she receives
a normalized utility of zero from payment processing. In summary, consumer
i’s utility from payments routed through a bank, a FinTech firm, or from using
cash are, respectively, v +bi , v and 0.
Figure 1 depicts the sequence of events.
At date t = 1, consumer j privately observes her bank affinity bj and her own
credit type θj . She then chooses a payment processor or remains a cash user.
The FinTech firms, acting as Bertrand competitors, charge zero for payment
processing (a normalization), whereas the bank chooses a price p. In practice,
the price p consists of account fees and below-market deposit interest rate,
among others. The timing reflects the fact that payments are ongoing and
choosing a payment processor is typically a long-term decision.
At t = 2, with probability ψ > 0 each consumer receives a liquidity shock and
applies for a loan at the bank. The bank engages in monopolistic screening,
and offers a menu of contracts, {(qj ,rj )}j =h, , with the contract (qh ,rh ) targeted

10 The large literature on relationship banking suggests that banks are able to exercise some market power in
lending to long-term consumers (see, e.g., Petersen and Rajan 1995). On the deposit side, Drechsler, Savov, and
Schnabl (2017) show that bank behavior following changes in the Federal funds rate is consistent with banks
having market power in deposits. More broadly, competition can be represented on a continuum, with the idea
that FinTech firms are more competitive than banks. For modeling simplicity, we consider the bank to be a
monopolist and FinTech firms to be perfectly competitive.
11 For households and individuals, other observable information includes (but is not limited to) income, wealth,
and credit score. For businesses, other observable information includes revenues and profits.

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Figure 1
Timing of events

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to the high credit type and the contract (q ,r ) targeted to the low credit type.
Here, qj represents the size of the loan offered to type j and rj the interest rate
on the loan. The consumer chooses at most one item from the menu.
At date t = 3, if the consumer receives a loan, she either fully repays the loan
by paying q(1+r) to the bank or defaults. For simplicity, in the latter case, we
assume that the bank recovers nothing from the consumer.
Key variables of the model, including those introduced here and in
subsequent sections, are tabulated in Appendix A for ease of reference.
Appendix B contains all proofs.

2. Loan Market
We begin by analyzing the loan market at time 2. Payoffs from this market will
affect both banks and customers in the payments processing market. Suppose
a consumer of credit type θ accepts a loan contract (q,r). Their utility from the
loan is:
λ
w(q,r | θ) = θ{Aq −q(1+r)}− (1−θ)q 2 , (1)
2
where A > 1 and λ > 0. Here, Aq is the utility earned from the project the funds
are used for. We assume that this utility is earned only if the consumer repays
the loan. The amount repaid is q(1+r). If the consumer defaults, which happens
with probability 1−θ , they incur a reputation penalty captured by the term λ2 q 2 .
This term ensures that defaulting is costly, and is more costly for low credit
type consumers.12
The profit of the bank from a loan (q,r) to a consumer with credit type θ is
γ
π(q,r | θ ) = θq(1+r)−q − q 2 . (2)
2
The first term on the right-hand side is the expected repayment. The second
term represents the opportunity cost of the loan. The last term represents a

12 Technically speaking, the quadratic default penalty ensures that the single-crossing property is satisfied. The slope

of an indifference curve of credit type θj is − ∂w/∂q 1 1 1

∂w/∂r = q {A−r −( θj −1)λq}. As θj increases, − θj increases,
so if λ > 0 the single-crossing property is satisfied.

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 When FinTech Competes for Payment Flows

capital charge against the loan. Here, γ > 0, so the capital charge is convex in
the size of the loan and independent of the type of the borrower.
The first-best outcome maximizes the total surplus between the bank and the
consumer, that is, the sum of equations (1) and (2). The total surplus for a given
θ is
λ γ 2
(θ A−1)q − (1−θ )+ q .
2 2
The first-order condition is (θA−1)−{γ +λ(1−θ )}q = 0, and it is immediate
to see that the second-order condition is satisfied.
Hence, the first-best quantity for credit type θj is

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f θj A−1
qj = . (3)
γ +λ(1−θj )
An increase in θj increases the loan quantity q f . That is, in the first-best
outcome, higher credit types receive larger loans.
The bank in the model has noisy information about a loan applicant, and acts
as a monopolistic screener. We solve for its optimal loan contract offers using
standard mechanism design techniques. Appealing to the revelation principle, in
order to screen consumers, the bank offers two possible contracts, one targeted
to each credit type. Crucial to its choice of menu is its belief about the credit
type of the consumer when she applies for a loan at the bank.
The bank’s prior at the start of the game is that a consumer has high credit
type with probability mh . This prior probability is updated in two ways. First,
as we show in Section 3 below, the relative mix of high and low credit types
who either use the bank for payment services or use an alternative payment
processing method can differ from the masses mh and m . Therefore, knowing
whether or not a consumer is a bank payment customer allows the bank to
update its beliefs. Second, as elaborated below, for its own payment customers,
the bank can extract an additional signal about credit type. Given its information
about a particular customer, let μh denote the posterior probability the bank
places on a loan applicant being the high credit type, with μ = 1−μh the
probability the applicant is the low credit type.
The optimal menu of loan contracts maximizes the bank’s expected profit
subject to incentive compatibility and individual rationality constraints on the
consumer. The bank’s problem is:

maxqh ,rh ,q ,r j =h, μj [θj qj (1+rj )−qj − γ2 qj2 ] (4)
subject to (I Ch ) wh (qh ,rh ) ≥ wh (q ,r ), (5)

(I C ) w (q ,r ) ≥ w (qh ,rh ), (6)

(I Rh ) wh (qh ,rh ) ≥ 0, (7)

(I R ) w (q ,r ) ≥ 0. (8)

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Here, inequalities (5) and (6) are the incentive compatibility conditions for types
θh and θ , and inequalities (7) and (8) are the individual rationality constraints.
We assume that the reservation utility of each credit type is zero.
We first show that the loan contracts the bank offers depend on its posterior
beliefs only through the likelihood ratio that the consumer is a high versus a low
credit type. Let κ = μμh denote this likelihood ratio when the consumer applies

for a loan.

Proposition 1. A bank with a posterior likelihood ratio κ optimally offers

two loan contracts, (qj ,rj ) for j = h,, with

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θ A−1 f
(i) q =  < q , and r is chosen to satisfy w (q ,r ) = 0.
θ 
γ +λ(1−θ )+λκ θh −1

f θh A−1
(ii) qh = qh = γ +λ(1−θ h)
, and rh is chosen to satisfy wh (qh ,rh ) = wh (q ,r ) > 0.

Consumers with credit type θh accept the contract (qh ,rh ), and consumers with
credit type θ accept the contract (q ,r ).

The optimal menu therefore induces complete separation, with the high and low
credit types accepting different loan contracts. The quantity offered to the low
credit type is distorted downward from the first-best quantity. The low credit
type receives zero surplus in the loan market, and the binding IR constraint
determines their interest rate. In contrast, the high credit type receives the first
f
best quantity, qh , and earns a positive surplus.
Note that the optimal menu of contracts in Proposition 1 is unique, as is
standard in monopolistic screening models. From the set of contracts that satisfy
the IC and IR constraints, the bank chooses the unique menu that maximizes
its profit. As expected, the low credit type is held down to its reservation utility,
whereas the IC constraint for the high credit type binds, allowing the latter to
earn an informational rent.
As is clear from Proposition 1 part (i), the degree to which the quantity for
the low credit type is distorted downward depends on the bank’s beliefs about
the customer, as captured by the likelihood ratio the customer is the high versus
the low credit type. The higher the chance a customer is the high credit type, the
more profitable it is to ensure that their IC constraint binds, and so the bigger
the distortion in the quantity offered to the low types.
We now describe how the bank updates its beliefs over credit types of loan
applicants. The initial likelihood ratio of an applicant being the high versus
the low credit type is m m
h
. After observing whether or not the applicant is
a bank payment customer, the likelihood ratio is updated to an intermediate
ratio ρ, which differs across bank payment customers and noncustomers. In
addition, in the base model, on its own payment customers the bank can
access and extract information from the payment data about the applicant,

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 When FinTech Competes for Payment Flows

which allows it to update the intermediate likelihood ratio ρ on its own

customers.13
The payment data of a consumer yield the bank a signal s ∈ {s ,sh } of the
consumer’s credit type. For some α ≥ 1,
α 1
P (s = sh | θh ) = P (s = s | θ ) = , P (s = sh | θ ) = P (s = s | θh ) = . (9)
1+α 1+α
Thus, after observing the payment signal, the bank updates the intermediate
likelihood ratio ρ to ρα if the signal is sh , and to αρ if the signal is s .
Here α captures the bank’s ability to extract useful information from the

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payment signal. If α = 1, the additional signal from payments is pure noise, and
as α → ∞, the signal perfectly reveals the credit type.
We say that a bank is “informed" (denoted by superscript I ) if it has access
to the consumer’s payment history, and “uninformed” otherwise (denoted by
superscript U ). Proposition 2 shows the consumer surplus and bank profit from
each credit type depending on the bank’s information status. From Proposition
1, there is a complete separation, with low credit types accepting the contract
(q ,r ) and high credit types accepting (qh ,rh ). Further, the loan quantity q
and interest rate r depends on the bank’s posterior likelihood ratio κ. In turn,
κ depends on the intermediate likelihood ratio ρ (after the bank has observed
whether the applicant is a payment customer, but before it has obtained the
payment signal), the signal obtained from payments s, and the precision of the
payment signal, α. For notational convenience, in Proposition 2, we write κ as
a function of the signal s.

Proposition 2. Let ρ be the intermediate likelihood ratio of the bank, before

it observes the signal from the loan applicant’s payment data, and κ(s) the
posterior likelihood ratio after observing payment signal s. Then:

(i) Among bank payment customers,

(a) Low credit type consumers receive zero surplus from the loan
market, that is, wI = 0. The bank’s expected profit from such a
consumer is

I
π = Es Aq (κ(s))−q (κ(s))(1+r (κ(s)))

λ(1−θ )+γ
− (q (κ(s)))2 | θ . (10)
2

13 The fact that payment data reside with the consumer’s bank further justifies the assumption that the bank has
market power in lending. If a consumer uses bank 1 for payments, bank 2 does not have access to this information
unless there is data portability by the consumer.

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 The Review of Financial Studies / v 35 n 11 2022

(b) High credit type consumers receive an expected surplus

θ λ
h
whI = −1 Es [(q (κ(s)))2 | θh ]. (11)
θ 2
The bank’s expected profit from such a consumer is
f f
πhI = Aqh −qh (1+Es [rh (κ(s)) | θh ])
λ(1−θ )+γ f 2
(qh ) −whI .
− (12)
2
(ii) Among consumers who adopt another payment option,

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(a) Low credit type consumers receive zero surplus from the loan
market, that is, wU = 0. The bank’s expected profit from such a
consumer is
λ(1−θ )+γ
πU = Aq (ρ)−q (ρ)(1+r (ρ))− (q (ρ))2 . (13)
2
(b) High credit types receive an expected surplus
θ λ
h
whU = −1 (q (ρ))2 . (14)
θ 2
The bank’s expected profit from such a consumer is
f f λ(1−θh )+γ f 2
πhU = Aqh −qh (1+rh (ρ))− (qh ) −whU . (15)
2

Notice that in part (a), an expectation is taken over signals given the credit
type. When the credit type is θh , the posterior likelihood ratio κ is equal to ρα
with probability 1+αα
and αρ with probability 1+α 1
, with the probabilities being
reversed when the credit type is θ .
The payoffs to the low and high credit type consumers follow immediately
from the optimal contracts presented in Proposition 1. The bank’s profit for
each type of consumer can then be determined as the total surplus generated
by the loan minus the surplus obtained by the consumer. As the low credit type
consumer is held down to their reservation constraint, the bank retains all the
surplus from the loan. In the case of the high credit type consumer, the bank
obtains the surplus from the loan less the high credit type’s information rent.
Observe that the high credit type’s information rent, whI or whU as the case
may be, is strictly decreasing in ρ, the intermediate likelihood ratio. That is,
all else equal, when applying for a loan the high credit type prefers to be in a
pool with a large number of low credit types, than in a pool with mostly high
credit types. If a consumer were revealed to be the high credit type for sure, the
monopolist bank lender would capture all the surplus from the loan contract,
holding the consumer down to their reservation utility.
An immediate corollary to Proposition 2 is that on a given loan applicant,
the bank earns a higher profit if it is informed, that is, has access to the payment
data.

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 When FinTech Competes for Payment Flows

Corollary 1. For all α > 1, when a consumer applies for a loan, the bank’s
profit from the loan is strictly higher if the bank is informed compared to when
it is uninformed.

3. Payment Market
Each payment service provider chooses a profit-maximizing price for its
services. For simplicity, we normalize the cost of providing payment services
to zero for both the bank and the FinTech firms. In the context of our model,

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the price charged by the bank for payment services, p, is the total economic
cost of maintaining a payment account at the bank. This includes account fees
and the below-market interest rate paid on deposits.
If a consumer of credit type θj and bank affinity b chooses the bank to process
payments, their overall utility is
Wjb = v −p +b +ψwjI , (16)
where v > 0 is the utility from using electronic payment services (as opposed to
using cash), and wjI is the utility from a loan offered by the bank. All consumers
face the same price p at time 1 because at time 1 the bank does not have any
information on the credit type of the consumer.
The bank affinity variable b admits different interpretations, and the
distribution can vary both across countries and across groups in the same
country.14 We use the affinity distribution to capture any reason a consumer may
prefer a bank or an alternative payment method, including intrinsic preference
or a cost of using either service. Thus, the bank affinity distribution not only
depends on the credit type but also should be viewed as country specific.
For example, consumers who value unmodeled bank services, such as wealth
management (say, older and wealthier consumers), have a positive and high b.
Conversely, those who have a high cost to accessing a bank (say, consumers
in rural India or Kenya15 who live far from the nearest bank branch), have a
large negative b. The variable b may also reflect a relative preference between
the bank and a FinTech firm, so it may be negative if the FinTech mobile app
is slicker and easier to use. Conversely, if a consumer worries about fraud or
data breaches with mobile payments, she would assign a high cost for using
FinTech firms, and would have a positive b.
The support of Fj , the distribution of b given credit type θj , is unbounded
to ensure that the bank’s optimal price for payment services remains finite. We

14 For example, Demirgüç-Kunt et al. (2018) report gender gaps among those who have bank accounts of 7% in
high-income countries and 9% in low-income countries and mention that “Globally, about 1.7 billion adults
remain unbanked — without an account at a financial institution or through a mobile money provider."
15 For example, regarding Kenya, Jack and Suri (2014) write: “In a country with 850 bank branches in total, roughly
28,000 M-PESA agents (as of April 2011) dramatically expanded access to a very basic financial service—the
ability to send and receive remittances or transfers.”

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assume that the demand goes to zero sufficiently rapidly as the price goes to
infinity.
Assumption 1. As the price of payment services becomes large, the bank’s
revenue from payment services goes to zero. Specifically, limp→∞ p(1−
Fj (p)) = 0 for each j = h,.

We consider both a benchmark case in which only the bank provides payment
services (with cash being the alternative) and a base case in which FinTech
firms compete with the bank in payment services. Intuitively, in each case high
affinity consumers use the bank and low affinity consumers use the alternative

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service. We further show that when FinTech services are available, no consumer
continues to use cash. The FinTech firms compete with each other in Bertrand
fashion, and charge a price of zero for payment services.
Recall that wjI (wjU ) is the surplus credit type θj obtains from a loan when
the bank is informed (uninformed).

Lemma 1. For each credit type θj , where j = h,, the threshold consumer
indifferent between using the bank and an alternative payment service is
given by
(i) bjm (p) = p −v −ψ(wjI −wjU ) when the bank is a monopoly provider of
payment services.
(ii) bjc (p) = p −ψ(wjI −wjU ) when FinTech firms also provide payment
services.
Consumers with bank affinity greater than the threshold use the bank for
payment services, and those with affinity lower than the threshold use cash
in case (i) and a FinTech firm in case (ii).

Given the type-dependent bank affinity distributions, the bank faces a

downward-sloping demand curve for its payment services. Let z represent the
incremental utility from bank payment services over the next best alternative
(where z = v if only the bank provides payment services and z = 0 after FinTech
entry). Then, we can write the demand for the bank’s payment services from
consumers with credit type θj as 1−Fj (p −z−ψ w w
j (p,z)), where j (p,z) =
wjI −wjU is the incremental surplus from a loan if the consumer uses the bank
rather than alternative payment service. That is, rational consumers incorporate
the value of a potential banking relationship when they make their choice. From
Proposition 2, wI = wU = 0, so it follows that w
 = 0. However, the demand from
high credit type consumers for payment services depends on the endogenous
incremental surplus from a loan when the bank is informed (i.e., on w h ). This
means that even if the two affinity distributions are the same, so that Fh = F ,
the induced distributions of who chooses the bank for payment services differ
between high and low types.

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 When FinTech Competes for Payment Flows

From a technical point of view, this feature implies that equilibrium entails
a fixed point in consumer demand, as w h in turn depends on the mass of each
credit type that use the bank for payment services. Observe that the intermediate
likelihood ratio for a bank payment customer who applies for a loan is ρ B =
mh 1−Fh (p−z−ψ w h (p,z))
m
× 1−F (p−z)
, recognizing that w  = 0. Similarly, the intermediate
 
F (p−z−ψ w (p,z))
likelihood ratio for a noncustomer of the bank is ρ N = m h
m
× h F (p−z)h .

Thus, the intermediate likelihood ratio ρ for each type of consumer depends
h = wh −wh , and in turn (as shown in Proposition 2), each of wh and wh
U U
on w I I

depend on ρ.
Given a price for bank payment services p and an incremental value of bank

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payment services over the next best alternative z ∈ {v,0}, define a mapping φ
from potential values of w w
h to realized values of h as follows. Let x denote a
real-valued number that is a potential value of h . Given w
w
h = x, determine the
intermediate likelihood ratios for bank customers (ρ B (x)) and noncustomers
(ρ N (x)). From these likelihood ratios, in turn determine the expected loan
surplus earned by the high credit type who uses the bank for payment services.
This surplus is determined using Equation (11) as
θ λ α 1 
h
whI (ρ B (x),α) = −1 q (ρ B (x)α)2 + q (ρ B (x)/α)2 , (17)
θ 2 1+α 1+α
after taking into account the probabilities of generating signals sh and s .
Similarly, the loan surplus earned by the high credit type who uses the alternative
payment technology is given by Equation (14), and may be written as
θ λ
h
whU (ρ N (x)) = −1 (q (ρ N (x)))2 . (18)
θ 2
Let φ(x) = whI (ρ B (x),α)−whU (ρ N ,α). Then, a fixed point of φ(x) represents a
value of w h that is internally consistent; given that value of
w
h , the demand
for bank payment services across the two credit types is such that indeed the
incremental loan surplus from using the bank for payment services works
out to w h . We first show that the mapping φ(·) has a unique fixed point,
which establishes that the bank’s demand function for payment services is
well-defined.
Lemma 2. For each price p for bank payment services and each z ∈ {v,0},
the mapping x  → φ(·) has a unique fixed point.

Given that the cost of providing payment services is zero, the bank’s total profit,
including its revenue from payment services and its profit from loans, is
 
= mj (1−Fj (p m −v −ψ w j ))(p +ψπj )+Fj (p −v −ψ j )ψπj .
m I m w U

j =h,
(19)
In what follows, we assume the second-order condition for profit
maxmization holds and the optimal price is unique. We verify this condition in
our numerical examples.

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While standard intuition is that competition lowers prices, we provide

sufficient conditions for the price of bank payment services to either increase
or decrease in the face of FinTech competition, compared to when the bank is
the only payment service provider. In particular, we consider the special case
that the bank affinity distribution is the same for both credit types. Note that
even in this case, different proportions of high and low credit type use the bank
for payment services, and the choice of payment provider is informative about
credit type. That is, the endogenous threshold consumer of each credit type
indifferent between using the bank and not, bjm (p) or bjc (p) as the case may
be, differs across the two credit types θh and θ . This point can be observed by
noting that w  = 0 and that in general h  = 0 in the expression for the threshold
w

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consumer in Lemma 1.

Proposition 3. Suppose the bank affinity distribution Fj is the same for each
j = h,, so that Fh (b) = F (b) = F (b) for all b. Then, there exists a ψ̄ > 0 such
that, for each ψ < ψ̄, comparing the case in which FinTech firms compete with
the bank in payment services to the case in which the bank is a monopolist
payment processor,

(i) The bank’s price for payment services decreases if the bank affinity
distribution F has an increasing hazard rate throughout.
(ii) The bank’s price for payment services increases if the bank affinity
distribution F has a decreasing hazard rate throughout.

In the industrial organization literature, Chen and Riordan (2008) characterize

conditions under which the price of a good can be higher under duopoly than
under monopoly. The trade-off is essentially between increasing market share
(which induces a lower price) and operating at an inelastic segment of the
demand curve (which could induce a higher price). In our framework, the
demand the bank faces is determined by both the price of its payments services
but also the consumers’ equilibrium perception of the surplus from a loan.
The condition of an increasing or decreasing hazard rate in Proposition 3
has its roots in the standard pricing problem of a monopolist. To illustrate the
intuition, suppose ψ = 0, and consider the simplified problem of a monopolist
bank maximizing its profit in the payment market alone when Fh = F = F . The
demand for payment services is 1−F (p −z), where z = v when the bank is
a monopolist. The bank’s profit is (1−F (p −z))p. Now, suppose the bank
increases its price p by a small amount. It earns the price increment on its
current consumers, who represent a mass 1−F (p). However, the consumers
who were just indifferent between using the bank and not now strictly prefer an
alternative, so the bank loses −f (p)p. The optimal price is found by trading

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 When FinTech Competes for Payment Flows

off these two effects.16 Now, competition by FinTech firms moves z from v to
0. Whether the first effect changes by more than the second one depends on
whether the hazard rate H (p −z) = 1−F f (p−z)
(p−z)
is increasing or decreasing.
In Proposition 3, we assume a low probability of a consumer needing a
loan. We show through a numerical example that even when (a) the affinity
distributions are different for the high and low credit types and (b) the
probability a consumer needs a loan (ψ) is high (set to one in our example),
the bank’s price for payment services can increase with competition. We fix the
bank affinity distribution for the low credit type consumer to be the exponential
distribution, and for the high credit type consumer to be a Weibull distribution.17

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We vary the first parameter of the Weibull distribution k between 0.5 and 1.5,
and set the second parameter λ to be 1. When k < 1, the distribution has a
decreasing hazard rate, and when k > 1 it has an increasing hazard rate. Figure 2
shows the prices both when the bank is a monopolist in payment services and
when it competes with FinTech firms. As can be seen from the figure, when
the hazard rate for the high credit type is decreasing, the price under FinTech
competition is greater than the monopoly price, with the converse being true
with an increasing hazard rate.

3.1 Welfare effects of FinTech competition

FinTech competition in payments affects both consumer welfare and the overall
surplus in our model through three channels: (1) the presence of FinTech pulls
cash users into the payment system (financial inclusion), (2) the change in the
bank’s price for payment services directly affects the welfare of consumers with
high bank affinity (who remain with the bank), and (3) there is an indirect effect
on welfare through the loan market, as the bank’s beliefs about both payment
customers and noncustomers changes with FinTech entry, which affects the
menu of loan contracts the bank offers.
The first effect is positive: the welfare of low bank affinity consumers
improves after FinTech entry due to access to electronic payments. From
Proposition 3 and Figure 2, one sees that the second effect may be positive
or negative. In particular, the bank’s price for payment services can increase
after FinTech entry, which hurts high bank affinity consumers, who are bank
payment customers even after FinTech entry. The third effect, the welfare in
the loan market, also may increase or decrease with FinTech competition.
The interaction of these three effects implies that the total impact of FinTech
competition is generally nuanced and ambiguous. Nonetheless, a few clear

16 The first-order condition for the optimal price is 1−F (p −z)−f (p −z)p = 0, which can be written as H (p −z)p =
f (p−z)
1, where H (p −z) = 1−F (p−z) is the hazard rate of the bank affinity distribution.
17 The Weibull distribution, which includes the exponential distribution as a special case, satisfies the assumption
that limp→∞ p(1−F (p)) = 0 made in Proposition 3. The distribution function for the Weibull distribution is
k
F (x | k,λ) = 1−e−(x/λ) , where k and λ are parameters of the distribution.

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Figure 2
FinTech competition can lead to higher or lower prices for the bank’s payment services
Here, A = 2,θh = 0.99,θ = 0.95,λ = 0.4,γ = 0.2,ψ = 1,α = 2,mh = m = 0.5. The bank affinity distribution for type 
is exponential. The bank affinity distribution for type h is Weibull, with first parameter k varying from 0.5 to 1.5,
and the second parameter set to λ = 1. The solid line pm ∗ represents the optimal price for bank payment services
when the bank is a monopolist, and the dashed line pc∗ represents the corresponding price when FinTech firms
compete with the bank.

predictions, as summarized in the following proposition, emerge from the

model.

Proposition 4. Comparing the cases of FinTech competition in payments to

the bank being a monopolist in payments,

(i) The profit of the bank is strictly lower.

(ii) The total surplus from loans to high credit type consumers is unchanged.
(iii) Among low credit type consumers,

(a) Those with low bank affinity b < min{bc (pc∗ ),bm (pm ∗
)} strictly
benefit from financial inclusion.
(b) Those with high bank affinity b > max{bc (pc∗ ),bm (pm
∗
)} benefit if
∗ ∗ ∗ ∗
pc < pm , and are hurt if pc > pm .

Part (i) of Proposition 4 predicts an unambiguous reduction in total bank

profit following FinTech competition. This is unsurprising but also nontrivial

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 When FinTech Competes for Payment Flows

because FinTech competition generally has an ambiguous impact on the bank’s

price for payment services and on loan market outcomes. For parts (ii) and
(iii), recall that loans to high credit type consumers always have the first-best
quantity, so the total surplus of such loans between the borrower and the lender is
not affected by FinTech competition. In comparison, low credit type consumers
always get zero surplus from the loan market, so the utility of those who stay
with the bank depends only on the price of payment services.
The total surplus from loans to low credit types (which includes both
consumer surplus and bank profit) and the consumer surplus accruing to high
credit types are generally ambiguous. To illustrate, we consider a numerical

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example. Appendix C presents the details of the example. In the example, we
use different distributions for bank affinity for the high and low credit types,
and show how the relative shape of these distributions affects the welfare
implications of FinTech entry. The main conclusions that emerge from the
example may be summarized as follows.

Observation 1. After FinTech entry:

(i) The expected loan surplus obtained by high credit type consumers may
increase or decrease.
(ii) The total surplus from loans to low credit consumers may increase or
decrease.

Broadly speaking, if FinTech competition leads to a sufficiently greater

proportion of high credit types using the bank for payment services, high
credit types who remain bank customers obtain worse loan terms. Conversely,
if FinTech competition results in proportionately more low credit types using
the bank’s payment services, high credit types who remain bank customers
obtain better loan terms. The effects on bank noncustomers similarly depend
on how FinTech competition affects the mix of high and low credit types who
stay away from the bank in the payment market. As before, the overall surplus
from a loan to low credit types is inversely related to the loan surplus obtained
by the high credit type.
Next, consider the comparative statics in α, the precision of the signal
extracted from payment data. As α → ∞, in the limit the type of the consumer
is fully revealed. At this point, the high credit type obtains zero surplus from
a loan, and the total surplus from a loan to the low credit type is equal to the
first-best surplus. More generally, for many parameter values, when the bank
is informed the expected loan surplus of the high credit type is decreasing in α.
The intuition is that when the bank knows that a given consumer is more likely
to be the high type, it can extract greater surplus from the consumer.
However, in some cases the high credit type’s loan surplus increases in α.
Suppose that the ex ante probability of high credit borrowers is very high, and
consequently, they receive a very small loan market surplus to start with. Then,

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Figure 3
Expected loan surplus of high credit type
This figure plots the expected loan surplus captured by credit type θh for different parameter values and payment
market structures. Here, A = 2,θh = 0.99,θ = 0.8,λ = 0.4,γ = 0.2,ψ = 1,α = 2,mh = 5,m = 0.5. The bank affinity
distribution for credit type θ is exponential, and for credit type type θh is Weibull with first parameter k = 2
(so the hazard rate is increasing). For each set of parameters, we find the optimal price for bank payment
services. The solid lines represent the bank is uninformed about the consumer, and the dashed lines represent
that the bank is informed.

the high signal from payment data has little effect on the menu of contracts
offered, and hence little effect on the loan surplus to the high credit type.
Conversely, the low payment signal can have a relatively large (and positive)
effect on this surplus. Although the likelihood of the low signal decreases in
α, the overall effect may still be that the loan surplus to the high credit type
increases in α. Figure 3 provides such an example.
In summary, when FinTech competes with banks for core banking services
it can affect consumer welfare through three possible channels. First, FinTech
competition can increase financial inclusion. Consumers who find it costly to
form a relationship with a bank are given access to electronic payments. Second,
banks will reprice their core banking services. As we have shown it is possible
for payment prices to increase or decrease as a result of changes in the mix of
customers. Finally, FinTech competition affects the flow of information in the
economy. Consumers may choose to move their payments away from the bank

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 When FinTech Competes for Payment Flows

because of the cheaper payment alternative, which affects information in the

loan market.

4. Using Nonbank Payment Data for Bank Lending

We now consider one market-based and one regulatory outcome, under which
information obtained from payments processed by FinTech firms may flow
back to the bank and be used in lending.

4.1 FinTechs sell data to bank

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Suppose that there is a private data market in which the stand-alone FinTech
firms sell customer data to the loan provider (the bank). Various institutional
arrangements are consistent with an active data market. In particular, our data
sales regime is consistent with the widespread practice of banks and FinTech
firms forming partnerships in which banks provide capital and FinTech firms
provide the user interface and data analytics.
To simplify the actual institutional arrangement in the data sales market, we
assume that the bank and each FinTech firm agree in advance on a fixed price
for the data of each consumer. In terms of the timeline in Figure 1, the first
stage at t = 1 is a negotiation between the bank and the FinTech firms over the
price of data per consumer. Figure 4 shows the new timeline.
It is immediate that, all else equal, access to payment data makes the bank
strictly better off whenever α > 1. Therefore, there exists a price y > 0 for data
transferred by a FinTech firm to the bank such that both the FinTech firms and
the bank are willing to participate in the data sales market. We do not model the
exact negotiation details between the bank and a FinTech firm. Instead, we take
the price for data y as given, and analyze the implications of the bank having
access to payment data from FinTech consumers.
From the FinTech point of view, each payment customer generates data
that it can sell with probability ψ. Given Bertrand competition, this extra
revenue will induce the FinTech firms to cross-subsidize their payments. Thus,
the FinTech payment price becomes −ψy per consumer. In other words, the

Figure 4
Timing of events with FinTech data sales

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FinTech customers receive “freemium” products which they value that also
generate data.
The equilibrium with data sales can be solved in a similar fashion as before.
Let bjs denote the bank affinity value of a consumer with credit type θj who is
indifferent between choosing the bank and a FinTech firm for payment services,
where the superscript s means data sales. Whichever payment service the
consumer chooses, the bank is informed about their payment history at the
time they seek a loan. Recall from Proposition 2 that the expected consumer
surplus earned by a high credit type from a loan, whI , depends on both the
likelihood ratio of a high-versus-low credit type before the payment signal is
obtained, ρ, and the precision of the signal from payments, α. Let ρ FT denote

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the likelihood ratio for a FinTech consumer, and ρ B the corresponding ratio
for a bank consumer, before the signal from payments is extracted. Then, bjs
satisfies
v −p +bjs +wjI (ρ B ,α) = v +ψy +wjI (ρ FT ,α), (20)

bjs (p) = p +ψy +(wjI (ρ FT ,α)−wjI (ρ B ,α)). (21)

A consumer with bank affinity b > bjs (b < bjs ) chooses the bank (a FinTech
firm) for payment processing.
The bank is now informed about all loan applicants. Given the price of buying
consumer data from a FinTech firm, y, the bank chooses its payment services
price p to maximize
 
s = mj (1−Fj (bjs (p)))(p +ψπjI (ρ B ,α))+Fj (bjs (p))(ψπjI (ρ FT ,α)−y) .
j
(22)
We show that in the special case that the bank affinity distribution is the same
for both credit types, the relative mass of high versus low credit types that uses
each payment service (bank or FinTech ) is the same. The further implication
is that there is no difference in the contract menu offered to bank and FinTech
payment customers.

Proposition 5. Suppose the bank affinity distribution is the same across the
two credit types θh and θ , that is, Fh (b) = F (b) = F (b) for all b. Then, for every
consumer data price y and bank price for payment services p:

(i) bhs (p) = bs (p), so that the demand for bank services, 1−Fj (bj (p)), is the
same across the two credit types.
(ii) ρ B = ρ FT = m h
m
. That is, whether a consumer is a bank or FinTech payment
customer does not convey any information about their credit type.

The arguments in Proposition 3 can be extended to the data sales case to

show that the price for the bank’s payment services may increase or decrease

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 When FinTech Competes for Payment Flows

when data sales occur, compared to the price in the base model with FinTech
competition but without data sales. As a result, the welfare effects of data sales
are nuanced. The presence of a data market introduces changes to the welfare
of both low and high bank affinity consumers.
Low bank affinity consumers benefit from the payment subsidy provided
by the FinTech firm, −ψy. The size of this subsidy depends on the price y
negotiated between the bank and the FinTech firms.18 The latter outcome is
qualitatively similar to a data tax, which the government could collect from the
data sales transaction and reimburse to FinTech consumers.
The loan offers received by consumers are different when the bank obtains

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the payment signal about FinTech consumers. As in Section 3, high credit type
consumers’ loan market surplus can go up or down, whereas low credit type
consumers’ loan market surplus still stays at zero.
High bank affinity consumers see a change in both the price for banking
payment services and the loan offers they receive. The latter occurs because
the presence of FinTech data sales affects the sorting of consumers into bank
payment customers and noncustomers, which in turn affects the bank’s beliefs
about their payment customers. As a result of these two effects, high bank
affinity consumers may be better off or worse off, regardless of their credit
type.

Observation 2. Comparing FinTech sales of data to the base model with

FinTech competition but no data sales:

(i) Overall expected surplus from the loan market is greater.

(ii) Consumers with low bank affinity and the low credit type are strictly
better off with FinTech sales of data.
(iii) Any of the following consumer groups, {high bank affinity, high credit
type}, {high bank affinity, low credit type}, and {low bank affinity, high
credit type}, may be better off or worse off.

Thus, although the standard intuition in economics is that introducing a missing

market alleviates an externality, the welfare effects of allowing the FinTech firm
to provide data to the bank are nuanced. In any equilibrium in which data sales
occur, the bank earns a higher profit than without data sales. However, consumer
welfare may be higher or lower. The fact that the high credit type consumers
who use a FinTech firm for payments can be worse off in the presence of an
information market provides a micro-foundation for a preference for privacy.
One interpretation of FinTech competition for payment customers and hence
data is that the FinTech company is a mechanism for the consumer to extract

18 An important assumption we make is that the FinTech firms make zero profit in expectation and pass the entire
price for data sales back to consumers. If the FinTech firms were imperfectly competitive, only part of the data
sales revenue would be passed to consumers.

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 The Review of Financial Studies / v 35 n 11 2022

rents from the bank in exchange for their data. As a vertically integrated
payments and lending company, the bank partially internalizes the benefit of
data. By contrast, competing FinTech firms directly pass the market value of
data back to the consumers through a payment subsidy.

4.1.1 FinTechs process data for the bank. If the FinTech firms have a
superior data analysis technology compared to the bank, then instead of
selling raw payment data to the bank, the FinTech firm can sell the data
processing technology to the bank so the bank can extract better signals from
its own customers’ payment data. The superior data processing capability of

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the FinTech firms can be thought of as an increase in α, the precision of the
signal from payment data.
Such a data processing arrangement inevitably leads to an outcome similar
to that in data sales, in the sense that when a consumer applies for a loan, the
bank always has access to the signal from payments. The difference is that
the signal is provided by the FinTech firm. Therefore, a FinTech firm can earn
revenues from the bank both for data sales on FinTech payment customers and
for data processing on bank payment customers. If FinTech firms are perfectly
competitive, as in our model, the fees they charge for processing data would
be their cost of doing so. Compared to the base model in which information on
FinTech customers is lost to the bank, the welfare effects are similar to those
for data sales.

4.2 Consumers own and port their data

Suppose that consumers control their own data, and can provide a credible
record of their payment history to a lender. Formally, in terms of the timeline in
Figure 1, at t = 2 if a consumer needs a loan, the bank asks the consumer to share
their payment history data. The consumer may then either share it or decline,
following which the bank chooses a menu of contracts for the consumer. Thus,
at the time of making a loan, the bank is potentially faced with three kinds of
consumers: those with high payment signals, those with low payment signals,
and those who have declined to share their payment history. In accordance
with Proposition 2, for each kind of consumer the bank will design a menu of
separating contracts, one contract for the high credit type and another for the
low credit type.
The key question is whether voluntary data porting actually leads to
consumers providing their data to the bank. We answer in the affirmative.
Because the bank makes a positive profit on each credit type, the bank can
offer loan applicants an infinitesimal inducement  > 0 if they provide their
payment history data to the bank. The low credit type obtains zero surplus from
the loan regardless of what they do, so will strictly prefer to provide their data.
At that point, any FinTech customers who decline to provide their data are easily
inferred to be the high credit type, and the monopolist bank can extract all the
surplus generated by a loan. Notice that if the high credit type also provides

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 When FinTech Competes for Payment Flows

their data, the bank cannot perfectly infer the credit type, as the payment signal
remains noisy. The high credit type is thus better off also providing their data.
In equilibrium, all consumers willingly port their data to the bank. In the limit
as  → 0, it remains an equilibrium for all consumers to share their data with the
bank. The nature of this equilibrium is reminiscent of unraveling. By sharing
data, consumers impose a data externality on everyone else. The externality is
strong enough that everyone shares data.
In what follows, we restrict attention to the equilibrium in which all
consumers port their data to the bank at no cost to the bank. In the absence of
an inducement to deliver their data, the low credit type is indifferent between

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giving their data to the bank and not doing so. Thus, depending on parameters,
there may also exist an equilibrium in which no FinTech consumer transfers
their data to the bank. However, this equilibrium is not robust to infinitesimal
inducements.
The bank’s optimal price for payment services can be derived in a similar
fashion as the case of data sales. Let bjo be the cutoff bank affinity value of
credit type j under data porting, or open banking. Because data are shared for
free, the marginal consumer’s calculation is

v −p +bjo +wjI (ρ B ,α) = v +wjI (ρ FT ,α) (23)

bjo (p) = p +(wjI (ρ FT ,α)−wjI (ρ B ,α)). (24)

A consumer with bank affinity b > bjo (b < bjo ) chooses the bank (a FinTech
firm) for payment processing. In particular, because low credit type consumers
always get zero surplus in the loan market, we have bo = p.
Likewise, the bank’s profit is

 
o = mj (1−Fj (bjo (p)))(p +ψπjI (ρ B ,α))+Fj (bjo (p))ψπjI (ρ FT ,α) .
j
(25)
By this point, it is transparent that consumers owning and voluntarily porting
data is a special case of FinTech data sales, with y = 0. Intuitively, if FinTech
firms sell consumer data at a zero price, it is equivalent to consumers porting
data at a zero price. Therefore, when compared to the base case with FinTech
competition but without data transfer, most qualitative effects of FinTech data
sales also apply to data porting. In particular, the overall loan market surplus
goes up due to information sharing, but the high credit type’s loan surplus
may increase or decrease. Also, the price for payment services may go up
or down.
Between data sales and data porting, which one is better for consumers?
In this economy, consumer surplus comes from payment services and loans.
Low credit type consumers always receive zero surplus in the loan market. If the

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 The Review of Financial Studies / v 35 n 11 2022

distribution of bank affinity is identical between high and low credit types, as in
Proposition 5, high credit type consumers also receive the same surplus between
data sales and data porting. This is because in both cases, the equilibrium
mix between the two credit types is identical to the prior, mh /m , and the
bank observes the consumer’s payment data when borrowing. Therefore,
the comparison in consumer welfare rests entirely on the price of payment
services. The following proposition shows conditions under which the bank’s
payment services under data sales is strictly better than that under (free) data
portability.

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Proposition 6. Suppose that (i) the bank affinity distribution is the same
across the two credit types θh and θ , that is, Fh (b) = F (b) = F (b) for all b,
and (ii) under data sales, the bank and each FinTech firm negotiate a price for
FinTech data sales ŷ > 0. Then

(i) The loan market outcomes are identical under data sales and under data
portability.
(ii) Both the bank and the FinTech firms have a strictly lower price for
payment services under FinTech data sales than under consumer data
portability.

Consequently, all consumers strictly prefer data sales to data portability.

The intuition behind Proposition 6 is straightforward. Under FinTech

data sales, consumers receive a fraction of the value of their data in the
form of subsidized payments from FinTech firms. Thus, the bank needs to
offer better prices to entice consumers to use the bank. But if data are
ported for free, the bank no longer has such an incentive, and the price
worsens.
To gain further intuition, we can write the bank’s profit with data porting,
given Fh = F = F and ρ B = ρ FT , as
   
o I mh mh
 = mj (1−F (p))p +ψπj = (1−F (p))p + mj ψπjI .
j
m  j
m
(26)
The second term in the profit expression, which comes from loans, has
nothing to do with the price of payment services, that is, there is a complete
decoupling of payment and credit if data are ported for free. The full
decoupling does not happen under data sales because the bank’s profit given
Fh = F = F is
  
I mh
s
 = mj (1−F (p +ψy))p +ψπj −ψF (p +ψy)y , (27)
j
m

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 When FinTech Competes for Payment Flows

where the last term is the cost of purchasing data from FinTech firms. In general,
(1−F (p +ψy))p −ψF (p +ψy)y = (1−F (p))p.
The results of this section highlight a data externality. In the presence of data
transfers, consumer welfare from the loan depends on their bargaining power
relative to the bank. Data sales are equivalent to the FinTech firm negotiating
with the bank on behalf of a block of consumers, whereas with data porting the
bank is able to “divide and conquer” consumers in one-on-one negotiations.
While the data externality seems stark in our two-credit-type setting, we expect
it to be a more general phenomenon even with N > 2 credit types. As before,
the bank is able to induce data sharing from the lowest credit type consumers.

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Once the lowest type is revealed, the bank can use the same inducement
on the lowest of the remaining N −1 types. So on it goes, and unraveling
ensues.
Our welfare result on consumers being better off under FinTech data sales,
as opposed to when they own their own data, depends on the market structures
in the payments and loan markets. In our model, the FinTech firms are Bertrand
competitors and so make zero profit, and the bank is a monopolist that retains
some of the surplus in the loan market (note that with noisy signals the high
credit type θh also earns a positive surplus). In a different context, Jones and
Tonetti (2020), show that it is nearly optimal for consumers to have property
rights over data, rather than firms, when a firm has an incentive to hoard data
to preserve its monopoly position.

5. Conclusion
New data processing technology has increased the economic importance of
data. Banks, through their joint role as payment processors and financial
service providers, have long enjoyed privileged access to consumers’ and
firms’ transaction data. We provide a flexible framework that points to the
complex effect that the loss of these data will have on both the payments and
financial services markets. Our analysis suggests that policy makers should take
a nuanced and country-specific approach to FinTech competition.
Much work still must be done to understand the optimal way in which
control rights to our large and growing data footprints should be allocated.
In our framework, a data market is always weakly preferred to consumer data
portability. This result is due to market power: with data sales, a FinTech firm
negotiates with the bank to extract part of the market value of the data which
it then reimburses to consumers. If multiple banks competed for the data,
presumably the FinTech firm would extract more of the value. By contrast,
individual consumers, each lacking market power, cannot do so. To the extent
that FinTech market power also becomes a concern—which it has, outside our
model—could a social planner do better by establish a data warehouse and
negotiating on behalf of consumers?

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 The Review of Financial Studies / v 35 n 11 2022

A. Table of Notation
θj Consumer’s repayment probability, with j = h,
v Consumer’s value for using electronic payment rather than cash
b Consumer’s bank affinity; negative b means a cost to access the bank
F,f Distribution and density of consumer’s bank affinity
ψ Probability that a consumer needs a loan in period 2
(q,r) Loan quantity and interest rate offered by the bank
α Quality of the signal about a consumer’s credit type extracted from payment data
wjU Consumer surplus to credit type θj from the loan when the bank is uninformed
wjI Expected consumer surplus to credit type θj from the loan when the bank is uninformed
w Expected change in consumer surplus from the loan for credit type θh when the bank is informed,
h
compared to when the bank is uninformed
πjU Bank’s expected profit from making a loan to credit type θj when the bank is uninformed
πjI

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Bank’s expected profit from making a loan to credit type θj when the bank is informed
p Price charged by bank for payment services
b∗ Threshold bank affinity of consumer who is indifferent between using the bank for payment
services and the alternative (depending on the case being considered, the alternative is to remain
unbanked or to use the FinTech firm for payment services)
y Price per consumer at which data are sold by FinTech firm to bank
m Superscript, benchmark case in which the bank is a monopolist provider of payment services
c Superscript, base case in which FinTech firms compete with the bank in providing payment
services
s Superscript, case in which FinTech firms can sell data to banks
o Superscript, case in which consumers own and port data

B. Proofs
B.1 Proof of Proposition 1
We proceed with a series of steps.

Step 1: At least one of the constraints I Rh and I R must bind.

Suppose not, so that we have an optimum in which both IR constraints are slack. Then two
subcases should be considered.

(i) One of the IC constraints is slack. Then, we can find a suitable increase in each of r and
rh such that the binding IC constraint is strictly satisfied, the slack IC constraint continues
to hold, and the IR constraints hold. This contradicts the assumption that we are at an
optimum.
(ii) Both IC constraints bind. Observe that we can write w(q,r | θ ) = θ {Aq −q(1+r)+ λ2 q 2 }−
λ 2
2 q . Therefore, the binding IC constraints I Ch and I C can respectively be written as
λ 1 λ 2 λ 1 λ 2
Aqh −qh (1+rh )+ qh2 − q = Aq −q (1+r )+ q2 − q (B.1)
2 θh 2 h 2 θh 2 
λ 1 λ 2 λ 1 λ 2
Aq −q (1+r )+ q2 − q = Aqh −qh (1+rh )+ qh2 − q (B.2)
2 θ 2  2 θ 2 h
Summing the two inequalities and simplifying, we have
1 2 1 2
(q −q2 ) ≥ (q −q2 ). (B.3)
θh h θ h
As θh > θ , it must be that qh = q . This further implies that rh = r (or the IC constraint
must be violated for at least one type), so the contract is a pooling contract.
Now, if the contract is a pooling contract and both IR conditions are slack, it is immediate
that a small increase in rh and r , increasing both by the same amount, leads to an increase
in profit for the lender while preserving all constraints. Again we have a contradiction that
the original contract was optimal.

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 When FinTech Competes for Payment Flows

Therefore, at the optimum contract, at least one IR constraint must bind.

Step 2: Optimal contract when I R binds.

Suppose I R binds at the optimal contract. Then θ (1+r )q = θ Aq −(1−θ ) λ2 q2 . Therefore,

θh  λ  λ θ
h
λ
wh (q ,r ) = θh Aq − θ Aq −(1−θ ) q2 −(1−θh ) q2 = −1 q2 . (B.4)
θ 2 2 θ 2
Hence, wh (q ,r ) > 0. From I Ch , it follows immediately that wh (qh ,rh ) > 0, so I Rh is slack.
Suppose also that I Ch is slack at the optimal contract. Then, for a small enough increase in
rh , I Ch and I Rh continue to hold, and the right-hand side (RHS) of I C is reduced, so I C must
continue to hold. There is no effect on I R . The increase in rh strictly increases the bank’s profit,
so the contract could not have been optimal. Thus, it must be that I Ch binds at the optimum. I Ch

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θ
binding implies that wh (qh ,rh ) = wh (q ,r ) = θh −1 λ2 q2 .

Now, the bank’s profit is
 γ
 = μj θj (1+rj )qj −qj − qj2 . (B.5)
2
j =h,

As noted above, I R binding implies that θ (1+r )q = Aθ q −(1−θ ) λ2 q2 . Further, from
 
θ
the binding I Ch constraint, we can write θh (1+rh )qh = Aθh qh −(1−θh ) λ2 qh2 − λ2 θh −1 q2 .

Substituting these expressions into the profit function,
λ γ
 = μ Aθ q −(1−θ ) q2 −q − q2
2 2
λ γ λ  θh 
+μh Aθh qh −(1−θh ) qh2 −qh − qh2 − −1 q2 . (B.6)
2 2 2 θ
The first-order condition in qh yields
Aθh −1
qh∗ = , (B.7)
γ +(1−θh )λ
which is the first-best quantity. Similarly, the first-order condition in q yields
Aθ −1 Aθ −1
q∗ =    =   (B.8)
μh θh θ
γ +λ 1−θ + μ θ −1 γ +λ(1−θ )+λκ θh −1
  

It is immediate to see that in each case the second-order condition is satisfied.

We have shown that I Rh is satisfied; what remains is to check I C . As w (q ,r ) = 0, I C here
reduces to w (qh ,rh ) ≤ 0, or θ Aqh −θ (1+rh )qh −(1−θ ) λ2 qh2 ≤ 0.
From the binding I Ch constraint, we obtain:
θ 1 λ λ θ  2
θ (1+rh )qh = θh (1+rh )qh = θ Aqh −θ −1 qh2 − 1− q . (B.9)
θh θh 2 2 θh 
Substituting the RHS for the term θ (1+rh )qh ) in w (qh ,rh ), we obtain
 θ  2
w (qh ,rh ) = − 1− (qh −q2 ) < 0, (B.10)
θh
where the last inequality follows from qh > q . To see that qh > q , observe that the first-best loan
quantity q f is strictly increasing in θ . Further, the optimal contracts feature qh∗ = qh and q∗ ≤ q ,
f f

so it must be that qh∗ > q∗ .

Therefore, starting with the assumption that I R binds, we have found a solution (qh∗ ,q∗ ) such
that the lender’s conditions for profit-maximization are satisfied, I Ch also binds, and I Rh and I C

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 The Review of Financial Studies / v 35 n 11 2022

are both satisfied as strict inequalities. It follows immediately that r∗ is chosen to satisfy I R , and
rh∗ to satisfy I Ch .

Step 3: It cannot be optimal for I Rh to bind.

Next, suppose that I Rh binds; that is, wh (qh ,rh ) = 0. Observe that for any feasible contract (q,r),
the borrower’s utility wj (q,r) = θ q{A−(1+r)+ λ2 q}− λ2 q 2 is strictly increasing in θj . Now, in any
feasible solution, it must be that 1+r < A. Otherwise, the borrower’s IR constraint is violated even
when λ = 0, and the loan will be rejected. When 1+r < A, it is immediate that wj (q,r) is strictly
increasing in θj .
Now it follows that if wh (qh ,rh ) = 0, then w (qh ,rh ) < 0. In conjunction with constraint I R
(which says that w (q ,r ) ≥ 0), it follows that I C is satisfied as a strict inequality.
Observe that I R implies that θ (1+r )q ≤ θ Aq −(1−θ ) λ2 q2 , so that

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θh θ λ
h
θh (1+r )q = θ (1+r )q ≤ θh Aq − −θh q2 . (B.11)
θ θ 2

Therefore,

λ
wh (q ,r ) = θh Aq −θh (1+r )q −(1−θh ) q2 (B.12)
2
θ λ
h
≥ −1 q2 . (B.13)
θ 2

As wh (qh ,rh ) = 0 when I Rh binds, to satisfy I Ch it must be that q∗ = 0. The solution in this case
Aθ −1
therefore has qh∗ = γ +λ(1−θ = qh , and rh chosen so that wh (qh ,rh ) = 0. Further, q∗ = 0, and we can
h f
h)
∗
arbitrarily set r = 0.
Now, observe that the solution above is a feasible solution when maximizing the profit function
in Equation (B.6) in the previous step. However, as shown above, this solution is inferior to the
Aθ −1
optimal solution of qh∗ = qh and q∗ =
f
  , with r∗ chosen to make I R bind and
θ h
γ +λ(1−θ )+λκ θ −1
rh∗ chosen to make I Ch bind.
Therefore, it cannot be optimal for I Rh to bind.

Step 4: Optimal contract.

It now follows from the above analysis that the optimal contract is the one found in Step
2, with the constraints I Rh and I C binding. This contract is exhibited in the statement of the
proposition.

B.2 Proof of Proposition 2

(i) (a) Consider bank payment customers. Observe from Proposition 1 that the loan contract menu
offered by the bank has w (q ,r ) = 0. That is, the low credit type obtains a zero surplus, or wI = 0.
The total surplus generated by the loan to a low credit type depends on the payment signal
obtained by the bank, s ∈ {sh ,s }. For a given signal s, this total surplus is given by AqI (κ(s))−
γ +λ(1−θ )
 (q I (κ(s)))2 . Conditional on the consumer being a low credit type,
qI (κ(s))(1+rI (κ(s)))− 2 
the expected surplus takes into account that the consumer generates the high signal with probability
1 α
1+α and the low signal with probability 1+α . The expected surplus may therefore be written as

γ +λ(1−θ ) I
Es [AqI (κ(s))−qI (κ(s))(1+rI (κ(s)))− (q (κ(s)))2 | θ ]. (B.14)
2

The expected profit of the bank, πI , is equal to the expected surplus, as the consumer obtains zero
surplus.

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 When FinTech Competes for Payment Flows

(b) From Equation

 (B.4)
 in the proof of Proposition 1, a high credit type consumer obtains a surplus
θ
wh (q ,r ) = θh −1 λ2 q (κ)2 . Now, q (κ), the quantity offered to the low credit type depends on

α
the payment signal s. Further, a high type consumer generates a high signal with probability 1+α
1
and a low signal with probability 1+α . Her expected consumer surplus may therefore be written as
θ λ
h
whI = −1) Es [q (κ(s))2 | θh ]. (B.15)
θ 2
f
Keeping in mind that the high credit type obtains the first-best loan quantity qh , the total surplus
f f γ +λ(1−θh ) f 2
generated by a loan to the high type given signal s is Aqh −qh (1+rh (κ(s)))− 2 (qh ) .
Taking an expectation over signal yields the total expected surplus, and subtracting the surplus
obtained by the high credit type leads to the expression for bank profit πhI in the statement of the

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lemma.

(ii) The proof of both parts (a) and (b) when the bank is uninformed mirror the proof of the
corresponding parts when the bank is informed. The expressions are simpler as in the case of the
uninformed bank, the posterior likelihood ratio κ equals the intermediate likelihood ratio ρ.

B.3 Proof of Corollary 1

Let ρ be the likelihood ratio of the high credit type versus the low credit type before the payment
signal is processed. Then, the bank’s expected profit from a consumer when the bank is uninformed
may be written as
ρ 1
π U (ρ) = πh (ρ)+ π (ρ). (B.16)
1+ρ 1+ρ
Now, when the bank has the payment signal, it is informed, and its profit is
ρ  α 1 
πI = πh (ρα)+ πh (ρ/α)
1+ρ 1+α 1+α
1  1 1 
+ π (ρα)+ π (ρ/α) . (B.17)
1+ρ 1+α 1+α
Observe that if the bank offers the contract (qj (ρ),rj (ρ)) to credit type θj for each j = h,, then
π I = π U . Further, if the bank strictly prefers to depart from this contract (which Proposition 1 shows
that it does when α > 1), the bank earns a strictly higher profit when informed, that is, π I > π U .

B.4 Proof of Lemma 1

(i) Consider a consumer with credit type θj and bank affinity b. Recall that wjI (wjU ) represents
the surplus that credit type θj obtains from a loan when the bank is informed (uninformed). The
overall utility of the consumer from using cash is thus

WjC = ψwjU . (B.18)

Similarly, the overall utility from using the bank, given that p is the price of the bank’s payment
services is

WjB = v +b −p +ψwJI . (B.19)

It follows that the consumer prefers the bank to cash if and only if WjB ≥ WjC , that is, if b ≥ bjm (p),
where

bjm (p) = p −v −ψ(wjI −wjU ). (B.20)

The statement of part (i) now follows.

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 The Review of Financial Studies / v 35 n 11 2022

(ii) When FinTech firms enter the payment market, they compete in Bertrand fashion with each
other, and so charge a price of zero. Thus, a consumer’s utility from using a FinTech firm for
payments is

WjFT = v +ψwjU . (B.21)

Observe that there cannot be any cash users in equilibrium. Recall that wI = wU = 0. Thus, low
credit type consumers obtain utility v from using a FinTech firm and utility zero from using cash,
so they strictly prefer to use a FinTech firm to using cash. Therefore, in equilibrium, any cash user
must be a high credit type. But as seen from Proposition 1, when μ = 0, the bank’s optimal menu
has q = 0, so credit type θh obtains zero surplus from the loan. If a cash-using high type deviates
to a FinTech firm for payment processing, they obtain a payment utility v > 0, and also obtain a

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strictly positive loan surplus. Therefore, in equilibrium, there cannot be any cash users in this case.
Now, a consumer prefers using the bank for payments rather than a FinTech firm if and only if
WjB ≥ WjFT , or b ≥ bjc (p), where

bjc (p) = p −ψ(wjI −wjU ). (B.22)

The statement of part (ii) now follows.

B.5 Proof of Lemma 2

Let z ∈ {0,v}, where z = v represents the case in which the nonbank alternative is cash, and z = 0 the
case in which the nonbank alternative is a FinTech firm, and let P be the price of the bank’s payment
services. The bank is uninformed about a fraction Fh (p −z−ψ w h ) of high credit type consumers
and a fraction F (p −z) of low credit type consumers, and is informed about (i.e., has payment data
for) a fraction 1−Fh (p −z−ψ w h ) of high credit type consumers and a fraction 1−F (p −z) of
α
low credit type consumers. When the bank analyzes payment data, with probability 1+α , it obtains
1
a correct signal about the customer, and with probability 1+α it obtains an incorrect signal.
h . Then, φ(x) = wh −wh , which can be written as
U
Now, let x represent an arbitrary value of w I

⎧
⎪
⎨
θh λ α/(1+α)
φ(x) = −1 (θ A−1)2 )   
θ 2 ⎪
⎩ θh m 1−Fh (p−z−ψx) 2
γ +λ(1−θ )+λ −1 mh
θ 1−F (p−z) α


1/(1+α)
+   (B.23)
θh m 1−Fh (p−z−ψx) 1 2
γ +λ(1−θ )+λ θ−1 mh 1−F (p−z) α

⎫
⎪
⎬
1
−  
θh mh Fh (p−z−ψx) 2 ⎪
⎭
γ +λ(1−θ )λ θ −1 m F (p−z)

The left-hand side of the previous equation increases in x. Further, Fh (p −z−ψx) decreases
in x, so that 1−F (p −z−x) increases in x. Hence, overall, the right-hand side decreases in x.
Therefore, for any p and z ∈ {0,v}, a unique value of x solves the equation φ(x) = x; that is, the
mapping x  → φ(x) has a unique fixed point.

B.6 Proof of Proposition 3

We first show that the proposition holds when ψ = 0, and then extend the proof to strictly positive
but small ψ.

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 When FinTech Competes for Payment Flows

Step 1: The proposition holds for ψ = 0.

Suppose first that ψ = 0. Then, it follows that bhm = bm = p m −v, and bhc = bc = p c . Noting that
the distribution of bank affinity F is the same for both credit types, the bank’s total profit under
payment monopoly is
m = (1−F (p −v))p, (B.24)

where we use the fact that mh +m = 1. The first-order condition is

1−F (p m −v)
1−F (p m −v)−f (p m −v)p m = 0 ⇒ pm = . (B.25)
f (p m −v)

Likewise, under FinTech competition, the bank’s first-order condition reduces to

1−F (p c )

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1−F (pc )−f (p c )p c = 0 ⇒ pc = . (B.26)
f (p c )
f
Now, suppose the distribution F has an increasing hazard rate throughout. Then, 1−F is
increasing, or 1−F
f is decreasing. Then, because v > 0,

1−F (p m −v) 1−F (pm )

pm = > ⇒ 1−F (pm )−f (p m )p m < 0. (B.27)
f (p m −v) f (p m )

Now, observe that the second-order condition in the FinTech competition case is that 1−F (p)−
f (p)p decreases in p. Thus, combining 1−F (p m )−f (p m )p m < 0 and 1−F (pc )−f (p c )p c = 0,
we know pm > pc .
f
Next, suppose the distribution F has a decreasing hazard rate. Then, 1−F is decreasing, or 1−F
f
is increasing. Then, because v > 0,

1−F (p m −v) 1−F (pm )

pm = < ⇒ 1−F (pm )−f (p m )p m > 0. (B.28)
f (p m −v) f (p m )

Again, the second-order condition in the FinTech competition case is that 1−F (p)−f (p)p
decreases in p. Thus, combining 1−F (p m )−f (p m )p m > 0 and 1−F (p c )−f (p c )p c = 0, we know
pm < pc .

Step 2: The proposition holds for small but strictly positive ψ.

The bank’s profit function when it is a monopolist in payment services is
 
m = mj (1−F (p −v −ψ w j ))(p +ψπj )+F (p −v −ψ j )ψπj .
I w U
(B.29)
j =h,

Denoting xj = πjI −F (p −v −ψ w )(π I

j j −πjU ), we can write the bank profit as
 
πm = mj (1−F (p −v −ψ w
j ))p +ψxj . (B.30)
j =h,

We show that the bank’s optimal price must lie within an interval [p, p̄]. First consider the upper
bound. When ψ = 0, the profit function reduces to (1−F (p −v))p = (1−F (p −v))(p −v)−(1−
F (p −v))v. Now, as p → ∞, F (p −v) converges to 1 as p → ∞, and by assumption, (1−F (p))p
converges to zero. Thus, (1−F (p −v))p converges to zero as p → ∞, so that the optimal price
when ψ = 0 must be finite.
f
Let Sj denote the first-best loan surplus for type θj . Then, xj = πjI −F (p −v −ψ w π
j ) j =
F (p −v −ψ j )πj +(1−F (p −v −ψ j )πj > 0, and πj ,πj , and j are each bounded above
w U w I U I w
f
by Sj . Now, by the continuity of m in ψ, we can find some ψ0 > 0 and some p > 0, such that for
any ψ < ψ0 , charging any price p > p is not optimal for the bank. This is easily seen by observing

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 The Review of Financial Studies / v 35 n 11 2022

that m > m maxp [(1−F (p −v))p], where 1−F (p −v) is the demand from the low credit type
for payment services at price (recall that w = 0).
It is equally easy to see that the bank’s optimal price has a lower bound. One possible lower
f
bound is −ψSh , that is, if in the payment market the bank reimburses the full surplus of the
loan to the high credit type consumer, the bank would make a loss. We denote such the lower
bound by p.
Now, recalling that w h depends on p, the first-order condition when the bank is a monopolist
in payment services is

  w 
d j dxj
0= mj 1−F (p m −v −ψ j )−f (p −v −ψ
w w
j )(1−ψ )p m +ψ . (B.31)
dp dp
j

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By the intermediate value theorem, we can write F (p m −v −ψ w
h ) = F (p −v)−ψ h f (p −
m w m

v −z1 ψ w h ), where z1 is between 0 and 1. We can also write f (p −v −ψ h ) = f (p −v)−

m w m

ψ w h f (p −v −z2 ψ j ), where z2 is between 0 and 1. The first-order condition can then be

m w

rewritten as

dy 
0 = 1−F (p m −v)−f (p m −v)p m +ψm +ψmh h f (p −v −z1 ψ
w m w
h) (B.32)
dp

d w d w dyh
+ w
hf (p m −v −z2 ψ w
h )(1−ψ
h
)p m − h
f (p m −v)p m +
dp dp dp

≡ 1−F (pm −v)−f (p m −v)p m +ψx m ,

 w
where x m = m
dy
+mh w f (p m −v −z ψ w )+ wf (p m −v −z2 ψ w )(1−ψ d h )p m −
dp h 1 h h h dp
d w dyh
dp
h f (p m −v)p m + . Because the relevant price p m is in a closed interval [p,p] and all
dp
functions are sufficiently smooth, we can find a uniform upper bound M > 0 for |x m |. Then,
1−F (p m −v)−f (p m −v)p m ∈ [−ψM,ψM].
If the hazard rate f/(1−F ) is strictly increasing, (1−F )/f is strictly decreasing. In the closed
interval p ∈ [p,p], the derivative of (1−F )/f is negative and has a lower bound, say −c, where
c > 0 is a constant. The first-order condition of the monopolist bank implies that there exists a
z3 ∈ [−1,1] such that

1−F (p m −v) ψM 1−F (p m ) ψM

pm = +z3 > +cv +z3
f (p m −v) f (p m −v) f (p m ) f (p m −v)

ψMf (p m )
⇒ 1−F (pm )−f (p m )p m < −cvf (p m )−z3 . (B.33)
f (p m −v)

In similar fashion, we can write the first-order condition of the bank under FinTech
competition as
0 = 1−F (p c )−f (p c )p c +ψx c , (B.34)

where the right-hand side is strictly decreasing in p, and x c is a collection of terms analogous
to x m . By an analogous argument that uses continuity, including establishing a closed interval in
which the relevant price resides in the competition case, we can find a constant C > 0 such that
1−F (p c )−f (p c )p c ∈ [−ψC,ψC], and 1−F (p)−f (p)p is decreasing in p over this interval.
Now, combining the conditions on p m and pc , we can choose a sufficiently small ψ so that
1−F (pm )−f (p m )p m < 1−F (pc )−f (p c )p c . Then, given that 1−F (p)−f (p)p is decreasing in
p, we have p m > pc .
The case for a strictly decreasing hazard rate is analogous.

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 When FinTech Competes for Payment Flows

B.7 Proof of Proposition 4

(i) Let p denote the price of the bank’s payment services, and let z denote the incremental difference
to consumer utility between the bank’s payment services and the next best alternative. Then, z = v
when the bank is a monopolist in payments, and z = 0 when there is FinTech competition.
Let w h (p,z) denote the solution to Equation (B.23). Then, it follows by inspection of Equation
(B.23) that w c w c c
h (p +v,v) = h (p ,0). That is, for any given price p under competition, if
the monopolist bank charges the price p c +v, the resultant value of w h remains unchanged.
Hence, bhm (p c +v) = p c −ψ hw = bhm (p c ), and bm (p c +v) = p c = bc (p c ). That is, under monopoly, the
threshold consumer of each credit type remains the same as in the competition case if p m = p c +v.
As a result, the loan contracts offered in the three cases of uninformed bank, informed bank with
high signal, and informed bank with low signal all remain the same as well, so that the profit from
the loan market is unchanged.

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Let R denote the bank’s profit from the loan market. Then, the bank’s overall profit under
competition is

c (p c ) = R + p c (1−F (bjc (p c ))). (B.35)
j =h,

Suppose the monopoly bank charges p m = p c +v.

As argued above, the bank’s profit from the loan
market is unchanged. Therefore, its overall profit is

m (p c +v) = R + (p c +v)(1−F (bjm (p c +v))). (B.36)
j =h,

But as argued above, bjm (p c +v) = bjc (p c ) for each j = h,. It therefore follows that whenever v > 0
and at least one of Fhc (bhc ) or Fc (bc ) is strictly less than one, we have m (p c +v) > c (p c ).
To complete the argument, note that if pm is the optimal price under monopoly, it must be that
m (p m ) ≥ m (p c +v), so it follows that m (p m ) > c (p c ).

(ii) This part follows immediately from noting that the menu of loan contracts offered by the bank
f
always has qh = qh , the first-best quantity for the high credit type, and that in equilibrium the high
credit type accepts the contract designed for it.

(iii) Observe that a low credit type earns zero surplus from a loan, regardless of the bank’s
information or of their bank affinity. Therefore, the change in welfare for this type is determined
solely by the surplus they obtain from payments. (a) Consider a low credit type consumer with
b < min{bc (p c ),bm (p m )}. When the bank is a payment monpolist, this consumer is unbanked, and
their overall utility is zero. When there is FinTech competition, this consumer earns the utility from
electronic payment services v > 0, and their overall utility is v as well. Thus, they are strictly better
off with FinTech competition.
(b) Consider a low credit type consumer with b > max{bc (p c ),bm (p m )}. This consumer uses the
bank to process payments both when the bank is a monopolist and under FinTech competition. Thus,
the overall utility of this consumer is b +v −pm under monopoly and b +v −pc under competition.
It follows that they are strictly better off under FinTech competition if p c < pm , and strictly worse
off if pc > pm .

B.8 Proof of Proposition 5

(i) As shown in Equation
 (11)
 in Proposition 2, the expected utility of the high credit type from a
θ
loan is equal to whI = θh −1 λ2 Es [q (κ(s))2 | θh ]. Let ρ be the intermediate likelihood ratio before

the payment signal is obtained. Then, we can write

θh λ α 1
whI (ρ,α) = −1 (q (ρα))2 + (q (ρ/α))2 . (B.37)
θ 2 1+α 1+α

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 The Review of Financial Studies / v 35 n 11 2022

From Proposition 1 part (i), q (κ) =

θ A−1
  is strictly decreasing in κ. Hence, it
θh
γ +λ(1−θ )+λκ θ −1
follows that q (ρα) and q (ρ/α) are each strictly decreasing in ρ, so that whI (ρ,α) is strictly
decreasing in ρ.
As the low credit type obtains zero surplus in all cases, we have wI (ρ,α) = 0. Therefore, bs (p) =
p +ψy.
Now, suppose that bhs (p) < bs (p) = p +ψy. Then, as the bank affinity distribution is the same
for both types, it follows that 1−F (bhs (p)) > 1−F (bs (p)) and F (bhs (p)) < F (bs (p)), so that
1−F (bs (p)) mh s
FT = F (bh (p)) mh . But w I (ρ,α) is strictly decreasing in ρ, so it follows
ρ B = 1−F (bhs (p)) m > ρ (b s m h that
 F  (p)) 
whI (ρ B ,α) < whI (ρ FT ,α), so that bhs = p +ψy +(whI (ρ FT ,α)−whI (ρ B ,α)) > bs = p +ψy, which
is a
contradiction.
A similar argument rules out the case that bhs (p) > bs (p), leaving only the possibility that

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bhs (p) = bs (p).

1−F (bs (p)) mh

(ii) This part follows immediately from part (i) on noting that ρ B = 1−F (bhs (p)) m and ρ FT =

s (p))
F (bh mh
F (bs (p)) m
.

B.9 Proof of Proposition 6

(i) Consider the equilibrium under data portability in which all consumers port their data to the
bank for free. As discussed in the text, this case is equivalent to data sales by the FinTech firm at a
price of zero. The proof of Proposition 5 applies for all values of the price of data under data sales,
including y > 0 and zero. Hence, it follows that the loan market outcomes are identical between
data sales and data portability.
(ii) Consider the data sales regime, and suppose the bank pays a price y to the FinTech firms for
acquiring payment data of FinTech customers. Write the bank’s expected profit from a loan to
credit type θj when it is informed as πjI (ρ,α), where ρ is the intermediate likelihood ratio before
the payment signal. Under the same affinity distribution between the two credit types, we have
bhs = bs = p +ψy, and ρ B = ρ FT = mh /m .
Then, the bank’s overall profit is simplified as
  mh
 = mj (1−F (p +ψy))p +ψ(1−F (p +ψy))πjI ,α
m
j

mh
+ψF (p +ψy) πjI ,α −y . (B.38)
m
The first-order condition for the optimal price is

0= mj [−f (p +ψy)(p +ψy)+1−F (p +ψy)]. (B.39)
j

Observe that this equation is of the form


0= mj [−f (x)x +1−F (x)], (B.40)
j

where x = p +ψy.
Let G(x) = −f (x)x +1−F (x). Then, by the implicit function theorem,
dp G (x) ∂x
∂y
=− = −ψ < 0. (B.41)
dy G (x) ∂x
∂p
That is, the bank’s price for payment services increases as y decreases. Hence, comparing data
sales (with a data price of ŷ > 0 and data portability (with a data price of zero), the bank’s price for
payment services is strictly greater under data portability.

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 When FinTech Competes for Payment Flows

The FinTech firms charge a price for payment services −ψ ŷ under data sales, and a price zero
under data portability. Hence, all consumers are paying strictly more for payment services under
data portability, whereas the loan market outcomes are identical in both the data sales and data
portability regimes. It follows that all consumers strictly prefer data sales to data portability.

C. Example: Effects of FinTech Competition on Loan Surplus

We set A = 2,θh = 0.99,θ = 0.8,λ = 0.4,γ = 0.2,ψ = 1,α = 2, and mh = 5 = m = 0.5. Figure C1 shows
the equilibrium loan surplus captured by credit type θh as a function of α, the precision of the
signal extracted from payments. Figure C2 shows the total surplus from a loan to the low credit
type in equilibrium as α varies. In each figure, the bank affinity distribution for the low credit type,

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F , is set to be exponential with mean 1. The bank affinity distribution for the high credit type, Fh
is Weibull with first parameter k = 2 (implying an increasing hazard rate) in panel (A) and k = 0.5
(implying a decreasing hazard rate) in panel (B). The second parameter of the Weibull distribution
is set to 1.
For each set of parameter values and payment market structure, we first compute the optimal
price of bank payment services. The numerical computation involves using Lemma 2 to pin down
a fixed point in w h for each p. The bank’s profit function can then be computed, and the optimal
price determined. The relative masses of consumers using the bank (and not using the bank) at the
optimal price determine the optimal menu of contracts in each case.
Bank payment customers obtain a menu based on the signal they have generated. Recall that
α 1
high credit types generate a high signal with probability 1+α and a low signal with probability 1+α ,
with the probabilities being reversed for low credit types. When the bank is informed, the loan
surplus calculations take these probabilities into account.
Consider Figure C1 (A), and start with the case in which the bank is a monopoly provider of
payment services. Given the parameters, at any price, the pool of consumers who use the bank
for payment services includes a larger proportion of high credit types than the prior probability of
0.5. Conversely, the pool of consumers who are not bank payment customers includes fewer high
credit types than the prior. Therefore, the bank extracts a higher rent from payment customers who

A Fh has increasing hazard rate B Fh has decreasing hazard rate

Figure C1
Expected loan surplus captured by credit type θh
This figure plots the expected loan surplus captured by credit type θh for different parameter values and payment
market structures. Here, A = 2,θh = 0.99,θ = 0.8,λ = 0.4,γ = 0.2,ψ = 1,α = 2,mh = 5,m = 0.5. The bank affinity
distribution for credit type θ is exponential with parameter 1. In panel A, the bank affinity distribution for
credit type θh is Weibull with first parameter k = 2. In panel B, the bank affinity distribution for credit type θh is
Weibull with first parameter k = 0.5. The second parameter of the Weibull is set to one in both cases. For each
set of parameters, we find the optimal price for bank payment services. The solid lines represent the bank is
uninformed about the consumer, and the dashed lines represent that the bank is informed.

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 The Review of Financial Studies / v 35 n 11 2022

A Fh has increasing hazard rate

B Fh has decreasing hazard rate

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Figure C2
Expected total surplus from loan to credit type θ
This figure plots the expected total surplus (i.e., the sum of bank profit and consumer surplus) from a loan to
credit type θ for different parameter values and payment market structures. Here, A = 2,θh = 0.99,θ = 0.8,λ =
0.4,γ = 0.2,ψ = 1,α = 2,mh = 0.95,m = 0.05. The bank affinity distribution for credit type θ is exponential. In
panel A, the bank affinity distribution for credit type θh is Weibull with first parameter k = 2. In panel B, the
bank affinity distribution for credit type θh is Weibull with first parameter k = 0.5. For each set of parameters,
we find the optimal price for bank payment services. The solid lines represent the bank is uninformed about the
consumer, and the dashed lines represent that the bank is informed.

have the high credit type. As a result, the latter have a lower utility from the loan. Conversely, high
credit types who do not use the bank for payment services benefit.
Now, consider the effects of FinTech competition. Relative to the bank monopoly case, FinTech
competition skews the pool of bank payment customers a little more toward the low credit type.
Thus, when the bank is uninformed, the high-credit type obtains less favorable terms and has an
even lower utility from the loan. That is, high credit types who are payment noncustomers are
worse off after FinTech entry. As a result, high-credit types who remain bank payment customers
obtain a lower surplus from the loan after FinTech competition.
Figure C1 (B) embodies similar reasoning. Here, the bank affinity distribution of high credit
types has an increasing hazard rate. FinTech competition skews the pool of bank payment customers
toward the high credit type, so that the high credit type obtains less favorable terms (compared
to the bank monopoly case) when the bank is informed. Therefore, bank payment customers are
worse off in the loan market under FinTech competition. Conversely, among high credit types,
bank payment noncustomers obtain a higher surplus from the loan under FinTech competition.
Figure C2 shows the total surplus from a loan to the low credit type. Recall that this loan surplus
is entirely captured by the bank. From Proposition 2, both the total surplus from a loan to the low
credit type and the amount of loan surplus captured by the high credit type depend on the quantity
offered to the low credit type. Thus, it is not surprising that the effect of FinTech competition on
the total surplus from the low credit type is similar to its effect in Figure C1. Keeping all else fixed,
when Fh has an increasing hazard rate, FinTech competition improves this surplus among bank
payment customers, and reduces it among noncustomers. The converse effects occur when Fh has
a decreasing hazard rate.
More surprisingly, the expected surplus from a loan to the low credit type payment customer is
nonmonotone in α, the precision of the signal extracted from payments. When α is high, the low
credit type is unlikely to generate a high signal. The high precision of the low signal allows the
bank to set the loan quantity for the low type close to its first-best level. Therefore, for high α, the
surplus from a loan to the low-credit type must be increasing in α. For values of α close to one,
the additional information from payments allows the bank to vary q with the signal in a nonlinear
way. As the low credit type still generates the high signal with sufficiently large probability for
such values of α, the overall expected surplus falls given our parameter values.

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 When FinTech Competes for Payment Flows

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