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Technology Adoption and Leapfrogging:
Racing for Mobile Payments
WP 21-05
Pengfei Han
Peking University
Zhu Wang
Federal Reserve Bank of Richmond
Technology Adoption and Leapfrogging:
Racing for Mobile Payments∗
Pengfei Han†and Zhu Wang‡
March 1, 2021
Abstract
Paying with a mobile phone is a cutting-edge innovation transforming the global
payments industry. However, some advanced economies like the U.S. are lagging
behind in mobile payment adoption.
We construct a dynamic model with se-
quential payment innovations to explain this puzzle, which uncovers how advanced
economies’ past success in adopting card-payment technology holds them back in
the mobile-payment race. Our calibrated model matches the cross-country adoption
patterns of card and mobile payments and also explains why advanced and developing countries favor different mobile payment solutions. Based on the model, we
conduct several quantitative exercises for welfare and policy analyses.
Keywords: Technology Adoption, Sunk Cost, Payments System, FinTech
JEL Classification: E4, G2, O3
∗
We thank Jeremy Greenwood, Zhiguo He, Chang-Tai Hsieh, Chad Jones, and Peter Klenow for
helpful comments, and Emily Emick for research assistance. The views expressed herein are solely those
of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Richmond or the
Federal Reserve System.
†
Affiliation: Guanghua School of Management, Peking University, Beijing, China. Email address:
pengfeihan@gsm.pku.edu.cn.
‡
Affiliation: Research Department, Federal Reserve Bank of Richmond, Richmond, VA, USA. Email
address: zhu.wang@rich.frb.org.
1
1
Introduction
The payments system is a key financial technological infrastructure of the aggregate economy. With the successful launch of general-purpose credit cards in the late 1950s and
debit cards in the early 1980s, the United States has been the leader of the card payment
revolution in the world. After maintaining the global leadership in the payments industry
for decades, however, the United States is falling behind in the recent mobile-phone-based
payment innovation (henceforth, “mobile payment”).
Kenya is an early success story for mobile payment adoption. Within four years after
being launched in 2007, mobile payment has been adopted by nearly 70% of Kenya’s adult
population (Jack and Suri, 2014). While the mobile payment technology in Kenya relies
on short message service (SMS), China has introduced an innovation based on smart
phones and QR (Quick Response) codes which experienced explosive growth of mobile
payments in recent years. In 2017, a total of 276.8 billion mobile payment transactions
were made in China, equivalent to 200 transactions per capita.1
As a stark contrast, the United States appears to be lagging in mobile payment adoption. To illustrate, Figure 1 compares the adoption rates of card and mobile payments
around 2017 in three countries: Kenya, China, and the United States. Figures 1A and 1B
report the percentage of the adult population (age 15 and above) having a debit card and
using a mobile payment service, respectively.2 As depicted in Figure 1A, card payment
adoption rate of the United States is remarkably higher than Kenya and China, reflecting
the global leadership of the United States in the card payment system. Figure 1B, however, shows that the mobile payment adoption rate of the United States is substantially
lower than Kenya and China. Therefore, while the United States maintained the global
leadership in the card payment era, it has been surpassed in the recent race of mobile
payment adoption.
This has raised concerns about the efficiency and competitiveness of the U.S. payments
system by the press, business leaders, and policymakers. With a headline of “China is
out-mobilizing the United States,” the Wall Street Journal (2018) was impressed by how
1
Source: Statistical Yearbook of Payment and Settlement of China.
Sources: Global Financial Inclusion (Global Findex) Database of the World Bank, and eMarketer.
See Appendix I for the data details.
2
2
“Chinese consumers are adopting mobile payments in a way that is making U.S. tech
companies green with envy.”3 Apple’s CEO, Tim Cook, noted in a speech that China
outdid the United States in the development of mobile payment technology.4 Leaders
of the Federal Reserve System recognized “that the U.S. retail payment infrastructure
lags behind many other countries” and “the gap between the transaction capabilities in
the digital economy and the underlying payment and settlement capabilities continues to
grow.”5
Figure 1. Adoption of Card and Mobile Payments (2017)
These observations and concerns lead to important questions: Why did developing
countries like Kenya and China lag behind in adopting the card payment but leapfrog
into the world frontier in the mobile payment stage? Has the United States lost the
global leadership in the payment area? Should the U.S. government implement policies
to boost mobile payment adoption?
This paper aims to address these questions. In doing so, we first compile a novel dataset
to uncover the general adoption patterns of card and mobile payments across countries.
3
See Wall Street Journal’s report on “China’s Great Leap to Wallet-Free Living,” January 18, 2018.
See Tim Cook’s speech at the eighteenth China Development Forum in Beijing on March 18, 2017.
5
See a speech by Lael Brainard, a Federal Reserve governor, on “Delivering Fast Payments for All”
on August 5, 2019.
4
3
The data shows that the overtaking in mobile payment adoption is a systematic pattern
between developing countries and advanced economies, beyond just Kenya, China, and the
United States. Moreover, the adoption rate of mobile payment shows a non-monotonic
relationship with per capita income: increasing in low-income countries, decreasing in
middle-income countries, and increasing again in high-income countries. This is in contrast with the card payment, for which the adoption rate increases monotonically in per
capita income across countries. Also, advanced economies and developing countries tend
to adopt different mobile payment solutions: The former favors those complementary to
card, while the latter favor those substituting card.
We then construct a theory to explain the early success of advanced economies in
adopting card payment, and how their advantage in card payment later hinders their
adoption of mobile payment. In our model, three payment technologies, cash, card, and
mobile, arrive sequentially. Newer payment technologies lower the variable costs of conducting payment transactions, but they require a fixed cost to adopt. As a result, when
card arrives after cash, high-income consumers find it more attractive to adopt, which
explains the high adoption rate in rich countries. However, when mobile arrives after
card, the adoption incentives are remarkably different between existing card users and
cash users. Since the fixed cost paid for adopting card is already sunk, card users have to
face a higher income threshold to adopt mobile payment than cash users. Also, the same
sunk cost makes it more attractive for card users to consider a mobile payment method
complementary to card, while cash users would favor a card-substituting solution. This
explains why most developing countries choose Mobile Money, a mobile payment method
bypassing card services, while most advanced economies use card-complementing mobile
solutions such as Apple Pay.
Our model calibration matches cross-country adoption patterns of both card and mobile payments well. Based on the calibrated model, we conduct quantitative analyses on
several welfare and policy issues. We find that lagging behind in mobile payment adoption
does not necessarily mean that advanced economies have fallen behind in overall payment
efficiency, even though they benefit less from the mobile payment innovation compared
with developing countries. Moreover, in our model economy, falling behind in adopting
mobile payment is an optimal choice for advanced economies, and we provide a quanti4
tative assessment of welfare loss of subsidizing mobile payment adoption. That said, our
model also suggests that greater technological advances in mobile payment are needed
for advanced economies to regain leading positions in the payment race, and governments
may play positive roles in facilitating technological progress and market coordination.
Our paper contributes to several strands of literature. The first one is the studies on
the payments system. Following the pioneering work of Rochet and Tirole (2002, 2003),
a fast growing body of literature has been developed for studying market structure and
pricing of retail payments system, especially card payments (see Rysman and Wright,
2014 for a literature review). However, most of those studies assume a static setting and
ignore adoption decisions of payment methods. Among very few exceptions, Hayashi, Li,
and Wang (2017) and Li, McAndrews, and Wang (2020) study payment system evolution
in dynamic settings, but they do not consider cross-country patterns, which is the focus
of this paper.
Our paper is also related to the literature studying how electronic payments affect
financial inclusion and social well-being. Jack and Suri (2014) find that M-PESA (a
mobile payment service in Kenya) reduced transaction costs of remittances and facilitated
the risk-sharing networks of households. Muralidharan, Niehaus, and Sukhtankar (2016)
show that biometrically authenticated cards enabled faster, more predictable, and less
corrupt payments process for beneficiaries of employment and pension programs in India.
Our paper complements those works in the sense that we study how cost savings brought
by electronic payments affect payment efficiency and drive different adoption patterns
between developing and advanced economies.
Finally, our paper contributes to the broad literature of technology diffusion. For a
long time, researchers in that field have been interested in the relationship between the
adoption of new technologies and the heterogeneity of potential adopters (e.g., Griliches,
1956). Some more recent works (e.g., Comin and Hobijn, 2004) explore cross-country
adoption patterns of major technologies and match them with alternative theoretical
explanations. We add to this literature a study of the diffusion of a latest payment
innovation and uncover a novel non-monotonic relationship between technology adoption
and per capita income.
The remainder of this paper is structured as follows. Section 2 provides the background
5
of mobile payment and summarizes stylized facts from a novel dataset regarding crosscountry adoption patterns. Section 3 introduces the model and solves the equilibrium
outcome. Section 4 calibrates the model and provides counterfactual exercises to illustrate
the implications of the model. Section 5 conducts welfare and policy analyses. Section 6
provides further discussions. Finally, Section 7 concludes.
2
Background and stylized facts
Following Crowe et al. (2010), we define a mobile payment to be a money payment
made for a product or service through a mobile phone, whether or not the phone actually
accesses the mobile network to make the payment. Mobile payment technology can also
be used to send money from person to person.
The very first mobile payment transaction in the world can be traced back to 1997,
when Coca-Cola in Helsinki came out with a beverage vending machine, where users
could pay for the beverage with just an SMS message. Around the same time, the oil
company Mobil, also came out with an RFID (Radio Frequency Identification) device
called Speedpass that helped its users to pay for fuel at gas stations. These two earliest
examples of mobile payment services were both based on the SMS and the payments were
made by a mobile account that was linked to the user’s device.
The mobile payment systems based on SMS soon evolved into the world’s first phonebased banking service launched by the Merita Bank of Finland in 1997. As time passed,
the mobile payment technology progressed with more user applications, such as buying
movie tickets, ordering pizza, and arranging travels. In 2007, Vodafone launched one
of the largest mobile payment systems in the world. It was based on SMS/USSD text
messaging technology and offered various kinds of macro and micro payments.6 Vodafone
launched this service in Kenya and Tanzania with the cooperation of the local telecom
operators.
2011 was the year which saw major technology firms like Google and Apple entering
6
SMS (short message service) and USSD (Unstructured Supplementary Service Data) are two methods
used by telecom companies to allow users to send and receive text messages. With SMS, messages are
sent to SMS centers, which store the message and then transmit the message to the recipient. In contrast,
USSD makes a direct connection between text message senders and recipients, making it more responsive.
6
the field of mobile payment. Google became the first major company to come up with its
digital mobile wallet solution. The wallet was based on the NFC (Near Field Communication) technology and allowed the customers to make payments, redeem coupons, and
earn loyalty points. In 2014, Apple launched its pay service in the United States called
Apple Pay compatible with iPhone 6, which allowed the users to simply tap their phone
against a contactless payment card terminal at the point of sale, paying instantaneously.
Before long, competitors to Apple, such as Google and Samsung, released their respective
mobile payment apps in the wake of Apple Pay’s success.
2.1
Alternative mobile payment technologies
While there are many mobile payment solutions, they fall into two basic categories: either bypassing or complementing the existing bank-related payment card systems. In
this paper, we name them card-substituting and card-complementing mobile payments,
respectively. The former is mainly used in developing countries like Kenya, and the latter
is popular in advanced economies like the United States.
2.1.1
Card-substituting mobile payment
Card-substituting mobile payment is epitomized by Kenya’s M-PESA model. M-PESA
is a mobile payment service launched by Safaricom and Vodafone in Kenya in 2007. MPESA users can deposit money into an account in their phones and send balances to other
users by SMS text messages. Hence, they can use a mobile phone to (i) deposit, withdraw,
and transfer money, (ii) pay for goods and services, and (iii) redeem deposits for regular
money. To deposit and withdraw money, M-PESA users rely on M-PESA agents (e.g.,
shops, gas stations, post offices). These agents in the M-PESA system are the analogs of
the ATMs and bank branches in the banking system, allowing the M-PESA operation to
bypass the banking system.
Achieving wild success in Kenya, M-PESA was emulated in many other developing
countries. This category of mobile payment methods is defined as the “Mobile Money”
payment by the Global System for Mobile Communications Association (GSMA) that
meets the following conditions: First, the payment method must include transferring
7
money as well as making and receiving payments using a mobile phone. Second, the
payment method must be available to the unbanked (e.g., people who do not have access
to a formal account at a financial institution). Third, the payment method must offer
a network of physical transactional points (that can include agents) widely accessible to
users. Fourth, mobile-banking-related payment services (such as Apple Pay and Google
Wallet) that offer the mobile phone as just another channel to access a traditional banking
product do not satisfy this definition of Mobile Money.
Figure 2. Global Adoption of Mobile Money Payment
The global adoption of Mobile Money payment in 2018 is illustrated in Figure 2.7 The
percentage numbers in the figure refer to the shares of registered mobile money customers.
The gray areas in the figure represent regions where the Mobile Money payment services
are unavailable. Most users of Mobile Money payment are concentrating in developing
countries, particularly sub-Saharan Africa (45.6%) and South Asia (33.2%). In contrast,
Mobile Money payment services are barely relevant for developed countries.
2.1.2
Card-complementing mobile payment
In developed countries, the popular mobile payment methods, created by technology firms
(e.g., Apple, Google, Samsung), rely heavily on banking and payment card networks.
7
Source: GSMA (2018), “State of the Industry Report on Mobile Money.”
8
Apple Pay is a leading example. Apple Pay was launched in 2014 as one of the first
mobile wallets — apps that enable people to connect credit cards, debit cards, and bank
accounts to mobile devices to send and receive money. Of the major mobile wallet services
— Google Pay (formerly Android Pay), Samsung Pay and Apple Pay – the Apple service
is the largest in terms of user adoption and market coverage.
Apple Pay represents a secure and sanitary payment option, since the app uses the
NFC technology to transmit an encrypted virtual account number to the point-of-sale
payment terminal. Originally being launched in the United States, Apple Pay debuted in
the United Kingdom, Australia, and Canada in 2015, and expanded to China, Switzerland, France, Singapore, and Japan in 2016. By 2020, Apple Pay has become available in
dozens of countries (marked dark blue in Figure 3), most of which are developed countries.8
Apple Pay supports both international payment card networks–such as American Express, Visa, Mastercard, and Discover–as well as country-specific domestic payment card
services like China’s UnionPay, Japan’s JCB, France’s Cartes Bancaires, and Canada’s
Interac.
Figure 3. Global Availability of Apple Pay
8
Source: https://en.wikipedia.org/wiki/Apple Pay#Supported countries.
9
2.2
Data and stylized facts
To study the global adoption pattern of mobile payments, we put together a novel dataset
on debit card and mobile payment adoption in 94 countries. The countries in our sample
accounted for 91.4% of world GDP in 2017.
The dataset are drawn from the following sources (See Appendix I for more details).
First, the data on the adoption rate of card-substituting mobile payment services in
2017 are based on the Global Financial Inclusion (Global Findex) Database of the World
Bank, which surveyed 76 countries with a visible presence of Mobile Money payment
services. Second, the data on the adoption rate of card-complementing mobile payments
around 2017, gathered from eMarketer, cover 23 countries with a visible presence of
mobile proximity payment services. Merging the two mobile payment data sources yields
a sample of 94 countries, among which five countries are covered in both data sources. We
also collect the adoption rate of debit cards for the 94 countries in 2017 from the Global
Findex Database of the World Bank. Finally, we obtain the data on per capita GDP for
each country in our sample from the World Bank.
Figure 4. Card and Mobile Payment Adoption across Countries
Figure 4 plots the adoption rates of debit card and mobile payments against log per
capita GDP in 2017. Fitting a simple linear regression line to the data shows that debit
10
card adoption rate strictly increases in per capita GDP across countries, while there
appears no clear relationship between mobile payment adoption and per capita GDP.
However, as we delve further into the mobile payment adoption data, some pattern
starts to emerge. First, we divide the sample into three income groups: low-income
countries (i.e., per capita GDP $2,500), middle-income countries (i.e., $2,500 ≤ per
capita GDP ≤ $30,000), and high-income countries (i.e., per capita GDP $30,000).
We then distinguish different payment technologies used in each country in the sample.
As shown in Figure 5A, there are clear differences in mobile payment technology choice:
Most low- and middle-income countries choose card-substituting mobile payment, while
most high-income countries choose card-complementing mobile payment.
Figure 5. Cross-Country Mobile Payment Adoption Pattern
Considering that mobile payment is a fairly recent technological innovation, it is possible that some countries (including those not covered by our dataset) may not have fully
introduced it due to information or coordination frictions. We then remove the observations that have very low adoption rate (i.e., 10%) and add back linear regression lines
by income-country group.9 The results are shown in Figure 5B. It becomes visible that
9
Removing observations with mobile payment adoption rate below 10% only affects countries from the
Global Findex Database that use Mobile Money payment services. Presumbly, the eMarketer dataset on
mobile proximity payment adoption has implicitly applied a similiar selection rule.
11
mobile payment adoption displays a non-monotonic relationship with per capita GDP:
increasing in low-income countries, decreasing in middle-income countries, and increasing again in high-income countries. We report the regression results in Appendix II,
and these patterns are robust for using a nonlinear regression model or an instrumental
variable approach.
To sum up, we have the following stylized facts on cross-country adoption patterns of
card and mobile payments:
1. Positive income effect on card adoption. — The adoption of card increases in per
capita income across countries.
2. Non-monotonic income effect on mobile payment adoption. — The adoption of mobile
payment increases in per capita income in low- and high-income countries, but
decreases in per capita income in middle-income countries.
3. Overtaking in mobile payment adoption. — Some low-income countries overtake
high-income countries in adopting mobile payment.
4. Different technology choices across countries. — For low- and middle-income countries, the mobile payment technologies adopted are almost entirely the card-substituting
ones, while in high-income countries, the dominant choices are the card-complementing
ones.
In the rest of the paper, we will construct a theory to explain these stylized facts
and conduct welfare and policy analyses. We will also provide discussions on the outlier
countries with very low mobile payment adoption rate (i.e., 10%) in Section 6.
3
3.1
Model
Setup
Our model studies the adoption of payment technologies across countries. In each country,
three payment technologies arrive sequentially, in the order of cash, card, and mobile.
12
Cash is a traditional paper payment technology, accessible to everyone in an economy.
Using cash incurs a cost per dollar of transaction, which includes handling, safekeeping,
and fraud expenses. In contrast, card and mobile are electronic payment technologies, each
of which requires a fixed cost of adoption but lowers variable costs of doing transactions
comparing with cash. We denote and as the one-time fixed adoption costs associated
with card and mobile, respectively. Those fixed costs may include time and resources spent
on joining banking or mobile payment networks plus any installation and learning costs.
The variable costs associated with using card and mobile are and per dollar of
transactions, respectively. To capture the technology progress between cash, card, and
mobile, we assume and .
Time is discrete with an infinite horizon. We consider an endowment economy, where
each agent receives an exogenous income at time . Without loss of generality, we
assume that income follows an exponential distribution across the population in the
economy, with the cdf function ( ) = 1 − exp(− ).10 Note that the exponential
distribution has a fixed Gini coefficient at 0.5 and the mean is . Over time, each agent’s
income grows at a constant rate , i.e., +1 = (1 + ). This implies that the mean
income of the economy also grows at the same rate, i.e., +1 = (1 + ). We normalize
the population size to unity.
An agent has a linear utility = , where is her consumption. We assume no storage
technology, so each agent consumes all her endowment net of payment costs each period.
We also assume payment services and merchant services are provided by competitive
markets, so that a consumer can always use her favorite payment technology to pay for
her consumption at the social cost of the payment method she chooses to use.11
3.2
Equilibrium
We derive the equilibrium adoption patterns of cash, card, and mobile payment technologies as they arrive sequentially in an economy.
10
The exponential distribution fits income distributions well (e.g., see Dragulescu and Yakovenko, 2001).
These simplifying assumptions allow us to focus on the technological side of payment innovations
and provide a good benchmark for understanding the key cross-country differences. We provide more
discussions in Section 6 on relaxing some of the assumptions.
11
13
3.2.1
Cash payment
The economy only has the cash technology before electronic payments are available. Cash
is accessible to everyone, so the adoption rate is 100%. In such a cash economy, the value
function of an agent depends on her income , and can be written as
( ) = (1 − ) + (+1 )
where
+1 = (1 + )
and is the discount rate. Accordingly, (+1 ) = (1 + ) ( ), and we derive
( ) =
3.2.2
(1 − )
1 − (1 + )
(1)
Card payment
At time , the payment card technology arrives as an exogenous shock. Each agent then
compares card and cash technologies and makes the adoption decision.
At any point of time ≥ , the value function of an agent who has income and
has adopted card can be written as
( ) = (1 − ) + (+1 )
which yields
( ) =
(1 − )
1 − (1 + )
(2)
The availability of the card technology also changes the value function of cash users
because it adds an option of adopting card in the future. Therefore, the value function of
an agent who has income and decides to continue using cash at time would be
( ) = (1 − ) + max{ (+1 ) (+1 ) − }
14
(3)
At each point of time ≥ , an agent would adopt card if and only if
( ) − ≥ ( )
(4)
Therefore, Eqs. (2), (3), and (4) pin down the minimum income level for card adoption,
which requires
(1 − ) (1 + )
(1 − )
− = (1 − ) + [
− ]
1 − (1 + )
1 − (1 + )
Accordingly, an agent would have adopted card by time ≥ if and only if her income
satisfies that
≥ =
(1 − )
( − )
(5)
The intuition of condition (5) is straightforward: An agent would adopt card if the flow
benefit of adoption ( − ) can cover the flow cost (1 − ) .
The payment card adoption rate, is determined as
¶
µ
(1 − )
= 1 − ( ) = exp −
( − )
(6)
It follows immediately from Eq. (6) that the payment card adoption rate increases in per
capita income (i.e., 0).
3.2.3
Mobile payment
Mobile payment arrives after card as another exogenous shock. In the following, we first
study a scenario where only a card-substituting mobile payment technology (e.g., Mobile
Money) is introduced, and we then study another scenario where a card-complementing
mobile payment technology (e.g., Apple Pay) also becomes available.
A card-substituting mobile payment technology At a point of time ,
a card-substituting mobile payment technology arrives. This mobile payment technology
allows users to replace or bypass the card technology, with a lower marginal cost
and a lower fixed cost . Each agent then compares three payment
technologies (i.e., cash, card, and mobile) to make the adoption decision.
15
At any point ≥ , the value function of an agent who has income is and has
adopted mobile can be written as
( ) = (1 − ) + (+1 )
which yields
( ) =
(1 − )
1 − (1 + )
(7)
Because mobile is a better payment technology than card, (i.e., and ),
an agent who has not adopted card by time − 1 (i.e., −1 ) would no longer
consider adopting card at time and afterwards. Instead, they would adopt mobile
payment at a point of time ≥ whenever
( ) − ≥ ( )
(8)
where the value function of a cash user ( ) now becomes
( ) = (1 − ) + max{ (+1 ) (+1 ) − }
(9)
Equations (7), (8), and (9) then pin down the minimum income level for mobile
payment adoption:
≥ =
(1 − )
( − )
(10)
Given and Eqs. (5) and (10) show , so the fraction of
agents who have switched from cash to mobile by time ≥ is
→ = −1 ( ) − ( ) = exp(− ) − exp(− −1 )
(1 − )
(1 − )
) − exp(−
)
= exp(−
( − )
( − ) −1
(11)
An agent who has adopted card by time − 1 (i.e., −1 ≥ ) would adopt mobile
payment at a point of time ≥ whenever
( ) − ≥ ( )
16
(12)
where the value function of a card user now becomes
( ) = (1 − ) + max{ (+1 ) (+1 ) − }
(13)
Equations (7), (12), and (13) pin down the income level 0 above which agents would
switch from card to mobile payment:
≥ 0 =
Assuming
−
,
−
(1 − )
( − )
(14)
we have 0 so the fraction of agents who have switched
from card to mobile by time ≥ is
→ = 1 − (0 ) = exp(−0 )
(1 − )
)
= exp(−
( − )
(15)
as long as some card adopters have not adopted mobile (i.e., → −1 ). Otherwise, → = −1
Combining Eqs. (11) and (15), the total fraction of agents who have adopted mobile
payments by time ≥ is
= → + → = exp(− ) − exp(− −1 ) + exp(−0 ) (16)
(1 − )
(1 − )
(1 − )
) − exp(−
) + exp(−
)
= exp(−
( − )
( − ) −1
( − )
as long as → −1 . Otherwise, = exp(− ) = exp(− ((1−)
). This result
− )
unveils the following subtle relationship between the mobile payment adoption rate and
per capita income: (i) taking the value of −1 as given, Eq. (16) yields 0,
which implies that a country’s mobile payment adoption rate increases over time due
to income growth; (ii) taking into account −1 = (1 + )− +1 , Eq. (16) shows
that the sign of has to depend on parameter values. As a result, the mobile
payment adoption rate may not show a monotonic relationship with per capita income
across countries; and (iii) in the long run, once all the card adopters eventually adopt
mobile (i.e., → = −1 ), we have = exp(− ) = exp(− ((1−)
), in which
− )
17
case the mobile payment adoption rate becomes strictly increasing in per capita income
across countries (i.e., 0).
A card-complementing mobile payment technology We now extend the model
to consider another scenario that at the same point of time , a card-complementing
mobile payment solution also becomes available in addition to the card-substituting one.
This mobile payment technology is an add-on upgrade to the existing card technology,
which allows an agent who has adopted card to pay an upgrading cost
to get the
mobile payment feature that lowers the variable cost of payments (i.e., ).
This add-on technology requires a lower fixed cost than adopting the card-substituting
mobile payment method (i.e.,
).
It is straightforward to see that in this scenario, agents who have adopted card before
would prefer adopting the card-complementing mobile payment technology because
, while agents who have not adopted card would bypass card and adopt the
card-substituting mobile payment technology because +
.
Therefore, agents who have switched from cash to mobile by time ≥ should have
chosen the card-substituting mobile payment technology. As shown in Eq. (11) above,
the fraction of these agents is
→ = −1 ( ) − ( ) = exp(−
(1 − )
(1 − )
) − exp(−
)
( − )
( − ) −1
On the other hand, agents who have chosen the card-complementing mobile payment by
time ≥ are those whose income have crossed the threshold
≥
0 =
(1 − )
( − )
(17)
The fraction of these card-mobile switchers is
→ = 1 −
(
0)
=
exp(−
0 )
(1 − )
= exp(−
)
( − )
(18)
as long as → ≤ −1 , a result similar to what is derived in Eq. (15) except that
replaces . Otherwise, → = −1
18
All together, the total fraction of agents who have adopted mobile payments by time
≥ is
= → + → = exp(− ) − exp(− −1 ) + exp(−
(19)
0 )
(1 − )
(1 − )
(1 − )
) − exp(−
) + exp(−
)
= exp(−
( − )
( − ) −1
( − )
as long as → −1 . Otherwise, = exp(− ) = exp(− ((1−)
)
− )
Again, Eq. (19) implies that depending on parameter values, the mobile payment
adoption rate may not have a monotonic relationship with per capita income across
countries. But once all the card adopters have adopted mobile so that = exp(− ) =
exp(− ((1−)
), the mobile payment adoption rate becomes strictly increasing in per
− )
capita income across countries.
4
Model calibration and implications
In this section, we calibrate the model to match the cross-country card and mobile payment adoption patterns. We then conduct several counterfactual exercises to explore the
model implications.
4.1
Model calibration
We first calibrate the model with two mobile payment options (i.e., the card-substituting
and card-complementing ones) using the parameter values as shown in Table 1. The
unit of time is year, and we set 2017 as the year when mobile payment becomes
available. Following convention, we set the discount factor = 095 and the annual
income growth rate = 2%. According to an ECB study (2012) on retail payment
costs in 13 participating countries, the average social cost of using cash is 2.3% of the
transaction value, while that of using debit cards is 1.4%, so we set the values of and
accordingly. We then calibrate = 500 to fit the cross-country card adoption pattern
in 2017. Finally, we calibrate the mobile payment variable cost = 1395% ( ) and
the fixed costs = 150 ( ) and
= 100 ( ) to fit the cross-country mobile
19
payment adoption pattern in 2017.12
Table 1. Parameter Values for Model Calibration
Parameter
Value
Description
Source of Identification
0.95
Discount factor
Standard
2%
Income growth rate
Standard
2.3%
Cash variable cost
ECB (2012)
1.4%
Card variable cost
ECB (2012)
500
Card adoption cost
Cross-country card payment adoption pattern, Figure 6A
1.395%
Mobile variable cost
Cross-country mobile payment adoption pattern, Figure 6B
150
Mobile adoption cost
Cross-country mobile payment adoption pattern, Figure 6B
100
Mobile add-on cost
Cross-country mobile payment adoption pattern, Figure 6B
Figure 6 shows that our calibration results fit the data well and match the first three
stylized facts identified above: (1) Positive income effect on card adoption; (2) Nonmonotonic income effect on mobile payment adoption; (3) Overtaking in mobile payment
adoption.
Figure 6. Model Fit with Data
12
In our model calibration, we treat per capita income/spending and per capita GDP interchangeable.
In reality, per capita income/spending could be a fraction of per capita GDP. To account for that, we can
simply rescale the payment adoption costs (i.e., , , and
) by the same fraction without affecting
any of the analysis and findings.
20
Figure 7 below shows that our calibration also matches the fourth stylized fact: (4) Different technology choice across countries.
ca sh -m obile s w itch er s
ca rd -m obile s w itch er s
total m o bile ado pter s
Mobile Payment Adoption Rate, %
10 0
pr ev io us ca sh us er s
pr ev io us ca rd us er s
80
60
40
20
0
300
10 00
2 500
1 000 0
300 00
10 000 0
P er C apita Inc om e at T m , $ (log sc ale)
Figure 7. Composition of Mobile Payment Adopters
In Figure 7, we decompose the fraction of total mobile payment adopters at = 2017
(red dash line) into cash-mobile switchers (green solid line) and card-mobile switchers
(blue solid line) by per capita income, and compare with the fractions of previous cash
users (green dot line) and card users (blue dot line) at −1. In the low-income countries
(i.e., $2 500) and most middle-income countries (i.e., $2 500 ≤ ≤ $30 000),
mobile payment adoption almost entirely relies on cash-mobile switchers who choose cardsubstituting technologies, while in most high-income countries (i.e., $30 000),
mobile payment adoption relies on card-mobile switchers who choose card-augmenting
technologies.
Moreover, Figure 7 helps explain the non-monotonic income effect on mobile payment
adoption. In the low-income countries, because most agents are cash users, the adoption
of mobile payments concentrates on card-substituting technologies and the adoption increases in per capita income. By contrast, in the middle-income countries, because more
agents are card users who are locked in by the card technology (i.e., their income cannot
justify switching to either card-substituting or card-complementing mobile payment tech21
nologies), the adoption of mobile payment decreases in per capita income. Finally, in the
high-income countries, most agents are card users and their incomes are high enough to
justify switching to the card-complementing mobile payment technology, so the adoption
of mobile payment again increases in per capita income.
4.2
Model implications
Our calibrated model matches the average cross-country pattern of mobile payment adoption. Based on that, we provide several counterfactual exercises to illustrate the implications of the model.
4.2.1
Mobile payment options
First, we check how the availability of different mobile payment technology options affect
the adoption pattern, as shown in Figure 8 below. The green dash line shows the mobile
payment adoption pattern if only the card-substituting option is available in each country.
The blue dot line shows the adoption pattern if only the card-complementing option is
available in each country. The red solid line, as seen above, shows the adoption pattern
when both mobile payment options are available in each country.
50
both mobile payment options
c ard-subs tituting option only
c ard-complementing option only
Mobile Payment Adoption Rate, %
45
40
35
30
25
20
15
10
5
0
3 00
1 000
25 00
1 000 0
Per C apita Income at T
m
30 000
, $ (log scale)
Figure 8. Mobile Payment Options and Adoption Patterns
22
10 000 0
The results in Figure 8 provide the following insights on the effects of mobile payment
technology options:
1. The availability of both mobile payment options in each country increases adoption
rate, especially for high-income countries (i.e., the red line is on top of both the
green dash line and the blue dash line).
2. Only having the card-substituting mobile payment option in each country would
not change much of the cross-country adoption pattern. Its effects on low- and
middle-income countries are almost entirely negligible, though it pushes down mobile
payment adoption in high-income countries almost by half.
3. Only having the card-complementing mobile payment option, however, would overturn the cross-country adoption pattern, making adoption increasing in per capita
income. Essentially, it would kill mobile payment adoption in most low- and middleincome countries, and it pushes down only slightly mobile payment adoption in
high-income countries.
4. With both mobile payment technologies being available, it is possible that each
country, depending on its per capita income, may only choose to supply one type of
mobile payment technology (e.g., there might exist a minimal scale requirement).
If that is the case, the adoption pattern would be given by the upper envelope of
the green dash line and the blue dot line. In this case, the cross-country adoption
pattern does not change much comparing with our calibrated model.13
4.2.2
Income growth
We now consider the effect of income growth. According to our theory, long-run income
growth would eventually take all the card adopters who exist before time to cross the
mobile payment adoption threshold. Once that happens, the mobile payment adoption
would solely depend on cash-mobile switchers, and mobile adoption rate would become
13
Note that an alternative way to calibrate our model is to assume that a country only supplies one type
of mobile payment technology, either the card-substituting one or the card-complementing one, whichever
would yield the higher adoption rate. However, as shown by Figure 8, this alternative calibration would
not change much of the data fitting, and the counterfactual analyses would be very similar.
23
increasing monotonically in per capita income. However, our quantitative exercise suggests that it would just take too long for income growth to overturn the non-monotonic
mobile payment adoption pattern.
10 0
Mobile Payment Adoption Rate, %
90
80
70
60
50
40
30
20
10
0
300
Tm
T m +100
T m +50
T m +180
100 0
2 500
10 000
30 000
10 000 0
P er C apita Inc om e at T m , $ (log sc ale)
Figure 9. Income Growth and Mobile Payment Adoption
Recall that we assume per capita income grows at 2% annually in each country. Figure
9 tracks each country by per capita income at time and plots mobile payment adoption
rates at year (red solid line), + 50 (pink dash line), + 100 (green dot line), and
+180 (blue dash-dot line).14 It shows that as per capita income grows, mobile payment
adoption increases in every country. Meanwhile, the adoption rate continues to be nonmonotonic in per capita income. Ultimately, it takes 180 years to converge to an adoption
curve that strictly increases in per capita income.
Figure 10 decomposes mobile payment adopters into cash-mobile switchers and cardmobile switchers. It shows that as per capita income grows over time, both cash-mobile
switchers and card-mobile switchers increase in every country. Eventually, after all the
( − )
Note that when −1 = (1 + )−( −1) 0 =
all the agents who have adopted card
( − )
at − 1 would have crossed the mobile payment adoption thresthold. Once that happens, the mobile
payment adoption rate only depends on the fraction of cash-mobile switchers so that = exp(− ) =
14
exp(− ((1−)
) which increases in per capita income . Based on our calibrated parameter values,
− )
this would take 180 years to happen.
24
previous card users have adopted mobile payment at year + 180 in every country, the
adoption rate of mobile payment is determined solely by cash-mobile switchers and it
strictly increases in per capita income.
A. Cash-Mobile Switchers
100
90
90
T m+50
T m+100
80
80
T m+180
Fraction of Population, %
Fraction of Population, %
B. Card-Mobile Switchers
100
cash users
Tm
70
60
50
40
40
20
10
10
10000
30000
0
300
100000
Per Capita Income at T m , $ (log scale)
T m +180
50
20
2500
T m +100
60
30
1000
T m +50
70
30
0
300
card users
Tm
1000
2500
10000
30000
100000
Per Capita Income at T m , $ (log scale)
Figure 10. Income Growth and Mobile Payment Adopters
4.2.3
Technology progress
Comparing with income growth, the effect of technology progress on mobile payment
adoption can be more striking. According to our theory, the main reason that advanced
economies are stuck with card payment is because the value added of mobile payment
is not substantial enough. Therefore, greater technological progress of mobile payment
not only would increase the adoption in every country, but also could restore advanced
economies to the leading positions in the mobile payment race if the technological progression is sufficiently large.
To see this, we conduct a counterfactual exercise with different values of . Figure
11 plots the result. It shows that with larger technological progress (i.e., smaller values
of ), the mobile payment adoption rate gets higher in every country and advanced
economies are especially benefitted. If the technology progress is sufficiently large, mobile
payment adoption becomes strictly increasing in per capita income across countries.
25
10 0
m
m
Mobile Payment Adoption Rate, %
90
= 1 .395 %
m
= 1 .37%
m
= 1.34%
= 1.3%
80
70
60
50
40
30
20
10
0
300
100 0
250 0
100 00
30 000
10 000 0
P e r C a p ita In c o m e a t T m , $ (lo g s c a le )
Figure 11. Technology Progress and Mobile Payment Adoption
Taking a step further, Figure 12 decomposes mobile payment adopters into cash-mobile
switchers and card-mobile switchers. One can see that technology progress mainly boosts
mobile payment adoption among previous card users, which explains why high-income
countries benefit more. Therefore, should some major technology progress occur down
the road, advanced economies might see their mobile payment adoption jump up and they
may even regain leading positions in the mobile payment race.
A . Cash-Mobile Sw itchers
100
c ash users
=1.395%
m
m
80
m
90
=1.37%
=1.3%
m
70
60
50
40
30
70
100 00
30 000
0
300
1 000 00
=1.3%
30
10
2 500
=1.34%
40
10
100 0
m
=1.37%
50
20
Per Capita Income at T m , $ (log s cale)
m
60
20
0
3 00
card users
=1.395%
m
m
80
=1.34%
Fraction of Population, %
90
Fraction of Population, %
B . Card-Mobile Sw itchers
10 0
10 00
250 0
10 000
Per C apita Income at T
m
3 000 0
, $ (log scale)
Figure 12. Technology Progress and Mobile Payment Adopters
26
100 000
5
Welfare and policy analyses
In this section, we use our calibrated model to conduct some welfare and policy analyses.
5.1
Payment efficiency
Given our model framework, an intriguing question is to evaluate which group of countries
might be the biggest winner in adopting new payment technologies. To address this
question, we conduct a welfare analysis. For ease of notation, we denote each agent by
her income level (without the time subscript) in the analysis.
We first consider a cash economy. Denote ̄ () as the value function of an agent
who would permanently use the cash technology. By Eq. (1), we know
̄ () =
(1 − )
1 − (1 + )
(20)
Accordingly, the present-value welfare of a cash economy, , at time ( ) is
=
Z
∞
̄ () () =
0
(1 − )
1 − (1 + )
(21)
At time , the card technology arrives as an exogenous shock. Denote ̄ () as the
value function of an agent who would permanently use the card technology. By Eq. (2),
we know
̄ () =
(1 − )
1 − (1 + )
(22)
Accordingly, we can derive the present-value welfare of the economy, at time :
= +
+
∞ Z
X
=1
where =
(1−)
( − )
Z
¢
̄ () − − ̄ () ()
∞¡
(1+)−1
(1+)
(23)
¢
¡
̄ ((1 + ) ) − − ̄ ((1 + ) ) ()
is given by Eq. (5). Note that the first term of the right-hand side
of Eq. (23) is the present value of welfare for all the agents if they continue using cash
forever. The second term is the additional welfare gains for card adopters at time , and
27
the last term is the additional welfare gains for future card adopters.
At time , the mobile payment technology arrives. Denote ̄ () as the value function of an agent who would permanently use the mobile payment technology. By Eq.
(7), we know
̄ () =
(1 − )
1 − (1 + )
(24)
We can then derive the present value of welfare for the economy, at time :
=
Z
0
+
+
(1+)
̄ () () +
∞ Z
X
Z=1∞
Z
(1+)−1
(1+)
̄ () () +
∞ Z
X
=1
where =
0
max(
(1+))
(1+)−1
0
max( (1+)
(1+))
(1−)
( − )
(25)
¢
¡
̄ ((1 + ) ) − − ̄ ((1 + ) ) ()
(1+)
+
¢
¡
̄ () − − ̄ () ()
(1+)
Z
∞
(1+))
max(
0
¢
¡
− ̄ () ()
̄ () −
¢
¡
̄ ((1 + ) ) −
− ̄ ((1 + ) ) ()
is given by Eq. (10), and
0 =
(1−)
( − )
is given by Eq. (17). Note
that the first term of the right-hand side of Eq. (25) is the present value of welfare for all
the cash users at time − 1 if they continue using cash at time and forever. The
second term is the additional welfare gains of cash-mobile switchers at time and the
third term is the additional welfare gains for future cash-mobile switchers. The fourth
term is the present value of welfare for all the card adopters by time − 1 if they
continue using card at time and forever. The fifth term is the additional welfare gains
of card-mobile switchers at time and the last term is the additional welfare gains for
future card-mobile switchers.
With the exponential income distribution, we can solve Eqs. (21), (23), and (25)
explicitly (see Appendix III). Define the payment efficiency of an economy, , as the
ratio between the present value of aggregate welfare with and without incurring payment
costs at time :
=
1−(1+)
(26)
Note that the first-best payment efficiency is 1 in a frictionless economy without any
28
payment costs, so gauges the fraction of the first-best welfare level that can be achieved
under available payment technologies at time .
Using the parameter values in Table 1, we can compare the change of payment efficiency across countries due to payment innovations. Consider a thought experiment
that the card technology arrives at , and the mobile payment technology arrives at
= + 1. Figure 13 plots the payment efficiency of each economy for (i.e., cash
only), = (i.e., card technology becomes available), and = (i.e., mobile payments
becomes available), according to their per capita income level at .
cash only
card arrives
m obile arrives
Payment Efficiency Ratio, %
98.6
98.4
98.2
98
97.8
97.6
300
10 00
2 500
1 000 0
30 000
1 000 00
Per Capita Income at T m , $ (log scale)
Figure 13. Payment Efficiency by Per Capita Income
Figure 13 shows that every country has the same payment efficiency when cash is
the only payment means (i.e., = 1 − ). Once the card technology arrives, the
payment efficiency improves in every country, and the welfare improvement increases in
per capita income across countries. Hence, high-income countries gain the most from the
card payment adoption. The arrival of mobile payment also benefits every country though
disproportionately. As shown in Figure 14, the relative welfare gain ( − )
peaks for countries with per capita income around $1,200. Figures 13 and 14 suggest
that while the richest countries appear to gain relatively little from their mobile payment
adoption, they remain leaders in terms of overall payment efficiency. In contrast, the
29
poorest countries do not gain much from both card and mobile payment innovations, and
they lag far behind in overall payment efficiency. Therefore, despite the promise of mobile
payments for financial inclusion, its benefits to poorest countries are limited at this stage.
In light of this, global financial inclusion may entail further innovations to reduce the
payment costs, especially the adoption costs.
50
payment efficiency gain (left)
mobile payment adoption (right)
0.4
45
40
0.35
35
0.3
30
0.25
25
0.2
20
0.15
15
0.1
10
0.05
0
300
Mobile Payment Adoption, %
Payment Efficiency Gain Due to Mobile, %
0.45
5
1000
2500
10000
30000
0
100000
Per Capita Income at T m , $ (log scale)
Figure 14. Payment Efficiency Gain by Per Capita Income
5.2
Subsidizing mobile payment adoption
In our model economy, with mobile payment technologies being given, the market outcome is socially efficient. Falling behind in the race for mobile payments could be an
optimal choice for advanced economies. However, policymakers in those countries have
been concerned about losing the race. Many argue that governments should play a more
active role in promoting mobile payment adoption.
As shown in Section 4.2.3, encouraging mobile payment technology progress might
be an effective way for advanced economies to restore leading positions in the mobile
payment race. To the extent that private firms may not internalize all the social welfare
gains in their R&D decisions, government intervention could be welfare improving.
On the other hand, given a fixed mobile payment technology, pushing up mobile payment adoption by providing subsidies would cause a welfare loss. To quantify this, we
30
conduct the following exercise. Based on our calibrated model, a country at the U.S.
per capita income level in 2017 ($53,356) would on average have a 94.8% card adoption
rate and a 19.0% mobile payment adoption rate. Assume that upon the arrival of mobile payment at time = 2017, the government offers each mobile payment adopter a
subsidy to reduce the adoption cost, and the subsidy is financed by income taxation.
Presumably, the subsidy would change the mobile payment adoption thresholds (i.e.,
and
0 ) for cash users and card users, but without changing the social costs (i.e., and
) of adoption. Therefore, we can calculate the present value of social welfare at time
under the subsidy by adapting Eq. (25) to the new adoption thresholds:
=
(1 − )( − )
( − )
and
0 =
(1 − )(
− )
( − )
Figures 15 and 16 show the effects of such a subsidy. In each figure, we normalize
the present value of social welfare under no subsidy to zero. We then plot the change of
welfare relative to the no-subsidy benchmark at different subsidy levels, ranging from $0
to $150 per adopter. Recall that in our calibration, it costs $100 for a card user to adopt
the card-complementing mobile payment technology, and it costs $150 for a cash user to
adopt the card-substituting one.
0
100
-10
90
Welfare Change, $
80
-30
70
-40
60
-50
50
40
-60
30
-70
20
welfare change (left)
mobile payment adoption (right)
-80
-90
0
10
50
100
Subsidy Per Adopter, $
Figure 15. Effects of Mobile Payment Adoption Subsidy
31
0
150
Mobile Payment Adoption, %
-20
Figure 15 reports the overall effects. As the amount of subsidy per adopter rises,
mobile payment adoption increases, but welfare falls at an increasing rate. However, the
welfare loss slows down and turns almost flat when the subsidy reaches $98 per adopter.
Eventually, as the subsidy increases to $150 per adopter, the mobile payment adoption
rate reaches 100%, and the welfare loss maximizes at $88.17 per capita. The reason that
the maximal welfare loss per capita is smaller than the subsidy per adopter is that a part
of the tax used to finance the subsidy is offset by the increased transaction efficiency from
using mobile payments.
100
90
70
Welfare Change, $
-30
60
-40
50
-50
40
-60
30
-70
20
-80
-90
0
50
100
8
7
-0.3
6
-0.4
5
-0.5
4
-0.6
3
-0.7
2
-0.8
10
welfare change (left)
card-mobile switchers (right)
9
-0.2
Welfare Change, $
80
-20
10
-0.1
Mobile Payment Adoption from Card Users, %
-10
Cash Users
0
0
150
-0.9
Subsidy Per Adopter, $
1
welfare change (left)
cash-mobile switchers (right)
0
50
100
0
150
Subsidy Per Adopter, $
Figure 16. Effects of Mobile Payment Subsidy on Card and Cash Users
Figure 16 decomposes the overall subsidy effects between card users and cash users. It
becomes clear that most of the subsidy effects come from the card users. In this economy,
right before time , 94.8% of agents are card users and 5.2% are cash users. Without
any subsidy, the mobile payment adoption rate at time would be 19.0%, among which
15.3% are card users and 3.6% are cash users. Should the subsidy per adopter increase
and reach $98 per adopter, all the 94.8% card users would have adopted mobile payments,
which would lead to a welfare drop of $87.32 per capita. In the meantime, another 4.6%
of adopters would come from cash users, resulting in a welfare loss of $0.36 per capita. If
32
Mobile Payment Adoption from Cash Users, %
Card Users
0
the subsidy goes above $98, no further changes would occur from card users, but mobile
payment adoption and welfare loss would continue to rise from cash users though the
magnitude would be small. Eventually, when the subsidy reaches $150 per adopter, all
the 5.2% cash users would adopt mobile payment, leading to a welfare loss of $0.85 per
capita.
The above exercise is based on the assumption that both mobile payment options, the
card-complementing one and the card-substituting one, are offered in the country. In an
alternative scenario where only the card-complementing option is available, we may just
need to exclude the small fraction of the cash-mobile switchers from the calculation. In the
end, the quantitative findings, because they are mainly driven by card-mobile switchers,
remain very similar.
6
Further discussions
While our model fits well the average cross-country pattern of mobile payment adoption,
it does not cover all the factors affecting payment adoption decisions. In this section, we
extend our model and provide some further discussions.
6.1
Two-sided market considerations
It is well known in the literature that the payment market is two-sided. A payment
technology needs to be adopted by both buyers and sellers before being widely used in
the economy. Our model so far has been explicit about consumers’ (buyers’) side of the
market but not much about the merchants’ (sellers’) side. We now extend our model to
the two-sided market setting and discuss the implications.
First, our model can be easily extended to a setting where merchants incur a zero
fixed cost for adopting a new payment technology. Consider that each consumer receives
an income of of the numeraire good at time , and follows an exponential distribution across the population of consumers. The numeraire good needs to be processed
and distributed through competitive merchants, where merchants’ processing and distributing costs are normalized to zero. Conducting a transaction between a merchant and
a consumer requires using a payment technology ∈ { }, for which the merchant
33
(seller) and the consumer (buyer) each incurs a variable cost and per dollar of
transactions, respectively. Assume merchants require customers to use a particular payment technology or they charge different prices based on payment means. Therefore, a
competitive merchant accepting payment technology would set price for selling the
good to break even:
=
1
1 −
and a consumer using payment technology at time would purchase and consume the
quantity of the good:
=
(1 − )
= (1 − )(1 − )
Assume that merchants incur no fixed cost for adopting a new payment technology, while
consumers need to pay and as the one-time fixed adoption costs associated with
adopting card and mobile payment technology, respectively. It is straightforward to see
the new model setting is equivalent to our original model by changing notations: For each
payment technology ∈ { }, we simply need to redefine the variable cost such
that
(1 − ) = (1 − )(1 − )
As before, to capture the technology progress between cash, card, and mobile, we assume
and .
More generally, our model can be extended to scenarios where merchants do incur a
fixed cost for adopting a new payment technology. In fact, as long as merchants can price
discriminate based on payment methods, they may find ways to transfer the adoption costs
to their customers, for example, by charging a one-time setup fee for customers to use a
new payment technology. However, in the case where merchants are heterogenous and do
not price discriminate based on payment methods, things become more complicated and
our model may serve as a first-order approximation (See Li, McAndrews, and Wang, 2020
for a detailed analysis).
Extending our model interpretation to the two-sided market setting does bring additional benefits. For one thing, the discussion makes it clear that one should take into
34
account payment costs of both merchants and consumers in the analysis. That is the
reason why we choose to calibrate our model using measures of social costs of payment
means instead of just consumers’ costs. Also, pending future data availability, it would
be valuable to model merchant heterogeneity and their payment adoption decisions and
match those with data.
Moreover, given that the payment market outcome depends on two sides’ decisions,
multiple equilibria can easily arise. The market outcome we discussed previously remains
a valid equilibrium, but it is no longer the unique one. For example, there could exist
another equilibrium where no merchant or consumer adopts a new payment technology
because they each expect no adoption from the other side. This so-called “chicken-egg”
dynamic often arises in network industries, and coordination becomes a relevant issue. In
terms of mobile payments, we observe in the data that some countries have an adoption
rate far below their peers, which might result from certain coordination failures among
relevant parties. In those cases, appropriate government interventions may have positive
welfare effects.
6.2
Kenya, China, and the U.S.
Kenya and China currently are world front-runners in mobile payment adoption. Their
extraordinary performance may have idiosyncratic components beyond the theory that
we offer to explain the average cross-country pattern.
Note that in our model calibration, we assume that all the countries in the sample
share the same set of parameter values, which provides useful model discipline. However,
this strict assumption is not intended to fit extreme cases, and our model provides some
clues on how things would differ when relaxing the assumption. According to our model
(cf. Eq. (19)), mobile payment adoption would be higher if mobile payment technology is
more efficient (i.e., a lower ) or less costly (i.e., a lower ), or the card technology is
less efficient (i.e., a higher ) or more costly (i.e., a higher ). These factors are certainly
relevant for the Kenya and China discussions. In both countries, it is well known that the
banking sectors have been quite inefficient, which suggests a higher or . In contrast,
the mobile payment service providers in each country, Safaricom in Kenya and Alibaba
and Tencent in China, are very innovative and successful players, which may suggest a
35
lower or .
Some factors outside our model may also play important roles. As a theoretical benchmark, our model assumes that payment services are provided by competitive firms, while
in reality some payment service providers may have market power. This may have additional implications on payment pricing and adoption decisions. Also, our model focuses
on the payment aspect of the mobile payment technology, while in reality the new technology may serve multiple functions. For example, Jack and Suri (2014) find that the
mobile payment innovation, M-PESA, is also popularly used for urban-rural remittances
in Kenya, providing an important risk-sharing function. In China, the two giant tech
firms, Tencent and Alibaba, have developed their mobile payment services, WeChat Pay
and Alipay, strategically to extend their business models, for instance, to cross-sell consumer and business loan services based on payments data (Hau et al., 2019). It would be
very valuable for future research to explore these additional factors.
In comparison, the United States has been lagging in mobile payment adoption. Its
performance, however, is not out of line with the cross-country average pattern explained
by our theory. Therefore, our model provides a useful framework for policy discussions in
the U.S. context. Our analysis shows that countries like the United States, the previous
card payment leaders, naturally tend to fall behind in the mobile payment race. Falling
behind is an optimal choice for such countries because the incremental improvement introduced by the current mobile payment technology does not provide a sufficient incentive for
them to switch. Given this finding, directly subsidizing mobile payment adoption would
be socially inefficient in those countries. Instead, policymakers may consider promoting
mobile payments in more productive ways, for example, by encouraging greater mobile
payment technology progress or reducing market frictions of coordination.
7
Conclusion
In this paper, we construct a quantitative theoretical framework to explain the crosscountry pattern of mobile payment adoption. With a novel dataset, we find that the
adoption rate of mobile payment has a non-monotonic relationship with per capita income.
This is in contrast with the card payment, for which the adoption increases monotonically
36
in per capita income across countries. Also, countries favor different mobile payment
solutions: advanced economies favor those complementary to the existing card payments,
while developing countries favor those substituting cards.
Our theory provides a consistent explanation for these patterns. In our model, three
payment technologies, cash, card, and mobile, arrive sequentially. Newer payment technologies lower the variable costs of conducting payments, but they require a fixed cost
to adopt. As a result, rich countries enjoyed advantages in adopting card payments for
replacing cash early on, but their sunk costs in adopting card payments later set a higher
threshold for adopting the mobile payment innovation. Also, the same sunk costs make
it more attractive for card-intensive countries to adopt mobile payment methods complementary to cards, while cash-intensive countries favor card-substituting mobile solutions.
Our model calibration matches cross-country adoption patterns of card and mobile
payments well. Based on the quantitative model, we find that lagging behind in mobile
payment adoption does not necessarily mean that advanced economies have fallen behind in overall payment efficiency. Moreover, slower adoption can be an optimal choice
given that the incremental benefit of switching from card payment to the current mobile
payment technology is not large enough. Down the road, greater technological advances
in mobile payments are needed for advanced economies to regain leading positions in
the payment race, and governments may play positive roles in facilitating technological
progress and market coordination.
References
[1] Comin, Diego, and Bart Hobijn. (2004). “Cross-country Technology Adoption: Making the Theories Face the Facts,” Journal of Monetary Economics, 51(1), 39-83.
[2] Crowe, Marianne, Marc Rysman, and Joanna Stavins. (2010). “Mobile Payments in
the United States at Retail Point of Sale: Current Market and Future Prospects,”
Review of Network Economics, 9(4), Article 2.
[3] Dragulescu, Adrian, and Victor M. Yakovenko. (2001). “Evidence for the Exponential
Distribution of Income in the USA,” European Physical Journal B 20(4): 585-589.
37
[4] Griliches, Zvi. (1957). “Hybrid Corn: An Exploration in the Economics of Technical
Change,” Econometrica, 25(4), 501-522.
[5] Hau, Harald, Yi Huang, Hongzhe Shan, and Zixia Sheng. (2019). “How FinTech
Enters China’s Credit Market,” AEA Papers and Proceedings, 109, 60-64.
[6] Hayashi, Fumiko, Bin Grace Li, and Zhu Wang. (2017). “Innovation, Deregulation,
and the Life Cycle of a Financial Service Industry,” Review of Economic Dynamics, 26, 180-203.
[7] Jack, William, and Tavneet Suri. (2014). “Risk Sharing and Transactions Costs:
Evidence from Kenya’s Mobile Money Revolution,” American Economic Review,
104(1), 183-223.
[8] Li, Bin Grace, James McAndrews, and Zhu Wang. (2020). “Two-sided Market, R&D,
and Payments System Evolution,” Journal of Monetary Economics, 115, 180-199.
[9] Muralidharan, Karthik, Paul Niehaus, and Sandip Sukhtankar. (2016). “Building
State Capacity: Evidence from Biometric Smartcards in India.” American Economic Review, 106(10), 2895-2929.
[10] Rochet, Jean-Charles, and Jean Tirole. (2002). “Cooperation among Competitors:
Some Economics of Payment Card Associations,” RAND Journal of Economics,
33(4), 549-570.
[11] Rochet, Jean-Charles, and Jean Tirole. (2003). “Platform Competition in Two-Sided
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38
Appendix
I. Data sources.
The mobile payment data introduced in Section 2.2 are drawn from two sources. First,
the data on the adoption rate for card-substituting mobile payment services in 2017 are
based on the Global Financial Inclusion (Global Findex) Database of the World Bank,
which surveyed 76 countries with a visible presence of Mobile Money payment services.
The Global Findex database was launched in 2011 and has been published every three
years since then. The 2017 version of the database is based on nationally representative
surveys of more than 150,000 adults (age 15 and above) in 144 economies. Among the 144
economies, 76 economies (where the GSMA MMU database indicates that mobile money
accounts were available at the time the survey was carried out) were surveyed for mobile
money adoption: “To identify people with a mobile money account, the 2017 Global
Findex survey asked respondents about their use of specific services available in their
economy – such as M-PESA, MTN Mobile Money, Airtel Money, or Orange Money –
and included in the GSM Association’s Mobile Money for the Unbanked (GSMA MMU)
database. The definition of a mobile money account is limited to services that can be
used without an account at a financial institution.”
Second, the data on the adoption rate for card-complementing mobile payments around
2017 were gathered from eMarketer’s public website. eMarketer is a market research
company headquartered in New York City. Its report on “Proximity Mobile Payment
Users Worldwide, 2019” estimates adult mobile proximity payment users (age 14+) in
23 countries where mobile proximity payments had a visible presence. According to
the European Payments Council, “mobile proximity payments are mobile payments in
which the payer and the payee are in the same location and where the communication
between their devices takes place through a proximity technology (such as Near Field
Communication (NFC), Quick Response (QR) codes, Bluetooth technology, etc.).” To be
more specific, the adoption rate of mobile proximity payments in the eMarketer data is
the adoption rate among mobile phone users, so we multiply that by the mobile phone
ownership rate of each country (obtained from GSMA) to obtain the mobile proximity
39
payment adoption rate in the population. As a sanity check, our estimate of the mobile
payment adoption rate in the eMarketer data is 24.6% for the United States, comparable
to the mobile payment adoption rate of 28.7% estimated from the U.S. Survey of Consumer
Payment Choice conducted by the Federal Reserve in 2017.
II. Regression results.
This appendix section provides the regression results related to Figures 4 and 5.
Table A1 reports the OLS results for estimating the card and mobile payment adoption.
Across the 94 countries in the sample, the regression (1) shows that the card adoption rate
in 2017 is significantly and positively related to per capita GDP in 2017. In contrast, the
regression (2) shows that the mobile payment adoption bears no significant relationship
with per capita GDP for the same sample. In fact, the adjusted 2 shows a negative value,
which implies that we would have had a better fit if we simply had run a regression with
only a constant. However, a pattern starts to emerge once we remove the countries that
have very low adoption rates of mobile payments (i.e., adoption rate 10%) and group
the remaining ones by income. The regression (3) shows that mobile payment adoption
increases in per capita GDP for low-income countries (i.e., per capita GDP $2,500) and
high-income countries (i.e., per capita GDP $30,000), but decreases in per capita GDP
for middle-income countries (i.e., $2,500 ≤ per capita GDP ≤ $30,000).
Specifically, the coefficient estimate of ln (GDP per capita) for the low-income countries is 0.113 and statistically significant. This suggests that doubling per capita GDP
would increase mobile payment adoption by 11.3% for the low-income countries. The
coefficient estimate of ln(GDP per capita) ×1{High Income} is small and not statistically
significant, suggesting that the marginal effect of per capita GDP on mobile payment
adoption in high-income countries is not different from that in low-income countries. On
the other hand, the coefficient estimate of ln(GDP per capita) ×1{Middle Income} is 0.163 and statistically significant. This implies that the marginal effect of per capita GDP
on mobile payment adoption in middle-income countries is significantly lower than that
in low-income (and high-income) countries. The coefficient difference, 0.113-0.163, suggests that doubling per capita GDP is associated with a 5% reduction in mobile payment
adoption rate among middle-income countries.
40
Table A1. Cross-Country Payment Adoption: OLS Regressions
Card
(1)
0.186***
(0.009)
ln(GDP per capita)
ln(GDP per capita)
×1{Middle Income}
ln(GDP per capita)
×1{High Income}
1{Middle Income}
1{High Income}
Constant
-1.179***
(0.079)
94
0.81
Observations
Adjusted 2
Mobile
(2)
(3)
0.001
0.113**
(0.010) (0.053)
-0.163*
(0.084)
-0.007
(0.133)
1.197*
(0.692)
-0.456
(1.365)
0.163*
-0.497
(0.083) (0.362)
94
59
-0.01
0.07
The results in Table A1 are based on the Ordinary Least Squares (OLS) models. The dependent
variable is the debit card adoption rate of 2017 in regression (1) or the mobile payment adoption rate
around 2017 in regressions (2) and (3). The independent variables include the GDP per capita of 2017 and
a constant in regressions (1) and (2), plus two dummy variables (i.e., Middle Income and High Income)
and their interaction terms with the GDP per capita in regression (3). Standard errors are reported in
the parentheses. *** Significance at 1% level, ** at 5% level, and * at 10% level.
For robustness checks, we re-run the regressions using the Fractional Logit (FL) model
to address the fractional nature of the dependent variable, which is bounded by 0 and 1.
The estimated marginal effects, shown in Table A2, are very similar to the OLS results
in Table A1.
We also re-run the regressions using the Two-Stage Least Squares (2SLS) model to
address a potential endogeneity concern that the adoption of a payment innovation may
have reverse impact on contemporaneous per capita GDP. To purify the potential reverse
impact, we bring in per capita GDP in 2004 (which is more than a decade ago and well
before the mobile payment was introduced) as an instrument for per capita GDP in 2017,
and the first-stage results are highly significant. The second-stage results, shown in Table
A3, are consistent with the OLS findings that card adoption has a positive relationship
with per capita income, while mobile payment adoption has a non-monotonic relationship.
41
Table A2. Cross-Country Payment Adoption: FL Regressions
Card
(1)
0.229***
(0.012)
ln(GDP per capita)
ln(GDP per capita)
×1{Middle Income}
ln(GDP per capita)
×1{High Income}
1{Middle Income}
1{High Income}
Observations
94
Mobile
(2)
(3)
0.001
0.106***
(0.008)
(0.039)
-0.155**
(0.070)
0.014
(0.061)
1.149*
(0.589)
-0.647
(0.575)
94
59
Regressions in Table A2 are based on the Fractional Logit (FL) models. The dependent and independent variables in the regressions are the same as in Table A1. The coefficient estimates are expressed
in terms of marginal effects evaluated at the means of the independent variables. Standard errors are
reported in the parentheses. *** Significance at 1% level, ** at 5% level, and * at 10% level.
Table A3. Cross-Country Payment Adoption: 2SLS Regressions
(Second-Stage Results)
Card
(1)
0.186***
(0.009)
ln(GDP per capita)
ln(GDP per capita)
×1{Middle Income}
ln(GDP per capita)
×1{High Income}
1{Middle Income}
1{High Income}
Constant
-1.179***
(0.079)
94
Observations
Mobile
(2)
(3)
0.002
0.100*
(0.010) (0.055)
-0.203**
(0.087)
0.039
(0.144)
1.592**
(0.723)
-0.891
(1.495)
0.155*
-0.407
(0.083) (0.373)
94
59
Regressions in this table are based on the Two-Stage Least Squares (2SLS) models. The dependent
and independent variables in the regressions are the same as in Table A1 except that the independent
variable ln(GDP per capita 2017) is instrumented by its value of 2004. Standard errors are reported in
the parentheses. *** Significance at 1% level, ** at 5% level, and * at 10% level.
42
III. Welfare calculation.
Eq. (21) shows that the present-value welfare of a cash economy at time ( ) is
=
(1 − )
.
1 − (1 + )
(27)
Eq. (23) implies that the present-value welfare when card technology arrives at is
µ
¶Z ∞
Z ∞
(1 − )
−
+
=
() −
()
1 − (1 + )
1 − (1 + )
µ
¶Z
Z
∞
∞
X
X
(1+)−1
(1+)−1
−
)
(1
+
)
(
+
() −
()
1
−
(1
+
)
=1
=1
(1+)
(1+)
Given the exponential distribution (), this yields
µ
¶
(1 − )
−
=
)( + ) − exp(−
) (28)
+
exp(−
1 − (1 + )
1 − (1 + )
⎞
⎛
µ
¶
∞
X
exp(− (1+) )( + (1+) )
( − ) (1 + ) ⎝
⎠
+
1
−
(1
+
)
)(
+
)
−
exp(−
=1
(1+)−1
(1+)−1
µ
¶
∞
X
−
exp(−
) − exp(−
)
(1 + )
(1 + )−1
=1
Denote that satisfies
0
(1+)
(1 + ) and
0
(1+)+1
≤ (1 + ) Eq. (25) implies
the present value of welfare when the mobile payment technology arrives at is
Z (1+)
Z (1+)
Z (1+)
(1 − )
( − )
=
() +
() −
()
1 − (1 + ) 0
1 − (1 + )
µ
¶ Z
Z −1
∞
∞
X
X
(1+)−1
(1+)
( − ) (1 + )
() −
()
+
1 − (1 + )
=1
=1
(1+)
(1+)
µ
¶Z ∞
Z ∞
Z ∞
( − )
(1 − )
() +
() −
()
+
1 − (1 + ) (1+)
1 − (1 + )
0
0
+
X
=1
+
( − ) (1 + )
1 − (1 + )
+1 (
+1
− ) (1 + )
1 − (1 + )
Z
0
(1+)−1
0
(1+)
Z
() −
0
(1+)
(1+)
() −
43
X
=1
+1
Z
Z
0
(1+)−1
0
(1+)
0
(1+)
(1+)
()
()
Given the exponential distribution (), this yields
¶
µ
(1 − )
(1 + )
=
)( + (1 + ))
(29)
− exp(−
1 − (1 + )
µ
¶
( − )
(1 + )
+
exp(−
)( + ) − exp(−
)( + (1 + ))
1 − (1 + )
µ
¶
(1 + )
− exp(−
) − exp(−
)
⎞
⎛
µ
¶
∞
X
exp(− (1+) )( + (1+) )
( − ) (1 + ) ⎝
⎠
+
1
−
(1
+
)
−
exp(−
)(
+
)
=1
(1+)−1
(1+)−1
µ
¶
∞
X
exp(−
) − exp(−
)
−
(1 + )
(1 + )−1
=1
(1 + )
(1 − )
exp(−
)( + (1 + ))
1 − (1 + )
µ
¶
( − )
0
0
+
)
exp(− )( +
0 ) − exp(−
1 − (1 + )
⎞
⎛
0
0
X
exp(− (1+) )( + (1+) )
( − ) (1 + ) ⎝
⎠
+
0
0
1
−
(1
+
)
− exp(− (1+)−1 )( + (1+)−1 )
=1
µ
¶
X
0
0
exp(−
) − exp(−
)
−
−1
(1
+
)
(1
+
)
=1
⎞
⎛
(1+)
+1
exp(− )( + (1 + ))
( − ) (1 + )
⎠
)⎝
+ +1
0
1 − (1 + )
− exp(− (1+)0 )( + (1+)
)
µ
¶
(1 + )
0
+1
exp(−
−
) − exp(−
)
(1 + )
+
44
@FedFRASER