The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Technology Adoption and Leapfrogging:
Racing for Mobile Payments
WP 21-05R
Pengfei Han
Peking University
Zhu Wang
Federal Reserve Bank of Richmond
Technology Adoption and Leapfrogging:
Racing for Mobile Payments∗
Pengfei Han†and Zhu Wang‡
August 31, 2021
Abstract
Paying with a mobile phone is a cutting-edge innovation transforming the global
payments landscape. Some advanced economies like the U.S., however, are lagging behind in mobile payment adoption. We construct a dynamic model with sequential 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, Leapfrogging, Payments System, FinTech
JEL Classification: E4, G2, O3
∗
We thank Mark Bils, Jeremy Greenwood, Zhiguo He, Chang-Tai Hsieh, Chad Jones, Boyan Jovanovic,
Peter Klenow, Dirk Krueger, Nitya Nayar, Shumiao Ouyang, Zheng (Michael) Song, Pengfei Wang,
Shang-Jin Wei, Wei Xiong, and participants at various seminars and conferences 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 an essential financial technology infrastructure of the aggregate
economy. With the successful launch of general-purpose credit cards in the late 1950s
and debit cards in the mid-1980s, the United States has been one of the leading countries
in deploying card payment technologies. However, the United States is falling behind in
adopting 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 a mobile payment innovation based
on smartphones and QR (Quick Response) codes which experienced explosive growth of
usage 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
In 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 shown by the figures, while the United States
boasts a much higher card payment adoption rate, it has been significantly surpassed by
Kenya and China in mobile payment adoption.
This has raised concerns by the press, business leaders, and policymakers about the
efficiency and innovativeness of the U.S. payments system. With a headline of “China
is out-mobilizing the United States,” the Wall Street Journal (2018) was impressed by
how “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
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.
3
See Wall Street Journal’s report on “China’s Great Leap to Wallet-Free Living,” January 18, 2018.
4
See Tim Cook’s speech at the eighteenth China Development Forum in Beijing on March 18, 2017.
2
2
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 relevant questions: Why did developing countries like Kenya and China lag in adopting card payments but leapfrog in adopting mobile
payments? Has the United States lost its leadership in the payment area? Should the
U.S. government implement policies to boost mobile payment adoption?
This paper addresses these questions. In doing so, we first compile a novel dataset to
uncover the general adoption patterns of card and mobile payments across countries. 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
5
See a speech by Lael Brainard, a Federal Reserve governor, on “Delivering Fast Payments for All”
on August 5, 2019.
3
to adopt different mobile payment solutions: The former favor 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. When card arrives
after cash, high-income consumers find it more attractive to adopt because they spend
more on purchases and, thus, can save more on the variable costs of payment transactions.
This explains the high adoption rate of card payments in rich countries. However, when
mobile arrives after card, the adoption incentives are different between existing card users
and cash users. Since the fixed cost for adopting card is already paid, card users face
a higher income threshold to adopt mobile payments than cash users. As a result, the
pre-mobile-payment composition of cash users and card users in each country leads to
a non-monotonic relationship between mobile payment adoption and per capita income
across countries, particularly the leapfrogging of low-income countries in mobile payment
adoption. Moreover, since both card and mobile payment adoption requires fixed costs,
cash users would favor mobile payments as a card-substituting solution, rather than paying the fixed costs to adopt both card and mobile payments. This explains why most
developing countries choose Mobile Money, the mobile payment method bypassing card
services. Card users, on the other hand, would more likely consider mobile payments
complementary to card, which is why 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 fall 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 quantitative assessment of welfare loss of subsidizing mobile payment adoption. That said, our
4
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.
It is worth noting that our model focuses on the role of income heterogeneity in driving
the adoption of payment technologies. In doing so, we largely abstract from network
externality considerations. This is an intentional modeling choice for a couple of reasons.
First, our paper aims to explain the steady-state payment adoption patterns rather than
characterizing transitional paths, so there is less need to elaborate on the feedback loops
among agents. Second, our approach, in the spirit of Ockham’s razor (or “the principle of
parsimony”), allows us to fit the cross-country data well with a parsimonious model, which
also facilitates the counterfactual and welfare analysis. Finally, we specify conditions in
Section 6.1 under which our model indeed incorporates two-sided market network effects
between consumers and merchants in terms of their payment choices. This interpretation
of the model allows us to discuss issues otherwise veiled in a one-sided market setting, such
as multiple equilibria and social versus private costs in adopting payment innovations. We
point out that our model may serve as a first-order approximation if some of the conditions
in Section 6.1 do not hold and we leave a full-blown two-sided market model for future
research.
Our paper contributes to several strands of literature. The first one is theories of
the payments system. Following the pioneering work of Baxter (1983), a fast growing
body of literature has been developed for studying market structure and pricing of retail
payments system, especially card payments (e.g., Rochet and Tirole, 2002, 2003, 2011,
Wright, 2003, 2012, and Shy and Wang, 2011, among others; 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 sequential innovations and leapfrogging,
which is the focus of this paper.
The second one is the empirical investigation of consumer payment choices. While
there is an abundance of literature studying domestic payment patterns (e.g., Rysman,
2007, Klee, 2008, Wang and Wolman, 2016, and Koulayev et al., 2016 for the U.S.),
5
cross-country studies on retail payments adoption are rather scarce and usually focus on
developed economies. Among the few examples, Humphrey et al. (1996) compare the use
of cash and noncash payment instruments in fourteen developed countries. Martikainen et
al. (2015) examine the convergence of the European retail payments market, and Bagnall
et al. (2016) document consumer cash use for seven developed countries using payment
diary surveys. Cross-country comparison of mobile payments, however, has not been
studied in this branch of literature. We fill this gap by compiling a novel dataset to study
cross-country adoption patterns of mobile versus card payments. Our dataset includes
both developed and developing economies, which allows us to uncover and address the
leapfrogging puzzle.
Our paper is also related to the literature that studies how electronic payments affect
financial inclusion and social well-being using large micro datasets. For example, 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 these works in the sense
that we take a quantitative macro approach to study how cost savings brought by electronic payments affect payment efficiency and drive different adoption patterns across
countries.
Finally, our paper contributes to the broad literature of technology diffusion. For a
long time, researchers have been interested in the relationship between the adoption of
new technologies and the heterogeneity of potential adopters (e.g., Griliches, 1957). While
some argue that the observed adoption lags are evidence of information or coordination
frictions, Manuelli and Seshadri (2014) among others have shown that the speed of adoption can be well explained by the moving equilibrium of frictionless models. Moreover,
in the presence of sequential innovations, some firms could get stuck with old technologies due to their past investments in technology-specific learning (e.g., Parente, 1994,
Jovanovic and Nyarko, 1996, and Klenow, 1998). Our paper extends this line of research
to a new context where consumers make frictionless adoption decisions on sequential payment innovations. We show high-income consumers or countries could be overtaken by
6
low-income counterparts in adopting mobile payments due to their past investments in
precedent card payment technologies. Taking the theory to data, our quantitative model
matches a non-monotonic relationship between mobile payment adoption and per capita
income across countries, which is a novel empirical finding to the existing literature (e.g.,
Comin and Hobijn, 2004).
The remainder of this paper is structured as follows. Section 2 provides the background
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 allowed 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. Later, 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
7
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.
The year 2011 witnessed major technology firms like Google and Apple entering the
field of mobile payment. Google became the first major company to come up with a
digital mobile wallet solution, Google Wallet. The wallet used the NFC (Near Field Communication) technology and allowed the customers to make payments, redeem coupons,
and earn loyalty points. In 2014, Apple launched its mobile payment 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 apps, Android Pay (later merged with Google Wallet and became Google
Pay) and Samsung Pay, in the wake of Apple Pay’s success.
As a cutting-edge payment innovation, mobile brings many additional benefits comparing with precedent card technologies, lowering both fixed and variable costs of making
payments. First, given that mobile phone has been widely adopted in most countries,
the fixed investment for adopting mobile payment is small for consumers and merchants.
Second, mobile payment is fast, convenient, and more secure. Apple Pay, for example,
enables the users to pay without unlocking their phones and the Touch/Face ID of an
iPhone adds extra security to authenticate a purchase. Apple Pay also encrypts payment
information by a tokenization technology, and, thus, enhances privacy and reduces the
odds of fraud (Gupta et al., 2015). Third, as the mobile payment technology becomes
more widespread, markets develop a system of complementary goods and services that
further enhance users’ benefits, such as financial planning, rewards programs, and price
competition (Crowe et al. 2010).7
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.
7
Crowe et al. (2010) provides detailed discussions on the long-run benefits of mobile payments. For
example, consumers could have their payments automatically logged in their financial planning software.
Also, they could upload warranties and instructional videos at the time of purchase. Merchants could
engage in sophisticated rewards programs, where consumers could access their status from their mobile
device and receive alerts when they are close to rewards thresholds. Also, consumers could compare
prices at nearby stores. If it is relatively easy to add new payment mechanisms to a mobile device and
to switch among options, one should see new entry and innovation in this arena.
8
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 and
withdraw money, (ii) pay for goods and services, and (iii) transfer money to other users.
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.
Following the 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
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.
The global adoption of Mobile Money payment in 2018 is illustrated in Figure 2.8 The
8
Source: GSMA (2018), “State of the Industry Report on Mobile Money.”
9
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.
Figure 2. Global Adoption of Mobile Money Payment
2.1.2
Card-complementing mobile payment
Card-complementing mobile payment is typically deployed in developed countries. The
popular types, created by technology firms (e.g., Apple, Google, Samsung), rely heavily
on banking and payment card networks. Because of using a proximity communication
technology (e.g., NFC or QR codes), these payment types are often referred to as mobile
proximity payment services.
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 launched in the United States, Apple Pay debuted in the
10
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.9 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
2.2
Data and stylized facts
To study the global adoption pattern of mobile payments, we assembled a novel dataset
on debit card and mobile payment adoption in 94 countries.10 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
9
Source: https://en.wikipedia.org/wiki/Apple Pay#Supported countries.
Debit card ownership is a good measure of consumers who have access to card-payment technologies
because credit card users almost surely own debit cards. For robustness checks, we also redid the analysis
using an alternative measure from the World Bank dataset on the percentage of the adult population
(age 15 and above) using a debit or credit card to make a purchase in the past year. The results are very
similar.
10
11
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
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.
12
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.11 The results are shown in Figure 5B. It becomes visible that
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.
Figure 5. Cross-Country Mobile Payment Adoption Pattern
To sum up, we have documented the following stylized facts on cross-country adoption
patterns of card and mobile payments:
1. Positive relation between per capita income and card adoption. — The adoption of
card increases in per capita income across countries.
2. Non-monotonic relation between per capita income and mobile payment adoption. —
11
Removing observations with mobile payment adoption rates below 10% only affects countries from the
Global Findex Database that use Mobile Money payment services. Presumably, the eMarketer dataset
on mobile proximity payment adoption has implicitly applied a similar selection rule.
13
The adoption of mobile payment increases in per capita income in low- and highincome 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. — Low- and middle-income countries
primarily adopt the card-substituting mobile payment technologies, while in highincome 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 rates (i.e., 10%) in Section 6.
3
Model
In this section, we provide a model with sequential payment innovations to explain the
stylized facts documented above. We outline the model environment in Section 3.1 and
then characterize the model equilibrium in Section 3.2.
3.1
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.
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.12 We denote and as the one-time fixed adoption costs
associated with card and mobile, respectively. Those fixed costs may include resources
spent on joining banking or mobile payment networks plus the costs of acquiring the
hardware and software for making electronic payments. The variable costs associated
12
A main reason for electronic payments to be used, despite of the fixed adoption costs, is that they
reduce the variable costs of payments (e.g., the time of dealing with handling, safekeeping, and fraud).
14
with using card and mobile are denoted as and per dollar of transaction, respectively. To capture the technology progress between cash, card, and mobile, we assume
and .
Time is discrete with an infinite horizon. We consider an economy where agents’ incomes are exogenous and heterogeneous (e.g., due to differences in productivity). Without
loss of generality, we assume that income at time follows an exponential distribution
across the population in the economy, with the cumulative distribution function (cdf)
( ) = 1 − exp(− ).13 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 + ), as does the mean income of the economy, 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 income 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 at its social cost.14
3.2
Equilibrium
We derive the equilibrium adoption patterns of cash, card, and mobile payment technologies as they arrive sequentially in an economy.
3.2.1
Cash payment
Cash is the only payment technology available in the economy before electronic payments
are introduced. 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 + )
13
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 these assumptions.
14
15
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 ) − }
(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 − )
( − )
16
(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.
At any point ≥ , the value function of an agent who has income 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
17
( ) − ≥ ( )
(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
( ) − ≥ ( )
(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 =
(1 − )
( − )
Equations (5) and (14) suggest that as long as
15
The condition
−
−
−
(14)
,
−
we have 0 .15 So
ensures that 0 , so only a fraction of the consumers who have
18
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
− )
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.
adopted card would cross the income threshold for adopting mobile. If this condition is violated, the
cost savings of mobile payment relative to card would be so large that all card users switch to mobile at
time . As a result, a country with a higher per capita income and thus a higher card adoption rate
would always have a higher rate of mobile adoption, so there would be no leapfrogging. In the empirical
study, we show that our calibrated model satisfies the condition and matches the non-monotonic mobile
payment adoption pattern across countries in the data.
19
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 ) = exp(−
(1 − )
)
( − )
(18)
as long as → ≤ −1 , a result similar to what is derived in Eq. (15) except that
replaces . Otherwise, → = −1
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
( − )
20
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 counterfactual analyses to explore the model
implications regarding different mobile payment options, income growth, and technological progress.
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.
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
Schmiedel et al. (2012)
1.4%
Card variable cost
Schmiedel et al. (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
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
21
annual income growth rate = 2%. According to an ECB study (Schmiedel et al., 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 payment adoption pattern in 2017.16,17
Figure 6. Model Fit with Data
Figure 6 shows that our calibration results fit the data well and match the first three
stylized facts identified above: (1) Positive relation between per capita income and card
adoption.; (2) Non-monotonic relation between per capita income and mobile payment
adoption; (3) Overtaking in mobile payment adoption.
16
To discipline the calibration, we assume that all countries share the same model parameter values
and the card-substituting and card-complementing mobile payment technologies share the same value of
. Relaxing such assumptions would provide additional degrees of freedom and, thus, allow the model
to fit the data targets even better.
17
In the 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
our analysis and findings. Similarly, note that the equilibrium adoption rates in our model all depend on
−
, and −
). In case that the calibrated values of , and
the ratios (i.e., −
−
that we use are mismeasured by a certain fraction, we can also rescale the payment adoption costs (i.e.,
, , and
) accordingly.
22
Figure 7 below shows that our calibration also matches the fourth stylized fact: (4)
Different technology choice across countries. 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 card-substituting technologies, while in most highincome countries (i.e., $30 000), mobile payment adoption relies on card-mobile
switchers who choose card-complementing technologies.
ca sh -m obile s w itch e r s
ca rd -m o bile s w it ch er s
t otal m o bile a do pter s
Mobile Payment Adoption Rate, %
10 0
p r ev io us ca sh us er s
p r 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
Moreover, Figure 7 helps explain the non-monotonic relation between per capita income and 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 middleincome 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 cardcomplementing mobile payment technologies), the adoption of mobile payment decreases
in per capita income. Finally, in the high-income countries, most agents are card users
23
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 the model, we provide several counterfactual exercises to illustrate the
implications of the model.
4.2.1
Mobile payment options
We first 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 m obile paym ent options
c ard-subs tituting option only
c ard-com plem enting 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
P er C apita Incom e at T
m
30 000
10 000 0
, $ (log scale)
Figure 8. Mobile Payment Options and Adoption Patterns
The results in Figure 8 provide the following insights on the effects of mobile payment
technology options:
24
First, the availability of both mobile payment options in each country increases adoption rate, especially for high-income countries. As shown in the figure, the red line is on
top of both the green dash line and the blue dash line.
Second, 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.
Third, 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 highincome countries.
Finally, 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., due to network effects or a minimum 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.18
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 the adoption rate would become 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.
Recall that we assume per capita income grows at 2% annually in each country. Figure
18
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, Figure 8 suggests that this alternative calibration would
not change much of the data fitting, and the counterfactual analyses would be very similar.
25
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). 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.19
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
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, once all the
previous card users have adopted mobile payment at year + 180 in every country, the
remaining adoption is determined solely by cash-mobile switchers and the overall mobile
payment adoption rate strictly increases in per capita income.
19
In our model simulation, with the 2% annual income growth rate, all the agents who have adopted
card by − 1 would have crossed the mobile payment adoption threshold in 180 years. Once that
happens, the mobile payment adoption rate is simply the fraction of agents whose incomes are greater
than (i.e., the income threshold for cash-mobile switchers), and it increases in per capita income .
Note that this process could speed up if our model introduces birth and death of agents.
26
A. Cash-Mobile Switchers
B. Card-Mobile Switchers
100
90
90
T m +5 0
T m +1 00
80
80
T m +1 80
Fraction of Population, %
Fraction of Population, %
100
cash u se rs
Tm
70
60
50
40
40
20
10
10
2 500
100 00
30 000
0
3 00
100 000
T m +18 0
50
20
10 00
T m +10 0
60
30
Per Capita Income at T m , $ (log scale)
T m +50
70
30
0
3 00
card u se rs
Tm
10 00
2 500
100 00
30 000
100 000
Per Capita Income at T m , $ (log scale)
Figure 10. Income Growth and Mobile Payment Adopters
4.2.3
Technological progress
Comparing with income growth, the effect of technological 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 . The
results are plotted in Figure 11. 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 technological progress is sufficiently
large, mobile payment adoption becomes strictly increasing in per capita income across
countries.
27
10 0
m
m
Mobile Payment Adoption Rate, %
90
= 1 .3 95 %
m
= 1 .3 7%
m
= 1.34%
= 1.3%
80
70
60
50
40
30
20
10
0
300
100 0
250 0
100 00
P e r C a p ita In c o m e a t T
m
30 000
10 000 0
, $ ( lo g s c a le )
Figure 11. Technological 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 technological progress mainly boosts
mobile payment adoption among previous card users who enjoy more cost savings than
cash users through a lower due to their higher income and spending. This explains why
high-income countries benefit more. Therefore, should some major technological 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 -M ob ile S w itchers
100
m
80
m
m
70
90
= 1.37%
= 1.3%
60
50
40
30
70
30 000
0
300
1 000 00
P er Capi ta Incom e at T m , $ (log s cale)
=1.3%
30
10
100 00
=1.34%
40
10
2 500
m
=1.37%
50
20
100 0
m
60
20
0
3 00
card users
=1.395%
m
m
80
= 1.34%
Fraction of Population, %
90
Fraction of Population, %
B . Card -M obile S w itchers
10 0
c ash users
= 1.395%
m
10 00
250 0
10 000
3 000 0
P er C apita Incom e at T m , $ (log scale)
Figure 12. Technological Progress and Mobile Payment Adopters
28
100 000
5
Welfare and policy analyses
In this section, we use our calibrated model to conduct welfare and policy analyses.
5.1
Payment efficiency
Given our model framework, an intriguing question is to identify the winners and losers
in adopting new payment technologies. To address this question, we conduct a welfare
analysis. We first evaluate payment efficiency for individual agents and then for aggregate
economies. For ease of notation, we denote each agent by her income level (without the
time subscript) in the analysis.
5.1.1
Individual agents
We first consider individual agents in a cash economy. Denote ̄ () as the value function
of an agent who would permanently use cash payment. By Eq. (1), we know
̄ () =
(1 − )
1 − (1 + )
(20)
so the present-value welfare of agent , denoted by (), equals ̄ () for any .
At time , the card technology arrives as an exogenous shock. Denote ̄ () as the
value function of an agent who would permanently use card payment. By Eq. (2), we
know
̄ () =
(1 − )
1 − (1 + )
(21)
The present-value welfare of agent at time , denoted by (), depends on the agent’s
income and the corresponding card adoption:
() =
⎧
⎪
⎪
̄ () −
⎪
⎨
⎡
⎤
̄ ((1 + ) )
⎣
⎪
⎦
̄
()
+
⎪
⎪
⎩
− − ̄ ((1 + ) )
Note that =
(1−)
( − )
if ≥ ;
if
(1+)
≤
,
(1+)−1
(22)
for ∈ {1 2 3 }
is given by Eq. (5). The top equation of (22) calculates the welfare
of an agent whose income crosses the card adoption threshold at time , and the bottom
29
equation calculates the welfare of an agent who would adopt card at a future time.
At time , the mobile payment arrives. Denote ̄ () as the value function of an
agent who would permanently use mobile payment. By Eq. (7), we know
̄ () =
(1 − )
1 − (1 + )
(23)
The present-value welfare of agent at time , denoted by (), depends on the
agent’s income and the corresponding mobile payment adoption:
⎧
⎪
̄ () −
⎪
⎪
⎪
⎡
⎪
⎪
⎪
⎪
̄ ((1 + ) )
⎪
⎣
⎪
()
+
̄
⎪
⎪
⎨
−
− ̄ ((1 + ) )
() =
⎪ ̄ () −
⎪
⎪
⎪
⎡
⎪
⎪
⎪
⎪
̄ ((1 + ) )
⎪
⎣
⎪
⎪ ̄ () +
⎪
⎩
− − ̄ ((1 + ) )
Note that =
(1−)
( − )
⎤
⎦
⎤
⎦
if ≥
0;
0
if max( (1+)
(1 + )) ≤
0
,
(1+)−1
for ∈ {1 2 3 };
if ≤ (1 + );
if
(1+)
≤
,
(1+)−1
for ∈ {1 2 3 }
is given by Eq. (10), and
0 =
(1−)
( − )
(24)
is given by Eq. (17).
The top equation of (24) calculates the welfare of a card-mobile switcher whose income
crosses the mobile adoption threshold at time , and the second equation is the welfare
of a card user who would adopt mobile at a future time. The third equation is the welfare
of a cash-mobile switcher at time , and the bottom equation is the welfare of a cash
user who would adopt mobile at a future time.
Define the payment efficiency of an agent , () as the ratio between the present
value of welfare at time with and without incurring the payment costs:
() =
Note that the denominator,
,
1−(1+)
()
1−(1+)
(25)
is the first-best welfare in a frictionless economy
without any payment costs, so () gauges the fraction of the first-best welfare level that
can be achieved by agent under available payment technologies at time .
Using the parameter values in Table 1, we can compare payment efficiency for individual agents at different income levels under each payment innovation. As before, we
30
assume that the mobile payment technology arrives at = 2017. We then assume that
the card payment arrives at = −3020 Figure 13 plots the payment efficiency of each
agent for (i.e., cash only), = (i.e., card becomes available), = (i.e., mobile
becomes available), according to their individual income level at . For a comparison,
we also plot a counterfactual case for = assuming mobile does not become available
then, which we denoted as ̃ .
98 .6
cash only for t<T d
card arrives at T d
mobile arrives at T
Payment Efficiency, %
98 .4
m
if mobile does not arrive at T
m
98 .2
98
97 .8
97 .6
10 0
500
250 0
10 000
5 000 0
250 000
Individual Income at T , $ (log scale)
m
Figure 13. Payment Efficiency by Individual Income
Figure 13 shows that every agent has the same payment efficiency when cash is the only
payment means (i.e., = 1− ). Once the card technology arrives at , the payment
efficiency improves for everyone, and it increases in agents’ income. A similar pattern holds
when the mobile payment arrives at . The intuition why payment efficiency measures
(i.e., and ) increase in agents’ income is as follows: It is always feasible for a
higher-income agent to mimic a lower-income agent’s adoption behavior. If that turns
out to be the optimal decision, the higher-income agent enjoys higher payment efficiency
than her lower-income counterpart because the adoption cost (i.e., , , or
) counts
20
The large-scale introduction of debit cards in the U.S. started in the mid-1980s (see Hayashi, Li, and
Wang, 2017), so we set = − 30. Note that the simulation results are robust if we use an alternative
year for because choosing an earlier (or later) would not change anything except adjusting down
(or up) the level of the payment efficiency given that the card adoption cost counts for a larger
(or smaller) share of agents’ income in an earlier (or later) year.
31
for a smaller share of her income. But if mimicking is not the optimal decision, the
higher-income agent must be able to achieve even higher payment efficiency by choosing
a payment method different from her lower-income counterpart.
Figure 13 also illustrates how payment efficiency evolves across income levels over time.
At time , agents either pay or expect to pay in the future the fixed cost to adopt
card, and the payment efficiency measure is a continuous and increasing function of
income. Then for any time ∈ ( ), card users who have paid off in the past no
longer count the fixed cost in their payment efficiency measure, so = 1 − for them.
Meanwhile, cash users who just meet or have not met the card adoption threshold need
to pay the fixed cost, so their payment efficiency displays a jump at the card adoption
threshold, as illustrated by the green dash-dot curve ̃ . For those cash users, their
payment efficiency does improve over time due to income growth and thus a declining
share of relative to their income. Comparing the two curves (the red solid one)
and ̃ (the green dash-dot one) shows that the introduction of mobile improves payment
efficiency for everyone (especially cash users) and makes the jump at the card adoption
threshold smaller.21
5.1.2
Aggregate economies
We now take a step further to compare the overall payment efficiency across countries
by aggregating over each country’s income distribution. With the exponential income
distribution, we can solve explicitly the present-value welfare of aggregate economies,
denoted by ( ), for (i.e., cash only), = (i.e., card becomes available), and
= (i.e., mobile becomes available). Appendix III provides the solution details.
Similar to the discussions above, we 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+)
21
(26)
For cash users, introducing mobile improves their payment efficiency substantially because of the
much reduced adoption cost comparing with card (recall that = 500 vs. = 150). For card
users, their payment efficiency only improves slightly somewhere between 1 − and 1 − (recall that
= 14% vs. = 1395%).
32
Using the parameter values in Table 1, we can now compare payment efficiency across
countries under each payment innovation. As before, we assume that the mobile payment
technology arrives at = 2017, and the card payment arrives at = − 30. Figure
14 plots the payment efficiency of each economy for , = , and = , according
to their per capita income level at .
ca sh on ly fo r t<T
9 8.6
ca rd arr ives a t T
d
d
mob ile a rrive s a t T m
Payment Efficiency, %
9 8.4
9 8.2
98
9 7.8
9 7.6
3 00
100 0
2 500
100 00
30 000
1 000 00
Per Capita Income at T m , $ (log scale)
Figure 14. Payment Efficiency by Per Capita Income
Figure 14 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 15, the relative welfare gain ( − )
peaks for countries with per capita income around $1,600. Figures 14 and 15 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
poorest countries do not gain much from either card or 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.
33
50
paym ent efficiency gain (left)
mobile payment adoption (right)
0 .5
45
40
35
0 .4
30
25
0 .3
20
0 .2
15
Mobile Payment Adoption, %
Payment Efficiency Gain Due to Mobile, %
0 .6
10
0 .1
5
0
30 0
100 0
25 00
10 000
3 000 0
0
10 000 0
Per Capita Income at T m , $ (log scale)
Figure 15. Payment Efficiency Gain by Per Capita Income
5.2
Policy considerations
While our model suggests that the market outcome is socially efficient, the framework
that we developed can be extended to discuss policy considerations. For example, we have
provided some quantitative analysis in Section 4.2.3 to show that technological progress
can 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 interventions that provide additional R&D
incentives could be welfare-improving. Policymakers can also help reduce payment costs
with improved regulations.22
On the other hand, pushing up mobile payment adoption by providing subsidies would
cause a welfare loss in our model framework. However, one may argue that such subsidies
might be justified, for instance, by some future technological breakthrough based on the
mobile payment platform and big data.23 To facilitate a meaningful cost-and-benefit
discussion, our model can be used to estimate the welfare cost of a subsidy policy, and
22
For example, the Check 21 Legislation appears to have been instrumental in reducing the costs of
checks in the United States (see Humphrey and Hunt, 2013).
23
Another argument for providing adoption subsidies is to encourage early adoption to align the expectations of potential adopters. We will discuss this consideration in Section 6.1, where the model is
extended to a two-sided market setting.
34
we provide a quantitative exercise as follows.
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 lump-sum 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 using
the new adoption thresholds (cf. Eq. (29) in Appendix III):
=
(1 − )( − )
( − )
and
0 =
− )
(1 − )(
( − )
Figures 16 and 17 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 16. Effects of Mobile Payment Adoption Subsidy
35
0
150
Mobile Payment Adoption, %
-20
Figure 16 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.
10 0
90
70
Welfare Change, $
- 30
60
- 40
50
- 50
40
- 60
30
- 70
20
- 80
- 90
0
50
10 0
8
7
- 0.3
6
- 0.4
5
- 0.5
4
- 0.6
3
- 0.7
2
- 0.8
10
welfar e c ha nge (left)
ca rd -m obile s witch er s ( r ig ht)
9
- 0.2
Welfare Change, $
80
- 20
10
- 0.1
Mobile Payment Adoption from Card Users, %
- 10
C ash Users
0
0
15 0
- 0.9
S ubsidy P er A dopter, $
1
we lfa re ch ang e ( le ft)
c as h- m ob ile s witc her s (r ight)
0
50
1 00
0
1 50
S ubs idy P er A dopter, $
Figure 17. Effects of Mobile Payment Subsidy on Card and Cash Users
Figure 17 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
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
36
Mobile Payment Adoption from Cash Users, %
C ard Users
0
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. At the
end, the quantitative findings, because they are mainly driven by card-mobile switchers,
are very similar. In either case, the welfare loss quantified in our analysis provides a
benchmark that one may use to compare with mobile payments’ potential future benefits
outside our model.
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 for 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
a two-sided market setting and explore policy implications.
As before, consider that each consumer receives an income at time , and follows
an exponential distribution across the population of consumers. The income is used to
purchase a numeraire good for consumption each period. The numeraire good is produced
at a unit cost and distributed through competitive merchants. Conducting a transaction
between a merchant and a consumer requires using a payment technology ∈ { (cash)
(card) (mobile)}, for which the merchant (seller) and the consumer (buyer) each incurs
a variable cost and per dollar of transactions, respectively. Merchants are each
37
at a sufficiently large size, so the fixed cost for a merchant to adopt card or mobile
payment technology is negligible on a per customer or per transaction basis. Assume
merchants can price discriminate based on payment method, for example, by specializing
in accepting a particular payment form or charging customers different prices based on
payment instruments. Therefore, a competitive merchant accepting payment technology
would set price for selling the numeraire 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 consumers need to pay and as the one-time fixed 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 .
Extending our model interpretation to the two-sided market setting brings additional
insights. For one thing, the discussion makes it clear that one should take into 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.
Moreover, given that the payment market outcome depends on two sides’ decisions,
multiple equilibria can 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-and-egg” dy-
38
namic often arises in network industries or for technologies featuring strong adoption
complementarity, and coordination becomes an important issue (see e.g., Buera et al.,
2021). In terms of mobile payments, we observe in the data that some countries have
an adoption rate far below their peers with similar per capita income levels, which might
result from certain coordination failures among relevant parties.24 In those cases, appropriate policy interventions, such as coordinating standard setting or providing incentives
for early adoption, may help align market expectations and enhance welfare.
The discussion above suggests that our model can apply to a two-sided market setting under the assumption of competitive merchants and price discrimination based on
payment method. In the cases where merchants have market power or do not price discriminate based on payment method, things become more complicated (e.g., see Li et al.,
2020 for a related analysis), and our model may serve as a simplified first-order approximation. We leave a full-blown two-sided market analysis for future research.
6.2
Kenya, China, and the U.S.
Kenya and China currently are front-runners in mobile payment adoption. Figure 18 suggests that their extraordinary performance may have idiosyncratic components beyond
the theory that we offer to explain the average cross-country pattern.
Figure 18. Model Fit: Kenya, China and the U.S.
24
For example, Aker, Prina and Welch (2020) show that mobile money has failed to take off in Niger
because of a chicken-and-egg problem: Agents need to be widespread for the service to be useful, but
putting agents everywhere isn’t viable until the service is widespread.
39
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 assumption is not intended to fit outlier 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 could be
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 and Vodafone in Kenya
as well as Alibaba and Tencent in China, are very innovative and successful players, which
may suggest a lower or .
Some factors outside our model may also play important roles. For example, our
benchmark model does not consider the variation of market structure and government
intervention across countries, which may also have driven some of the adoption pattern.
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) highlight the role of M-PESA in urban-rural remittances in Kenya, which provides
an important risk-sharing function.25 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 in 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
25
Recent studies suggest that the unique urban-rural remittance pattern in Kenya may help explain
its exceptionally wide adoption of M-PESA. Therefore, Kenya’s success in adopting mobile payment
should be regarded as an outlier rather than normative (see Piper, Kelsey (September 11, 2020). What
Kenya can teach its neighbors – and the US – about improving the lives of the “unbanked.” Vox). This
is consistent with our model’s prediction, which underestimates the mobile payment adoption rate of
Kenya but fits well the adoption rates of Kenya’s neighboring countries.
40
payment leaders, naturally tend to fall behind in the mobile payment race. Falling behind can be 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. In this context, subsidizing mobile payment adoption could
cause welfare losses.26 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
This paper provides a quantitative theoretical framework to explain the adoption of card
and mobile payments within and across countries. 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 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 enjoy advantages in adopting card payments for replacing cash early on, but this success later hinders their adoption of the mobile payment
innovation. Also, the fixed-cost considerations 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 fall behind in
overall payment efficiency. Moreover, slower adoption can be an optimal choice given that
26
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 that distorts payment
pricing and adoption. In the latter case, certain government interventions might be warranted.
41
the incremental benefit of switching from card 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.
While our paper focuses on payment services, the mobile payment innovation may
have impact beyond payments. For example, it may help extend financial services to
the unbanked population and reduce poverty. Meanwhile, the rise of nonbank payment
service providers, particularly telecom companies and fintech firms, may pose new challenges to financial stability and regulations. Those would be interesting topics for future
research. On the other hand, leapfrogging is a relevant issue for the adoption of other
major innovations. For example, mobile phones have enabled developing countries to skip
the old fixed-line technology and move straight to the mobile technology, and solar energy technologies may allow developing countries to skip an energy infrastructure based
on fossil fuels but jump directly into the Solar Age. Our analysis derives conditions for
leapfrogging to occur in a payment context, which might help shed light on the broad
issue on rank-preserving versus leapfrogging in adopting new technologies.
42
References
[1] Aker, Jenny C., Silvia Prina, and C. Jamilah Welch. (2020). “Migration, Money
Transfers, and Mobile Money: Evidence from Niger.” AEA Papers and Proceedings, 110, 589-93.
[2] Baxter, William (1983). “Bank Interchange of Transactional Paper: Legal Perspectives.” Journal of Law and Economics 26, 541-588.
[3] Bagnall, John, David Bounie, Kim P. Huynh, Anneke Kosse, Tobias Schmidt, and
Scott Schuh. (2016). “Consumer Cash Usage: A Cross-Country Comparison with
Payment Diary Survey Data.” International Journal of Central Banking, 12(4),
1-61.
[4] Buera, Francisco, Hugo Hopenhayn, Yongseok Shin, and Nicholas Trachter. (2021).
“Big Push in Distorted Economies.” NBER Working Paper No. 28561.
[5] Comin, Diego, and Bart Hobijn. (2004). “Cross-country Technology Adoption: Making the Theories Face the Facts.” Journal of Monetary Economics, 51(1), 39-83.
[6] 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.
[7] 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.
[8] Griliches, Zvi. (1957). “Hybrid Corn: An Exploration in the Economics of Technical
Change.” Econometrica, 25(4), 501-522.
[9] Gupta, Sunil, Shelle Santana, and Margaret L. Rodriguez. (2016). “Apple Pay.”
Harvard Business School Case 516-027.
[10] Hau, Harald, Yi Huang, Hongzhe Shan, and Zixia Sheng. (2019). “How FinTech
Enters China’s Credit Market.” AEA Papers and Proceedings, 109, 60-64.
[11] 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.
43
[12] Humphrey, David B., and Robert Hunt. (2013). “Cost Savings from Check 21 Electronic Payment Legislation.” Journal of Money, Credit and Banking, 45(7), 14151429.
[13] Humphrey, David B., Lawrence B. Pulley, and Jukka M. Vesala. (1996). “Cash,
Paper, and Electronic Payments: A Cross-Country Analysis,” Journal of Money,
Credit and Banking, 28(4), 914-939.
[14] 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.
[15] Jovanovic, Boyan, and Yaw Nyarko. (1996). “Learning by Doing and the Choice of
Technology.” Econometrica, 64(6), 1299-1310.
[16] Klee, Elizabeth. (2008). “How People Pay: Evidence from Grocery Store Data.”
Journal of Monetary Economics, 55(3), 526-541.
[17] Klenow, Peter. (1998). “Learning Curves and the Cyclical Behavior of Manufacturing
Industries.” Review of Economic Dynamics, 1, 531-550.
[18] Koulayev, Sergei, Marc Rysman, Scott Schuh, and Joanna Stavins. (2016). “Explaining Adoption and Use of Payment Instruments by US Consumers.” RAND
Journal of Economics, 47(2), 293-325.
[19] 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.
[20] Manuelli, Rodolfo, and Ananth Seshadri. (2014). “Frictionless Technology Diffusion:
The Case of Tractors.” American Economic Review, 104(4), 1368-91.
[21] Martikainen, Emmi, Heiko Schmiedel, and Tuomas Takalo. (2015). “Convergence of
European Retail Payments.” Journal of Banking and Finance, 50, 81—91.
[22] Muralidharan, Karthik, Paul Niehaus, and Sandip Sukhtankar. (2016). “Building
State Capacity: Evidence from Biometric Smartcards in India.” American Economic Review, 106(10), 2895-2929.
[23] Parente, Stephen. (1994). “Technology Adoption, Learning by Doing and Economic
Growth.” Journal of Economic Theory, 63, 346-369.
44
[24] Rochet, Jean-Charles, and Jean Tirole. (2002). “Cooperation among Competitors:
Some Economics of Payment Card Associations.” RAND Journal of Economics,
33(4), 549-570.
[25] Rochet, Jean-Charles, and Jean Tirole. (2003). “Platform Competition in Two-Sided
Markets.” Journal of the European Economic Association, 1(4), 990-1029.
[26] Rochet, Jean-Charles, and Jean Tirole. (2011). “Must-take Cards: Merchant Discounts and Avoided Costs.” Journal of the European Economic Association, 9
(3), 462—495 .
[27] Rysman, Marc. (2007). “An Empirical Analysis of Payment Card Usage.” Journal of
Industrial Economics, 55(1), 1-36.
[28] Rysman, Marc, and Julian Wright. (2014). “The Economics of Payment Cards.”
Review of Network Economics, 13(3), 303-353.
[29] Schmiedel, Heiko, Gergana Kostova, and Wiebe Ruttenberg. (2012). “The Social
and Private Costs of Retail Payment Instruments: A European Perspective.”
Occasional Paper Series 137, European Central Bank.
[30] Shy, Oz , and Zhu Wang. (2011). “Why Do Payment Card Networks Charge Proportional Fees?” American Economic Review, 101(4), 1575-1590.
[31] Wang, Zhu and Alexander Wolman. (2016). “Payment Choice and Currency Use:
Insights from Two Billion Retail Transactions.” Journal of Monetary Economics,
84, 94-115.
[32] Wright, Julian. (2003). “Optimal Card Payment Systems.” European Economic Review, 47, 587-612.
[33] Wright, Julian. (2012). “Why Payment Card Fees Are Biased Against Retailers.”
RAND Journal of Economics, 43(4), 761-780.
45
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
46
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, we estimate the coefficient of ln(GDP per capita) ×1{Middle Income}
to be -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, (0.1130.163), suggests that doubling per capita GDP is associated with a 5% reduction in mobile
payment adoption rate among middle-income countries.
47
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.
48
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.
49
III. Present-value welfare of aggregate economies.
This appendix section calculates the present-value welfare of aggregate economies.
Recall that ̄ () is the value function of an agent who would permanently use the
cash technology, given by Eq. (20). Accordingly, the present-value welfare of a pure cash
economy, , at any time is
Z
=
∞
̄ () () =
0
(1 − )
1 − (1 + )
(27)
Thus, the present-value welfare of an economy, denoted by , equals for any .
Recall that ̄ () is the value function of an agent who would permanently use the
card technology, given by Eq. (21). Accordingly, the present-value welfare of the economy,
at time when card technology arrives is
= +
+
∞ Z
X
=1
where =
(1−)
( − )
Z
¢
̄ () − − ̄ () ()
∞¡
(1+)−1
(1+)
(28)
¢
¡
̄ ((1 + ) ) − − ̄ ((1 + ) ) ()
is given by Eq. (5). Note that the first term of the right-hand side
of Eq. (28) 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
the last term is the additional welfare gains for future card adopters.
Given the exponential distribution () = 1 − exp(− ), Eq. (28) yields that
µ
¶Z ∞
Z ∞
−
(1 − )
+
=
() −
()
1 − (1 + )
1 − (1 + )
µ
¶Z
Z
∞
∞
X
X
(1+)−1
(1+)−1
( − ) (1 + )
() −
()
+
1 − (1 + )
=1
=1
(1+)
(1+)
µ
¶
−
(1 − )
)( + ) − exp(−
)
+
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
50
Recall that ̄ () is the value function of an agent who would permanently use the
mobile payment technology, given by Eq. (23). We can then derive the present value of
welfare for the economy, at time when mobile technology arrives:
=
Z
(1+)
̄ () () +
0
+
+
∞ Z
X
Z=1∞
Z
(1+)−1
(1+)
̄ () () +
∞ Z
X
=1
where =
0
max(
(1+))
(1+)−1
0
max( (1+)
(1+))
(1−)
( − )
¢
¡
̄ () − − ̄ () ()
(29)
¢
¡
̄ ((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. (29) is the present-value welfare for all the
cash users at − 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 welfare for all the card adopters at −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.
Denote that satisfies
0
(1+)
(1 + ) and
0
(1+)+1
≤ (1 + ) Eq. (29) implies
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+)
¶Z ∞
µ
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+)
0
(1+)
Z
(1+)
51
() −
() −
X
=1
+1
Z
Z
0
(1+)−1
0
(1+)
0
(1+)
(1+)
()
()
Given the exponential distribution () = 1 − exp(− ), this yields
¶
µ
(1 − )
(1 + )
=
)( + (1 + ))
− 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+)
X µ
exp(−
−
(1+)
¶
)
0
0
)
−
exp(−
−1
(1 + )
(1 + )
=1
⎛
⎞
(1+)
+1
exp(− )( + (1 + ))
( − ) (1 + )
⎠
+ +1
)⎝
0
0
1 − (1 + )
− exp(− (1+) )( + (1+) )
µ
¶
(1
+
)
0
+1
exp(−
−
) − exp(−
)
(1 + )
52
@FedFRASER