No. 10-03

Merchant fees and reward programs generate an implicit monetary transfer to credit card

users from non-card (or “cash”) users because merchants generally do not set differential

prices for card users to recoup the costs of fees and rewards. On average, each cash-using

household pays $149 to card-using households and each card-using household receives $1,133

from cash users every year. Because credit card spending and rewards are positively

correlated with household income, the payment instrument transfer also induces a regressive

transfer from low-income to high-income households in general. On average, and after

accounting for rewards paid to households by banks, the lowest-income household ($20,000 or

less annually) pays $21 and the highest-income household ($150,000 or more annually)

receives $750 every year. We build and calibrate a model of consumer payment choice to

compute the effects of merchant fees and card rewards on consumer welfare. Reducing

merchant fees and card rewards would likely increase consumer welfare.

Scott Schuh is Director of the Consumer Payments Research Center and a senior economist in the research

department at the Federal Reserve Bank of Boston. Oz Shy is a senior economist and a member of the Consumer

Payments Research Center and Joanna Stavins is a senior economist and policy advisor and a member of the

Consumer Payments Research Center, both in the research department at the Federal Reserve Bank of Boston. Their

This paper, which may be revised, is available on the web site of the Federal Reserve Bank of Boston at

We thank Tamás Briglevics for most valuable research assistance, analysis, and advice. We also thank Santiago

Carbó Valverde, Dennis Carlton, Bob Chakravorti, Alan Frankel, Jeff Fuhrer, Fumiko Hayashi, Bob Hunt, Suzanne

Lorant, John Sabelhaus, Irina Telyukova, Bob Triest, Lotta Väänänen, Zhu Wang, Paul Willen, and Michael Zabek,

as well as seminar participants at the Boston Fed and at the Economics of Payments IV conference (New York Fed,

May 2010), the conference on Platform Markets (ZEW Mannheim, June 2010), and the conference on Payment

Markets (University of Granada, June 2010) for valuable comments and suggestions on earlier drafts.

The views and opinions expressed in this paper are those of the authors and do not necessarily represent the views

of the Federal Reserve Bank of Boston or the Federal Reserve System.

1. Introduction

The typical consumer is largely unaware of the full rami cations of paying for goods and

services by credit card. Faced with many choices|cash, check, debit or credit card, etc.|

consumers naturally consider the costs and bene ts of each payment instrument and choose

accordingly. For credit cards, consumers likely think most about their bene ts: delayed

payment|\buy now, pay later"|and the rewards earned|cash back, frequent ier miles,

or other enticements. What most consumers do not know is that their decision to pay by

credit card involves merchant fees, retail price increases, a nontrivial transfer of income from

cash to card payers, and consequently a transfer from low-income to high-income consumers.

In contrast, the typical merchant is acutely aware of the rami cations of his customers'

decisions to pay with credit cards. For the privilege of accepting credit cards, U.S. merchants

pay banks a fee that is proportional to the dollar value of the sale. The merchant's bank

merchants seek to pass the merchant fee to their customers. Merchants may want to recoup

the merchant fee only from consumers who pay by credit card. In practice, however, credit

card companies impose a \no-surcharge rule" (NSR) that prohibits U.S. merchants from

mark up their retail prices for all consumers by enough to recoup the merchant fees from

credit card sales.

This retail price markup for all consumers results in credit-card-paying consumers being

subsidized by consumers who do not pay with credit cards, a result that was rst discussed

in Carlton and Frankel (1995), and later in Frankel (1998), Katz (2001), Gans and King

proportional merchant fees (rather than xed, per-transaction fees). The amount of surplus that card

networks can extract increases with the degree of merchants' market power.

U.S. merchants to give cash discounts under certain restrictions. However, cash discounts are not widely

observed. Frankel (1998) argues that a prohibition on credit card surcharges can have e
ects di
erent from

those resulting from a prohibition on cash discounts, because card surcharges allow merchants to vary their

charges according to the di
erent merchant fees they pay on di
erent cards, whereas a cash discount is taken

from a single card price.

1

(2003), and Schwartz and Vincent (2006). For simplicity, we refer to consumers who do

not pay by credit card as cash payers, where \cash" represents all payment instruments

merchant fees are passed on to all buyers in the form of higher retail prices regardless of the

means of payments buyers use to pay. Thus, cash buyers must pay higher retail prices to

cover merchants' costs associated with the credit cards' merchant fees. Because these fees

are used to pay for rewards given to credit card users, and since cash users do not receive

rewards, cash users also nance part of the rewards given to credit card users.

If the subsidy of card payers by cash payers results from heterogeneity in consumer

preferences and utility between cash and card payments, the subsidy may be innocuous

in terms of consumer and social welfare. However, U.S. data show that credit card use is

very positively correlated with consumer income. Consequently, the subsidy of credit card

payers by cash payers also involves a regressive transfer of income from low-income to high-

income consumers. This regressive transfer is ampli ed by the disproportionate distribution

Frankel (1998, Footnote 85) was the rst to connect the wealth transfers to average income

of groups of consumers (that is, poorer non-cardholders subsidizing wealthier cardholders).

This idea was later discussed in Carlton and Frankel (2005, pp. 640{641) and Frankel and

Our contribution to this line of research is that we are the rst to compute who gains

and loses from credit card payments in the aggregate economy. We compute dollar-value

estimates of the actual transfers from cash payers to card users and from low-income to

card to cash users) in cases where merchants' cost of handling cash exceeds merchants' card fees. McAndrews

and Wang's de nition of cards includes debit cards, which are less costly than credit cards, whereas in our

paper debit cards are considered part of \cash." Humphrey et al. (1996) and Humphrey et al. (2006)

also provide evidence that electronic payment instruments, such as debit cards, are less costly than paper

instruments, such as cash or check. Again, however, we focus only on credit cards, which have high merchant

fees and are more costly than other payment instruments, paper or electronic.

Pay Same Price," October 1, 2009; and by Ron Lieber, \The Damage of Card Rewards," January 8, 2010.

2

high-income households. A related paper by Berkovich (2009) estimates the total amount

transferred from non-rewards consumers to rewards consumers in the United States resulting

We propose a simple, model-free accounting methodology to compute the two transfers

by comparing the costs imposed by individual consumer payment choices with actual prices

paid by each buyer. On average, each cash buyer pays $149 to card users and each card

buyer receives $1,133 from cash users every year, a total transfer of $1,282 from the average

cash payer to the average card payer. On average, and after accounting for rewards paid

to households by banks, when all households are divided into two income groups, each

low-income household pays $8 to high-income households and each high-income household

receives $430 from low-income households every year. The magnitude of this transfer is

even greater when household income is divided into seven categories: on average, the lowest-

among income groups are smaller than those between cash and card users because some

low-income households use credit cards and many high-income households use cash. Finally,

about 79 percent of banks' revenue from credit card merchant fees is obtained from cash

payers, and disproportionately from low-income cash payers.

To conduct welfare and policy analysis of these transfers, we construct a structural model

of a simpli ed representation of the U.S. payments market and calibrate it with U.S. micro

data on consumer credit card use and related variables. Parameters derived from the model

are notably reasonable given the simplicity and limitations of the model and data. High-

income households appear to receive an inherent utility bene t from credit card use that

is more than twice as high as that received by low-income households. Eliminating the

merchant fee and credit card rewards (together) would increase consumer welfare by 0.15 to

on low-income minorities and to resemble a regressive tax on consumption. These estimates focus exclusively

on rewards transfers and do not account for the full range of transfers from low- to high-income consumers

resulting from merchant fees.

3

0.26 percent, depending on the degree of concavity of utility, which also can be interpreted

in an aggregate model as the degree of aversion to income inequality in society.

Our analysis is consistent with, but abstracts from, three features of the U.S. payments

market. First, we focus on the convenience use of credit cards (payments only) and do not

incorporate a role for revolving credit, which is an important feature of the total consumer

credit card spending is surprisingly similar across income groups, so it is unlikely that interest

income plays a major role in the transfers. This fact supports working with a static model

that is more tractable for data analysis. Second, we abstract from the supply-side details

of the payments market for both cash and cards. We take as given the well-established,

seminal result of Rochet and Tirole (2006) concerning the critical role of an interchange fee

between acquiring and issuing banks in the two-sided credit card market, a result that notes

merchant fees and card rewards rates, we can assume that the interchange fee lies between

these rates and is set internally in the banking sector to the optimal level conditional on

fees and rewards. Finally, we do not incorporate a role for the distribution of bank pro ts

from credit card payments to households that own banks, because of a lack of sucient micro

data. Given these three simpli cations, we can assess only the consumer welfare implications

of the payment instrument transfers but not the full social welfare implications.

We want to be clear that we do not allege or imply that banks or credit card compa-

nies have designed or operated the credit card market intentionally to produce a regressive

transfer from low-income to high-income households. We are not aware of any evidence to

income in the face of income and wealth shocks and achieve optimal consumption plans. However, the

actual impact of credit card borrowing on consumer and social welfare is complicated, as can be seen from

literature, including Brito and Hartley (1995), Gross and Souleles (2002), Chatterjee et al. (2007), and

Cohen-Cole (Forthcoming).

reader can consult Chakravorti and Shah (2003), Gans and King (2003), Rochet (2003), Wright (2003),

Roson (2005), Evans and Schmalensee (2005), Armstrong (2006), Schwartz and Vincent (2006), Bolt and

Chakravorti (2008), Hayashi (2008), Rysman (2009), and Verdier (Forthcoming). For a comprehensive

empirical study of interchange fees, see Prager et al. (2009).

4

non-trivial regressive transfer in the credit card market may be a concern that U.S. individ-

uals, businesses, or public policy makers wish to address. If so, our analysis suggests several

principles and approaches worth further study and consideration, which we discuss briey at

the end of the paper. Recent U.S. nancial reform legislation, motivated by concerns about

competition in payment card pricing, gives the Federal Reserve responsibility for regulating

interchange fees associated with debit (but not credit) cards. Our analysis provides a di
er-

ent but complementary motivation|income inequality|for policy intervention in the credit

card market.

Section 2 documents three basic facts about card card use. Section 3 demonstrates a

simple \accounting" of transfers from cash to card users and from low-to high-income buy-

ers. Section 4 presents an analytical model, which is then used in Section 5 to calibrate

the welfare-maximizing merchant fees and rewards to card users, and to compute changes

in welfare associated with a total elimination of card reward programs and merchant fees.

Policy implications are explored in Section 6. Section 7 subjects our computations of income

transfers to a wide variety of tests associated with additional modi cations of the data. Sec-

tion 8 concludes. An appendix provides data details and sensitivity analysis of the calibrated

model.

2. Basic Facts about Credit Cards

This section establishes three basic facts about credit cards: 1) consumer credit card use

has been increasing; 2) consumer credit card use and rewards are positively correlated with

household income; and 3) credit card use varies across consumers due to heterogeneity in

nonpecuniary bene ts from cards, even within income groups. These facts motivate our

analysis and modeling of transfers among consumers, associated with convenience use of

cards.

5

2.1 Credit cards in the economy

Over the last two decades, payment cards have enjoyed increased popularity in all sectors of

the economy. Our research focuses on credit and charge cards issued by banks, stores, and

gas stations and used by consumers only. Figure 1 shows that the fraction of households who

have a credit card (adopters) has been steady at about 70{75 percent during the past two

decades, reecting the maturity of the market. However, the percentage of total consumption

expenditure paid for by credit card increased from about 9 percent to 15 percent during the

spending, also increased. Consumer credit card spending accounts for approximately half of

0 20 40 60 80 100

Percentage of households

8 10 12 14 16 18

Percentage of consumption expenditure

1990 1995 2000 2005 2010

Consumption spending

volume (left scale)

Credit card adoption

rate (right scale)

Sources: Survey of Consumer Finances 1989−2007

Credit Card Usage

6

2.2 Card use and income

Although previous literature found a positive relationship between income and credit card

adoption (Stavins (2001), Mester (2003), Bertaut and Haliassos (2006), Klee (2006), Zinman

(2009a), Schuh and Stavins (2010)), there has been less focus on the relationship between

income and credit card use. Publicly available data sources, such as the 2007 Survey of

Consumer Finances, typically provide only the dollar amounts charged on credit cards, which

we de ne here as use. However, data on the number of transactions consumers make with

credit cards are available from the new 2008 Survey of Consumer Payment Choice (SCPC).

The data reveal a strong positive correlation between consumer credit card use and house-

hold income, as shown in Table 1. (The unequally sized income categories are as reported

in published aggregate data from the Consumer Expenditure Survey.) The proportion of

households who hold (have adopted) at least one credit card increases monotonically with

income ( rst column). Average new monthly charges on all credit cards held by a household

also increases monotonically with income among households who have adopted credit cards

The data also reveal a strong positive correlation between consumer credit card rewards

and household income, as shown in Table 2. The share of credit card holders earning any

type of rewards increases monotonically with income. A similar pattern is visible for each of

the major types of rewards as well: cash back, frequent yer miles, discounts, and others.

In most of our analysis, we split the consumer population into two income groups: house-

roughly how much were the new charges made to these [Visa, MasterCard, Discover, or American Express]

accounts?" Because merchant fees are proportional to the amount charged on credit cards, regardless of

whether the cardholder pays his monthly balance or carries it over to the next month, total new credit card

charges for each household is the relevant measure of credit card use.

because the marginal propensity to consume falls with household income.

7

Average monthly cc Share of cc spending

Annual income Have cc charge by adopters in consumption

is motivated by the need for parsimony in modeling, by the signi cant di
erences in credit

card behavior between these two broad income groups shown in Tables 1 and 2, and by

our desire to put the focus more on the transfer to higher-income households (and less on

the transfer from lower-income households). Table 1 shows that credit card spending by

high-income consumers is nearly ve times higher than credit card spending by low-income

consumers, and Table 2 shows that high-income consumers are 20 percentage points more

likely to receive credit card rewards. The di
erence between the lowest-income (less than

$20,000 per year) and the highest-income ($150,000 per year or more) households' credit

card spending and rewards is markedly greater.

2.3 Non-income factors a
ecting credit card use

Income is not the only factor that is positively correlated with credit card use. Schuh and

Stavins (2010) estimated the use of payment instruments as a function of various characteris-

tics of these instruments, employing a 2006 survey of U.S. consumers. They found that, after

controlling for income, the characteristics of convenience, cost, and timing of payment have

a statistically signi cant e
ect on credit card use. Using the more extensive 2008 SCPC,

we re-estimated the e
ects of payment instrument characteristics on consumer adoption and

8

Income Any Reward Cash Back Airlines Miles Discounts Other Rewards

Under $20,000 48 27 17 13 8

$20,000{49,999 50 28 17 11 10

$50,000{79,999 62 35 26 13 12

$80,000{99,999 68 38 36 15 11

$100,000{119,999 71 37 33 16 15

$120,000{149,999 82 44 39 19 25

Over $150,000 75 33 48 15 19

Whole sample 61 33 27 13 12

Consumer Finance Monthly survey conducted by the Ohio State University.

use of credit cards, using the following speci cation:

Table 3 shows the distribution of credit card use, calculated as a share of credit card

payments in all payments for each consumer. The share of credit card transactions is higher

for the over $100K income group than for the under $100K income group across the whole

distribution. However, there is substantial variation within each income group. For example,

among the high-income consumers, the 10th percentile of credit card users pay for 4 percent

of their transactions with credit cards, compared with 70 percent of transactions for the 90th

percentile of users. Therefore, there is variance in credit card use within income groups that

needs to be explained.

Several relative payment-instrument characteristics have a signi cant e
ect on credit card

9

Percentile Under $100K Over $100K Whole Sample

Based on the 2008 Survey of Consumer Payment Choice, and weighted using the population

weights from the 2008 SCPC.

use. Table 4 shows the estimated coecients on payment-instrument characteristics from

estimating equation (1) for three di
erent samples. While the cost of credit cards (which

includes rewards as well as interest rates and fees) is signi cant in all speci cations and for

both income groups, other attributes of credit cards also are important determinants of credit

card use, conditional on cost. Controlling for income categories (column 1 of Table 4), ease

of use and record keeping have a strong and statistically signi cant e
ect on credit card use.

In separate regressions by household income category, record keeping and cost have much

stronger e
ects on higher-income consumers (column 3) than on lower-income consumers

(column 2), while ease of use was not statistically signi cant for the higher-income group.

The preceding results indicate that payment-instrument characteristics are valued dif-

ferently by consumers both within and between income groups. The model in Section 4

captures consumers' nonpecuniary bene ts from using credit cards relative to cash, such as

eter turns out to be an important factor determining the choice of cash versus credit card

for payments.

3. Transfer Accounting

This section demonstrates a simple, model-free approach to computing two implicit monetary

transfers between U.S. consumers that result when some buyers pay with credit cards and

others do not. One transfer is from cash buyers to credit card buyers; the other is from

10

(1) (2) (3)

Explanatory Variables Whole Sample Under $100K Over $100K

Income categories included? Yes No No

Consumer Payment Choice. *** signi cant at the 1% level, ** signi cant at the 5% level.

low-income buyers to high-income buyers. Our methodology decomposes national income

account data on consumption into consumer groups de ned by payment choice and income

level, using micro data on consumption, credit card spending, and related variables (along

with the benchmark estimates of payment costs). Humphrey, Kaloudis, and wre (2004)

use an analogous methodology to estimate cash use in Norway.

3.1 The payments market

Figure 2 illustrates a simpli ed version of the U.S. payments market that frames the computa-

tion of aggregate transfers. There are three types of agents: buyers (consumers), merchants,

and \banks." Buyers can have high or low incomes and pay by credit card or cash (all other

non-credit card payments). A representative merchant sells a representative good to all con-

sumers. This assumption is not strictly true for all markets, so we explore the implications

of relaxing it in Section 7. However, it is a good approximation for most transactions and

it is necessary to compute the transfers, given the lack of micro data on payment choice

that provides credit card payment services. It includes banks that issue cards to consumers

consumers, merchants, and goods|a level of detail for which proper data are not currently available

anyway|in addition to payment choice.

11

(\issuers"), banks that receive card payments from merchants (\acquirers"), and card com-

panies (Visa or MasterCard are examples) that facilitate interactions among banks and be-

of the \banks" and merchant markets but tends to abstract from consumer heterogeneity,

restricting analysis of transfers among consumers. Our analysis takes the opposite approach.

























Issuer Acquirer



6

?









=

\Banks"

High-income card users

#

"

!

Merchant Low-income cash users

High-income cash users

#

"

!



p

Payments occur as follows. Buyers purchase a good for an endogenously determined price,

The merchant incurs a cost with either payment choice. For cash, the merchant bears a cost,

banks (acquirers) that is proportional to card sales. Thus, the merchant's cost of accepting

MasterCard in 2006.

interpreted as average cost that includes possible xed costs because the data do not distinguish well between

xed and marginal costs.

12

The merchant fee and reward rate are closely related to pricing decisions internal to banks.

fees involve the xing of fees by competing card issuers, they have triggered many debates and

the transfers among consumers requires only the merchant fee and reward rate and not the

inclusion of the interchange fee.

Regardless of whether buyers choose cash or credit card, U.S. merchants tend to charge

the no-surcharge rule, merchants cannot charge credit card buyers a higher price than the

However, under certain conditions card companies do allow the merchant to o
er a discount

some U.S. merchants have o
ered cash discounts from time to time, they generally do not do

so widely or consistently. One reason may be the cost of o
ering two prices. Another reason

may be concerns about adverse customer reactions to di
erential pricing and especially to

penalizing card buyers, who tend to be higher-income households and to buy more goods.

The simpli ed payments market in Figure 2 covers only convenience use of credit cards

and not the revolving credit feature of cards. In reality, banks also receive revenue from

consumers through interest payments on revolving debt and from credit card fees (annual,

over-the-limit, etc.), so it is possible that card rewards may be funded from sources of

or interest from revolving credit card debt. Funding of rewards is discussed more later.

may o
er a discount as an inducement for a Cardholder to use a means of payment that the Merchant prefers,

provided that the discount is clearly disclosed as a discount from the standard price and, non-discriminatory

as between a Cardholder who pays with a Visa Card and a cardholder who pays with a `comparable card'."

See also Footnote 2.

13

below suggest that these alternative sources of credit card revenue are unlikely to alter

our qualitative conclusions about transfers. Furthermore, the welfare e
ects of credit card

borrowing and lending are extremely dicult to identify in economic theory and practice|

revolving debt may be welfare improving, even at very high interest rates|whereas the

welfare e
ects of transfers among consumers associated with convenience use of credit cards

are less so.

3.2 Data and assumptions

The payments market discussed in Section 3.1 generates implicit monetary transfers between

consumers, regardless of whether revolving credit is extended for card purchases. Calculation

of these transfers does not require a formal economic model, only data and arithmetic|

on three key economic assumptions described below.

The quantitative fees and costs portrayed in Figure 2 represent \benchmark" estimates

of recent conditions in the U.S. payments market. The limited available data suggest that

a reasonable, but very rough, estimate of the per-dollar merchant e
ort of handling cash

transaction (the average check transaction) is $0.43 (or 0.8 percent) if it is a cash transaction and $1.22

(or 2.25 percent) if it is paid by a credit/charge card. The study by Bergman, Guibourg, and Segendorf

(2007) for Sweden found that the total private costs incurred by the retail sector from handling 235 billion

Swedish Crown (SEK) worth of transactions was 3.68 billion SEK in 2002, which would put our measure

estimates that private costs of handling 62.1 billion Norwegian Crown (NOK) worth of cash transactions

percent of the U.S. credit card sales for that same year in the Call Report data for depository institutions.

Actual merchant fees are complex and heterogeneous, varying over cards and merchants. We estimate

merchant fees across cards as follows: general purpose (Visa, MasterCard, and Discover) 2 percent; American

14

to Table 2, only 55 percent of low-income credit card holders receive rewards, compared

with 75 percent of high-income card holders. For this reason, the average card user in either

In addition to the benchmark speci cations, the only data needed to calculate the trans-

tion from the National Income and Product Accounts (NIPA) and Consumer Expenditure

sumption does not involve a payment choice for consumers, for example, imputed rental

of owner-occupied housing, employer-provided health insurance, and fees paid for nancial

income households and credit card spending data are obtained from the Survey of Consumer

actual reward rate could be even lower, because holders of reward credit cards may not claim all of their

rewards or the rewards may expire, but we do not have data on the rate at which consumers actually claim

their rewards.

and Jay Zagorsky (Boston University) for helping us clarify whether credit cards can be used for mortgage

payments.

credit card charges and fairly well on account balance totals.

15

It is well known that consumption and income are distributed unevenly across households,

and this situation is evident in Table 5. Low-income buyers account for 81 percent of all

households but only 58 percent of transactions. Low-income buyers also tend to favor cash

payments: 70 percent of all households are low-income cash buyers, and 50 percent of all

transactions are conducted by low-income cash buyers. In addition, high-income households

than their population share (19 percent). All this shows that high-income households make

Distribution of Households Distribution of Transactions

Cash buyers 70 13 83 50 29 79

Card buyers 12 6 17 8 13 21

Total 81 19 100 58 42 100

Three assumptions are needed to de ne the implicit transfers among households.

that is, the merchant does not charge di
erent prices to cash buyers and card buyers.

ities.

The validity of these assumptions is an empirical matter and the data needed to verify them

are not available. One needs data on individual transactions that identify not only the

payment instrument but also the consumer who uses it and the merchant who receives it.

obtain a parsimonious aggregate representation of the data for modeling purposes. Households without

credit cards are literally cash-only households (where cash means non-credit-card). However, there are no

households that strictly use credit cards only, and most households use both cash and credit cards. Our

aggregate transfer calculations cannot account for this within-household heterogeneity, a re nement we leave

for future research.

16

Such matched consumer-merchant data are extremely rare, and may not even be sucient.

If consumers of di
erent income groups buy di
erent products within merchants, and if

merchants price those products not only according to their price elasticities of demand but

also by their probabilities of being paid for by cash versus credit, then consumer-merchant

data are needed at the level of detailed individual products (goods and services) as well.

Future research based on such rich and nely graded data would provide valuable re nements

of our calculations. However, Section 7 considers some alternative calculations that explore

the e
ects of relaxing these assumptions on the transfers.

3.3 Transfer de nitions

Our goal is to measure the actual transfers in the U.S. payments market and their e
ects on

consumer welfare. Thus, we de ne each transfer as the di
erence between the actual money

paid by a household toward merchant payment costs, on one hand, and the reference value

(amount of money) the household would pay if it faced the full cost of its payment choice in

the current payment environment, on the other. The actual money paid is the household's

payment depends on the marginal cost of the good for the household. As shown in Section 4,

marginal cost of payment varies across households according to the household's payment

With this transfer de nition in mind, consider rst the transfer between cash and credit



S

􀀀

is what cash users actually pay toward total merchant payment costs: the cash share of total

17

Similar to (2), the transfer (or subsidy received, if the transfer is negative) made by credit



S

􀀀

)



payment costs net of the rewards they receive. The rst term inside the braces is their

times the total merchant cost of transactions. The second term inside the braces adjusts for

is the total merchant cost of credit card transactions, which equals banks' fee revenue from

all credit card transactions.

The credit card transfer, equation (3), contains two components. One is the point-of-sale

(POS) transfer, which occurs at the merchant:



S

􀀀

d

), which are subtracted

from the POS transfer because rewards are rebated to credit card users by banks and reduce

the contribution of card users to total merchant payment costs. The rewards adjustment

to the POS transfer captures the portion of the overall transfer that occurs because credit

card users do not pay the full value of the rewards they receive. Instead, cash users pay for

part of the rewards, and this rewards-related transfer varies across income groups. Thus,

the POS transfer, which excludes rewards, understates the actual transfer occurring as a

18

lower-bound estimate of the transfer, so we report both estimates. Furthermore, the POS

transfer would be the appropriate measure if credit card users paid the full value of their

Section 2.2 established a positive correlation between card use and income, which moti-

vates calculation of the transfer between low-income and high-income households. Similar

to the transfer de nitions given by (2) and (3), the transfers paid by each household income

group are



S

􀀀





S

􀀀



The rst terms in braces are what households actually pay toward total merchant payment

) = $23 billion.

Note that the total (aggregate) transfer among households by income level is the same as

between cash-using and card-using households:

Similar to equation (4), the POS transfers between low-income and high-income house-

Paul Willen for helping us to clarify our thinking about the transfer de nitions, especially the central and

crucial de nition in equation (3).

credit card users for their rewards at the POS and then rebate the full rewards instantly to households using

the full merchant fee and having banks pay rewards to households later.

19

holds are

L



S

􀀀

) (8)

H



S

􀀀

) (9)

and they omit the adjustment for rewards, which varies by income group. At the household

level, the relative magnitudes of the income group transfers are determined primarily by two

3.4 Transfer estimates

Applying the benchmark speci cation and data described in Section 3.2 to the transfer

equations de ned in Section 3.3 yields the central results of this paper. Table 6 displays the

transfer estimates in billions of 2007 dollars and on a per household basis. These two types

of estimates are qualitatively equivalent but we focus on the latter. Recall that positive

(negative) numbers indicate that households using a payment instrument paid a transfer

(received a subsidy).

Total ($ Billions) Per household, total ($)

POS only ($ Billions) Per household, POS ($)

To our knowledge, the results in Table 6 are the rst quantitative estimates for the

aggregate economy of theoretical measures of transfers between buyers stemming from the

choice of payment instrument. Two main conclusions can be drawn from the results.

20

2007.

The annual transfer gap (di
erence) between the average low-income household and the

of median income across low-income households in 2007. By far, the bulk of the transfer

Although low-income credit card buyers also receive a subsidy ($613) and high-income cash

buyers pay a larger transfer ($352) than low-income cash buyers, the greater use of credit

cards and receipt of rewards gives high-income households a non-trivial subsidy each year.

These transfer estimates, based on only two income categories (de ned by a cuto
of

highest-income households. Dividing households into seven income categories instead, as

in Table 7, reveals that the transfer gap between the lowest-income households (less than

each year. The average lowest-income household pays $21 each year, and the average highest-

income household receives $750 each year, from the convenience use of credit cards. In

between, the transfer gap is nonlinear across groups|relatively at until household income

a large number of lower-income households pays a relatively small dollar amount of transfer,

21

while each household of a small number of higher-income groups receives a relatively large

Transfers paid

Income range POS Total

Section 4 develops a model to quantify the potential loss to consumer welfare result-

ing from these transfers. Before doing so, let us put the payment transfer estimates into

perspective by viewing them in the context of another public policy issue. The literature

on ination nds that the potential welfare gain of reducing steady-state ination from 10

and Lucas (2000)). These estimates translate into an annual per household cost of $243 to

to merit attention from policy makers similar to that devoted to controlling ination.

3.5 Sources of banks' income

sources of revenue from each of the four buyer groups. We multiply gross income (revenue)

results appear in the rst panel of Table 8. We then compute rewards paid to credit card

a higher cuto
level is more representative of the transfer paid by the highest income groups. If the cuto

household receives $200 instead of $430.

22

users in the second panel of the table. The third panel reports the net income of banks from

merchant fees, that is, gross income ( rst panel) minus rewards (second panel).

Revenue from Merchant Fees

Total ($ billions) Per household ($)

Rewards to Consumers (expenditure)

Cash payers 0 0 0 0 0 0

Net ($ billions) Net Per household ($)

From Table 8 we can derive the following results about sources of banks' income from

merchant fees:

of credit cards because they tend to use cash more often than high-income households. Cash

one-fourth as much.

23

spite the fact that the high-income group uses credit cards more than the low-income group

Overall, the picture painted by these data and results is one in which low-income cash payers

account for the bulk of the costs (merchant fee revenue) imposed by the payment choices

(credit card purchases) of mostly high-income households.

4. A Model of Cash and Card Users

To investigate the welfare consequences associated with the redistribution of income among

households, we construct an analytical model and then calibrate it. Endogenously deter-

mined variables will be denoted by lower case letters. Exogenous parameters will be denoted

by roman capital and Greek letters.

4.1 Buyers

paying with a card relative to paying with cash, as illustrated in Figure 3 and described

paying with cash over card.

Buyers have an endogenous choice of paying with cash or paying with a card. Banks

24

(

(10)

8>><

>>:



paying with a card



p

paying cash,

Equation (11) implies that a buyer's utility is increasing with the number of transactions

(income divided by price). In addition, if the buyer pays with a card, the buyer gains an

0

-

0

-

z }| {

z }| {

low-income buyers).

paying with a card are found by solving



=



p

who otherwise prefer to pay cash to use their cards in order to collect rewards.

25

The remainder of this section computes the number of card and cash payers as well as

the number of transactions made with each payment instrument. Recall that superscripts

In view of the \indi
erent" buyers described in (12) and Figure 3, the number of buyers

which is the total number of buyers (both income groups combined) who pay cash.

which is the total number of buyers (both income groups combined) who pay with cards.

4.2 Merchants

Merchants supply one \good," which could be either a product or a service. Free entry

results in normal (zero) pro ts. Similar to Wang (2010), we model a \mature" card market

in the sense that we assume that all merchants accept payment cards and cash. Thus, we

assume for simplicity that consumers do not have to search for a merchant who accepts their

cash transaction relative to a card transaction. Thus, the merchant's disutility from handling

"

1

#

26

card acquirer.

4.3 Calibrations

We rst use the model to calibrate the number of cash and card users within each group,

consumption expenditures because savings are not modeled.

Next, in view of Figure 3, the key parameters to be calibrated are the maximal bene ts

equations (13) and (14), assuming the card reward rates reported in Section 3.1. Transactions

data from the Survey of Consumer Payment Choice (SCPC) show that credit cards accounted

values obtained under the above computations.

4.4 Equilibrium price and markup

Substituting the calibrated parameters from Table 9 into (13){(16), the equilibrium price

(16) becomes



p



which is the Lerner's index commonly used for measuring markup over marginal cost. Thus,

our calibrations imply the following result:

27

Parameter Notation Value Procedure

To assess the sensitivity of this result, Figure 4 plots the retail price markup as a function

depicted by the shaded triangle on the oor of the three-dimensional graph. Each relationship

between the markup and the two parameters is each approximately linear, but the markup

is more sensitive (steeper slope) to the merchant fee than to the reward rate. The reason

for this result follows from equation (16), which shows that the merchant fee a
ects price

directly because it is a cost for the merchant, whereas the reward rate has only an indirect

e
ect by making credit cards more attractive, thereby increasing the number of card users,

see equation (14).

28

through dark blue, the lowest).

who pay cash. On the other hand, rewards have a much smaller e
ect on the markup; the

4.5 Banks' income from consumer credit cards

transfers analyzed in previous sections, banks' net income is nonlinear with respect to the

merchant fee and reward rate. Banks' income from consumer credit card payments, net of

from merchant fees, while consumers receive 35 percent in rewards.

in the markup comes directly from the change in the merchant fee.

29

Figure 5 displays banks' net income from credit card spending as a function of the

Thus, banks can keep the same net income using di
erent combinations of merchant fee

Figure 6. The dashed line shows the combinations of parameters for which bank pro ts are

0 1 2 3 4 5

0

1

2

3

4

5

Merchant fee (%)

Reward rate (%)

zero|combinations of reward rates and merchant fees to the left of this line would result

30

are both less than one, the slope of the iso-pro t curves is greater than one, meaning that

banks could o
er a higher reward rate than the merchant fee, since they earn merchant

fees on every credit card payment while they have to give rewards for only a fraction of

these transactions. The solid line, which runs through the benchmark point, shows the

not alter bank pro ts, but would result in a lower retail price markup, as explained in the

previous subsection.

5. Consumer Welfare Calibrations

The analytical framework developed in this paper enables us to calibrate the consequences of

merchant fees and card rewards on consumer welfare stemming from the implicit monetary

8<

:



p



9=

because buyers derive di
erent bene ts from card use). Therefore, total buyer welfare as a

consumption demand, because we do not have micro data on bank ownership (stocks). For this reason, we

do not extend this analysis to include social welfare. However, if household ownership of banks is increasing in

income too, then taking bank pro ts into consideration would likely magnify our central results. Section 7.3

and Appendix B discuss the implications of income changes due to redistribution of banks' pro ts.

31

The reason for this result is that rewards are pure windfalls received by the households

from the banks in this partial equilibrium setup. On the other hand, consumer welfare

falls very fast with an increase in the merchant fee. More precisely, the elasticity of the

the merchant fee (while leaving rewards unchanged) would increase aggregate consumer

decline in aggregate consumer welfare.

Using these elasticities, we can infer the welfare implications of certain changes in the pay-

ment fee structure. If, for example, the merchant fee is cut in half to 1 percent, the economy

welfare. However, Figure 7 reveals that this is not the maximum attainable level of welfare.

32

sumer welfare, although this move would raise welfare by a smaller amount than the move

gain from another 1-percent reduction in the merchant fee and the welfare loss from the

percent increase in consumer welfare compared with the benchmark starting point.

because the marginal utility loss from the low-income transfer becomes larger, while the

marginal utility gain from the high-income subsidy gets smaller. When applied to aggregate

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

−0.5

0

0.5

1

1.5

2

2.5

a

Merchant fee, reward rate (%)

zero bank pro ts)

Figure 8 plots the welfare-maximizing values of the merchant fee and reward rate for

33

with an increase in the degree of concavity of buyers' utility function (11) with respect to the

Result 7 highlights the distortion in the income distributions caused by the merchant fee and

from low- to high-income buyers has a greater impact on low-income buyers. For low values

linear utility, the loss to low-income buyers is smaller than the gain to high-income buyers,

so positive merchant fees and rewards become optimal.

Finally, Figure 9 illustrates the combinations of merchant fee and card rewards such that

6. Policy Implications

Our model and analysis suggest that aggregate consumer welfare likely can be increased

by reducing transfers between consumers, especially between low-income and high-income

welfare e
ects of zero banks' net income are magni ed.

34

1 2 3 4 5

109.6784

109.6785

109.6786

Merchant fee (%)

Consumer Welfare (log scale)

consumers. While it is natural to consider public policy initiatives in this endeavor, our

research and discussions suggest preemptive actions that private sector agents (households,

merchants, and banks) could take that would reduce the transfers. However, if private

agents are not willing or able to take these actions to reduce the transfers, then public policy

makers may wish to enact policies that would do so. Given the limitations of our model and

analysis, we cannot provide precise policy recommendations that would necessarily optimize

social welfare. Nevertheless, our research suggests some general principles and implications

pertaining to consumer welfare that may be useful for policy deliberations:

payment instruments. Policies that would allow and encourage merchants to charge

di
erential prices according to the costs imposed by payment instruments could help

to reduce the transfers by reducing payment cross subsidies. Eliminating the NSR

would seem to be an obvious option, but it may not be a sucient incentive to induce

di
erential pricing (for example, see Bolt and van Renselaar (2009)).

mation about about merchant fees and other aspects of payment costs that have an

impact on retail prices and consumer welfare. Policies that would require merchants,

banks, or credit card companies to fully disclose fees, costs, and price markups to

35

consumers could help to reduce transfers by giving consumers the incentive to make

optimal payment choices.

using tax policies to redistribute money from high-income households according to

credit card use and receipt of rewards. Direct methods may be complicated and costly,

but tax deductions for reward contributions may be feasible.

ernment e
orts to promote alternative payment instruments could help to reduce the

transfers. Expanding access to low-cost existing networks, such as the Automatic

Clearing House (ACH), is one possibility.

merchant fee, but two important caveats apply. First, economists would caution as

usual that regulators may have diculty determining the optimal fee, so regulation

of the merchant fee could actually reduce consumer welfare if the wrong level of the

fee were selected. Second, and unique to our analysis, regulators should consider the

merchant fee and reward rate simultaneously.

Of course, these policy implications and ideas would require more research and formulation

before they could be considered and adopted.

Finally, these policies to reduce transfers are closely related to recent policies enacted to

regulate payment card interchange fees worldwide. Policy makers in Australia and Spain, as

well as the European Commission, have already taken actions to limit the interchange fees

associated with credit cards. Actions taken by various countries are discussed in Bradford and

Hayashi (2008). The recent U.S. nancial reform bill (ocially, the \Dodd-Frank Wall Street

Reform and Consumer Protection Act" of 2010), signed into law on July 21, 2010, includes

the Durbin Amendment, giving the Federal Reserve responsibility for regulating interchange

fees associated with debit cards. In each of these cases, regulation of interchange fees was

36

motivated in part by concerns over an alleged lack of competition in payment card markets.

Our analysis provides a di
erent but complementary motivation|income inequality|for

policy intervention.

Given that policy makers have been and will be focusing on regulating interchange fees, we

can provide some potentially helpful information about the properties of merchant fees and

rewards for policy makers who wish to take these parameters into consideration. Table 10

summarizes the key elasticities with respect to the merchant fee and the reward rate in

the model. Recall from Section 4.4 that regulating the merchant fee without changing the

Variable Merchant Fee Reward rate

reward rate would have a much larger e
ect on the price markup and consumer welfare

than regulating the reward rate without changing the merchant fee ( rst and last lines

of Table 10). However, it is important to remember that optimal policy would require

simultaneous regulation of the merchant fee and the reward rate. It would also require an

analysis and treatment of household claims to banks' pro ts, which we have not considered

here.

Table 11 provides a guide to the e
ects of policy changes by showing the percentage

changes in consumer welfare associated with reductions in merchant fee and reward rates

indicates an increase in consumer welfare. The maximum possible increases in consumer

welfare are found at the top of each column where banks' net income is the smallest for the

column.

37

7. Quali cations and Extensions

Our analysis relies on several assumptions and simpli cations imposed due to lack of data

or for tractability. Relaxing these restrictions could alter the magnitudes of the transfer

estimates. This section explores the potential impact of these restrictions, and provides

some quali cations and extensions to the central results.

7.1 Transfer accounting assumptions

Section 3.2 lists three key assumptions underlying the estimates of the transfers between

cash and card payers and between low-income and high-income households. In reality, each

assumption may not hold exactly. So we designed some alternative transfer calculations to

approximate more realistic conditions in the payments market that would occur if we relaxed

the assumptions. Table 12 reports the results of our alternative transfer calculations and

their deviations from the benchmark estimates based on two household income categories.

To simplify the analysis, columns three and four report only the transfer gap, which we

de ned earlier as the di
erence between the average transfer per low-income household and

the average transfer per high-income household. The remaining two columns report the

percentage change for the alternative transfer estimate relative to the benchmark estimate.

38

Transfer Gap ($) Change (%)

Assumption Alternative Card Income Card Income

First, we relaxed assumption A-1, one price for all buyers, and instead allowed for partial

price di
erentiation between cash and credit card buyers. Price di
erentiation could arise for

many reasons, including the following: the representative merchant could surcharge credit

cards or discount cash purchases; there may exist heterogeneous merchants and/or products

for which only cash or only credit cards are accepted; or low-income and high-income house-

holds may shop at di
erent merchants so that cash and credit card purchases are segregated.

Each of these reasons can be simulated in observationally equivalent fashion by excluding a

percent of consumption from broad NIPA categories that are likely paid for by cards only or

3.7 percent and the income transfer gap falls by 16.7 percent.

Next, we relaxed assumption A-2, complete (100 percent) pass-through of the merchant

fee to consumers, and instead allowed for the pass-through to be more or less than complete

by introducing two forms of imperfect competition. One form is classic market power for

the merchant, which results in a traditional price markup over marginal costs and the cost

of the payment instrument. The transfer formula for this price markup is:



S

\air transportation," and \accommodations," which are likely paid mostly with credit cards.

39

other form is market power held by a very large merchant (for example, Walmart) over

banks, giving the merchant leverage in bargaining over the merchant fee. We simulated

this possibility by reducing the aggregate merchant fee 0.5 percentage points to 1.5 percent.

the pass-through of payment costs in the retail price is more than 100 percent; the card

transfer gap is only slightly higher. In contrast, bargaining power over the merchant fee

Combining these two di
erent e
ects of market power, we see that imperfect competition

Finally, we relaxed assumption A-3, no funding of credit card rewards from revolving

debt activity, and instead assumed that interest revenue from revolving debt held by high-

income households is used to fund rewards paid to low-income households. As we show in

more detail below, this alternative transfer calculation is not supported well by the data,

even though it is often alleged in the literature. In any case, this alternative does not a
ect

direct transfer of interest payments from high-income to low-income household rewards.

One clear overall conclusion emerges from these alternative transfer calculations: both

transfers remain economically signi cant even after adjusting for alternative conditions in

the payments market. Although relaxing some assumptions leads to reductions in some of

the estimates, the adjusted transfers are still about three-quarters (or more) as large as their

benchmark values. Furthermore, we have omitted from the benchmark transfer calculations

two very important features of credit card markets|redistribution of bank pro ts (discussed

the transfer estimates. We believe that these increases to the transfer estimates are most

likely greater (in absolute value) than the reductions reported in Table 12.

40

7.2 Revolving credit

It is important to emphasize once more that our model and analysis focus on the convenience

use of credit cards and do not incorporate a role for revolving credit. Revolving credit is an

important part of the value of credit cards to the economy, and we support future research

that expands our analysis in this direction. We also recognize that debt activity could be

another source of revenue for banks and credit card companies. This subsection explores the

evidence on this issue further to reassure the reader that we have not grossly mischaracterized

the transfers.

High interest and penalties paid by credit card borrowers on revolving debt may directly

or indirectly fund some of the bank issuers' expenses on card rewards. In fact, Chakravorti

and Emmons (2003) demonstrate an equilibrium in the market for credit cards (as opposed

to debit and charge cards) in which the \convenience use" of credit cards by nonborrowing

consumers is subsidized by liquidity-constrained consumers who borrow on their credit cards

and pay high interest. Chakravorti and Emmons's results explain that borrowers pay high

interest rates on credit card debt because this interest is used to reward all credit card users,

including those who avoid interest charges by paying their full balances on time. However,

the evidence suggests that rewards are funded at least partly by merchant fees. Levitin

(2007) reports that 44 percent of interchange fees goes to fund reward programs. Hayashi

(2009) also investigates the degree to which card reward programs are nanced by merchant

fees, but does not draw de nite conclusions. In our calculations, rewards make up about 35

The SCF provides data on credit card revolving debt, reported in Table 13, that help one

to evaluate the idea of Chakravorti and Emmons (2003). The survey poses two questions

related to revolving credit, and both show surprisingly little di
erence between low-income

and high-income households. First, the SCF asks whether respondents usually pay o
their

41

revolving credit between income groups belies the conventional notion that credit card debt

is predominantly a problem for low-income households.

Low-income High-income

Annual interest payment (debt rate) $788 $1316

The remainder of Table 13 shows the implications of revolving credit for interest revenues

to banks. Among revolvers, high-income households carry about twice as much revolving

debt as low-income households, but their credit cards have interest rates about 1 percentage

enough interest to cover the credit card rewards earned by the group. Thus, it seems unlikely

that interest from either group cross-subsidizes the rewards of the other, so we conclude that

the transfer calculations based only on convenience use of credit cards are likely accurate.

7.3 Other extensions

We close this section with a brief discussion of some extensions to our model and some

analysis that we leave for future research.

average for all revolvers (the second rate shown). The other gures in the table, except for those shown in

the last two rows, are averages over the entire income group.

42

credit card services, which would be distributed to households in reality. Because the wealth-

iest 20 percent of the U.S. population holds the majority of all stocks, bank pro ts from

merchant fees likely would be distributed disproportionately to high-income households.

Thus, incorporating household ownership of banks is likely to increase the transfers from

low-income to high-income households.

Report data on total U.S. credit card transactions indicate that total credit card spending

by business (and including government) is about equal to consumer credit card spending. If

businesses used credit cards at the same establishments as consumers, they would impose

further costs on the merchants and raise retail prices even more. If businesses (and their

pro ts) are more likely to be owned by high-income households, then incorporating business

use of credit cards into the analysis is likely increase the transfers from low-income to high-

income households.

impose more costs on merchants' sales sta
s than on card users. If cash transactions take

signi cantly longer to handle than credit card transactions, cash users may impose an ex-

ternality on card users by slowing them down at the point of payment. This externality

would o
set, at least partly, the transfer from cash users to card users. However, the avail-

able data on the time it takes to handle a transaction by payment method do not provide

highway toll booths, as discussed in Amromin, Jankowski, and Porter (2007). But electronic

Cost Study of Retail Payments," a credit card transaction takes longer to handle than a cash transaction:

49 seconds compared to 29 seconds. However, a 2006 study by MasterCard International titled \MasterCard

PayPass: The Simpler Way to Pay," nds that the average cash transaction is slower than the average credit

card transaction if no signature is required: 34 seconds compared to 27 seconds.

43

toll transponders that serve as a faster alternative to cash are not credit cards, and the

proportion of toll payments is relatively small.

rewards that could a
ect the transfer estimates. If credit card holders pay for their rewards

with high annual fees, then our transfer calculations would overstate the transfers. However,

this possibility is unlikely to be a major factor. According to the 2003 Synergistics Credit

The preceding list of extensions suggests that the magnitudes of our estimates and results

for transfers from low-income to high-income consumers may be altered quantitatively by

future research. However, if anything, the qualitative nature of the regressive transfer is

almost surely robust and the quantitative estimates are likely to increase relative to our

benchmark.

8. Conclusion

We proposed an accounting methodology to calculate two types of implicit monetary transfers

occurring in a simpli ed representation of the U.S. payments market: 1) the transfer between

cash buyers and credit card buyers; and 2) the transfer between low-income and high-income

households. Both of these transfers are estimated to be economically signi cant and robust

to potential changes in the assumptions underlying the accounting methodology.

We also built an empirically tractable theoretical model of payment for consumption that

includes all of the salient and economically important features of U.S. credit card payments.

We calibrated this model with the best, most detailed data available to us and derived

estimates of the average payment, retail price markup over marginal cost, and nonpecuniary

44

utility bene t of card use over cash use. The results are remarkably plausible given the

relative simplicity of our data and model.

Extending our model and analysis with better data and more realistic features of the

credit card market surely would provide more re ned quantitative estimates of the two

transfers. However, we are con dent that the qualitative existence of these two transfers is

robust to changes in the model and data. On balance, our estimates of the transfers likely

understate the true values of the transfers, especially between income classes. Taking into

account the quantitative impact of all potential improvements and extensions to the data

and model, it is most likely that including in future research the factors we omitted from

this analysis will yield higher estimates of the transfers.

Appendix A Data

To get total consumption expenditure, we looked at the National Income and Product Ac-

counts (NIPA) for 2007. From the Personal Consumption Expenditure gure, we subtracted

a number of subcategories, where we believe that the transfers analyzed in the paper did

not take place, because assumption A-1 was not satis ed. Table 14 below details these

calculations for our benchmark model and for the alternative simulation with partial price

drawback of using NIPA data is that we cannot break down consumption expenditure by

income categories. To do that, we used the 2008 edition of the Consumer Expenditure

Survey (CEX). Tables 2 and 2301 of the 2008 CEX contain the most detailed breakdown

available of consumption by income. To make our calculations consistent with our NIPA

consumption spending gure we had to take the same spending categories out of the CEX

consumption gure as we took out of the NIPA. Unfortunately, the subcategories in the CEX

and the NIPA do not map into each other one-for-one. So, from the CEX \Average annual

expenditure" gure, we took out the entire \Healthcare" category as well as \Mortgage and

45

Line Category name Amount ($ Billions)

Benchmark model

Partial price di
erentiation

interest charges," \Property taxes," \Rented dwellings," \Cash contributions," and \Pen-

sions and Social Security." (Expenditures on nancial services are not measured in the CEX

at all.) Once we had the relevant consumption and income gures from the CEX (readily

available in Tables 2 and 2301 of the CEX publication), we could construct the average

propensity to consume by each income category (except for the bottom income group). For

the lowest income group, where consumers' average income was negative, the average total

consumption expenditure per weighted respondent was matched so that it was equal to that

of the second-lowest group. These average propensities could then be multiplied by the in-

come gure in the Survey of Consumer Finances (SCF) 2007 to yield an estimate of total

consumption expenditure by income group. We measured household income as the sum of

multiplied the resulting number by a scalar so that it matched our adjusted total Personal

46

Consumption Expenditures gure.

Total annual credit card spending was computed as the sum of the values data gathered

in response to questions in the SCF asking about consumers' total use of credit cards in the

nation scenario we subtracted \Other lodging" and \Household furnishings and equipment"

spending by income group from their respective total credit card spending. The gures for

total annual credit card transactions were taken from Table 19 (monthly credit card use

multiplied by 12) in SCPC 2008 (Foster et al. (2009)).

Appendix B Transfer Accounting Details

To understand better why it is appropriate to adjust the POS transfer for rewards, consider

the aggregate accounting of the complete ow of funds among households, merchants, and

banks. The revenue from merchant fees is paid to banks, which then distribute rewards to

Viewed this way, credit card rewards act as a claim on banks' pro ts that is paid to credit card

users only, rather than to all owners of banks, and the distribution of rewards precedes the

or privately), banks' pro ts ultimately are income for households. Thus, rewards represent

a transfer of pro ts and dividend income from owners of banks to credit card users who may

After rewards are paid to credit card holders, the distribution of pro ts to the owners of

banks is

are perfectly competitive, then these pro ts would be zero.

claims. However, this would be irrelevant if credit card users were the sole owners of banks.

47

Because our computations omit the distribution of banks' pro ts given in (21), the sum of

transfers equals the negative amount of rewards,

rather than zero. Therefore, estimates of the full aggregate transfer between cash-paying

and card-paying households depends crucially on the structure of ownership of banks by

households. In contrast, the sum of transfers at the point of sale,

does equal zero and does not depend on the ownership of banks.

Data on household ownership of banks by household payment choice and household in-

come are not available, so we cannot estimate the full aggregate transfer. However, unless

cash-paying households own a large portion of the banks, the full aggregate transfer likely is

greater than the POS transfer for two reasons: (1) the dividend income of cash-paying house-

holds is reduced by the payment of rewards to credit card users; and (2) the post-rewards

distribution of dividend income to households may not be proportional to the payment costs

imposed on merchants by household payment choices. The credit card transfer, equation (3),

includes rewards as an estimate of (1), but it does not include an estimate of (2). However, if

the ownership of banks is positively correlated with income, the net e
ects of bank ownership

on total (pre-reward) pro ts is likely to make the full aggregate transfer at least as large as

the rewards-adjusted transfer. The rewards-adjusted transfer also allows evaluation of the

independent e
ects of changes in the merchant fees versus changes in rewards. Clearly, more

data and additional research in this area would produce more complete and re ned estimates

of the full aggregate transfer.

Transfer equations (2) and (3) can be rewritten using the de nitions above to clarify the

.

Merchant fee revenue is divided between credit card users (in the form of rewards) and owners

48

Substituting this identity into the transfer equations, and then collecting and rearranging

terms, yields



)



􀀀

The structure of the rewritten transfer equations mirrors the original equations. In both

equations, the rst term in braces represents what payment users actually pay toward total

merchant payment costs, and the second term (outside braces) represents the merchant cost

of the household's payment choice. With regard to rewards, it is now clear from equation

(25) that the credit card transfer represents the amount of imbalance between the rewards

portion paid by credit card users clearly shows that card users do not pay the full value of

Appendix C Sensitivity Analysis

assumption that richer people derive higher utility from using credit cards a
ects our results.

Also, as noted above, some empirical studies nd values that di
er from our estimates for the

costs of handling the payment instruments that we labeled as \cash," and these di
erences

could have important implications for our results.

When thinking about the welfare implications of di
erent parameter values, one has to

look carefully at the utility of all four groups in the model: (i) low-income cash users, (ii) low-

income card users, (iii) high-income cash users and (iv) high-income card users. The di
erent

parameter values considered below lead to di
erent estimates of the transfers between these

49

groups. In general, since our social welfare function is utilitarian, a redistribution to groups

with higher marginal utility will be desirable. With our concave individual utility functions,

in card users' utility will raise their marginal utility above cash users' within their respective

income groups.

high-income group (see equation (14)) and (ii) a higher average marginal utility of card

card-payer transfer will amplify the redistribution of income between the income groups as

well. Intuitively, there will be more card payers who underpay in the high-income group,

so the cash payers (in both income categories) will have to overpay by more, but with the

result in a cross-subsidy from low-income households to their high-income counterparts. For

concave utility functions, this redistribution will lower total consumer welfare. At the same

users to card users within the high-income group. Remember that in both income groups

until the marginal utilities of cash and card users within the income groups are equalized.

redistribution of income from low- to high-income groups.

consumer welfare function. The mean change in the consumer welfare function has the exact

50

of the consumer welfare function drastically, so we expect our results to remain robust to

stays fairly constant.

0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3

11.7

11.8

11.9

12

12.1

12.2

12.3

Percentage (%)

Change in consumer welfare compared to benchmark

Mean change

0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3

−20

−10

0

10

20

Dollar billions

Change of XL

leads to a relatively higher number of card payers among the rich, and thus more of the cash-

to-card-payer redistribution becomes also low-income-to-high-income redistribution. Since

curtail the amount of cash-to-card-payer redistribution.

51

panel of Figure 12 suggests that the shape of the consumer welfare function does not change

@

=

S

=

S

income households' contribution to the costs imposed and to the costs paid by roughly the

same amount. A rise in the cost of handling cash leads to a redistribution from card to cash

payers, just as the increase in the merchant fee leads to a transfer from cash payers to card

payers. Again, the no-surcharge rule forces merchants to recover the higher costs imposed by

users will increase, even though their purchases do not impose any additional costs to the

merchants. Since this transfer means a redistribution from high- to low-income households

between the income groups. As can be seen from Figure 11, however, this redistribution can

fee to redirect some of the transfer to low-income households back to high-income households.

52

0.5 1 1.5

11.8

11.9

12

12.1

12.2

Percentage (%)

Change in consumer welfare compared to benchmark

Mean change

0.5 1 1.5

0

15

Dollar billions

Change in XL

still not warrant a positive merchant fee to maximize consumer welfare. Also, as noted above,

for high cash-handling costs the optimal merchant fee changes markedly with di
erent values

the two income groups) increases the between-income group redistribution. If there were no

redistribution between income groups, the transfer resulting from cash-handling costs would

decrease welfare, since it would channel income from (high marginal utility) card payers to

more desirable, as it becomes a subsidy from high-income to low-income households, while

the redistribution caused by the merchant fee becomes less desirable, since it works in the

Cash-handling costs play an important role in determining the markup. Because of the

high fraction of cash payers (approximately 86 percent in the low- and 69 percent in the high-

53

as a function of cash-handling costs and the merchant fee. Note that while the merchant

fee goes from 0 to 5 percent, cash-handling costs vary only between 0.5 and 1.6 percent.

Keeping this in mind, Figure 13 shows that the markup is almost ve times more responsive

Appendix D Discussions of the NSR

(NSR). Under the NSR, merchants sign an agreement under which they cannot charge con-

sumers an additional fee for using a card. Over the years, formal NSR agreements have been

declared illegal by several antitrust authorities but not in the United States. Most merchants

in the United States still do not impose a surcharge on card payments and many do not give

discounts for cash payments. Bolt and van Renselaar (2009) provide an empirical analysis

of the e
ect of surcharging card payments on actual payment behavior in the Netherlands,

where surcharging is currently allowed.

54

There are a number of explanations for why merchants do not surcharge buyers for card

payments, despite having to pay a high fee for each card transaction.

Buyers may suspect that the sole purpose of a card surcharge is to enhance merchants'

pro t with no cost justi cation. Clearly, educating consumers may solve this problem.

a surcharge on cards may require placing two labels. By itself, this should not be a

big problem; however, when a sale is declared, merchants will have diculties with

marking down di
erent prices associated with the di
erent means of payment.

for merchants, in which no merchant can pro tably deviate by refusing to accept card

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