An empirical analysis of ownership multihoming and usage

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					An empirical analysis of ownership multihoming and
        usage multihoming of credit cards


          Exploiting an extensive dataset on Chinese credit card holders, we analyze the de-
      terminants of credit card multihoming behavior of different types of credit card holders
      with a nested logit model. The top level decision is on the usage type; not using the
      card, only transacting or both transacting and revolving. The bottom level is the own-
      ership and usage multihoming decision. Higher merchant acceptance, ownership of a
      debit card and being a credit card holder for a longer period all positively impact the
      conditional probability to multihome, while the reverse is true for having a loan.

1    Introduction
This paper analyses the determinants of credit card multi-homing behavior by different types
of credit card holders by exploiting a unique dataset on Chinese credit card holders. The term
multihoming is introduced in the literature on two-sided markets (e.g. Rochet & Tirole 2003)
to indicate that consumers (or merchants) use credit cards of multiple credit card associa-
tions. When a consumer only uses one credit card he is said to singlehome. The degree of
multihoming on one side of the market has an important impact on the market power that the
platform has on the other side of the market.
    Rysman (2007) has shown that while many consumers in the U.S. hold cards of different
credit card associations, they tend to concentrate their credit card spending on a single plat-
form; in other words, ownership multihoming does not necessarily implicate that a consumer
will also multihome in usage. One possible explanation is that although consumers have a
preferred platform, they are also willing to use a less-preferred platform when merchants do
not accept the preferred card. Even when the less-preferred card is not used, consumers value
the option it offers in terms of having an alternative available when the preferred card is not

accepted. If this option value is sufficiently high, the consumer will decide to multihome in
    The two-sided market literature only looks at the payment function of the credit card;
the decision to hold none, one or more credit cards is solely based on the expected value of
the option to use the cards for payment purposes. A credit card, of course, also has another
function: at the end of each payment period (typically one month), the credit card holder
is only required to make a minimum payment. The remaining balance is revolved to the
next period at the cost of an interest charge determined by the card holder’s bank. When
deciding on ownership multihoming, the consumer also takes into account the value of the
option to use the card for borrowing purposes. When a consumer values both the payment
and the borrowing option of the credit card, we expect that he is more likely to hold multiple
credit cards; the preferred card for transactions, does not necessarily offer a low credit card
rate. The actual circumstances the credit card holder is in, determine whether he will use the
options of the credit cards he holds.
    The dataset we use is both unique and extensive: it has data on more than hundred thou-
sand Chinese credit card holders. The empirical analysis is based on the estimation of a
nested multinomial logit model. The top level decision is on usage type: a consumer has the
choice between not using the credit cards, only using the cards for payments and using the
card for both payments and borrowing. Conditional on this decision, the consumer decides
on multihoming in ownership and in usage. We find that holding a debit card, being a long
time credit card user and living in a large city are positively correlated to the probability
of multihoming for both transacting and revolving credit card holders. Having a loan has a
negative effect on the conditional probability to multihome.
    The paper is structured as follows. In the next two sections the two different functions
of the credit card are discussed separately and the multihoming decision based on both func-
tions is described. Section 4 connects both functions and the implications for multihoming
decisions. Section 5 gives the detail of the methodology used for the empirical analysis. The
dataset used for the analysis is described in the next section. The decision and explanatory
variables are defined in this section and the summary statistics are briefly discussed. The
results are reported in section 7, followed by a concluding section.

2    Credit cards as a payment instrument
In a typical credit card transaction five participants are involved: the consumer (cardholder),
the consumer’s bank (or issuer), the merchant, the merchant’s bank (or acquirer) and the credit
card network (e.g. Visa, MasterCard). The merchant receives the funds from the merchant’s
bank at the cost of paying a merchant discount fee. Similarly the acquirer pays an interchange
fee, set by the card network, to the issuing bank. At the end of each payment period (usually
one month), the consumer receives an invoice for all credit card purchases in that period.
Paying by credit card thus implies that the consumer enjoys an interest-free period or grace
period. The per transaction fee charged to the consumer by the issuer is often zero or even
negative when the consumer enjoys benefits such as frequent flyer miles, extended guarantees
and warranties on their purchases and car rental and travel insurance. However, a fixed annual
fee is not uncommon.
    The credit card market is a typical example of a two-sided market. Rochet & Tirole (2006)
define two-sided markets as “markets in which one or several platforms enable interactions
between end-users and try to get the two (or multiple) sides “on board” by appropriately
charging each side”. An alternative definition focuses on the presence of cross-group ex-
ternalities or “the net utility on side i increases with the number of members on side j”. In
the credit card market, the end-users are the merchants and consumers. The level of the
interchange fee determines the level of fees faced by merchants and cardholders. A higher
interaction fee raises the costs of acquirers, resulting in higher merchant discounts and lower
merchant acceptance, and it lowers the costs for issuers, resulting in lower consumer fees (or
higher card benefits) and encouraging card ownership and usage. By appropriately setting
the interchange fee, the credit card network can determine the total number of transactions
on the platform.
    Initially the literature on two-sided markets focused on monopolistic platforms and more
specifically on the balancing of prices to get the two sides on board. The analysis of com-
petition between platforms is complicated by the possibility of multi-homing. The prices on
one side of the market depend on the degree of multihoming on the other side. For example,
in a situation with two credit card associations, if one platform reduces its merchant fee mer-
chants will be tempted to turn down the more costly card of the other platform when a large
fraction of cardholders multihomes. In other words, multihoming of cardholders intensifies
competition on the other side (Rochet & Tirole 2003).
    The paper of Rysman (2007) is one of the few empirical studies of credit card holders’
multihoming behavior. Based on the analysis of a dataset on U.S. consumers’ credit card us-
age in the period 1998-2001 he concludes that although two-thirds of the consumer hold cards

from different networks, only few of them actually use all cards. Consumers tend to concen-
trate their spending on a single payment network. The choice of this network is correlated
with the amount of local merchant acceptance of that network. This shows that multihom-
ing can be considered at two levels: ownership and usage and that ownership multihoming
does not necessarily imply that all the cards will actually be used or in other words that the
cardholder will also multihome in usage.
    In the context of a credit card as a payment instrument, the decision to hold a credit card
is based on the trade-off between the annual fee and the expected net-benefits of holding the
card or put differently the valuation of the option to use the card for transactions. The payment
option value of a given card is determined by two factors: the merchant acceptance rate
and the expected transactional net-benefit of using the credit card. The higher the merchant
acceptance rate, the more opportunities the cardholder has to use the card and consequently
the higher the expected net-benefit of the card. The transactional net-benefit is the difference
between the per transaction fee (which can be negative: see before) and the gross utility from
a payment with credit card. If the transactional net-benefit of the credit card is higher than
those of other available payment instruments (e.g. cash, cheques, debit cards), the cardholder
will prefer to use the credit card for the transaction. In sum, a high merchant acceptance rate
and high expected transactional net-benefits make the credit card more attractive in terms
of both more potential transactions and a higher utility from each of those transactions; the
consumer highly values holding card and thus the option to use the card for payments.
    The merchant acceptance rate and the transactional benefits are not the same for all con-
sumers and for one consumer they may not be the same for all transactions. First look at the
transactional benefits: different consumers have different preferences for the available pay-
ment instruments. For example, one consumer can have a large negative utility of going to an
ATM for cash withdrawal and consequently prefers using a credit card to using cash for pay-
ment purposes, while another consumer lives very close to an ATM and has a smaller utility
loss of visiting it; his transactional benefit of using a credit card compared to using cash is
lower. Also for the same consumer the benefits of using different payment instruments can
differ between transactions; if the price to be paid at a merchant is unexpectedly high and the
consumer does not have enough cash in his wallet, he can use his credit card even when in
other circumstances he prefers using cash. Another example follows from the comparison of
the benefits of credit cards and debit cards. They share a number of common characteristics,
but the debit card does not provide an interest free period. However, a consumer does not al-
ways experience this as a negative feature; the immediate credit of his deposit account when
using a debit card can be an advantage in terms of avoiding late payments and the associated
penalty fees and loosing track of the total liquidity position. For large purchases this disad-

vantage of credit cards versus debit cards may be offset by the larger benefit of the interest
free period.
    Secondly, merchant acceptance of credit cards of a given credit card network may be
not the same in all regions and consequently consumers from different regions are confronted
with different merchant acceptance rates. If a consumer travels a lot, he will not only take into
account the merchants acceptance rate in his own regions, but also the ones in the regions he
plans to visit. Merchants selling different types of goods also can have different preferences
for credit card transactions, and consequently the acceptance rates between sectors might also
be heterogeneous.
    In conclusion, the option to use credit cards as a payment instrument depends on the
expectations about merchant acceptance and transactional benefits; the magnitude of both
depends on the consumer characteristics and on the type of transactions. The consumer will
decide to apply for a credit card when the option value it offers is larger than the annual
fee. The ownership multihoming decision depends on the option value an additional card
offers, which is lower than the one of the first card. Consumers’ expectations on the usage
intensity of this card are lower than those of the first card. The additional card will only be
used when it is not possible to use the more preferred card; for example when the preferred
card is not accepted or when the credit limit is exceeded. The actual usage of the credit cards
depends on the situation the consumer is confronted with; he can either use all cards (usage
multihoming), only one card (usage singlehoming) or not use his cards at all.

3    Credit cards as a credit instrument
In the previous section, we implicitly assumed that the credit cards are only used for payment
purposes. At the end of each payment period, the cardholder pays off the balance in full.
This type of cardholder is known as a convenience user or transactor. However, a credit card
holder is only required to make a minimum payment; the remaining balance is revolved to
the next period at the cost of an interest charged on the outstanding balance. Consumer that
use the credit function are referred to as revolvers.
    As a credit instrument, the credit card offers the possibility of uncollateralized borrowing.
This type of borrowing allows for a lot of freedom. The consumer can decide on the amount
of borrowing, restricted by the credit limit, on the timing of borrowing and on the size and
timing of the repayments, although a minimum payment is required at the end of each pay-
ment period. Therefore borrowing on credit cards is more flexible than its closest substitute;
a short to medium term bank loan. However the credit card interest rate often is higher than

the ones on bank loans; the consumer pays a price for the higher flexibility. The consumer
will choose to borrow on credit cards when his valuation of the higher flexibility of credit
card borrowing outweighs the increased interest costs.
    Park (1997 & 2004) provides another explanation why consumers prefer credit cards to
loans. The default probability of consumers changes over time. Card issuers, of course, can
adapt the interest rates when the cardholder becomes riskier, but continuously monitoring
the cardholders’ creditworthiness in unfeasible. Therefore, cardholders can borrow before
card issuers raise the credit card rates, allowing him to borrow at an interest rate that does
not correct for his increased riskiness. However, when applying for a loan, the bank will
evaluate the present creditworthiness and consequently, the consumer needs to pay a price
for his riskiness. When a consumer becomes high-risk, he will prefer to borrow on credit
cards. The issuer calculates the interest rate taken into account the expected riskiness of the
mix of borrowers. As a result, the interest rate on credit cards will be higher than the rate on
bank loans for low-risk consumers. The transaction costs on loans are generally higher than
those for obtaining a credit card. If the transaction costs for loans are high enough, even a
low-risk consumer will prefer to borrow on credit cards.
    The above shows that a consumer has different reasons to prefer credit card borrowing
to obtaining a loan. The consumers’ valuation of the option to borrow offered by a credit
card increases when his valuation of borrowing on credit cards relative to loans increases and
when his probability to have borrowing needs increases. A consumer will decide to obtain a
credit card when this option of borrowing is high enough so as to offset the annual card fee.
The main factor in his choice of credit card, will be the credit card rate; the platform is only
of lesser importance. Comparable to the case of the credit card as a payment instrument, also
here the expected value of an additional credit card is lower than that of the first one; since
the consumer already has a credit card and thus a credit line, the issuer will only offer a credit
card with a higher interest rate, decreasing its attractiveness relative to loans. The consumer
values the extra credit line the card offers, but will only use it when the limit of the first card
is reached. The total number of credit cards and accordingly the total credit line a consumer
can obtain is restricted by its creditworthiness. The actual usage depends on the realization
of the borrowing needs and the situation of the consumer at that time.

4     Credit cards as a bundle of payment and credit instru-
Since a credit card is a bundle of a payment instrument and a credit instrument, ownership
multihoming is based on the valuation of both the option for payment and the option for bor-
rowing that the credit cards offer. Because consumers are heterogeneous in the valuation of
both options (as is described before), their ownership multihoming decisions will be different
and even when the same multihoming decision is made, the underlying reasons can be dif-
ferent. When consumers only value the option for borrowing or only the option for payment,
we refer to the previous sections for the analysis of their multihoming decisions. However,
consumer may have a positive option value for both functions. Since the preferred card for
payments and the card with the lowest interest rate are not always the same, we expect that
they will be more tempted to obtain multiple cards; one for revolving and one for transacting.
Again, usage multihoming depends on the actual realization of the parameters that determine
whether one wants to use a card (e.g. if there is a borrowing need, or for the “less-preferred
card” if the consumer needs to buy goods from a merchant that does not accept his preferred

5     Methodology
To analyze the multihoming behavior of different types of consumers, we use a nested multi-
nomial logit model (NMNL). We first describe the nesting in the model, based on the decision
tree, and then give the econometric details of the model and conclude this section with a note
on the estimation of marginal effects.

5.1    Decision tree
From the previous sections, we can conclude that consumers will base their decision to mul-
tihome or singlehome on expectations on how the cards will be used. Figure 1 represents
the two-step decision process of the cardholders. The consumers will first decide on the us-
age type (the top “branches”) and conditional on that choice, determine their multihoming
behavior. Because we can not observe the consumers’ expectations, we will instead look at
the actual usage type; the credit card holder can either only use the cards for transactions and
always pay off the balance in full (transactor), or he can revolve his balance (revolver). Some
consumers do not use their cards at all (inactive).

     Secondly, conditional on the usage type chosen at the first level, the consumer decides
on ownership multihoming and usage multihoming. The choice for an inactive card holder
is limited to the one between ownership singlehoming and ownership multihoming. Since he
does not use his cards, there is no usage multihoming decision. A transactor can either hold
one card or multiple cards, and in the latter case he uses either one or more cards. Compared
to a transactor, a revolver has an extra choice; two types of multihoming in both ownership
and usage are possible (indicated as type 1 and type 2 in figure 1). Type 2 represent the
decision to use multiple cards for revolving, while type 1 indicates that one card is used for
revolving, while the other will be used solely for transacting.

                                     Figure 1: Decision tree

5.2   Econometric model
The NMNL procedure allows groups of alternatives to be similar to each other in an un-
observed way or in other words to have correlated error terms. As described before, the
consumer first chooses its usage type; three different choices are available represented by i
(i=1, 2, 3). Conditional on the type that was chosen, in the second step he has a number of
available choices for multihoming: j = 1, ...Ji . We assume that the utility from choosing
usage type i and multihoming type j depend on the explanatory variables x in the following

                       Vi j = x βi j + εi j with i = 1, ..., 3 and j = 1, ...Ji

The consumer chooses the alternative that gives him the highest utility. We assume that the
error terms follow a type of generalized extreme-value distribution as described byMcFadden
(1978). Under these assumptions the joint probability of observing a consumer choosing
usage type i and multihoming type j can be written as:
                                                        eVi j
                                     Pi j =                  J|k
                                          ∑i ∑m=1 eVkm
However, we are interested in the multihoming behavior, given the choice for a usage type or
in other words, the conditional probability of choosing j given i.
                                                        eVi j
                                        Pj|i =         J|i
                                                  ∑m=1 eVi j
Now define the inclusive value as:
                                        IVi = ln       ∑ eVim
Then the probability of choosing usage type i can be written as:
                                                 eτi IVi
                                        Pi =
                                               ∑i eτk IVk
    The parameters βi j and τi are estimated by working backwards on the decision tree. First,
the βi j ’s are estimated for each usage type decision by a multinomial logit of the membership
choice on the explanatory variables. The estimated βi j ’s are then used to construct the in-
clusive values for each usage type, using the expression for the inclusive value given above.
In the second step the τi ’s are estimated by regressing the usage type choice on the inclusive

5.3    Estimating the marginal effects
After the description of the dataset and explanatory variables in the next section, the results
of the estimation of our model will be given. However, instead of reporting the βi j ’s , we will
present the marginal effects of the explanatory variables on both the conditional probability,
Pj|i , and the unconditional probability Pi . As the following equation shows, the marginal
effect does not always have the same sign as βi j :

                                          = Pj|i βi j(k) − βi(k)
                                with βi(k) =   ∑ Pm|iβim(k)

6    Data description
To analyze the multihoming behavior, we use a very rich dataset consisting of information
on 125 863 consumers of a large Chinese bank in 2005. The dataset is a sample of the credit
card holders of this bank. The information is not limited to the credit cards, debit cards and
loans the consumer has at this bank, but also at the other banks.
     The percentages at the usage type node in figure 1 give the percentage of consumers
that choose this usage type. The largest group is the one of the transactors; these are the
consumers that used one or more credit cards for payments in the last 12 months and paid
off their balance in full at the end of each payment period. About one third of the consumers
had a revolving balance at some point in the past 12 months on at least one card, while in the
same period a quarter of the cardholders did not use their card at all.
     The percentages at the ownership and usage multihoming nodes, give the percentage of
users that choose this type of homing behavior, conditional on the usage type choice in the
top nodes. As could be expected, the majority of the inactive cardholders singlehomes. More
than two thirds of the transactors singlehome, and the group of transactors using multiple
cards is larger than the one of transactors that hold multiple cards but only use one. The
situation for revolvers is a bit different. The fraction of ownership singlehomers is lower (a
little less than half of the revolvers), while the second largest group are the revolvers that
multihome in ownership and use one card for revolving and the other for transacting. These
findings are consistent with the assumption that the consumers who value both functions of
the credit card will be more inclined to multihome in ownership as well as in usage.
     Table 1 gives the definitions of the explanatory variables and table 2 presents the summary
statistics of these variables, for each of the different choices. Income is highest for the group
of revolvers, especially for those who hold multiple cards. The latter can be partly explained
by a supply effect; higher income consumers are considered to be more creditworthy and
banks are more inclined to approve their applications for extra credit cards (and consequently
a higher credit limit) than for lower income users.
     The group of revolving credit card holders is the youngest of the three groups; this is
consistent with the idea that younger cardholders borrow now in anticipation of higher future
incomes. The fact that the inactive users are older on average also has a logical explana-
tion: credit cards are relatively new in China and older consumers do not easily change their
payment habits. The interaction variable of gender and marital status indicates that singles
are more likely to revolve than the cardholders that are married. The dummy variable city is
included to control for merchant acceptance; we expect that this will be higher in the more
populated regions. A smaller fraction of the inactive users lives in a large city compared to

transactors and revolvers.
    The group of multihoming consumers has a larger fraction of debit card holders than
the one that singlehomes and more revolving than transacting cardholders also hold a debit
card. This suggests that consumers that highly value credit cards also value debit cards. The
fraction of credit card holders that also has a short loan is very small, while most of them
have a long term loan. The former can be a substitute for credit card revolving, while the
latter is usually a collateralised loan and controls for the fact that a consumer that needs to
repay a loan has less income left to spend for other purposes. The variable maxline is the
credit limit on the consumer’s card with the highest limit. The age of the oldest card proxies
for the time that someone is a credit card holder.

7    Results
Table 3 gives the marginal effects of the explanatory variables on the probability of choosing a
given usage type, calculated at the sample mean. Almost all variables are highly significant,
which can be explained by the high number of observations used to estimate the model.
When interpreting the results one should not focus on this statistical significance, but on the
economical significance. An extra 1 000 RMB of yearly income increases the probability to
transact and to revolve with only 0,03 percentage points. Controlling for other factors, income
has a very limited impact on the usage type decision. The coefficients for age indicate that an
older person has a higher probability of being inactive and to a lesser extent also to transact
than to revolve. Most of the coefficient for the gender*marital status variables are not (highly)
significant and their effect on the probabilities is only of lesser importance.
     At the sample mean, living in a large city increases the probability of both revolving and
transacting. The higher merchant acceptance in the most populated regions seems to activate
credit card holders. Holding a debit card increases the probability of choosing to transact
with 3.73 percentage points confirming that credit card holders with a high valuation of credit
cards also highly value debit cards. The short term loan variable has a positive impact on the
probability to revolve; consumers with a short term need to borrow will use both credit cards
and short term loans. However, the same is not true for having a long term loan. The variable
age oldest card indicates that the longer someone is a card holder, the more likely it is that he
will revolve. However, we also see a positive marginal effect for inactive credit card users.
It is possible that the age of the oldest card is not a good proxy for the time during which
someone is a credit card holder; it is not unreasonable to assume that an active credit card
holder will more often switch its cards, because he has a larger benefit from switching than

                              Table 1: Variable definitions

Variable                    Definition
Dependent variables
Type                        Top level of nested logit model:
                            Inactive, transactor or revolver
Alternative                 Bottom level of nested logit model:
                            Single vs multiple holding
                            Single vs multiple use

Explanatory variables
Income                      Yearly income (thousands RMB)
Age                         Age of the person (in 10 years)
Gender and marital status   Dummy variables for gender and marital status:
Singlemale                  Not married and male
Singlefemale                Not married and female
Marriedmale                 Married and male
Marriedfemale               Married and female
City                        1 if live in a city with population larger than 1 000 000
                            0 if not
Has debit                   1 if person has debit card(s)
                            0 if person has no debit cards
Hasshortloan                1 if person has loans with total duration 2 years or less
                            0 if not
Haslongloan                 1 if person has loans with total duration of more than
                            2 years
                            0 if not
Maxline                     The credit line of the credit card which has the highest
                            credit line in thousands RMB
Age oldest card             Age of the oldest credit card in years

                                             Table 2: Summary statistics for explanatory variables
     Variable                    Inactive                          Transactors                                     Revolvers                        Total
                       Single    Multiple    Total   Single    Multiple   Multiple    Total   Single    Multiple   Multiple    Multiple    Total
                       holding   holding             holding   holding    holding             holding   holding    holding     holding
                                                     Single     Single    Multiple            Single     Single    Multiple    Multiple
                                                      use        use        use                use        use        use         use
                                                                                                                   (type 1)    (type 2)
     Income            53.23      61.67     53.91    60.68      62.88      58.27     60.37    58.13      76.71      69.68       74.42      65.16    60.29
     Income2           7834.7    8905.4     7921.5   9942.2    10627.5    8980.2     9794.2   8998.3    14357.8    12496.9     13417.2    11058.3   9730.3
     Age                3.85      3.884     3.853    3.775      3.666      3.582     3.717      3.6      3.548      3.441       3.454      3.528    3.689
     Age2              15.41      15.81     15.44    14.85      14.02      13.41     14.41     13.5      13.15      12.35       12.45      12.98     14.2

     Singlemale        17.10%    17.00%     17.10%   20.10%    18.20%     19.00%     19.60%   23.70%    26.60%     24.10%      30.60%     24.70%    20.60%
     Singlefemale      7.16%      8.20%     7.25%    9.75%      9.93%     11.40%     10.10%   10.20%    12.90%     14.50%      12.80%     12.10%    10.10%
     Marriedmale       54.80%    51.60%     54.50%   49.00%    46.60%     42.00%     47.10%   47.60%    40.10%     38.00%      40.40%     43.00%    47.60%
     Marriedfemale     21.00%    23.20%     21.20%   21.20%    25.20%     27.60%     23.20%   18.50%    20.50%     23.40%      16.20%     20.20%    21.70%
     City              9.36%      7.33%     9.19%    11.20%     8.57%     12.20%     11.10%   11.30%     8.92%     11.00%       8.69%     10.70%    10.50%
     Has debit         22.40%    31.60%     23.10%   22.40%    32.90%     36.90%     27.10%   25.20%    31.90%     36.60%      34.10%     30.50%    27.20%
     Hasshortloan      5.31%      3.08%     5.13%    5.10%      4.03%      3.51%     4.60%    7.14%      4.75%      4.59%       7.32%     6.07%     5.22%
     Haslongloan       97.50%    84.90%     96.50%   92.30%    69.90%     66.40%     83.50%   92.90%    80.40%     67.20%      73.60%     81.30%    86.10%
     Maxline           10.31      16.08     10.78    8.937      14.87      18.4      11.87    11.87      19.12      21.69       17.7       16.38    13.09
     Age oldest card   1.485      2.21      1.544    0.611      1.935      1.364     0.944    1.043      2.035      1.687       1.787      1.417    1.256
do the inactive credit card holders.
    Tables 4 to 6 give the marginal effects of the explanatory variables of the probability of
the homing choices, conditional on the usage type choice. Although statistically highly sig-
nificant, the income variable only has a very limited impact on the multihoming choices for
all usage types. An increase in age of one year increases the probability of singlehoming for
all usage types, while a decrease significantly increases the probability of ownership multi-
homing combined with using one card for transacting and one for revolving, conditional on
the choice to revolve. The gender*marital status variables only have a small effect on the
conditional probabilities and are in general not highly significant.
    For transactors, the probability of multihoming in both ownership and usage is signif-
icantly higher for a cardholder living in a large city. The higher merchant acceptance in
higher populated regions encourages to credit card usage for payments. For revolvers, living
in a large city increases the probability of using one card for transactions and one for revolv-
ing with 7.53 percentage points. When merchant acceptance is higher, the card can be used
more often for transactions and consequently the transactional benefits that the card offers
will be more important. On the other hand, the credit card holder will also revolve and thus
wants a credit card with a low credit card rate. It is beneficial for the card holder to have two
cards; one for transacting and one mainly for revolving.
    The effects of debit cards on the conditional probabilities are comparable to those of city.
A plausible explanation is that credit card holders with a high valuation for the transaction
function of credit cards, also highly value debit cards and will use both credit and debit
cards, depending on the situation. Having a short term loan and having a long term loan both
increase the conditional probability to singlehome for both transactors and revolvers. One
possible explanation is that having a loan implies liquidity constraints, a lower creditworthi-
ness and consequently a lower probability to be granted an extra credit card. Given the choice
to revolve on credit cards, a credit card holder is more likely to singlehome if he has a short
term loan. He does value the credit function of the credit card, but not enough to borrow the
full amount on credit cards rather than a short term loan.
    The age of the oldest card has a negative effect on the conditional probability to single-
home for both usage types, while all types of multihoming and especially usage multihoming
are more likely when the age of the oldest card is higher. This suggest that the longer some-
one owns credit cards, the more likely it is that he will get an extra credit card and the more
likely that he uses both of these cards.

Table 3: Marginal effects of the explanatory variables on Pr(i) evaluated at sample means

                                Inactive               Transactor        Revolver
              Income            -0.0006***             0.0003***         0.0003***
                                (0.0000)               (0.0000)          (0.0000)
              Income  2         0.0000***              -0.0000***        -0.0000***
                                (0.0000)               (0.0000)          (0.0000)
              Age               0.1599***              0.1002***         -0.2600***
                                (0.0146)               (0.0173)          (0.0168)
              Age 2             -0.0122***             -0.0094***        0.0216***
                                (0.0018)               (0.0022)          (0.0021)
              Singlefemale (d)  -0.0172***             0.0075            0.0097
                                (0.0050)               (0.0058)          (0.0054)
              Marriedmale (d)   0.0422***              -0.0091*          -0.0332***
                                (0.0037)               (0.0044)          (0.0042)
              Marriedfemale (d) 0.0119**               0.0105*           -0.0224***
                                (0.0043)               (0.0050)          (0.0046)
              City (d)          -0.0279***             0.0163***         0.0116*
                                (0.0039)               (0.0049)          (0.0048)
              Has debit (d)     -0.0562***             0.0373***         0.0189***
                                (0.0027)               (0.0035)          (0.0033)
              Hasshortloan (d)  0.0630***              -0.0773***        0.0142*
                                (0.0066)               (0.0066)          (0.0066)
              Haslongloan (d)   0.2180***              -0.1187***        -0.0993***
                                (0.0024)               (0.0046)          (0.0045)
              Maxline           -0.0066***             0.0014***         0.0052***
                                (0.0001)               (0.0001)          (0.0001)
              Age oldest card   0.1586***              -0.2380***        0.0794***
                                (0.0017)               (0.0024)          (0.0020)
              Standard errors between brackets
              ***p < 0.01, **p < 0.05, *p < 0.10.
              (d) is for discrete change of dummy variable from 0 to 1

Table 4: Marginal effects of the explanatory variables on Pr(i|inactive)

                          Single holding             Multiple holding
        Income            -0.0000                    0.0000
                          (0.0000)                   (0.0000)
        Income  2         0.0000*                    -0.0000*
                          (0.0000)                   (0.0000)
        Age               0.0558***                  -0.0558***
                          (0.0108)                   (0.0108)
        Age 2             -0.0065***                 0.0065***
                          (0.0013)                   (0.0013)
        Singlefemale (d)  -0.0039                    0.0039
                          (0.0047)                   (0.0047)
        Marriedmale (d)   -0.0012                    0.0012
                          (0.0032)                   (0.0032)
        Marriedfemale (d) -0.0090*                   0.0090*
                          (0.0039)                   (0.0039)
        City (d)          -0.0031                    0.0031
                          (0.0040)                   (0.0040)
        Has debit (d)     -0.0061*                   0.0061*
                          (0.0025)                   (0.0025)
        Hasshortloan (d)  0.0422***                  -0.0422***
                          (0.0017)                   (0.0017)
        Haslongloan (d)   0.4381***                  -0.4381***
                          (0.0213)                   (0.0213)
        Maxline           -0.0015***                 0.0015***
                          (0.0001)                   (0.0001)
        Age oldest card   -0.0878***                 0.0878***
                          (0.0022)                   (0.0022)
        Standard errors between brackets
        ***p < 0.01, **p < 0.05, *p < 0.10.
        (d) is for discrete change of dummy variable from 0 to 1

Table 5: Marginal effects of the explanatory variables on Pr(i|transactor)

                  Single holding             Multiple holding   Multiple holding
                    Single use                 Single use        Multiple use
Income              0.0007***                 -0.0001***         -0.0005***
                     (0.0001)                   (0.0000)           (0.0001)
Income2            -0.0000***                   0.0000*           0.0000***
                     (0.0000)                   (0.0000)           (0.0000)
Age                 0.1701***                    -0.0171         -0.1531***
                     (0.0313)                   (0.0148)           (0.0257)
Age 2               -0.0124**                    0.0009           0.0116***
                     (0.0040)                   (0.0018)           (0.0033)
Singlefemale (d)    -0.0346**                    0.0080            0.0266**
                     (0.0108)                   (0.0054)           (0.0090)
Marriedmale (d)      -0.0093                     0.0069             0.0024
                     (0.0083)                   (0.0040)           (0.0069)
Marriedfemale (d)  -0.0889***                  0.0189***          0.0700***
                     (0.0094)                   (0.0047)           (0.0080)
City (d)           -0.0573***                    -0.0077          0.0650***
                     (0.0088)                   (0.0041)           (0.0078)
Has debit (d)      -0.0709***                    -0.0022          0.0732***
                     (0.0064)                   (0.0028)           (0.0054)
Hasshortloan (d)    0.1678***                 -0.0445***         -0.1234***
                     (0.0094)                   (0.0040)           (0.0076)
Haslongloan (d)     0.4555***                 -0.1255***         -0.3301***
                     (0.0066)                   (0.0049)           (0.0066)
Maxline            -0.0122***                  0.0023***          0.0099***
                     (0.0003)                   (0.0001)           (0.0002)
Age oldest card    -0.4073***                  0.1450***          0.2623***
                     (0.0052)                   (0.0024)           (0.0041)
Standard errors between brackets
***p < 0.01, **p < 0.05, *p < 0.10
(d) is for discrete change of dummy variable from 0 to 1

           Table 6: Marginal effects of the explanatory variables on Pr(i|revolver)

                        Single holding       Multiple holding   Multiple holding   Multiple holding
                          Single use           Single use        Multiple use       Multiple use
                                                                    (type 1)           (type 2)
Income                    -0.0005***            0.0002***            0.0001          0.0002***
                            (0.0001)              (0.0000)         (0.0001)           (0.0000)
Income2                    0.0000***            -0.0000***          -0.0000         -0.0000***
                            (0.0000)              (0.0000)         (0.0000)           (0.0000)
Age                        0.4164***            -0.0542***       -0.3041***         -0.0581***
                            (0.0354)              (0.0163)         (0.0315)           (0.0170)
Age2                      -0.0427***            0.0070***         0.0294***           0.0063**
                            (0.0045)              (0.0021)         (0.0040)           (0.0022)
Singlefemale (d)          -0.0358***               -0.0001        0.0491***          -0.0133**
                            (0.0103)              (0.0050)         (0.0096)           (0.0046)
Marriedmale (d)             0.0250**             -0.0108**           0.0034         -0.0176***
                            (0.0084)              (0.0041)         (0.0077)           (0.0040)
Marriedfemale (d)         -0.0450***               -0.0042        0.0773***         -0.0281***
                            (0.0094)              (0.0046)         (0.0089)           (0.0041)
City (d)                  -0.0596***               -0.0043        0.0753***           -0.0114*
                            (0.0091)              (0.0049)         (0.0090)           (0.0048)
Has debit (d)             -0.0849***               -0.0044        0.0841***             0.0052
                            (0.0065)              (0.0032)         (0.0060)           (0.0033)
Hasshortloan (d)           0.1653***            -0.0239***       -0.1367***            -0.0047
                            (0.0126)              (0.0056)         (0.0100)           (0.0058)
Haslongloan (d)            0.4322***            -0.0203***       -0.3582***         -0.0536***
                            (0.0048)              (0.0041)         (0.0065)           (0.0045)
Maxline                   -0.0097***            0.0008***         0.0081***          0.0008***
                            (0.0003)              (0.0001)         (0.0002)           (0.0001)
Age oldest card           -0.3367***            0.0809***         0.1972***          0.0586***
                            (0.0047)              (0.0017)         (0.0037)           (0.0018)
Standard errors between brackets
***p < 0.01, **p < 0.05, *p < 0.10
(d) is for discrete change of dummy variable from 0 to 1

8    Conclusion
We analyzed the multihoming behavior of credit card holders, conditional on the usage type
decision they made, using a rich dataset on Chinese credit card holders. We argue that when
making an ownership decision, consumers take into account the value of the option a credit
card offers in terms of options for payment and credit. The actual usage depends on the
circumstances the credit card holder is in.
    A NMNL model was estimated, in which the first decision was the usage type. Credit card
holders can either use their card for transaction purposes only or they can also use the credit
function. Alternatively a user can decide to not use its cards. Conditional on this decision, the
multihoming decision is made; both in terms of ownership and usage. Explanatory variables
include person characteristics (age, income, gender,...), the ownership of a debit card, having
loans, how long someone is a cardholder and a proxy for merchant acceptance.
    We find that the largest group of credit card holders uses credit cards for payment pur-
poses only. Furthermore the multihoming decision depends on the usage type; more trans-
actors than revolvers choose to multihome. Living in a large city, and thus in a region with
higher merchant acceptance, increases the probability of multihoming both for transactors
and revolvers. Higher merchants acceptance increases the potential benefits of a credit card,
since there will be more opportunities to use it, consequently the valuation of credit cards
is higher and he will be more likely to hold multiple cards. Although debit cards and debit
cards share common characteristics, holding a debit card does not lead to less credit card use
and ownership; but on the contrary debit card holders are more likely to multihome, both
when they revolve and when they transact. Consumers that highly value credit cards also
value debit cards and vice versa; debit card ownership is positively correlated with credit
card multihoming.
    Having a loan (both short term and long term) is positively correlated with the probability
of singlehome for both usage types. An interesting fact is that when someone holds a credit
card for a longer time, he will have a higher probability of being inactive. However, when he
does decide to use credit cards, either for revolving or transacting, he will be more likely to

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