Manajemen | Fakultas Ekonomi Universitas Maritim Raja Ali Haji 073500107000000133
Journal of Business & Economic Statistics
ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20
Consumer Search Behavior in the Changing Credit
Card Market
Sougata Kerr & Lucia Dunn
To cite this article: Sougata Kerr & Lucia Dunn (2008) Consumer Search Behavior in the
Changing Credit Card Market, Journal of Business & Economic Statistics, 26:3, 345-353, DOI:
10.1198/073500107000000133
To link to this article: http://dx.doi.org/10.1198/073500107000000133
Published online: 01 Jan 2012.
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Date: 12 January 2016, At: 17:57
Consumer Search Behavior in the Changing
Credit Card Market
Sougata K ERR
Consumer Risk Modeling and Analytics, JP Morgan and Chase Co., Columbus, OH 43240
(sougata.kerr@chase.com)
Lucia D UNN
Downloaded by [Universitas Maritim Raja Ali Haji] at 17:57 12 January 2016
Department of Economics, Ohio State University, Columbus, OH 43210 (Dunn.4@osu.edu )
This article investigates whether search costs inhibit consumers from searching for lower credit card interest rates. The results provide evidence that the credit card search environment has changed since the
mid-1990s. Using the 2001 Survey of Consumer Finances, we model consumers’ propensity to search and
their probability of being denied credit simultaneously and find that larger credit card balances induce
cardholders to search more even though they face a higher probability of rejection. This result may be related to the high volume of direct solicitation, combined with disclosure requirements, which has lowered
the cost of search to find lower interest rates.
KEY WORDS: Revolving credit; Search costs; Switch costs.
1. INTRODUCTION
Credit card balance switching and the consumer search involved in this process have become important issues in the
banking community as more cardholders seek to move their
revolving credit to lower cost lenders. Throughout the 1980s
and early 1990s, research in this area tended to focus on consumers’ lack of interest rate sensitivity and the inhibiting effect
of high search costs in this market. These were among the main
reasons put forward to explain the lack of interest rate competition in the credit card market and persistent high rates in
this period. We find that consumer behavior has changed since
the early 1990s. Consumers now display more willingness to
shop around for lower rates. Easy access to rate information on
the Internet and in the large volume of mailed solicitations, as
well as disclosure requirements such as those in the Truth in
Lending Act (officially the “Fair Credit and Charge Card Disclosure Act” of 1988), have contributed to this changing environment by providing easier access to interest rate information
and thus facilitating the “search and switch” behavior of consumers. These and other factors may be partially responsible
for the more competitive environment in the 1990s credit card
market.
Here we will examine the determinants of consumer search
propensities with particular emphasis on those cardholders who
carry a high balance. High-balance cardholders are of special
interest because they potentially have the most to gain from
search; and at the same time, they face a higher probability of
rejection. Previous researchers have argued that a greater likelihood of rejection is likely to deter the search propensity of
the high-balance-carrying consumer due to substantial search
costs in this market. We will analyze (a) the effect of large balances on the consumer’s probability of credit application rejection, and (b) how these factors—large balances and rejection
probability—affect consumers’ search propensities. In testing
the search-cost hypothesis, we deal with the issue of endogeneity between consumers’ search and the likelihood of rejection
with a simultaneous equations model.
Our results show that consumers in the current credit card
market are interest-rate sensitive. Furthermore, we find no evidence that search costs deter consumer search for lower rates.
Whereas credit application rejection is found to have a dampening effect on search, the possible interest savings from a sufficient amount of balances is found to overcome the effect of
the rejection. In the next section we review the relevant literature on this market and recent changes in the market environment. Section 3 discusses our methodology and improvements
in available data. Section 4 presents our empirical results, and
Section 5 summarizes our findings and conclusions.
2. BACKGROUND AND PREVIOUS LITERATURE ON
THE CREDIT CARD MARKET
Consumer revolving credit, which includes credit card debt
as its principal component, has been the fastest growing segment of the U.S. consumer loan market in recent years (Durkin
2000). In the 1980s a peculiar feature of this market was the
lack of price competition between issuers, as credit card rates
remained high (around 18%) and downwardly sticky. This behavior was puzzling given the fact that the market was functionally deregulated by 1982 and saw the entry of nearly 4,000
firms during the ensuing decade.
Early work on credit card markets presented consumer
search, or the lack of it, as an important factor in the high
and sticky interest rates of that period. Ausubel (1991) argued
that many consumers underestimated their borrowing potential,
which made them less sensitive to interest rates. In addition to
interest rate insensitivity, he cited the inhibiting nature of high
search costs, which prevented consumer search for lower rates
and allowed issuers to keep rates high in this market. (For other
developments in search models, see Mortensen and Pissarides
1999.)
Other researchers explained the observed high levels of interest rates by pointing to various unique features of credit card
debt such as the noncollaterized characteristic of credit cards
(Mester 1994); open-ended revolving credit lines (Park 1997);
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© 2008 American Statistical Association
Journal of Business & Economic Statistics
July 2008, Vol. 26, No. 3
DOI 10.1198/073500107000000133
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346
and the liquidity services offered by credit cards under consumption uncertainty (Brito and Hartley 1995). However, the
lack of price competition was considered the dominant factor
in this literature.
The major empirical article on credit card search by Calem
and Mester (1995) used 1989 Survey of Consumer Finances
(SCF) data and found results that were consistent with consumers’ reluctance to search for lower rates due to high search
costs in this market. That research did not model consumer
search explicitly but reached this conclusion by examining the
determinants of credit card balances, one of which was consumer search. They found (a) that credit rejection is positively related to the level of balances because large outstanding balances send a signal of high risk to banks. More importantly, they found (b) that the level of credit card balances
is negatively related to search, indicating that high-balancecarrying consumers are less willing to search for lower rates.
Together these results were indicative of both consumer insensitivity to interest rates and high search costs in this market. According to the search-cost hypothesis, the impact of
past rejections on the search propensity of the consumer would
depend crucially on the magnitude of search costs prevailing
in the market. If search costs are negligible, then a higher
likelihood of rejection is unlikely to have a major impact
on consumers’ search behavior. On the other hand, if these
costs are high, then a high probability of rejection will adversely affect the search propensities of balance-carrying consumers. The negative relation between card balances and consumer search led Calem and Mester to conclude by inference
that higher balance cardholders, facing a greater risk of rejection, will have higher expected search costs and will search
less.
Other research that suggested search costs are an issue to
consumers in this period is that of Stango (2002). He used
data from the Card Industry Directory (listing data for the 250
largest card issuers) for the period from 1989 to 1994 and found
that switching costs explain over one-quarter of the within-firm
variation in credit card interest rates for commercial banks.
2.1 Relevant Changes in the Credit Card Market
Beginning in 1991, credit card interest rates started to decline
after remaining stable at around 18% for the previous 20 years.
According to the Federal Reserve Board’s 2001 Annual Report, rates declined gradually until 1994, and thereafter the
average rate has fluctuated in accordance with the prime rate
(reflecting the marginal cost of funds). This decline in credit
card interest rates during the 1990s was in part a result of
price competition as banks pursued a strategy to attract customers by offering introductory low rates on easily implemented balance transfers, thereby encouraging customers to
roll over balances from competing firms. The number of direct solicitations reached 5 billion annually by the year 2001,
almost four solicitations per month per American household
(see Federal Reserve Board Annual Report, 2001). This increased competition among banks may have been responsible for a somewhat reduced differential between the prime
rate and the average credit card rate over the decade of the
1990s. Credit card rates had been stuck around the 18% level
Journal of Business & Economic Statistics, July 2008
throughout the 1980s up to 1991. The year 1991 makes for
an easy comparison since the prime rate (cost of funds) in
1998 was about the same as in 1991, around 8.5%. However,
the credit card rate was 4 percentage points lower in 1998
compared to 1991, from 18% to 14%. Hence the spread between credit card rates and the prime rate decreased over that
decade.
At the same time, consumer revolving credit outstanding became the fastest growing component of the consumer loan market, doubling between 1991 and 1997, from $247 billion to
$514 billion (Yoo 1998). Black and Morgan (1998) and Yoo
(1998) showed that democratization of credit, and later an increase in overall indebtedness of U.S. households, were responsible for this growth. This prompted a growing literature
on the issue of obtaining and utilizing credit limits and the
question of consumers being credit-constrained. Research in
this area includes work by Jappelli (1990), Jappelli, Pischke,
and Souleles (1998), Dunn and Kim (1999), Gross and Souleles (2002a,b), Haliassos and Reiter (2003), and Castronova
and Hagstrom (2004). In addition to providing evidence that
consumers are credit-constrained, some of these studies have
also found indications that consumers have target utilization
rates.
With these new factors in the credit card market, researchers
have begun to re-examine the search and switch cost issue.
Crook (2002) modeled the effect of (a) credit rejection on balances and (b) balances on search behavior separately, repeating Calem and Mester’s test using the 1998 SCF, and he did
not find a significant relationship between high balances and
search. Furthermore, based on results from a search model, he
concluded that the problem of adverse selection in the credit
card market may have abated in recent years, as the search
propensities of consumers with poor payment histories are not
different from the search propensities of consumers with better payment histories. The current article differs from earlier
work by modeling search behavior explicitly on both past rejections and card balances, as well as exploring the possible
endogeneity that may exist between shopping behavior and frequency of credit rejections. This specification allows us to test
the countereffects of balance-carrying and credit rejection and
checks whether the indirect effect of large balances through
credit rejection is sufficient to deter the direct benefit achieved
from search. Kim, Dunn, and Mumy (2005) used a new set of
credit card data from a monthly household survey taken from
1996 to 2002 to examine the equilibrium interest rates resulting from the different search motives of convenience-users and
borrowers in this market. They found that borrowers end up
with lower interest rates than convenience-users. Berlin and
Mester (2004) examined a variety of consumer search models with 1981–1986 bank data to see if, in the time period
when search costs were presumably higher, such theoretical
models could explain the distribution of credit card interest
rates that prevailed. Berlin and Mester concluded that a drop
in switching costs may not be the main explanation for the
decline in credit card interest rates in the 1990s. Calem, Gordy,
and Mester (2006) looked at adverse selection and switching
costs in the credit card market using more recent SCF data
and the following novel treatments: (a) controls for the possibility that households that are temporarily liquidity-constrained
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Kerr and Dunn: Consumer Search Behavior
will run up larger balances, and (b) incorporation of a “pseudo
credit score” which the authors themselves constructed for sample members. Their findings suggested that some informationbased barriers to switching may still exist, but that the level of
credit card balances at which they become effective may have
increased.
In the current article, we use the 2001 SCF data to simultaneously model search propensity and likelihood of credit card
rejection. We hypothesize that there is a trade-off for consumers
between the cost of search and likelihood of rejection on the
one hand and the potential savings from lower finance charges
on the other hand. Past turndown and high credit card balances
should have a significant negative impact on shopping behavior, as it raises the likelihood of future rejection; but high credit
card balances, although also potentially signaling risk, should
not deter shopping behavior if the expected savings from lower
finance charges are sufficiently high. We thus directly test the
issue of how the factors of balance-carrying and credit rejection
affect search. We find that in recent years the balance-carrying
consumers search for better credit terms in spite of the dampening effect of past credit card denials. These results are probably
related to the large volume of solicitations and federal disclosure requirements, which forced issuers to report upfront their
most important contract terms. These phenomena have made
comparison shopping for credit card terms much easier and less
costly. This also suggests that a factor in the increased price
competition in the last decade may have been a change in consumer behavior, with greater consumer sensitivity to credit card
interest rates and more interest rate search by debt-carrying
credit card users. Our results are consistent with the results of
Gross and Souleles (2002a) who found that credit card debt has
become increasingly interest-elastic and, more importantly, approximately half of the effect is the result of balance switching.
3. THE EMPIRICAL INVESTIGATION
3.1 Data
Here we use data from the 2001 Survey of Consumer Finances, a more recent round of the SCF than was used in some
of the earlier work cited here. These data used the SCF sample weights, and all results are based upon the average of the
five SCF implicates. See Montalto and Sung (1996), and Kennickell (1998). This dataset contains improved variables specifically formulated for the credit card market. The proxy for consumer search used in this paper, Shop, is constructed from the
question that collects information on consumers’ propensity to
search before making decisions related to credit and borrowing only. The responses to the shopping question range from
“almost no shopping” through “moderate level of shopping” to
“a great deal of shopping.” Shop is assigned the value 1 for
“moderate to high level of shopping” and 0 for all other categories. Prior rounds of the SCF lumped search for credit or
loan products together with search for deposit products (savings/investments), and this inability to distinguish between the
two types of search in the data created unavoidable measurement error in earlier research on credit card search behavior.
347
The response to the current Shop question could apply to several types of credit products, but we assume that the propensities to shop in different credit markets should be correlated.
Although one might argue that the likely gains from shopping
would be greater for a mortgage (making them more likely
to be a target for shopping), the transactions costs associated
with shopping for mortgages are also correspondingly much
higher than for credit cards in the current environment of unsolicited mail offers. This cost factor would work against this
argument. Also, in our empirical analysis, we control for other
types of credit instruments through a Monthly Payment to Income variable which includes mortgage payments and auto payments.
Another important SCF variable used here is credit card rejection, Turndown. This credit card-specific variable is also
available only in recent rounds of the SCF, whereas a variable
that referred to rejection for all credit products was used in earlier works. Turndown equals 1 if a credit card application has
been rejected and 0 otherwise.
Detailed information on a broad array of assets and liabilities
held by consumers, such as forms of account ownership, minimum required payments on loans, frequency of these payments,
and so on, allows us to construct the relevant variables that capture the income and expenditure stream of each consumer along
with their search propensities, credit access, and demographic
information. The sample used here focuses only on those households that have at least one bank credit card (Visa, MasterCard,
Amex, and Discover).
3.2 Methodology
The approval of credit depends on a lender’s a priori estimate
of the default thresholds of consumers based on various signals
of credit risk. Therefore, the lender’s rejection of a credit application is modeled using an index function of creditworthiness
for consumer ‘i,’ Ci (X1i ), that depends on a vector capturing
an individual’s credit characteristics, X1i . A credit application
is rejected when Ci (X1i ) < C̄, where C̄ is the threshold level for
granting credit. Writing Ci (X1i ) as a first-order approximation
of the variables and normal error, we get the following probit
model for Turndown:
Ti∗ = C̄ − C(X1i ) = δ1 · X1i + ε1i ,
(1)
where Ti∗ > 0 results in rejection and Ti∗ ≤ 0 results in credit
approval.
On the other hand, a consumer searches for better credit
terms if the utility derived from search through lower finance
charges (after adjusting for search costs) outweighs his utility from not searching. The search behavior of consumer i is
therefore modeled using the latent variable Si∗ = Vsi (X2i , φi ) −
Vnsi (X2i , 0), where Vsi and Vnsi denote the utility derived from
searching and not searching, respectively. The utility from
search depends on a vector of individual specific characteristics X2i and also on φi , which represents both pecuniary and
nonpecuniary costs of search and in itself depends on X2i . Writing the utilities as a linear approximation of the individual specific characteristics and a normal error, the determinants of consumer search can then be analyzed with the following probit
equation:
Si∗ = Vsi (X2i , φi ) − Vnsi (X2i , 0) = δ2 · X2i + ε2i ,
(2)
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Journal of Business & Economic Statistics, July 2008
where individual i engages in search if Si∗ > 0 and does not
search when Si∗ ≤ 0.
Since outstanding card balances and a consumer’s past rejections, Turndowni , are included in X2i , (2) provides a direct
test for the hypothesis that consumers with large balances, who
are more subject to rejection, will be inhibited from shopping
around for credit terms because of their higher expected cost of
search.
Variable (SE)
Turndown
Intercept
−.41∗∗
Shop
Turndown
Balances
3.3 Endogeneity
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Table 1. Independent probit estimates for Turndown and Shop
It can be argued that because the underlying hypothesis is
that a higher probability of rejection makes high-balance consumers reluctant to comparison shop, then (2) should include
the latent variable Ti∗ rather than the indicator variable for rejection Turndown. Also, it might be argued that consumers with
a higher search propensity subject themselves to more rejection.
To account for this latter possibility, we explore the endogeneity between Shop and Turndown. Rewriting X1i = (Si∗ , Z1i ) and
X2i = (Ti∗ , Z2i ), we estimate the following two probit equations
simultaneously using a two-step maximum likelihood procedure (Mallar 1977):
Ti∗ = α1 · Si∗ + β1 · Z1i + ε1i ,
Si∗ = α2 · Ti∗ + β2 · Z2i + ε2i .
(3)
We follow Murphy and Topel (1985) to calculate the asymptotic variance–covariance matrix of the second-stage coefficients. This accounts for the interdependence of the error
terms and the fact that the unobservable regressors have been
estimated in calculating the second-step coefficients (see App.
A for details).
4. RESULTS
Table 1 presents the results of the separate probits in (1)
and (2). Column 1 is the fit of the credit card rejection variable Turndown (1) to the search variable Shop and outstanding
balances. Column 2 presents the fit of Shop (2) to Turndown
and outstanding balances. Turndown and Shop are both binary
variables taking the value 1 for having incurred credit application rejection and engaging in search behavior, respectively.
We also include control variables for income, bankruptcy and
delinquency histories, average monthly payments on consumer
loans and monthly rents to income, liquid assets, homeownership, and socioeconomic characteristics. A detailed description
of variables is presented in Appendix B, Table B.1, and the correlations between regressors are presented in Appendix B, Table B.2.
We see from Table 1 that the level of outstanding balances
has a positive and highly significant effect on credit card rejection, consistent with the hypothesis that banks regard highbalance consumers as high risks. (Note that the variable representing consumer search—Shop—is not significant in the fit
for credit card rejection.) Also, column 2 shows that credit rejection has a negative effect on search (although not quite at the
10% significance level). Nevertheless, the level of outstanding
Balances still has a positive and significant effect on consumer
search even in the face of rejection. Also, it is important to consider the relative magnitude of the effects. The coefficients on
Bankruptcy
Delinquency
Income
Liquid assets
Monthly payments/income
Home ownership
Age
Gender
(.14)
−.10
(.084)
—
—
2.06∗∗
(.45)
.78∗∗
(.098)
.43∗∗
(.061)
−.084
(.060)
−.008
(.033)
—
−.32∗∗
(.078)
−.019∗∗
(.003)
—
—
Education 1
—
Education 2
—
Education 3
Marital status
—
—
Shop
1.35∗∗
(.12)
—
−.147
(.091)
.79∗
(.48)
—
—
−.002
(.012)
−.004
(.007)
.19∗
(.10)
.31∗∗
(.064)
−.017∗∗
(.002)
−.23∗∗
(.083)
−.16∗
(.091)
−.12∗∗
(.061)
−.17∗∗
(.069)
.33∗∗
(.073)
NOTE: ∗∗ Significant at 5% level of confidence. ∗ Significant at 10% level of confidence.
N = 3,193.
Balances and Turndown imply that the negative impact from
each one-percentage point increase in the expected probability of turndown is offset by an extra $190 in credit card balances. (The average credit card balance among revolvers was
$9,205 in 2004 according to Bankrate.com.) Thus, even though
rejection is a factor in the credit card market, our results are
in contrast to the earlier hypotheses that balance-carrying consumers (a) are insensitive to interest rates, and (b) are impeded
by costs from searching in this market. In today’s environment,
finance charge considerations appear to offset the search and
switch costs that might exist for high-balance consumers. Even
though high-balance consumers are more likely to be denied
credit, this does not deter them from searching for lower interest rates.
4.1 Two-Stage Estimates
We now explore the link between Turndown and Shop further by estimating the equations accounting for endogeneity between consumers’ search and the likelihood of rejection, since
greater search is also likely to expose a consumer to more rejection. For identification purposes, bankruptcy and delinquency
are used as instruments for Turndown and omitted from the
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Kerr and Dunn: Consumer Search Behavior
Shop equation. Clearly, consumers with a past record of bankruptcies and delinquencies are more likely to get rejected by
credit issuers. On the other hand, there is no theory or solid empirical evidence suggesting that past bankruptcy filings or delinquency actually affect shopping behavior of individuals. Even
if there is a discouraging effect, it should be through the Turndown variable. The strength of bankruptcy and delinquency in
the Turndown reduced-form equation (App. C) supports their
use as instruments for Turndown.
Likewise, the consumer’s average monthly payments to income, along with gender, education, and marital status, are included as instruments in the Shop equation and are omitted from
the Turndown equation. Consumers having to make high average monthly payments relative to income will be sensitive to
the price portion of any credit contract and will be more likely
to search for lower interest rates. On the other hand, average
monthly payments to income need not convey a signal of credit
risk to banks—especially since reliable income data are not
available to credit card banks—and hence are excluded from
the Turndown equation. Likewise, there is no evidence suggesting that the socioeconomic variables should affect Turndown.
(Age is not used as an instrument for Shop because it can affect Turndown. Unlike other demographic characteristics, Fair
Lending Laws are explicit against discrimination to older applicants, but this does not prevent lenders from rejecting younger
applicants.) The reduced-form results, which are presented in
Appendix C, show that all instruments for Shop are significant
in the Shop equation but not significant in the Turndown equation.
Finally, it has been suggested to us that those with a history
of delinquency in the last 12 months (as ascertained in the SCF)
may have a different attitude toward credit card search than
those without this history. We have therefore reestimated the
Shop equation with the latent variable Turndown decomposed
into two components: one that reflects the effect of a history
of delinquency and holds all other factors constant; and one
that holds delinquency constant at zero and considers all other
factors. These results, which are equivalent to removing delinquency as an instrument, are presented in Appendix D for those
who would like to further examine the effect of delinquency.
The maximum likelihood estimates of the simultaneous twoequation probit model are reported in Table 2. The results do
not indicate the presence of endogeneity.
5. SUMMARY AND CONCLUSIONS
Credit card debt has been the fastest growing segment of the
U.S. consumer loan market in the last two decades. One line
of research on credit cards has focused on cardholder search
behavior as a primary factor behind the lack of price competition in this market until the early 1990s. Since that period, a
large volume of direct solicitations featuring full disclosure of
rate and other contract terms, as required by the Truth in Lending Act of 1988, has become common; and this has contributed
to a change in consumer behavior. Here we examine consumer
search behavior using the more recent data of the 2001 Survey
of Consumer Finance and a direct model specification for consumer search. We also investigate the possible endogeneity of
349
Table 2. Structural ML estimates of Shop and Turndown
Dependent variable (SE)
Turndown
Shop
Intercept
−.43∗∗
1.32∗∗
(.12)
—
(.16)
−.056
(.078)
—
Shop (latent)
Turndown (latent)
Balances
Bankruptcy
Delinquency
Income
Liquid assets
Monthly payments/income
Home ownership
Age
Gender
2.10∗∗
(.45)
.78∗∗
(.099)
.429∗∗
(.061)
−.086
(.061)
−.007
(.032)
—
−.31∗∗
(.082)
−.020∗∗
(.003)
—
Education 1
—
Education 2
—
Education 3
—
Marital status
—
.035
(.090)
.65
(.51)
—
—
.0014
(.015)
−.003
(.008)
.18∗
(.10)
.33∗∗
(.072)
−.016∗∗
(.002)
−.23∗∗
(.083)
−.16∗
(.092)
−.12∗
(.061)
−.18∗∗
(.070)
.33∗∗
(.074)
NOTE: ∗∗ Significant at 5% level of confidence. ∗ Significant at 10% level of Confidence.
N = 3,193.
consumer search and the probability of rejection for the highbalance cardholders.
We find that in the current market, high-balance-carrying
consumers search for lower credit card rates in spite of their
higher likelihood of rejection. Our results show that the negative impact from each one-percentage-point increase in the expected probability of turndown is offset by an extra $190 in balances. Thus, interest savings on large credit card balances can
outweigh the discouraging effect of credit rejection on search
in this market.
APPENDIX A: CORRECTED ASYMPTOTIC
VARIANCE–COVARIANCE MATRIX
FOR TWO–STEP MLE
The reduced-form equations of the model in (3) are as follows:
Ti∗ = 1 · Zi + e1i ,
(3a)
Si∗ = 2 · Zi + e2i ,
(3b)
where Zi = (Z1i , Z2i ). First, consistent estimates of the reducedform parameters are obtained by maximizing the marginal likelihood functions constructed from (3a) and (3b) separately. Let
350
Journal of Business & Economic Statistics, July 2008
L1 be the likelihood function for the first-stage reduced-form
equation for Turndowni ,
L1 =
n
Ti · log{F(1 · Zi )} + (1 − Ti ) · log{1 − F(1 · Zi )} .
i=1
Writing θ2 = (α2 , β2 ), the correct asymptotic variance–
covariance matrix for the second-stage parameters (Murphy and
Topel 1985) is given as
var(θ2 ) = V2−1 + V2−1 [CV1−1 C/ − RV1−1 C′ − CV1−1 R]V2−1 ,
where
ˆ 1 · Zi ). Second, this estimated probMaximizing L1 gives T̂i∗ (
ability is substituted for its unobserved counterpart in the structural equation, and the likelihood function for the structural
equation is then maximized with respect to its parameters. If L2
is the likelihood function for the second-stage structural equaˆ 1 · Zi ) for Turndowni in L2
tion for Shop, then substituting T̂i∗ (
gives
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L2 =
∂ 2 L1
,
∂1 ∂′1
∂L2 ∂L2 ′
V2 = E
,
∂θ2 ∂θ2
∂L2 ∂L2 ′
C=E
,
∂1 ∂θ2
∂L1 ∂L2 ′
R=E
.
∂1 ∂θ2
V1 = −E
n
Si · log F(α2 · T̂i∗ (1 · Zi ) + β2 · Z2i )
i=1
+ (1 − Si ) · log 1 − F(α2 · T̂i∗ (1 · Zi ) + β2 · Z2i ) .
Maximizing L2 gives consistent estimates (α̂2 , β̂2 ).
These matrices are replaced by their estimated counterparts in
the calculation of the standard errors. The above procedure is
followed for the structural equation Turndown also.
APPENDIX B: VARIABLE DEFINITIONS AND CORRELATIONS
Table B.1. Definitions of variables
Variable
Definition
Shop
1—Consumer shops around before making credit decisions (mean = 76.6%)
0—Otherwise
Turndown
1—Turned down specifically for a credit card or denied increase in credit line
(mean = 8.5%)
0—Otherwise
Outstanding balances on bank cards (MC, Visa, Discover, AMEX) in units of
$100,000 (mean = $2,308)
Balances
Bankruptcy
Delinquency
Income
Liquid assets
Monthly
payments/income
Home ownership
Age
Gender
Marital status
Education
1—Declared bankruptcy in the past (mean = 7.8%)
0—Has not declared bankruptcy
0—No loans or have loans but never missed a payment (mean = 89.0%)
1—Sometimes missed payments but never by more than 2 months (mean = 8.0%)
2—Behind on payments by 2 months or more (mean = 3.0%)
Annual household income in units of $100,000 (mean = $81,488)
Liquid assets held; checking, savings, money market deposit accounts, CDs,
mutual funds in units of $100,000 (mean = $67,763)
Avg. monthly payments/monthly income, where payments includes mortgage
payments, rent, auto, lease (mean = 28.1%)
1—Owns home (mean = 76.8% )
0—Rents
Age of respondent in years (mean = 49.5 years)
1—Male (mean = 78.4%)
0—Female
1—Married (mean = 66.7%)
0—Unmarried
1—Less than high school (mean = 8.7%)
2—High school diploma (mean = 29.5%)
3—Some college, no degree (mean = 19.2%)
4—College degree (mean = 42.7%)
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Kerr and Dunn: Consumer Search Behavior
Table B.2. Correlations between regressors for both equations
Weighted Correlation matrix
_NAME_
Balances
Income
Liquid assets
Monthly
Payments/
Income
Home
ownership
Age
Gender
Marital status
Education
Bankruptcy
Delinquency
Monthly
payments/
income
.005
−.017
−.009
1.000
Home
ownership
−.035
.105
.073
−.055
Balances
1.000
.021
−.048
.005
Income
.021
1.000
.331
−.017
Liquid
assets
−.048
.331
1.000
−.009
−.035
.105
.073
−.055
1.000
−.094
.022
.016
.038
.007
.068
.004
.108
.114
.155
−.042
−.052
.104
.034
.044
.090
−.043
−.040
−.038
.000
−.041
−.004
−.002
.095
.279
.209
.289
.019
−.054
−.143
Gender
.022
.108
.034
.000
Marital
status
.016
.114
.044
−.041
Education
.038
.155
.090
−.004
Bankruptcy
.007
−.042
−.043
−.002
Delinquency
.068
−.052
−.040
.095
.279
.209
.289
.019
−.054
−.143
1.000
−.055
−.005
−.126
−.026
−.133
−.055
1.000
.710
.067
−.044
−.061
−.005
.710
1.000
.038
−.019
−.039
−.126
.067
.038
1.000
−.077
−.075
−.026
−.044
−.019
−.077
1.000
.032
−.133
−.061
−.039
−.075
.032
1.000
Age
−.094
.004
.104
−.038
351
352
Journal of Business & Economic Statistics, July 2008
APPENDIX: C: FIRST–STEP REDUCED-FORM
ESTIMATES FOR TWO–STEP ML
ESTIMATES OF Shop AND Turndown
APPENDIX D: ALTERNATIVE STRUCTURAL ML
ESTIMATES OF Shop USING TWO COMPONENTS
FOR TURNDOWN—WITH AND WITHOUT
DELINQUENCY HISTORY
Table C.1.
Turndown
Shop
Intercept
−.47
(.14)
2.05∗∗
(.44)
−.009
(.010)
.78∗∗
(.099)
.44∗∗
(.062)
−.087
(.065)
−.009
(.035)
−.30∗∗
(.082)
−.019∗∗
(.003)
.043
(.11)
−.036
(.14)
−.14
(.088)
.010
(.091)
−.10
(.10)
1.32
(.12)
.77
(.48)
.19∗
(.10)
.19∗
(.10)
−.096
(.059)
−.002
(.012)
−.003
(.007)
.31∗∗
(.064)
−.016∗∗
(.002)
−.22∗∗
(.083)
−.15∗
(.092)
−.12∗∗
(.061)
−.17∗∗
(.069)
.33∗∗
(.073)
Balances
Monthly payments/income
Bankruptcy
Delinquency
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Table D.1.
Variable (SE)
Income
Liquid assets
Home ownership
Age
Gender
Education 1
Education 2
Education 3
Marital status
∗∗ Significant at 5% level of confidence. ∗ Significant at 10% level of confidence.
NOTE:
N = 3,193.
[Received February 2004. Revised January 2007.]
Dependent variable (SE)
Intercept
Turndown (latent)—with delinquency history
Turndown (latent)—without delinquency history
Balances
Monthly payments/income
Income
Liquid assets
Home ownership
Age
Gender
Education 1
Education 2
Education 3
Marital status
Shop
1.44∗∗
(.13)
−.22
(.14)
.24∗
(.12)
.28
(.54)
.19∗
(.10)
.019
(.017)
−.001
(.008)
.38∗∗
(.076)
−.012∗∗
(.003)
−.24∗∗
(.083)
−.14
(.092)
−.087
(.063)
−.20∗∗
(.070)
.35∗∗
(.074)
NOTE: ∗∗ Significant at 5% level of confidence. ∗ Significant at 10% level of confidence.
N = 3,193. Table suggests that consumers who have been turned down because of past
delinquency are discouraged from shopping, whereas those turned down because of other
credit risk factors, including high balances, are not.
REFERENCES
Ausubel, L. M. (1991), “The Failure of Competition in the Credit Card Market,”
American Economic Review, 81, 50–81.
Berlin, M., and Mester, L. J. (2004), “Credit Card Rates and Consumer Search,”
Review of Financial Economics 13, 179–198.
Black, S., and Morgan, D. P. (1998), “Risk and the Democratization of Credit
Cards,” Research Paper 9815, Federal Reserve Bank of New York.
Brito, D. L., and Hartley, P. R. (1995), “Consumer Rationality and Credit
Cards,” Journal of Political Economy, 103, 400–433.
Calem, P. S., Gordy, M. B., and Mester, L. J. (2006), “Switching Costs and
Adverse Selection in the Market for Credit Cards: New Evidence,” Journal
of Banking and Finance, 30, 1653–1685.
Calem, P. S., and Mester, L. J. (1995), “Consumer Behavior and Stickiness of
Credit Card Interest Rates,” American Economic Review, 85, 1327–1336.
Castronova, E., and Hagstrom, P. (2004), “The Demand for Credit Cards:
Evidence From the Survey of Consumer Finances,” Economic Inquiry 42,
304–318.
Crook, J. (2002), “Adverse Selection and Search in the Bank Credit Card Market,” working paper, Credit Research Centre, University of Edinburgh.
Dunn, L. F., and Kim, T. H. (1999), “An Empirical Investigation of Credit Card
Default: Ponzi Schemes and Other Behavior,” Working Paper 99-13, Ohio
State University, Dep. of Economics.
Durkin, T. A. (2000), “Credit Cards: Use and Consumer Attitudes,” Federal
Reserve Bulletin, 86, 623–634.
Federal Reserve Board (2001), “88th Annual Report 2001,” Board of Governors
of the Federal Reserve System.
Gross, D. B., and Souleles, N. S. (2002a), “Do Liquidity Constraints and Interest Rates Matter for Consumer Behavior? Evidence From Credit Card Data,”
Quarterly Journal of Economics, 117, 149–185.
(2002b), “An Empirical Analysis of Personal Bankruptcy and Delinquency,” Review of Financial Studies, 15, 319–347.
Haliassos, M., and Reiter, M. (2003), “Credit Card Debt Puzzles,” working paper, University of Cyprus and Universitat Pompeu Fabra.
Jappelli, T. (1990), “Who Is Credit Constrained in the U.S. Economy,” Quarterly Journal of Economics, 105, 219–234.
Jappelli, T., Pischke, J.-S., and Souleles, N. S. (1998), “Testing for Liquidity
Constraints in Euler Equations With Complementary Data Sources,” Review
of Economics and Statistics, 80, 251–262.
Kennickell, A. B. (1998), “Multiple Imputation in the Survey of Consumer Finances,” Federal Reserve Board SCF Bibliography, available at
www.federalreserve.gov/pubs/oss/oss2/papers/impute98.pdf.
Kim, T. H., Dunn, L. F., and Mumy, G. E. (2005), “Bank Price Competition and
Asymmetric Consumer Responses to Credit Card Interest Rates,” Economic
Inquiry, 43, 344–353.
Mallar, Ch. D. (1977), “The Estimation of Simultaneous Probability Models,”
Econometrica, 45, 1717–1722.
Mester, L. J. (1994), “Why Are Credit Card Rates Sticky?” Economic Theory,
4, 505–530.
Montalto, C. P., and Sung, J. (1996), “Multiple Imputation in the 1992 Survey
of Consumer Finance,” Financial Counseling and Planning, 7, 133–146.
Kerr and Dunn: Consumer Search Behavior
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Mortensen, D. T., and Pissarides, C. (1999), “New Developments in Models of
Search in the Labor Market,” in Handbook for Labor Economics (3B), eds.
O. Ashenfelter and D. Card, Amsterdam: North-Holland.
Murphy, K. M., and Topel, R. H. (1985), “Estimation and Inference in TwoStep Econometric Models,” Journal of Business & Economic Statistics, 3,
370–379.
353
Park, S. (1997), “Option Value of Credit Lines as an Explanation of High Credit
Card Rates,” Research Paper 9702, Federal Reserve Bank of New York.
Stango, V. (2002), “Pricing With Consumer Switching Costs: Evidence From
the Credit Card Market,” Journal of Industrial Economics, 50, 475–492.
Yoo, P. S. (1998), “Still Charging: The Growth of Credit Card Debt Between
1992 and 1995,” business review, Federal Reserve Bank of St. Louis.
ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20
Consumer Search Behavior in the Changing Credit
Card Market
Sougata Kerr & Lucia Dunn
To cite this article: Sougata Kerr & Lucia Dunn (2008) Consumer Search Behavior in the
Changing Credit Card Market, Journal of Business & Economic Statistics, 26:3, 345-353, DOI:
10.1198/073500107000000133
To link to this article: http://dx.doi.org/10.1198/073500107000000133
Published online: 01 Jan 2012.
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Date: 12 January 2016, At: 17:57
Consumer Search Behavior in the Changing
Credit Card Market
Sougata K ERR
Consumer Risk Modeling and Analytics, JP Morgan and Chase Co., Columbus, OH 43240
(sougata.kerr@chase.com)
Lucia D UNN
Downloaded by [Universitas Maritim Raja Ali Haji] at 17:57 12 January 2016
Department of Economics, Ohio State University, Columbus, OH 43210 (Dunn.4@osu.edu )
This article investigates whether search costs inhibit consumers from searching for lower credit card interest rates. The results provide evidence that the credit card search environment has changed since the
mid-1990s. Using the 2001 Survey of Consumer Finances, we model consumers’ propensity to search and
their probability of being denied credit simultaneously and find that larger credit card balances induce
cardholders to search more even though they face a higher probability of rejection. This result may be related to the high volume of direct solicitation, combined with disclosure requirements, which has lowered
the cost of search to find lower interest rates.
KEY WORDS: Revolving credit; Search costs; Switch costs.
1. INTRODUCTION
Credit card balance switching and the consumer search involved in this process have become important issues in the
banking community as more cardholders seek to move their
revolving credit to lower cost lenders. Throughout the 1980s
and early 1990s, research in this area tended to focus on consumers’ lack of interest rate sensitivity and the inhibiting effect
of high search costs in this market. These were among the main
reasons put forward to explain the lack of interest rate competition in the credit card market and persistent high rates in
this period. We find that consumer behavior has changed since
the early 1990s. Consumers now display more willingness to
shop around for lower rates. Easy access to rate information on
the Internet and in the large volume of mailed solicitations, as
well as disclosure requirements such as those in the Truth in
Lending Act (officially the “Fair Credit and Charge Card Disclosure Act” of 1988), have contributed to this changing environment by providing easier access to interest rate information
and thus facilitating the “search and switch” behavior of consumers. These and other factors may be partially responsible
for the more competitive environment in the 1990s credit card
market.
Here we will examine the determinants of consumer search
propensities with particular emphasis on those cardholders who
carry a high balance. High-balance cardholders are of special
interest because they potentially have the most to gain from
search; and at the same time, they face a higher probability of
rejection. Previous researchers have argued that a greater likelihood of rejection is likely to deter the search propensity of
the high-balance-carrying consumer due to substantial search
costs in this market. We will analyze (a) the effect of large balances on the consumer’s probability of credit application rejection, and (b) how these factors—large balances and rejection
probability—affect consumers’ search propensities. In testing
the search-cost hypothesis, we deal with the issue of endogeneity between consumers’ search and the likelihood of rejection
with a simultaneous equations model.
Our results show that consumers in the current credit card
market are interest-rate sensitive. Furthermore, we find no evidence that search costs deter consumer search for lower rates.
Whereas credit application rejection is found to have a dampening effect on search, the possible interest savings from a sufficient amount of balances is found to overcome the effect of
the rejection. In the next section we review the relevant literature on this market and recent changes in the market environment. Section 3 discusses our methodology and improvements
in available data. Section 4 presents our empirical results, and
Section 5 summarizes our findings and conclusions.
2. BACKGROUND AND PREVIOUS LITERATURE ON
THE CREDIT CARD MARKET
Consumer revolving credit, which includes credit card debt
as its principal component, has been the fastest growing segment of the U.S. consumer loan market in recent years (Durkin
2000). In the 1980s a peculiar feature of this market was the
lack of price competition between issuers, as credit card rates
remained high (around 18%) and downwardly sticky. This behavior was puzzling given the fact that the market was functionally deregulated by 1982 and saw the entry of nearly 4,000
firms during the ensuing decade.
Early work on credit card markets presented consumer
search, or the lack of it, as an important factor in the high
and sticky interest rates of that period. Ausubel (1991) argued
that many consumers underestimated their borrowing potential,
which made them less sensitive to interest rates. In addition to
interest rate insensitivity, he cited the inhibiting nature of high
search costs, which prevented consumer search for lower rates
and allowed issuers to keep rates high in this market. (For other
developments in search models, see Mortensen and Pissarides
1999.)
Other researchers explained the observed high levels of interest rates by pointing to various unique features of credit card
debt such as the noncollaterized characteristic of credit cards
(Mester 1994); open-ended revolving credit lines (Park 1997);
345
© 2008 American Statistical Association
Journal of Business & Economic Statistics
July 2008, Vol. 26, No. 3
DOI 10.1198/073500107000000133
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346
and the liquidity services offered by credit cards under consumption uncertainty (Brito and Hartley 1995). However, the
lack of price competition was considered the dominant factor
in this literature.
The major empirical article on credit card search by Calem
and Mester (1995) used 1989 Survey of Consumer Finances
(SCF) data and found results that were consistent with consumers’ reluctance to search for lower rates due to high search
costs in this market. That research did not model consumer
search explicitly but reached this conclusion by examining the
determinants of credit card balances, one of which was consumer search. They found (a) that credit rejection is positively related to the level of balances because large outstanding balances send a signal of high risk to banks. More importantly, they found (b) that the level of credit card balances
is negatively related to search, indicating that high-balancecarrying consumers are less willing to search for lower rates.
Together these results were indicative of both consumer insensitivity to interest rates and high search costs in this market. According to the search-cost hypothesis, the impact of
past rejections on the search propensity of the consumer would
depend crucially on the magnitude of search costs prevailing
in the market. If search costs are negligible, then a higher
likelihood of rejection is unlikely to have a major impact
on consumers’ search behavior. On the other hand, if these
costs are high, then a high probability of rejection will adversely affect the search propensities of balance-carrying consumers. The negative relation between card balances and consumer search led Calem and Mester to conclude by inference
that higher balance cardholders, facing a greater risk of rejection, will have higher expected search costs and will search
less.
Other research that suggested search costs are an issue to
consumers in this period is that of Stango (2002). He used
data from the Card Industry Directory (listing data for the 250
largest card issuers) for the period from 1989 to 1994 and found
that switching costs explain over one-quarter of the within-firm
variation in credit card interest rates for commercial banks.
2.1 Relevant Changes in the Credit Card Market
Beginning in 1991, credit card interest rates started to decline
after remaining stable at around 18% for the previous 20 years.
According to the Federal Reserve Board’s 2001 Annual Report, rates declined gradually until 1994, and thereafter the
average rate has fluctuated in accordance with the prime rate
(reflecting the marginal cost of funds). This decline in credit
card interest rates during the 1990s was in part a result of
price competition as banks pursued a strategy to attract customers by offering introductory low rates on easily implemented balance transfers, thereby encouraging customers to
roll over balances from competing firms. The number of direct solicitations reached 5 billion annually by the year 2001,
almost four solicitations per month per American household
(see Federal Reserve Board Annual Report, 2001). This increased competition among banks may have been responsible for a somewhat reduced differential between the prime
rate and the average credit card rate over the decade of the
1990s. Credit card rates had been stuck around the 18% level
Journal of Business & Economic Statistics, July 2008
throughout the 1980s up to 1991. The year 1991 makes for
an easy comparison since the prime rate (cost of funds) in
1998 was about the same as in 1991, around 8.5%. However,
the credit card rate was 4 percentage points lower in 1998
compared to 1991, from 18% to 14%. Hence the spread between credit card rates and the prime rate decreased over that
decade.
At the same time, consumer revolving credit outstanding became the fastest growing component of the consumer loan market, doubling between 1991 and 1997, from $247 billion to
$514 billion (Yoo 1998). Black and Morgan (1998) and Yoo
(1998) showed that democratization of credit, and later an increase in overall indebtedness of U.S. households, were responsible for this growth. This prompted a growing literature
on the issue of obtaining and utilizing credit limits and the
question of consumers being credit-constrained. Research in
this area includes work by Jappelli (1990), Jappelli, Pischke,
and Souleles (1998), Dunn and Kim (1999), Gross and Souleles (2002a,b), Haliassos and Reiter (2003), and Castronova
and Hagstrom (2004). In addition to providing evidence that
consumers are credit-constrained, some of these studies have
also found indications that consumers have target utilization
rates.
With these new factors in the credit card market, researchers
have begun to re-examine the search and switch cost issue.
Crook (2002) modeled the effect of (a) credit rejection on balances and (b) balances on search behavior separately, repeating Calem and Mester’s test using the 1998 SCF, and he did
not find a significant relationship between high balances and
search. Furthermore, based on results from a search model, he
concluded that the problem of adverse selection in the credit
card market may have abated in recent years, as the search
propensities of consumers with poor payment histories are not
different from the search propensities of consumers with better payment histories. The current article differs from earlier
work by modeling search behavior explicitly on both past rejections and card balances, as well as exploring the possible
endogeneity that may exist between shopping behavior and frequency of credit rejections. This specification allows us to test
the countereffects of balance-carrying and credit rejection and
checks whether the indirect effect of large balances through
credit rejection is sufficient to deter the direct benefit achieved
from search. Kim, Dunn, and Mumy (2005) used a new set of
credit card data from a monthly household survey taken from
1996 to 2002 to examine the equilibrium interest rates resulting from the different search motives of convenience-users and
borrowers in this market. They found that borrowers end up
with lower interest rates than convenience-users. Berlin and
Mester (2004) examined a variety of consumer search models with 1981–1986 bank data to see if, in the time period
when search costs were presumably higher, such theoretical
models could explain the distribution of credit card interest
rates that prevailed. Berlin and Mester concluded that a drop
in switching costs may not be the main explanation for the
decline in credit card interest rates in the 1990s. Calem, Gordy,
and Mester (2006) looked at adverse selection and switching
costs in the credit card market using more recent SCF data
and the following novel treatments: (a) controls for the possibility that households that are temporarily liquidity-constrained
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Kerr and Dunn: Consumer Search Behavior
will run up larger balances, and (b) incorporation of a “pseudo
credit score” which the authors themselves constructed for sample members. Their findings suggested that some informationbased barriers to switching may still exist, but that the level of
credit card balances at which they become effective may have
increased.
In the current article, we use the 2001 SCF data to simultaneously model search propensity and likelihood of credit card
rejection. We hypothesize that there is a trade-off for consumers
between the cost of search and likelihood of rejection on the
one hand and the potential savings from lower finance charges
on the other hand. Past turndown and high credit card balances
should have a significant negative impact on shopping behavior, as it raises the likelihood of future rejection; but high credit
card balances, although also potentially signaling risk, should
not deter shopping behavior if the expected savings from lower
finance charges are sufficiently high. We thus directly test the
issue of how the factors of balance-carrying and credit rejection
affect search. We find that in recent years the balance-carrying
consumers search for better credit terms in spite of the dampening effect of past credit card denials. These results are probably
related to the large volume of solicitations and federal disclosure requirements, which forced issuers to report upfront their
most important contract terms. These phenomena have made
comparison shopping for credit card terms much easier and less
costly. This also suggests that a factor in the increased price
competition in the last decade may have been a change in consumer behavior, with greater consumer sensitivity to credit card
interest rates and more interest rate search by debt-carrying
credit card users. Our results are consistent with the results of
Gross and Souleles (2002a) who found that credit card debt has
become increasingly interest-elastic and, more importantly, approximately half of the effect is the result of balance switching.
3. THE EMPIRICAL INVESTIGATION
3.1 Data
Here we use data from the 2001 Survey of Consumer Finances, a more recent round of the SCF than was used in some
of the earlier work cited here. These data used the SCF sample weights, and all results are based upon the average of the
five SCF implicates. See Montalto and Sung (1996), and Kennickell (1998). This dataset contains improved variables specifically formulated for the credit card market. The proxy for consumer search used in this paper, Shop, is constructed from the
question that collects information on consumers’ propensity to
search before making decisions related to credit and borrowing only. The responses to the shopping question range from
“almost no shopping” through “moderate level of shopping” to
“a great deal of shopping.” Shop is assigned the value 1 for
“moderate to high level of shopping” and 0 for all other categories. Prior rounds of the SCF lumped search for credit or
loan products together with search for deposit products (savings/investments), and this inability to distinguish between the
two types of search in the data created unavoidable measurement error in earlier research on credit card search behavior.
347
The response to the current Shop question could apply to several types of credit products, but we assume that the propensities to shop in different credit markets should be correlated.
Although one might argue that the likely gains from shopping
would be greater for a mortgage (making them more likely
to be a target for shopping), the transactions costs associated
with shopping for mortgages are also correspondingly much
higher than for credit cards in the current environment of unsolicited mail offers. This cost factor would work against this
argument. Also, in our empirical analysis, we control for other
types of credit instruments through a Monthly Payment to Income variable which includes mortgage payments and auto payments.
Another important SCF variable used here is credit card rejection, Turndown. This credit card-specific variable is also
available only in recent rounds of the SCF, whereas a variable
that referred to rejection for all credit products was used in earlier works. Turndown equals 1 if a credit card application has
been rejected and 0 otherwise.
Detailed information on a broad array of assets and liabilities
held by consumers, such as forms of account ownership, minimum required payments on loans, frequency of these payments,
and so on, allows us to construct the relevant variables that capture the income and expenditure stream of each consumer along
with their search propensities, credit access, and demographic
information. The sample used here focuses only on those households that have at least one bank credit card (Visa, MasterCard,
Amex, and Discover).
3.2 Methodology
The approval of credit depends on a lender’s a priori estimate
of the default thresholds of consumers based on various signals
of credit risk. Therefore, the lender’s rejection of a credit application is modeled using an index function of creditworthiness
for consumer ‘i,’ Ci (X1i ), that depends on a vector capturing
an individual’s credit characteristics, X1i . A credit application
is rejected when Ci (X1i ) < C̄, where C̄ is the threshold level for
granting credit. Writing Ci (X1i ) as a first-order approximation
of the variables and normal error, we get the following probit
model for Turndown:
Ti∗ = C̄ − C(X1i ) = δ1 · X1i + ε1i ,
(1)
where Ti∗ > 0 results in rejection and Ti∗ ≤ 0 results in credit
approval.
On the other hand, a consumer searches for better credit
terms if the utility derived from search through lower finance
charges (after adjusting for search costs) outweighs his utility from not searching. The search behavior of consumer i is
therefore modeled using the latent variable Si∗ = Vsi (X2i , φi ) −
Vnsi (X2i , 0), where Vsi and Vnsi denote the utility derived from
searching and not searching, respectively. The utility from
search depends on a vector of individual specific characteristics X2i and also on φi , which represents both pecuniary and
nonpecuniary costs of search and in itself depends on X2i . Writing the utilities as a linear approximation of the individual specific characteristics and a normal error, the determinants of consumer search can then be analyzed with the following probit
equation:
Si∗ = Vsi (X2i , φi ) − Vnsi (X2i , 0) = δ2 · X2i + ε2i ,
(2)
348
Journal of Business & Economic Statistics, July 2008
where individual i engages in search if Si∗ > 0 and does not
search when Si∗ ≤ 0.
Since outstanding card balances and a consumer’s past rejections, Turndowni , are included in X2i , (2) provides a direct
test for the hypothesis that consumers with large balances, who
are more subject to rejection, will be inhibited from shopping
around for credit terms because of their higher expected cost of
search.
Variable (SE)
Turndown
Intercept
−.41∗∗
Shop
Turndown
Balances
3.3 Endogeneity
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Table 1. Independent probit estimates for Turndown and Shop
It can be argued that because the underlying hypothesis is
that a higher probability of rejection makes high-balance consumers reluctant to comparison shop, then (2) should include
the latent variable Ti∗ rather than the indicator variable for rejection Turndown. Also, it might be argued that consumers with
a higher search propensity subject themselves to more rejection.
To account for this latter possibility, we explore the endogeneity between Shop and Turndown. Rewriting X1i = (Si∗ , Z1i ) and
X2i = (Ti∗ , Z2i ), we estimate the following two probit equations
simultaneously using a two-step maximum likelihood procedure (Mallar 1977):
Ti∗ = α1 · Si∗ + β1 · Z1i + ε1i ,
Si∗ = α2 · Ti∗ + β2 · Z2i + ε2i .
(3)
We follow Murphy and Topel (1985) to calculate the asymptotic variance–covariance matrix of the second-stage coefficients. This accounts for the interdependence of the error
terms and the fact that the unobservable regressors have been
estimated in calculating the second-step coefficients (see App.
A for details).
4. RESULTS
Table 1 presents the results of the separate probits in (1)
and (2). Column 1 is the fit of the credit card rejection variable Turndown (1) to the search variable Shop and outstanding
balances. Column 2 presents the fit of Shop (2) to Turndown
and outstanding balances. Turndown and Shop are both binary
variables taking the value 1 for having incurred credit application rejection and engaging in search behavior, respectively.
We also include control variables for income, bankruptcy and
delinquency histories, average monthly payments on consumer
loans and monthly rents to income, liquid assets, homeownership, and socioeconomic characteristics. A detailed description
of variables is presented in Appendix B, Table B.1, and the correlations between regressors are presented in Appendix B, Table B.2.
We see from Table 1 that the level of outstanding balances
has a positive and highly significant effect on credit card rejection, consistent with the hypothesis that banks regard highbalance consumers as high risks. (Note that the variable representing consumer search—Shop—is not significant in the fit
for credit card rejection.) Also, column 2 shows that credit rejection has a negative effect on search (although not quite at the
10% significance level). Nevertheless, the level of outstanding
Balances still has a positive and significant effect on consumer
search even in the face of rejection. Also, it is important to consider the relative magnitude of the effects. The coefficients on
Bankruptcy
Delinquency
Income
Liquid assets
Monthly payments/income
Home ownership
Age
Gender
(.14)
−.10
(.084)
—
—
2.06∗∗
(.45)
.78∗∗
(.098)
.43∗∗
(.061)
−.084
(.060)
−.008
(.033)
—
−.32∗∗
(.078)
−.019∗∗
(.003)
—
—
Education 1
—
Education 2
—
Education 3
Marital status
—
—
Shop
1.35∗∗
(.12)
—
−.147
(.091)
.79∗
(.48)
—
—
−.002
(.012)
−.004
(.007)
.19∗
(.10)
.31∗∗
(.064)
−.017∗∗
(.002)
−.23∗∗
(.083)
−.16∗
(.091)
−.12∗∗
(.061)
−.17∗∗
(.069)
.33∗∗
(.073)
NOTE: ∗∗ Significant at 5% level of confidence. ∗ Significant at 10% level of confidence.
N = 3,193.
Balances and Turndown imply that the negative impact from
each one-percentage point increase in the expected probability of turndown is offset by an extra $190 in credit card balances. (The average credit card balance among revolvers was
$9,205 in 2004 according to Bankrate.com.) Thus, even though
rejection is a factor in the credit card market, our results are
in contrast to the earlier hypotheses that balance-carrying consumers (a) are insensitive to interest rates, and (b) are impeded
by costs from searching in this market. In today’s environment,
finance charge considerations appear to offset the search and
switch costs that might exist for high-balance consumers. Even
though high-balance consumers are more likely to be denied
credit, this does not deter them from searching for lower interest rates.
4.1 Two-Stage Estimates
We now explore the link between Turndown and Shop further by estimating the equations accounting for endogeneity between consumers’ search and the likelihood of rejection, since
greater search is also likely to expose a consumer to more rejection. For identification purposes, bankruptcy and delinquency
are used as instruments for Turndown and omitted from the
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Kerr and Dunn: Consumer Search Behavior
Shop equation. Clearly, consumers with a past record of bankruptcies and delinquencies are more likely to get rejected by
credit issuers. On the other hand, there is no theory or solid empirical evidence suggesting that past bankruptcy filings or delinquency actually affect shopping behavior of individuals. Even
if there is a discouraging effect, it should be through the Turndown variable. The strength of bankruptcy and delinquency in
the Turndown reduced-form equation (App. C) supports their
use as instruments for Turndown.
Likewise, the consumer’s average monthly payments to income, along with gender, education, and marital status, are included as instruments in the Shop equation and are omitted from
the Turndown equation. Consumers having to make high average monthly payments relative to income will be sensitive to
the price portion of any credit contract and will be more likely
to search for lower interest rates. On the other hand, average
monthly payments to income need not convey a signal of credit
risk to banks—especially since reliable income data are not
available to credit card banks—and hence are excluded from
the Turndown equation. Likewise, there is no evidence suggesting that the socioeconomic variables should affect Turndown.
(Age is not used as an instrument for Shop because it can affect Turndown. Unlike other demographic characteristics, Fair
Lending Laws are explicit against discrimination to older applicants, but this does not prevent lenders from rejecting younger
applicants.) The reduced-form results, which are presented in
Appendix C, show that all instruments for Shop are significant
in the Shop equation but not significant in the Turndown equation.
Finally, it has been suggested to us that those with a history
of delinquency in the last 12 months (as ascertained in the SCF)
may have a different attitude toward credit card search than
those without this history. We have therefore reestimated the
Shop equation with the latent variable Turndown decomposed
into two components: one that reflects the effect of a history
of delinquency and holds all other factors constant; and one
that holds delinquency constant at zero and considers all other
factors. These results, which are equivalent to removing delinquency as an instrument, are presented in Appendix D for those
who would like to further examine the effect of delinquency.
The maximum likelihood estimates of the simultaneous twoequation probit model are reported in Table 2. The results do
not indicate the presence of endogeneity.
5. SUMMARY AND CONCLUSIONS
Credit card debt has been the fastest growing segment of the
U.S. consumer loan market in the last two decades. One line
of research on credit cards has focused on cardholder search
behavior as a primary factor behind the lack of price competition in this market until the early 1990s. Since that period, a
large volume of direct solicitations featuring full disclosure of
rate and other contract terms, as required by the Truth in Lending Act of 1988, has become common; and this has contributed
to a change in consumer behavior. Here we examine consumer
search behavior using the more recent data of the 2001 Survey
of Consumer Finance and a direct model specification for consumer search. We also investigate the possible endogeneity of
349
Table 2. Structural ML estimates of Shop and Turndown
Dependent variable (SE)
Turndown
Shop
Intercept
−.43∗∗
1.32∗∗
(.12)
—
(.16)
−.056
(.078)
—
Shop (latent)
Turndown (latent)
Balances
Bankruptcy
Delinquency
Income
Liquid assets
Monthly payments/income
Home ownership
Age
Gender
2.10∗∗
(.45)
.78∗∗
(.099)
.429∗∗
(.061)
−.086
(.061)
−.007
(.032)
—
−.31∗∗
(.082)
−.020∗∗
(.003)
—
Education 1
—
Education 2
—
Education 3
—
Marital status
—
.035
(.090)
.65
(.51)
—
—
.0014
(.015)
−.003
(.008)
.18∗
(.10)
.33∗∗
(.072)
−.016∗∗
(.002)
−.23∗∗
(.083)
−.16∗
(.092)
−.12∗
(.061)
−.18∗∗
(.070)
.33∗∗
(.074)
NOTE: ∗∗ Significant at 5% level of confidence. ∗ Significant at 10% level of Confidence.
N = 3,193.
consumer search and the probability of rejection for the highbalance cardholders.
We find that in the current market, high-balance-carrying
consumers search for lower credit card rates in spite of their
higher likelihood of rejection. Our results show that the negative impact from each one-percentage-point increase in the expected probability of turndown is offset by an extra $190 in balances. Thus, interest savings on large credit card balances can
outweigh the discouraging effect of credit rejection on search
in this market.
APPENDIX A: CORRECTED ASYMPTOTIC
VARIANCE–COVARIANCE MATRIX
FOR TWO–STEP MLE
The reduced-form equations of the model in (3) are as follows:
Ti∗ = 1 · Zi + e1i ,
(3a)
Si∗ = 2 · Zi + e2i ,
(3b)
where Zi = (Z1i , Z2i ). First, consistent estimates of the reducedform parameters are obtained by maximizing the marginal likelihood functions constructed from (3a) and (3b) separately. Let
350
Journal of Business & Economic Statistics, July 2008
L1 be the likelihood function for the first-stage reduced-form
equation for Turndowni ,
L1 =
n
Ti · log{F(1 · Zi )} + (1 − Ti ) · log{1 − F(1 · Zi )} .
i=1
Writing θ2 = (α2 , β2 ), the correct asymptotic variance–
covariance matrix for the second-stage parameters (Murphy and
Topel 1985) is given as
var(θ2 ) = V2−1 + V2−1 [CV1−1 C/ − RV1−1 C′ − CV1−1 R]V2−1 ,
where
ˆ 1 · Zi ). Second, this estimated probMaximizing L1 gives T̂i∗ (
ability is substituted for its unobserved counterpart in the structural equation, and the likelihood function for the structural
equation is then maximized with respect to its parameters. If L2
is the likelihood function for the second-stage structural equaˆ 1 · Zi ) for Turndowni in L2
tion for Shop, then substituting T̂i∗ (
gives
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L2 =
∂ 2 L1
,
∂1 ∂′1
∂L2 ∂L2 ′
V2 = E
,
∂θ2 ∂θ2
∂L2 ∂L2 ′
C=E
,
∂1 ∂θ2
∂L1 ∂L2 ′
R=E
.
∂1 ∂θ2
V1 = −E
n
Si · log F(α2 · T̂i∗ (1 · Zi ) + β2 · Z2i )
i=1
+ (1 − Si ) · log 1 − F(α2 · T̂i∗ (1 · Zi ) + β2 · Z2i ) .
Maximizing L2 gives consistent estimates (α̂2 , β̂2 ).
These matrices are replaced by their estimated counterparts in
the calculation of the standard errors. The above procedure is
followed for the structural equation Turndown also.
APPENDIX B: VARIABLE DEFINITIONS AND CORRELATIONS
Table B.1. Definitions of variables
Variable
Definition
Shop
1—Consumer shops around before making credit decisions (mean = 76.6%)
0—Otherwise
Turndown
1—Turned down specifically for a credit card or denied increase in credit line
(mean = 8.5%)
0—Otherwise
Outstanding balances on bank cards (MC, Visa, Discover, AMEX) in units of
$100,000 (mean = $2,308)
Balances
Bankruptcy
Delinquency
Income
Liquid assets
Monthly
payments/income
Home ownership
Age
Gender
Marital status
Education
1—Declared bankruptcy in the past (mean = 7.8%)
0—Has not declared bankruptcy
0—No loans or have loans but never missed a payment (mean = 89.0%)
1—Sometimes missed payments but never by more than 2 months (mean = 8.0%)
2—Behind on payments by 2 months or more (mean = 3.0%)
Annual household income in units of $100,000 (mean = $81,488)
Liquid assets held; checking, savings, money market deposit accounts, CDs,
mutual funds in units of $100,000 (mean = $67,763)
Avg. monthly payments/monthly income, where payments includes mortgage
payments, rent, auto, lease (mean = 28.1%)
1—Owns home (mean = 76.8% )
0—Rents
Age of respondent in years (mean = 49.5 years)
1—Male (mean = 78.4%)
0—Female
1—Married (mean = 66.7%)
0—Unmarried
1—Less than high school (mean = 8.7%)
2—High school diploma (mean = 29.5%)
3—Some college, no degree (mean = 19.2%)
4—College degree (mean = 42.7%)
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Table B.2. Correlations between regressors for both equations
Weighted Correlation matrix
_NAME_
Balances
Income
Liquid assets
Monthly
Payments/
Income
Home
ownership
Age
Gender
Marital status
Education
Bankruptcy
Delinquency
Monthly
payments/
income
.005
−.017
−.009
1.000
Home
ownership
−.035
.105
.073
−.055
Balances
1.000
.021
−.048
.005
Income
.021
1.000
.331
−.017
Liquid
assets
−.048
.331
1.000
−.009
−.035
.105
.073
−.055
1.000
−.094
.022
.016
.038
.007
.068
.004
.108
.114
.155
−.042
−.052
.104
.034
.044
.090
−.043
−.040
−.038
.000
−.041
−.004
−.002
.095
.279
.209
.289
.019
−.054
−.143
Gender
.022
.108
.034
.000
Marital
status
.016
.114
.044
−.041
Education
.038
.155
.090
−.004
Bankruptcy
.007
−.042
−.043
−.002
Delinquency
.068
−.052
−.040
.095
.279
.209
.289
.019
−.054
−.143
1.000
−.055
−.005
−.126
−.026
−.133
−.055
1.000
.710
.067
−.044
−.061
−.005
.710
1.000
.038
−.019
−.039
−.126
.067
.038
1.000
−.077
−.075
−.026
−.044
−.019
−.077
1.000
.032
−.133
−.061
−.039
−.075
.032
1.000
Age
−.094
.004
.104
−.038
351
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Journal of Business & Economic Statistics, July 2008
APPENDIX: C: FIRST–STEP REDUCED-FORM
ESTIMATES FOR TWO–STEP ML
ESTIMATES OF Shop AND Turndown
APPENDIX D: ALTERNATIVE STRUCTURAL ML
ESTIMATES OF Shop USING TWO COMPONENTS
FOR TURNDOWN—WITH AND WITHOUT
DELINQUENCY HISTORY
Table C.1.
Turndown
Shop
Intercept
−.47
(.14)
2.05∗∗
(.44)
−.009
(.010)
.78∗∗
(.099)
.44∗∗
(.062)
−.087
(.065)
−.009
(.035)
−.30∗∗
(.082)
−.019∗∗
(.003)
.043
(.11)
−.036
(.14)
−.14
(.088)
.010
(.091)
−.10
(.10)
1.32
(.12)
.77
(.48)
.19∗
(.10)
.19∗
(.10)
−.096
(.059)
−.002
(.012)
−.003
(.007)
.31∗∗
(.064)
−.016∗∗
(.002)
−.22∗∗
(.083)
−.15∗
(.092)
−.12∗∗
(.061)
−.17∗∗
(.069)
.33∗∗
(.073)
Balances
Monthly payments/income
Bankruptcy
Delinquency
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Table D.1.
Variable (SE)
Income
Liquid assets
Home ownership
Age
Gender
Education 1
Education 2
Education 3
Marital status
∗∗ Significant at 5% level of confidence. ∗ Significant at 10% level of confidence.
NOTE:
N = 3,193.
[Received February 2004. Revised January 2007.]
Dependent variable (SE)
Intercept
Turndown (latent)—with delinquency history
Turndown (latent)—without delinquency history
Balances
Monthly payments/income
Income
Liquid assets
Home ownership
Age
Gender
Education 1
Education 2
Education 3
Marital status
Shop
1.44∗∗
(.13)
−.22
(.14)
.24∗
(.12)
.28
(.54)
.19∗
(.10)
.019
(.017)
−.001
(.008)
.38∗∗
(.076)
−.012∗∗
(.003)
−.24∗∗
(.083)
−.14
(.092)
−.087
(.063)
−.20∗∗
(.070)
.35∗∗
(.074)
NOTE: ∗∗ Significant at 5% level of confidence. ∗ Significant at 10% level of confidence.
N = 3,193. Table suggests that consumers who have been turned down because of past
delinquency are discouraged from shopping, whereas those turned down because of other
credit risk factors, including high balances, are not.
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