The demand for credit cards: evidence from the survey of consumer finances.

Castronova, Edward ; Hagstrom, Paul

I. INTRODUCTION

The credit card market has expanded rapidly over the past 20 years. In 1983, 65% of households held at least one card; by 1998, about 74% did so. The size of real balances on these cards more than tripled in this period. Analysts have proposed a number of explanations for the increase, but untangling the main causes is complicated by the unique nature of the credit card financial product. An individual who obtains a credit card has obtained the right to borrow a certain amount, called the limit, with no questions asked, under predetermined payback rules. Thus credit cards involve both assets and liabilities. The available limits are best thought of as assets, which can be used by a consumer to hedge against future income shortfalls or just to facilitate paying for goods and thereby reducing the need to carry cash.

The asset and limit components of credit cards makes them similar to financial instruments. For example, the asset component is essentially an option, a subject that has been studied extensively in the corporate finance literature. The seminal work is Black and Scholes (1973), who developed a method for valuing an option. Washam and Davis (1998) extend this method to the problem of valuing the liquidity of credit resources. This body of literature suggests that for some people, a credit card can be viewed as a source of liquid funds for business purposes. Moreover, once a credit card is used, it becomes a debt liability. In effect, these are loans that the user has taken on to cover an income shortfall or simply to make a purchase for which borrowing makes sense. Again, a corporate equivalent would be line-of-credit borrowing; see Myers (1989), or Miller et al. (1998) for an introduction.

These similarities raise the question of what sort of sample one should analyze for a study of consumer use of credit cards. In all likelihood, many average consumers who use credit cards are actually business entrepreneurs who use the cards to finance small business. Considering that wealth is an important element of any study of credit cards, one faces the further problem that small business wealth is hard to measure accurately. Some research (Lindh and Ohlsson 1998) suggests that access to liquid credit, such as credit cards, can make the difference between becoming self-employed or not. Dunn and Holtz-Eakin (2000) argue that family financial capital can ease the transition to self-employment; although they do not discuss credit availability in their study, their results are strong evidence that credit cards would also ease that transition. Other studies that focus on the role of liquid credit and entrepreneurial activity include Meyer (1990), Blanchflower and Oswald (1998), Cox and Japelli (1990), and Evans and Jovanovich (1989).

Our focus here is not on the use of credit cards as a business financing tool, however, it is apparent from this literature that business finance certainly plays a powerful role in determining the use of credit cards by some owners. The research suggests that entrepreneurs would be more likely to be using credit cards for financing business rather than for consumer purposes. For this reason, it is important to separate the self-employed from the non-self-employed in our sample.

Looking specifically at consumers, the unusual nature of the credit card financial product raises interesting questions for empirical researchers who hope, as we do, to provide some estimates of the responsiveness of the credit card demand to standard price and income effects. The object of this article is to raise these questions and then answer some of them, estimating regression models using data from the Survey of Consumer Finances (SCF). Specifically, we make two empirical approaches. First, we model credit card demand as a two-stage process, with a consumer obtaining limits in the first stage and then borrowing some fraction of those limits in the second. We estimate this model with a nested tobit procedure. Second, we model the demand for limits (not balances) as one equation in a two-equation supply-demand model. We estimate this model with simple two-stage least squares (2SLS), instrumenting for the price variable, that is, the interest rate. The two approaches are connected in that the results of the first model suggest that most of the action in the market is in the demand for limits, not the demand for balances. Our first-stage results suggest, in fact, that consumers tend to borrow a constant fraction of the limits they have obtained. (1) Exploring this possibility further, we find that it may be related to the practice of self-employed respondents using credit cards to borrow for small business needs. In any case, the market for limits seems to have a great influence on both the aggregate amount of outstanding limits as well as the aggregate amount of credit card debt. Our analysis of the limit market suggests that limits are indeed responsive to price, income, and wealth effects.

Our article is organized in seven sections. Section II gives an overview of the credit card market, its growth, its extension into lower regions of the income distribution, and the current state of the literature regarding the market forces behind these developments. Section III discusses data issues and the selection of variables for regressions. Section IV presents results from nested tobit regressions with limit demand in the first stage and limit usage in the second stage. Section V presents results from 2SLS regressions on credit card limits, where the price is endogenous. In section VI, we address policy concerns related to the possibility that poor people react in a different way to the availability of credit cards. Section VII wraps up.

II. THE CREDIT CARD MARKET

We will explore the demand for credit cards using a cross-section from the 1998 SCF. The SCF is a weighted, nationally representative sample of households maintained by the Board of Governors of the Federal Reserve and is intended to give a reliable snapshot of the wealth holdings and debt of U.S. consumers. It contains extensive data on households' credit card holdings, including number of cards owned, balances on the cards, and the card interest rates. The data also record the household's income and wealth situation, as well detailed information on household characteristics, such as age of the head, sex, race, and so on.

>From the basic SCF data we draw a sample of 3,229 bank credit card holders for analysis. In the entire 1998 SCF sample, of the 4,305 households, 3,449 held some type of credit card, including gas cards and store cards. Of these, only 220 households did not hold or report a credit limit on a bank credit card. Of those with a bank-type credit card, 40.6% maintained a positive balance after their last payment. Of these households, the average remaining bank card balance is $4,809 (1998 dollars). (2)

Table 1 shows some descriptive statistics from different waves of the SCF from 1983 to 1998, the most recent data available. The basic story, which has been found in a number of reports on these data and other sources, is that credit card usage has gone up dramatically over the past 20 years. (3) More consumers than ever now own at least one card; the average balance on these cards has steadily risen. Limits are higher, as well as utilization rates. The expansion of the market has not been limited to middle- and upper-income consumers, however; credit card holdings and usage among the poor have also risen rapidly (Bird et al. 1999). Because the SCF includes a considerable number of high-wealth households with low or negative incomes, for the purposes of this article we define poverty as having income below the federal poverty line and having less than $100,000 in nonhousing wealth.

Following the 1991-92 recession, which put many debt-burdened consumers in bankruptcy court, the suggestion arose that credit card interest rates were too high and that perhaps the market was in some way broken (e.g., Ausubel 1991). For a brief time there was even discussion of explicit legislated limits on credit card interest rates, but the end result has instead been a series of regulations on the information reported on statements and credit card offers. Durkin (2000) reports that most consumers seem to know pretty well the terms of their own credit card arrangements and in any case do not think the information would be all that hard to find out. A study by Brito and Hartley (1995) constructs theoretical models that explain most of the features of the credit card market without resorting to market-failure arguments. Moreover, empirical work by Calem and Mester (1995) and Cargill and Wendel (1996) argues against the idea that credit card consumers are irrational; Nash and Sinkey's (1997) data suggest that credit card banks do not make extraordinary profits given the risks. Overall, the evidence suggests that the credit card market is not broken.

Although it may not be broken, however, the credit card market is unusual. The credit card is composed of two products: an asset (or insurance) product in the form of the remaining unsecured credit line, and a debt, in the form of the outstanding monthly balance. Econometric work on the demand for these two interrelated products is limited. Duca and Whitesell (1995) estimate the simultaneous choice of monetary assets and card ownership using the SCF. Their study focuses on the basic choice of whether to have a card, and the results argue most strongly that those who do have cards are likely to have less demand for transaction balances. In other words, the evidence suggests indirectly that some part of the demand for credit cards involves their use as a payment vehicle. The study leaves open, however, questions about the sensitivity of demand, for both limits and balances, to income and price variables.

Gross and Souleles (1999) go further in investigating the peculiar nature of credit cards, exploring the response of balances both to changes in limits as well as changes in interest rates. Using rich panel data on hundreds of thousands of credit card accounts (rather than households), they show that account balances tend to increase when limits increase and decrease when account-specific interest rates increase. They also show that consumers seem to set a target level of utilization, in that the balance on a card tends to be a roughly constant fraction of the available limit. The trajectory of borrowing in response to a limit change tends to return the ratio of debt to limit to its initial level. Gross and Souleles argue that such behavior can be explained through models of rational saving and risk-taking, however. Our approach differs from theirs in two main ways. First, we use the SCF, in which the unit of observation is the household rather than the account, as is the case in the Gross and Souleles (1999) work. This gives us access to more data on the specific circumstances of the credit card holder, including the aggregate credit card balances held by individual households. Second, consistent with the difference in the data, Gross and Souleles are interested mostly in tracking the response of balances on a given account to changes in that account, whereas we will estimate the response of the demand for limits and balances to changes in the account terms (i.e., the interest rate) as well as consumer characteristics (income, wealth).

III. DATA

Tables 2 and 3 present descriptive statistics from the 1998 SCF on the 3,229 households holding bank credit cards for a number of variables that we will use in our regression analyses. For comparison, Table 2 provides means from the sample of poor households holding credit cards. Poor households have lower total limits and less total debt, but their utilization (DEBT RATIO) is higher, and they face higher interest rates. These figures, and those reported in Table 1, motivate us to make some effort to see whether credit-seeking behavior is different at the lower tail of the income distribution. For further comparison and to follow up on the importance of keeping the self-employed separate, Table 3 shows descriptive statistics across samples. These figures suggest that the self-employed are indeed using credit cards in a different way, in that they hold much higher limits. Interestingly (and we will see more of this shortly), the self-employed have similar utilization rates to the non-self-employed. Unpacking this further, we found that the self-employed who do carry a balance carry, on average, a balance of 72% of the limit. This, combined with the fact that comparatively fewer self-employed do carry a balance, results in a similar utilization rate on average. The self-employed are less likely to carry a balance, but when they do, it is a large share of the limit.

As for what kind of credit-seeking we are looking for, there are two outcome variables in our analysis. The first is LIMIT, which is the sum of the borrowing limits available to the household on all bank credit cards. (The SCF also contains data on other kinds of interest-bearing rotating credit accounts, but we have chosen to focus on bank credit cards alone. Only bank credit cards have an interest rate reported in the data.) The second outcome variable is DEBT, which is the amount of the limit that has been left as an outstanding balance on the card. Some consumers place charges on their cards and pay them off each month, resulting in zero credit card debt. Any charges that are not paid off have been borrowed. Our DEBT variable consists of all charges remaining after the household's, last payment. For econometric reasons we will usually express the debt variable as a fraction of the available limit, defining DEBT RATIO = DEBT/LIMIT. (4)

As for independent variables, we are interested in the response of credit card demand to standard economic influences: price, income, and wealth. The price variable in the credit card market is the interest rate on card balances. The SCF does not report the interest rates on all cards, but it does report (in 1998) the interest rate on the card with the largest current balance. We assume that this rate is also the marginal rate facing the consumer and define the variable RATE as the interest rate on the bank card with the largest current balance. (5)

For income, we recognize that household income may fluctuate a great deal from year to year, but we assume, as is common in the precautionary savings literature, that permanent income is the appropriate budget constraint in the demand for assets (Hubbard et al. 1995; Skinner 1988). Permanent income is ordinary income that is purged of transitory fluctuations. The content of the assumption is that a consumer's demand for limits on credit cards is part of the consumer's medium- to long-run financial planning.

The easiest way to estimate permanent income would be to estimate fixed or random effects model on panel data, which would in principle be possible because the SCF does have some panel characteristics: some households in the 1983 sample were reinterviewed for the 1989 sample. However, we cannot use the 1983-89 panel for our study because the key price variable, the credit card interest rate, doesn't appear in the SCF until the 1995 cross-section. Moreover, the SCF panel is now almost 12 years old.

Nonetheless, we are able to construct a permanent income estimate in the 1998 cross-section data using a method updated from King and Dicks-Mireaux (1982) (KDM). KDM take a cross-section income regression and divide the residual of the regression into a permanent and transitory component based on out of sample results. They do this by reviewing a number of panel data income studies that report fixed-effects estimates of household income. For each study KDM calculate the transitory component, the average ratio of transitory variance to total variance. For the studies they review, the transitory share of the residual averages about 0.5 of the total residual. This they treat as a constant; then, in their own cross-section data, they assign one-half the cross-section residual to transitory income and the other half to permanent income. Their definition of permanent income reduces to the fitted value of the income regression plus one-half of the residual. (6)

We follow a similar procedure, except that we update it to our data rather than just apply the KDM parameter of 0.5. Our estimates are based on random-effects models on the 1983 89 panel of the SCF. Our analysis of income dynamics in this sample suggests that the average ratio of permanent to total variance is 0.79. We then tested the results from random-effects models for heterogeneity, regressing the permanent/total variance ratio of each respondent on a vector of his or her characteristics. We conclude from this regression that, in fact, the ratio of permanent to total variance does not vary systematically across the population. Thus we define permanent income as the fitted value of a cross-section regression of income on a large vector of individual characteristics plus 0.79 times the regression residual. (7)

Wealth variables present fewer problems. Previous studies have shown that there is a difference in the response of credit cards to liquid and nonliquid wealth, so we use two corresponding measures. LWEALTH is the net worth of the respondent in terms of liquid assets and debts (cash savings, CDs, stocks, bonds, short-term loans). HOME is an indicator of whether the respondent is a homeowner.

As will be seen, our results depend significantly on whether or not the respondent is self-employed. This variable can be directly observed in the SCF, because each respondent is asked to indicate whether or not they are self-employed. The variable abbreviation we use for this is SELFEMP.

Other than this, we use a series of standard sociodemographic variables, such as sex, age, race, and education. We also look at two self-reported variables that attempt to directly measure parts of the preference profile of the respondent. RISK A VERSE is an indicator of the respondent's attitude toward risk-taking. Respondents were asked whether their household would be willing to take risks to obtain higher returns, and those who responded that they either would never take risks or that they would take only average risks to obtain average returns are coded as 1 in RISK A VERSE. Households who would take larger risks or "substantial" risks are coded 0. Finally, respondents were asked how they viewed the state of the economy in the next year--good, bad, or average. OPTIMIST is coded 1 for respondents who said it would be good, and 0 otherwise.

IV. THE DEMAND FOR CREDIT CARDS: DEBT

We begin by analyzing the debt aspect of demand. Here the structure of the decision-making process leads us to a particular formation of the econometric model. Consumers obtain limits, and then they have the option of borrowing as much of the limit as they wish, at any time. Whatever they borrow must be paid back, but only under fairly generous repayment rules. There is a fixed minimum payment required each month, usually a small percentage of the outstanding balance. However, the consumer may pay any amount greater than that if he or she chooses. In essence, consumers make decisions in two stages: first they obtain limits, then they choose what fraction of those limits to keep as balances.

This structure calls for a nested estimation model. The first-stage dependent variable, LIMIT, is a simple continuous variable censored at zero. The second stage variable, the debt choice, is a censored continuous variable, with the censoring occurring at zero and at the maximum debt level, that is, the limit. Because the limit varies across respondents, one approach would be a nested model with a heterogeneous upper limit in the second stage. We were unable to find an estimator with these features. A simpler approach is possible, however, if we define debt as the ratio of the outstanding balance to the maximum possible limit. This variable, DEBT RATIO, is also continuous between 0 and 1, but it has a homogenous upper limit at 1. We use a sequential nested tobit model to estimate a two-stage decision process with a continuous first stage and a homogeneously censored second stage.

Specifically, we estimate the model:

(1) LIMIT * = [[beta]'.sub.1][X.sub.1] + [[epsilon].sub.1],

LIMIT = max(LIMIT *, 0)

(2) DEBT RATIO * = [[beta].sub.2][X.sub.2] + [[epsilon].sub.2],

DEBT RATIO

= max(DEBT RATIO *, 0)

(3) where, [[epsilon].sub.1], [[epsilon].sub.2] ~ N(0, 0, [[sigma].sub.1], [[sigma].sub.2], [rho]).

The independent variables [X.sub.1] in the LIMIT regression include all information known to the individual and to the credit lending institutions through credit applications and credit reports, including the price of borrowing. In other words, it incorporates both demand and supply factors. At the second stage we include RATE, the price of borrowing, and individual characteristics, not all of which are known to the lending institution.

With this approach, we have the best opportunity given the data available to directly estimate the characteristics of the demand for credit card debt. Note that a direct regression of credit card debt on price, income, and demographic characteristics will not identify demand effects from supply effects. If, for example, debt rises with income, it will not be clear whether that happens because richer consumers demand more debt or because richer consumers are offered higher limits on better terms from suppliers. This same reasoning also applies to the first stage in the nested tobit: if limits rise with income, it will not be clear whether this is because richer consumers demand higher limits or because richer consumers are granted higher limits by suppliers. In this section we will not try to sort out the demand and supply effects in the first stage regression (they will be addressed later). Instead, we will simply note that once the limit is determined in the first stage, the second stage is a pure demand effect. Consumers may borrow whatever fraction of the limit they wish. Their borrowing is not constrained by their credit-worthiness, the cost of funds to the suppliers, or any other supply-side factor. Thus the second-stage regression directly reveals the demand for credit card debt per se.

Table 4 (top) provides the results of the nested tobit procedure on our SCF cross-section. The first stage has the log of LIMIT as the dependent variable, and almost all of the variables have statistically significant effects. Interpretation of the coefficients is problematic, however, for the reasons just given: are these demand or supply effects? Passing on to the second stage, however, we have purely demand effects. The surprising result here is that none of the coefficients has a statistically significant effect, and their substantive effect is also small. This result is robust to a very large number of variations in the structure of the two equations. We have been generally unable to find regression specifications in which the degree of responsiveness and change in the second equation come even close to that in the first equation. Based on these results, it seems that the debt ratio is roughly constant across the population.

An economic rationale for this (see Gross and Souleles 1999) is that consumers who wish to borrow more simply obtain more cards or higher limits on existing cards rather than max out the cards they now have. If this is the case, then it would seem that the action in this market is at the level of limits and not debts. Certainly it is no surprise that the supply side of the market would focus on limits, because the limits constitute one of the terms under which suppliers precommit themselves to making loans. It is only surprising that consumers also look at credit cards the same way, also viewing limits as one of the terms under which they are apparently precommitting to borrow. There is no requirement in the contract that they precommit to borrow in this way, but in practice they apparently do so. As a result, the supply and demand for limits end up determining the equilibrium quantity of not just limits but debts as well.

However, it may also be the case that some of this borrowing behavior is not about consumer credit at all but about business credit, specifically self-employed respondents borrowing for small business. (8) To explore this possibility further, the middle and bottom of Table 3 repeat the analysis for separate self-employed and non-self-employed samples. The results for the self-employed can only be indicative. The SCF does not include the data necessary to conduct a fully specified analysis of the self-employed's use of credit. Although the data does allow us to identify the self-employed separately for the non self-employed, it does not give us enough information about the self-employed to render their behavior in great detail. For example, self-employed credit card users can deduct interest on their cards as business expense, thereby affecting the relevant price of credit. We have no way of knowing how common this practice is in our sample, nor how much it affects borrowing behavior. The SCF does not report the share of borrowing that is business-related nor the amount of interest that is deductible.

The results indicate, indeed, that much of the noise in the DEBT RATIO equation occurs because of the borrowing patterns of self-employed respondents; Table 3 shows that when these respondents are removed from the sample, several of the variables are statistically significant. Though there appears to be no price effect, there is an evident positive income effect on borrowing, as well as a substitution effect versus other forms of wealth. Larger families seem to induce more borrowing--a result that would be intuitive for most parents. The bottom part Table 4, by contrast, shows that the self-employed seem to borrow for reasons unrelated to the variables listed. Overall, the two tables suggest that self-employed borrowing is driven by the needs of small business, not by consumer and household finances. It also suggests that although most of the action in credit cards occurs in the limit market, consumer utilization of their limits does respond to some economic variables.

V. THE DEMAND FOR CREDIT CARDS: LIMITS

With this in mind, we proceed to a study of the market for limits. Here we can pay more attention to supply and demand issues, because the structure of decision making is much more simple. Essentially, we view limits as an unbounded continuous variable, representing the quantity in the market. The interest rate represents price. In a standard supply and demand model, the quantity and price are both endogenous; identifying price effects in the quantity demanded regression requires that the price variable be instrumented. The instruments should be things that determine supply and not demand. Here there are natural candidates, namely, the aspects of creditworthiness that credit card companies observe but that play no role in the household's current desire for credit.

In the SCF, there is a wealth of supply-side instruments for the interest rate. These include whether the household has been bankrupt, whether it has been more than two months late in making payments, whether they regularly pay off the entire credit card balance every month, and the household's occupation category (card applications usually ask for profession). (9)

Using 2SLS, we then ran the limit equation with the same independent variables as in the first stage of the nested tobit, as well as the instrumented interest rate variable. The results are presented in Table 5. The first column reports a regression on the entire sample. They are not substantially different from the first-stage regression in the tobit results, but in contrast to those results, they do lend themselves to interpretation as demand effects. Thus, an increase of one point in the interest rate reduces the demand for limits by 0.0281 log points, indicating an own-price elasticity of about -0.4. The income coefficients indicate that limits rise with income at an increasing rate over the range of positive income. There is also a substantive, positive liquid wealth effect, as well as a positive effect of homeownership. Thus, as resources rise, the demand for limits rises. (10) Looking at other variables, we find that nonwhites, female-headed households, and risk-averse households have lower demand for limits, whereas respondents with higher education, married respondents, and older respondents have higher demands.

Table 5 report the 2SLS regressions on the non-self-employed sample and the self-employed sample. Interestingly, here, the two groups seem roughly similar in their response to the standard price, income, and wealth variables. Self-employed people seem more sensitive to the interest rate on their credit cards, perhaps a sign of their access to other forms of finance. However, the self-employed are much less strongly affected by demographic variables (marriage, kids, education), which fits with our interpretation that these folks use cards for business purposes primarily. This leaves the consumer as the group who might use their cards as consumption buffers, and it is consistent with that view that the non-self-employed sample continues to show significant effects of family, marriage, children, and education.

Overall, these results suggest that the demand for limits responds strongly and in intuitive ways to standard economic influences. Limit demand rises with income and wealth and falls with the interest rate.

VI. THE DEMAND FOR CREDIT CARDS: ARE THE POOR DIFFERENT?

Evidently the self-employed are somewhat different from the non-self-employed in their use of credit cards; what about the poor? We are not able to answer this question by breaking out a poverty sample as we did with the self-employed sample, because there are only about 100 poor credit card holding respondents in the SCF (as compared with almost 1,000 self-employed people). However, we can include regressions with poverty interactions to capture some information. We do this mostly out of recognition that there is a growing interest in the use of more or less sophisticated financial instruments by the poor.

We define a poor household as one whose income falls below the federal poverty line for a family of that size. We also exclude the family from poverty status if it has assets worth more than $100,000. For this analysis, we are also looking only at the non-self-employed sample, because the preceding tables seemed to suggest that the self-employed should probably be analyzed from a small business perspective; an analysis of the poor has to approach credit cards as consumer finance. (11)

In Tables 6 and 7, we repeat the nested tobit and the 2SLS limit demand equations, this time interacting the key price and income variables with the poverty indicator. In Table 6, we see that there is very little change caused by the presence of the poor-interacted variables. The poor do seem to have higher limits, all else equal (stage 1), but they borrow less against them (stage 2). One partial explanation of this is the turbulent nature of income streams. It is well known that periods of poverty are often transitional (see Naifeh 1998; Stevens, 1999; Rank and Hirschl 2001). Here we have defined poverty according to an ordinary income standard, but our income regressor is a permanent income concept, as is standard in the literature (Hubbard et al. 1995). This mixing of income concepts, combined with what is known about savings behavior in the face of income uncertainty, provides a rather complex interpretation of the poverty-interacted income coefficients in these tables. The coefficients suggest that people who are poor according to a disposable income concept do acquire higher limits because their permanent income is higher. However, the poor also borrow less against these limits as their permanent income increases. The first coefficient makes sense under consumption-insurance theory, but the second does not. A person who is poor by ordinary-income standards but has a high permanent income must view the current poverty state as transitory. Theory suggests that this person would acquire more limits and borrow against them to raise current consumption. The data suggest that the limit effect is present in these data, but the induced borrowing effect is not. It appears that the same uncertainty that encourages the poor to have obtained higher limits prevents or discourages them from using the available credit. After all, these data are still consistent with the idea that the poor may hold on to credit as a contingency against dire emergency. Reconciling these findings fully would require a more extensive model of permanent and transitory income shocks for the poor than is feasible with the SCF data. This will have to remain an avenue for future work.

Only one of the poverty-interacted variables is statistically significant (income) at the second stage; more generally, it seems once again that there is not as much movement in terms of utilization as there is in terms of limit acquisition. Perhaps the strongest evidence of this is in the variable that, to economists, would be critical: the price. Table 6, stage 1, shows that LIMIT responds negatively to RATE among all respondents and that there is no statistically significant difference between the poor and nonpoor on that score. Stage 2 shows, however, that utilization does not respond to RATE for either the poor or the nonpoor. Thus there seems to be more responsiveness at the level of credit card limits than at the level of borrowing against those limits.

Table 7 repeats the 2SLS analysis of the limit market with poverty interactions. The coefficient POOR is positive, large, and statistically significant, which suggests that poor households, all else equal, have higher limit demand. The interaction of POOR and RATE yields a statistically insignificant coefficient, which suggests that poor and nonpoor households respond similarly to the interest rate. However, poor households do not seem to change their limits significantly in response to changes in income--the interacted coefficient is the same size and opposite sign as the noninteracted coefficient. This means that the increase we see for poor relative to nonpoor households occurs discretely at the transition from nonpoor to poor. Once one is poor, changes in income do not seem to have further significant effects. As for wealth, the poor-interacted variable has the opposite sign but is not as large as the noninteracted coefficient, suggesting that the poor have less sensitivity to wealth than nonpoor households do.

These results suggest that the poor are different in several senses. All else equal, a poor household will demand more limits than other households. However, poor households do treat the debt ratio as a constant, just as other households do. In the limit equation, poor households have about the same interest sensitivity as nonpoor households and less income and wealth sensitivity. The broader implications of this similarity between poor and nonpoor are not really very surprising; we would be more surprised if poor people behaved in a way that seemed fundamentally different and irrational relative to the nonpoor. The simple fact that poor people do respond rationally to the availability of credit may nonetheless have significant implications for a number of policies. It may well be the case that if public assistance becomes more difficult to obtain, poor households may instead use a credit card/bankruptcy route to get through their hard times. All of this suggests that analyses of welfare reform concepts may need to include some financial aspects as well.

VII. CONCLUSIONS

Our analysis of data from the SCF has yielded two general findings. First, we have found that the demand for limits responds in intuitive ways to standard economic variables. The own-price elasticity is about -0.40; and the demand for limits rises with income and other wealth.

Second, we have found that most of the demand responsiveness in the credit card market appears to be at the level of limits, not debts. Consumers seem to hold a certain fraction of their limits as debt. This fraction does not seem to vary systematically in the population. Thus it appears that those who want to borrow more will acquire more cards or higher limits, rather than max out the limits on the cards they currently hold. Certainly, the limit is the critical item for suppliers, but our results suggest it is also the critical item for demanders. If this is so, then analysts interested in this market should at least begin with a study of the supply and demand for limits.

ABBREVIATIONS

2SLS: Two-Stage Least Squares

KDM: King and Dicks-Mireaux

SCF: Survey of Consumer Finances

TABLE 1

Growth of the Credit Card Market, 1983-98

 1983 1989 1992
All households
 Percent holding at least one credit card 65 70 74
 Average balance among cardholders 802 1455 1465
 Average new charges per month -- 588 460
 Median limit-bank type cards 9300
 Average debt ratio-bank-type cards -- -- 0.134
 Sample size 4262 3143 3906
Poor households
 Percent holding at least one credit card 17 20 34
 Average balance among cardholders 834 364 1166
 Average new charges per month -- 197 124
 Sample size 485 338 445

 1995 1998

All households 77 74
 Percent holding at least one credit card 1979 2610
 Average balance among cardholders 663 749
 Average new charges per month 11,765 16,043
 Median limit-bank type cards 0.181 0.197
 Average debt ratio-bank-type cards 4299 4305
 Sample size
Poor households 36 32
 Percent holding at least one credit card 1476 1979
 Average balance among cardholders 195 289
 Average new charges per month 482 490
 Sample size

Source: SCF, various years. All money figures in 1998 $US. Note these
figures include debts and charges on all credit cards, but our
regressions use only bank credit cards. Interest rate data exist only
for bank cards. Households defined as poor (POOR) meet two conditions:
(a) income falls below the federal poverty line for a family of that
size, and (b) nonhousing wealth below $100,000.

Note:--indicates no data available.

TABLE 2

Descriptive Statistics for Credit Card Holders

Variable Name Mean SD Median

LIMIT 26,114 64,116 15,000
DEBT 1959 5996 0
DEBT RATIO 0.197 1.832 0
RATE 14.54 4.54 15
INCOME 52,902 100,851 73,606
LWEALTH 133,326 912,055 11.571
SELFEMP 0.31 -- 0
HOME 0.80 -- 1
FEMALE 0.16 -- 0
NONWHITE 0.12 -- 0
EDUC 14.47 2.47 16
MARRIED 0.73 -- 1
FAMSIZE 2.62 1.38 2.00
AGE 50.81 15.17 50
RISK AVERSE 0.66 -- 1
OPTIMIST 0.22 -- 0
POOR 3.44 -- 0

Observations 3229
Status of Poor
Households
with Credit
Cards
LIMIT 7744 12,217 3000
DEBT 1881 5383 370
DEBT RATIO 0.392 1.126 0.156
RATE 15.267 4.41 17
INCOME 10,791 5712 9776
LWEALTH 6373 10,756 1650
SELFEMP 0.072 -- 0
HOME 0.342 -- 0
FEMALE 0.441 -- 0
NONWHITE 0.378 -- 0
EDUC 12.676 3.39 13
MARRIED 0.396 -- 0
FAMSIZE 2.775 1.78 2.00
AGE 41.66 19 37
RISK AVERSE 0.874 -- 1
OPTIMIST 0.333 -- 0

Variable Name Description

LIMIT Sum of limits on all bank credit cards
DEBT Sum of debts on all bank credit cards
DEBT RATIO Ratio of DEBT to LIMIT
RATE Interest rate on card with highest
 balance,in percent
INCOME Household permanent income
LWEALTH Household liquid net worth
SELFEMP Equals 1 if respondent is
 self-employed, 0 otherwise
HOME Equals 1 if respondent owns home,
 0 otherwise
FEMALE Equals 1 if respondent is female,
 0 otherwise. Respondent is typically
 head of household
NONWHITE 1 if respondent is nonwhite,
 0 otherwise
EDUC Respondent's years of schooling
MARRIED 1 if respondent is married,
 0 otherwise
FA MSIZE Family size
AGE Respondent's age
RISK AVERSE 1 if respondent is risk averse
 (self-reported), 0 otherwise
OPTIMIST 1 if respondent thinks economy will
 be good next year, 0 otherwise
POOR 1 if respondent household income
 falls below federal poverty
 guidelines for a family of that size,
 and has less than $100K nonhousing
 wealth; 0 otherwise
Observations
Status of Poor
Households
with Credit
Cards
LIMIT Sum of limits on all bank credit cards
DEBT Sum of debts on all bank credit cards
DEBT RATIO Ratio of DEBT to LIMIT
RATE Interest rate on card with highest
 balance, %
INCOME Household permanent income
LWEALTH Household liquid net worth.
SELFEMP Equals 1 if respondent is
 self-employed, 0 otherwise
HOME Equals 1 if respondent owns home,
 0 otherwise
FEMALE Equals 1 if respondent is female,
 0 otherwise. Respondent is typically
 head of household
NONWHITE 1 if respondent is nonwhite,
 0 otherwise
EDUC Respondent's years of schooling
MARRIED 1 if respondent is married,
 0 otherwise
FAMSIZE Family size
AGE Respondent's age
RISK AVERSE 1 if respondent is risk averse (self-reported),
 0 otherwise
OPTIMIST 1 if respondent thinks economy will be good
 next year, 0 otherwise

TABLE 3

Descriptive Statistics by Self-Employment Status

 Non-Self-Employed

 Mean SD Median

LIMIT 21,642 70,537 10,000
DEBT 1896 4970 0
DEBT RATIO 0.196 0.57 0
RATE 14.46 4.61 15
INCOME 179,710 797,058 54,635
LWEALTH 96,970 727,424 6450
HOME 0.752 0.432 1
FEMALE 0.209 0.407 0
NONWHITE 0.145 0.353 0
EDUC_R 14.16 2.49 14
MARRIED 0.676 0.468 1
FAMSIZE 2.52 1.38 2
AGE_R 50.06 16.34 49
RISKAVER 0.702 0.457 1
OPTIMIST 0.230 0.421 0
Observations 2234

 Self-Employed

 Mean SD Median

LIMIT 36,153 45,021 23,000
DEBT 2098 7823 0
DEBT RATIO 0.200 3.19 0
RATE 14.71 4.38 15.90
INCOME 633,395 2,081,052 200,230
LWEALTH 321,219 1,551,675 26,000
HOME 0.919 0.274 1
FEMALE 0.0047 0.213 0
NONWHITE 0.0074 0.263 0
EDUC_R 15.18 2.28 16
MARRIED 0.852 0.355 1
FAMSIZE 2.85 1.36 2
AGE_R 52.49 11.99 52
RISKAVER 0.552 0.498 1
OPTIMIST 0.211 0.408 0
Observations 995

Notes: Sample is limited to credit card holders only. All money figures
in 1998 (US).

Source: SCF 1998.

TABLE 4

Nested Tobit Results

 Stage 1: ln(LIMIT) Stage 2: DEBT RATIO

Variable Beta SE Beta SE

RATE -0.0274 * 0.0039 -0.0016 0.0227
ln(INCOME) -0.0049 * 0.0012 0.0127 0.0081
ln[(INCOME).sup.2] 0.0046 * 0.0011 -0.0115 0.0073
LWEALTH 0.0977 * 0.0098 -0.0743 0.0561
HOME 0.3008 * 0.0514 -0.0149 0.3055
SELFEMP 0.1274 * 0.0449 0.0408 0.2437
AGE 0.0501 * 0.0078 0.0434 0.0433
AG[E.sup.2] -0.0004 * 0.0001 -0.0005 0.0004
FEMALE -0.2197 * 0.0663 0.1110 0.3781
MARRIED 0.1076 0.0665 0.1841 0.3574
FAMSIZE -0.0311 0.0172 0.0334 0.0919
EDUC 0.0611 * 0.0085 -0.0016 0.0498
NONWHITE -0.2291 * 0.0516 0.0044 0.3057
OPTIMIST 0.0611 0.0426 0.1390 0.2413
RISK AVERSE -0.0911 * 0.0421 -0.1015 0.2377
Constant 5.5165 * 0.2313 0.6903 1.2913
[Sigma.sub.1] 0.969
[Sigma.sub.2] 0.339
Rho -0.721
N 3229
Log likelihood -8640.537
Non-self-employed sample
 RATE -0.0250 * 0.0047 0.0107 0.0062
 ln(INCOME) -0.0062 * 0.0016 0.0091 * 0.0025
 ln[(INCOME).sup.2] 0.0060 * 0.0014 -0.0088 * 0.0022
 LWEALTH 0.0826 * 0.0121 -0.0898 * 0.0148
 HOME 0.2924 * 0.0592 -0.1087 0.0804
 AGE 0.0530 * 0.0089 0.0410 * 0.0111
 AG[E.sup.2] -0.0005 * 0.0001 -0.0006 * 0.0001
 FEMALE -0.2100 * 0.0762 0.1740 * 0.0856
 MARRIED 0.1482 0.0818 0.1537 0.0899
 FAMSIZE -0.0674 * 0.0212 0.0620 * 0.0223
 EDUC 0.0656 * 0.0102 -0.0082 0.0134
 NONWHITE -0.2486 * 0.0598 0.0063 0.0704
 OPTIMIST 0.0315 0.0523 0.0754 0.0646
 RISK AVERSE -0.1008 0.0531 0.0103 0.0647
 Constant 5.3178 * 0.2713 0.7815 * 0.3255
 [Sigma.sub.1] 0.959
 [Sigma.sub.2] 1.143
 Rho -0.107
 N 2234
 Log likelihood -5116.658
Self-employed sample
 RATE -0.0341 * 0.0070 -0.0085 0.0949
 ln(INCOME) -0.0040 * 0.0020 0.0171 0.0294
 ln[(INCOME).sup.2] 0.0034 * 0.0016 -0.015 0.0258
 LWEALTH 0.1251 * 0.0175 -0.0792 0.2562
 HOME 0.2681 * 0.1210 0.0104 1.5483
 AGE 0.0324 0.0200 0.0468 0.2833
AG[E.sup.2] -0.0003 0.0002 -0.0005 0.0027
FEMALE -0.2289 0.1731 0.0593 2.0738
MARRIED 0.0126 0.1205 0.3277 1.5426
FAMSIZE 0.0389 0.0307 0.0100 0.4042
EDUC 0.0492 * 0.0162 0.0046 0.1975
NONWHITE -0.1125 0.1105 0.0868 1.4216
OPTIMIST 0.1480 0.0749 0.1612 1.0177
RISK AVERSE -0.0769 0.0696 -0.2550 0.9177
Constant 6.4773 * 0.5573 0.8689 7.4000
[Sigma.sub.1] 1.005
[Sigma.sub.2] 0.162
Rho -0.077
N 995
Log likelihood -2496.383

TABLE 5

2SLS results

 Full Sample Non-Self-Employed

Variable Beta SE Beta SE

RATE -0.0283 * 0.0040 -0.0261 * 0.0048
ln(INCOME) -0.0051 * 0.0012 -0.0065 * 0.0016
In[(INCOME).sup.2] 0.0047 * 0.0010 0.0063 * 0.0014
LWEALTH 0.1009 * 0.0105 0.0861 * 0.0127
HOME 0.3105 * 0.0555 0.3050 * 0.0629
SELFEMP 0.1315 * 0.0440 -- --
AGE 0.0517 * 0.0079 0.0552 * 0.0088
AG[E.sup.2] -0.0005 * 0.0001 -0.0005 * 0.0001
FEMALE -0.2267 * 0.0695 -0.2189 * 0.0786
MARRIED 0.1111 0.0651 0.1546 0.0787
FAMSIZE -0.0321 0.0168 -0.0703 * 0.0205
EDUC 0.0630 * 0.0086 0.0684 * 0.0104
NONWHITE -0.2365 * 0.0582 -0.2592 * 0.0665
OPTIMIST 0.0631 0.0441 0.0328 0.0532
RISK AVERSE -0.0941 * 0.0412 -0.1051 * 0.0518
Constant 5.6943 * 0.2291 5.5444 * 0.2627
N 3229 2234
[R.sup.2] 0.3435 0.3267

 Only Self-Employed

Variable Beta SE

RATE -0.0339 * 0.0072
ln(INCOME) -0.0040 * 0.0018
In[(INCOME).sup.2] 0.0034 * 0.0016
LWEALTH 0.1245 * 0.0192
HOME 0.2669 * 0.1250
SELFEMP -- --
AGE 0.0323 0.0193
AG[E.sup.2] -0.0003 0.0002
FEMALE -0.2278 0.1724
MARRIED 0.0126 0.1160
FAMSIZE 0.0387 0.0299
EDUC 0.0489 * 0.0156
NONWHITE -0.1120 0.1235
OPTIMIST 0.1473 0.0781
RISK AVERSE -0.0766 0.0673
Constant 6.4471 * 0.5432
N 995
[R.sup.2] 0.2234

Notes: * indicates statistical significance at the 95% level,
two-tailed test. Dependent variable is ln(LIMIT). RATE is instrumented
by credit-worthiness indicators.

Source: SCF 1998.

TABLE 6

Nested Tobit Results with Poverty Interactions, Non-Self-Employed
Sample

 Stage 1: ln(LIMIT) Stage 2: DEBT RATIO

Variable Beta SE Beta SE

POOR 1.2636 * 0.4459 -3.1295 * 0.6667
RATE -0.0239 * 0.0049 0.0083 0.0064
RATE x POOR -0.0066 0.0210 0.0278 0.0322
ln(INCOME) 0.0938 * 0.0302 -0.1986 * 0.0356
ln(INCOME) x POOR -0.0938 * 0.0304 0.1986 * 0.0359
LWEALTH 0.0952 * 0.0127 -0.1041 * 0.0148
LWEALTH x POOR -0.0571 0.0362 0.0946 0.0539
HOME 0.2863 * 0.0601 -0.0997 0.0808
AGE 0.0522 * 0.0090 0.0436 * 0.0110
AG[E.sup.2] -0.0004 * 0.0001 -0.0006 * 0.0001
FEMALE -0.2113 * 0.0766 0.1730 * 0.0872
MARRIED 0.1547 0.0819 0.1594 0.0885
FAMSIZE -0.0610 * 0.0214 0.0621 * 0.0222
EDUC 0.0677 * 0.0102 -0.0061 0.0130
NONWHITE -0.2417 * 0.0600 0.0088 0.0698
OPTIMIST 0.0323 0.0526 0.0784 0.0670
RISK AVERSE -0.0977 0.0535 0.0023 0.0661
Constant 4.7773 * 0.3346 2.0907 * 0.4314
[Sigma.sub.1] 0.9583
[Sigma.sub.2] 1.1474
Rho -0.1086
N 2234
Log likelihood -5109.940

Notes: * indicates statistical significance at the 95% level,
two-tailed test. Household defined as poor (POOR) meet two conditions:
(a) income falls below the federal poverty line for a family of that
size, and (b) nonhousing wealth below $100,000. First-stage dependent
variable is ln(LIMIT). Second-stage dependent variable is DEBT RATIO.

Source: SCF 1998.

TABLE 7

2SLS Results with Poverty Interactions,
Non-Self-Employed Sample

Variable Beta SE

POOR 1.3186 * 0.5152
RATE -0.0250 * 0.0049
RATE x POOR -0.0069 0.0247
ln(INCOME) 0.0979 * 0.0309
ln(INCOME) x POOR -0.0978 * 0.0309
LWEALTH 0.0993 * 0.0130
LWEALTH x POOR -0.0596 0.0421
HOME 0.2988 * 0.0633
AGE 0.0545 * 0.0089
AG[E.sup.2] -0.0005 * 0.0001
FEMALE -0.2205 * 0.0788
MARRIED 0.1614 0.0788
FAMSIZE -0.0636 * 0.0207
EDUC 0.0706 * 0.0104
NONWHITE -0.2522 * 0.0667
OPTIMIST 0.0337 0.0533
RISK AVERSE -0.1020 * 0.0519
Constant 4.9852 * 0.3296
N 2234
[R.sup.2] 0.3255

Notes: * indicates statistical significance at the 95%
level, two-tailed test. Households defined as poor
(POOR) meet two conditions: (a) income falls below
the federal poverty line for a family of that size, and (b)
nonhousing wealth below $100,000. Dependent variable
is ln(LIMIT). RATE is instrumented by credit-worthiness
indicators.

Source: SCF 1998.

(1.) Gross and Souleles (1999) find a similar result in a different data set with different methods.

(2.) This figure ($4,809) is the average debt on all credit cards, among all who have a positive debt. In Table 1, the 1998 average balance ($2,440) includes all who have a card; hence it includes those with a zero balance. In Table 2, DEBT ($1,959) is the average balance on bank credit cards only, among those who have a card. Thus, bank credit card debt represents the overwhelming majority of all debt--over 80%. In our regressions we use the DEBT variable because we do not have price data (interest rates) on cards other than bank credit cards. This also limits us to using the 1998 SCF; the price variable is not available in other years.

(3.) See Bird et al. (1999), Evans and Schmalensee (1999), Yoo (1997; 1998), Canner et al. (1995), Kennickell and Starr-McCluer (1994), Canner and Luckett (1992).

(4.) We experimented with the number of credit cards as a dependent variable. These runs only seemed to suggest that decisions were not being made along that dimension. The sample seemed much more responsive to overall debt and limits, not to the number of cards.

(5.) Credit cards also have other price and cost variables associated with them, annual fees, membership fees, and so on. see Sinkey and Nash (1993). It would be ideal to include these, but we do not have these data in the SCF. We do believe, however, that the interest rate is the most important price variable, because it indicates the marginal cost to the consumer of taking on one more dollar of debt.

(6.) KDM also assign a cohort effect to income. To compare permanent incomes across cohorts, they define permanent income as expected income at the specific age of 45. In other words, they estimate an income equation that includes age, and then they define permanent income as the fitted value of this equation with age set to 45 for all respondents. We felt this procedure was not appropriate for our study. We are not doing a cohort analysis, and conversely it is of interest to us to examine the differences in credit card demand by age. Thus, although we also estimate an income equation and take permanent income as the fitted value (with a KDM-like adjustment for the permanent component of the error), we make the imputation using the respondent's current age, not a standardized age of 45.

(7.) As a further check, we constructed a transitory income variable as the difference between ordinary income and permanent income. Then we compared this variable to a self-reported variable in the data in which the respondent indicates whether she feels that income was high, low, or normal this year. In our sample, 70% of those reporting a good year had transitory income that was positive, and 63% of those reporting a bad year had negative transitory income. We infer from this that our estimates of permanent and transitory income are fairly accurate, at least relative to self-reported income states.

(8.) We thank referees of a previous draft for pointing out this possibility.

(9.) Our instrumenting equation for the interest rate (available on request) showed expected patterns--people with bankruptcies and delinquencies had much higher interest rates on their credit card portfolios.

(10.) We have treated all the income and wealth resources as exogenous, mostly because it would be nearly impossible to find instruments for them. Moreover, we did not have price information for other assets. Future research could build on this by taking the limit market as the critical part of the credit card market and studying the joint demand for limits and other assets.

(11.) One aspect of poor people's credit that would be worth studying is the use of secured credit cards. There are no data on these in the SCF, however.

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EDWARD CASTRONOVA and PAUL HAGSTROM *

* We thank participants in the session Credit Cards: Equity and Efficiency at the 2001 American Economics Association Annual Meetings for helpful comments on our first draft.

Castronova: Associate Professor of Economics, California State University at Fullerton, Fullerton, CA 92834. Phone 1-714-278-4458, Fax 1-714-278-3097, E-mail [email protected]

Hagstrom: Associate Professor of Economics, Hamilton College, Clinton NY 13244. Phone 1-315-859-4146, Fax 1-315 859 4632, E-mail [email protected]