Modeling credit card borrowing: a comparison of type I and type II Tobit approaches.

• Author: Min, Insik

1. Introduction

   More than 11,000 bank and nonbank holding companies issued credit cards in 1997. Among these firms, the top 50 issuers' market share is 90.4%, and the 10 largest credit card issuers hold 57.3% of total outstanding balances. Bank holding company revenue from interest on outstanding balances is $57.5 billion, which is 77.8% of the total revenue of $73.9 billion. Moreover, about 80% of 102 million U.S households own at least one credit card. Demand for credit cards consists of two components, one being the demand as a transaction medium and the other being the demand as a borrowing medium. Over 68% of bank-type credit card holders use their credit cards only as a transaction medium, (1) which means that they pay off their balances in full each month (Cargill and Wendel 1996). However, other credit card holders use their cards as a source of short-term, low-amount borrowing or as an instrument for consumption smoothing. This study focuses on credit cards as a borrowing medium.

   Total household debts have been investigated in other studies relating household debt levels to credit or liquidity constraints. Using a two-step selection approach, Duca and Rosenthal (1993) examine the extent to which borrowing constraints restrict household access to debt and the manner in which lenders vary debt limits across borrowers. Crook (2001) investigates the determinants of credit constraints and the factors in the amount of household debt with a multistage model. However, it is necessary to separate the credit card debt from other household debts in the sense that every credit card user could borrow without incurring a transaction cost. Brito and Hartley (1995) provide a theoretical model in which the equilibrium interest rate can be very high and inflexible under the assumptions of rational consumers and competitive markets. They show that by introducing transaction costs in borrowing from other financial institutions, rational individuals finance a substantial fraction of consumption with credi t card debts.

   Because of a substantial number of zero balances, the credit card debt function has been estimated by a type I Tobit model, the traditional Tobit model. One shortcoming of the type I Tobit model is that it restricts coefficients on the choice to borrow and the balance level chosen to have the same sign because the coefficients of two different decisions are coming from estimating the same equation. However, without a priori information, this restriction could result in possible model misspecification.

   In Table 1, the 1998 Survey of Consumer Finance data show the following patterns between income and credit card borrowing: Relative income level is negatively correlated with the probability to hold a positive credit card balance but is positively correlated with the level of card debt. (2) We could infer that a lower income household is more likely to borrow with a credit card and that the balance level is smaller partly because of limited credit availability compared to a higher-income household.

   In place of the type I Tobit approach, an alternative type II Tobit technique is used to separately model whether to borrow (the first step) and how much to borrow (the second step). By estimating the first and second steps as reduced-form functions, this estimation procedure will yield more consistent results with other studies and quantify the behavior of credit card users for practical uses.

   The remainder of this study is as follows. Section 2 briefly describes the data and provides theoretical foundations. In section 3, the econometric methodology of type I Tobit and type II Tobit models is discussed. Section 4 provides empirical results, whose implications are examined in section 5, which concludes the paper.

2. SCF Data and Theoretical Background

   Data Source and Descriptions

   The data used in our empirical analysis are from the 1998 Survey of Consumer Finance (S CE). The survey is designed to provide detailed information on U.S. household assets, liabilities, incomes, and use of financial institutions and instruments such as credit cards and mutual funds. This survey studies a random sample of U.S. households, with an oversampling of relatively high-income and high-wealth households, because income and wealth are concentrated among a small number of households, so a random sample of the population will miss too many high-income households (for details, see Kennickell and Starr-McCluer 1994).

   The original sample size in the 1998 survey was 4309 households. We require that households have at least one bank-type credit card, such as Visa, MasterCard, Discover, or Optima. In addition, households with more than $1,000,000 in income or with negative income are excluded from our analysis in that they are not likely to be typical credit card holders. (3) As a consequence, there are 2904 households in our sample. Detailed variable descriptions and summary statistics are provided in Table 2.

   Theoretical Background

   A specification for credit card balances can be formalized in the context of conventional supply-demand theory. In the credit card market, when deciding on debt ceilings, suppliers (lenders) consider a number of borrower characteristics that are also included in the demand function specification. Therefore, credit card balances are determined by the confluence of supply and demand considerations. Specifically, equilibrium debt levels can be described by

   [D.sub.i] = f([P.sub.i], [I.sub.i], [S.sub.i], [T.sub.i], [R.sub.i], [E.sub.i]),

   where [P.sub.i] is the price of credit card borrowing defined as the interest rate charged on outstanding balances, [I.sub.i] is a household income, [S.sub.i] is a volume of liquid assets, [T.sub.i], is a taste variable, [R.sub.i] denotes a risk aversion factor, and [E.sub.i] contains some environmental proxies.

   Intuitively, the demand for borrowing with credit cards should decline as the interest rate increases. However, as Ausubel (1991) pointed out, consumers may not be very responsive to interest rate cuts partly because of switch/search costs. (4) Another key determinant is the household income ([I.sub.i]). We can predict that a household with low income is relatively constrained to the available credit limit; that is, their possible borrowing levels are restricted by suppliers. Traditional demand theory suggests that, ceteris paribus, higher-income households should have a higher demand for credit card borrowing than lower-income families.

   Liquid assets ([S.sub.i]) are included in the specification because they can be used to finance consumption instead of borrowing from credit cards with high interest rates. Accordingly, households that are likely to be liquidity constrained (those holding few liquid assets) are probably more likely to use credit cards to finance unexpected expenditures. Contrary to our intuition about the effect of this variable, Morrison (1998) and Gross and Souleles (2002) show that a considerable fraction of households (about 33%) not only have credit card balances outstanding but also have accumulated liquid assets that exceed one month of income.

   Laibson, Repetto, and Tobacman (2000) find that the median household borrows aggressively on credit cards but still manages to carry a substantial amount of illiquid wealth. In other words, consumers do not act consistently, acting patiently with regard to retirement accumulation and impatiently in the credit card market. (5) They describe this inconsistency as "a debt puzzle." They suggest that the resolution to this puzzle is to assume that households have hyperbolic time preferences.

   An implication of their analysis is that illiquid assets such as retirement savings should have no significant effect on credit card debts. In our study, we consider three types of assets: (i) checking balances (highly liquid); (ii) saving accounts, total money market accounts (MMAs). and call accounts at brokerages (CALL) (less liquid); and (iii) pensions and the cash value of life insurance (illiquid)

   In general, the tastes or preferences ([T.sub.i]) of each individual should enter the demand for credit card borrowing. Some variables that can be presumed as attitudes toward financing with credit cards are found in SCF data. For instance, questionnaires included in SCF survey are as follows: "In general, do you think it is a good idea for people to buy things on the installment plan?" or "Do you think it is a good idea to cover the expenses of a vacation trip and to purchase a fur coat or jewelry with credit cards?" Intuitively, higher preferences toward borrowing in general may be associated with a higher demand for credit card borrowing.

   We consider the risk aversion factor ([R.sub.i]) in the consumer's utility function. Brito and Hartley's (1995) simulation results show that the relative risk aversion of consumers has little effect on the probability of financing with credit cards but has a negative effect on the amount of credit card balances. Similarly, we include the proxy for the risk aversion in specifying the borrowing decision and the credit card debt level functions.

   Finally, environmental proxies ([E.sub.i]) contain demographic variables such as age, ethnicity and gender, and the variable closely associated with credit constraints. Intuitively, credit constrained households have a higher effective demand for credit card borrowing because they are likely to be denied other forms of credit.

3. Econometric Methodology

   The type I Tobit approach has been employed to estimate the credit card debt function (Duca and Rosenthal 1993; Calem and Mester 1995). To overcome the main shortcoming of type I Tobit model, the two-step approach (type II Tobit) has been used to model cigarette consumption (Blaylock and Blisard 1992) and expenditure on food consumed away from home (Byrne, Capps, and Saha 1996). In addition, we pay more attention to the marginal effect (elasticity) in the debt balance function, which has...