Modeling credit card borrowing: a comparison of type I and type II Tobit approaches.1. Introduction More than 11,000 bank and nonbank non·bank adj. Of, relating to, or done by a business or an institution that is not a bank but performs similar services. 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 A liquidity constraint in economic theory is a form of imperfection in the capital market. It causes difficulties for models based on intertemporal consumption. Many economic models require individuals to save or borrow money from time to time. . Using a two-step selection approach, Duca and Rosenthal (1993) examine the extent to which borrowing constraints CONSTRAINTS - A language for solving constraints using value inference. ["CONSTRAINTS: A Language for Expressing Almost-Hierarchical Descriptions", G.J. Sussman et al, Artif Intell 14(1):1-39 (Aug 1980)]. 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 mul·ti·stage adj. 1. Functioning in more than one stage: a multistage design project. 2. Relating to or composed of two or more propulsion units. model. However, it is necessary to separate the credit card debt Credit card debt is an example of unsecured consumer debt, accessed through ISO 7810 plastic credit cards. Debt results when a client of a credit card company purchases an item or service through the card system. from other household debts in the sense that every credit card user could borrow without incurring in·cur tr.v. in·curred, in·cur·ring, in·curs 1. To acquire or come into (something usually undesirable); sustain: incurred substantial losses during the stock market crash. 2. a transaction cost. Brito and Hartley (1995) provide a theoretical model in which the equilibrium equilibrium, state of balance. When a body or a system is in equilibrium, there is no net tendency to change. In mechanics, equilibrium has to do with the forces acting on a body. interest rate can be very high and inflexible under the assumptions of rational consumers and competitive markets. They show that by introducing transaction costs Transaction Costs Costs incurred when buying or selling securities. These include brokers' commissions and spreads (the difference between the price the dealer paid for a security and the price they can sell it). 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 Tobit Model is an econometric, biometric model proposed by James Tobin (1958) to describe the relationship between a non-negative dependent variable , the traditional Tobit model. One shortcoming short·com·ing n. A deficiency; a flaw. shortcoming Noun a fault or weakness Noun 1. 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 a priori In epistemology, knowledge that is independent of all particular experiences, as opposed to a posteriori (or empirical) knowledge, which derives from experience. 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 cor·re·late v. cor·re·lat·ed, cor·re·lat·ing, cor·re·lates v.tr. 1. To put or bring into causal, complementary, parallel, or reciprocal relation. 2. 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 estimation In mathematics, use of a function or formula to derive a solution or make a prediction. Unlike approximation, it has precise connotations. In statistics, for example, it connotes the careful selection and testing of a function called an estimator. procedure will yield more consistent results with other studies and quantify Quantify - A performance analysis tool from Pure Software. 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 e·con·o·met·rics n. (used with a sing. verb) Application of mathematical and statistical techniques to economics in the study of problems, the analysis of data, and the development and testing of theories and models. 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 SCF Service Canadien des Forêts (Canadian Forest Service) SCF Stem Cell Factor SCF Scientific Committee on Food (European Commission) SCF Service Canadien de la Faune 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 Creating a more accurate digital representation of an analog signal. In order to work with real-world signals in the computer, analog signals are sampled some number of times per second (frequency) and converted into digital code. 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 for·mal·ize tr.v. for·mal·ized, for·mal·iz·ing, for·mal·iz·es 1. To give a definite form or shape to. 2. a. To make formal. b. 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 confluence /con·flu·ence/ (kon´floo-ins) 1. a running together; a meeting of streams.con´fluent 2. in embryology, the flowing of cells, a component process of gastrulation. 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 Cash, or property immediately convertible to cash, such as Securities, notes, life insurance policies with cash surrender values, U.S. savings bonds, or an account receivable. , [T.sub.i], is a taste variable, [R.sub.i] denotes a risk aversion risk aversion The tendency of investors to avoid risky investments. Thus, if two investments offer the same expected yield but have different risk characteristics, investors will choose the one with the lowest variability in returns. 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 determinant, a polynomial expression that is inherent in the entries of a square matrix. The size n of the square matrix, as determined from the number of entries in any row or column, is called the order of the determinant. is the household income ([I.sub.i]). We can predict that a household with low income is relatively constrained con·strain tr.v. con·strained, con·strain·ing, con·strains 1. To compel by physical, moral, or circumstantial force; oblige: felt constrained to object. See Synonyms at force. 2. to the available credit limit; that is, their possible borrowing levels are restricted by suppliers. Traditional demand theory suggests that, ceteris paribus Ceteris Paribus Latin phrase that translates approximately to "holding other things constant" and is usually rendered in English as "all other things being equal". In economics and finance, the term is used as a shorthand for indicating the effect of one economic variable on , 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 intuition, in philosophy, way of knowing directly; immediate apprehension. The Greeks understood intuition to be the grasp of universal principles by the intelligence (nous), as distinguished from the fleeting impressions of the senses. 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 ac·cu·mu·late v. ac·cu·mu·lat·ed, ac·cu·mu·lat·ing, ac·cu·mu·lates v.tr. To gather or pile up; amass. See Synonyms at gather. v.intr. To mount up; increase. 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 Illiquid An asset or security that cannot be converted into cash very quickly (or near prevailing market prices). Notes: A house is a good example of an illiquid asset. See also: Cash, Liquidity Illiquid In the context of finance. wealth. In other words Adv. 1. in other words - otherwise stated; "in other words, we are broke" put differently , consumers do not act consistently, acting patiently with regard to retirement accumulation and impatiently im·pa·tient adj. 1. Unable to wait patiently or tolerate delay; restless. 2. Unable to endure irritation or opposition; intolerant: impatient of criticism. 3. in the credit card market. (5) They describe this inconsistency in·con·sis·ten·cy n. pl. in·con·sis·ten·cies 1. The state or quality of being inconsistent. 2. Something inconsistent: many inconsistencies in your proposal. as "a debt puzzle “Puzzle solving” redirects here. For the concept in Thomas Kuhn's philosophy of science, see normal science. A puzzle is a problem or enigma that challenges ingenuity. ." They suggest that the resolution to this puzzle is to assume that households have hyperbolic hy·per·bol·ic also hy·per·bol·i·cal adj. 1. Of, relating to, or employing hyperbole. 2. Mathematics a. Of, relating to, or having the form of a hyperbola. b. 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 jewelry, personal adornments worn for ornament or utility, to show rank or wealth, or to follow superstitious custom or fashion. The most universal forms of jewelry are the necklace, bracelet, ring, pin, and earring. 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 ethnicity Vox populi Racial status–ie, African American, Asian, Caucasian, Hispanic 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 con·sume v. con·sumed, con·sum·ing, con·sumes v.tr. 1. To take in as food; eat or drink up. See Synonyms at eat. 2. a. 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 been often ignored in other studies. Type I Tobit Model The type I Tobit model is of the form [Y.sup.*.sub.i] = [X.sub.i][beta]+[[xi].sub.i], [[xi].sub.i] ~ N(0,[[sigma].sup.2.sub.[xi]]), where [Y.sup.*.sub.i] is a latent variable In statistics, Latent variables (as opposed to observable variables), are variables that are not directly observed but are rather inferred (through a mathematical model) from other variables that are observed and directly measured. that may imply the desired stock of borrowing. [Y.sup.*.sub.i] is not always observable ob·serv·a·ble adj. 1. Possible to observe: observable phenomena; an observable change in demeanor. See Synonyms at noticeable. 2. . We observe [Y.sub.i] = [Y.sup.*.sub.i] if [Y.sup.*.sub.i] > 0 and[Y.sub.i] = 0 if [Y.sup.*.sub.i] [less than or equal to] 0. Explanatory ex·plan·a·to·ry adj. Serving or intended to explain: an explanatory paragraph. ex·plan variables ([X.sub.i]) include interest rate, income, preference, and other factors described in the previous section. Under the normality normality, in chemistry: see concentration. assumption of the error term [[xi].sub.i], we have Pr[[Y.sub.i] >0] = Pr[[xi].sub.i]>-[X.sub.i][beta]/[[sigma].sub.[xi]] = [PHI phi n. Symbol  The 21st letter of the Greek alphabet.PHI, n See health information, protected. ]([X.sub.i][beta]/[[sigma].sub.[xi]]), and E[Y.sub.i]/[Y.sub.i]>0] = [X.sub.i][beta]+[[sigma].sub.[xi][phi]([X.sub.i][beta]/[[sigma].sub.[ xi]])/[PHI](X.sub.i][beta]/[[sigma].sub.xi]]. In type I Tobit analysis, McDonald and Moffitt (1980) suggest a useful decomposition decomposition /de·com·po·si·tion/ (de-kom?pah-zish´un) the separation of compound bodies into their constituent principles. de·com·po·si·tion n. 1. of [partial]E[[Y.sub.i]/[X.sub.i]][partial][x.sub.ik]. Following their decomposition, two marginal effects can be derived: [partial]Pr[[Y.sub.i] > 0]/[partial][x.sub.ik] = [partial][PHI]([X.sub.i][beta]/[[sigma].sub.[xi]])/ [partial][x.sub.ik] = [[beta].sub.k]/[[sigma].sub.[xi]].[phi]([X.sub.i][beta]/[[sigma].sub. [xi]]), (1) and [partial]E[[Y.sub.i]/[Y.sub.i] > 0]/[partial][x.sub.ik] = [[beta].sub.k] - [[beta].sub.k].[PHI]([X.sub.i][beta]/[[sigma].sub.[xi]])/[PHI]([X.sub .i][beta]/[[sigma].sub.[xi]])[([X.sub.i][beta]/[[sigma].sub.[xi]]) + [PHI]([X.sub.i][beta]/[[sigma].sub.[xi]])/ [PHI]([X.sub.i][beta]/[[sigma].sub.[xi]])], (2) where [phi](.) and [PHI](.) are the standard normal probability density function Probability density function The function that describes the change of certain realizations for a continuous random variable. and cumulative distribution function, respectively. Equation 1 represents the marginal effect of variable [x.sub.ik] on the binary Meaning two. The principle behind digital computers. All input to the computer is converted into binary numbers made up of the two digits 0 and 1 (bits). For example, when you press the "A" key on your keyboard, the keyboard circuit generates and transfers the number 01000001 to the borrowing decision, and Equation 2 yields the marginal effect of [x.sub.ik] on the amount of credit card borrowing conditional on households using credit cards as a borrowing medium. Type II Tobit Model The type II Tobit model with sample selection is motivated mo·ti·vate tr.v. mo·ti·vat·ed, mo·ti·vat·ing, mo·ti·vates To provide with an incentive; move to action; impel. mo by the specification of Heckman (1979): selection equation: [Y.sup.*.sub.1i] = [X.sub.1i][alpha] + [v.sub.i] (3) main equation: [Y.sub.2i] = [X.sub.2i][gamma] + [u.sub.i], (4) where [Y.sup.*.sub.1i] is a latent variable and [Y.sub.2i] is the amount of credit card debt, which is observable only when [Y.sub.1i] = 1. We observe [Y.sub.1i] = 1 if a household is currently borrowing with credit cards and [Y.sub.1i] = 0 if a household has a zero credit card balance. The error ([v.sub.i], [u.sub.i]) is assumed to have a bivariate bi·var·i·ate adj. Mathematics Having two variables: bivariate binomial distribution. Adj. 1. normal distribution with correlation coefficient Correlation Coefficient A measure that determines the degree to which two variable's movements are associated. The correlation coefficient is calculated as: [[rho].sub.vu]. Identification conditions are chosen as [[sigma].sub.v], [[sigma].sub.u], [[rho].sub.vu]] = [1, [[sigma].sub.u], [[rho].sub.vu]]. The conditional expectation In probability theory, a conditional expectation (also known as conditional expected value or conditional mean) is the expected value of a real random variable with respect to a conditional probability distribution. of [Y.sub.2i] given [Y.sub.1i] = 1 in Equation 4 is E[[Y.sub.2i] / [Y.sub.1i] = 1] = E[[Y.sub.2i] / [v.sub.i] > - [X.sub.1i][alpha]] = [X.sub.2i][gamma]] + E[[u.sub.i] / [v.sub.i] > [X.sub.1i][alpha]], (5) where E([u.sub.i]/[v.sub.i] > - [X.sub.1i][alpha]] [not equal to] 0 because of correlation between [v.sub.i] and [u.sub.i]. The bivariate normal assumption implies that E([u.sub.i]/[v.sub.i] > - [X.sub.1i][alpha]] = [[rho].sub.vu]] [[sigma].sub.u][[PHI]([X.sub.1i][alpha]])/ [[PHI]([X.sub.1i][alpha]])], where [phi]([X.sub.1i][alpha])/ [[PHI]([X.sub.1i][alpha]]) is known as the inverse Mills ratio The inverse Mills' ratio is a concept in statistics. It is the ratio of the probability density function over the cumulative distribution function of a distribution. (MILLS). (6) When we estimate Equation 5 by OLS OLS Ordinary Least Squares OLS Online Library System OLS Ottawa Linux Symposium OLS Operation Lifeline Sudan OLS Operational Linescan System OLS Online Service OLS Organizational Leadership and Supervision OLS On Line Support OLS Online System with a selected subsample sub·sam·ple n. A sample drawn from a larger sample. tr.v. sub·sam·pled, sub·sam·pling, sub·sam·ples To take a subsample from (a larger sample). , the inverse Mills ratio should be included as an additional regressor. From Equations 3 and 4, one obtains Pr[[Y.sub.1i] = 1] = Pr[[Y.sup.*.sub.1i] > 0] = [[PHI]([X.sub.1i][alpha]), and E[[Y.sub.2i]/[Y.sub.1i] = 1] = [X.sub.2i][gamma] + [[rho].sub.vu]] [[sigma].sub.v][[PHI](-[X.sub.1i][alpha]])/ 1 - [[PHI](-[X.sub.1i][alpha]]). In this type II Tobit model, we can derive comparable marginal effects on borrowing decision and the level of balance. The marginal effect of [x.sub.ik] on the binary borrowing decision is [partial]Pr[[Y.sub.li] = 1]/[partial][x.sub.ik] = [partial][PHI]([x.sub.1I][alpha])/[partial][x.sub.ik] = [[alpha].sub.k][phi]([X.sub.1i][alpha]), and the marginal effect on the positive level of credit card balance is [partial]E[[Y.sub.2i]\[Y.sub.li] = 1]/[partial][x.sub.ik] = [[gamma].sub.k] - [p.sub.vu][[sigma].sub.11][[alpha].sup.k] [phi]([X.sup.li][alpha])/[PHI]([X.sub.li][alpha])[[X.sub.li][alpha] + [phi]([X.sub.li][alpha]/[PHI](X.sub.li][alpha])]. 4. Empirical Results Model Specification For the type I Tobit model specification, we estimate the reduced form In social science and statistics, particularlly econometrics, a reduced form equation is a method of dealing with endogeneity. A reduced form equation is defined by James Stock & Mark Watson (2007) in the following way: of the supply-demand Equation 6 on the basis of the theoretical foundations discussed in the earlier section: [Y.sup.*.sub.i] = [X.sub.i][beta] + [[xi].sub.i] = [[beta].sub.0] + [[beta].sub.1][INT.sub.i] + [[Beta].sub.2][LINC.sub.i] + [[beta].sub.3][HSIZE.sub.i] + [[beta].sub.4][AGE.sub.i] + [[beta].sub.5][SEX.sub.i] + [[beta].sub.6][EDUC EDUC Education EDUC Commission for Culture and Education (COR) .sub.i] + [[beta].sub.7][HOME.sub.i] + [[beta].sub.8][MAR.sub.i] + [[beta].sub.9][RACE.sub.i] + [[beta]sub.10][WORK.sub.i] +[[beta].sub.11][LLIQ1.sub.i] + [[beta].sub.12][[LLIQ2.sub.i] + [[beta].sub.13][LLIQ3.sub.i] + [[beta].sub.14][RISK.sub.i] + [[beta].sub.15][SHOP.sub.i] + [[beta].sub.16][INST.sub.17][EMER.sub.i] + [[beta].sub.18][VACA VACA Virginia Animal Control Association VACA Virginia Contracting Activity .sub.i] + [[beta].sub.19][LUX A unit of measurement of the intensity of light. It is equal to the illumination of a surface one meter away from a single candle. See candela. .sub.i] + [[beta].sub.20][CC.sub.i] + [[beta].sub.21][NCC NCC See National Clearing Corporation (NCC). .sub.i] + [[xi].sub.i], (6) where variables are defined (with their summary statistics) in Table 2. For the dependent variable, we observe a positive credit card balance (CC[B.sub.i] [Y.sup.*.sub.i]) if the latent variable [Y.sup.*.sub.i] > 0 and a zero credit card balance ([CC[B.sub.i] 0) if [Y.sup.*.sub.i] 0. The dummy variable This article is not about "dummy variables" as that term is usually understood in mathematics. See free variables and bound variables. In regression analysis, a dummy variable for credit constraint Constraint A restriction on the natural degrees of freedom of a system. If n and m are the numbers of the natural and actual degrees of freedom, the difference n - m is the number of constraints. ([CC.sub.i]) is 1 if the respondent In Equity practice, the party who answers a bill or other proceeding in equity. The party against whom an appeal or motion, an application for a court order, is instituted and who is required to answer in order to protect his or her interests. has experienced a rejection for credit card application or credit line increase at least once in the past five years. For a type II Tobit model, we estimate two regression equations Regression equation An equation that describes the average relationship between a dependent variable and a set of explanatory variables. , the selection equation (Eqn. 7) and the main equation (Eqn. 8) are given here: [Y.sup.*.sub.1I] = [X.sub.1i] [alpha] + [v.sub.i] = [[alpha].sub.0] + [[alpha].sub.0] + [[alpha].sub.1][INT.sub.i] + [[alpha].sub.2][LINC.sub.i] + [[alpha].sub.3][HSIZE].sub.i] + [[alpha].sub.4][AGE.sub.i] [[alpha].sub.5][SEX.sub.i] + [[alpha].sub.6][EDUC.sub.i] + [[alpha].sub.7][HOME.sub.i] + [[alpha.sub.8][MAR.sub.i] + [[alpha.sub.9][RACE.sub.i] + [[alpha.sub.10][WORK.sub.i] + [[alpha.sub.11][LLIQ1.sub.i] + [[alpha.sub.12][LLIQ2.sub.i] + [[alpha.sub.13][LLIQ3.sub.i] + [[alpha.sub.14][RISK.sub.i] + [[alpha.sub.15][SHOP.sub.i] + [[alpha.sub.16][INST.sub.i] + [[alpha.sub.17][EMER.sub.i] + [[alpha.sub.18][VACA.sub.i] + [[alpha].sub.19][LUX.sub.i] + [[alpha.sub.20][CC.sub.i] + [v.sub.i], (7) where we observe the borrowing decision ([BD.sub.i]) [BD.sub.i] = 1 if [Y.sup.*.sub.1i] > 0 and [BD.sub.i] = 0 if [Y.sup.*.sub.1i] [less than or equal to] 0. and [Y.sub.2i] = [X.sub.2I][gamma] + [u.sub.i] = [[gamma].sub.0] + [[gamma].sub.1][INT.sub.i] + [[gamma].sub.2][LINC.sub.i] + [[gamma].sub.3][HSIZE.sub.i] [[gamma].sub.4][AGE.sub.i] + [[gamma].sub.5][SEX.sub.i] + [[gamma].sub.6][EDUC.sub.i] + [[gamma].sub.7][HOME.sub.i] + [[gamma].sub.8][MAR.sub.i] + [[gamma].sub.9][RACE.sub.i] + [[gamma].sub.10][WORK.sub.i] + [[[gamma].sub.11][LLIQ1.sub.i] + [[gamma].sub.12][LLIQ2.sub.i] + [[gamma].sub.13][LLIQ3.sub.i] + [[gamma].sub.14][RISK.sub.i] + [[gamma].sub.15][NCC.sub.i] + [u.sub.i], (8) where [Y.sub.2i] is defined as the amount of credit card balance ([CCB CCB Calcium channel blocker, see there .sub.i) conditional on [BD.sub.i] = 1. To satisfy the identification condition given by Maddala (1983, p. 233), we include some taste (preference) variables and the credit constraint dummy Sham; make-believe; pretended; imitation. Person who serves in place of another, or who serves until the proper person is named or available to take his place (e.g., dummy corporate directors; dummy owners of real estate). ([CC.sub.i]) only in [X.sub.1i]. However, the variables excluded from the main equation can still affect the level of credit card debt borrowed through the inverse Mills ratio. Exogeneity Test for Credit Constraint ([CC.sub.i]) The simultaneity between credit constraint and household debt has been investigated in previous studies using sample selection technique (Duca and Rosenthal 1993; Crook 2001). Exogeneity of [CC.sub.i] is required to guarantee consistent parameter (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind. estimates. A two-stage conditional maximum likelihood (ML) approach is used to test whether [CC.sub.i] should be treated as an endogenous variable Endogenous variable A value determined within the context of a model. Related: Exogenous variable. . First, a Probit model In statistics, a probit model is a popular specification of a generalized linear model, using the probit link function. Probit models were introduced by Chester Ittner Bliss in 1935. is estimated, where [CC.sub.i] is regressed on additional instrumental variables. (7) Second, generalized gen·er·al·ized adj. 1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain. 2. Not specifically adapted to a particular environment or function; not specialized. 3. residuals derived from the first-order conditions are used to construct the ML estimates needed to implement the exogeneity test (Smith and Blundell 1986; Rivers and Vuong 1988), where the test statistic statistic, n a value or number that describes a series of quantitative observations or measures; a value calculated from a sample. statistic a numerical value calculated from a number of observations in order to summarize them. is a likelihood-ratio (LR) statistic. In this study, we test if [CC.sub.i] is exogenous Exogenous Describes facts outside the control of the firm. Converse of endogenous. in the selection equation of the type H Tobit model. The LR test statistic is 0.46 ~ [chi square chi square (kī), n a nonparametric statistic used with discrete data in the form of frequency count (nominal data) or percentages or proportions that can be reduced to frequencies. ](1), with a p-value of 0.49, indicating that exogeneity of [CC.sub.i] is not rejected. Marginal Effect (Elasticity) and Prediction Performance From the third column of Table 3, it can be concluded that sample selection bias exists because the coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int) 1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities. 2. for the inverse Mills ratio (MILLS) is significant. Because estimated coefficients reported in Table 3 from two models have implications only about qualitative effects, we compute To perform mathematical operations or general computer processing. For an explanation of "The 3 C's," or how the computer processes data, see computer. the marginal effect of a determinant at the sample mean to explicitly quantify the behavior of credit card users. Two types of marginal effects can be estimated using type I and type II Tobit models. The first set includes the marginal effects of variables on whether to borrow with a credit card, and the second set includes the marginal effects on how much credit card debt to borrow. Two types of marginal effects in each model are presented in Table 4. Marginal effects on whether to borrow with credit cards are given in the first two columns. It is noteworthy that the coefficients from the two models are very close and that there is no qualitative difference between the two models. The interest rate (INT) has, as expected, a significantly negative effect on the probability of borrowing. From the first two columns in Table 4, a 1-percentage-point increase in the interest rate leads to a 0.6- to 0.7-percentage-point decrease in the probability of borrowing, which implies that households are not very responsive to interest rate changes. Income (LINC) as another key determinant negatively affects the borrowing likelihood. More specifically, a 1% increase in income induces an 8.7-0% decrease in the probability of borrowing. Younger households are more likely to use credit cards to borrow than older families, as reflected in the negative coefficient on the credit card holder's age (AGE). This result is consistent with the fact that younger families have more limi ted access to other financial instruments. Furthermore, it can explain why credit card issuers have recently increased their marketing efforts to attract younger customers. The probability of borrowing is negatively correlated to schooling years (EDUC) and to nonwhite non·white n. A person who is not white. non  white adj. racial status (RACE), which is
consistent with evidence that minorities face tighter debt limits than
white households in loan markets (Duca and Rosenthal 1993).
Turning to the effect of assets, checking balance (LLIQ1) and illiquid assets (LLIQ3) do not significantly affect the probability of borrowing, in accordance Accordance is Bible Study Software for Macintosh developed by OakTree Software, Inc.[] As well as a standalone program, it is the base software packaged by Zondervan in their Bible Study suites for Macintosh. with Laibson, Repetto, and Tabacman's (2000) argument discussed in the previous section. In contrast, households with more saving and mutual fund assets Fund assets The total value of a portfolio's securities, cash, and other holdings, minus any outstanding debts. (LLIQ2) are less inclined to borrow with credit cards. In addition, the risk aversion (RISK) factor has little effect on the probability of borrowing, consistent with simulation results from Brito and Hartley (1995). As expected, a tendency to shop for better borrowing and financing terms (SHOP) has a significantly negative effect on borrowing likelihood, consistent with the negative effect of interest rates (INT). Among the preference variables for credit card borrowing, a tendency to purchase with installment plans (INST) and a tendency to finance a vacation trip by borrowing (VACA) significantly raise the probability of borrowing. Nonetheless, the most crucial variable for determining credit card borrowing is the credit constraint (CC), whose coefficient implies a 20-30% higher probability of borrowing if a household has experienced the credit constraint in the past five years. While the two approaches yield very similar results for the probability of using credit cards as a borrowing medium, substantial differences arise when estimating the amounts borrowed conditional on using credit card debt. For three key variables (interest rate, age, and income), we test if there is a statistical difference between the two marginal effects presented in the third and fourth columns of Table 4. The null hypothesis null hypothesis, n theoretical assumption that a given therapy will have results not statistically different from another treatment. null hypothesis, n of no difference is rejected at the 5% significance level: Test statistics are -2.00, -5.01, and -6.08, respectively. One of the key variables, interest rate (INT), has a statistically significant, negative effect on the borrowing level in the type I Tobit model, whereas this variable is insignificant according to according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. the type II Tobit model. This result exactly elucidates the reason the interest rate has been so sticky Refers to an application or service that keeps you on a Web site. For example, stock quotes, glossaries, educational material, chat rooms and similar offerings give you reason to remain on the site, while it allows the company to show you more ads or proprietary messages. and relatively high in the credit card market, which seems to be perfectly competitive. Even though households respond to an interest rate cut when deciding to borrow, they react very little to interest rate changes when determining how much to borrow. For household income (LINC), a qualitative difference between the two models is also apparent. While a household with higher income borrows less according to the type I Tobit model, household income is significantly and positively related to credit card balances according to the type II Tobit model. The type I model implies that a household with average income reduces its credit card balance by 0.5% for every 1% rise in income, whereas the increase is notably smaller at 015% in the type II Tobit model. The coefficient from the type II Tobit model is more consistent with Table 1, in which the average balance for the bottom three income quantiles is $3905 and the average balance for the top three quantiles $9035. Differences also arise for demographic variables. For example, the marginal effect of a respondent's age (AGE) is significantly negative according to the type I Tobit model, which indicates that older households have less credit card debt. However, according to the type II Tobit model, a credit card holder's age (AGE) has no significant effect on the amount of credit card debt held. For another demographic variable, the borrowing level is negatively associated with a respondent's years of schooling (EDUC) for the type I Tobit model, but this negative relationship is not found while using the type II Tobit approach. Moreover, there is a qualitative change in marginal effects for the other two variables: marital status marital status, n the legal standing of a person in regard to his or her marriage state. (MAR) and nonwhite racial status (RACE). In particular, the type I Tobit model predicts that a nonwhite household will borrow 28.8% more than a white household. (8) In contrast, the type II Tobit model finds that ethnicity has no significant effect on the amount of credit card debt held. With respect to asset holding effects, the two approaches yield quantitatively different findings. For example, the volume of less liquid assets (LLIQ2) significantly decreases credit card balance levels in both the type I and the type II Tobit model, but the elasticity from the type II Tobit model is just half as much as that in the type I Tobit model. A more risk-averse household borrows less with a credit card in the type II Tobit model, and the percentage change due to the characteristic of risk aversion is around 28.3%, which means that a risk-averse household borrows 28.3% less compared to a risk-neutral or risk-inclined household. It is noted that the accumulation of illiquid assets (LLIQ3) has nothing to do with credit card balances in either model. Like the debt puzzle proposed by Laibson, Repetto, and Tobacman (2000), inconsistent behavior of a credit card user in credit card borrowing and accumulation for retirement is observed for both type I and type II Tobit models.9 It is noted that there is no qualitative difference between two models with regard to taste or preference variables (SHOP, INST, VACA, EMER, and LUX). In addition, as expected, credit-constrained households (CC) having more credit cards (NCC) borrow more. In terms of marginal effects, the type II Tobit model seems to be notably more consistent with simple cross-section correlations and with results of other, related studies. In this subsection subsection Noun any of the smaller parts into which a section may be divided Noun 1. subsection - a section of a section; a part of a part; i.e. , a comparison is carried out between the two approaches to investigate which model yields better insample and out-of-sample predictions. First, we divide the data into two parts. We use the first 2500 observations as the in-sample data to estimate the coefficients. These estimated coefficients are used to predict the credit card borrowing behaviors for the remaining out-of-sample 404 households. Prediction results are provided in Table 5. The Count [R.sup.2], which represents the prediction performance for the binary borrowing decision, is defined as the proportion of households correctly predicted to use credit cards for borrowing purposes. For the prediction of credit card balances among borrowers, the mean squared prediction error In statistics the mean squared prediction error of a smoothing procedure is the expected sum of squared deviations of the fitted values  from the (unobservable) function (MSPE MSPE Medical Student Performance EvaluationMSPE Michigan Society of Professional Engineers MSPE Minnesota Society of Professional Engineers MSPE Mean Square Prediction Error MSPE Mercenaries Spies & Private Eyes (game) ) is compared. In in-sample prediction, the type II Tobit model predicts slightly better according to both the Count [R.sup.2] and the MSPE. In out-of-sample prediction, the type I Tobit model has an inferior INFERIOR. One who in relation to another has less power and is below him; one who is bound to obey another. He who makes the law is the superior; he who is bound to obey it, the inferior. 1 Bouv. Inst. n. 8. prediction performance compared to that of the type II Tobit model in terms of MSPE. For credit card issuers, out-of-sample predictability is more important in evaluating potential customers using historical data. Simulation for the Mean Household's Behavior Using a simulation based on historical data, we show how the mean household responds to changes in the key variables. In Figure 1, the predicted probability of borrowing is given against the change in interest rates (INT). As shown in Table 4, three key variables--interest rate, age, and income--have negative marginal effects on the probability of borrowing. Thus, our simulated graph for the mean household has a negative slope, and there is no noticeable difference between the two models in this figure. (10) The obvious difference between the two models can be seen in the next three figures, in which the predicted balance level is illustrated for changes in other key determinants. In Figure 2, the type II Tobit model predicts that the mean household borrows with credit cards up to a 13% interest rate and that their balance level is not sensitive to interest rates. Considering that this is for the mean household, the result is consistent with the fact that the average credit card interest rate was roughly 15.5% between 1997 and 2001. (11) On the other hand, the type I Tobit model produces suspicious simulation outcomes in that the mean household still holds credit card balances up to a rate of 22%, and the expected borrowing level is very small, even at a 0% interest rate. In Figure 3, the result from the type II Tobit model implies that the mean household slightly increases its credit card debt as it gets older. In contrast, the type I Tobit model predicts a negative relationship with the mean household's age. Figure 4 clearly reveals that the type II Tobit specification yields more reasonable results than the type I Tobit model. To illustrate the distinction in the mean household's behavior, Figure 4 is drawn with households whose predicted balances are under $10,000. The type I Tobit model predicts $7770 to $8800 balances for lower income households, which is an infeasible borrowing amount due to lender-imposed credit limits. However, balances of approximately $650 to $670 are predicted for the same income range by the type II Tobit model. Also, the type II Tobit model predicts that the mean household significantly increases the credit card balance as income rises, but the type I Tobit finds a reduction in credit card debt as income rises. 5. Conclusions Modeling credit card borrowing requires analyzing some distinguishing characteristics Noun 1. distinguishing characteristic - an odd or unusual characteristic distinctive feature, peculiarity characteristic, feature - a prominent attribute or aspect of something; "the map showed roads and other features"; "generosity is one of his best of credit cards. For example, the interest rate for credit card borrowing has been sticky and relatively high over the past 20 years, even when the cost of funds Cost of Funds The interest rate paid on an outstanding loan. Notes: Money isn't free! Cost of funds is the cost of borrowing money. See also: Interest Rate Cost of funds Interest rate associated with borrowing money. that is the primary determinant of the marginal cost Marginal cost The increase or decrease in a firm's total cost of production as a result of changing production by one unit. marginal cost The additional cost needed to produce or purchase one more unit of a good or service. of lending has generally been low. In order to explain these peculiarities, a type II Tobit model is proposed and compared with a traditional Tobit model. By separately estimating the borrowing decision (the first step) and the balance level decision (the second step) using the type II Tobit approach, different marginal effects for borrowing likelihood and the level of credit card debt can be estimated. By describing a reduced-form supply-demand model for credit card debts, a particular coefficient reflects the overall effects of a certain variable through the supply and demand for credit. The balance of supply and demand effects need not be the same in the first and second steps. This unbalanced supply-demand effect may explain why the type I and type LI Tobit models yield different results in the second step. For example, the demand effects of higher income are weaker in the first step and the supply effects of higher income stronger in the second step. As a result, a household with higher income reduces the probability of using a high cost credit card as a borrowing medium. But for those who do end up borrowing with credit cards, perhaps there is a tendency to borrow up to the credit lines predetermined pre·de·ter·mine v. pre·de·ter·mined, pre·de·ter·min·ing, pre·de·ter·mines v.tr. 1. To determine, decide, or establish in advance: by suppliers. In this case, a household with higher income increases the credit card debts incurred. Simulation results show that the mean household is not sensitive to interest rate cuts up to 13%. As expected, the lower-income group is more inclined to depend on credit card borrowing than the higher-income group, while debt levels grow in response to an income increase. These features are not captured by a type I Tobit model where the same directional In one direction. Contrast with omnidirectional. effect is a restriction on the borrowing likelihood and debt level functions. Disparity dis·par·i·ty n. pl. dis·par·i·ties 1. The condition or fact of being unequal, as in age, rank, or degree; difference: "narrow the economic disparities among regions and industries" across the marginal effects on probability of card borrowing and card balance levels is also found for other demographic variables, such as ethnicity, marital status, gender, and home ownership. On the other hand, preference variables or attitudes toward credit card borrowing are positively related to borrowing likelihood and balance levels. In addition, a household facing a binding credit constraint has a significantly higher probability of borrowing and debt level compared with a household that has not experienced a binding credit constraint. As a consequence, the type I I Tobit model used in our study is more appropriate for analyzing the behavior of credit card users and for predicting a household's credit card balance. Appendix Probit Model Estimation for [CC.sub.i] Equation Variable Coefficient LINC -0.069 (0.038) * HSIZE -0.025 (0.020) AGE -0.024 (0.002)** SEX 0.006 (0.069) EDUC -0.026 (0.012) ** HOME -0.271 (0.077) ** MAR 0.037 (0.069) RACE -0.216 (0.079) ** LLIQ3 -0.021 (0.007) ** RISK 0.311 (0.111) ** INST 0.043 (0.063) VACA 0.215 (0.077) ** EMER 0.158 (0.058) ** LUX 0.131 (0.111) WORKYEAR 0.004 (0.003) CHECK 0.162 (0.098) * SAVING 0.004 (0.059) LATE60 1.173 (0.145) ** DIRATIO 0.007 (0.004) Count [R.sup.2] 0.816 * and ** indicate 10% and 5% significance levels, respectively. Standard errors are in parentheses. Model specification: [Z.sup.*.sub.i] = [X.sub.31] [delta]+[[eta].sub.i] = [[delta].sub.0] + [[delta].sub.1] LINC + [[delta].sub.2]HSIZE + [[delta].sub.3]AGE + [[delta].sub.4]SEX + [[delta].sub.5]EDUC + [[delta].sub.6]HOME + [[delta].sub.7]MAR + [[delta].sub.8]RACE+ [[delta].sub.9]TIME + [[delta].sub.10]RISK [[delta].sub.11]INST + [[delta].sub.12]VACA + [[delta].sub.13]EMER + [[delta].sub.14]LUX + [[delta].sub.15]WORKERYEAR + [[delta].sub.16]CHECK + [[delta].sub.17]SAVING + [[delta].sub.18]LATE60 + [[delta].sub.19]DIRATIO + [[eta].sub.i] where we observe [CC.sub.i] = 1 if [Z.sup.*.sub.i] > 0 and [CC.sub.i] = 0. Count [R.sup.2] is defined as the proportion of households correctly predicted using the usual threshold value 0.5. [FIGURE 1 OMITTED] [FIGURE 2 OMITTED] [FIGURE 3 OMITTED] [FIGURE 4 OMITTED]
Table 1
Percentage of Households with Credit Card Balances and Average Credit
Card Balances by Income Percentile
Income Percentile Percentage of Households with Average Credit
Credit Card Balance Card Balance (a)
0-10 65.7 3267
10-20 59.6 3535
20-30 61.4 4915
30-40 55.0 4754
40-50 61.3 6202
50-60 56.0 4434
60-70 48.3 6500
70-80 39.0 7757
80-90 22.6 8072
90-100 14.6 11,278
Source: 1998 SCF data.
(a)It is calculated by averaging credit card balances that only
uncensored observations carry.
Table 2
Defined Variables and Summary Statistics
Standard
Variable Definition Mean Deviation
CCB Logarithm of credit card balance 3.64 3.93
BD 1 if a household currently carries 0.48 0.49
credit card debt
INT (a) Interest rate charged on credit 14.52 4.53
card balance (100*percent)
LINC Logarithm of household income 11.10 1.09
HSIZE The number of household 2.65 1.41
AGE Age of a respondent 50.02 15.27
SEX 1 if a respondent is male 0.76 0.42
EDUC Schooling years 14.32 2.48
HOME 1 if a respondent owns a home 0.78 0.41
MAR 1 if married 0.70 0.45
RACE 1 if white 0.86 0.33
WORK 1 if employed 0.76 0.42
LLIQI Logarithm of liquid asset (checking 6.89 2.85
account)
LLIQ2 Logarithm of less liquid assets 6.69 4.24
(saving + MMA + CALL)
LLIQ3 Logarithm of illiquid assets 8.18 4.80
(pension + life insurance)
RISK (b) 1 if risk averse 0.06 0.24
SHOP 1 if often shops for best terms for 0.35 0.47
and saving
INST 1 if feels a good idea to use 0.67 0.46
installment plan
VACA 1 if feels a good idea to borrow 0.15 0.36
for vacation
EMER 1 if feels a good idea to borrow 0.42 0.49
for emergency cost
LUX 1 if feels a good idea to borrow to 0.06 0.25
buy jewelry of fur coat
CC 1 if experienced credit constraint 0.20 0.40
past five years
NCC The number of credit cards 2.48 1.74
Additional variables for exogeneity test
WORKYEAR Working years at current job 9.54 10.99
CHECK 1 if a respondent has a checking 0.89 0.31
account
SAVING 1 if a respondent has a saving 0.57 0.49
account
LATE6O 1 if recently experienced 0.03 0.18
difficulties in paying its debt
DIRATIO (total household debt)/(household 1.29 4.89
income)
(a)Interest rate charged on a zero balance is replaced with that on a
respondent's most recent credit card
(b)Related questionnaire: "Which of the statements on this page comes
closest to the amount of financial risk that you are willing to take
when you save or make investments?"
Table 3
Coefficient Estimates for Type I Tobit and Type II Tobit Models
Type II Tobit
Type I Tobit Selection Equation Main Equation
INT -0.096 (0.028) ** -0.019 (0.005) ** 0.013 (0.008)
LINC -1.326 (0.170) ** -0.252 (0.034) ** 0.317 (0.065) **
HSIZE 0.087 (0.093) 0.019 (0.019) -0.001 (0.031)
AGE -0.124 (0.009) ** -0.024 (0.001) ** 0.009 (0.004) **
SEX 0.652 (0.307) ** 0.119 (0.063) * 0.031 (0.101)
EDUC -0.284 (0.057) ** -0.057 (0.012) ** 0.038 (0.019) **
HOME 0.595 (0.352) 0.034 (0.076) 0.293 (0.108) **
MAR 0.750 (0.314) ** 0.193 (0.065) ** -0.173 (0.105) *
RACE -0.837 (0.362) ** -0.212 (0.079) ** 0.297 (0.112) **
WORK -0.206 (0.306) -0.044 (0.063) -0.057 (0.099)
LLIQ1 -0.002 (0.049) -0.001 (0.009) -0.018 (0.018)
LLIQ2 -0.222 (0.033) ** -0.040 (0.006) ** -0.016 (0.012)
LLIQ3 -0.002 (0.031) -0.003 (0.006) 0.010 (0.010)
RISK -0.650 (0.534) -0.083 (0.110) -0.279 (0.172) *
SHOP -0.402 (0.266) -0.091 (0.054) *
INST 1.237 (0.281) ** 0.259 (0.057) **
VACA 1.388 (0.351) ** 0.337 (0.076) **
EMER 0.223 (0.259) 0.062 (0.053)
LUX 0.699 (0.502) 0.118 (0.109)
CC 3.248 (0.315) ** 0.795 (0.072) **
NCC 0.586 (0.072) ** 0.316 (0.021) **
MILLS -0.987 (0.188) **
* and ** indicate 10% and 5% significance levels, respectively. Standard
errors are in parentheses.
Table 4
Marginal Effects in Type I Tobit and Type II Tobit Models
Borrowing Decision Amount of Borrowing
Type I Tobit Type II Tobit Type I Tobit
INT -0.006 (0.001) ** -0.007 (0.002) ** -0.037 (0.010) **
LINC -0.087 (0.011) ** -0.101 (0.013) ** -0.520 (0.066) **
HSIZE 0.005 (0.006) 0.007 (0.007) 0.034 (0.036)
AGE -0.008 (0.0006) ** -0.009 (0.0007) ** -0.048 (0.003) **
SEX 0.043 (0.020) ** 0.047 (0.025) * 0.251 (0.120) **
EDUC -0.018 (0.003) ** -0.022 (0.004) ** -0.111 (0.022) **
HOME 0.039 (0.023) ** 0.013 (0.030) 0.229 (0.138) *
MAR 0.049 (0.020) ** 0.076 (0.025) ** 0.289 (0.123) **
RACE -0.054 (0.023) ** -0.084 (0.031) ** -0.339 (0.142) **
WORK -0.014 (0.022) ** -0.017 (0.025) -0.081 (0.120)
LLIQ1 -0.0001 (0.003) -0.0007 (0.003) -0.0009 (0.019)
LLIQ2 -0.014 (0.002) ** -0.016 (0.002) ** -0.087 (0.013) **
LLIQ3 0.0001 (0.002) -0.001 (0.002) -0.009 (0.012)
RISK -0.043 (0.035) -0.033 (0.043) -0.248 (0.209)
SHOP -0.026 (0.017) * -0.036 (0.021) * -0.157 (0.104) *
INST 0.081 (0.018) ** 0.102 (0.022) ** 0.475 (0.110) **
VACA 0.090 (0.023) ** 0.133 (0.029) ** 0.571 (0.138) **
EMER 0.014 (0.017) 0.024 (0.021) 0.087 (0.101)
LUX 0.045 (0.033) 0.047 (0.043) 0.282 (0.197)
CC 0.205 (0.020) * 0.303 (0.025) ** 1.402 (0.123) **
NCC 0.038 (0.004) ** 0.230 (0.028) **
Amount of Borrowing
Type II Tobit
INT 0.001 (0.009)
LINC 0.157 (0.069) **
HSIZE 0.011 (0.033)
AGE -0.005 (0.004)
SEX 0.107 (0.109)
EDUC 0.002 (0.020)
HOME 0.315 (0.118) **
MAR -0.049 (0.113)
RACE 0.166 (0.121)
WORK -0.085 (0.107)
LLIQ1 -0.017 (0.019)
LLIQ2 -0.042 (0.013) **
LLIQ3 0.008 (0.011)
RISK -0.333 ()0.187) *
SHOP -0.058 (0.035) *
INST 0.167 (0.038) **
VACA 0.206 (0.044) **
EMER 0.039 (0.033)
LUX 0.073 (0.066)
CC 0.462 (0.033) **
NCC 0.316 (0.021) **
Standard errors computed by delta method are in parenthese. * and **
indicate 10% and 5% significance levels, respectively. Marginal effects
are computed at the sample mean. For a dummy variable, the discrete
change from 0 to 1 is considered to be the marginal effect. Results that
qualitatively or quantitatively differ to a noteworthy extent are in
bold
Table 5
Prediction Performance
In-Sample Prediction Out-of-Sample
Prediction
Type I Tobit Type II Tobit Type I Tobit
Count [R.sup.2] 0.731 0.737 0.767
MSPE 16.61 16.25 19.02
Out-of-Sample
Prediction
Type II Tobit
Count [R.sup.2] 0.740
MSPE 17.93
Count [R.sup.2] is defined as the proportion of households correctly
predicted borrowing decision. MSPE = (1/[n.sup.p]) [summation over
(n.sup.p]/i =1)] [[[Y.sub.i] - E([Y.sub.i]/ [Y.sub.i] > 0)]].sub.2],
where [n.sub.p] is the observation number used in the prediction
procedure ([n.sub.p] = 404). In the out-of-sample experiment, the first
2,500 observations are used to predict the Last 404 observations.
Received April 2002; accepted September 2002. (1.) Demand for credit cards as a transaction medium is discussed by Duca and Whitesell (1995). (2.) Income is defined as the total household income in 1997 from all sources before taxes and other deductions are made, Credit card debt is defined as the balance still owed on credit card accounts after the last payments were made on these accounts. (3.) Calem and Mester (1995) omitted households with more than $1 million in liquid assets or $250,000 annual income because they are not considered representative of typical credit card users, From 1998 SCF data, it is found that only 3% of households with more than $1 million income carry credit card balances and that the average balance is approximately $1777. This result seems to deviate from the typical pattern of credit card users. (4.) Switch/search costs may include (i) the information cost of finding which cards are offering lower interest rate, (ii) the forgone benefit (a better credit rating or higher credit limit by holding the same card) if one switches to other cards, and (iii) the cost in time, effort, and energy in filling out an application form for a new card. (5.) Another motivation for retirement saving could be a tax consideration such as Tax Deferred Account Plan or Individual Retirement Accounts (Poterba, Venti, and Wise 1995). (6.) For detailed derivations, see Johnson and Kotz (1994). (7.) The additional variables included in the [CC.sub.i] equation are given in Table 2, and the regression regression, in psychology: see defense mechanism. regression In statistics, a process for determining a line or curve that best represents the general trend of a data set. output is provided in the Appendix. (8.) Since the dependent variable is the logarithm logarithm (lŏg`ərĭthəm) [Gr.,=relation number], number associated with a positive number, being the power to which a third number, called the base, must be raised in order to obtain the given positive number. of a household's credit card balance, a simple transformation is necessary to compute the percentage change due to the impact of the dummy variable: percentage change = exp exp abbr. 1. exponent 2. exponential (ME) - 1, where ME is the marginal effect from the dummy variable given in Table 4. (9.) The so-called debt puzzle (households with positive retirement saving and interest-bearing credit card balances) may not necessarily reflect irrational ir·ra·tion·al adj. Not rational; marked by a lack of accord with reason or sound judgment. irrational adjective Unreasonable, illogical or ill-informed behavior if the tax advantages or the employer-thrift plan match of retirement account (sometimes 100% or more of an employee's contribution) are sufficiently large In mathematics, the phrase sufficiently large is used in contexts such as:
envisage, ideate, imagine households that made contributions to retirement accounts that later encountered an unexpected and pressing need to borrow. In such a case, there may not be an ex ante debt puzzle. (10.) We found similar graphical patterns with respect to other key variables (age and income) that are not reported here to save space. (11.) Source: Federal Reserve Statistical Board's G. 19 Release (January 1997-December 2001), Federal Reserve Bulletin (Washington, DC: Board of Governors of the Federal Reserve System Board of Governors of the Federal Reserve System The managing body of the Federal Reserve System, which sets policies on bank practices and the money supply. ). References Ausubel, Lawrence M. 1991. The failure of competition in the credit card market. American Economic Review 81:50-81. Blaylock, James R., and W. Noel Blisard. 1992. U.S. cigarette consumption: The case of tow-income women. American Journal of Agricultural Economics Agricultural economics originally applied the principles of economics to the production of crops and livestock - a discipline known as agronomics. Agronomics was a branch of economics that specifically dealt with land usage. 74:698-705. Brito, Dagobert L., and Peter R. Hartley. 1995. Consumer rationality and credit cards. Journal of Political Economy 103:400-33. Byrne, Patrick J., Oral Cappa, and Atanu Saha. 1996. Analysis of food-away-from-home expenditure patterns for U.S. households, 1982-89. American Journal of Agricultural Economics 78:614-27. Calem, Paul S., and Loretta J. Mester. 1995. Consumer behavior and the stickiness See sticky. of credit-card interest rates. American Economic Review 85:1327-36. Cargill, Thomas F., and Jeanne Wendel. 1996. Bank credit cards: Consumer irrationality versus market forces. Journal of Consumer Affairs 30:373-9. Crook, Jonathan. 2001. The demand for household debt in the USA: Evidence from the 1995 Survey of Consumer Finance. Applied Financial Economics 11:83-91. Duca, John V., and Stuart S. Rosenthal. 1993. Borrowing constraints, household debt, and racial discrimination in loan markets. Journal of Financial Intermediation 3:77-103. Duca, John V., and William C. Whitesell. 1995. Credit cards and money demand: A cross-sectional study cross-sectional study n. See synchronic study. cross-sectional study, n the scientific method for the analysis of data gathered from two or more samples at one point in time. . Journal of Money, Credit, and Banking 27:604-23. Gross, David B., and Nicholas S Nicholas, Russian grand duke Nicholas (Nikolai Nikolayevich) (nyĭkəlī` nyĭkəlī`əvĭch), 1856–1929, Russian grand duke and army officer; first cousin of Czar Alexander III and grandson of Czar . Souleles. 2002. Do liquidity constraints and interest rates matter for consumer behavior? Evidence from credit card data. Quarterly Journal of Economics The Quarterly Journal of Economics, or QJE, is an economics journal published by the Massachusetts Institute of Technology and edited at Harvard University's Department of Economics. Its current editors are Robert J. Barro, Edward L. Glaeser and Lawrence F. Katz. 117:149-85. Heckman, James J. 1979. Sample selection bias as a specification error. Econometrica 47:153-62. Johnson, Norman, and Samuel Kotz. 1994. Continuous univariate distributions In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector. See also
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of : John Wiley John Wiley may refer to:
Kennickell, Arthur B., and Martha Starr-McCluer. 1994. Changes in family finances from 1989 to 1992: Evidence from the Survey of Consumer Finances The Survey of Consumer Finances (SCF) is a triennial survey of the balance sheet, pension, income, and other demographic characteristics of U.S. families. The survey also gathers information on the use of financial institutions. The study is sponsored by the U.S. . Federal Reserve Bulletin, 861-82. Laibson, David, Andrea Repetto, and Jeremy Tobacman. 2000. A debt puzzle. NBER NBER National Bureau of Economic Research (Cambridge, MA) NBER Nittany and Bald Eagle Railroad Company Working Paper No. 7879. Maddala, G. S. 1983. Limited-dependent and qualitative variables in econometrics econometrics, technique of economic analysis that expresses economic theory in terms of mathematical relationships and then tests it empirically through statistical research. . New York: Cambridge University Press Cambridge University Press (known colloquially as CUP) is a publisher given a Royal Charter by Henry VIII in 1534, and one of the two privileged presses (the other being Oxford University Press). . McDonald, John F., and Robert A. Moffitt. 1980. The uses of Tobit analysis. Review of Economics and Statistics 62:318-21. Morrison, Anne K. 1998. An anomaly Abnormality or deviation. Pronounced "uh-nom-uh-lee," it is a favorite word among computer people when complex systems produce output that is inexplicable. See software conflict and anomaly detection. in household consumption and savings behavior: The simultaneous borrowing and lending of liquid assets. Mimeo, University of Chicago. Poterba, James M., Steven F. Venti, and David A. Wise. 1995. Do 401(k) contributions crowd out other personal saving? Journal of Public Economics 58:1-32. Rivers, Douglas, and Quang H. Vuong. 1988. Limited information estimators and exogeneity tests for simultaneous probit models. Journal of Econometrics 39:347-66. Smith, Richard J., and Richard W. Blundell. 1986. An exogeneity test fat a simultaneous equation Tobit model with an application to labor supply. Econometrica 54:679-86. Insik Min * Jong-Ho Kim + * Department of Economics, Texas A&M University, 3035 Academic Building-West, Texas A&M University, College Station, TX 77843-4222, USA; E-mail i0m5376@neo.tamu.edu; corresponding author. + Department of Economics, Texas A&M University, 3035 Academic Building-West, Texas A&M University, College Station, TX 778434228, USA; E-mail jkim@econmail.tamu.edu. We would like to thank a coeditor and two anonymous referees for their valuable comments. |
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