Credit Card Debt Puzzles and Debt Revolvers for Self Control - SSRN

Credit Card Debt Puzzles and Debt Revolvers for Self Control∗ Carol C. Bertaut, Michael Haliassos, and Michael Reiter† Board of Governors of the Federal Reserve System; Goethe University Frankfurt, CFS, MEA, NETSPAR; Institute for Advanced Studies, Vienna and CESIfo

September 24, 2008

∗

We are grateful to Editor Peter Bossaerts, Giuseppe Bertola, Chris Carroll, Tullio Jappelli, Christos Koulovatianos, David Laibson, Nick Souleles, and to an anonymous referee for helpful suggestions. We thank participants in the Economics of Consumer Credit conference at the European University Institute, the AS.S.E.T. conference, and the NBER Summer Institute where very preliminary findings were presented. We acknowledge funding from the European Community’s Human Potential Program under contract HPRNCT-2002-00235, [AGE], the CFS Program on Household Wealth Management, HERMES, the Leventis Foundation, and the Spanish ministry of Science and Technology under grant SEC2002-01601. The views presented in the paper are the authors’ own and do not necessarily represent those of the US Federal Reserve System. † Bertaut: Board of Governors of the Federal Reserve System, International Finance Division, 20th Street and Constitution Avenue NW, Washington, DC 20551, USA. Email: [email protected]. Haliassos: School of Economics and Business Administration, House of Finance, Goethe University Frankfurt, Grueneburgplatz 1, PF H32, D-60323, Germany. Email: [email protected]. Reiter: Institute for Advanced Studies (IHS), Department of Economics and Finance, Stumpergasse 56, A-1060 Vienna, Austria. Email: [email protected].

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Credit Card Debt Puzzles and Debt Revolvers for Self-Control September 24, 2008 Abstract Most US credit card holders revolve high-interest debt, often combined with substantial (i) asset accumulation by retirement, and (ii) low-rate liquid assets. Hyperbolic discounting can resolve the former but not the latter puzzle (Laibson et al., 2003). This paper combines, updates, and extends the theoretical and empirical analysis of the "accountant-shopper" setup originally presented in Bertaut and Haliassos (2002) and Haliassos and Reiter (2005). It shows that the separation of accounting and shopping made possible by credit cards can generate both types of co-existence and target credit card utilization rates consistent with Gross and Souleles (2002), even when accountant and shopper are engaged in a rational, dynamic game. When the shopper is more impatient than the accountant, it is not necessarily optimal for the accountant to sell assets to pay off debt: the impatient shopper can charge more and restore debt to its previous level. We show that the accountant-shopper setup can match both the observed incidence of debt revolvers with substantial assets and median asset holdings for modest relative impatience. Matching other moments is likely to require heterogeneity in presence and degree of spending control problems among households. We present empirical evidence consistent with a role for spending control considerations, where present, after controlling for standard factors influencing credit card debt. JEL Classification: E210, G110. Key Words: Credit cards, debt, self control, household portfolios.

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Introduction

In all Surveys of Consumer Finances between 1995 and 2004, more than half of bank-type credit card holders revolve debt on their cards. Of those that revolve debt, nearly half declare that they “hardly ever” pay off the balance in full, despite paying a median interest rate of 15 percent and not relying on automatic payment facilities.1 Thus, it is hard to attribute debt revolving to ignorance, inertia, teaser interest rates or accident. About one third of debt revolvers have liquid assets (excluding cash not measured in the data) greater than their card balance, at least $1,200 in 2004 dollars, and at least one-half monthly income. More than two thirds of those declare that they do not typically pay off their card balance. The size of liquid assets excluding cash makes it unlikely that co-existence of debt with assets can be attributed simply to a cash transactions motive. Despite these tendencies to revolve debt, US households exhibit considerable median levels of total net worth by the time they reach the 55-64 age range. The surprising portfolio coexistence of high-interest credit card debt, low-interest liquid asset holdings, and substantial accumulation of assets for retirement is a challenge for the modern theory of saving. Gross and Souleles (2002) identified these two co-existence puzzles. Laibson, Repetto, and Tobacman (2003) proposed an explanation of one, namely that despite heavy credit card borrowing, US households aged 50 to 59 attain median ratios of total wealth (net of credit card debt, mortgages, and education loans) to annual total after-tax income of the order of 3.5.2 Bertaut and Haliassos (2002) sketched an ‘accountant-shopper’ model to explain coexistence of debt with liquid assets and provided some empirical evidence. Both papers introduced ‘self-control’ considerations.3 Haliassos and Reiter (2005) developed a full accountant-shopper model, where the shopper is both impatient and not fully financially sophisticated, and showed that it can generate both types of co-existence as well as behavior consistent with Gross and Souleles4 even under exponential discounting. This paper combines, updates and extends the two working papers on ‘accountant-shopper’ models to present in an article a version as close to ra1

Only 2 percent of debt revolvers rely on automatic payment facilities. This is the average of the median ratios for this age group obtained for the Survey of Consumer Finances in 1983, 1989, 1992, and 1995. 3 Gross and Souleles (2002) had also hinted at the possibility of resolving the co-existence puzzles using such considerations. 4 Using a proprietary administrative data set, Gross and Souleles found that line increases not requested by account holders lead them to return to utilization rates of the limit observed prior to the increase, normally within four to five months. 2

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tional models as possible, but still generating co-existence. In Haliassos and Reiter (2005), the impatient shopper is modeled as also exhibiting limited awareness of the financial consequences of his spending actions. Here, we model the shopper as fully rational, engaged in a dynamic game with the rational accountant, and explore how far this takes us. Our key point is that the separation of purchase from payment made possible by credit cards creates potential for differential impatience between the entities responsible for the two actions: the ‘shopper’ and the ‘accountant’. If these two entities are a single person, the model has a self-control interpretation. If they are not, the model simply departs from the unitary framework. Since our setup in this paper collapses to the standard model when accountant and shopper share the same rate of time preference, we can think of the population of credit card holders as heterogeneous in differential impatience between accountant and shopper. For some, this difference is zero and the unitary model applies. In deciding how much credit card debt to revolve, the accountant takes into consideration all standard factors (e.g., life-cycle, precautionary, borrowing constraints, etc.) but also that a higher unpaid balance leaves less room to the shopper for charging on the credit card. The accountant may choose not to use all liquid assets to pay off the card balance, because the more impatient shopper will then be able to charge more on the card, consistent with the shopper’s utilization target. Separation of the unitary household into two entities with differential time preference turns out to be sufficient to generate co-existence between credit card debt and substantial liquid assets, even if both entities are rational and financially sophisticated. Our model allows for the fact that debt may be revolved also for consumption smoothing or other purposes. It does not imply that a given household continuously revolves debt and holds substantial liquid assets: fluctuations in debt and asset amounts do occur over the life cycle. Our simulations make clear that revolving a credit card balance is costly, as are lack of spending control itself and alternative self-control methods (such as switching to debit cards). This is consistent with data, presented below, that households often revolve debt and use debit cards simultaneously. Our approach can be applied to issues involving consumer lines of credit in general but is not necessarily applicable to all types of loan purchases. For example, a house purchase backed by a mortgage is lumpy and important enough to induce coordination between accountants and shoppers in the decision making rather than separation of the accounting from the purchase decision. Credit card behavior is special in allowing such separation, and its potential for generating spending control problems is often stressed in

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household surveys.5 The paper is structured as follows. Section 2 places the current paper in the literature. Section 3 describes credit card debt revolving in Survey of Consumer Finances data. Section 4 presents the accountant-shopper model, calibration choices, and simulation results. Section 5 reports econometric results on the relevance of spending control considerations for credit card debt revolvers using Survey of Consumer Finances data from successive waves. Section 6 offers concluding remarks. The solution algorithm and calibration details are described in Appendices.

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Recent Literature on Debt-Asset Coexistence

Our model is in the tradition of ‘planner-doer’ models pioneered by Shefrin and Thaler (1988). Laibson, Repetto and Tobacman (2003) proposed a hyperbolic discounting model involving control of future selves by the current self, with each self having full responsibility for all household decisions. They showed that a standard model with credit cards and exponential discounting could not account simultaneously for households revolving card debt and for the considerable pre-retirement ratios of total wealth to total after-tax, non-asset income. In their self-control model, the current self discounts the immediate future considerably, thus justifying high-interest credit card borrowing, but discounts the distant future by less than he anticipates his future incarnations to discount it. So, he accumulates illiquid assets, imposing heavy (in the limit, infinite) liquidation costs to the future selves. In the LRT model, card borrowing is intended for short-term consumption smoothing, while accumulation of illiquid assets is used as an instrument for controlling future selves. As recognized by the authors, hyperbolic discounting cannot simultaneously address the co-existence of credit card debt with low-interest liquid assets. Our model differs in at least three ways. First, it can refer to self-control or to separation of roles within the household. Second, the two selves or actors are contemporaneous and neither has full decision-making powers. Third, credit card debt, rather than illiquid assets, is used as an instrument of control. Lehnert and Maki (2001) had proposed an alternative explanation for coexistence of liquid assets with card debt, namely the generous provisions of 5 For example, data on attitudes of credit card holders in the 2001 Survey of Consumers show that about forty percent of card holders perceive control problems emanating from credit cards and the possibility of overspending (Durkin, 2002).

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bankruptcy law in some states. These allow households declaring bankruptcy to rescue part of their assets, which they would not have available had they used it to pay off credit card debt. However, the widespread nature of coexistence, shown below, and the potential for drawing a cash advance prior to defaulting instead of continuously paying interest costs cast doubt on the wide applicability of this explanation.6 In our empirical section, we include a control for strategic default considerations. Teluykova (2007) and Zinman (2007) invoke the need to purchase cash (rather than credit) goods as motivation for holding liquid assets along with credit card debt. These papers do not account fully for observed accumulations of liquid assets, even without cash holdings (which serve the purpose but are not measured in the survey) and under very favorable assumptions regarding the timing of cash payments relative to the time of survey interview. At any rate, our paper, as indeed Gross and Souleles (2002), focuses on households with liquid assets above a generous threshold (half monthly income and at least $1,200), which together with unmeasured cash holdings should cover typical cash needs within the month. A number of authors from different fields, such as Marketing or Consumer Psychology, have argued in favor of spending- or self-control considerations in borrowing behavior. Hoch and Loewenstein (1991) argue that self-control problems occur when the benefits of consumption occur earlier and are dissociated from the costs. The findings of Shefrin and Thaler (1988), Prelec and Simester (2001), and Wertenbroch (2002) suggest that liquidity enhances both the probability of making a purchase and the amount one is willing to pay for a given item being purchased, over and above any effects due to relaxation of liquidity constraints. Soman and Cheema (2002) present experimental and survey evidence that consumers interpret available credit lines as indications of future earnings potential when deciding consumption expenditures.7 Costly self-rationing as a means of self-control has been stressed in Marketing and in research on mental accounting.8 The single person interpretation of our model has a similar flavor with mental accounting, but mental accounting is not assumed for either actor in the two-person interpretation. 6

See also the discussion in Gross and Souleles (2002). Credit cards may lead to overspending even without self-control considerations, because they provide absent-minded consumers with less information on spending flows than cash transactions do (Caplin and Leahy, 2004). 8 See Thaler (1980), Thaler and Shefrin (1981), Schelling (1992), Ariely and Wertenbroch (2002), Wertenbroch (1998, 2002). 7

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3

Credit Card Debt Revolving in the Data

We use data from the 1995, 1998, 2001, and 2004 Surveys of Consumer Finances to study credit card behavior and debit card use.9 Combining these waves, we have comprehensive data on 17,564 households, including household assets, debts, and income along with detailed demographic information. Table 1 shows the prevalence of credit card debt revolving among U.S. households with at least one bank-type credit card. Although card ownership increased notably in the 1980s and early 1990s,10 it grew less rapidly between 1995 and 2001, from about 66 percent to 73 percent, and then edged down by one percentage point in 2004. Despite these changes in ownership, the fraction of cardholder households that reported revolving a balance after paying last month’s bill remained remarkably steady at about 55 percent. Although revolving of high-interest credit card debt could simply reflect a need to borrow due to limited finances, almost a third of credit card debt revolvers also have liquid assets (checking, saving, or money market account balances, excluding any cash) that exceed their card balance and are at least $1,200 (in 2004 dollars) and at least one-half of average monthly income (column 3). It is conceivable that some households have only temporarily revolved a balance, e.g., to meet temporary needs or take advantage of temporarily low ("teaser") rates. However, more than two thirds of credit card debt revolvers with substantial liquid assets admit that they ‘typically’ do not pay off the balance in full (column 4). For debt revolvers with substantial liquid assets, the median interest rate charged was 14 percent, and for less than 10 percent was the interest rate below 6 percent. Credit card debt revolving is not confined to the young or the less educated. Although it tends to be less prevalent after 55 years and among college graduates, almost half of credit card holders in the 55-64 age range and almost half of those with college degree at any age, revolve credit card debt. The more puzzling behavior, of also holding sizable liquid financial assets, is exhibited by about one third of debt revolvers in all age ranges above 35 (column 3). The incidence of this rises with education, with almost half of college graduates in this group. About two thirds of credit card debt revolvers with substantial liquid assets habitually revolve debt, in all age and education groups (column 4). Table 2 reports median amounts of revolving card debt and of various 9

We restrict our sample to these more recent waves of the SCF because the questions on debit cards capture debit card use (rather than ownership) beginning with the 1995 Survey. 10 Bertaut and Haliassos (2006) report growth in credit card use from 43 percent in 1983 to 62 percent by 1992.

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assets for debt revolvers with substantial liquid assets, all in 2004 dollars. In 2004, the median amounts of debt, liquid financial assets, and financial assets in this category were 1,400, 10,000 and 48,000 dollars, respectively (top panel). Median credit card debt is even higher among habitual debt revolvers (bottom panel), while median assets drop only marginally. Moreover, recall that recorded asset holdings exclude cash. Such figures make it difficult to argue that our puzzling households were systematically revolving credit card debt because they were unable to pay it off or because the interest benefits from doing so would be lower. Debit cards provide another way to limit overspending, by making sure that the funds in the account linked to the debit card are limited. By 2004, only 15% of US households were left with neither a debit card nor a bank type credit card (Table 3). The proportion of households using only a debit card grew during the period, but has remained remarkably small (even in 2004, it was under 14 percent) and it drops with age and education. Among those with a bank type credit card, almost half were also using a debit card. These figures suggest that debit cards are complementary to credit cards for many households. Indeed, if credit cards are used partly for self-control purposes, there is no reason to think that the same households may not be using debit cards as well, in the effort to impose spending control.

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An Accountant-Shopper Model

We depart from models of unitary households and allow each household to consist of two entities, representing either two different people or two ‘selves’, the “accountant” and the “shopper”. We will be using ‘he’ for both, to avoid gender interpretations. The accountant manages household assets and debts, including the extent of debt repayment. The shopper chooses consumption, taking as given the size of the unused credit card line as determined by the accountant. In the reported version, both agents are fully rational but the shopper discounts the future more than the accountant. This is to show that limited financial awareness is not necessary for co-existence of assets with debt.11 Accountant and shopper are engaged in a repeated dynamic game. The accountant knows how the shopper’s consumption is related to the unused line and takes this into account in making payments. The shopper tends to overspend relative to what the accountant desires, because of differential 11

The working paper by Haliassos and Reiter describes results from a model in which the accountant is fully financially sophisticated but the shopper is impulsive, both in the sense of discounting the future more heavily and in the sense of ignoring the consequences of today’s spending on the payments into the account made by the accountant next month.

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time preference. In deciding consumption, the shopper takes into consideration the optimal payment response of the accountant to the shopper’s purchases.

4.1

The Accountant’s Problem

The accountant’s objective is to maximize expected lifetime utility of the household, which is a function of real household consumption, Ct , and of effective household size, nt , assumed exogenous and computed as n = adults + κ · children: Ã t−1 ! T +N−1 X Y U(C0 , n0 )+E0 βt sj [st U(Ct , nt ) + (1 − st )W (At , Bt )] , 0 < β < 1 t=1

j=1

(1) where Et is the conditional expectations operator, β is the discount factor, At is net assets excluding credit card debt, Bt is unsecured revolving debt on the credit card at the beginning of period t, W is terminal utility based on the size of bequests of assets and of debt, and st is the probability that the accountant-shopper pair will survive in period t given that it has survived in period t − 1.12 Felicity is of the constant relative risk aversion form: ⎡ ³ ´1−ρ ⎤ Ct − 1⎥ ⎢ nt (2) U (Ct , nt ) = nt ⎣ ⎦ 1−ρ

At the beginning of each period t, the accountant receives the credit card bill showing the outstanding balance, Bt , and chooses how much to pay into the credit card account, Pt . Given the unused credit limit, the shopper visits the stores and charges an amount Ct to the credit card.13 The transition equation governing the evolution of the credit card balance is: Bt+1 = (Bt − Pt + Ct ) Rtc

(3)

where Rtc is the credit card rate that applies to any outstanding balance between the beginning of period t and that of period t + 1. The relationship 12

For simplicity, we assume that the accountant and shopper die at the same time, which of course holds exactly when we refer to two selves. 13 Assuming that all consumption is charged to the credit card simplifies the model without restricting overall consumption. If the accountant’s desired consumption exceeds the credit limit, then he can deposit enough to leave a positive balance, which can then be used by the shopper.

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between Bt and Pt determines the applicable interest rate: ⎧ h if Pt < Bt ⎨ R c Rt = ⎩ 1 if Pt ≥ Bt

(4)

If the accountant decides to revolve debt, he pays an amount Pt that falls short of the outstanding balance. The remaining balance, Bt − Pt , plus any new purchases Ct made by the shopper are charged the (high) credit card rate Rh . If the accountant pays off the entire balance (or more), then new purchases by the shopper, Ct , are subject to a grace period and are charged zero rate of interest (a gross rate of 1).14 The rational accountant can compute the policy function that relates shopper consumption expenditure to the unused credit line available to him, and he internalizes this policy function. The borrowing limit on the credit card is set by the bank and taken as given by the accountant: Bt ≤ B t (5) Following Laibson et al., we assume that this borrowing limit is related to the average labor income earned by the population group that has the same education as the accountant. Before retirement, it is a constant fraction of average labor income: Bt = λ Y t (6) At retirement, income drops instantaneously, but the credit card limit does not. We assume a simple adaptive process for the credit card limit after retirement: i h Ret Ret Bef Ret (7) B t = λ ρt−t Y t + (1 − ρt−t ) Y t

where (t − tRet ) measures the time elapsed since retirement (in years), and Bef Ret Yt is average income immediately before retirement. We chose ρ = 0.7. The evolution of stocks of the liquid asset, A, that offers a riskless interest rate Rt is given by At+1 = (At + Yt − Pt ) Rt (8) where Yt is labor income received at the beginning of period t. At the beginning of each period t, the accountant observes the outstanding stock of assets, At , and receives labor income, Yt . For each dollar of payment into the card account, Pt , the accountant is giving up the return Rt that he would 14

If the accountant decides to pay more into the account than necessary to pay off the balance, this extra amount earns no interest.

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obtain from the liquid asset, but he saves Rtc , as shown by (3). We abstract from explicit consideration of illiquid assets for simplicity.15 We introduce a borrowing constraint at the (low) riskless rate R: At ≥ 0 ∀ t

(9)

The constraint that the household can only borrow using the credit card if it is to finance purchases of the consumption good economizes on the need to model alternative modes of financing. It will not be binding typically for households we focus on, namely those who have liquid assets but revolve credit card debt. Income Yt (called loosely “labor income”) represents all after-tax income from transfers and wages, and its logarithm during working life (20 ≤ t ≤ T ) behaves as yt = f W (t) + ut + vtW (10) where f W (t) is a cubic polynomial in age, ut is a Markov process, and vtW is iid and normally distributed with mean 0 and variance σ 2v,w . During retirement (T ≤ t ≤ T + N), yt = f R (t) + vtR (11) where f R (t) is linear in age, and the shock is iid and normally distributed N(0, σ 2v,R ). The parameters of the “labor income” processes are calibrated differently depending on the education category of the accountant, who is the household head for finances, but our benchmark calibration is reported for high-school graduates. Thus, the state variables of the problem facing the accountant are the credit card balance Bt , liquid assets At , labor income Yt , and the value of the Markov income shock ut . The accountant’s control variable is the amount of payment into the card account, Pt .

4.2

The Shopper’s Problem

Modeling of shopper behavior is motivated by empirical findings surveyed in the introduction. Existing literature suggests that the separation of purchase from payment made possible by a credit card tends to make shoppers behave more impatiently than if they were forced to run down cash balances, but also that the tendency of credit card holders to overspend is not linked to 15

In a preliminary version of the Haliassos Reiter working paper, we showed that portfolio co-existence of liquid assets, illiquid assets, and credit card debt can also be obtained in a model that allows for illiquid asset purchases. Unlike in the Laibson et al (2000) model, though, illiquid assets are not necessary to exercise self control.

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ignorance of credit card terms (see Durkin, 2000) or to period-by-period maximization (see Gross and Souleles on target credit limit utilization rates generally below unity). We formalize these implications by assuming that the shopper has a higher rate of time preference than the accountant but otherwise has the same horizon, preferences, and knowledge of interest rates and of the transition equation linking his purchases to credit card debt. Formally, the preferences of the shopper take again the form (1), except that the discount factor β is replaced by β S < β to allow for greater shopper impatience. The extent of relative impatience will be important for the amount of revolving debt predicted by the model. As this is not a parameter for which estimates exist, we present below sensitivity analysis for different possible degrees of shopper impatience relative to the accountant. The shopper’s felicity is given by equation (2), as for the accountant. The shopper’s problem is dynamic, because the shopper is assumed to understand the terms of his account and to perceive the credit card limit B t given by equation (6), as well as how the credit card balance changes when he charges an extra dollar on the credit card today (3). When the shopper charges an extra dollar on the credit card, he faces two consequences: a higher outstanding balance for given payments by the accountant, equal to the gross interest rate on the credit card; and any change in the size of payments induced by this higher balance: ¡ ¢ ∂ B t+1 − Bt+1 + Pt+1 ∂Pt+1 = −RtC + (12) ∂Ct ∂Bt+1 Understanding the first consequence simply requires knowledge of account terms, which the shopper is assumed to possess. In this paper we allow the shopper to be fully financially sophisticated and to be able to compute also the second term, based on the overall financial condition of the household and on optimal accountant behavior. Even with such ability, the shopper will choose to leave a fraction of the credit card line unused as a buffer, in a fashion similar to a buffer stock saving model (Carroll, 1997) and consistent with credit line utilization rates found by Gross and Souleles (2002). This is because the shopper has a ‘precautionary saving’ motive, as he realizes that the accountant’s payments into the credit card account are stochastic, in response to the shocks facing the household.

4.3

Equilibrium

Given their respective rates of time preference, both accountant and shopper are assumed to behave optimally. Accountant and shopper enter into a dynamic game, sharing the same information. The accountant knows that the shopper is more impatient and that he responds to the size of the unused 11

credit line. The shopper knows that the accountant can use the credit card balance to restrain his spending and that he responds to the amount charged by the shopper in this way. Within each period, the accountant decides first, paying the bills at the start of the month, and the shopper subsequently carries out his spending. This corresponds naturally to the payment cycle of the credit card account: the bill is paid at the start of the month and the size of the payment relative to the previously outstanding balance determines whether new charges by the shopper enjoy the grace period or are subject to interest payments right away. Formally, the action of the accountant, the payment Pt , depends on liquid assets At and on credit card debt Bt at the beginning of the period. The action of the shopper, consumption Ct , depends on credit card debt after payment Bt − Pt , and liquid assets left after payment, At − Pt . There is a final period, since the death probability in the last month of year 90 is 1. The game can be solved backwards: 1. In the last period (call it T ), the shopper spends as much as the credit card limit allows, because credit card debt is assumed not to affect the size of bequests. This determines the shopper’s policy function CT (AT − PT , BT − PT ). 2. In any period t, knowing the shopper’s future policy functions Ct+i (At+i − Pt+i , Bt+i − Pt+i ), i = 0, 1, . . ., the accountant chooses his optimal payment Pt (At , Bt ). 3. In any period t < T , the shopper chooses his policy function Ct (At − Pt , Bt − Pt ) based on the future policy functions Pt+i (At+i , Bt+i ), i = 1, 2, . . . of the accountant. The information regarding future periods is effectively contained in the accountant’s value function Vt (At − Pt , Bt − Pt ) and the shopper’s value function V˜t (At , Bt ), and the model can be solved by backward iteration in the standard way.

4.4

Calibration

In this section we present calibrating parameters and stochastic processes used in the numerical implementation of the model. Our calibration choices for a model based on time periods of one year are intentionally kept as close as possible to those of Laibson et al (2003). Since we are modeling the month-to-month interaction between an accountant and a shopper, we need to calibrate a model where the time period is one month long (see Appendix). 12

4.4.1

Demographics

The household is assumed to consist of an accountant and of a shopper of the same age. The accountant and the shopper live for up to 90 years, and face conditional probabilities of survival given by the 1998 United States Life Tables (National Vital Statistics Report, 2001). Effective household size is computed as in Laibson et al (2003), using their estimated numbers of dependent adults (in addition to head and spouse) and of children based on the PSID.16 Our benchmark runs are reported for high-school graduates.17 Household size is computed as the sum of the number of adults and of the weighted number of children (under 17), with 0.4 used as the weight. 4.4.2

Incomes

Income is defined as after-tax non-asset income, and includes labor income, government transfers, bequests, and lump-sum windfalls. Separate income regressions are used for each of the three education categories, and for working and retired households of the same education category. For working households, the age polynomial is cubic, while for retired households it is linear. The regressions allow for age, separately for the number of each of the three components of the household (head and spouse, number of dependent adults, and number of children), cohort dummies (based on year of birth and split into five-year cohorts), and the unemployment rate in the household’s state of residence (as a proxy for time effects).18 The stochastic part of annual pre-retirement income is modeled as the sum of a household fixed effect, an autoregressive process of order 1, and a purely transitory shock: W W ξW it = ζ i + uit + ν it = ζ i + αuit−1 + εit + ν it

(13)

The variances of ε and of ν W , as well as the value of α, are estimated using the residuals from the regressions for income during working years and applying a weighted GMM procedure that minimizes the distance between the theoretical and the empirical first seven autocovariances of the change in the W stochastic part, E(∆ξ W t ∆ξ t−k ). Different estimates are obtained and used 16

Their non-linear least squares regression estimates are reported in their Table 3. The profile for each category is obtained by using these regression estimates and setting the errors equal to zero. 17 We have also considered high-school dropouts and college graduates. This does not change our qualitative findings and we therefore do not report these results. 18 The regression estimates used are in Table 4 of Laibson et al.

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for the three different education categories.19 The transitory noise in annual retirement income is modeled as the sum of a household fixed effect and of a purely transitory shock: R ξR it = ϑi + ν it

(14)

The variance of ν R is estimated using the residuals from the regressions for income during retirement years.20 The retirement age for high-school dropouts is set to 61, for high-school graduates to 63, and for college graduates to 65, based on mean ages observed in the data. 4.4.3

Assets and Debts

The credit card limit is assumed equal to 30 percent of the average annual income for the current year and for the education category to which the household belongs. The after-tax real gross interest rate on liquid assets, R, is set to 1.0375.This reflects higher than typical estimates of the riskless rate that are close to 1.01, to allow for the fact that households typically have better investment opportunities. Since we simplify by assuming that asset returns are riskless, we ought to think of the asset as a well-diversified portfolio of stocks and bonds. The real gross interest rate on revolving credit card balances, RCC , is set to 1.1075, three percentage points below the mean debt-weighted real interest rate measured by the Federal Reserve Board, to allow for an effect of bankruptcy that is absent from our model (as from the Laibson et al benchmark model). 4.4.4

Preferences

As noted above, we postulate a felicity function that exhibits constant relative risk aversion. The degree of relative risk aversion, ρ, is set to 2, close to empirical estimates commonly used in the consumption-saving literature. The discount rate of the accountant, β, is set to 0.952 annually, such that we get asset-to-income ratios similar to what we find in the data. The spendingcontrol problem is only characterized by the shopper having higher discount 19

The vector of estimates for (α, σ 2ε , σ 2ν W ) is (0.881, 0.024, 0.041) for high-school dropouts; (0.782, 0.029, 0.026) for high-school graduates; and (0.967, 0.019, 0.014) for college graduates. In the simulations, the household fixed effect is set to zero, and uit is represented with a symmetric, two-state Markov process and symmetric transition probability p between the states q {−θ, +θ}. This process matches the estimated variance and σ2

α+1 ε autocovariance of uit if θ = 1−α 2 and p = 2 . 20 2 The estimates of σ ν R for high-school dropouts, high-school graduates, and college graduates are, respectively, 0.077, 0.051, 0.042. In simulations, household fixed effects are set to zero.

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rate than the accountant, β S > β. We examine a range of values for differential impatience, β − β S ∈ {0.05, 0.1, 0.2}. We parameterize the accountant’s bequest function as follows: B(Xt ) = (R − 1) · max {0, Xt } ·

U1 (y, 0, n) 1−δ

(15)

Here, y and n are the mean values for income and household size over the life cycle that apply to the education category of the household, and U1 (y, 0, n) = ¡ y ¢−ρ . This formulation of bequests essentially views the bequest recipient as n having total consumption approximately equal to y, effective household size equal to n, and as consuming bequeathed wealth in the form of an annuity. Finally, Appendix B describes the adjustments made to convert the model from annual to monthly frequency.

4.5

Numerical Results

We report numerical results for simulations of households with high-school certificates: results are qualitatively similar for the other categories of educational attainment. Figure 1 presents policy functions of a fifty year old accountant in terms of liquid assets, for the low and high states of the twostate Markov process designed to approximate the AR(1) part in the income process. We assume that the beginning-of-period credit card debt is $5,000. As expected, a household with no difference in account-shopper rates of time preference never revolves credit card debt if there are sufficient assets to repay the debt, because of the difference in interest rates.21 In contrast, if the shopper is more impatient than the accountant, the accountant decides to roll over a significant amount of credit card debt, for a wide range of asset levels. Interestingly, the policy function of a household with symmetric time preferences across shopper and accountant is smooth, but if the shopper is relatively impatient and engages in a fully rational, dynamic game with the accountant, the optimal policy of the accountant is highly irregular.22 This feature of the solution makes simulation results easier to interpret than policy functions; in our discussion below we focus on simulation results. Figures 2 and 3 plot sample averages from a simulation of 100,000 households where shoppers have relative impatience of 10 percentage points. Figure 2 shows median income, consumption and credit card payments. Figure 21

The slightly negative levels of credit card debt (credit balance on the credit card account) are due to the discrete approximation. 22 The Working Paper by Haliassos and Reiter shows a much more limited incidence of irregularities when the shopper is characterized not only by relative impatience but also by limited awareness of the financial consequences of his spending decisions.

15

3 shows that households accumulate sizeable liquid assets before retirement. The median credit card balance before payment stays strictly below the borrowing limit, implying less than full utilization, Consistent with empirical findings, this result reflects buffer-stock behavior of the shopper who does not want to exhaust, on average, the credit card line.23 The median card balance after payment (i.e., the size of revolving credit card debt) is rather strongly positive for middle-aged households, but is close to zero after retirement. Note that assets and debt are measured on different axes in the Figure; sizable holdings of assets thus coexist with considerable levels of credit card debt. This model is minimalistic as a model of spending control: the only difference between accountant and shopper is in the discount factor, the shopper is fully financially sophisticated, and accountant and shopper enter into a complicated dynamic game. Nevertheless, this small departure from the standard unitary model, coupled with relative shopper impatience of 10pp, generates results consistent with a number of empirical observations: co-existence of revolving credit card debt with liquid assets and substantial retirement accumulation; a tendency to keep a fraction of the credit line unutilized as a buffer; and a reduced tendency of the elderly to revolve credit card debt. At the same time, accountant-shopper considerations do not seem to interfere with other key properties of standard models, such as consumption smoothing. Clearly, a key parameter is the relative impatience of the shopper. To gain some understanding of its quantitative importance, we simulate the model for different values of this parameter, ranging from 5 to 50 percentage points (Table 4). As the first panel shows, the (endogenous) proportion of households with spending control problems which revolve credit card debt rises with relative impatience of the shopper. The second panel shows that this also holds for the endogenous proportion of debt revolvers with assets above our threshold. Intuitively, although credit card debt is held for various reasons, including consumption smoothing, households with relative shopper impatience are more likely to revolve debt, both unconditionally and conditionally on having substantial assets, the more serious is the spending control problem they face. As we look across the life cycle (first two panels), both endogenous proportions exhibit a hump shape, reaching their peak during the later stages of working life and going down substantially during retirement. As was seen above, an important contributing factor is the hump-shaped 23

Note, however, that the credit line is exhausted by individual households in periods of extremely unfavorable income shock realizations. Indeed, it is for such occasions that the unused credit line is kept as a buffer.

16

profile of credit card limits over the life cycle. The third and fourth panels of the Table report median amounts of revolving credit card debt and of financial assets among debt revolvers with sufficient assets to pay off the card debt and to pass the threshold. We see that revolving credit card debt rises with relative impatience. Financial assets initially get somewhat smaller as we increase impatience, but this is reversed as we move to more extreme cases of relative impatience. When spending control problems are particularly serious (shopper impatience is 50pp above that of the accountant), we observe quite wealthy households revolving credit card debt. How well do these model predictions compare with observed proportions of debt revolving and asset accumulation in Tables 1 and 2? As the first column of Table 4 shows, relative impatience of only 5 percentage points is sufficient to generate a simulated fraction of debt revolvers who have substantial assets equal to the observed value of 30 percent (column 3 of Table 1). The second column of Table 4 shows that if all credit card holders exhibit relative impatience of 10 percentage points, median assets are about $40,000 (panel 4) and the proportion of debt revolvers about 55 percent (panel 1), as in the data (Tables 1 and 2). However, the model with identical degrees of relative impatience across households generates somewhat greater proportions of debt revolvers with assets above the threshold and greater median amounts of revolving credit card debt among holders of sizeable assets than are found in the data. We also compare proportions of debt revolvers and amounts of credit card debt over the life cycle in the simulations to those of different age groups in the data.24 For differential impatience of 10 percentage points, the model tends to exhibit less debt-revolving by young households than is actually observed, but more debt revolving for greater impatience. These findings suggest that a data matching exercise, beyond the scope of the present paper, should probably consider heterogeneity in presence and intensity of spending control problems: not all credit card holders face such problems, and those who do are likely to differ in intensity. A lesson for empirical work (see next section), is that it should allow for multiple reasons for revolving credit card debt and test whether indicators of spending control problems continue to be significant. A further issue is that card debt revolving is costly. Figure 4 shows that spending control problems, even in the limited sense of differential impatience between accountant and shopper, are themselves costly. The figure displays 24

We would not expect exact matches regardless of the quality of the theoretical model, in view of the difficulty of separating age from cohort and time effects in cross-sectional data.

17

the value function of a household at the beginning of economic life (20 years, with low value of ut ), as a function of liquid assets. As expected, the value function shifts down as the impatience of the shopper increases. With relative shopper impatience of 5pp., the household needs around $8,000 of liquid assets to be as well off as a household with zero assets but no differential impatience. Thus, the observation that a control mechanism (debt revolving) is costly is not sufficient to rule out its use to fight a problem that also entails costs. But is credit card debt revolving too costly to be used at all if we allow households to switch to a debit card, for example? We note a priori that alternatives, such as switching to a debit card, also entail costs:the household gives up the ability to borrow on the credit card, to float new charges, and to have other benefits we do not model (such as bonus points on the credit card, various insurance and protection options, etc.). Moreover, it has to maintain a balance on the account linked to the debit card at minimal interest rates, as there is no floating. Figure 5 compares value functions if the household is forced to choose at the start of economic life to pursue only one spending control option: either credit card debt revolving or debit card use. Households that start off economic life with zero assets (the assumption often made in simulated models of asset accumulation) or with limited assets would actually find it disadvantageous to rely entirely on the debit card because they have to give up the borrowing facility offered by the credit card, even though we do not include the full list of advantages of credit cards (bonus points and the like). As initial financial assets increase and the borrowing option of the credit card is less important for consumption smoothing, using a credit card becomes progressively less advantageous, but the advantage of debit cards is rather small unless initial assets are sizeable. Recall that these estimated amounts not only ignore some advantages of credit cards and rule out combination with debit cards, but also assume full information, asset knowledge, and financial sophistication of both accountants and shoppers. In view of these findings, we see no reason to rule out credit card debt revolving a priori as a means of controlling spending, especially when its costs can be reduced by combining it with use of debit cards. Indeed, combined use of credit and debit cards is a feature of the data, as described above.

5

An Empirical Exercise

Our theoretical analysis introduced a spending-control role for revolving credit card debt in addition to the roles typically associated with finances over 18

the life cycle (e.g., consumption smoothing). Controlling for other factors, we would expect to find the following two patterns. First, factors involving spending control considerations should encourage debit card use and discourage ownership of credit cards that involve separation of purchases from payments and the potential for overspending. Second, conditional on having a credit card, spending control considerations should make it more likely that credit card owners revolve debt on their cards, controlling for remaining factors that influence debt behavior. In this Section, we use data from the 1995, 1998, 2001, and 2004 waves of the SCF to uncover such patterns. We first look at the joint decisions to own a credit card and to use a debit card; and then, at the decision to revolve debt on the credit card systematically, conditional on owning a credit card. For obvious reasons, there are no direct questions on whether people suffer from spending-control problems in a population-wide survey. We use instead responses to behavioral and attitudinal questions about spending behavior and impulsiveness. These include attitudes about buying on credit, sources of investment advice, ability to save, tendency to "shop around" for the best terms when making purchases or investments, being behind on payments on other types of revolving credit; and smoking.25

5.1

Credit Card Ownership and Debit Card Use

We first consider the joint decision of bank-type credit card ownership and debit card use: both are useful payment media and potential spending-control devices. In our bivariate probit estimation, we allow for unobserved factors influencing both outcomes (Table 4).26 Consistent with the descriptive statistics presented in Table 1, households with higher levels of education are more likely to use either type of card even controlling for other factors, but differences in estimated coefficients are more pronounced for having a credit card. Higher income prospects associated with higher education may encourage credit card issuers to offer cards more readily to those with higher levels of education. On the demand side, households with higher education may be in better position to appreciate the advantages of having a credit card for 25

For a recent investigation of the usefulness of smoking as an indicator of self-control problems prompted by use of this variable in the Bertaut and Haliassos working paper, see Milde (2007). 26 As usual, these regressions are reduced-form equations, and coefficients can represent the interaction of demand and supply considerations. Results for debit card ownership may be more clearly attributable to demand considerations, as we explicitly controlled for whether the household has a checking account. Even in 1995, many checking accounts offered debit cards.

19

consumption smoothing, floating, and accumulating points; they may also be more confident in their ability to control spending, and thus more willing to acquire a credit card, despite the potential for overspending. Controlling for income, financial assets, and homeownership, younger households are significantly more likely to use debit cards; the estimated effect on credit cards is negative but marginally insignificant. Both demand and supply effects are likely to be at play: younger households may be less likely to be offered credit cards because of limited credit histories and less job stability, but they may also prefer to use debit cards instead of credit cards for their transactions. The life-cycle stage of young households would seem to favor the use of a credit card, given that it offers the possibility for consumption smoothing through revolving debt. To the extent that this opposite empirical result reflects demand-side considerations, it is consistent with the idea that young households are influenced by a need to control their spending when opting for debit cards. Older households are significantly less likely to use either type of card, most likely reflecting the limited availability and popularity of such instruments in the formative years of their economic life. As we control for perceptions that buying on a credit card is a ’bad idea’ and related attitudes, supply considerations rather than cultural factors likely contribute to the result that nonwhite or Hispanic households are significantly less likely to have a bank-type credit card. This probably results from being less targeted by the financial sector. Controlling for other factors, nonwhite households are neither more nor less likely to use debit cards. Controlling for age and education, higher income contributes positively to having a credit card, but negatively to using a debit card. Similarly, (controlling for having a checking account), households with larger liquid financial assets are more likely to have either type of card, but holding higher amounts of investment assets (either relatively "safe" investment assets in the form of CDs or bonds or amounts held in retirement accounts) or having home equity increase the probability of having a bank-type credit card but reduce the probability of using a debit card. As with education, credit supply considerations likely account in part for the greater credit card ownership among higher-income and higher-wealth households. But demand considerations are also likely to play a role, as these households’ income and assets make them more likely to pay off their balances and "float" using credit cards, an option not offered by debit cards. Controlling for income and assets, households who receive professional investment advice and those in professional or technical occupations are significantly more likely both to have a bank-type credit card and to use a debit card. This is likely to arise mainly from greater familiarity with the instruments. Being self-employed per se contributes negatively to the likelihood 20

of using a debit card, without having any significant effect on credit card ownership. With riskier incomes, the self-employed are more likely to value the potential to borrow on the credit card to smooth consumption. On the negative side, credit card providers tend to value income stability and may be more reluctant to grant credit cards to self employed with particularly volatile incomes. Although it is conceivable that the self employed may be more concerned about losing control of their expenditures as a result of using a credit card, the operation of such a motive is hard to reconcile with the estimated negative effect on debit card use. We now turn to responses on attitudinal or behavioral factors. Statistical significance of spending control considerations, as well as the pattern of signs across debit and credit card ownership are both relevant. For example, spending control considerations that lead households not to take a credit card in the first place could lead the household to use a debit card instead. Households that report being liquidity constrained are significantly less likely to have a bank-type credit card and more likely to use a debit card. This is entirely consistent with a spending-control explanation: households that find borrowing problematic are particularly likely to want to control their expenses. They avoid the credit cards that can get them into trouble (e.g., through the separation of shopping from payment) and are more likely to opt for a debit card. They do so, even though credit cards themselves might help relax borrowing constraints. One may suspect that this result arises trivially from the supply side with demand having nothing to do with it, but such a simple explanation does not seem fully consistent with the data. Only about one-fourth of liquidity-constrained households were specifically denied credit for a credit card, and of those that were turned down for this reason, nearly 70 percent already had at least one other type of bank-type card. It seems plausible that credit cards are unpopular with many liquidityconstrained households because they fear they will end up borrowing on unfavorable rates if they do get one. Even controlling for liquidity constraints, households that are currently 60 days or more delinquent on at least one revolving credit or charge account at a retail store are somewhat less likely to have a bank-type credit card but significantly more likely to use a debit card. Households having difficulty with payments shy away from the credit card involving separation of purchases from payments and favor debit cards instead; a pattern quite consistent with a spending control motive. Interestingly, those who "shop around" for the best investment terms are significantly less likely to use debit cards, while those that "shop around" for purchases are significantly more likely to use them, even after controlling for resources and liquidity constraints. “Shopping around” for purchases may signal a need to control 21

spending, whereas financially alert investors see no particular benefit to using a debit card when they can benefit from floating and other advantages of credit cards. Households who respond that "buying on the installment plan is usually a bad idea" are significantly less likely to have a bank-type credit card and somewhat more likely to use a debit card. Since they are not forced to revolve credit card debt, this decision can signal concern that owning a credit card may induce them to borrow at high rates. The coefficient on whether the household head is a smoker — a habit often linked to general lack of self control — is significant and negative in the credit card equation, controlling for age, race, education, income, and financial assets. While it is unlikely that smokers are systematically denied credit cards compared to non-smoking households with similar remaining characteristics, the result is consistent with smokers electing not to have credit cards because of their known problem of self control in other spheres. We do not find a statistically significant effect on use of debit cards as their spending control method. It is possible that they are more likely to resort to an even more extreme mode of spending control, namely using cash only, but this hypothesis cannot be tested in the SCF, as it does not collect data on cash holdings. Our regression results point to the rapid growth in the use of debit cards between 1995 and 2004 even for households of given characteristics: the year dummies have significant, positive, and successively larger coefficients in the debit card equation. In contrast, credit card ownership has changed little over these years and the year dummies are notably smaller and typically insignificant. The coefficient on rho is significant and positive, indicating that unobserved characteristics contribute positively both to use of debit cards and to ownership of bank-type credit cards.

5.2

Revolving Credit Card Debt Conditional on Card Ownership

Our second set of regressions focuses on the decision to revolve credit, conditional on having a bank-type credit card (Table 6, Model 6.A). We look for sign reversals, i.e. factors that make a household less likely to have a credit card, but more likely to revolve debt if it does have a card. If the tendency to revolve credit debt is motivated instead by a need to make ends meet, this should show up both as an increased tendency to have a card and to borrow, instead of a reversal in sign. We estimate a bivariate probit model, using the same basic specification for the ownership equation as in Table 5. The second equation is estimated as a selection model of households who respond

22

that they typically do not pay off the balance in full on their most frequently used card at the end of the billing period. In addition to the demographic and behavioral variables in the first equation, we control for the interest rate charged on the most frequently used card and for factors likely to contribute to a need to borrow for financial reasons. These include whether income received in the past year was unusually low, and whether the household head or spouse was fair or poor health. We also include two additional variables, not available in the 1995 Survey: whether the household has previously filed for bankruptcy, and the number of years since the bankruptcy filing. Although we can no longer use the 1995 wave, this introduces default considerations: knowledge and experience of default, as well as a proxy for social stigma and current penalties (since both diminish with time since default).27 Households that are younger, with more children, less education, and fewer resources are less likely to acquire bank-type credit cards, but significantly more likely to revolve credit card balances if they do have them. For some, the sign reversal could reflect in part limited access to credit or lack of information about other forms of credit, e.g. because of limited marketing to them. However, we already control for the presence of liquidity constraints and general difficulties in obtaining loans, and these variables continue to be significant. The reversal in sign could be due, in part, to spending control issues, as belonging to these categories makes it more likely that there is greater need to avoid overspending. Having a higher interest rate on the card most frequently used makes a significant negative contribution to borrowing, consistent with the idea that households do respond to the terms of their credit card contract. Households that have ever filed for bankruptcy are significantly more likely to hold credit cards, especially if the bankruptcy filing was several years ago. However, such households are significantly less likely to revolve the card balance if they do have a card, suggesting that they may have learned to use their cards with caution. Being liquidity-constrained, late on payments on revolving debt, and unable to save — factors that make ownership of credit cards less likely in the first place — contribute significantly to revolving balances on cards if households do own them. A combination of supply-side restrictions in the provision of credit cards, combined with lack of cheaper forms of loans for those who do obtain the credit cards, probably contribute to these findings. However, spending-control considerations may also be contributing to the findings, as all these factors also imply that the household needs to control 27

Excluding the 1995 wave and including the bankruptcy variables have very limited effects on the size and significance of other coefficients in the credit card ownership equation.

23

its spending. A potentially stronger indicator of general self-control problems is whether the financial respondent smokes. Smokers are significantly more likely to revolve credit card balances — even after controlling for age, race, education, and income. As it is difficult to imagine that smokers would be more likely than nonsmokers to be in financial difficulties (the cost of cigarettes cannot be making such a difference across the entire range of financial resources of US respondents), this result gives considerable support to the idea that spending-control considerations play a role. Model 5.B replaces the dummy variables for ever filed for bankruptcy, liquidity constrained, late on payments, not a saver, and smoking with corresponding ones interacted with a dummy signalling that the household has liquid financial assets over the threshold (at least $1,200 in 2004 dollars and half average monthly income). The idea is that such factors are more likely to be capturing spending-control considerations if they are significant for households above the threshold amount of liquid assets. In this specification, the interacted version of previous bankruptcy has a sizable positive and significant coefficient, behavior that is not inconsistent with a strategic default motive. However, the interacted versions of remaining behavioral variables continue to contribute to habitual credit card debt revolving, even after allowing for default considerations. To gain understanding of the potential magnitude of effects, Table 7 presents estimated probabilities for debit card use, credit card ownership, and card balance revolving (conditional on card ownership) for a "typical" young, high-school educated single female with one child, and for a "typical" middle-aged married male with a professional or technical education and a college degree. In both cases, their liquid assets are not below the threshold. The predicted probability of debit card use for the hypothetical young female is .24 in 1995, but rises to .68 by 2004. In contrast, her predicted credit card ownership is much higher than that of her debit card use in 1995, but is roughly the same in 2004. Conditional on card ownership, she is quite likely to revolve credit (probability of .78). If in addition she is a smoker, her predicted probability of debit card use is about unchanged, but the probability of credit card ownership falls to just under 60 percent, while the probability of revolving the card balance conditional on card ownership increases to about .81. If she is liquidity constrained, her predicted probability of debit card use increases to about .32 in 1995 and to more than .75 in 2004. Her predicted probability of credit card ownership falls to about .59, while that of revolving the balance increases to about .89. The chosen male is slightly less likely to use a debit card than the chosen female in either year, but has much larger predicted probability of credit card 24

ownership (nearly .98 in both years) and a fairly low estimated probability of revolving the card balance (about .35 in both years). If he is also a smoker, the probabilities of either type of card use are virtually unchanged, but that of revolving the credit card balance increases to about .42 in both years. If he is liquidity constrained, the predicted probability of using a debit card increases to .28 in 1995 and to nearly .72 in 2004. The effect on credit card ownership is negative but very small, while that on revolving the credit card balance is fairly sizable, increasing to more than .54 in both years. Thus, as both examples illustrate, factors such as smoking (that captures general problems of self-control) or liquidity constraints (that are more likely to be associated with control problems for households above the threshold amount of liquid assets), reduce the probability of credit card ownership and increase that of habitual debt revolving if a credit card is obtained by amounts that are statistically and economically significant. All in all, the econometric results in this section are consistent with the hypothesis that spending-control considerations play a role in credit card ownership and card debt revolving among households with substantial liquid assets, even after controlling for the usual life-cycle factors and for a possible link to default considerations.

6

Concluding Remarks

The co-existence of substantial, low-interest liquid assets and high-interest credit card debt that characterizes a number of households questions fundamental notions of arbitrage. The co-existence of credit card debt with substantial accumulation of assets for retirement among some households makes them appear impatient with respect to some objectives and much more patient with respect to others. Households who revolve credit card debt appear to have target utilization rates of their credit card limits rather than a specific amount of debt necessary to finance consumption needs. In order to deal with cases that do not fit our standard rational models, we have presented a model that distinguishes between an accountant and a shopper function in the household and recognizes the potential role that credit card debt can play in disciplining the consumption behavior of the shopper, in addition to consumption smoothing. Clearly, the distinction between accountant and shopper is not necessary for households that do not face overspending: there, accountant and shopper share the same rate of time preference and the unitary model works well. But when overspending is a problem, low-interest assets can co-exist with higher-interest credit card debt, because if the assets were used to pay it off, the shopper would adjust his consumption behavior, frustrating the attempt 25

of the accountant to reduce the amount of credit card debt. Since credit card debt is not held simply because of impatience but has a role to play in moderating consumption, its existence is quite consistent with objectives to build up assets for retirement. Shoppers, who are uncertain about their future ability to make purchases, maintain an unused portion of their credit line as a buffer to future consumption. Accountants can exploit this behavior to control the amount of consumption by manipulating the size of the credit line that remains free. Our simulations of a minimalistic accountant-shopper model, in which the only departure from the standard model is differential impatience between the accountant and the shopper, suggest that the setup is a powerful one for generating coexistence of assets and debts even for limited differences in impatience. Although detecting spending- or self-control problems in survey data is a formidable task, we have presented considerable empirical evidence that is at least consistent with a role for spending control considerations even after controlling for a host of typical factors governing credit card debt. All in all, it seems that the accountant-shopper framework, with its many possible variants, could provide a useful tool for future attempts to match the quite heterogeneous and often puzzling debt-asset structure of modern households.

A A.1

Appendix Outline of the Solution Algorithm

Since this model is a complicated nonconvex game between the accountant and the shopper, it seems unavoidable to discretize the action spaces of the players in order to get a reliable, if not necessarily very precise solution. Both the accountant’s and the shopper’s action can be seen as a choice of the credit card balance, the balance before and after consumption takes place, respectively. We therefore choose a discrete grid of possible values of Bt (the grid changes with age to account for the changing credit card limit). Liquid assets A are a continuous variable. The value function is stored at discrete points of A, and between grid points it is approximated by piecewise-linear interpolation. For the reported results, we have used a grid of 100 points for A and 400 points for B. The solution is then computed by backward induction, solving each period first the shopper’s problem and then the accountant’s problem.

26

A.2

Conversion from Annual to Monthly Frequency

In this Appendix, we describe the adjustment that we made to convert the model from annual to monthly frequency. A parameter related to the monthly calibration is denoted by a tilde, a parameter without tilde refers to the annual calibration. For the death probabilities we assume, for simplicity, that they are constant within a year. Therefore if PD (y) denotes the probability of surviving from year y to y +1, the probability PD (y˜ : m) of surviving from month y : m to the next month (which is y : m + 1 or y + 1 : 1 if m = 12), is equal to PD (y˜ : m) = PD (y)1/12 The discount factor β and the interest rates R and RCC are converted to e = β 1/12 etc. monthly rates by the formula β We now turn to the adjustment of the parameters of the individual income processes. The deterministic part of log income is adjusted simply by substracting log 12. More problematic is the adjustment of the stochastic part, since the shocks to these processes are i.i.d. For the parameters of the two-state Markov process governing the serially correlated income shock, uit , we set α ˜ = α1/12 and σ˜2 = σ 2 /12. These parameter choices then determine θ and p.We use a transitory income shock, ν, that is i.i.d. at the monthly level such that the variance of annual income is unchanged. This probably leads to a series of monthly income that is too volatile, but it is unavoidable unless we want to introduce serial autocorrelation in these income shocks, which is against the spirit of the annual income calibration.28 We therefore adjusted the parameter by applying the formula σ˜2ν = 12σ 2ν for both working and retired population (i.e., for both ν W and ν R shocks). To understand this, note that σ 2ν is the shock to the logarithm √ of income. Since the standard deviation of income has to be divided by 12 when going from annual to monthly frequency, the √ standard deviation of income in percentage terms has to be multiplied by 12, which leads to the above formula. 28

Introducing serial correlation would also complicate the computation substantially because it implies introducing an extra continuous state variable.

27

References [1] Ariely, Dan and Klaus Wertenbroch (2002). “Procrastination, Deadlines, and Performance: Self-Control by Precommitment”, forthcoming in Psychological Science. [2] Bertaut, Carol C. and Michael Haliassos (2002). “Debt Revolvers for Self-Control”, mimeo. [3] Bertaut, Carol C. and Michael Haliassos (2006). “Credit Cards: Facts and Theories”, in G. Bertola, R. Disney, and C. Grant, The Economics of Consumer Credit, Cambridge: MIT Press, 181-237. [4] Caplin, A., and J. Leahy (2004). “Absentminded consumer”, NBER Working Paper 10216. [5] Carroll, C.D. (1997). “Buffer Stock Saving and the Life Cycle / Permanent Income Hypothesis,” Quarterly Journal of Economics CXII , 3-55. [6] Durkin, Thomas (2000). “Credit Cards: Use and Consumer Attitudes, 1970-2000”, Federal Reserve Bulletin, September 2000, 623-34. [7] Durkin, Thomas (2002). “Consumers and Credit Disclosures: Credit Cards and Credit Insurance”, Federal Reserve Bulletin, April 2002, 20113. [8] Frederick, Shane, George Loewenstein, and Ted O’Donoghue (2002).“Time Discounting and Time Preference: A Critical Review”, Journal of Economic Literature, XL, 351-401. [9] Gross, David and Nicholas Souleles (2002). “Do Liquidity Constraints and Interest Rates Matter for Consumer Behavior? Evidence from Credit Card Data”, Quarterly Journal of Economics, 117, 149-85. [10] Hoch, Stephen J. and George F. Loewenstein (1991). “Time-Inconsistent Preferences and Consumer Self-Control”, Journal of Consumer Research, 17(4), 492-507. [11] Laibson, David, Andrea Repetto, and Jeremy Tobacman (2003). “A Debt Puzzle”, in Philippe Aghion, Roman Frydman, Joseph Stiglitz, and Michael Woodford (Eds), Knowledge, Information, and Expectations in Modern Economics: In Honor of Edmund S. Phelps, 228-266.

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[12] Lehnert, Andreas and Dean M. Maki (2001). “Consumption, Debt, and Portfolio Choice: Testing the Effect of Bankruptcy Law”, mimeo, Board of Governors of the Federal Reserve System. [13] Milde, Christopher (2007). Credit Card Borrowing, Illiquid Assets, and Self-Control Problems, Unpublished PhD dissertation, European University Institute. [14] Prelec, Drazen and Duncan Simester (2001). “Always Leave Home Without It: A Further Investigation of the Credit-Card Effect on Willingness to Pay”, Marketing Letters, 12, 5-12. [15] Schelling, Thomas C. (1992). “Self-Command: A New Discipline”, in Loewenstein, G. and J. Elster (eds), Choice Over Time, New York: Russell Sage Foundation, 167-176. [16] Shefrin, Hersch M. and Richard H. Thaler (1988). “The Behavioral LifeCycle Hypothesis”, Economic Inquiry, 26, 609-43. [17] Soman, Dilip and Amar Cheema (2002). “The Effect of Credit on Spending Decisions: The Role of the Credit Limit and Credibility”, Marketing Science, 21, 32-53. [18] National Vital Statistics Report, 2001, Vol. 48, No. 18, February 7, 2001. [19] Telyukova, Irina (2007). "Household Need for Liquidity and the Credit Card Debt Puzzle." Working Paper. [20] Thaler, Richard H. (1980). “Toward a Positive Theory of Consumer Choice”, Journal of Economic Behavior and Organization, 1, 39-60. [21] Thaler, Richard H. and Hersch M. Shefrin (1981). “An Economic Theory of Self-Control”, Journal of Political Economy, 89, 392-406. [22] Wertenbroch, Klaus (1998). “Consumption Self-Control via Purchase Quantity Rationing of Virtue and Vice”, Marketing Science, 17, 317337. [23] Wertenbroch, Klaus (2002). “Self-Rationing: Self-Control, Overconsumption, and Consumer Choice,” forthcoming in Loewenstein, G., R. Baumeister, and D. Read (eds), Time and Decision, New York, NY: Russell Sage Foundation. [24] Zinman, Jonathan (2007). “Household Borrowing High and Lending Low Under No-Arbitrage", Working Paper. 29

Table 1: Percentage of households with bank-type credit cards and percentages of households that typically revolve credit card debt. Source: 1995, 1998, 2001, and 2004 Surveys of Consumer Finances

Percent with bank-type credit card

Percent of card holders with balance remaining after last billing period

Percent of card holders with balance who have liquid assets > balance and > threshold amount*

Percent of card holders with balance and liquid assets > card balance and > threshold amount* and who do not usually pay off balance in full

By year: 1995 1998 2001 2004 All

66.5 67.2 72.6 71.5 69.5

55.9 54.8 53.4 56.1 55.0

26.0 30.9 32.1 31.2 30.1

74.6 69.7 68.1 65.7 68.7

by age: less than 35 35-54 55-64 65 +

60.4 74.7 75.6 65.5

68.6 63.1 47.7 28.6

21.1 32.6 37.7 35.2

68.5 71.9 65.5 59.4

by education: less than high school high school degree college degree

36.7 68.6 89.0

57.2 62.1 46.7

13.6 27.1 45.1

67.2 69.6 68.0

*Checking, saving, or money market account balances of at least $1,200 (in 2004 dollars) and at least one-half of average monthly income.

30

Table 2: Median bank-type credit card balances remaining after last payment, median liquid financial assets, and median financial wealth of households that revolve card balances and have liquid assets greater than card balance and greater than threshold. Median card balance

Median liquid financial assets

Median financial wealth

1995 1998 2001 2004

1,231 1,159 1,065 1,400

7,017 8,695 8,521 10,000

39,393 40,694 44,415 48,000

All

1,231

8,521

43,392

Median card balances, median liquid financial assets, and median financial wealth of households that revolve card balances, have liquid assets greater than threshold and greater than card balance, and do not usually pay off balance in full. 1995 1998 2001 2004

1,600 1,507 1,278 1,800

7,140 8,000 7,456 8,800

38,778 36,172 37,023 40,200

All

1,507

7,988

37,697

Source: 1995, 1998, 2001, and 2004 Surveys of Consumer Finances Amounts in 2004 dollars.

31

Table 3: Percentage of households that have bank-type credit card and that use debit cards. Source: 1995, 1998, 2001, and 2004 Surveys of Consumer Finances

Neither type card

Debit user only

Has bank-type credit card Does not use debit

Uses debit card

1995

30.4

3.1

52.0

14.5

1998

25.7

7.2

40.7

26.5

2001

18.2

9.2

34.8

37.8

2004

15.1

13.4

25.5

46.0

all years

22.1

8.4

37.8

31.7

less than 35

25.7

14.0

22.8

37.5

35-54

16.8

8.5

37.3

37.4

55-64

18.1

6.3

44.7

30.9

65 +

31.0

3.4

50.8

14.8

less than high school

52.5

10.8

25.0

11.7

high school degree

40.8

19.9

76.0

63.3

college degree

6.1

4.9

44.3

44.5

by age:

by education:

32

Table 4: Model Results

Impatience of shopper: 5%

10%

20%

50%

0.540 0.518 0.721 0.777 0.324

0.833 0.829 0.950 0.983 0.687

0.972 0.999 1.000 1.000 0.926

0.447 0.199 0.542 0.900 0.342

0.677 0.476 0.739 0.961 0.636

0.940 0.900 0.983 0.999 0.908

5983 6396 9925 7172 2133

6551 8537 10214 7035 2374

36897 15242 34714 76035 35987

72789 21590 75084 148924 71269

Fraction of debt revolvers in population All: All age= 65

-0.406

0.059

0.000

Age >= 75

-0.499

0.056

0.000

Lt high school education

-0.452

0.043

0.000

Lt high school education

0.065

0.061

0.288

College degree

0.240

0.039

0.000

College degree

-0.237

0.033

0.000

ln(income)

0.078

0.013

0.000

ln(income)

-0.092

0.011

0.000

Has home equity ln(liquid financial assets)

0.336

0.037

0.000

-0.188

0.039

0.000

0.104

0.007

0.000

Has home equity ln(liquid financial assets)

-0.169

0.007

0.000

ln(safe investment assets)

0.017

0.003

0.000

-0.021

0.003

0.000

ln(retirement account assets)

0.028

0.003

0.000

Has checking account

0.365

0.042

0.000 0.030

0.039

0.438

-0.212

0.036

0.000

Health of head or spouse fair or poor

0.031

0.035

0.376

Shops around when making purchases

-0.055

0.029

0.060

ln(safe investment assets)

Income last year unusually low Head is self-employed

Shops around for investment advice

0.013

0.045

0.763

-0.049

0.035

0.161

Shops around when making purchases

0.062

0.035

0.072

Uses professional investment advice

0.163

0.038

0.000

36

Head is selfemployed

Table 6A continued has professional or technical occupation

0.168

0.041

0.000 Interest rate on credit card

-0.522

0.256

0.041

0.495

0.042

0.000

-0.181

0.037

0.000

Is liquidity constrained

-0.152

0.039

0.000

Is liquidity constrained

Buying on credit "bad idea"

-0.265

0.032

0.000

Buying on credit "bad idea"

Doesn't save

-0.037

0.033

0.258

Doesn't save

0.322

0.033

0.000

Late 60 days or more on revovling credit

-0.036

0.058

0.528

Late 60 days or more on revovling credit

0.454

0.082

0.000

Head is smoker

-0.185

0.036

0.000

Head is smoker

0.225

0.035

0.000

Ever filed for bankruptcy

0.090

0.018

0.000

Ever filed for bankruptcy

-0.057

0.013

0.000

No. years ago filed for bankruptcy

0.023

0.006

0.000

0.013

0.035

0.357

D2001

0.107

0.037

0.004

D2001

-0.042

0.035

0.240

D2004

-0.016

0.037

0.664

D2004

-0.037

0.036

0.304

RHO(1,2)

-0.642

0.101

0.000

N

13266

N (selected from those with bank-type credit card)

10198

Log likelihood

-9157.555

37

Table 6 continued Model 6.B: Behavioral variables interacted w/ has liquid financial assets > threshold amount Equation 2: Does not usually pay off balance on bank-type credit card

Equation 1: Dependent variable: has bank-type credit card Coeff.

Std.Err.

P-value

Coeff.

Std.Err.

P-value

Constant

-1.930

0.159

0.000

Constant

2.864

0.160

0.000

Married

0.167

0.046

0.000

Married

0.161

0.049

0.001

Single Female

0.027

0.049

0.585

Single Female

0.220

0.053

0.000

No. children

-0.048

0.015

0.001

No. children

0.075

0.014

0.000

Nonwhite or Hispanic

-0.205

0.038

0.000

Nonwhite or Hispanic

0.150

0.039

0.000

Age lt 40

-0.067

0.038

0.083

Age lt 40

0.042

0.036

0.244

Age 65-74

-0.157

0.052

0.003

Age >= 65

-0.484

0.057

0.000

Age >= 75

-0.489

0.057

0.000

Lt high school education

-0.453

0.043

0.000

Lt high school education

0.049

0.065

0.452

College degree

0.242

0.039

0.000

College degree

-0.250

0.034

0.000

ln(income)

0.077

0.013

0.000

ln(income)

-0.077

0.012

0.000

Has home equity ln(liquid financial assets) ln(safe investment assets)

0.347

0.037

0.000

-0.227

0.040

0.000

0.106

0.007

0.000

-0.224

0.007

0.000

0.017

0.003

0.000

Has home equity ln(liquid financial assets) ln(safe investment assets)

-0.023

0.003

0.000

ln(retirement account assets)

0.030

0.003

0.000

Has checking account

0.359

0.042

0.000 0.084

0.040

0.036

-0.216

0.036

0.000

Health of head or spouse fair or poor

0.072

0.036

0.045

Shops around when making purchases

-0.067

0.030

0.024

Credit card interest rate

-0.045

0.262

0.862

Income last year unusually low Head is self-employed

Shops around for investment advice

0.012

0.045

0.797

-0.036

0.035

0.298

Shops around when making purchases

0.060

0.035

0.085

Uses prof. investment advice

0.163

0.038

0.000

Has professional or technical occupation

0.171

0.042

0.000

Head is self-employed

38

Model 6B continued Is liquidity constrained

-0.108

0.039

0.005

Is liquidity constr. & liq assets > threshold

0.510

0.057

0.000

Buying on credit "bad idea"

-0.268

0.032

0.000

Buying on credit "bad idea" & liq. assets > threshold

-0.198

0.037

0.000

Doesn't save

0.001

0.033

0.964

Doesn't save & liq. assets > threshold

0.231

0.039

0.000

Late ≥60 days on revolving credit

0.011

0.056

0.841

Late ≥60 days & liquid assets>threshold

0.315

0.144

0.029

-0.166

0.035

0.000

Head smoker & liq. assets > threshold

0.182

0.045

0.000

Ever filed for bankruptcy

0.086

0.017

0.000

Filed for bankruptcy & liq. assets > threshold

0.198

0.069

0.004

No. years ago filed for bankruptcy

0.024

0.006

0.000

D2001

0.107

0.038

0.005

D2001

-0.032

0.036

0.368

D2004

-0.019

0.037

0.614

D2004

-0.010

0.036

0.785

RHO(1,2)

-0.505

0.116

0.000

Head is smoker

N N (selected from those with bank-type card) Log likelihood

13266 10198 9251.921

39

Table 7. Estimated probabilities of using debit card, having bank-type credit card, and revolving balance on bank-type card (conditional on ownership). Using estimated coefficients from Table 5 (has debit card and has debit card) and Table 6, Model 6.B 1. Single white female, 1 child, age lt 40, with high-school education, checking account but no home equity Probability of using debit card 1995

Probability of having credit card

2004

1995

2004

Probability of revolving balance 1998

2004

Baseline probability

0.244

0.678

0.681

0.669

0.759

0.756

if smoker if liquidity constrained if doesn’t save if late on payments if ever filed for bankruptcy additional assumptions: income: liquid financial assets safe investment assets retirement account assets

0.237

0.671

0.597

0.584

0.812

0.809

0.323

0.757

0.588

0.575

0.887

0.885

0.254 0.327

0.689 0.761

0.665 0.645

0.653 0.632

0.825 0.845

0.822 0.843

0.816

0.813

20,000 1,200 1,000 0

40

Table 7 continued 2. Married white male, 2 children, age 40-64, college education, professional or technical occupation, checking account and home equity Probability of having credit card

Probability of using debit card 1995

2004

1995

2004

Probability of revolving balance 1998

2004

Baseline probability

0.207

0.632

0.977

0.975

0.350

0.346

if smoker if liquidity constrained if doesn’t save if late on payments if ever filed for bankruptcy additional assumptions: income: liquid financial assets safe investment assets retirement account assets

0.201 0.280

0.624 0.717

0.962 0.960

0.959 0.957

0.420 0.550

0.416 0.546

0.216 0.283

0.644 0.720

0.975 0.971

0.972 0.969

0.439 0.472 0.426

0.435 0.468 0.422

80,000 7,000 19,000 28,000

41

5000

4000

Balance after payment

3000

2000

1000

0 Rational,low u

t

Rational,high u

−1000

t

Impat,low u

t

Impat,high u

t

−2000

0

1

2

3

4

5 Assets

6

Figure 1: Policy function, 50 year old

42

7

8

9

10 4

x 10

12000

50000 45000

10000 40000

medians

8000

6000

35000

Assets (right axis) Limit Balance Payments

30000 25000

4000 20000 15000

2000

10000 0 5000 -2000 20

0 30

40

50

60

70

age Figure 2: Model simulations

43

80

90

5500

5000

4500

medians

4000

3500

3000

2500

2000

1500

Income Consumption Payments

1000 30

40

50

60

age Figure 3: Model simulations

44

70

80

90

−0.51 Rational Impat=0.05 Impat=0.1 Impat=0.2 Impat=0.5

−0.515

−0.52

−0.525

−0.53

−0.535

−0.54

−0.545

0

0.2

0.4

0.6

0.8

1 Assets

Figure 4: Value functions

45

1.2

1.4

1.6

1.8

2 4

x 10

Welfare gain of debit card 10000 Low ut High u

t

8000

2004 dollars

6000

4000

2000

0

−2000

3

4

10

10 Assets of debit card holder Figure 5: Value loss

46