Learning in the Credit Card Market Sumit agarwal, John C. Driscoll. Xavier Gabaix, and David Laibson* pril23,2011 Abstract Agents with more experience make better choices. We measure learning dynamics using a panel with four million monthly credit card statements. We study add-on fees specifically cash advance, late payment, and overlimit fees. New credit card accounts generate fee payments of S15 per month. Through negative feedback-ie paying a fee consumers learn to avoid triggering future fees. Paying a fee last month reduces the likelihood of paying a fee in the current month by about 40%. Controlling for account fixed effects, monthly fee payments fall by 75% during the first three years of account life. We find that learning is not monotonic. Knowledge effectively depreciates about 10% per month, implying that learning displays a strong recency effect. The speed of net learning is about twice as great for higher-income borrowers than it is for lower- income borrowers; the rate of knowledge depreciation, or forgetting, is about half as fast for high- relative to low-income borrowers. Middle-aged borrowers have the same advantageous learning dynamics relative to older borrowers. JEL: D1, D4, D8, G2 Agarwal: Federal Reserve Bank of Chicago. sagarwalofrbchi. org. Driscoll: Federal Reserve Board, john. c. driscollafrb. gov. Gabaix: New York University and NBER, xgabaix @stern. nyu. edu Laibson: Harvard University and NBER, dlaibson harvard. edu. Gabaix and Laibson acknowledg support from the National Science Foundation(DMS-0938185). Laibson acknowledges financial support from the National Institute on Aging(RO1-AG-1665). The views expressed in this paper are those of the authors and do not represent the policies or positions of the Board of Governors of the Federal Reserve System or the Federal Reserve Bank of Chicago. Ian Dew-Becker, Keith Er icson, Mike Levere, Tom Mason and Thomas Spiller provided outstanding research assistance. The authors are grateful to the editor and the referees, and to Murray Carbonneau, Stefano dellavigna Joanne Maselli, Nicola Persico, Devin Pope, Matthew Rabin, and seminar participants at the aeA Berkeley, EUI and the NBER(Law and Economics) for their suggestions. This paper previously circulated under the title"Stimulus and Response: The Path from Naivete to Sophistication in the Credit card market
Learning in the Credit Card Market Sumit Agarwal, John C. Driscoll, Xavier Gabaix, and David Laibson∗ April 23, 2011 Abstract Agents with more experience make better choices. We measure learning dynamics using a panel with four million monthly credit card statements. We study add-on fees, specifically cash advance, late payment, and overlimit fees. New credit card accounts generate fee payments of $15 per month. Through negative feedback — i.e. paying a fee — consumers learn to avoid triggering future fees. Paying a fee last month reduces the likelihood of paying a fee in the current month by about 40%. Controlling for account fixed effects, monthly fee payments fall by 75% during the first three years of account life. We find that learning is not monotonic. Knowledge effectively depreciates about 10% per month, implying that learning displays a strong recency effect. The speed of net learning is about twice as great for higher-income borrowers than it is for lowerincome borrowers; the rate of knowledge depreciation, or forgetting, is about half as fast for high- relative to low-income borrowers. Middle-aged borrowers have the same advantageous learning dynamics relative to older borrowers. (JEL: D1, D4, D8, G2) ∗Agarwal: Federal Reserve Bank of Chicago, sagarwal@frbchi.org. Driscoll: Federal Reserve Board, john.c.driscoll@frb.gov. Gabaix: New York University and NBER, xgabaix@stern.nyu.edu. Laibson: Harvard University and NBER, dlaibson@harvard.edu. Gabaix and Laibson acknowledge support from the National Science Foundation (DMS-0938185). Laibson acknowledges financial support from the National Institute on Aging (R01-AG-1665). The views expressed in this paper are those of the authors and do not represent the policies or positions of the Board of Governors of the Federal Reserve System or the Federal Reserve Bank of Chicago. Ian Dew-Becker, Keith Ericson, Mike Levere, Tom Mason and Thomas Spiller provided outstanding research assistance. The authors are grateful to the editor and the referees, and to Murray Carbonneau, Stefano Dellavigna, Joanne Maselli, Nicola Persico, Devin Pope, Matthew Rabin, and seminar participants at the AEA, Berkeley, EUI and the NBER (Law and Economics) for their suggestions. This paper previously circulated under the title “Stimulus and Response: The Path from Naiveté to Sophistication in the Credit Card Market.” 1
Introduction Economists often motivate optimization and equilibrium as the outcome of learning Learning is a key mechanism that underpins economic theories of rational behavior. Accord- ingly, many economic studies have analyzed learning in the lab, and in the field. 2 Because of data limitations, only a few papers measure learning with household- panel data. Such household studies, usually find that households learn to optimize over time. For example, Miravete(2003)and Agarwal, Chomsisengphet, Liu and Souleles(2006) espectively show that consumers switch telephone calling plans and credit card contracts te minimize monthly bill payments. A few papers are able to identify the specific information Hows that elicit learning. For instance, Fishman and Pope(2006) study video stores, and find that renters are more likely to return their videos on time if they have recently been fined for returning them late. Ho and Chong(2003)use grocery store scanner data to estimate a model in which consumers learn about product attributes. Their learning model has greater predictive power, with fewer parameters, than forecasting models used by retailers.3 In the current paper, we study individual households that learn to avoid add-on fee the credit card market. We analyze a panel dataset that contains three years of credit card statements, representing 120,000 consumers and 4.000.000 credit card statements. We focus our analysis on credit card fees -late payment, over limit, and cash advance fees. Some observers argue that account holders do not optimally minimize such fees. We want to know whether credit card holders change the way they use their credit cards -e. g, paying For example, Van Huyck, Cook and Battalio(1994), Crawford(1995), Roth and Erev(1995),Camerer (2003), and Wixted(2004) 2For example, see Bahk and Gort(1993), Marimon and Sunder(1994). Thornton and Thompson(2001) LEmieux and MacLeod(2000) study the effect of an increase in unemployment benefits in Canada They find that the propensity to collect unemployment benefits increases as a consequence of a previous unemployment spell. Odean, Strahlevitz and Barber(2010) find evidence that individual investors tend to repurchase stocks that they previously sold for a gain. Dellavigna(2009) surveys the field evidence on behavioral phenomena 4 Ausubel(1991, 1999), Shui and Ausubel(2004)and Kerr and Dunn(2008)analyze the magnitude of interest payments and fees in the credit card market ple, Frontline reports that "The new billions in revenue reflect an age-old habit of human behavior: Most people never anticipate they will pay late, so they do not shop around for better late fees"(http://www.pbs.org/wgbh/pages/frontline/shows/credit/more/rise.html)thereisalsoanascent academic literature that studies how perfectly rational firms interact in equilibrium with imperfectly rational consumers. See Shui and Ausubel(2004), Della vigna and Malmendier(2004). Mullainathan and Shleifer (2005), Oster and Morton(2005), Gabaix and Laibson(2006), Jin and Leslie(2003), Koszegi and Rabin (2006), Malmendier and Shanthikumar(2007), Grubb(2009), and Bertrand et al.(2010). See Spiegler (2011)for an overview
1 Introduction Economists often motivate optimization and equilibrium as the outcome of learning. Learning is a key mechanism that underpins economic theories of rational behavior. Accordingly, many economic studies have analyzed learning in the lab,1 and in the field.2 Because of data limitations, only a few papers measure learning with household-level panel data. Such household studies, usually find that households learn to optimize over time. For example, Miravete (2003) and Agarwal, Chomsisengphet, Liu and Souleles (2006) respectively show that consumers switch telephone calling plans and credit card contracts to minimize monthly bill payments. A few papers are able to identify the specific information flows that elicit learning. For instance, Fishman and Pope (2006) study video stores, and find that renters are more likely to return their videos on time if they have recently been fined for returning them late. Ho and Chong (2003) use grocery store scanner data to estimate a model in which consumers learn about product attributes. Their learning model has greater predictive power, with fewer parameters, than forecasting models used by retailers.3 In the current paper, we study individual households that learn to avoid add-on fees in the credit card market.4 We analyze a panel dataset that contains three years of credit card statements, representing 120,000 consumers and 4,000,000 credit card statements. We focus our analysis on credit card fees – late payment, over limit, and cash advance fees. Some observers argue that account holders do not optimally minimize such fees.5 We want to know whether credit card holders change the way they use their credit cards — e.g., paying 1For example, Van Huyck, Cook and Battalio (1994), Crawford (1995), Roth and Erev (1995), Camerer (2003), and Wixted (2004). 2For example, see Bahk and Gort (1993), Marimon and Sunder (1994), Thornton and Thompson (2001). 3Lemieux and MacLeod (2000) study the effect of an increase in unemployment benefits in Canada. They find that the propensity to collect unemployment benefits increases as a consequence of a previous unemployment spell. Odean, Strahlevitz and Barber (2010) find evidence that individual investors tend to repurchase stocks that they previously sold for a gain. Dellavigna (2009) surveys the field evidence on behavioral phenomena. 4Ausubel (1991, 1999), Shui and Ausubel (2004) and Kerr and Dunn (2008) analyze the magnitude of interest payments and fees in the credit card market. 5For example, Frontline reports that “The new billions in revenue reflect an age-old habit of human behavior: Most people never anticipate they will pay late, so they do not shop around for better late fees.” (http://www.pbs.org/wgbh/pages/frontline/shows/credit/more/rise.html) There is also a nascent academic literature that studies how perfectly rational firms interact in equilibrium with imperfectly rational consumers. See Shui and Ausubel (2004), DellaVigna and Malmendier (2004), Mullainathan and Shleifer (2005), Oster and Morton (2005), Gabaix and Laibson (2006), Jin and Leslie (2003), Koszegi and Rabin (2006), Malmendier and Shanthikumar (2007), Grubb (2009), and Bertrand et al. (2010). See Spiegler (2011) for an overview. 2
fewer fees- as they gain experience We find that fee payments are very large in the first few months after the opening of an ccount. We find that new accounts generate direct monthly fee payments(not including interest payments)that average S15 per month. b However, these payments fall by 75 percent during the first four years of account life These learning effects may be driven by many different channels. Consumers learn more about the existence and magnitude of fees when they knowingly or accidentally trigger them Painful fee payments may also train account holders to be more vigilant in their card usage As a result of many different learning pathways, card holders sharply cut their fee payments over time We find that the learning dynamics are not monotonic. Card holders act as if their knowl- edge depreciates-i.e, learning patterns exhibit a recency effect. 7 A late payment charge from the previous month engenders vigilant fee avoidance this month, and this response is much stronger than the vigilance engendered by a late payment charge that was paid further back in time. We estimate that the learning effect of a fee payment effectively depreciates at a rate of between 10 and 20 percent per month. At first glance, such depreciation may seem counter-intuitive. However, if attention is a scarce resource, attention may wander as the salience of a past fee payment fades. After making any significant mistake(e.g, getting a speeding ticket), people are likely to pay attention and avoid the mistake; however as the key event recedes into history, vigilance fades There are several papers that have also documented forgetting effects, though the sett of these papers are quite different from our credit card application. For instance, Benkard (2000)finds evidence for both learning and forgetting - that is, depreciation of productivity over time- in the manufacturing of aircraft, as do argote, Beckman and Epple(1990), in shipbuilding We analyze the mechanisms that may explain the fee dynamics that we measure. W mOreover, this understates the impact of fees, since some behavior -e. g. a pair of late payments not only triggers direct fees but also triggers an interest rate increase, which is not captured in our $15 calculation. Suppose that a consumer is carrying $2,000 of debt. Changing the consumer's interest rate from 10% to 20% is equivalent to charging the consumer an extra $200. Late payments also may prompt a report to the credit bureau, adversely affecting the card holder's credit accessability and creditworthness The average consumer has 4.8 cards and 2.7 actively used card 7See Lehrer(1988), Aumann, Hart and Perry(1997) and Besanko et al.(2010) for some theoretical models of forgetfulness
fewer fees — as they gain experience. We find that fee payments are very large in the first few months after the opening of an account. We find that new accounts generate direct monthly fee payments (not including interest payments) that average $15 per month. 6 However, these payments fall by 75 percent during the first four years of account life. These learning effects may be driven by many different channels. Consumers learn more about the existence and magnitude of fees when they knowingly or accidentally trigger them. Painful fee payments may also train account holders to be more vigilant in their card usage. As a result of many different learning pathways, card holders sharply cut their fee payments over time. We find that the learning dynamics are not monotonic. Card holders act as if their knowledge depreciates — i.e., learning patterns exhibit a recency effect.7 A late payment charge from the previous month engenders vigilant fee avoidance this month, and this response is much stronger than the vigilance engendered by a late payment charge that was paid further back in time. We estimate that the learning effect of a fee payment effectively depreciates at a rate of between 10 and 20 percent per month. At first glance, such depreciation may seem counter-intuitive. However, if attention is a scarce resource, attention may wander as the salience of a past fee payment fades. After making any significant mistake (e.g., getting a speeding ticket), people are likely to pay attention and avoid the mistake; however as the key event recedes into history, vigilance fades. There are several papers that have also documented forgetting effects, though the settings of these papers are quite different from our credit card application. For instance, Benkard (2000) finds evidence for both learning and forgetting — that is, depreciation of productivity over time — in the manufacturing of aircraft, as do Argote, Beckman and Epple (1990), in shipbuilding. We analyze the mechanisms that may explain the fee dynamics that we measure. We 6Moreover, this understates the impact of fees, since some behavior – e.g. a pair of late payments – not only triggers direct fees but also triggers an interest rate increase, which is not captured in our $15 calculation. Suppose that a consumer is carrying $2,000 of debt. Changing the consumer’s interest rate from 10% to 20% is equivalent to charging the consumer an extra $200. Late payments also may prompt a report to the credit bureau, adversely affecting the card holder’s credit accessability and creditworthness. The average consumer has 4.8 cards and 2.7 actively used cards. 7See Lehrer (1988), Aumann, Hart and Perry (1997) and Besanko et al. (2010) for some theoretical models of forgetfulness. 3
first explore several explanations that are not consistent with our preferred explanation of learning /forgetting-for example, that card usage might be negatively autocorrelated-and find that these explanations are not consistent with the data. On the other hand, we find support for mechanisms that support the learning/forgetting interpretation. Notably, we find that in the month after paying a late fee, account holders are especially likely to make their next payment more than two weeks before the due date. This suggests that a late payment fee acts as a wake up call that induces earlier fee payment. We also find that the speed of (i) net learning, (ii) the magnitude of the recency effect, and(iii) the speed of forgetting all differ across borrower characteristics. Higher-income borrowers learn more than twice as fast, have a recency effect double the size, and forget about three-times as slowly as lower-income borrowers. Likewise, middle-aged borrowers have similar learning dvantages relative to older borrowers In summary, our findings imply that a high rate of knowledge depreciation offsets learning Nevertheless, learning dominates knowledge depreciation. On average, fees fall over the life the credit card. These learning dynamics are most advantageous for high-income and middle-aged borrowers We organize our paper as follows, Section 2 summarizes our data and presents our basic evidence for learning and backsliding/forgetting. Section 3 analyzes various alternative(non- learning) explanations for our finding Section 4 discusses extensions to our analysis on learning and forgetting, including results on the demographics of learning. In Section 5, we draw some conclusions 2 Two Patterns in Fee Payment In this section, we describe the data. We then show that fee payments decline sharply with account tenure. We also show that the learning dynamics exhibit a recency effect: a late payment charge from the previous month is strongly associated with fee avoidance this month, and this elasticity sharply declines as the time gap increases between the previous fee payment and the current period
first explore several explanations that are not consistent with our preferred explanation of learning/forgetting—for example, that card usage might be negatively autocorrelated—and find that these explanations are not consistent with the data. On the other hand, we find support for mechanisms that support the learning/forgetting interpretation. Notably, we find that in the month after paying a late fee, account holders are especially likely to make their next payment more than two weeks before the due date. This suggests that a late payment fee acts as a wake up call that induces earlier fee payment. We also find that the speed of (i) net learning, (ii) the magnitude of the recency effect, and (iii) the speed of forgetting all differ across borrower characteristics. Higher-income borrowers learn more than twice as fast, have a recency effect double the size, and forget about three-times as slowly as lower-income borrowers. Likewise, middle-aged borrowers have similar learning advantages relative to older borrowers. In summary, our findings imply that a high rate of knowledge depreciation offsets learning. Nevertheless, learning dominates knowledge depreciation. On average, fees fall over the life of the credit card. These learning dynamics are most advantageous for high-income and middle-aged borrowers. We organize our paper as follows, Section 2 summarizes our data and presents our basic evidence for learning and backsliding/forgetting. Section 3 analyzes various alternative (nonlearning) explanations for our findings. Section 4 discusses extensions to our analysis on learning and forgetting, including results on the demographics of learning. In Section 5, we draw some conclusions. 2 Two Patterns in Fee Payment In this section, we describe the data. We then show that fee payments decline sharply with account tenure. We also show that the learning dynamics exhibit a recency effect: a late payment charge from the previous month is strongly associated with fee avoidance this month, and this elasticity sharply declines as the time gap increases between the previous fee payment and the current period. 4
2.1 Data We use a proprietary panel dataset from a large U. S. bank that issues credit cards na- tionally. The dataset contains a representative random sample of about 128,000 credit card accounts followed monthly over a 36 month period(from January 2002 through December 2004). The bulk of the data consists of the main billing information listed on each ac- count's monthly statement, including previous payment, purchases, credit limit, balance debt, amount due, purchase APR, cash advance APR, date of previous payment, and fees incurred. At a quarterly frequency, we observe each customer's credit bureau rating(FICO score) and a proprietary (internal) credit 'behavior'score. We have credit bureau data for the number of other credit cards held by the account holder, total credit card balances, and mortgage balances. We have data on the age, gender and income of the account holder collected at the time of account opening. Further details on the data, including summary statistics and variable definitions, are available in the appendix. We focus on three important types of fees, described below: late fees, over limit fees, and ash advance fees. 8 1. Late Fee: a direct late fee of $30 or S35 is assessed if the borrower makes a payment beyond the due date on the credit card statement. If the borrower is late by more than 60 days once, or by more than 30 days twice within a year, the bank al impose indirect late fees by raising the APR to over 24 percent. Such indirect fees are referred to as penalty pricing The bank may also choose to report late payments to credit bureaus, adversely affecting consumers' FICO scores. Our analysis measures only direct late fees(and therefore excludes consumer costs associated with penalty pricing) 2. Over Limit Fee: a direct over limit fee. also of S30 or $35. is assessed the first time sOther types of fees include annual, balance transfer, foreign transactions, and pay by phone. All of these fees are relatively less important to both the bank and the borrower. Fewer issuers(the most notable exception being American Express)continue to charge annual fees, largely as a result of increased competition for new borrowers(Agarwal et al., 2006). The cards in our data do not have annual fees. A balance transfer fee of 2-3% of the amount transferred is assessed on borrowers who shift debt from one card to another ers repeatedly transfer balances, borrower response to this fee will not allow us to study learning about fee payment. The foreign transaction fees and pay by phone fees together comprise less than three percent of the total fees collected by banks. PIf the borrower does not make a late payment during the six months after the last late payment, the APR will revert to its normal (though not its promotional) level
2.1 Data We use a proprietary panel dataset from a large U.S. bank that issues credit cards nationally. The dataset contains a representative random sample of about 128,000 credit card accounts followed monthly over a 36 month period (from January 2002 through December 2004). The bulk of the data consists of the main billing information listed on each account’s monthly statement, including previous payment, purchases, credit limit, balance, debt, amount due, purchase APR, cash advance APR, date of previous payment, and fees incurred. At a quarterly frequency, we observe each customer’s credit bureau rating (FICO score) and a proprietary (internal) credit ‘behavior’ score. We have credit bureau data for the number of other credit cards held by the account holder, total credit card balances, and mortgage balances. We have data on the age, gender and income of the account holder, collected at the time of account opening. Further details on the data, including summary statistics and variable definitions, are available in the appendix. We focus on three important types of fees, described below: late fees, over limit fees, and cash advance fees.8 1. Late Fee: A direct late fee of $30 or $35 is assessed if the borrower makes a payment beyond the due date on the credit card statement. If the borrower is late by more than 60 days once, or by more than 30 days twice within a year, the bank may also impose indirect late fees by raising the APR to over 24 percent.9 Such indirect fees are referred to as ‘penalty pricing.’ The bank may also choose to report late payments to credit bureaus, adversely affecting consumers’ FICO scores. Our analysis measures only direct late fees (and therefore excludes consumer costs associated with penalty pricing). 2. Over Limit Fee: A direct over limit fee, also of $30 or $35, is assessed the first time 8Other types of fees include annual, balance transfer, foreign transactions, and pay by phone. All of these fees are relatively less important to both the bank and the borrower. Fewer issuers (the most notable exception being American Express) continue to charge annual fees, largely as a result of increased competition for new borrowers (Agarwal et al., 2006). The cards in our data do not have annual fees. A balance transfer fee of 2-3% of the amount transferred is assessed on borrowers who shift debt from one card to another. Since few consumers repeatedly transfer balances, borrower response to this fee will not allow us to study learning about fee payment. The foreign transaction fees and pay by phone fees together comprise less than three percent of the total fees collected by banks. 9 If the borrower does not make a late payment during the six months after the last late payment, the APR will revert to its normal (though not its promotional) level. 5
the borrower exceeds his or her credit limit in a given month. Penalty pricing also results from over limit transactions. As above, our analysis measures only direct over limit fees 3. Cash Advance Fee: a direct cash advance fee of 3 percent of the amount advanced or S5(whichever is greater) is levied for each cash advance on the credit card. Unlike the first two types of fees, a cash advance fee can be assessed many times per month Cash advances do not invoke penalty pricing. However, the APR on cash advances is typically greater than that on purchases, and is usually 16 percent or more. Our analysis measures only direct cash advance fees(and not subsequent interest charges 2.2 Fee payment by account tenure Figure 1 reports the frequency of each fee type as a function of account tenure. The regression-like all those that follow -controls for time effects, account fixed effects, and time-varying attributes of the borrower(e. g, variables that capture card utilization each pay ycle). The data plotted in Figure 1 is generated by estimating fit= a+oi+vtime Spline(Tenure. +n, Purchase. t +n2 Activei.t +n3 Bille ristit-l +yUtilit-1+Ei. The dependent variable fit is a dummy variable that takes the value l if a fee of type j is paid by account i at tenure t. Note that t indexes account tenure- not calendar time. When we refer to calendar time we use subscript time. Fee categories, j, include late payment fees filate-over limit fees-fouer-and cash advance fees--f Aduance. Parameter a is a con- stant;i is an account fixed effect; vtime is a time fixed-effect; Spline(Tenure. t) is a spline lo that takes account tenure(time since account was opened) as its argument; Purchasi.t is the total quantity of purchases in the current month: Activei. t is a dummy variable that re- The spline has knots every 12 months through month 72. We have also tried replacing the spline with dummies for each month of account tenure; the results are quantitatively similar. We report results with a spline as our baseline specification because the reduction in the number of parameters meaningfully decreases the computation time required to estimate the model; each regression has 4,000,000 observations of credit card statements
the borrower exceeds his or her credit limit in a given month. Penalty pricing also results from over limit transactions. As above, our analysis measures only direct over limit fees. 3. Cash Advance Fee: A direct cash advance fee of 3 percent of the amount advanced or $5 (whichever is greater) is levied for each cash advance on the credit card. Unlike the first two types of fees, a cash advance fee can be assessed many times per month. Cash advances do not invoke penalty pricing. However, the APR on cash advances is typically greater than that on purchases, and is usually 16 percent or more. Our analysis measures only direct cash advance fees (and not subsequent interest charges). 2.2 Fee payment by account tenure Figure 1 reports the frequency of each fee type as a function of account tenure. The regression – like all those that follow – controls for time effects, account fixed effects, and time-varying attributes of the borrower (e.g., variables that capture card utilization each pay cycle). The data plotted in Figure 1 is generated by estimating, (1) = + + + ( ) + 1 + 2 + 3−1 +1 −1 + The dependent variable is a dummy variable that takes the value 1 if a fee of type is paid by account at tenure . Note that indexes account tenure — not calendar time. When we refer to calendar time we use subscript . Fee categories, include late payment fees – – over limit fees – – and cash advance fees – Parameter is a constant; is an account fixed effect; is a time fixed-effect; ( ) is a spline10 that takes account tenure (time since account was opened) as its argument; is the total quantity of purchases in the current month; is a dummy variable that re- 10The spline has knots every 12 months through month 72. We have also tried replacing the spline with dummies for each month of account tenure; the results are quantitatively similar. We report results with a spline as our baseline specification because the reduction in the number of parameters meaningfully decreases the computation time required to estimate the model; each regression has 4,000,000 observations of credit card statements. 6
fects the existence of any account activity in the current month; Bille risti t-1 is a dummy variable that reflects the existence of a bill with a non-zero balance in the previous balance Utili t. for utilization. is debt divided by the credit limit: Eit is an error term. Table 1 provides the regression results Figure 1 plots the expected frequency of fees as a function of account tenure, holding the other control variables fixed at their means. This analysis shows that fee payments are fairly common when accounts are initially opened, but that the frequency of fee payments declines rapidly as account tenure increases. In the first four years of account tenure, the monthly frequency of cash advance fees drops from 57% of all accounts to 13% of all accounts The frequency of late payment fees drops from 36% to 8%. Finally, the frequency of over limit fees drops from 17% to 5% To establish that the estimated pattern is robust to alternative specifications, we estimate several variants. We estimate equation 1 as a conditional logit; the results are qualitatively similar. We also repeat the analysis controlling for behavior and FICO scores, both lagged by three months to reflect the fact that they are only computed quarterly. The coefficients on the spline of tenure are almost unchanged. Finally, to eliminate the possibility that attrition from the sample has distorted the results, we have tried restricting the sample te only those account present for all 36 months; the results are little changed It is also of interest to know how the amount of fees paid vary by account tenure. For the late fee and over limit fees. the fee amount is constant, while for the cash advance fee the fee amount can vary over time. Figure 2 reports the average value of each fee type as a function of account tenure, conditional on other factors that might affect fee payment. The data plotted in Figure 2 is generated by estimating Vit =a+oi+vtime SplineTenure t) +n, Purchase t +n2 Activei. t n3 bille risti t-l +1Util;t-1+∈;t The dependent variable Vit is the value of fees of type j paid by account i at tenure t. All other variables are as before. Table 2 reports the regression results II Tenure in all figures starts at month two since borrowers cannot, by definition, pay late fees or over limit fees in the first month their accounts are op
flects the existence of any account activity in the current month; −1 is a dummy variable that reflects the existence of a bill with a non-zero balance in the previous balance; , for utilization, is debt divided by the credit limit; is an error term. Table 1 provides the regression results. Figure 1 plots the expected frequency of fees as a function of account tenure, holding the other control variables fixed at their means.11 This analysis shows that fee payments are fairly common when accounts are initially opened, but that the frequency of fee payments declines rapidly as account tenure increases. In the first four years of account tenure, the monthly frequency of cash advance fees drops from 57% of all accounts to 13% of all accounts. The frequency of late payment fees drops from 36% to 8%. Finally, the frequency of over limit fees drops from 17% to 5%. To establish that the estimated pattern is robust to alternative specifications, we estimate several variants. We estimate equation 1 as a conditional logit; the results are qualitatively similar. We also repeat the analysis controlling for behavior and FICO scores, both lagged by three months to reflect the fact that they are only computed quarterly. The coefficients on the spline of tenure are almost unchanged. Finally, to eliminate the possibility that attrition from the sample has distorted the results, we have tried restricting the sample to only those account present for all 36 months; the results are little changed. It is also of interest to know how the amount of fees paid vary by account tenure. For the late fee and over limit fees, the fee amount is constant, while for the cash advance fee, the fee amount can vary over time. Figure 2 reports the average value of each fee type as a function of account tenure, conditional on other factors that might affect fee payment. The data plotted in Figure 2 is generated by estimating, (2) = + + + ( ) +1 + 2 + 3−1 +1 −1 + The dependent variable is the value of fees of type paid by account at tenure . All other variables are as before. Table 2 reports the regression results. 11Tenure in all figures starts at month two since borrowers cannot, by definition, pay late fees or over limit fees in the first month their accounts are open. 7
S. Figure 2 shows that, when an account is opened, the card holder pays $6, 65 per month in ash advance fees, $5.63 per month in late fees, and $2.46 per month in over limit fees. These numbers understate the total cost incurred by fee payments, as these numbers do not include interest payments on the cash advances, the effects of penalty pricing (i.e, higher interest rates), or the adverse effects of higher credit scores on other credit card fee structures. Like Figure 1, Figure 2 shows that the average value of fee payments declines rapidly with account Figures 1 and 2 imply that fee payments fall substantially with experience. We next turn to a second pattern in our data 2. 3 The impact of past fee payment on current fee payment There are four reasons to expect fee payments of agent i to be correlated(positively or negatively) at two arbitrary dates t and t+k First, the(cross-sectional) type of the card holder (e.g. forgetful) may influence fee paying behavior. If person i pays a fee in period t then person i is more likely to be of the type that pays fees in general, implying that person i has a higher likelihood of paying a fee in period t+ h relative to other subjects in our sample. As long as the cross-sectional type of the account holder is a fixed characteristic, this first source of intertemporal linkage could be modeled as a fixed effect. If the true fixed effect is added to the model the residual variation is no longer correlated across time. however as we discuss below nickell bias (1981)introduces a wrinkle when the fixed effect needs to be estimated Second, transitory shocks that persist over more than one month(for instance, an un- employment spell) may influence fee paying behavior, causing fees to be positively autocor- hird, transitory shocks that are negatively correlated across months(for instance,an annual summer vacation) will cause fees to be negatively autocorrelated Fourth, fee payments may engender learning, causing fees to be negatively autocorrelated One natural approach to estimating the force of these four effects would be to estimate in autoregressive model, in which current fee payment would be allowed to depend on lagged fee payment, controlling for account fixed effects and time-varying characteristics. However Nickell(1981)showed that including fixed effects in dynamic panel data models causes the autoregressive coefficients to exhibit a bias of order-1/T, where T is the number of time
Figure 2 shows that, when an account is opened, the card holder pays $6.65 per month in cash advance fees, $5.63 per month in late fees, and $2.46 per month in over limit fees. These numbers understate the total cost incurred by fee payments, as these numbers do not include interest payments on the cash advances, the effects of penalty pricing (i.e., higher interest rates), or the adverse effects of higher credit scores on other credit card fee structures. Like Figure 1, Figure 2 shows that the average value of fee payments declines rapidly with account tenure. Figures 1 and 2 imply that fee payments fall substantially with experience. We next turn to a second pattern in our data. 2.3 The impact of past fee payment on current fee payment There are four reasons to expect fee payments of agent to be correlated (positively or negatively) at two arbitrary dates and + . First, the (cross-sectional) type of the card holder (e.g. forgetful) may influence fee paying behavior. If person pays a fee in period then person is more likely to be of the type that pays fees in general, implying that person has a higher likelihood of paying a fee in period + relative to other subjects in our sample. As long as the cross-sectional ‘type’ of the account holder is a fixed characteristic, this first source of intertemporal linkage could be modeled as a fixed effect. If the true fixed effect is added to the model, the residual variation is no longer correlated across time. However, as we discuss below, Nickell bias (1981) introduces a wrinkle when the fixed effect needs to be estimated. Second, transitory shocks that persist over more than one month (for instance, an unemployment spell) may influence fee paying behavior, causing fees to be positively autocorrelated. Third, transitory shocks that are negatively correlated across months (for instance, an annual summer vacation) will cause fees to be negatively autocorrelated. Fourth, fee payments may engender learning, causing fees to be negatively autocorrelated. One natural approach to estimating the force of these four effects would be to estimate an autoregressive model, in which current fee payment would be allowed to depend on lagged fee payment, controlling for account fixed effects and time-varying characteristics. However, Nickell (1981) showed that including fixed effects in dynamic panel data models causes the autoregressive coefficients to exhibit a bias of order -1, where is the number of time 8
eries observations. We thus adopt two approaches to deal with this problem. The first to calculate the following statistic E[f1|f-k=1] k EIf Probability of paying a fee at tenure t given the agent paid a fee k periods ago Probability of paying a fee at tenure t without conditioning on the RHS variables from the previous subsection(most importantly, we do not use person fixed effects to calculate Lt k). Specifically, E It is just the average frequency of fee payments in period t. 2 Likewise, E It I ft-k= l is the average frequency of fee payments in period t among the account holders who paid a fee at time t-k Conditioning on this sparse information, a consumer who paid a fee k periods ago has a probability of paying a fee equal to the baseline probability, E It, multiplied by Ltk.A value of 1 for Lt k indicates that having paid a fee k periods does not change the expected probability of paying a fee this period; a value less than one indicates lagged fee payment is associated with a reduction in the expected probability, and a value greater than one indicates lagged fee payment are associated with an increase in the expected probability For example, if Lt 1=0.6, a consumer who paid a fee last month has a probability of paying a fee this month that is 40% below the baseline probability We report averages of Lt k L Hence, Lk is the average relative likelihood of paying a fee, if the account holder paid a fee k periods ago. The Lk statistic illustrates some important time series properties in our data while avoiding econometric problems associated with estimating probit or logit models with fixed effects for a large n dataset Figure 3 plots Lk for all three types of credit card fees for values of k ranging from 1 to 35. All three lines start below 1, indicating that a fee payment last month is associated with a less than average likelihood of making a fee payment this month. For both cash advance and late fees, having paid a fee one month ago is associated with a 40 percent reduction in the likelihood of paying a fee in the current month. For over limit fees, having paid a fee Observations used for the calculation of Lk are from subjects who are in our sample at both date t and date t-k
series observations. We thus adopt two approaches to deal with this problem. The first is to calculate the following statistic: ≡ [ | − = 1] [] = Probability of paying a fee at tenure given the agent paid a fee periods ago Probability of paying a fee at tenure (3) without conditioning on the RHS variables from the previous subsection (most importantly, we do not use person fixed effects to calculate ). Specifically, [] is just the average frequency of fee payments in period 12 Likewise, [ | − = 1] is the average frequency of fee payments in period among the account holders who paid a fee at time − Conditioning on this sparse information, a consumer who paid a fee periods ago has a probability of paying a fee equal to the baseline probability, [] multiplied by . A value of 1 for indicates that having paid a fee periods does not change the expected probability of paying a fee this period; a value less than one indicates lagged fee payment is associated with a reduction in the expected probability, and a value greater than one indicates lagged fee payment are associated with an increase in the expected probability. For example, if 1 = 06, a consumer who paid a fee last month has a probability of paying a fee this month that is 40% below the baseline probability. We report averages of : ≡ 1 X =1 Hence, is the average relative likelihood of paying a fee, if the account holder paid a fee periods ago. The statistic illustrates some important time series properties in our data while avoiding econometric problems associated with estimating probit or logit models with fixed effects for a large dataset. Figure 3 plots for all three types of credit card fees for values of ranging from 1 to 35. All three lines start below 1, indicating that a fee payment last month is associated with a less than average likelihood of making a fee payment this month. For both cash advance and late fees, having paid a fee one month ago is associated with a 40 percent reduction in the likelihood of paying a fee in the current month. For over limit fees, having paid a fee 12Observations used for the calculation of are from subjects who are in our sample at both date and date − 9
last month is associated with a 50 percent reduction in the likelihood of paying a fee in the current month The Lk plots rise with k indicating that as a given fee payment recedes into the past the negative association between this fixed lagged fee payment and current fee payments is diminished. By the time one year has passed, the association between the lagged fee payment and current fee payment has almost vanished For large values of k, all three graphs rise above 1. This asymptotic property reflects the variation in fee payments that is driven by cross-sectional variation in the(persistent) type of the borrower. Some individuals have a relatively high long- run likelihood of paying fees For instance, imagine that 20 percent of consumers never pay a fee(maybe because they are rery disciplined), while the others have a long- run monthly probability b>0 of paying a fee Then, the long run Lk is 1/ 0.8=1.25. 3 2.3.1 Dynamic panel models with fixed effects Our second approach to estimating the impact of past fee payments on current fee pay ments is to estimate dynamic panel data models with fixed effects for each fee, while using Monte Carlo simulations to bound the size of the bias. As noted above, Nickell(1981)ana- lytically derived that the size of the bias for an ar(1) with fixed effects is of order -1/T Since in our estimation, T=36, the implied bias is approximately -1/36=-.028. This amount is much too small to explain the large reduction in fee frequency this month as- sociated with a fee payment last month. However, we are interested in the impact of fe payments at longer lags than one month on current fee payment; no analytical results exist for determining the size of the bias for higher-order autoregressive models. We thus use Monte Carlo simulations to determine the size of the bias in such cases Specifically, we first draw 10,000 times from a uniform(0, 1) distribution; call each draw ai,where i=1,.,10, 000. For each i, we then draw 36 times from a uniform(0, 1), recoding the results as l if the draw is less than ai and 0 otherwise. This algorithm simulates 36 i.i.d draws from a binomial distribution with probability of success a;(for 10,000 households). On these N=10,000 and T=36 observations, we then estimate an ar(1), AR(12 and AR(18 with fixed effects. We repeat the whole process 5,000 times, and report mean and standa 13The numerator of(3)is b, while the denominator is 0.8b. So Lk=b/(0.8b)=1/0.8
last month is associated with a 50 percent reduction in the likelihood of paying a fee in the current month. The plots rise with , indicating that as a given fee payment recedes into the past, the negative association between this fixed lagged fee payment and current fee payments is diminished. By the time one year has passed, the association between the lagged fee payment and current fee payment has almost vanished. For large values of all three graphs rise above 1. This asymptotic property reflects the variation in fee payments that is driven by cross-sectional variation in the (persistent) type of the borrower. Some individuals have a relatively high long-run likelihood of paying fees. For instance, imagine that 20 percent of consumers never pay a fee (maybe because they are very disciplined), while the others have a long-run monthly probability 0 of paying a fee. Then, the long run is 108=125. 13 2.3.1 Dynamic panel models with fixed effects Our second approach to estimating the impact of past fee payments on current fee payments is to estimate dynamic panel data models with fixed effects for each fee, while using Monte Carlo simulations to bound the size of the bias. As noted above, Nickell (1981) analytically derived that the size of the bias for an AR(1) with fixed effects is of order −1. Since in our estimation, = 36, the implied bias is approximately −136 = −028. This amount is much too small to explain the large reduction in fee frequency this month associated with a fee payment last month. However, we are interested in the impact of fee payments at longer lags than one month on current fee payment; no analytical results exist for determining the size of the bias for higher-order autoregressive models. We thus use Monte Carlo simulations to determine the size of the bias in such cases. Specifically, we first draw 10,000 times from a uniform (0,1) distribution; call each draw , where = 1 10 000. For each , we then draw 36 times from a uniform (0,1), recoding the results as 1 if the draw is less than and 0 otherwise. This algorithm simulates 36 i.i.d. draws from a binomial distribution with probability of success (for 10,000 households). On these =10,000 and = 36 observations, we then estimate an AR(1), AR(12) and AR(18) with fixed effects. We repeat the whole process 5,000 times, and report mean and standard 13The numerator of (3) is , while the denominator is 08. So = (08)=108. 10
