deviations. Note that, if there were no Nickell bias, all of the autoregressive coefficients should be zero Table 3 reports the mean values of those coefficients for all three cases. The Ar(1)case shows a bias of about -.028, confirming the analytical results of Nickell(1981). The AR(12) and AR(18)cases show somewhat larger biases- for the first lag, about -0.06 and -0.10 respectively - that decline in absolute value with the lag. 4 Although this declining pattern does mimic in a qualitative fashion the recency effects we see above, the magnitude of the bias is again not nearly sufficient to explain the size of the recency effects that we measure We show this in table 4. which estimates fit a+oi+vtime +a(lfit_l +n, Purchase. t +n2 Activei. t n& Bille risti t-l +71Util;t-1+∈i where A(L)is a twelfth-order lag polynomial for each of the three kinds of fees. As with e Lk measure, all three sets of results show a strong recency effect, far larger than can be explained by Nickell bias. The coefficients decrease in absolute value with lag, reaching zero by the eleventh or twelfth lag. For late fees, the coefficient on the first lag shows that having paid a fee one month ago is associated with nearly a 50 percent reduction in the frequency of current fee payments -or about a 45 percent reduction once the bias resulting from the Monte Carlo simulations is subtracted. For the over limit and cash advance fees the reductions are slightly over 40 percent and 30 percent, respectively(again controlling for the bias). These large reductions are all within ten percentage points of those associated with the Lk approach estimated above e note that a third way of estimating the recency effect would be to use the instrumental variables approach of Arellano and Bond(1991)or the conditional logit estimators derived by Chamberlain(1993) and Honore and Kyriazidou(2000), which allow for the presence of lagged endogenous variables. We do not follow these approaches because they all limit the extent to which the disturbance terms may be serially correlated We think it likely that agents do face autocorrelated shocks that may affect their likelihood of fee payment. Honore and Kyriazidou(2000) also require that there not be time effects; we in turn think that agents 1 We are grateful to Devin Pope for pointing out this pattern of bias in higher-order autoregressive models
deviations. Note that, if there were no Nickell bias, all of the autoregressive coefficients should be zero. Table 3 reports the mean values of those coefficients for all three cases. The AR(1) case shows a bias of about −028, confirming the analytical results of Nickell (1981). The AR(12) and AR(18) cases show somewhat larger biases — for the first lag, about −006 and −010, respectively — that decline in absolute value with the lag.14 Although this declining pattern does mimic in a qualitative fashion the recency effects we see above, the magnitude of the bias is again not nearly sufficient to explain the size of the recency effects that we measure. We show this in Table 4, which estimates: = + + + () −1 (4) +1 + 2 + 3−1 +1 −1 + where () is a twelfth-order lag polynomial for each of the three kinds of fees. As with the measure, all three sets of results show a strong recency effect, far larger than can be explained by Nickell bias. The coefficients decrease in absolute value with lag, reaching zero by the eleventh or twelfth lag. For late fees, the coefficient on the first lag shows that having paid a fee one month ago is associated with nearly a 50 percent reduction in the frequency of current fee payments — or about a 45 percent reduction once the bias resulting from the Monte Carlo simulations is subtracted. For the over limit and cash advance fees, the reductions are slightly over 40 percent and 30 percent, respectively (again controlling for the bias). These large reductions are all within ten percentage points of those associated with the approach estimated above. We note that a third way of estimating the recency effect would be to use the instrumental variables approach of Arellano and Bond (1991) or the conditional logit estimators derived by Chamberlain (1993) and Honoré and Kyriazidou (2000), which allow for the presence of lagged endogenous variables. We do not follow these approaches because they all limit the extent to which the disturbance terms may be serially correlated We think it likely that agents do face autocorrelated shocks that may affect their likelihood of fee payment. Honoré and Kyriazidou (2000) also require that there not be time effects; we in turn think that agents 14We are grateful to Devin Pope for pointing out this pattern of bias in higher-order autoregressive models. 11
may face different shocks at different times-for example, due to changing macroeconomic conditions 2. 4 Summary The data exhibit a robust time-series pattern. Paying a fee last month is associated with a sharply reduced likelihood of paying a fee this month (relative to other members of your account holding cohort). Paying a fee a year ago has little relationship to the likelihood of paying a fee now (relative to other members of your account holding cohort). Paying a fee two years ago is associated with a 20% elevation in the likelihood of paying a fee now (relative to other members of your account holding cohort) Our findings imply that the there must be a mechanism that produces the short-run negative association(or recency effect). Moreover, this mechanism must be strong enough to temporarily overwhelm the positive long-run association in fee payments driven by type variation15 3 Alternative Explanations The patterns of fee payments that we document is explained by a model in which con- sumers learn to avoid fees by first experiencing them. The learning dynamics are complicated by partial backsliding or forgetting. In our view, this is like the effect of getting a speeding ticket; a driver may slow down for a few weeks, but will partially revert to type and speed again.6 In our credit card analysis, the net effect of learning and backsliding appears to be positive, since fee payments do fall on average with tenure On the other hand, some or all of the data patterns that we observe may be explained by mechanisms other than learning and forgetting. In this section, we first discuss a few alter- native explanations: we find that the available evidence does not support these alternative IsThe short-run drop in Lk would be even bigger if it were not offset by the positive autocorrelation in fees produced by both variation in types and transitory(multi-month) variation in fee-paying propensities 16 We are grateful to Devin Pope for suggesting this analogy
may face different shocks at different times—for example, due to changing macroeconomic conditions. 2.4 Summary The data exhibit a robust time-series pattern. Paying a fee last month is associated with a sharply reduced likelihood of paying a fee this month (relative to other members of your account holding cohort). Paying a fee a year ago has little relationship to the likelihood of paying a fee now (relative to other members of your account holding cohort). Paying a fee two years ago is associated with a 20% elevation in the likelihood of paying a fee now (relative to other members of your account holding cohort). Our findings imply that the there must be a mechanism that produces the short-run negative association (or recency effect). Moreover, this mechanism must be strong enough to temporarily overwhelm the positive long-run association in fee payments driven by type variation.15 3 Alternative Explanations The patterns of fee payments that we document is explained by a model in which consumers learn to avoid fees by first experiencing them. The learning dynamics are complicated by partial backsliding or forgetting. In our view, this is like the effect of getting a speeding ticket; a driver may slow down for a few weeks, but will partially revert to type and speed again.16 In our credit card analysis, the net effect of learning and backsliding appears to be positive, since fee payments do fall on average with tenure. On the other hand, some or all of the data patterns that we observe may be explained by mechanisms other than learning and forgetting. In this section, we first discuss a few alternative explanations; we find that the available evidence does not support these alternatives. 15The short-run drop in would be even bigger if it were not offset by the positive autocorrelation in fees produced by both variation in types and transitory (multi-month) variation in fee-paying propensities. 16We are grateful to Devin Pope for suggesting this analogy. 12
3. 1 Potential correlation between financial distress and credit card tenure The tendency to observe declining fees may reflect a tendency for new account holders to experience more financial/personal distress than account holders with high tenure. To test this hypothesis, we determined whether FICO scores and behavior scores(two inverse measures of financial distress) correlate with account tenure Figure 4 plots FICO scores and behavior scores by account tenure, demeaned and nor- malized. To calculate the FIco variable. a single Fico mean is calculated for all accounts over all periods in our sample. This mean is used for the demeaning. A single FICO stan- dard deviation is calculated for all accounts over all periods in our sample. This standard deviation is used for the normalization. An analogous method is used for the behavior score No time trend is apparent in the normalized data. To more formally measure the FICO-tenure relationship, we predict FICO with an account-tenure spline using annual knots (controlling for account and time fixed effects). The estimated tenure spline exhibits slopes that bounce around in sign and are all very small in magnitude. For example, at a horizon of 5 years, the spline predicts a total (accumulated) change in the FICO score of 18 units since the account was opened. At a horizon of 10 years the spline predicts a total (accumulated) change in the FICO score of-004 units since the account was opened. Recall that the mean FICO score is 732 and the standard deviation of the Fico score is 81. Hence. financial distress does not show significant variation with account tenure 3.2 Movers Moving to a new home could potentially cause both patterns of fee payment that we se Disruptions associated with the move and additional needs for cash could lead to payment of late, over limit, and cash advance fees. Over time, consumers would revert to their normal pattern of fee payment To test for this possibility, since we know when account holders move, we examine the difference between the frequency of fee payment during the move(defined as payment from two months before to two months after the move date) and fee payment in all other months 17 A high FICO or behavior score implies that the individual is a reliable creditor. A behavior score is a proprietary measure of credit risk calculated by the card-issuing institution
3.1 Potential correlation between financial distress and credit card tenure. The tendency to observe declining fees may reflect a tendency for new account holders to experience more financial/personal distress than account holders with high tenure. To test this hypothesis, we determined whether FICO scores and behavior scores (two inverse17 measures of financial distress) correlate with account tenure. Figure 4 plots FICO scores and behavior scores by account tenure, demeaned and normalized. To calculate the FICO variable, a single FICO mean is calculated for all accounts over all periods in our sample. This mean is used for the demeaning. A single FICO standard deviation is calculated for all accounts over all periods in our sample. This standard deviation is used for the normalization. An analogous method is used for the behavior score. No time trend is apparent in the normalized data. To more formally measure the FICO-tenure relationship, we predict FICO with an account-tenure spline using annual knots (controlling for account and time fixed effects). The estimated tenure spline exhibits slopes that bounce around in sign and are all very small in magnitude. For example, at a horizon of 5 years, the spline predicts a total (accumulated) change in the FICO score of 18 units since the account was opened. At a horizon of 10 years the spline predicts a total (accumulated) change in the FICO score of -0.04 units since the account was opened. Recall that the mean FICO score is 732 and the standard deviation of the FICO score is 81. Hence, financial distress does not show significant variation with account tenure. 3.2 Movers Moving to a new home could potentially cause both patterns of fee payment that we see. Disruptions associated with the move and additional needs for cash could lead to payment of late, over limit, and cash advance fees. Over time, consumers would revert to their normal pattern of fee payment. To test for this possibility, since we know when account holders move, we examine the difference between the frequency of fee payment during the move (defined as payment from two months before to two months after the move date) and fee payment in all other months. 17A high FICO or behavior score implies that the individual is a reliable creditor. A behavior score is a proprietary measure of credit risk calculated by the card-issuing institution. 13
We find that account holders are only about 1 percent more likely to pay late or over limit fees during the move, and 2 percent more likely to pay cash advance fees. These small differences are not enough to account for the large reductions in fee payment by tenure or the recency effects 3.3 Potential correlation between purchasing patterns and credit card tenure The tendency to observe declining fees may reflect a tendency for new account holders to spend more than account holders with high tenure. To test this hypothesis, we determined if purchases correlate with account tenure. Figure 4, which plots the demeaned and normalized level of purchases, again shows no economically significant time trend 3.4 Non-utilization of the card The fee dynamics that we observe could be driven by consumers who temporarily or permanently stop using the card after paying a fee on that card. We look for these effects by estimating a regression model in which the outcome of"no purchase in the current month predicted by dummies for past fee payments and control variables, including account and time fixed effects as well FICO, Behavior, and Utilization. We find very small effects of past fee payments on subsequent card use. For example,(controlling for account fixed effects) somebody who paid a fee every month for the past six months is predicted to be only 2% less likely to use their card in the next month relative to somebody with no fee payments in the last six months. Such small effects cannot explain our learning dynamics, which are over an order of magnitude larger. Figure 5 also plots the absolute level of utilization(demeaned and normalized), which exhibits no time-series pattern 3.5 Time-varying financial service needs Time-varying financial service needs may also play an important role in driving fee dy- namics. To illustrate this idea, let vt represent a time-varying cost of time, so that
We find that account holders are only about 1 percent more likely to pay late or over limit fees during the move, and 2 percent more likely to pay cash advance fees. These small differences are not enough to account for the large reductions in fee payment by tenure or the recency effects. 3.3 Potential correlation between purchasing patterns and credit card tenure. The tendency to observe declining fees may reflect a tendency for new account holders to spend more than account holders with high tenure. To test this hypothesis, we determined if purchases correlate with account tenure. Figure 4, which plots the demeaned and normalized level of purchases, again shows no economically significant time trend. 3.4 Non-utilization of the card. The fee dynamics that we observe could be driven by consumers who temporarily or permanently stop using the card after paying a fee on that card. We look for these effects by estimating a regression model in which the outcome of “no purchase in the current month” is predicted by dummies for past fee payments and control variables, including account and time fixed effects as well FICO, Behavior, and Utilization. We find very small effects of past fee payments on subsequent card use. For example, (controlling for account fixed effects) somebody who paid a fee every month for the past six months is predicted to be only 2% less likely to use their card in the next month relative to somebody with no fee payments in the last six months. Such small effects cannot explain our learning dynamics, which are over an order of magnitude larger. Figure 5 also plots the absolute level of utilization (demeaned and normalized), which exhibits no time-series pattern. 3.5 Time-varying financial service needs. Time-varying financial service needs may also play an important role in driving fee dynamics. To illustrate this idea, let represent a time-varying cost of time, so that (5) Pr ( = 1) = 14
where vt is an exogenous process, that causes fee use, but is not caused by it. To explain our recency effect, one needs vt to be negatively autocorrelated at a monthly frequency. To see this, consider the regression (6) ft=0ft-1+ controls If (5)holds, then the regression coefficient is 0=cov(vt, Vt-1)/var(t-1) We run this regression, including all of our usual control variables, that is, time- and account-fixed effects, a tenure spline, Purchase, Active, Bille rist, and Util. We also include Behavior and FICO. 18 f it-1+a+o,+vtime Spline (Tenure.t) +n, Purchasi. t +n2 Activei. t n3 Bille risti t-l +n4FICOi t-3 +ns Behave, t-3 +n Utili.t +Eit Results for the three types of fees are given in Table 5. We find that 6 is -0.75 for the late fee, -0.52 for the over limit fee, and -0.28 for the cash advance fee. We call this the"recency effect, since the payment of a fee last month greatly reduces the probability that a fee will be paid this month. 9 The empirical finding of 0 0 implies corr (vt, Vt-1)<0. Hence, to explain the"recency effect"with time-varying financial needs, it would need to be the case that vt is negatively autocorrelated. The autocorrelation of vt would need to be not only negative. but also greater than 0.75 (in the case of the late fee) in absolute value: corr (vt, Ut-1)<0=-07520 We think that such a very strong negative autocorrelation of monthly needs is unlikely. 21 s The results do not differ if we instead begin the regressions in month 2 and exclude the behavior and FICO scores 19There is a potential small sample bias(Nickell 1981), to which we thank Peter Fishman and Devin Pope for drawing our attention. To see how large it is, we note that if ft is i.i.d., then in the regression ft= 0ft-1+constant, done over a T periods, the expected value of 0 is -1/T. With T= 24, the bias is -0.05. We conclude that, in our study, the small sample bias is very small compared to the large negative 0 that we find 2 It is easy to see that under(5),cou(t, ft-1)=cou(vt, Vt-1), and var(+)=E[v](1-ElvtD)2EV2 Evt (ut), as vt E 0, 1. So, 0= cou(t, ft-1)/var (t-1) satisfies 0< cow(vt, vt-1)/var(vt) Icorr(vt, Vt-1), and 0 and corr(vt, Vt-1) have the same sign The least implausible type of negatively autocorrelated process in economics is a"periodic spike"process which take a value of a every K periods, and bf a otherwise. It has an autocorrelation of -1/(K-1). We fail to find evidence for such a pattern in credit card use other than fees. For instance, expenses across time
where is an exogenous process, that causes fee use, but is not caused by it. To explain our recency effect, one needs to be negatively autocorrelated at a monthly frequency. To see this, consider the regression, (6) = −1 + controls. If (5) holds, then the regression coefficient is = ( −1) (−1). We run this regression, including all of our usual control variables, that is, time- and account-fixed effects, a tenure spline, , , , and . We also include and . 18 = −1 + + + + ( ) + 1 + 2 + 3−1 + 4−3 + 5−3 + 6 + Results for the three types of fees are given in Table 5. We find that is -0.75 for the late fee, -0.52 for the over limit fee, and -0.28 for the cash advance fee. We call this the “recency effect,” since the payment of a fee last month greatly reduces the probability that a fee will be paid this month.19 The empirical finding of 0 implies ( −1) 0. Hence, to explain the “recency effect” with time-varying financial needs, it would need to be the case that is negatively autocorrelated. The autocorrelation of would need to be not only negative, but also greater than 0.75 (in the case of the late fee) in absolute value: ( −1) ≤ = −075. 20 We think that such a very strong negative autocorrelation of monthly needs is unlikely.21 18The results do not differ if we instead begin the regressions in month 2 and exclude the behavior and FICO scores. 19There is a potential small sample bias (Nickell 1981), to which we thank Peter Fishman and Devin Pope for drawing our attention. To see how large it is, we note that if is i.i.d., then in the regression = −1+constant, done over a periods, the expected value of is −1. With = 24, the bias is −005. We conclude that, in our study, the small sample bias is very small compared to the large negative that we find. 20 It is easy to see that under (5), ( −1) = ( −1), and () = [] (1 − []) ≥ £ 2 ¤ − [] 2 = (), as ∈ [0 1]. So, = ( −1) (−1) satisfies || ≤ | ( −1)| () = | ( −1)|, and and ( −1) have the same sign. 21The least implausible type of negatively autocorrelated process in economics is a “periodic spike” process, which take a value of every periods, and 6= otherwise. It has an autocorrelation of −1 ( − 1). We fail to find evidence for such a pattern in credit card use other than fees. For instance, expenses across time 15