Macroeconomic factors, consumer behavior, and bankcard default rates

Introduction

Credit card delinquencies, and consumer credit problems in general, have been the subject of considerable interest and debate in the popular press, in professional banking journals, and in The Federal Reserve Bulletin. The popular business press, for instance, frequently raises the possibility that credit problems result from an over-eagerness to solicit new business (see Frank 1997, for example). It also has been argued that credit card issuers are becoming more adept at the avoidance of bad credit risks (Womack 1998). As a general statement, though, it is widely held that an increase in debt levels relative to income, and/or debt payment obligations relative to income, can lead to increased credit problems (Canner et al. 1995; Luckett 1988; Paquin and Weiss 1998.)

To our knowledge, however, the specific issue of how consumer credit delinquency rates relate to various macroeconomic variables has received little attention in the academic literature, particularly in terms of empirical testing.

Paquin and Weiss (1998) offer some interesting insights into consumer credit problems, and in particular the personal bankruptcy rate. After examining a host of potential explanatory variables, they conclude that variations over time in personal bankruptcies are best explained by a set of four variables.

The explanatory variables are the supply of consumer credit, as measured by the annual change in the number of bankcard accounts; consumers' capacity to service debt, gauged by the household debtto-income ratio; the condition of the job market, as proxied by initial unemployment insurance claims; and interest rate levels, based on the yield on one-year Treasury bills. These test variables are lagged from one to nine quarters, using the combination of variable lags that maximizes the model's overall explanatory power. The four test variables, along with an autoregressive (AR) term, explain 98 percent of the variation in the personal bankruptcy rate.

Paquin and Weiss also note that bankruptcies are an issue of import to the credit card industry, since many credit card chargeoffs appear to result from bankruptcies.'

Our paper takes a somewhat different approach, examining bank credit card payment problems directly, and using delinquencies rather than chargeoffs as the variable of interest. Based on the apparent success of Paquin and Weiss in explaining their chosen measure of credit problems (bankruptcy rates), we select a set of test variables designed to reflect the aforementioned issues of credit supply, capacity to service debt, job market conditions, and interest rates.

Initially we find that our set of test variables explains a high proportion of the variation in bankcard delinquencies. However, diagnostic tests reveal serious violations of underlying model assumptions. Thus, the seemingly impressive explanatory power of the model is suspect.

Fortunately, we find that the statistical violations can be eliminated by modeling the first differences of our dependent and explanatory variables, as opposed to the levels of those variables. Thus, we can examine the one-quarter change in the bankcard delinquency rate as a function of the one-quarter changes in our explanatory variables. We examine these one-quarter changes in both absolute and relative terms. Since the delinquency rates themselves are provided in both per-account and per-dollar terms, testing absolute and relative changes in each of these measures allows a total of four models.

The resulting test statistics are more modest than in our initial models, but the models remain sufficiently strong to provide a reasonable degree of explanatory power. Overall model significance is 5 percent or better in all four cases. Further, the revised models are statistically better behaved, and hence more reliable, than the initial models.

In addition, we perform some tests regarding the notion of selective default. It seems reasonable that consumers will choose credit card delinquency prior to other types of debt default when funds for repayment are scarce, and it is widely believed that this is a typical course of action (Greenberg 1997). The results of our tests are consistent with the idea that consumers will default selectively. One quarter after an increase in the consumer debt ratio, there is an increase in the extent to which the bankcard default rate exceeds the default rate on a more general measure of consumer credit.

The remainder of the paper is organized as follows. The second section describes our data and methodology. The third section details the results of our statistical tests. The fourth section concludes the paper.

Data and Methodology Data

This paper includes tests of both the delinquency rate for bankcard debt and the difference between this delinquency rate and delinquencies on a composite measure of consumer credit.2 The American Bankers Association (ABA) provided information on both the bankcard and composite delinquency rates. Bankcard delinquency rates are provided both in dollar terms (dollars in delinquent accounts relative to total dollars of loans outstanding, expressed hereafter as Bcarddol) and in terms of the number of accounts (delinquent accounts over total accounts, hereafter Bcardnum). Likewise, delinquency rates on the composite measure of consumer credit are provided based on both dollars of credit (Compdol) and the number of accounts (Compnum).

Regardless of whether it is reporting its delinquency rates in dollars or in numbers of accounts, the ABA defines delinquent accounts as those that are overdue by 30 days or more. The ABA notes that all numbers are reported as percentages; for instance, in the fourth quarter of 1981, Bcarddol was 2.26 percent; this is reported as 2.26.

As a proxy for the overall supply of credit, we use total revolving credit outstanding, expressed in billions of dollars (Rdebt).3 To gauge consumers' ability to service debt, we use the consumer debt ratio (consumer debt as a percentage of disposable income, hereafter Cdr). The Federal Reserve Board in Washington, D,C., provided information regarding these two variables. The interest rate environment is represented by the average rate on 30-year fixed-rate conventional mortgages, in percent, as reported by Freddie Mac (Mtg).4 To assess job market conditions, we use the unemployment rate (Ue); these data come from the Bureau of Labor Statistics.

Finally, in our tests of the difference between the bankcard default rate and the composite default rate, we refer to the level of consumer credit (Concr). These data come from The Federal Reserve Bulletin.

The time frame for the study is the 19-year period from 1981-1999, inclusive. This test period was chosen to allow for complete information on each of the variables of interest. With quarterly data, we have 76 observations on each variable and 75 observations on the first differences.

Table 1 provides a synopsis of our variables and data sources.

Methodology

Except where otherwise noted, we employ ordinary least squares (OLS) regression for model testing. The OLS assumes that the variables are stationary and that the errors are mean zero with a finite variance. Accordingly, the variables are first tested for the presence of a unit root using an augmented Dickey-Fuller test of the form

If gamma = 0 in equation 1, then a unit root is present and the variable y is non-stationary, implying that the mean, variance, and auto-covariance of the variable is not constant over time. Accordingly, the ADF test examines the null hypothesis of a unit root. In addition, if a single unit root is present, taking the first difference of the series can usually induce stationarity. In other words, the ADF statistic would be insignificant for the series of observations on the variable itself, but significant for the first difference of the series. As detailed later (in Table 3), all of the variables in our sample are nonstationary and are shown to have a single unit root, so taking the first differences induces stationarity. We test each model for serial correlation in the error terms using Ljung-Box Q and Breusch-- Godfrey tests. Where appropriate to mitigate the effects of serial correlation, we employ an autoregressive moving average (ARMA) model. Since we have quarterly data, an ARMA (4,1) model is used to adjust for any possible seasonal effects. Here, the model takes the form

Results

Initial Tests of Delinquency Rates

Our first test examines how the two measures of the bankcard delinquency rate (Brarddol and Bcardnum) relate to our set of test variables. Table 2 displays the results of these regressions.

The overall explanatory power of the model appears impressive. Sixty-four percent of variability in Bcarddol can be explained by the set of test variables, and the F-statistic is easily significant at the 1 percent level. All four test variables are significant at the I percent level; Mtg displays a negative coefficient, while Cdr, Ue, and Rdebt all have positive coefficients. Thus, bankcard delinquencies are highest when the absolute level of revolving debt, the consumer debt ratio, and the unemployment rate are highest and when mortgage rates are lowest

The model also explains more than 61 percent of the variability in Bcardnum, and again the overall model significance level is better than I percent. The regression coefficients for Cdr, Ue, and Rdebt are all positive at the 1 percent level.

Overall, our results-and particularly the consistently positive relationships of both Bcarddol and Bcardnum to Cdr, Ue, and Rdebt-seem intuitively appealing. However, any inferences from the model are questionable, as highly significant serial correlation exists in the error terms. The Ljung-- Box Q and Breusch-Godfrey statistics are used to test the null hypothesis of no serial correlation. This hypothesis is consistently rejected at a probability level of 1 percent. This is not particularly surprising, as Augmented Dickey-Fuller (ADF) tests, which receive more detailed attention in Table 3 below, find significant stationarity problems with the delinquency rate measures and with each of the test variables.

Consequently, as appealing as the initial results may seem, they are spurious. This finding also raises a question in our minds as to whether similar statistical tests of the Paquin and Weiss (1998) model for bankruptcy rates might show the same flaws.

Fortunately, we find that this statistical problem can be adjusted with a relatively simple correction: we take the first differences of both the dependent and explanatory variables. The first differences can be expressed as the absolute change from the prior period, designated by preceding each variable with "D"; for instance, if Rdebt rises from 500 to 510, then D-Rdebt is 10. Or, the first differences can be expressed as the relative change from the prior period, specified by preceding each variable with "R-." In the example above, R-Rdebt equals 10 divided by 500, or 0.02.

Table 3 shows that for the "level" variables used in Table 2, the ADF tests are consistently unable to reject the null hypothesis of a unit root. The table also shows that in testing the absolute first differences of these variables, the null hypothesis of a unit root is consistently rejected at the 5 percent level, and in every case but one at the I percent level. Thus, the use of first differences appears to eliminate the problem of time-dependent distribution statistics, which were present when the level variables were used. Summary statistics for the absolute first differences are also provided in Table 3, and similar information is provided for other variables that are examined in later tests.

Tests of First Differences

The results of the regression models using first differences, and using the full set of test variables, are displayed in Tables 4 and 5. In Table 4, absolute first differences in delinquencies are regressed on absolute first differences of the test variables. In Table 5, relative first differences in delinquencies are regressed on relative first differences of the test variables.

The overall model is fairly strong, producing F-statistics that are consistently significant at a significance level of 5 percent or better. However, the specific test variables displaying statistically significant regression coefficients vary, depending on how the delinquency rate is calculated and on the use of absolute or relative first differences.

Probably the most important finding regarding the individual test variables is as follows. When the delinquency rate is calculated based on the number of accounts, the consumer debt ratio (D-Cdr or R-Cdr) is positive and significant at the 5 percent level; the total dollar amount of revolving debt (D-- Rdebt or R-Rdebt) is not significant. When the delinquency rate is calculated based on the number of dollars outstanding, the total dollar amount of revolving debt is significantly positive, but the consumer debt ratio is not.

While this contrast is intriguing, on reflection it is not overly surprising. It would seem to make sense that the percentage of accounts in default would be tied to the consumer debt ratio. All else being equal, when debt payment obligations become too high relative to disposable income for the population as a whole, more borrowers will be unable to service their debts. On the other hand, if total debt levels go up I percent, and monthly debt payment obligations likewise go up I percent, but disposable income goes up 2 percent, then consumers as a group are actually better able to afford to service their debts than before, and per-account default rates should drops

However, in dealing with default rates that have been calculated based on the absolute amount of dollars outstanding, the situation is somewhat different For instance, for each of the 76 quarters in our sample period, the level of the raw variable Bcarddol is higher than the level of the raw variable Bcardnum. (Average levels of these variables are 3.83 percent for Bcarddol and 2.80 percent for Bcardnum.) Since Bcarddol and Bcardnum are both expressed in percentage terms, it would be mathematically impossible for this to occur unless higher-dollar accounts default at a greater rate than do lower-dollar accounts. Thus, the higher-dollar accounts are, on average, disproportionately prone to default.7

Now, suppose that the total amount of revolving debt increases. And, for lack of more specific information, suppose that this increase in revolving debt is spread equally among high-balance and low-balance accounts. It seems plausible that the increase in debt levels will be more likely to push those borrowers whose balances are already relatively high into default, especially given the fact that these borrowers are, on average, the ones who default most often.

Thus, all else being equal, an increase in the total amount of revolving debt outstanding leads to more defaults among high-dollar borrowers, and thereby leads to an increase in the default rate, as calculated based on the number of dollars of credit outstanding.

For the unemployment variable, the significance of the results does not depend on which default rate is being used, but rather on how the first differences are calculated. Table 5 shows that when relative first differences are used, the variable R-Ue is positive and significant at the 5 percent level. Table 4 shows that when absolute first differences are used, the variable D-Ue does not attain significance at the 5 percent level. In no case does the mortgage variable (D-Mtg or R-- Mtg) attain significance at the 5 percent level.

Relative Default Rates and the Selective Default Notion

Next we test the notion of selective default; in other words, do individual borrowers rationally choose credit card default over default on other types of loans when they find themselves having trouble making payments? It is widely perceived that this is exactly what borrowers do (Greenberg 1997).

To examine the selective default idea, we take the difference of the default rate on bank credit cards (Bcarddol) and the composite default rate (Compdol). This difference is identified as "BD minus CD," or "Bdmcd." As shown in Table 3, B&ncd has the same problem with serial correlation that was previously described for the other variables in the study. Thus, we express the first difference of this variable in both absolute (D-Bdmcd) and relative (R-B&ncd) terms. Tables 6 and 7 show the results of our tests.

In the first model in each table, we regress the first difference of the gap between the two default rates on the first difference of revolving debt (Rdebt). One would expect consumers to encounter greater problems with credit after a period of increased borrowing; however, the effect may not be immediate. Thus we were not surprised to find that the strongest evidence of selective default seems to take place one quarter after an increase in revolving debt. That is, D-Bdmcd is positively related to a one-period lag on the variable D-Rdebt; R-B&ncd is positively related to a one-period lag on the variable R-Rdebt. The significance level is 5 percent or better in both cases.

So, one quarter after revolving debt levels go up, there tends to be an increase in the occurrence of defaults on credit cards, relative to the occurrence of defaults on consumer credit in general. While this clearly does not offer definitive proof of selective default on the part of individual borrowers, the result is consistent with what the idea of selective default would lead us to expect

As a follow-up to this finding, we conducted a secondary test of the dependent variable B&ncd. In this test, we took the ratio of Rdebt to a broader measure of total consumer credit outstanding (Concr), obtaining a variable that we called Rdccr. Consistent with the rest of our tests, we took the absolute first difference (D-Rdccr) and relative first difference (R-Rdccr) of this variable. The first difference of Rdccr tells us whether revolving debt is increasing relative to total consumer credit, or vice versa.

We would expect to find a significantly positive relationship with a one-period lag. That is, as consumers' use of credit card lending increases, relative to their use of lending in general, we would expect to find an increase in the credit card default rate, relative to the default rate on a more general measure of consumer debt. But we would expect to find that this relationship exists with a slight lag, as people generally do not default immediately after taking out a loan.

In both Tables 6 and 7, our results are consistent with this prediction. When D-&D-ncd (R-Bdmcd) is regressed on D-Rdccr (R-Rdccr), the regression coefficient on the one-period lag is positive, and is significant at the 1 percent level.8

Conclusion

This paper uses, as its starting point, the findings of Paquin and Weiss (1998) regarding personal bankruptcies. Based on those findings, and the observation of Paquin and Weiss that the bankruptcy issue is of interest to credit card issuers, we chose to address credit card payment problems directly, specifically by examining delinquency rates.

Our initial tests, if accepted at face value, seem to have a high degree of explanatory power regarding bankcard delinquencies. Bankcard delinquency rates are significantly, positively related to the supply of consumer credit, the consumer debt ratio, and the unemployment rate, and are significantly, negatively related to the current level of interest rates.

However, the results are not statistically valid, as the underlying assumption of no serial correlation in the error terms is violated. We deal with this problem by using the first differences of our dependent and explanatory variables. We find that the consumer debt ratio is strongly related to changes in the bankcard default rate, when the default rate has been calculated based on the number of accounts. But when the bankcard default rate has been calculated based on dollars of debt outstanding, the total amount of revolving debt outstanding becomes a more useful explanatory variable, and the consumer debt ratio becomes less useful.

Further testing provides evidence in line with what we would expect to find if consumers selectively default on credit card debt prior to defaulting on other types of debt. However, while our evidence is consistent with the idea of selective default, the aggregated nature of our data means that we are unable to investigate the behavior of individual consumers. An interesting topic for future research would involve examination of the default patterns of individual borrowers, to see whether these borrowers are indeed more likely to selectively default after measures of their personal debt levels go up.