Journal of Credit Risk

Risk.net

Bankcard performance during the Great Recession: a consumer-level analysis

Paul Calem, Julapa Jagtiani and Loretta Mester

  • This paper offers a “deep dive” examination of consumer default on credit card debt during the Great Recession.
  • We estimate a model that provides the best in-sample predictions of default for prime and below-prime customers, using all available relevant data from 2000-2008. The model fits the data very well in-sample but fails to accurately predict card defaults out-of-sample during the Great Recession period (2008-2013).
  • Default rates during the Great Recession are markedly under-predicted for prime consumers, but default rates are over-predicted for subprime borrowers.
  • This experience highlights the importance of identifying and managing model risk, particularly when venturing into “uncharted territory” as was the case in the credit boom prior to the Great Recession.

This paper investigates factors associated with high credit card loss rates during the period 2008–11 associated with the Great Recession. We examine default at the individual consumer (as opposed to the account) level. Using data available from consumer credit records for the period March 2000–March 2008, we develop and estimate segment-level logistic regression equations to predict default outcomes through 2013. The model fits the data very well in-sample but fails to accurately predict defaults out-of-sample for the Great Recession. On the one hand, default rates throughout the Great Recession are markedly underpredicted for prime consumers, especially those granted large credit limits during the credit expansion that characterized 2000–2008. On the other hand, default rates are overpredicted for subprime borrowers, indicating that lenders’ losses during the Great Recession would have been significantly larger if the repayment performance of subprime borrowers had aligned with extrapolation based on historical performance data.

1 Introduction

Credit cards are one of the largest sources of consumer finance. Credit card origination volume has grown rapidly since 2010, and the aggregate credit limits of new cards reached USD33.6 billion as of July 2018.11 1 For more information, visit the Consumer Financial Protection Bureau website: https://bit.ly/2TVq0im. Historically, credit losses on bank-issued credit cards (bankcards) have been characterized by cyclical episodes of elevated delinquency and loss rates, separated by five years or more and mostly associated with macroeconomic downturns (Figure 1). In particular, credit card delinquency peaked during the Great Recession (2008–9) and sharply declined after 2010.

Here, we examine factors associated with the high credit card loss rates during the Great Recession. This paper is distinct from previous studies on credit card default because we examine default at the individual consumer level (as opposed to at account level), and we identify some new empirical relationships with interesting implications. Although understanding and predicting account-level delinquency is paramount for financial institutions that fund bankcard credit lines or manage customer accounts, a consumer-level analysis can offer new insights. Modeling bankcard delinquency at the consumer level provides a more direct view of aggregate bankcard default, that is, of default tied to shifts in consumers’ behavior across all of the cards they hold.

Our analysis uses a national sample of credit bureau records, representative of all US consumers who have credit cards, combined with relevant economic data. We examine trends in consumer bankcard borrowing, and then develop and estimate a set of segment-specific logistic regression equations based on data from the period March 2000–March 2008 in order to predict consumer default outcomes through 2013.

Percentage of balances ninety or more days past due: all commercial banks. Source: Board of Governors of the Federal Reserve System, available via the FRED database (Federal Reserve Bank of St Louis).
Figure 1: Percentage of balances ninety or more days past due: all commercial banks. Source: Board of Governors of the Federal Reserve System, available via the FRED database (Federal Reserve Bank of St Louis).

Specifically, we model the likelihood that an individual with at least one (active) bankcard account will become seriously delinquent on at least one bankcard. We then examine how the model performs in predicting default rates during the Great Recession (the out-of-sample period), particularly within individual consumer segments differentiated by risk score, total card balances, and whether the consumer has a mortgage loan.

Consistent with Canals-Cerdá and Kerr (2015), our estimated model of borrowers’ repayment performance based on data prior to the Great Recession does not accurately predict segment-level default rates through the downturn. The size and direction of the prediction errors vary across segments; for prime borrowers with large balances, default rates are substantially underpredicted. The prediction errors may be attributed to the unprecedented rise in unemployment during the Great Recession, which necessitates extrapolation well outside of the sample, and to the emergence of new risk relationships from this transition.

Our analysis also yields new findings that are not documented in previous studies. On the one hand, we find that the default rates are markedly underpredicted for a subset (not all) of prime borrowers: those with large credit card balances. This finding suggests that the credit expansion to prime borrowers that occurred between 2000 and 2008 had adverse consequences that likely would not have been anticipated. On the other hand, default rates are overpredicted for all low-balance borrowers, whether they are subprime, near-prime or prime, and for high-balance subprime borrowers. This result suggests that lenders’ losses during the Great Recession would have been significantly larger if the repayment performance of subprime borrowers had aligned with extrapolations based on historical performance.

The analysis does not provide direct evidence that lenders overextended card credit during the pre-downturn period. In light of the findings, however, we suspect that the pre-downturn expansion of credit could have been excessive in the sense that the attendant risks were underweighted by lenders. For instance, lenders may have been inattentive to any model risk related to quantifying borrower repayment risk on the basis of historical data lacking observations of how borrowers perform under severe downturn conditions. In other words, lenders may have entered into “uncharted territory” during the pre-downturn period, with insufficient regard for the risks associated with the expansion of card credit.22 2 In these respects, the experience in the bankcard market can be seen as similar to that of the mortgage market. For instance, Mian and Sufi (2014) argue that the 2003–6 mortgage credit expansion left many households with unmanageable debt burdens. Acharya et al (2009) characterize the financial crisis as being tied to large financial institutions during 2003–7 that were taking on “excessive leverage in the form of manufacturing tail risks that were systemic in nature”.

The rest of the paper is organized as follows. Section 2 provides a brief review of the literature on the default risk of credit card borrowers. Section 3 describes our data, and Section 4 discusses our statistical model of the transition from current status into delinquency status. Sections 5 and 6 present our results, and Section 7 presents conclusions and policy implications.

2 Brief recap of the literature

Past research on bankcard delinquency confirms an association between bankcard repayment performance and macroeconomic conditions, such that credit card losses are positively associated with rising unemployment rates. Laderman (1996) documents the cyclical nature of card default, such that the default rate increases when employment growth slows. Bellotti and Crook (2009 and 2013) find that inclusion of macroeconomic factors in a duration model of card default, alongside measures of borrower behavior, significantly improves model fit and predictive accuracy.

Other previous studies, however, highlight the limited predictability of bankcard delinquency and loss rates. For instance, Gross and Souleles (2002) find that models of bankcard delinquency based on measurable factors may be subject to instability even over relatively short periods with modest variation in economic conditions. Specifically, they estimate duration models for card default during 1995–7 and assess the relative importance of various measurable factors in predicting default. They find, after accounting for observable risk composition and other standard economic variables, that the propensity to default increased significantly and somewhat inexplicably between 1995 and 1997.

The paper by Canals-Cerdá and Kerr (2015) is most similar to ours, in that it, too, focuses on the poor performance of out-of-sample prediction of default rates during the Great Recession. They find that default projection models based on pre-2007 account-level data (inclusive of the historical downturn episode in 2001) significantly underpredict losses when used to forecast defaults during the period 2008–10, conditional on realized economic conditions. They also find that prime borrowers were affected by the economic downturn more severely than below-prime consumers. As a result, they attribute the model’s underprediction of credit card losses largely to the prime borrowers. Our paper revisits the limitations of the quantitative modeling of bankcard default rates during the Great Recession by using data at the individual consumer level and by applying a more granular analysis.

Some previous studies examine credit card balances in relation to the pricing or availability of card credit rather than in relation to default.33 3 Agarwal and Zhang (2015) provide an expansive review of the literature on consumer behavior with credit cards, including topics such as consumer behavior in searching for switching to new card accounts; the determinants of borrower behavior; and the extent to which behavioral biases drive consumer behavior. Credit card default/loss is the subject of a modest number of prior studies. For instance, Calem et al (2006) find that for consumers with lower risk scores, a large credit card balance represents an impediment to obtaining a better interest rate.44 4 Calem and Mester (1995) find that high-balance customers face a lower probability of approval on new credit applications, and that they are more likely to fall behind on payments. The authors attribute this to switching costs tied to informational barriers (issuers not knowing which applicants for new credit intend to switch and which intend to add to their existing card balances). Kerr and Dunn (2008) find that larger credit card balances induce cardholders to search more for lower interest rates but that they face a higher probability of rejection.55 5 Bellotti and Crook (2012) and Dermine and de Carvalho (2006) find a significant, negative correlation between the balance at default and recovery rate.

Finally, to our knowledge we are the first nonproprietary study using US consumer credit reporting data to test the relationship between borrower income (using neighborhood median income as a proxy) and the likelihood of default on bankcards, conditional on risk score and other risk measures. Consistent with Bellotti and Crook (2013), we find a significant inverse relationship between income and the probability of delinquency.

3 Analytical framework, data sources and notable historical trends

3.1 Consumer-level framework

An important and distinguishing aspect of our analysis is that it is conducted at the consumer level rather than at the account level (which are not one and the same, because many consumers have more than one bankcard account). Although understanding and predicting account-level delinquency is paramount for financial institutions that fund bankcard credit lines or manage customer accounts, a consumer-level analysis can offer new insights.

In particular, modeling bankcard delinquency at the consumer level provides a more direct view of aggregate bankcard default and loss patterns. The aggregate exposure of financial institutions and consumers to bankcard charge-offs is determined by (1) individual consumers falling behind on their payments for at least one of their bankcard accounts; (2) the proportion of total bankcard balances associated with delinquent accounts; and (3) consumers failing to cure their delinquencies, resulting in balances being charged-off.

For example, an account-level analysis might indicate a strong positive relationship between account balance and the likelihood of default. However, this might be due to consumers with one large-balance account and one or more small-balance accounts typically remaining current on the small-balance accounts in the event of defaulting on at least one account. In this case, at the consumer level, the relationship between total bankcard balance and the likelihood of default may be less pronounced.

Moreover, it is helpful to model bankcard delinquency at the consumer level in order to identify and aptly characterize sources of model risk that derive from shifts in consumer behavior. In other words, accounts do not change behavior, consumers do.

Formally, our framework represents a consumer’s expected contribution to aggregate losses in period t+2, conditional on being nondelinquent at t, as the product of

  1. (1)

    a probability of default (PD), which is the probability that the consumer will be at least sixty days late on at least one bankcard account in period t+1;

  2. (2)

    an exposure at default (EAD), which is the total balance in period t+1 in the consumer’s delinquent account(s); and

  3. (3)

    a probability of charge-off (PCO), which is the probability that these balances will be charged off as of period t+2.

Thus,

  EL=PD×EAD×PCO.   (3.1)

Alternatively, we can express (3.1) in terms of a loss rate relative to the current (period t) total balance:

  ELratio=PD×EADratio×PCO,   (3.2)

where ELratio=EL/balance at t, and EADratio=delinquent balance at t+1/balance at t.66 6 Note that EAD is the total balance in the customer’s delinquent bankcard accounts at t+1, while the denominator of the EAD ratio is the customer’s total balance in all bankcard accounts at t (none of which are yet delinquent). These EAD constructs fit the context of modeling loss at the customer level.

The major focus in this paper is on the PD component; we briefly examine EAD and PCO after concluding our analysis of PD.

3.2 Federal Reserve Bank of New York Consumer Credit Panel/Equifax

We develop our empirical analysis using a 5% random sample of primary consumers in the Federal Reserve Bank of New York Consumer Credit Panel/Equifax (FRBNY Equifax CCP).77 7 A primary consumer is a consumer who has been followed throughout the data set. Their household members are also followed as long as they continue to be a household member of the primary consumer. Household members may get dropped from the sample if they later become a household member of a nonprimary consumer. The FRBNY Equifax CCP is a panel data set comprising quarterly updates of the credit reports of a fixed sample of individual consumers (and their household members), where the overall population size is maintained through resampling to replace individuals who exit the credit reporting system.88 8 The Equifax panel of “primary” individuals itself constitutes a 5% random sample of all individuals with a Social Security number and a credit record, totaling about 12 million records each quarter. The full Equifax panel also incorporates individuals residing in the same household as the “primary” individual; these “secondary” individuals are excluded from our sample. See Wardrip and Hunt (2013) for a more detailed description of the Equifax panel.

The data set contains information aggregated to the borrower level about all active bank credit card accounts that each primary consumer has as of the reporting date (quarterly). This information includes, for example, age (in months) of the oldest and newest accounts; total balance across all accounts; total amount sixty or more days past due (as well as amounts thirty or more days and ninety or more days past due). The data set provides similar information about mortgage and installment accounts. In addition, the FRBNY Equifax CCP includes a continually updated consumer risk score, such that higher risk scores indicate lower risk of defaulting on a credit obligation. The state, county and census tract location of the consumer’s mailing address are also provided.

Our sample covers the period March 1, 2000–December 1, 2013. The initial panel sample consists of about thirty-three million (panel) observations, from which we exclude individuals with fewer than five quarters of data and those with substantial gaps between quarterly observations, leaving about thirty-one million observations.99 9 As explained by Wardrip and Hunt (2013), such exclusions consist primarily of individuals with fragmentary records and individuals who have only a few trades or public records, who only temporarily meet the inclusion criteria used to assemble the panel.

We further limit the sample to observations such that the individual in that quarter is current on all bankcard payments, retaining forward information for modeling transitions to delinquency.1010 10 About 900 000 observations are excluded by this criterion. In addition, we drop about 300 000 observations that are missing forward information on payment status. In addition, we require that each individual consumer have at least one open bankcard account and a total bankcard balance exceeding USD10. This is done because individuals with a zero or near-zero total balance (mostly associated with inactive accounts) contribute minimally to overall default rates and might erode the explanatory power of the model.1111 11 Reported positive balances of USD10 or less are also excluded on the basis of questionable reliability. Finally, we exclude a few outlier observations associated with individuals with total card balances exceeding USD1 million. After these exclusions, the final sample size is 15 460 121 observations, corresponding to a cross-section of 510 628 individuals observed over the sample period.

3.3 Economic factors

The above consumer credit panel data is merged with quarterly state-level unemployment rate and first-time unemployment insurance claim data, and with a quarterly, state-level house price index (HPI), obtained from Haver Analytics and from CoreLogic Solutions, respectively. We also construct a quarterly measure of per capita personal income at the census tract level by interpolating data from several sources: census tract-level data from the United States Census of 2000; annual “five-year estimates” over 2009 to 2013 from the American Community Survey (ACS); and annual county-level data from the US Bureau of Economic Analysis.

Note that each five-year estimate from the ACS is based on sampling over a five-year period; for example, the 2009 ACS value is based on the sampling period 2005–9. Thus, the point of departure for our interpolation procedure was to convert the five-year estimate into an estimate assigned to the third year of the five-year period, basing this conversion on county-level trends. For instance, we converted the five-year estimate from the 2009 ACS for a given census tract into a 2007 estimate by applying the ratio of per capita personal income in the county in 2007 to the average of county-level personal income for 2005 through 2009. It then remained for us to interpolate six missing annual census tract values between 2000 and 2007, and to extrapolate values for 2012 and 2013, which were not yet available. This interpolation allows the data to reflect the dynamics of county-level income growth between 2000 and 2007 while matching the tract-level endpoints. The annual estimate constructed by this interpolation method was applied to all four quarters in the panel.

We inflation adjust all dollar values, including card balances, census tract per capita personal income and credit limits. We adjust to 2012 US dollars using the quarterly personal consumption expenditures chain-weighted price index (PCE) from the Department of Commerce, Bureau of Economic Analysis.

3.4 Notable historical trends

Risk score and census tract per capita income

Changes over the study period in average consumer credit quality, as measured by average risk score (with the average calculated in two ways: with and without weighting by balance), are shown in Figure 2. Without balance weighting, average risk scores for consumers in our sample (calibrated along the left axis of the figure) rose about 10 points, from 712 as of March 2000 to about 722 as of March 2008. In contrast, the balance-weighted risk scores rose significantly more (about 30 points) during the same period, from about 690 in 2000 to 720 in 2008. These patterns are consistent with the previous observation that card balances were rising disproportionately among consumers with higher risk scores.

Sample average risk score and average tract per capita income. Source: FRBNY Equifax CCP and ACS.
Figure 2: Sample average risk score and average tract per capita income. Source: FRBNY Equifax CCP and ACS.

In addition, Figure 2 shows the average census tract per capita income (measured in 2012 US dollars) associated with the consumers in our sample, by quarter. The average income in the neighborhoods where the consumers reside trends upward during 2003 through 2007. This trend, along with the trend of rising average risk scores over this period, suggests the improving credit quality of the population with at least one active bankcard account (and no delinquent bankcard accounts). Notably, average income in the neighborhoods where the consumers reside declines during the Great Recession, which suggests that consumers residing in higher-income neighborhoods had a greater likelihood of exiting the sample during this period.1212 12 We choose not to show balance-weighted average tract income, as weighting by total bankcard balance simply shifts the time series upward (in the range of USD3000 to USD4000) without notably affecting the pattern of movement through time.

Credit card balance

(a) Card balances per consumer by consumer's risk score segment and (b) distribution of bankcard balances by consumer's risk score and balance category. Excludes consumers with zero total bankcard balance. Source: FRBNY Equifax CCP. Balances measured in 2012 dollars using the PCE.
Figure 3: (a) Card balances per consumer by consumer’s risk score segment and (b) distribution of bankcard balances by consumer’s risk score and balance category. Excludes consumers with zero total bankcard balance. Source: FRBNY Equifax CCP. Balances measured in 2012 dollars using the PCE.

Figure 3(a) shows the quarterly average across consumers of total bankcard balances (standardized to 2012 US dollars using the PCE) by risk score segment. On average, balances of prime borrowers (risk score >720) in our sample had trended up prior to the Great Recession and were at historically high levels going into the downturn. In contrast, the average balance in the subprime segment (<660) had been trending down, while that in the middle range had been roughly constant prior to the downturn. After the recession, average balances declined for all segments; this is consistent with Santucci (2016), who finds that 75% of revolving card balances in March 2009 were paid off by February 2013, with three-quarters of that decline paid off by deleveraging borrowers.

Figure 3(b) shows the composition of bankcard balances by quarter, as distributed across six consumer segments: specifically, across “high-balance” and “low-balance” ranges within each of the three risk score segments (<660, 660–720 and >720). High-balance consumers are defined as those with total bankcard balances exceeding USD4000, USD6000 and USD9000 (the June 2007 mean balances), respectively, in the three risk score segments.1313 13 Likewise, low-balance consumers are defined as consumers with bankcard balances below the June 2007 mean balance for their risk score segment. Between 2000 and 2009, the share of the high-balance, high risk score cohort nearly doubled, while that of the other cohorts declined. As we shall see, these trends are of particular interest in relation to the out-of-sample performance of our default prediction model.1414 14 In addition, over this period the median balance within the high-balance range (measured in 2012 US dollars) of the high risk scores segment increased from USD10 968 to USD13 259, and the 75th percentile balance increased from USD16 960 to USD22 207.

Card utilization ratio

Consumer credit reporting agencies historically have had incomplete information on bankcard credit limits, which would have been ideal for calculating utilization ratios. In the FRBNY Equifax CCP, the variable “high credit” is the credit limit if reported by the lender, or the highest historical balance if the actual credit limit is not reported. To gain a sense of the degree to which rising limits may have contributed to rising balances pre-downturn, we track bankcard utilization rates (total balance to total “credit limit”). To the extent that rising balances are offset by rising limits, we expect to observe relatively stable utilization rates.

Proportion of consumers with utilization rate >75% by consumer's risk score segment. Source: FRBNY Equifax CCP.
Figure 4: Proportion of consumers with utilization rate >75% by consumer’s risk score segment. Source: FRBNY Equifax CCP.

Figure 4 shows the percentage of consumers with high utilization rates (at least 75%) by quarter and range of risk score. Among consumers with high risk scores, the percentage with high utilization rates remained roughly unchanged pre-downturn, despite rising balances in this cohort, suggesting that these rising balances were offset by rising limits. The opposite is observed for consumers in the middle risk score range post-downturn, for whom we observe declining average card balances but a rising proportion with high utilization rates.

Unemployment insurance claims

Figure 5 depicts the variation over our period of study in employment conditions, as measured by the year-over-year percent change in first-time claims for unemployment insurance. This is shown in Figure 5 both for the aggregate United States and for a few individual states selected for illustrative purposes.

Unemployment insurance first-time claims year-over-year percent change: United States and selected states.
Figure 5: Unemployment insurance first-time claims year-over-year percent change: United States and selected states.

Employment conditions at the state level show wide variation, with the year-over-year percent change in first-time claims ranging between -50% and 140% for the selected states. During both downturn periods, we observe a rising incidence of claims. Relative to the official commencement date of each downturn, the rise in claims began somewhat earlier for the 2001 downturn compared with the Great Recession.

Consumer default rates

We quantify historical rates of default on bankcard accounts by constructing quarterly default “roll rates”: these represent the proportion of consumers who transition from current on all accounts as of quarter t to seriously delinquent (sixty or more days past due) on at least one account as of quarter t+1. We calculate this default roll rate (PD) in two ways: as the unweighted (individual) roll rate, and as the balance-weighted roll rate (weighted by the consumer’s total bankcard balance at t).1515 15 The first measure is calculated as the number of individuals who are current on all accounts (have no balances thirty or more days past due) as of quarter t and at least one seriously delinquent account at t+1, divided by the total number of individuals who are current at t. The second measure is the total balances as of quarter t of individuals who are current at t and have at least one seriously delinquent account at t+1, divided by the total balances at t of individuals who are current at t.

Delinquency roll rates: individual versus balance weighted. (a) Full sample. (b) Low-balance segment. (c) High-balance segment. Source: FRBNY Equifax CCP.
Figure 6: Delinquency roll rates: individual versus balance weighted. (a) Full sample. (b) Low-balance segment. (c) High-balance segment. Source: FRBNY Equifax CCP.

Figure 6 displays the time series of the individual and balance-weighted roll rate measures for the (a) overall sample and for the (b) low- and (c) high-balance cohorts. The quarters where we observe elevated default roll rates roughly coincide with the periods in Figure 5 where we observe rising first-time unemployment claims.

Within the low-balance range, the two measures coincide during 2009 and 2010, but otherwise the individual roll rate mostly exceeds the balance-weighted roll rate. Within the high-balance range, the two measures coincide except in 2008 through 2010, when the balance-weighted delinquency roll rate rises sharply above the unweighted roll rate. Default roll rates within the high-balance segment consistently exceed those within the low-balance segment. For the overall sample, the balance-weighted roll rate tends to exceed the individual roll rate.

During the Great Recession, balance-weighted roll rates within the high-balance segment increase more sharply than those within the low-balance segment. Consequently, we observe a sharp divergence between the individual and balance-weighted roll rates during the Great Recession for the overall sample. Thus, large-balance consumers comprised a disproportionate share of the population of seriously delinquent borrowers during the Great Recession.

4 Multivariate statistical model of transition to default

In this section, we construct a set of segment-level logistic regression equations for bankcard roll rates (PD). These equations will be estimated using the portion of our sample through March 1, 2008, and then applied to generate out-of-sample predictions for the downturn and post-downturn parts of our sample period.

4.1 Risk segments of consumers

Six logistic regression equations are estimated, corresponding to six segments of consumers. First, we account for the potentially different responses of homeowners and nonhomeowners to financial and economic variables by segmenting our sample between consumers who have a mortgage (as reported in the FRBNY Equifax CCP data) and those who do not.

Since the Great Recession was tied to a deep housing market downturn with severely adverse consequences for home values and mortgage default, we expect that it may have affected homeowners or mortgagees differently from nonhomeowners or those without mortgage debt. Moreover, individuals with and without a mortgage tend to have differing financial strengths and vulnerabilities. Homeowners (indicated by having a mortgage) typically have higher incomes and wealth than renters, and home equity can serve as a backup source of liquidity in the event of a temporary financial setback. Homeowners also bear a greater risk of a decline in home value, unexpected property maintenance expenses and large property tax increases. Therefore, we do not wish to constrain these two groups to be similarly situated with respect to behavior with credit card debt.

Next, within each mortgage status category, we segment consumers using three ranges of the risk score: <620, 620–720 and >720.1616 16 When it is available, we use the four-quarter lagged value of the individual’s risk score for slotting to segments, to mitigate simultaneity with the dependent variable. If the four-quarter lagged risk score is not available, we use the furthest available lagged risk scores up to four quarters. Relationships between borrower characteristics and likelihood of default can differ by risk score range. For example, Ash et al (2007) report that, with accounts segmented into two bands based on origination risk score, the default probability for higher risk accounts increases with loan age to about eighteen months and then flattens out, and for lower risk accounts it increases with loan age to about thirty-three months and then declines.

The frequency distribution of the estimation sample across the six risk segments (regressions) is reported in Table 1. The majority (about 56%) of observations are in the high risk score segments, and about 60% of observations are individuals with at least one active mortgage account.

Table 1: Distribution of observations by risk score range and with/without a mortgage. [All values given as percentages. Source: FRBNY Equifax CCP and United States Census Bureau.]
    ???    
  Risk score risk score Risk score  
  <??? ??? >??? All
With mortgage 11.1 19.2 29.8 060.1
Without mortgage 03.1 10.4 26.4 039.9
All 14.15 29.6 56.25 100.0

4.2 Variable definitions

The general form of our logistic regression equation for each of the six segments is

  Yi,t=a+bXi,t+ei,t,   (4.1)

where the dependent variable Yi,t is a binary roll-to-delinquency indicator for consumer i during quarter t. Thus, Yi,t is equal to 1 if consumer i transitions from being current at time t into being at least sixty days past due at time t+1; it takes a value of 0 otherwise.

Prior studies, such as Bellotti and Crook (2013) and Canals-Cerdá and Kerr (2015), have identified account age, age of the borrower or of the borrower’s oldest account, account balance, credit line utilization, and local economic conditions as factors related to the likelihood of becoming seriously delinquent on bankcard payments. Our vector of independent variables Xi,t incorporates these or similar factors.

Lagged risk scores

In addition to distinguishing the three risk score segments for separate regression equations, we include the consumer’s lagged risk scores as a continuous variable in each regression (Lag_Risk_Score). As described by Equifax, the risk score is derived from a comprehensive statistical model “designed to help predict the likelihood of a consumer becoming 90+ days delinquent within 24 months”, and this is “based on length of credit history, depth of credit information and delinquency history”.1717 17 See https://bit.ly/3l5atso. We use the four-quarter lagged risk score if available; otherwise, we use the furthest available lagged risk scores up to four quarters.

Income

Higher-income households tend to be more financially stable, as they tend to have a larger amount of accumulated liquid assets and their incomes tend to be less volatile. We use quarterly per capita personal income at the census tract level (Tract_Income) as a proxy for the unobserved incomes of the individuals in our sample.

Bankcard balance ranges

Each consumer’s total bankcard balance is slotted to a balance range based on the December 2000 sample distribution of card balances. The relationship between balance range and likelihood of default reflects conflicting factors and may not be monotonic. On the one hand, a larger card balance tends to be associated with higher-income households, implying a lower likelihood of default. On the other hand, a larger card balance requires larger monthly debt payments, which could imply a greater likelihood of default.

Table 2: Balance range boundaries. [Source: FRBNY Equifax CCP and United States Census Bureau.]
  Card balance segments
   
  1 2 3 4 5 6 7 8 9 10
Percentile 0 55th 60th 65th 70th 75th 80th 85th 90th 95th
lower bound                    
Amount (dollars) 25 524 866 1354 2051 3052 4523 6675 10 274 17 652
lower bound                    

For our initial specification testing, we allowed for ten ranges (Bal_Range), defined by the boundaries shown in Table 2. Thus, for example, individuals in the highest range have a total balance greater than USD17 652. For our final model, we consolidated these into fewer ranges and specified range 10, the top balance range, to be the base case.1818 18 For these regressions, we retain only two segments in the low risk score range: the top range (segment 10) and all others combined. For the middle risk score range, we combine segments 3, 4 and 5 into one segment. For the high risk score range, we merge segments 2 through 5.

Log balance

The top balance range is expansive, bounded at the upper end by the sample’s upper limit of USD1 000 000. Therefore, we included the natural log of balance interacted with an indicator for a balance exceeding the 95th percentile threshold (ln_LargeBal).

Utilization ratio

We distinguish categories of consumers with relatively high bankcard utilization rates or relatively small credit lines, with the expectation that they face tighter liquidity constraints and therefore could have a higher likelihood of default. Thus, we include three categorical variables: an indicator for consumers with a total credit limit below USD500; an indicator for consumers with a limit of at least USD500 and a utilization ratio below 75%, and an indicator for a limit of at least USD500 and a utilization ratio greater than 90%. The base case is a consumer with a total credit limit of at least USD500 and a utilization ratio between 75% and 90%.

Changes in card balances

A large change in a consumer’s total bankcard balance (relative to a year before) may indicate a change in the consumer’s financial condition. For instance, a large increase in the balance may indicate declining household liquidity and thus a weakening financial situation. Alternatively, it might also reflect a jump in household income and spending, consistent with improved financial health. Since we do not have individual household income, this is an empirical question. We account for the direction of the changes by including the two separate measures Bal_Chg_Pos and Bal_Chg_Neg:

  Bal_Chg_Pos  
    ={ln(Bal-Lag_Bal)/(100+Lag_Bal)if Bal-Lag_Bal>100,0otherwise,  
  Bal_Chg_Neg  
    ={ln(Lag_Bal-Bal)/(100+Lag_Bal)if Lag_Bal-Bal>100,0otherwise,  

where Bal denotes the individual’s current total bankcard balance (at time t) and Lag_Bal denotes the individual’s lagged balance (at time t-4).1919 19 If the four-quarter lag is not available, then the furthest lagged value observed within the past year is substituted.

New card indicator in the past year

Similar to an increasing balance, adding a new card account, such as in response to solicitations received in the mail, may indicate a change in the consumer’s financial condition. For instance, adding a new card account may reflect a need for liquidity, potentially indicating an increase in delinquency risk. We include a dummy variable (New_Card) that takes a value of 1 if the individual’s current number of bankcards exceeds his or her number of bankcards as of four quarters ago, and 0 otherwise.2020 20 Again, when the four-quarter lagged count is not available, we use the furthest lagged value observed within the past year.

Age of the oldest/newest bankcard accounts

We expect that consumers who have more experience managing their debt, as reflected in having older card accounts, would be less likely to default. We enter the ages of the oldest and newest accounts in months as continuous variables (Age_Oldest and Age_Newest), allowing for slope changes via spline points. In the final model specification (after exploring alternative thresholds), for age of the oldest account spline points are placed at twenty-four months (Age_Oldest_Spline24) and sixty months (Age_Oldest_Spline60), while for age of the newest account a spline point is placed at twelve months (Age_Newest_Spline12).

Local employment conditions

We expect a positive association between the local unemployment rate and credit card delinquency due to the impact of job loss and reduced incomes on the ability of individuals to meet their debt payment obligations. In the equations for the middle risk score segment, we include percentage change in first-time state unemployment claims over the previous quarter (Claims_Qtrchange). In each of the other equations we include the percentage change in first-time state unemployment claims between the current year and the previous year (Claims_Yrchange).2121 21 We tested various alternative measures of unemployment level and change, including level and change in the unemployment rate at the state and county levels, prior to selecting these measures for our final specification.

Local housing market conditions

Changes in home values directly affect the wealth of homeowner households. Consequently, we expect that the association between local house price appreciation and bankcard delinquency might differ between households with a mortgage and those without a mortgage. For example, households that are seeing their wealth accumulate through appreciating home value might reduce their holdings of liquid assets in the expectation that they can draw on their home equity if the need arises. If the house price appreciation unexpectedly reverses, these households may be in a relatively precarious position, having less liquidity.

Local house prices are affected by the demand for home purchases, which is affected by changes in household income and wealth. Thus, local house price appreciation rates not only indicate the strength of the local housing market but may also serve, alongside the unemployment rate, as an additional indicator of local economic conditions. Therefore, local house price appreciation rates may be inversely related to the likelihood of delinquency on both mortgage and nonmortgage consumer credit. Conceivably, however, a change in home values could correlate with rent increases for nonhomeowners, and the resulting increase in their monthly payment obligations could increase their risk of default on credit card debt. Thus, the overall relationship of house price appreciation to the likelihood of default for nonhomeowners is a priori ambiguous.

We include in each regression equation the one-year percentage change in the state HPI, distinguishing between increasing and declining house price environments.2222 22 A small proportion of sample observations (6%) are associated with a local area one-year house price decline. The mean decline in this cohort is 3.2%; the steepest decline is 10.2%. That is,

  HPI_Yrchange_Pos ={HPI_Yrchangeif HPI_Yrchange>0,0otherwise,  
  HPI_Yrchange_Neg ={-HPI_Yrchangeif HPI_Yrchange<0,0otherwise.  

Home equity loans

In the equations for individuals with a mortgage, we include an indicator of whether the individual has an open home equity line of credit (HELOC). Borrowers with a HELOC may be more or less prone to bankcard delinquency, other factors held constant. On the one hand, the presence of a HELOC may mitigate bankcard delinquency risk, as it provides a backup source of liquidity. On the other hand, borrowers with a HELOC might have a higher risk of delinquency on a bankcard, as they may choose to prioritize their HELOC payment over their bankcard payment.

We distinguish between first- and second-lien HELOCs in the analysis by using categorical variables because there may be differences in the financial strength or resilience of the corresponding borrower groups. Thus, we include indicators for no HELOC and for a second-lien HELOC; individuals with a first-lien HELOC are the base case.

Consumer Bankruptcy Act

We include an indicator for June 2005 (June2005_BK_Spike) to control for the potential impact of the implementation in October 2005 of the Consumer Bankruptcy Act, which placed stricter conditions on consumer bankruptcy filing. Its implementation incentivized a rush to file for bankruptcy before the new law took effect, which caused a spike in the roll rate to delinquency between June 2005 and September 2005.

Seasonality

We include dummy indicators for the June observation date (D_June) and the September date (D_Sept) to capture quarterly seasonal effects.

5 Empirical results: probability of default model

5.1 Default prediction model estimation

The estimation (model development) sample for our logistic regression equations consists of quarterly cohorts of individuals who are current on all bankcards (have zero balances thirty or more days past due) beginning with the March 1, 2000 cohort and ending with the December 1, 2007 cohort. We model the likelihood that an individual will transition from current to default, that is, to being sixty or more days past due on at least one bankcard as of the following quarter.

The regression equations are estimated with all observations equally weighted: we do not balance weight. It is of general interest to explore the factors associated with defaults of individual customers without disproportionately weighting any particular segment, although accurate prediction of credit loss, as previously discussed, might favor balance weighting. We opt instead to estimate the regression equations without balance weighting, but with the inclusion of a set of indicator variables for balance range to capture potential differences in default roll rate patterns in relation to a consumer’s total card balance. We revisit this issue below in our discussion of model fit.

Table 3: Mean values of categorical variables by risk score range and with/without a mortgage. [Source: FRBNY Equifax CCP and United States Census Bureau.]
    Credit limit Credit limit      
    ?????? ??????      
  Credit limit and utilization and utilization   Second-lien First-lien
  <?????? <75% >90% New_Card HELOC HELOC
No mortgage, 14.2 27.1 16.9 47.2
risk score < 620            
No mortgage, 03.05 14.1 11.3 40.1
620 risk score 720            
No mortgage, 00.3 01.3 01.4 26.8
risk score > 720            
Has mortgage, 07.0 27.9 18.2 39.4 05.9 05.7
risk score < 620            
Has mortgage, 00.8 13.8 11.8 36.2 14.4 10.7
620 risk score 720            
Has mortgage, 00.1 01.7 02.05 29.7 20.0 13.95
risk score > 720            

Table 3 reports the frequency distributions in the model development sample for the discrete variables High_Util, New_Card and HELOC, by risk segment. For instance, a relatively high bankcard utilization rate is most frequently observed among individuals with risk scores of 620 or lower, and relatively rare among individuals with risk scores greater than 720. HELOCs are more common among individuals with higher risk scores.

Census tract per capita personal income is unknown for 4.9% of the full sample and 5.4% of the pre-2008 quarterly cohorts of individuals who make up the estimation sample. Few observations have missing values for any of the other independent variables described above.2323 23 About two-thirds of the cases of missing census tract per capita income are due to unknown tract. The ages of the oldest and newest bankcard accounts are missing for about 0.5% of the full sample. After excluding observations with missing values, the pre-2008 model development sample contains 7 793 947 observations, corresponding to a cross-section of 444 413 individuals.2424 24 The model’s estimated coefficients, in-sample fit and out-of-sample predictions are robust to including observations with missing tract income (by means of including an indicator variable for those observations after setting the missing values to zero). In addition, the estimated coefficients and out-of-sample predictions are robust to dropping the first three quarters (in 2000) from the sample.

Table 4: Logistic regression results. [Dependent variable is the binary variable indicating whether a consumer rolls from current status at time t to a delinquency status at time t+1. Source: FRBNY Equifax CCP and United States Census Bureau.]
(a) For consumers without a mortgage
      Risk score >???    
  Risk score ??? and ??? Risk score >???
       
    Odds   Odds   Odds
Variable Coefficient ratio Coefficient ratio Coefficient ratio
Intercept 1.393**   4.765**   7.811**  
Lag_Risk_Score -0.006** 0.994 -0.012** 0.988 -0.016** 0.984
Age_Oldest -0.017** 0.983 -0.012** 0.988 -0.008 0.992
Age_Oldest_Spline24 0.014** 1.015 0.010** 1.01 -0.005 0.995
Age_Oldest_Spline60 0.001* 1.001 0.002* 1.002 0.014** 1.014
Age_Newest -0.009** 0.991 -0.013** 0.987 -0.014** 0.965
Age_Newest_Spline12 0.008** 1.008 0.012** 1.012 -0.035** 1.037
Bal_Range < 10 0.051 1.107        
Bal_Range = 1     -0.001 1.504 0.250** 2.013
Bal_Range in (2,3,4,5)         -0.335** 1.122
Bal_Range = 2     0.116** 1.7    
Bal_Range in (3,4,5)     -0.071** 1.409    
Bal_Range = 6     -0.030 1.475 -0.037 1.51
Bal_Range = 7     0.015 1.536 0.011 1.585
Bal_Range = 8     0.122** 1.709 0.132* 1.789
Bal_Range = 9     0.269** 1.981 0.427** 2.403
Credit limit < 500 dollars 0.266** 1.843 0.501** 2.161 0.475** 1.825
Credit limit 500 dollars and utilization < 75% -0.235** 1.116 -0.751** 0.618 -1.027** 0.407
Credit limit 500 dollars and utilization > 90% 0.314** 1.934 0.521** 2.205 0.680** 2.241
HPI_Yrchange_Neg 0.020** 1.02 0.034** 1.034 0.051** 1.053
HPI_Yrchange_Pos -0.008** 0.992 -0.006** 0.994 0.006* 1.006
Claims_Ychange 0.002** 1.002     0.002 1.002
Claims_Qtrchange     0.003* 1.003    
Tract_Income -0.005** 0.995 -0.006** 0.994 -0.006** 0.994
Log_LargeBal 0.035** 1.035 0.108** 1.114 0.133** 1.142
Bal_Chg_Pos 0.133** 1.142 0.170** 1.185 0.221** 1.247
Bal_Chg_Neg -0.173** 0.841 -0.017 0.983 0.033 1.033
New_Card 0.078** 1.081 0.203** 1.225 0.314** 1.369
D_June 0.144** 1.155 0.081** 1.084 -0.026 0.974
D_Sept 0.131** 1.14 0.104** 1.11 0.042 1.043
June2005_BK_Spike 0.022 1.022 0.098* 1.103 0.082 1.085
(b) For consumers with at least one mortgage
      Risk score >???    
  Risk score ??? and ??? Risk score >???
       
    Odds   Odds   Odds
Variable Coefficient ratio Coefficient ratio Coefficient ratio
Intercept 0.734**   5.340**   6.427**  
Lag_Risk_Score -0.006** 0.994 -0.014** 0.986 -0.016** 0.985
Age_Oldest -0.016 0.994 -0.008 0.992 0.01 1.01
Age_Oldest_Spline24 0.014 1.001 0.008 1.008 -0.018 0.982
Age_Oldest_Spline60 0.004** 1.004 -0.001 0.999 0.009 1.009
Age_Newest 0.023** 1.024 0.009* 1.009 -0.027** 0.973
Age_Newest_Spline12 -0.026** 0.975 0.011** 0.989 0.024** 1.024
Bal_Range < 10 0.011 1.022        
Bal_Range = 1     0.227** 1.667 0.350** 2.476
Bal_Range in (2,3,4,5)         -0.204** 1.423
Bal_Range = 2     0.089 1.452    
Bal_Range in (3,4,5)     -0.116** 1.182    
Bal_Range = 6     -0.108* 1.192 -0.062 1.64
Bal_Range = 7     -0.078* 1.228 0.582 1.85
Bal_Range = 8     0.083* 1.443 0.196** 2.124
Bal_Range = 9     0.187** 1.601 0.219** 2.173
Credit limit < 500 dollars 0.172** 1.476 0.466** 1.926 0.562** 2.077
Credit limit 500 dollars and utilization < 75% -0.213** 1.005 -0.724** 0.586 -0.999** 0.436
Credit limit 500 dollars and utilization > 90% 0.259** 1.61 0.448** 1.891 0.606** 2.171
HPI_Yrchange_Neg 0.038** 1.038 0.100** 1.105 0.086** 1.09
HPI_Yrchange_Pos -0.018** 0.982 -0.020** 0.98 0.001 1.001
No HELOC 0.080** 1.107 0.080** 1.042 0.01 0.92
Second-lien HELOC 0.059 0.963 0.120** 0.853 -0.103** 0.822
Claims_Ychange 0.003** 1.003     0.003* 1.003
Claims_Qtrchange     0.005* 1.005    
Tract_Income -0.002** 0.998 -0.004** 0.996 -0.005** 0.995
Log_LargeBal 0.018 1.018 0.085** 1.088 0.153** 1.165
Bal_Chg_Pos 0.083** 1.087 0.100** 1.104 0.176** 1.193
Bal_Chg_Neg -0.159** 0.853 -0.070** 0.933 -0.007 0.993
New_Card 0.218** 1.244 0.234** 1.264 0.220** 1.247
D_June 0.128** 1.136 0.101** 1.107 0.022 1.022
D_Sept 0.136** 1.146 0.085** 1.088 0.130** 1.139
June2005_BK_Spike 0.041 1.042 0.175* 1.191 0.078 1.081

The estimated coefficients along with their associated odds ratios are reported in Table 4(a) for segments of consumers without a mortgage, and in Table 4(b) for segments of consumers with at least one mortgage. We considered several alternative model specifications; in our view, within the confines of the information available in the consumer credit panel data set, our variable selection and model specification represent a “best practice” model.2525 25 Among the alternative specifications considered were inclusion of the following additional variables: adding a spline point at zero for percentage change in first-time unemployment claims; adding the interaction of the latter variable to the balance ranges; adding the number of active bankcards of the individual; allowing for spline points in the relationships to twelve-month balance change; and including three-month in addition to twelve-month balance change. The additional variables were not statistically significant. We also tested substituting the ratio of balance to tract income in place of tract income; absolute balance change in place of log change; and alternative spline points for age and risk score. These substitutions had no noticeable impact on the in-sample fit or out-of-sample predictions.

Risk scores

As expected, for all six segments the estimated coefficients of the lagged risk score are significantly negative: a higher risk score implies lower odds of default. The estimated odds ratios for the middle and high risk score segments indicate increases in the odds of default in the range of 22.5% to 28% for a twenty-point increase in the risk score. For subprime borrowers (those in the lowest risk score segment), the likelihood of default is less steeply related to risk score; the estimated odds ratio indicates (roughly) an 11% increase in the odds of default for a twenty-point increase in the risk score.

Utilization ratio

Consumers with a total credit limit of less than USD500 have a relatively high likelihood of default on their card balances, consistently for all six segments, as indicated by the estimated odds ratios. In most cases, these consumers exhibit about double the odds of default relative to those with larger credit lines. For consumers with a total credit limit of at least USD500, the likelihood of default is greatest for those who have a utilization ratio of 90% or higher, again for all six segments, and again in most cases their odds of default are about double those of others. For the four middle or high risk score segments, consumers with a utilization rate below 75% have materially lower odds of default relative to other consumers.

Bankcard balance

The estimated odds ratios for the balance range dummy variables indicate some differences in the likelihood of default by balance range for the four middle or high risk score segments, but we observe no statistically significant differences in terms of balance range for the two subprime segments. For the four middle or high risk score segments, consumers in the top balance range (10), which is the omitted category, overall have lower odds of default relative to those with smaller balances. However, the estimated coefficient on ln_LargeBal indicates that within the top balance range of each of these four segments, the likelihood of default increases with balance. Also, for these four segments, consumers in the two balance ranges just below the top range (8 and 9) have materially higher odds of default relative to other consumers.

Change-in-balance

Consumers with an increased balance relative to the previous year have a greater likelihood of default, consistently for all six segments, as indicated by statistically significant, positive estimated coefficients. Reduced balance relative to the year before is statistically significant for three segments: the two subprime segments and the middle risk score segment of consumers with a mortgage. In these cases, a reduced balance is associated with a lower likelihood of default.

Other risk factors

Individuals with an additional card relative to a year before (New_Card = 1) have an increased likelihood of default. Based on the estimated odds ratios, having an additional card is associated with an 8% increase in the odds of default for the low risk score segment of borrowers without a mortgage, and at least a 20% increase in the odds of default for the other segments.

Consistent with our expectation that neighborhood per capita income is a proxy for household income, and that higher-income households are more financially stable, the estimated coefficients of census tract per capita income are significantly negative for all six segments. Consumers are more likely to default on their credit card if they live in a lower-income neighborhood, all else being equal.

The estimated coefficients on percent change in home values when values are declining are significantly positive for all six segments. The corresponding odds ratios indicate a larger impact on the odds of default for consumers with a mortgage versus those without.

The estimated coefficients on percentage change in home values in rising home price environments are significantly negative for the four low or middle risk score segments, consistent with rising home values signifying generally positive economic conditions. Again, the corresponding odds ratios indicate a greater impact on the odds of default for consumers with a mortgage.2626 26 For the high risk score segment of consumers without a mortgage, the estimated coefficient on percent change in home values in rising home price environments is positive and statistically significant, consistent with an impact of rising rental expenses, although the corresponding estimated odds ratio indicates that the magnitude of the effect is small.

Finally, as expected, we find that in all risk segments, the likelihood of card default increases with a rise in state-level unemployment claims. The estimated odds ratios indicate a modest but material association; for instance, an estimated odds ratio of 1.003, as is observed for several segments, implies that a doubling of claims increases the odds of default by about 35%.

5.2 Analysis of in-sample and out-of-sample model fit

Table 5 reports in-sample (March 1, 2000 through December 1, 2007) and out-of-sample (March 1, 2008 through September 1, 2013) C-statistics for each of the estimated equations. As with our previous look at quarterly default roll rates (see Figure 2), we report C-statistics two ways: with and without balance weighting.

Table 5: In-sample and out-of-sample C-statistics for the segment-level regression equations. [Source: FRBNY Equifax CCP and United States Census Bureau.]
  Without mortgage With mortgage
     
    ???     ???  
  Risk score risk score Risk score Risk score risk score Risk score
  <??? ??? >??? >??? ??? >???
Number of observations 861 978 1 495 94 2 324 370 241 111 811 184 2 059 367
C-statistic (in-sample unweighted) 0.67 0.731 0.751 0.657 0.727 0.751
C-statistic (in-sample weighted) 0.667 0.724 0.729 0.653 0.719 0.733
C-statistic (out-of-sample unweighted) 0.67 0.718 0.81 0.658 0.718 0.846
C-statistic (out-of-sample weighted) 0.663 0.708 0.787 0.653 0.71 0.833

The in-sample C-statistics reported in Table 5 indicate that, despite the limitation of having no information about the consumer other than what can be assembled from the FRBNY Equifax CCP, the model differentiates risk within the development data fairly well. The equations are more informative for the middle and upper risk score ranges than for the lower range, based on a comparison of the C-statistics across segments; this is consistent with the occurrence of default being more idiosyncratic among individuals with lower risk scores.

Because the model is estimated unweighted, the balance-weighted C-statistics, both in-sample and out-of-sample, are only marginally smaller than the corresponding unweighted C-statistics. Thus, the dummy variables for balance range adequately capture differences in default roll rate patterns in relation to a consumer’s total card balance.

The C-statistics for the out-of-sample fit of the model are larger than the in-sample C-statistics for the high risk score segments, and equal to or slightly smaller than the corresponding in-sample C-statistics for the other segments. Thus, the model’s ability to differentiate (rank order) default probabilities remains strong out-of-sample, indicating that for the purpose of “scoring” consumer default risk, the model is quite robust.

Visual analysis of model fit

We further explore model fit by dividing each risk score segment into low-balance and high-balance ranges based on its 2007 mean balance, as was done previously for Figure 3(b), and plotting quarterly actual (observed) roll rates by segment. Figure 7(a)–(f) provides these visual comparisons for the six segments, respectively, over the full period comprising the quarterly cohorts from March 1, 2000 through December 1, 2013.

Observed versus fitted default rates: balance-weighted. (a) High risk score, high-balance segment. (b) Medium risk score, high-balance segment. (c) Low risk score, high-balance segment. Source: FRBNY Equifax CCP. Continued. (d) High risk score, low-balance segment. (e) Medium risk score, low-balance segment. (f) Low risk score, low-balance segment. Source: FRBNY Equifax CCP.
Figure 7: Observed versus fitted default rates: balance-weighted. (a) High risk score, high-balance segment. (b) Medium risk score, high-balance segment. (c) Low risk score, high-balance segment. (d) High risk score, low-balance segment. (e) Medium risk score, low-balance segment. (f) Low risk score, low-balance segment. Source: FRBNY Equifax CCP.

The actual and fitted roll-rates from nondelinquent to default shown in Figure 7 are balance weighted.2727 27 Thus, the observed default rate at time t is the ratio of total balances as of quarter t of all individuals who transition from current to delinquent (who have no delinquent accounts at t and at least one seriously delinquent account at t+1) to total card balances as of quarter t of all individuals who are current at t. The fitted (predicted) default rate for quarter t is the weighted sum of the probabilites of all individuals who are current at t of transitioning from current to delinquent, such that individuals are weighted by their total bankcard balance as of quarter t. Very similar patterns are observed for individual roll rates within each segment (that is, without balance weighting), although actual and fitted roll rates may together shift up or down with removal of the weighting, depending on the segment.

For our Figure 7 comparisons, we aggregate consumers with and without mortgages within each segment in order to economize on the number of visual comparisons. When we further split the sample based on whether the consumer has a mortgage, we observe qualitatively similar model fit patterns between cohorts with and without a mortgage.

In all six panels, the model’s fitted default roll rates align reasonably well with actual default roll rates during the in-sample period (March 2000 to December 2007). However, we see a marked deterioration of model fit out-of-sample. Thus, while the model is robust for purposes of rank ordering default risk, it does not succeed as a forecasting model.

Out-of-sample, beginning in 2009, the model widely underpredicts default roll rates for consumers with high risk score and high balances (Figure 7(a)). Conversely, beginning in 2008, the model markedly overpredicts default roll rates for low-balance consumers in each risk score range (Figure 7(d)–(f)) and for high-balance consumers with low risk scores (Figure 7(c)).2828 28 As previously stated, we do not observe major differences between cohorts with and without a mortgage when we further split the sample by this criterion. The most notable difference is that in each small balance range, the model more widely overpredicts 2008 and 2009 default roll rates for individuals with mortgages. In the remaining segment, comprised of high-balance consumers with risk scores in the middle range, the model moderately underpredicts default roll rates for most of 2009 and overpredicts them after 2010 (Figure 7(b)). In sum, extrapolation of the historical relationships captured by our model does not accurately predict segment-level consumer default rates through the downturn and beyond.

Combining the low-/high-balance and high risk score cohorts, we find that, with balance weighting, model fit for the high risk score segment overall resembles that observed in Figure 6(a) for the high-balance cohort; in particular, out-of-sample default roll rates are widely underpredicted beginning in 2009.2929 29 With respect to unweighted roll rates for the high risk score segment overall, the model underpredicts peak roll rates in 2008 and tends to overpredict throughout 2009 and 2010. Combining the low- and high-balance cohorts within the low and middle risk score segments, respectively, we find that the model overpredicts overall default roll rates for these segments, beginning in 2008, with or without balance weighting. This finding is consistent with previous research by Canals-Cerdá and Kerr (2015), which documents the underprediction of account-level default frequency in the prime segment during the Great Recession. We find at the consumer level that prime borrowers with large balances are the source of the underprediction.

Discussion

Investigation of the underlying reasons for the out-of-sample divergence of realized default roll rates from model predictions is outside the scope of our study, as our data is not adequate for that purpose. However, our results suggest that the out-of-sample deterioration in model fit at least in part reflects changes in consumer behavior that are unanticipated by the model.

As noted, we observe a sizable underprediction of default roll rates for the high-balance, high risk score cohort (Figure 6(a)) starting in 2009 and persisting through 2010. However, most of the run-up in first-time unemployment claims during the Great Recession occurred prior to 2009, with the one-year percent change peaking early in 2009 (Figure 5.) Thus, the deterioration in model fit does not seem entirely attributable to the model’s inability to extrapolate beyond the range of historical data with regard to rising unemployment claims.

More likely, the underprediction reflects other unprecedented effects of the Great Recession on employment or on household financial conditions, or changes in borrower behavior unanticipated by the model.3030 30 For instance, the Great Recession was characterized by an unprecedented lengthening of unemployment spells. Average duration of unemployment, which had remained below fifteen weeks during the 2001 downturn, increased from seventeen to twenty-three weeks during the Great Recession and continued to increase through the end of 2010, peaking at about forty weeks. For instance, deleveraging may help explain the persistent gap between predicted and actual roll rates in the high-balance, high risk score cohort for 2009 through 2010. That is, deleveraging (as reflected in the declining average balances in Figure 3(a)) may have generated a selection effect, such that consumers who did not deleverage were higher risk, causing balance-weighted roll rates to diverge relative to individual roll rates.

Also as noted, we observe overprediction of default roll rates for the low-balance segments, which is immediate in 2008. As such, this overprediction commences well before the rise in first-time unemployment claims for the low-balance cohorts had exceeded historical experience. Thus, again, the inaccurate fit of the model cannot be attributed to the rise in unemployment claims being outside the range of historical experience. Rather, the deterioration in model fit seems attributable to unanticipated aspects of borrower behavior.

6 Empirical results: exposure-at-default and probability of charge-off

We briefly examine the two other components of the EL ratio in equation (3.2). These are the exposure-at-default (EAD) ratio and the probability of charge-off (PCO).

The EAD ratio is simply the fraction of a consumer’s total bankcard balance (summed across all accounts) that is associated with the defaulting account(s) when the consumer transitions from current to default. The PCO quantifies the likelihood that a consumer who has defaulted on at least one bankcard account will transition to having at least one account charged off. To simplify the analysis, we equate charge-off with an account becoming 120 days or more past due.

EAD ratio

The numerator of the EAD ratio is the consumer’s ex post total balance on defaulted bankcard accounts (immediately following the consumer’s transition from current to default). The denominator is the consumer’s ex ante total bankcard balance (immediately prior to the default transition) one quarter prior to the default event.

EAD ratio by risk score range and balance segment. (a) Low risk score range. (b) Medium risk score range. (c) High risk score range. Source: FRBNY Equifax CCP.
Figure 8: EAD ratio by risk score range and balance segment. (a) Low risk score range. (b) Medium risk score range. (c) High risk score range. Source: FRBNY Equifax CCP.

Quarterly EAD ratios by balance segment and risk score range are plotted in Figure 8 for the (a) low, (b) middle and (c) high risk score ranges.3131 31 We do not observe major differences between cohorts with and without a mortgage when we further split the sample by this criterion. We display four-quarter moving averages of the quarterly ratios to smooth out variability and help highlight patterns.

EAD ratios for the low-balance cohorts appear inversely related to risk score: they mostly range between 40% and 60% in the high risk score segment; between 60% and 75% in the middle risk score segment; and between 85% and 95% in the low risk score segment. The EAD ratios for the high-balance cohorts are more similar across risk score segments: they mostly range between 45% and 60% in the low and middle risk score segments and between 55% and 70% in the high risk score segment.

With the exception of the low-balance, high risk score cohort, EAD ratios during and after the Great Recession materially exceed pre-downturn EAD ratios (on average), and in most cases this reflects upward trends during 2000 through 2009 or 2010. To the extent that these elevated EAD ratios were tied to shifts in consumer behavior that were not anticipated by predictive models, realized EAD and losses during the Great Recession would have been larger than predicted.3232 32 In particular, lenders that simply relied on historical average EAD ratios by risk segment to quantify EAD would have underpredicted the realized EAD. Investigation of this issue is outside the scope of our study.

Charge-off and cure probabilities

Probability of (a) charge-off and (b) cure, balance weighted, by balance segment. Source: FRBNY Equifax CCP.
Figure 9: Probability of (a) charge-off and (b) cure, balance weighted, by balance segment. Source: FRBNY Equifax CCP.

A consumer who is current on all bankcard accounts in period t-1 and transitions to default (sixty or more days past due on at least one account) in period t may subsequently transition to charge-off (become 120 or more days past due on at least one account) or to cure from default (return to being current on all accounts), or they may remain in default (transition to neither cure nor charge-off). Quarterly balance-weighted rates of charge-off and cure by balance segment, conditional on having transitioned to default over the preceding quarter, are plotted in Figure 9 in parts (a) and (b), respectively.3333 33 We weight by the consumer’s total ex ante, bankcard balance. We do not observe major differences by risk score range or between cohorts with and without a mortgage when we further split the sample by these criteria. The case of neither cure nor charge-off is relatively infrequent (as can be inferred from summing the quarterly charge-off and cure rates) and therefore is not plotted. These are calculated by observing the status of the loans (whether charged-off or cured) both in the following quarter and (since not all defaults are resolved within one quarter) as of four quarters forward.

We find that the high-balance segment is characterized by a higher PCO and lower probability of cure compared with the low-balance segment, although for both segments charge-off is consistently the more likely outcome. During 2006 through 2008, charge-off rates trended up while cure rates declined, leading to substantially higher charge-off rates.

Consequently, charge-off rates were materially higher (and cure rates lower) during 2008 through 2010 than before 2006. To the extent that the increased charge-off rates were tied to shifts in consumer behavior that were not incorporated into predictive models prior to 2008, realized losses during the Great Recession would have been larger than predicted.3434 34 In particular, lenders that simply relied on historical average EAD ratios by risk segment to quantify EAD would have underpredicted the realized EAD. Again, investigation of this issue is outside the scope of our study.

7 Conclusions

This paper offers a “deep dive” examination of consumer default on credit card debt during the Great Recession. We estimate a model that provides the best in-sample predictions of default for prime and below-prime customers, using all available relevant data from March 2000 to March 2008. The model fits the data very well in-sample but fails to accurately predict card defaults out-of-sample during the Great Recession period (2008–13). Default rates during the Great Recession are markedly underpredicted for the subset of prime consumers carrying large credit card balances, whose share of total bankcard balances grew substantially prior to the Great Recession.

Although the analysis does not provide direct evidence that lenders overextended card credit during the pre-downturn period, we suspect that the pre-downturn expansion of credit could have been excessive in the sense of underweighting risks associated with prime borrowers. This is a typical model risk associated with use of historical data from a period of economic expansion when credit lines and outstanding balances increased to historically unprecedented levels. The historical data provided little insight into how borrowers would perform under severe downturn conditions. This experience highlights the importance of identifying and managing model risk, particularly when venturing into “uncharted territory”, as was the case in the credit boom prior to the Great Recession.

Another inference we can draw from the analysis is that lenders’ losses during the Great Recession would have been significantly larger if the repayment performance of subprime borrowers had aligned with extrapolations based on historical performance data. We find that default rates are overpredicted for all low-balance borrowers, whether they are subprime, near-prime or prime, and for all subprime borrowers.

We also identify a long-term behavioral trend for the EAD ratio: the ratio of delinquent to lagged nondelinquent balances of borrowers transitioning to serious delinquency. Average EAD ratios by risk segment increased continually from 2000 through 2009, implying that for consumers who defaulted there was a higher share of defaulted balances relative to total card balances. This contributed to elevated loss rates during the downturn. The reasons for this behavioral shift merit further investigation that is beyond the scope of this study.

Declaration of interest

The views expressed here do not necessarily represent those of the Federal Reserve Bank of Philadelphia, the Federal Reserve Bank of Cleveland, or the Federal Reserve System.

Acknowledgements

Paul Calem participated in this research in his prior position at the Federal Reserve Bank of Philadelphia. We thank Quinn Maingi and Erik Dolson for their dedicated research assistance. Thanks also to Ron Borzekowski, Kenneth Brevoort and participants at the CFPB seminar.

References

  • Acharya, V., Philippon, T., Richardson, M., and Roubini, N. (2009). Prologue: a bird’s-eye view. The financial crisis of 2007–2009: causes and remedies. Financial Markets, Institutions, and Instruments 18(2), 89–137 (https://doi.org/10.1111/j.1468-0416.2009.00147_2.x).
  • Agarwal, S., and Zhang, J. (2015). A review of credit card literature: perspectives from consumers. Report, UK Financial Conduct Authority. URL: https://bit.ly/2TWt0v1.
  • Ash, D., Kelly, S., Lang, W., Nayda, W., and Yin, H. (2007). Segmentation, probability of default and Basel II capital measures for credit card portfolios. Working Paper, August, Federal Reserve Bank of Philadelphia.
  • Bellotti, T., and Crook, J. (2009). Credit scoring with macroeconomic variables using survival analysis. Journal of the Operational Research Society 60(12), 1699–1707 (https://doi.org/10.1057/jors.2008.130).
  • Bellotti, T., and Crook, J. (2012). Loss given default models incorporating macroeconomic variables for credit cards. International Journal of Forecasting 28, 171–182 (https://doi.org/10.1016/j.ijforecast.2010.08.005).
  • Bellotti, T., and Crook, J. (2013). Forecasting and stress testing credit card default using dynamic models. International Journal of Forecasting 29, 563–574 (https://doi.org/10.1016/j.ijforecast.2013.04.003).
  • Calem, P., and Mester, L. J. (1995). Consumer behavior and the stickiness of credit-card interest rates. American Economic Review 85(5), 1327–1336.
  • Calem, P., Gordy, M., and Mester, L. J. (2006). Switching costs and adverse selection in the market for credit cards: new evidence. Journal of Banking and Finance 30(6), 1653–1685 (https://doi.org/10.1016/j.jbankfin.2005.09.012).
  • Canals-Cerdá, J., and Kerr, S. (2015). Forecasting credit card losses in the Great Recession: a study in model risk. The Journal of Credit Risk 11(1), 29–57 (https://doi.org/10.21314/JCR.2015.187).
  • Dermine, J., and de Carvalho, C. N. (2006). Bank loan losses-given-default: a case study. Journal of Banking and Finance 30, 1219–1243 (https://doi.org/10.1016/j.jbankfin.2005.05.005).
  • Gross, D. B., and Souleles, N. S. (2002). Do liquidity constraints and interest rates matter for consumer behavior? Evidence from credit card data. Quarterly Journal of Economics 17(1), 149–185 (https://doi.org/10.1162/003355302753399472).
  • Kerr, S., and Dunn, L. (2008). Consumer search behavior in the changing credit card market. Journal of Business and Economic Statistics 26, 345–353 (https://doi.org/10.1198/073500107000000133).
  • Laderman, E. (1996). What’s behind problem credit card loans? Economic Letter 96-21, July, Federal Reserve Bank of San Francisco.
  • Mian, A., and Sufi, A. (2014). House of Debt: How They (and You) Caused the Great Recession, and How We Can Prevent It from Happening Again. Chicago University Press (https://doi.org/10.7208/chicago/9780226277509.001.0001).
  • Santucci, L. (2016). What happened to the revolving credit card balances of 2009? Discussion Paper 16-01, Federal Reserve Bank of Philadelphia.
  • Wardrip, K., and Hunt, R. (2013). Residential migration, entry, and exit as seen through the lens of credit bureau data. Discussion Paper, Payment Cards Center, Federal Reserve Bank of Philadelphia (https://doi.org/10.2139/ssrn.2365794).

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