The Review of Financial Studies/v 26 n 9 2013 Descriptive statistics Mean Median tatement balance(E) 633 Debt(E 615.6 Interest rate(%) Income(E) 0.26604 15,910 41.0 Hom No other card (%) ation(November 2007). The total number of individuals is 39, 883. variables edit limit, interest rates, self-reported income, and age. The table also reports the mposition of the sample in terms of marital and employment status, home ownershi in February 2008. We have data until May 2008, so we can measure the effect of interest rate changes over the three months following the implementation, that is, from February to April 2008. We lose one month because of lagging for the construction of our outcome variables The experimental sample was not chosen from the lender's full client base Accounts that are flagged for reasons such as default, several months of delinquency, or inactivity are excluded before the selection of the sample. Furthermore the lender excluded individuals who have been with the lender for less than seven months at the time of the design. Table 1 presents the characteristics of the individuals in the sample at the time of the randomization (November 2007) The median income reported at the time of application is f15, 500. Given that the median individual income for the United Kingdom is about f19,000 individuals in our sample represent the lower end of the income distribution The average monthly utilization rate, defined as outstanding monthly balance divided by the credit limit, is about 79.4%o with the median value of 94.8%. The average utilization rate for all U.K. credit card borrowers is approximately 34%(see the Data monitor[2008]report). Interest rates and credit limits are the two other variables highlighting the differences between our average borrower versus the average U. K. borrower. The mean(median) interest rate is 30.9% 30.0% pa). These interest rates are significantly higher than the rates on typical U.K. credit cards(approximately 15%0-18% pa). The mean(median) credit limit is f1, 082(f1, 000), which is much lower than the average U. K credit card limit of f5. 129 in 2007 As Table I shows, the average monthly purchase value is about 576 with the median value of fo. It is worth drawing attention to the size of revolving debt in the table. This figure is calculated as the balance appearing on the 2358 Downloadedfromhttps://academic.oupcam/rfs/article-abstract/26/9/2353/166253
[16:30 29/7/2013 RFS-hht029.tex] Page: 2358 2353–2374 The Review of Financial Studies / v 26 n 9 2013 Table 1 Descriptive statistics Mean Median SD Utilization rate (%) 79.4 94.8 33.4 Statement balance (£) 848.7 726.6 633.4 Debt (£) 743.2 628.5 615.6 New transactions (£) 76.1 0.0 182.4 Credit limit (£) 1,182 1,000 796.8 Interest rate (%) 30.9 30.0 2.3 Income (£) 17,866 15,500 15,910 Age 42.1 41.0 11.8 Married (%) 56 – – Employed (%) 63 – – Self employed (%) 10 – – Home owner (%) 34 – – No other card (%) 42 – – The table presents the descriptive statistics of the individuals in the sample at the time of the randomization (November 2007). The total number of individuals is 39,883. Variables include utilization rate, statement balance, outstanding credit card debt, new transactions, credit limit, interest rates, self-reported income, and age. The table also reports the composition of the sample in terms of marital and employment status, home ownership, and ownership of other credit cards. in February 2008. We have data until May 2008, so we can measure the effect of interest rate changes over the three months following the implementation, that is, from February to April 2008. We lose one month because of lagging for the construction of our outcome variables. The experimental sample was not chosen from the lender’s full client base. Accounts that are flagged for reasons such as default, several months of delinquency, or inactivity are excluded before the selection of the sample. Furthermore, the lender excluded individuals who have been with the lender for less than seven months at the time of the design. Table 1 presents the characteristics of the individuals in the sample at the time of the randomization (November 2007). The median income reported at the time of application is £15,500. Given that the median individual income for the United Kingdom is about £19,000, individuals in our sample represent the lower end of the income distribution. The average monthly utilization rate, defined as outstanding monthly balance divided by the credit limit, is about 79.4% with the median value of 94.8%. The average utilization rate for all U.K. credit card borrowers is approximately 34% (see the Data monitor [2008] report). Interest rates and credit limits are the two other variables highlighting the differences between our average borrower versus the average U.K. borrower. The mean (median) interest rate is 30.9% pa (30.0% pa). These interest rates are significantly higher than the rates on typical U.K. credit cards (approximately 15%–18% pa). The mean (median) credit limit is £1,082 (£1,000), which is much lower than the average U.K. credit card limit of £5,129 in 2007. As Table 1 shows, the average monthly purchase value is about £76 with the median value of £0. It is worth drawing attention to the size of revolving debt in the table. This figure is calculated as the balance appearing on the 2358 Downloaded from https://academic.oup.com/rfs/article-abstract/26/9/2353/1662534 by Fudan University user on 14 December 2017
Subprime Consumer Credit Demand November 2007 statement minus the payments made toward that balance in the following month(December 2007). This is the debt revolved from November to December, to which the interest charge is applied. The mean revolving debt in November 2007 is approximately f743, with the median value of 5628. This is quite a large figure given a monthly interest rate of about 2.5%o. It is clear that a significant portion of the individuals in our data set use their card for borrowing purposes. To be precise, approximately 81% of the individuals in our sample revolved debt every month between November 2007 and April 2008 2.1 Experimental design erhaps the most intriguing feature of our data is that the lender had changed Its clients interest rates through randomized trials since 2006. They carried out the randomization as a block design in which a sample of individuals were assigned to blocks(cells, henceforth) defined by the interaction of utilization rates and an internally developed behavior score that summarizes individuals,risk characteristics. Individuals were allocated into cells according to their utilization rates and behavioral scores as of november 2007. After the allocation, the randomization was performed within cells. Such designs well known in the statistical, medical, and experimental economics literatures Simple randomization to treatment and controls is rarely employed in real randomized control trials for a number of reasons. For example, block designs reduce the variance of the experimental estimates(see, e.g., List, Sadoff, and Wagner[2011]or Duflo, Glennerster, and Kremer [2006]). This design implies that within cells, there is no selection problem, and conditional on cells, interest rate changes are exogenous o Table 2 presents the cell design, the sample sizes of each cell, and the number of individuals allocated into the treatment and control groups. In each cell, individuals in the treatment group(approximately 93.5% of the individuals) received a five percentage point increase in interest rates. For example, cell 1 contains individuals who had high utilization rates and low behavior scores high default risk) in November 2007. In this cell, 4, 319 individuals were allocated in the treatment group, whereas 280 individuals were in the control group. Similarly, cell 9 contains individuals who had low utilization rates and high behavior score(low default risk). In this cell, 4,030 individuals received a five percentage point increase in interest rates, whereas 276 individuals were in the control group. Note that the control size is quite small. However, as we show and discuss in the results section, these data give us a reasonable statistical power to estimate the economically significant impact. Note also that a 50 /50 llocation to treatment and control is not necessary and in general not optimal (see List, Sadoff, and Wagner 2011). For cells 2, 3, 5, and 6, the lender did 8 Internally developed credit scoring systems eatures of our lender' s scoring system, but we were informed practice for credit card issuers. We do not know the exact ed that it is a continously updated, multivariate orithm Downloadedfromhttps://academic.oupcam/rfs/article-abstract/26/9/2353/166253
[16:30 29/7/2013 RFS-hht029.tex] Page: 2359 2353–2374 Subprime Consumer Credit Demand November 2007 statement minus the payments made toward that balance in the following month (December 2007). This is the debt revolved from November to December, to which the interest charge is applied. The mean revolving debt in November 2007 is approximately £743, with the median value of £628. This is quite a large figure given a monthly interest rate of about 2.5%. It is clear that a significant portion of the individuals in our data set use their card for borrowing purposes. To be precise, approximately 81% of the individuals in our sample revolved debt every month between November 2007 and April 2008. 2.1 Experimental design Perhaps the most intriguing feature of our data is that the lender had changed its clients’ interest rates through randomized trials since 2006. They carried out the randomization as a block design in which a sample of individuals were assigned to blocks (cells, henceforth) defined by the interaction of utilization rates and an internally developed behavior score that summarizes individuals’risk characteristics.8 Individuals were allocated into cells according to their utilization rates and behavioral scores as of November 2007. After the allocation, the randomization was performed within cells. Such designs are well known in the statistical, medical, and experimental economics literatures. Simple randomization to treatment and controls is rarely employed in real randomized control trials for a number of reasons. For example, block designs reduce the variance of the experimental estimates (see, e.g., List, Sadoff, and Wagner [2011] or Duflo, Glennerster, and Kremer [2006]). This design implies that within cells, there is no selection problem, and conditional on cells, interest rate changes are exogenous. Table 2 presents the cell design, the sample sizes of each cell, and the number of individuals allocated into the treatment and control groups. In each cell, individuals in the treatment group (approximately 93.5% of the individuals) received a five percentage point increase in interest rates. For example, cell 1 contains individuals who had high utilization rates and low behavior scores (high default risk) in November 2007. In this cell, 4,319 individuals were allocated in the treatment group, whereas 280 individuals were in the control group. Similarly, cell 9 contains individuals who had low utilization rates and high behavior score (low default risk). In this cell, 4,030 individuals received a five percentage point increase in interest rates, whereas 276 individuals were in the control group. Note that the control size is quite small. However, as we show and discuss in the results section, these data give us a reasonable statistical power to estimate the economically significant impact. Note also that a 50/50 allocation to treatment and control is not necessary and in general not optimal (see List, Sadoff, and Wagner 2011). For cells 2, 3, 5, and 6, the lender did 8 Internally developed credit scoring systems are general practice for credit card issuers. We do not know the exact features of our lender’s scoring system, but we were informed that it is a continously updated, multivariateprobit-type algorithm. 2359 Downloaded from https://academic.oup.com/rfs/article-abstract/26/9/2353/1662534 by Fudan University user on 14 December 2017
The Review of Financial Studies /v 26 n 2013 LL1CELL T=5pp T=5p T=5pp igh #C=2804C=573#C=95 CELL 2 CELLS T=3.252 #C=0 CELL3 CELL6 CELL 9 137#=1,065#T=4030 C=0 #C=276 vior Score(Bscore cell design of the experiment, the sample sizes of each cell, and the numbere tis deont (r)and control( C)groups. The lender classifies individuals according the clients riskiness(low, medium, or high) and their redit cards(low, medium, or high). In each cell, individuals in the treatment group(approximatel individuals)received a five percentage point in not allocate individuals to a control group, making them unavailable for our purposes 2.2 Implementation Unlike studies using randomized field experiments(mainly in development economics), we were not involved in the design orimplementation of the experi- ment on which our analysis is based. Although randomized experiments are now standard practice among credit card companies and they have every incentive to implement them correctly, we need to make sure that the randomization was carried out properly to ensure the internal validity of our results. We perform mean equality tests on a range of variables including,our outcome variable. These tests are carried out using the variables measured in November 2007(the date of the randomization). Table 3 presents the means of tested variables for the treated and control. The p-values obtained from mean equality tests are displayed in parentheses. As shown in the table, we could not detect any statistically significant difference between the treated and control groups in any cell(as would be expected when randomization is carried out Even though the randomization was carried out properly, there may be ther challenges to the internal validity of our experimental estimates. Sample attrition, for example, would be of particular concern if it were caused by the treatment. This could happen if the treatment initiated delinquency nd eventually default, making the remaining treatment sample no longer comparable to the control sample(a dynamic selection problem). If the treatment caused some accounts to be charged off, our treatment effect estimates may be biased toward finding insensitivity to interest rates. Alternatively, if the 2360 Downloadedfromhttps://academic.oupcam/rfs/article-abstract/26/9/2353/166253
[16:30 29/7/2013 RFS-hht029.tex] Page: 2360 2353–2374 The Review of Financial Studies / v 26 n 9 2013 Table 2 Descriptive statistics 100% Utilization Rate CELL 1 CELL 4 CELL 7 High T= 5pp T= 5pp T= 5pp #T= 4319 #T= 8,072 #T= 14,418 #C= 280 #C= 573 #C= 995 Mid CELL 2 CELL 5 CELL 8 T= 5pp T= 5pp T= 5pp #T= 281 #T= 3,252 #T= 6469 #C= 0 #C= 0 #C= 451 Low CELL 3 CELL 6 CELL 9 T= 5pp T= 5pp T= 5pp #T= 137 #T= 1,065 #T= 4,030 #C= 0 #C= 0 #C= 276 0 Low Mid High Behavior Score (Bscore) The matrix presents the cell design of the experiment, the sample sizes of each cell, and the number of individuals allocated into the treatment (T) and control (C) groups. The lender classifies individuals according to a behavior score (Bscore) that is designed to measure the client’s riskiness (low, medium, or high) and their utilization of credit cards (low, medium,or high). In each cell, individuals in the treatment group (approximately 93.5% of the individuals) received a five percentage point increase in interest rates (T= 5pp). not allocate individuals to a control group, making them unavailable for our purposes. 2.2 Implementation Unlike studies using randomized field experiments (mainly in development economics), we were not involved in the design or implementation of the experiment on which our analysis is based.Although randomized experiments are now standard practice among credit card companies and they have every incentive to implement them correctly, we need to make sure that the randomization was carried out properly to ensure the internal validity of our results. We perform mean equality tests on a range of variables including, our outcome variable. These tests are carried out using the variables measured in November 2007 (the date of the randomization). Table 3 presents the means of tested variables for the treated and control. The p-values obtained from mean equality tests are displayed in parentheses. As shown in the table, we could not detect any statistically significant difference between the treated and control groups in any cell (as would be expected when randomization is carried out correctly). Even though the randomization was carried out properly, there may be other challenges to the internal validity of our experimental estimates. Sample attrition, for example, would be of particular concern if it were caused by the treatment. This could happen if the treatment initiated delinquency and eventually default, making the remaining treatment sample no longer comparable to the control sample (a dynamic selection problem). If the treatment caused some accounts to be charged off, our treatment effect estimates may be biased toward finding insensitivity to interest rates. Alternatively, if the 2360 Downloaded from https://academic.oup.com/rfs/article-abstract/26/9/2353/1662534 by Fudan University user on 14 December 2017