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The Quarterly Journal of Economics
, Volume 133 (1) – Feb 1, 2018

62 pages

/lp/ou_press/do-banks-pass-through-credit-expansions-to-consumers-who-want-to-WfAS1TVwR6

- Publisher
- Oxford University Press
- Copyright
- Published by Oxford University Press on behalf of the President and Fellows of Harvard College 2017.
- ISSN
- 0033-5533
- eISSN
- 1531-4650
- D.O.I.
- 10.1093/qje/qjx027
- Publisher site
- See Article on Publisher Site

Abstract We propose a new approach to studying the pass-through of credit expansion policies that focuses on frictions, such as asymmetric information, that arise in the interaction between banks and borrowers. We decompose the effect of changes in banks’ cost of funds on aggregate borrowing into the product of banks’ marginal propensity to lend (MPL) to borrowers and those borrowers’ marginal propensity to borrow (MPB), aggregated over all borrowers in the economy. We apply our framework by estimating heterogeneous MPBs and MPLs in the U.S. credit card market. Using panel data on 8.5 million credit cards and 743 credit limit regression discontinuities, we find that the MPB is declining in credit score, falling from 59% for consumers with FICO scores below 660 to essentially zero for consumers with FICO scores above 740. We use a simple model of optimal credit limits to show that a bank’s MPL depends on a small number of parameters that can be estimated using our credit limit discontinuities. For the lowest FICO score consumers, higher credit limits sharply reduce profits from lending, limiting banks’ optimal MPL to these consumers. The negative correlation between MPB and MPL reduces the impact of changes in banks’ cost of funds on aggregate household borrowing, and highlights the importance of frictions in bank-borrower interactions for understanding the pass-through of credit expansions. JEL Codes: D14, E51, G21. I. Introduction During the Great Recession, policy makers sought to stimulate the economy by providing banks with lower-cost capital and liquidity. One goal was to encourage banks to expand credit to households and firms that would, in turn, increase their borrowing, spending, and investment.1 Yet empirically analyzing the strength of this “bank lending channel” is challenging. For example, there was a large drop in U.S. banks’ cost of funds in the fall of 2008, when the Federal Funds Rate was cut to zero in response to the financial crisis. However, this was exactly the period when lenders and borrowers were updating their expectations about the economy, making it practically impossible to use time-series analysis to isolate the effect of the change in monetary policy on borrowing volumes. In this article, we propose a new empirical approach to studying the bank lending channel that focuses on frictions, such as asymmetric information, that arise in bank-borrower interactions. Our approach is based on the observation that the effect on aggregate borrowing of a change in banks’ (shadow) cost of funds—for example, due to an easing of monetary policy, a reduction in capital requirements, or a market intervention that reduces financial frictions—can be expressed as a function of the supply and demand for credit by different agents in the economy. This approach is empirically useful because it allows us to quantify the pass-through of credit expansion policies by decomposing the overall effect into objects that can be estimated using micro-data on lending and quasi-exogenous variation in contract terms. This approach is also conceptually useful because understanding the relative importance of these supply and demand factors is independently important for designing effective policies. We apply our framework to the U.S. credit card market. As we discuss below, in this market credit limits are a key determinant of credit supply and the primary margin of adjustment to changes in the cost of funds. Let c denote the banks’ cost of funds, CLi the credit limit of consumer i, and qi the borrowing of that consumer. The effect of a change in c on total borrowing q can be expressed as the product of banks’ marginal propensity to lend (MPL) to consumer i and that consumer’s marginal propensity to borrow (MPB), aggregated across all the consumers in the economy: \begin{equation} - \frac{ d q}{d c} = \int _i \quad \underbrace{-\frac{d CL_i}{d c}}_{\text{MPL}} \times \underbrace{\frac{d q_i}{d CL}_i}_{\text{MPB}}. \end{equation} (1)We operationalize our framework by estimating heterogeneous MPBs and MPLs using panel data on all credit cards issued by the eight largest U.S. banks. These data, assembled by the Office of the Comptroller of the Currency (OCC), provide us with monthly account-level information on contract terms, utilization, payments, and costs for more than 400 million credit card accounts between January 2008 and December 2014. The data are merged with credit bureau information, allowing us to track balances across consumers’ broader unsecured credit portfolios. Our research design exploits the fact that banks sometimes set credit limits as discontinuous functions of consumers’ FICO credit scores. For example, a bank might grant a $${\$}$$2,000 credit limit to consumers with a FICO score below 720 and a $${\$}$$5,000 credit limit to consumers with a FICO score of 720 or above. We show that other borrower and contract characteristics trend smoothly through these cutoffs, allowing us to use a regression discontinuity strategy to identify the causal impact of providing extra credit at prevailing interest rates. We identify a total of 743 credit limit discontinuities in our data, which are distributed across the range of the FICO score distribution. We observe 8.5 million new credit cards issued to borrowers within 50 FICO score points of a cutoff. Using this regression discontinuity design, we estimate substantial heterogeneity in MPBs across the FICO score distribution. For the least credit-worthy consumers (FICO ≤ 660), a $${\$}$$1 increase in credit limits raises borrowing volumes on the treated credit card by 58 cents at 12 months after origination. This effect is due to increased spending and is not explained by a shifting of borrowing across credit cards. For the highest FICO score consumers (>740), we estimate a 23% effect on the treated card that is entirely explained by a shifting of borrowing across credit cards, with an increase in credit limits having no effect on total borrowing. We next analyze how banks pass through credit expansions to different consumers. As discussed above, estimating the MPL directly using observed changes in the cost of funds is challenging, because such changes are typically correlated with shifts in the economic environment that also affect borrowing and lending decisions. We use economic theory and our quasi-exogenous variation in credit limits to address this identification problem. In particular, we write down a simple model of optimal credit limits to show that a bank’s MPL depends on a small number of “sufficient statistics” that can be estimated directly using our regression discontinuities. Our approach involves a trade-off. To avoid the standard identification problem, we need to assume that banks respond optimally to changes in the cost of funds and that we can measure the incentives faced by banks. We think both assumptions are reasonable: credit card lending is highly sophisticated and our estimates of bank incentives are fairly precise. Indeed, we show that observed credit limits are close to the optimal credit limits implied by the model. In our model, banks set credit limits at the level where the marginal profit from a further increase in credit limits is zero. A decrease in banks’ cost of funds reduces the cost of extending a given unit of credit and corresponds to an outward shift in the marginal profit curve. As shown in Figure I, a reduction in the cost of funds has a larger effect on optimal credit limits when the marginal profit curve is relatively flat (Panel A) than when it is relatively steep (Panel B). Figure I View largeDownload slide Pass-Through of Reduction in Cost of Funds into Credit Limits Figure shows marginal profits for lending to observationally identical borrowers. A reduction in the cost of funds shifts the marginal profit curve outward, and raises equilibrium credit limits (CL* → CL**). Panel A considers a case with a relatively flat marginal profit curve; Panel B considers a case with a steeper marginal profit curve. The vertical axis is divided by the MPB because a given decrease in the cost of funds induces a larger shift in marginal profits when credit card holders borrow more on the margin. See Section VI for more details. Figure I View largeDownload slide Pass-Through of Reduction in Cost of Funds into Credit Limits Figure shows marginal profits for lending to observationally identical borrowers. A reduction in the cost of funds shifts the marginal profit curve outward, and raises equilibrium credit limits (CL* → CL**). Panel A considers a case with a relatively flat marginal profit curve; Panel B considers a case with a steeper marginal profit curve. The vertical axis is divided by the MPB because a given decrease in the cost of funds induces a larger shift in marginal profits when credit card holders borrow more on the margin. See Section VI for more details. What are the economic forces that determine the slope of marginal profits? One important factor is the degree of adverse selection. With adverse selection, higher credit limits are disproportionately taken up by consumers with higher probabilities of default. These higher default rates lower the marginal profit of lending, thereby generating more steeply downward-sloping marginal profits. Higher credit limits can also lower marginal profits holding the distribution of marginal borrowers fixed. For example, if higher debt levels have a causal effect on the probability of default—as they do, for example, in the strategic bankruptcy model of Fay, Hurst, and White (2002)—then higher credit limits, which increase debt levels, will also raise default rates. As before, this lowers the marginal profit of lending, generating more steeply downward-sloping marginal profits.2 The effect of these (and other) frictions in the bank-borrower relationship on the pass-through of credit expansions is fully captured by the slope of the marginal profit curve. Indeed, by estimating this slope, we can quantify the pass-through of credit expansion policies without requiring strong assumptions on the underlying micro-foundations of consumer behavior. This approach of estimating sufficient statistics rather than model-dependent structural parameters builds on approaches that are increasingly popular in the public finance literature (see Chetty 2009). How do we estimate the slope of marginal profits? Conceptually, each quasi-experiment provides us with two moments at the prevailing credit limit: marginal profits, which can be estimated using our regression discontinuities, and average profits, which can be directly observed in our data and which correspond to the area under the marginal profit curve in Figure I. With these two moments, we can identify any two-parameter curve for marginal profits. Intuitively, for a given credit limit, larger average profits correspond to a steeper slope of the marginal profit curve. To obtain quantitative estimates of the MPL, we parameterize the marginal profit curve using a linear functional form. We find that marginal profits are most steeply downward-sloping for consumers with the lowest FICO scores, consistent with significant asymmetric information in this segment of the population. Consequently, a one percentage point reduction in the cost of funds increases optimal credit limits by $${\$}$$253 for borrowers with FICO scores below 660, compared with $${\$}$$1,224 for borrowers with FICO scores above 740. While these precise estimates rely on our linear functional form assumption, we prove that, given the moments in our data, our finding of larger pass-through to higher FICO score borrowers is qualitatively robust to any functional form that satisfies an appropriately defined single-crossing condition. Taken together, our estimates imply that MPBs and MPLs are negatively correlated across consumers. This negative correlation is economically significant. Suppose one incorrectly calculated the impact of a decrease in the shadow cost of funds as the product of the average MPL and the average MPB in the population. This would generate an estimate of the effect on total borrowing that is approximately twice as large as an estimate that accounts for this correlation. We view our article as making three contributions. First, our article builds on a literature that has estimated marginal propensities to consume (MPCs) and MPBs using shocks to income and liquidity. Our finding of substantial heterogeneity in MPBs by FICO score complements recent papers by Parker et al. (2013) and Jappelli and Pistaferri (2014) that have shown substantial heterogeneity in MPCs out of income shocks, and recent work by Mian and Sufi (2011) and Mian, Rao, and Sufi (2013), who have shown substantial heterogeneity in MPCs out of shocks to housing prices and wealth. Most closely related are Gross and Souleles (2002), who estimate MPBs using time-series variation in credit limits but do not have the power to identify heterogeneous effects, and Aydin (2017), who estimates MPBs using a credit limit experiment in Turkey.3 We advance this literature by providing the first joint estimates of consumers’ MPBs and banks’ MPLs. Estimating both objects together is important because it allows for an evaluation of credit expansion policies that are intermediated by banks. We show that the interaction between MBPs and MPLs across different types of consumers is key to understanding the aggregate impact of these policies.4 Second, our approach to estimating banks’ MPLs highlights the importance of frictions in bank-borrower interactions—such as asymmetric information—in determining the strength of the bank lending channel. This complements research on how variation in capital and liquidity levels or risk across banks mediates the strength of the bank lending channel (see, among others, Kashyap and Stein 1994; Kishan and Opiela 2000; Jiménez et al. 2012, 2014; Acharya et al. 2015; Dell’Ariccia, Laeven, and Suarez 2016).5 In our model, forces like liquidity levels affect banks’ shadow cost of funds, c, and are therefore conceptually separable from the bank-borrower interactions that we focus on. Third, our article contributes to a literature that has identified declining household borrowing volumes as a proximate cause of the Great Recession.6 Within this literature, there is considerable debate over the relative importance of supply versus demand factors in explaining the reduction in aggregate borrowing. Our estimates suggest that both explanations have merit, with credit supply being the limiting factor at the bottom of the FICO score distribution and credit demand being the limiting factor at higher FICO scores. There are a number of caveats for using our estimates to obtain a complete picture of the effectiveness of monetary policy during the Great Recession. First, we only study one market. While the credit card market is of stand-alone interest because credit cards are the marginal source of credit for many U.S. households, other markets, such as mortgage lending and small-business lending, are probably more important channels for monetary policy transmission.7 However, we think that our finding of lower pass-through to less creditworthy borrowers—for example, because of asymmetric information—is likely to apply across this broader set of markets, all of which feature significant potential for adverse selection and moral hazard.8 A second caveat is that our article does not assess the desirability of stimulating household borrowing from a macroeconomic stability or welfare perspective. For example, while extending credit to low FICO score households might lead to more borrowing and consumption in the short run, we do not evaluate the consequences of the resulting increase in household leverage. Our results also do not capture general equilibrium effects that might arise from the increased spending of low-FICO-score households. The rest of the article proceeds as follows. Section II presents background information on the determinants of credit limits and describes our credit card data. Section III discusses our regression discontinuity research design. Section IV verifies the validity of this research design. Section V presents our estimates of the marginal propensity to borrow. Section VI provides a model of credit limits. Section VII presents our estimates of the marginal propensity to lend. Section VIII concludes. II. Background and Data Our research design exploits quasi-random variation in the credit limits set by credit card lenders (see Section III). In this section, we describe the process by which banks determine these credit limits and introduce the data we use in our empirical analysis. We then describe our process for identifying credit limit discontinuities and present summary statistics on our sample of quasi-experiments. II.A. How Do Banks Set Credit Limits? Most credit card lenders use credit-scoring models (also called “scorecards”) to make their pricing and lending decisions. These models are developed by analyzing the correlation between cardholder characteristics, contract terms, and outcomes such as default and profitability. Banks use both internally developed and externally purchased credit-scoring models. The most commonly used external credit scores are called FICO scores, which are developed by the Fair Isaac Corporation. FICO scores are used by the majority of financial institutions and take into account a consumer’s payment history, credit utilization, length of credit history, and the opening of new accounts. Scores range between 300 and 850, with higher scores indicating a lower probability of default. The vast majority of the population has scores between 550 and 800. Each bank develops its own policies and risk tolerance for credit card lending, with lower credit limits generally assigned to consumers with lower credit scores. Setting cutoff scores is one way that banks assign credit limits. For example, banks might split their customers into groups based on their FICO scores and assign each group a different credit limit (FDIC 2007). In Online Appendix B, we show how such a contract-setting process can be optimal in the presence of fixed costs for determining optimal contract terms for a set of observationally similar individuals. We also show that the magnitude of profits forgone by suboptimally pricing individuals close to credit limit discontinuities is small relative to industry estimates of the fixed cost of determining optimal contract terms for similar individuals. II.B. Data Our main data source is the Credit Card Metrics (CCM) data set assembled by the U.S. Office of the Comptroller of the Currency (OCC).9 The CCM data set has two components. The main data set contains account-level panel information on credit card utilization (e.g., purchase volume, measures of borrowing volume such as ADB), contract characteristics (e.g., credit limits, interest rates), charges (e.g., interest, assessed fees), performance (e.g., chargeoffs,10 days overdue), and borrower characteristics (e.g., FICO scores) for all credit card accounts at the eight largest U.S. banks. The second data set contains portfolio-level information for each bank on items such as operational costs and fraud expenses across all credit cards managed by these banks. Both data sets are submitted monthly; reporting started in January 2008 and continues through the present. We use data from January 2008 to December 2014 for our analysis. In the average month, we observe account-level information on over 400 million credit cards. See Agarwal et al. (2015b) for more details on these data and summary statistics on the full sample. To track changes in borrowing across the consumers’ broader credit portfolios, we merge the CCM data to quarterly credit bureau data using a unique identifier. The credit bureau data we observe were collected to study credit card borrowing and contain rich information on individuals’ unsecured-borrowing behavior across all lenders (e.g., the total number of credit cards, total credit limits, total balances, length of credit history, and credit performance measures such as whether the borrower was ever more than 90 days past due on an account). We do not observe borrowing on secured credit products such as mortgages or auto loans. II.C. Identifying Credit Limit Discontinuities In our empirical analysis, we focus on credit cards that were originated during our sample period, which started in January 2008. Our data do not contain information on the credit supply functions of banks when the credit cards were originated. Therefore, the first step involves backing out these credit supply functions from the observed credit limits offered to individuals with different FICO scores. To do this, we jointly consider all credit cards of the same type (co-branded, oil and gas, affinity, student, or other), issued by the same bank, in the same month, and through the same loan channel (preapproved, invitation to apply, branch application, magazine and internet application, or other). It is plausible that the same credit supply function was applied to each card within such an “origination group.” Since our data end in December 2014, we only consider credit cards originated until November 2013 to ensure that we observe at least 12 months of postorigination data for each account. For each of the more than 10,000 resulting origination groups between January 2008 and November 2013, we plot the average credit limit as a function of the FICO score. Panels A to D of Figure II show examples of such plots. Since banks generally adjust credit limits at FICO score cutoffs that are multiples of 5 (e.g., 650, 655, 660), we pool accounts into such buckets. Average credit limits are shown with dark lines; the number of accounts originated are shown with gray bars. Panels A and B show examples where there are no discontinuous jumps in the credit supply function. Panels C and D show examples of clear discontinuities. For instance, in Panel C, a borrower with a FICO score of 714 is offered an average credit limit of approximately $${\$}$$2,900, while a borrower with a FICO score of 715 is offered an average credit limit of approximately $${\$}$$5,600. Figure II View largeDownload slide Credit Limit Quasi-Experiments: Examples and Summary Statistics Panels A to D show examples of average credit limits by FICO score for accounts in “origination groups” with and without credit limit quasi-experiments. Origination groups are defined as all credit cards of the same product-type originated by the same bank in the same month through the same loan channel. The horizontal axis shows FICO score at origination. The dark line plots the average credit limit for accounts in FICO score buckets of 5 (left axis); gray bars show the total number of accounts originated in those buckets (right axis). Panels E and F show summary statistics for the quasi-experiments. Panel E plots the number of quasi-experiments at each FICO score cutoff. Panel F plots the number of accounts within 50 FICO score points of these quasi-experiments for each FICO score cutoff. Figure II View largeDownload slide Credit Limit Quasi-Experiments: Examples and Summary Statistics Panels A to D show examples of average credit limits by FICO score for accounts in “origination groups” with and without credit limit quasi-experiments. Origination groups are defined as all credit cards of the same product-type originated by the same bank in the same month through the same loan channel. The horizontal axis shows FICO score at origination. The dark line plots the average credit limit for accounts in FICO score buckets of 5 (left axis); gray bars show the total number of accounts originated in those buckets (right axis). Panels E and F show summary statistics for the quasi-experiments. Panel E plots the number of quasi-experiments at each FICO score cutoff. Panel F plots the number of accounts within 50 FICO score points of these quasi-experiments for each FICO score cutoff. Although continuous credit supply functions are significantly more common, we detect a total of 743 credit limit discontinuities between January 2008 and November 2013. We refer to these cutoffs as “credit limit quasi-experiments” and define them by the combination of origination group and FICO score. Panel E of Figure II shows the distribution of FICO scores at which we observe these quasi-experiments. They range from 630 to 785, with 660, 700, 720, 740, and 760 being the most common cutoffs. Panel F shows the distribution of quasi-experiments weighted by the number of accounts originated within 50 FICO score points of the cutoffs, which is the sample we use for our regression discontinuity analysis. We observe more than 1 million accounts within 50 FICO score points of the most prominent cutoffs. Our experimental sample has 8.5 million total accounts, or about 11,400 per quasi-experiment. II.D. Summary Statistics Table I presents summary statistics for the accounts in our sample of quasi-experiments at the time the accounts were originated. In particular, to characterize the accounts that are close to the discontinuities, we calculate the mean value for a given variable across all accounts within 5 FICO score points of the cutoff for each quasi-experiment. We then show the means and standard deviations of these values across the 743 quasi-experiments in our data. We also show summary statistics separately for each of the four FICO score groups that we use to explore heterogeneity in the data: ≤660, 661–700, 701–740, and >740. These ranges were chosen to split our quasi-experiments into roughly equal-sized groups, but we show in Online Appendix E that our conclusions are not sensitive to the exact grouping of experiments. In the entire sample, 28% of credit cards were issued to borrowers with FICO scores up to 660; 16% and 19% were issued to borrowers with FICO score ranges of 661–700 and 701–740, respectively; and 37% of credit cards were issued to borrowers with FICO scores above 740 (see Online Appendix Figure A.I). TABLE I Quasi-Experiment-Level Summary Statistics, at Origination Average Std. dev. Average Std. dev. Credit limit on treated card ($${\$}$$) Total balances across all credit cardaccounts ($${\$}$$) Pooled 5,265 2,045 Pooled 9,551 3,469 ≤660 2,561 674 ≤660 5,524 2,324 661–700 4,324 1,090 661–700 9,956 2,680 701–740 4,830 1,615 701–740 10,890 3,328 >740 6,941 1,623 >740 9,710 3,326 APR on treated card (%) Credit limit across all credit cardaccounts ($${\$}$$) Pooled 15.38 3.70 Pooled 33,533 14,627 ≤660 19.63 5.43 ≤660 12,856 5,365 661–700 14.50 3.65 661–700 26,781 7,524 701–740 15.35 3.11 701–740 32,457 8,815 >740 14.70 2.52 >740 44,813 12,828 Number of credit card accounts Number times 90+ DPD in last24 months Pooled 11.00 2.93 Pooled 0.17 0.30 ≤660 7.13 1.18 ≤660 0.51 0.31 661–700 10.22 1.68 661–700 0.21 0.16 701–740 11.12 2.34 701–740 0.14 0.10 >740 12.63 2.92 >740 0.05 0.08 Age oldest account (months) Number accounts currently 90+ DPD Pooled 190.1 29.1 Pooled 0.03 0.03 ≤660 162.0 26.3 ≤660 0.10 0.05 661–700 180.1 19.9 661–700 0.02 0.02 701–740 184.7 24.0 701–740 0.02 0.02 >740 208.6 25.7 >740 0.01 0.01 Average Std. dev. Average Std. dev. Credit limit on treated card ($${\$}$$) Total balances across all credit cardaccounts ($${\$}$$) Pooled 5,265 2,045 Pooled 9,551 3,469 ≤660 2,561 674 ≤660 5,524 2,324 661–700 4,324 1,090 661–700 9,956 2,680 701–740 4,830 1,615 701–740 10,890 3,328 >740 6,941 1,623 >740 9,710 3,326 APR on treated card (%) Credit limit across all credit cardaccounts ($${\$}$$) Pooled 15.38 3.70 Pooled 33,533 14,627 ≤660 19.63 5.43 ≤660 12,856 5,365 661–700 14.50 3.65 661–700 26,781 7,524 701–740 15.35 3.11 701–740 32,457 8,815 >740 14.70 2.52 >740 44,813 12,828 Number of credit card accounts Number times 90+ DPD in last24 months Pooled 11.00 2.93 Pooled 0.17 0.30 ≤660 7.13 1.18 ≤660 0.51 0.31 661–700 10.22 1.68 661–700 0.21 0.16 701–740 11.12 2.34 701–740 0.14 0.10 >740 12.63 2.92 >740 0.05 0.08 Age oldest account (months) Number accounts currently 90+ DPD Pooled 190.1 29.1 Pooled 0.03 0.03 ≤660 162.0 26.3 ≤660 0.10 0.05 661–700 180.1 19.9 661–700 0.02 0.02 701–740 184.7 24.0 701–740 0.02 0.02 >740 208.6 25.7 >740 0.01 0.01 Notes. Table shows quasi-experiment-level summary statistics at the time of account origination, both pooled across our 743 quasi-experiments and split by FICO score groups. For each quasi-experiment, we first calculate the mean value for a given variable across all of the accounts within five FICO score points of the cutoff. We then show the means and standard deviations of these values across our 743 quasi-experiments. We follow the same procedure to obtain the means and standard deviations by FICO score group. View Large At origination, accounts at the average quasi-experiment have a credit limit of $${\$}$$5,265 and an annual percentage rate (APR) of 15.4%. Average credit limits increase from $${\$}$$2,561 to $${\$}$$6,941 across FICO score groups, while average APRs decline from 19.6% to 14.7%. In the merged credit bureau data, we observe utilization on all credit cards held by the borrower. At the average quasi-experiment, account holders have 11 credit cards, with the oldest account being more than 15 years old. Across these credit cards, account holders have $${\$}$$9,551 in total balances and $${\$}$$33,533 in credit limits. Total balances are hump-shaped in FICO score, while total credit limits are monotonically increasing. In the credit bureau data, we also observe historical delinquencies and default. At the average quasi-experiment, account holders have been more than 90 days past due (90+ DPD) 0.17 times in the previous 24 months. This number declines from 0.51 to 0.05 across the FICO score groups. III. Research Design Our identification strategy exploits the credit limit quasi-experiments identified in Section II using a fuzzy regression discontinuity (RD) research design (see Lee and Lemieux 2010). In our setting, the “running variable” is the FICO score. The treatment effect of a $${\$}$$1 change in credit limit is determined by the jump in the outcome variable divided by the jump in the credit limit at the discontinuity. We first describe how we recover the treatment effect for each quasi-experiment and then discuss how we aggregate across the 743 quasi-experiments in the data. For a given quasi-experiment, let x denote the FICO score, $$\overline{x}$$ the cutoff FICO level, cl the credit limit, and y the outcome variable of interest (e.g., borrowing volume). The fuzzy RD estimator, a local Wald estimator, is given by: \begin{equation} \tau = \frac{\lim _{x \downarrow \overline{x}} E[y|x] - \lim _{x \uparrow \overline{x}} E[y|x]}{\lim _{x \downarrow \overline{x}} E[cl|x] - \lim _{x \uparrow \overline{x}} E[cl|x]}. \end{equation} (2)The denominator is always nonzero because of the known discontinuity in the credit supply function at $$\overline{x}$$. The parameter τ identifies the local average treatment effect (LATE) of extending more credit to people with FICO scores in the vicinity of $$\overline{x}$$. We estimate the limits in equation (2) using locally linear regressions. Specifically, let i denote a credit card account and $$\mathbb {I}$$ the set of accounts within 50 FICO score points on either side of $$\overline{x}$$. For each quasi-experiment, we fit a locally linear regression that solves the following objective function separately for observations i on either side of the cutoff, d ∈ {l, h}, for the variables, $$\tilde{y} \in \lbrace cl, y\rbrace$$: \begin{equation} \min _{\alpha _{\tilde{y},d}, \beta _{\tilde{y},d}} \sum _{i \in \mathbb {I}} [\tilde{y_i} - \alpha _{\tilde{y},d} - \beta _{\tilde{y},d} (x_i - \overline{x})]^2 {\bf 1}_{\left(|x_i - \overline{x}| < b \right)} \quad \text{for} \,\, d \in \lbrace l,h\rbrace . \end{equation} (3)In our baseline results we use the optimal bandwidth b from Imbens and Kalyanaraman (2011).11 For those quasi-experiments where we identify an additional jump in credit limits within our 50-FICO-score-point window, we include an indicator variable in equation (3) that is equal to 1 for all FICO scores above this second cutoff; Online Appendix C shows that this approach allows us to recover unbiased estimates of the actual treatment effect. Given these estimates, the LATE is given by: \begin{equation} \tau = \frac{\hat{\alpha }_{y,h} - \hat{\alpha }_{y,l}}{\hat{\alpha }_{cl,h} - \hat{\alpha }_{cl,l}}. \end{equation} (4) III.A. Heterogeneity by FICO Score Our objective is to estimate the heterogeneity in treatment effects by FICO score (see Einav et al. 2015, for a discussion of estimating treatment effect heterogeneity across experiments). Let j indicate quasi-experiments, let τj be the LATE for quasi-experiment j estimated using equation (4), and let FICOk, k = 1, …, 4 be indicator variables that take on a value of 1 when the FICO score of the discontinuity for quasi-experiment j falls into one of our FICO score groups (≤660, 661–700, 701–740, >740). We recover heterogeneity in treatment effects by regressing τj on the FICO score group dummies and controls: \begin{equation} \tau _j = \Bigg ( \sum _{k = 1}^4\beta _{k} FICO_{j,k} \Bigg ) + X_j^{\prime } \delta _X + \epsilon _j. \end{equation} (5)In our baseline specification, Xj includes fully interacted controls for origination quarter, bank, and a “zero initial APR” dummy that captures whether the account has a promotional period during which no interest is charged, and additively separable fully interacted loan channel by “zero initial APR” fixed effects.12 The βk are the coefficients of interest and capture the mean effect for accounts in FICO score group k, conditional on the other covariates. In Online Appendix Section E, we examine the relationship between our LATEs and FICO scores using nonparametric binned scatter plots, and show our results are robust to the choice of FICO score groups in the baseline analysis. We construct confidence intervals by bootstrapping over the 743 quasi-experiments. In particular, we draw 500 samples of local average treatment effects with replacement, and estimate the coefficients of interest, βk, in each sample. Our reported 95% confidence intervals give the range from the 2.5th percentile of estimates to the 97.5th percentile of estimates. Conceptually, we think of the local average treatment effects τj as “data” that are drawn from a population distribution of treatment effects. We are interested in the average treatment effect in the population for a given FICO score group. Our confidence intervals can be interpreted as measuring the precision of our sample average treatment effects for the population averages. IV. Validity of Research Design The validity of our research design rests on two assumptions: First, we require a discontinuous change in credit limits at the FICO score cutoffs. Second, other factors that could affect outcomes must trend smoothly through these thresholds. Below we present evidence in support of these assumptions. IV.A. First-Stage Effect on Credit Limits We first verify that there is a discontinuous change in credit limits at our quasi-experiments. Panel A of Figure III shows average credit limits at origination within 50 FICO score points of the quasi-experiments together with a local linear regression line estimated separately on each side of the cutoff. Initial credit limits are smoothly increasing except at the FICO score cutoff, where they jump discontinuously by $${\$}$$1,472. The magnitude of this increase is significant relative to an average credit limit of $${\$}$$5,265 around the cutoff (see Table II). Panel A of Figure IV shows the distribution of first-stage effects from RD specifications estimated separately for each of the 743 quasi-experiments in our data. These correspond to the denominator of equation (4). The first-stage estimates are fairly similar in size, with an interquartile range of $${\$}$$677 to $${\$}$$1,755 and a standard deviation of $${\$}$$796.13 Figure III View largeDownload slide Credit Limits and Cost of Credit Around Credit Limit Quasi-Experiments and Placebo Experiments Figure plots average credit limits (Panels A and B), average APR (Panels C and D), and average number of months with zero introductory APR (Panels E and F; limited to originations with zero introductory APR). The left column plots these outcomes around our 743 pooled quasi-experiments. We also control for other quasi-experiments within 50 FICO score points in the same origination group. The right column plots the same outcomes around the same FICO score cutoffs but for “placebo experiments” originated in the same month as the quasi-experiments in the left column but for origination groups with no quasi-experiments at that FICO score. The horizontal axis shows FICO score at origination, centered at the FICO score cutoff. Scatter plots show means of outcomes for 5-point FICO score buckets. Dashed lines show predicted values from locally linear regressions estimated separately on either side of the cutoff using the Imbens and Kalyanaraman (2011) optimal bandwidth. Figure III View largeDownload slide Credit Limits and Cost of Credit Around Credit Limit Quasi-Experiments and Placebo Experiments Figure plots average credit limits (Panels A and B), average APR (Panels C and D), and average number of months with zero introductory APR (Panels E and F; limited to originations with zero introductory APR). The left column plots these outcomes around our 743 pooled quasi-experiments. We also control for other quasi-experiments within 50 FICO score points in the same origination group. The right column plots the same outcomes around the same FICO score cutoffs but for “placebo experiments” originated in the same month as the quasi-experiments in the left column but for origination groups with no quasi-experiments at that FICO score. The horizontal axis shows FICO score at origination, centered at the FICO score cutoff. Scatter plots show means of outcomes for 5-point FICO score buckets. Dashed lines show predicted values from locally linear regressions estimated separately on either side of the cutoff using the Imbens and Kalyanaraman (2011) optimal bandwidth. Figure IV View largeDownload slide Effect of FICO Score Cutoff on Credit Limits Panel A shows the distribution of credit limit increases at the FICO score cutoffs across our 743 credit limit quasi-experiments. Panel B shows regression discontinuity estimates of the effect of a $${\$}$$1 increase in initial credit limits on credit limits at different time horizons after account origination. Estimates are shown for FICO score groups, defined at account origination. The corresponding estimates are shown in Table III. Figure IV View largeDownload slide Effect of FICO Score Cutoff on Credit Limits Panel A shows the distribution of credit limit increases at the FICO score cutoffs across our 743 credit limit quasi-experiments. Panel B shows regression discontinuity estimates of the effect of a $${\$}$$1 increase in initial credit limits on credit limits at different time horizons after account origination. Estimates are shown for FICO score groups, defined at account origination. The corresponding estimates are shown in Table III. Panel B of Figure IV examines the persistence of the jump in the initial credit limit. It shows the RD estimate of the effect of a $${\$}$$1 increase in initial credit limits on credit limits at different time horizons following account origination. The initial effect is highly persistent and very similar across FICO score groups, with a $${\$}$$1 higher initial credit limit raising subsequent credit limits by $${\$}$$0.85 to $${\$}$$0.93 at 36 months after origination. Table III shows the corresponding regression estimates. In the analysis that follows, we estimate the effect of a change in initial credit limits on outcomes at different time horizons. A natural question is whether it would be preferable to scale our estimates by the change in contemporaneous credit limits instead of the initial increase. We think the initial increase in credit limits is the appropriate denominator because subsequent credit limits are endogenously determined by household responses to the initial increase. We discuss this issue further in Section VI.D. IV.B. Other Characteristics Trend Smoothly through Cutoffs For our research design to be valid, the second requirement is that all other factors that could affect the outcomes of interest trend smoothly through the FICO score cutoff. These include contract terms, such as the interest rate (Assumption 1), characteristics of borrowers (Assumption 2), and the density of new account originations (Assumption 3). Because we have 743 quasi-experiments, graphically assessing the validity of our identifying assumptions for each experiment is not practical. Therefore, we show results graphically that pool across all of the quasi-experiments in the data, estimating a single pooled treatment effect and pooled locally linear regression line. In Table II, we present summary statistics on the distribution of these treatment effects across the 743 individual quasi-experiments. Assumption 1. Credit limits are the only contract characteristic that changes at the cutoff. The interpretation of our results requires that credit limits are the only contract characteristic that changes discontinuously at the FICO score cutoffs. For example, if the cost of credit also changed at our credit limit quasi-experiments, an increase in borrowing around the cutoff might not only result from additional access to credit, but could also be explained by lower borrowing costs. Panel C of Figure III shows the average APR around our quasi-experiments. APR is defined as the initial interest rate for accounts with a positive interest rate at origination, and the “go-to” rate for accounts which have a zero introductory APR.14 As one would expect, the APR is declining in the FICO score. Importantly, there is no discontinuous change in the APR around our credit limit quasi-experiments. This is consistent with the standard practice of using different models to price credit (set APRs) and manage exposure to risk (set credit limits).15Table II shows that, for the average (median) experiment, the APR increases by 1.7 basis points (declines by 0.5 basis point) at the FICO score cutoff; these changes are economically tiny relative to an average APR of 15.4%. Panel E of Figure III shows the length of the zero introductory APR period for the 248 quasi-experiments with a zero introductory APR. The length of the introductory period is increasing in FICO score, but there is no jump at the credit limit cutoff.16 Assumption 2. All other borrower characteristics trend smoothly through the cutoff. We next examine whether borrowers on either side of the FICO score cutoff looked similar on observable characteristics in the credit bureau data when the credit card was originated. Panels A and B of Figure V show the total number of credit cards and the total credit limit on those credit cards, respectively. Both are increasing in the FICO score, and there is no discontinuity around the cutoff. Panel C shows the age of the oldest credit card account for consumers, capturing the length of the observed credit history. We also plot the number of payments for each consumer that were 90 or more days past due (90+ DPD), both over the entire credit history of the borrower (Panel D), as well as in the 24 months prior to origination (Panel E). These figures, and the information in Table II, show that there are no discontinuous changes around the cutoff in any of these borrower characteristics.17 Figure V View largeDownload slide Initial Borrower Characteristics around Credit Limit Quasi-Experiments Figure plots average borrower characteristics around our 743 pooled credit limit quasi-experiments. The horizontal axis shows FICO score at origination, centered at the FICO score cutoff. The vertical axis shows the number of credit card accounts (Panel A), total credit limit across all credit card accounts (Panel B), age of the oldest account (Panel C), number of payments ever 90+ days past due (Panel D), number of payments 90+ days past due in last 24 months (Panel E), and the total number of accounts opened in the origination group where we observe the credit limit quasi-experiment (Panel F). All borrower characteristics are as reported to the credit bureau at account origination. Scatter plots show means of outcomes for 5-point FICO score buckets. Dashed lines show predicted values from locally linear regressions estimated separately on either side of the cutoff using the Imbens and Kalyanaraman (2011) optimal bandwidth. Figure V View largeDownload slide Initial Borrower Characteristics around Credit Limit Quasi-Experiments Figure plots average borrower characteristics around our 743 pooled credit limit quasi-experiments. The horizontal axis shows FICO score at origination, centered at the FICO score cutoff. The vertical axis shows the number of credit card accounts (Panel A), total credit limit across all credit card accounts (Panel B), age of the oldest account (Panel C), number of payments ever 90+ days past due (Panel D), number of payments 90+ days past due in last 24 months (Panel E), and the total number of accounts opened in the origination group where we observe the credit limit quasi-experiment (Panel F). All borrower characteristics are as reported to the credit bureau at account origination. Scatter plots show means of outcomes for 5-point FICO score buckets. Dashed lines show predicted values from locally linear regressions estimated separately on either side of the cutoff using the Imbens and Kalyanaraman (2011) optimal bandwidth. Assumption 3. The number of originated accounts trends smoothly through the cutoff. Panel F of Figure V shows that the number of originated accounts trends smoothly through the credit score cutoffs. This addresses a number of potential concerns with the validity of our research design. First, regression discontinuity designs are invalid if individuals are able to precisely manipulate the forcing variable. In our setting, the lack of strategic manipulation is unsurprising. Since the banks’ credit supply functions are unknown, individuals with FICO scores just below a threshold are unaware that marginally increasing their FICO scores would lead to a significant increase in their credit limits. Moreover, even if consumers knew of the location of these thresholds, since the FICO score function is proprietary, it would be very difficult for consumers to manipulate their FICO scores in a precise manner. A second concern in our setting is that banks might use the FICO score cutoff to make extensive margin lending decisions. For example, if banks relaxed some other constraint once individuals crossed a FICO score threshold, more accounts would be originated for households with higher FICO scores, but households on either side of the FICO score cutoff would differ along that other dimension. In Figure III, we already documented that there are no changes in observable characteristics around the FICO score cutoffs. The smooth trend in the number of accounts further indicates that banks do not select borrowers on an unobservable dimension as well. Finally, we would observe fewer accounts to the left of the threshold if there was a “demand response,” whereby consumers were more likely to turn down credit card offers with lower credit limits. However, in this market, consumers do not know their exact credit limits when they apply for a credit card and only learn of their credit limits when they have been approved and receive a credit card in the mail. Since consumers have already paid the sunk cost of applying, it is not surprising that consumers with lower credit limits do not immediately cancel their cards, which would generate a discontinuity in the number of accounts. V. Borrowing and Spending Having established the validity of our research design, we turn to estimating the causal impact of an increase in credit limits on borrowing and spending, focusing on how these effects vary across the FICO score distribution. V.A. Average Borrowing and Spending We start by presenting basic summary statistics on credit card utilization. The left column of Table IV shows average borrowing by FICO score group at different time horizons after account origination. To characterize the credit cards that identify the causal estimates, we again restrict the sample to accounts within 5 FICO score points of a credit limit quasi-experiment. TABLE IV Quasi-Experiment-Level Summary Statistics, Postorigination FICO score group FICO score group FICO score group ≤660 661–700 701–740 >740 ≤660 661–700 701–740 >740 ≤660 661–700 701–740 >740 Credit limit ($${\$}$$) Cumulative purchase volume ($${\$}$$) Cumulative cost of funds ($${\$}$$) After 12 months 2,617 4,370 4,964 6,980 After 12 months 2,212 2,579 2,514 2,943 After 12 months 14 16 16 15 After 24 months 2,414 4,306 4,946 7,071 After 24 months 2,447 3,956 3,791 4,374 After 24 months 23 29 28 25 After 36 months 2,301 4,622 5,047 7,005 After 36 months 3,240 5,023 4,253 4,521 After 36 months 28 38 36 31 After 48 months 2,252 4,525 4,985 6,944 After 48 months 3,741 5,154 4,919 4,845 After 48 months 31 43 41 34 After 60 months 2,290 4,449 4,601 6,839 After 60 months 4,524 5,598 5,121 5,626 After 60 months 33 46 44 36 ADB ($${\$}$$) Cumulative total costs ($${\$}$$) Cumulative total revenue ($${\$}$$) After 12 months 1,260 2,160 2,197 2,101 After 12 months 122 172 169 147 After 12 months 233 192 181 175 After 24 months 1,065 1,794 1,719 1,524 After 24 months 281 451 433 304 After 24 months 474 503 439 347 After 36 months 1,164 1,734 1,481 1,343 After 36 months 459 710 644 395 After 36 months 740 793 663 449 After 48 months 1,079 1,501 1,260 1,064 After 48 months 588 845 808 488 After 48 months 953 971 863 563 After 60 months 1,050 1,465 1,097 1,084 After 60 months 712 962 901 583 After 60 months 1,148 1,126 965 669 Average interest bearing debt ($${\$}$$) Cumulative chargeoffs ($${\$}$$) Cumulative interest charge revenue ($${\$}$$) After 12 months 864 903 811 672 After 12 months 47 67 61 35 After 12 months 106 61 52 42 After 24 months 1,040 1,676 1,557 1,294 After 24 months 178 259 245 124 After 24 months 297 295 243 159 After 36 months 1,068 1,615 1,344 1,135 After 36 months 306 443 403 190 After 36 months 484 520 420 243 After 48 months 1,044 1,416 1,144 924 After 48 months 403 552 524 261 After 48 months 625 669 578 340 After 60 months 1,020 1,388 1,001 941 After 60 months 483 634 602 322 After 60 months 760 794 657 429 Cumulative prob positive interest-bearing debt (%) Cumulative prob 60+ DPD (%) Cumulative fee revenue ($${\$}$$) After 12 months 58.4 36.1 31.6 26.9 After 12 months 6.4 4.1 3.6 1.6 After 12 months 73 79 79 74 After 24 months 75.4 73.0 64.9 50.3 After 24 months 12.0 9.3 8.2 3.8 After 24 months 129 129 121 101 After 36 months 84.0 79.4 72.3 61.6 After 36 months 15.1 12.2 10.9 5.2 After 36 months 192 173 157 116 After 48 months 87.4 84.0 78.1 69.8 After 48 months 16.5 13.6 12.2 5.9 After 48 months 254 199 187 126 After 60 months 90.1 86.3 81.3 75.2 After 60 months 17.2 14.4 12.9 6.2 After 60 months 364 310 211 101 Total balances across all cards ($${\$}$$) Cumulative prob 90+ DPD (%) Cumulative profits ($${\$}$$) After 12 months 6,155 10,546 11,411 10,528 After 12 months 4.8 3.3 2.9 1.3 After 12 months 111 21 12 30 After 24 months 5,919 10,521 11,307 10,703 After 24 months 10.2 8.1 7.2 3.2 After 24 months 194 56 9 46 After 36 months 6,387 10,716 11,702 11,267 After 36 months 13.2 10.9 9.7 4.5 After 36 months 281 91 23 59 After 48 months 6,698 10,437 11,665 11,137 After 48 months 14.5 12.2 10.9 5.1 After 48 months 365 126 55 75 After 60 months 7,566 10,591 11,972 12,490 After 60 months 15.2 12.9 11.5 5.4 After 60 months 436 164 63 87 FICO score group FICO score group FICO score group ≤660 661–700 701–740 >740 ≤660 661–700 701–740 >740 ≤660 661–700 701–740 >740 Credit limit ($${\$}$$) Cumulative purchase volume ($${\$}$$) Cumulative cost of funds ($${\$}$$) After 12 months 2,617 4,370 4,964 6,980 After 12 months 2,212 2,579 2,514 2,943 After 12 months 14 16 16 15 After 24 months 2,414 4,306 4,946 7,071 After 24 months 2,447 3,956 3,791 4,374 After 24 months 23 29 28 25 After 36 months 2,301 4,622 5,047 7,005 After 36 months 3,240 5,023 4,253 4,521 After 36 months 28 38 36 31 After 48 months 2,252 4,525 4,985 6,944 After 48 months 3,741 5,154 4,919 4,845 After 48 months 31 43 41 34 After 60 months 2,290 4,449 4,601 6,839 After 60 months 4,524 5,598 5,121 5,626 After 60 months 33 46 44 36 ADB ($${\$}$$) Cumulative total costs ($${\$}$$) Cumulative total revenue ($${\$}$$) After 12 months 1,260 2,160 2,197 2,101 After 12 months 122 172 169 147 After 12 months 233 192 181 175 After 24 months 1,065 1,794 1,719 1,524 After 24 months 281 451 433 304 After 24 months 474 503 439 347 After 36 months 1,164 1,734 1,481 1,343 After 36 months 459 710 644 395 After 36 months 740 793 663 449 After 48 months 1,079 1,501 1,260 1,064 After 48 months 588 845 808 488 After 48 months 953 971 863 563 After 60 months 1,050 1,465 1,097 1,084 After 60 months 712 962 901 583 After 60 months 1,148 1,126 965 669 Average interest bearing debt ($${\$}$$) Cumulative chargeoffs ($${\$}$$) Cumulative interest charge revenue ($${\$}$$) After 12 months 864 903 811 672 After 12 months 47 67 61 35 After 12 months 106 61 52 42 After 24 months 1,040 1,676 1,557 1,294 After 24 months 178 259 245 124 After 24 months 297 295 243 159 After 36 months 1,068 1,615 1,344 1,135 After 36 months 306 443 403 190 After 36 months 484 520 420 243 After 48 months 1,044 1,416 1,144 924 After 48 months 403 552 524 261 After 48 months 625 669 578 340 After 60 months 1,020 1,388 1,001 941 After 60 months 483 634 602 322 After 60 months 760 794 657 429 Cumulative prob positive interest-bearing debt (%) Cumulative prob 60+ DPD (%) Cumulative fee revenue ($${\$}$$) After 12 months 58.4 36.1 31.6 26.9 After 12 months 6.4 4.1 3.6 1.6 After 12 months 73 79 79 74 After 24 months 75.4 73.0 64.9 50.3 After 24 months 12.0 9.3 8.2 3.8 After 24 months 129 129 121 101 After 36 months 84.0 79.4 72.3 61.6 After 36 months 15.1 12.2 10.9 5.2 After 36 months 192 173 157 116 After 48 months 87.4 84.0 78.1 69.8 After 48 months 16.5 13.6 12.2 5.9 After 48 months 254 199 187 126 After 60 months 90.1 86.3 81.3 75.2 After 60 months 17.2 14.4 12.9 6.2 After 60 months 364 310 211 101 Total balances across all cards ($${\$}$$) Cumulative prob 90+ DPD (%) Cumulative profits ($${\$}$$) After 12 months 6,155 10,546 11,411 10,528 After 12 months 4.8 3.3 2.9 1.3 After 12 months 111 21 12 30 After 24 months 5,919 10,521 11,307 10,703 After 24 months 10.2 8.1 7.2 3.2 After 24 months 194 56 9 46 After 36 months 6,387 10,716 11,702 11,267 After 36 months 13.2 10.9 9.7 4.5 After 36 months 281 91 23 59 After 48 months 6,698 10,437 11,665 11,137 After 48 months 14.5 12.2 10.9 5.1 After 48 months 365 126 55 75 After 60 months 7,566 10,591 11,972 12,490 After 60 months 15.2 12.9 11.5 5.4 After 60 months 436 164 63 87 Notes. Table shows quasi-experiment-level summary statistics at different horizons after account origination by FICO score group. For each quasi-experiment, we calculate the mean value for a given variable across all of the accounts within 5 FICO score points of the cutoff. We then show the means and standard deviations of these values across the available quasi-experiments. Since later quasi-experiments are observed for shorter periods of time only, the set of experiments contributing to the averages across different horizons is not constant. FICO score groups are defined at account origination. View Large TABLE II Validity of Research Design: Discontinuous Increase at FICO Cutoff Distribution of jump across quasi-experiments Average Median Standard devation Baseline Credit limit 1,472 1,282 796 5,265 APR (%) 0.017 −0.005 0.388 15.38 Months to rate change 0.027 0.016 0.800 13.37 Number of credit cardaccounts 0.060 0.031 0.713 11.00 Total credit limit—allaccounts 151 28 2,791 33,533 Age oldest account (months) 1.034 0.378 11.072 190.11 Number times 90+ DPD—last24 months 0.010 0.002 0.111 0.169 Number accounts 90+DPD—at origination 0.001 0.001 0.017 0.026 Number accounts 90+DPD—ever 0.004 0.003 0.095 0.245 Number of accounts originated 10.21 4.38 47.61 580.12 Distribution of jump across quasi-experiments Average Median Standard devation Baseline Credit limit 1,472 1,282 796 5,265 APR (%) 0.017 −0.005 0.388 15.38 Months to rate change 0.027 0.016 0.800 13.37 Number of credit cardaccounts 0.060 0.031 0.713 11.00 Total credit limit—allaccounts 151 28 2,791 33,533 Age oldest account (months) 1.034 0.378 11.072 190.11 Number times 90+ DPD—last24 months 0.010 0.002 0.111 0.169 Number accounts 90+DPD—at origination 0.001 0.001 0.017 0.026 Number accounts 90+DPD—ever 0.004 0.003 0.095 0.245 Number of accounts originated 10.21 4.38 47.61 580.12 Notes. Table shows the reduced-form discontinuous increase (“jump”) in credit limits and outcome variables at the FICO score cutoff (see equation (4)). All variables are measured at account origination, allowing us to inspect the validity of the research design. We present the average, median, and standard deviation of this jump across our 743 quasi-experiments. We also present the average value of the variable at the cutoff (“baseline”), allowing us to judge the economic significance of any differences. View Large TABLE III Persistence of Credit Limit Effect Months after account origination 12 24 36 48 60 FICO ≤660 0.93 0.92 0.93 0.93 0.97 [0.91, 0.96] [0.87, 0.96] [0.86, 0.99] [0.83, 1.04] [0.79, 1.19] 661–700 0.94 0.90 0.85 0.78 0.78 [0.90, 0.94] [0.88, 0.93] [0.86, 0.90] [0.71, 0.85] [0.67, 0.90] 701–740 0.95 0.93 0.89 0.82 0.80 [0.94, 0.97] [0.90, 0.94] [0.86, 0.90] [0.77, 0.87] [0.67, 0.90] >740 0.95 0.92 0.91 0.88 0.93 [0.94, 0.96] [0.90, 0.94] [0.87, 0.93] [0.81, 0.94] [0.83, 1.11] Months after account origination 12 24 36 48 60 FICO ≤660 0.93 0.92 0.93 0.93 0.97 [0.91, 0.96] [0.87, 0.96] [0.86, 0.99]