Consumer Demand for Credit Card Services - Google Sites

Consumer Demand for Credit Card Services* Alexei Alexandrov„

¨ Ozlem Bedre-Defolie…

Daniel Grodzicki§

Abstract We estimate how demand for credit card transacting, borrowing, and late payment responds to the interest rate and late payment fee. We find that lower rates increase borrowing and lower fees increase late payments. Prime cardholders demand for all services is decreasing in any price. In contrast, subprime cardholders borrow less when fees drop, a response consistent with models of limited attention. We calculate that a 2 percentage point rise in the Federal Funds rate decreases borrowing by 16 percent, or $130 billion, that this effect is greater in higher income communities, and that it exhibits geographic agglomeration. JEL Codes: D12, G41

* This

paper was formerly circulated under the title “The Effects of Interest Rate Changes and Addon Fee Regulation on Consumer Behavior in the US Credit Card Market.” The views expressed are those of the authors and do not necessarily reflect those of the Consumer Financial Protection Bureau or the United States. We would like to thank Paul Heidhues and Johannes Johnen for thoughtful comments and suggestions. We would also like to thank the participants and our discussants at the International Industrial Organization Conference, European Economic Association, European Association for Research in Industrial Economics, American Economic Association conference, and Boulder Summer Conference on Consumer Financial Decision Making and at the Consumer Financial Protection Bureau’s, European School of Management and Technology’s, the Pennsylvania State University’s, and Boston Federal Reserve Bank’s internal seminars. The authors are solely responsible for any remaining errors. „ [email protected]. … European School of Management and Technology (ESMT), Berlin, and CEPR, [email protected]. § The Pennsylvania State University and Consumer Financial Protection Bureau, [email protected].

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Introduction

Consumer financial products often require users to make complex choices. This is in part because they offer an array of services and related prices that interact in increasingly sophisticated ways. Diversity of services enhances the potential value and subsequent popularity of these products to consumers, but it also raises the scope for users to make mistakes. This trade off has motivated a discussion among academics and policymakers alike regarding the extent to which consumers successfully navigate these complexities and the ways in which their failure to do so is exploited by sellers. A key element of this discussion, which has received relatively little attention in the empirical literature, is consumer demand. More specifically, how does consumers’ usage of a financial product respond to the collection of interest rates and fees that comprise the eventual cost of using it? We study empirically consumers’ demand for credit card services in the US. Credit cards in the US are ubiquitous as a tool for managing household finances. About 4 in 5 US households use a card, resulting in $2 trillion in annual transaction volume, $780 billion in outstanding debt, and $4 trillion in committed credit. In addition to its size and importance to households, the US credit card market has been cited for the increasing sophistication of the products it offers and the potential effects of these on usage and subsequent welfare (Consumer Financial Protection Bureau, 2015). Our demand study begins by providing direct evidence on how cardholders’ usage of various credit card services responds to the combination of rates and fees attached to those services. Tying in to the broader discussion on the relationship between complexity and usage, we then evaluate the extent to which observed demand accords with existing theories of consumer choice. Finally, we draw implications of our findings for potential aggregate and distributional effects of monetary policy on consumer borrowing. Our analysis is carried out using a de-identified account level monthly panel of large banks’ credit card portfolios. These data are compiled in the Consumer Financial Protection Bureau’s (CFPB) Credit Card Database (CCDB) and include nearly 85 percent of all credit card accounts in the United States. This provides a unique opportunity to measure cardholders’ response to prices for nearly the entire US market. Specifically, we study demand responses to interest rates (APR) and late payment fees (LF) of the three most common services: (1) transacting (purchases), (2) revolving (balances), and (3) late payment. Given the size and richness of the CCDB, we are able measure demand responses separately for prime and subprime cardholders. Much of the academic and policy concerns regarding consumers’ ability to optimally respond to contract complexities have centered on differences in demand behavior between these groups. We contribute to these discussion by documenting these differences. A challenge in demand estimation is identifying price movements that are unrelated to 2

factors governing demand. Our analysis considers two prices and therefore employs two distinct identification strategies. First, to identify supply driven movements in APR we use lenders’ account repricing decisions. We detect account repricing by leveraging the panel dimension of the data and estimating an average account’s response to changes in its own APR. We show that these lender repricing decisions are uncorrelated with demand observables and seemingly unanticipated by consumers, but that they are associated with movements in the cost of funds. We note that often repricing is a result of changes in risk and repayment, and exclude such penalty repricing in our analysis. Second, to isolate supply driven variation in LF we use the LF ceiling implemented as part of the Credit Card Accountability Responsibility and Disclosure (CARD) Act in August 2010. This mandated price ceiling was binding and similarly affected nearly all cardholders, lowering their LF from $39 to $25. Fewer than half of cardholders make any purchases or revolve balances in a given month. Moreover, users cannot ordinarily hold negative balances (lend) or make negative purchases (sell) on their credit card. As a result, purchases and balances are heavily censored in the data. Given its prevalence, not accounting for this censoring may severely bias any estimates of demand. Our empirical design explicitly incorporates this censoring into the fixed effects framework. Conceptually, we interpret this as cardholders making decisions along intensive and extensive margins in their demand for these services. In addition to providing a consistent estimate of demand, allowing for censoring makes it possible to disentangle demand effects separately along these two margins. We use this margin decomposition to further clarify potential mechanisms underlying price effects on demand. We find that a rise in their APR prompts cardholders to hold fewer balances, with elasticities of -1.97 and -1.08 for the median subprime and prime cardholder, respectively. Stronger price effects among subprime cardholders echoes a theory of adverse selection cited as a driver of high prices in this market during the 1980s (Ausubel, 1991). Moreover, it is largely inconsistent with older theories of rationing, whereby credit constraints mitigate risky consumers’ response to interest rates (Juster and Shay, 1964). We further find that the propensity to pay late is decreasing in LF, with elasticities of -0.24 and -0.30 for the median subprime and prime cardholders, respectively. The rising complexity of credit card pricing in recent years has helped establish the common view that ‘back-end’ fees, such as LF, are for the most part non-salient or hidden from consumers (Government Accountability Office, 2006). Our estimates suggest that, in the absence of regulatory pressure, LF would have likely been higher. Given the already high cost, this indicates a substantial degree of non-salience of LF among cardholders. However, our findings also illustrate a statistically significant and economically meaningful response of late payments to LF. Moreover, in line with theoretical work on non-salience in consumer mar-

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kets (Ellison, 2005; Gabaix and Laibson, 2006; Ru and Schoar, 2016), we find that prime cardholders, arguably more sophisticated users of credit, are on average more sensitive to these fees. Consistent with standard models of rational consumer choice, prime cardholders’ demand for all services is decreasing in both APR and LF. In contrast, subprime cardholders reduce balances given a decline in LF. This response is difficult to predict within the standard rational consumer model, but is consistent with theories of limited attention (Mullainathan and Shafir, 2013). Such theories predict that, when fees are high, cardholders with limited attention may focus on making on-time payments, potentially losing track of finance charges to their account. A decline in fees may then shift cardholders’ attention toward interest payments. As further evidence in favor of this view, we find a 25 percent larger balance reduction given a decline in fees among subprime cardholders residing in low income counties, where the incidence of financial hardship is likely higher. Moreover, subprime cardholders’ demand for balances is more sensitive to APR in the year following the price cap, when LF is lower. This increase in sensitivity to APR aligns with recent theoretical work on competition when consumers have limited attention, which predicts a rise in consumer shopping following a cap on add-on fees (Heidhues et al., 2017). Using our demand estimates, we explore effects of a hypothetical rise in the Federal Funds rate (FFR) on the demand for consumer credit. As the US economy stabilizes following the Great Recession, the Federal Reserve is poised to begin a campaign of increasing its benchmark Federal Funds rate. Because 9 in 10 credit card contracts carry a variable APR defined as a fixed markup over a benchmark rate, a rise in the FFR means a similar and nearly immediate increase in almost all credit card APRs. We analyze the effect of this increase on borrowing, holding all other variables constant. Secondary effects through employment, wages, and prices may take some time to percolate through the economy, while credit card APRs rise almost immediately. We interpret our results as a pure APR effect, which may be construed as a good guess of these effects in the short to medium term. We calculate that, all else equal, a 2 percentage-point increase in the FFR decreases credit card borrowing by 15 and 22 percent for prime and subprime cardholders, respectively. In the aggregate, debt decreases by $130 billion and annual finance charges decline by nearly $20 billion. While substantial in the aggregate, these effects vary across income groups and regions. Specifically, the quintile of cardholders residing in the highest income counties are between 25 and 50 percent more responsive to this policy than the remaining 80 percent of cardholders. This suggests that households in lower income areas, who may not have the ability to pay down or reorganize their debt, may be those more likely left holding expensive debt when rates rise. Putting these heterogeneous effects into perspective, we calculate that, all else equal, were all cardholders to respond like those in high income counties,

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annual finance charges would further decline by $6.5 billion, or 30 percent. Lastly, we note substantial agglomeration in borrowing response to APR across US States. We conjecture that income differences alone may not be enough to explain the variance in responses across geographic regions. This is in large part because much of this heterogeneity is driven by differences in persistent tastes, or fixed effects, for maintaining balances. The analyses in this paper complement a growing body of empirical work on borrowing behavior in consumer financial markets. One strand of this literature studies the extent to which borrowing decisions are congruent with canonical models of permanent income, measuring cardholders’ propensity to borrow out of new liquidity (Gross and Souleles, 2002; Agarwal et al., 2015a). These studies find that, contrary to classical predictions, the propensity to borrow out of new credit is substantial, even for cardholders who are not borrowing constrained. Adding to this work, we measure how credit card borrowing responds to changes in price. Looking at both direct price changes through interest rates and indirect price changes via fees, we explore the degree to which these responses correspond to standard models of consumer choice. Another strand of this literature has sought to measure the presence, and potential impacts, of adverse selection and moral hazard in credit card lending (Agarwal et al., 2010; Ausubel, 1999; Karlan and Zinman, 2009) and to better understand cardholders’ default and delinquency decisions (Ausubel, 1997). Our analysis contributes to these studies by exploring price response among cardholders of varying risk profiles. Specifically, we show that subprime cardholders are indeed more responsive to interest rate changes, lending empirical support to previous hypotheses of adverse selection (Ausubel, 1991). Other studies have further looked into how consumers shop for credit cards (Stango and Zinman, 2015) and the manner by which lenders choose to offer card products to potential customers (Ru and Schoar, 2016; Han et al., 2013). Related work aims to further understand how cardholders react to complex pricing schemes, such as teaser rates and the bundling of rewards (Ching and Hayashi, 2010; Simon et al., 2010; Agarwal et al., 2010) as well as the process by which they learn to navigate these complications (Agarwal et al., 2011). This paper complements this strand of previous work by analyzing the steady state responses of existing customers. In particular, we show that while prime cardholders on average exhibit rationalizable behavior, subprime cardholders response to prices cannot be wholly rationalized. The remainder of the paper is organized as follows. We describe the relevant aspects of credit card pricing and regulation in Section 2. In Section 3 we describe the data. Our empirical design is laid out in section 4, and our identification argument is presented in 5. In Section 6 we discuss our results. Section 7 concludes.

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2

Recent Changes in Card Pricing and Regulation

Over the past decades the US credit card market has grown significantly. This growth materialized alongside substantial changes in the way lenders interact with consumers, how they structure and price their products, and the way in which their business practices are regulated by financial authorities. By the late 1980s a majority of banks issued cards, a plurality of merchants accepted them as payment, and purchase and outstanding credit volumes were in the hundreds of millions of dollars. Nevertheless, the credit card remained a relatively straight-forward product, providing access to a pre-determined credit line and charging fixed annual fees and interest rate on outstanding balances. Annual fees constituted a bulk of the fee revenue, while a great majority of overall revenue came from cardholders paying finance charges on balances. In the 1990s, lenders began adopting sophisticated credit scoring technologies. Better screening led to lower interest rates and an expansion of consumer credit. It also influenced how credit card products were structured and priced. Among these changes, up front annual fees gave way to back-end, often termed behavioral, fees like LF and over-the-limit (OTL) fees.1 This change accelerated following the 1996 US Supreme Court decision in Smiley v. Citibank that prevented individual states from regulating LF and OTL charged by nationally chartered banks. By the end of the decade LF and OTL became a prominent source of lender revenue, especially among the growing subprime segment (Ausubel, 1997; Zywicki, 2000; Furletti, 2003).2 In 2004, the Office of the Comptroller of the Currency (OCC) issued an advisory letter (OCC AL 2004-10), warning banks of pricing practices which may be considered unfair and deceptive.3 Then, in October 2006, the US Government Accountability Office (GAO), released a highly cited study documenting the rapid increase in the late payment fees. Following the GAO report, the rise in lender fees abated.4 In February 2008, a bill to curb deceptive practices was introduced in the US Congress (H.R. 5244 110th Congress). A version of that bill eventually became the CARD Act, which was signed into law in May 2009. The CARD Act had multiple provisions, which took effect in three phases: Phase I on August 20, 2009, Phase II on February 22, 2010, and Phase III on August 22, 2010 1

These were charged to cardholders who failed to make the minimum payment by the due date or who outspent their credit limit during the cycle. 2 The Supreme court decision upheld a US Office of the Comptroller of the Currency regulation and was in effect an extension of the Marquette v. First of Omaha decision that did the same for interest rates. In the a decade following the decision, fees grew rapidly from around $5-$10 to $39 for almost all large issuers (United States Government Accountability Office, 2006). 3 An example was lenders changing LF ex-post without warning or reason, even when the initial contract specified that the issuer has the unilateral right to do so. 4 Fees in 2009 seemed to be effectively unchanging for years, and not customized like interest rates had been for decades, despite massive changes in economic conditions.

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(Consumer Financial Protection Bureau, 2013). Phase I implemented provisions concerning rate increases on new balances, requiring lenders to notify their customers at least 45 days in advance of any rate change. Phase II restricted rate increases on existing balances. Rate increases were limited to those contractually agreed upon via a variable contract rate or as a result of delinquency triggering ‘penalty’ rates. Even for delinquent cardholders, issuers were obligated to restore the original rate after six consecutive on time payments. Phase II also restricted OTL, which could now only be charged if the cardholders opted in to this service. In absence of customer opt in, lenders had to reject the transaction or to allow it without penalty.5 . Phase III further restricted OTL and placed a binding price ceiling on LF. In August 2010 LF were effectively capped at $25, down from $39, previously the modal fee for the largest issuers.6 In contrast to LF, other than through limitations on re-pricing, the CARD Act made no provisions to limit how lenders set APR on new accounts.

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Data

For our demand analysis, we use a de-identified monthly panel of credit card accounts from large banks’ credit card portfolios. These data are compiled in the Consumer Financial Protection Bureau’s (CFPB) Credit Card Database (CCDB), which contains information on the consumer and small business credit card portfolios of 13 lenders and covers approximately 85 percent of all credit card accounts in the US. Account information includes borrowing interest rates (APR), fees, purchase volume, balances, payments, available credit, and an updated credit score associated with each cardholder. Account information in the database cannot be tied to any particular consumer or household nor can multiple accounts in the database that may belong to a single consumer or household be linked. As a result, our analyses are carried out at the account, rather than individual or household, level. We use a 1 percent random sample of accounts in the CCDB. We restrict attention to general purpose accounts originated on or before January 2009 and which remain in existence until August 2011, a balanced panel.7 To avoid misclassified interest rate movements resulting from expired promotion and/or new delinquency, we exclude accounts with regular non-introductory rates below 7 percentage points, accounts experiencing a month-to month rate change greater than 5 percentage points, and accounts ever more than 60 days past due. We further abstract away from accounts whose utilization is ever 5

This reduced the proportion of accounts charged an over-limit fee at least once in a year from 12 percent to about 1 percent (Consumer Financial Protection Bureau, 2013) 6 The rule also allowed issuers to charge consumers a higher LF if the consumers previously paid late within the last six months. 7 These are the bulk of accounts. We recognize that small business cards, students cards, certain affinity cards, and especially private label cards are important segments of this market. However, we believe these are very different products and fall outside the scope of this study.

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more than 90 percent.8 The remaining accounts are divided into prime (Credit Score > 660) and subprime (Credit Score ≤ 660) based on the cardholders’ credit score as of September 2009, the beginning of the analysis period.9 We classify approximately 5 percent of remaining accounts as subprime and 95 percent as prime. To equilibrate the sample size across 5 ≈ 5.26%.10 Lastly, types, we randomly draw from the prime accounts sample at a rate 95 our analysis period ranges from September 2009 to August 2011, inclusive. This range constitutes one year before and one year after the fee cap implemented by the CARD Act. It allows us to mitigate any potential seasonal effects of late payment propensities and/or long term economic effects resulting from the recession and/or recovery. The CCDB provides information on the contract APR for regular purchases. Contract late fees are not observed. Nevertheless, the data provide information on the late fees assessed to individuals paying late. Assessed fees can vary for any number of reasons. Credits can be provided from a previous overpayment and/or additional fees can be added given the account status. Nevertheless, these occurrences are rare, and the vast majority of accounts assessed a late fee pay the contract price. As a result, we define the contracted listed late fee as the most common, or modal, late payment fee assessed to cardholders paying late. Since in practice these fees might vary across lenders, account origination vintages, and by risk, we allow for the modal fee paid to vary across these categories. Lastly, we consider separately the most commonly assessed fee for each risk category before and after the CARD Act implementation. Figure 1 shows trends in prices throughout our sample period. The top panels show monthly average rates for subprime accounts (left) and prime accounts (right). The bottom panel shows average LFs for each of these. The vertical lines mark CARD Act implementation dates. As can be seen in the top panel of the figure, interest rates were stable during our period of analysis, and Prime cardholders on average paid about 4 percent lower APRs on balances than subprime cardholders. Moreover, dispersion in interest rates was significant during this time, and substantially less pronounced among prime cardholders. The bottom panel of figure 1 shows trends in late fees. Prior to the fee cap, nearly all cardholders were charged $38 for a late payment, with little variation across cardholders and over time. After the fee cap, this charge decreased to $25, again for almost all cardholders in the market. 8

The vast majority of accounts are never close to their limit. Moreover, we do not study changes in credit supply here. Excluding these accounts helps focus the estimation on interest rate and late fee changes as distinct from changes in individuals’ credit availability (see below section 5). 9 We choose risk categories to conform with Consumer Financial Protection Bureau (2013). 10 Note that 5 percent is a much lower rate of subprime accounts than in the population. This is because we exclude accounts based on activities, such as delinquency and over limit, which are more prevalent among subprime cardholders. To avoid possibility of effects being disproportionately driven by outliers (e.g. cardholders with extremely high balances and/or purchase) we exclude a further 1 percent of accounts with very large balances/purchases.

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Figure 1: Trends in Interest Rates (APR) and Late Payment Fees (LFs) Note: Data are from the CFPB’s Credit Card Database (CCDB). The figure shows trends in APRs and LFs given our sample over the implementation period.

Table 1 shows summary statistics on credit card demand variables for subprime and prime cardholders, respectively. Throughout, our measure of balances exclude all balances in promotion, balances resulting form cash withdrawals, or balances assessed at the penalty rate.11 As shown in the table, subprime and prime cardholders differ substantially in the way they use their credit card. Compared to prime cardholders, subprime cardholders make fewer purchases on their card, but are more likely to hold a balance and utilize a higher proportion of available credit on average. Nevertheless, average balances for the average subprime revolver are still substantially less than for the average prime revolver. In addition, subprime cardholders are three times more likely to pay late in any given month than prime cardholders. The data also provides information on account origination dates. We use this information as a proxy for account maturity, which likely matters for demand behavior. As shown in the table, prime accounts in our sample are on average 3 years, or 33 percent, older, 11

Specifically, balances are defined as non-promo non-penalty balances at the end of the cycle net of any payments made in the following cycle, as technically payments are applied to previous cycles’ balances.

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Table 1: Summary Statistics Subprime Mean 25th Pctl. 75th Pctl. (1) (2) (3) 353.67 44.07 389.08 33.07

Purchase Volume for Users % with Purchases

Prime Mean 25th Pctl. (4) (5) 820.82 97.96 56.24

75th Pctl. (6) 996.40

Balance for Revolvers (Non-Intro) 1,598.63 % Revolving Balances 42.55

287.79

2,108.63

2,007.36 32.11

265.72

2,770.36

Credit Limit

800.00

5,915.00 13,405.05

6,300.00

17,500.00

4,502.22

% Paying Late

6.14

Account Age (Years)

7.77

4.00

10.00

10.39

5.00

15.00

0.62 -0.14

-4.75 -2.02

6.77 2.36

0.65 0.12

-5.25 -2.00

6.45 2.31

19,947 24

19,947 24

19,947 24

19,885 24

19,885 24

19,885 24

%∆ Average Wage (County) %∆ Employment (County) Number of Accounts (N) Number of Months (T)

2.39

Notes: Data are from the CFPB’s CCDB and based on a sample of credit card accounts between September 2009 and August 2011, inclusive. Revolving balances exclude any balances in promotion, resulting form cash withdrawals, or those assessed at the penalty rate. Data on wages and employment comes are merged to the CCDB from the Quarterly Census of Employment and Wages (QCEW) vary at the country-quarter level.

or more mature than subprime accounts. Lastly, to account for the effects of time varying local economic conditions on demand, we match data on average wages and employment from the Bureau of Labor Statistics’ (BLS) Quarterly Census of Employment and Wages (QCEW). These data vary at the CountyQuarter level. As shown in the table, there is substantial variation in both the percent quarterly change in average wage in a county and the percent change in county level employment. On average, all counties in the sample experienced small increases in average wages. However, counties in which subprime cardholders reside saw slight reduction in employment. In contrast, counties in which prime cardholders reside saw small gains in employment and wages during the analysis periods.

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Empirical Design

The aim of the empirical analysis is to measure how cardholders’ demand for credit card services responds to changes in the APR and LF. To this end, we model a cardholder i at each month t as making three choices: (1) how much to use her credit card for purchases (2) the amount of balances to keep unpaid (revolving balances), and (3) whether to pay late, that is, not to pay the minimum payment corresponding to her balances by the due date. 10

Each of these choices can be made deliberately given some decision rule or as a result of mistakes on the part of the cardholder. Our model does not specify a specific decision rule. Instead, we measure cardholders’ responses to prices along the usage of these three services. Let U , C, and L denote respectively credit card purchases, revolving balances (credit card debt), and late payment. We define the demand for service S ∈ {U, C, L} as Dit∗S = hS (Pit , Xit ; θS ) + g S (t) + αiS + Sit ,

(1)

where Pit = {APR, LF} is a vector of prices and Xit is a vector of time-varying account specific and community level controls. Account level controls include a second order polynomial of an account’s age, which allows for demand to vary flexibly with account maturity, or experience, as well as any changes in an accounts available credit line. The community level controls include the quarterly percent changes in counties’ average weekly wage and employment. Community controls allow for demand to vary with changes in the local economy. The function g S (t) controls for time varying effects that are common across all accounts and is a third order polynomial on the months passed since the fee cap implementation date (September 2010).12 The variable αiS is a time-invariant account specific taste parameter, or account fixed effect. The variable Sit is an additively separable monthly consumption, or spending, shock. This shock can arise from fluctuations in income and/or purchase needs of cardholders over time, for example, an unexpected health problem. Consumption shocks are assumed to be independently and identically distributed across accounts and over time Sit ∼ N (0, σS2 ) and orthogonal to demand observables Sit ⊥ Xit , Pit , g S (t), αiS

(2)

We specify hS (Pit , Xit , θS ) as being linear in prices and controls according to hS (Pit , Xit ; θS ) = β S LFit + γ S AP RitS +

6 X

S S γ−j AP Rt−j + Xit0 δ S

(3)

j=1 12

For a month before the implementation date the trend variable is negative and for a month after the implementation date the trend variable is positive. We allow time trend to have non-linear effects by using a third-degree polynomial of the trend variable. We would prefer to control for time non-parametrically, e.g., by time fixed effects. However, we cannot do so since we observe only a one time change in LF. We attempt to compensate for this by allowing for as much flexibility as possible to control for time effects that would affect usage of the credit card services. We have tried several orders of our polynomial, from 1 to 4, and our results are robust to this.

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Linearity of h(·) is necessary due to a lack of variation in late payment fees within account over time, which occurs only once during our period (see Figure 1). However, following Gross and Souleles (2002), we allow for past APRs to affect current demand. In other words, we allow cardholders to adjust their credit card demands over time, with a delay of up to 6 months, due to a change in the interest rate. We then define the long-run response to the APR changes as the sum of the current and past responses, whereby γTSot

6 X S =γ + . γ−j S

j=1

We note that our framework is static, as we are most interested in measuring steady-state price responses. However, our choice to model demand as static with time invariant types is motivated by evidence that cardholders exhibit strong preferences for certain types of services that persist over time (Fulford and Schuh, 2015) and that credit card use is relatively stable over time for individuals with varying characteristics (Klee, 2006).13

4.1

Demand for Purchases and Revolving Balances

A credit card is strictly for borrowing and/or purchasing. Cardholders cannot systematically carry negative balances across months (cannot lend to the lender) nor can they make negative purchases on the card (sell to the lender/vendor). Nevertheless, it is common for cardholders to make no new purchases and/or revolve no balances in a given month. As a result, an important feature of the data is that in any given month a large portion of cardholders do not revolve a balance and/or make new purchases (see Table 1). We model this feature as a truncated (dependent) random variable and interpret this truncation as cardholders locating at a corner (e.g. zero balances).14 Let DitU ∗ and DitC∗ be account i’s latent unconstrained demand for purchases and revolving balances, respectively, in month t. Observed demands can be written as DitB = max(0, DitB∗ ), (4) with B ∈ {U, C}. The expected demand of account i in month t is then E[DitB |·] = (hB (·) + g B (t) + αiB ) · Φ(hB (·) + g B (t) + αiB ) + φ(hB (·) + g B (t) + αiB ), 13

(5)

This feature of persistent tastes has parallels in other consumer markets as well. As an example, were we to model demand for soft drinks, we may observe that some consumers choose Pepsi a majority of the time. A dynamic model may suggest that a consumer is choosing Pepsi today because she chose Pepsi yesterday. However, absent learning or stockpiling, perhaps a more appropriate explanation is that she chose Pepsi more often because of a time invariant preference for Pepsi (Hendel and Nevo, 2006; Shin et al., 2012). 14 The analysis does not include accounts that are borrowing at their credit limit. As a result, we only consider truncation at zero and not at the credit limit.

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where hB (·) is defined in equation (3). Φ(·) and φ(·) refer to the cumulative distribution and probability density functions of the Normal distribution, respectively, with variance σB2 .

4.2

Demand for Late Payment

Unlike purchasing and borrowing, late payment is a binary outcome; cardholders may pay late or on time. We therefore model demand for late payment using a standard binary choice latent variable framework. As such, this approach measures the extent to which cardholders incorporate knowledge of their interest rate and late payment fee into their decision making process regarding late payment. Specifically, let account i derive some indirect utility DitL∗ from not making her minimum payment by the due date t and let this indirect utility be as described in equation (1). Late payment occurs whenever DitL∗ > 0 and observed late payment behavior can be written as DitL = 1(DitL∗ > 0).

(6)

cardholder i’s propensity to pay late in month t is then E[DitL |·] = Φ(hL (·) + g L (t) + αiL ),

(7)

where hL (·) is defined in equation (3) and Φ(·) refers to the cumulative distribution function of the standard Normal distribution.

4.3

Estimation

Equations (5) for B ∈ {U, C} and equation (7) comprise the demand system that we estimate separately via (limited information) maximum likelihood. Given our normality assumption, DU and DC , specified in equation (5), are estimated using a Tobit likelihood (Amemiya, 1984). DL is estimated using a standard Probit likelihood.15 The large number of account fixed effects makes the estimation of these non-linear demand functions numerically complicated. Moreover, they introduce an asymptotic bias. This bias is exacerbated in short panels, small T , with a large number of fixed effects, large N , and is commonly referred to as the incidental parameters problem. The problem arises from sampling error in the estimation of the fixed effects carrying over to the estimates of the parameters of interest, whereby the resulting asymptotic distribution is no longer centered around 0, even if T grows at the same 15

The Tobit likelihood is transformed according to Olsen (1978) in order to ensure global concavity, and thus convergence, of the objective function. The Probit likelihood remains unchanged, but the variance of the error is normalized to 1 as it is standard in binary choice models.

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rate as N .16 To reduce the asymptotic bias, we use an analytical bias reduction described in Hahn and Newey (2004) and Arellano and Hahn (2007). This method derives the asymptotic bias and subtracts this term from the likelihood equation.17 We then estimate our adjusted likelihood using an efficient Newton-Raphson algorithm laid out in Hospido (2012). Exact details of our estimation procedure are laid out in Appendix B. Lastly, we estimate the demand equations separately for subprime and prime. As our data is comprehensive, covering the majority of accounts in the market, we are not constrained to pooling accounts across risk categories or controlling for risk category of an account with added regressors. Instead, we are able to analyze price effects for the subprime market as distinct from the prime market. As aforementioned, academic and policy discussions regarding cardholders’ costs of evaluating complex credit card prices and potential nonsalience to back-end fees have centered on differences in behavior between these two types of cardholders. We analyze these issues by exploring how these groups differ in their demand responses to price changes.

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Identification

A common problem in estimating demand is isolating price movements due to supply from those driven by variation in demand. We are interested in the demand response to movements in two prices: (1) APR and (2) LF. To this end we use two different strategies to identify supply driven price effects, one for each relevant price.

5.1

Movements in APR and LF

We identify supply driven changes in interest rates by exploiting lenders’ repricing of accounts around the time of the CARD Act. These episodes are detected using the fixed effects in our estimation equations. By conditioning on time invariant type, we eliminate all cross sectional variation in the effect of prices. As a result, price movements reflect changes in cardholders’ own rate, or within account, change over time. This is precisely a repricing episode. Our within estimator can be interpreted as the average response to a change in cardholders’ own interest rate. Prior to the CARD Act, accounts were repriced for a variety of reasons. A primary cause of repricing was a delinquency on the card, at times even a ’hair-trigger’ delinquency, or a 16

For a discussion of asymptotic bias resulting from an incidental parameters problem see Arellano and Hahn (2007). 17 Simpler “automatic” forms of bias reduction, such as jackknife methods, are not suitable to our application because we only observe a price change in late fees once during the sample period. As a result, we appeal to the shape of the objective function and use an analytic reduction technique.

14

universal default (e.g. default or delinquency on an unrelated line of credit appearing in a cardholder’s credit report). In such instances, APRs were often increased to the contractual penalty rate, mostly an increase of 10 percentage points or more, and applied to existing as well as forward balances. In our analysis we eliminate effects of this type of repricing. We do so by restricting our sample to accounts who never face an APR change greater than 5 percentage points and by excluding accounts who are ever more than 60 days delinquent on their payments.18 Moreover, we use downward as well as upward movements in APR to identify demand. Our identification thus relies on small repricing events that often occur via decision rules that are unknown to cardholders. We check whether these repricing episodes are correlated with observed demand side variables such as baseline risk and/or usage and whether that they are anticipated. We find that in both cases they are not. However, we find that these changes are associated with movements in the cost of funds, as measured by the 1-year Treasury rate.19 As such we conclude these rate movements may be plausibly exogenous to individual demand decisions. Table 2 shows prevalence in repricing, both upward and downward, before and after the CARD Act implementation. It further relates within account interest rate movements to demand side variables, specifically risk category and revolving balance amount, to test whether there is some connection between demand side behavior and the likelihood of experiencing repricing. The table shows the results from nine separate regressions. In each regression we estimate separately the relationship between three types of APR changes: an overall month-to-month APR change (column 1), an APR increase (column 2), and an APR decrease (column 3), and three demand characteristics: whether an cardholder is revolving in the last 3 months (revolver), her current revolving balance amount, or whether she is a prime cardholder. First, the table shows that repricing episodes are fairly common across lenders. The monthly propensity to be repriced prior to the CARD Act was approximately 3.7 percent.20 Assuming independence, this implies that the probability of being repriced at least once over 1 year was 36.4 percent (= 1−(1−0.037)12 ). Moreover, we see that repricing of rates includes both upward and downward rate movements, so the responsiveness of the demands to APR changes are not identified only from movements in one direction. The CARD Act’s Phase II provisions, which were implemented in February 22, 2010, largely restricted repricing by lenders. As is evident in the table, this mandate reduced upward repricing significantly (from 2.9 percent to 0.5 percent), but have had a more modest effect downward repricing. Overall, 18

We have also estimated our demand equations using cardholders who are at all times during our sample current on their payment (e.g. never 30 days or more delinquent). We find our results are robust to this pruning. 19 Ours is not the first to consider the 1-year Treasury rate as a proxy for the cost of funds (Ausubel, 1991). Our results are robust to using other maturities as well. 20 Note that the constant is the average of the bank fixed effects.

15

Table 2: APR Changes and Demand Observables Depvar Revolver Post CARD Act Constant Non-Introductory Balance ($1, 0000 s) Post CARD Ac Constant Prime (Credit Score > 660) Post CARD Act Constant Lender FE Observations

APR Change (1) 0.0023 (0.0098) -0.0152* (0.0066) 0.0385* (0.0035) 0.0030 (0.0031) -0.0151* (0.0066) 0.0371* (0.0029) 0.0053 (0.0088) -0.0152* (0.0066) 0.0365* (0.0056) X 955,968

APR Increase (2) 0.0024 (0.0039) -0.0241* (0.0091) 0.0289* (0.0044) 0.0012 (0.0012) -0.0241* (0.0091) 0.0288* (0.0043) 0.0012 (0.0031) -0.0242* (0.0091) 0.0290* (0.0044) X 955,968

APR Decrease (3) -0.0001 (0.0069) 0.0090+ (0.0053) 0.0096* (0.0022) 0.0018 (0.0019) 0.0090+ (0.0053) 0.0083* (0.0028) 0.0041 (0.0059) 0.0090+ (0.0054) 0.0075 (0.0054) X 955,968

Notes: Data using the estimation sample of prime and subprime accounts described in section 3. All regressions include lender fixed effects. The constant is the average of the fixed effects in the regression. Standard errors are clustered at the lender level. + = significant at the 10% level and * = significant at the 5% level.

the CARD Act has significantly decreased repricing, but has not eliminated it.21 Second, the table shows that within account movements in APR are largely uncorrelated with observable demand side (account) characteristics. There is no statistically significant difference between a revolver and a transactor in their likelihood of experiencing a change in their APR. Moreover, the estimated coefficient is small relative to the baseline repricing propensity, nearly an order of magnitude smaller. Similarly, the amount of revolving balances and risk category of a given account both fail to predict whether that account will see an APR change in any given month. Overall, we find little evidence that interest rate changes are correlated with account level demand characteristics. In other words, within account changes in interest rates are likely not driven by individual account behavior, but rather are algorithmically decided and/or applied to a large portfolio of accounts. Much of our variation with regards to upward and downward repricing derives from the 21

The monthly propensity to be repriced has become 2.2% (=0.037−0.015), where −0.015 is the coefficient of Post CARD Act in the first column estimations in Table 2. Thus, the probability of being repriced at least once over 1 year has become 1 − (1 − 0.022)12 = 23.4%.

16

first year in our data. As such, figure 2 shows movements cardholders’ revolving balances given an APR changes in the middle months of that year (e.g. January - March 2010). The figure shows trends in balances from 5 months prior to 6 months following the repricing. It further compares trends for those whose APR changed (Treatment) those whose APR did not change (Control). As shown in the figure, upward (downward) repricing leads to a

Figure 2: Unanticipated Balance Response to Changes in APR Notes:The figure shows trends in balances for cardholders whose APR changes (Treatment) as compared to those for who the APR remains the same (Control). Data include APR changes during January, February, and March of 2010. The month of the APR change is normalized to 0 and trends spann five months prior to six months following the change.

sharp decrease (increase) in balances following the changes.22 Moreover, these lower (higher) balances persists for at least six months following the changes. Overall, the figure suggests that these repricing episodes are largely unanticipated by cardholders and that their effects are significant and persistent following the change. We next look the extent to which minor repricing episodes are associated with the cost of funding accounts. We do so by measuring the degree to which an existing accounts’ APR is adjusted in response to a change in the 1-year constant maturities (CMT) Treasury rate, our proxy for the cost of funds. This is similar to the method used in (Ausubel, 1991) to measure cost pass through in this market.23 Table 3 shows how movements in the cost of funds are associated with account repricing. As can be seen in the table, account APRs are 22

We acknowledge that for upward repricing episodes balances begin to decrease prior to the rate change. We suspect this is likely due to CARD Act rule enacted in August 2009 which required lenders to notify borrowers of this change at least 45 days in advance. 23 Ausubel also used the 1-year CMT Treasury rate as a proxy for the cost of funds. However, in contrast to Ausubel, who used lenders’ most commonly offered rates at quarterly intervals, we use individual account rates and measure within account changes monthly.

17

Table 3: Interest Rates and the Cost of Funds DepVar =

∆APR (OLS) (1)

APRt−1 1-Yr Treasury Rate

APR (OLS) (2) 0.7404** (0.0221) 0.2932** (0.1187)

APR (IV) (3) 0.7875** (0.0044) 0.2290** (0.0050)

∆[1-Yr Treasury Rate]

0.2579 (0.2128) Constant 0.0232 4.3352** 3.4382** (0.0130) (0.3667) (0.0748) Arellano-Bond (1991) Test for Zero Correlation in First Differenced Errors 1st Order -76.5060** nd 2 Order -1.7332 Account Fixed Effects X X Lender Clustered SE X X Observations 866,544 907,808 866,544 R2 0.0005 0.9959 Notes: This table shows the relationship between changes in APR and the cost of funds, as measured the the 1-year constant maturities Treasury rate. Data are using our CCDB balance panel (table 1). + = significant at the 10% level and * = significant at the 5% level.

highly responsive to the cost of funds, as measured by the 1-year CMT Treasury rate. The correlation in differences (column 1) suggests that a 100 basis point change in the cost of funds is associated an expected 26 basis point increase in APR. Moreover, the adjustment rate is quite high as well. As shown in column 2, the monthly adjustment rate of APR to the cost of funds is approximately 29 percent.24 To account for the dynamic panel bias (Nickell, 1981), we estimate the same relationship using the instrumental variable estimator of Arellano and Bond (1991). As shown in column 3, accounting for the bias reduces the adjustment rate to 23 percent. Nevertheless, this effect is still economically significant. Overall, we find evidence that these minor repricing episodes were, at least in part, driven by cost side considerations. Finally, to isolate supply driven variation in late fees we use the late fee cap imposed by the CARD Act in September 2010. Prior to the regulation, the majority of lenders charged $39 dollars for late payments and there was very little variation over time and across lenders. The regulation capped late fees at $25 dollars and the cap was binding for almost all accounts (see Figure 1). Thus, the late fee change affected all cardholders independently of their individual demand behavior. It follows that estimated demand response to movements in 24

In contrast, using aggregate data Ausubel (1991) measures a 5 percent adjustment rate, quarterly, during the 1980’s, while Grodzicki (2012) measures a 26 percent adjustment rate biannually between 1994 and 2008. It is important to note that previous work has measured the price to cost adjustment in the context of offered rates, rather than movements in rates on existing accounts. Consequently, our results are not directly comparable.

18

late fees are identified from this one-time decrease.

5.2

Potential Threats to Identification

A number of confounding influences may affect our interpretation of the results. One important factor to consider is a change in the macroeconomic environment during our sample period. Such a change could affect cardholders’ demand for the credit card services via movements in their consumption patterns over time. We assuage this concern by parametrically accounting for time effects in our specification. Moreover, by including changes in county level wages and employment we control for cardholders’ demand responses to local economic conditions.25 There may be still be other local environmental factors affecting demands for which we do not control. However, as we discuss later in the paper (Section 6), we believe that wages and unemployment account for a large portion of the macroeconomic impact on demand for credit card services. There have also been several other market changes mandated by the CARD Act that may influence demand in a way not directly accounted for in our specification. For example, provisions restricting upward repricing were mostly eliminated by the CARD Act and this change may have indirectly affected demand for borrowing over the period. Nevertheless, these were imposed on all cardholders. As a result, any indirect (non-price) effects are likely accounted for in our parametric time effects. It is also possible that demand responses to the late fee are influenced by the CARD Act mandated opt-in requirement for over-limit fees.26 For example, a consumer might use her card more because, if she pays her bill late, the LF is lower, but the same consumer could also be using her card more because, if she happens to reach her credit limit without noticing, she will not have to pay the over-limit fee given that she did not opted-in the over-limit service. We believe that this may not be a large concern for four main reasons. First, we restrict the sample to cardholders that never use more than 90 percent of their credit line. These cardholders are unlikely to be responsive to over-limit fee changes, since 18 months prior to the opt-in implementation they were never in danger of reaching their limit.27 Second, the over-limit fee requirement came into effect six months prior to the fee cap. As a result, any remaining effects are likely absorbed by our time trend. Third, to the extent that changes in borrowing limits may have interacted with this mandate, we control for these explicitly in the regression. Lastly, a comparison 25

However, due to the unavailability of data on account-level demographics, we cannot control for the effect of the cardholder’s wage and employment changes on her demands for the credit card services. 26 This change mandated that issuers could not charge the cardholder an over-limit fee unless the cardholder opted-in for the over-limit service. 27 It is possible that there is a buffer stock effect of consumers being hesitant to even approach the limit, see Carroll (1997), but the vast majority of cardholders are far from anything even reasonably approaching the limit.

19

of subprime and prime cardholders finds that subprime cardholders are much more likely be close to their limit; yet, we do not find subprime cardholders’ balances and usage to be considerably more responsive to the change in late fee (Section 6). The CARD Act also mandated minimum payment disclosure requirements that oblige credit card issuers to display on credit card bills the costs of repayment and 3-year amortization totals for minimum payments. Given that a cardholder has to pay the late fee only if she fails to pay the minimum payment amount corresponding to her revolving balance, one would expect the minimum payment disclosure to affect cardholders’ propensity to pay late. 28 Thus, our estimates of the demand response to the LF change could potentially pick up some of this effect. We believe this may not be a significant factor in our setting. First, previous studies document that, because of an ’anchoring’ effect, minimum payment disclosures may be associated with lower repayment rates and/or have only a modest effect on repayment rates overall.29 Second, our sample consists of cardholders that are somewhat experienced and our specification flexibly controls for account age, which should largely soak up any remaining effects of this disclosure.

6

Results

In this section we present and discuss implications of demand responses from our estimated regressions. Our exposition unfolds as follows. In 6.1 we present our main results for the three demand components, purchases, balances, and late payment, as laid out in section 4. For each component we distinguish between own and cross effects of prices on demand. Specifically, we call the effects of APR on balances and LF on late payments own effects. We call the effects of LF on purchases/balances and APR on purchases/late payment cross effects. In section 6.2 we further explore the mechanisms underlying these differences by decomposing demand responses into an extensive and an intensive margin and by measuring how usage is correlated across the three services. Lastly, in section 6.3 we study the impacts of a rising Federal Funds rate on the demand for credit card borrowing. 28

The minimum payment amount is typically 1-4 percent of the unpaid balances. In an experimental study with 400 participants from UK Stewart (2009) finds that removing the minimum repayment information (of 5.42 pounds) led to a significant increase in payment by 75 percent, from 99 to 175 pounds. Navarro-Martinez et al. (2011) confirmed the previous result qualitatively in an experimental study using 127 randomly selected adults from US. Agarwal et al. (2015b) find that the CARD Act’s minimum payment disclosure provisions increased the number of accounts paying at a rate that would repay their balance within 3 years by a modest 0.5 percentage points. In a related study Keys and Wang (2016) document that 29 percent of accounts regularly make payments at or near (within $50 range of) the minimum payment amount and only less than 1 percent of accounts stick to the three-year repayment amount after the CARD Act’s disclosure provisions. They argue that this modest effect of the regulation might be due to many people anchoring at the minimum payment amount or making their repayment without seeing the display of the 3-year repayment amount (as they are not displayed on online statements) or without paying attention to this new display. 29

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6.1

Demand for Credit Card Services

Table 4 presents the demand elasticities implied by the estimated regression equations 5 and 7 in section 4.30 The top and bottom panels of the table show the elasticity measures for subprime and prime cardholders, respectively. Columns (1) and (2) show the elasticities of Table 4: Demand Elasticities

Subprime Cardholders Prime Cardholders

DU ,AP R DU ,LF (1) (2) Median 0.01 -0.01 IQR 0.01 0.01 Median -0.15 -0.07 IQR 0.12 0.05

DC ,AP R DC ,LF DL ,AP R DL ,LF (3) (4) (5) (6) -1.97 0.83 0.24 -0.24 1.77 0.66 0.14 0.10 -1.08 -0.12 -0.53 -0.30 0.85 0.08 0.25 0.16

Notes: This table presents the demand elasticities implied by estimation of the regression equations, 5 and 7. For full regression results, see Appendix A. The table shows median and interquartile range of elasticities. DU ,AP R refers to the elasticity of credit card usage volume (purchases) with respect to interest rate, DU ,LF refers to the elasticity of purchases with respect to late payment fee, DC ,AP R refers to the elasticity of credit card borrowing volume (balances) to interest rate, DC ,LF refers to the elasticity of balances to late payment fee, DL ,AP R refers to the elasticity of late payment demand to interest rate, and DL ,LF refers to the elasticity of late payment demand to late payment fee. Data are from the CFPB’s CCDB for the sample period September 2009 - August 2011, inclusive. See Section 3 for details.

demand for purchases (DU ) with respect to APR and LF, respectively. Columns (3) and (4) show the elasticities of demand for balances (DC ) with respect to APR and LF, respectively. Columns (5) and (6) show the elasticities of demand for late payment (DL ) with respect to APR and LF, respectively. The table shows the median and inter-quartile range (IQR) of price responses among all cardholders within each respective risk group. Making purchases (transacting) on a credit card does not necessarily imply paying an interest rate on balances or incurring a late payment fee. Nevertheless, purchases can lead to greater debt and a higher propensity to incur fees. Consequently, changes in rates and/or fees alter the expected cost of transacting on a card. As shown in Columns (1) and (2) of Table 4, the median prime cardholder is responsive to this change and reduces purchase activity when rates and fees rise. In contrast, the median subprime cardholders’ purchase decisions seem less affected by changes in rates and fees. Overall, subprime cardholders’ propensity to carry balances and pay late is substantially higher than for prime cardholders (Table 1). Mitigated price response among this group of cardholders suggests potentially less flexibility in their ability to change their purchase patterns on a card, perhaps because they only have one card, and/or an underestimate of the propensity of purchases to lead to debt and fees (Laibson, 1997; O’Donoghue and Rabin, 1999). 30

Full regression results are shown in Appendix A.

21

Unlike purchases, credit card balances are generally assessed finance charges. Moreover, failure to pay the minimum payment by the due date incurs a fee. As shown in Column (3) of Table 4, for both prime and subprime cardholders, an increase in APR lowers the demand for balances, with stronger price effects among subprime cardholders.31 This greater sensitivity to interest rates among subprime cardholders echoes a conjecture in Ausubel (1991) arguing that, because high risk cardholders more often intend to use their cards for borrowing (Table 1), they may be more sensitive to borrowing rates.32 This finding also contrasts with earlier hypotheses of consumer rationing which argue that high risk constrained cardholders may care more about monthly payments than interest rates and so should be less sensitive to changes in APR (Juster and Shay, 1964).33 Among prime cardholders, a decrease in LF leads to a modest rise in demand for balances, the cross effect (Column (4) of Table 4). Like for purchases, a lower LF reduces the expected price of borrowing. This finding is consistent with standard models of rational consumer choice, with the modest effect potentially due to a low probability of late payment (∼ 2%). However, for subprime cardholders, a decrease in LF leads to a reduction in balances. In other words, when the expected cost of borrowing decreases, so does demand. This response is difficult to predict within the framework of standard models of rational consumer choice. We argue that this finding is consistent with theories of limited attention. Studies on cognitive scarcity (Mullainathan and Shafir, 2013; DellaVigna, 2009) demonstrate how consumers in strained financial conditions are limited in their ability (attention) to process all the information available to them. As a result, they form rules of thumb, prioritizing certain information streams over others. When making purchase and repayment choices, cardholders must consider a number of factors such as their APR, LF, total unpaid balances and minimum payment amount due. Cardholders who find it too costly to negotiate 31

Our results are comparable to Gross and Souleles (2002), who also document how cardholders’ demand for balances responds to interest rates. Going beyond their previous work we document that subprime borrowers are more sensitive to interest rates than prime borrowers. In contrast to their study, our analysis is carried out at the account level, not at the consumer or at the household level. As a result we cannot measure balance shifting across cards. However, this may work to strengthen our result. To the extent that prime cardholders are more likely to hold a portfolio of credit cards and transfer debt between them, we may be overestimating the responsiveness of prime cardholders’ demand for balances with respect to APR. In contrast, subprime cardholders’ are much less likely to hold more than one card or have opportunities for transferring balances to newly originated cards. As a result, the pay down in balances we observe more likely accords to a true reduction in household leverage. 32 In contrast, low risk (prime) customers, who likely enjoy cheaper credit alternatives, use their cards more heavily for transacting (Table 1) so may care less about the cost of borrowing. Ausubel (1991) argued that when lenders could not differentiate between these types of consumers, a unilateral reduction in rates by a lender would adversely select riskier and less profitable customers, and so lead to persistently high prices. This argument was used in part to explain a failure of competition in the credit card market during the 1980s. 33 In our analysis we eliminate accounts ever close to the credit limit. Nevertheless, this finding is robust to including those accounts as well.

22

all these terms simultaneously may focus their attention on paying some sufficient and fixed amount by the due date to avoid high fees, often at the expense of attentiveness to revolving balances and incurred finance charges. A decrease in fees may lead to a shift in attentional resources toward interest rate charges, prompting debt pay down.34 For example, using data from a field experiment in Brazil, (Medina, 2017) shows that a reminder for timely credit card payment leads a large fraction of consumers to incur checking account overdraft fees instead and argues that this finding is consistent with theories of selective attention, such as Bordalo et al. (2013). The above mentioned theories of limited attention predict that cognitive scarcity should be more acute among individuals in greater financial distress. As a result, we would expect estimated cross effects to be stronger among lower income and more financially distressed cardholders. Relatedly, greater focus on avoiding fees may imply that individuals who are less likely to pay late may also exhibit stronger response of balances to lower fees, as their attention now shifts toward the cost of holding balances. In line with this logic, more recent theoretical work on markets with multi-price contracts and consumers with limited attention describes how a policy limiting add-on, or hidden, fees, such as LF, can shift consumer’s attention away from these ‘hidden’ prices and thereby increase their sensitivity to products’ main, or headline, prices, e.g. APR (Heidhues et al., 2017).35 We test these predictions within our setting by calculating own and cross effects of demand for balances separately for cardholders residing in low income communities and cardholders who never pay late within our two year window. We also measure own effects of demand for balances separately for the year before and the year following the CARD Act mandated LF cap. First, in columns (1) and (2) of Table 5 we confirm the prediction that cross effects (DC ,LF ) should be stronger among individuals more likely to be financially distressed. As shown in the table, this effect is approximately 25 percent larger among cardholders whose account billing address is in the bottom quartile of county average income. Next, as further corroborating evidence, Columns (3) and (4) of Table 5 show similar differences in cross effects when separating out subprime cardholders who never paid late during our sample period. Moreover, own effects (DC ,AP R ) are diminished for cardholders residing in low income communities as well as for those who are never late during the sample, a 34

Our argument is closely related to work documenting cardholders anchoring payments at the minimum payment amount when fees are high (Keys and Wang, 2016; Stewart, 2009; Navarro-Martinez et al., 2011). These studies show that anchoring is substantial among constrained borrowers, largely impervious to ’nudges’ on repayment patterns, and costly to consumers. 35 Heidhues et al. (2017) lay out a model in which inattentive consumers must either study one lender’s add-on fee in detail or ‘browse’ many sellers headline prices while largely ignoring add-on fee costs. Their model predicts an equilibrium in which low-value consumers choose to study one provider’s add-on fee in detail, but fail to browse the ‘headline’ price across different firms. An important implied comparative static is that a reduction in the add-on price (e.g. a mandated price cap) increases low value consumers’ relative benefit of browsing ‘headline’ prices, increasing the sensitivity of these consumers to this price.

23

Table 5: Heterogeneity in Elasticities of balances by Cardholder Type and Over Time

Subprime Cardholders Prime Cardholders

DC ,AP R DC ,LF  C Median D ,AP R DC ,LF Median

High Income Low Income Sometimes Late Never Late Pre (1) (2) (3) (4) (5) -1.99 -1.91 -3.41 -0.28 -1.34 0.78 1.01 0.65 1.01 -1.11 -0.98 -1.54 -0.75 -1.28 -0.11 -0.08 -0.17 -0.08

Post (6) -4.40 -0.52

Notes: This table presents the elasticities of balances implied by estimation of the regression equation (5) separately for high and low income cardholders, or residing in the lowest quintile of county average income, cardholders who paid late at least once during the period (sometimes-late), and cardholders who never paid late at any point in the sample (never-late). It also shows the elasticities of balances with respect to APRs separately for the months prior to the LF cap implementation (Pre) and for the months following (Post). See Appendix A for full regression results.

finding congruent with the notion that greater focus on avoiding fees comes at the expense of paying less attention to the price of carrying balances.36 Splitting the sample into the period prior to and following the mandated LF cap, we find that the median own effect for APR on borrowing among subprime cardholders rose substantially after the regulation (Columns (5) and (6) in Table 5). As aforementioned, this finding is in line with our previous argument that the LF cap shifted subprime cardholders’ attention toward APR, prompting them to pay down their balances.37 It is also consistent with Heidhues et al. (2017) which predicts an increased sensitivity to a product’s main, or headline, price resulting from regulation of add-on fees, a regulation which they claim is potentially welfare enhancing.38 Finally, we turn to the effect of APR and LF on the incidence of late payment. While economists traditionally expect that the law of demand holds, policy makers and researchers alike have recently argued that back end fees may not be salient to cardholders, whose late payment results from mistakes, e.g. when they accidentally trip the wire by forgetting to pay 36

Alternatively, it may be the case that our results are driven by a prevalence of self control problems among subprime (unsophisticated) consumers. In their model of credit markets with naive consumers, Heidhues and K˝ oszegi (2010) predict that unsophisticated consumers, who are naive and lack self control, will pay late more often and, as a result, respond to the LF cap by reducing their borrowing. However, this prediction is inconsistent with our finding that subprime cardholders who never pay late reduce their borrowing more in response to the cap than those who never pay late during our sample. Combined with the pre and post differences in own effects (see below), this suggests that self control may not be the primary mechanism underlying the positive cross effects observed among subprime cardholders. 37 In contrast, prime consumers’ sensitivity to rates declined following the fee cap, a potentially rational response to the reduction in the overall cost of borrowing. 38 Our finding of an upward sloping cross effect of demand might seem reminiscent of a similar result in Alan et al. (2015). In that study on bank overdrafts in Turkey, the authors argue that an increase in the demand for overdrafts following an announcement of a price decrease may result from consumers becoming newly aware of the cost of over-drafting, in essence amounting to a price rise. However, we note that, in our setting, a reduction in LF, the own effect, leads to a greater incidence of late payments, both among prime and subprime cardholders (Table 4). This is inconsistent with the increased salience documented in their study. We are grateful to Johannes Johnen for pointing out this alternative mechanism to us.

24

(Gabaix and Laibson, 2006). Consequently, the frequency of, or demand for, late payment might not be downward sloping in its own price, LF. Nevertheless, Column (6) of Table 4 shows that when late fees decline the frequency of late payment among cardholders rises, a negative own effect. Although this in no way rules out the prevalence of accidental late payments, it does show that all cardholders pay late more often when it is less expensive to do so, with prime cardholders seemingly more sensitive in this dimension. To the extent that prime cardholders are more sophisticated users of credit, the difference in responsiveness across these groups does provide evidence supporting predictions in recent theoretical work which defines a notion of unsophisticated consumers and shows these are more likely to incur such fees (Table 1) and less likely to alter their behavior when it becomes more or less costly to do so (DellaVigna and Malmendier, 2004; Ellison, 2005; Gabaix and Laibson, 2006; Ru and Schoar, 2016). Looking at the cross effects, Column (5) of Table 4 shows that, like for purchases and balances, prime cardholders’ frequency of late payment decreases when their APR increases. In contrast, higher APR leads to a modest increase in late payment propensity among subprime cardholders. This positive response is likely due to a related rise in minimum payment amount, which some subprime cardholders may find more difficult to pay before its due. However, we calculate this effect is likely quite small and may impact few users.39

6.2 6.2.1

Demand Decompositions The Extensive vs. Intensive Margin

Cardholders who carry balances are often termed revolvers, while those who do not are either called transactors, if they make purchases, or inactive, if they do not use their card at all. Our demand specification captures these possibilities, allowing us to decompose demand decisions into an extensive margin, that is the propensity to use a service at all, and the intensive margin, the quantity of that service to use when using. More specifically, from the Tobit functional form and using Bayes rule it follows that E[DitB |P, X] = E[DitB > 0|P, X] · E[DitB |DitB > 0, P, X], 39

(8)

Minimum payments are usually 1-2 percent of balances. We calculate that a one-percentage-point increase in APR for an average subprime account leads to 0.84 percent increase in minimum payment, which can explain the small effect.

25

where B ∈ {U, C}. By taking derivatives of both sides with respect to prices and normalizing by the level we obtain E[DB |P, X],P = E[DitB >0|P, X],P + E[DitB |DitB >0, P, X],P , | {z } | {z } | it{z } T otal

Extensive

(9)

Intensive

which we re-write as Extensive TDotal + Intensive . B ,P = D B ,P DB ,P

(10)

Normalizing both sides by the total elasticity (TDotal B ,P ) gives the relative, or proportional, importance of each margin for the total effects of prices on each demand. Note that these margins are identified from movements into and out of purchasing/revolving over time and across accounts. We carry out this decomposition for the elasticity of purchases with respect to LF (DU ,LF ) and the elasticity of balances with respect to LF (DC ,LF ), which we are shown in Table 6. As

Table 6: Decomposition: Extensive and Intensive Margins

Subprime Cardholders Prime Cardholders

DU ,LF Extensive Intensive (1) (2) Median -73.6% -26.4% Median -68.1% -31.9%

DC ,LF Extensive Intensive (3) (4) 67.5% 32.5% -72.6% -27.4%

Notes: “Extensive” refers to the elasticity at the extensive margin, that is, the percentage change in the expected probability of having a positive purchase/balance volume when the late payment fee increases by 1%. “Intensive” refers to the elasticity at the intensive margin, that is, the percentage change in the demand for purchases/balances when the late payment fee increases by 1%, conditional on having a positive purchase/balance prior to the late fee change.

discussed in section 6.1, a decrease in LF leads to more purchasing among prime cardholders, a response consistent with a model of rational consumer choice. A feature of credit card pricing is that late payment fees are largely unrelated to the volume of purchase.40 This means that the greatest change in expected cost of usage occurs at the extensive margin. As a result, we would expect that cardholders respond to an LF decrease mostly by using their card more often, rather than more intensely. Consistent with this notion, we find that for the median prime cardholder nearly 70 percent of the effect of LF on prime accounts’ credit card usage is attributed to the extensive margin. Using a similar reasoning, we expect that the effect of late fees on balances should come primarily through the extensive margin. Indeed we find that nearly 73 percent of the effect of LF on prime accounts’ balances stems from a reduction in the probability of revolving. 40

This is not true for very high purchase or debt volumes, however, it applies for the vast majority of users.

26

Recall that subprime cardholders’ balances decrease in response to a reduction in LF. We argued that this positive response might be consistent with the theories of limited attention and/or anchoring at the minimum payment amount. Our decomposition result for subprime cardholders shows that nearly 70 percent of the response comes from the extensive margin, or a decline in the probability of revolving. This is consistent with subprime cardholders increased sensitivity to finance charges leading to lower propensity to revolve balances at all. 6.2.2

Correlation of Demand Across Services

In principle, one may expect time invariant characteristics (fixed effects) of cardholders’ behavior to positively covary, for example those who are high volume purchasers might also borrow more. One may also expect monthly shocks to propagate across services, such as if a cardholder were compelled to make large purchases on a card in a given month she may also then borrow more than is customary. Similarly, large purchase or greater borrowing relative to a cardholder’s norm may also mean a higher propensity to pay the bill late. Our empirical strategy uses a limited information maximum likelihood approach. In other words, we do not directly estimate coefficients of correlation for tastes and shocks to demand across services. Nevertheless, we utilize fixed effects and calculated generalized residuals (Chesher and Irish, 1987; Gourieroux et al., 1987) from our estimated demand equations to measure indirectly how tastes are correlated across services and how shocks filter through different usage decisions. Table 7 shows pairwise correlation patterns across equations for both tastes (fixed effects) and shocks (residuals), and across risk and income groups. Specifically, we calculate the pairwise correlation for each of the three demand equaTable 7: Correlation of Demand Across Services

FE (Rank) Subprime Cardholders Shock FE (Rank) Prime Cardholders Shock

(All) (Low (All) (Low (All) (Low (All) (Low

Income) Income) Income) Income)

ρ(U, C) ρ(U, L) ρ(C,L) (1) (2) (3) 0.06 -0.03 0.08 0.02 -0.11 0.34 0.16 0.06 0.14 0.20 0.07 0.17 0.18 0.09 0.29 0.12 -0.04 0.24 0.21 0.06 0.20 0.16 0.06 0.17

Notes: This table shows pairwise correlations for (1) fixed effect rank (2) generalized residuals (Chesher and Irish, 1987; Gourieroux et al., 1987) using estimated demand equations (Appendix A). Column (1) show correlations between purchases (U) and balances (C), Column (2) shows correlations between purchases and late payment (L), and column (3) shows correlations between balances and late payment.

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tions on (1) rank of fixed effect (taste) and (2) generalized residual (shock). Column (1) shows correlations between purchasing (U) and borrowing (C), column (2) shows correlations between purchasing and late payment (L), and column (3) shows correlations between borrowing and late payment. As shown in the table, for the most part both time invariant tastes and shocks positively covary across all services and groups. One notable exception is tastes for purchasing and paying late among subprime cardholders. Still, we find substantial differences in the degree of correlation across tastes and shocks and for various cardholder groups. For example, subprime cardholders’ tastes exhibit very little correlation across types of usage. One exception is the correlation between borrowing and paying late for low income households, a finding highlighting a strain to make on-time payments because of tight budgets. In contrast, prime cardholders’ tastes are more correlated across usage types. Higher correlation in tastes among this group may be an indication that credit card usage is more incorporated into the broader lifestyle of prime consumers leading to more entrenched tastes in usage in this group.41 For both prime and subprime, although still somewhat low, we generally find a higher correlation in shocks (residuals) across services than in tastes. Moreover, we find few differences in the correlation of shocks among these two cardholder types. Our estimates thus reveal modest spillover effects of shocks into usage of different services. For example, for a prime cardholder, a 1 standard deviation increase in purchasing relative to expectation (”shock”) is commensurate with a 0.20 standard deviation increase in the level of borrowing. To translate this into dollar amounts, a shock sufficient for a prime cardholder to increase purchase volume by $500 relative to normal is correlated an increase roughly $100 in balances. We can perform a similar calculation for borrowing and late payment, whereby a shock sufficient for a prime cardholder to increase their balance by $5,000 is commensurate with an 0.60 percentage point (≈ 10 to 25 percent) increase in the probability of paying late. Notably, these effects are not materially different across risk or income types.

6.3

Monetary Policy and Demand for Consumer Credit

Using our demand estimates we calculate the impact of a hypothetical 200 basis point (bp) increase in the FFR on credit card revolving balances. As noted in Section 2, the majority of accounts carry variable APRs and so credit card issuers contractually commit to pass all of the increases in their prime rate onto existing accounts’ APRs.42 To focus on the direct 41

They may also be different types of card offering various rewards program that target certain types of users. 42 APR on an account is calculated as a fixed markup over the prime rate, which is defined as 300bp plus the FFR.

28

effect of the FFR change on revolving balances, what we call the pure APR effect, we hold constant all other variables affecting demand for credit card balances.43 We first document the average effects for prime and subprime cardholders and then illustrate how these averages vary across different regions. Finally, we discuss some caveats of our analysis with respect to holding constant other factors governing demand for credit card balances. 6.3.1

Aggregate Effects

Table 8 shows the average effects of a 200 bp increase in the FFR on credit card balances.44 The table shows average percentage point and absolute effects, Columns (1) and (2). Using the expressions derived in section 6.2.1, it also shows separately the effect of the policy on cardholders’ propensity to revolve, carry, balances, Columns (3) and (4). As shown in the Table 8: Effects of the rise in Federal Funds rate on credit card borrowing. Revolving Balances Percent of Revolvers Percent Change Percentage Point Change Percent Change (1) (2) (3) Subprime -21.78% -3.94% -16.21% Prime -14.84% -2.54% -11.06% Notes: This table shows the average effects of a hypothetical 200 basis point rise in the Federal Funds rate on the estimated credit card balance demands of prime and subprime accounts.

top row of the table, we calculate that the average subprime cardholder reduces her balances by about 22 percent and that about 1 in 25 accounts stop revolving balances altogether. This corresponds to a nearly 16 percent decrease in the likelihood of revolving among these cardholders. For prime cardholders, the bottom row, we document a 15 percent average reduction in revolving balances given a similar rise in FFR. According to the New York Fed Consumer Credit Panel/Equifax, total outstanding balances among cardholders were approximately $784 billion in 2017Q2, and according to Consumer Financial Protection Bureau (2015), at the end of 2015 with prime cardholders accounted for 81 percent of the balances outstanding. Assuming this fraction stayed the same, prime cardholders held $635 billion of the debt. From this, we calculate that a 200 bp increase in the FFR will lead to a $635 × 15% = $95 billion and a $149 × 22% = $33 billion decrease in credit card balances in the prime and subprime markets, respectively. Altogether, 43

Using our estimates, an interested reader can also calculate the effect of the 200 bp increase in FFR on the propensity to pay late. 44 Note that, as should be evident from Table 4, the main economic impact of the change in rates is from a reduction in average balances. Moreover, the effects of interest rates on consumer credit is especially important component of interest rate setting for policy makers. As a result we focus on this particular effect.

29

we calculate that total credit card debt will decrease by approximately $128 billion.45 This reduction in balances implies $95 × 14% = $13 billion and $33 × 18% = $6 billion reduction in yearly finance charges among prime and subprime customers, respectively.46 6.3.2

Heterogeneous Effects

Contractionary monetary policies, such as a rise in the FFR, may have a heterogeneous impact on consumers. For example, Coibion et al. (2012) show that such policies may affect low income households differently from those with high income. One channel through which this is may occur is by benefiting savers, who are more likely to be high income households, and hurting borrowers, who are more often low income households (Doepke and Schneider, 2006). Another reason may be credit market frictions, which are more damaging to the credit prospects of low income consumers. Heterogeneous effects may occur for reasons other than income as well. Previous studies have also argued that regional heterogeneous effects in the transmission of monetary policy may arise due to the bank lending channel of monetary policy (Carlino and DeFina, 1998; Owyang et al., 2005).47 We explore potential heterogeneous effects of a rise in FFR by estimating demand responses separately for cardholders residing in low and high income communities and exploiting differential demand responses driven by the account fixed effects (types) in our model. Our results contribute to an emerging literature on pass-through of monetary policy changes via consumer finance channels.48 Figure 3 plots the distribution of model predicted response of balances to a 200bp FFR increase across the 5 income quintiles during the final month of the sample (August 2011).49 Each graph shows the mean and interquartile range of cardholders’ response. The top panels show responses in overall balances whereas the bottom panels show effects on the propensity to revolve balances (the extensive margin). As shown in the figure, cardholders residing in the richest counties, the top quintile, reduce their balances more than those in poorer counties. This holds for both the prime and subprime group. For example, we find that subprime cardholders residing in the highest quantile would reduce their balances by almost 50 percent more on average (30 percent vs. 20 percent) relative to cardholders in the poorer communities. Despite this consistent pattern, however, the interquartile ranges are wide, indicating that communities of varying 45

Additionally, millions of accounts will respond on the extensive margin, by not holding any balance at

all. 46

Interest payment reductions are calculated using the average interest rates faced by each risk type, respectively. See Figure 1. 47 Regional differences in reaction to monetary policy may be an even more important topic in the European Union, see for example Lane (2012) 48 See, for example, Agarwal et al. (2015a) and Di Maggio et al. (2015). 49 Income quintiles are measured as average weekly wages in a county.

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Figure 3: Heterogeneous Effects of Monetary Policy by County Income Notes: The figure shows the relationship between distribution of predicted reduction of balances in a county and county income during the final month of the sample (August 2011). Each graphs shows the mean and inter quartile range of consumer response to a rise in rates using our estimated regressions, equations 5 and 7, separately for each quintile of county income. Average weekly wages are from the QCEW as described in section 3.

income by be affected other ways which our data does not allow us to measure.50 Overall, these results suggest that borrowers in higher income areas may possess a greater ability to adjust, or re-optimize, their debt portfolio as credit card borrowing rates rise (e.g., relative prices change). In contrast, borrowers in low income areas, who may be more likely to borrow and/or face greater adjustment frictions, may be left paying high levels of now more expensive debt for longer periods of time reducing their already low income.51 50

Without a deeper analysis, one can try to see other patterns arising from these graphs. For example, in three of the four charts the second highest point is the first quintile counties, suggesting a possible U-shaped relationship. However, we believe that drawing any other conclusions warrants a deeper analysis that goes beyond the scope of this paper. 51 There are many reasons why lower income cardholders face greater difficult in adjusting their debt portfolio. One simple reason may be that they have access to a narrower set of available substitutes to credit cards. Alternatively, they may want to pay down their debt, but do not have the savings or income flow to do so.

31

The magnitude of the effects becomes clearer once we perform the following back-of-theenvelope calculation. Consider a counterfactual where the 80 percent of cardholders residing in lower income Counties respond to the policy identically to the quintile of cardholders residing in the highest income Counties, all else equal. For subprime cardholders, this would result in an additional $12 billion dollars of debt repaid and $2 billion dollars in fewer finance charges. For prime consumers, this would lead to an in additional $31 billion in balance reduction and approximately $4.5 billion less in interest payments each year.52 Despite a clear relationship between balance adjustments in response to the rate change and income, much of the variation in demand adjustments remains unexplained. Figure 4 shows how responses of demand for balances to rising rates vary across states in the US using the regression with the full sample and exploiting response heterogeneity resulting from persistent tastes for balances, e.g. fixed effects. The left panels show adjustments in net balances for subprime (top) and prime (bottom) cardholders. The right panels show reduction in percentage of revolvers for subprime (top) and prime (bottom) accounts. As shown in the figure, there is substantial variation across states in the adjustments of balances as a reaction to the rate increase. We find economically meaningful dispersion in average adjustments across states, indicating substantial agglomeration in time invariant tastes across regions. Reductions in net balances range from 13 to 16 percent for prime and from 18 to 25 percent for subprime, while reductions in percentages of revolvers range from 9 to 12 percent for prime and from 12 to 19 percent for subprime (as in, we estimate 12 to 19 percent fewer revolvers.). Looking across regions, we find that cardholders residing in non-coastal Western states adjust their balances more than cardholders residing in other regions. This is true both for adjustments at the extensive and intensive margins, as well as both for prime and subprime cardholders. Conversely, cardholders residing in the South Eastern states adjust much less when rates rise. Coastal states in the West and North East or Mid Atlantic show varying levels of adjustments on each margin and across the risk types. As aforementioned, one reason for this dispersion may be differences across regions in their transmission of monetary policy through the bank-lending channel. However, as aforementioned, in our analysis this heterogeneity is driven by persistent differences in preferences for maintaining a balance, which appear to be strongly associated with geographic location. Moreover, our results indicate that only a portion of this variation is explained by income differences. We conjecture that perhaps local preferences and/or norms may be important determinants of demand for credit card borrowing and potentially a factor driving heterogeneous effects of the monetary policy change. 52

For this back-of-the-envelope calculation, we compared the effect that we estimated in Figure 3 with what would have occurred had each quintile responded as the highest quintile (separately for prime and subprime).

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Figure 4: Heterogeneous Response Across US States Notes: The figure shows variation in adjustment rates across US States. Adjustment rates are derived using the entire sample (See Table A.1 in Appendix A.)

6.3.3

Substitutes, Macroeconomic Effects, and the Supply Side

In the above exercise, we analyze the effects of a rise in FFR only in as much as it affects demand through an increase in cardholders’ account APRs. One caveat to this approach is that we estimate the demand response of individual accounts as opposed to an increase across the board for all credit cards. Many cardholders could potentially switch to a different card, in which case we may be overestimating the response to a true across-the-board interest rate increase. Similarly, cardholders may switch to other credit products such as a home equity line of credit. The CCDB cannot speak to changes in cardholders’ debt choice in other products, although rates on those products are likely to rise as well. Regardless, APRs on existing accounts adjust quickly, and in the short to medium run consumers may have few substitutes for credit card borrowing. As a result, our approximation might be reasonable for many cardholders for shorter time horizons and more so if other credit card debt is less substitutable. Another caveat is that FFR increases likely affect a multitude of macroeconomic variables, which would in turn affect consumers’ demand for credit card balances. Such general equi33

librium effects on consumers’ balances are most apparent through changes in employment and wages, often via productivity and price level changes. A number of empirical studies have analyzed effects of monetary policy on wages, employment, and output (Bernanke et al., 2005; Uhlig, 2005). These studies have found mostly modest effects in the short run.53 Reconciling previous approaches, Coibion (2012) shows that an FFR increase leads to small drop in prices and industrial production, and a modest rise in unemployment. These changes take about one to two years to take full effect. For example, following a 100 bp rise in the FFR, it takes about 1 year for unemployment to rise by 0.5 percent. Moreover, it takes 18 months for a similar shock to reduce industrial production by 1.5 percent; prices take about 2 years before any adjustment takes place.54 It is likely that unemployment, prices, and production, the latter affecting wages, are the most important general equilibrium contributors to the effects of monetary policy on consumer credit. Both productivity and price level drop eventually result in an average wage decrease, the timing of which may be difficult to predict given wage rigidities. As a result, despite a productivity slowdown following a rise in FFR, the effect on wages may take time to percolate through the system. In all, we suspect that the effects of an FFR rise on credit card balances through employment and wages would be small at first. Short term first-order effects of this shock would be through APRs. A rise in the FFR might also affect consumption directly, through expectations perhaps, which could in turn affect the demand for credit card balances. Bernanke et al. (2005) reports small direct effects FFR movements on consumption. Finally, we do not take into account other supply-side reactions by credit card issuers. Agarwal et al. (2015a) analyze the question of pass-through of monetary expansions to consumers, and suggest that issuers increase credit limit of prime cardholders, while keeping the credit limit of subprime cardholders virtually unchanged. For a contractionary monetary policy, this would suggest a decrease in prime consumers’ credit limit. However, Agarwal et al. (2015a) note that prime cardholders’ marginal propensity to consume out of the changed credit limit is low, suggesting low overall effect on credit card balances. Subprime cardholders would likely be unaffected by this supply change. 53

An exception is Romer and Romer (2004). In this study, the authors use different data for measurement (records from the Federal Open Market Committee meetings and internal Fed forecasts) and find considerably larger effects. Coibion (2012) shows that several plausible assumptions make the differences between the two approaches considerably smaller than they initially appeared. 54 Keys, Tobacman, and Wang (WP 2017) study specifically the effects of consumption smoothing through credit card use over the business cycle. See their paper for a better understanding of this effect.

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7

Conclusion

In this paper we study how demand for credit card services in the US responds to the collection of prices the comprise the total cost of utilizing those services. We find that the law of demand holds for all prices and among all cardholders. Specifically, cardholders reduce balances when their APR increases and they pay late more often when the LF decreases. We note significant quantitative differences in response intensity across risk types. Tying in to the broader debate on complex pricing and consumer decision making, We discuss these difference within the context of existing theories of consumer choice. In that spirit, we further find that cross price responses differ qualitatively between for prime and subprime cardholders. Whereas prime cardholders responses are consistent rational consumer behavior, subprime cardholders’ responses cannot be wholly rationalized and are better approximated by a model of consumers with limited attention. Using our estimates, we calculate the pure APR effect of a simulated two percentage point rise in the FFR, holding all else equal. We find that, on average, this decreases borrowing and interest rate payments by $130 billion and $20 billion, respectively. Moreover, the policy reduces borrowing more in higher income communities, leaving lower income cardholders with higher levels of expensive debt. We calculate that, were all cardholders to reduce balances at the rate of those in highest quintile, annual finance charges would further decline by $6.5 billion, or 30 percent. Given potential difficulties for low income households to properly adjust their level of debt, a sharp rise in FFR may further exacerbate income inequality across communities. In addition, the degree of demand adjustment to higher APR exhibits geographic agglomeration. We conjecture that perhaps external neighborhood factors may contribute to this heterogeneity. Our study focuses on existing cardholders’ steady state, or static, demand response to changes in rates and fees. As a result, we are unable to consider a number of important elements governing consumer choice in this market. These include dynamic pricing behavior, such as promotional rates, rewards, consumer default, learning, or competition. Moreover, our reduced form approach is largely agnostic about specific preference structures. Taking an informed stand on the exact model of consumer choice would also allow for a discussion of the impact of a larger set of policies on consumer welfare. We leave such analysis for future work.

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A

Main Regression Results

Table A.1 shows our main regression results. Columns (1) & (2) show results for the purchase equation, columns (3) & (4) for balances, and columns (5) & (6) for purchase volume. For Table A.1: The Response of Consumer Demand for Credit Card Services to Price Changes Depvar

Late Payment Fee APRT ot (Account Age) (Account Age)2 %∆(Wage) %∆(Emp.) %(Line ↓)t−1 %(Line ↑)t−1 Trend Trend2 Trend3 σ N T LL

Purchase Subprime (1) -0.0015 (0.0073) 0.0018 (0.0269) -0.0076 (0.0112) 0.0005 (0.0002) -0.0131 (0.0353) -0.2205 (0.0790) 0.0125 (0.0056) -0.0117 (0.0031) -0.0028 (0.0193) 0.0515 (0.0074) -0.0318 (0.0167) 0.5563 (0.0034) 14,719 24 -53,971

Volume Balances Prime Subprime Prime (2) (3) (4) -0.0177 0.2224 -0.0431 (0.0067) (0.0075) (0.0083) -0.0790 -0.9021 -0.9143 (0.0262) (0.0334) (0.0332) 0.0323 -0.0006 0.0578 (0.0093) (0.0104) (0.0115) -0.0002 -0.0008 -0.0005 (0.0002) (0.0002) (0.0002) -0.0070 0.1123 0.1558 (0.0288) (0.0337) (0.0371) -0.2045 -0.1308 -0.3615 (0.0608) (0.0629) (0.0598) 0.0985 -0.0127 0.0668 (0.0071) (0.0061) (0.0087) -0.0154 -0.0097 -0.0018 (0.0046) (0.0035) (0.0054) -0.0675 0.2010 -0.0158 (0.0179) (0.0183) (0.0221) 0.0279 -0.0530 0.0252 (0.0063) (0.0071) (0.0079) 0.0050 -0.2587 -0.0695 (0.0149) (0.0162) (0.0187) 0.9605 1.0437 1.6988 (0.0015) (0.0021) (0.0012) 18,398 15,287 13,436 24 24 24 -182,835 -172,634 -214,510

Late Payment Subprime Prime (9) (11) -0.0466 -0.0587 (0.0129) (0.0196) 0.0711 -0.1961 (0.0456) (0.0646) 0.0557 0.0529 (0.0188) (0.0255) -0.0014 -0.0010 (0.0004) (0.0005) 0.0769 -0.0419 (0.0612) (0.0802) -0.2812 0.1120 (0.0942) (0.1008) 0.0029 0.0492 (0.0127) (0.0197) -0.0056 -0.0112 (0.0057) (0.0100) -0.2638 -0.1094 (0.0328) (0.0507) 0.2107 0.1280 (0.0127) (0.0182) 0.0792 -0.0291 (0.0288) (0.0431)

9,347 24 -73,138

5,480 24 -35,157

Notes: The table shows full regressions results used to calculate elasticity distributions in table 4. APRT ot row shows the ”long-run” response to the APR changes, which is the sum of the current and delayed responses up to six months. LPF row shows the current response to the late payment fee changes.

reasons of scaling, balances and purchased volume are measured in $1000s and LF and APR are measured in 10 percentage or points (APR = 14.99% → 1.499) or dollar (LF = $39 → 3.9) units, respectively. Account age is measured in years and the trend is the number of years from September 2010. Line increases (%(Line ↑)t−1 ) and line decreases (%(Line ↓)t−1 ) as measured as a percent change in accounts’ available credit line as of the previous month. Table A.2 shows full regression results for the balances equation (Equation 5 in section 4). Like above, all prices are scaled for the purposes of stable computation. 41

42

Purchase High Income Subprime Prime (1) (2) 0.2102 -0.0410 (0.0086) (0.0093) -0.9207 -0.9458 (0.0381) (0.0381) 0.0048 0.0744 (0.0120) (0.0132) -0.0002 -0.0014 (0.0003) (0.0002) 0.1878 0.2064 (0.0395) (0.0430) -0.3977 -0.6627 (0.1045) (0.1138) -0.0092 0.0727 (0.0070) (0.0098) -0.0109 0.0018 (0.0038) (0.0059) 0.1546 -0.0121 (0.0208) (0.250) -0.0438 0.0101 (0.0080) (0.0089) -0.2436 -0.0851 (0.0180) (0.0210) 1.0503 1.7056 (0.0024) (0.0015) 12,176 10,704 24 24 -137,890 -170,420

Volume Low Income Subprime Prime (3) (4) 0.2747 -0.0306 (0.0177) (0.0182) -0.8592 -0.8157 (0.0711) (0.0696) -0.0540 -0.0694 (0.0230) (0.0254) -0.0032 0.0036 (0.0005) (0.0005) -0.2493 -0.1527 (0.0739) (0.0789) 0.1489 -0.0613 (0.0841) (0.0806) -0.0260 0.0467 (0.0128) (0.0191) -0.0040 -0.0184 (0.0081) (0.0125) 0.4185 0.0605 (0.0451) (0.0499) -0.0926 0.0725 (0.0158) (0.0174) -0.2997 -0.0182 (0.0365) (0.0410) 1.0176 1.6717 (0.0050) (0.0026) 3,111 2,732 24 24 -34,635 -44,053

Balances Sometimes Late Never Subprime Prime Subprime (5) (6) (7) 0.1786 -0.0696 0.2662 (0.0104) (0.0138) (0.0111) -1.5274 -1.3570 -0.1323 (0.0584) (0.0570) (0.0390) -0.0157 0.1406 0.0166 (0.0149) (0.0190) (0.0147) 0.0008 -0.0027 -0.0028 (0.0003) (0.0004) (0.0003) 0.0614 0.0785 0.1643 (0.0482) (0.0605) (0.0476) 0.0111 -0.1661 -0.3463 (0.0812) (0.0772) (0.1015) -0.0174 0.0462 -0.0103 (0.0093) (0.0141) (0.0082) -0.0134 -0.0064 -0.0049 (0.0047) (0.0081) (0.0049) 0.1954 0.0042 0.2094 (0.0261) (0.0363) (0.0261) -0.1412 -0.0789 0.0393 (0.0104) (0.0132) (0.0096) -0.1526 0.0261 -0.3582 (0.0229) (0.0311) (0.0234) 1.0501 1.7945 1.0324 (0.0037) (0.0020) (0.0026) 7,221 4,741 8,066 24 24 24 -83,547 -79,887 -88,090

Late Payment Late Pre CARD Act Post CARD Act Prime Subprime Prime Subprime Prime (8) (9) (10) (11) (12) -0.0283 (0.0104) -0.6115 -0.5335 -0.8588 -1.3496 -0.3385 (0.0416) (0.0435) (0.0358) (0.1368) (0.1161) 0.0019 0.0569 0.1031 0.1010 0.1991 (0.0148) (0.0200) (0.0388) (0.0247) (0.0267) 0.0008 0.0007 0.0008 -0.0012 -0.0014 (0.0003) (0.0005) (0.0004) (0.0005) (0.0004) 0.1709 0.1115 -0.0954 0.0039 0.1510 (0.0475) (0.0499) (0.0581) (0.0499) (0.0301) -0.6129 0.3185 -0.1581 0.0943 -0.0544 (0.1019) (0.1061) (0.0715) (0.1207) (0.0679) 0.0798 -0.0299 0.0337 -0.0110 0.0390 (0.0111) (0.0093) (0.0118) (0.0085) (0.0134) 0.0018 -0.0073 0.0115 0.0048 -0.0101 (0.0071) (0.0041) (0.0066) (0.0082) (0.0104) -0.0176 -0.0272 1.6595 -0.1025 0.6173 (0.0280) (0.1357) (0.5795) (0.0596) (0.2476) 0.0834 -0.0418 3.3580 -1.1729 -3.3018 (0.0098) (0.2862) (1.2104) (0.4647) (0.9474) -0.1167 -0.2049 1.7476 1.0934 2.7539 (0.0235) (0.1681) (0.6612) (0.3808) (0.7407) 1.6404 0.8705 1.3316 0.7104 1.3537 (0.0017) (0.0032) (0.0065) (0.0059) (0.0068) 8,695 15,287 13,436 15,287 13,436 24 12 12 12 12 -134,130 -61,911 -82,619 -32,499 -80,204

Notes: The table shows full regressions results used to calculate elasticity distributions in table 5. APRT ot row shows the ”long-run” response to the APR changes, which is the sum of the current and delayed responses up to six months. LPF row shows the current response to the late payment fee changes.

N T LL

σ

Trend3

Trend2

Trend

%(Line ↑)t−1

%(Line ↓)t−1

%∆(Emp.)

%∆(Wage)

(Account Age)2

(Account Age)

APRT ot

Late Payment Fee

Depvar

Table A.2: Heterogeneous Response of Consumer Demand for Balances to Price Changes

B

Estimation Details

In this section we detail the procedure described in Section 4 for estimating equations 5 and 7. Equation 5 corresponds to the purchase and balance equations for B ∈ {U, C}, respectively, and is a type I Tobit. Equation 7, corresponding to the late payment equation L, is a binomial Probit. For each equation, we first posit its likelihood function and respective Score (S) and Hessian (H). We then derive the analytical bias adjustment term (Hahn and Newey, 2004; Arellano and Hahn, 2007). Finally, we describe the iterative Efficient NewtonRaphson (ENR) procedure used for estimation (Hospido, 2012) and relevant standard error calculations.

B.1

Likelihood Equations

The Tobit likelihood, corresponding to the purchase volume and revolving balance equations 5 for B ∈ {U, C}, respectively, takes the following form: h  lb − xθ − α i h √ (y − xθ − αi )2 i i + (1 − c ) · ln Φ LitB = cit · − ln( 2π) − ln(σ) − it 2 2σ σ

(1)

where cit = 1(yit > lb) and lb is the censored lower bound, in this case lb = 0. Moreover, θ is a (J − 1) × 1 vector of parameters and αi (i = 1, ..., N ) and σ are scalars. As shown in Olsen (1978), the above likelihood is not globally concave in the parameter space. To ensure global concavity, we transform LitB as follows h i h i √ 1 LitB,O = cit · − ln( 2π) + ln(δ) − (δy − xβ − ηi )2 ) + (1 − cit ) · ln Φ(0 − xβ − ηi ) (2) 2 where β = σθ , ηi = ασi , and δ = σ1 . Then we can write the Score (S B,O ) and Hessian (H B,O ) of the likelihood as (J + N ) × 1 and (J + N ) × (J + N ) matrices, respectively with

S B,O

 N T  i XX j h x · cit · (y − xβ − ηi ) − (1 − cit ) · Λ(ϕit )     ∂L B,O   i=1 t=1 it     ∂βj         N T i h XX  B,O    1 ∂L    = cit · − yit (δyit − xit β − ηi )  ∂δ  =   δ     i=1 t=1       ∂L B,O   T ∂ηi  X h i    · cit · (y − xβ − ηi ) − (1 − cit ) · Λ(ϕit ) t=1

43

(3)

 ∂ 2 L B,O ∂βj ∂βk

H B,O

   ∂ 2 L B,O =  ∂δ∂βj   ∂ 2 L B,O ∂ηi ∂βj

∂ 2 L B,O ∂βj ∂δ ∂ 2 L B,O ∂δ 2 ∂ 2 L B,O ∂ηi ∂δ

∂ 2 L B,O ∂βj ∂ηi



   2 B,O ∂ L  ∂δ∂ηi   

(4)

∂ 2 L B,O ∂ηi ∂ηj

and  N T h i XX j k xit xit · − cit − (1 − cit ) · Λ(ϕit ) · (ϕit + Λ(ϕit ))    i=1 t=1         ∂ 2 L B,O    N T X X   j ∂βj ∂βk  c it · xit · yit          i=1 t=1  2 B,O    ∂ L     ∂βj ∂δ       T h i  X j      2 B,O   x − c − (1 − c ) · Λ(ϕ ) · (ϕ + Λ(ϕ )) it it it it it  it ∂ L     ∂βj ∂ηi   t=1      =    2 B,O    N X T 1  ∂ L 2   X   ∂δ   2  − cit · 2 + yit     δ     t=1 i=1  ∂ 2 L B,O         ∂δ∂ηi       T  X     cit · yit   ∂ 2 L B,O   ∂ηi ∂ηj t=1         T h i X   1(i = j) · − cit − (1 − cit ) · Λ(ϕit ) · (ϕit + Λ(ϕit )) t=1

where ϕit ≡ −(xit β + ηi ) and Λ(x) ≡

φ(x) . Φ(x)

The Probit likelihood, corresponding to the late payment equation 7, takes the following form     LitL = dit · ln Φ(xθ + αi ) + (1 − dit ) · ln 1 − Φ(xθ + αi ) (5) where, because it is not identified, the variance of the Φ is normalized to σ = 1 and Ψit ≡

44

xit θ + αi . The Score (S L ) is given by  N T  XX j  ∂L L   xit (dit · Λ(Ψit ) − (1 − dit ) · Λ(−Ψit ))   ∂θ i=1 t=1   j   L   S = =   X  T h ∂L L i   ∂αi dit · Λ(Ψit ) − (1 − dit ) · Λ(−Ψit )

(6)

t=1 φ(x) . We write the Hessian (H L ) as a (K + N ) × (K + N ) symmetric where, as above, Λ(x) ≡ Φ(x) matrix with the following form

" HL =

∂2L L ∂θj ∂θk ∂2L L ∂αi ∂θk

∂2L L ∂θj ∂αi ∂2L L ∂αi ∂αj

#

"

L L Hθα Hθθ = L L Hαα Hαθ

# (7)

then let   Γit = dit · Λ(Ψit ) · (−Ψit − Λ(Ψit )) − (1 − dit ) · Λ(−Ψit ) · (−Ψit + Λ(−Ψit ))

(8)

and write 

 N X T X xj xk · Γit     ∂ 2 L L   i=1 t=1 it it   ∂θj ∂θk           T  ∂2L L   X  j   = · Γ x it it  ∂θj ∂αi        t=1       ∂2L L   T ∂αi ∂αj   X   1(i = j) · Γit

(9)

t=1

These above equations thus characterize the unadjusted likelihoods of interest and their respective Score and Hessian expressions.

B.2

Analytically Adjusted Likelihood

To correct for the asymptotic bias resulting from small T and large N , the incidental parameters problem, we use an analytically derived bias correction of the concentrated likelihood as described in Hahn and Newey (2004); Arellano and Hahn (2007). Although there are other simpler methods of bias reduction, such as automatic jackknife methods, we use the analytical method because we have only one change in the price of the late fees. As a result,

45

we must rely more on the structure of the likelihood in our identification. Following Arellano and Hahn (2007), the asymptotic bias term of the concentrated likelihood is given by h ∂ 2 L (θ, α(θ)) i−1 h ∂L (θ, α(θ))2 i 1 1 −1 bi (θ) = · H(α) i (θ) · Υ(α) i (θ) = · Ei − · Ei 2 2 ∂α2 ∂α

(10)

Then, following Hospido (2012), we reformulate the above expression in terms of the original, un-concentrated likelihood, as an input into the estimation. Given this approach, we write down the following estimator of the bias term ˆbi (θ, α) = − 1 · 2

"

T X ∂ 2 Lit (θ, α)

#−1 " ·

∂α2

t=1

T X ∂Lit (θ, α) 2 t=1

# (11)

∂α

We then subtract the bias from the original likelihood to arrive at the adjusted likelihood N X T T X X L (θ, α) = Lit (θ, α) − bi (θ, α) A

i=1 t=1

(12)

t=1

From above, it follows that S A = S − S b and H A = H − H b where S b and H b are the Score and Hessian of the bias term, respectively. It follows that we can write   ∂Υ(α) i −1 H · − bi · (α) i ∂θ N N ∂θj X X  1    Sb =  =− ·   2 ∂Υ(α) i ∂bi i=1 i=1 −1 − bi · H · ∂αi (α) i ∂α  ∂b  i

∂H(α) i ∂θ

∂H(α) i ∂α

   

(13)

and

Hb = −

N X



1   2 i=1

∂ 2 bi ∂θj ∂θk ∂ 2 bi ∂αi ∂θj

∂ 2 bi ∂θj ∂αi ∂ 2 bi ∂αi ∂αj

 (14)

 

where 

∂ 2 bi ∂θj ∂θk





−1 H(α) i

h

∂ 2 Υ(α) i ∂θj ∂θk

− bi

∂ 2 H(α) i ∂θj ∂θk



−



∂bi ∂θj

·

∂H(α) i ∂θk

+

∂bi ∂θk

·

∂H(α) i ∂θj

i



          h   i  ∂2b    ∂ 2 Υ(α) i ∂ 2 H(α) i ∂H(α) i ∂H(α) i −1 ∂bi ∂bi i     H(α) i ∂θj ∂αi − bi ∂θj ∂αi − ∂θj · ∂αi + ∂αi · ∂θj  ∂θj ∂αi  =           h   i   2Υ 2H ∂ 2 bi ∂ ∂ ∂H ∂H (α) i (α) i (α) i (α) i −1 ∂bi ∂bi 1(i = j) · H(α) − b − · + · ∂αi ∂αj i i ∂αi ∂αj ∂αj ∂αi ∂αj ∂αi ∂αi ∂αj

46

(15)

This completes the characterization the adjusted likelihood L A (θ, α) for the Probit and Tobit likelihoods.

B.3

Efficient Newton-Raphson (ENR)

Given the smoothness and convexity of our objective functions, we estimate the model parameters using an efficient Newton-Raphson (ENR) algorithm laid out in Hospido (2012). This method exploits the block structure of the Hessian matrix of the log likelihood function and provides significantly increased estimation speed.55 In what follows, denote Θ = (θ, α). The Kth step of the ENR algorithm is "

Θ[K]

∂ 2 L (Θ[K−1] ) = Θ[K−1] − ∂Θ∂Θ0

#−1 "

∂L (Θ[K−1] ) · ∂Θ

# (16)

Where the Score and Hessian in their block form can be expressed as follows 

  SθA Hθθ |{z} |{z}  J×J J×1  ∂L A  ∂ 2L A    SA = = =   and H A = 0  A  0 ∂Θ ∂Θ∂Θ  Sα   Hθα |{z} |{z} N ×J

N ×1

 Hθα |{z} J×N     Hαα  |{z}

(17)

N ×N

Given the block nature of H A , re-write the K th step of the ENR algorithm in two parts as

A A A −1 A −1 A A −1 A θ[K] = θ[K−1] − [Hθθ − Hθα (Hαα ) Hαθ ] · [SθA − Hθα (Hαα ) Sα ]

−1 α[K] = α[K−1] − Hαα · [SαA + Hαθ (θ[K] − θ[K−1] )]

(18)

Note that in the Tobit case, the parameter θ includes the shape parameter of the normal distribution, whereas in the Probit case it does not as the variance is normalized to 1. 55

Currently with this method we can estimate the adjusted Tobit with 20k+ fixed effects and 13 parameters in approximately 10 minutes. Using a commercially available optimization routine this would take one or two days of computation time.

47

B.4

Standard Error Calculations

The above estimator is consistent and asymptotically normal under our assumption of i.i.d errors. It follows that √ T

θˆ − θ0 α ˆ i − αi0

!

Iθ,θ Iθ,αi d → − N 0, Iαi ,θ Iαi ,αi

!−1 ! (19)

It follows that   √ d −1 T (θˆ − θ0 ) → − N 0, (Iθ,θ − Iθ,αi Iα−1 I ) i ,αi αi ,θ where Iθ,θ Iθ,αi Iαi ,θ Iαi ,αi

! =

−E −E

∂2L ∂(θ)2
∂2L ∂αi ∂θ




−E −E

∂2L ∂θ∂αi
∂2L ∂(αi )2

(20)


! (21)

and where we use sample means as consistent estimators. We recover confidence intervals of the original parameters using the delta method.

48