Payment Choice and Currency Use: Insights from Two Billion Retail Transactions

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1 Payment Choice and Currency Use: Insights from Two Billion Retail Transactions Zhu Wang, Alexander L. Wolman October, 215 Abstract Using three years of transactions data from a discount retailer with thousands of stores, we study payment variation along three dimensions: transaction size and location; weekly and monthly frequencies; and longer time horizons. In each case, we connect empirical patterns to theories of money demand and payments. We show that cross-sectional and time-series payment patterns are consistent with a theoretical framework in which individual consumers choose between cash and noncash payments based on a threshold transaction size, and we evaluate factors that may determine the variation of threshold distributions across locations and time. Keywords: Payment choice; Money demand; Consumer behavior JEL Classification: E41; D12; G2 Research Department, Federal Reserve Bank of Richmond; zhu.wang@rich.frb.org and alexander.wolman@rich.frb.org. The views expressed here are those of the authors and do not represent the views of the Federal Reserve Bank of Richmond or the Federal Reserve System. The data used in this study is proprietary and has been provided to us by the Payment Studies Group at the Federal Reserve Bank of Richmond. We are grateful to the members of that group for their efforts in putting together this data. In addition, we would like to thank members of FRB Richmond s IT department for their critical role in putting the data in manageable form. Sam Marshall and Joe Johnson have provided outstanding research assistance, and Liz Marshall and Sabrina Pellerin provided us with valuable input. For helpful comments, we would like to thank Fernando Alvarez, Dave Beck, Evren Damar, Itay Goldstein, Tom Holmes, Boyan Jovanovic, Marc Rysman, Joanna Stavins, Matti Viren, Mark Watson and participants at various conferences and seminars. 1

2 1 Introduction The U.S. retail payments system has been undergoing fundamental changes in the past few decades, migrating from paper payment instruments, namely cash and check, to electronic forms such as debit and credit cards. Amidst these changes, a large empirical literature has developed to study consumer payment choice, with the broader goals of understanding payments system functioning and the transaction demand for currency. For researchers and policymakers working on these issues, one major impediment is the lack of data on consumers use of cash. Given the difficulties of tracking cash use, most studies have relied on data from consumer surveys. 1 While this research has greatly improved our understanding of how consumers choose to pay, consumer survey data has its limitations: Most surveys have relatively small samples (hundreds or thousands of participants at most) and lack broad coverage of location and time. Our paper helps to fill the gap. We report new evidence on cash use in retail transactions, as well as on credit, debit, and check use, based on a large merchant transaction dataset. The data, provided by a discount retail chain, covers every transaction in the three years starting in April 21, in each of the chain s thousands of stores across most of the country. In total, we have about 2 billion transactions, which involve millions of consumers. 2 With this rich dataset we explore three themes: (i) payment variation across payment sizes and locations, (ii) payment variation at weekly and monthly frequencies, and (iii) payment variation over the longer term. In each case, we link our empirical findings to theoretical work on money demand and payment choice, indicating which of our findings are consistent with existing theories, and which suggest directions for extending those theories. A natural reference point for our work is Klee (28), which also used merchant transaction records to study consumer payment choices. However, by exploring a dataset with richer geographic and time coverage (thousands of zip codes versus 99 census tracts, and three years versus 9 days), we are able to investigate cross-sectional and time-series payment variation not addressed in Klee s study. Our analytical approach also differs from Klee (28). Because our data set is so large we do not work with the transaction data directly, instead aggregating it up to the shares of transactions for each payment type on 1 For example, Borzekowski et al (28), Borzekowski and Kiser (28), Zinman (29), Ching and Hayashi (21), Arango et al (211), Koulayev et al (212), Cohen and Rysman (212), Schuh and Stavins (212). 2 If we assume a consumer visits a store once a week, the data would cover more than twelve million consumers; even if we assume daily shopping, it would still cover almost two million consumers. 2

3 each day in each zip code. Aggregation allows us to use all transactions, and it smooths out the noise in individual transactions. Finally, our data is especially informative about cash use. The stores are located in relatively low-income zip codes where the customer base is more likely to be unbanked or underbanked. The stores also have a large share of small-dollar transactions, for which cash has remained stubbornly popular: The median sale value is around $7 and the mean is about $11. In contrast, Klee s (28) sample is from large grocery stores located in much higher income zip-codes with larger transaction sizes (the average sale value is $29, and she omits transactions below $5). Although our data likely overstates the proportion of cash use in U.S. retail transactions, this very fact meansthatitprovidesvaluableinsightsintothenature of cash use. Our data only identifies transactions, not customers. However, we link the empirical model to theories of money demand and payments by assuming that the demographic and economic characteristics of the zip code in which each store is located reflect the demographic characteristics of the store s customers and the economic environment in which they live. Money demand theories dating back at least to Baumol (1952) and Tobin (1956) and including Sidrauski (1967) and Lucas (1982), emphasize opportunity cost, especially foregone interest, as a factor in households decisions of how much cash to hold. Those early models have only one means of payment, but Prescott (1987), Freeman and Kydland (2) and Lucas and Nicolini (215) among others, have allowed for multiple means of payment in models where non-cash payments require a fixed per-transaction cost. 3 This fixed cost then implies a consumer-specific threshold transaction size below which cash is used, with the threshold depending on the consumer s characteristics, as well as the economic environment. Motivated by these theories, we include variables in our empirical model that proxy for the costs of using cash relative to other means of payment. 4 In addition, because a nontrivial fraction of the U.S. population is unbanked or underbanked and thus without easy access to non-cash means of payment, we include several zip-code-level variables in the empirical model that are likely to be correlated with consumers adoption of non-cash payments. We also include demographic variables (e.g., age, race, education) that may be related to both the choice of how to pay and the choice of whether to adopt non-cash means of payment. 3 For example, consumers may face certain fees, restrictions or risks of identity theft that are related to using non-cash payment means (such as check or payment cards). Those are typically fixed per-transaction costs regardless of the transaction size. 4 Although there was little time-series variation in short-term interest rates over the period of our sample, the opportunity cost of holding cash varies across individuals according to the availability and cost of banking services, risks of robbery and theft, and other considerations. 3

4 Our initial analysis includes transactions of all sizes in a single regression, where the dependent variables are shares of each payment type for each zip-code day. According to the threshold hypothesis, the shares of cash transactions represent the fraction of shoppers for each zip-code day whose transaction size was below their threshold. We then group the data by transaction size and estimate separate models for each group, thereby allowing coefficient estimates to vary across transactions of different sizes. These transaction-size regressions allow us to estimate the entire distribution of cash thresholds at each location: The share of non-cash transactions for a given transaction size is the cumulative distribution of cash thresholds, evaluated at that transaction size, and it is a function of the location-specific variables and calendar time. Recent research has also incorporated payment innovations and heterogeneous households into Baumol-Tobin style models that explicitly account for the sequential interplay between payments and cash balances (e.g., Alvarez and Lippi 29, 215). In turn, these models have predictions for how cash use varies over time, in relation to the shopper s cash inventory. To date, these models have not incorporated variation or heterogeneity in transaction sizes, but we conjecture that extensions along these lines would yield a threshold transaction size like Prescott (1987) and Lucas and Nicolini (215). Below we will relate our findings to both types of models. Our empirical model fits the data well and allows us to evaluate certain implications of theories of money demand. In terms of zip-code-level variables, our findings confirm that variables reflecting a higher opportunity cost of holding cash are negatively associated with cash shares, as are variables proxying for access to, or adoption of non-cash payments. We find that as transaction size increases, in a given zip-code location the fraction of cash payments decreases but those of debit, credit and check increase. This relationship supports the threshold hypothesis: If each consumer has a threshold transaction size below (above) which they use cash (non-cash means of payment), then the aggregate fraction of cash transactions must be decreasing in transaction size. We also find that the cross-location dispersion of the payment mix increases with transaction size, which indicates that the threshold distributions across locations exhibit more variation for larger transaction sizes. Using a quantitative decomposition, we then study the determinants of the threshold distributions, both within and across locations. Turningtotheshort-runtimeeffects, there are interesting day-of-week and day-ofmonth patterns. Over the course of the week, the cash and debit fractions are nearly mirror images of each other, whereas over the month credit comes closer to mirroring 4

5 cash. We also find that the number of transactions shares time patterns similar to those for cash shares. We interpret the high correlation between number of transactions and the cash share of transactions as indicating that consumers are subject to time-varying financial or liquidity constraints through the week and month (likely related to their frequency of pay), which then affect their shopping patterns and payment choices. Finally, our month-of-sample dummies identify seasonal cycles and longer-run trends in the payment mix. Over the longer term, the shares of cash and check transactions decline steadily, while debit and credit s shares rise. The overall cash fraction of transactions is estimated to have declined by 2.46 percentage points per year in our three-year sample period, largely replaced by debit. We find that the decline in cash at this particular retailer was likely not driven by transitory shocks, and if the decline were to continue, only a relatively small fraction could be explained by forecasted changes in the zip-codelevel variables, including age-cohort composition. This leaves a large fraction of the time trend to be explained, with prime candidates being technological progress in debit and changing consumer perceptions of debit relative to cash. The structure of the paper is as follows. Section 2 describes the transactions data and the zip-code-level explanatory variables. Section 3 introduces the empirical model and estimation method, and presents an overview of the estimation results. The next three sections explore the three themes introduced above: payment variation across locations andtransactionsizesinsection4;weeklyandmonthlypaymentpatternsinsection5;and longer-run payment variation in Section 6. Section 7 concludes and suggests directions for future research. 2 Data The transactions data is from a large discount retailer with thousands of stores, covering most U.S. states. The stores sell a wide variety of goods in various price ranges, with household consumables such as food and health and beauty aids accounting for a majority of sales. The unit of observation is a transaction, and the time period is April 1, 21 through March 3, 213. For each transaction, the data includes means of payment, time, location, and amount. We include only transactions that consist of a sale of goods, with one payment type used, where the payment type is cash, credit card, debit card, or check the four general-purpose means of payment. 5 The retailer also provides cash- 5 Data limitations prevent us from distinguishing credit cards from signature debit and prepaid cards. However, our estimates reveal time variation in what we report as credit cards that is significantly 5

6 back services, and the purchase components of cash-back transactions are included in our analysis. In contrast, transactions made with special-purpose means of payment such as EBT, coupons and store return cards are excluded. All told, our empirical analysis covers 94% of the total transactions in the sample period. Our summary of the data in this section will refer to all stores; the zip-code-level data introduced below and used in the empirical analysis covers most of those stores zip codes, but we will need to omit some of the retail outlets from that analysis because the zip-code-level data is unavailable. 2.1 Transactions Data Figure 1A presents payment variation across time in our sample. The data are plotted at the daily level, displaying the fraction of all the transactions accounted for by each payment type. Note that while cash is measured on the left axis, and debit, credit, and check are all measured on the right axis, both axes vary by.35 from bottom to top, so fluctuations for each payment type are displayed comparably. The figure shows that cash is the dominant payment instrument at this retailer, followed by debit, credit and check. Over the sample period, the fractions of cash and check are trending down, with debit and credit trending up. There seems to be a weekly pattern in both the cash and debit shares, with the two moving in opposite directions. Credit displays a monthly pattern, rising over the course of the month. We will allow for these patterns in the econometric model by including day-of-week, day-of-month and month-of-sample dummies. We turn now to payment variation across locations. Figure 1B restricts attention to the last full month of the sample, March 213, aggregates the data by zip code, and displays smoothed estimates of the density functions for fraction of transactions conducted with cash, debit, credit, and check. 6 We use only one month because of the time trend evident in Figure 1A. The ranking from Figure 1A is also apparent in Figure 1B: Cash is the dominant form of payment, followed by debit, credit, and check. The main message of Figure 1B, however, is that there is significant variation across zip-code locations in cash and debit use, and to a lesser extent in credit use as well. This variation highlights the need for including location-specific variables in our econometric model. different from the variation in PIN debit. Because signature debit and prepaid cards are close substitutes for PIN debit, in that they rely on consumers account balances rather than borrowed funds, we can reasonably assume the estimated time patterns are primarily driven by the true credit cards. 6 Note that the estimated kernel density for checks is truncated in Figure 1B. The check fractions are concentrated near zero, so the figure would be uninformative about the other payment instruments if we extended the y-scale to include the entire check density. 6

7 A. Fraction of Transactions by Payment Type cash, left axis debit, right axis credit, right axis check, right axis Apr 21 Aug 21 Dec 21 Apr 211 Aug 211 Dec 211 Apr 212 Aug 212 Dec 212 B. Kernel Density for Fractions by Zip Code, March 213 Density check credit debit cash Fraction of Transactions Figure 1. Payment variation across time and location. In Figure 2 we show how the payment mix varies with transaction size, again restricting attention to March 213. To construct Figure 2, for each zip-code day we group the data by transaction size, using $1 bins between $1 and $15, $5 bins between $15 and $5, and combining all transactions above $5 into one bin. These categories were chosen to ensure a sufficient number of transactions in each bin. For transactions in a given size bin, we calculate the shares of the four payment types on each zip-code day. The solid lines represent the median across zip-code days of the payment shares, and the dashed lines represent the 5th and 95th percentiles of the distribution. The overall message of Figure 2 is twofold: Cash is relatively more important for small transactions; and 7

8 the distribution of payment shares across zip-code days exhibits increasing dispersion for higher transaction sizes, as reflected by the fanning out of the 5th and 95th percentiles. Our analysis will show how these patterns relate to the threshold hypothesis, and what factors may determine the empirical distributions of the thresholds. A. Cash B. Debit th Percentile Median 95th Percentile th Percentile Median 95th Percentile $ $ C. Credit D. Check th Percentile Median 95th Percentile th Percentile Median 95th Percentile $ $ Figure 2. Payment variation across transaction sizes. Figure 2 shows that the payment mix varies systematically with transaction size. Thus, the overall composition of payments should be related to the transaction size distribution. Figure 3 provides information about the size distribution of transactions in March 213, without regard to means of payment. Figure 3A displays a smoothed density function, by transaction size, for all 74,465,1 transactions in our sample in March 213. The prevalence of small transactions helps to explain the large fraction of cash transactions in Figures 1A and 1B. Figure 3B plots the distribution of median transaction sizes across zip-code days, also for March 213 (representing 178,315 zip-code days). Figure 3B complements Figure 1B in showing that there is substantial heterogeneity across location and time with respect to size of transaction, as well as payment mix. Transaction size thus needs to be taken into account in our empirical model of the payment mix. 8

9 A. Individual Transaction Size B. Median Transaction Size Density Density $ $ Figure 3. Kernel densities of transaction size in March Zip-code-level Explanatory Variables The heterogeneity evident in Figures 1B, 2 and 3 indicates the quantitative importance of including location-specific variables in an econometric model of means of payment. We include variables that describe the economic environment consumers face, as well as the characteristics of households. Many of these variables are chosen for their potential to explain the distribution of threshold transaction sizes, which determines payment shares in a given zip code. Table 1 lists summary statistics for the zip-code-level explanatory variables we will use in the regressions, fixed at their 211values. 7 We also list summary statistics for zip-code-level explanatory variables for the entire country in Table A1 in the Appendix so that we can contrast our sample to the United States as a whole Economic Environment: Cash Holding and Payment Choice Several of the explanatory variables represent aspects of the economic environment that have direct bearing on the cash holding and payment choice behavior considered in the theoretical literature. These include the banking competition measure, bank branches per capita, and the robbery rate. According to the threshold hypothesis, cash use should decrease in banking-sector competition and the robbery rate (which increase consumers opportunity costs of using cash), but increase in bank branches per capita (which reduces 7 Most of our zip-code-level variables come from the U.S. Census s American Community Survey (ACS) and the FDIC s Summary of Deposits. The robbery data is from the FBI s Uniform Crime Report. We fix zip-code-level explanatory variables at their 211 values (5-year estimates), because the ACS provides only 5-year estimates for areas with less than 2, residents, and the median zip code in our sample has less than 18, residents. In Section 6, where we study longer-run payment variation, we will explicitly account for the effects of time variation in zip-code-level explanatory variables. 9

10 consumers costs of replenishing cash balances). Following the banking literature and antitrust tradition, we measure banking-sector concentration by the Herfindahl-Hirschman Index (HHI) in each MSA or rural county. 8 According to Tables 1 and A1, the distribution of HHI in our sample is comparable with the overall nation, and banking markets are significantly more concentrated in rural counties than in MSAs. However, the average number of bank branches per capita in our sample appears smaller than that in the entire U.S. We measure the robbery rate at the county level (and will have to discard some zip codes from our analysis because of missing robbery data), and the robbery rate in our sample is not appreciably different than in the nation as a whole Household Characteristics: Adoption of Non-cash Payments Adoption of non-cash payments is an important factor in explaining payment patterns, and two of the variables we include, median household income and deposits per capita, may be correlated with the likelihood that consumers have bank accounts or own credit or debit cards. There is a clear sense in which adoption represents the extensive margin, compared to the intensive margin associated with cash holding and payment choice. For our purposes however, a consumer who has not adopted any non-cash forms of payment can simply be thought of as having an extremely high threshold transaction size. When we aggregate across the transactions of heterogeneous consumers, the fraction of cash transactions will be increasing in the fraction of non-adopters. 9 The mean value of median household income is 2 percent lower in our sample than in the U.S. as a whole. Figure 4 provides additional detail, plotting kernel smoothed density functions for median income in our sample of zip codes and in the United States. Mean deposits per capita are dramatically lower in our sample than in the entire country, but the nationwide value is likely driven by a small number of zip codes with extremely large bank branches. We also include population density as an explanatory variable. 8 Both the theoretical literature and antitrust practice typically assume that the relevant geographic banking market is a local area where banks compete to offer financial services to households and small businesses. That market area is often approximated by a metropolitan area (MSA) in urban areas and by a county in rural areas. The most commonly used measure of market concentration is the Herfindahl- Hirschman Index (HHI), calculated by squaring each bank s share of deposits in a market and then summing these squared shares. 9 Note that our classification of variables should not be taken as exclusive; banking competition, prevalence of bank branches, and the robbery rate may also affect household s choices of whether to adopt non-cash forms of payment. Likewise, while we classified deposits and income as adoption variables, to the extent that they proxy for the opportunity costs of households time, they may also fall into the intensive margin category: Households with a high opportunity cost of time face higher costs of replenishing their cash balances, and will therefore use cash less often. 1

11 As McAndrews and Wang (212) point out, replacing traditional paper payments with electronic payments requires merchants and consumers to each pay a fixed cost but reduces marginal costs for doing transactions. Their work suggests that adoption and usage of electronic payment instruments should be higher in areas with a high population density or more business activity. The zip codes in our sample are somewhat less densely populated than in the broader U.S. Table 1. Summary statistics of zip-code variables Variable (unit) Mean Std. dev. 1% 99% C ash holding and paym ent choice Banking HHI Metro Banking HHI Rural Branches per capita (1/1 3 ) Robbe ry rate (1/1 5 ) Adoption of non-cash payments Median household income ($) 4,623 11,389 19,37 76,85 Dep osits per capita ($) , ,765 Population density (per m ile 2 ) ,21 Demographics (%) Family households Housing: Renter-occupied Owner-occupied Vacant Fem ale Age Race w hite black Hispanic Native Asian Pac-Islr other multiple Ed uc below high school high school some college college

12 2.2.3 Demographics We include a range of demographic variables in the regressions under the assumption that these variables may be systematically related to payment adoption and usage. Relative to theunitedstatesaverage,thezipcodesinoursamplehavealowpercentageofowneroccupied dwellings, with little variation. The racial composition of these zip codes also differs markedly from the rest of the country: There is a higher percentage of Blacks, Hispanics, and Native Americans and a lower percentage of Whites and Asians. Also, there is a relatively low percentage of college graduates. However, the age, gender and family profiles of our sample are not significantly different from the nation as a whole. Density e+ 1e-5 2e-5 3e-5 4e-5 Our Sample United States $ Figure 4. Distribution of median household income across zip codes. 3 Empirical Analysis: Estimating Payment Shares In the preceding section we documented substantial variation in the composition of payments across time and location, as well as transaction size. We turn now to an empirical model aimed at explaining this variation. In our first specification we aggregate all transactions by zip-code day, and include median transaction size for each zip-code day as an explanatory variable. In the second specification we omit median transaction size, but estimate separate regressions for 22 different transaction size bins. 12

13 3.1 Empirical Model The data is analyzed using a fractional multinomial logit model (FMLogit). The dependent variables are the fractions of each of the four payment instruments used in transactions at stores in one zip code on one day between April 1, 21, and March 31, The explanatory variables comprise the economic and demographic variables listed above, plus time dummies (day of week, day of month, and month of sample) and state-level dummies. The FMLogit model addresses the multiple fractional nature of the dependent variables, namely that the fraction of payments for each instrument should remain between and 1, and the fractions add up to The FMLogit model is a multivariate generalization of the method proposed by Papke and Wooldridge (1996) for handling univariate fractional response data using quasi-maximum likelihood estimation. Mullahy (21) provides more econometric details. Formally, consider a random sample of =1 zip code-day observations, each with outcomes of payment shares. In our context, =4, which correspond to cash, debit, credit, and check. Letting represent the outcome for observation, and, =1, be a vector of exogenous covariates. The nature of our data requires that [ 1] =1 ; Pr( = ) and Pr( =1 ) ; X and =1 for all =1 Given the properties of the data, the FMLogit model provides consistent estimates by enforcing conditions (1) and (2), [ ] = ( ; ) ( 1) =1 ; (1) 1 In our sample, more than three quarters of zip codes have only one store. Because we measure the fraction of payment instruments at the zip code level, we do not distinguish locations with one store from those with multiple stores. In the latter case, we simply sum up the transactions of all the stores in the zip code. 11 Note that when dealing with fractional responses, linear models do not guarantee that their fitted values lie within the unit interval nor that their partial effect estimates for regressors extreme values are good. The log-odds transformation, ln[ (1 )], is a traditional solution to recognize the bounded nature, but it requires the responses to be strictly inside the unit interval. The approach we take directly models the conditional mean of the responses as an appropriate nonlinear function, so that it can provide a consistent estimator even when the responses take the boundary values. 13

14 X [ ] =1; (2) =1 and also accommodating conditions (3) and (4), Pr( = ) =1 ; (3) Pr( =1 ) =1 ; (4) where =[ 1 ] Specifically, the FMLogit model assumes that the conditional means have a multinomial logit functional form in linear indexes as [ ] = ( ; ) = exp( ) =1 (5) X exp( ) =1 As with the multinomial logit estimator, one needs to normalize =for identification purposes. Therefore, Eq (5) can be rewritten as ( ; ) = 1+ exp( ) 1 X =1 exp( ) =1 1; (6) and ( ; ) = 1+ 1 X =1 1 exp( ) (7) Finally, one can define a multinomial logit quasi-likelihood function ( ) that takes the functional forms (6) and (7), and uses the observed shares [ 1] in place of the binary indicator that would otherwise be used by a multinomial logit likelihood function, such that Y Y ( ) = ( ; ) (8) =1 =1 The consistency of the resulting parameter estimates ˆ then follows from the proof in Gourieroux et al. (1984), which ensures a unique maximizer. In the following analysis, we use Stata code developed by Buis (28) for estimating the FMLogit model Similar to the Multinomial logit (MLogit) model, the FMLogit model imposes some restrictions on the substitution patterns between categories of the dependent variables. For a robustness check, we redo 14

15 3.2 Estimates for All Transaction Sizes Together In Table 2 we report estimation results for the first specification, where we model payment shares at the zip-code day level, including all transactions greater than $1. The coefficient estimates are expressed in terms of marginal effects evaluated at the means of the explanatory variables Cash Holding and Payment Choice Considerations As suggested by theory, we assume that each consumer has a threshold transaction size (possibly time-varying), below which they only use cash. Aggregating transactions within azip-codeday,wethenexpecttofind that an upward shift in the size distribution of transactions corresponds to a lower share of cash transactions. Using median transaction size as a convenient summary of the size distribution, we find the expected result: Evaluating at the mean of median sale value, $6.86, the marginal effects indicate that a $1 increase in median sale value reduces the predicted cash share by 1.8 percentage points but raises debit by 1.2 percentage points, credit by.5 percentage points, and check by.1 percentage points. While these results reflect the sensitivity of the payment mix to the distribution of transaction sizes, in Section 3.3 we use a similar framework to investigate in detail how the payment mix varies across individual transaction sizes. We find that higher banking concentration corresponds to a higher cash share (lower card shares) in rural areas. However, higher concentration corresponds to a lower cash share (higher card shares) in MSAs. We conjecture that in rural areas HHI does a good job proxying for banking market power, whereas in metro areas it may not: In metro areas, banking is inherently competitive, and a high level of concentration (as measured by HHI) may simply indicate the presence of one or more especially efficient banks. 14 the analysis by grouping payment types into two: cash and non-cash (combining debit, credit and check), and the results are essentially unchanged. 13 For continuous variables, the marginal effects are calculated at the means of the independent variables. For dummy variables, the marginal effects are calculated by changing the dummy from zero to one, holding the other variables fixed at their means. 14 When interpreting the relationship between market performance and HHI, two hypotheses are often tested. One is the Structure-Conduct-Performance (SCP) hypothesis, which assumes that the ability of banks in a local market to set relatively low deposit rates or high fees depends positively on market concentration. The other is the Efficient-Structure (ES) hypothesis, which takes an opposite view and argues that a concentrated market may reflect the efficiency advantages of leading banks in the market, so it may instead be associated with lower prices for banking services. The empirical evidence on these two hypotheses is mixed (Gilbert and Zaretsky [23] provides a comprehensive literature review). Our findings suggest that both hypotheses are relevant for our sample, with the SCP hypothesis supported by the rural market evidence and the ES hypothesis supported by the MSA evidence. 15

16 Quantitatively, a one-standard-deviation increase of HHI in the rural market (i.e., an increase of.145) raises the fraction of cash use by.44 percentage points. 15 A higher robbery rate is associated with less cash use and more debit use. Our estimates show that a one-standard-deviation increase in the robbery rate (i.e., three more robbery incidences per ten thousand residents) reduces the predicted cash share by.16 percentage points but raises debit by.19 percentage points. 16 In contrast, higher bank branches per capita are associated with a higher cash share, mainly at the expense of debit and credit: A one-standard-deviation increase raises the predicted cash share by.15 percentage points but reduces debit by.11 percentage points and credit by.9 percentage points Adoption of Non-cash Payments For the variables that we classified as relating to the adoption decision, our coefficient estimates also have the expected signs. The predicted fractions of debit and credit purchases increase with income while cash decreases. The magnitude of these effects implies that for a $1, increase in median household income (i.e., about a one-standard-deviation increase) from its mean, the predicted cash share drops by.33 percentage points while credit and debit rise by.36 and.5 percentage points respectively. Similarly, a $1, increase in deposits per capita (i.e., about a half-standard-deviation increase ) reduces the predicted cash share by.6 percentage points, but it raises debit by 1.6 percentage points. We find that higher population density is associated with lower shares of paper payments, especially checks, and higher shares of card payments. This is consistent with McAndrews and Wang s (212) theory of the scale economies of adopting relatively new payment instruments. A one-standard-deviation increase in population density reduces the predicted check share by.35 percentage points and cash by.1 percentage points, but it raises debit by.21 percentage points and credit by.24 percentage points. Although the stores in our sample accept both credit and debit cards, consumers adoption decisions should be related to the policies of other stores, and those may vary systematically with population density. 15 As a robustness check, we also use HHI of urban counties instead of MSAs. Again, banking markets are less concentrated in urban counties than rural counties, and the regression results based on HHI of urban counties are consistent with those based on MSAs. 16 Consistent with our results, Judson and Porter (24) find that local crime seems to depress overall demand for currency, as measured by payment and receipt growth at 37 Federal Reserve Cash Offices. 16

17 Table 2. Marginal effects for zip-code-level variables Variable Cash Debit Credit Check Cash holding and payment choice Median sale value -.18*.12*.5*.1* Banking HHI.3* -.23* -.1*.3* Banking HHI*Metro -.5*.32*.24* -.5* Branches per capita.7* -.5* -.4*.1* Robbery rate -.54*.63*. -.1* Adoption of non-cash payments Median household income -.33*.5*.36* -.8* Deposits per capita -.6*.16*. -.1* Population density -.38*.79*.91* -.131* Demographics Family households -.98*.89*.16* -.6* Housing Owner-occupied -.2*.6*.6*.8* Vacant -.4*.11*.26*.4* Female -.52*.8* -.5* -.23* Age *.163*.34* -.13* *.115*.53* -.16* *. -.13* -.18* * -.38*.54*.7* Race black.55* -.25* -.2* -.11* Hispanic.24* -.19*.3* -.7* Native.133* -.74* -.52* -.7* Asian -.18*.8*.32* -.22* Pac-Islr -.311*.55* -.23* -.36* other.91* -.42* -.48* -.1* multiple -.81*.19*.5* -.32* Edu high school -.22*.138*.57*.7* some college -.322*.233*.88*.1* college -.225*.14*.79*.7* Pseudo 2 (incl state, time) (excl state) (excl time) (excl state, time) Zip code-day observations 4,55,642 4,55,642 4,55,642 4,55,642 Note: *1% significance level based on robust standard errors. The dependent variables are the fractions of each of the four general payment instruments used in transactions at stores in a zip code on a day between April 1, 21, and March 31, 213. The independent variables take their values in 211. Banking HHI index is calculated by squaring each bank s share of deposits in a market (a MSA or a rural county) and then summing these squared shares. Metro is a dummy variable taking the value one when the banking market is a MSA, otherwise equal to zero. Branches per capita is measured as the number of bank branches per 1 residents in a zip code. Robbery rate is defined as the number of robberies per 1 residents in a county. Median household income is measured in the unit of $1, per household in a zip code. Deposits per capita is measured in the unit of $1, deposits per resident in a zip code. Population density is measured in the unit of 1, residents per square mile in a zip code. All the demographic variables are expressed as fractions. 17

18 3.2.3 Demographics Consistent with previous studies based on consumer surveys, we find that demographic characteristics such as age, race, and education are systematically related to consumer payment choices. Table 2 shows that a higher presence of older age groups is associated with greater useofpaymentcardsrelativetothebaselineagegroup,under15.thismightbesimply because minors do not have access to non-cash payments, or because families with children tend to use more cash or checks. However, the age profile with respect to cash and checks is non-monotonic. A higher presence of the age group is associated with a significantly higher cash fraction, while a higherpresenceofpeopleatage7andolder is associated with a higher check fraction. These findings suggest that the age variables may be standing in primarily for cohort effects: Older people tend to be cash users not because they are older but because they did not have access to cards when they first reached adulthood. For the purpose of projecting future cash use as we do in Section 6, the distinction between cohort and age interpretations is important, and we will adopt the cohort interpretation except for the youngest age group. Table2alsoshowsthatahighershareofBlack,HispanicorNativeAmericanpopulation is associated with a higher cash fraction compared with White and Asian. A more educated population (i.e., high school and above) is associated with a lower cash fraction relative to the baseline education group (i.e., below high school) State and Time Effects The regression also includes dummy variables for state, for day-of-week, day-of-month, and month-of-sample. The estimates for state dummies reveal substantial payment variation across states (Figure A1 in the Appendix plots histograms of state dummies for each payment type). Conditioning on the other variables, the cross-state variation appears largest in the fraction of debit, with a maximum difference of 14.8 percentage points; credit ranks second (9.93 percentage points) and cash ranks third (9.41 percentage points). The cross-state variation is smallest for checks with a maximum difference of merely.72 percentage points, reflecting the fact that checks only account for 2 percent of all transactions. We defer discussion of the time effects until Sections 5 and 6 below. Table2reportspseudoR 2 values when the time and state dummies are either included or excluded. Our full model explains 59 percent of the variation in cash fractions, and that number falls by 23 percentage points when both state and time effects are removed. 18

19 The contributions of state and time dummies are nearly additive; that is, removing state and time effects is close to removing state effectsplusremovingtimeeffects. Time effects have small contributions, especially for credit. On the other hand, state effects are important, but more so for the debit vs. credit margin than for the cash vs. non-cash margin. 3.3 Estimates by Transaction Size Class We now turn to an analysis based on individual transaction sizes by estimating separate regressions for the 22 transaction size bins used in Figure 2, again aggregating to the zip-code day level. As a result, we will produce an estimated counterpart to Figure 2 and explain payment variation across transaction sizes and locations Estimation Approach We subdivide the sample by transaction size class before aggregating to the day and zipcode level. This allows us to use FMLogit regressions as before, but based on subsamples accordingtodifferent transaction sizes. In the background, we continue to be motivated by the threshold hypothesis: The fraction of cash payments at a particular transaction size for a given zip-code-day represents the fraction of shoppers whose threshold for cash use lies above that transaction size. By conditioning on transaction size, we focus here on marginal payment shares instead of the total payment shares. With heterogeneous consumers, the payment share at a particular transaction size still depends on the distribution of consumer characteristics, the economic environment and calendar time. In the exercise, we allow all coefficient estimates to vary across transaction size regressions. A more restrictive approach would impose common coefficients on zip-code level variables, allowing only the constant terms to vary across each transaction size regression. We will see in Section 4 that the data do not appear consistent with common coefficients. The sensitivity of both level and dispersion of payment shares, shown in Figure 2, is attributed overwhelmingly to variation across transaction size in the coefficients on zip-code-level variables. For the sake of space, we only plot marginal effects for cash here in Figure 5, leaving the others to the Appendix. We highlight the findings from the estimates by transaction size in what follows. 19

20 Marginal effect Marginal effect HH Income Deposits -.2 Pop Density Robbery Value of sale Marginal effect Family -.3 Homeowner -.4 Vacant Female Value of sale Black Hispanic Native Asian Value of sale Marginal effect Marginal effect Marginal effect HHI Rural HHI MSA Branches Value of sale -.4 Age Value of sale High School -.6 Some College College Value of sale Figure 5. Cash marginal effects by transaction size Findings: Marginal Effects and Amplification Most zip-code-level explanatory variables show a sign consistent with our estimates for the overall zip-code-day shares. In fact, our marginal-effect estimates from the overall regression in Section 3.2 closely match those from the $6-$7 transaction size regression (Recall that for our overall sample, the mean value of zip-code-day level median sales is $6.86). Therefore, the discussion of our marginal-effect estimates above also applies here for the appropriate size transactions. Moreover, as transaction size increases, the marginal effects for most explanatory variables are increasing in absolute value (we refer to this pattern as amplification). Such patterns are found for cash, debit, credit and check alike, as shown in Figures 5 and A3-A5. In a few cases, the amplification of marginal effects is more subtle. For example, in Figure 5, population density shows a small and decreasing effect on cash use as transaction size increases. However, a careful look into the results in the Appendix (Figures A3-A5) shows that population density mainly affects the substitution between cards and check, while cash only captures a small residual effect. In fact, the marginal effects of population 2

21 density clearly amplify with transaction sizes for debit, credit and check. Thestateandtimeeffects also amplify with transaction sizes. We provide histograms of state fixed effects in Figure A6 in the Appendix, and again defer discussion of the time effects until Sections 5 and 6. 4 Payment Variation across Transaction Sizes and Locations In Figure 2 we showed that the fraction of cash (non-cash) transactions is decreasing (increasing) in transaction size, and that the dispersion of these fractions across locations is increasing in transaction size. In this section we investigate the counterpart to Figure 2 implied by our estimated model. We begin this section by confirming that the estimated counterpart replicates the patterns in Figure 2. We then provide an interpretation based on the cash thresholds of individual shoppers. Finally, we provide a decomposition showing that the estimated relationship between transaction size and payment fractions (level and dispersion) is accounted for not by a fixed transaction size effect, but rather by the amplifying effect of the zip-code-level variables. 4.1 Threshold Distributions Figure 6 displays the estimated counterpart to the raw data of Figure 2. For each size class, we plot the median, 5th, and 95th percentiles of the distribution of predicted values for the four payment shares. Comparing the two figures, it is clear that the estimated models for each transaction size are successful at replicating both (i) the relationship between transaction size and the level of payment composition, and (ii) the relationship between transaction size and the dispersion of payment composition across zip-code days. Our model estimates yield empirical counterparts to the cash threshold distributions implied by theory. Specifically, the sum of all three non-cash payment fractions shown in Figure 6 (or one minus the cash fractions) provides the empirical bounds for locationspecific cumulative distribution functions of the cash thresholds in our sample. The figures show that for $1 transactions, about 9 percent of shoppers are under their cash thresholds in most locations. As transaction size increases, more and more shoppers pass their cash thresholds, and the dispersion of cdf functions increases across locations. Eventually, for $5 dollar and above transactions, 58 percent of shoppers have passed their cash thresholds 21

22 in the median location, while the fraction is 45 percent in 5th percentile location and 7 percent in the 95th percentile location. 17 A. Cash B. Debit th Percentile Median 95th Percentile th Percentile Median 95th Percentile $ $ C. Credit D. Check th Percentile Median 95th Percentile th Percentile Median 95th Percentile $ $ Figure 6. Predicted payment variation across transaction sizes. 4.2 Determinants of Threshold Distributions We now discuss how those relationships are related to the amplifying effects of explanatory variables. We first divide the explanatory variables into two groups: One comprises constant terms, which include the intercept and time and state-level fixed effects, and the other comprises all zip-code-level variables. We wish to quantify the relative contributions of the two groups of variables to the levels and dispersion of the payment mix across transaction sizes. In Section 3 we found that zip-code days with larger transactions were associated with a lower share of cash payments, but that finding is consistent with either the constant terms or zip-code-level variables driving the share levels in the transaction 17 It is useful to compare our model-predicted payment choice probabilities with those in Klee (28) and Briglevics and Schuh (214). Those two studies focus on grocery transactions, one using data from a grocery store chain in 21 and the other using 212 Diary of Consumer Payment Choice (DCPC) data. Their results show that in the past decade, there has been a dramatic decline in cash and check use in grocery transactions, and a substantial increase in credit and debit use (See Figure A2 in the Appendix for the comparison). For example, considering a $5 transaction, the probability of cash use was 3% in 21 but dropped to 15% in 212, while check use dropped from more than 3% to almost zero. Meanwhile, credit use (including signature debit) increased from less than 2% to 55%, and PIN debit use increased from 2% to 3%. Comparing with their results, estimates based on our sample show a much higher probability of cash and PIN debit use, both about 4% for a $5 transaction in the median location. 22