Convenient prices, cash payments and price rigidity

Economic Modelling 41 (2014) 329–337

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Economic Modelling journal homepage: www.elsevier.com/locate/ecmod

Convenient prices, cash payments and price rigidity☆ Y. Bouhdaoui a, D. Bounie b,⁎, A. François c a b c

APEC — C2.33, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium Telecom ParisTech, Economics and Social Sciences, 46 rue Barrault, 75634 Paris Cedex 13, France EM Strasbourg Business School-Strasbourg University (LaRGE), and Telecom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France

a r t i c l e

i n f o

Article history: Accepted 21 May 2014 Available online 17 June 2014 Keywords: Convenient prices Cash payments Price rigidity

a b s t r a c t Recent works suggest that convenient prices that match monetary denominations exhibit above-average price rigidity and are set up by firms that have incentives to be paid in cash. The relationship between convenient prices and cash usage has however never been explicitly examined. This paper proposes a model that relates convenient prices to cash usage and exploits to test it a unique dataset in 2011 on cash payments and prices by a representative sample of French consumers. In line with the model, estimation results bring direct evidence that individuals' shares of cash payments increase with convenient prices. This finding confirms that price rigidity can be in part explained by the use of cash to pay convenient prices. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Several recent works have attempted to explain why firms have incentives to set price points or convenient prices. Convenient prices are round prices that usually match monetary denominations while price points are odd prices such as 9-ending prices (Knotek, 2008). Price points and convenient prices are of a significant importance because they are in turn accused of being one of the sources of price rigidity (Blinder et al., 1998; Kashyap, 1995; Knotek, 2011; Levy et al., 2011) which supposedly influences the monetary policy, the aggregate price level (Aoki, 2001; Carvalho, 2006) and the output (Nakamura and Steinsson, 2008). In the economics literature, the existence of price points and convenient prices has been addressed in two main contributions.1 In a first study, Levy et al. (2011) relate price points to consumer behaviors. They argue that consumers ignore the rightmost digits of retail prices (consumer inattention) and then may offer a plausible explanation for the existence of price points. In a second study,

☆ This research benefited from financial support from the Groupement des Cartes Bancaires “CB”. ⁎ Corresponding author. E-mail addresses: [email protected] (Y. Bouhdaoui), [email protected] (D. Bounie), [email protected] (A. François). 1 There is an important literature in management that analyzes how price endings affect buyer's decisions; see Stiving and Winner (1997).

http://dx.doi.org/10.1016/j.econmod.2014.05.030 0264-9993/© 2014 Elsevier B.V. All rights reserved.

Knotek (2011) argues that convenient prices deal with the pricesetting of firms. He reports three key factors that encourage firms to set convenient prices: transactions made with cash, items that are sold alone or with a few similar items and high-traffic transactions. The factor that relates convenient prices to cash usage is worth focusing. Indeed, firms may set convenient prices and be paid in cash to expedite transactions at point-of-sale, avoid sales taxes or credit card fees. Conversely, it can be also profitable for a firm to set price points to avoid cash payments when the cost of handling cash is high or risky (theft, etc.) compared to the costs of other payment instruments. The same reasoning applies to consumers who also face transaction and holding costs when they use cash or other payment instruments. For instance, Whitesell (1989) has shown that consumers may prefer cash to other payment instruments for low value transactions. However, to the best of our knowledge, the relation between cash usage and convenient prices has never received an explicit economic analysis. Indeed, based on the study of the prices of several product groups in various types of establishments, Knotek (2011) infers the existence of a relation between convenient prices and goods and services “typically” purchased in cash. Unfortunately, the author has no indication on the way convenient prices are paid in the surveyed establishments since the use of payment instruments is not observed. As a result, the impact of convenient prices on the use of payment instruments is not clearly established and could be due to other factors (high-traffic transactions, etc.). Similarly, Kim and Lee (2012) analyze in a standard search-based model of exchange how a trade-off between cash and debit card can provide one of the possible micro-foundations for price rigidity in response to monetary policy. However, the authors

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do not specifically connect cash payments to convenient prices and outline that “empirical studies with extensive data on the payment patterns should be indispensable to understand the importance of the mechanism for nominal price rigidity associated with means of payment”. The goal of this paper is precisely to examine the link between convenient prices and the use of cash in transactions. To this end, we first extend the model of Whitesell (1989) by including a cost of paying non convenient prices in cash. This model outlines that the share of cash payments should increase with convenient prices since transaction costs of cash are lower than the ones of the alternative payment instrument. Second, we exploit a unique dataset of payments reported in shopping diaries in 2011 by a representative sample of 1106 French individuals of 18 years and older. This method is standard in empirical research in payment economics and considered as promising in research on demand for cash (Alvarez and Lippi, 2009). Diary survey data have indeed the advantage to collect accurate information on individual cash (and non cash) transactions, their volume and value, the types of products purchased, the types of establishment visited, the purchases that involve single or multiple items, etc., information that are not well known by central banks. Using different econometric tests and controlling for transaction and individual characteristics, we show that individuals' shares of cash payments increase with convenient prices. This finding therefore proves the Knotek's conjecture according to which convenient prices exhibit above-average price rigidity because firms have incentives to be paid in cash. The remainder of the paper is structured as follows. In Section 2, we refine the model of Whitesell (1989) by including a cost of paying cash non convenient prices. In Section 3, we describe the data used to explain the relation between cash usage and convenient prices and in Section 4, we present and comment on the econometric tests, the results and their robustness. Finally, in Section 5, we conclude. 2. A model of convenient prices and cash usage

case that the optimal domain of cash is compact and located in low value transactions.3 Now, we extend the initial framework to account for convenient prices. As outlined in Knotek (2011), price points are indeed not easy to process for consumers and require to carry more tokens during shopping trips. Therefore, these factors affect the consumer's trade-off between payment instruments. In the following, computational and carrying costs of cash are referred to as “transaction costs of cash”. We associate them, in practice, to the number of tokens exchanged in transactions.4 Formally, we consider a currency system s composed of J denominations of face values vs(j) with j ∈ {1, …, J}, and assume, as in standard theoretical and empirical works, that agents pay cash following the “principle of least effort”.5 This principle states that consumers and merchants exchange a minimum number of coins and notes to pay a given amount of cash. Namely, a transaction of size t is paid by exchanging rs(t, j) token(s) for each denomination vs(j): t¼

X

rs ðt; jÞvs ð jÞ;

ð3Þ

j

such that the number of monetary units exchanged rs(t) = ∑ j|rs(t, j)| is minimum.6 The parameter rs(t) is a direct measure of the convenience of a price.7 As argued previously, we define the transaction cost of cash, based on rs(t), as w ⋅ rs(t), where w is the unit cost of exchanging a token. The cost of cash defined in Eq. (1) can then be extended as follows: 0

C ð1Þ ¼ nb þ

X i X tþw rs ðt Þ: 2n t∈D t∈D ð1Þ

By adding up C′(1) and C(2), the consumer's problem can be written as: 8 9 < = X X i X tþw r s ðt Þ þ ðu F þ uV t Þ ; minDð1Þ ∈℘ðDÞ nb þ : ; 2n t∈D t∈D t∈D∖D ð1Þ

In developed countries, most consumers hold several payment instruments such as cash, credit and debit cards, etc. Each time they face a price, consumers have then to decide which payment instrument to use. Whitesell (1989) has proposed a framework to model the choices between payment instruments. In this model, consumers face a predetermined set of transaction D payable either with cash or with an alternative payment instrument. When using cash, consumers are supposed to incur a withdrawal fee, b, and an opportunity cost for holding cash that equals the interest rate, i, times the average cash holding over the purchasing period. Regarding the alternative payment instrument, consumers incur a fixed cost per transaction, uF, and a variable cost, uV. Formally, a consumer making n withdrawals incurs a cost of cash that can be written as: C ð1Þ

i X ¼ nb þ t; 2n t∈D

ð1Þ

where Dð1Þ is a subset of D that refers to the transactions paid in cash over the period.2 The complementary set D∖Dð1Þ , payable with an alternative payment instrument, induces the cost: X

ðu F þ uV t Þ:

ð2Þ

t∈D∖Dð1Þ

The consumer problem is then to minimize C(1) + C(2) by making the optimal choices of payment instruments. Whitesell (1989) shows in this 2

The term 2ni ∑t∈Dð1Þ t refers to the interest earnings foregone over the period.

ð1Þ

ð5Þ

ð1Þ

with ℘ðDÞ, the powerset of D. According to Eq. (5), the consumer's problem consists in minimizing the costs of transactions by determining the optimal set of cash payments Dð1Þ , given that the complementary set of transactions is carried out using the alternative payment instrument. The first order condition related to the number of cash withdrawals, n, is written as follows: b−

i X t ¼ 0: 2n2 t∈Dð1Þ

ð6Þ

Therefore, the optimal number of withdrawals is:

ð1Þ

C ð2Þ ¼

ð4Þ

ð1Þ

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u i X  t: n ¼t 2b t∈D

ð7Þ

ð1Þ

3 As shown in Whitesell (1989), the alternative payment instrument will not be used for low-value transactions because of the fixed cost of transaction. 4 Beside the processing cost of transactions, there is a wide agreement in the economics literature according to which the carrying cost of money is an essential element in studying cash payment patterns (Lee, 2009; Van Hove and Heyndels, 1996). 5 The principle of least effort was introduced by Caianiello et al. (1982) and subsequently refined by Cramer (1983). More recently, Franses and Kippers (2007) have shown that the principle of least effort constitutes a reasonable approximation of the Dutch public payment behavior. 6 Absolute values indicate that overpayment and return of change are allowed. 7 rs(t) takes low values for convenient prices as they require to exchange fewer tokens, and vice versa.

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Table 1 Examples of costs of payments. Options of payment (C = Cash and A = Alternative payment instrument) D ¼ f5; 7:5; 10g

{C, C, C} pffiffiffiffiffiffiffi 4:5 þ 14 0 16.12

C(1)′ C(2) Total costs of payments

{C, C, A} pffiffiffiffiffiffiffi 2:5 þ 12 11 24.58

{C, A, C} pffiffiffi 3þ4 8.5 14.23

{C, A, A} pffiffiffi 1þ2 19.5 22.5

The other parameters are given in plain text.

Replacing Eq. (7) in (4) and rearranging the terms, we obtain: 0

C ð1Þ ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X X 2ib tþw r s ðt Þ: t∈Dð1Þ

3.1. Methodology of the survey and sample ð8Þ

t∈Dð1Þ

Therefore, the consumer's problem becomes: 8 9
ð1Þ

ð9Þ

ð1Þ

Based on Eq. (9), several comments can be made. First, conversely to Whitesell (1989) where the domain of cash is compact and delimited by a specific upper bound value, the domain of cash here can be non-compact and composed of spaced intervals. As an illustration, let us consider a currency system composed of four denominations s = {0.25, 1, 5, 10} and the set of prices D ¼ f5; 7:5; 10g. The model parameters are set as: i = 5%, b = w = 2 and uF = uV = 1. In this example, the agent has eight choices to settle the three prices depending on whether they are paid in cash or with another payment instrument. In Table 1, we report the four least costly options.8 In the first one, {C, C, C}, all the prices are paid in cash; in the second one, {C, C, A}, the two first ones are paid with cash and the last one with an alternative payment instrument; and so forth. We measure the costs of payments for each option. In accordance with Eq. (8), the costs of cash payments are partly based on the convenience of prices: rs(5) = 1, rs(7.5) = 5 and rs(10) = 1.9 As a result, the costs of cash payments are comparatively high in options 1 and 2 where the least convenient price t = 7.5 is paid in cash. Overall, the third option {C, A, C}, where cash is used to pay the lowest and the highest prices, proves to be the least costly. This result shows that accounting for the transaction cost of cash can lead to optimal configurations where the preference domain of cash is non-compact, contrasting therefore with the initial framework of Whitesell (1989). This finding is clearly in line with the cash payment patterns described in empirical studies such as Bouhdaoui and Bounie (2012). Second, it also results from Eq. (9) that a convenient price is more likely to have a higher impact on the transaction costs of the alternative payment instrument than on the ones of cash (see C(1)′). As a result, the model predicts that the share of cash payments should increase with convenient prices. In the previous example, the optimal choice illustrates this observation, as the first and third prices, both matching a face value of the currency system, are paid in cash, whereas the second one is paid with the alternative payment instrument. 3. Data description In this section, we present the data used to examine the relation between cash usage and price convenience at an individual level. 8 The first four options where t = 0.25 is paid with the alternative payment instrument turn out to be too costly, we therefore only report the remaining choices. 9 The transaction t = 7.5 requires five tokens: t = 5 + 2 × 1 + 2 × 0.25 = 10 − 2 × 1 − 2 × 0.25.

We conducted a survey in 2011 on a representative sample of 1106 French individuals of 18 years and older. The survey is structured in two parts. The first is a questionnaire designed to collect, during face-to-face interviews, payment methods, individuals' finances and demographics (such as gender, age, income and profession). The second is an 8-day shopping diary10 in which each respondent reports information on daily point-of-sale payments.11 Each purchase in the diary is characterized by several pieces of information such as the amount to be paid, the type of payment instrument used (cash, check, payment card, etc.), the type of product purchased (in 9 categories),12 the type of establishment in which the transaction took place (in 7 categories)13 and the number of products (items) purchased during the transaction (in two categories: one or more than one). In comparison to previous studies such as Knotek (2011), the use of diaries allows us to identify the payment instrument used, the number of items purchased and, on top of this, the socioeconomic characteristics of the agents. Out of 1106 respondents, 1056 have completed the diaries. Since we are interested in examining the relation between the price of a single product and the use of a payment instrument, we exclusively focus on transactions that involve the purchase of a single item. Moreover, we exclude from the sample all purchases realized on the Internet, by phone or by mail where cash cannot be used. We have then a final sample of 909 individuals totalizing 4852 point-of-sale payments.14

3.2. Description of the global data set The distribution of all purchases paid in cash or with an alternative payment instrument is plotted in Fig. 1. Two comments can be made. First, the largest part of transactions is low value purchases; more precisely, 34.5% of all transactions are lower than 2 euros, 56.3% lower than 10 euros and 69.7% lower than 20 euros. The mode of the distribution amounts exactly to 0.80 cents euros. This distribution is consistent with other studies in different countries (Boeschoten and Fase, 1989; Klee, 2008; Mooslechner et al., 2006). Second, the distribution exhibits a higher frequency of transactions for convenient prices that either match monetary denominations or are simple combinations of them such as 10 €, 20 €, 30 €, 50 €, etc. Based on the principle of least effort described in Section 2, we calculate the number of tokens exchanged to cover each price observed in the distribution. As displayed in Fig. 2, 14.1% of all prices are paid using one

10 The method of the diary is common to several international studies (see Boeschoten and Fase, 1989; Jonker et al., 2012; Mooslechner et al., 2006; Von Kalckreuth et al., 2009; Wakamori and Welte, 2012). 11 Professional expenses and bill payments were excluded from diaries. 12 The categories are: 1) Food and beverages; 2) Equipment and personal services; 3) Press, tobacco and gambling; 4) Home furnishing; 5) Medical/Health; 6) Transport; 7) Leisure and culture; 8) Restaurant, cafe and hotel; 9) Other. 13 The categories are: 1) Small retail stores (retail daily consumption products); 2) Department stores; 3) Drugstore, cosmetics; 4) Hypermarket (superstore); 5) Home services; 6) Administration; 7) Other. 14 11 prices above 1000 euros have been dropped from the samples. These prices are considered as outliers.

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Fig. 1. Percentage of transactions as a function of the transaction size (logarithmic scale).

Fig. 2. Percentage of transactions as a function of the number of tokens.

token, 44.5% need two tokens, 27.4% three tokens and a very low proportion of prices requires four or more tokens. As a consequence, a large fraction of prices can be considered as convenient prices. 3.3. Description of consumer payments As our model in Section 2 is centered on consumer choices, we now describe the data set to characterize consumer payments. To begin with, the shopping diaries show that consumers face on average 4.5 transactions per week for a total value per consumer of about 93 euros.15 Out of 4.5 transactions, 3.1 are paid on average in cash (64.7%) for a total value of about 20 euros. The distribution of the number of tokens that should be exchanged on average by individuals to cover all transactions, i.e. paid in cash or with an alternative payment instrument, is depicted in Fig. 3. It shows that most transactions faced by consumers require to exchange two or three tokens.16 Finally, in relation with our research question, we can provide a first outlook of the relation between the share of cash payments and price convenience. Fig. 4 depicts the average share of cash payments of consumers as a function of the average number of tokens exchanged in transactions. It confirms that prices that require a high number of tokens to be exchanged are less often paid in cash.17 This finding is in line with the model described above. Indeed, when people face non convenient prices that require a high number of tokens, they are more likely to opt for alternative payment instruments to avoid the transaction costs of cash. In the next part, we present a multivariate analysis to control for various individual and transaction characteristics.

Fig. 3. Distribution of the number of tokens exchanged in transactions by individual.

4. Impact of convenient prices on cash payments In this part, we first present the econometric test and second we discuss the robustness of the estimation results. 15

A summary of the key descriptive variables is provided in Appendix A.1. Using the principle of least effort, we first calculate the number of tokens exchanged for each transaction and then, for each individual, the average number of tokens per transaction. The average number of tokens per transaction exchanged by individuals is 2.4. 17 We distinguish seven categories: 1) less than 1.5 tokens (71 observations, 7.8%), 2) between 1.501 and 2 tokens (257 obs., 28.3%), 3) between 2.01 and 2.5 tokens (236 obs., 26.0%), 4) between 2.501 and 3 tokens (235 obs., 25.8%), 5) between 3.01 and 3.5 tokens (52 obs., 5.7%), 6) between 3.501 and 4 tokens (52 obs., 5.7%), and 7) more than 4 tokens (6 obs., 0.7%). 16

Fig. 4. Average share of cash payments as a function of the number of tokens per transaction.

Y. Bouhdaoui et al. / Economic Modelling 41 (2014) 329–337

4.1. Econometric test and results This part aims at specifying and testing the relation between convenient prices and the use of cash in payments. To do that, we use a linear and a generalized linear regression model that explains for each individual of the sample the share of their cash payments (dependent variable). The generalized linear model (GLM) is used to account for the fact that our dependent variable is bounded between 0 and 1 (and thus predictions can fall outside the unit interval). In this case, Papke and Wooldridge (1996) suggest to use a GLM with a binomial distribution and a logit link function, which they coin the ‘fractional logit’ model. As we will discuss later, the linear and the generalized linear regression models provide very similar results. The simple linear regression model can be written as follows: Si ¼ αX i þ βZ i þ γT i þ error;

ð10Þ

with Si the share of cash payments of the individual i, Xi, the average number of tokens used in transactions by the individual i, Zi a vector of transaction characteristics, Ti a vector of individual characteristics and, finally, α, β and γ the parameters to be estimated. Standard OLS are used to estimate the parameters. In Eq. (10), the average number of tokens per transaction serves as a proxy to capture price convenience and is used to explain the

333

individual's share of cash payments. Accordingly with the model and the preliminary data analysis, we expect a negative impact of the average number of tokens on the share of cash payments since convenient prices reduce the transaction costs of cash. We also introduce several control variables related to transactions such as the average transaction size, the shares of cash payments realized in each type of establishment and for different categories of products. First, the transaction size is expected to have a negative impact on the share of cash payments (Whitesell, 1989). Second, according to research on price rigidity (Nakamura and Steinsson, 2008), the types of good and establishment are unequally impacted by price movements. In this regard, we expect to have a positive effect of some typical products and establishments that use extensively cash. Descriptive statistics provided in Table 3 in Appendix A.1 show, for instance, that cash is widely used in small retail stores visited for daily consumption. Finally, several individual characteristics such as sex, age, monthly income, education level and size of the living area are also used as control variables. The results of the estimations are reported in Table 2. We find that the standard and the generalized linear models provide very similar results. As the signs and the statistical significance of the coefficients of the explanatory variables are stable, we only comment on hereafter the OLS outcomes. As expected, we find a negative and statistically significant effect of the average number of tokens per transaction on the share of cash payments of individuals. In other words, the lower the number of tokens to be

Table 2 Estimation of the share of cash payments. Model

OLS standard Model A

Average value of a transaction Average number of tokens per transaction % of cash payments made … Food and beverages Personal equipment/services Press/tobacco/gambling Home furnishing Medical/health Transport Leisure/culture Restaurant/cafe/hotel Other Small retail stores Department stores Drugstore/cosmetics Hypermarket Home services Administration Other Sex (1 if male) Age Monthly income: b1500 € N1501 € and b3000 € N3001 € Do not know/refuse Education: no diploma Before university University Area: small cities Large city Paris and agglomeration Constant Observations Adj. R2/AIC

GLM fractional logit Model B

Model C

Model A

Model B

Model C

−0.12⁎⁎⁎ (0.023) – – −0.16⁎⁎⁎ (0.023) −0.012⁎⁎⁎ (0.0038) −9.64⁎⁎⁎ (1.43) −11.5⁎⁎⁎ (1.41) – – −0.55⁎⁎⁎ (0.10) −0.69⁎⁎⁎

(0.10)

Reference −0.35⁎⁎⁎ 0.054 −0.21⁎⁎⁎ −0.42⁎⁎⁎ −0.49⁎⁎⁎ −0.27⁎⁎⁎ −0.37⁎⁎⁎ −0.31⁎⁎⁎

(0.05) (0.04) (0.07) (0.06) (0.05) (0.07) (0.06) (0.07)

Reference −0.28⁎⁎⁎ (0.05) −0.22⁎⁎⁎ (0.06) −0.20⁎⁎⁎ (0.04) −0.12 (0.15) 0.22⁎⁎ (0.10) −0.20⁎⁎⁎ (0.05) 3.74⁎⁎ (1.82) −0.022 (0.06) Reference −6.60⁎⁎⁎ (2.14) −10.9⁎ (5.82) 1.21 (3.24) Reference −2.35 (2.92) −10.1⁎⁎⁎ (3.51) Reference 1.73 (1.95) 1.14 (2.71) 119.7⁎⁎⁎ (5.59) 909 0.48/–

−0.37⁎⁎⁎ 0.053 −0.31⁎⁎⁎ −0.42⁎⁎⁎ −0.52⁎⁎⁎ −0.28⁎⁎⁎ −0.38⁎⁎⁎ −0.35⁎⁎⁎

−0.36⁎⁎⁎ 0.024 −0.23⁎⁎⁎ −0.49⁎⁎⁎ −0.49⁎⁎⁎ −0.29⁎⁎⁎ −0.40⁎⁎⁎ −0.37⁎⁎⁎

(0.05) (0.04) (0.07) (0.06) (0.05) (0.07) (0.06) (0.07)

−0.28⁎⁎⁎ (0.05) −0.32⁎⁎⁎ −0.24⁎⁎⁎ (0.06) −0.21⁎⁎⁎ −0.21⁎⁎⁎ (0.04) −0.22⁎⁎⁎ −0.13 (0.15) −0.11 0.12 (0.10) 0.24⁎⁎ −0.24⁎⁎⁎ (0.05) −0.17⁎⁎⁎ 3.93⁎⁎ (1.85) 3.60⁎

(0.05) (0.06) (0.04) (0.15) (0.10) (0.05) (1.87) (0.06)

−0.011

(0.05) (0.04) (0.07) (0.06) (0.05) (0.07) (0.06) (0.07)

(0.06) −0.024

−7.32⁎⁎⁎ (2.17) −7.28⁎⁎⁎ (2.19) −12.6⁎⁎ (5.91) −12.7⁎⁎ (5.96) 1.53 (3.29) 1.00 (3.32) −2.32 (2.96) −1.74 (2.99) −10.3⁎⁎⁎ (3.57) −9.33⁎⁎⁎ (3.60) 2.47 0.83 122.7⁎⁎⁎ 909 0.47/–

(1.98) 1.28 (2.75) 2.69 (5.65) 99.0⁎⁎⁎ 909 0.46/–

Standard errors in parentheses. The GLM is a fractional logit with a binomial distribution and a logit link function. ⁎ p b 0.10. ⁎⁎ p b 0.05. ⁎⁎⁎ p b 0.01.

(2.00) (2.77) (4.79)

Reference −0.020⁎⁎⁎ 0.0025 −0.013⁎⁎⁎ −0.023⁎⁎⁎ −0.026⁎⁎⁎ −0.014⁎⁎⁎ −0.021⁎⁎⁎ −0.016⁎⁎⁎

(0.0038) (0.0033) (0.0046) (0.0044) (0.0039) (0.0044) (0.0036) (0.0043)

−0.022⁎⁎⁎ 0.0025 −0.017⁎⁎⁎ −0.023⁎⁎⁎ −0.028⁎⁎⁎ −0.015⁎⁎⁎ −0.022⁎⁎⁎ −0.019⁎⁎⁎

Reference −0.013⁎⁎⁎ (0.0038) −0.014⁎⁎⁎ −0.010⁎⁎ (0.0047) −0.012⁎⁎ −0.011⁎⁎⁎ (0.0032) −0.012⁎⁎⁎ −0.0060 (0.012) −0.0071 0.015 (0.0094) 0.0059 −0.012⁎⁎⁎ (0.0034) −0.014⁎⁎⁎ 0.28⁎⁎ (0.12) 0.27⁎⁎ −0.0017 Reference −0.45⁎⁎⁎ −0.57⁎⁎ 0.071 Reference −0.22 −0.69⁎⁎⁎ Reference 0.12 0.12 4.04⁎⁎⁎ 909 –/0.84

(0.0035) −0.0015

−0.015⁎⁎⁎

(0.0041)

(0.0037) (0.0035) (0.0045) (0.0043) (0.0037) (0.0044) (0.0037) (0.0042)

−0.020⁎⁎⁎ 0.0011 −0.013⁎⁎⁎ −0.026⁎⁎⁎ −0.025⁎⁎⁎ −0.014⁎⁎⁎ −0.022⁎⁎⁎ −0.019⁎⁎⁎

(0.0038) (0.0035) (0.0047) (0.0042) (0.0039) (0.0043) (0.0037) (0.0041)

(0.0038) (0.0048) (0.0031) (0.012) (0.0071) (0.0034) (0.12) (0.0034)

−0.015⁎⁎⁎ (0.0037) −0.0097⁎⁎ (0.0043) −0.012⁎⁎⁎ (0.0032) −0.0051 (0.011) 0.016⁎ (0.0086) −0.010⁎⁎⁎ (0.0034) 0.27⁎⁎ (0.12) −0.0015 (0.0034) −0.48⁎⁎⁎ −0.65⁎⁎⁎ 0.074

(0.12) (0.25) (0.20)

(0.12) (0.24) (0.20)

−0.48⁎⁎⁎ −0.70⁎⁎⁎ 0.067

(0.12) (0.25) (0.20)

(0.21) (0.24)

−0.24 −0.69⁎⁎⁎

(0.21) (0.24)

−0.19 −0.63⁎⁎⁎

(0.22) (0.24)

(0.12) (0.18) (0.40)

0.16 0.065 4.29⁎⁎⁎

(0.12) (0.18) (0.40)

0.093 0.22 2.80⁎⁎⁎

(0.12) (0.18) (0.30)

909 –/0.85

909 –/0.85

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exchanged in transactions, the higher the share of cash payments. The magnitude of the effect is quite high since one more token in transactions decreases the share of cash payments by more than 9.3 points of percentage or, said differently, an increase of 1% of the average number of tokens per transaction decreases the share of cash payments by 0.36%. Turning to the transaction size dimension, we find that an increase of 10 euros of the average transaction size decreases the share of cash payments by 9 points of percentage. Finally, as stated previously, we find that the share of cash payments significantly varies across products and establishments that extensively use cash: more precisely, the share of cash payments is significantly higher for the base categories “Food and beverages” and “Small retail stores” that use extensively cash compared to other categories.18

4.2. Discussion and robustness of the results The effect of convenient prices on cash payments outlined in the previous section is robust for several reasons. First, this is not an artifact due to a possible correlation with the price variable. Indeed, the pairwise correlation coefficient between the average value of a transaction and the average number of tokens is low (around 0.31). Moreover, the estimated coefficients are fairly stable when we exclude successively from the regression one of the two main predictors (see Models B and C in Table 2). Finally, the mean of the variance inflation factor (VIF) of the estimation is low 1.41, with a VIF associated to the average value of the transaction at 1.4; our results therefore are not affected by a multicollinearity issue. Second, estimation results are not altered by different measures of price convenience or cash payments. Indeed, we ran different estimations with various measures of price convenience such as the total number of tokens exchanged in transactions, the logarithm of the average number of tokens, the average number of tokens with dummy variables (as depicted in Fig. 4) and the average number of tokens (continuous variable). Whatever the considered measure, the results are similar: the individual's share of cash payments decreases with convenient prices. Moreover, we ran another estimation with the share of the value of cash payments for each individual. We observe once again that the estimation results are very close to what we observe when the dependent variable is the share of the number of cash payments.19 Third, our results are also robust to extreme observations. Some individuals in the sample have not indeed realized any cash payments over the 8-day period, while others have paid all their transactions in cash. These extreme values could undermine the quality of the estimations since they could distort the distribution of the variable. We account for this issue by excluding from the regression the people with a share of cash payments equal to 0 (150 individuals) or 100 (342 individuals). The results of the new estimation are reported in Appendix A.2. Once again, the results are fairly stable; convenient prices have still a positive and significant effect on the share of the number of cash payments. Finally, as a final robustness check, we decided to change the empirical strategy. All the previous regressions are tested at the level of the individual to remain in line with standard microeconomic models of consumer payment choices. This strategy leads therefore to collapse information by individual and then to lose information on transactions. To test the validity of the results at the

18 Two categories do not differ significantly from the others, namely “Press/Tobacco/ Gambling” and “Home services”. As reported in Table 3, cash is also widely used in the first category. 19 The results are not reported in the text and are available upon request.

level of the transaction, we also ran a probit regression on each transaction, including individual, good, and establishment characteristics, along with explanatory variables related to convenience and the size of the transaction. The objective of the regression is to check if the probability of paying cash a transaction is positively correlated to its convenience. The estimation results, presented in Appendix A.3, are similar to the previous ones: the probability of paying cash a transaction increases with the convenience of a price and the effect is also statistically significant at the 1% level. This final regression therefore confirms the robustness of our results.

5. Conclusion Previous research have hypothesized a relation between cash usage and convenient prices. This relation is all the more important since convenient prices are related to price rigidity (Knotek, 2008, 2011). However, these empirical research did not directly tackle the supposedly relation between cash usage and convenient prices mainly because of the lack of data. Indeed, to bring evidence of such relation, micro-level data on the use of payment instruments and prices are required. In this respect, scanner data available in most retailers could be exploited but they mainly suffer from the absence of individual characteristics (Klee, 2008). An alternative option is to use surveys and individual payment diaries produced by several central banks around the world (Jonker et al., 2012; Wakamori and Welte, 2012). We use such individual payment diaries to study the relation between cash usage and prices. In this study, we exclusively focus on single item purchases. Exploiting a unique dataset in 2011 on cash payments and prices by a representative sample of French consumers, estimation results bring direct evidence that the share of cash payments increases with convenient prices. We find that these results are robust to a change of the measure of the share of cash payments (in value) and to different measures of price convenience. In the end, this paper confirms that price rigidity can be in part explained by the use of cash to pay convenient prices. Based on our results, we suggest three main directions for future research. One is to propose a macroeconomic model that explicitly provides a micro-foundation for price rigidity in connection with convenient prices. Indeed, to the exception of Blinder et al. (1998) that mention convenient prices as a potential source of price rigidity, there is no macroeconomic model that studies such a relationship. This model would be all the more important as Kim and Lee (2012) have shown a distortionary effect of inflation on relative price between cash trade and debit card trade. The other is related to the impact of technological innovations on price rigidity (debit and credit cards, contactless technologies, etc.). As outlined in several empirical studies, the market share of the debit card for instance increases to the detriment of that of cash as the debit card becomes less costly for consumers and merchants (Bolt et al., 2010; Borzekowski et al., 2008). The decline of cash in the next years could then reduce the occurrence of convenient prices in economies which should affect in turn price rigidity. Finally, from a strict technical standpoint, Knotek (2008, 2011) only focuses on firms and finds evidence that they set convenient prices for items that are typically purchased with cash. In the same vain, our paper sheds light on the only consumer payment choices and shows that convenient prices are more often paid in cash at pointof-sale. A further research could be done to study simultaneous payment decisions of both sides, consumers and merchants. However, as far as we know, there are no data sets or surveys that incorporate at the same time information on consumer and merchant payment decisions.

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Appendix A A.1. Statistical description of the variables Table 3 Key summary of the variables. Variable

Mean

Std. Dev.

Min

Max

Share of cash payments (number) Share of cash payments (value) Average number of tokens per transaction Average value of a cash payment % of cash payments made… Type of product Food and beverages Personal equipment/services Press/tobacco/gambling Home furnishing Medical/health Transport Leisure/culture Restaurant/cafe/hotel Other Type of establishment Small retail store Department store Drugstore/cosmetics Hypermarket Home services Administration Other Sex (1 if male) Age Monthly income Less than 1500 € Between 1501 and 3000 € More than 3000 € Do not know or refuse Education No diploma Before university University Living area: Small cities Large cities Paris and agglomeration

64.74 48.38 2.44 24.96

36.73 43.80 0.68 44.62

0 0 1 0.3

100 100 5 799

41.40 9.19 11.32 4.78 8.27 9.70 4.55 5.42 4.64

36.30 20.08 22.25 14.34 20.60 21.99 14.74 16.54 14.98

0 0 0 0 0 0 0 0 0

100 100 100 100 100 100 100 100 100

61.33 8.56 6.57 11.13 0.76 2.16 9.03 0.45 46.96

36.08 19.67 17.83 23.47 5.98 9.73 21.38 0.50 17.00

0 0 0 0 0 0 0 0 18

100 100 100 100 100 100 100 1 91

0.59 0.29 0.03 0.09

0.49 0.46 0.16 0.28

0 0 0 0

1 1 1 1

0.11 0.66 0.23

0.31 0.47 0.42

0 0 0

1 1 1

0.42 0.43 0.15

0.49 0.50 0.36

0 0 0

1 1 1

A.2. Estimation of the share of cash payments excluding extreme values This appendix presents new estimations when extreme values are excluded. Extreme values refer to individual's shares of cash payments that amount to 0 or 100. In the first model, we estimate the coefficients using a standard OLS. In the second model, we use a maximum likelihood (ML) of a two-parameter beta distribution. Table 4 Estimation of the share of cash payments excluding extreme values. Model

Average value of a transaction Average number of tokens per transaction % of cash payments… Food and beverages Personal equipment/services Press/tobacco/gambling Home furnishing Medical/health Transport Leisure/culture Restaurant/cafe/hotel Other Small retail stores Department store Drugstore/cosmetics Hypermarket

OLS

ML of beta distribution

Coef.

(se)

Coef.

(se)

−0.043 −5.41⁎⁎⁎

(0.027) (1.55)

−0.0019 −0.24⁎⁎⁎

(0.0012) (0.065)

Reference −0.18⁎⁎⁎ 0.067 −0.20⁎⁎⁎ −0.20⁎⁎⁎ −0.16⁎⁎⁎ −0.16⁎⁎ −0.20⁎⁎⁎ −0.18⁎⁎⁎

(0.055) (0.049) (0.071) (0.070) (0.056) (0.071) (0.060) (0.069)

−0.0074⁎⁎⁎ 0.0032 −0.0082⁎⁎⁎ −0.0085⁎⁎⁎ −0.0066⁎⁎⁎ −0.0062⁎⁎ −0.0078⁎⁎⁎ −0.0075⁎⁎⁎

(0.0023) (0.0020) (0.0029) (0.0030) (0.0023) (0.0029) (0.0025) (0.0028)

Reference −0.29⁎⁎⁎ −0.24⁎⁎⁎ −0.23⁎⁎⁎

(0.054) (0.071) (0.050)

−0.012⁎⁎⁎ −0.0095⁎⁎⁎ −0.0095⁎⁎⁎

(0.0023) (0.0030) (0.0021) (continued on next page)

336

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Table (continued) 4 (continued) Model

OLS

ML of beta distribution

Coef. Small retail stores Home services Administration Other Sex (1 if male) Age Monthly income: b1500 € Monthly income: N1501 € and b3000 € Monthly income: N3001 € Monthly income: do not know/refuse Education: no diploma Education: before university Education: university Area: small cities Area: large city Area: Paris and agglomeration Constant ln ϕ ϕ Observations Adj. R2

Reference −0.37⁎⁎ 0.024 −0.17⁎⁎⁎ 3.38⁎⁎ 0.071 Reference −1.00 −5.93 6.28⁎⁎ Reference −1.48 −5.39 Reference −0.14 −1.33 88.7⁎⁎⁎ – – 417 0.39

(se)

Coef.

(se)

(0.15) (0.094) (0.056) (1.58) (0.050)

−0.015⁎⁎⁎ 0.0014 −0.0070⁎⁎⁎ 0.14⁎⁎ 0.0033

(0.0059) (0.0039) (0.0023) (0.066) (0.0021)

(1.79) (4.87) (2.73)

−0.035 −0.27 0.27⁎⁎

(0.074) (0.20) (0.12)

(2.84) (3.30)

−0.089 −0.26⁎

(0.12) (0.14)

(1.66) (2.45) (5.76)

−0.011 −0.068 1.66⁎⁎⁎ 2.29⁎⁎⁎

(0.069) (0.10) (0.25) (0.066) (0.658)

9.91 –

Standard errors in parentheses. ⁎ p b 0.10. ⁎⁎ p b 0.05. ⁎⁎⁎ p b 0.01.

A.3. Estimation of the probability of cash payment This appendix presents the results of the estimations of the probability of cash payment. Table 5 Probit estimations of the probability of cash payment. Model

Log of the value of transaction Average number of tokens per transaction Type of good (food and beverages as reference) Personal equipment/services Press/tobacco/gambling Home furnishing Medical/health Transport Leisure/culture Restaurant/cafe/hotel Other Type of merchant (small retail stores as reference) Department stores Drugstore/cosmetics Hypermarket Home services Administration Other Sex (1 if male) Age Monthly income (less than 1500 € as reference) N 1501 € and b3000 € N 3001 € Do not know/refuse Education (no diploma as reference) Before university University Area (small cities as reference) Large city Paris and agglomeration Constant Observations Pseudo R2 Standard errors in parentheses. ⁎ p b 0.10. ⁎⁎ p b 0.05. ⁎⁎⁎ p b 0.01.

(1)

(2)

(3)

Model A

Model B

Model C

−0.71⁎⁎⁎ −0.12⁎⁎⁎

(0.030) (0.032)

– −0.40⁎⁎⁎

– (0.028)

−0.74⁎⁎⁎ –

(0.029) –

−0.21⁎ 0.40⁎⁎⁎ −0.21 −0.56⁎⁎⁎ −0.38⁎⁎⁎

(0.11) (0.12) (0.13) (0.13) (0.12) (0.14) (0.12) (0.15)

−1.24⁎⁎⁎ 0.12 −1.00⁎⁎⁎ −1.38⁎⁎⁎ −1.48⁎⁎⁎ −0.92⁎⁎⁎ −1.12⁎⁎⁎ −0.95⁎⁎⁎

(0.093) (0.10) (0.12) (0.12) (0.10) (0.13) (0.10) (0.12)

−0.18⁎ 0.39⁎⁎⁎ −0.21 −0.56⁎⁎⁎ −0.30⁎⁎⁎

(0.11) (0.12) (0.13) (0.13) (0.11) (0.14) (0.12) (0.15)

(0.11) (0.13) (0.097) (0.28) (0.19) (0.11) (0.062) (0.0019)

−1.01⁎⁎⁎ −0.75⁎⁎⁎ −0.87⁎⁎⁎ −0.86⁎⁎⁎

(0.10) (0.12) (0.086) (0.26) (0.17) (0.100) (0.054) (0.0017)

−0.15 −0.60⁎⁎⁎ −0.17 −0.77⁎⁎⁎ −0.44⁎⁎⁎ −0.43⁎⁎⁎ −0.076 −0.097 −0.27⁎⁎ 0.13⁎⁎ 0.00019 −0.16⁎⁎ −0.49⁎⁎⁎

−0.23 −0.58⁎⁎⁎ 0.19⁎⁎⁎ 0.00063 −0.22⁎⁎⁎ −0.54⁎⁎⁎

0.095

(0.073) (0.18) (0.11)

−0.24⁎⁎ −0.52⁎⁎⁎ 0.091 0.069 2.95⁎⁎⁎ 4024 0.54

−0.10 −0.59⁎⁎⁎ −0.14 −0.79⁎⁎⁎ −0.44⁎⁎⁎ −0.44⁎⁎⁎ −0.020 −0.13 −0.24⁎⁎ 0.13⁎⁎ 0.000038

(0.11) (0.13) (0.097) (0.28) (0.19) (0.11) (0.062) (0.0019)

−0.17⁎⁎ −0.49⁎⁎⁎

0.022

(0.062) (0.15) (0.095)

0.095

(0.072) (0.18) (0.11)

(0.10) (0.12)

−0.22⁎⁎ −0.48⁎⁎⁎

(0.092) (0.11)

−0.24⁎⁎ −0.52⁎⁎⁎

(0.10) (0.12)

(0.066) (0.093) (0.18)

0.11⁎⁎ −0.0059 2.62⁎⁎⁎

(0.057) (0.080) (0.16)

0.088 0.088 2.69⁎⁎⁎

(0.065) (0.093) (0.17)

4024 0.39

4024 0.53

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References Alvarez, F., Lippi, F., 2009. Financial innovation and the transactions demand for cash. Econometrica 77 (2), 363–402. Aoki, K., 2001. Optimal monetary policy responses to relative-price changes. J. Monet. Econ. 48 (1), 55–80. Blinder, A.S., Elie, R., Canetti, D., Lebow, D., Rudd, J., 1998. Asking About Prices: a New Approach to Understanding Price Stickiness. Russell Sage Foundation, New York, NY. Boeschoten, W.C., Fase, M.M.G., 1989. The way we pay with money. J. Bus. Econ. Stat. 7, 319–326. Bolt, W., Jonker, N., van Renselaar, C., 2010. Incentives at the counter: an empirical analysis of surcharging card payments and payment behaviour in the Netherlands. J. Bank. Financ. 34, 1738–1744. Borzekowski, R., Kiser, E.K., Ahmed, S., 2008. Consumers' use of debit cards: patterns, preferences, and price response. J. Money Credit Bank. 40 (1), 149–172. Bouhdaoui, Y., Bounie, D., 2012. Modelling the share of cash payments in the economy: an application to France. Int. J. Cent. Bank. 8 (4), 175–195. Caianiello, E.R., Scarpetta, G., Simoncelli, G., 1982. A systemic study of monetary systems. Int. J. Gen. Syst. 8, 81–92. Carvalho, C., 2006. Heterogeneity in price stickiness and the real effects of monetary shocks. Berkeley Electron. Press Front. Macroecon. 2 (1), 1–56. Cramer, J.S., 1983. Currency by denomination. Econ. Lett. 12, 299–303. Franses, P.H., Kippers, J., 2007. An empirical analysis of euro cash payments. Eur. Econ. Rev. 51, 1985–1997. Jonker, N., Kosse, A., Hernández, L., 2012. Cash usage in the Netherlands: how much, where, when, who and whenever one wants? DNB Occas. Stud. 10 (2). Kashyap, A.K., 1995. Sticky prices: new evidence from retail catalogs. Q. J. Econ. 110 (1), 245–274. Kim, Y.S., Lee, M., 2012. Price rigidity and means of payment. Seoul J. Econ. 25 (1), 111–135.

337

Klee, E., 2008. How people pay: evidence from grocery store data. J. Monet. Econ. 55, 526–541. Knotek II, E.S., 2008. Convenient prices, currency, and nominal rigidity: theory with evidence from newspaper prices. J. Monet. Econ. 55 (7), 1303–1316. Knotek II, E.S., 2011. Convenient prices and price rigidity: cross-sectional evidence. Rev. Econ. Stat. 93 (3), 1076–1086. Lee, M., 2009. Carrying cost of money and real effects of denomination structure. J. Macroecon. 32, 326–337. Levy, D., Lee, D., Chen, H., Kauffman, R.J., Bergen, M., 2011. Price points and price rigidity. Rev. Econ. Stat. 93 (4), 1417–1431. Mooslechner, P., Stix, H., Wagner, K., 2006. How are payments made in Austria. Results of a survey on the structure of Austrian households' use of payment means in the context of monetary policy analysis. Monet. Policy Econ. 2, 111–134. Nakamura, E., Steinsson, J., 2008. Five facts about prices: a reevaluation of menu cost models. Q. J. Econ. 123 (4), 1415–1464. Papke, L.E., Wooldridge, J.M., 1996. Econometric methods for fractional response variables with an application to 401(K) plan participation rates. J. Appl. Econ. 11, 619–632. Stiving, M., Winner, R.S., 1997. An empirical analysis of price endings with scanner data. J. Consum. Res. 24, 57–67. Van Hove, L., Heyndels, B., 1996. On the optimal spacing of currency denominations. Eur. J. Oper. Res. 90, 547–552. Von Kalckreuth, U., Schmidt, T., Stix, H., 2009. Choosing and using payment instruments: evidence from German microdata. Working Paper Series 1144. European Central Bank. Wakamori, N., Welte, A., 2012. Why do shoppers use cash? evidence from shopping diary data. Working Paper 2012-24. Bank of Canada. Whitesell, W., 1989. The demand for currency versus debitable accounts. J. Money Credit Bank. 21 (2), 246–251.