Cash versus Card: Payment Discontinuities and the Burden of Holding Coins Heng Chen∗
Kim Huynh∗ ∗ Bank
Oz Shy
of Canada
Bank of Canada Seminar Ottawa, September 18, 2017 The views expressed in this presentation are those of the presenters and do not necessarily represent the views of the affiliated institutions.
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Motivation and goals of this research Cash is the preferred method of payment for small value transactions (generally less than $25). We provide new theoretical and empirical insights into payment choice by decomposing cash-use into banknotes and coins. Previous research analyzed how factors, such as transaction value, cost, and demographic attributes, affect consumer payment choice between non-cash instruments and cash (banknotes and coins combined). We use the 2013 Bank of Canada Method-of-Payments Survey to identify discontinuities in cash-use at $5 and $10 transaction values. Main policy implication: Structure of currency denomination matters for consumer payment choice!
Introduction
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Our approach: Count the change! For each (tax-inclusive) transaction value v ∈ {$0.05, $0.10, . . . , $24.95, $25.00}, we analyze payment choice by comparing the cost of paying cash and paying with cards as follows: I. compute the amount of change II. and corresponding buyers’ burden of receiving coins (wallet’s weight, size, sorting time). III. Compare with the cost of paying with cards. IV. Identify decision thresholds transaction values. V. Use regression-discontinuity design (RDD) to estimate the effect of receiving coins on the probability of paying with banknotes. Method: We cannot observe the cost of paying with cards, but it is likely to be smooth w.r.t. transaction value. Hence, we identify the decision thresholds by examining the transaction values where there are jumps in the amount of coins received as change. Introduction
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Introduction
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Ratio of cash value to total cash and cards value
Red curve is a nonparametric local linear fit. Introduction
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Nonparametric regression-discontinuity plots (rdplot package in R). ●
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Introduction
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Digression: The importance of transaction value (“Amount”) in payment choice Amount >= 20 < 20
Other 55%
Educ = Grd,S_U,Tch,Unv Elm,Hgh
Other 10%
Amount >= 35 < 35
Ccard
Other
24%
12%
Left: Classification tree. Right: Random Forests’ variable importance chart. Note: “Amount” is always significant in any discrete choice regression. Introduction
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Structure of currency denomination Our research shows that the structure of denomination has significant effects on consumer payment choice.
Canada (CAN) Coins Notes 0.05 5 0.10 10 0.25 20 0.50 50 1.00 100 2.00
Europe (Euro) Coins Notes 0.01 5 0.02 10 0.05 20 0.10 50 0.20 100 0.50 200 1.00 500 2.00
U.S. (USD) Coins Notes 0.01 1 0.05 2 0.10 5 0.25 10 0.50 20 1.00 50 100
Only the U.S. circulates $1 notes Terminology for Canadian coins: Large coins : $1 and $2 Small coins : 5c/, 10c/, 25c/, and 50c/.
Introduction
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Transaction v = $0.80 =⇒ 2 coins change $0.10 + $0.10 Transaction v = $0.35 =⇒ 3 coins change $0.05 + $0.10 + $0.50 Transaction v = $0.05 =⇒ 4 coins change $0.05 + $0.10 + $0.10 + $0.50 Theory
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Measuring burden of large coins ($1 and $2)
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Suppose the consumer pays with a $5 paper note. Then, Transaction v = $4.05 =⇒ 0 large coins change (only small coins) Transaction v = $2.05 =⇒ 1 large coin change $2 (+ small coins) Transaction v = $0.05 =⇒ 2 large coins change $2 + $2 (+ small coins) Theory
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Measuring burden of coins: Buyers’ cost functions δS (δL ) denote dis-utility from receiving one small (large) coin. Need not specify whether δS < δL or δS ≥ δL . i ∈ Z+ = {0, 1, 2, . . .} is a non-negative integer representing the dollar component of each transaction value, such as $0, $1, and $2 . cS (v ) = 0 δS 2δS 3δS 4δS
Theory
if if if if if
v v v v v
= i × $1.00 ∈ {$0.50, $0.75, $0.90, $0.95} + i × $1.00 ∈ {$0.25, $0.40, $0.45, $0.65, $0.70, $0.80, $0.85} + i × $1.00 ∈ {$0.15, $0.20, $0.30, $0.35, $0.55, $0.60} + i × $1.00 ∈ {$0.05, $0.10} + i × $1.00. if $4.05 ≤ v ≤ $5.00 + i × $5.00 0 cL (v ) = δL if $2.05 ≤ v ≤ $4.00 + i × $5.00 2δL if $0.05 ≤ v ≤ $2.00 + i × $5.00. 11/22
Consumers’ choice of a payment instrument: Identification of decision thresholds We look for transaction values (discontinuities) v for which ( H (cash) if v ∈ [b v − , vb] def S(v ) = D (card) if v ∈ (b v , vb + ]. where is a small number. Therefore, consumers minimizes cost if ( H (cash) if cS (v − ) + cL (v − ) ≤ cD (v − ) min C (v ) = H,D D (card) if cS (v + ) + cL (v + ) > cD (v + ), cD (v ) (unknown function) is the consumer’s cost of paying with a card for transaction value v , which is a smooth function with no jumps. cS (·) + cL (·) (cost of receiving coins) has jumps. =⇒ It is sufficient to focus on the discontinuities of this function (see graph next slide). Theory
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We analyze the “major” discontinuities of cS (v ) + cL (v ): $10, $15, $20, $25. Theory
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Regression-discontinuity design (RDD) Angrist and Lavy (1999) test classroom performance given a 40-student limit on class size. Beyond that, schools were forced to open an add’l classroom (smaller size). Similarly, we test: Y = S(B, v , u), where B = I {v > vb} is the “coin burden” binary treatment variable. Y = 1 (pay banknote), Y = 0 (card), I = (indicator function) u = unobserved covariate vector, vb ∈ {5, 10, 15, 20, 25}. Since cD (v ) is continuous, only the discontinuities of cS (v ) + cL (v ) matter. Hence, lim E (Y |v ) − lim E (Y |v ) 6= 0. v ↓b v
v ↑b v
The figure on the previous slide reveals negative jumps around the thresholds. Regression-discontinuity design
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Sharp RDD estimates We obtain the linear auxiliary regression: Y = g (v ) + δB + ,
where
g (v ) is an unknown nonparametric continuous function and E (|v ) = 0, and δ = lim E (Y |v ) − lim E (Y |v ). v ↓b v
v ↑b v
However, because the 1c/coin was eliminated, the limits “just below” and “just above” cannot be compared. Hence, we restrict g (v ) to be a parametric polynomial so that Y = β0 + β1 v + β2 v 2 +δB + . {z } | g (v )
Regression-discontinuity design
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Two estimation specifications Y = β0 + β1 v + β2 v 2 + δ5 I {v > 5} + αX + ε, Y = β0 + β1 v + β2 v 2 + δ10 I {v > 10} + αX + ε, Y = β0 + β1 v + β2 v 2 + δ15 I {v > 15} + αX + ε, Y = β0 + β1 v + β2 v 2 + δ20 I {v > 20} + αX + ε, Y = β0 + β1 v + β2 v 2 + δ25 I {v > 25} + αX + ε;
Y = β0 + β1 v + β2 v 2 + δ5 I {v > 5} + δ10 I {v > 10} + δ15 I {v > 15} + δ20 I {v > 20} + δ25 I {v > 25} + αX + ε where X is a vector of other observed covariates, such as, age, gender and cash holding. Remark: Note the discontinuity from the “right” “>” (and not “≥”). Estimation
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The Bank of Canada Method of Payments Survey
The MOP includes a three-day diary. 3,663 survey respondents and 2,596 diary respondents. Survey was in the field from Mid-October to early-December 2013. For 3 days, respondents (consumers) recorded: 1. 2. 3. 4.
Dollar amount of each purchase. Payment instrument (cash, card, check, etc.). Merchant type (fast food, transportation, grocery store, etc.). ATM withdrawals, and more...
The 2013 diary recorded 13,196 transactions and 1,078 withdrawals.
Data
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Data requirements The obtained sample was restricted as follows: 1. Transactions that can be paid with cash and cards. 2. Individuals with accurate cash flow information ±5CAN. 3. Transactions in which the payer has not made any change in cash flow (such as ATM withdrawals or deposits). 4. Only the first transaction of the person’s diary (so we know the precise initial stock of notes and coins). 5. Only transactions that individuals did not initially hold any coin (to be able to measure the cost of receiving change).1 We are left with 518 transaction records for the RDD.
1 Data
Because we do not model the dynamic optimization of minimizing coin accumulation. 18/22
Table 2: RDD Estimates of Cash Denomination Thresholds Age over 55
Purchase amount
$5 0.162∗∗∗ (0.053)
$10 0.156∗∗∗ (0.053)
−0.011∗∗∗ (0.002)
−0.012∗∗∗ (0.002)
ALL 0.155∗∗∗ (0.053) −0.007∗∗ (0.004)
Purchase amount2
0.0001∗∗∗ (0.00001)
0.0001∗∗∗ (0.00001)
0.00005∗∗∗ (0.00002)
Cash holding before transaction
0.001∗∗∗ (0.0002)
0.001∗∗∗ (0.0002)
0.001∗∗∗ (0.0002)
Threshold at $5
−0.192∗∗∗ (0.054)
−0.194∗∗∗ (0.061) −0.119∗ (0.065)
Threshold at $10
−0.123 (0.087)
Threshold at $15
0.184∗ (0.102)
Threshold at $20
−0.148 (0.121) 0.181
Adjusted R2 Estimation
0.178
0.163
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Estimation results (conclusions)
1. Transaction values $5 and $10 exhibit the largest and significant reduction in the probability of paying cash with 2. marginal effects −0.192 (≈ 19%) and −0.119 (≈ 12%). 3. The ATE δ declines with v (v = $15 may be an exception). δ5 < δ10 < δ20 < δ25 < 0. This may be a consequence of the decline in D (v ) < 0. the cost of paying with cards w.r.t. transaction value: ∆c∆v 4. Single regressions (OLS and Logit) with all the discontinuities generate similar results (larger estimates in absolute value).
Estimation
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But, what about other transaction values?
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Running 25 regressions at $1, $2, . . . , $25 discontinuity thresholds reveals: low probabilities of switching from cash to cards (“local” peaks) at: ($5 − ), ($10 − ), ($15 − ), and ($20 − ) transaction values. Estimation
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Conclusion and policy implications We identify discontinuities (decline) in cash-use at $5 and $10 transaction values. Policy markers must take into account the burden of change when designing the structure of currency denomination. And also the burden on merchants (future research):
Picture on the right: A laundromat owner who got stuck with coins because banks refuse to accept them.
The theory and the RDD methodology are general and could be easily applied to other countries. Try it! Thanks for listening. Conclusion
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