Customers and Retail Growth
Liran Einav, Stanford and NBERPete Klenow, Stanford and NBER
Jonathan Levin, Stanford and NBERRaviv Murciano-Goroff, Boston University
April 2021
University of Houston Macro Seminar
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What we do
1 Quantify the role of customer growth in the growth of retail merchants and storesusing Visa, Inc. data in the U.S. from 2016–2019
2 Trace aggregate retail sales changes to merchants with rapidly-growing vs.rapidly-shrinking numbers of customers
3 Model firm growth through innovation and customer acquisition to see how thecustomer margin might affect aggregate growth
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Some related papers
ModelsI Arkolakis (2010, 2016)I Perla (2019)
EvidenceI Foster, Haltiwanger and Syverson (2008, 2016)I Hottman, Redding and Weinstein (2016)I Fitzgerald and Priolo (2018), Fitzgerald, Haller and Yedid-Levi (2019)I Baker, Baught and Sammon (2020)
BothI Gourio and Rudanko (2014)I Eslava, Tybout, Jinkins, Krizan and Eaton (2015)I Bornstein (2018)I Bernard, Dhyne, Magerman, Manova and Moxnes (2019)I Afrouzi, Drenik and Kim (2020)
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Visa data
Transaction amount and day
Unique card identifiers (credit and debit)
Unique merchant identifiers (firms with one or more stores)
Store industry (3-digit NAICS)
Store location (address)
January 2016 through December 2019
No detail on items bought or prices paid
Cannot tie multiple card numbers to single households
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Visa data confidentiality
All results have been reviewed to ensure that no confidential information about Visamerchants or cardholders is disclosed.
Cards are anonymized, and we report no data on individual cards. Cardholder informationis based solely on the card’s transactions.
We report no data on specific merchants or recent months (nothing from 2020 onward).
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Visa summary statistics
U.S. annual averages from 2007 through 2019
430 million cards
32 billion transactions
24% of all consumption
60% credit, 40% debit
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Visa samples
All NAICS
Retail (+ restaurant) NAICS
Offline retail (card present transactions) – our baseline sample
“Named” merchants back to 2007 (instead of just 2016–2019)
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Decomposing sales
Sales ≡ Cards · TransactionsCards
· SalesTransactions
For merchants, we can further decompose cards:
Cards ≡ Stores · CardsStores
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Sales regressions
We take logs and regress each RHS variable on the LHS (log of Sales).
Coefficients decompose sales:
Across merchants in 2019 (with NAICS fixed effects)
Across stores within merchants in 2019 (with merchant fixed effects)
Over time within stores/merchants 2016–2019 (store/merchant and year fixed effects)
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Decomposing sales across merchants in 2019
Each entry is from a single univariate log-log regression on Sales
Dep. var. → Cards Trans/Cards Sales/Trans # obs.
All NAICS 0.743 0.037 0.221 2.18m
Online 0.673 0.073 0.254 606k
Offline 0.813 0.031 0.159 1.79m
Offline retail 0.812 0.035 0.166 954k
The coefficients in each row add up to 1 by construction.
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Decomposing sales in offline retail
Dependent variable→ Cards Trans/Cards Sales/Trans # obs.
Across merchants in 2019 0.812 0.035 0.166 954k
Within merchants 2016–2019 0.844 0.101 0.055 3.91m
Across stores within merchants 2019 0.843 0.079 0.078 2.02m
Within stores 2016–2019 0.818 0.137 0.045 8.19m
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Decomposing 2019 merchant sales growth, by NAICS
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Decomposing store growth over time (by store age)
Cards Trans/Cards Sales/Cards
Age 1-2 years 0.736 0.080 0.184(0.001) (
Ventile Figures
For each variable, subtract any fixed effects in logs
Sort observations (merchant-years or store-years) into 20 groups based on their sales
For each variable, compute its average within each ventile
Exponentiate the average in each ventile, and normalize the lowest ventile to 1
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Across merchants in 2019
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Within merchants over time, 2016–2019
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Stores vs. cards per store across merchants in 2019
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Stores vs. cards per store over time within merchants, 2016–2019
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Across stores within merchants in 2019
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Within stores over time, 2016–2019
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Growth in spending per returning customer, merchants 2016–2019
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Merchant contributions to aggregate sales changes, 2016–2019
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Cumulative merchant contributions, 2016–2019
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Merchant contributions to sales changes over 2016–2019, by NAICS
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The importance of customers in the tails
A merchant’s sales changes can be decomposed as:
∆Sit ≡ ∆Nit · S/N it + ∆(S/N)it ·N it
whereN it ≡
Nit +Ni,t−12
and
S/N it ≡Sit/Nit + Si,t−1/Ni,t−1
2
Use this to gauge role of customers for sales growth of top and bottom firms
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Customers vs. sales/customer and firm sales changes, 2016–2019
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Visa patterns and a model
1 The number of customers drive Visa merchant growth
2 Rapid-growers and shrinkers dominate aggregate Visa sales changes
Motivates a model with these features:
1 Heterogeneous firm innovation
2 The number of customers responds strongly to innovation
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Consumer preferences
A unit mass of customers have the following preferences over consumption:
U =
∞∑t=0
βtC
1−1/σt
1− 1/σ
Consumption is an aggregate of varieties:
Ct =
(∫ 10nit (qitcit)
θ−1θ di
) θθ−1
.
Note the fixed unit mass of varieties i ∈ [0, 1], with variety i having quality qit.nit ∈ [0, 1] is the probability that a consumer has the option to purchase variety i.cit is the quantity of variety i purchased by each consumer with access to i.
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Customer demand and the aggregate price index
Per customer demand conditional on access to variety i:
cit =
(pitPt
)−θqθ−1it Ct
Resulting ideal price index
Pt ≡(∫ 1
0nit
(pitqit
)1−θdi
) 11−θ
.
Total demand facing firm j, summed across its customers:
yit = nit · cit
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Production, customer acquisition, and static profit maximization
Each firm uses production labor lit to produce its single variety:
yit = lit
It uses marketing labor mit to reach fraction nit of customers:
nit =
(γ
φ· mitMt
)1/γwhere γ > 1 and Mt ≡
∫ 10mitdi.
Normalizing the nominal wage to 1, the firm’s static profit maximization problem is:
maxpit,mit
(pit − 1) yit −mit
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Firm pricing and relative quality
Through monopolistic competition, firms choose pricing:
pit =θ
θ − 1 ≡ µ
Aggregate quality and relative quality:
Qt ≡(∫ 1
0q
Γ(θ−1)it di
) 1Γ(θ−1)
where zit ≡qitQt
and Γ ≡ γγ − 1
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Customers and variable profits
nit = min
(γzΓ(θ−1)
φ
) 1γ
, 1
πit =z
Γ(θ−1)it
Γ(θ − 1) · Lt
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Innovation
A firm with absolute quality qit and relative quality zit that hires research labor sit sees itsquality follow a controlled binomial process with probability xit ∈ [0, 1]:
qit+1 =
{qite
∆ w/ prob. xitqit w/ prob. 1− xit
and sit = λ log(
1
1− xit
)zζit
∆, λ and ζ are all strictly positive
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Firm value and growth
A firm’s value function is given by:
Vt (z) = πt (z) + maxx∈[0,1]
{R−1t
[xVt+1
(ze∆−gt
)+ (1− x)Vt+1
(ze−gt
)]− st (z, x)
}
The growth rate of this economy is:
1 + gt =
(∫x(z)zΓ(θ−1)
(e∆Γ(θ−1) − 1
)dF (z) + 1
) 1Γ(θ−1)
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Recap on firm decisions
In each period, a firm makes the following ordered decisions:
1. Hire marketing labor m(z) to access customers n(z)
2. Hire production labor l(z) to sell to their customers
3. Hire research labor to achieve a probability of research success x(z) ∈ [0, 1]
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Labor market clearing
Lt =
∫lt (z) dFt (z)
Mt =
∫mt (z) dFt (z)
St =
∫st (z) dFt (z)
Lt +Mt + St = 1
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Aggregates
Lt =γ (θ − 1) (1− St)γ (θ − 1) + 1
Mt =1− St
γ (θ − 1) + 1
Ct = (γ/φ)1
γ(θ−1) · Lt ·Qt
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Parameter values
Symbol Parameter Value Target
σ IES 0.5 Hall (2009)
θ CES between varieties 3 Aghion et al. (2019)
β Discount factor 0.992 Farhi and Gourio (2018)
φ Scale of marketing costs 3.57 ·1037 Largest firms have n = 0.5γ Markeing cost elasticity 1.25 Visa sales decomposition
∆ Quality step size 0.06 Twice average growth
λ Linear research cost 0.094 2.9% BLS growth rate
ζ Convex research cost 10.04 Top 1% contribution in Visa
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Intensive and extensive margin elasticities
The elasticity of sales with respect to quality is the sum of the elasticity of customers andthe elasticity of spending per customer with respect to quality:
ξy,q = ξn,q + ξc,q =θ − 1γ − 1 + θ − 1
With our calibration (γ = 1.25 and θ = 3), the customer share of the sales elasticity is80%, which matches our finding in the Visa data.
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Steady state values of endogenous variables
Symbol Variable Baseline No customers
g Growth rate 2.90% 3.22%
r Interest rate 6.70% 7.38%
L Production labor 67.9% 93.3%
M Marketing labor 27.2% 0.0%
S Research labor 4.9% 6.7%
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Törnqvist growth decomposition
Baseline No customers
True growth rate 2.90% 3.22%
Approximated growth rate 2.95% 3.26%
First order term 2.49% 3.17%
Second order term 0.46% 0.09%
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Customers and firm quality
1000 2000 3000 4000 5000z
0.0
0.2
0.4
0.6
0.8
1.0
n
Baseline
No customers
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Customers and firm value
−1.0 −0.5 0.0 0.5 1.0log(z)
−10
−5
0
5
10
log(V)
Baseline
No customers
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Customers and firm innovation
0.0 0.5 1.0 1.5 2.0z
0.0
0.2
0.4
0.6
0.8
1.0
x
Baseline
No customers
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The distribution of sales
1 2 3 4z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
f (y)
Baseline
No customers
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Firm contributions to aggregate sales changes
B1 B5 B10 B25 T25 T10 T5 T1Firms grouped by sales changes
0
20
40
60
80
100
%Baseline
No customers
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Conclusion
We looked at Visa debit and credit card data on transactions at all offline retailmerchants from 2016–2019
We documented a dominant role for the customer extensive margin in the dispersionof sales and sales growth across merchants
In a simple growth model, the customer margin stimulates innovation and marketingby large firms but actually reduces overall innovation and growth
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