Unequal Expenditure Switching:Evidence from the 2015 Swiss Franc Appreciation

By Raphael Auer, Ariel Burstein, Sarah Lein, Jonathan Vogel

November, 2020

Questions

How do consumers adjust expenditures and how does welfare respond tochanges in foreign prices?

Margins of adjustment:

I Imports vs. domestic goods

I Cross-border (CB) shopping vs. domestic shopping

How do these responses vary across households...

I ... with different incomes?

I ... at different distances to CB shopping?

Focus on Switzerland:1 Data availability

2 Characteristics lending itself to important role of CB shopping

3 January 2015 Swiss Franc appreciation

January 2015 Swiss Franc Appreciation

11.0

51.1

1.1

51.2

1.2

5

EU

R/C

HF

1/1/2013 1/1/2014 1/1/2015 1/1/2016 1/1/2017

date

January 2015 Swiss Franc Appreciation

Sept. 6, 2011: After sharp appreciation of the Swiss franc (CHF), SwissNational Bank (SNB) introduced a min. exchange rate of 1.20 CHF per EUR

Late 2014, early 2015: Foreign developments (e.g., anticipation of large QEprogram in the euro area) raised perceived cost of sustaining CHF policy

Jan. 15, 2015: SNB unexpectedly abandons minimum exchange rateI ⇒ Large and sudden appreciation of the CHF

Subsequent appreciation episode is unique in a number of ways

1 Policy change triggered by foreign developments

2 Followed a period of exchange rate stability

3 Exchange rate movement was large in magnitude

4 Appreciation occurred against the backdrop of a stable Swiss economy

Heterogeneous price implicationsAverage log price by month for imports, domestic goods, and cross-border purchases

weighted by total expenditures in 2014

Increases in import and CB expenditure shares accompany these price changes

Heterogeneous expenditure-side effects

Identify heterogeneous effects of price shock across agents arising from

initial exposure (initial expenditure shares on imports, CB shopping)

responsiveness (elasticities of substitution btw import, domestic, CB)

associated with differences in

income (e.g. non-homotheticity)

distance to the border (e.g. different costs of CB shopping)

Using detailed Swiss non-durable consumption data

Heterogeneity in initial exposure in 2014

CB expenditure share M expenditure shareProximity to the border + 0Income 0 0

Heterogeneity in responsiveness 2014-2015

CB expenditure share M expenditure shareProximity to the border 0 0Income 0 –

Implications for welfare (and employment)

Leveraging the 2015 appreciation

1 Estimate differences in import elasticities by income

2 Calibrate level of import elasticity and CB elasticity

Construct equivalent variation by income, distance to CB shopping in response toobserved (CHF appreciation and 2020 border closure), counterfactual foreign shocks

1 Income: Low income households substitute more btw imports and domestic goods ⇒they benefit more (or lose less) from large changes in import prices

2 Distance to the border: Those near CB shopping have higher CB shares ⇒ theybenefit more (or lose more) from changes in foreign prices

For example, welfare impact of 20%↑ in cost of imports and CB shopping

Far from CB shopping Near CB shoppingHigh income −5.2 −6.5Low income −4.1 −5.5

Spatial heterogeneity in CB shopping also has implications for employmentresponses to foreign price shocks

I Retail employment 2015/14 falls in 4-digit zip codes relatively closer to CB shopping

Relation to literature: Heterogeneity across income

Differential price effect across income groups of international shocks

Previous research: do not observe trade shares by income, so fill gaps in data byI structural model to infer shares from aggregate trade flows (Fajgelbaum-Khandelwal, 2016)

I common trade shares and elasticities w/in “sector,” diffs in expenditure across (Cravinoand Levchenko 17; Jaravel and Sager, 19; Borusyak and Jaravel, 18; Caroll and Hur, 19; Hottman and Monarch, 20)

I do not estimate elasticities, measure price indices by group using S-V weights —assume no demand shocks of any form over time (Bai and Stumpner, 2019)

Differential price effect across income groups of domestic shocks Jaravel (2019); Faber and Fally (2020)

Price sensitivity and income in macro models Kaplan-Menzio (2016); Alessandria and Kaboski (2011)

Expenditure switching due to income effects, using product-level data Bems and Di Giovanni (2016)

We observe import share by income, estimate import elasticity by income

Limitation: Data on a small set of goods (supermarkets and drugstores)

Relation to literature: Heterogeneity across space

Cross border shopping and exchange rate movements

Measures of CB shopping: same-day trips across border (Chandra, Head, and Tappata, 2004)

Cross-border shopping and price level differences w/in EU (Beck, Kotz, and Zabelina, 2020)

Retail employment and proximity to the border in response to exchange ratemovements (Campbell and Lapham, 2004; Baggs, Fung, and Lapham, 2015)

Data and models of spatial shopping Agarwal, Jensen, Monte (2020), Miyauchi, Nakajima and Redding (2020), Allen, Fuchs,

Ganapati, Graziano, Madera, Montoriol-Garriga (2020)

Spatial taxes and shopping Agrawal (2017), Baker, Johnson, Kueng (2020), Goolsbee (2000), Liran, Knoepfle, Levin, Sundaresan(2014)

Data: We observe large xrate shock + CB expenditures, trips, transactionsby household, income, region

We study the impact of foreign price shocks on welfare and employmentacross space

Data requirements and sources

Data requirements and sources

Data requirements

Household income (and size) and distance to CB shopping

Household-level panel data on expenditures by product & country of purchase

Product-country-of-purchase-specific panel on prices

For products purchased in Switzerland, data on production location

Data sources

AC Nielsen homescan: Retail prices and (offline) expendituresI Covers a demographically, regionally representative sample of ≈ 3,000

households in Switzerland Jan. 2013 - Dec. 2016, Jan. 2019 - July 2020F 7 income bins, 9 size bins, 76 two-digit zip codes

I Participating households record purchases in supermarkets and drugstores(food, beverages, personal and household items)

I Observation is a transaction:F household ID, barcode (European Article Number, or EAN) of product, quantity,

price (net of good-specific discounts), date of purchase, name of retailer

F whether purchase occurred in Switzerland or abroad (Austria, France, Germany)

Data requirements and sources

Data requirements

Household income (and size) and distance to CB shopping

Household-level panel data on expenditures by product & country of purchase

Product-country-of-purchase-specific panel on prices

For products purchased in Switzerland, data on production location

Data sources

codecheck.info: info on country of production for a subset of goodsI 63% of goods, 72% of exp. in Nielsen in 36 months surrounding appreciation

I import share in expenditures 27% in 2014, similar to total import share inconsumption reported in in SFSO (2014)

Household income and size

At sample entry, household reports binned income (Top) and size (Bottom)

1 Some income and size bins are small

2 Income distribution closely reflects that of countryI Annual wages in 2014 by percentile (Swiss Earnings Structure Survey):

F 20th 29.3K , 50th 52.8K , 80th 75.8K

I Annual disposable income in 2014 by percentile (Federal Statistical Office):F 25th 35.8K , 50th 49.2K , 75th 67.5K , 90th 91.2K

3 Income is predictive of expenditures income vs expenditure

Expenditure shares on products in our dataFrom the Federal Statistical Office, 2015-17

Expenditures on product categories in our data account for ≈ 20% of aggregateexpenditure

I However, import share on product categories in our data similar to overall importshare (on goods and services)

Share of total expenditure on product categories in our data and goods morebroadly decreases with household income

I Another source of heterogeneous exposure (from which we abstract)I see e.g. Cravino and Levchenko 17; Borusyak and Jaravel, 18

Driving time to CB shopping

Driving time measurement for each 2-digit (or 4-digit) zip code, z

I Identify supermarkets close to Swiss border in Germany, France, Italy, Austria

I Identify the largest town by population in each z , tz

I Use viamichelin.ch (similar to google maps) to measure min. driving time toand from tz to foreign supermarkets, keeping only minimum

ImportsHomogeneous initial exposure

Heterogeneous responsiveness

Homogeneous initial import exposureNo differences across households in import shares by income or distance

Import share in our data is 26.9% in 2014 and 27.8% in 2015

Question: How does it vary with HH characteristics?

XMht /(XD

ht + XMht ) = αt + β1t ln(inch) + β2t ln(sizeh) + β3t ln(driveh) + εht

(1) (2) (3) (4)log income 0.006 -0.004 0.002 -0.011

[0.005] [0.006] [0.005] [0.007]log HH size -0.019∗∗∗ -0.014∗ -0.021∗∗∗ -0.009

[0.006] [0.008] [0.005] [0.006]log drive time -0.007∗ -0.009∗ 0.003 -0.003

[0.004] [0.005] [0.003] [0.004]Adjusted R2 0.01 0.01 0.01 0.00year 2014 2015 2014 2015Observations 3302 2918 3302 3300weighted Y Y N N

(weighing h share of expenditure w/in (income, size) × # of h in (income, size))

Income insignificant

Distance effects are economically small, statistically not robust

Average import responsiveness across all householdsIncrease in import relative to domestic expenditure at the HH level starting after appreciation

ln

(XMht

XDht

)= α+ FEh + FEt + εht

In this and all HH-level regressions we:

cluster by (income, size) bins Import share Alt. weight

weight: h share of expenditure w/in (income, size) × # of h in (income, size)I each (income, size) gets weight given by number of householdsI within (income, size), relative weights across h given by expenditure in 14

Common interval of months in all t (starting with January 15th) b/c of seasonalityI eg, in month 5, XM

ht = expenditure on imports btw Jan 15th-May 15th in year t

(weighing h share of expenditure w/in (income, size) × # of h in (income, size))

Heterogeneous import responsivenessImport share ↑ more for low income groups following 2015 appreciation

ln

(XM

ht

XDht

)= FEt + FEh +

∑y 6=2014

βtIy=txh + [Controlsht ] + εht

where xh equals either I{Inch>42.5K} or ln(Inch) η calibration

High Income Dummy Ln(Income)

(1) (2) (3) (4) (5) (6)

Income 2013 -0.047∗∗ -0.052∗∗ -0.052∗∗ -0.030∗ -0.034∗ -0.034∗[0.018] [0.022] [0.022] [0.015] [0.019] [0.019]

Income 2015 -0.067∗∗∗ -0.073∗∗∗ -0.073∗∗∗ -0.057∗∗∗ -0.064∗∗∗ -0.064∗∗∗[0.020] [0.025] [0.025] [0.010] [0.013] [0.013]

Income 2016 -0.083∗∗∗ -0.077∗∗ -0.077∗∗ -0.071∗∗∗ -0.067∗∗∗ -0.068∗∗∗[0.031] [0.031] [0.032] [0.022] [0.022] [0.022]

HH Size 2013 0.011 0.011 0.010 0.011[0.022] [0.022] [0.023] [0.023]

HH Size 2015 0.014 0.015 0.019 0.019[0.019] [0.018] [0.018] [0.018]

HH Size 2016 -0.013 -0.013 -0.008 -0.008[0.024] [0.024] [0.020] [0.020]

Distance 2013 -0.005 -0.005[0.013] [0.013]

Distance 2015 -0.006 -0.006[0.020] [0.020]

Distance 2016 -0.003 -0.003[0.021] [0.021]

Observations 11577 11577 11577 11577 11577 11577

Adjusted R2 0.780 0.780 0.780 0.780 0.780 0.780

Negative 2013 coefficient: import shares ↑ more for high Y groups btw 2013/2014

no evidence of continuation of pre-existing trends

Heterogeneous import responsivenessResults hold at more aggregate level and within product groups

Aggregate to the HH income × size groupadditionally estimating w/in product groups

Within product group

High inc. Ln(income) High inc. Ln(income)

(1) (2) (3) (4) (5) (6) (7) (8)

Income 2013 -0.044 -0.053∗ -0.015 -0.021 -0.029 -0.043 0.007 -0.002[0.028] [0.030] [0.022] [0.024] [0.027] [0.028] [0.029] [0.032]

Income 2015 -0.071∗∗ -0.083∗∗∗ -0.058∗∗∗ -0.071∗∗∗ -0.071∗∗∗ -0.079∗∗∗ -0.061∗∗∗ -0.071∗∗∗[0.028] [0.030] [0.022] [0.024] [0.021] [0.025] [0.020] [0.025]

Income 2016 -0.087∗∗∗ -0.083∗∗∗ -0.091∗∗∗ -0.092∗∗∗ -0.058 -0.056 -0.074∗∗ -0.077∗[0.028] [0.030] [0.022] [0.024] [0.040] [0.040] [0.036] [0.040]

HH Size Control No Yes No Yes No Yes No Yes

Observations 211 211 211 211 9954 9954 9954 9954

Adjusted R2 0.720 0.722 0.737 0.736 0.935 0.935 0.935 0.935

Aggregating across h at the income × size group level (Columns 1-4)

ln

(XM

ht

XDht

)= FEt + FEh +

∑y 6=2014

βtIy=txh + [Controlsht ] + εht

and estimating at the income × size group level by product group g (Columns 5-8)

ln

(XM

hgt

XDhgt

)= FEgt + FEhg +

∑y 6=2014

βtIy=txh + [Controlsht ] + εht

Heterogeneous import responsiveness: robustness exercisesResults are robust to the following

Replace ln(XMht

/XD

ht ) with XMht

/(XD

ht + XMht ) Go

Don’t weigh observations Go

Replace income and size with income per capita Go

Horizons from 1-12 (baseline is 12)

I Household aggregation Go

I Income × size aggregation Go

I Income × size aggregation within product group Go

Cross-border shoppingHeterogeneous initial exposure

Homogeneous responsiveness

Price gaps between shopping domestically and CBQuarterly series using balanced sample of EAN codes

Median price gap between identical EAN codes purchased in Switzerland andforeign countries, using Swiss Nielsen data only (left) or Swiss + German, Italian,Austrian Nielsen data (right)

Price gap using purchases made bySwiss only

Price gap using purchases made bySwiss and neighbors

Prices are lower abroad

The gap in prices grows after appreciation

Three measures of CB shares in 2014

Three measures of CB shares (out of total) by time horizon in 2014

1 Expenditures

2 Transactions: count of a HH’s purchases (EAN code-day-location)

3 Trips: count of days on which a HH purchases anything CB model

Share is btw 1.4% and 2.6% across horizons and measures

Share of HHs engaged in CB shopping in 2014 (by horizon)

Share increases from 12% to 33% with horizon

Heterogeneous initial exposure to CB shoppingHigher CB shares closer to CB shopping (by 2-digit zip code) in 2014 (and all years)

Driving time Expenditure share

Trip share Transaction share

Heterogeneous initial exposure to CB shoppingHigher CB shares closer to CB shopping (by 2-digit zip code) in 2014 (and all years)

Expenditure share

Trip share Transaction share

Heterogeneous initial exposure to CB shoppingHigher CB exposure closer to the border (but no differences across income or size)

yht = αt + β1t ln(inch) + β2t ln(sizeh) + β3t ln(driveh) + εht

where yht : HH’s share of expenditures, trips, transactions abroad

Expenditures Trips Transactions

(1) (2) (3) (4) (5) (6)log income -0.001 -0.002 -0.001 -0.002 -0.001 -0.002

[0.002] [0.002] [0.002] [0.003] [0.003] [0.004]log HH size 0.001 0.003 0.002 0.003 0.002 0.004

[0.001] [0.002] [0.002] [0.002] [0.002] [0.003]log drive time -0.016∗∗∗ -0.017∗∗∗ -0.018∗∗∗ -0.020∗∗∗ -0.030∗∗∗ -0.032∗∗∗

[0.002] [0.002] [0.002] [0.002] [0.003] [0.003]Adjusted R2 0.04 0.04 0.05 0.05 0.09 0.09year 2014 2015 2014 2015 2014 2015Observations 3309 2921 3309 2921 3309 2921weighted Y Y Y Y Y Y

(weighing h share of expenditure w/in (income, size) × # of h in (income, size))

Average CB responsiveness across all householdsIncrease in CB shares starting after appreciation

XCBht

Xht= α + FEh + FEt + εht

Expenditures

Transactions Trips

Homogeneous responsiveness of CB shopping

yht = FEt + FEh +∑

y 6=2014

Iy=t

(βt ln(incomeh) + ρt ln(sizeh) + γt ln(disth)

)+ εht

Defining yht as

I the share,XCBhtXht

, Go

I or log ratio, ln(

1+XCBht

1+XnonCBht

)... Go

...for Xht defined as Trips, Transactions, or Expenditures...

...we find no evidence of robust heterogeneous responsiveness across incomes,distance, or size

Welfare (and employment) implications

Motivating theoretical framework

What are the distributional effects of factual

I exchange rate appreciation of January 15th, 2015?

I COVID-related border lockdown?

and counterfactual changes in prices of imports and CB shopping?

Simple model consistent with empirical observations

I Standard framework w/ known welfare aggregation

I Direct structural interpretation of reduced-form coefficients

I Highlight measurement issues in CB expenditure shares and provide resolution

I Imposes a number of restrictions that we relax in robustness

Roadmap

1 Imports only (limit of baseline model in which CB is zero)

2 Add cross-border shopping

Model with imports and domestic goods, no CB shopping

If a household h only shops locally, price index Pht = PDMht is given by

PDMht =

(ζht(PMht

)1−ηh+ (1− ζht)

(PDht

)1−ηh)1/(1−ηh)

which arises from CES aggregator with elasticity ηh

Letting y = y ′/y for any y and XDht , X

Mht denote expenditures,

PDMht =

(XD

ht

XDht + XM

ht

(PDht

)1−ηh+

XMht

XDht + XM

ht

(PMht

)1−ηh) 1

1−ηh

We report (proportional) equivalent variation [“welfare”]

EV ≡ 100× ln

(E(p0, u1)

E(p0, u0)

)= 100× ln

(E(p0, u1)

E(p1, u1)

)which is simply

EV = −100× log PDMht

Baseline model discussion: I

Introduce endogenous differences in ηh (non-homothetic preferences) in robustness

I As in limit, consider consumers who do not CB shop Go

Easy to introduce outside good

I Abstract from it in quantification

F Not overstating aggregate welfare effects of international shocks, since importshare similar in our data and in overall consumption

F However, abstracting from heterogeneity in outside good shares abstracts fromcomponents of inequality featuring in e.g., Cravino and Levchenko (2017) and

Borusyak and Jaravel (2018) Go

We abstract from product group heterogeneityI Changes in import shares are largely driven within categories within product

I In estimation robustness, we incorporate multiple product groups

I (For CB: not sufficient cross-border shopping data)

Baseline calibration of ηh: I

Model implication

ln

(XMht

XDht

)= (1− ηh) ln

(PMht

PDht

)+ ln

(ζht

1− ζht

)Baseline assumptions

1 Common ln(PMht /P

Dht) across households

ln

(XMht

XDht

)= (1− ηh) ln

(PMt

PDt

)+ ln

(ζht

1− ζht

)

2 Parametrization: ηh =

{ηP for lowest two income groups

ηR for highest five income groupsIncome distr.

Baseline calibration of ηh: II

Expressing the previous equation in differences (btw 2014-15)

∆ ln

(XM

h15

XDh15

)= α + βIInch>y + εh (1)

where α ≡ (1− ηP)∆ ln(PM15/P

D15), β ≡ (ηP − ηR)∆ ln(PM

15/PD15), εh ≡ ∆(ζh15/(1− ζh15))

(1) is equivalent to our reduced-form regression (in differences) RF regs

Structural parameters ηP and ηR

At 12 month horizon, βOLS = −0.067 (SE = −0.020), αOLS = 0.082 (SE= 0.018),

∆ ln(PM

15/PDD

)= −0.021 prices

If demand shocks uncorrelated with income ⇒ ηP − ηR = 3.19

If average demand shock is zero ⇒ ηP = 4.73⇒ ηR = 1.54

Higher values of ηs, alternative functional form (ηh = γ0 − γ1 ln(Inch)), prices varying by

HH characteristicsI Defer robustness of calibration, combine with robustness of results

Changes in import prices and income-group-specific welfareEquivalent variation for various import price changes (for HHs engaged in no CB shopping)

log change import price 2.10 10 20 30 40 50 10000

Changes in welfareEV low income -0.55 -2.35 -4.10 -5.38 -6.29 -6.94 -8.44EV high income -0.56 -2.65 -5.19 -7.63 -9.98 -12.23 -58.28EV high / low income 1.02 1.12 1.26 1.42 1.58 1.76 6.91

Initial import share (given elasticities) at which income groups have common EVImport share low income 27.7 30.2 33.5 36.8 40.1 43.3 88.6Import share high income 26.3 24.0 21.4 19.1 17.2 15.6 4.5

Poor being more elastic, suffer less from given import price increase

I To a first-order approximation, import elasticity irrelevantI Gap in welfare changes grow with size of shock

Import share for (e.g.) low income at which ∆ welfare for low and high income are equated

I Higher than actual common import share of 27%I With this initial import share growing in the size of the shock

Robustness

1 Non-homothetic preferences and endogenous changes in ηh Go

I Smaller welfare losses from import price ↑ w/ non-homothetic demandF HHs become poorer ⇒ substitute away from imports even more

2 Higher values of ηs holding fixed ηP − ηR Go

I Relative welfare changes smaller the higher are import elasticities

I However, only quantitatively relevant for large import price changes

3 Alternative functional form: ηh = γ0 − γ1 ln(Inch)− [γ2 ln(sizeh)] Go

I Multiple ηs simply smooths effects across income distribution

I Incorporating size (or not) has little effect

4 Prices varying by HH income × size Go

I Differences in elasticities across incomes (and hence results) very similar to baseline

Baseline model incorporating CB expenditureAssumptions

Within period, HH makes a continuum of shopping trips, z , and maximizes

Ch =

∫ 1

0

(∑s

Ush × (εsh(z))1−κ × C s

h (z)

) ρ−1ρ

dz

ρρ−1

for shopping location s ∈ {CB,DM}, subject to budget constraint

Inch =∑s

P shV

sh

∫ 1

0

C sh (z)× (εsh(z))−κdz

(interest rate 6= 0 within period and time discounting has no effect on results)

I Ush : systematic demand shifter (e.g. amenity, time) for shopping in location s

I (εs(z))1−κ: idiosyncratic demand shifter for shopping in location s in trip z

I Psh : retail price index per unit of consumption when shopping in location s

I V sh : systematic non-retail, monetary cost shifter associated with shopping in s

I (εs(z))−κ: idiosyncratic non-retailer monetary cost shifter of shopping in s in trip z

εs(z) distributed Frechet, G (ε) = exp(−ε−θ

)θ > ρ− 1

I Abstract from differences in CB elasticities by income given empirical results

Baseline model incorporating CB expenditureImplications: trip and expenditure shares

Model limits to trade-only model when either UCBh = 0 or V CB

h =∞

HH chooses location s for shopping trip z ⇐⇒ Ushε

sh(z)

V shPsh> maxs′ 6=s

{Us′h ε

s′h (z)

V s′h

Ps′h

}Let πs

h denote the share of trips HH makes in location s

πsh =

[Ush/ (P s

hVsh )]θ∑

s′[Us′

h /(P s′h V s′

h

)]θMonetary cost borne by HH is P s

hVsh (εsh(z))−κ

Distribution of expenditures across trips in s determined by distribution ofC sh (z)P s

hVsh (εsh(z))−κ conditional on shopping in s in trip z

I This distribution is independent of s ⇒ πh(s) is also expenditure shareI Not true of distribution of mismeasured expenditures (using P s

h for price)F If κ 6= 0, then the elasticity of mismeasured expenditures is not θ

F If κ = 0,V CBh > VDM

h , mismeasured CB expend. share < true version Data

Baseline model incorporating CB expenditureImplications: welfare

Letting Ph = Ch/Inch, we obtain Ph = γ[∑

s (V shP

sh/U

sh)−θ

]−1θ

In response to a change in retailer prices, (letting x = x ′/x for any x)

Ph =

[∑s

πsh

(P sh

)−θ]−1θ

Implications:

Constructing factual or counterfactual changes in welfare requires:

1 cross border shopping elasticity θ

2 initial expenditure (equivalently, trip) share by shopping location, πsh

3 changes in retail price index by shopping location, Psh

Measure πsh using trip share, which equals true expenditure shares

Similarly, parametrize θ using trip share

Baseline model additional implications and discussion

Additional implications that are consistent with our data

If we observe a random discrete sample of trips per HH per month, share ofHHs engaged in CB shopping rises with a longer horizon

In response to CHF appreciation (i.e. reduction in PCBh )

1 Share of CB trips rises

2 If we observe a random discrete sample of trips per HH, share of HHs engagedin CB shopping rises

Discussion of modeling choices

Instead of continuum of trips, can assume a fixed, finite number of trips,χ = 1 (implies common expenditure across trips), unknown realizations of εs

I Household welfare (and whether it shops abroad) is random each period

I Aggregating across continuum of agents yields same welfare expression

I Share of HHs engaged in CB shopping rises with CHF appreciation

No fixed cost of CB shopping or dynamic HH inventoriesI Dividing products by perishability, for all three CB measures: perishable

I While CB shares are higher (2-3×) for non-perishable items...

I ...both fall with distance

I ...and responsiveness to appreciation very similar (+ not statistically different)

Baseline calibration of θ using trips share

ln

(πCBht

πDMht

)= −θ ln

(PCBht

PDMht

)+ θ ln

(UCBht /V

CBht

UDMht /V DM

ht

)Baseline assumption

Common ln(PCBht /P

DMht ) across households (true in model to a first order)

Expressing the previous equation in differences (btw 2014-15)

∆ ln

(πCBh15

πDMh15

)= α + ιht where α ≡ −θ∆ ln

(PCB

15

PDM15

)Structural parameter θ

At 12 month horizon, αOLS = 0.095 (SE= 0.032) and ∆ ln(

PCB15

PDM15

)= −0.062.

If average demand shock is zero ⇒ θ = 1.53Alternatives leading to robustness of θ ∈ [1, 2.5]

1 Use ↑ aggregate CB trip share (0.026 to 0.029): ⇒ θ = 2.10

2 Using transactions: θ = 1.18 or 2.20 using regression or aggregate

3 Using expenditures: θ = 1.00 or 1.28 using regression or aggregate

4 At horizon of 3 months using CB trip share: θ = 1.28 or 2.13 using...

5 CB trip share in zip codes w/in 30 minutes of CB: θ = 1.92 or 2.02 using...

Change in welfare in response to 2015 appreciationIncorporating both imports and CB shopping

Feed in 12-month-horizon changes in CB and DM price indices

Measure πCBh14 using share of CB trips transactions

Equivalent variation for low income

Those closer to CB shopping gain substantially more employment effects

Values of θ and ηh (hence, heterogeneity in ηh) matter little for EV with small shocks

Closing of the border for CB shopping

Switzerland closed its borders to and from the Schengen area fornon-essential traffic to mitigate spread of Covid 19

TimelineI March 17: Borders to Austria, France, and Germany closed

I March 17 - April 26: Lockdown

I April 27 - May 10: Partial reopening

I May 11 - June 15: All shops reopened

I June 16: Borders to EU reopened

Calculate welfare effects across space of this border closing

Closing of the border for CB shoppingCB shares across space fall to close to 0 during lockdown

Debit card data

Closing of the border for CB shoppingCB shares across space fall to, or almost to, zero during lockdown

Transactions Expenditures

Closing of the border for CB shoppingChange in domestic+import prices across space during lockdown

No systematic changes in non-CB prices across space within Switzerland

⇒ We evaluate welfare given fixed non-CB prices

Closing of the border for CB shoppingWelfare falls substantially close to the border

Closing of the border for CB shoppingSensitivity to CB elasticity θ

Conclusions

Unequal effects of internationally-induced price changes

Spatial variation by distance to cross-border shopping

I Largely absent in the literature

I Those living closer to border benefit more from foreign price reductionI Quite important for Switzerland; more generally, relevant margin for

F small countries, countries w/ substantial populations along borders (Canada)

F regional tax changes

F spatial shopping literature

Variation by household income

I This is the heart of a large international trade literature

I We find large variation in price sensitivities (lower income more price sensitive),a margin from which the literature largely abstracts (due to data limitations)

I Lower income benefit more (or suffer less) from large price changes

Appendix

Average expenditure by income group (bin scatter)Income bin is predictive of expenditure

(weighted by number of HHs)

Income and expenditure at the HH levelIncome bin is predictive of expenditure

Estimate separately by year:

ln(expht) = αt + β1t ln(inch) + β2t ln(sizeh) + β3t ln(driveh) + εht

(1) (2)log income 0.115∗∗∗ 0.120∗∗∗

[0.020] [0.026]log HH size 0.375∗∗∗ 0.354∗∗∗

[0.019] [0.025]log drive time 0.037∗∗ 0.047∗∗

[0.017] [0.022]Adjusted R2 0.15 0.10year 2014 2015Observations 3309 2921weighted Y Y

back

Import responsiveness by horizonHorizon robustness at household aggregation

Replicating HH aggregation, Columns 3 and 6 for each horizon

ln

(XMht

XDht

)= FEt + FEh +

∑y 6=2014

βtIy=txh + Controlsht + εht

High income ln income

Back

Import responsiveness by horizonHorizon robustness at income × size aggregation

Replicating income×size aggregation, Columns 2 and 4 for each horizon

ln

(XMht

XDht

)= FEt + FEh +

∑y 6=2014

βtIy=txh + Controlsht + εht

High income ln income

Back

Import responsiveness by horizonHorizon robustness at income × size aggregation within product group

Replicating income×size aggregation within product group, Columns 6 and 8 foreach horizon

ln

(XMhgt

XDhgt

)= FEgt + FEhg +

∑y 6=2014

βtIy=txh + [Controlsht ] + εht

High income ln income

Back

Cross border responsiveness of CB shopping: baseline(XCB

ht

Xht

)= FEt + FEh +

∑y 6=2014

βtIy=txh + Controlsht + εht

where xh equals either I{Inch>42.5K} or ln(Inch), for three measures of Xht

Expenditures Trips Transactions

High inc. Ln(income) High inc. Ln(income) High inc. Ln(income)

(1) (2) (3) (4) (5) (6)

Income 2013 0.001∗∗ 0.001∗ 0.001∗ 0.001∗ 0.001 0.000[0.001] [0.001] [0.001] [0.001] [0.001] [0.001]

Income 2015 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001[0.001] [0.001] [0.001] [0.001] [0.001] [0.001]

Income 2016 -0.000 -0.001 -0.001 -0.001 -0.001 -0.002∗[0.001] [0.001] [0.002] [0.001] [0.002] [0.001]

HH Size 2013 -0.001 -0.001 -0.000 -0.001 0.000 0.000[0.001] [0.001] [0.001] [0.001] [0.001] [0.001]

HH Size 2015 0.002∗ 0.002∗ 0.002 0.002 0.002 0.002∗[0.001] [0.001] [0.001] [0.001] [0.001] [0.001]

HH Size 2016 0.001 0.001 0.002 0.002 0.002 0.002[0.001] [0.001] [0.002] [0.002] [0.002] [0.002]

Distance 2013 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001[0.001] [0.001] [0.001] [0.001] [0.001] [0.001]

Distance 2015 -0.001 -0.001 -0.002∗ -0.002∗ -0.002∗ -0.002∗[0.001] [0.001] [0.001] [0.001] [0.001] [0.001]

Distance 2016 -0.002 -0.002 -0.002 -0.002 -0.001 -0.001[0.001] [0.001] [0.002] [0.002] [0.002] [0.002]

Observations 11646 11646 11646 11646 11646 11646

Adjusted R2 0.786 0.786 0.806 0.806 0.848 0.848

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Cross border responsiveness of CB shopping: robustness

ln

(1 + XCB

ht

1 + X nonCBht

)= FEt + FEh +

∑y 6=2014

βtIy=txh + Controlsht + εht

where xh equals either I{Inch>42.5K} or ln(Inch), for three measures of Xht

Expenditures Trips Transactions

High inc. Ln(income) High inc. Ln(income) High inc. Ln(income)

(1) (2) (3) (4) (5) (6)

Income 2013 -0.183 -0.180 -0.031 -0.041 -0.010 -0.029[0.138] [0.125] [0.049] [0.047] [0.032] [0.027]

Income 2015 -0.142 -0.089 -0.031 -0.023 0.003 -0.001[0.144] [0.122] [0.056] [0.044] [0.036] [0.028]

Income 2016 -0.191 -0.063 -0.057 -0.027 -0.029 -0.020[0.180] [0.155] [0.061] [0.044] [0.042] [0.029]

HH Size 2013 0.041 0.060 -0.029 -0.022 -0.021 -0.013[0.099] [0.087] [0.035] [0.029] [0.023] [0.020]

HH Size 2015 0.105 0.101 0.022 0.023 0.035∗ 0.036∗[0.109] [0.093] [0.041] [0.036] [0.021] [0.019]

HH Size 2016 0.192 0.165 0.041 0.036 0.021 0.020[0.173] [0.164] [0.055] [0.054] [0.031] [0.029]

Distance 2013 0.116 0.116 -0.009 -0.009 -0.002 -0.002[0.108] [0.108] [0.034] [0.034] [0.021] [0.022]

Distance 2015 0.261∗ 0.262∗ 0.041 0.041 0.020 0.020[0.148] [0.149] [0.041] [0.041] [0.021] [0.021]

Distance 2016 -0.013 -0.011 0.006 0.006 0.021 0.021[0.147] [0.147] [0.043] [0.042] [0.024] [0.024]

Observations 11646 11646 11646 11646 11646 11646

Adjusted R2 0.717 0.717 0.804 0.804 0.814 0.814

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Prices intro

We assume

1 No product entry or exit

F Small Homescan sample, particularly at HH income, HH size, geographic levels

F Regressions often at household level

2 We observe a representative sample of products

For estimation, use a first-order approximation of price indices PMt , PD

t

I Laspeyres: initial period shares

Prices details

Detailed product price (eancode) change by CB status and horizon

I monthly price: by detailed product, and CB status of purchase, takeunweighted geometric average price across transactions

I price for given horizon: simple geometric average across months in horizon

I take ln changes across years w/in common horizon, eancode, and CB status

Aggregate across eancodes to construct price indices for

D domestic purchases of domestically produced goods

M domestic purchases of imported goods

CB cross border purchases

Robustness:

I Sato-Vartia weights rather than first-order approximation

I Income and size-specific expenditures as weights across products

Back to η calibration

Change in retail employmentWhat are the implications of CB shopping for retail employment?

In response to CHF appreciation, DM expenditure decreases

XCBh

XDMh

=

(UCBh /

(V CBh PCB

h

)UDMh /

(V DMh PDM

h

))θ

and XCBh + XDM

h = Inch ⇒

d lnXDMh = πCB

h θd ln

(PCBh

PDMh

)and if θ > 0 ↓ by more the greater is the initial share of expenditure in CB

I Expenditure = retail revenue if κ = 0 and either V CBh = V DM

h or V DMh = 1

⇒ Impact on Swiss retail revenue is larger closer to CB shopping

If employment is increasing in revenue, same holds for employment

We test this hypothesis around the 2015 appreciation, obtaining industryemployment by 4-digit zip codes from the Business Census (“STATENT”)

Change in retail employmentBinscatter across 4-digit zip codes of 2-year ln changes in retail employment: 2014-16

(no controls, weighing by total employment of 4-digit zip in 2014)

Retail employment ↓ closer to the border (relatively) around CHF appreciation

Spatial heterogeneity in CB shopping has implications for employment responses toforeign price shocks

Change in non-retail employmentBinscatter across 4-digit zip codes of 2-year ln changes in non-retail employment: 2014-16

(no controls, weighing by total employment of 4-digit zip in 2014)

Reallocation towards non-retail employment closer to the border

Change in retail (and non-retail) employmentWhat are the implications of CB shopping for retail employment across 4-digit zip codes?

We stack 4-digit zip codes, z , and years, t (2013-16), and estimate

ln(empzt) = αt + αz + βt ln(distz) + γt ln(incz) + εzt

separately for retail employment and non-retail employment back

(weighing by total employment of 4-digit zip in 2014, over 2600 zip codes)

Average import responsiveness across all householdsIncrease in import expenditure share at the HH level starting after appreciation

XMht

XDht + XM

ht

= α + FEh + FEt + εht

(weighing h share of expenditure w/in (income, size) × # of h in (income, size))

Back

Average import responsiveness across all householdsIncrease in import relative to domestic expenditure at the HH level starting after appreciation

ln

(XMht

XDht

)= α + FEh + FEt + εht

(weighing h by expenditure in 2014)

Back

Decomposition

Decompose changes in aggregate import share ωt over time

I Let g denote product categories, XM ,XDM exp on M and M + D

I Aggregate import sharet : ωt ≡ XMt

XDMt

=∑

g

XMgt

XDMgt

XDMgt

XDMt

∆ωt =∑g

∆

(XM

gt

XDMgt

)Avg

(XDM

gt

XDMt

)︸ ︷︷ ︸

within

+∑g

Avg

(XM

gt

XDMgt

)∆

(XDM

gt

XDMt

)︸ ︷︷ ︸

between

I Within share of aggregate change by horizon always dominates between

Does relative importance of within share vary with income per capita?

I Construct ∆ωjt by j = HH income × HH size bins and regress on ln incomej

I Insignificant relationship in all horizons

Decomposition

Within share of aggregate change by horizon always large

Back

Change in welfare in response to 2015 appreciationImports and CB for low income households: robustness using transaction share

Equivalent variation for low income

back

Import responsiveness: robustness exercises 1 and 2

Dep var import share Unweighted

High inc. Ln(income) High inc. Ln(income)

(1) (2) (3) (4)Income 2013 -0.009∗∗ -0.041∗∗ -0.049∗∗ -0.041∗∗

[0.004] [0.020] [0.024] [0.020]Income 2015 -0.012∗∗∗ -0.071∗∗∗ -0.076∗∗∗ -0.071∗∗∗

[0.004] [0.019] [0.023] [0.019]Income 2016 -0.013∗∗ -0.065∗∗∗ -0.051 -0.065∗∗∗

[0.006] [0.021] [0.034] [0.021]Observations 11630 12057 12057 12057Adjusted R2 0.770 0.731 0.731 0.731

Columns 1 and 2: Replace ln(XMht

/XDht ) with XM

ht

/(XD

ht + XMht )

Columns 3 and 4: Don’t weigh observations

All regressions include HH size and distance interacted with year

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Import responsiveness: robustness exercise 3

Household aggregation Income x size aggregation

Within product group

(1) (2) (3)Ln(Income/HH size) 2013 -0.022 -0.019 -0.014

[0.019] [0.020] [0.028]Ln(Income/HH size) 2015 -0.041∗∗∗ -0.053∗∗∗ -0.047∗

[0.014] [0.020] [0.024]Ln(Income/HH size) 2016 -0.029 -0.046∗∗ -0.042

[0.020] [0.020] [0.028]Observations 11577 211 9954Adjusted R2 0.779 0.717 0.935

Replace income and size with income per capita

All regressions include distance interacted with year

Back

Non-homotheticityFor a household with no CB shopping

Following Fally (...) and Faber and Fally (....), utility is implicitly defined by

f (Cht)η(Cht )−1

η(Cht ) =

(ζ

1η(Cht )

ht

(CMht

) η(Cht )−1

η(Cht ) + (1− ζht)1

η(Cht )(CDht

) η(Cht )−1

η(Cht )

)where η(C ) = γ0 − γ1 ln(C )

Since utility is ↑ function of income, in initial eqm normalize Cht = Incγ2

htI pins down f (C) for any γ2 > 0 (results on EV invariant to γ2)

Focus on poorest (Inch = 20K and second-richest Inch = 135K ) groupsI Choose γ0, γ1 to match—in initial eqm—ηP and ηR (from CES calibration)

I in calibration, as in counterfactuals, assume fixed CHF income

Choose ζht s.t. import shares are 27% for all HHs in initial eqm

Now import elasticities respond to shocksI ↑ in foreign prices ⇒ real income ↓ ⇒ elasticity ↑ ⇒ Welfare losses are smaller

Measure welfare changes using equivalent variation

back to discussion back to robustness

Non-homotheticityFor a household with no CB shopping

log change import price 2.1 10 20 30 40 50 10000

CES demand systemEV low income -0.55 -2.35 -4.10 -5.38 -6.29 -6.94 -8.44EV high income -0.56 -2.65 -5.19 -7.63 -9.98 -12.23 -58.28

non-homothetic demand systemEV low income -0.55 -2.35 -4.08 -5.33 -6.21 -6.82 -8.14EV high income -0.56 -2.64 -5.16 -7.53 -9.74 -11.79 -30.15

new low income elast 4.74 4.77 4.80 4.82 4.83 4.84 4.87new high income elast 1.55 1.58 1.63 1.67 1.70 1.74 2.04

For small shocks, CES and non-homothetic results are very similar

I To a first-order approximation, elasticities irrelevant

Smaller welfare losses from import price increases in non-homothetic demand

I HHs become poorer ⇒ substitute away from imports even more

back to robustness

Changes in import prices and income-group-specific welfareRobustness to higher ηh for fixed gap between rich and poor

Robustness: ηh =

{1.54→ 3 lowest two income groups

4.73→ 6.19 highest five income groups

For HH not engaged in CB shopping:

log change import price 2.10 10 20 30 40 50 10000

Changes in welfareEV low income -0.54 -2.23 -3.69 -4.62 -5.19 -5.54 -6.06EV high income -0.56 -2.51 -4.66 -6.50 -8.05 -9.36 -15.74EV high / low income 1.02 1.12 1.26 1.41 1.55 1.69 2.60

For a given gap between rich and poor import elasticities (ηR − ηP = 3.19), relative welfarechanges smaller the higher are import elasticities

However, this change only quantitatively relevant for large import price changes

Back

Changes in import prices and income-group-specific welfareAlternative functional form relating elasticity to income

ηh = γ0 − γ1 ln(Inch)− [γ2 ln(sizeh)]⇒ estimating equation becomes Back

∆ ln

(XMh15

XDh15

)= α+ β ln(Inch) + [β1 ln(sizeh)] + εh

βOLS = −0.057 (SE = .010) changes to −0.064 including ln(sizeh)I including size has little effect (size itself is insignificant)

Excluding richest very richest income group (very few HHs), set ηmin = 1.54

Implies ηh = 1.54− 0.0570.021

ln(

Inch135,000

)= 1.54− 2.71 ln

(Inch

135,000

)I ⇒ ηh ∈ [1.54, 6.71] (compared to ηh ∈ {1.54, 4.73})

Changes in import prices and income-group-specific welfarePrices varying by HH income × size (different weights)

∆ ln

(XMh15

XDh15

)= (1− ηh)∆ ln

(PMh15

PDh15

)+ ιh15

where we assume either Back

ηh =

{ηP for Inch ≤ 42.5K

ηR for Inch > 42.5Kor ηh = γ0 − γ1 ln(Inch)

ηP − ηR γ1

Perishability

Perishable product groups (coded by hand):

I fruits

I vegetables

I fish

I bread and other bakery items

I ...

Change in log CB share in 2015 (relative to 2014) measured using

Expenditures: Transactions: Trips:

PerishabilityCross border responsiveness of CB shopping by perishability

Perishable:Expenditures Trips Transactions

(1) (2) (3)

log income -0.000 0.000 0.000[0.001] [0.001] [0.002]

log HH size 0.000 0.000 0.003[0.001] [0.002] [0.002]

log drive time -0.009∗∗∗ -0.012∗∗∗ -0.022∗∗∗[0.001] [0.001] [0.002]

Adjusted R2 0.03 0.03 0.07year 2014 2014 2014Observations 3302 3302 3302weighted Y Y Y

Nonperishable:Expenditures Trips Transactions

(1) (2) (3)

log income -0.001 -0.001 -0.001[0.002] [0.002] [0.003]

log HH size 0.002 0.003 0.002[0.002] [0.002] [0.002]

log drive time -0.020∗∗∗ -0.023∗∗∗ -0.029∗∗∗[0.002] [0.003] [0.003]

Adjusted R2 0.05 0.05 0.09year 2014 2014 2014Observations 3303 3303 3303weighted Y Y Y

Back

Debit card data on CB shopping

Debit card expenditures by Swiss on Food and supermarket, Accommodation,Restaurants, Fuel, Personal services, Entertainment, and Transport

http://monitoringconsumption.org/switzerland

Ratio of CB expenditures / Swiss expenditures ≈ 5%-7%

Debit card expenditures 2019-20Italy

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Debit card expenditures 2019-20Germany

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Debit card expenditures 2019-20Germany groceries

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Debit card expenditures 2019-20France

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Debit card expenditures 2019-20Austria

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Debit card expenditures 2019-20Switzerland

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