Unequal expenditure switching:
Evidence from Switzerland*
Raphael Auer

Ariel Burstein

Sarah Lein

Jonathan Vogel

BIS

UCLA

Uni Basel

UCLA

June 2023

Abstract
What are the unequal effects of changes in consumer prices on the cost of living? In thecontext of changes in import prices (driven by, e.g., changes in trade costs or exchange
rates), most analyses focus on variation across households in initial expenditure shareson imported goods. However, the unequal welfare effects of non-marginal foreign pricechanges also depend on differences in how consumers substitute between imported anddomestic goods, on which there is scant evidence. Using data from Switzerland surrounding the 2015 appreciation of the Swiss franc, we provide evidence that lower-income
households have higher price elasticities. We quantify the contribution of heterogeneous
elasticities for the unequal welfare effects of observed price changes between 2014–15 andfor counterfactual shocks to the mean and dispersion of import price changes.

* The views presented in this paper are those of the authors and not necessarily those of the Bank forInternational Settlements. We thank David Atkin, David Baqaee, Kirill Borusyak, Javier Cravino, Pablo Fajgelbaum, Thibault Fally, Isabel Martínez, Katheryn Russ, Andres Santos, and David Weinstein for helpfulcomments. We thank Santiago Alvarez for excellent research assistance.

1

Introduction

What are the unequal effects of changes in consumer prices on the cost of living? In thecontext of changes in prices of imported goods (due to, e.g., changes in trade costs or
exchange rates), most attempts to answer this question have focused on variation acrosshouseholds in initial expenditure shares on imported goods; see, e.g., Fajgelbaum andKhandelwal (2016), Cravino and Levchenko (2017), and Borusyak and Jaravel (2021).1
However, the unequal welfare effects of non-marginal foreign price changes also dependon differences in how consumers substitute between imported and domestic goods (unequal expenditure switching), on which there is scant evidence. As noted by Deaton (1997,
page 187):
Since my main interest here is in the distributional effects of price changes...,these [second-order] effects will change the conclusions only to the extent thatthe elasticities ... differ systematically between poor and rich. Although there
is no reason to rule out such effects a priori, there is no reliable evidence on
the topic.
In this paper, we document large differences in price elasticities across the income distribution and quantify their contribution to the unequal welfare effects of import priceshocks.
In Section 2, we begin by describing the setting in which we measure both initial expenditure shares on imported goods across households as well as unequal expenditureswitching. We focus on Switzerland in a period surrounding the abrupt appreciation of
the Swiss franc on January 15, 2015, which markedly reduced import relative to domestic retail prices; see Figure 1.2 We measure initial import exposure across the income
distribution using data on expenditure shares by household income groups across 296
consumption categories (using the Swiss Household Budget Survey) and import sharesacross 217 slightly more aggregated consumption categories (using the disaggregateddata underlying the Swiss CPI). To study unequal expenditure switching, we turn tohigher-frequency and more detailed barcode-level Swiss Nielsen Homescan data, cov1 See also Friedman and Levinsohn (2002), Porto (2006), and Carroll and Hur (2020).
2 The Swiss National Bank (SNB) adopted a minimum exchange rate of 1.20 CHF per EUR in September 2011.

Developments abroad in late 2014 and early 2015 prompted the SNB to unexpectedly abandon this policy
on January 15, 2015. The subsequent appreciation episode came after a period of remarkable exchange ratestability, was significant (the EUR/CHF appreciated by 14.7 percent by the end of June), and—in contrast to
many episodes with large swings in international relative prices—occurred against the backdrop of stableeconomic aggregates and nominal income inequality in Switzerland. Import prices fell by more at theborder than at the retail level (Auer et al., 2021); we focus on the latter given our emphasis on expenditureswitching and welfare at the consumer level.

1Figure 1: Swiss franc appreciation and resulting price changes
January 2015 Swiss franc appreciation(relative to the euro)

Retail price changes for imported anddomestically produced purchases

Notes: The left-hand panel displays the CHF per EUR exchange rate with a vertical line at January 15, 2015; source: Swiss National
Bank (2016). The right-hand panel displays retail price differences relative to December 2014 separately for imports and domestically
produced purchases (and associated 95% confidence intervals) from estimating equation (A5); source: Nielsen Switzerland (2016).
Observations are weighted by product expenditure in 2014 and confidence intervals are constructed using robust standard errors
clustered at the product level.

ering individual household purchases of food, beverages, personal care, and household
supplies in supermarkets and drugstores. We merge these data with information onwhether individual barcode products are produced domestically or imported (as reported
on product labels).3 In response to the 2015 CHF appreciation, the import share within
the Homescan data rises and this increase is greater for lower-income households; thisdifferential change in import shares across incomes is not driven by a larger decline inimport prices for lower-income households. Finally, we document that the 2015 CHF appreciation was accompanied by an increase in the dispersion of price changes within theset of imported goods.
In Section 3, we characterize a set of sufficient statistics to answer our motivating
question: What are the unequal welfare effects of changes in consumer prices (morespecifically, changes in import relative to domestic prices in our quantitative applications)through their impact on the cost of living? A large literature has addressed this question
by applying a first-order approximation of the expenditure function and, hence, focusing
on variation across households in initial expenditure shares on different goods. We apply known results in microeconomic theory—see, e.g., Hausman (1981) and more recently
Baqaee and Burstein (2023)—to provide an exact answer to this question for non-marginal
3 In terms of measuring initial import shares across the income distribution, our paper is most closely related

to Borusyak and Jaravel (2021), who also use detailed data on consumer expenditures and import sharesacross the full economy rather than for aggregate industries and directly observe household-specific importshares on consumer packaged goods (and motor vehicles).

2price changes, taking expenditure switching into account. The sufficient statistics to calculate a household’s compensating variation in response to a given change in income andprices are initial expenditure shares across products and compensated cross-price elasticities (i.e. cross-price elasticities along the initial indifference curve).4 The unequal effects ofprice changes on the cost of living are shaped by differences in initial expenditure sharesand differences in compensated cross-price elasticities, and these effects increase in thedispersion of price changes across goods. In practice, estimating cross-price elasticities(compensated or uncompensated) between all goods in the economy is infeasible without additional assumptions. We therefore impose nested, generalized non-homothetic
CES preferences, building on Matsuyama (2019), Fally (2022) and Comin et al. (2021). Income elasticities can be non-unitary; and elasticities of substitution between goods withina sector can vary between indifference curves, but (as in standard trade models) are constant along any indifference curve.
In Section 4 we estimate how elasticities of substitution between goods in the Homescan data vary with income, taking two approaches that leverage distinct sources of variation. In our first approach, we use variation in changes in import relative to domestic
expenditures between 2014 and 2015 (surrounding the appreciation) across higher- andlower-income households. Our identification assumption is that import demand shocks
in 2015 are not systematically different across incomes. In our second approach, we use
variation in changes in expenditures across individual barcode products and variation in
product price changes. In this case, we control for product-specific demand shocks andhousehold-specific import demand shocks. We instrument for the interaction between
initial household income and the product-specific price change using an interaction between household income and a product “cost shifter.” Our cost shifter exploits variation
across border groups—an aggregation of products—in the invoicing currency of imports.
Specifically, we measure the share of imported goods in each border group that are denominated in EUR, using information from the goods-level survey underlying the calculation of the official Swiss import price index. Because of the stickiness of import prices
at the border in their invoicing currency, Swiss retail prices of imported goods are more
responsive to the appreciation if imports are denominated in EUR rather than in CHF; see
Auer et al. (2021). Given additional controls and our instrumentation strategy, the exclusion restriction in the second approach is substantially weaker than in the first approach.
4 There are well known price indices (e.g.

Törnqvist or Sato-Vartia) that incorporate information on observed expenditure shares over time and—under strong assumptions—measure welfare beyond first-orderapproximations. For recent alternative approaches, see Atkin et al. (2020), Jaravel and Lashkari (2022), andBaqaee et al. (2022). In contrast to all of these approaches, we calculate changes in welfare in response tocounterfactual changes in prices and income; see Section 5.

3

In spite of these differences, we obtain very similar quantitative results across approaches. The elasticity of substitution between goods in the Homescan data is substantially lower for higher-income households: for example, the difference between the elasticities of substitution between two households, where one has an income three times
that of the other, is 2.4 under the first approach and 2.1 under the second approach. These
approaches identify differences in elasticities across incomes. To estimate the level of theseelasticities, we make stronger identification assumptions, and the resulting estimates vary
more across the two approaches. However, in our analytic and quantitative results weshow that, conditional on differences in price elasticities across households, the unequal
welfare effects of price changes are not very sensitive to elasticity levels.
Our estimates of higher price elasticities for lower-income households are qualitatively consistent with demand system estimates in industrial organization—see, e.g., Berryet al. (2004) among many others—and findings on shopping behavior in macroeconomics—see, e.g., Kaplan and Menzio (2016) and Aguiar and Hurst (2007)—all of which support
Harrod’s (1936) Law of Diminishing Elasticity of Demand, which postulates that demand
elasticities decrease in income.5 In the spatial economics literature, there is scant and conflicting evidence on differences in elasticities across household incomes. Argente and Lee(2021) and Faber and Fally (2022) find very small differences. Handbury (2021) finds differences in elasticities across incomes very similar to our estimates when controlling forthe fact that higher-income households have a greater willingness to pay for quality but
finds opposite results when not; our approach incorporates these differences in willingness to pay for quality (by incorporating household × barcode product-specific demand
shifters that cancel out when estimating demand elasticities using changes rather thanlevels of household expenditure shares by income).6 Moreover, whereas these papers use
either Hausman instruments or the approach developed by Feenstra (1994) and Broda
and Weinstein (2006), we exploit exogenous variation in price responsiveness to an exchange rate shock.7
Finally, in Section 5 we quantify how differences in price elasticities estimated using
5 Bems and di Giovanni (2016) document that a large aggregate decrease in income in Latvia reduced importshares (since high-quality imports are more income elastic), and Coibion et al. (2015) show that households
switch expenditures toward low-price stores when local economic activity falls. Rather than focusing on
expenditure switching due to changes in income, we focus on heterogeneous expenditure switching acrossthe income distribution in response to changes in relative prices.
6 While Handbury (2021) calculates regional differences in price indices abstracting from her estimated differences in price elasticities, we show that differences in elasticities are quantitatively important in shaping
the unequal welfare effects of large price changes.
7 When we use a Hausman instrument, we find small differences. In Appendix B.2 we show that the Hausman instrument may be endogenous in our Swiss context (where there is little spatial variation in pricechanges).

4the Homescan data shape the unequal welfare effects of changes in prices.8 For these
exercises, we consider households at three distinct income levels ranging from 20,000
to 120,000 CHF per year with respective elasticities of 6.6, 4.4, and 3. We first calculatechanges in the welfare-relevant price index over grocery products in the Homescan data
in response to observed price changes between 2014 and 2015, following the CHF appreciation. Prices fell on average by 1.2% between 2014 and 2015. The welfare-relevant
price index (taking expenditure switching into account) declined by 1.6% for householdswith income of 120,000 CHF and by 2.2% for households with income of 20,000 CHF. Thisgap between income groups is accounted for by unequal expenditure switching between
imports and domestic goods as well as between products with different price changes
within the set of imports and domestic goods. If price elasticities were equal across income groups, then the gap in price indices would be small and of the opposite sign.
We then calculate changes in welfare in response to counterfactual changes in importrelative to domestic prices, considering, first, only uniform price changes within each setof goods and, second, incorporating variation in price changes within each set of goods.
To conduct these counterfactuals, we use our measures of import shares for each income
across all consumer goods and we impose that our estimated differences in price elasticities across incomes within our Homescan data apply more broadly. To highlight the nonlinearities from expenditure switching, we consider import price shocks that are larger
than the one induced by the 2015 CHF appreciation.9 Uniform import price increases
harm higher-income households more than lower-income households in Switzerland for
two reasons: (i) higher-income households have higher initial import shares (since they
spend relatively more on non-grocery goods, which are more tradable than groceries) and(ii) they substitute away from imported goods less.10 For large changes in prices, the impact of unequal expenditure-switching on welfare is substantial. For example, consider
8 Bai and Stumpner (2019) and Jaravel and Sager (2019) construct income-group and product-category-specific inflation rates and project these on changes in import penetration induced by China. Hottman
and Monarch (2020) focus on differences in import price inflation rates across US households. Relative tothese papers, we estimate differences in import elasticities across income groups, which we then use toquantify welfare changes for observed and counterfactual price shocks.
9 Given our focus on the expenditure-side effects of foreign price shocks, in the counterfactuals we abstractfrom changes in the income distribution. There is a large empirical and theoretical literature on the impact ofinternational trade on income inequality with multiple factors; see e.g. Burstein and Vogel (2017), Cravino
and Sotelo (2019), Galle et al. (2022), and Adao et al. (2022). See, e.g., He (2018) and Borusyak and Jaravel(2021) for papers incorporating both income and expenditure-side inequality induced by trade.
10 Variation of import shares with household income differs across countries depending, among other things,
on whether the country is high or low income and has a comparative advantage in goods with high- or lowincome elasticities. For example, Borusyak and Jaravel (2021) document that imports are flat throughout
the income distribution in the US. Therefore, if we applied our counterfactuals to the US context, unequal
expenditure switching would be the only channel inducing unequal welfare effects (via variation in cost ofliving).

5

a 20% uniform increase in import prices relative to domestic prices, which is not uncommon in the context of large exchange rate devaluations; see, e.g., Burstein et al. (2005) andCravino and Levchenko (2017). In response to this shock, welfare of a household with annual income of 20,000 CHF falls by about one third less than for a household with annual
income of 60,000 CHF. Almost half of this differential is accounted for by differences inprice elasticities. In practice, the variance of price changes within imports and domestic
goods rose during the 2015 CHF appreciation. If in our counterfactuals we additionallyconsider an increase in price dispersion within imported and domestic goods, then theimportance of unequal expenditure switching can be substantially larger.
In summary, we make four main contributions. First, we document heterogeneity
across incomes in expenditure switching in response to an exogenous shock to importprices. Second, we estimate differences in elasticities of substitution across incomes using
plausibly exogenous variation resulting from this shock to import prices and its heterogeneity across product groups. Third, we apply results in welfare economics to characterize differential welfare changes due to heterogeneous price elasticities in response toforeign-induced price changes. Fourth, we show quantitatively that unequal expenditureswitching contributes substantially to differences in welfare across the income distribution in response to observed Swiss price changes and to plausible counterfactual shocks
to the mean and dispersion of import price changes.

2

Data and stylized facts

2.1

Data

In this section we provide an overview of the main data sets employed in the paper.
Details and additional data sources are described in Appendix A.
AC Nielsen Homescan data and import status. AC Nielsen Homescan, Nielsen Switzerland (2016), includes information on household (HH) characteristics and shopping transactions of a demographically and regionally representative sample in Switzerland during
the period surrounding the 2015 appreciation: January 2013 to December 2016. The data
includes approximately 3,300 households in 2014.
Participating households record purchases—of food, beverages, personal care (healthand beauty aids), and other selected general merchandise—in supermarkets and drugstores (we refer to these goods as groceries). Individual products are identified by theirbarcode (European Article Number or EAN, which we often refer to as a product). In the
appendix, we describe a number of adjustments we make to the data, such as dropping6

likely recording errors by households. In the raw data, an observation is a transactionthat includes the household identifier, EAN code, quantity purchased, price paid (net of
good-specific discounts due to e.g. coupons), date of the shopping trip, and the name of
the retailer. We drop all transactions that occur abroad. See Burstein et al. (2022) for ananalysis of cross-border shopping in Switzerland using the Homescan data. We measureeach product’s price as an average of transaction-level log prices in the correspondingtime period, weighing transactions by expenditures.
The Homescan data come with a rich set of socioeconomic characteristics for eachhousehold, summarized in Table A2 in Appendix A for the year 2014, including the twodigit zip code of residence, the educational level of the household’s main earner, thenumber of household members (and the number of those under 10 and over 70 years
old), and total household pre-tax annual income reported in seven bins. Given each ofthese characteristics, we infer a level of household pre-tax income in 2014 for each Homescan household using additional data from the Swiss Household Panel (FORS). We do soby projecting the level of 2014 pre-tax household income in FORS on a set of household
characteristics available both in FORS and Homescan, including indicator variables forthe seven pre-tax income bins available in Homescan (and which can be constructed in
FORS). We then predict household income in Homescan using these coefficients.
We augment the Homescan data with information on whether individual products areimported or produced domestically. Whereas EANs provide information on the country in which a product has been registered, in many instances this is not the country inwhich the product has been produced. However, that information is disclosed on the label of each product. We use the label information that Auer et al. (2021) collected fromcodecheck.info. Coverage is not complete and notably excludes most fruits and vegetables, EANs assigned by store managers locally, and goods that are only occasionally soldin grocery stores such as toys, clothing, or household electronics. Our measure of importstatus for each individual product is fixed over time, as obtained from codecheck.info
between October 2015 and March 2016.11 We drop products for which import status is
unknown.
Comparing columns 1 and 2 of Table A1 in Appendix A, we see that out of 69, 088
unique goods and expenditure of CHF 11.1 million, there are 8, 409 unique goods andexpenditure of CHF 4.2 million with known import status; the share of expenditure for

11 Roughly 90% of imported goods in our data are from the European Union. Our results are robust to drop-

ping imports from other origins.

7which the production location is known is approximately 38%.12,13 We further divide
products with known import status into imports and domestically produced goods incolumns 3 and 4. A similar number of unique imported and domestically produced goods
were purchased and the import share (at retail prices) of expenditures was 26.9%.
Expenditure and import shares by income group and sector. To calculate expenditure
shares and import shares by income group across each consumption category, we use twodata sets provided by the Swiss Federal Statistical Office (SFSO).
The first data set, the Swiss Household Budget Survey (HBS), reports information
about consumption expenditures by income group and consumption category for the periods 2012–14 and 2015–18 based on roughly 250 households per month randomly selected from a large and representative registry. At the lowest level of disaggregation,
there are 296 consumption categories for goods and services, such as “rice”, “pasta”, or“tickets for public transport.” The SFSO collects expenditures on these consumption categories separately for each of five income groups. We use data for the pre-appreciation period 2012–14 to construct sectoral expenditure shares for each group. While we constructthese sectoral expenditure shares by income group for each of the 296 disaggregated consumption categories, Table 1 displays expenditure shares in the aggregate and separately
for each income group, aggregated up to three sectors: groceries (matching as close as
possible our Homescan goods), non-grocery goods, and services.
The second data set contains a cross section of import shares by disaggregated productcategory, obtained by the SFSO via firm surveys published in 2016 based on informationfrom previous years. These shares, used by the SFSO to calculate a CPI for imported
goods, are available at a similar disaggregation to the ones in the HBS data. We combine
these import shares—which vary across disaggregated category—with the HBS data—
which vary across disaggregated category and income group—to construct import sharesby income group within each of our three aggregate sectors. To do so, we assume thatdifferent income groups have common import shares within each disaggregated productcategory, an assumption we do not impose in the Homescan data since we observe theimport status of individual products. Table 1 displays the resulting import shares by

12 Many of the products for which we do not observe import status appear in the Homescan data for only ashort period of time. If we keep only those products that were purchased at least once per year between
2013 and 2016, the share of expenditure on goods with known origin is 47% instead of the 38% we observein our baseline sample.
13 One concern might be that expenditure on products for which we do not observe import status is correlatedwith household income. However, in Table A3 in Appendix A we show that household income is not
significantly correlated with the household’s share of expenditure in 2014 on products for which we do not
observe import status.

8

Table 1: Expenditure and import shares by income group and sector
Expenditure shares
Annual income– 60,252
60,252 – 88,032
88,032 – 119,736
119,736 – 164,244
164,244 –All

Grocery
20.1
18.6
18.0
17.1
15.1
17.2

Other goods
18.5
21.6
23.4
24.3
25.6
23.5

Services
61.4
59.8
58.6
58.6
59.3
59.3

Import shares
Grocery
36.6
37.2
36.6
37.4
40.2
37.9

Other goods
66.9
71.1
72.6
74.7
75.3
73.3

Services
2.2
3.3
3.6
4.2
5.1
4.0

All
21.1
24.2
25.7
27.0
28.3
26.1

Notes: Expenditure shares by income range and sector—aggregated to groceries, other non-grocery goods, and services—are fromSFSO using the years 2012–14. Import shares are constructed from import shares in disaggregated product categories and expenditure
shares by income across these categories. The final row represents the value of each column across all households and the final column
represents the import share of each income group across all sectors.

income group, by aggregate sector, and by income group × aggregate sector.14
Currency of invoicing of import prices at the border. Our instrument in Section 4 exploits variation across imported goods in the invoicing currency of prices at the border.
We match individual barcode products in the Homescan data to groups of imported products at the border (border groups) and measure the share of imported products in each border group in 2014 that are denominated in EUR (out of those denominated in either EUR
or CHF), using information from the goods-level survey underlying the calculation of theofficial Swiss import price index. For additional information, see Auer et al. (2021).

2.2

Stylized facts

In this section we present our five stylized facts (SFs), indicating in brackets for each fact
the data set that we use to calculate it. Facts 2–5 use Homescan rather than SFSO data
because the SFSO data are not available at annual frequency. In Appendix A we provide
additional information.
SF 1 (SFSO): Import shares before the 2015 CHF appreciation were higher among higherincome households.
The right-most column of Table 1 displays the aggregate import share—across all consumption categories—for each of the five income groups in the SFSO data (for the 2012–14
period). Higher-income households had higher aggregate import shares in Switzerland,with the share rising monotonically from 21% to 28% between the bottom and top income
14 The aggregate import share for groceries in the SFSO sample (37.9%) is higher than in the Homescan data

(26.9%). In Appendix A, we show that this is due to expenditures in the SFSO data being comparatively
concentrated in categories with high import shares. Applying common expenditure weights across categories in the SFSO and Homescan data yields more similar aggregate import shares.

9

Figure 2: Aggregate import responsiveness and heterogeneity across incomes in Homescan data

Notes: Import shares by year aggregated across all households (All), households with incomes below our sample median (Low income), and households with income above our sample median (High income). Point estimates and ten percent confidence intervals
for each income group and year are calculated by regressing separately across household h within the low-income group and the
XhM
on a constant, weighing h by XhM + XhD and clustering by income quantile (of which there are
high-income group 100 × X +hM XhD
fifty).

groups in the SFSO data. This pattern is accounted for by two relationships. First, the import share was much higher for non-grocery goods (across all income groups) than forgroceries or services, and higher-income households spent a higher share of their incomein this sector. Second, higher-income households had a higher import share within the
non-grocery goods aggregate sector and, to a lesser extent, within services.15
On the other hand, import shares within groceries were not strongly correlated withincome. This is evident in the SFSO data from Table 1. The same (weak) relationshipholds within our product-level Homescan data, as shown in Table A6 in Appendix B.1.
SF 2 (Homescan): The import share increased following the 2015 CHF appreciation.
The aggregate import share in the Homescan data increased from 26.9% to 27.5% between 2014 and 2015, as shown in Figure 2. To show that this occurred within individual households—rather than from a change in the composition of expenditures acrosshouseholds—we regress each household’s import share of expenditure in each year on
household effects and year effects, excluding the year 2014. These year effects identify
the change, within households, in the import share of expenditures between each yearand 2014. We find no economically or statistically significant differences between 2013
and 2014. On the other hand, within households the import share was higher in 2015
than it was in 2014 and continues increasing into 2016; see Figure A1 in Appendix B.1,
which reports the rise in year effects estimated separately over all monthly time horizons
within the year (we define horizon j as the first j months in year t and in 2014).
SF 3 (Homescan): Import shares increased less for higher-income households following the 2015 CHF appreciation.
15 This is largely because high-income groups have higher budget shares on cars and cars in Switzerland tend

to be imported.

10

Table 2: Heterogeneous expenditure switching towards importslog(Income)High income

Income 2013(1)
-0.472∗[0.266](2)-0.489∗[0.265](3)-0.496∗[0.261](4)-0.213[0.288](5)-0.179[0.271](6)-0.184[0.278]

Income 2015

-0.727∗∗[0.272]-0.813∗∗∗[0.279]-0.835∗∗∗[0.291]-0.698∗∗[0.293]-0.750∗∗[0.316]-0.778∗∗[0.325]

Income 2016

-0.953∗∗∗[0.321]11630-0.970∗∗∗[0.339]11630
X-1.002∗∗∗[0.336]11630
X
X-0.383[0.382]11630-0.284[0.424]11630
X-0.327[0.433]11630
X
X

Observations
Control size
All controlshiNotes: Results of estimating XhMt /(XhMt + XhDt ) = FEt + FEh + ∑y6=2014 Iy=t β t Inch + [ζ t0 Kh ] + ε ht , where XhMt and XhDt are household h’s expenditure on imports and domestic goods in year t; FEt and FEh are year and household fixed effects; Inch is either the logarithm ofhousehold income (columns 1–3) or an indicator that equals one if HH income is greater than the median in our sample of 57, 647 CHF(columns 4–6); Income y displays the coefficient on β y . In columns 2 and 5, we control for HH size interacted with year. In columns 3
and 6 we additionally include an indicator for whether there is a child under 10 and and an indicator if everyone in the HH is older
than 70, each interacted with year. Robust standard errors are clustered by income quantile (of which there are fifty) and observations
are weighted by the product of the number of households in the income quantile and the household’s share of expenditure in 2014
within its income quantile. *p<.1; **p<.05; ***p<.01

Figure 2 displays the import share by year separately for high- and low-income households (those with annual incomes above and below our sample median of approximately
57, 600 CHF).16 Between 2014 and 2015 the import share of low-income households increased more than that of high-income households. The difference between the importshares of low- and high-income households expanded from approximately 0.5 to 1.1 percentage points between 2014 and 2015. This gap rose further to 1.2 percentage points
in 2016. Figure 2 shows no evidence of pre-trends in the difference between low- andhigh-income import shares.
This greater increase in import shares among low-income households occurred within
individual households, rather than from a change in the composition of expenditures
across households. To show this, we estimate the differential change across householdincomes in the import share of expenditures between each year and 2014 at the household
level, controlling for household fixed effects. To measure income we use either the log ofhousehold income or an indicator for household incomes above the median.
Table 2 shows that import shares increased substantially less for high- than low-income
households after the exchange rate appreciation. For example, a household with an income three times than that of another experienced a roughly 0.7 percentage point smaller
16 The higher import share for low-income households in 2014 displayed in Figure 2 appears inconsistent with

SF 1. However, the difference is not statistically significant, as revealed by the wide confidence in the figure
and the results in Table A6.

11increase in its import share between 2014 and 2015. This is not a continuation of preexisting trends: the coefficients in Table 2 indicate that the gap between the import sharesof low- and high-income households did not rise between 2013 and 2014 (see the first row
of columns 1 and 4) before rising between 2014 and 2015. Changes between 2014 and2015 also do not appear to be reversion to the mean: the coefficient in row 1 of column
4 is insignificantly different from zero and the coefficient in row 1 of column 1, whilemarginally significant, is much smaller than in row 2. These results are robust to including progressively more household-level controls interacted with year; see columns 2, 3, 5,
and 6.
SF 4 (Homescan): The price of imported relative to domestic goods fell following the2015 CHF appreciation. Neither import nor domestic price changes varied systematically with household income.
Regressing individual product prices on product fixed effects and month fixed effects(omitting a fixed effect for the month preceding the CHF appreciation) separately forimports and domestic goods, we find that import prices fell by approximately 2% relative
to domestic prices following the appreciation (averaging the change between December
2014 and each month in 2015); see Figure 1 in the Introduction.
In Appendix B.1, we run a related regression that separates prices paid for each product by household income. We find no differential changes in import or domestic prices
across income, either economically or statistically; see Figure A2 in Appendix B.1.17 Thispattern is robust to further disaggregating prices by region in Switzerland and including region fixed effects in the regression. This implies that the pattern of heterogeneouschanges in import shares across households with different incomes described in SF 3 is
not driven by lower-income households facing greater declines in relative import prices.
SF 5 (Homescan): The dispersion of price changes across goods was greater between
2014–15 than between 2013–14 and than between 2015–16, especially within the set ofimported goods.
Table 3 displays the standard deviation across barcode products of annual log pricechanges within the set of imported goods, domestic goods, and all goods between years
t and t + 1 for t = 2013, 2014, and 2015. The standard deviation of log price changes rosefrom 5.8% to 7.6% for imported and from 4.2% to 4.8% for domestic goods between 2013–14 and 2014–15; each approximately reverts to its initial level between 2015–16. We showthat these patterns are robust to various alternative choices in Figure A7 in Appendix B.1.
17 We also find no relationship between income and the level of the price paid within individual barcode

products. Relatedly, defining products as aggregations of barcodes, Handbury (2021) finds that most of the12Table 3: Standard deviation of log price annual changes across barcode products

2013–142014–15
2015–16

Imports

Domestic

All

0.058
0.076
0.061

0.042
0.048
0.041

0.047
0.058
0.047

Notes: Expenditure-weighted standard deviation of annual log price change across barcode products between t and t + 1 for t = 2013,2014, and 2015, for imported goods (column 1), domestic goods (column 2), and all goods (column 3) .

We will show that this increase in the dispersion of price changes—together withgreater expenditure switching of lower-income households—contributes significantly tothe unequal welfare effects of the 2015 CHF appreciation.

3

Welfare impacts of price changes

Our objective is to construct a measure of the change in welfare for different households,
starting from an initial observed period, in response to factual or counterfactual changes
in income and in the prices of consumption goods. In Section 3.1 we provide sufficient
statistics for this calculation under general preferences, building on results in micro theory. In Section 3.2 we restrict these preferences to a particular parametric form, which weuse in the following sections to estimate differences in elasticities of substitution acrosshouseholds and to perform our quantitative applications.

3.1

General formulation

Household h’s preferences over N consumption goods, indexed by ζ (taste shifters), canbe represented by the expenditure function eh (p, u; ζ ), which indicates the minimum costof achieving utility u given a vector of prices p. The associated budget share on good
i is denoted by bhi (p, u; ζ ), which by Shephard’s lemma equals ∂ log eh (p, u; ζ )/∂ log pi .
Given income I (which we assume is equal to expenditures), the indirect utility function
is vh (p, I; ζ ).
We consider a change in household h’s income from Iht0 to Iht1 , prices, from pht0 to
pht1 , and taste shifters from ζ ht0 to ζ ht1 . Our welfare measure is the compensated variation
evaluated at initial preferences, CVh , which is implicitly defined byvh (pht0 , Iht0 ; ζ ht0 ) = vh (pht1 , e−CVh Iht1 ; ζ ht0 ).
variation in prices paid across incomes is accounted for by differences in products purchased.

13

In words, CVh is the reduction in income (in logs) under the final budget set that makes
the household with initial preferences equally well-off as under the initial budget set.
Household h is better off under the final than initial budget set if and only if CVh > 0.
We can express CVh using the expenditure function as!
eh pht1 , uht0 ; ζ ht0
CVh = log
eh pht0 , uht0 ; ζ ht0(1)


where the second equality uses the fact that eh pht , vh (pht , Iht ; ζ th0 ); ζ ht0 = Iht and whereuht ≡ vh (pht , Iht ; ζ ht ) represents utility achieved under the time t budget set and preferences. Welfare changes equal the change in household nominal income deflated by
the change in the expenditure function in response to changes in prices, evaluated along
the initial indifference curve. The deflator is evaluated at the initial indifference curve
because, by the definition of CVh , the income compensation it receives at t1 leaves thehousehold on that indifference curve.
To understand what one needs to know in order to construct the price deflator in (1),consider any smooth path of prices from pht0 to pht1 , where t indexes “time” (or, moregenerally, increments along which prices change between two points t0 and t1 ). Using
Shephard’s lemma, (1) can be expressed as (see Lemma 1 in Baqaee and Burstein, 2023)

!


Iht1
eh pht1 , vh (pht1 , Iht1 ; ζ th0 ); ζ th0
 = log

− log
Iht0
eh pht1 , vh (pht0 , Iht0 ; ζ th0 ); ζ ht0
CVh = log

Iht1
Iht0



−

Z t1

CV
bhi
(pht )∑
t0id log piht
dt,
dt

(2)

CV ( p ) ≡ b ( p , u ; ζ ) represents household h’s budget share on good i atwhere bhihhi
h ht0 ht0
prices ph along its initial indifference curve. Equation (2) implies that welfare changes fora consumer with non-homothetic preferences that are subject to taste shocks are identicalto welfare changes for a fictional consumer with homothetic and stable preferences withCV ( p ).18
budget shares as a function of prices given by bhi
hDiscussion. Equations (1) and (2) hold globally—for changes in prices and incomes ofany size. According to equation (2), in order to measure CV (for given price changes) weCV ( p ). Given
only need to know compensated budget shares as a function of prices, bhi
ht
the path of prices from t0 to t1 , these budget shares can be constructed from initial budget
CV ( p ), and cross-price elasticities between all goods along the initial indiffershares, bhi
ht0
ence curve. Given these cross-price elasticities, measuring CVh does not require income

18 That is, bCV ( p ) corresponds to the budget shares of a fictional consumer with homothetic preferences rephi
resented by the expenditure function eCVh ( p, u ) = eh ( p, u ht0 ; ζ t0 ) u.

14

elasticities or taste shifters.19 However, in estimating these cross-price elasticities, shifts indemand induced by income effects and taste shocks cannot be ignored, as we discuss in
Section 4.
In our quantification of the welfare impacts of factual or counterfactual changes inprices, we directly measure initial budget shares over consumption goods in our Swissdata. We specify particular preferences to estimate cross-price elasticities along the initial
indifference curve using the price changes induced by the 2015 CHF appreciation.

3.2

Non-homothetic CES preferences

In what follows, we restrict the general setup of Section 3.1 by imposing non-homothetic
CES preferences. There are multiple sectors, indexed by s, and within each sector there is a
fixed set of goods, indexed by i ∈ I(s), some imported and some produced domestically.
The expenditure function is given by"eh (pht , u; ζ ht ) = f h (u)∑ ζ hst u# 1
γs( Phst )

1− ρ

1− ρ

(3)

s





1
1− ηs ( u )Phst =  ∑ ζ hit uγi ( phit )1−ηs (u) (4)i ∈I(s)where f h (·) > 0 and ρ, ηs (·) ∈ [0, 1) ∪ (1, ∞).20 By Shephard’s lemma, the budget shareof any good i ∈ I(s) isγbhit =1−η (uht )ζ hit uhti phit sγ 0 1−ηs (uht )∑i0 ∈I(s) ζ hi0 t uhti phi0 t

× bhst(5)where bhst ≡ ∑i∈I(s) bhit is the share of sector s in h’s budget at time t, given byγbhst =1− ρζ hst uhts Phst
γ0

1− ρ

∑s0 ζ hs0 t uhts Phs0 t.

(6)

19 If we used the equivalent (rather than compensating) variation under final (rather than initial) preferences,then computing welfare changes requires budget shares as a function of prices along the final (rather thaninitial) indifference curve. Since in our applications we consider the welfare implications for Swiss consumers of counterfactual price changes starting in 2014, it is more convenient to focus on CV (which requires estimates of price elasticities in 2014) rather than EV (which requires budget shares and estimates of
price elasticities in an unobserved initial period such as autarky).
20 These preferences reduce to nested homothetic CES if, for example, η ( u ) is independent of u, γ = γ = 0ssifor all i and s, and f h0 (u) > 0.

15

As described in detail below, in mapping our model to the data we consider three aggregate sectors s listed in Table 1. Within each sector we either map each i to a homothetic
aggregator across domestic products and a homothetic aggregator across imported products (we do not introduce notation for these aggregators to simplify presentation) or we
map each i to individual barcode products. In the first approach, ηs (u) is the elasticity of
substitution between the aggregate domestic good and the aggregate imported good in
sector s. In the second approach, ηs (u) is the elasticity of substitution between any pair ofbarcode products in sector s, irrespective of import status.
CV ( p ) are obtained by fixing utility at
Welfare changes. Compensated budget shares bhihuht0 and tastes at ζ hit0 and ζ hst0 . We express compensated budget shares as a simple function of initial expenditure shares, initial elasticities of substitution, and changes in prices:CVbhi(ph ) = bhit0 ×





pbhi
Pbhs

1−ηhst

0

×

1− ρ
Pbhs
1− ρ
∑s0 bhs0 t0 Pbhs0



bhit0
( pbhi )1−ηhst0 bi ∈I(s) hst0

Pbhs ≡  ∑11−ηhst

(7)

0

(8)

where xb ≡ x/xt0 for any x; ρ is the elasticity of substitution along the initial indifference
curve between sectors, which we assume is common across all households and constant;and ηhst0 is the elasticity of substitution along the initial indifference curve for household
h between goods within sector s.
Given compensated budget shares, the expression for welfare changes in the general
setup, (2), simplifies to 
CVh = log b
Ih −

1
log
1−ρ

"



∑ bhst0 Pbhs

1− ρ

#
(9)

s

where Pbhs is defined by equation (8).
We use (9) to construct changes in welfare in response to factual and counterfactual
income and price changes. Constructing CVh for household h requires the value of theelasticity of substitution between sectors, ρ, expenditure shares across sectors in the initial period, bhst , income changes, b
Ih , and sectoral price changes Pbhs . Constructing Pbhs
0in equation (8) for household h requires expenditure shares within sector s in the initialperiod, bhit0 , and the elasticity of substitution in the initial period t0 , ηhst0 .

16

To a second-order approximation, and setting ρ → 1, equation (9) can be expressed as
h
i
h
i 1
 

CVh ≈ log b
Ih − Ebht log Pb + ∑ bhst0 ηhst0 − 1 Varbht |s log Pb
0
0
2 s
|
{z
} |
{z
}
First-order effect(10)

Expenditure-switching effecthiwhere Ebht log Pb is the budget-share weighted average of log price changes and whereh 0 i
Varbht |s log Pb is the budget-share weighted variance of log price changes within sector0s; see Baqaee and Burstein (2023). The approximation error in expression (10) vanishes
as price changes become smaller and as ηhst0 → 1. The literature on the unequal effects of price changes has largely focused on the first-order effects in equation (10). The
expenditure-switching effect, which is the focus of our paper, raises welfare if the elasticity of substitution ηhst0 is greater than one, and is increasing in ηhst0 . That is, households
that are more price sensitive benefit more from volatility in prices (or lose less if ηhst0 < 1).
Unequal expenditure switching. Here, we provide two special cases that highlight theimportance of differences in elasticities, ηh0 st0 − ηhst0 , for differences in CVh0 and CVh . In
both cases, we set ρ → 1.
First, consider two households with common expenditure shares in the initial period
and arbitrary changes in product prices. To a second-order approximation, the differencein the expenditure switching effect between these households is
h
i

1
b
0
log
P
b
η
−
η
Var
hst0
hst0
h st0
bht0 |s2∑s(11)

which depends on the difference in their elasticities of substitution in the initial period,
ηh0 st0 − ηhst0 . Conditional on this difference, the levels of these elasticities do not matter toa second-order approximation. It is precisely this difference in elasticities that we estimate
in Section 4.21
Second, consider two households with (potentially) different expenditure shares within
sectors and assume that the distribution of log price changes, log pbhit , in each sector is
normal with mean µs and standard deviation σs . In this case, equation (10) is exact. Moreover, if expenditure shares across sectors are common across households, then the differ21 Allowing for differences in initial budget shares, the differences in the expenditure-switching effect includes

the additional term
h
i
h
io
n
1
b
b
Var
log
P
η
−
1
b
Var
log
P
−
b
0
0
hst0
h st0
h st0
bh 0 t | s
bht0 |s2∑0sThis additional term depends on the level of the elasticity. However, since the differences in price variancesacross households is small in our quantitative application, this additional term is small.

17

ence in theswitching effect between them is given by equation (11), whereh expenditurei
Varbht |s log Pb is simply σs2 . Conditional on differences in ηh0 st0 − ηhst0 , the levels of these0elasticities do not matter, now globally.
Discussion of preferences. The non-homothetic CES preferences we consider are general
in a number of ways. First, they allow for non-unitary income elasticities that vary acrossgoods within sectors as can be seen in equation (5), driven by differences in γi acrossgoods and the dependence of price elasticities on u, and also across sectors as can be seenin equation (6). As shown in equation (2) and discussed in Section 3.1 in the generalformulation, income elasticities play no role in the construction of the CV conditionalon knowing initial expenditure shares and compensated cross-price elasticities. Second,
these preferences allow for elasticities of substitution that vary across households as afunction of utility uh , as in Fally (2022).22 As shown in equation (9), calculating CVhrequires values for these elasticities of substitution in the initial period.
Contrary to this generality, these preferences impose strong restrictions. Elasticities
of substitution are constant along any indifference curve as in standard CES models. We
make this assumption for three reasons. First, we estimate these elasticities of substitution leveraging the 2015 Swiss franc appreciation, which does not contain sufficient pricevariation to estimate them globally. Second, this restriction has an appealing theoreticalproperty: it implies that the integral over prices in equation (2) simplifies substantially, as
shown in equation (9). It additionally implies that compensated budget shares in equations (7) and (8) and the CV in equation (9) for a particular household are identical tothose in a model in which the household has homothetic and stable CES preferences withhousehold-specific, exogenously given, and constant demand shifters and elasticities.23
Third, this restriction implies that only a small subset of preference parameters are required for measuring CV, as opposed to other demand systems, e.g. the Almost Ideal
Demand System, in which the same parameters control both income and cross-price elasticities.
The other strong restriction we impose is that for any household there is a single elasticity, ρ, that shapes substitution between sectors and a single elasticity, ηhst , that shapes
22 Fally (2022) establishes sufficient conditions for the rationalization of non-homothetic CES demand whenthe elasticity of substitution is a decreasing function of u, which is the empirically relevant case in ourdata. In Appendix C we show—under certain assumptions—that these conditions are satisfied under theparameterization of η (u) that we assume to derive our main estimating equation. We also describe numerical simulations for which the expenditure function is monotonically increasing in u for a wide range ofparameters.
23 It is standard to calculate changes in price indices across households imposing homothetic CES preferenceswith demand shifters and elasticities that vary across households but are fixed in the counterfactuals (see,e.g., Handbury 2021). Our results show that this is equivalent to calculating changes in the welfare-relevant
deflator when preferences are generalized non-homothetic CES.

18

patterns of substitution between goods within sector s. This dramatically reduces the dimensionality of the problem. This formulation is equivalent to one with additional nests(e.g. product categories) under the assumption that the elasticity of substitution withinnests is equal to the one between nests.

4

Elasticities of substitution and income

In this section we estimate differences in compensated price elasticities across incomesusing the Homescan data, where we observe household-product-specific expenditure
shares and prices.

4.1

Estimating equation

To estimate how elasticities of substitution vary with income, we must take into accountthat changes over time in budget shares reflect not only price changes but also income
effects and demand shifters. For any continuing good, differentiating equation (5) at t0
yields∂ηsd log bhit = d log ζ hit + γi −u log phit0∂uh ht0
d log uht + (1 − ηhst0 )d log phit + ψhst (12)
γ 0 1− η ( u )where ψhst ≡ d log bhst ∑i0 ∈I(s) ζ hi0 t uhti phi0 t s ht and all derivatives (in the previous
and subsequent equations) are evaluated at t0 . Differentiating Iht = eh (pht , u; ζ ht ),d log uht =∂ log eh∂ log uh

 −1



I
× d log ht − ε̄ ht
Pht


(13)

where d log( Iht /Pht ) is the change in income deflated by a household-specific weighted
average of price changes across goods in all sectors d log Pht ≡ ∑i bhit0 d log phit , and ε̄ ht ≡∑i ∂ log eh ∂ζ hi dζ hit is the shift in the expenditure function due to taste shifters; see
Appendix C for derivations. We refer to d log( Iht /Pht ) as the change in real income forhousehold h. Substituting (13) into (12) yields
d log bhit =∂ log eh∂ log uh

 −1



∂ηs
× γi −
log phit0∂ log uh

+ d log ζ hit + (1 − ηhst0 )d log phit + ψhstI× d log ht − ε̄ ht
Pht


(14)

To estimate how elasticities of substitution vary with initial income, we impose two
19

restrictions (in Appendix C we provide a cardinalization of the utility function that microfounds these two restrictions). These restrictions play no role for our counterfactual
welfare calculations conditional on estimates of elasticities of substitution; we impose
these restrictions to facilitate the estimation of these elasticities. First, we assume thathousehold h’s income elasticity for good i at t0 , ∂log bhit /∂ log Ih , can be expressed as thesum of a good i-specific term that is common for all households, which we denote by κi ,and a household-sector-specific term. This assumption holds if the term multiplying thechange in real income in expression (14) evaluated at t0 can be written as∂ log eh∂ log uh

 −1



∂ηs
× γi −
log phit0∂ log uh= κi + κhs(15)

Second, we assume a log-linear relation between the elasticity of substitution in sector s
and household income in the initial period,
ηhst0 ≡ η̄s + ηs log Iht0 .

(16)

If ηs < 0, then a higher-income household is less price sensitive in sector s at t0 .
Under these two additional restrictions, equation (14) can be expressed asd log bhit = νhit + κi d log

Iht
Pht





+ 1 − η̄s − ηs log( Iht0 ) d log phit + ψehst .

(17)

The first term, νhit ≡ d log ζ hit − κi ε̄ ht , corresponds to household h’s demand shifter forgood i due to taste shocks. The second term captures the interaction between the goodi-specific component of the income elasticity and the change in real income for householdh, giving rise to a demand shifter for good i due to income effects. The third term corresponds to the compensated price elasticity for good i in the initial period interacted withehst , groups all factors that vary at thethe change in the price of good i. The last term, ψsector × household level.24
We can decompose the demand shifter νhit —without loss of generality—into the component of the demand shock for good i that is common across all households, a demand
shock for imports that varies freely across households, and a household-good-specificf hst I M + νehit , where I M is an indicatordeviation from these. Specifically, νhit ≡ νit + FEii
24 Setting changes in income, tastes, and prices of goods j 6 = i equal to zero, equation (17) resembles the fa-

miliar Slutsky equation relating Marshallian, Hicksian, and income elasticities. Our baseline approach toestimating differences in Hicksian price elasticities does not require estimating income elasticities for eachgood using cross-sectional data. In Appendix B.2 we consider an alternative procedure that relaxes restriction (15) but requires first estimating income elasticities in the cross section under additional assumptions.

20

variable that equals one if good i is imported. This yields our baseline estimating equation
 
Iht
M
− ηs log( Iht0 )d log phit + ι hit .
(18)
d log bhit = FEit + FEhst + κi d log
Pht
In equation (18), the product-fixed effect FEit is the sum of the average product-specificdemand shock across households, νit , and the common impact of the average price changeM
f hst I M is afor product i across households, (1 − η̄s )d log pit ; the term FEhst≡ ψhst + FEihousehold × import status fixed effect; and finally, the term ι hit ≡ ν̃hit + (1 − η̄s )(d log phit −d log pit ) is a residual that includes both the household’s demand-shock deviation for
product i (relative to the average across households and, if i is imported, the household’s average demand shock for imported goods) as well as the common effect of thehousehold-specific deviation in the change in product i’s price relative to its averagechange across households.
We estimate variation in elasticities of substitution across households, ηs , using equation (18) in two different ways leveraging distinct sources of variation. In our first approach, we use variation in changes in import relative to domestic expenditures acrosshigher- and lower-income households, similar to the variation in SF 3. In our second approach, we use variation in changes in expenditures across individual barcode products
and variation in product price changes across aggregations of higher- and lower-income
households. The advantages of the first approach are simplicity, the ability to estimate
equation (18) at the household level, and the straightforward connection to SF 3. We view
this as a first pass. The benefit of the second approach is that it substantially relaxes ouridentification assumption: it is valid in the presence of entry and exit of products andin the presence of import demand shocks that vary systematically with income (which
we cannot a priori rule out, even though the 2015 CHF appreciation was triggered by apolicy response to foreign events and took place in the context of a stable Swiss economy both in terms of aggregates and nominal income inequality). In both approaches,
we estimate equation (18) taking differences between 2014 and 2015. Even though these
two approaches leverage entirely distinct sources of variation to identify ηs , they yieldremarkably similar results.

4.2

Approach 1: Import and domestic expenditures by household

In our first approach, we assume that there are only two goods within groceries: an imported good i = M and a domestic good i = D.25 In this case, whereas we can control
25 To map this first approach to our data (in which there are multiple imported and domestic goods), we

assume that each of the two goods is itself a stable homothetic aggregator across a fixed set of imported and21

for an aggregate import demand shock (contained in FEit in equation 18), we cannot
control for a household-specific import demand shock, since there is only one imported
Mgood. Hence, FEhst
reduces to a household effect. Since there are only two goods, wetake differences across the imported and domestic goods and, since there are only twotime periods, we also replace the time effect with a constant and estimate

d log

bhMt
bhDt





= α + κd log

Iht
Pht





− ηs log( Iht0 )d log

p Mt
p Dt



+ ι ht(19)

Here, α, κ, and ι ht all represent differences of the parameters in equation (18) across imported and domestic goods: α ≡ FE Mt − FEDt , κ ≡ κ M − κ D , and ι ht ≡ ι hMt − ι hDt .
We measure bhDt and bhMt as the expenditure shares on domestic and imported goods
within each individual household. The price changes for imported and domestic goods
are measured as weighted averages of annual changes in national prices of products
weighted by expenditures per product across all consumers in 2014, separately for imports and domestic goods. By using a single national relative import price change, ourestimating equation in approach 1 is very similar to that used in columns 1–3 of Table 2,
where we documented SF 3. We measure household h’s inflation rate (across all sectors),
d log Pht , using disaggregated price data in the CPI as measured by the SFSO (these pricechanges are common across households) and income group-specific expenditure sharesacross these disaggregated categories. We measure annual changes in nominal income
by household using a Swiss household panel on income (FORS); details are available inAppendix A.
Identification. We identify differences in elasticities across household incomes from changes
in import expenditure shares that are correlated with household income. We do not instrument for price changes since we have only one value of d log ( p Mt /p Dt ). The identification assumption estimating regression (19) using OLS is that household-specific importdemand shock deviations from the aggregate import demand shock between 2014 and2015 are uncorrelated across household incomes in 2014. We relax this restriction in Approach 2.
Results. Whereas we estimate regression (19) at the household level, we cluster standard
errors by 50 income bins defined by quantiles of the household income distribution in
our sample in 2014. We do so to allow for the possibility of correlated imported demand
shocks across households in the same income bin; however, as stated above, we continue
domestic varieties. In constructing import and domestic prices within groceries to use in the estimation,
we use a first-order approximation of the expenditure function of any homothetic aggregator within each
import status.

22

Table 4: Estimation of ηs in Approach 1 using equation (19)log( Iht0 )d log( p Mt /p Dt )Constant
Observations
Baseline
No winsorizing
Winsorize 5%
Unweighted
Expenditure weight
No income effects
HH size(1)2.189∗∗∗[0.554](2)2.207∗∗∗[0.567](3)
1.838∗∗∗[0.478](4)
1.981∗∗∗[0.618](5)2.041∗∗∗[0.672](6)
2.172∗∗∗[0.540](7)2.361∗∗∗[0.591]0.553∗∗∗[0.129]2901
X

0.557∗∗∗[0.132]2901

0.469∗∗∗[0.110]2901

0.492∗∗∗[0.144]2901

0.516∗∗∗[0.157]2901

0.550∗∗∗[0.126]2901

0.581∗∗∗[0.131]
2901

X
X
X
X
X
X

Notes: The estimating equation is (19). We report −ηs and α. Observations are households and the dependent variable is the log
change in import-relative-to-domestic expenditures across all Homescan products between 2014 and 2015. In our baseline in column
1, robust standard errors are clustered by 50 household bins according to household income in 2014, observations are weighted by the
product of the number of households in each of the 50 bins and the share of each household’s expenditures among households withinthat bin, and we winsorize the dependent variable at the first percentile in both tails. Columns 2–7 each make one change relative tothe baseline in column 1. In column 2 we do not winsorize, in column 3 we instead winsorize at the 5th percentile, in column 4 we do
not weigh observations, in column 5 instead weigh observations by expenditures in 2014, in column 6 we omit changes in real income
from the regression specification, and in column 7 we control for household size. *p<.1; **p<.05; ***p<.01

to require that import demand shocks between 2014 and 2015 across income bins are notsystematically related to income. We weigh observations (households) by the product of
the number of households in each of the 50 bins and the share of household h’s expenditures among households within that bin and winsorize the dependent variable at the first
percentile in both tails. We revisit each of these choices in robustness.
The first column of Table 4 displays our baseline results. In all tables we report theestimated coefficient, which is −ηs . We find ηs = −2.19, which implies a substantiallylower elasticity of substitution for higher-income households. For example, the elasticity
of substitution of a household with 2014 income of 60,000 CHF is approximately 2.4 (≈2.19 × log 3) lower than a household with income of 20,000 CHF. This gap shapes the
non-linear effects of import price changes in our quantification.

4.3

Approach 2: Product-level expenditures by income group

In our second approach, each i is an individual barcode product.26 Given the granularityof this definition of a product i relative to our first approach, the household-productlevel data are sparse. Hence, to estimate equation (18) we aggregate product-level data
across groups of households, as is standard in demand estimation. Specifically, we group
26 Our baseline sample is the set of products that were purchased at least once per month (nationally) in the

year-and-a-half before and after the CHF appreciation.

23

households into 50 income bins defined by quantiles of the household income distribution
in our sample in 2014; h ∈ {1, ..., 50} now denotes the income bin. Within each bin, we
take the median value of 2014 income and the median annual change in nominal income
between 2014 and 2015 across individual households. We measure inflation and changes
in income at the household level as described above.
In our baseline we use a common price change across households at the product level,d log phit = d log pit . In robustness we consider a more disaggregated household aggregation that incorporates spatial variation; in this case, we measure a common d log phit for
all households within a one-digit zip code and allow these price changes to vary acrossspace.
Identification. In our second approach, we identify differences in elasticities across households from differences across the income distribution in the relationship between changes
in expenditure shares and prices at the barcode product level. In this case, we can explicitly incorporate import demand shocks that are specific to each of the fifty household
aggregates.
There are two remaining endogeneity concerns. The first is measurement error, which
generates attenuation bias. The second is an economic argument for endogeneity. Suppose that high-income households are less price sensitive, consistent with our findingsin Approach 1. Consider a product that faces demand shocks that are higher for higherincome households (we control for the average demand shock across households, so only
deviations from the average remain in the residual). In response, the firm will face a moreinelastic demand and will, therefore, charge a higher markup. Hence, there is a positive correlation between household-specific demand shock deviations (i.e., the residual)
and the interaction between product-specific price changes and household initial income(the independent variable of interest). This implies that under the hypothesis that highincome households are less price sensitive, OLS is upward biased.
We address these concerns by constructing an instrument using an interaction between a product-specific cost shifter and initial household income. Our cost shifter exploits variation across imported goods in the invoicing currency of prices at the border.
As described in Section 2.1, we match products to border groups and measure the shareof imported products in each border group that are denominated in EUR (out of thosedenominated in either EUR or CHF) in 2014, which we denote by shareit0 . Because of the
stickiness of import prices at the border in their invoicing currency, Swiss retail prices ofimported goods are more responsive to the CHF appreciation if imports are denominatedin EUR rather than in CHF; see Auer et al. (2021).
Since the expected reduction in Swiss retail prices in response to the CHF apprecia24

Table 5: Estimation of ηs in Approach 2 using equation (18)log( Iht0 ) × d log pit

(1)
OLS
0.018
[0.134]log( Iht0 ) × shareit0 × IiMObservations
K-P F Stat (first stage)

95,325(2)RF-0.140∗∗[0.068]95,325(3)
2SLS1.930∗∗[0.867]

95,325
13.1

Notes: The estimating equation is (18). Observations are barcode product × household aggregates, where households are aggregatedinto 50 bins according to initial income. The dependent variable is the log change in expenditures between 2014 and 2015. Column 1reports OLS results, column 2 reports reduced-form results in which we replace log( Iht0 )d log pit with log( Iht0 )shareito IiM , and column
3 reports 2SLS results in which we instrument for log( Iht0 )d log pit with log( Iht0 )shareito IiM . Robust standard errors are two-way
clustered at the level of household income bin and, separately, the interaction between import status and the share of imported goods
denominated in EUR in the border group; observations are weighted by the product of the number of households in each aggregationand the share of expenditures among households within that aggregation on product i; and we winsorize changes in log expendituresat the first percentile (both in the right and left tails). *p<.1; **p<.05; ***p<.01

tion is greater for imported products that belong to border groups with a higher fractionof border prices invoiced in EUR, we construct our instrument as the interaction between(i) the share of imported goods in the corresponding border group that are denominatedin EUR, shareit0 , (ii) an import indicator variable, IiM , and (iii) the logarithm of initialhousehold income, log( Iht0 ). If we restrict our sample to imported goods, as we do in robustness, then the instrument is the interaction between (i) and (iii) alone: log( Iht0 )shareit0 .
In this case, we leverage the fact that the expected reduction in Swiss retail prices among
imported goods in response to the CHF appreciation is greater for those goods belonging
to border groups with a higher fraction of border prices invoiced in EUR.27
In some border groups, the number of border price observations denominated in either EUR or CHF with which to construct (i)—the share of imported goods that are denominated in EUR (out of those denominated in EUR or CHF)—is small and, therefore,
the share is unreliable. Hence, in our baseline we restrict the sample of products to thosein border groups with more than 28 border price observations in 2014 and vary this cutoff
in robustness. This leaves 35 border groups in our baseline estimation sample, 7 of whichhave no imported goods denominated in EUR (i.e., shareit0 = 0 for all products i in these
7 border groups).
Results. In our baseline, we weigh observations by the product of the number of households in each aggregation h and the share of expenditures among households within that
27 There is a large literature (see, e.g., Gopinath and Itskhoki 2022) arguing that the data on invoicing currencyof export and import prices are consistent with models in which firms’ invoicing currency choices are basedon desired pass-through to exchange rate movements. A sufficient condition for our exclusion restriction isthat heterogeneity in anticipated relative demand shocks across the income distribution between 2014 and2015 does not shape pre-shock invoicing currency choices.

25

aggregation on product i.28 In constructing changes in log expenditure shares, we winsorize changes in log expenditures at the first percentile (both in the right and left tails).
Finally, we two-way cluster standard errors at the level of household income (there are 50
such clusters) and, separately, the interaction between import status and the value of theshare of imported goods denominated in EUR in the corresponding border group (there
are 54 such clusters). We revisit each of these choices in robustness.
Table 5 displays our baseline results, focusing on the parameter of interest: ηs . The
first column reports results from estimating equation (18) using OLS, where we find an
economically small and statistically insignificant estimate. Column 2 reports results fromestimating the reduced-form specification, in which we replace the change in productprice interacted with the logarithm of initial household income with the instrument. We
find that, between 2014 and 2015, higher-income households increased their expendituresby less on imported goods within border groups with a higher share of products invoiced
in EUR (those with a larger decline in border and retail prices in response to the 2015 CHF
appreciation) conditional on real income changes, import demand shocks that vary freely
across household income groups, and other covariates. This is the expected sign of the
reduced-form relationship.
Column 3 reports the baseline version of our main empirical result, the two-stage leastsquares estimate of ηs . The first-stage coefficient is −0.073 (implying that, on average, theprice of an imported product in a border group that is entirely invoiced in EUR fell by
7.3% more than a product in a border group entirely invoiced in CHF in response to
the roughly 14% appreciation of the CHF) and the associated F statistic is 13.1.29 The
second-stage coefficient of interest, ηs = −1.93, is very similar to the estimate in our first
approach, which leverages an entirely distinct source of identification. The bias of the
OLS estimate is as expected both due to measurement error and the economic argument
described above (recall that we display the negative value of the OLS coefficient, since
this is the structural parameter of interest).

4.4

Robustness and sensitivity

Table 4 displays robustness across a range of choices in our first approach. In column
2 we do not winsorize the dependent variable; in column 3 we instead winsorize at the
fifth percentile. In column 4 we do not weigh observations and in column 5 we instead
28 This approach puts equal weight on each underlying household rather than giving a higher weight to thosehousehold aggregations with higher expenditures (since our objective is to estimate how price sensitivities
vary with income).
29 Throughout, we report the Kleibergen-Paap Wald rk F statistic when there is only one endogenous variable.

26

Table 6: Robustness of Approach 2log( Iht0 ) × shareit0 × IiM(1)-0.14∗∗[0.07](2)-0.00[0.07](3)-0.10[0.08](4)-0.14∗[0.07]

log( Iht0 ) × d log pit
Observations
Baseline
Outcome period
Imports only
Additional controls I
Additional controls II
F Stat (first stage)

95,325
X

98,65278,800

13-14

15-16

27,128

(5)

(6)

(7)

(8)

1.93∗∗[0.87]
95,325X

1.93∗∗[0.88]
27,1282.19∗∗[0.87]
95,325

2.15∗∗[0.87]
95,325

X

X
X
17.1

X

X

13.1

12.8

15.6

Notes: Column 1 replicates our baseline RF specification shown in column 2 of Table 5. Columns 2 and 3 report the same specification,
but in which the outcome variable is defined over the period 2013–14 (column 2) and 2015–16 (column 3). Column 4 displays estimatesof the RF specification on a sample restricted to imported goods alone (so that IiM = 1 for all observations). Column 5 replicates ourbaseline 2SLS specification shown in column 3 of Table 5. Column 6 displays estimates of the 2SLS specification on a sample restricted
to imported goods alone. Column 7 incorporates two additional controls interacted with year: the 2014 import share as well as the2014 expenditure share on each border group. Column 8 additionally incorporates one more control interacted with year: the 2014
average price of each individual product. In columns 5–8 we report the KP F statistic. *p<.1; **p<.05; ***p<.01

weigh by household expenditure in 2014. In column 6 we omit changes in real income
from the estimating equation.30 Finally, in column 7 we control for household size in case
it is correlated with income and elasticities vary with household size. Results are largely
robust to these choices.
The majority of our robustness exercises focus on our second approach. Most ofthese—such as incorporating spatial variation into the estimation, varying choices in theconstruction of household income, and determining whether particular income groups
drive our results—are contained in Appendix B.2. Here, we describe a small number ofsensitivity and robustness exercises, with results displayed in Table 6.
Recall from Table 2 in Section 2.2 that the gap between the import shares of lowand high-income households fell between 2013–14 and rose both between 2014–2015 and2015–2016. Changes between 2013–14 might suggest pre-existing trends that would callinto question our baseline results. Changes between 2015–16 might suggest mechanisms
generating lags in expenditure-switching responses.
Here, we begin by showing that there are no such pre-trends in Approach 2. Column 1 of Table 6 replicates our baseline reduced-form specification. Column 2 of Table 6
documents an absence of pre-existing trends in the reduced-form specification; we cannot study pre-trends in the structural specification since our instrument has no power
30 In additional sensitivity on income effects in Appendix B.2, mentioned in footnote 24, we use an alterna-

tive approach that relaxes restriction (15), but requires estimating cross-sectional income elasticities understrong assumptions. We apply this in Approach 1 and show that results are robust in Table A8.

27

before the CHF appreciation, given that the CHF-EUR exchange rate is stable between
2013–14. Whereas in our baseline we obtain a coefficient of −0.14 that is significant at
the 5% level, running the same regression but replacing changes in expenditure shares
between 2014–15 with changes between 2013–14 yields a coefficient that is three ordersof magnitude smaller and statistically insignificant; see column 2 of Table 6. We interpret
this lack of differential pre-existing trends as strengthening the structural interpretationof our baseline results.31
Another concern is that the share of imported goods in each border group that are
denominated in EUR is correlated with some other product characteristic and that thisother product characteristic is driving the differential patterns of substitution for higherand lower-income households. Here we show that controlling for additional triple interactions in which we replace the share of imported goods in the border group that are
denominated in EUR with other border group or product characteristics (the 2014 importshare of each border group, the 2014 expenditure share of each border group, and the 2014
average price of each individual product) does not substantially change our results. Column 5 of Table 6 replicates our baseline 2SLS estimate from column 3 of Table 5. Columns
7 and 8 of Table 6 show that including these additional controls has little effect on results.
Finally, in our baseline, we include both imported and domestically produced goods
in our estimation sample. However, the instrumented change in price is common for
all domestic goods. Columns 4 and 6 display reduced-form and 2SLS results when we
restrict the sample to imports.32 Results are largely unchanged, although we only have
26 clusters in one dimension.

4.5

Estimating η̄sNeither of the two approaches in Section 4 identify the intercept η̄s defined in equation(16). However, under stronger assumptions they can be adjusted to do so; see Appendix
B.3 for details.
In Approach 1, we can identify η̄s if we assume that the average import demand shifterνit is zero between 2014 and 2015. This yields η̄s ≈ 26.6. In Approach 2, we can identify η̄s
31 Column 3 similarly replicates our baseline reduced-form specification using changes in expenditure shares

between 2015–16. As in the 2013–14 period, we find statistically insignificant results. However, the estimated coefficient is closer to the baseline value. This could represent evidence of dynamics in expenditureswitching responses, which we do not explore further.
32 Restricting the sample to imported goods requires replacing our household-import indicator fixed effectwith a household fixed effect, since there is no need (or possibility) to control for differential import demand
shocks across income groups. And our instrument reduces to the interaction between the log of householdincome and the share of imported goods denominated in EUR in the border group.

28

if we do not control for the average product-specific demand shock νit and, instead, moveit to the residual. This yields η̄s = 20.87. The first (second) approach implies that theelasticity of substitution is 4.92 (1.76) for a household with income of 20,000 CHF and that
this elasticity remains positive for all household incomes below approximately 190,000(50,000) CHF.
To sum up, we impose weaker assumptions estimating ηs than η̄s and our estimatesof ηs are much more similar across approaches 1 and 2 than are our estimates of η̄s . For
these reasons, in our quantitative analyses in Section 5, we present results for a range ofη̄s and show that differences in welfare across incomes do not depend crucially on thesevalues within a broad range, consistent with our analytic results in Section 3.2.

5

Quantification

In this section, we use our estimates in Section 4 to assess the role of heterogeneous expenditure switching in shaping the welfare implications—measured using equation (9)—of
factual and counterfactual changes in prices. In Section 5.1 we quantify changes in thewelfare-relevant price index for groceries using observed price changes in the Homescan
data. In Section 5.2 we consider changes in welfare in response to counterfactual changes
in import relative to domestic prices across all consumer goods.
We make the following choices in both sections. The initial period, t0 , is 2014. Differences in within-grocery elasticities of substitution across incomes, ηs = −2, match ourHomescan-based grocery estimates in Section 4. We consider households at three income
levels within the range of incomes in our sample—20,000, 60,000, and 120,000 CHF—andchoose η̄s so that the lowest elasticity of substitution across the income groups that we
consider (at 120,000 CHF) is equal to 3.

5.1

Heterogeneous effects of observed Homescan price changes

In this section we quantify changes in the welfare-relevant price index, Pbhs in equation(8), for the grocery sector in response to observed price changes of individual products in
the Homescan data between 2014 and 2015. We do not include non-groceries because weonly observe price changes at the CPI level, which is much more aggregated than in theHomescan data, where we observe price changes at the barcode level. We measure thesebarcode-specific national price changes as described in Section 4.3.33
33 To reduce the role of abnormally large price changes on the price index, we drop products with year-to-year

price ratios above 3 or below 1/3. This has almost no impact on the 2014–15 results.

29

Table 7: Welfare-relevant grocery price changes 2014–15
IncomeHeterogeneous elasticities
Elasticity 1st-order Switching Exact

Homogeneous elasticities
Elasticity 1st-order SwitchingExact

1: 20,000
2: 60,000
3: 120,000

6.6
4.4
3.0

6.6
6.6
6.6

-2.2
-2.2
-2.3

-1.1
-1.2
-1.3

-1.0
-0.6
-0.3

-2.2
-1.7
-1.6

-1.1
-1.2
-1.3

-1.0
-0.9
-0.9

Notes: This table displays changes in the welfare-relevant price index, Pbhs in equation (8), for the grocery sector in response to observed
price changes of individual products in the Homescan data between 2014 and 2015. Rows 1–3 display results for households withincomes of 20,000 CHF, 60,000 CHF, and 120,000 CHF. Columns 1–3 use heterogeneous elasticities (6.6, 4.4, and 3) whereas columns 4–
6 impose common elasticities (all set to 6.6). Columns 1 and 4 display the first-order effects, columns 2 and 5 display the second-ordereffect, and columns 3 and 6 display the exact change.

To calculate Pbhs in equation (8), we need expenditure shares and elasticities of substitution by income group in 2014. To measure expenditure shares, we divide households
into three equal-sized bins based on 2014 income: the lowest, middle, and top bins contain households with 2014 annual income of 20,000 CHF, 60,000 CHF, and 120,000 CHF.
For each bin, we calculate the expenditure share on each product and assign this expenditure share to the corresponding household; in sensitivity analysis we show that our
main results are robust to using common expenditure shares across all households. The
elasticities required to compute the price index are calculated as described above, yielding elasticities of 6.6, 4.4, and 3 for households with incomes of 20,000 CHF, 60,000 CHF,
and 120,000 CHF, respectively; in sensitivity analysis we show that our main results arerobust to varying η̄s so that the elasticity for households with incomes of 120,000 CHF
ranges between 1.5 and 5.
The left-hand panel of Table 7 contains our baseline results with heterogeneous elasticities. The first column displays the first-order welfare effect of price changes in groceries(using the second-order approximation in equation 10), which is simply the expenditureshare-weighted average of product price changes within groceries. These range from -1.1
percent for households with incomes of 20,000 CHF to -1.3 percent for households withincomes of 120,000 CHF. The second column displays the expenditure-switching welfare
effect of price changes, which is (1 − ηhst0 ) times half the expenditure-share-weighted
variance of price changes within groceries. Whereas these effects are smaller than thefirst-order terms (they range from -1.0 percent for households with incomes of 20,000
CHF to -0.3 percent for households with incomes of 120,000 CHF), their variation acrossincomes is larger. These differences in expenditure switching are driven almost entirely
by differences in elasticities; in particular, the weighted variance is very similar acrossincome groups. The third column shows the full non-linear effect, which is very similar to the sum of the first-order and expenditure-switching effects. The price change for30low-income households is -2.2 percent, which is about 50% larger than the price change
for high-income households. This gap is almost identical to the gap in the expenditureswitching effect.
Another way to see the importance of the expenditure-switching effect is to set all
elasticities to be equal. In the right-hand panel of Table 7, we display results in which
we impose the elasticity of the lowest-income households, 6.6, for all three householdgroups. The first-order effect, displayed in column 4, is obviously unchanged. However,
now the expenditure-switching effect is very similar across households, unlike in column
2; it is not identical across households because of small differences in the expenditureshare-weighted variance of price changes. Differences in the price index across income
groups, displayed in column 6, are much smaller (and of the opposite sign) than thoseunder heterogeneous elasticities reported in column 3.
In Table 7, we have focused on 2014–15. In the left-hand panel of Table A15 in Appendix D we display results for price changes the year before the CHF appreciation (2013–14). The variance of price changes between 2014–15 is one-and-a-half times the varianceof price changes between 2013–14, as implied by SF 5 above. Hence, the gap between income groups in the expenditure-switching effect is similarly one-and-a-half times larger
in 2014–15 than in 2013–14.
Sensitivity. In the right-hand panel of Table A15 in Appendix D.1 we display results
imposing common expenditure shares across households. Whereas the first-order effects are, obviously, now identical across households, the second-order effects are littlechanged from our baseline. In Table A16 in Appendix D.1 we display results for alternative levels of η̄s —so that the elasticity for households with income of 120,000 CHF ranges
between 1.5 and 5—while holding the differences in elasticities across households fixed.
Greater substitution generates larger declines in the welfare-relevant price index; however, differences between income groups are not very sensitive even for the large rangeof η̄s considered.

5.2

Heterogeneous effects of counterfactual import price changes

In this section we quantify the effect of counterfactual changes in import prices acrossall consumer goods. Our focus here on import price changes contrasts with our focus in
Section 5.1 on observed price changes between 2014 and 2015, which reflect not only the
CHF appreciation but also price changes that would have occurred in its absence. Our focus here on all consumer goods contrasts with our focus in Section 5.1 on groceries alone,where import shares do not vary systematically with income and the first-order effects of31

import price changes are mechanically very similar across households. At the aggregate
level, import shares in 2014 are higher among higher-income households, as shown in SF
1, yielding heterogeneous first-order effects of import price changes. Finally, to highlightthe non-linearities induced by expenditure switching, we consider larger import priceshocks like those induced by much larger exchange rate changes (see, e.g., Cravino andLevchenko, 2017) or a movement to autarky.
To model counterfactual price changes, we assume that the price change of any imported j = M or domestic j = D product i in any sector s is given bylog pbi = log pbj + σj ei(20)

where log pbj is the uniform component of price changes across all imported or domestic
products and σj ei is the product-level idiosyncratic component of price changes, with ei ∼N (0, 1).
Given our focus on the expenditure-side effects of foreign price shocks, we assume
that the log change in income for all households, b
Ih , is equal to the average change inthe log price of domestic goods, pbD , as in single-factor trade models without imported
intermediate inputs.34
Under these assumptions, changes in welfare in (9) are given by
CVh = −

1
log ∑ bhst01−ρsbhjst0bj∈ M,D hst0∑



pbj 1 σ2 (1−ηhst )
0
e2 j
pbD

1−ηhst ! 1−1η−hstρ
0


0




(21)

where bhjst0 /bhst0 is the share of expenditure in sector s on either imports j = M or domestic goods j = D. According to (21), a higher variance σj2 increases CVh (for ηhst0 > 1), in asimilar way that a lower log pbj does, and this effect is stronger the larger ηhst0 is. Whereas
we use equation (21) in our analysis below, we gain further intuition in the special case inwhich σj = σ and ηhst0 = ηht0 , where changes in welfare are given by
CVh = −

1log ∑ bhst01−ρs|bhMst0
bhst0



pbM
pbD
{z

1−ηhtuniform component! 1−1−η ρ 
ht00bhDst0
+
+
bhst0
}

1 2
σ (ηht0 − 1)
2
|
{z
}

(22)

idiosyncratic component

34 In estimating compensated price elasticities, we do not impose this restriction, but instead use actualchanges in retail prices by good. In our counterfactuals, if all domestic goods have a common imported
intermediate share, then differences between households in welfare changes do not depend on the value of
this share, for any given change in import to domestic prices.

32

In this case, changes in welfare are additively separable in the uniform and idiosyncraticcomponents of price changes.
We consider three sectors s: groceries, non-grocery goods, and services. For each of thethree income groups (20,000, 60,000, and 120,000 CHF), we construct import shares in eachof these aggregate sectors and expenditure shares across them using data on expendituresand import shares within highly disaggregated consumer categories in the SFSO data (seeTable 1 in Section 2.1).35 Aggregating up to three sectors has no effect on our measure ofoverall import shares by income. We impose a value of ρ very close to one, ρ = 0.99, andvary this parameter in sensitivity analysis. We choose values for ηhst0 as described above.
We quantify the impact of import price shocks, ∆ ≡ log pbM − log pbD , for different
values of ∆ > 0 ranging from ∆ = 2.2% (the size of the reduction of import prices relative
to domestic prices in 2015) to 1,000% (a movement to autarky, which is a focus of thequantitative trade literature). We begin by imposing σj2 = 0, so that only the uniform
component in equation (22) is active.
Uniform price changes within M and D. The first panel of Table 8 reports the welfare
implications for each household of import price increases of various sizes.
Higher-income groups are harmed more by import price increases for two reasons.
First, they have higher import shares, which shape the first-order effect displayed inequation (10). The import shares in 2014 are 21%, 24%, and 27% for households withincomes of 20,000, 60,000, and 120,000 CHF, respectively, as displayed in Table 1. Second,
they have lower initial elasticities of substitution, which shape the expenditure-switchingeffect.
The bottom two panels of Table 8 highlight the increasing importance of the expenditureswitching effect as the size of the change in import prices ∆ grows. The middle panel
displays the percent difference between the CV of the lowest-income household and theCV of the middle- and highest-income households. For a 10% import price increase, thewelfare of the middle- and high-income households fall by approximately 22% and 41%,
respectively, more than for the low-income household. When import prices rise by more,
the differences in welfare changes between incomes and the contribution of heterogeneous elasticities to these differences grow substantially.
To quantify the importance of the expenditure-switching effect, we consider an alternative parameterization in which we impose a common price elasticity across incomesequal to that of households with income of 20,000 CHF (which is 6.6). The bottom panel
35 In practice, in assigning import shares in each of these three sectors and expenditure shares across them forour household with income of 60,000 CHF, we use an income of 60,252 CHF instead of 60,000 CHF. This is
the cutoff separating the first and second income brackets in Table 1.

33

Table 8: Compensating variation of counterfactual import price shocks+2.2

Import price shock+10 +20 +40 +1000
σ=0

+2.2
σ>0

-0.4
-0.5
-0.6

-1.8
-2.2
-2.6

-3.2
-4.1
-5.0

-4.7
-7.0
-9.1

-5.6
-11.1
-22

-0.2
-0.4
-0.5

16
30

22
41

31
57

50
95

99
295

83
148

44
41

62
60

79
86

69
67

Annual income
1: 20,000 elasticity 6.6
2: 60,000 elasticity 4.4
3: 120,000 elasticity 3.0% difference in CV btw
income groups 2 and 1
income groups 3 and 1

Contribution of heterogeneous ηs
income groups 2 and 1
income groups 3 and 1

8
7

28
26

Notes: Percent changes are 100× the log of the relative price change. “% difference in CV btw income group j and 1” is (CVj −
homog

homog

homog

CV1 )/CV1 for income group j. “Contribution of heterogeneous elasticities” is 1 − (CVj
− CV1)/(CVj − CV1 ) where CVj
is the compensating variation of income group j in our alternative counterfactual in which elasticities are common across income
groups and set to the value for a household with income of 20,000 CHF. All columns but the last impose σj2 = 0. In the final column,
we set σj2 for j = D and j = M to match the observed increase in idiosyncratic volatilities between 2013–14 and 2014–15.

of Table 8 displays the contribution of heterogeneous elasticities (comparing heterogeneous elasticities and import shares to heterogeneous import shares alone) in shaping
differences in welfare changes for the middle- and high-income groups compared to the
low-income group.36 Differences in elasticities between the low- and high-income groups
explain only 8% (middle vs low income) and 7% (high vs low income) of the differencein welfare changes when the import price rises by 2.2%. However, when the import pricerises by 20%, differences in elasticities explain 44% and 41% of the differences in welfarechanges. The larger is the increase in import prices, the higher is the contribution of differences in elasticities to the unequal welfare changes across incomes. For a movement toautarky, the expenditure-switching effect accounts for the vast majority (79% and 86%) of
the unequal welfare effects.
Dispersed price changes within M and D. To this point in Section 5.2, we have considered the uniform component of import price shocks ∆ ≡ log pbM − log pbD imposing azero variance for idiosyncratic price changes within imported j = M and domestic goods
36 For income group j, this is simply 1 − (CV homog − CV homog ) / (CV − CV ) where CV homog is CV of income
1
j
1
j
j

group j in our alternative parameterization with homogeneous elasticities. Another way to quantify thecontribution of heterogeneous elasticities is to compare results with heterogeneity in both elasticities andimport shares to results with heterogeneity in elasticities alone. These results are very similar to thosereported in the bottom panel of Table 8.

34

Table 9: Compensating variation of a 10% import price shock

Annual income

Ratio of variance of idiosyncratic price changes
to the calibrated variance with a 2.2% shock
0
1
1.5
2
2.5
3

1: 20,000 elasticity 6.6
2: 60,000 elasticity 4.4
3: 120,000 elasticity 3.0

-1.8
-2.2
-2.6

-1.6
-2.1
-2.5

-1.5
-2
-2.4

-1.4
-1.9
-2.4

-1.3
-1.9
-2.3

-1.1
-1.8
-2.3

22
41

30
55

35
63

40
73

47
85

55
99

% difference in CV btw
income groups 2 and 1
income groups 3 and 1

Notes: All columns display results that correspond to the top two panels of the second column of Table 8 (using a 10% import price2 = σ2 = 0, we set σ2 = x × 0.0005 and σ2 = x × 0.0025 (as described in footnote 37), for values of x
shock). But instead of setting σDMDM
displayed at the top of each column. Column 1 corresponds to column 2 of Table 8.

2 = σ2 , the welfare impact due to idiosynj = D. Recall from equation (22) that if σMDcratic price changes is additively separable from the uniform component. To evaluate theoverall effect, we must calibrate σj2 .
We first consider an import price shock of size ∆ = 2.2%, which is the size of the average decline in import relative to domestic prices observed between 2014–15. Rather thansetting σj2 to the observed variance of price changes between 2014–15 (which includes
price changes that would have occurred in the absence of the import price shock), we set
it to the observed increase in the variance of price changes between 2013–14 and 2014–15.37
The final column of Table 8 shows that the welfare loss of the lowest-income household is smaller than for the middle- and highest-income households, and more than twothirds of the differences across incomes is driven by heterogeneity in ηs across households. These results contrast with the first column of Table 8 (no idiosyncratic pricechanges), where relative differences in welfare across households are smaller and mostly
driven by heterogeneous import shares. Intuitively, the price volatility associated with
the import price shock reduces its welfare costs for all households, but does so disproportionately for more elastic households.
37 To motivate why we set the counterfactual variance equal to the difference in variance between 2013–14 and2014–15, suppose that the idiosyncratic component of price changes is the sum of a component induced by
the import price shock, σ1j e1i , and a component that is orthogonal to the import price shock, σ2j e2i , wheree1i and e2i are i.i.d. and normally distributed. The sum of the two components can be written as in equation
2 + σ2 . For our counterfactual import price shocks, we set σ = 0. To assign σ for a(20), where σj2 = σ1j2j
1j2j
2 and the2.2% import price shock, we assume that the variance of price changes between 2013–14 equals σ2j
2 + σ2 . Thus, σ2 equals the variance of price changes
variance of price changes between 2014–15 equals σ1j
2j
1j
between 2014–15 minus the variance of price changes between 2013–14. Specifically, from Table 3, we obtain
2 = 0.0058 − 0.0033 = 0.0025 and σ2 = 0.0023 − 0.0018 = 0.0005.
σM
D

35

Finally, we consider a larger import price shock, of size ∆ = 10%. Since the idiosyncratic price volatility generated by such a shock is unobserved, we consider a wide rangeof volatilities. Each column in Table 9 considers a value of σj2 that is a factor x of ourcalibrated variance under the ∆ = 2.2% shock for various values of x. The first column(x = 0) corresponds to the second column of Table 8, where we set the idiosyncratic pricevariance to zero. The second column (x = 1) imposes the same idiosyncratic varianceas under the smaller, ∆ = 2.2% shock. As x increases from 0 to 3, differences in welfare between incomes grow. This growth is entirely driven by the expenditure-switchingeffect.
Sensitivity. We consider a range of robustness exercises in Appendix D.2. First, we consider import price declines rather than increases. In this case, high-income households
benefit more from the first-order effect (they have higher initial import shares) whereas
low-income households benefit more from the expenditure-switching effect (they havehigher price elasticities). If σj = 0, the expenditure-switching effect dominates for large
import price declines; it also dominates for our smallest import price decline of 2.2% if σj
is calibrated to match its observed increase in 2014–15. Second, we set ηs = −1.5, which
is at the lower end of our estimates of differences in elasticities of substitution across incomes, rather than ηs = −2. This slightly reduces differences in welfare across incomes
induced by expenditure switching. Third, we vary η̄s so that the lowest elasticity of substitution (that for the highest-income household, with income of 120, 000 CHF) is equal
to 1.5 or 5, instead of equal to 3. This leaves the differences in welfare across households
largely unchanged (except for the extreme shock to import prices that essentially resultsin autarky). Fourth, we set the elasticity of substitution between sectors to ρ = 0.2 insteadof ρ = 0.99, which does not have a strong impact on our results. Finally, we consider alternative assumptions on the value of ηs in non-grocery sectors s. Even when households
share common elasticities within the service sector we obtain very similar results.

6

Conclusions

In this paper we revisit a classic question: what are the distributional implications ofchanges in foreign prices? We focus on differential changes in costs of living across households.
Theoretically, we show that differences across households in compensating variationin response to given income and price changes are shaped by initial expenditure sharesacross products and initial compensated cross-price elasticities. Empirically, we use de-36

tailed Swiss data to document that lower-income households engaged in significantly
more expenditure switching towards imported goods in response to the 2015 Swiss franc
appreciation. Leveraging these data and imposing generalized, non-homothetic CES
preferences, we estimate substantially higher elasticities of substitution for lower-income
households.
Import price increases in Switzerland harm higher-income households more than lowerincome households both because higher-income households have higher initial importshares (the standard channel considered by the literature) and because they engage inless expenditure switching between imported and domestic goods (a channel from which
the literature has abstracted). Quantitatively, we show that for large and dispersed pricechanges, unequal expenditure switching generates substantial differences in welfare acrossthe income distribution.
Unequal expenditure switching can be relevant for the distributional consequences ofhigh-inflation episodes, if these coincide with a rise in the dispersion of price changes (forevidence on the relation between inflation and price dispersion, see, e.g., Alvarez et al.,2019). We leave this for future research.

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A

Data appendix

Processing the Homescan data. Households record if a purchase occurs within Switzerland or at a retailer abroad. We drop all transactions that occur abroad. Throughout theanalysis, we focus on prices including the local VAT.
For expositional purposes, to examine the period around the January 2015 appreciation we shift the data of all transactions by 15 days, so that the appreciation coincides
with the change in the calendar year. For example, what is referred to as 2015 (or the firstquarter of 2015) includes the actual calendar dates January 15, 2015 through January 14,
2016 (January 15, 2015 through April 14, 2015).
Participating households manually enter data on their transactions. We remove potential errors in the data using a two-step procedure. First, for each transaction we calculate
the unweighted average log price across all other transactions of the same product. We
then identify all transactions with a price level exactly equal to 1 and, within this set oftransactions, drop any transaction for which the absolute value of the log average priceexcluding this transaction is greater than 2; we do this because it appears that some transactions are accidentally coded as having a price of 1. Second, on the remaining sample,
for each transaction we re-calculate the unweighted average log price across all othertransactions in the same product and drop each transaction for which the absolute valueof the log price minus the log average price excluding this transaction within the productis greater than 2. These transactions may correspond to instances in which quantity andprice have been switched. This two-step procedure drops very few transactions: e.g., 274
in 2014 and 613 in 2015.
Whereas EANs are generally product-specific rather than retailer-specific, a block of
numbers—all EANs starting with the number 2, termed “in-store” EANs—is reserved for
assignment by the retailer. In-store EANs have a variety of uses. They can be assigned by
the retail chain, for example if a specific good is sold exclusively by the respective retailchain. However, they can also be assigned at the outlet level, for example when applying
a discount to food approaching its expiration date. The same in-store EAN could be used
for different products across the different outlets of a retail chain. In-store EANs are thus
dropped, unless we can find a product description on codecheck.info that allows us touniquely map the in-store EAN to a product and its origin.
There exist 93 different two-digit zip codes in Switzerland, which uniquely identify
cities such as Basel or Zurich, or, in rural areas, smaller regions such as such “Engadin
and Val Müstair.” The education groups identified in the Homescan data are definedas 1 = obligatory school (9 years) “obligatorische Schule”, 2 = vocational education and

A1

Table A1: Homescan data summary statistics in 2014
All
All
Number of products
Expenditures
Transactions

69,088110.7
234.6

Known origin
Imported Domestic

8,409
41.9
110.4

4,084
11.3
27.7

4,325
30.6
82.7

Notes: The sample is all purchases made within Switzerland in 2014 across all households in the Homescan data. The first column
includes all purchases made within Switzerland in 2014, the second column includes all such purchases for which the production
location of the good is known, and the third and fourth columns decompose the second column into imported and domestically
produced purchases. Number of Products is the number of distinct barcode products that are sold within each sample. Expenditures
and Transactions are total expenditures (in hundreds of thousands of CHF).

Table A2: Household summary statistics by Homescan income bin in 2014
Income bin

0-35k35-50k50-70k

70-90k90-110k

110-160k

>160k

Total

Median income
No. of households
Avg household size
Share with kids
Share elderly HH
Share higher education
Median expenditure

15,069
398
1.7
7
22
12
735

45,410
554
2.1
8
21
15
935

55,566
733
2.5
13
13
17
1,043

76,005
739
2.9
17
9
24
1,252

96,569
391
3.1
20
5
33
1,246

128,035
458
3.2
20
3
53
1,292

257,259
29
3.8
24
0
45
1,617

3,302
2.6
14
12
17
1,270

Notes: Household characteristics by income bin in the Homescan data (for our sample of households with positive expenditure in 2014
on products with known production locations). Share higher education is the share of household main earners who have university orcollege degrees. Share with kids is the share of HHs with at least one child under the age of 10. Share elderly HH is the share of HHs
in which all members are over the age of 70. Each HH’s total pre-tax annual income is constructed using the relationship between HH
characteristics and the level of total household pre-tax annual income in FORS. Median income reports the median value within eachHomescan income bin.

Table A3: Relationship between household income and expenditure share on productswith known import status in 2014
log(Income)Observations
Control size
All controls

(1)
0.25
[0.25]
3308

(2)
-0.00
[0.26]
3308
X

(3)
0.07
[0.26]
3308
X
X

Notes: Estimation of equation (A2), replacing the dependent variable with the share of household expenditure on products with known
import status. Column 2 controls for household size. Column 3 additionally controls for an indicator for whether there is a child under
10 and an indicator if everyone in the HH is older than 70. Robust standard errors are clustered by income quantile (of which there
are fifty) and observations are weighted by the product of the number of households in each quantile × the household’s share of
expenditure in 2014 within its income quantile. *p<.1; **p<.05; ***p<.01

A2

training “Berufsausbildung”, 3 = university entrance qualification “Matura”, 4 = collegeof higher education “hoehere Berufsausbildung”, 5 = college “hoehere Fachschule”, 6 =university “Hochschule/Universitaet”, 7 = other “andere Ausbildung.”
We restrict our sample to households with positive expenditures inside Switzerland in2014 on products with known import status; this yields a sample of 3,302 households.A1
Household pre-tax income. The Homescan data includes a comprehensive set of household socioeconomic characteristics, as reported in Table A2. However, a household’s total pre-tax annual income is reported only in seven bins. We construct a more granularmeasure of household pre-tax income by using information from a supplementary dataset, the Swiss Household Panel compiled by the Swiss Centre of Expertise in the Social
Sciences (FORS). Our approach is to estimate the relationship between household characteristics and total pre-tax income in 2014 in the FORS data and to use this relationship to
predict the level of household income for all households in the Homescan sample.A2 We
also predict the change in each household’s income between 2014–15 following a similar
procedure (using the panel structure of FORS).A3
We use the following socioeconomic characteristics from the Homescan and FORS
databases: an indicator variable for each of the seven income bins in the Homescan data,
an indicator variable for the household’s canton of residence, the education of the household’s main earner, the number of household members, the number of household members under 10, and the number of household members over 70.A4
To concord the Homescan and the FORS data, we adjust the FORS survey waves tocorrespond to calendar years. FORS is conducted once each year, but the surveying takes
place from September to February, with e.g. the 2013 survey wave being sampled from
09/2013 to 02/2014 and the 2014 survey wave being sampled from 09/2014 to 02/2015.
The survey includes the date each household was interviewed on, and we thus allocate
incomes to calendar years rather than survey waves. We may observe two surveys per
calendar year for a household when a household is surveyed between January and FebruA1 We construct the first column of Table A1 including all households with positive expenditures in 2014

without restricting to those with positive expenditures on products with known import status.
A2 In practice, the predicted level of household income falls within the relevant Homescan income bin for eachhousehold.
A3 When regressing changes of income on household characteristics, to address potential measurement error

in income in the FORS data, the 2014 income bins in FORS are instrumented with bins corresponding toaverage income during the period 2013–16. We also remove outliers of income changes.
A4 The FORS data provides information on the canton of residence. Cantons are more aggregated geographies
than two-digit zip codes. However, in some instances two-digit zip codes do not map uniquely to Cantons.
Of the 76 two-digit zip codes in the Homescan data, 22 map into 2 cantons and 7 map into 3. In these cases,
we allocate the respective canton fixed effects to two-digit zip codes weighing equally the respective fixed
effects.

A3

ary in one wave and between September and December in the following wave. In suchcases, we use only the later survey. For the year 2014, the resulting data set contains information on the socioeconomic characteristics of 6,658 households interviewed during
January, February, September, October, November, and December 2014.
FORS surveys household members regarding their total annual net income in CHF
at the time of the survey. The sum of all household members’ net income is defined as
the sum of labor earnings, asset income, private transfers, public transfers, and social
security pensions, all net of taxes.A5 From the data, we calculate household-specific income for calendar years and the socioeconomic characteristics of the household’s mainearner (which we observe in the Homescan data). Last, we use weights that adjust for
non-responses to the household questionnaire in the FORS survey. The population FORS
is sampling from is representative, but the response rates differ by socioeconomic characteristics, so FORS has developed weights to adjust for these differences in response rates,
which we employ; see Kuhn (2018) for a description.
SFSO data. In our analysis, we require budget shares across three sectors by income
group, inflation rates by income group, and import shares by income group within eachof our three sectors. We construct these using three data sets provided by the SFSO. In
these data sets, products are defined at a much more disaggregated level than at our
sector level. Here, we describe how we concord the three data sets provided by the SFSO
and how we construct these variables for the five income groups within the SFSO data.
The first data set, the Swiss Household Budget Survey (HBS), includes informationon consumption expenditures by income group and consumption category.A6 The HBS
is collected by the SFSO via a rotating and non-overlapping survey, randomly sampledthroughout the year from the SFSO’s register of all Swiss households. Around 250 households participate each month and record consumption expenditures during the following
month for 296 HBS consumption categories. The latter include both goods and services,in categories such as “rice”, “pasta”, or “tickets for public transport.” The survey alsocollects data on households’ socioeconomic characteristics, including income. The SFSO
publishes HBS category-specific expenditure shares averaged over a three-year horizon
for each of five income groups. The expenditure share data we use in our analysis covers
A5 There are two types of surveys sent to each household. One is a questionnaire for the household as a whole.

The other one includes individual questionnaires for each member of the household. FORS judges theindividual responses for income to be more reliable, and we thus use the income measure that is summed
over individual incomes. FORS conducts manual checks when the individual responses and the household
responses are very inconsistent. See Kuhn (2018) for further explanations.
A6 See Swiss Federal Statistical Office (2014) and Swiss Federal Statistical Office (2013) for a detailed description. One purpose of the survey is to calculate the category weights underlying the consumer price index.

A4

the years 2012–14.A7
The second data source is the disaggregated data underlying the Swiss CPI, which isalso published by the SFSO and described in Swiss Federal Statistical Office (2016). It includes price indices for 217 disaggregated CPI consumption categories. The data includes
annual price index levels, from which we calculate the category-specific annual inflation
rate. We use the data from the 2016 release, which includes the annual rate of inflation
for the years 2013–16. Finally, we also use data from the SFSO that reports import shares
per CPI consumption category. These import shares are collected periodically via firm
surveys. They are used by the SFSO to publish an inflation rate for imported consumer
goods.
We concord the HBS expenditure categories with the CPI expenditure categories. Many
CPI expenditure categories are identical to the ones from the HBS data. However, not all
categories are identical in the two data sets. Therefore, we rely on coarser categories toconcord the HBS and CPI schemes.A8 The resulting concordance includes 187 consumption categories.A9
To compute (i) inflation rates by income group and (ii) import shares by income groupwithin each of our three broad sectors, we use the expenditure shares by income groupacross the 187 consumption categories as an income-group-specific weight. We construct
the inflation rate by income group in each year as the income-group-specific weighted
average of inflation rates across the 187 consumption categories (using the 2012-2014 expenditure shares). We construct the import share in each of our three aggregate sectors foreach income group as the income-group-specific weighted average of the import sharesof each of the 187 consumption categories within the relevant aggregate sector. Hence,variation across income groups in aggregate inflation rates and in import shares withineach of our three aggregated sectors arises exclusively from differences across income
groups in expenditure shares across the 187 consumption categories (inflation rates andimport shares are assumed to be identical across income groups within each of the 187
consumption categories).
When aggregating from the 187 consumption categories into our three broad sectors—
groceries, non-grocery goods, and services—we divide goods as follows. Groceries include all food and beverages at home as well as additional products that are included in
A7 Due to data sparsity, the SFSO does not publish expenditure shares for all income group-category combina-

tions. We impute missing income group-category expenditure shares by the overall expenditure share forthe category.
A8 When using coarser HBS categories, we sum the expenditures of the HBS categories we aggregate. Whenusing coarser CPI categories, we use the CPI weights to aggregate the CPI categories.
A9 This concordance is available in the replication material.

A5

the Homescan data, such as “cleaning articles”, or “soaps and foam baths.” Non-groceries
includes all other goods categories.
Comparing the import share in groceries across Homescan and SFSO. Table 1 showsthat the aggregate import share for groceries is substantially higher in the SFSO sample(37.9%) than in the 2014 Homescan data (26.9%); we reproduce these numbers in column
1 of Table A4. Here, we show that more disaggregated import shares—at the productcategory level—are broadly similar in the SFSO and Homescan data. The difference inthe aggregate import share is mostly due to expenditures in the SFSO data being concentrated in sectors with high import shares, particularly in goods other than food andnon-alcoholic beverages (that is, alcohol, tobacco, and non-food grocery items).
To compare import shares at a disaggregated level, we concord Homescan “productgroups” with SFSO “product names,” resulting in a data set of 44 common categories. We
then separately calculate Homescan and SFSO expenditure and import shares for thesecategories using the 2014 Homescan micro data and the SFSO data underlying Table 1.
In this sample of matched categories (which does not comprise the entire sample), theweighted import share is 37.9% in the SFSO (the SFSO import share reported in column
3 of Table A4) and 26.2% in the Homescan data (the Homescan import share reported incolumn 4 of Table A4). Hence, we obtain the same discrepancy between Homescan and
SFSO grocery import shares in our matched data set as in the full data set.
Using this matched sample, we now provide evidence that the discrepancy between
these grocery import shares is driven by differences in expenditure shares across categories rather than differences in import shares within them. As a first exercise, we calculate the correlation coefficient between these category-level import shares. This correlation is 0.63 (significant at the 0.1 percent level). As a second exercise, we construct theunweighted import share across categories in the SFSO data and in the Homescan data.
These shares, reported in the second column of Table A4, are substantially more similar,
43.5% in the SFSO data and 39.4% in the Homescan data. Column 3 reports weighted average import shares across categories in the SFSO and Homescan data using expenditure
shares from the SFSO data and column 4 replicates this exercise using expenditure sharesfrom the Homescan data. Each of these columns reports shares that are more similar thanusing different expenditure weights (i.e., compared to the first column).
These differences in expenditure shares are largely accounted for by expenditures on
items other than food and non-alcoholic beverages. The latter category has a high importshare (56.4% in the SFSO data). While these categories account for 31.2% of expendituresin the SFSO data, they represent only 21.3% of expenditures in the Homescan data. Such
differences may reflect that the SFSO adjusts expenditure shares for tobacco or that the
A6

Table A4: Import shares in groceries using SFSO and Homescan data

SFSO import shares
Homescan import shares

All categories
Own weights

Unweighted

37.9
26.9

43.5
39.4

Matched categories
SFSO weights Homescan weights
37.9
31.0

26.4
26.2

Notes: Column 1 displays the grocery import share in SFSO and in Homescan data. Column 2–4 use a subset of each data set (44 common categories) that can be matched. Column 2 displays the unweighted average import share across common categories. Columns
3 and 4 display the weighted average import share across common categories weighted using expenditure weights from SFSO data incolumn 3 and from Homescan data in column 4.

Homescan sample captures food and beverage expenditures better than non-food grocery expenditures (e.g., medicines, household equipment, cosmetics, personal care appliances), which also tend to be purchased in non-grocery retail outlets.
Alternative price changes. In column 7 of Table A9, we construct price changes between
the fourth quarter of 2014 and the first quarter of 2015 using an alternative approach. In
our baseline, we calculate an expenditure-weighted average price across all transactions
by year for each product. Here, we instead use the approach of Auer et al. (2021): foreach product, we first calculate average retail prices by region, retailer, and month, thenaverage these across regions and retailers by month, and finally average monthly prices
by quarter.
Prices across regions within Switzerland. Average prices across individual products do
not systematically vary much across regions within Switzerland. To document this fact,
we estimate
log pij = α + FEi + FE j + ε ij
(A1)where log pij is the weighted average log price for domestic purchases in 2014 of producti within one-digit-zip code j, FE j is a one-digit zip-code specific fixed effect, and FEi is a
product-specific fixed effect. We weigh observations by expenditure in 2014 and cluster
by product.
Table A5 displays our estimated one-digit-zip code fixed effects. The omitted fixed
effect is for the most populous one-digit zip (which contains Zurich). There are at mosttiny systematic differences in average prices across regions (conditioning on the range ofoffered products), with the greatest difference from Zurich being half of one log point.

A7

Table A5: A lack of systematic price variation across space

Region FEs(1)
Geneva&Valais
0.005∗∗∗(0.001)(2)
Neuchatel
0.002∗(0.001)(3)
Berne
0.003∗∗∗(0.001)

(4)
Basel
0.000
(0.001)(5)
Aarau-0.000(0.001)(6)
Central CH-0.005∗∗∗(0.001)(7)
Grisons-0.001(0.001)(8)
Eastern CH-0.002∗(0.001)

Notes: Estimation of equation (A1). Observations weighted by expenditure in 2014. Clustered by product. The one-digit zip code
containing Zurich (which is the most populous) is omitted.

B

Empirical appendix

B.1

Details on stylized facts

Here we provide additional details, tables, and figures associated with our stylized facts
presented in Section 2.2.
SF 1 Part 2 (SFSO and Homescan): Import shares within groceries before the 2015 CHF
appreciation were not strongly correlated with income.
In Section 2.2 we show that import shares are higher among higher-income households in the 2012–14 SFSO data. On the other hand, we state that import shares within
groceries are not strongly correlated with income.
This is evident in the SFSO data from Table 1. We next show that import shares arealso not significantly correlated with income in the product-level Homescan data. To doso, we estimate
100 ×

XhM
= α + β log( Incomeh ) + [ζ 0 Kh ] + ε h
XhM + XhD

(A2)

where XhM and XhD are household h’s expenditure on imports and domestic goods in2014, log( Incomeh ) is the logarithm of household h’s income in 2014, and Kh is a vector of household controls. Robust standard errors are clustered by income quantiles (ofwhich there are fifty) and observations are weighted by the product of the number ofhouseholds in each income quantile times the household’s share of expenditure in 2014
within its quantile. The coefficient β identifies the difference in import shares in 2014
between higher- and lower-income households. Table A6 displays the results, which are
insignificantly different from zero whether or not we control for additional household
characteristics.
SF 2 (Homescan): The import share increased following the 2015 CHF appreciation.
The aggregate import share increased from 26.9% to 27.5% between 2014 and 2015. To
A8

Table A6: Household income and import shares in Homescan in 2014
log(Income)Observations
Control size
All controls

(1)
-0.06
[0.46]
3302

(2)
0.50
[0.51]
3302
X

(3)
0.42
[0.52]
3302
X
X

Notes: Estimation of equation (A2). Column 2 controls for household size. Column 3 additionally controls for an indicator
for whether there is a child under 10 and an indicator if everyone in the HH is older than 70. Robust standard errors are
clustered by income quantile (of which there are fifty) and observations are weighted by the product of the number of households in each quantile × the household’s share of expenditure in 2014 within its income quantile. *p<.1; **p<.05; ***p<.01

show that this rise occurred within individual households—rather than from a change inthe composition of expenditures across households—we estimate the following regression
XhMt= α + FEh + ∑ β t Iy=t + ε ht
(A3)
100 ×
XhMt + XhDt
y6=2014
where XhMt and XhDt are expenditures on imports and domestic goods for household hin year t, FEh is a household fixed effect that controls for systematic differences acrosshouseholds in import shares, and Iy=t is an indicator that equals one if y = t. Robust
standard errors are clustered by income quantiles (of which there are fifty) and observations are weighted by the product of the number of households in each income quantile
times the household’s share of expenditure in 2014 within its quantile. The coefficients β tidentify the change within households in the share of expenditures on imports between
year t and 2014.
Figure A1 displays our estimated year fixed effects, β t , together with their associated
95% confidence intervals when estimating regression (A3) separately for each of twelve
horizons, where we define horizon j as the first j months in year t and in 2014; our annual
regressions are equivalent to horizon 12. Over the full year, there are no economicallyor statistically significant differences between 2013 and 2014. On the other hand, withinhouseholds the import share was higher in 2015 than it was in 2014—the increase in theimport share in 2015 is largely stable over all twelve horizons—and this persists through2016.
SF 3 (Homescan): Import shares increased less for higher-income households following the 2015 CHF appreciation.
Table 2 reports results from estimating the following household level regression
100 ×

h
i
XhMt
= FEt + FEh + ∑ Iy=t β t Inch + [ζ t0 Kh ] + ε ht
XhMt + XhDt
y6=2014
A9(A4)

Figure A1: Plotting β t by time horizon from equation (A3)

Notes: Estimation of equation (A3) separately by horizon (for horizons 1–12), showing estimated coefficients, β y , and associated 95%
CIs. Robust standard errors are clustered by income quantiles (of which there are fifty) and observations are weighted by the productof the number of households in each income quantile times the household’s share of expenditure in 2014 within its quantile.

where FEh and FEt are household and time fixed effects that soak up any systematicdifferences in import shares across households or years, Iy=t is an indicator that equals
one if y = t, Kh is a vector of household controls, and Inch is a measure of household
h’s income in 2014.A10 The coefficient β t identifies the difference-in-difference—between
year t and 2014 and between higher relative to lower-income households—in the log ofimports relative to domestic purchases.
SF 4 (Homescan): The price of imported relative to domestic goods fell following the2015 CHF appreciation. Neither import nor domestic price changes varied systematically with household income.
We measure the monthly log price of each barcode product as the average of log prices
across all transactions, weighing transactions by expenditures within the relevant month.
The average change in log prices—relative to December 2014—within the set of domestic
goods and, separately, the set of imports is identified estimating the following regression
separately for domestic and imported goods,
log pim = α + FEi +∑Im0 =m β m + ε im(A5)

m0 6=Dec 2014

where i indexes product and m indexes month. We weigh each observation by total exA10 The additional controls that are interacted with year are: household size, an indicator for whether there isa child under 10, and an indicator if everyone in the HH is older than 70.

A10

Figure A2: Price changes and household income

Notes: Estimation of (A6) displaying estimated coefficient β q and associated 95% confidence interval for each quarter q. Coefficientsfor imported and domestic goods are estimated separately. Robust standard errors are clustered by product and observations areweighted by 2014 expenditures by group j on product i.

penditure on that product in 2014. The coefficient β m identifies the average difference inproduct prices—separately for imported and domestic goods—between month m and December 2014. Figure 1 in the Introduction displays our results with robust standard errors
clustered at the product level. Before the 2015 appreciation, import prices and domestic
prices moved together. Following the appreciation, import prices fell by approximately
2.1% relative to domestic prices (averaging the change between December 2014 and eachmonth in 2015).
Did prices paid change differentially for households with different incomes? Separately on the sample of imported goods and domestic goods, we estimate
log pihq = α + αih + αq +∑Iy=q β q log( Incomeh ) + ε ihq(A6)

y6=2014Q4

where pihq is the level of the price of product i paid by household aggregation h (defined as the 50 income quantiles) in quarter q.A11 We measure this price as the geometricweighted average product price across transactions within hq, weighing by expendituresin the current quarter. We weigh observations in (A6) by 2014 expenditures by household
aggregation h on product i and cluster standard errors by product. The coefficient β qidentifies the difference-in-difference—between quarter q and the fourth quarter of 2014
and between higher- relative to lower-income households—in the average log price.
Results for the differences-in-differences coefficients, β q , are displayed visually in FigA11 We aggregate up from months in (A5) to quarters in (A6) given the finer disaggregation across incomes in

(A6).

A11

Table A7: Standard deviation of log price changes across barcode products
Balanced all years

2013–142014–15
2015–16

Expend. weight 2014

Imports

DomesticAll

Imports

Domestic

All

0.054
0.074
0.061

0.042
0.048
0.041

0.046
0.057
0.047

0.053
0.074
0.062

0.045
0.048
0.042

0.048
0.057
0.048

Notes: Expenditure-weighted standard deviation of annual log price change across barcode products for imported goods, domestic
goods, and all goods. The left panel includes only products purchased in all years 2013, 2014, 2015, and 2016. The right panel
additionally uses common weights (given by 2014 expenditures) across years.

ure A2. As indicated in the figure, point estimates are economically small and statisticallyinsignificantly different from zero. Changes in prices paid at the individual product level
surrounding the 2015 appreciation do not differ systematically across incomes.A12
SF 5 (Homescan): The dispersion of price changes across goods was greater between
2014–15 than between 2013–14 and than between 2015–16, especially within the set ofimported goods.
For each barcode product we calculate an expenditure-weighted average log priceacross all transactions for each year t. For each product and each t in 2013, 2014, and 2015
we then calculate the change in log price between t and t + 1. For each t, we restrict oursample either to imported (column 1), domestic (column 2), or all goods (column 3). To
reduce the role of abnormally large price changes, we drop products with year-to-year
price ratios above 3 or below 1/3. We then construct the weighted standard deviationof log price changes for each t, weighting by expenditures in year t. Results are shownin Table 3. Restricting the sample to the set of products that were purchased in all three
years, or additionally imposing common weights (given by 2014 expenditures) across t
leaves results broadly unchanged, as shown in Table A7.

B.2

Additional details for robustness of estimation of ηs

In this section, we describe a range of additional robustness and sensitivity exercises focusing on our second approach to estimating ηs . In the first exercise, we consider an alternative estimation approach—using cross-sectional income elasticities—that allows us
to relax the restriction that the good-specific component of income elasticities is common
across households in the initial period. In the second set of exercises, we vary specific
A12 A related observation, documented in Appendix A, is that average price levels do not vary much acrossregions in Switzerland, either in 2014 or in 2015.

A12

baseline choices and show that our baseline point estimate is robust. Third, we show that
our results are robust if we do not infer household income using household characteristics
beyond Homescan income bin or if we drop high- or low-income households from ourestimation (both in approaches 1 and 2). In the final set of exercises, we demonstrate that
our results are robust to incorporating spatial variation in both expenditures and prices.
Using cross-sectional income elasticities. In our baseline approach, we estimate differences in Hicksian elasticities without the need to first estimate income elasticities in
the cross section. This approach leverages restriction (15), which imposes that the goodspecific component of income elasticities is common across households in the initial period. In this sensitivity (mentioned in footnotes 24 and 30), we consider an alternative
estimation approach that allows us to relax this restriction. This alternative approach
involves first estimating cross-sectional income elasticities. We apply this alternative procedure in Approach 1 and obtain very similar results.
Define∂ηs∂ log eh −1
× γi −
log phit0
κ hi ≡∂ log uh∂ log uhwhere all derivatives in this section are evaluated at t0 . In our baseline procedure, we
assume κ hi = κi + κ hs , so that the income elasticity for good i at t0 can be expressed as
the sum of κi , which is common for all households, and a household-sector-specific term.
Here we drop this restriction. Equation (18) becomesM
d log bhit = FEit + FEhst+ κhi d log



Iht
Pht



− ηs log( Iht0 )d log phit + ι hit .

(A7)

In our modified procedure, we first estimate κ hi from the cross section and then estimate
ηs .
We implement this procedure in Approach 1, where we only need to estimate a single
income elasticity, that of imports relative to domestic goods: κ hMD ≡ κ hM − κ hD .A13 Givenan estimate of κ hMD , we obtain ηs from a modified version of equation (19):

d log

bhMt
bhDt



− κhMD d log



Iht
Pht





= α − ηs log( Iht0 )d log

p Mt
p Dt



+ ι ht(A8)

To estimate κ hMD , we estimate a standard Engel-curve regression for the share of imports

A13 In Approach 2, we would have to estimate thousands of income elasticities at the barcode product level.

A13

Table A8: Robustness of Approach 1: Using cross-sectional Engel curves
Linearlog( Iht0 )d log( p Mt /p Dt )Observations
Control size
All controls(1)2.17∗∗∗[0.54]
2901(2)
2.16∗∗∗[0.54]
2901
X

Quadratic(3)
2.17∗∗∗[0.54]
2901
X
X

(4)
2.09∗∗∗[0.54]
2901(5)
2.06∗∗∗[0.54]
2901
X(6)
2.08∗∗∗[0.54]2901
X
X

Notes: Results of estimating equation (A8) using estimates of κ hMD estimated using equation (A9) (in 2014 data) under the assumptionthat β 2 = 0 in columns 1-3 and without this assumption in columns 4–6. Columns 1 and 4 include no controls. Columns 2 and5 include household size controls. Columns 3 and 6 additionally include an indicator for whether there is a child under 10 and an
indicator for whether everyone in the HH is older than 70. The regression (A8) is clustered and weighted as in the baseline of Approach
1. The regression (A9) is unweighted. Standard errors in this table do not correct for the fact that the dependent variable depends onan estimated coefficient. *p<.1; **p<.05; ***p<.01

relative to domestic goods by household in t0 = 2014,

log

bhMt0
bhDt0



= β 0 + β 1 log( Iht0 ) + β 2 log( Iht0 )2 + Xh0 γ + ι ht0(A9)

where we have imposed that κ hMD = β 1 + 2 × β 2 log( Iht0 ). Tastes for imports relative todomestic goods at t0 must be uncorrelated with income conditional on other controls, Xh .
We do not require this assumption in our baseline approach.
If we impose β 2 = 0, we are back to our baseline assumption that the good-specificcomponent of income elasticities is common across households. However, even in thiscase, the approach differs from our baseline approach, as we estimate κ hMD using crosssectional rather than time-series variation. In the case of β 2 = 0, regression (A9) isbhMt

rather thanvery similar to regression (A2), where the dependent variable is b +b0
hMt0
hDt0
b

hMt
log b 0 .
hDt0Table A8 displays estimates of ηs obtained using this procedure. Columns 1–3 contain results imposing β 2 = 0 varying the set of controls and columns 4–6 contain results
without this restriction. Across specifications, estimates are very similar to our baseline.
Standard errors should be interpreted with caution since we do not adjust for the fact thatthe left-hand side of equation (A8) depends on a coefficient estimated in the first step of
the procedure.
Varying baseline choices. Column 1 of Table A9 displays our baseline 2SLS estimate
and the remaining columns display results from various robustness exercises. In ourbaseline we winsorize changes in log expenditures at the first percentile (in the top andbottom tails). In columns 2 and 3 we instead winsorize at the 5th percentile and not atall. Our baseline sample only includes products if they were purchased at least once per
A14

Table A9: Robustness of Approach 2: Varying baseline choiceslog( Iht0 ) × d log pit
Observations
Baseline
Winsorize 5%
No winsorizing
Unbalanced sample
Sample >20 border prices
Sample >32 border prices
Prices rel to 14Q4
K-P F Stat (first stage)(1)
1.93∗∗[0.87]
95,325X(2)
1.80∗∗[0.73]
95,325(3)
1.87∗[0.97]
95,325(4)
2.03∗[1.12]
120,889(5)
1.61∗[0.94]
97,366(6)
1.89∗∗[0.89]
92,383(7)
1.87∗[0.99]
95,325

X
X
X
X
X
13.1

13.1

13.1

16.1

8.7

13.9

X
12.1

Notes: Column 1 replicates our baseline 2SLS estimate of ηs in column 3 of Table 5. Columns 2–7 each vary one choice in our baseline
specification. Column 2 winsorizes at the 5th percentile whereas column 3 does not winsorize at all. Column 4 drops the sample
restriction that a product is only included if it was purchased at least once per month in the year and a half before and after the CHF
appreciation. Column 5 (column 6) includes products in border groups with more than 20 (more than 32) border price observations.
Column 7 defines dlogpit as the log price change between 2015 and the fourth quarter of 2014. *p<.1; **p<.05; ***p<.01

Table A10: Robustness of Approach 2: Varying baseline choiceslog( Iht0 ) × d log pit
Observations
Baseline
Horizon 3mHorizon 6mHorizon 9m
Percent change
Omit d log( Iht /Pht )All inv. currencies
HH size interaction
K-P F Stat (first stage)(1)
1.93∗∗[0.87]
95,325X(2)
3.55[2.23]
43,559(3)
2.62∗∗[1.10]
67,179(4)
2.27∗∗[1.01]
82,995(5)
1.97∗∗∗[0.62]
116,930(6)
1.62∗[0.94]
95,325(7)
1.83∗∗[0.85]
95,325(8)
2.35∗[1.33]
95,325

X
X
X
X
X
X
13.1

7.6

8.6

11.4

12.8

12.8

12.7

X
14.6

Notes: Column 1 replicates our baseline 2SLS estimate of ηs in column 3 of Table 5. Columns 2–7 each vary one choice in our baseline
specification. Columns 2–4 use price and expenditure changes measured over the first 3, 6, and 9 months of 2014 and 2015. Column
5 replaces log changes in expenditures and in prices with percent changes. Column 6 omits the covariate d log( Iht /Pht ) from theregression. Column 7 uses an alternative instrument using the share of non-CHF invoiced border prices, including all currencies.
Column 8 includes a control for household-size interacted with the change in product price, instrumented using a version of ourbaseline instrument replacing the log of household income with household size. In column 8, the reported F statistic is the SW F onlog( Iht0 )d log pit . The unreported SW F stat on the household-size interaction is over 14. *p<.1; **p<.05; ***p<.01

A15

month in the year-and-a-half before and after the CHF appreciation. In column 4 we drop
this sample restriction. Our baseline sample only includes products in border groups forwhich there are more than 28 border price observations in 2014. In columns 5 and 6 weinclude additional border groups (those with more than 20 border price observations) andfewer border groups (those with more than 32 border price observations). In our baseline,
we use price changes and expenditure changes defined using the full years of 2014 and2015. In column 7 we use retail price changes between the fourth quarter of 2014 and thefirst quarter of 2015 as calculated in Auer et al. (2021) (and described in Appendix A) andchanges in expenditures over the full years of 2014 and 2015. Each of these choices has
little effect on either first-stage or second-stage results.
Column 1 of Table A10 again displays our baseline 2SLS estimate and the remainingcolumns display results from additional robustness exercises. In columns 2, 3, and 4 weuse price changes and expenditure changes measured over the first 3, 6, and 9 monthsof 2014 and 2015. In all cases, changes in real income are still measured over the fullyear given data availability. Results remain largely stable across these specifications; theelasticity difference is larger when estimated using changes in expenditures and prices
over the first 3 months, but it is not precisely estimated.
In our baseline, we use log changes in prices and in expenditure shares. This approach
drops all observations for which initial (i.e. 2014) or terminal (i.e. 2015) expenditures are
zero. In column 5, we replace log changes in expenditures and in prices with percent
changes. This alternative approach keeps any observation for which consumption in 2014is positive (as long as any household in any income group consumes the product in 2015).
Our main result is largely unchanged. In our baseline, we control for changes in real income. If we omit this covariate, our estimated difference in elasticities falls; see column
6. Our baseline instrument uses the share of imported goods in each border group thatare denominated in EUR out of all goods denominated in either EUR or CHF. If we instead use the share of non-CHF invoiced border prices including all currencies, results arelargely unchanged as shown in column 7. Another concern is that household income iscorrelated with household size and that households of different sizes have different elasticities. In column 8 we control for the interaction between household size and the log
product price change and instrument for this interaction using a version of our baseline
instrument in which we replace log income with household size. The SW F stats for bothendogenous variables are above 14 and our main result is largely unchanged.
In our baseline, we two-way cluster standard errors at the level of household income
and, separately, the interaction between import status and the value of the share of imported goods denominated in EUR in the corresponding border group. Here, we report
A16

how the first-stage F statistic and the second-stage standard error vary with these choices.
If we two-way cluster standard errors at the level of household income and, separately,
the barcode product, the first-stage F statistic is approximately 25. If we two-way cluster
standard errors at the level of household income and, separately, the interaction between
import status and the border group (rather than by the share of imported goods denominated in EUR in the border group, which makes a difference because 7 of the 35 bordergroups have a common EUR invoicing share equal to zero), the first-stage F statistic isapproximately 6. If we one-way cluster standard errors at the level of the triple interaction between import status, the share of products denominated in EUR in the bordergroup, and household income, the first-stage F statistic is well over 100. If we one-way
cluster standard errors at the level of the interaction between import status and the shareof products denominated in EUR in the border group, the first-stage F statistic is largely
unchanged. In all cases, the second-stage standard error is very similar to its value in ourbaseline.
Household income. In our baseline in approaches 1 and 2, we infer household income
and changes in income combining Homescan information on household characteristics—
including income group, size, etc.—and the Swiss Household Panel (FORS). Here, we
replicate our baseline estimation of both approaches using only Homescan income data,assigning a common value of income to all households in the same Homescan incomebin. Because we do not use FORS to infer household income, we similarly do not use it
to infer changes in household income; hence, we omit the covariate measuring changes
in real income from both approaches in this robustness. Finally, because we only have 7
income bins in these exercises, we do not two-way cluster including income; instead, we
one-way cluster.
To assign a value of income to each household, we use data on the distribution of annual taxable household income of natural persons in 2014—from Swiss Federal Tax Administration (2014) (henceforth SFTA)—to measure the median household income levelassociated with each of the Homescan income bins. Taxable household income is equal
to total pre-tax household labor income minus social security contributions and other tax
deductions.
We calculate the median income within each Homescan household income bracket
using the 2014 national distribution of household pre-tax income from the federal tax
administration. Specifically, the SFTA records the number of Swiss households for each
10,000 CHF income step (and steps of 100,000 for incomes above 200,000 CHF). We split
the 30,000-40,000 step in the SFTA data and allocate the number of households equally to
the 0–35,000 and 35,000–50,000 CHF brackets in the Homescan data. The resulting median
A17

Table A11: Robustness of approaches 1 and 2 to inferring household income

log( Iht0 )d log( p Mt /p Dt )(1)
Approach 1
2.14∗∗∗[0.54]

log( Iht0 ) × d log pit
Observations
K-P F Stat (first stage)

2,901

(2)
Approach 2

2.29∗∗∗[0.72]
19,881
11.2

Notes: Columns 1 and 2 replicate our baseline in approaches 1 and 2, respectively, without inferring household income. Instead, we
use only the seven income bins in the Homescan data and allocate each household to the median income in that bin as described in
the text. In both columns we omit the covariate measuring changes in real income. In column 2, we do not include income in ourclustering. *p<.1; **p<.05; ***p<.01

income levels within each Homescan bracket are 15,0000, 45,000, 55,000, 75,000, 95,000,
125,000, and 250,000 CHF. Assigning households to these incomes leaves our baseline
results largely robust, as shown in Table A11.
Are the specific income groups driving the variation that identifies differences in elasticities particularly high- or low-income households? In Tables A12 and A13 we replicate
our baseline estimation of approaches 1 and 2, respectively, dropping either all households in the lowest Homescan income group, the two lowest Homescan income groups,
the highest Homescan income group, or the two highest Homescan income groups (outof the seven income groups). Across the eight cases (two approaches and dropping four
distinct sets of households), we obtain a positive coefficient. This coefficient is very similar to our baseline estimates in all cases but one (dropping the two lowest income groups
in Approach 1, where we lose almost 30% of our observations). Our estimates, however,are less precise when we drop the lowest income groups. We conclude that the negative
relationship between incomes and price elasticities is not driven by either high- or lowincome households; although for precision, low-income households play an importantrole.
Incorporating spatial variation. In our baseline we did not incorporate geography atall. We aggregated households by 2014 income alone and, therefore, used common pricechanges within each individual product across household aggregates.
Here, we show that further disaggregating our household groups by both geography
and income leaves our results largely unchanged. Column 1 of Table A14 replicates ourbaseline 2SLS result from column 3 of Table 5. In the remaining columns in Table A14
we disaggregate households both across 50 income quantiles (as before) and across eachof 9 one-digit zip codes in Switzerland; our regression specification incorporates correspondingly more disaggregated household fixed effects, where h is now the interaction
A18

Table A12: Robustness of Approach 1 dropping household income ranges

log( Iht0 )d log( p Mt /p Dt )Constant
Observations(1)
Drop lowest
1.58[1.29](2)
Drop 2 lowest
0.72[1.55](3)
Drop 2 highest
2.52∗∗∗[0.42](4)
Drop highest
2.52∗∗∗[0.46]

0.41[0.31]
2569

0.19[0.37]
2085

0.63∗∗∗[0.10]
2460

0.63∗∗∗[0.11]
2872

Notes: Each column of this table replicates column 1 of Table 4 while omitting a subset of the estimation sample. Column 1 drops
all households in the lowest Homescan income bin whereas column 2 additionally drops the second-lowest income bin. Column 4drops all households in the highest Homescan income bin whereas column 3 additionally drops the second-highest income bin. *p<.1;**p<.05; ***p<.01

Table A13: Robustness of Approach 2 dropping household income ranges

log( Iht0 ) × d log pit
Observations
K-P F Stat (first stage)(1)
Drop lowest
1.80[1.61]
85,60711.5(2)Drop 2 lowest
2.88[1.73]
71,02911.3(3)
Drop 2 highest
1.69∗∗[0.80]
93,12613.2(4)
Drop highest
1.89∗[1.08]
80,89314.0

Notes: Each column of this table replicates column 3 of Table 5 (the baseline 2SLS estimate in Approach 2) while omitting a subset ofthe estimation sample. Column 1 drops all households in the lowest Homescan income bin whereas column 2 additionally drops thesecond-lowest income bin. Column 4 drops all households in the highest Homescan income bin whereas column 3 additionally drops
the second-highest income bin. *p<.1; **p<.05; ***p<.01

between the income quantile and zip code. Column 2 displays the results of estimating
the baseline specification—continuing to use a common price change within each good—using this more disaggregated data; first- and second-stage results are largely unchanged.
In column 3, we additionally use price changes measured separately within each of the 9
one-digit zip codes. Incorporating price variation across regions leads to a modest attenuation in our baseline estimate of ηs (from −1.93 to −1.54) and our instrument remains
strong.
Finally, we describe an alternative instrument leveraging spatial price variation, aHausman instrument interacted with household income. Using this instrument, we findmuch smaller differences in elasticities across incomes. We also show that this Hausman
instrument may be endogenous in our particular Swiss setting (where there is little pricevariation across space).
In a first step, we omit our cost-shock instrument and use an alternative: the interaction between a Hausman instrument and initial log income. Specifically, for households
in a particular income quantile h ∈ {1, ..., 50} living in a particular one-digit zip codej ∈ {1, ..., 9}, we instrument for the interaction between the income of quantile h and the
product-specific price change in one-digit zip code j using the income of quantile h andA19

Table A14: Robustness of Approach 2: Incorporating spatial variationlog( Iht0 ) × d log pit(1)1.930∗∗[0.867](2)2.170∗∗∗[0.663]log( Iht0 ) × d log phit
Observations
Baseline
Spatial variation: outcome
Spatial variation: priceK-P F Stat (fist stage)

95,325X

134,596
X

13.1

12.4

(3)

1.542∗∗∗[0.572]
134,596
X
X
18.5

Notes: Columns 1 replicates our baseline 2SLS estimate of ηs in column 3 of Table 5 in which an observation is a product × householdincome quantile (of which there are fifty). In columns 2 and 3 we further disaggregate households by one-digit zip code and in column
3 we measure product-specific price changes separately across each one-digit zip code. In Columns 2 and 3 we two-way cluster by
the interaction between import status and the share of imported goods that are denominated in EUR and, separately, the household
aggregation (income quantile × one-digit zip code). *p<.1; **p<.05; ***p<.01

the product-specific price change measured outside of j. The instrument is very strong,with an F statistic of over 250. The very strong first stage can be understood by the factthat there is very little variation in regional prices of individual products set by the major national retailers in Switzerland. This also explains why this specification yields very
similar estimates to the baseline OLS using common national price changes displayed incolumn 1 of Table 5. In particular, the second-stage coefficient of interest, ηs = 0.093, isover an order of magnitude smaller than our baseline 2SLS estimate.
The exclusion restriction when using a Hausman instrument—without interactingwith income—is that there are no product-specific demand shocks at the national levelthat are correlated with price changes whereas the exclusion restriction when using a
cost-shock instrument is that the cost shock is uncorrelated with demand shocks. Given
that we are over-identified—with two instruments and one endogenous variable—we
can use Hansen’s (1982) J test, an over-identification test of all instruments: the joint null
hypothesis is that all instruments are valid. Estimating (18) using both instruments, we
obtain a Hansen J statistic of 5.739 and a Chi-sq p value of 0.0166, thus rejecting the null
hypothesis that both instruments are exogenous. Given that cost-based instruments are
the gold-standard in demand estimation—or ‘textbook instrumental variables’ as Nevo
(2000) refers to them—one conclusion might be that the Hausman-based instrument isendogenous in our setting. Of course, even if the Hausman-based instrument is endogenous in our setting, that does not imply endogeneity in other contexts.

A20

B.3

Details of estimating η̄sNeither of the two approaches in Section 4 identify the intercept η̄s defined in equation(16). However, under stronger assumptions they can be adjusted to do so.
In our first approach in Section 4.2 using equation (19), if we assume that the average
import demand shifter νit is zero between 2014 and 2015, then η̄s is identified from theconstant α as η̄s = 1 − α/ (d log ( p Mt /p Dt )). Given d log ( p Mt /p Dt ) = −0.0216 and theconstant displayed in column 1 of Table 4, we obtain η̄s ≈ 26.6. Together with our estimateof ηs = −2.189 from this approach, this implies that the initial elasticity of substitution is
4.92 for a household with income of 20,000 CHF and that this elasticity remains positive
for all household incomes below approximately 190, 000 CHF.
In our second approach in Section 4.3 we cannot recover η̄s without moving the average product-specific demand shock νit to the residual. In this case, rather than re-estimate
ηs under a stronger exclusion restriction, we subtract the estimated price interaction fromboth the left- and right-hand sides of equation (18) and then instrument for the log change
in product price using our cost shifter. In our baseline we obtain η̄s = 20.87. In combination with the baseline estimate of ηs = −1.930, the initial elasticity of substitution for ahousehold with income of 20,000 in 2014 is 1.76 and this elasticity remains positive for all
household incomes below approximately 50,000 CHF.
The levels of initial elasticities of substitution (e.g., 4.92 and 1.76 in approaches 1 and
2 for a household with income of 20,000) are much less stable than the implied differences
across household incomes across approaches (e.g., 2.40 and 2.12 in approaches 1 and 2
comparing across households with income differences of a factor of three).A14 For thisreason, in our counterfactual analyses we impose different values of η̄s that imply reasonable price elasticities for high-income households and show that relative differencesin welfare depend crucially on the value of ηs but are not substantially affected by the
choice of η̄s .

C

Theoretical appendix

We use a particular formulation of the non-homothetic CES preferences presented in Fally(2022). Given the consumption bundle cht and preference parameters ζ ht for household h
A14 In addition to instability of the estimated levels across approaches, each estimate has its own confidence

interval. In the first approach, the estimated value of η̄ is highly sensitive to the estimated constant. A one
standard deviation change in the regression constant (0.129), moves the level of η̄ by 5.97 ≈ 0.129/0.0216.
In the second approach, we do not report standard errors because it is not straightforward to do so with adependent variable that depends on previous estimates, two-way clustering, and a large set of fixed effects.

A21

at time t, utility u is implicitly given by
ρ −1

ρ −1

1

f h (u) ρ = ∑ (ζ hst uγs ) ρ (chst ) ρ ,

(A10)

s

where

∑ (ζ hit u )γichst =1ηs ( u )(chit )ηs (u)−1ηs ( u )! ηs ( u )ηs (u)−1

,

(A11)

i

f h (·) > 0 and ρ, ηs (·) ∈ [0, 1) ∪ (1, ∞). These preferences reduce to nested homothetic CESif, for example, ηs (u) is independent of u, γi = γs = 0, and f h0 (u) > 0. The householdchooses {chit } to maximize u subject to the budget constraint Iht = ∑i pit chit . The expenditure function associated with these preferences is given by (3). The maximum utility
achieved by household h at time t is vh ( pht , Iht ; ζ ht ) ≡ uht where e ( pht , uht ; ζ ht ) = Iht . We
discuss below conditions that ensure that the expenditure function is monotonic in u.
Deriving equation (13). Log-linearizing Iht = eh (pht , uht ; ζ ht ) at t0 yields
d log Iht =where ε̄ ht ≡ ∑i

∂ log ehd log uht + ∑ bhit0 d log phit + ε̄ ht ,∂ log uhi∂log eh∂ζ hi dζ hit and derivatives are evaluated at t0 . Solving for d log u ht yields

d log uht =∂ log eh∂ log uh −1

× d log Iht − ∑ bhit0 d log phit − ε̄ ht

!
(A12)

i

This is equation (13) in the text.
Deriving equation (17). Substituting equation (A12) into equation (12) yields
d log bhit =∂ log eh∂ log uh

 −1



∂ηs
× γi −
log phit0∂ log uhd log Iht − ∑ bhit0 d log phit − ε̄ hti+ d log ζ hit + (1 − ηhst0 )d log phit + ψhst
The previous expression and assumption (15) yieldd log bhit = (κi + κ hs )d log Iht − ∑ bhit0 d log phit − ε̄ hti+ d log ζ hit + (1 − ηhst0 )d log phit + ψhst

A22

!

!

Note that the only i-specific term multiplying changes in real income is κi . This implies
that household h’s income elasticity for good i in sector s in the initial period can be
expressed as the sum of a good-specific and a household-sector specific component. The
previous expression and assumption (16) yieldd log bhit =(κi + κ hs )d log Iht − ∑ bhit0 d log phit − ε̄ ht!

i+ d log ζ hit + (1 − η̄s − ηs log Iht0 )d log phit + ψhst
The previous expression is equation (17) given the definitions νhit ≡ d log ζ hit − κi ε̄ ht andehst ≡ ψhst + κ hs (d log( Iht /Pht ) − ε̄ ht ). The demand shifter νhit combines the taste shifterψfor good i, d log ζ hit , and the change in utility due to taste shifters, ε̄ ht interacted with theutility elasticity κi .
Assumptions (15) and (16). We consider a cardinalization of the utility function thatsatisfies two properties. First, the elasticity of substitution η is log-linearly related to uht ,ηhst ≡ η̄˜ s + η̃s log(uht ).

(A13)

If η̃s < 0, then a household that attains a higher indifference curve is less price sensitivein sector s. In combination with the assumption that initial prices of individual goods
within s are given by log phit0 = log pit0 + log phst0 we obtain∂ηslog phit0 = η̃s log pit0 + log phst0∂ log uh
The second property of our utility function is that the elasticity of the expenditure function with respect to uht in the initial period is common across households. To achieve thisoutcome, we assume that f h (·) introduced in (3) is"
f h ( x ) = a0 x

a1

∑ ζ hst x# 1
γs( Phs ( x ))

1− ρ

ρ −1

(A14)

s

with a0 > 0 and a1 > 0 and where

Phs ( x ) =  ∑ ζ hit0 x γi phit0i ∈I(s)A23 1− ηs ( x )11− ηs ( x )

(A15)



a1
and ∂ log eh ∂ log uh = a1 when evalIn this case, eh pht0 , uht0 ; ζ ht0 = Iht0 = a0 × uht
0uated at t0 . These cardinalization assumptions imply equation (16), where η̄s ≡ η̄˜ s −a1−1 η̃s log( a0 ) and ηs ≡ a1−1 η̃s , and also imply equation (15), where κi ≡ a1−1 γi − ηs log pit0
and κ hs ≡ −ηs log phst0 .
Monotonicity of the expenditure function. For any constant u, the shape of the indifference curves implied by the non-homothetic utility function (A11) is the same as underhomothetic CES. Similarly, for any given u, the shape of the expenditure function (3) andcorresponding Hicksian demand under non-homothetic CES is the same as under homothetic CES. In order for our utility function to be well-defined there must be a uniquesolution for u in equations (A10)–(A11). In order for our expenditure function to be welldefined, there must be a unique u that solves e ( p, u; ζ ) = I, and the expenditure must be
increasing in u to ensure budget exhaustion.
We examine these properties first analytically—applying results in Fally (2022)—and
then numerically. We focus on the empirically relevant case in which the elasticity of
substitution is decreasing in u, in a specification with a single sector (or, equivalently, allsectors are symmetric). In this case, the utility function (A10) is
f (u)η (u)−1η (u)= ∑ (ζ i u )
γi

i

1
η (u)

η (u)−1η (u)ciwhere we have dropped household and time sub-indices, ζ i ≥ 0 for all i and ∑i ζ i = 1.
1

To use the notation of Fally (2022), define Gi (u) ≡ f (u) (ζ i uγi ) 1−η (u) , and re-express theutility function as η (u)−1(A16)
1 = ∑ ci Gi (u) η (u)ithe expenditure function ase ( p, u; ζ ) =∑ (Gi (u) pi )!
1− η ( u )11− η ( u )

,

(A17)

i

and demand for good i as
pi ci
=
I



Gi (u) piI 1− η ( u )
(A18)



G ( u ) p 1− η ( u )with ∑i i I i= 1.
Proposition 4 in Fally (2022) states that a sufficient condition for the demand system

A24

(A18) with η 0 (u) < 0 to be integrable is(η (u) − 1)2 Gi0 (u)K (u) ≡ ∑ exp
η 0 (u)
Gi (u)
i




< 1.

(A19)

The proof of Proposition 4 in Fally (2022) shows that if condition (A19) is satisfied, thenthere is a unique solution u in (A16) and u in e ( p, u; ζ ) = I, and that around each of thosevalues of u the expenditure function is increasing in u.
We prove that (A19) is satisfied under our functional form assumption η (u) = η̄ +1
 1
η log(u) with η̄ 6= 1, η < 0, and f (u) = (uk1 ) 1−η (u) . In this case, Gi (u) = ζ i uγ̃i 1−η (u) ,where γ̃i ≡ γi + k1 .A15 Hence, (1 − η (u)) γ̃i
Gi0= log ζ i uγ̃i +Gi
η 0 (u)uCombining the previous expression with the definition of K (u) yields
K (u) ≡ ∑ ζ i u exp
γ̃i

i



γ̃i 1 − η (u)u η 0 (u)Using the functional form η (u) = η̄ + η log(u), the previous expression implies
K (u) = K = ∑ ζ i exp γ̃ii

1 − η̄
η

Since ∑i ζ i = 1, K is a weighted average of exp( xi ) for xi ≡ γ̃i (1 − η̄ )/η. If η̄ > 1, then(1 − η̄ )/η > 0 and exp( xi ) < 1 for all i if γ̃i < 0 for all i. Hence, if k1 < − maxi {γi }then condition (A19) is satisfied. If η̄ < 1, then (1 − η̄ )/η < 0 and exp( xi ) < 1 for all i if
γ̃i > 0 for all i. Hence, if k1 > − mini {γi } then condition (A19) is satisfied. For any η̄ 6= 1,
condition (A19) can always be ensured to hold since the level of k1 and γi are not pinned
down by observable choices (which only depend on differences in γi ) and do not affectchanges in welfare.
1

The functional form f (u) = (uk1 ) 1−η (u) used in the previous result differs from as
sumption (A14) used in deriving the estimation equation (which gives (∂ log eh ) (∂ log uh ) =a1 at t0 prices). In order to check whether the expenditure function is increasing in u under (A14) away from t0 prices, we resort to numerical simulations. We consider a range
A15 As in Fally (2022), we do not consider the case of η ( u ) = 1.

To maintain η (u) > 1, we could assume
η (u) = max{δ, η + η1 log(u)} for some δ > 1. Here, we do not make this assumption and simply show that
(A19) holds in a neighborhood of any u for which η (u) > 1.

A25

of incomes I from 15,000 to 250,000 CHF and elasticities of substitution as a function ofincome η ( I ) = 3 − 2 × log( I/250, 000). We consider 10 goods and draw random utility
elasticities γi ∼ U (0, 2), initial prices pi ∼ U (0, 1), and initial taste shifters ζ ∼ U (0, 1);
we then renormalize to satisfy ∑ ζ i = 1. We set a0 = 1 and a1 = 1, 000. For small deviations in prices relative to their t0 levels, the expenditure function is approximately equal
to a0 u a1 . To allow for larger price changes, we draw price changes from a log-normal distribution with mean zero and standard deviation 0.3. Across a large number (4,280,000)
random simulations, only 108 (or 0.0025%) contain a non-increasing portion of the expenditure function (across a large range of utilities). As with quadratic or translog utility, inthese cases one must restrict the space of feasible choices or prices to ensure that we arein the monotonic region of the expenditure function.

D

Quantitative appendix

D.1

Additional results from Section 5.1

Here we present the additional results described briefly in Section 5.1.
In the right-hand panel of Table A15 we display results imposing common expenditure shares across households, using the expenditure share calculated across all households. Whereas the first-order effects are, obviously, now identical across households, thesecond-order effects are little changed from our baseline.
In Table A16 we display the full non-linear effect of price changes for alternative levelsof η̄s —so that the elasticity for households with income of 120,000 CHF ranges between
1.5 and 5—while holding the differences in elasticities across households fixed. Greater
substitution generates larger declines in the welfare-relevant price index; however, differences between income groups are not very sensitive even for the large range of η̄sconsidered.

D.2

Sensitivity analysis of results from Section 5.2

First, in response to import price declines (compared to increases displayed in Table 8),
the first-order and expenditure-switching effects push welfare of higher- relative to lowerincome households in opposite directions. High income households benefit more fromthe first-order effect because they have higher initial import shares. On the other hand,
low-income households benefit more from the expenditure-switching effect because they
have higher price elasticities. If we assume σj = 0, which mitigates the expenditure
A26

Table A15: Welfare-relevant grocery price changes: Additional results I
Annual income
1: 20,000 elasticity 6.6
2: 60,000 elasticity 4.4
3: 120,000 elasticity 3.0
Difference between
income groups 3 and 1

2013–14 Heterogeneous elasticities
1st-order Switching Exact

2014–15 Common exp. shares
1st-order Switching Exact

1.2
1.1
1.0

-0.6
-0.4
-0.2

0.4
0.7
0.7

-1.2
-1.2
-1.2

-0.9
-0.6
-0.3

-2.2
-1.8
-1.5

0.2

-0.4

-0.3

0.0

-0.6

-0.7

Notes: The left panel replicates the left panel of Table 7, but using 2013–14 changes. The right panel replicates the left panel of Table 7,
but imposing common expenditure shares across HHs (calculated across all HHs).

Table A16: 2014–15 Exact welfare-relevant grocery price changes: Additional results II
Annual income
1: 20,000 elasticity η High,s + 3.6
2: 60,000 elasticity η High,s + 1.4
3: 120,000 elasticity η High,sDifference between
income groups 3 and 1

Varying high-income elasticity (η High,s )η High,s = 1.5
η High,s = 3
η High,s = 5
-1.9
-1.5
-1.3

-2.2
-1.7
-1.6

-2.7
-2.1
-2.0

-0.5

-0.6

-0.8

Notes: Column 2 exactly replicates column 3 of the left panel of Table 7. Columns 1 and 3 display results for alternative values of theelasticity of substitution for the highest-income household.

switching effect, then the first channel dominates for small import price declines and thesecond channel dominates for larger import price declines. If we set σj > 0, then lowerincome households gain slightly more in response to the 2.2% import price decline. Thisis because the observed increase in the variance of price changes in 2014–15 is sufficiently
strong to make the expenditure-switching effect dominate. Table A17 displays the results.
Second, in our baseline we choose ηs = −2. Table A18 reports results in which we useηs = −1.5, which is at the lower end of our estimates. We maintain the assumption thatthe elasticity of substitution for the highest-income household equals 3, which pins downη̄. As expected, the importance of heterogeneous elasticities for shaping the unequal
welfare implications of foreign prices is smaller.
Third, in our baseline we choose η̄s so that the lowest initial elasticity of substitution(that for the highest-income household with income of 120, 000 CHF) is equal to 3. Tables
A19 and A20 report results in which we use an elasticity of substitution for the highestincome household equal to 1.5 and 5, respectively. Lower levels of price elasticities imply
much larger welfare losses for every income group. However, except for the movement toautarky experiment, the percentage difference in CV between income groups and the contribution of heterogeneous elasticities are not very sensitive to the level of the elasticities
A27

Table A17: Import price declines

Annual income

Import price shock-2.2 -10 -20 -40
-2.2
σ=0
σ>0

1: 20,000 elasticity 6.6
2: 60,000 elasticity 4.4
3: 120,000 elasticity 3.0

0.47
0.53
0.59

2.4
2.6
2.8

5.4
5.6
5.8

13.2
12.7
12.6

0.73
0.70
0.69

13
25

9
17

4
9

-4
-4

-5
-6

% difference in CV btw
income groups 2 and 1
income groups 3 and 1

Notes: This table replicates the exercise in Table 8 but studying import price declines. We omit the contribution of heterogeneous ηsbecause the first-order and higher-order effects move in opposite directions.

Table A18: Smaller differences in elasticities of substitution
+10

-0.4
-0.5
-0.6

-1.9
-2.3
-2.6

-3.3
-4.2
-5.0

-5.1
-7.2
-9.1

-6.6
-12.4
-22.0

-0.2
-0.4
-0.5

16
30

20
38

27
49

41
77

86
232

58
104

37
34

55
52

76
82

62
59

Annual income
1: 20,000 elasticity 5.7
2: 60,000 elasticity 4.0
3: 120,000 elasticity 3.0

Import price shock+20 +40 +1000
σ=0

+2.2

+2.2
σ>0

% difference in CV btw
income groups 2 and 1
income groups 3 and 1

Contribution of heterogeneous ηs
income groups 2 and 1
income groups 3 and 1

6
5

23
20

Notes: This table replicates the exercise in Table 8 but imposing ηs = 1.5 rather than ηs = 2, while maintaining that the lowest elasticity
of substitution (that for the highest-income household with income of 120, 000 CHF), ηhst0 , is equal to 3.

A28

Table A19: Elasticity of substitution of high-income group = 1.5+2.2

Import price shock+10 +20 +40
+1000
σ=0

+2.2
σ>0

-0.4
-0.5
-0.6

-1.9
-2.3
-2.7

-3.4
-4.5
-5.3

-5.5
-8.1
-10.4

-7.6
-20.0
-87.3

-0.3
-0.4
-0.6

16
30

22
40

30
54

48
89

163
1047

63
112

44
41

62
60

87
96

67
65

Annual income
1: 20,000 elasticity 5.1
2: 60,000 elasticity 2.9
3: 120,000 elasticity 1.5% difference in CV btw
income groups 2 and 1
income groups 3 and 1

Contribution of heterogeneous ηs
income groups 2 and 1
income groups 3 and 1

8
7

28
25

Notes: This table replicates the exercise in Table 8 but imposing the lowest elasticity of substitution (that for the highest-income
household with income of 120, 000 CHF), ηhst0 , is equal to 1.5 rather than 3.

keeping the elasticity difference between income groups unchanged.
Fourth, in our baseline we choose ρ = 0.99 so that expenditure shares across sectors
are essentially fixed. Table A21 reports results in which we use a much lower value ofρ = 0.20.
Finally, in our baseline we choose elasticities of substitution in the service sector andthe other non-grocery goods sector to match those we estimated within the grocery sector;
we do so because estimates of income-group-specific price elasticities are not available
outside of our Homescan data on groceries. Tables A22 and A23 report results in which
we impose a common price elasticity across all income groups within the service sector
and within both the service and other non-grocery goods sectors, respectively. In bothcases, the contribution of heterogeneous elasticities falls relative to that in our baseline.
Nevertheless, since import shares within the service sector are relatively low, results inTable A22 are very similar to those in our baseline.

A29

Table A20: Elasticity of substitution of high-income group = 5
+10

-0.4
-0.5
-0.6

-1.7
-2.1
-2.5

-2.8
-3.8
-4.5

-3.8
-5.7
-7.5

-4.1
-7.0
-11

-0.1
-0.3
-0.4

16
31

23
42

32
60

50
99

70
168

153
272

44
42

60
60

71
75

72
70

Annual income
1: 20,000 elasticity 8.6
2: 60,000 elasticity 6.4
3: 120,000 elasticity 5.0

Import price shock+20 +40 +1000
σ=0

+2.2

+2.2
σ>0

% difference in CV btw
income groups 2 and 1
income groups 3 and 1

Contribution of heterogeneous ηs
income groups 2 and 1
income groups 3 and 1

8
7

28
26

Notes: This table replicates the exercise in Table 8 but imposing the lowest elasticity of substitution (that for the highest-income
household with income of 120, 000 CHF), ηhst0 , is equal to 5 rather than 3.

Table A21: Elasticity of substitution across sectors = 0.2
+10

-0.4
-0.5
-0.6

-1.9
-2.3
-2.6

-3.2
-4.2
-5.1

-4.8
-7.3
-9.5

-5.8
-11.9
-25.2

-0.2
-0.4
-0.5

16
30

22
41

31
58

51
98

106
335

83
148

44
41

62
61

80
87

69
67

Annual income
1: 20,000 elasticity 6.6
2: 60,000 elasticity 4.4
3: 120,000 elasticity 3.0

Import price shock+20 +40 +1000
σ=0

+2.2

+2.2
σ>0

% difference in CV btw
income groups 2 and 1
income groups 3 and 1

Contribution of heterogeneous ηs
income groups 2 and 1
income groups 3 and 1

8
7

28
26

Notes: This table replicates the exercise in Table 8 but imposing ρ = 0.2 rather than ρ = 0.99.

A30

Table A22: Homogeneous elasticities within the service sector
+10

-0.4
-0.5
-0.6

-1.8
-2.2
-2.6

-3.2
-4.1
-4.9

-4.8
-7.0
-9

-5.7
-11.1
-21.5

-0.2
-0.4
-0.5

16
30

21
39

29
54

47
89

94
275

54
97

42
39

60
58

79
85

60
58

Annual income
1: 20,000
2: 60,000
3: 120,000

Import price shock+20 +40 +1000
σ=0

+2.2

+2.2
σ>0

% difference in CV btw
income groups 2 and 1
income groups 3 and 1

Contribution of heterogeneous ηs
income groups 2 and 1
income groups 3 and 1

7
6

26
23

Notes: This table replicates the exercise in Table 8 but imposing that within the service sector all income groups have a common importelasticity equal to that of income group 2 in our baseline (ηhst0 = 4.4 for s = services for all h).

Table A23: Homogeneous elasticities within the service and other goods sectors+2.2

Import price shock+10 +20 +40 +1000
σ=0

+2.2
σ>0

-0.4
-0.5
-0.6

-1.9
-2.2
-2.5

-3.4
-4.1
-4.8

-5.5
-7.0
-8.3

-8.1
-11.1
-14.6

-0.3
-0.4
-0.4

15
29

18
34

22
40

28
52

37
80

32
56

26
23

41
38

61
65

42
38

Annual income
1: 20,000
2: 60,000
3: 120,000% difference in CV btw
income groups 2 and 1
income groups 3 and 1

Contribution of heterogeneous ηs
income groups 2 and 1
income groups 3 and 1

4
3

16
13

Notes: This table replicates the exercise in Table 8 but imposing that within the service sector and the other goods sector all income
groups have a common import elasticity equal to that of income group 2 in our baseline (ηhst0 = 4.4 for s = services and other goods
for all h).

A31