Schulz-Gebha d, Jan; Ipsen, Leonha d
Wo king Pape
Poo households and he weigh o in la ion
FMM Wo king Pape , No. 106
P o ided in Coope a ion wi h:
Mac oeconomic Policy Ins i u e (IMK) a he Hans Boeckle Founda ion
Sugges ed Ci a ion: Schulz-Gebha d, Jan; Ipsen, Leonha d (2024) : Poo households and he weigh
o in la ion, FMM Wo king Pape , No. 106, Hans-Böckle -S i ung, Mac oeconomic Policy Ins i u e
(IMK), Fo um o Mac oeconomics and Mac oeconomic Policies (FMM), Düsseldo
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FMM WORKING PAPER
No. 106 • Augus 2024 • Hans-Böckle -S i ung
POOR HOUSEHOLDS AND
THE WEIGHT OF INFLATION
Jan Schulz
1
, Leonha d Ipsen
2
ABSTRACT
Public opinion and he pe cep ions o poo e households consis en ly indica e ha he poo
a e mos exposed o in la ion. Meanwhile, he empi ical li e a u e on income-dependen
in la ion inequali y emains ambiguous. In his pape , we explo e wo di e en explana ions
o his in la ion-inequali y puzzle. Fi s , we examine he ole o sec o ial he e ogenei y in
modula ing he impac o cos -push shocks on households. An Inpu -Ou pu analysis o 21
EU coun ies wi hin he global p oduc ion ne wo k shows he income-dependen impac o a
p ice shock o be highly con ingen on he sec o o o igin. While hese indings sugges a
pa ial explana ion o he ambiguous esul s on in la ion inequali y, hey do no poin o a
consis en o e exposu e o lowe -income households. As a second explana ion, we p opose
he income-weigh ing o p ice shock e ec s as opposed o he con en ional expendi u e-
weigh ing. This app oach conside s he sha e o income alloca ed o consump ion and hus
di ec ly a ec ed by a change in p ices. Using a u ili y amewo k, we demons a e ha unde
bounded a ionali y he decline in u ili y is indeed p opo ional o he a e age p opensi y o
consume imes he change in p ices. In oducing hese income-weigh s in ou empi ical
analysis, we ind lowe -income households o be disp opo ionally a ec ed by e e y sec o ial
p ice shock, ully explaining he in la ion-inequali y puzzle.
—————————
1 Economics Ins i u e, Uni e si y o Bambe g, jan.schulz-gebha d@uni-bambe g.de
2 Bambe g Resea ch T aining G oup on Bounded Ra ionali y, He e ogenei y and Ne wo k E ec s,
unded by he Hans Böckle Founda ion, leonha d.ipsen@uni-bambe g.de
Poo Households and he
Weigh o In la ion
Jan Schulz1 Leonha d Ipsen1, 2
jan.schulz-gebha d@uni-bambe g.de
leonha d.ipsen@uni-bambe g.de
1Economics Ins i u e, Uni e si y o Bambe g
2Bambe g Resea ch T aining G oup on Bounded Ra ionali y, He e ogenei y and Ne wo k E ec s,
unded by he Hans Böckle Founda ion
Abs ac
Public opinion and he pe cep ions o poo e households consis en ly indica e ha he poo a e mos
exposed o in la ion. Meanwhile, he empi ical li e a u e on income-dependen in la ion inequali y
emains ambiguous. In his pape , we explo e wo di e en explana ions o his in la ion-inequali y
puzzle. Fi s , we examine he ole o sec o ial he e ogenei y in modula ing he impac o cos -push
shocks on households. An Inpu -Ou pu analysis o 21 EU coun ies wi hin he global p oduc ion
ne wo k shows he income-dependen impac o a p ice shock o be highly con ingen on he sec o
o o igin. While hese indings sugges a pa ial explana ion o he ambiguous esul s on in la ion
inequali y, hey do no poin o a consis en o e exposu e o lowe -income households. As a second
explana ion, we p opose he income-weigh ing o p ice shock e ec s as opposed o he con en ional
expendi u e-weigh ing. This app oach conside s he sha e o income alloca ed o consump ion and
hus di ec ly a ec ed by a change in p ices. Using a u ili y amewo k, we demons a e ha unde
bounded a ionali y he decline in u ili y is indeed p opo ional o he a e age p opensi y o consume
imes he change in p ices. In oducing hese income-weigh s in ou empi ical analysis, we ind lowe -
income households o be disp opo ionally a ec ed by e e y sec o ial p ice shock, ully explaining
he in la ion-inequali y puzzle.
Keywo ds: In la ion, Inpu -ou pu Analysis, Eu ope, Inequali y
JEL: E31, D31, C15, C67, D90
Acknowledgemen s: We hank F ank Wes e ho , Geo g Max on, he pa icipan s o he mee ing o
he Keynes Socie y, and pa icipan s o he Wo kshop on Economics wi h He e ogeneous
In e ac ing Agen s o aluable commen s a c ucial junc ions o his in es iga ion. We hank Luis
D echsel o excellen esea ch assis ance. Funding by he Hans-Böckle -Founda ion h ough g an
PK045 is g a e ully acknowledged.
1. In oduc ion
Public opinion and he pe cep ions o poo e households consis en ly indica e
ha he poo a e mos exposed o in la ion. Meanwhile, he empi ical li e a u e
on he pe sis ence, di ec ion, and magni ude o income-dependen in la ion
inequali y emains ambiguous. In his pape , we explo e wo di e en
explana ions o his in la ion-inequali y puzzle. Fi s , we examine he ole o
sec o ial he e ogenei y in modula ing he impac o cos -push shocks on
households. An Inpu -Ou pu analysis o 21 EU coun ies wi hin he global
p oduc ion ne wo k shows he income-dependen impac o a p ice shock o be
highly con ingen on he sec o o o igin. While hese indings sugges a
pa ial explana ion o he ambiguous esul s on in la ion inequali y, hey only
show lowe -income households o be o e exposed o in la iona y p essu e o
some sec o ial shocks. As a second explana ion, we p opose he income-
weigh ing o p ice shock e ec s as opposed o he con en ional expendi u e-
weigh ing. Since he poo consume a much la ge sha e o hei income han
he ich, hei exposu e o he same shock on hei consump ion baske should
hus also be highe . Following his a gumen , analyzing in la ion inequali y
needs o conside he income-dependen p opensi ies o consume. In a
pa simonious u ili y amewo k, we demons a e ha unde bounded
a ionali y he decline in u ili y is indeed p opo ional o he a e age
p opensi y o consume (APC) imes he change in p ices, while unde a ional
expec a ions he APC does no a ec he change in u ili y. In pa icula , i
boundedly a ional agen s do no conside he e ec s o a shock o he
1
agg ega e p ice le el on hei u u e consump ion, he e ec o a p ice le el
change on hei u ili y will be weigh ed by hei indi idual APC. Finally,
in oducing hese income-weigh s in ou empi ical analysis, we ind lowe -
income households o be disp opo ionally a ec ed by li e ally e e y sec o ial
p ice shock. Taken oge he , we sugges and empi ically subs an ia e an
explana ion o he con es ing esul s on in la ion inequali y and show why
poo e households may indeed be o e ly exposed o in la ion.
The pape p oceeds as ollows: Sec ion 2 ou lines he ela ed li e a u e o ou
s udy. Sec ion 3 desc ibes he da a and model used o conduc ou empi ical
analysis. Sec ion 4 p esen s he esul s. Sec ion 5 discusses he ole o he APC
o in la ion inequali y based on a u ili y amewo k. Sec ion 6 p esen s he
esul s o ou empi ical analysis, his ime conside ing he income-weigh ing
a gumen . Sec ion 7 concludes wi h a inal discussion and pe spec i es o
u he esea ch.
2. Rela ed Li e a u e
Ou s udy connec s o di e en s ands o exis ing li e a u e. Mos impo an ly,
i aims o p o ide a pa ial explana ion o wha can be called he in la ion-
inequali y puzzle. While unequal in la ion exposu e can mani es along a
mul i ude o dimensions such as weal h (Doepke and Schneide , 2006), age
(Adam and Zhu, 2016), idiosync a ic consump ion o p ice di e ences
(Kaplan and Schulho e -Wohl, 2017; S asse e al., 2023), o ace (Hobijn and
Lagakos, 2005), we ocus on income-dependen in la ion inequali y o
2
households. The exis ing li e a u e on his p o ides inconclusi e esul s on he
exis ence and di ec ion, depending on he obse a ional pe iod and a ea
(Ga cima ín e al., 2021). I u he mo e epo s low pe sis ency o
asymme ic exposu e ac oss ime (Hobijn and Lagakos, 2005; S asse e al.,
2023), while again p o iding inconclusi e esul s on whe he o no highe
in la ion a es also lead o highe in la ion inequali y (Claeys and Gue a-
Jean enaud, 2022; C aw o d and Old ield, 2002; Hobijn and Lagakos, 2005).
Meanwhile, he pe cep ions o poo e households consis en ly indica e ha he
poo a e mos exposed o in la ion (Eas e ly and Fische , 2001; S an che a,
2024).
We p opose wo explana ions o his appa en misma ch: sec o ial
asymme ies in p ice shock p opaga ion and he conside a ion o a ec ed
income sha es, as opposed o ocusing only on expendi u e sha es. The i s
claim is mo i a ed by ounda ional esea ch om Webe e al. (2024). As hei
s udy showed o he US and subsequen ly was con i med in a simila s udy
by Ipsen e al. (2023) o he EU, a class o ew sec o s domina es he o e all
p ice le el o consume s. The la e also p o ide sugges i e e idence ha
poo e EU coun ies ace g ea e exposu e o ola ile and ising p ices, calling
o a mo e ho ough in es iga ion o his channel. Bo h s udies emphasize ha
he size o a sec o o i s sha e in inal consump ion may be an insu icien
p edic o o i s ac ual impo ance in de e mining he p ice le el. O en
o e looked, a sec o 's ole in he p oduc ion ne wo k cons i u es ano he key
3
a iable, as i modula es he p opaga ion o shocks. In hei le e , Ipsen and
1
Schulz (2024) build on a simila Leon ie Inpu -Ou pu model o unco e hese
p oduc ion ne wo k e ec s o in la ion inequali y. They show o he same se
o coun ies as in ou s udy ha he global p oduc ion ne wo k dampens
asymme ies in in la ion exposu e be ween lowe - and highe -income
households. Ye , in mos cases, his happens a he expense o poo e
households. In he p esen , ela ed s udy, we pick up upon hei wo k o u he
explo e he ole o sec o ial asymme ies o in la ion inequali y, going beyond
hei ocus on p oduc ion ne wo ks. Niki o os e al. (2024) also build upon he
a o emen ioned Inpu -Ou pu model o Webe e al. (2024) o analyze he
impac o p ice shocks on he unc ional dis ibu ion o income, namely p o i
e sus wage sha es. Ou s udy now p o ides he o he side o his coin by
showing ha p ice shocks also asymme ically a ec households dependen on
hei pe sonal income. Some pa allels o ou wo k can also be ound in he
analysis p o ided by Cucigna o e al. (2023), who y o decompose he shock
p opaga ion o he la es ene gy p ice shock o h ee Eu opean coun ies, also
conside ing he unde lying p oduc ion ne wo k. Ou wo k goes beyond his in
se e al aspec s. Fi s , we conside shocks p opaga ing in he global p oduc ion
ne wo k. Second, we analyze he ele an impo ance o all sec o classes, no
only he ene gy sec o s. Mos impo an ly, we ocus on dis ibu ional
consequences along he income dis ibu ion o a much la ge se o 21 EU
coun ies.
The sho age o semi-conduc o s is an illus a i e example, ha cos a mul i ude wo h o
1
p oduc ion ela i e o i s inpu p ice.
4
Conce ning ou second p oposi ion, he ole o he APC in in la ion inequali y,
ela ed li e a u e is somewha sca ce. Aucle (2019) add esses he impo ance
o di e ences in he p opensi y o consume, howe e , ocusing on mone a y
policy ansmission. Analysing in la ion inequali y in he eu o a ea, S asse e
al. (2023) men ion he p opensi y o consume as one aspec o consump ion
he e ogenei y bu do no explo e his aspec u he . Commonly, empi ical
analyses o in la ion inequali y a e based on expendi u e sha es (see, o
example, A gen e and Lee, 2021; Gü e and Weichen iede , 2020; Hobijn and
Lagakos, 2005; Kaplan and Schulho e -Wohl, 2017). While hese expendi u e
sha es cap u e he e ogenei ies in spending pa e ns, hey do no conside he
sha e o income used o expendi u es. As poo e households consis en ly
spend la ge sha es o hei a ailable income o consump ion pu poses, i.e.
ha e a highe APC (Fishe e al., 2016; Eu os a , 2021a), ocusing solely on
expendi u e sha es migh mask a subs an ial sou ce o ealized in la ion
inequali y. This a gumen ela es o a s and o li e a u e ha is conce ned wi h
he nexus o households’ expendi u e sha es and income, da ing back a leas
o Engel (1857). By now known as Engel’s Law, i es ablishes ha wi h
inc easing income, he ela i e income sha e spen on ood dec eases, albei a
la ge absolu e amoun is spen . Simila ly o ou app oach, pa s o his
li e a u e indeed appea o use ood’s income sha e in se e al p ominen
pape s (Engel and Kneip, 1996; Hamil on, 2001; Lese , 1963), al hough using
ood’s expendi u e sha e is s ill much mo e common (c . Lewbel and
Hou hakke , 2008 o a su ey). While heo e ical models o Engel’s law
indeed sugges income-weigh ing (Hamil on, 2001), empi ical pape s ypically
5
build on expendi u e sha es o no con ound hei es ima es o expendi u e
decisions o di e en goods’ ca ego ies wi h he decision o spend o sa e a
all (Ba igozzi e al., 2012). In ou pa simonious u ili y amewo k, we build on
a Cobb-Douglas unc ional o m o sa ings decisions, implying ha op imal
sa ings decisions a e independen o he p ice le el o add ess his issue. This
amewo k allows us o in e p e he expendi u e- and income-weigh ing cases
as pe aining o he u ili y e ec s o p ice shocks o ull and boundedly
a ional decision-making wi hou any con ounding e ec o he sa ings
decision. We a e, o he bes o ou knowledge, he i s o p o ide a sys ema ic
analysis o he impo ance o income-dependen asymme ies in he p opensi y
o consume o ealized in la ion inequali y as an agg ega e phenomenon no
cons ained o speci ic goods ca ego ies.
3. Empi ical S a egy
In his sec ion, we will discuss he da a and model used o ou empi ical
analysis. Ou global p oduc ion ne wo k, he sha es o inal demand o a
2
coun yc in sec o i o coun ya, as well as he sec o -speci ic p ice shocks a e
based on he Wo ld Inpu Ou pu Da abase (WIOD). I p o ides annual panel
Inpu -Ou pu da a o he yea s 2000 o 2014 o 43 coun ies wi h 56 sec o s
each and co e s economic ac i i y ha accoun s o mo e han 85 pe cen o
wo ld GDP (Timme e al., 2015).
To be able o analyze income-dependen in la ion, we o se he inal demand
da a o he WIOD wi h sec o -le el da a on consump ion by pu pose
Da a and code a e a ailable unde h ps://gi hub.com/ip5490/In la ion-Inequali y.
2
6
In Figu e 5 we map sec o s on a ou -quad an cha . Sec o classi ica ions can
be ound in Appendix C. The e ical axis co esponds o he o al e ec
es ima e o a sec o , indica ing whe he a p ice shock o his sec o is
equalizing (inc easing exposu e wi h income) o disequalizing (dec easing
exposu e wi h income). The ho izon al axis shows whe he he p oduc ion
ne wo k ampli ies o dampens in la ion inequali y. We compu e his media ing
e ec o each sec o as
.
I his di e ence is posi i e (nega i e), he p oduc ion ne wo k dampens
(ampli ies) in la ion inequali y ela i e o he di ec e ec o a p ice shock. In
o he wo ds, i posi i e, he p oduc ion ne wo k pushes he es ima e close o
he ze o line – he neu al e ec benchma k – ela i e o he di ec e ec . The
opposi e is ue o a nega i e media ing e ec .
While Figu es 2 - 4 al eady poin o signi ican asymme ies in he e ec s o
p ice shocks, Figu e 5 shows ha he ole o he p oduc ion ne wo k in
dis ibu ing hese shocks is a om uni o m ei he . In sum, ou esul s sugges
ha he income-dependen in la ion inequali y a ising om a p ice shock is
highly con ingen on he sec o o o igin. Thus, om a sec o ial pe spec i e,
ambiguous esul s on in la ion inequali y o di e en pe iods and places a e
no su p ising bu o be expec ed.
Media ing!E ec =|Di .!E ec !Es ima e|−|Ind.!E ec !Es ima e|
13
(3)
Wha does his mean o he ac ual in la ion a es and inequali ies a he
household le el? A e lowe - o highe -income households mo e a ec ed?
Figu e 6 p o ides an agg ega e answe o ou 21 coun ies unde
conside a ion. I shows he a e age mean e ec o a sec o in pe cen age
poin s. Red (inequali y enhancing) and blue (inequali y educing) con as
10
he dis ibu i e e ec o a p ice shock o a gi en sec o . The da ke (ligh e )
colo ing shows he a e age ela i e e ec size o he di ec (indi ec ) e ec o
a p ice shock o a gi en sec o . The a io o he o al e ec o inequali y
educing p ices o inequali y enhancing p ices sugges s an app oxima ely
equal exposu e ac oss incomes (51:49), unde lining he sys emic impo ance
o a se o ew sec o s o he o e all p ice le el (Webe e al., 2024). Ipsen
and Schulz (2024) p o ide a mo e de ailed decomposi ion o he income-
We i s compu e he a e age e ec o a sec o class conside ing sec o s om all supply-
10
coun ies (i.e. globally) o each income quin ile o each o he 21 demand-coun ies. We hen
compu e he mean o hese o each sec o class.
14
Fig. 5. Each quad an delimi s a dis inc e ec o a sec o ial p ice shock on
in la ion inequali y. The e ical axis epo s he o al e ec es ima es, whe e
nega i e (posi i e) alues indica e ha a p ice shock is inequali y enhancing
( educing). The ho izon al axis epo s he sum o
, whe e nega i e (posi i e) alues indica e ha
he p oduc ion ne wo k ampli ies (dampens) in la ion inequali y. Sec o s a e
labeled acco ding o ISIC Re . 4 classi ica ion. See Appendix C o a able
wi h sec o desc ip ions.
|To al E ec
Es ima e|
−|Indi ec E ec
Es ima e|
dependen e ec sizes, inding he o al exposu e o p ice shocks o e en il
sligh ly agains lowe -income households.
15
Fig. 6. A e age mean di ec (da ke ) and indi ec (ligh e ) e ec o each
sec o in pe cen age poin s. Red ma ks sec o s whose o al e ec is
inequali y enhancing, blue ma ks inequali y educing sec o s. Sec o s wi h
insigni ican e ec a e ma ked in g ay. To al e ec a io o Inequali y
Reducing P ices o Inequali y Enhancing P ices sugges s an app oxima ely
equal exposu e ac oss incomes (51:49).
All in all, a sec o ial pe spec i e on in la ion inequali y unco e s conside able
he e ogenei y in income-dependen in la ion exposu e, p o iding a p omising
explana ion o ambiguous esul s in p e ious s udies. I is no able, howe e ,
o subs an ia e he pe cep ions o poo e households ha hey a e consis en ly
mos exposed o in la ion. We discuss a second explana ion o his misma ch
in he ollowing.
5. The Role o Income-weigh s o In la ion
Inequali y
Empi ical s udies on in la ion inequali y commonly base hei analysis on
di e ences in expendi u es. While his app oach is able o cap u e income-
dependen he e ogenei y in he consump ion baske , i ails o conside he
ac ual income ha is alloca ed o consump ion and is hus di ec ly a ec ed by
a p ice change in his baske . As he p opensi ies o consume om a ailable
income a y subs an ially along weal h- and income-le els, ocusing solely on
di e ences in expendi u es migh mask a subs an ial sou ce o ealized
in la ion inequali y. In his sec ion, we use a s aigh o wa d u ili y amewo k
o show how unde bounded a ionali y he ma ginal g ow h a e o u ili y is
p opo ional o he p ice change imes he a e age p opensi y o consume.
We assume a Cobb-Douglas ype u ili y unc ion wi h and e lec ing
he weigh s on cu en and expec ed u u e consump ion o cap u e in e -
empo al mo i es, i.e., he u ili y unc ion is gi en by
α
(1 −α)
U
16
wi h as he a e age p opensi y o consume, as a ailable cu en income,
and as he p ice le el. He e, only en e s he cu en consump ion e m
(le ). As a consequence, agen s conside he e ec o he p ice le el o hei
cu en consump ion, while only conside ing he nominal income o he
u ili y hey gain ou o hei sa ings. This implies ha agen s ac boundedly
a ional, since he p ice le el will also a ec hei u u e consump ion and
hence, should a ec he u ili y gained ou o hei sa ings. Indeed, a ecen
eu o a ea su ey da a p o ides some e idence o his beha io , as he mos
common eac ion o he ecen in la iona y su ge was o modi y consump ion
beha io , while no e en hal o he esponden s epo ed adjus ing hei
sa ings (Bobasu e al., 2024).
By he FOC, he op imal p opensi y o consume is gi en by,
which implies he canonical esul ha expendi u es a e a cons an ac ion o
income. Op imizing gi es he u ili y unc ion o
U(γ;Y,α,p) = (γ⋅Y
p)α
⋅((1 −γ)Y)1−α
γ
Y
p
p
Y
γ*
∂U
∂γ
!
= 0 ⇒γ* = α,
γ*
U*(Y,α,p) = (αY
p)α
⋅((1 −α)Y)1−α.
17
(4)
(5)
(6)
Taking he loga i hmic de i a i e and app oxima ing by he disc e e g ow h
a e in u ili y o e he disc e e g ow h a e in he p ice le el yields
Fo ou applica ion case, all ini ial p ice le els a e no malized o uni y. This
implies ha we can exp ess he ma ginal g ow h a e o u ili y in esponse o a
p ice shock as
Thus, i agen s solely ocus on he consump ion e ec o a change in p ices,
he ma ginal g ow h a e o u ili y is indeed p opo ional o he p ice change
imes he a e age p opensi y o consume. The abo e equa ion (8) nes s he
usual use case o expendi u e weigh s o . This case co esponds o a
si ua ion, whe e agen s do no gain any u ili y ou o sa ings and hus, in e -
empo al mo i es do no ma e . Wi hin he same amewo k, Appendix D
shows ha unde a ull a ionali y assump ion, he p opensi y o consume does
no a ec he eac ion in u ili y.
Empi ically, as Table 1 shows, a signi ican sha e o households epo APCs
well o e 90 pe cen o a ailable income. Fo income-quin ile one, only
Cyp us epo s an APC o below 100 pe cen . A guably, hese cash-
cons ained households will only be conce ned wi h p esen consump ion and
dlog U*
dlog p=−α
p≈Δu*/u*
Δp/p.
Δp
Δu*/u
Δp=−α⇔ − Δu*
u=α⋅ Δp.
α= 1
18
(7)
(8)
canno conside he e ec o a change in p ices on hei sa ings. Since we a e
in e es ed in why poo e households a e indica ed o be disp opo ionally
a ec ed by in la ion, conside ing he APC seems o be well-g ounded.
6. Empi ical Resul s o Income-weigh ed
In la ion Inequali y
To empi ically in es iga e he impac o APCs on he ealiza ion o income-
dependen in la ion inequali y, we e un ou Inpu -Ou pu analysis, his ime
using income-weigh ed expendi u e sha es. The e o e, we compu e he sha e
o expendi u e in a gi en sec o as a a io o he o al income as opposed o he
o al expendi u es. We compu e hese o e e y coun y-income pai as
wi h as he a e age expendi u es o income quin ileq o coun yc on
goods p oduced in sec o j and as he mean disposable income o
quin ileq o coun yc (see Appendix A o he coun y speci ic APCs and
Eu os a (2021a) o in o ma ion on he da a collec ion. We can now eplace
he expendi u e sha es o ou ini ial Inpu -Ou pu se up wi h hese income-
weigh ed sha es.
exj,c,q×APCc,q=exj,c,q
n
∑
j=1
exj,c,q
×
n
∑
j=1
exj,c,q
Incomec,q
=exj,c,q
Incomec,q
,
exj,c,q
Incomec,q
19
(9)
Figu es 7 - 9 epo he es ima es (poin s) and 95 pe cen con idence in e als
(whiske s) o he di ec , indi ec , and o al e ec , espec i ely. I shows ha i
we a e o conside he di e ences in he APCs o in la ion inequali y, e e y
sec o ial p ice shock disp opo ionally a ec s lowe -income households. The
massi e di e ences in he APCs be ween income g oups e en ou weigh
di e ences in expendi u e pa e ns in he o he di ec ion. These indings a e
consis en wi h he indica ion ha poo e households a e consis en ly
o e exposed o in la ion.
20
Fig. 7. Es ima es o income-dependen in la ion exposu e o he e ec o a
p ice shock o he inal goods p oduced by a sec o (di ec e ec ). Whiske s
gi e he 95 pe cen con idence in e al. Es ima es below ze o a e Inequali y
Enhancing P ices, as he in la ion exposu e o households owa ds hese
sec o s is educed wi h inc easing income. Posi i e es ima es acco dingly
show Inequali y Reducing P ices, as exposu e ises wi h inc easing income.
Based on income-weigh ed expendi u e sha es.
21
Fig. 8. Es ima es and 95 pe cen con idence in e al o income-dependen
in la ion exposu e o he e ec o a p ice shock o he in e media e goods
p oduced by a sec o (indi ec e ec ). Based on income-weigh ed
expendi u e sha es.
Fig. 9. Es ima es and 95 pe cen con idence in e al o income-dependen
in la ion exposu e o he e ec o a p ice shock o all goods p oduced by a
sec o ( o al e ec ). Based on income-weigh ed expendi u e sha es.
7. Conclusion
The empi ical li e a u e on income-dependen in la ion inequali y p o ides
con es ing esul s abou i s di ec ion, magni ude, and pe sis ence. Meanwhile,
he pe cep ions o poo e households consis en ly indica e ha hey a e mos
exposed o in la ion. We p opose and empi ically subs an ia e wo possible
explana ions o his in la ion-inequali y puzzle. Fi s , we show o a se o 21
EU coun ies embedded in he global p oduc ion ne wo k, ha he income-
dependen impac o a p ice shock is highly con ingen on he sec o o o igin.
This sec o ial pe spec i e poses a p omising con es e o explaining
ambiguous esul s on in la ion inequali y. Condi ional on he a ailabili y o
da a, u u e esea ch could es he explana o y powe o ou sec o -le el
es ima es o he ealized in la ion-inequali y in p e ious s udies. Ou esul s
di ec ly imply he es able hypo hesis ha poo households' pe cep ions o
in la ion should eac he s onges , whene e in la iona y p essu es o igina e
in sec o s like housing and ag icul u al p oduc s. Moni o ing sec o ial p ices
could gi e policy-make s a head s a in mi iga ing in la ion and especially in
p e en ing unnecessa y ha d-ship o lowe -income households.
Second, we p opose ha income-dependen di e ences in he p opensi ies o
consume ma e o ealized in la ion inequali y. Focusing solely on
di e ences in expendi u es ails o conside he ac ual income ha is alloca ed
o consump ion and hus di ec ly a ec ed by a p ice change in he
consump ion baske . Using a u ili y amewo k, we show ha o agen s who
ocus hei conce n on he consump ion e ec o a change in p ices, he
22
Appendix A: A e age P opensi y o Consume
29
GEO
Q1 (%)
Q2 (%)
Q3 (%)
Q4 (%)
Q5 (%)
Aus ia
129.8
97.9
85
75.9
59.4
Belgium
118.9
92.1
73.8
63.3
50
Bulga ia
113.9
89.6
75
62.2
44.1
C oa ia
121
107.7
88.4
80
63
Cyp us
89.3
87
86.5
82.6
65.2
Denma k
117.5
85.6
74.8
62.3
46.5
Es onia
108.3
81.9
69.9
54
45.3
F ance
114.1
84.9
78.7
72
55.3
Ge many
143.4
91.6
84.4
77.5
63.4
G eece
168
110.4
101.5
88.6
72
Hunga y
113.4
94.8
83.3
74.8
66.2
La ia
114
88.7
78
72.4
56.9
Li huania
110.7
82.1
69.5
51.8
39.4
Luxembou g
112.9
86.8
80.4
63.8
52.8
Mal a
136.2
94.6
87.6
74.4
53.9
Ne he lands
148.2
104.3
83.6
68.3
52.9
Poland
104.1
60.6
53.5
47.2
38.8
Romania
195.4
126.6
104.1
86
65.6
Slo akia
103
89.2
79.6
71.3
55
Slo enia
116.5
95.7
87
78.2
64.3
Spain
129.3
90.6
76
65.8
50.6
Mean
124.2
92.5
81.0
70.1
55.3
Table 1: A e age P opensi y o Consume o each income
quin ile in 21 EU coun ies o he yea 2020. Based on Eu os a
(2021a).
Appendix B: Leon ie P ice Model De i a ion
We base his sec ion on he Leon ie p ice models used in Ipsen and Schulz
(2024), Valadkhani and Mi chell (2002) and Webe e al. (2024). Equa ion (i)
shows he model’s p inciple case o he p ice o being a linea
unc ion o he p ices o inpu s imes he echnical coe icien s plus he
alue added . Since ou da a comp ises global ade da a, we need no
addi ional impo and expo a iables. The echnical coe icien s a e
compu ed as he a io o alue o inpu s om o he o e all alue o
ou pu . Wi h no malizing he ou pu o , (i) gi es he p ice pe
uni o ou pu . A change in p ices is hus o be in e p e ed as pe cen age
changes.
Fo sec o s, his becomes a sys em o linea equa ions.
Since we wan o simula e he down-s eam p opaga ion o shocks, we need o
ake he anspose o he echnical coe icien ma ix . In ma ix no a ion, his
gi es
Pj
sec o j
Pi≠j
aij
Vj
aij
sec o i
sec o j
sec o j
Pj=a1jP1+ . . . + aij Pi+ . . . + anj Pn+Vj
n
P1
P2
⋮
Pn
=
a11a21 ⋯an1
a12a22 ⋯an2
⋮ ⋮ ⋱ ⋮
a1na2n⋯ann
P1
P2
⋮
Pn
+
1
2
⋮
n
A
30
(i)
(ii)
As a nex s ep, we single ou he sec o which we wan o expose o an
exogenous p ice shock. This spli s (iii) in o
11
wi h he p ice ec o o he shocked sec o and as he p ice ec o s o
he emaining endogenous sec o s. Since is de e mined by ou exogenous
shock, we a e only in e es ed in
cap u es how he p ices in he endogenous sec o s depend on he p ice
o he exogenous sec o . cap u es how he p ices in he endogenous
sec o s depend on each o he . I we sol e o , we ge
Assuming no subs i u ion, he quan i y o inpu s emains unchanged ollowing
a change in p ices. Thus, ollowing a change in p ices in he exogenous sec o
, he p ice change in he emaining sec o s, , is gi en by
P=A′ P+ .
[PX
PE]=[A′
XXA′
EX
A′
XEA′
EE][PX
PE]+[ X
E]
PX
PE
PX
PE=A′
XE PX+A′
EE PE+ E.
A′
XE PX
A′
EE PE
PE
PE= (I−A′
EE)−1A′
XE PX+ (I−A′
EE)−1 E.
ΔPx
ΔPE
ΔPE= (I−A′
EE)−1A′
XEΔPX.
Recall ha we compu e he p ice shock o as i s a e age pe cen age change o e ou
11
pe iod o obse a ion.
sec o j
31
(iii)
(i )
( )
( i)
( ii)
A his poin , we in oduce he expendi u e sha es. ep esen s he
expendi u e sha e o o in he exogenous .
ep esen s he expendi u e sha e o o in he endogenous
sec o . We a e now able o decompose he e ec o a p ice shock o he
inal goods p oduced by a sec o in o
and he e ec o a p ice shock o he in e media e goods p oduced by a sec o
in o
The o al e ec o a p ice shock o a sec o is hen gi en by
These di ec , indi ec and o al p ice shock e ec s o a sec o a e used as he
dependen a iable o compu e he elas ici y es ima es acco ding o equa ion
(2) in Sec ion 3.
esx,q,i
quin ileq
coun yi
sec o x
ese,q,i
quin ileq
coun yi
e≠x
Δπdi ec
q,i,x=esx,q,iΔPx
Δπindi ec
q,i,x=∑
e≠x
ese,q,iΔPe.
Δπ o al
q,i,x=esx,q,iΔPx+∑
b≠x
ese,q,iΔPe.
32
( iii)
(ix)
(x)
Appendix C: Sec o Classi ica ions
33
Table 2
Sec o
Label
Desc ip ion
Sec o
Label
Desc ip ion
A01
C op and animal p oduc ion,
hun ing and ela ed se ice
ac i i ies
C25
Manu ac u e o ab ica ed me al
p oduc s, excep machine y and
equipmen
A02
Fo es y and logging
C26
Manu ac u e o compu e , elec onic
and op ical p oduc s
A03
Fishing and aquacul u e
C27
Manu ac u e o elec ical equipmen
B
Mining and qua ying
C28
Manu ac u e o machine y and
equipmen n.e.c.
C10-C12
Manu ac u e o ood
p oduc s, be e ages and
obacco p oduc s
C29
Manu ac u e o mo o ehicles,
aile s and semi- aile s
C13-C15
Manu ac u e o ex iles,
wea ing appa el and lea he
p oduc s
C30
Manu ac u e o o he anspo
equipmen
C16
Manu ac u e o wood and o
p oduc s o wood and co k,
excep u ni u e; manu ac u e
o a icles o s aw and
plai ing ma e ials
C31/C32
Manu ac u e o u ni u e; o he
manu ac u ing
C17
Manu ac u e o pape and
pape p oduc s
C33
Repai and ins alla ion o machine y
and equipmen
C18
P in ing and ep oduc ion o
eco ded media
D35
Elec ici y, gas, s eam and ai
condi ioning supply
C19
Manu ac u e o coke and
e ined pe oleum p oduc s
E36
Wa e collec ion, ea men and
supply
C20
Manu ac u e o chemicals
and chemical p oduc s
E37-E39
Sewe age; was e collec ion,
ea men and disposal ac i i ies;
ma e ials eco e y; emedia ion
ac i i ies and o he was e
managemen se ices
C21
Manu ac u e o basic
pha maceu ical p oduc s and
pha maceu ical p epa a ions
F
Cons uc ion
C22
Manu ac u e o ubbe and
plas ic p oduc s
G45
Wholesale and e ail ade and epai
o mo o ehicles and mo o cycles
C23
Manu ac u e o o he non-
me allic mine al p oduc s
G46
Wholesale ade, excep o mo o
ehicles and mo o cycles
C24
Manu ac u e o basic me als
G47
Re ail ade, excep o mo o ehicles
and mo o cycles
34
Sec o
Label
Desc ip ion
Sec o
Label
Desc ip ion
H49
Land anspo and anspo
ia pipelines
L68
Real es a e ac i i ies
H50
Wa e anspo
M69/
M70
Legal and accoun ing ac i i ies;
ac i i ies o head o ices;
managemen consul ancy ac i i ies
H51
Ai anspo
M71
A chi ec u al and enginee ing
ac i i ies; echnical es ing and
analysis
H52
Wa ehousing and suppo
ac i i ies o anspo a ion
M72
Scien i ic esea ch and de elopmen
H53
Pos al and cou ie ac i i ies
M73
Ad e ising and ma ke esea ch
I
Accommoda ion and ood
se ice ac i i ies
M74/
M75
O he p o essional, scien i ic and
echnical ac i i ies; e e ina y
ac i i ies
J58
Publishing ac i i ies
N
Adminis a i e and suppo se ice
ac i i ies
J59/J60
Mo ion pic u e, ideo and
ele ision p og amme
p oduc ion, sound eco ding
and music publishing
ac i i ies; p og amming and
b oadcas ing ac i i ies
O84
Public adminis a ion and de ence;
compulso y social secu i y
J61
Telecommunica ions
P85
Educa ion
J62/J63
Compu e p og amming,
consul ancy and ela ed
ac i i ies; in o ma ion
se ice ac i i ies
Q
Human heal h and social wo k
ac i i ies
K64
Financial se ice ac i i ies,
excep insu ance and pension
unding
R/S
O he se ice ac i i ies
K65
Insu ance, einsu ance and
pension unding, excep
compulso y social secu i y
T
Ac i i ies o households as
employe s; undi e en ia ed goods-
and se ices-p oducing ac i i ies o
households o own use
K66
Ac i i ies auxilia y o
inancial se ices and
insu ance ac i i ies
U
Ac i i ies o ex a e i o ial
o ganiza ions and bodies
Appendix D: U ili y Maximiza ion unde Full
Ra ionali y
The u ili y unc ion is gi en by
wi h as he a e age p opensi y o consume, as a ailable cu en income,
and as he p ice le el. In his e sion, en e s bo h he e m ela ing o
cu en consump ion (le ) and in he sa ings ( igh ). Thus, in his se up,
agen s co ec ly an icipa e bo h he consump ion as well as weal h e ec o a
change in .
By he FOC, we can de i e he op imal a e age p opensi y o consume
Op imizing gi es he u ili y unc ion o
Taking he loga i hmic de i a i e and app oxima ing by he disc e e g ow h
a e in u ili y o e he disc e e g ow h a e in he p ice le el yields
U
U(γ;Y,α,p) = (γ⋅Y
p)α
⋅((1 −γ)Y
p)1−α
,
γ
Y
p
p
p
γ*
∂U
∂γ
!
= 0 ⇒γ* = α.
γ*
U*(Y,α,p) = (αY
p)α
⋅((1 −α)Y
p)1−α
.
35
(i)
(ii)
(iii)
Assumeíng ha he ini ial p ice le el is , han he ma ginal g ow h a e
o u ili y is gi en by
In his case, he model sugges s ha i agen s co ec ly an icipa e he e ec o
a change in p ices on hei consump ion and sa ings beha io , hen he e ec
o a p ice shock on u ili y is no media ed by he a e age p opensi y o
consume.
dlog U*
dlog p=−1
p≈Δu*/u*
Δp/p.
p= 1
Δu*/u
Δp=−1⇔ − Δu*
u=Δp.
36
(i )
( )
Imp in
Publishe
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