Do e n, Jonas; Glas, Alexande ; Kenny, Geo
A icle — Published Ve sion
Tes ing o di e ences in su ey‐based densi y
expec a ions: A composi ional da a app oach
Jou nal o Applied Econome ics
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Sugges ed Ci a ion: Do e n, Jonas; Glas, Alexande ; Kenny, Geo (2024) : Tes ing o di e ences
in su ey‐based densi y expec a ions: A composi ional da a app oach, Jou nal o Applied
Econome ics, ISSN 1099-1255, Wiley, Hoboken, NJ, Vol. 39, Iss. 6, pp. 1104-1122,
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Recei ed: 4 June 2023 Re ised: 11 Janua y 2024 Accep ed: 29 Ap il 2024
DOI: 10.1002/jae.3080
RESEARCH ARTICLE
Tes ing o di e ences in su ey-based densi y expec a ions:
A composi ional da a app oach
Jonas Do e n1Alexande Glas2Geo Kenny3
1School o Business, Economics and
Socie y, F ied ich-Alexande -Uni e si ä
E langen-Nü nbe g, Nu embe g,
Ge many
2Pensions and Sus ainable Financial
Ma ke s, ZEW – Leibniz Cen e o
Eu opean Economic Resea ch,
Mannheim, Ge many
3Eu opean Cen al Bank, F ank u am
Main, Ge many
Co espondence
Jonas Do e n, School o Business,
Economics and Socie y,
F ied ich-Alexande -Uni e si ä
E langen-Nü nbe g, Lange Gasse 20,
90403 Nu embe g, Ge many.
Email: [email p o ec ed]
Summa y
We p opose o ea su ey-based densi y expec a ions as composi ional da a
when es ing ei he o he e ogenei y in densi y o ecas s ac oss di e en g oups
o agen s o o changes o e ime. Mon e Ca lo simula ions show ha he p o-
posed es has mo e powe ela i e o bo h a boo s ap app oach based on he
KLIC and an app oach ha in ol es mul iple es ing o di e ences o indi id-
ual pa s o he densi y. In addi ion, he es is compu a ionally much as e han
he KLIC-based one, which elies on simula ions, and allows o compa isons
ac oss mul iple g oups. Using densi y expec a ions om he ECB Su ey o P o-
essional Fo ecas e s and he US Su ey o Consume Expec a ions, we show he
use ulness o he es in de ec ing possible changes in densi y expec a ions o e
ime and ac oss di e en ypes o o ecas e s.
KEYWORDS
composi ional da a, densi y o ecas s, disag eemen , su ey o ecas s
1INTRODUCTION
Expec a ions a e cen al bo h o mic oeconomic decision-making and o mac oeconomic dynamics. Hence, i is no su -
p ising ha a la ge body o li e a u e s udies he p ope ies o expec a ions in a ious economic con ex s. In ecen yea s,
he use o su ey-based expec a ion da a has become inc easingly mo e common. This p ocess is pa icula ly s ong in
mac oeconomics whe e mo e and mo e su eys a e se up o s udy he mac oeconomic expec a ions o p i a e house-
holds (Con ad e al., 2022; Coibion e al., 2024; D'Acun o e al., 2021; Kim & Binde , 2023), i ms (And ade e al., 2022;
Coibion e al., 2018, 2020; Do e n e al., 2023; Kuma e al., 2023), and p o essional o ecas e s (Glas & Ha mann, 2022;
Rich & T acy, 2021).
We obse e wo endencies in his li e a u e ha we wan o b ing oge he in ou pape . On he one hand, he e is a
g owing ocus on unde s anding he easons o and he e ec s o he e ogenei y o mac oeconomic expec a ions a leas
since he seminal con ibu ion by Mankiw e al. (2003). On he o he hand, he e is a endency owa d he analysis
o p obabilis ic (densi y) expec a ions ha o e a mo e comple e pic u e o expec a ions ela i e o con en ional poin
expec a ions (Manski, 2018). Wha is missing, so a , a e majo e o s o combine hese wo impo an aspec s. Rich
and T acy (2021) use he Wasse s ein dis ance as a measu e o he e ogenei y in expe s' densi y o ecas s. Howe e ,
hey do no compa e dis inc g oups o o ecas e s and do no es o s a is ical di e ences. Mi chell and Hall (2005)
and Clemen s (2018) use Diebold–Ma iano- ype es s based on he Kullback Leible In o ma ion C i e ion (KLIC) as
sugges ed by Bao e al. (2007). Mi chell and Hall (2005) compa e he densi y o ecas s (“ an cha s”) o in la ion in he
Uni ed Kingdom epo ed by he Bank o England and he Na ional Ins i u e o Economic and Social Resea ch and ind
This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion-NonComme cial-NoDe i s License, which pe mi s use and dis ibu ion in any medium,
p o ided he o iginal wo k is p ope ly ci ed, he use is non-comme cial and no modi ica ions o adap a ions a e made.
© 2024 The Au ho s. Jou nal o Applied Econome ics published by John Wiley & Sons, L d.
wileyonlinelib a y.com/jou nal/jae J Appl Econ. 2024;39:1104–1122.
1104
ha he o me end o be mo e accu a e han he la e . Clemen s (2018) es s whe he expe s' densi y o ecas s ou -
pe o m uncondi ional benchma k densi ies. While his app oach could be used o es o (c oss-sec ional) expec a ion
he e ogenei y, bo h s udies ely on ime se ies a ia ion in o ecas pe o mance o compa e di e en densi y expec a ions.
Ou pape 's con ibu ion is o sugges a me hod ha can be used o es o he e ogenei y o p obabilis ic expec a ions.
Such p obabilis ic expec a ions a e usually elici ed by asking agen s o assign p obabili ies o in e als o po en ial ou -
comes. Ou cen al insigh is ha hese ec o s o p obabili ies a e composi ional da a. Composi ional da a consis o
ec o s o p opo ions (he e: p obabili ies) ha a e subjec o he cons ain ha he sum o all elemen s mus equal a
ixed alue (he e: one); see Ai chison (1982, 1986). We p opose o use es s ha ha e been de eloped o composi ional
da a o es o di e ences in p obabilis ic expec a ions ac oss di e en g oups o indi iduals o su ey wa es.
Using Mon e Ca lo simula ions, we compa e he p oposed composi ional app oach o an al e na i e boo s ap-based
app oach ha builds on he mo e adi ional way o compa ing (expec a ion) dis ibu ions using dis ance measu es such
as he KLIC. The esul s om he Mon e Ca lo simula ions sugges ha he es s designed o composi ional da a ha e
highe powe agains al e na i es ha imply only mode a e di e ences in densi y expec a ions be ween wo subpopula-
ions, especially when he sample size is ela i ely small. Mo eo e , ou p oposed es is much as e because i does no
equi e simula ions due o he ac ha he dis ibu ion o he es s a is ic is known unde he null hypo hesis. In addi-
ion, he es allows o a join compa ison o mul iple g oups, whe eas he KLIC-based app oach can only be used o
compa e wo g oups a a ime.
We hen apply he me hod o i e di e en esea ch ques ions ha ha e ecen ly been discussed in he li e a u e.
Speci ically, we es o he e ogenei y o expec a ions and changes o e ime among di e en g oups o p o essional
mac oeconomic o ecas e s (based on da a om he Eu opean Cen al Bank's Su ey o P o essional Fo ecas e s, SPF) and
p i a e households (based on da a om he Fede al Rese e Bank o New Yo k's Su ey o Consume Expec a ions, SCE).
We show ha (i) p o essional o ecas e s quickly changed hei sho - e m in la ion densi y o ecas s in esponse o he
ecen pe iod o ising in la ion a es, whe eas long- e m expec a ions eac ed mo e g adually, (ii) in mos su ey wa es,
bo h in la ion and GDP g ow h expec a ions di e signi ican ly be ween expe s ha ound hei p obabili y s a emen s
and hose ha do no , (iii) he e is s ong e idence agains he hypo hesis ha p i a e households' in la ion expec a ions
epo ed by men and women a e equal, (i ) households lea n abou concep s hey a e ini ially un amilia wi h—such as
in la ion— ia epea ed su ey pa icipa ion as ecen ly highligh ed by Kim and Binde (2023), and ( ) o a sizeable ac-
ion o pe iods in ou sample, households om di e en egions epo signi ican ly di e en densi y expec a ions o he
u u e change o na ionwide house p ices.
Fi s and o emos , ou wo k ela es o o he s udies ha analyze he e ogenei y o mac oeconomic expec a ions ac oss
indi iduals o i ms. Fo example, Malmendie and Nagel (2011, 2016) show ha US households who expe ienced low
s ock ma ke e u ns and/o high in la ion a es du ing hei li e ime end o be mo e pessimis ic wi h espec o u u e
s ock ma ke de elopmen s and/o in la ion han indi iduals wi h mo e mode a e li e ime expe iences. Simila ly, Kuchle
and Za a (2019) ind ha local house p ice expe iences a ec households' expec a ions abou u u e house p ice changes.
In pa icula , he expe ience o ola ile house p ices leads o a highe dispe sion o house p ice expec a ions. Wi h espec
o i m expec a ions, Kuma e al. (2015) ind ha he in la ion expec a ions o i m manage s in New Zealand a e hea ily
dispe sed, a odds wi h he no ion o ancho ed o ully a ional expec a ions. A common ea u e sha ed by hese s udies
is ha hey ocus on poin o ecas s. Ou con ibu ion is o p o ide me hods ha allow us o analyze he e ogenei y o
densi y expec a ions and, hus, o mo e beyond he analysis o he e ogenei y o poin expec a ions.
In e ms o he me hodology used, ou wo k ela es o—and bo ows hea ily om— he li e a u e on composi ional da a.
Ai chison (1986) and Filzmose e al. (2018) o e comp ehensi e o e iews o me hodological aspec s ha a e impo -
an when dealing wi h such da a. The me hods a e widely applied in many disciplines, including geochemis y (e.g.,
Buccian i, 2018; Reimann e al., 2012), sedimen ology (Wel je & on Eyna en, 2004), demog aphy (Lloyd e al., 2012),
and medicine (B aga & Feingenbaun, 2020; Ki ano e al., 2020). In economics, me hods o composi ional da a ha e been
used, o ins ance, o analyze income o expendi u e sha es (F y e al., 1996) and how ime budge s a e sha ed o di -
e en ac i i ies (Gup a e al., 2020). Ou con ibu ion is o show ha hese me hods a e also ele an and help ul when
dealing wi h p obabilis ic expec a ions.
The es o his pape is s uc u ed as ollows. Sec ion 2 b ie ly summa izes he basics o composi ional da a and
desc ibes he es s ha we p opose o use o he analysis o he e ogenei y and empo al s abili y in p obabilis ic expec-
a ions. Sec ion 3 p esen s he esul s om he Mon e Ca lo simula ions ha we use o assess he p ope ies o he es s.
Sec ion 4 desc ibes he applica ions o he p oposed me hod. Sec ion 5 concludes.
DOVERN ET AL.1105
2METHODOLOGY
We conside su ey-based p obabilis ic densi y expec a ions epo ed by indi iduals i=1,…,Na ime =1,…,T
o some u u e (mac oeconomic) ou come in pe iod +hso ha hindica es he o ecas ho izon. In p ac ice, hese
densi y expec a ions a e mos commonly elici ed by asking subjec s o assign p obabili ies o a se o Kdi e en ou come
in e als (o “bins”). The assigned alues indica e he p obabili ies by which subjec s expec he ou come o all in o
he co esponding in e als. Hence, each p obabilis ic densi y expec a ion is epo ed in he o m o a his og am ha is
ep esen ed by a ec o pi, ,h=(pi, ,h,1,…,pi, ,h,K)′wi h nonnega i e elemen s pi, ,h,k o k=1,…,K. Since he union o
all in e als co e s he en i e ou come space, a na u al cons ain (which is usually en o ced by he su ey design) is ha
pi, ,h,1+pi, ,h,2+…+pi, ,h,K=1.
We a e in e es ed in he ollowing p oblem: Gi en wo se s o densi y o ecas s om di e en g oups o o ecas -
e s, deno ed as g∈{A,B}, we wan o es —based on he sample o a ailable his og ams— he null hypo hesis
ha indi iduals om bo h g oups d aw hei p obabilis ic expec a ions om he same dis ibu ion. Mo e o mally, le
(𝜇g
,h,1,𝜇
g
,h,2,·; ·𝜇g
,h,K)′
=𝝁g
,h=E(pg
i, ,h)deno e he expec ed alue o he ec o o in e al p obabili ies o any indi id-
ual om g oup g.1No e ha he de ini ion and he numbe o in e als, K, need o be he same o bo h g oups because
he es is going o compa e ec o s ha need o be o he same leng h. Usually, his is gi en au oma ically because expec-
a ions o bo h g oups come om he same su ey. Ou null hypo hesis hen is H0:𝝁A
,h=𝝁B
,hagains he al e na i e
hypo hesis ha H1:𝝁A
,h≠𝝁B
,h. We wan o es his hypo hesis abou he wo popula ion momen s using wo samples o
obse ed his og am o ecas s o size NAand NB(wi h NA+NB=N).2
In he ollowing subsec ions, we i s p opose a es o analyzing di e ences o his og am o ecas s ac oss g oups o
indi iduals ha we bo ow om he li e a u e on composi ional da a. We hen desc ibe wo al e na i e app oaches. The
i s al e na i e b eaks down ou null hypo hesis in o Kin e al-speci ic es able hypo heses and uses he Bon e oni
co ec ion o con ol o he size o he es o he p ima y null hypo hesis. The second al e na i e is a boo s ap-based
app oach ha is based on he adi ional way o measu ing he dissimila i y be ween wo dis ibu ions using he KLIC.
2.1 Composi ional da a app oach
T ea ing expec a ions o he o m conside ed in his pape as composi ional da a s a s om he insigh ha he sum o
all p obabili ies mus equal one. Wi h espec o he s a is ical modeling o he dis ibu ion o he ec o s o p obabili ies
pi, ,h, his implies ha he sample space is no simply he K-dimensional space o nonnega i e eal numbe s RK
+bu he
so-called K−1-dimensional simplex de ined by
SK−1={(pi, ,h,1,…,pi, ,h,K)∶pi, ,h,1≥0,…,pi, ,h,K≥0;pi, ,h,1+…+pi, ,h,K=1}.(1)
Failing o ake accoun o his—by applying “s anda d” s a is ical me hods—will lead o a ious p oblems, including
p oblema ic in e p e a ion o he co a iance o he in e al p obabili ies (see Ai chison, 1986, chap e 3).
Ins ead, one needs o apply a p ope one- o-one ans o ma ion ha leads o a ec o o andom a iables ha one can
handle mo e easily. Commonly, he addi i e log a io ans o ma ion is used, and we adop his choice in ou pape , oo.3
Choosing he K h p obabili y as he e e ence (wi hou loss o gene ali y because i does no ma e which elemen o pi, ,h
is used), he ans o med expec a ion da a is gi en by
1In economic e ms, his expec a ion deno es he consensus expec a ion in he popula ion, ha is, he a e age expec a ion ha e lec s common
in o ma ion a e all idiosync a ic ac o s—such as p i a e in o ma ion, di e en p io s, and di e en expec a ion- o ma ion models—has been
in eg a ed ou .
2Ins ead o wo king wi h he su ey his og ams, one could i a pa ame ic dis ibu ion o he su ey p obabili ies, o example, a no mal dis ibu ion
(Gio dani & Söde lind, 2003), he gene alized be a dis ibu ion (Engelbe g e al., 2009), o a skew dis ibu ion (Ganics e al., 2024). Howe e , choosing
a pa icula pa ame ic dis ibu ion is di icul due o he la ge deg ee o he e ogenei y equen ly obse ed in su ey da a. This is especially ue o
household su eys ha also su e om i egula i ies such as bimodal esponses and disjoin ed se s o nonze o p obabili ies. A majo ad an age o he
app oaches discussed in his pape is ha hey do no equi e any pa ame ic assump ions o i ing p ocedu e.
3This choice implies ha we equi e s ic ly posi i e p obabili ies o simpli y he analysis. Hence, we eplace all ze o en ies by e y small ( andom)
numbe s in he applica ions and adjus he o he en ies acco dingly o ensu e ha he uni cons ain is s ill me . Gi en ha ounding is an eminen
ea u e o su ey-based p obabilis ic expec a ions (Binde , 2017; Clemen s, 2021; Glas & Ha mann, 2022; Reiche & Meyle , 2022), ea ing ze o en ies
as ounded app oxima ions o small p obabili ies seems a easonable modeling choice. Ma ín-Fe nández e al. (2003) and Filzmose e al. (2018) discuss
a ious s a egies o dealing wi h ze oes and missing alues in composi ional da a.
DOVERN ET AL.
1106
pi, ,h,k=ln (pi, ,h,k
pi, ,h,K) o k=1,…,K−1.(2)
This ans o ma ion makes he cons ain ha elemen s mus add up o one obsole e. Ins ead, he sample space o he
ans o med objec
pi, ,h=(
pi, ,h,1,…,
pi, ,h,K−1)′is RK−1. The abo e s a ed hypo hesis es ansla es in o a simple es o
equali y o he ans o med popula ion means, ha is, H0:
𝝁A=
𝝁B e sus H1:
𝝁A≠
𝝁B, supp essing he indices o he
ime pe iod and expec a ion ho izon o he emainde o his subsec ion o simpli y he no a ion.
We assume ha he co esponding K−1×K−1 popula ion co a iance ma ix, 𝜮, is he same in each subpopula ion (an
assump ion ha we could elax easily). 𝜮 e e s o wi hin-g oup a ia ion ac oss su ey pa icipan s. I can be in e p e ed,
o ins ance, as e lec ing he e ogenei y in densi y expec a ions caused by idiosync a ic in o ma ion o o he in o ma ion
igidi ies such as s icky in o ma ion. No e ha i is no a measu e o unce ain y o indi idual densi y expec a ions.
In his se ing, he null hypo hesis can be implemen ed by a Ho elling es using he es s a is ic
2=NANB
NA+NB(
pA−
pB)′S−1(
pA−
pB),(3)
whe e
pA=1
NA
NA
∑
i=1
pi,
pB=1
NB
NB
∑
𝑗=1
p𝑗
and
S=1
NA+NB(NA
∑
i=1(
pi−
pA)(
pi−
pA)′
+
NB
∑
𝑗=1(
p𝑗−
pB)(
p𝑗−
pB)′)
deno e he maximum likelihood es ima es o he popula ion pa ame e s. The es s a is ic 2in Equa ion (3) asymp o i-
cally ollows a 𝜒2dis ibu ion wi h K−1 deg ees o eedoms.4
Fo ini e samples, we can use a ela ed s a is ic i we assume ha
pi, ,h ollows a mul i a ia e no mal dis ibu-
ion (
𝝁 ,h,𝜮 ,h), implying ha he o iginal ec o o p obabili ies pi, ,h ollows an addi i e logis ic no mal dis ibu ion
acco ding o he de ini ion in Ai chison (1986, p. 113). In pa icula ,
=NA+NB−K
(NA+NB−2)(K−1)2
ollows an Fdis ibu ion wi h K−1andNA+NB−Kdeg ees o eedom in his case.
One ad an age o ea ing his og am expec a ions as composi ional da a when es ing o mean di e ences ac oss
g oups is ha we can easily ex end he app oach o allow o a join compa ison o mo e han wo g oups. This can be
done by applying an ANOVA- ype analysis o es he null hypo hesis H0∶
𝝁1=
𝝁2=…=
𝝁Gagains he al e na i e
ha a leas one mean is di e en om he o he s. Ano he bene i is ha he compu a ions necessa y o his app oach
a e e y as , which is an ad an age o e he KLIC-based app oach discussed below in Sec ion 2.3.
2.2 Mul iple es ing Bon e oni app oach
The second app oach o es ing he null hypo hesis desc ibed abo e decons uc s he his og ams and compa es he p ob-
abilis ic expec a ions in e al by in e al. The p ima y null hypo hesis implies o all k=1,…,K ha Hk
0∶𝜇A
,h,k=𝜇B
,h,k
is ue. The al e na i e in each case is Hk
1∶𝜇A
,h,k≠𝜇B
,h,k. Fo each k, we can use a s anda d wo-sample - es o es his.
The p ima y null hypo hesis is ejec ed i we can ejec he implied null hypo hesis o a leas one o he bins. To ensu e
good small sample p ope ies, we apply he es o he log p obabili ies, ha is, ln(pi, ,h,k) o k=1,…,K.
4See Ai chison (1986, p. 125) o he sui able cen al limi heo em.
DOVERN ET AL.1107
Because his app oach ge s us in o a mul iple- es ing se up, we ha e o apply a co ec ion o he signi icance le el used
o he indi idual - es s o con ol he o e all size o ou es ing app oach. A common app oach o do so is he Bon e oni
co ec ion ha implies using a signi icance le el o 𝛼∕K o each indi idual hypo hesis Hk
0,whe e𝛼is he o e all size ha
should be achie ed.
Simila o he Ho elling es om he p e ious subsec ion, he app oach desc ibed he e can deal wi h mo e han
wo g oups and does no equi e much compu ing powe . A d awback o his app oach is ha he Bon e oni co ec-
ion is known o be conse a i e (“unde sized”) when he indi idual es s a is ics a e co ela ed, which—due o he
composi ional na u e o ou da a—is he case in ou con ex . This educes he powe o he es ing app oach.
2.3 KLIC-based app oach
The hi d app oach o es ing he p ima y null hypo hesis s a s om he ac ha he KLIC is commonly used o com-
pa e p obabili y dis ibu ions. The KLIC desc ibes he expec ed alue o he loga i hmic di e ence be ween wo se s o
p obabili y dis ibu ions (Mi chell & Hall, 2005). Fo disc e e p obabili y dis ibu ions, such as he his og am o ecas s
desc ibed abo e, he KLIC is de ined as
KLIC (pA
,h,pB
,h)=
K
∑
k=1
pA
,h,kln (
pA
,h,k
pB
,h,k).(4)
In Equa ion (4), he elemen s o he ec o s pA
,h=(1∕NA)∑NA
i=1pi, ,hand pB
,h=(1∕NB)∑NB
i=1pi, ,h ep esen he a e age
(non ans o med) p obabili y mass assigned o bin kbased on all indi iduals in a pa icula g oup.
Unde he null hypo hesis de ined abo e, he agg ega e dis ibu ions o bo h g oups a e e y simila o ini e g oup sizes
and asymp o ically iden ical. In his case, he KLIC om Equa ion (4) is close o ze o. The mo e
pA
,h,kand
pB
,h,kde ia e om
each o he , he la ge he alue o KLIC (pA
,h,pB
,h). To es whe he KLIC (pA
,h,pB
,h)is signi ican ly di e en om ze o
and, hence, he null hypo hesis should be ejec ed, we use a boo s ap app oach. Speci ically, we d aw Z andom samples
o size Nwi h eplacemen om he a ailable expec a ion da a. We hen andomly assign NAo he d awn his og ams
o g oup Aand NBd awn his og ams o g oup B. Fo each boo s ap sample, we hen calcula e he KLIC as desc ibed in
Equa ion (4). We conclude ha KLIC (pA
,h,pB
,h)is signi ican ly di e en om ze o whene e i exceeds he 95%-quan ile
o he Zboo s apped KLIC alues.5
The use o he KLIC o compa ing his og am o ecas s has se e al disad an ages. Fi s , he KLIC can only be used o
compa e he p obabili y dis ibu ions o wo g oups. In case he numbe o g oups exceeds wo, only pai wise compa isons
can be ca ied ou . Second, calcula ion o he boo s apped KLICs is compu a ionally in ensi e. Thi d, he esul s o he
KLIC-based es a e sensi i e o he o de ing o he wo g oups, ha is, KLIC (pA
,h,pB
,h)≠KLIC (pB
,h,pA
,h), al hough i
should be no ed ha he es is co ec ly sized in bo h cases (i a pa icula o de is chosen ex an e). O e all, hese a e
impo an sho comings ela i e o he p e iously discussed al e na i es.
3MONTE CARLO SIMULATIONS
We now assess he p ope ies o he es ing app oaches discussed in he p e ious sec ion by means o Mon e Ca lo simula-
ions. In pa icula , we compa e he ejec ion equencies o he Ho elling es , he mul iple es ing Bon e oni app oach,
and he KLIC-based es unde he null hypo hesis o equal subpopula ion means and a ious al ena i es.
5This app oach is simila o Clemen s (2022) who p oposes a es o he e ogenei y in he e isions o GDP g ow h expec a ions in he US Su ey o
P o essional Fo ecas e s. In o de o add ess po en ial issues due o small sample size, Clemen s (2022) simula es a se o imagina y SPF pa icipan s
by andomly d awing om he se o o ecas e isions epo ed in a gi en su ey wa e. While his boo s ap app oach ocuses on e isions o poin
o ecas s, we andomly d aw and eassign en i e densi y o ecas s. In an ea lie s udy, Clemen s (2018) implemen s he abo e-men ioned al e na i e
app oach ha es s o di e ences be ween a e age expec a ions o a g oup o o ecas e s and a model-based benchma k by exploi ing a ia ion ac oss
ime. Fo ou pu pose, his al e na i e is no sui able o wo easons. Fi s , many o he new household su eys wi h la ge c oss-sec ions s ill ha e a
sho ime dimension. Second, he al e na i e does no allow o analyze changes o g oup di e ences ac oss ime.
DOVERN ET AL.
1108
3.1 Simula ion se up
Fo he Mon e Ca lo e alua ion, we calib a e ou benchma k his og ams o he one-yea -ahead in la ion his og ams om
he 2020Q1 wa e o he SPF (see Sec ion 4 o de ails on he su ey). We i s ob ain an es ima e o 𝜮by applying he
addi i e log a io ans o ma ion in Equa ion (2) o he indi idual his og ams and calcula ing he co esponding co a i-
ance ma ix. To ob ain
𝝁A, we i a no mal dis ibu ion o he agg ega e SPF his og am. To do so, we i s calcula e he
mean and s anda d de ia ion o he agg ega e his og am by assuming ha he p obabili y mass in each bin is cen e ed a
he midpoin and use hose pa ame e s as s a ing alues o he op imiza ion.6We hen calcula e he p obabili y mass
o each bin using he i ed no mal densi y and apply he addi i e log a io ans o ma ion o hese p obabili ies.
Fo each scena io desc ibed below, we simula e S=2000 a i icial da a se s o his og ams.7We hen apply he Ho elling
es , he Bon e oni-adjus ed - es s, and he KLIC-based es as desc ibed in he p e ious sec ion and calcula e he ejec-
ion equencies in each case. Fo he KLIC-based es , we se he numbe o boo s ap eplica ions o Z=250. Finally,
we choose a nominal le el o 𝛼=0.05.
In p ac ice, he SPF his og ams a e ela i ely coa se, and many indi idual his og ams do no closely esemble a no -
mal dis ibu ion. Fo he one-yea -ahead in la ion expec a ions, almos wo hi d o he SPF pa icipan s assign nonze o
p obabili y o a mos i e bins. The e o e, a possible conce n could be ha he choice o a Gaussian dis ibu ion o he
simula ions is no app op ia e o indi idual su ey esponses and, hus, migh yield a misleading imp ession o he es s'
p ope ies in eal applica ions. To assess how de ia ions om no mali y a ec he size and powe o he es s, we conduc
a second se o simula ions wi h a da a gene a ing p ocess (DGP) ha mimics his da a ea u e. In pa icula , we ans-
o m he simula ed his og ams in o mo e coa se e sions wi h nonze o p obabili y assigned only o he ( wo o i e) bins
wi h he highes p obabili ies. Fo each indi idual his og am, we andomly d aw he p ecise numbe o bins wi h nonze o
p obabili y wi h selec ion p obabili ies equal o he ela i e equency o obse a ions in he SPF wi h wo o i e bins
( escaled o sum o uni y).8We e e o he wo se ings as he Gaussian se up and he unca ed-p obabili ies se up below.
3.2 Resul s o Gaussian se up
In a i s s ep, we analyze whe he he di e en es s a e co ec ly sized o a ying g oup size. Fo each g oup, we conside
g oup sizes o 10, 25, 50, 75, 100, 200, and 500 indi iduals. While a g oup size o app oxima ely 25 indi iduals seems o
be a good desc ip ion o su eys among p o essional o ecas e s, a g oup size o 500 indi iduals is mo e ep esen a i e o
a ypical household su ey.
Table 1 shows he ejec ion equencies o all h ee es s unde he null hypo hesis. While Panel A shows he esul s
o ou baseline calib a ion o he co a iance ma ix ha de e mines he wi hin-g oup he e ogenei y, Panels B and C
p esen indings o lowe /highe wi hin-g oup he e ogenei y. In hese se ings, we mul iply 𝜮by a ac o c,whe ec
equals 0.5 (Panel B) o 5 (Panel C). Fo bo h he Ho elling es o composi ional da a and he KLIC-based app oach (and
o all sample sizes and le els o wi hin-g oup he e ogenei y), he empi ical size is e y close o he nominal size o 0.05.
In con as , he mul iple es ing Bon e oni app oach is, as expec ed, unde sized. Wi h espec o he speed o he MC
simula ions, pe o ming he KLIC-based es 2000 imes akes a li le mo e han 14 hou s on a s anda d desk op compu e
while 2000 Ho elling es s ake only nine seconds.
Nex , we u n o an assessmen o he powe o he es s. Unless explici ly s a ed o he wise, we se he g oup sizes o
NA=NB=25. Because he Bon e oni app oach is oo conse a i e in he sense ha i su e s om size dis o ions, we
epo size-adjus ed powe s a is ics o his app oach.
We i s conside shi s in he expec ed i s momen o he his og ams. Unde H0, all his og ams ha e he same expec ed
alue. We hen shi he expec ed alue o he his og ams o one g oup. We conside he ollowing shi s: H1a:0.05,H1b:
0.1,H1c:0.2,H1d:0.3,H1e:0.4,H1𝑓:0.5,H1g: 0.75, and H1h: 1.00. Nex , we change he popula ion s anda d de ia ion o he
6Figu e A.1 o he suppo ing in o ma ion shows he agg ega e SPF his og am ( epo ing densi ies ins ead o bin p obabili ies) based on he p edic ions
epo ed by 46 su ey pa icipan s. Mean and s anda d de ia ion based on he “mass-a -midpoin ”-app oach a e 1.26 pe cen age poin s and 0.60 pe -
cen age poin , espec i ely. The black line shows he i ed no mal dis ibu ion, which has a mean o 1.25 pe cen age poin s and a s anda d de ia ion
o 0.54 pe cen age poin .
7This numbe was chosen because p elimina y simula ions had indica ed ha his is a numbe su icien ly la ge o gi e us s able es ima es o he
empi ical sizes o es s and o he powe cu es. Lowe alues o Swould ha e been possible, o cou se, o cu down on compu a ional cos —a he
expense o he p ecision o esul s.
8These equencies a e 9.9%, 20.0%, 16.4%, and 15.1% o he one-yea -ahead in la ion expec a ions in he SPF.
DOVERN ET AL.1109
TABLE 1 Mon e Ca lo simula ion esul s: Size analysis.
G oup size (NA=NB) 10 25 50 75 100 200 500
Panel A: Gaussian se up, baseline wi hin-g oup he e ogenei y
Composi ional 0.055 0.052 0.056 0.048 0.046 0.046 0.048
Bon e oni 0.053 0.050 0.049 0.043 0.033 0.038 0.033
KLIC 0.062 0.050 0.063 0.049 0.054 0.047 0.049
Panel B: Gaussian se up, low wi hin-g oup he e ogenei y ( ela i e o baseline)
Composi ional 0.055 0.048 0.048 0.042 0.051 0.057 0.045
Bon e oni 0.035 0.040 0.043 0.040 0.039 0.040 0.038
KLIC 0.047 0.049 0.042 0.051 0.047 0.066 0.050
Panel C: Gaussian se up, high wi hin-g oup he e ogenei y ( ela i e o baseline)
Composi ional 0.052 0.049 0.051 0.050 0.058 0.054 0.050
Bon e oni 0.048 0.044 0.042 0.037 0.043 0.037 0.039
KLIC 0.038 0.053 0.047 0.052 0.047 0.052 0.055
Panel D: T unca ed-p obabili ies se up, baseline wi hin-g oup he e ogenei y
Composi ional 0.050 0.047 0.044 0.038 0.049 0.046 0.045
Bon e oni 0.061 0.043 0.043 0.044 0.042 0.041 0.040
KLIC 0.048 0.046 0.052 0.046 0.053 0.045 0.049
No e: The panels show ejec ion equencies o he Ho elling es o composi ional da a, he mul iple
es ing app oach, and he KLIC-based es unde he null hypo hesis o no expec a ion di e ence be ween
wo g oups o a ying g oup size. In he simula ions, all es s a e used wi h a nominal size o 0.05. Panel A
p esen s esul s o he Gaussian se up wi h baseline wi hin-g oup he e ogenei y. Panels B and C show
ejec ion a es when we mul iply he baseline 𝜮by 0.5 and 5, espec i ely. Panel D p esen s ou indings o
he unca ed-p obabili ies se up wi h baseline wi hin-g oup he e ogenei y.
his og ams o one g oup by mul iplying he s anda d de ia ion unde H0by a ac o unequal o one. We conside he
ollowing ac o s: H2a:1.05,H2b:1.1,H2c:1.2,H2d:1.3,H2e:1.4,H2𝑓:1.5,H2g:1.75,H2h:2.00,H2i: 2.50, and H2𝑗: 3.00. Nex ,
we change he g oup sizes unde he assump ion o a mode a e mean shi o 0.05 (i.e., unde H1a). Finally, we conside
changes in he wi hin-g oup he e ogenei y by adjus ing he co a iance ma ix 𝜮(again assuming a mean shi o 0.05
as in H1a). In pa icula , we conside a ange o se ings o c𝜮,whe ecassumes he ollowing alues in he di e en
al e na i e scena ios: H3a:0.5,H3b:0.75,H3c:1.0,H3d:1.25,H3e:1.5,H3𝑓:1.75,H3g:2.0,H3h:2.5,H3i:3.0,andH3𝑗: 10.0.
The plo in he uppe le o Figu e 1 shows he ejec ion equencies o he se o al e na i es o which we shi
he mean expec a ions o one g oup. E iden ly, he pe o mances o he h ee app oaches a e e y di e en . While he
Ho elling es o composi ional da a ejec s he null hypo hesis in abou 70% o cases al eady o a small shi o 0.05, he
KLIC-based es p oduces much lowe ejec ion equencies o small de ia ions om he null hypo hesis. I ma ches he
pe o mance o he Ho elling es only o e y la ge mean shi s o 0.75 o mo e. The size-adjus ed powe o he Bon e oni
app oach lies somewhe e in be ween, ma ching he powe o he Ho elling es o mean shi s o 0.3 o mo e.
The uppe - igh plo o Figu e 1 shows analogous ejec ion a es o he second se o simula ions ha analyze he
es pe o mance agains al e na i es ha de ia e om he null hypo hesis due o di e ences in he popula ion s anda d
de ia ion o he densi y expec a ions ac oss g oups. The al e na i es ange om mode a e de ia ions ( o which he a io
o he implied s anda d de ia ion o he wo g oups is 1.05) o ex eme ( a io o 3). Again, he Ho elling es yields high
ejec ion equencies o all al e na i es excep H2a. The Bon e oni app oach he e shows e y simila (size-adjus ed)
powe o he composi ional app oach. In con as , ejec ion equencies o he KLIC-based es a e low o he al e na i es
ha do no di e much om he null hypo hesis; we obse e ejec ion equencies abo e 25% only o al e na i es ha
a e based on a a io o he s anda d de ia ions o 1.5 o la ge .
Nex , we assess how he g oup size a ec s he ejec ion equencies. We analyze his o he al e na i e H1a,which
implies a mean shi o 0.05 o mean expec a ions in one o he g oups. The esul s in he lowe -le plo show ha inc eas-
ing he sample size—e en o numbe s ha would be common in household su eys—does no subs an ially inc ease he
ejec ion equency o he KLIC-based es . Rejec ion equencies a e much highe o he Ho elling es — o small sam-
ple sizes and inc easingly so o la ge sample sizes. Again, he Bon e oni app oach is somewhe e in-be ween, exhibi ing
e y low (size-adjus ed) powe o small o medium sample sizes bu ca ching up wi h he Ho elling es o la ge sample
sizes o NA=NB=500.
Finally, he lowe - igh plo o Figu e 1 shows how he le el o wi hin-g oup he e ogenei y a ec s ejec ion equencies.
I is e iden ha he KLIC-based es and he Bon e oni app oach ha e no powe agains H1aindependen ly o he le el
o wi hin-g oup he e ogenei y. Fo he Ho elling es , we obse e ha —no su p isingly—i has good powe agains a
DOVERN ET AL.
1110
0.00
0.25
0.50
0.75
1.00
H0 H1a H1b H1c H1d H1e H1 H1g H1h
Mean shi
0.00
0.25
0.50
0.75
1.00
H0 H2a H2b H2c H2d H2e H2 H2g H2h H2i H2j
Shi in s anda d de ia ion
0.00
0.25
0.50
0.75
1.00
n=10 n=25 n=50 n=75 n=100 n=200 n=500
Va ying g oup size
0.00
0.25
0.50
0.75
1.00
H3a H3b H3c H3d H3e H3 H3g H3h H3i H3j
In a−g oup he e ogenei y
Composi ional Bon e oni KLIC
FIGURE 1 Mon e Ca lo simula ion esul s: Powe analysis o Gaussian se up. No e: The plo s show ejec ion equencies based on he
Gaussian se up o he Ho elling es o composi ional da a (solid ed lines), he mul iple es ing app oach (dashed blue lines), and he
KLIC-based es (do ed black lines) unde a ious al e na i es. The uppe -le plo co esponds o al e na i e hypo heses wi h di e ences in
means o densi y expec a ions (H1a:0.05,H1b:0.1,H1c:0.2,H1d:0.3,H1e:0.4,H1𝑓:0.5,H1g: 0.75, and H1h: 1.00). The uppe - igh plo
co esponds o al e na i e hypo heses wi h di e ences in he s anda d de ia ion o densi y expec a ions (H2a:1.05,H2b:1.1,H2c:1.2,H2d:
1.3,H2e:1.4,H2𝑓:1.5,H2g:1.75,H2h:2.00,H2i: 2.50, and H2𝑗: 3.00). The lowe -le plo co esponds o simula ions wi h a ying g oup size,
assuming mean di e ences as in H1a. The lowe - igh plo co esponds o simula ions wi h a ying wi hin-g oup he e ogenei y o which we
mul iply ou baseline calib a ion o he co a iance ma ix by a ac o c,whe ecassumes he ollowing alues: H3a:0.5,H3b:0.75,H3c:
1.0,H3d:1.25,H3e:1.5,H3𝑓:1.75,H3g:2.0,H3h:2.5,H3i:3.0,andH3𝑗: 10.0 (again assuming mean di e ences as in H1a). In he simula ions, all
es s a e used wi h a nominal size o 0.05.
small di e ence in he expec ed alue o he his og ams implied by H1awhen he he e ogenei y wi hin g oups is small,
bu less so when i is high. Rejec ion equencies decline conside ably om almos 100% o a ound 10% o e he scena ios
conside ed in ou simula ions. S ill, o any le el o wi hin-g oup he e ogenei y, he ejec ion equencies a e subs an ially
highe han hose o he KLIC-based es and he Bon e oni app oach.
The numbe o bins in he SPF ques ionnai e changes o e ime. To assess whe he he powe o he es s depends on
he speci ics o he su ey design, we agg ega e he bin p obabili ies o wo adjacen bins in ano he se o simula ions.
The eby, we e ec i ely educe he numbe o bins om wel e o six. Using he changed se ing, we e-es ima e ejec ion
equencies. Figu e 2 shows ha his p ocedu e sligh ly educes he powe o he es s. Howe e , he ejec ion equencies
o he Ho elling es emain high and domina e hose o he o he es s.
DOVERN ET AL.1111
FIGURE 5 p- alues o
he e ogenei y es s (SCE): Panel
condi ioning e ec s. No e:Theplo
shows he p- alues om he
Ho elling es o composi ional da a
(solid ed line), he mul iple es ing
app oach (dashed blue line), and he
KLIC-based es (do ed black line)
o he analysis o panel
condi ioning e ec s in in la ion
expec a ions (le ) and pe sonal
income expec a ions ( igh ). Fo he
mul iple es ing app oach, we epo
( he minimum o one and) he
smalles p- alue mul iplied by he
numbe o bins o make i
compa able. The sample pe iod is
om June 2013 o Decembe 2021.
0.00
0.25
0.50
0.75
1.00
2014 2016 2018 2020 2022
In la ion expec a ions
0.00
0.25
0.50
0.75
1.00
2014 2016 2018 2020 2022
Income expec a ions
Composi ional Bon e oni KLIC
he scope o lea ning is mo e limi ed. We supplemen his e idence by es ing o sys ema ic di e ences in p obabilis ic
in la ion and income densi y expec a ions (Q24) be ween i s - ime su ey pa icipan s e sus mo e expe ienced pa ic-
ipan s. The sample is he same as he one used in he p e ious applica ion. The le plo in Figu e A.4 o he suppo ing
in o ma ion shows ha he numbe o i s - ime esponden s in each wa e is a ound 150–200 wi h he excep ion o Augus
2013 whe e 740 new pa icipan s en e ed he SCE. The plo s a he bo om o Figu e A.5 o he suppo ing in o ma ion
show he agg ega e dis ibu ions o bo h g oups.
The le plo o Figu e 5 shows clea e idence ha i s - ime pa icipan s d aw hei p obabilis ic in la ion expec a ions
om a di e en dis ibu ion han mo e expe ienced panelis s. Consis en wi h he indings o Kim and Binde (2023),
Figu e A.7 o he suppo ing in o ma ion indica es a highe s anda d de ia ion o i s - ime esponden s (and a no iceably
lowe ku osis). In con as , he igh plo o Figu e 5 shows only limi ed e idence o panel condi ioning e ec s o he
income expec a ions. Indeed, Figu e A.8 o he suppo ing in o ma ion shows ha he di e ences in his og am momen s
a e much less p onounced o income expec a ions. In sum, ou indings con i m he e idence o panel condi ioning
e ec s documen ed by Kim and Binde (2023) and ha such e ec s a e much less p onounced o expec a ions o a iables
like pe sonal income g ow h ha households a e likely o be e y amilia wi h.
4.5 Regional di e ences in na ional house p ice expec a ions
In his inal applica ion, we demons a e ha he KLIC-based app oach ceases o be easible in se ups whe e expec a ions
o mo e han wo g oups need o be compa ed. The choice is mo i a ed by he inding o Kuchle and Za a (2019) ha
di e ences in local house p ice dynamics end o ansla e in o dispe sed o ecas s o u u e na ionwide house p ices
changes, a inding ha appea s inconsis en wi h ull in o ma ion a ional expec a ions.
We es o di e ences o house p ice expec a ions ac oss households om he 50 US s a es and Washing on D.C.—o ,
al e na i ely, om ou b oade egions (“Wes ,” “Midwes ,” “No heas ,” and “Sou h”; see Figu e A.4 o he numbe o
households om each egion). In pa icula , we es he hypo hesis ha he densi y expec a ions om all s a es ( egions)
a e om he same popula ion in an ANOVA amewo k. The da a a e again om he SCE, and we ocus on expec a ions
o he change o a e age house p ices na ionwide (C1). The uppe igh plo in Figu e A.5 o he suppo ing in o ma ion
shows he agg ega e his og ams o he di e en egions. Figu e A.9 o he suppo ing in o ma ion shows he ime se ies
o he momen s o he agg ega e his og ams. The igu es do no e eal clea e idence o di e ences wi h one excep ion:
The mean o he agg ega e his og am o he “Wes ” egion is no iceably highe han hose o he o he egions in he
i s couple o su ey wa es.
The plo s in Figu e 6 p esen he esul s based on egions (le plo ) and s a es ( igh plo ). E iden ly, he e is mo e
ime a ia ion in he p- alues han o he di e ences in in la ion expec a ions in he wo p e ious applica ions. Fo he
Ho elling es , we ejec he null hypo hesis o no di e ences in he house p ice expec a ions ac oss egions (s a es) o
DOVERN ET AL.
1118
0.00
0.25
0.50
0.75
1.00
2014 2016 2018 2020 2022
Regions
0.00
0.25
0.50
0.75
1.00
2014 2016 2018 2020 2022
S a es
Composi ional Bon e oni
FIGURE 6 p- alues o
he e ogenei y es s (SCE): Local
di e ences in house p ice
expec a ions. No e: The plo shows
he p- alues om he Ho elling es
o composi ional da a (solid ed
line) and he mul iple es ing
app oach (dashed blue line) o he
analysis o di e ences in house p ice
expec a ions ac oss egions (le ) o
s a es ( igh ). Fo he mul iple
es ing app oach, we epo ( he
minimum o one and) he smalles
p- alue mul iplied by he numbe o
bins o make i compa able. The
sample pe iod is om June 2013 o
Decembe 2021.
28 (26) o he 103 su ey wa es. The e idence o he mul iple es ing app oach is simila . The pe iods wi h signi ican ly
di e en house p ice expec a ions a e dis ibu ed wi hou any ob ious sys ema ic pa e n, al hough pa icula ly o he
s a e-le el analysis we obse e mo e di e ences in he beginning o he sample be ween 2013 and 2015. This is likely due
o he highe mean expec a ions o he “Wes ” egion du ing his pe iod.
5CONCLUSION
We p opose a new es o he e ogenei y and di e ences in densi y expec a ions. This es builds on he insigh ha p ob-
abilis ic su ey o ecas s a e composi ional da a. Fo no mally dis ibu ed da a, ou Mon e Ca lo simula ions show he
supe io pe o mance o his es ela i e o a mo e adi ional boo s ap-based app oach using he KLIC as a dis ance
measu e be ween wo densi ies and an app oach ha in ol es mul iple es ing o di e ences o indi idual pa s o he
densi y. The no el es has high powe especially when in ag oup he e ogenei y is ela i ely low. Fo se ings ha mimic
mo e closely he coa se densi y expec a ions obse ed in many su eys, all es s ha e e y simila powe . Howe e , he
no el es is always much as e compa ed o he KLIC-based es because i does no ely on simula ions. In addi ion, i
has he addi ional ad an age ha i allows o compa isons ac oss mo e han wo g oups.
In i e applica ions, we analyze su ey-based densi y expec a ions o p o essional o ecas e s and households. Fi s , we
show ha he sho - e m in la ion expec a ions o expe s adjus ed apidly in esponse o ising in la ion a es in he eu o
a ea a e 2021. Long- e m expec a ions we e no ully ancho ed bu changed less s ongly and mo e g adually. Second,
we ind ha o mos pe iods, sho - un in la ion and g ow h expec a ions signi ican ly di e be ween o ecas e s ha
ound hei p obabili y s a emen s and hose ha do no . Thi d, we ind e y s ong e idence agains he hypo hesis ha
in la ion expec a ions o male and emal household heads a e equal, con i ming ea lie esul s in he li e a u e based on
poin o ecas s. Fou h, we show ha he in la ion expec a ions o households who jus en e ed he su ey panel di e
om hose o mo e expe ienced pa icipan s. Finally, consis en wi h a ole o local de elopmen s and in o ma ion se s
in luencing subjec i e expec a ions da a o agg ega e ou comes, we show ha o a sizeable ac ion o pe iods in ou
sample, households om di e en egions epo signi ican ly di e en densi y expec a ions o he u u e change o
na ionwide house p ices.
Ou analysis shows ha i is bene icial o ea su ey-based densi y expec a ions as composi ional da a. This migh be
ele an also in o he con ex s whe e such su ey da a a e used.
Ou esul s could be ex ended by using he panel s uc u e o mos expec a ion su eys. So a , we ha e analyzed each
su ey wa e as sepa a e da a samples, bu one could also join ly analyze he ull sample o expec a ion da a. Fo ins ance,
by adop ing a dynamic model o he composi ional expec a ion da a. Fu he mo e, one could, o cou se, eplace he
KLIC by o he dis ance measu es—such as he Wasse s ein dis ance (Dob ushin, 1970), he Jensen–Shannon di e gence
(Lin, 1991), o symme ic e sions o he KLIC— o gene a e al e na i e benchma k es s.
DOVERN ET AL.1119
Las ly, Basse i e al. (2022) p opose a nonpa ame ic al e na i e o es ima ing he unde lying densi y expec a ions om
a c oss-sec ion o a ailable su ey-based his og am o ecas s. In p inciple, ha would also be an app oach upon which
one could build an analysis o he e ogenei y ac oss g oups. Howe e , o he SPF, he numbe o a ailable his og ams pe
g oup is a he small—likely oo small o he applica ion o his nonpa ame ic me hod. We lea e a compa ison o ou
me hod wi h nonpa ame ic app oaches o u u e esea ch.
ACKNOWLEDGEMENTS
We hank he edi o , Michael McC acken, and h ee anonymous e e ees o e y help ul commen s. Ou esea ch has also
been imp o ed h ough aluable commen s and sugges ions by Ch is ian Con ad, Mal e Knüppel, and Fabian K üge .
We a e esponsible o any emaining e o s. This pape should no be epo ed as ep esen ing he iews o he Eu opean
Cen al Bank (ECB). The iews exp essed a e hose o he au ho s and do no necessa ily e lec hose o he ECB.
OPEN RESEARCH BADGES
This a icle has been awa ded Open Da a Badge o making publicly a ailable he digi ally-sha eable da a necessa y o
ep oduce he epo ed esul s. Da a is a ailable a h ps://doi.o g/10.15456/jae.2024132.1553917996.
DATA AVAILABILITY STATEMENT
We use da a om he Eu opean Cen al Bank' Su ey o P o essional Fo ecas e s (SPF) and he Fede al Rese e
Bank o New Yo k's Su ey o Consume Expec a ions (SCE). The da a a e a ailable om h ps://www.ecb.
eu opa.eu/s a s/ecb_su eys/su ey_o _p o essional_ o ecas e s/h ml/all_da a.en.h ml and h ps://www.newyo k ed.
o g/mic oeconomics/da abank.h ml, espec i ely. Replica ion da a a e a ailable om h ps://jou nalda a.zbw.eu/
da ase / es ing- o -di e ences-in-su ey-based-densi y-expec a ions-a-composi ional-da a-app oach.
ORCID
Jonas Do e n h ps://o cid.o g/0000-0003-0890-8809
Alexande Glas h ps://o cid.o g/0000-0003-2229-1112
Geo Kenny h ps://o cid.o g/0000-0002-4627-1928
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