Fiscal consolida ion
p og ams and income
inequali y
Ped o B inca
Miguel H. Fe ei a
F ancesco F anco
Hans A. Hol e
Lau ence Mala y
Wo king Pape
# 617
2017
Fiscal Consolida ion P og ams and Income Inequali y∗
Ped o B inca ‡† Miguel H. Fe ei a ‡F ancesco F anco ‡
Hans A. Hol e §Lau ence Mala y ¶
No embe 15, 2017
Abs ac
Following he G ea Recession, many Eu opean coun ies implemen ed iscal con-
solida ion policies aimed a educing go e nmen deb . Using h ee independen da a
sou ces and h ee di e en empi ical app oaches, we documen a s ong posi i e e-
la ionship be ween highe income inequali y and s onge ecessi e impac s o iscal
consolida ion p og ams ac oss ime and place. To explain his inding, we de elop
a li e-cycle, o e lapping gene a ions economy wi h uninsu able labo ma ke isk. We
calib a e ou model o ma ch key cha ac e is ics o a numbe o Eu opean economies, in-
cluding he dis ibu ion o wages and weal h, social secu i y, axes and deb , and s udy
he e ec s o iscal consolida ion p og ams. We ind ha highe income isk induces
p ecau iona y sa ings beha io , which dec eases he p opo ion o c edi -cons ained
agen s in he economy. C edi -cons ained agen s ha e less elas ic labo supply e-
sponses o iscal consolida ion achie ed h ough ei he ax hikes o public spending
cu s, and his explains he ela ionship be ween income inequali y and he impac o
iscal consolida ion p og ams. Ou model p oduces a c oss-coun y co ela ion be ween
inequali y and he iscal consolida ion mul iplie s, which is qui e simila o ha in he
da a.
Keywo ds: Fiscal Consolida ion, Income Inequali y, Fiscal Mul iplie s, Public Deb ,
Income Risk
JEL Classi ica ion: E21, E62, H31, H50
∗We hank Anmol Bhanda i, Michael Bu da, Gau i Egge sson, Mi chel Ho man, Loukas Ka aba bounis,
Robe Ki kby, Di k K uege , Pe K usell, Ellen McG a an, William Pe e man, Rica do Reis, Vic o Rios-
Rull, Ma celo San os, Chima Simpson-Bell and Kje il S o esle en o help ul commen s and sugges ions.
We also hank semina pa icipan s a Bi beck College, Humbold Uni e si y, IIES, New Yo k Uni e si y,
Uni e si y o Be gen, Uni e si y o Minneso a, Uni e si y o Oslo, Uni e si y o Pennsyl ania, Uni e si y
o Vic o ia-Welling on, and con e ence pa icipan s a he 2017 Junio Symposium o he Royal Economic
Socie y, ADEMU, he 6 h edi ion o Lub amac o, he 11 h Mee ings o he Po uguese Economic Jou nal,
he 70 h Eu opean Mee ings o he Econome ic Socie y, ASSET 2017 and he Sp ing Mid-Wes Mac o
Mee ing 2017. Ped o B inca is g a e ul o inancial suppo om he Po uguese Science and Technology
Founda ion, g an s numbe SFRH/BPD/99758/2014, UID/ECO/00124/2013 and UID/ECO/00145/2013.
Miguel H. Fe ei a is g a e ul o inancial suppo om he Po uguese Science and Technology Founda ion,
g an numbe SFRH/BD/116360/2016. Hans A. Hol e is g a e ul o inancial suppo om he Resea ch
Council o No way, G an numbe 219616; he Oslo Fiscal S udies P og am.
†Cen e o Economics and Finance a Uni e sidade o Po o
‡No a School o Business and Economics, Uni e sidade No a de Lisboa
§Depa men o Economics, Uni e si y o Oslo
¶Depa men o Economics, S ockholm Uni e si y
1 In oduc ion
The 2008 inancial c isis led se e al Eu opean economies o adop coun e -cyclical iscal
policy, o en inanced by deb . Go e nmen de ici s exceeded 10% in many coun ies, and
his c ea ed an u gency o iscal consolida ion policies as soon as imes e u ned o no mal.
Many coun ies designed plans o educe hei deb h ough aus e i y, ax inc eases, o mo e
commonly a combina ion o he wo, see Blancha d and Leigh (2013), Alesina e al. (2015a).
The p ocess o iscal consolida ion ac oss Eu opean coun ies, howe e , aised a numbe
o impo an ques ions abou he e ec s on he economy. Is deb consolida ion ul ima ely
con ac iona y o expansiona y? How la ge a e he e ec s and do hey depend on he s a e
o he economy? How does he impac o consolida ion h ough aus e i y di e om he
impac o consolida ion h ough axa ion? In his pape we con ibu e o his li e a u e,
bo h empi ically and heo e ically, by p esen ing e idence on a dimension ha can help
explain he he e ogeneous esponses o iscal consolida ion obse ed ac oss coun ies: income
inequali y and in pa icula he ole o uninsu able income isk.
We begin by documen ing a s ong posi i e empi ical ela ionship be ween highe income
inequali y and s onge ecessi e impac s o iscal consolida ion p og ams ac oss ime and
place. We do his by using da a and me hods om h ee ecen , s a e-o - he-a , empi ical
pape s, which co e a ious coun ies and ime pe iods and make use o di e en empi ical
app oaches: i) Blancha d and Leigh (2013) ii) Alesina e al. (2015a) iii) Ilze zki e al. (2013)1.
Nex we s udy he e ec s o iscal consolida ion p og ams, inanced h ough bo h aus e -
i y and axa ion, in a neoclassical mac o model wi h he e ogeneous agen s and incomple e
ma ke s. We show ha such a model is well-sui ed o explain he ela ionship be ween in-
come inequali y and he ecessi e e ec s o iscal consolida ion p og ams. The mechanism
we p opose wo ks h ough idiosync a ic income isk. In economies wi h lowe isk, he e a e
mo e c edi cons ained households and households wi h low weal h le els, due o less p e-
1While he i s wo pape s s udy iscal consolida ion p og ams in Eu ope, Ilze zki e al. (2013) s udy
go e nmen spending mul iplie s using a g ea e numbe o coun ies. We include his s udy o comple eness.
1
cau iona y sa ing. Impo an ly, hese c edi cons ained households ha e less elas ic labo
supply esponses o inc eases in axes and dec eases in go e nmen expendi u es.
Ou empi ical analysis begins wi h a eplica ion o he ecen s udies by Blancha d and
Leigh (2013) and Blancha d and Leigh (2014). These s udies ind ha he In e na ional
Mone a y Fund (IMF) unde es ima ed he impac s o iscal consolida ion ac oss Eu opean
coun ies, wi h s onge consolida ion causing la ge GDP o ecas e o s. In Blancha d and
Leigh (2014), he au ho s ind no o he signi ican explana o y ac o s, such as p e-c isis deb
le els2o budge de ici s, banking condi ions, o a coun y’s ex e nal posi ion, among o he s,
can help explain he o ecas e o s. In Sec ion 3.1 we ep oduce he exe cise conduc ed by
Blancha d and Leigh (2013), now augmen ed wi h di e en me ics o income inequali y.
We ind ha du ing he 2010 and 2011 consolida ion in Eu ope he o ecas e o s a e la ge
o coun ies wi h highe income inequali y, implying ha inequali y ampli ied he ecessi e
impac s o iscal consolida ion. A one s anda d de ia ion inc ease in income inequali y,
measu ed as Y10/Y90 3leads he IMF o unde es ima e he iscal mul iplie in a coun y by
66%.
Fo a second independen analysis, we use he Alesina e al. (2015a) iscal consolida ion
episodes da ase wi h da a om 12 Eu opean coun ies o e he pe iod 2007-2013. Alesina
e al. (2015a) expands he exogenous iscal consolida ion episodes da ase , known as IMF
shocks, om De ies e al. (2011) who use Rome and Rome (2010) na a i e app oach o
iden i y exogenous shi s in iscal policy. Again we documen he same s ong ampli ying
e ec o inequali y on he ecessi e impac s o iscal consolida ion. A one s anda d de ia ion
inc ease in inequali y, measu ed as Y25/Y75, inc eases he iscal mul iplie by 240%.
Ou hi d empi ical analysis eplica es he pape by Ilze zki e al. (2013). These au ho s
use ime se ies da a om 44 coun ies (bo h ich and poo ) and a SVAR app oach o s udy
he impac s o di e en coun y cha ac e is ics on iscal mul iplie s. We ind ha coun ies
2In Sec ion 8.1 we show ha , in line wi h ou p oposed mechanism, household deb ma e s i an in e -
ac ion e m be ween deb and he planned iscal consolida ion is included in he eg ession.
3Ra io o op 10% income sha e o e bo om 10% income sha e.
2
wi h highe income inequali y expe ience signi ican ly s onge declines in ou pu ollowing
dec eases in go e nmen consump ion.
To explain hese empi ical indings, we de elop an o e lapping gene a ions economy wi h
he e ogeneous agen s, exogenous c edi cons ain s and uninsu able idiosync a ic isk, simila
o ha in B inca e al. (2016b). We calib a e he model o ma ch da a om a numbe o
Eu opean coun ies along dimensions such as he dis ibu ion o income and weal h, axes,
social secu i y and deb le el. Then we s udy how hese economies espond o g adually
educing go e nmen deb , ei he by cu ing go e nmen spending o by inc easing labo
income axes.
Ou pu alls when deb educ ion is inanced h ough ei he a dec ease in go e nmen
spending o inc eased labo income axes. In bo h cases, his is caused by a all in labo
supply. In he case o educed go e nmen spending, he ansmission mechanism wo ks
h ough a u u e income e ec . As go e nmen deb is paid down, he capi al s ock and hus
he ma ginal p oduc o labo (wages) ise, and hus expec ed li e ime income inc eases. This
will lead agen s o enjoy mo e leisu e and dec ease hei labo supply oday, and ou pu o all
in he sho - un, despi e he long un e ec s o consolida ion on ou pu being posi i e. C edi
cons ained agen s and agen s wi h low weal h le els do, howe e , ha e a lowe ma ginal
p opensi y o consume goods and leisu e ou o u u e income ( o cons ained agen s he
MPC o u u e income is ze o4). Cons ained agen s do no conside changes o hei li e ime
budge , only changes o hei budge in he cu en ime pe iod. Agen s wi h low weal h
le els a e also less esponsi e o u u e income changes because hey will be cons ained
in se e al u u e s a es o he wo ld. Inc eases in expec ed u u e consump ion and leisu e
le els will hus ha e a smalle e ec on hei labo supply oday.
In he case o consolida ion h ough inc eased labo income axes he e will also be a
nega i e income e ec on labo supply oday, h ough highe u u e wages and inc eased
li e- ime income. Fo cons ained agen s, who do no conside hei li e- ime budge bu
4The ac ha cons ained agen s also e y sligh ly change hei labo supply in ou model simula ions
is due o gene al equilib ium e ec s (p ice changes) oday.
3

only hei budge oday, he ax would ins ead cause a d op in a ailable income in he sho -
un, leading o a labo supply inc ease. Howe e , he ax also induces a nega i e subs i u ion
e ec on wages oday, bo h o cons ained and uncons ained agen s. I u ns ou ha all
agen s dec ease hei labo supply, bu he esponse is weake o cons ained and low-weal h
agen s.
When highe income inequali y e lec s highe uninsu able income isk, he e exis s a
nega i e ela ionship be ween income inequali y and he numbe o c edi cons ained agen s.
G ea e isk leads o inc eased p ecau iona y sa ings beha io , hus dec easing he sha e o
agen s wi h liquidi y cons ain s and low weal h le els. Since uncons ained agen s ha e
mo e elas ic labo supply esponses o he posi i e li e ime-income e ec om consolida ion,
labo supply and ou pu will espond mo e s ongly in economies wi h highe inequali y.
Th ough simula ions in a benchma k economy, ini ially calib a ed o Ge many, we show
ha a ying he le el o idiosync a ic income isk s ongly a ec s he ac ion o c edi
cons ained agen s in he economy and he iscal mul iplie , bo h o consolida ion h ough
axa ion and aus e i y. I we ins ead change inequali y by changing he a iance o ini ial
condi ions, p io o en e ing he labo ma ke (pe manen abili y and he age-p o ile o wages
in he model), he e is e y li le e ec on he ac ion o c edi cons ained agen s o on he
iscal mul iplie .
In a mul i-coun y exe cise, we calib a e ou model o ma ch a wide ange o da a and
coun y-speci ic policies om 13 Eu opean economies, and ind ha ou simula ions ep o-
duce he an icipa ed c oss-coun y co ela ion be ween income inequali y and iscal mul ipli-
e s. Mo eo e , we show ha in ou model, coun ies wi h highe idiosync a ic uninsu able
labo income isk ha e a smalle pe cen age o cons ained agen s and ha e la ge mul iplie s,
con i ming ou analysis and mechanism o he benchma k model calib a ed o Ge many.
We pe o m wo empi ical exe cises o es he alidi y o he mechanism desc ibed abo e.
Fi s , in ou calib a ed model, highe le els o household deb a e associa ed wi h a highe
numbe o c edi cons ained households. This implies ha coun ies wi h highe le els o
4
deb should ha e expe ienced less ecessi e impac s o iscal consolida ion p og ams. We
show ha such ela ionship exis s in he da a, by again pe o ming a simila exe cise o
Blancha d and Leigh (2013).
Second, he mechanism we p opose implies ha iscal consolida ions lead o dec eases in
labo supply, and ha hese a e ampli ied by income inequali y. We ollow Alesina e al.
(2015a) bu now look a he impac s o iscal consolida ion and income inequali y on hou s
wo ked. We ind, p ecisely in line wi h ou simula ions, ha iscal consolida ion p og ams
ha e a nega i e impac on hou s wo ked and ha his impac is ampli ied by inc eases in
income inequali y.
In Sec ion 9, we conduc a inal alidi y es o he mechanism by using ou model. In
he empi ical analysis we make he case ha he IMF o ecas s did no p ope ly ake income
inequali y in o accoun . In his sec ion we show ha using da a om ou model, ob ained
by simula ing he obse ed iscal consolida ion shocks in he da a, we ge simila esul s o
Blancha d and Leigh (2013) when we shu down all labo income isk in ou model. The
di e ence be ween he ou pu d op ha ou calib a ed model p edic s bo h wi h and in he
absence o isk (which is ou p oxy o he o ecas e o ), is explained by he size o he
iscal shock and i s in e ac ion wi h he same income inequali y me ics as in ou eplica ion
o he Blancha d and Leigh (2013) expe imen ( ound in Sec ion 3.1). The esul ing pa e n
o eg ession s a is ics a e s ikingly simila o Blancha d and Leigh (2013).
The emainde o he pape is o ganized as ollows: We begin by discussing some o he
ecen ele an li e a u e in Sec ion 2. In Sec ion 3we assess he empi ical ela ionship be-
ween income inequali y and he iscal mul iplie s associa ed wi h consolida ion p og ams. In
Sec ion 4we desc ibe he o e lapping gene a ions model, de ine he compe i i e equilib ium
and explain he iscal consolida ion expe imen s. Sec ion 5desc ibes he calib a ion o he
model. In Sec ion 6we inspec he ansmission mechanism, ollowed by he c oss-coun y
analysis in Sec ion 7. In Sec ion 8we empi ically alida e he mechanism and in Sec ion 9
we eplica e he Blancha d and Leigh (2014) exe cise wi h model da a. Sec ion 10 concludes.
5
2 Rela ed Li e a u e
The e has been a su ge in he li e a u e s udying he impac s o iscal consolida ion p og ams.
Guaja do e al. (2014) ocus on sho - e m e ec s o iscal consolida ions on economic ac i i y
o a sample o OECD coun ies, using he na a i e app oach as in Rome and Rome (2010),
inding ha a 1% iscal consolida ion shock causes GDP o o decline by 0.62%; Yang e al.
(2015) build a sample o iscal adjus men episodes in OECD coun ies o e he pe iod om
1970 o 2009 and ind a somewha smalle ecessi e impac : a 1% iscal consolida ion shock
leads o a 0.3% all in ou pu . Blancha d and Leigh (2013) and Blancha d and Leigh (2014)
ind a nega i e e ec o iscal consolida ion p og ams on ou pu and shows ha his e ec
is unde es ima ed by he IMF. The conclusions in Alesina e al. (2015b) suppo p e ious
s udies, emphasizing ha ax-based consolida ions p oduce deepe and longe ecessions han
spending based ones. Pappa e al. (2015) s udy he impac o iscal consolida ion episodes in
an en i onmen wi h co up ion and ax e asion, and ind e idence ha iscal consolida ion
causes la ge ou pu and wel a e losses. They ind ha much o he wel a e loss is due o
inc eases in axes, which c ea es he incen i es o p oduce in he less p oduc i e shadow
sec o . Dupaigne and F`e e (2016) ocus on how he pe sis ence o go e nmen spending can
shape he sho - un impac s on ou pu h ough he esponse o p i a e in es men . Mo e
pe sis en go e nmen spending leads o g ea e iscal mul iplie s.
Ou pape is also mo e b oadly ela ed o he la ge li e a u e s udying iscal mul iplie s,
i.e. he esponse o ou pu o changes in iscal policy, and in pa icula he li e a u e ocusing
on how hese esponses depends on income and weal h inequali y. Hea hco e (2005) s udies
he e ec s o changes in he iming o income axes and inds ha ax cu s can ha e la ge
eal e ec s and ha he magni ude o he e ec depends c ucially on he deg ee o ma ke
incomple eness. Hagedo n e al. (2016), in a New Keynesian model, p esen u he e idence
o he ele ance o ma ke incomple eness in de e mining he size o iscal mul iplie s. Fe ie e
and Na a o (2016) p o ide empi ical e idence showing ha in he pos -wa U.S., iscal
expansions a e only expansiona y when inanced by inc eases in ax p og essi i y. Like in
6
B inca e al. (2016b), Fe ie e and Na a o (2016) can eplica e his empi ical inding using
a neoclassical amewo k. B inca e al. (2016) p o ide empi ical e idence ha highe weal h
inequali y is associa ed wi h s onge impac s o inc eases in go e nmen expendi u es and
show ha an o e lapping gene a ions model wi h uninsu able income isk calib a ed o ma ch
key cha ac e is ics o a numbe o OECD coun ies, can eplica e his empi ical pa e n.
K uege e al. (2016) assess how weal h, income and p e e ence he e ogenei y ac oss
households ampli ies agg ega e shocks. K uege e al. (2016) conclude ha , in an economy
wi h he weal h dis ibu ion consis en wi h he da a, he d op in agg ega e consump ion in
esponse o a nega i e agg ega e shock is 0.5 pe cen age poin s la ge han in a ep esen a i e
household model. This is condi ional on he economy ea u ing a su icien ly la ge sha e o
agen s wi h low weal h. Ande son e al. (2016) ind ha in he con ex o he U.S. economy,
indi iduals espond di e en ly o unan icipa ed iscal shocks depending on age, income le el,
and educa ion. The beha io o he weal hies agen s, in pa icula , is consis en wi h
Rica dian equi alence bu poo households show e idence o non-Rica dian beha io .
Rela edly Ca oll e al. (2014) measu e ma ginal p opensi ies o consume o a la ge panel
o Eu opean coun ies, and hen calib a e a model o each coun y using ne weal h and
liquid weal h. The au ho s ind ha he highe he p opo ion o inancially cons ained
agen s in an economy, he highe he consump ion mul iplie . Kaplan and Violan e (2014)
p opose a model wi h wo ypes o asse s ha p o ides a a ionale o ela i ely weal hy
agen s’ choice o being c edi cons ained. In a con ex o po olio op imiza ion wi h one
high- e u n illiquid asse and one low- e u n liquid asse , ela i ely weal hy indi iduals may
end up c edi cons ained. Kaplan e al. (2014), using mic o da a om se e al coun ies,
hen a gue ha he pe cen age o inancially cons ained agen s can be well abo e wha is
ypically he ou come o models whe e e y ew agen s ha e hei weal h ied up in illiquid
asse s. An unes and E colani (2016) also highligh he ele ance o bo owing cons ain s
o he dynamics o public deb .
7
he median, he ecessi e impac s o dec eases in go e nmen consump ion expendi u es a e
s onge and s a is ically di e en om he impac s o he g oup o coun ies wi h income
inequali y me ics below he median.
The objec i e is o es ima e he ollowing sys em o equa ions
AYn =
K
X
k=1
CkYn, −k+un, (4)
whe e Yn is a ec o con aining he endogenous a iables o coun y n in qua e . The
a iables conside ed a e he same as in Ilze zki e al. (2013): go e nmen consump ion,
ou pu , cu en accoun in pe cen age o GDP and he na u al loga i hm o he eal e ec i e
exchange a e. Ckis a ma ix o lag own and c oss e ec s o a iables on hei cu en
obse a ions. Gi en ha A is no obse able we canno es ima e his eg ession di ec ly.
We need o p e-mul iply e e y hing by A−1and, using OLS, we can eco e he ma ix
P=A−1Ckand en, =A−1un, . So we es ima e he sys em
Yn =
K
X
k=1
A−1CkYn, −k+A−1un, (5)
To be able o es ima e he e ec s o iscal consolida ion, we need mo e assump ions on A
so ha we can iden i y he inno a ions by sol ing en, =A−1un, . We use he same assump ion
used by Ilze zki e al. (2013) and i s in oduced by Blancha d and Pe o i (2002), o iden i y
he esponses o ou pu o go e nmen consump ion expendi u es: go e nmen consump ion
canno eac o shocks in ou pu wi hin he same qua e . The plausibili y o his assump ion
comes om he ac ha he go e nmen ’s budge is ypically se on a yea ly basis and can
only eac o changes in ou pu wi h a lag. Fo he o de ing o he emaining a iables,
we also ollow Ilze zki e al. (2013) and le he cu en accoun ollow ou pu and he eal
exchange a e ollow he cu en accoun . Gi en his, we can iden i y he impulse esponses
o a p imi i e shock in go e nmen spending. In Figu es 1,2and 3we plo he cumula i e
ou pu mul iplie o a go e nmen consump ion shock, de ined as:
14

cummula i e mul iplie G(T) = P =T
=0 1
(1+ m) ∆Y
P =T
=0 1
(1+ m) ∆G
(6)
mis he e he median in e es a e in he da a sample. The ou pu mul iplie s shown in
Figu es 1,2and 3sugges ha in coun ies wi h highe income inequali y, con ac ions in
go e nmen spending ha e a mo e ecessi e impac .
Figu e 1: Cumula i e ou pu mul iplie , as de ined in (6), o a go e nmen consump ion shock (90% e o bands in g ay)
Figu e 2: Cumula i e ou pu mul iplie , as de ined in (6), o a go e nmen consump ion shock (90% e o bands in g ay)
15
Figu e 3: Cumula i e ou pu mul iplie , as de ined in (6), o a go e nmen consump ion shock (90% e o bands in g ay)
The empi ical indings in Sec ion 3 oge he sugges ha income inequali y is a ele an
dimension o ake in o accoun when s udying he e ec s o iscal policy. In pa icula ,
hey sugges ha highe inequali y ampli ies he ecessi e impac s o iscal consolida ion and
dec eases in go e nmen expendi u es. In o de o unde s and he mechanism h ough which
income inequali y may play such ole, we build a s uc u al model ha is in oduced in he
nex sec ion.
4 Model
In his sec ion, we desc ibe he model we will use o s udy he e ec s o a iscal consolida ion
in di e en coun ies. Ou model is a ela i ely s anda d li e-cycle economy wi h he e oge-
neous agen s and incomple e ma ke s. I is simila o he model in B inca e al. (2016b),
excep ha we ha e in oduced a beques mo i e o ge a mo e ealis ic dis ibu ion o weal h
o e he li e-cycle.
Technology
The e is a ep esen a i e i m, p oducing ou pu wi h a Cobb-Douglas p oduc ion unc ion:
Y (K , L ) = Kα
[L ]1−α(7)
16
whe e K is he capi al inpu and L he labo inpu in e iciency uni s. The e olu ion o
capi al e olu ion is gi en by:
K +1 = (1 −δ)K +I (8)
whe e I is g oss in es men and δ he capi al dep ecia ion a e. Each pe iod, he i m hi es
labo and capi al o maximize i s p o i s:
Π =Y −w L −( +δ)K .(9)
In a compe i i e equilib ium, he ac o p ices will be equal o hei ma ginal p oduc s gi en
by:
w =∂Y /∂L = (1 −α)K
L α
(10)
=∂Y /∂K −δ=αL
K 1−α
−δ(11)
Demog aphics
The economy is popula ed by Jo e lapping gene a ions o ini ely li ed households11. All
households s a li e a age 20 and en e e i emen a age 65. Le jdeno e he household’s
age. Re i ed households ace an age-dependen p obabili y o dying, π(j) and die o ce ain
a age 100.12. A model pe iod is 1 yea , so he e a e a o al o 40 model pe iods o ac i e
wo k li e. We assume ha he size o he popula ion is ixed ( he e is no popula ion g ow h).
We no malize he size o each new coho o 1. Using ω(j)=1−π(j) o deno e he age-
dependen su i al p obabili y, by he law o la ge numbe s he mass o e i ed agen s o age
j≥65 s ill ali e a any gi en pe iod is equal o Ωj=Qq=J−1
q=65 ω(q).
In addi ion o age di e ences, households a e he e ogeneous wi h espec o asse hold-
ings, idiosync a ic p oduc i i y, and hei subjec i e discoun ac o , which o each house-
hold is cons an o e ime bu akes one ou o he h ee alues β∈ {β1, β2, β3}; he dis-
11Recen wo k by Pe e man and Sage (2016) makes he case o ha ing a li e-cycle dimension when
s udying he impac s o go e nmen deb .
12This means ha J= 81.
17
ibu ion o discoun ac o s is uni o mly dis ibu ed ac oss agen s in each coho . Finally,
hey also di e in e ms o a pe manen abili y componen , i.e., hey ha e a s a ing le el o
p oduc i i y ha is ealized a bi h. E e y pe iod o ac i e wo k-li e hey decide how many
hou s o wo k, n, how much o consume, c, and how much o sa e, k. Re i ed households
make no labo supply decisions bu ecei e a social secu i y paymen , Ψ .
The e a e no annui y ma ke s, so ha a ac ion o households lea e unin ended beques s
which a e edis ibu ed in a lump-sum manne be ween he households ha a e cu en ly
ali e. We use Γ o deno e he pe -household beques . Re i ed households’ u ili y is inc easing
in he beques hey lea e when hey die. This helps us calib a e he asse holdings o old
households.
Labo Income
The wage o an indi idual depends on his/he own cha ac e is ics: age, j, pe manen abili y,
a∼N(0, σ2
a), and idiosync a ic p oduc i i y shock, u, which ollows an AR(1) p ocess:
u +1 =ρu + +1,  ∼N(0, σ2
) (12)
These cha ac e is ics will dic a e he numbe o e icien uni s o labo he household is
endowed wi h. Indi idual wages will also depend on he wage pe e iciency uni o labo w.
Thus, indi idual i’s wage is gi en by:
wi(j, a, u) = weγ1j+γ2j2+γ3j3+a+u(13)
γ1ι,γ2ιand γ3ιcap u e he age p o ile o wages.
18
P e e ences
The momen a y u ili y unc ion o a household, U(c, n), depends on consump ion and wo k
hou s, n∈(0,1], and akes he ollowing o m:
U(c, n) = c1−σ
1−σ−χn1+η
1 + η.(14)
Re i ed households gain u ili y om he beques hey lea e when hey die:
D(k) = ϕlog(k) (15)
Go e nmen
The go e nmen uns a balanced social secu i y sys em whe e i axes employees and he
employe ( he ep esen a i e i m) a a es τss and ˜τss and pays bene i s, Ψ , o e i ees. The
go e nmen also axes consump ion and labo and capi al income o inance he expendi u es
on pu e public consump ion goods, G , which en e sepa ably in he u ili y unc ion, in e es
paymen s on he na ional deb , B , and a lump-sum edis ibu ion, g . We assume ha
he e is some ou s anding go e nmen deb and ha go e nmen deb - o-ou pu a io, BY=
B /Y , does no change o e ime. Consump ion and capi al income a e axed a la a es
he τcand τk. To model he non-linea labo income ax, we use he unc ional o m p oposed
in Benabou (2002) and ecen ly used in Hea hco e e al. (2017) and Hol e e al. (2017):
τ(y) = 1 −θ0y−θ1(16)
whe e ydeno es p e- ax (labo ) income and τ(y) he a e age ax a e gi en a p e- ax income
o y. The pa ame e s θ0and θ1go e n he le el and he p og essi i y o he ax code,
espec i ely.13.Hea hco e e al. (2017) a gue ha his unc ion i s he U.S. da a well.
In a s eady s a e, he a io o go e nmen e enues o ou pu will emain cons an . G ,
13A u he discussion o he p ope ies o his ax unc ion is p o ided in he appendix
19

g , and Ψ mus also emain p opo ional o ou pu . Deno ing he go e nmen ’s e enues
om labo , capi al, and consump ion axes by R and he go e nmen ’s e enues om social
secu i y axes by Rss
, he go e nmen budge cons ain in s eady s a e akes he ollowing
o m:
g 45 + X
j≥65
Ωj!=R−G− B, (17)
Ψ X
j≥65
Ωj!=Rss.(18)
Recu si e Fo mula ion o he Household P oblem
A any gi en ime a household is cha ac e ized by (k, β, a, u, j), whe e kis he household’s
sa ings, β∈β1, β2, β3, is he ime discoun ac o , ais pe manen abili y, uis he idiosyn-
c a ic p oduc i i y shock, and jis he age o he household. We can o mula e he house-
hold’s op imiza ion p oblem o e consump ion, c, wo k hou s, n, and u u e asse holdings,
k0, ecu si ely as ollows:
V(k, β, a, u, j) = max
c,k0,n hU(c, n) + βEu0V(k0, β, a, u, j + 1)i
s. .:
c(1 + τc) + k0= (k+ Γ) (1 + (1 −τk)) + g+YL
YL=nw (j, a, u)
1 + ˜τss 1−τss −τlnw (j, a, u)
1 + ˜τss 
n∈[0,1], k0≥ −b, c > 0 (19)
He e, YLis he household’s labo income a e social secu i y axes and labo income axes.
τss and ˜τss a e he social-secu i y con ibu ions paid by he employee and by he employe ,
espec i ely. The p oblem o a e i ed household, who has a p obabili y π(j) o dying and
20
gains u ili y D(k0) om lea ing a beques , is:
V(k, β,j) = max
c,k0hU(c, n) + β(1 −π(j))V(k0, β, j + 1) + π(j)D(k0)i
s. .:
c(1 + τc) + k0= (k+ Γ) (1 + (1 −τk)) + g+Ψ,
k0≥0, c > 0 (20)
S a iona y Recu si e Compe i i e Equilib ium
Le he measu e o households wi h he co esponding cha ac e is ics be gi en by Φ(k, β, a, u, j).
The s a iona y ecu si e compe i i e equilib ium is de ined by:
1. Gi en he ac o p ices and he ini ial condi ions he consume s’ op imiza ion p oblem
is sol ed by he alue unc ion V(k, β, a, u, j) and he policy unc ions, c(k, β, a, u, j),
k0(k, β, a, u, j), and n(k, β, a, u, j).
2. Ma ke s clea :
K+B=ZkdΦ
L=Z(n(k, β, a, u, j)) dΦ
ZcdΦ + δK +G=KαL1−α
3. The ac o p ices sa is y:
w= (1 −α)K
Lα
=αK
Lα−1
−δ
21
4. The go e nmen budge balances:
gZdΦ + G+ B =Z τk (k+ Γ) + τcc+nτlnw(a, u, j)
1 + ˜τss !dΦ
5. The social secu i y sys em balances:
ΨZj≥65
dΦ = ˜τss +τss
1 + ˜τss Zj<65
nwdΦ!
6. The asse s o he dead a e uni o mly dis ibu ed among he li ing:
ΓZω(j)dΦ = Z(1 −ω(j)) kdΦ
Fiscal Expe imen and T ansi ion
The iscal expe imen s ha we analyze in his pape is 50 pe iods o educ ion in go e nmen
deb , B, ei he inanced h ough a dec ease in go e nmen spending, G, by 0.2% o bench-
ma k GDP14, o an inc ease in he labo income ax τl, by 0.1% o all agen s. The economy
is ini ially in a s eady s a e and he 50 pe iods o iscal consolida ion is unan icipa ed un il
i is announced15. A e he 50 pe iods ei he he go e nmen spending o he labo ax go
back o he ini ial le el. The lumpsum ans e , gis se o clea he go e nmen budge , and
we assume ha he economy akes an addi ional 50 pe iods o con e ge o he new s eady
s a e equilib ium, wi h lowe deb o GDP a io.
To sa e space, he de ini ion o a ansi ion equilib ium a e he iscal expe imen is
s a ed in Appendix 11.2. The key change compa ed o he s eady s a e is ha he dynamic-
p og amming p oblem o households need ano he s a e a iable: ime, , cap u ing all he
changes in policy and p ice a iables ele an in his maximiza ion p oblem. The nume ical
solu ion o he model necessi a es guessing on pa hs o all he a iables ha will depend
14The o al e enue a ailable o deb epaymen o e he 50-yea pe iod is hus 10% o benchma k GDP
15In Sec ion 3.2, we ound ha unan icipa ed bu no an icipa ed iscal consolida ions ha e a s a is ically
signi ican nega i e e ec on ou pu .
22
on ime and hen sol ing his maximiza ion p oblem backwa d, a e which he guess is
upda ed; he me hod is simila o ha used in B inca e al. (2016b) and K usell and Smi h
(1999).
De ini ion o he Fiscal Mul iplie in he Con ex o a Fiscal Consolida ion
Shock
In he expe imen wi h deb educ ion inanced by a educ ion in G, we de ine he impac
mul iplie as:
impac mul iplie G =∆Y0
∆G0
(21)
whe e ∆Y0is he change in ou pu om pe iod 0 o pe iod 1 and ∆G0is he change
in go e nmen spending om pe iod 0 o pe iod 1. The cumula i e mul iplie a ime Tis
de ined as:
cummula i e mul iplie G(T) = P =T
=0 Πs=
s=0 1
(1+ s)∆Y
P =T
=0 Πs=
s=0 1
(1+ s)∆G
(22)
whe e ∆Y is he change in ou pu om pe iod 0 o pe iod and ∆G0is he change in
go e nmen spending om pe iod 0 o pe iod When he consolida ion is inanced h ough
an inc ease in he labo income ax, τl, we de ine he impac mul iplie as:
impac mul iplie τl=∆Y0
∆R0
(23)
whe e ∆Y0is he change in ou pu om pe iod 0 o pe iod 1 and ∆R0is he change
in go e nmen e enue om pe iod 0 o pe iod 1. Go e nmen spending, Gand lumpsum
edis ibu ion, g, a e kep cons an du ing his consolida ion. Fo he ax-based consolida ion
we de ine he cumula i e mul iplie as:
23
6.1 Illus a ing he Mechanism: Compa ing Fiscal Consolida ion in Ge -
many and he Czech Republic
To illus a e he impac o di e ences in inequali y, we i s compa e he e ec s o consolida-
ion in Ge many and in he Czech Republic, wo Eu opean coun ies on he opposi e side o
he spec um in e ms o wage inequali y. Ge many wi h he second highes a iance o log
wages, 0.354, and Czech Republic wi h he lowes alue, 0.174. These wo coun ies di e
along se e al dimensions, bu he eason why we choose Ge many and Czech Republic is due
o hei di e ences in wage inequali y, idiosync a ic isk and he pe cen age o cons ained
agen s. In he Czech Republic he calib a ed a iance o he idiosync a ic isk is 0.145 and
he pe cen age o cons ained agen s is 7.39%, while Ge many has a highe a iance o isk,
0.439, and a lowe pe cen age o cons ained agen s, 3.41%. We ind wha ou mechanism
sugges s ha he ou pu mul iplie ollowing he unan icipa ed iscal consolida ion shock is
la ge in Ge many han in Czech Republic.
Figu e 6: Labo ax consolida ion: Ou pu cumula i e mul iplie (le panel) and Labo Supply cumula i e mul iplie ( igh
panel) in he i s h ee pe iods in Ge many (dashed line) and Czech Republic (solid line)
In Figu es 6and 7we plo he cumula i e ou pu mul iplie and labo supply esponse o
labo ax and go e nmen spending consolida ions espec i ely, o he wo coun ies. Bo h
he labo supply esponses and he ou pu mul iplie s a e signi ican ly la ge in he Ge man
economy, whe e wage inequali y is highe . As Ge many has a smalle sha e o cons ained
and low-weal h agen s, he ou pu d op is mo e p onounced. One should also no e ha
he consolida ion h ough inc eased labo income axes causes deepe ecessions han he
30

Figu e 7: Go e nmen spending consolida ion: Ou pu cumula i e mul iplie (le panel) and Labo Supply cumula i e
mul iplie ( igh panel) in he i s h ee pe iods in Ge many (dashed line) and Czech Republic (solid line)
consolida ion inanced by a educ ion in go e nmen spending. This is consis en wi h he
esul s by Alesina e al. (2017).
6.2 Inequali y: Va iance o Risk s. Va iance o Abili y s. Age P o iles
Nex , we pe o m h ee expe imen s in ou Ge man benchma k economy o e i y he mech-
anism desc ibed abo e. We ocus on unde s anding he ole o he di e en pa ame e s ha
d i e wage inequali y in ou model, σ,σa, and γ1,γ2,γ3. These pa ame e s go e n he
a iance o idiosync a ic wage shocks, he a iance o pe manen abili y and he shape o
he age-p ogile o wages. We ind ha he co ela ion be ween wage inequali y and iscal
mul iplie s ha we documen ed in he empi ical sec ion can only be explained by di e ences
in idiosync a ic isk and no by p ede e mined di e ences in abili y o in he age-p o ile o
wages. We pe o m h ee di e en expe imen s:
1. We g adually change V a (ln w) om in he benchma k model by changing he a iance
o he inno a ions o he s ochas ic income p ocess, σ2
, om low o high.
2. We g adually change V a (ln w) in he benchma k model calib a ed o Ge many, by
changing he a iance o abili y, σ2
a, om low o high.
3. We g adually change V a (ln w) in he benchma k model calib a ed o Ge many, by
mul iplying he age-p o ile o wages, go e ned by γ1,γ2,γ3, by a Scala , going om
low o high.
31
In all cases we adjus γ0by a cons an o gua an ee ha a e age p oduc i i y in he
economy s ays unchanged. Then o each alue o σu,σaand he Scala we pe o m ou
wo iscal consolida ion expe imen s: i) consolida ion h ough go e nmen spending and ii)
consolida ion h ough he labo income ax.
Figu e 8: Impac mul iplie o he labo ax consolida ion in he benchma k model o Ge many when changing he a iance
o isk (le panel), he a iance o abili y (middle panel), and he age p o ile o wages ( igh panel).
In Figu e 8we plo he impac mul iplie in he expe imen wi h iscal consolida ion
h ough labo income axes o di e en alues o σ,σaand he Scala . In he le panel
we obse e ha he iscal mul iplie is e y sensi i e o changes in income isk. When we
change he a iance o he inno a ions o he idiosync a ic shock, , om 0 o 0.45 he impac
mul iplie alls om abou -1.40 o -1.95. In he middle and igh panels we obse e ha i
is ela i ely inelas ic wi h espec o changes in abili y and he s eepness o he age-p o ile
o wages19.
Figu e 9: Impac mul iplie o he consolida ion h ough go e nmen spending in he Ge man benchma k economy when
changing he a iance o isk (le panel), he a iance o abili y (middle panel), and he age p o ile o wages ( igh panel).
19Ge many has one o he s eepes age-p o iles in ou sample o coun ies. We he e o e le he scala go
om 0 o 1, cap u e he e ec o going om a s eep age-p o ile o a comple ely la age-p o ile.
32
The expe imen wi h consolida ion h ough go e nmen spending gene a es simila e-
sul s. In he le panel o Figu e 9, we obse e ha as we change he a iance o he
inno a ions o he idiosync a ic shock, go e ned by σ, om 0 o 0.45 he impac mul iplie
inc eases om abou 0.41 o 0.47. In he middle and he igh panels o he igu e we ob-
se e ha he changes in he mul iplie induced by changing he a iance o abili y and he
s eepness o he age-p o ile o wages a e small. We conclude ha only h ough changes in
income isk can we gene a e a posi i e ela ionship be ween he impac o iscal consolida ion
p og ams and income inequali y.
The analysis in Figu es 8and 9co e s changes in isk ha go om ze o o he highes
alue ob ained in ou calib a ion o he model o 13 di e en Eu opean coun ies. In ou
calib a ion exe cise, he lowes alue o he a iance o isk was ob ained o G eece and
equal o 0.12 and he highes was equal o 0.5, o F ance. One should no e ha he ela i e
magni ude o changes in he mul iplie induced by changing he isk is la ge o ax-based
han o spending-based consolida ion. Going om he lowes o he highes le el o isk,
implies a 30% inc ease in he impac mul iplie o he ax-based consolida ion and an 8%
inc ease in he impac mul iplie o he spending-based consolida ion. As men ioned be o e
i is wo h no ing ha he ac ual consolida ions s udied in Sec ion 3include bo h changes
in axes and spending.
In Figu e 10 we e i y ou hypo hesis abou he ela ionship be ween income isk and he
iscal consolida ion mul iplie s s emming om he ac ha economies wi h highe income
isk ha e a lowe sha e o c edi -cons ained agen s. In he le panel o he igu e we
documen a s ong, nega i e ela ionship be ween he a iance o isk and he p opo ion
o c edi cons ained agen s in he economy. In he middle panel we see ha changing
he a iance o abili y does no a ec he sha e o agen s wi h liquidi y cons ain s, as we
an icipa ed. A s eepe age-p o ile o wages leads o mo e liquidi y-cons ained agen s (as
one would expec 20) bu he e ec is e y weak compa ed o he impac o income isk.
20Wi h a s eepe age p o ile agen s will sa e less ea ly in he li e-cycle.
33
Figu e 10: Sha e o c edi -cons ained agen s in he Ge man benchma k economy when changing he a iance o isk (le
panel), he a iance o abili y (middle panel), and he age p o ile o wages ( igh panel).
In Figu e 11 we illus a e he ela ionship be ween he sha e o agen s wi h liquidi y
cons ain s and he impac mul iplie , o bo h spending-based and ax-based iscal consol-
ida ion, as we change income isk. We obse e ha he e is a s ong nega i e ela ionship
be ween he sha e o c edi cons ained agen s and he iscal consolida ion mul iplie s.
Figu e 11: Impac mul iplie o he G-consolida ion (le panel) and o he τl-consolida ion ( igh panel) plo ed agains he
sha e o c edi -cons ained agen s in he Ge man benchma k economy, when dec easing he a iance o isk.
Finally, as a las obus ness es o e i y ha he ela ionship be ween inequali y and
iscal mul iplie s comes om he a iance o isk we conduc he ollowing expe imen : we
keep wage inequali y cons an by choosing di e en combina ions o isk and abili y, going
om one ex eme, whe e all wage inequali y (excep om he age-p o ile) is due o he
a iance o isk, o he o he ex eme, whe e wage inequali y is ully explained by a iance
o abili y. Figu e 16 in he Appendix shows ha he mul iplie is la ges when all inequali y
is explained by income isk and smalles when all inequali y is explained by he a iance o
34
abili y, o bo h ax-based and expendi u e-based consolida ions.
7 C oss-coun y Analysis
In he p e ious Sec ion we demons a ed ha ou model is able o ep oduce he empi ical
ela ionship be ween income inequali y and iscal mul iplie s, h ough a ia ion in income
isk. In his Sec ion we pe o m a c oss-coun y analysis o show ha his mechanism
is s ong enough o ma e empi ically. We calib a e ou model o ma ch a wide ange
o di e en coun y cha ac e is ics, whe e, in addi ion o he dis ibu ions o income and
weal h, we ma ch da a on axes, social secu i y and go e nmen deb . We show ha e en
when in oducing subs an ial coun y he e ogenei y, we a e able o ep oduce he c oss-
coun y ela ionship be ween bo h ax- and spending-based iscal consolida ion and income
inequali y.
The model is calib a ed o 13 Eu opean coun ies21 using coun y-speci ic age-p o iles
o wages, keeping he a iance o he pe manen abili y ixed and changing he a iance
o he idiosync a ic shock o ma ch he a iance o log wages in he da a. Tables 10 and
14 summa ize he weal h dis ibu ion, he o he coun y speci ic da a used o calib a e
he model, and he coun y speci ic pa ame e s es ima ed ou side o he model. Table 15
summa izes he coun y speci ic pa ame e s es ima ed h ough he simula ed me hod o
momen s, as desc ibed in Sec ion 5. Pa ame e s kep cons an o all he coun ies, a e
summa ized in Table 16.
Figu e 12 e eals ha ou model is able o ep oduce he c oss-coun y empi ical ela ion-
ship be ween income inequali y and he impac s o iscal consolida ion: coun ies wi h highe
inequali y expe ience la ge ou pu d ops on impac , bo h o ax and spending based con-
solida ions. These e ec s a e la ge and economically meaning ul, in pa icula o ax-based
21Fo his exe cise we use only coun ies which ac ually wen h ough iscal consolida ion p ocesses a e
2009. Compa ed o Blancha d and Leigh (2013), we a e o ced o exclude Belgium, Cyp us, Denma k,
I eland, Mal a, No way, Poland, Romania and Slo enia due o da a limi a ions. The esul s in Sec ion 3.1
a e, howe e , obus o conside ing only hese 13 coun ies. See Table 12 in Appendix.
35

consolida ions. Using he coe icien ound when eg essing he mul iplie on income inequal-
i y, we ind ha he esponse be ween he coun y wi h he lowes income inequali y (Czech
Republic) and he highes (F ance) leads o a 90% inc ease in he ax-based mul iplie . One
should also no e ha ax-based consolida ions in gene al p oduce deepe ecessions ac oss
coun ies han spending based consolida ions.
Figu e 12: Impac mul iplie and Va (ln(w)). On he le panel we ha e he c oss-coun y da a o a consolida ion done by
dec easing G (co ela ion coe icien 0.35 , p- al 0.25 ), while on he igh panel we ha e he c oss-coun y da a o a consolida ion
done by inc easing he labo ax (co ela ion coe icien -0.60 , p- al 0.03 ).
In he p e ious sec ion we a gued ha he mechanism h ough which highe income
isk ansla es in o la ge mul iplie s is h ough changes in he sha e o c edi -cons ained
agen s. In Figu e 13 his ela ion is documen ed o he 13 economies o which we calib a e
he model. Coun ies wi h a highe s anda d de ia ion o he inno a ions o idiosync a ic
income isk, σ, ha e a smalle sha e o cons ained agen s.
As a gued be o e, he labo supply o cons ained agen s is less elas ic wi h espec o he
iscal shock, and he la ge he pe cen age o cons ained agen s he smalle he mul iplie .
In Figu e 14 his ela ionship is documen ed o he c oss coun y analysis. Coun ies wi h
a la ge sha e o liquidi y cons ained agen s expe ience a smalle ou pu d op o bo h
spending- and ax-based consolida ions.
36
Figu e 13: Pe cen age o agen s cons ained in he y-axis and a iance o idiosync a ic isk on he x axis. Co ela ion coe icien
o -0.73 and p- alue o 0.00
Figu e 14: Impac mul iplie and pe cen age o agen s cons ained. On he le panel we ha e he c oss-coun y da a o a
consolida ion done by dec easing G (co ela ion coe icien -0.68 , p- al 0.01 ), while on he igh panel we ha e he c oss-coun y
da a o a consolida ion done by inc easing he labo ax (co ela ion coe icien 0.55 , p- al 0.06 )
8 Empi ical Valida ion o he Mechanism
In Sec ion 3we es ablished ha income inequali y ampli ies he ecessi e e ec s o iscal
consolida ions. In Sec ion 6we s udy a mechanism ha leads o his ampli ica ion e ec :
37
labo supply esponds s onge in coun ies wi h highe income inequali y, leading o a la ge
ou pu d op.
In his sec ion we p esen wo pieces o empi ical e idence ha suppo s ou mechanism.
Fi s , we use he ac ha household deb and he sha e o c edi -cons ained agen s a e
s ongly co ela ed in ou benchma k economy. I ou mechanism is co ec , he ou pu d op
in esponse o iscal consolida ions should be smalle in coun ies wi h highe household
deb because hey ha e mo e cons ained agen s. We expand he Blancha d and Leigh
(2014) eg ession wi h an in e ac ion e m be ween household deb and he planned iscal
consolida ion and ind exac ly his: household deb diminishes he ecessi e e ec s o iscal
consolida ion. The la ge he household deb , he smalle he o ecas e o .
Then, o es how income inequali y a ec s he labo supply esponse o iscal consoli-
da ion p og ams, we use he Alesina e al. (2015a) da ase bu ins ead o conside ing GDP
g ow h a es as ou dependen a iable, we use annual hou s wo ked pe capi a. We ind
ha o coun ies wi h highe income inequali y, labo supply is mo e esponsi e o iscal
consolida ion p og ams, jus as ou mechanism sugges s.
8.1 Household Deb
Blancha d and Leigh (2014) es whe he p e-c isis household deb was one o he dimensions
he IMF did no ake p ope ly in o conside a ion when o ecas ing he GDP g ow h a es.
Like all he o he a iables hey es , hey ind ha deb does no a ec he o ecas e o .
Howe e , ou mechanism sugges s ha deb should ha e a ec ed he ecessi e impac s o
iscal consolida ion p og ams. Dec easing isk, induces less p ecau iona y sa ings, which
esul s in highe household deb and consequen ly in a highe sha e o c edi -cons ained
agen s, as can be seen in Figu e 15. Highe household deb should, acco ding o ou model,
ansla e in o smalle mul iplie s.
To es whe he household deb helps o explain he impac s o iscal consolida ion p o-
g ams, besides ex ending Equa ion (1) wi h p e-c isis household deb , as al eady done by
Blancha d and Leigh (2014), we also include an in e ac ion e m be ween planned iscal
38
Figu e 15: The ac ion o liquidi y cons ained agen s (y-axis) and household deb le el (x-axis), when changing he le el o
idiosync a ic isk in he Ge man benchma k economy.
consolida ion and p e-c isis household deb . The equa ion ha we es ima e is:
∆Yi, : +1 −ˆ
E{∆Yi, : +1|Ω }=α+βˆ
E{Fi, : +1| |Ω }+γHDi, −1+
ι(( ˆ
E{Fi, : +1| |Ω })(HDi, −1−µHD)) + i, : +1 (27)
HDi, −1is he e p e-c isis household deb in coun y i, measu ed as o al inancial liabili ies
in pe cen o household disposable income. We use p e-c isis household deb so ha i is
exogenous o he iscal shocks and o he ou pu a ia ion. Once again, we epa ame ize
he in e ac ion e m.
The esul s in Table 5a e consis en wi h ou mechanism. The in e ac ion e m is posi i e
and s a is ically signi ican . Mo eo e , he R2is subs an ially highe han in he speci ica ion
wi hou he in e ac ion e m, and he coe icien associa ed wi h he planned consolida ion is
mo e nega i e and s a is ically di e en om he speci ica ion wi hou he in e ac ion. This
sugges s ha du ing he consolida ions in he Eu opean coun ies in 2010 and 2011, highe
p e-c isis household deb con ibu ed o diminish he ecessi e e ec s o iscal consolida ion
p og ams, jus as ou mechanism sugges s. Inc easing p e-c isis household deb by one
s anda d de ia ion dec eases he ecessi e impac s o iscal consolida ion by 52%.
39
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48
11 Appendix
11.1 Tax Func ion
26 Gi en he ax unc ion
ya =θ0y1−θ1
which we employ, he a e age ax a e is de ined as
ya = (1 −τ(y))y
and hus
θ0y1−θ1= (1 −τ(y))y
and hus
1−τ(y) = θ0y−θ1
τ(y) = 1 −θ0y−θ1
T(y) = τ(y)y=y−θ0y1−θ1
T0(y) = 1 −(1 −θ1)θ0y−θ1
Thus he ax wedge o any wo incomes (y1, y2) is gi en by
1−1−τ(y2)
1−τ(y1)= 1 −y2
y1−θ1
(29)
and he e o e independen o he scaling pa ame e θ0.Thus by cons uc ion one can aise
a e age axes by lowe ing θ0and no change he p og essi i y o he ax code, since (as
26This appendix is bo owed om Hol e e al. (2017)
49
long as ax p og essi i y is de ined by he ax wedges) he p og essi i y o he ax code27 is
uniquely de e mined by he pa ame e θ1.
11.2 De ini ion o a T ansi ion Equilib ium a e he Unan icipa ed Fiscal
Consolida ion Shock
We de ine a ecu si e compe i i e equilib ium along he ansi ion be ween s eady s a es as
ollows:
Gi en he ini ial capi al s ock, he ini ial dis ibu ion o households and ini ial axes,
espec i ely K0, Φ0and {τl, τc, τk, τss,˜τss} =∞
=1 , a compe i i e equilib ium is a sequence o
indi idual unc ions o he household, {V , c , k0
, n } =∞
=1 , o p oduc ion plans o he i m,
{K , L } =∞
=1 , ac o p ices, { , w } =∞
=1 , go e nmen ans e s {g ,Ψ , G } =∞
=1 , go e nmen
deb , {B } =∞
=1 , inhe i ance om he dead, {Γ } =∞
=1 , and o measu es {Φ } =∞
=1 , such ha o
all :
1. Gi en he ac o p ices and he ini ial condi ions he consume s’ op imiza ion p oblem
is sol ed by he alue unc ion V(k, β, a, u, j) and he policy unc ions, c(k, β, a, u, j),
k0(k, β, a, u, j), and n(k, β, a, u, j).
2. Ma ke s clea :
K +1 +B =Zk dΦ
L =Z(n (k , β, a, u, j)) dΦ
Zc dΦ +K +1 +G = (1 −δ)K +Kα
L1−α
27No e ha
1−τ(y) = 1−T0(y)
1−θ1
>1−T0(y)
and hus as long as θ1∈(0,1) we ha e ha
T0(y)> τ(y)
and hus ma ginal ax a es a e highe han a e age ax a es o all income le els.
50
3. The ac o p ices sa is y:
w = (1 −α)K
L α
=αK
L α−1
−δ
4. The go e nmen budge balances:
g ZdΦ +G + B =Z τk (k + Γ ) + τcc +n τln w (a, u, j)
1 + ˜τss !dΦ + (B +1 −B )
5. The social secu i y sys em balances:
Ψ Zj≥65
dΦ =˜τss +τss
1 + ˜τss Zj<65
n w dΦ !
6. The asse s o he dead a e uni o mly dis ibu ed among he li ing:
Γ Zω(j)dΦ =Z(1 −ω(j)) k dΦ
7. Agg ega e law o mo ion:
Φ +1 =Υ (Φ )
11.3 Desc ip ion o Da a used in Sec ions 3,8, and 9
The da a se ies used in Sec ions 3.1 and 3.2 o he inequali y measu es a e om he Eu-
opean Union S a is ics on Income and Li ing Condi ions (EU-SILC). The EU-SILC is a
su ey aiming a collec ing c oss-sec ional and longi udinal mic oda a on income, po e y,
social exclusion and li ing-condi ions. Da a collec ed is based on a na ionally ep esen a-
i e p obabili y sample o he popula ion esiding in p i a e households wi hin he coun y.
C oss-sec ional da a se ies used is g oss income - o al mone a y and non-mone a y income
ecei ed by he household be o e deduc ion o axes.
51

The g ow h o ecas e o and planned iscal consolida ion se ies a e aken om Blancha d
and Leigh (2014), who use da a om he IMF’s WEO da abase. The o ecas s used we e
made o he Eu opean Economies in ea ly 2010. The g ow h o ecas e o consis on he
di e ence be ween ac ual cumula i e g ow h in 2010-11 and he IMF o ecas p epa ed o
he Ap il 2010 WEO. The planned iscal consolida ion is he IMF o ecas o he cumula i e
changes o s uc u al iscal balance as pe cen o po en ial GDP, also p epa ed o he Ap il
2010 WEO. The household deb a iable used in Sec ion 6also comes om Blancha d and
Leigh (2014), who ake i om he da ase o he Ap il 2012 WEO chap e on household
deb . Household deb consis s on o al inancial liabili ies in pe cen o household disposable
income.
The da a se ies used in Sec ion 3.3 a e aken om Ilze zki e al. (2013). The da a se ies
consis o qua e ly obse a ions (no in e pola ed) on eal go e nmen consump ion, GDP,
he a io o cu en accoun o GDP, and he eal e ec i e exchange a e o 44 coun ies,
oughly balanced be ween de eloped and de eloping economies (see Table 9 o he lis
o included coun ies). Nominal se ies a e de la ed using a GDP de la o when a ailable
(and CPI when no ). Consump ion, GDP, and exchange a e a iables a e ans o med by
aking na u al loga i hms. These se ies a e de-seasonalized and analyzed as de ia ions om
hei quad a ic end gi en hey exhibi s ong seasonali y and a e non-s a iona y. Da a in
Table 9comes om he Wo ld Bank’s Wo ld De elopmen Indica o s o he yea s o 2009 o
Bo swana and Malaysia, 2010 o Aus alia, Canada and Is ael, 2011 o Ge many and Sou h
A ica, 2012 o Belgium, Bulga ia, C oa ia, Czech Republic, Denma k, Es onia, Finland,
F ance, G eece, Hunga y, Iceland, I eland, I aly, La ia, Li huania, Mexico, Ne he lands,
No way, Po ugal, Slo akia, Slo enia, Spain, Sweden and Uni ed Kingdom, and 2013 o all
he o he coun ies.
52
Table 9: Income Inequali y measu es o 44 Selec ed Coun ies
Coun y Income Gini Y20/Y80 Y10/Y90
A gen ina 0.42 9.8 19.1
Aus alia 0.35 5.9 10.2
Belgium 0.28 4.2 6.7
Bo swana 0.61 23.1 45.0
B azil 0.53 17.4 41.8
Bulga ia 0.36 6.9 13.7
Canada 0.34 5.8 9.5
Chile 0.51 12.3 24.4
Colombia 0.54 17.1 38.1
C oa ia 0.33 5.7 9.6
Czech Republic 0.26 3.8 5.7
Denma k 0.29 4.4 8.4
Ecuado 0.47 11.5 22.8
El Sal ado 0.43 9.1 16.4
Es onia 0.33 5.7 10.1
Finland 0.28 3.9 5.7
F ance 0.33 5.3 8.6
Ge many 0.30 4.6 7.0
G eece 0.37 7.6 15.7
Hunga y 0.31 4.9 8.0
Iceland 0.27 4.0 6.0
I eland 0.33 5.3 8.3
Is ael 0.43 10.3 18.4
I aly 0.35 6.7 13.8
La ia 0.36 6.7 12.1
Li huania 0.35 6.5 11.7
Malaysia 0.46 11.2 19.2
Mexico 0.48 11.0 20.5
Ne he lands 0.28 4.2 6.6
No way 0.26 3.8 5.8
Pe u 0.45 11.3 22.3
Poland 0.33 5.2 7.8
Po ugal 0.36 6.6 12.6
Romania 0.28 4.1 6.0
Slo akia 0.26 4.1 6.6
Slo enia 0.26 3.7 5.7
Sou h A ica 0.63 27.6 57.0
Spain 0.36 7.2 15.2
Sweden 0.27 4.2 6.7
Thailand 0.38 6.5 10.1
Tu key 0.40 8.0 13.9
Uni ed Kingdom 0.33 5.4 8.5
Uni ed S a es 0.41 9.1 17.8
U uguay 0.42 9.3 16.3
Sample median 0.35 6.5 10.9
53
11.4 Eu osys em Household Finance and Consump ion Su ey - Summa y
Weal h S a is ics
Table 10 p esen s he cumula i e weal h dis ibu ions o he coun ies in he Eu osys em
Household Finance and Consump ion Su ey. We include ou addi ional coun ies’ weal h
dis ibu ions, om he Luxembou g Weal h S udy’s compila ion o a ious household weal h
su eys.
Table 10: Cumula i e Dis ibu ion o Ne Weal h
25% 50% 75%
HFCS samplea
Aus ia -1.0 2.2 18.6
F ance 0.1 5.4 26.2
Ge many -0.4 2.7 17.9
G eece 1.1 12.5 36.7
I aly 0.9 10.2 32.4
Ne he lands -2.5 5.0 30.3
Po ugal 0.6 8.2 26.6
Slo akia 5.5 20.7 45.0
Spain 1.7 12.9 34.2
O he sou cesb
Czech Republicc0.4 6.1 22.1
Iceland 0.5 7.7 27.6
Sweden -9.9 -7.8 11.5
UK -0.7 5.4 27.0
aCumula i e dis ibu ion o ne weal h (su ey a iable designa-
ion: DN3001) o a selec ion o coun ies om he i s wa e o
he ECB’s HFCS.
bSou ced om Luxembou g Weal h S udy’s mos ecen en y o
each espec i e coun y (su ey a iable designa ion: nw1).
cSou ced om he S ie li e al. (2014). We use 2009 da a p o ided
by he au ho s.
54
11.5 Addi ional Figu es and Tables
Table 11: Blancha d and Leigh (2013) Reg essions wi h GDP as he Dependen Va iable
Coe icien s Blancha d-Leigh Y25/Y75 Y20/Y80 Y10/Y90 Y5/Y95 Y2/Y98 Income Gini
β-1.556*** -1.116** -1.078** -0.901** -0.901** -1.026*** -1.696***
(0.467) (0.441) (0.436) (0.379) (0.339) (0.339) (0.406)
γ-0.402 -0.302 -0.170 -0.039 0.019 0.286
(0.578) (0.444) (0.191) (0.053) (0.050) (0.169)
ι-0.405 -0.365 -0.229* -0.116*** -0.098** -0.000
(0.388) (0.304) (0.113) (0.036) (0.035) (0.115)
Cons an 3.763*** 6.545* 6.335* 6.264** 4.938*** 3.612*** -6.990
(0.576) (3.760) (3.493) (2.578) (1.302) (1.057) (6.402)
Obse a ions 26 26 26 26 26 26 26
R-squa ed 0.465 0.533 0.544 0.607 0.634 0.587 0.542
a*** p<0.01, ** p<0.05, * p<0.1. Robus s anda d e o s in pa en heses.
bThe able displays he esul s om es ima ing he eg ession in (1) wi h GDP as he dependen a iable.
cY25/Y75, Y20/Y80, Y10/Y90, Y5/Y95 and Y2/Y98 ep esen he sha e o income o he op 25%, 20%, 10%, 5% and 2%
di ided by he sha e o he bo om 25%, 20%, 10%, 5% and 2%.
Table 12: Blancha d and Leigh (2013) Reg essions o he Coun ies in Sec ion 7
(1) (2) (3) (4) (5) (6) (7)
Coe icien s Blancha d-Leigh Y25/Y75 Y20/Y80 Y10/Y90 Y5/Y95 Y2/Y98 Income Gini
β-1.430*** -1.161*** -1.170*** -1.204*** -1.286*** -1.259*** -1.378***
(0.182) (0.131) (0.134) (0.172) (0.164) (0.176) (0.204)
γ-0.490 -0.303 -0.033 0.031 0.048 0.365**
(0.750) (0.534) (0.165) (0.034) (0.046) (0.120)
ι-0.122 -0.119 -0.073 -0.039* -0.040** -0.053
(0.187) (0.134) (0.047) (0.017) (0.017) (0.063)
Cons an 1.207* 4.304 3.553 1.712 0.616 0.228 -12.831**
(0.567) (5.167) (4.552) (2.709) (1.233) (0.840) (4.458)
Obse a ions 13 13 13 13 13 13 13
R-squa ed 0.715 0.755 0.750 0.736 0.736 0.748 0.919
a*** p<0.01, ** p<0.05, * p<0.1. Robus s anda d e o s in pa en heses.
bThe able displays he esul s om es ima ing he eg ession in (1) jus o he coun ies in Sec ion 7. These a e he coun ies
o which we ha e enough da a o calib a e he model.
cY25/Y75, Y20/Y80, Y10/Y90, Y5/Y95 and Y2/Y98 ep esen he sha e o income o he op 25%, 20%, 10%, 5% and 2%
di ided by he sha e o he bo om 25%, 20%, 10%, 5% and 2%.
55