Heterogeneous household finances and the effect of fiscal policy

Transcription

1 Heerogeneous household finances and he effec of fiscal policy Javier Andrés a, José E. Boscá a,b, Javier Ferri a,b and Crisina Fuenes-Albero c a Universiy of Valencia b FEDEA c Federal Reserve Board February, Absrac This paper analyses he link beween fiscal policy, heerogeneous household finances, and households consumpion response. Our model economy is populaed by six ypes of households wih idenical labour income, bu differen balance shee composiion. We show ha heerogeneiy in he srucure of household finance is key o undersanding he effecs of fiscal shocks. In paricular, we conclude ha: 1 he marginal propensiy o consume is negaively correlaed wih ne worh; 2 he size of fiscal effecs is posiively correlaed wih wealh inequaliy; and 3 he welfare effecs among heerogeneous households depend heavily on he composiion of ne worh. Keywords: household finances, fiscal policy, heerogeneiy. JEL Classificaion: E21, E Inroducion Wealh ownership in many advanced counries has always been concenraed in he hands of a small minoriy of he populaion. In fac, wealh inequaliy increased in he Grea Moderaion period in he US and oher developed counries and coninued o do so during he Grea Recession. The wealh share of he U.S. s op 3 percen see Federal Reserve Board Survey of Consumer Finances, 2014 rose from 44.8 percen of he counry s wealh This work was suppored by Fundación Rafael del Pino; BBVA Research; and he Spanish Minisry of Economy and Compeiiveness gran ECO R.

2 2 in 1989 o 51.8 percen in 2007 and 54.4 percen in In he U.S., wealh held by he op 3 percen of he populaion is wice as much as ha in he hands of he poores 90 percen. During he Grea Moderaion period, his issue received lile aenion from economic researchers, given ha, a he same ime, consumpion differences across households were reduced. The financial secor was playing a key role favouring ha wealhy people big savers provided loans o finance consumpion of he less favoured par of he populaion and, hus, reducing he differences in consumpion across households. As a resul consumpion inequaliy was reduced, alhough wealh inequaliy increased. However, he financial urmoil in 2008 brough abou an imporan recomposiion of he balance shees of many households. The crisis exered a devasaing effec on he abiliy of households o obain credi and also on he prices of many financial and real asses. While he value of privae secor asses, in paricular real sae, plummeed, deflaion increased he real value of deb. The subsequen fiscal responses in many counries were hus carried ou agains he backdrop of economies wih households characerised by very differen asses/liabiliies posiions han he ones prevailing before he crisis. For his reason, researchers and policy makers have made subsanial effors o assess o wha exen fiscal mulipliers are now very differen from he ones esimaed before he crisis see e.g. he surveys by Ramey, 2011 and Spilimbergo e. al., The mos recen economic lieraure has gone a sep furher combining macroeconomic and microeconomic empirical and heoreical analysis o shed some ligh on he links beween fiscal policy, heerogeneous household finances and heir consumpion responses o shocks. The main idea of his srand of he lieraure consiss in using microeconomic daa, coming from differen surveys, o mach he sylised facs regarding he composiion of households finances. This ype of approach will allow a beer undersanding of he reacion of economies o fiscal and oher kinds of shocks. In his paper, we carry ou a macroeconomic analysis of hese issues wihin he framework of a general equilibrium model populaed by six ypes of consumers. Households differ in he composiion of heir balance shees. These households caegories have been used individually, or in differen combinaions, in many macroeconomic models developed in he general equilibrium lieraure. 1 Specifically, we idenify sandard Ricardian opimising households R, ypical hand-o-mouh or rule-of-humb consumers HNH ha hold neiher asses nor liabiliies, wealhy HM consumers HH ha hold asses bu no liabiliies, borrowers wih eiher high or low capaciy o access credi backed by collaeral BL and BH, respecively and, finally, wha we call Eggersson-Krugman ype of consumers EK ha do no posses collaeralisable asses and borrow agains heir fuure 1 See Eggersson and Krugman 2012, Gali, López-Salido and Vallés 2007, Iacoviello 2015, and Andrés, Boscá and Ferri 2015 and 2016.

3 3 labour income. Idenifying marginal propensiies o consume using wealh changes is difficul because individuals differ in labour income, employmen saus, produciviy, educaion, ec. Our heoreical model limis he scope of heerogeneiy among households only o heir balance shee posiion. The paper aims o isolae ne worh effecs of fiscal shocks and, o ha end, we assume perfec insurance o unemploymen. In paricular, labour income is idenical across individuals in a search and maching environmen. Thus, afer a governmen expendiure shock, all households in he economy face he same variaion in heir labour income, bu idiosyncraic reacions of heir ne worh. This framework allows us o look in deail a he general equilibrium mechanism underlying he consumpion reacion o specific ne wealh variaions of he various agens in he economy, and in urn o he aggregae consumpion and oupu effecs of fiscal policy. The model is calibraed o mach he mos salien feaures of he U.S. economy. We inspec he mechanism considering alernaive heoreical wealh disribuions and access o credi among he populaion. We hen give he simulaed model a more solid empirical foundaion by improving he calibraion of he model wih he share of hese ypes of households idenified in he Panel Sudy of Income Dynamics PSID. We idenify differen ypes of consumers ha are heerogenous in erms of he composiion of heir balance shees and ha mach o some exen he feaures of he individuals in our heoreical model. We conclude ha maching sylised facs regarding households finances is key o undersand he reacion of economies o fiscal shocks. Our resuls show ha changing he composiion of he populaion according o heir financial posiions has imporan effecs on he aggregae marginal propensiy o consume and he oupu muliplier. A he individual level, he marginal propensiy o consume is negaively relaed wih ne worh. Model simulaions show ha he size of he fiscal effec is posiively correlaed wih wealh inequaliy. Finally, we compue he effec in our model of fiscal shocks on household s welfare, showing ha welfare effecs depend heavily on he composiion of ne worh. Summing up, we conclude ha households in he lowes par of he ne wealh disribuion HH, HNH and EK households in our economy can affec imporanly he magniude of he aggregae marginal propensiy o consume, he value of he fiscal muliplier and he disribuional consequences of fiscal shocks. Secion 2 presens a succinc review of he recen empirical lieraure on he macroeconomic implicaions of alernaive household balance shees. Secion 3 inroduces he model and is calibraion. The simulaion exercises are presened in Secion 4. Secion 5 conains a descripion of he daa se, he crieria used o idenify he differen house-

4 4 holds caegories and some addiional simulaion exercises based on his daa. Secion 6 concludes. 2. Lieraure review Kaplan, Violane and Weidner 2014 use survey daa on household porfolios for he U.S., Canada, Ausralia, he U.K., Germany, France, Ialy, and Spain o documen he shares of he so called hand-o-mouh HM households across counries, heir demographic characerisics and he composiion of he asses side of heir balance shees. They idenify wo ypes of HM households: poor hand-o-mouh wih lile or no liquid wealh and no illiquid wealh and he wealhy hand-o-mouh wih lile or no liquid wealh, bu significan amouns of illiquid asses. Using daa of he Survey of Consumer Finances for he U.S., hey conclude ha abou 30% of he populaion is HM, from which one-hird is poor HM and he remainder is wealhy HM. The auhors find ha boh wealhy and poor HM households have significanly sronger responses o ransiory income shocks han non-hm households. They show ha ignoring ha wealhy hand-o-mouh can use illiquid asses o buffer large negaive shocks oversaes he overall financial fragiliy of HM households. In a similar vein, Angrisani, Hurd and Rohwedder 2015 use panel daa spanning he years on a complee invenory of household spending and asses. They esimae he response of privae spending o negaive wealh shocks in he US due o unexpeced declines in house and sock marke prices. Their main finding is ha he marginal propensiy o consume ou of an unexpeced housing wealh change is seven cens per dollar, and abou four cens per dollar ou of financial wealh. So, hey find ha consumpion was reduced in he Grea Recession because of losses in housing wealh and also, alhough less precisely esimaed, because of financial wealh losses. Oher auhors pu he emphasis on he imporance of he composiion of he liabiliies side of he balance shee of households o undersand he consumpion responses of individuals o income shocks. For example, Cloyne and Surico 2014 use household expendiure daa from 1978 o 2009 of he UK s Living Coss and Food Survey commonly known as he Family Expendiure Survey o show ha households wih morgage deb exhibi large and persisen consumpion responses o changes in heir income. In conras, homeowners wihou a morgage do no appear o reac, independenly of he ime horizon considered. The references above look eiher a he asses or he liabiliies side of balance shees. Bu boh sides of he T-accoun are imporan in shaping he effecs of shocks on households consumpion and, hus, on aggregae oupu in he economy. Oher papers have also looked a he ne worh, defined as he value of households asse holdings ne of

5 5 deb, rying o undersand he evoluion of consumpion over he recen years. Jaramillo and Chailloux 2015 base heir analysis on an unbalanced panel daase for 14 advanced economies, from 1998 o They separae he effecs on privae final consumpion expendiure of he subcomponens of disposable income labor income, social benefis, personal income axes and social securiy conribuions and of differen caegories of ne wealh financial asses, housing asses, and household deb, finding a significan longerm relaion beween consumpion and he differen componens of income and wealh. While labor income remains he main driver of consumpion, financial asses and housing asses are found o have a posiive coefficien, while household deb has a negaive one. Furhermore, hese auhors resuls sugges ha he conribuion o consumpion from an increase in financial or housing asses would be more han offse if financed fully hrough increases in household deb. Carroll, Slacalek and Tokuoka 2014 documen he imporance of maching sylised facs a he household level o inerpre he reacion of economies o shocks. Using daa from 15 European counries, hey find ha wealh inequaliy and differences in he dynamics of household income affec he response of economies o fiscal simuli in an economically relevan way. In heir sample hey rack down subsanial heerogeneiy in ne wealh o income raios boh across and wihin counries. Counries in which households end o hold more ne wealh respond less srongly o ransiory income shocks, while counries wih more unequal wealh disribuions have a higher aggregae marginal propensiy o consume MPC and also a larger dispersion of MPCs across households and, hus, respond more srongly o shocks. Finally, Anderson, Inoue and Rossi 2015 presen empirical evidence based on a narraive approach, finding ha individuals whose consumpion levels are mos negaively affeced by a posiive governmen spending unexpeced shock are he wealhies and working-age individuals, whereas consumpion of he poores increases he mos. Thus, he ineresing conclusion is ha posiive governmen spending policy shocks end o decrease consumpion inequaliy. Overall, he mos imporan implicaion of his burgeoning mosly empirical lieraure is ha he ne wealh posiion of households is a major deerminan of heir spending decisions, and hence ha he disribuion of wealh in an economy ineracs wih affecs and is affeced by fiscal policy shocks in a non rivial manner. This is rue no only for he case of ax changes, whose incidence on household wealh is more direc, bu also following changes in public spending, hrough heir macroeconomic effecs on boh he asse and he liabiliies sides of he balance shee. 3. The model This secion presens a sylised version of our model economy. A complee descripion of

6 6 he model can be found in he Appendix 1. The economy is populaed by six differen ypes of households, being N he oal size of he working-age populaion. Households differ in erms of some few characerisics, as housing enancy, he degree of impaience, or he abiliy o accessing credi. Le N i denoe he i-ype household mass, wih i denoing an elemen of he se I = {R, HNH, HH, BL, BH, EK}. The meaning of he previous acronyms is as follows: R sands for Ricardian households; HNH are hand-o-mouh households wih no access o financial markes and no real or financial asses; HH capures hand-o-mouh households ha can purchase and own houses, bu, as for HNH households, oal expendiures are equal o curren income every period ; BL represens households ha are able o borrow agains a low proporion of he expeced value of a collaeralised housing asse; BH sands for households ha are able o collaeralise a higher par of he nex-period expeced value of heir housing; and EK sands for households ha are allowed o borrow agains heir fuure labour income. Define τ i = Ni N τ i = 1 as he weigh of he i-ype household in he oal populaion. For convenience, we also define differen subses of households belonging o I. Firs, le ĩ be he index for he households in he subse Ĩ = {HNH, HH, BL, BH, EK} referring o he differen households facing a high degree of impaienness. Second, define he subse Î = {R, BL, BH, EK}, whose elemens are indexed by î, as he subse for hose households ha have access o financial markes. Finally, consider I = {R, HH, BL, BH}, indexed by i, as he subse of households ha own houses. Financially unconsrained Ricardian households R have been during a long ime he main characer in represenaive agen macroeconomic models. These households are ypically savers/lenders ha own asses, bu do no have liabiliies. In our economy, Ricardian consumers coexis wih financially consrained individuals, who are characerised by having a higher degree of impaience. Typical hand-o-mouh consumers HNH were popularised by Galí, López-Salido and Vallés 2007 o obain a posiive response of aggregae consumpion o a governmen spending shock. Conrary o Ricardian consumers, hese households have no asses, bu also no liabiliies, so heir ne worh is zero. More recenly, Kaplan, Violane and Weidner 2014 defined he wealhy hand-o-mouh households as hose ha consume all heir disposable income every period bu have sizable amouns of wealh in illiquid asses his is he role played by our HH households. BL and BH households are of he ype designed by Kiyoaki and Moore 1997 and Iacoviello These individuals own boh asses and liabiliies and display a posiive ne wealh in he long run which is lower he higher he capaciy o borrow. The ype of households ha are able o borrow agains heir fuure labour income EK were used by Eggersson and Krugman 2012 o illusrae he power of fiscal policy in highly leveraged economies. i I

7 7 Compared o Ricardian consumers, hese households are locaed in he oher exreme regarding he composiion on heir ne worh, as hey have only liabiliies bu no asses. In order o emphasize he imporance of household ne wealh heerogeneiy on he effecs of fiscal policy, we assume ha all households in he economy receive he same labour income. In paricular, we assume ha all workers are equally producive and delegae o a rade union he negoiaion wih firms, so ha in equilibrium all of hem receive he same wage, work he same number of hours and display idenical employmen raes. 3.1 Households problem The opimisaion problem faced by a household of ype i can be expressed as, max c i,bî,xi,dr,kr,jr E β i [ln c i +φ i x ln x i +n i -1 φ 1-l 1 1 η 1 1-η =0 +1-n i -1 φ 1-l 2 1-η ] 2 1-η 1 subjec o: c i +j R 1+ φ 2 j R k R 1 +q x i -x i 1 +r k R 1 +w n i 1 l 1+bî+d R + f R +rh = -1+r n 1 b î -1 1+π + dr -1 1+π 2 k R = j R + 1 δk R 1 3 [ ] b i ϕ i m i q π +1 x i E 1 + r n i Ĩ Î [ ] +1 ϕ i m EK E 1 + π+1 w +1 n i l r n 4 n i = 1 σn i 1 + ρi 1 ni 1 5 Variables in his problem are normalised by he wihin-group working-age populaion N i. The index i in variables and parameers poins o a specific financial srucure of he household. Those wih a ĩ superscrip refers o he subse of financial consrained consumers, and he ones indexed by R affecs only o consumers from Ricardian households. Non-indexed variables and parameers are common o all households in he model economy.

8 8 The meaning of he variables implied in he uiliy funcion 1 is he following: c i, xi,ni 1 and 1 ni 1 represen, respecively, consumpion, housing holdings, and he beginning of period employmen and unemploymen raes of differen households. The ime endowmen is normalised o one and, hence, l 1 and l 2 are an index of hours worked per employee and hours devoed o job seeking by he unemployed. While here is a process of bargaining over l 1, he amoun of ime devoed o job seeking l 2 is assumed o be exogenous and he same among workers. The discoun rae parameer, β i, and he preferences on housing, φ i x, can differ depending on he household class he consumer belongs. However, he Frisch elasiciy of he labour supply, relaed wih η, and he valuaion of leisure by employed φ 1 and unemployed φ 2 workers are assumed o be he same for all he agens. Regarding he budge consrain 2 all consumers earn labour income w n i 1 l 1, where w sands for hourly real wages. Laer on we will commen ha under our assumpions n i 1 = n 1 for all i I, so ha labour income is homogeneous across all household ypes. Also, all consumers receive pay he same amoun of lump sum ransfers axes from o he governmen rh. When rh is negaive i is considered a ax. Consumpion is represened by c i. Ricardian consumers, who are more paien han he res of agens and, hus, are characerised by a high value of β i, are he only lenders in he economy. Ricardians lend in real erms b i o he privae secor implying ha bi is negaive when i = R and dr o he public secor. Deb conracs are se in nominal erms and hey earn an amoun 1 + r 1 n b 1 R from financial asse holdings, where r 1 n is he nominal ineres rae 1+π + dr 1 1+π on loans beween 1 and. These paien consumers are also assumed o be he only ones who own physical capial k R ha yields r 1k 1 R, where r represens he gross reurn on physical capial. Capial accumulaes according o 3, where j R sands for producive invesmen and δ is he depreciaion rae. Invesmen is subjec o increasing marginal coss of adjusmen which are conrolled by he parameer φ. Moreover, given ha firms make exraordinary profis, we assume ha lenders receive hese in he form of dividends f R. The res of consumers in he economy, hose belonging o he subse Ĩ, are assumed o be more impaien han Ricardians and face he same discoun facor, βĩ < β R. From he subse of impaien consumers only hose belonging o Î have access o credi, alhough in a resricive way. These are households of ype BL, BH, EK. Loans have differen consideraion depending on he degree of securiizaion. There is deb backed by collaeral bu also no morgaged deb in he economy, and he possibiliy of access each of hem depends on he parameer ϕ i. We assume ha for BL, BH households ϕ i = 1, which means ha he oal amoun of deb hey can ge is a fracion of he liquidaion value

9 9 of heir housing sock. However for he EK consumers we assume ha ϕ i = 0 so ha hey can ake loans up o a proporion of he discouned expeced omorrow s labour income. 2 The impaien households ineremporal subsiuion is limied as represened by he corresponding Euler equaion in consumpion, 1 + r λ1 i = β i n E λĩ1+1 + µ i 1 + π 1 + rn 6 i Ĩ Î +1 where µ i is he shadow price associaed wih he consrain 4. There is a fixed amoun of real esae in he economy and he erm q x i xi 1 denoes housing invesmen, where q is he real housing price. The remaining consrain faced by households concerns he law of moion for employmen. Each period, jobs are desroyed a he exogenous rae σ. Likewise, new employmen opporuniies come a he rae ρ w ha represens he probabiliy ha one unemployed worker will find a job, which is aken as exogenous by individual workers bu is endogenously deermined a aggregae level. Acually, ρ w can be defined as he number of mached workers during period over he volume of unemployed workers a he beginning of period, ρ w 1 n 1 = χ 1 v χ 2 [1 n 1 l 2 ] 1 χ 2 7 where v sands for he number of acive vacancies during period, being χ 1 and χ 2 he parameers in he maching funcion. For laer use we define he marginal value of employmen for a worker λ i h as, W i n i 1 λ i h =λi 1 w 1-l l 1 + φ 1 1 η 1-l 2 1 η 1 -φ 1-η σ-ρ w 1-η βi E λ i h+1 8 where W i Ω i represens he value funcion of households maximum uiliy. λi h measures he marginal conribuion of a newly creaed job o he uiliy of he household. The firs erm capures he value of he cash-flow generaed by he new job in, i.e. he labour income measured according o is uiliy value in erms of consumpion λ1 i is he marginal uiliy of consumpion. The second erm on he righ-hand side of 8 represens he ne uiliy semming from he newly creaed job. Finally, he hird erm represens he "capial value" of an addiional employed worker, given ha he employmen saus will persis in he fuure, condiional o he probabiliy ha he new job will no be los. 2 Alernaively we could have allowed for differen ypes of loans for all impaien households, wih a proporion refereing o morgaged deb and he res being jus backed by expeced labor income. We find our modeling choice easier o handle wihou much loss of accuracy in he exercises berlow.

10 Firms problem For convenience, producion is organised in hree differen levels: 1 a wholesale secor indexed by j where firms use labour and capial o produce a homogenous good ha is sold in a compeiive flexible price marke a a price P w ; 2 an inermediae secor whose firms indexed by j operaes in a monopolisically compeiive fashion in which prices are sicky. These firms buy he homogenous good and ransform i, wihou he use of any oher inpu, ino a firm-specific variey; 3 a compeiive reail aggregaor ha buys differeniaed varieies from he inermediae secor a a price and sells a y j P j homogeneous final good y a price P. The compeiive reail secor The compeiive reail aggregaor buys differeniaed goods from firms in he inermediae secor and sells a homogeneous final good y a price P. Each variey is purchased a a y j price. Profi maximisaion by he reailer implies P j Max y j { P y } P j y j d j subjec o, [ 1 1/θ y = y j d j ] θ θ 1 9 where θ > 1 is a parameer ha can be expressed in erms of he elasiciy of subsiuion beween inermediae goods κ, as θ = 1 + κ /κ. The reailer s price is given by: [ 1 P = 0 ] 1 1 θ 1 θ P j d j 10 The monopolisically compeiive inermediae secor The monopolisically compeiive inermediae secor comprises j = 1,... J firms, each of which buys he producion of compeiive wholesale firms a a common price P w and sells a differeniaed variey a price o he final compeiive reailing secor described y j P j above. Variey producers sagger prices. In keeping wih Calvo 1983, only some firms se heir prices opimally each period. Those firms ha do no rese heir prices opimally a adjus hem according o a simple indexaion rule o cach up wih lagged inflaion. Thus, each period a proporion ω of firms simply se = P j 1 + π 1 ς P j 1 wih ς represening he degree of indexaion and π 1 he inflaion rae in 1. The fracion of

11 11 firms of measure 1 ω ha se he opimal price a seek o maximise he presen value of expeced profis. Consequenly, 1 ω represens he probabiliy of adjusing prices each period, where ω can be inerpreed as a measure of price rigidiy. The soluion o choice of he opimal price for he represenaive variey producer is E s=0 P θ = θ-1 E s=0 [ ] s β R ω λ R s -θ 1+s mc +s P +s θ y +s 1+π +s -1 ς s =0 [ ] s β R ω λ R s 1-θ 11 1+s P +s θ-1 y +s 1+π +s -1 ς s =0 where P is he price se by he represenaive opimizing firm a ime, and mc represens he real marginal cos. In accordance wih he ownership srucure of he economy, fuure profis are discouned a he relevan rae β R s λr 1+s of he paien household. λ1 R Taking ino accoun 10 and ha θ is assumed ime invarian, he corresponding aggregae price level is given by, P = [ ω P 1 π ς 1 θ ω P 1 θ] 1 θ 1 12 The compeiive wholesale secor The compeiive wholesale secor consiss of j = 1,...J firms, each selling a differen quaniy of a homogeneous good a he same price P w o he monopolisically compeiive inermediae secor. Firms in he perfecly compeiive wholesale secor carry ou he acual producion using labour and capial. Capial demand and vacancy posing are decided by solving he cos minimisaion problem faced by he represenaive compeiive producer, min E k,v =0 subjec o he producion funcion β R λr 1+1 r 1 k 1 + w n 1 l 1 + κ v v 13 λ R 1 and he law of moion for employmen y = Ak 1 α 1 n 1l 1 α 14 n = 1 σn 1 + ρ f v 15

12 12 From he firms poin of view, labour is homogeneous regardless of he ype of household ha provides i and ρ f is he probabiliy ha a vacancy will be filled in any given period. The probabiliy of filling a vacan pos ρ f is exogenous from he perspecive of he firm. However, as far as he overall economy is concerned, his probabiliy is endogenously deermined according o he following Cobb-Douglas maching funcion: ρ f v = χ 1 v χ 2 [1 n 1 l 2 ] 1 χ 2 16 The soluion o he opimisaion program above generaes he following firs-order condiions for privae capial and he number of vacancies r = 1 αmc +1 y +1 k 17 κ v ρ f = β l E λ l 1+1 λ l 1 V +1 n 18 Expression 18 reflecs ha firms choose he number of vacancies in such a way ha he marginal recruiing cos per vacancy, κ v, is equal o he expeced presen value of opening he vacancy β R λ1+1 E R ρ f V +1 λ1 R n, where V +1 n addiional job ha is defined as represens he nex period marginal value of an λ f V y = αmc w l n 1 n σβ l λ1+1 l E 1 λ1 l V f +1 n 19 where he marginal conribuion of a new job o profis equals he marginal produc ne of he wage rae, plus he capial value of he new job in, correced for he probabiliy ha he job will coninue in he fuure. 3.3 Trade in he labour marke: he labour conrac We assume, as in Boscá e al. 2011, ha alhough households ypes may differ in heir reservaion wages, hey delegae wage and hour bargaining o a rade union. This rade union maximises he aggregae marginal value of employmen for workers and disribues employmen according o heir shares in he working-age populaion. Thus, all workers receive he same wage, work he same number of hours and have he same unemploymen raes. Following sandard pracice, he Nash bargaining process maximises he weighed

13 13 produc of he paries surpluses from employmen. max w, l 1 λ w τ i λi h i I λ1 i λ f 1 λ w = max λ h λ w 1 λ w λ f w, l 1 20 where λ w [0, 1] reflecs workers bargaining power. The erm λ h represens he average worker s surplus, whereas he erm λ f is he firm s surplus. More specifically, λ i h /λi 1 denoe he earning premium in erms of consumpion of employmen over unemploymen for a ype-i household, respecively. Solving he Nash maximisaion problem we ge he opimal real wage and hours worked [ w l 1 = λ w mc α y ] κ v v + n 1 1 n 1 [ +1 λ w 1 l 2 1 η φ 2 1 η +1 λ w 1 σ ρ w τ i λĩh+1 E ĩ Ĩ λĩ1+1 1 l φ 1 1 η 1 1 η β R λr 1+1 λ R 1 i I τ i λ i 1 ] βĩ λĩ1+1 λĩ1 21 mc α y n 1 l 1 = φ 1 1 l 1 η i I τ i λ i Policy insrumens and resources consrain We assume he exisence of a cenral bank ha follows a Taylor s rule, 1 + r n = 1 + r 1 n rr 1 + π 1+r π ry 1 rr y 1 + r n 23 y where y and r n are seady-sae levels of oupu and ineres rae, respecively. The parameer r R capures he exen of ineres rae ineria, and r π and r y represen he weighs given o inflaion and oupu objecives. Revenues and expendiures are made consisen by means of he governmen ineremporal budge consrain: b p = g + rh rn π b p 1 24 In order o make he deb o GDP raio saionary, he following fiscal policy reacion funcion is imposed:

14 14 rh = rh 1 ψ 1 [ b gdp ] [ b b ψ gdp 2 gdp b 1 gdp 1 ] 25 where ψ 1 > 0 capures he speed of adjusmen from he curren raio owards he desired. The value of ψ 2 > 0 is chosen o ensure a smooh adjusmen of curren deb b gdp arge owards is seady-sae level. Finally, he aggregae resource consrain guaranees ha he sum of demand componens plus he cos of posing vacancies be equal o aggregae oupu, y = A k 1 α 1 n 1l 1 α = c + j 1 + φ j + g + κ v v 26 2 k Calibraion The calibraion sraegy for our benchmark model consiss in using sandard values in he lieraure for some parameers and maching some relevan daa momens for he US economy. In Table 1 we presen he values of hose parameers ha allow us o idenify he six differen ypes of households ha populae our benchmark economy. Thus, firs we define he shares of he households caegories in he oal populaion, assuming ha Ricardian households represen 50 percen of he populaion τ R = 0.5 and he oher five ype of individuals amoun each o 10 percen of i τ HNH = τ HH = τ BL = τ BH = τ EK = 0.1. The subjecive ineremporal discoun rae of paien households is β R = 0.99, while all oher five ypes are more impaien, presening a discoun facor of 0.95 see Iacoviello, All individuals ha own houses in our economy share he same preferences parameer on housing, φ i x = This value, as well as he he oal sock of housing, X, depend on he value we assign o he raio of asses of paien households b R o oal oupu y in he seady sae, ha we se following also Iacoviello 2005 such ha he oal sock of housing over yearly oupu is 140 percen. Finally, ϕ i is se o one for BL and BH households, indicaing ha hese individuals ake credi using housing as collaeral, and o zero for EK individuals, indicaing ha hey borrow agains heir fuure labour income. Loan-o-value raios are se o for BL households and for BH and EK individuals, values ha are slighly lower and higher han hose in Iacoviello and Neri The remaining se of parameers is shown in Table 2. We ake very sandard values for he Cobb-Douglas parameer α = 0.7 and he depreciaion rae of physical capial δ = The elasiciy of maching o vacan poss χ 2 = 0.5 comes from Monacelli e al 2010, whereas he exogenous ransiion rae from employmen o unemploymen,

15 15 Table 1. Parameerizaion of househols Type τ i β φ i x ϕ i m i R HNH HH BL BH EK σ = 0.15, is aken from Andolfao 1996 and Cheron and Lango These auhors also provide some average seady-sae values, such as he probabiliy of a vacan posiion becoming a producive job, which is assumed o be ρ f = 0.9, he fracion of ime spen working, l 1 = 1/3, and he fracion of ime households spend searching l 2 = 1/6. The long-run employmen raio is compued o be n = 0.75 as in Choi and Rios-Rull Furhermore, we assume ha equilibrium unemploymen is socially-efficien see Hosios, 1990 and, as such, λ w = 0.5 is equal o 1 χ 2. For he ineremporal labour elasiciy of subsiuion, we consider η = 2 implying ha average individual labour supply elasiciy η 1 1/l 1 1 is equal o 1, he same as in Andolfao The adjusmen coss parameer for producive invesmen φ = 5.5, is aken from QUEST II, which considers he same funcion as ours for capial insallaion coss. Parameers affecing he New Phillips Curve are also sandard in he lieraure. We se a value of θ = 6 for he elasiciy of final goods implying a seady sae markup of = 1.2. Hence, he seady sae value for he marginal cos is obained as mc = θ 1 θ. The probabiliy of no changing prices, ω, is se o 0.75, meaning ha prices change every four quarers on average, whereas we ake an inermediae value, ς = 0.4, for inflaion indexaion. Regarding Taylor s rule, he parameers r R = 0.73 and r π = 0.27 are aken from Iacoviello We choose a value of 0, for he parameer measuring he ineres rae reacion o oupu r y. θ θ 1 We normalise boh seady-sae oupu y and real housing prices q o one. Seadysae governmen expendiure g/y, is se o 17 per cen of oupu, maching US daa. We obain he long-run value for vacancies from 19 v = σn/ρ f. Then, we calibrae he raio of recruiing expendiures o oupu κ v v/y o represen 0.5 percenage poins of oupu, as in Cheron and Lango 2004 or Choi and Rios-Rull 2008, and very close o he value of 0.44 implied by he calibraion of Monacelli e al From his raio we obain a value of κ v = 0.04 and using he seady-sae version of he equaion 18, we can solve for he value of wages w. The seady-sae value of maching flows in he economy equals he flow of jobs ha are los σn and we use he equaliy σn = χ 1 v χ 2 [1 n l 2 ] 1 χ 2 o solve for he scale parameer of he maching funcion χ 1 = The long-run value of oal facor produciviy, A = 1.50, is calibraed from he

16 16 Table 2. Parameer values Preferences: Labour elasiciy, η 2 Leisure preference empl., φ Leisure preference unempl., φ Technology: Labour share in producion, α 0.7 Depreciaion rae of capial, δ Elasiciy of final goods, θ 6 Enry fixed cos, κ f Fricions: Probabiliy of no changing prices, ω 0.75 Invesmen adjusmen coss, φ 5.5 Inflaion indexaion, ς 0.4 Labour marke: Maching elasiciy, χ Transiion rae, σ 0.15 Workers bargaining power, λ w 0.5 Cos of vacancy posing, κ v 0.04 Scale parameer maching, χ Policy: Fiscal reacion parameer, ψ Fiscal reacion parameer, ψ Ineres rae smoohing, r R 0.73 Ineres rae reacion, r π 0.27 Ineres rae reacion, r y 0 producion funcion o obain he seady-sae value of Tobin s q raio, λ l 2 λ l 1. The reurn on capial r comes from he firs-order condiions and he seady-sae value for capial sock k from 17. Capial sock, ogeher wih he depreciaion rae and he adjusmen cos parameer, allows us o calculae he value of gross invesmen for he seady sae and, using he aggregae consrain, he level of consumpion c. The seady-sae value of he nominal ineres rae r n, is relaed o he ineremporal discoun rae of Ricardian households hrough he seady-sae version of he firs-order condiion for consumpion. The value for he lump-sum ransfers in he seady sae is such ha from he governmen budge consrain he resuling deb-o-oupu raio is 93 per cen on annual erms. In order o compue κ f, we use he following equaliy beween he source of income and aggregae spending where κ f = 1 τ b d R. c + j 1 + δ φ + g = nwl + rk + κ 2 f Seady-sae levels of he marginal uiliies of consumpion of he differen ypes of consumers, λ R 1, λ HNH 1, λ HH 1, λ BL 1, λ BH 1, and λ EK 1 come from heir respecive firs-order condiions. As regards leisure preference parameers in he household uiliy funcion, φ 1 = 1.59 is calculaed from he seady-sae version of expression 22. A sysem of seven equaions implying he seady sae of expressions 8 for he six caegories of individuals and 21 is solved for φ 2, λ R h, λ HNH h, λ HH h, λ BL h, λ BH h, and λ EK h. The resuling value for φ 2 is

17 Therefore he calibraed values for φ 1 and φ 2 imply ha he value aribued o leisure by an employed worker is well above ha aribued by an unemployed worker. 4. Simulaion resuls 4.1 The disribuion of ne wealh across households Table 3 presens seady sae levels of consumpion, labour income and ne wealh and is disribuion beween asses and liabiliies across all six household caegories in our economy. The model assumpions on he labour marke warran he same labour income across all household ypes second column of Table 3 so ha, as Table 3 shows, here is a very unequal seady sae disribuion of ne wealh bu a more egaliarian disribuion of consumpion. Ricardian consumers own he bulk of asses and mos ne wealh in he economy, wih a raio of ne worh over labour income close o sixy. This is no surprising, as in our model hese households are he only ones ha save, provide credi funds and own all producive capial. Bu ne wealh is also very differen among hose household ypes ha are subjec o some kind of borrowing consrain, depending on he composiion of heir balance shees. In paricular, and focusing on asses and liabiliies holdings, we cover a wide range of combinaions ha range from households wih asses and no liabiliies our R households or Ricardian consumers o he Eggerssson and Krugman households ype wih liabiliies and no asses our EK households, hrough consumers wih neiher asses nor liabiliies our HH or RoT households, or hose households ha hold asses and liabiliies in differen proporions depending on heir easiness of access o credi our BL and BH or he Iacoviello ype households. Also, alhough our HH consumers share wih Ricardians a posiive ne worh, given ha boh do no hold liabiliies, hey differ in heir inabiliy o smooh consumpion over ime, so ha hey exhaus all heir income every period. Thus, alhough he wealhy-hand-o-mouh individuals of Kaplan e al. 2014, hold presumably much more oal wealh han our HH households, he fac ha hey chose o save mos of ha wealh in highly illiquid asses, clearly differeniaes heir paern of consumpion wih respec o Ricardian consumers. Overall, he picure ha arises from Table 3 wih respec o he disribuion of ne worh and labour income, summarised in he las column of he able represening he raio of ne wealh over labour income, is in line wih empirical esimaes by Carroll e al These auhors use daa from he European Household Finance and Consumpion Survey o show subsanial heerogeneiy in wealh-o-permanen income raios, boh across and wihin counries. Regarding he seady sae levels of consumpion across

18 18 Table 3. Seady sae consumpion, labour income and ne wealh Cons Lab income Ne wealh Asses Liabiliies Raio /2 R HNH HH BL BH EK agens, presened in column 1 of he able, no surprisingly Ricardian consumers display he highes levels of per capia consumpion across households, since hey hold mos asses in he economy and have no liabiliies. Boh ypes of hand-o-mouh consumers are he ones who achieve he highes consumpion levels among he resriced household ypes in our seing. This is so, because in he seady sae hey consume all heir labour income and, given ha hey do no have liabiliies on heir balance shees, hey do no need o make any ineres rae paymens noice also ha in he seady sae here is no housing invesmen, so HH consumers do no spend on housing. Finally, among he household ypes ha paricipae in he credi marke per capia consumpion levels are inversely relaed wih he amoun of liabiliies hey hold. Thus, EK consumers consume more han borrowers wih a low capaciy o ge credi, and hese more han he ones wih easy access o loans. In he seady sae indebed households have o disribue heir incomes beween consumpion and deb ineres paymens. So, given equal labour incomes, heavily indebed households will reach lower consumpion levels. 4.2 Consumpion dynamics In his subsecion, we analyze he role played by household balance-shee heerogeneiy in shaping he shor-run response of consumpion o a ransiory governmen spending shock. Figure 1 shows he impulse response funcions of oupu and consumpion for he benchmark parameerizaion. Upon impac, he response of oupu o a 1% increase is governmen spending is larger han 1%. Therefore, he oupu muliplier is larger han 1. The governmen spending shock generaes a crowding-in effec in consumpion. This aggregae response of consumpion, however, hides a very heerogeneous reacion of consumpion and ne wealh for he differen households. The exreme cases are: i he consumpion by EK households increases by abou 4% upon impac and ii he consumpion by Ricardian households declines upon impac. Figure 2 shows he response of consumpion wih respec o is seady sae, labor income, and ne worh for each ype of household. Consumpion is a funcion

19 19 5 Consumpion 5 Ne Wealh Oupu and Consumpion BL BH RH RNH 0 1 C Y EK O 5 10 BL BH RH EK O Figure 1: Impulse-response o a 1 percen GDP increase in governmen spending relaive variaion of labour income and ne worh. As he movemen of labour income is he same all across households, he response of ne wealh becomes cenral o undersand differen consumpion mulipliers. Ricardian households are affeced by he deerioraion in heir ne worh caused by he fall of he price of real sae and producive capial. The fac ha deb conracs are se in nominal erms reinforces he negaive wealh effec as he real value of deb bî 1 1+π + dr 1 1+π is eroded as a consequence of he rise in curren inflaion π. Alhough labour income increases afer he shock, he fall in he value of he large amoun of wealh held by Ricardians consumers dominaes, causing a downward adjusmen in heir spending. Turning now o he oher households caegories, heir oal spending capaciy depends on curren labour income, ne wealh and he new credi flow. From 2, oal spending capaciy can be rewrien as: c i + q x i = b i }{{} new credi flow + q x i rn 1 bi π } {{ } ne financial wealh + w l 1 n 1 }{{} + + rh curren labour income 27 Ne wealh also falls for households BL and BH due basically o he downward movemen of he price of housing q, he only asse available for hem. However, his effec is parially compensaed by a deb deflaion induced by he rise in inflaion, which affecs negaively he erm bi 1 1+π. The effec on ne financial wealh is negaive bu less pronounced for

20 20 2 R 2 BL 2 BH Consumpion Income Ne Wealh Periods HH 2 HNH 2.5 EK Figure 2: Response of consumpion by household ype o a 1 percen GDP increase in governmen spending per capia absolue variaion lowly leveraged borrowers. Acually, alhough BL households are less leveraged han BH households b 1 BL < bbl 1, so ha he Fisher effec has less punch on real deb for hem, hey also demand less housing x 1 BL < xbh 1, implying ha he fall in q has a weaker effec on lowly indebed households. Considering jus he response of labour income and ne financial wealh, we would expec a more mued response of consumpion for BH han for BL households. However, Figure 2 shows he opposive. The explanaion for his resul relies in he new credi flow erm, b i, ha responds very differenly for indebed consumers. The fiscal shock increases he expeced value of he collaeral E q +1 x b and 1+r reduces he real ineres rae in, n 1+π e, which according o 4 faciliaes he access o +1 credi. This effec is sronger for BH household since hey have a higher loan-o-value raio m b. For EK households, he erm q x 1 i is absen from he spending resricion. Thus, hey do no suffer he drop in he value of asses, bu sill hey ake advanage of he erosion of heir real ousanding deb which makes ne wealh o jump iniially. Also, hey can easily call for more credi because he increase in he expeced omorrow s labour income. As a consequence, hese households are he ones wih a sronger response of consumpion on impac.

21 21 Households HH and HNH do no have access o credi, so hey canno accumulae deb so he erms b i and bi 1 1+π do no appear as consumpion drivers in he equaion above. A ypical hand-o-mouh consumer, as i has been considered in he lieraure, does no possess asses, so for HNH households erms q x HNH and q x 1 HNH disappear and consumpion replicaes he evoluion of curren income, which simulae a sizable response in he firs period. Wealhy hand-o-mouh households HH suffer he decline in he value of heir asses wih no compensaion by he oher side of heir balance shee and, hence, heir consumpion response is he lowes one among he financially consrained households. 4.3 Marginal propensiies o consume From expression 27, we can obain he differen sources for he marginal propensiy o consume ou of labour income MPC as, c i lab i = 1 + bi lab i + nwi lab i q x i lab i 28 where nw is he erm q x i rn 1 bi 1 1+π represening he financial ne wealh and lab i is he curren income. From expression 28, we conclude ha he change in consumpion in response o he change in curren income induced by he shock will be 1 for a household wih no access o fresh credi, no ne worh and no houses our HNH households. However, for he oher caegories of households he marginal propensiy o consume depends on he induced effec ha he change in labour income produces on new deb, ne wealh and housing invesmen. Table 4 quanifies he imporance of he sources behind he MPC for each ype of household. A firs conclusion from Table 4 is he large heerogeneiy across households in he consumpion expendiure response o he increase in labour income induced by he shock. We have ordered households according o heir iniial wealh, so ha comparing he firs and he las column we see a clear negaive relaionship beween he marginal propensiy o consume, ou of curren labour income, and he wealh of he household. Households wih less wealh respond more srongly o an increase in governmen spending induced income, a resul which is consisen wih some recen empirical linking wealh and consumpion Carroll e al., 2014; Kaplan e al., 2014; Angrisani e al, The cenral columns acually corroborae ha balance shees are pivoal in he disinc reacion of household consumpion, an idea ha has already been documened empirically by Parker e al, 2013; Agarwal and Qian, 2014; Acconcia e al., 2015; Sahm e al., 2015; Surico and Trezzi, 2015.

22 22 Table 4. Sources of he marginal propensiies o consume ou of curren income c i nw i lab i b i q lab i x i NW SS lab i lab i R HH BL BH HNH EK In our model, he negaive response of Ricardian households consumpion is mosly driven by he drop in ne worh, whereas he inense fall in housing invesmen prevens consumpion spending o go down by more. On he oher exreme he ne worh muliplier o labour income is no large for EK consumers, bu in his case is effec on consumpion is reinforced by he addiional credi ha he increase in expeced income makes available. Fresh credi is he main driver explaining he differences beween BL and BH consumers spending decisions. Also, a comparison beween he wo caegories of hand-o-mouh households RoTs, HNH, and wealhy hand-o-mouh, HH makes clear he wo channels pulling down he MPC of HH households: declining wealh and, more imporanly, diversion of spending owards addiional housing. 4.4 Fiscal mulipliers The disincive reacion of household consumpion induced by he governmen spending generaes a clear correlaion paern linking he composiion of he populaion and he aggregae oupu muliplier. In Table 5, we calculae he oupu and consumpion impac muliplier o a fiscal shock under differen scenarios regarding he disribuion of households among he six ypes considered. In he firs row we assume an economy populaed enirely by a represenaive Ricardian consumer. The governmen spending increase riggers he sandard crowding ou effec in consumpion and an oupu muliplier lower han one. In he following rows we keep he share of Ricardian in a 50 percen and disribue he remaining 50 percen equally among he differen ypes of non Ricardian consumers in a sequenial way. For example, he second row populaion is spli on equal proporions beween Ricardian and HH households, whils in he las row he differen class of non Ricardian households represen each a 10 percen of he oal populaion. The paricular sequence we have chosen for his exercise implies a coninuos change in he size of he muliplier as we are adding new households caegories o he economy. This exercise offers a rough indicaor of wha we miss in erms of he effec of fiscal policy by no providing enough deail on he households side. Overall, he oupu muliplier o a governmen spending shock augmens by more han 50 percen if we compare he resul

23 23 Table 5. Fiscal mulipliers y g c g R R+HH R+HH+BL R+HH+BL+BH R+HH+BL+BH+RNH R+HH+BL+BH+RNH+EK of a represenaive Ricardian household economy o ha from an economy wih a sensible disribuion of a wide variey of household caegories. 4.5 Wealh inequaliy and he fiscal muliplier We can also derive from our model some implicaions regarding he relaionship beween wealh inequaliy and he fiscal muliplier. This relaes o he work of Carroll e al who posulae a posiive associaion beween wealh inequaliy and he aggregae MPC. We explore his issue in Figure 3 ploing he impac oupu muliplier agains a Gini coefficien represening differen scenarios abou he disribuion of households caegories in oal populaion. In paricular, we sar by represening he Gini coefficien and he aggregae oupu muliplier corresponding o he benchmark calibraion he Bench poin in he figure and proceed as follows: we increase τ HH for HH households from 0.1 o 0.2 and reduce correspondingly τ R for he Ricardians from 0.5 o 0.4, and hen compue for his new disribuion he Gini coefficien and he oupu muliplier poin HH in he Figure 3. We repea he same exercise for he res of households in our model. The resuls esablish a clear associaion beween he oupu muliplier and wealh dispersion. Fiscal policy in a more unequal economy would display larger effecs in erms of oupu, as he posiive slope in regression line indicaes. This relaionship is no more han he reflecion of he heerogeneiy in he MPC ha we have explained in Table Welfare effecs The heerogeneiy in our model allows us o compare he effec of a governmen spending change on he consumpion response across households caegories. Bu households uiliy also depends on heir real sae holdings. To assess he disribuional consequences of he policy in a more global way we compue is effec on household s welfare. We define welfare V i as he discouned sum of a household i period uiliy, condiional on he economy being a he seady sae in period 0 common o all he experimens and