Does government spending composition matter for welfare? The case of Brazil

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1 Does governmen spending composiion maer for welfare? The case of Brazil Absrac: The aim of his work is o conribue o sudies abou welfare consequences of a given srucure of governmen expendiure by analysing he effecs of wo alernaive measures of public spendin income ransfers and invesmen in public capial, on household welfare. To his end, we use DSGE modeling. Our resuls show ha governmen spending biased owards public invesmen, coupled wih reduced curren public expendiure, is he opion yielding he greaes reurns o he economy as a whole. Even hough households are found o be worse off hroughou a ime span of 0 quarers, he larger oupu ha ensues from his policy measure will render fuure generaions beer off. Thus, if policymakers care equally abou all generaions, hey will elec o underake public invesmens, while if more weigh is aached o presen generaions han o fuure ones, hey will be more willing o embark on income ransfers. Celso José Cosa Junior Alejandro C. Garcia-Cinado 2 Armando Vaz Sampaio 3 São Paulo School of Economics - FGV/EESP and Pona Grossa Sae Universiy - UEPG, cjcosaj@yahoo.com.br 2 Pablo de Olavide Universiy, agcinado@upo.es 3 Federal Universiy of Paraná - UFPR, avsampaio@ufpr.br Keywords: DSGE Models, Welfare, Public Expendiure and Income ansfers. Código JEL: C63, E37, E62.

2 8 Does governmen spending composiion maer for welfare? The case of Brazil 4 Income ransfer programs are mean o raise he income of he poor unil some minimum accepable level is reached. 5 In Economics, invesmen refers o he use of capial in he producion process so as o increase producion capaciy. Public invesmen concerns he capial invesed by he public secor in order o improve people s qualiy of life. For example, invesmen in infrasrucure such as roads, bridges, hospials, pors, saniaion and schools, which gives rise o higher poenial growh and beer life perspecives overall, hinges almos exclusively on public invesmen. Oher uses include public invesmens in social, urban, ranspor and producive facors. 6 The esimaion of DSGE models poses some major challenges. Iniially, calibraing he parameers was common pracice. However, his approach is deemed o be inappropriae as he values obained hrough i are always condiional on a paricular model. In his regard, DSGE models esimaion via Bayesian mehodology has become he primary ool among macroeconomiss, for i is known o be powerful, coheren and sufficienly flexible, and i is he one we op for in his aricle. 7 Impulse response funcions race he effec of a one-ime shock o each of he endogenous variables. These responses are obained as follows: iniially, all variables mus be a heir seady-sae levels. A some ime = 0, an endogenous variable akes a value equal o is seady-sae level over an increase (impulse) in size equal o one sandard deviaion, and are calculaed as all variables evolve afer ha.. Inroducion Brazil has winessed six decades of unprecedened expansion of is public secor. Available daa indicae ha, beween 948 and 202, oal public expendiures rose from 7% of GDP o 40% (IMF, 203). Several sudies dealing wih he dynamic behavior of his variable have been conduced. Among hem, i is worh highlighing Wagner s conribuions (Bird, 970), and Peacock and Wiseman (970), who pu forward some hypoheses argeed a explaining he ime evoluion of he public secor. Boh aricles reveal he shorcomings ha a pure empirical sraegy for idenifying he drivers of he expansion of governmen expendiures would presen. I may be worhwhile o emphasize, however, ha he size of he governmen does no ighly associae iself wih he level of efficiency wih which his operaes. As a maer of fac, here are counries whose public secors accoun for more han 50% of GDP (generally viewed as big governmens) and ye, hey rank prey high on he liss measuring he mos efficien saes around he world. Examples of his are he Scandinavian counries. By he same oken, counries wih low governmen spending o GDP raios, such as many in Lain America or Africa, are ofen cied as hose wih more scleroic and inefficien public secors. So, he main lesson o be learned from his circumsance can reduce o i is no really abou how much he governmen can and does acually spend as a proporion of GDP, bu abou how i does ha and wha sor of expendiure i prioriizes over he alernaives. Tha is o say, irrespecive of how much he public secor may have grown over ime, he key policy variable ha may be decisive in providing informaion abou he effec of he size of he public secor on welfare is he composiion of governmen spendin so paricular aenion should be devoed o i. However, i is worh poining ou ha in an ineremporal framework assessing consumer welfare in a pos-shock siuaion is a ad more inricae ha i may seem. In effec, increases in curren governmen spending are hough o lead o lower economic growh over ime (and evenually o lower welfare) han say a higher invesmen in public infrasrucure, which are known o have a posiive impac on oal facor produciviy. Bu in he shor run he former fiscal policy is assumed o have a greaer impac on consumer welfare han he laer. Neverheless, as any oher economic agen, he governmen is also subjec o a (boh inra- and iner-emporal) budge consrain, implying ha here clearly is an opporuniy cos in erms of he expendiure iem foregone every ime he policymaker makes a decision as o which spending iem, and by how much, should be increased. In his regard, i is consanly faced wih he rade-off arising from he desirabiliy of choosing one ype of public expense over he remaining ones, which ineviably leaves some groups of people unsaisfied. Alhough his lieraure for Brazil comprises a myriad of sudies on how ax changes affec welfare over ime (Paes and Bugarin, 2006; Mussolini and Kanczuk, 20; Cavalcani and Silva, 200), here sill is a gap concerning he welfare effecs of variaions in he composiion of governmen expendiures. Wih he purpose of helping fill his void, his work aims o assess he effec of wo kinds of governmen expendiures on he main macroeconomic variables. For ha maer, wo governmen spending shocks embedded in a DSGE model are considered. The firs shock akes he form of governmen ransfers of income o households 4. The second one involves he governmen increasing public invesmens 5. The model parameers will be calibraed and esimaed using Bayesian approach 6 and he focus will be placed on he analysis of he impulse-response funcions 7. These wo differen spending iems have no been chosen in a vacuum, and hus he raionale for using hem in our paper is ha governmen ransfers are he ools

3 Celso José Cosa Junior; Alejandro C. Garcia-Cinado; Armando Vaz Sampaio 9 on which he Brazilian fiscal auhoriies have relied on a permanen basis for reducing income inequaliy and povery, which have long plagued he counry. The leading ransfer program in Brazil is he famous Bolsa-família 8, which sands ou in lifing people ou of povery a a relaively low cos. In addiion o his, here are several oher ransfer programs whose records in erms of efficiency leave a lo o be desired and are casually considered poenial sources of wase and corrupion (for example, many of he subsidies ha he Brazilian Developmen Bank, BNDES 9, disburses o some secors of he economy are said o fall ino his caegory 0 ). On he oher hand, owing o he piiable sae in which public infrasrucure, such as roads, highways, bridges, pors, ec. are in he counry, public invesmen is ofen brough up in casual conversaions as an inegral par of more comprehensive package aimed a puing he Brazilian economy back on he growh rack, as well as i is also called for by prominen economiss and analyss alike as one of he main levers policymakers should fall back on in order o accomplish he aforemenioned goal. No only is his measure aken o be a sabilizaion policy, since i succeeds in simulaing he economy in he shor run, bu i is also a growh policy in ha i raises produciviy and herefore long-run growh. I should be menioned ha here exiss an aricle akin o ours where he auhors, by means of a DSGE model applied o Euro-Area counries, aemp o accoun for he welfare behavior of reallocaions of expendiures beween differen public spending iems (Sraub and Tchakarov, 2007). The lieraure disinguishes wo differen avenues hrough which public expendiures can be inroduced ino DSGE models. On one hand, governmen expendiures can be hough of as a componen of aggregae spendin which enails ha households uiliy will no be affeced by hem. This is he approach chosen for example by Chrisiano and Eichenbaum (992) and Ljungqvis and Sargen (2004), o menion jus a few. Among he Brazilian auhors who op for his sraegy, we should sress Casro e al. (20), Gadelha and Divino (203a), and Gadelha and Divino (203b). I is worh pausing a bi here o briefly commen on hese hree laer aricles since he Brazilian economy consiues he focus of our work. The firs aricle covers in deail a medium-sized DSGE model named SAMBA developed by economiss from he Cenral Bank of Brazil. I is a small open economy model combining sandard feaures - price and wage sickiness, adjusmen coss, habi formaion, Ricardian and Non-Ricardian consumers -- wih more specific characerisics of he Brazilian economy - counry-specific fiscal rule, adminisered prices, ec. The auhors find ha he impulse-responses o sandard shocks are well-behaved and fall wihin he range i would be expeced for his economy. By allowing for disorionary axes and pro-cyclical fiscal policy rules, he aricles by Gadelha and Divino seek o improve over he model by Galí, López-Salido and Vallés (2007) in order o see wheher he "governmen spending puzzle" holds in he Brazilian economy. They find no evidence of i whasoever. Ineresingly, hey also uncover a negaive relaionship beween hours worked and a posiive produciviy shock, as well as a well-defined pro-cyclical behavior of fiscal revenues and spending. On he oher hand, assuming ha governmen spending is neural o individuals uiliy does no appear o be he mos suiable conjecure. An alernaive roue is o hink of public expendiures as goods consumed by privae agens, herefore enering households uiliy funcion. Our work pursues his laer approach by employing he funcional form used by Mussolini and Kanczuk (20), Barro (98), Aschauer (985) and Aiyagari e al. (992), whereby household s aggregae consumpion is a linear combinaion of privae consumpion and governmen consumpion 2. Despie his governmen s crucial role in carrying ou invesmen in infrasrucure o suppor he privae secor, here are few references abou his opic. 8 Bolsa-família, or in English, Family Allowance, is a ransfer program of he Brazilian governmen, seeking o provide financial aid o povery-sricken Brazilian families condiional on having heir children aend school and vaccinaed. Is primary goals are o boh reduce povery and raise human capial. 9 From is sie: The Brazilian Developmen Bank (BNDES) is he main financing agen for developmen in Brazil. The Bank offers several financial suppor mechanisms o Brazilian companies of all sizes as well as public adminisraion eniies, enabling invesmens in all economic secors. In any suppored underakin from he analysis phase up o he moniorin he BNDES emphasizes hree facors i considers sraegic: innovaion, local developmen and socio-environmenal developmen. 0 I is dubbed Bolsa-empresário. The governmen spending puzzle refers o he posiive response of privae consumpion o a posiive shock o governmen spending. According o RBC posulaes, he opposie effec should prevail. 2 I should be acknowledged ha no all economiss agree on his assumpion as being compleely reasonable. However, i does no seem odd a all o asser ha beer public services -enhanced public safey, saniaion, ransi, ec.- lead o more saisfied people, increasing heir level of uiliy.

4 0 Does governmen spending composiion maer for welfare? The case of Brazil During he 970s, several heoreical sudies incorporaed public capial ino he aggregae producion funcion, some examples being hose by Arrow and Kurz (970), Weizman (970) and Pesieau (974). This nowihsandin i was no unil afer Barro (990) ha hese iniial ideas were recovered. Over he following years, a number of aricles in he same spiri as he former such as Barro and Sala-i-Marin (992), Finn (993), Glomm and Ravikumar (994), Cashin (995) and Bajo (2000), among ohers, followed sui. As for empirical sudies ha deploy his same approach, one can highligh Mera (973), Raner (983) and Aschauer (989). The resuls we obain in his aricle are he following: he shock o public invesmen booss economic growh and hus fuure consumer welfare, a he expense of presen welfare. On he conrary, he income-ransfer shock increases welfare on impac, bu has a negaive effec on growh, hereby leading o lower fuure welfare. When a policy consising of higher public invesmen combined wih decreased curren governmen spending is carried ou, ineremporal welfare is maximized. In addiion o his inroducion, his work is srucured as follows. The nex secion describes he DSGE model, he subsequen one conducs he empirical analysis, and he wo final secions presen he resuls and conclude, respecively. 2. Model The model consiss of an economy inhabied by hree sors of economic agens. The firs one is he represenaive household who chooses he value of is ineremporal consumpion and he amoun of labor i is willing o offer. I also owns he capial sock which firms ren o use i in heir producion processes. The represenaive household's sources of income are wages and reurns on capial in exchange for labor services and rening services, respecively. The second agen is he represenaive firm ha combines capial and labor o produce oupu and sell i on he marke. An imporan feaure of our model is he environmen in which he represenaive firm operaes. The marke srucure is assumed o be monopolisic compeiion, ha is, he firm enjoys marke power in ha i is able o se he price over he marginal cos and make an exraordinary profi (mark-up). The hird agen is he Governmen which finances is aggregae spending hrough ax collecion, and whose decision over he kind of expendiure i leans oward deermines he final composiion of is spending. Specifically, he laer can be grouped ino hree differen caegories: curren public spendin income ransfers, and public invesmen. Finally, wo addiional feaures of he model bear menioning: he economy is closed, and here is no financial sysem. 3 We have oped o leave fricions, such as price and wage rigidiies, consumpion habis, adjusmen coss, and financial fricions, ou of our model. These absences do no affec he resuls. However, monopolisic compeiion consiues a crucial elemen in our aricle as one of our primary arges is o look ino he behavior of Brazilian firms mark-ups in he face of a change in he public spending composiion. 4 The Brazilian economy can be regarded as a relaively closed one, so i is safe o say ha his srong assumpion is applicable in our work. 5 The oal available ime is spli ino hours of leisure and of work (Leisure + Work = ), so he decision abou how many hours are devoed o leisure amouns o choosing how much ime o work. 2. Households There is a coninuum of infiniively-lived idenical households ha maximize heir uiliy semming from consumpion and leisure 5. In paricular, he sand-in consumer's lifeime uiliy is represened by: E = 0 β ( C + ηg ) σ σ + L + where E is he expecaions operaor, β is he discoun facor, C is consumpion, L is he number of hours worked, G is he curren governmen expendiure, η Gis he sensiiviy of he uiliy o curren governmen expendiure, σ and are he parameers ha measure he elasiciy of marginal uiliy of consumpion wih respec o is level and he marginal disuiliy of work relaive o he labor supply, respecively. ()

5 Celso José Cosa Junior; Alejandro C. Garcia-Cinado; Armando Vaz Sampaio In addiion, he represenaive consumer faces he following budge consrain in every period: α+ α 2 + α3 = α 2 = 0.6 α3 = 0.4 α (, )( τ ) ( τ ), ( τ ) C + I + P = W L + R K + rans p c l p k where + I p, denoes privae invesmen, W is he wage, R is he reurn on capial, K p, is he sock of privae capial, rans is he income ransfers o households by governmen, + τ c ), τ l ), τ k are ax raes on consumpion, on labor income and on capial income, respecively, and P refers o he price level ha is normalized o one, P=. (2) Privae capial accumulaes according o he following rule: ( δ ) K = p, p K + + p, I (3) p, where is he depreciaion rae of privae capial. The consumer hen maximizes () subjec o (2) which yields he following firs order condiions: σ τ l ( C + ηg ) L = W (4) + τ c 2.2 Firms β σ C + ηg τ ( δ ) + + k = E p + R + C + ηg + τ c As menioned above, firms behave in a monopolisically compeiive fashion. The economy's producive secor is divided ino wo pars: an inermediae-good secor, and a final-good secor. The inermediae-good secor is composed of a large number of firms, each producing slighly differeniaed goods, and deciding he quaniy of producive facors o be hired and he price hey are willing o charge. This seup relies on he works by Cassou and Lansing (998), Lansing (998), Baxer and King (993) and Ambler and Paque (996), where he public capial sock is insered ino he producion funcion. In he final-good secor, here exiss one company in charge of aggregaing he inermediae goods ino a single good ha will be consumed by economic agens. Thus, he producion funcion is depiced by he following expression: α α 2 α 3 Y = A K p, L K (6) where K g is he sock of public capial, α, α 2 +, α 3 are paricipaions of capial, of labor and of public capial in he producion of good j, respecively 6. Toal facor produciviy, A 7, follows a sochasic log-linear AR () described below: log A = ρ log A + ε (7) where ε ~ ( 0, σ ε ). (5) The sock of public capial obeys he law of moion: ( δ ) where depreciaion rae of public capial. K = g K + + I (8) I is he governmen's invesmen in public capial asses, and is he The demand for inpus funcions are direcly derived from he firms' profimaximizing behavior: φ α 2 Y L = (9) φ α+ α 2 W δ g 6 Firms are subjec o consan reurns o scale, α+ α 2 + α3 =, based on Cassou and Lansing (998), corroboraed by empirical sudies by Aschauer (989) and Ai and Cassou (995). 7 The resuls ensuing from he produciviy shock will no be presened here, because our goal is o focus only on shocks o governmen expendiures.

6 2 Does governmen spending composiion maer for welfare? The case of Brazil φ α Y K = φ α+ α 2 K (0) where φ is he elasiciy of subsiuion among differeniaed goods. 2.3 Governmen The governmen eners he picure by spending on curren expendiure iems (G), by giving ransfers of income (rans), by underaking public invesmens ( I ) and by collecing axes. Income ransfer paymens follow a sochasic process described below: wih, rans = χ S Y () log S = ρ log S + ε (2), where S is sochasic and χ is a saic parameer ha accouns for income ransfers as a share of GDP and. ( ) ε ~ 0, σ ε By he same oken, he governmen invesmen follows, wherein, I = χ S Y (3) Ig Ig log S ( ) ε ~ 0, σ ε, where, S is sochasic and he share of public invesmen in GDP. Ig Ig = ρ log S + ε (4) χ Ig is he saic parameer capuring In all periods, by assumpion, he governmen mus abide by is budge consrain. Thus: ( ) τ τ τ ( δ ) C + I P + W L + K R = G P + rans + I P (5) p, c l p, k p Lasly, he aggregae equilibrium condiion (aggregae demand = aggregae supply) mus be me: Y = C + G + I + I (6) p, 8 X2-ARIMA was developed by US Census Bureau as an exended and improved version of he X- ARIMA mehod of Saisics Canada. The program runs hrough he following seps. Firs he series is modified by any user-defined prior adjusmens. Then he program fis a regarima model o he series in order o deec and adjus for ouliers and oher disoring effecs for improving forecass and seasonal adjusmen. The program hen uses a series of moving averages o decompose a ime series ino hree componens. In he las sep a wider range of diagnosic saisics are produced, describing he final seasonal adjusmen, and giving poiners o possible improvemens which could be made. 9 firs log-difference X ( X ) = ln X 3. Empirical Analysis In his secion we proceed o presen he empirical par of our sudy. I begins by describing he daa used in he esimaion of he sandard deviaion parameers included in he sochasic shocks. I nex shows he calibraed parameers, priori and poseriori of he parameers o Bayesian esimaion. 3. Daa We esimaed he model using quarerly daa spanning from 2003Q o 203Q4 (44 daa poins). We use 3 model variables as observables: GDP (Y); governmen consumpion (G); and governmen revenues on consumpion (( C + I p ) τ cp ). To prepare he daa for he model esimaion, we deflaed using he IPCA, derened and seasonally adjused non saionary series using he sofware X2-ARIMA 8 and applied firs log-difference Calibraed Parameers, Priori and Poseriori Disribuions We resor o calibraing he parameers which are no direcly relaed o he shocks,

7 Celso José Cosa Junior; Alejandro C. Garcia-Cinado; Armando Vaz Sampaio 3 whereas hose relevan ones for he analysis of he shocks propagaion are esimaed via Bayesian mehodology. Wih regard o hese Bayesian esimaions, he prior disribuion reflecs he beliefs abou he values of he parameers. A large sandard deviaion of hese values implies lile confidence in he priori value used. In order o conduc a proper esimaion of he disribuion parameers, we avail ourselves of he mean and sandard deviaion values in common use in he Brazilian economic lieraure. The daa regarding he facor shares corresponding o boh capial and labor 20, he value of ρ, and he sensiiviy of preferences relaive o public expendiure ( η) Gwere aken from Mussolini (20), on he grounds of he close similariies his abovemenioned work and ours exhibi. Privae and public depreciaion values ( δ p and δ g ), respecively), he ineremporal discoun rae ( β ), he parameers measuring he elasiciy of marginal uiliy of consumpion wih respec o is level and he marginal disuiliy of labor relaive o he amoun of working hours supplied ( σ and ) were obained from Cavalcani and Vereda (20). In his aricle hese auhors ake a in-deph look a he dynamic properies of a DSGE model for Brazil, so hese priori values can herefore be considered o have esed reliabiliy. Similarly, we ake he saic parameer ha accouns for public invesmen as a share of GDP ( χ Ig ) from Resende (200) as he describes in deail he composiion of he Brazilian public expendiures a he end of he 990s. According o his auhor, he average shares of governmen expendiure (in percenage erms) hroughou he period were: social securiy, 53%; public goods, 8,%; educaion spendin 7,3%; and public infrasrucure, 2,3%. So making use of a sensiiviy parameer of around 2,3% of GDP in our sudy seems o be warraned. Finally, our sudy ress on Araújo and Ferreira (999) as regards ax raes on consumpion + ( τ c ), on labor income ( τ l ) and on capial income ( τ k ). Concerning he elasiciy of subsiuion beween he differeniaed goods (φ ), we use he same figure as in Araújo e al. (2006). Hence, Table shows he calibraed parameers of he model. We employ he series Benefícios Assisenciais (LOAS e RMV 2 ) and Cuseio e Invesimeno so as o calculae he parameer values of χ rans using he relaionship = 0.007, respecively. Table 2 shows he poserior disribuions. Y Table. Calibraed parameers and prior disribuion of he model Parameer Average Source α 0.32 Mussolini (20) β Cavalcani and Vereda (20) σ 2 Cavalcani and Vereda (20).5 Cavalcani and Vereda (20) δ g Cavalcani and Vereda (20) δ p Cavalcani and Vereda (20) τ l Araújo and Ferreira (999) ϕ 6 Araújo e al (2006) Source: Prepared by he auhors. E E β = 0 = 0 σ ( C ( C+ η+ Gη G) ) β σ + + L L σ σ α+ αα + 2α + 2α + 3α = 3 = α 2α = 20.6 = 0.6, so α3α = 30.4 = 0.4 α α ( ( )( )( ) ) ( ( ) ) ( ( ) ) 2 C C + I+ I p, p, + τ + τ c PThe c = P W= erms W L L LOAS τ τ l + and l R+ K RMV K p, sand p, τ for τ k + rans Lei k + rans Orgánica de Assisência Social (Organic Law of Social Assisance in English) K K = p, + ( =, ( δ p p ) δkp ) Kand + p, I Renda + p, I Mensal Vialícia (Monhly + p, p, Annuiy in English), respecively. σ σ C σ τ + ηg σ + τ C + + ηg + l l = = β Eβ E ( C( C + ηg ) ) L R. Bras. = W ( δ + ηg L = Eco. de W ( Emp. + τ 206; 6(2): 7-24 C + ηg + c τ C + ηg c α α α 2 α 2α 3 α 3 Y Y= A= KA KL p, LK K p,

8 ,,,, 4 Does governmen spending composiion maer for welfare? The case of Brazil Table 2. Poserior disribuion of he model. Parameer Average Confidence Inerval τ c τ k χ Ig χ η ρ ρ Ig ρ ε A ε Ig ε ( ) σ + C + ηg L E β Source: Prepared by he auhors. ( ) σ + C + ηg L = 0 E σ + β = 0 σ + α+ α 2 + α3 = α 2 = 0.6 α3 = 0.4 α α + α 2 + α 3 α 2 = 0.6 α3 = 0.4 α ( C 4. Resuls + I p, )( + τ c ) P = W L ( τ l ) + R K p, ( τ k ) + rans ( C + I p, )( + τ c ) P = W L ( τ l ) + R K p, ( τ k ) + rans K =, ( p δ p ) K 22 Compensaing ( + + p, I p, K =, p Variaion δ p ) K + + p, I p, is he amoun σ of consumpion σ τ C + + ηg + k l o be delivered = β E σ ( C or + ηg ) L = W + + η wihdrawn from consumers C σ τ + + p + ηg + k l ( C = β under + + ηg ) + τ = β E p + L = c C + ηg + W c he new rules o mainain + τ he + η same C + ηg + + α α 2 α 3 c c Y = A K p, L K level of uiliy αhey α 2 α 3 Y = A K enjoyed previously., L K, Thus, he variaion p g log A of consumpion = ρ log A + ε is measured log A as log he value CV solving = ρ A + ε for he ε ~ ( 0, following σ ε ) equaion which represens ε ~ ( 0, he σ ε ) K insananeous uiliy funcion =, ( Kof g δ g ) K = he ( agen: + + I ) 4. Welfare Analysis + δ g K + I φ α 2 Y L = U ( C*, G*, L* ) U φ ( C α 2 φ shocks, G Y shocks L, Lshocks, VC ) = α+ α 2 W φ α+ α 2 W φ α Y K σ = ( ) ( ) σ + φ + C VC C * + ηg φ * L + α Y * shocks, + K ηgshocks, L = α+ α 2 K g shocks, = φ α+ α 2 K g σ rans = + χ S Y σ + rans = χs Y Variables log S = ρ log wih S + ε, subscrip * are measured log S a = ρ seady log S + ε, ε sae, while he ~ ( 0, σ ε ) variables ε wih ~ subscrip (shocks) are ( 0, σ ε ) Ig evaluaed I afer occurrence of shocks g = χigs Y Ig (Ferreira Iand Araujo, 999). g = χigs Y ε Ig ~ ( 0, σ ε Ig ) 23 I considers ε Ig ~ ( 0, a σ ε Ig measure ) ha would be ideal ( C + I p, for ) τ cp + W Lτ l + K p, τ k welfare changes. ( R δ p ) = G P + rans + I P So i would like o have ( C + I p, a ) τ cp + W Lτ l + K p, τ k measure of ( R δ p he ) = G P + rans + I P change in Y = C + G + I uiliy resuling, + I g p by, any policy. Suppose Y = C + G + I here are wo X endowmen g, + I p, U ( C*, G*, L * ) and ( X ) = ln U ( Cshocks, Gshocks, Lshocks, VC X). I is convenien o hink ( X X ) = ln of U ( C*, G*, L * ) as Xhe rans value a seady sae and U ( C= shocks, Gshocks, Lshocks, VC ) rans as an amendmen. Y Then, he obvious = measure of change Y of Uwelfare ( C*, G*, L* ) = Uinvolved ( Cshocks, Gshocks, Lshocks in, VChe ) passage U ( C*, G*, LU )( C*, Go *, L* ) = U ( Cshocks, Gshocks, Lshocks, VC ( C ) is only *, G*, L * ) ( Cshocks, Gshocks, Lshocks ) he difference ( C*, G*, L * ) ( Cshocks, in G indirec shocks, Lshocks ) uiliy: σ + σ ( Cshocks, + ηg + shocks, ) L ( ) shocks σ, C* + ηg* L * Welfare = + σ ( Cshocks, + ηg + shocks, ) L shocks, ( C* + ηg* ) L * Welfare = σ + σ + σ + σ + If his difference in uiliy is posiive (negaive), hen he policy change increases (decreases) he welfare of households (Varian, 992). 24 Composiion of household consumpion (C), and governmen consumpion (G), hereinafer he composiion of spending. This secion examines he welfare consequences of he model. I seeks o answer some quesions such as: how do variables behave in response o shocks? Does he τ ( σδ represenaive ) R τ + τ τ household gain or lose in erms of welfare afer a given shock? Is he δ ( δ ) + R + τ τ model sable in he sense ha he endogenous variables end up reurning o heir seady saes? If so, do hese variables compleely adjus wihin a reasonable ime span? Alhough he main objecive of he presen work is o idenify he effecs of (by heir very naure permanen) changes in he composiion of governmen expendiures on welfare, we only deal wih emporary shocks. Neverheless, i is our view ha he response of he macroeconomic variables o such shocks provides an inuiive way o gauge welfare variaions. These changes in welfare come abou hrough boh he ineremporal - i.e., how consumpion evolves over ime as a resul of sochasic shocksand he inraemporal channels - i.e., how demand for leisure reacs o such shocks. In order o measure hese changes, wo differen mehodologies are uilized. The firs one, due o Ferreira and Araujo (999), draws upon he concep of compensaing variaion of consumpion (VC) 22 ; and he second one consiss of he difference beween he uiliy funcion of households afer each shock and he uiliy funcion of households a seady sae ( Welfare ) 23. In regards o he shock o public invesmen (Figure.a), he fall in curren spending (Figure.b) helps he represenaive agen balance is budge (Equaion 8). Since a rise in public invesmen mus be accommodaed by cuing anoher spending iem, i is noiceable ha even wih an increase in privae consumpion (Figure.c), oal consumpion (sum of privae and public consumpion) 24 goes down (Figure.d). The decreasing levels of he laer variable and leisure boh drag down welfare levels (Figure.e). Oupu rises, however (Figure.f), hereby allowing for a greaer fuure welfare. On he oher hand, he shock o income ransfers (Figure.g) leads o higher oal consumpion (Figure.d), even hough governmen expendiure falls (Figure.b). Addiionally, i is worh menioning ha, as a resul of his shock, households supply less labor (more leisure) (Figure.h), which makes hem beer off a presen (Figure.e), bu

9 Celso José Cosa Junior; Alejandro C. Garcia-Cinado; Armando Vaz Sampaio 5 worse off in he fuure via a lower oupu (Figure.f). The resuls also show ha, as far as he public invesmen shock is concerned, he compensaing variaion is posiive (Figure.i), because he lower curren expendiure (Figure.b) should be offse by a greaer value of privae consumpion (see equaion in foonoe 5). In his respec, households would find his fiscal policy undesirable, hus advocaing agains is implemenaion. Regarding he shock on income ransfers, i becomes clear ha he compensaing variaion is negaive (Figure.i). This ransfer policy is welfare-improving as boh consumpion and leisure are greaer afer he shock (Figure.e), and hence, i would be advocaed for by households. In summary, he fall in consumer welfare riggered by he public invesmen shock is compensaed for by an increase in oupu, whereas he welfare gain resuling from he shock o income ransfers reduces oupu. In he firs case, consumers would engage in ineremporal consumpion subsiuion, giving rise o a replacemen of presen welfare for fuure welfare as hey ake advanage of he higher oupu growh. In he second case, households would be beer off by consuming more a presen, even if his preference for oday's consumpion harms economic growh. The decision o work is anamoun o deciding how o spend ime. An opional use of he available ime is o spend i on enjoyable leisure aciviies. The alernaive o i is o work. Hence, one can characerize he decision wheher or no o work as a choice beween leisure and work 25. I follows hen ha shocks on oal consumpion will exer an influence over he supply of labor in he wake of a change in household income. On impac, he public invesmen shock lowers welfare by squeezing oal consumpion (Figure.d). In he ransiion of hese variables owards heir seady saes, o raise privae consumpion and make up for he decline in governmen consumpion, households supply more labor. This excess of labor depresses he wage level. Correspondingly, workers are less willing o work han before he shock, which pushes wages back up. This process whereby wages increase as labor supply decreases is referred o as income effec (IR). 25 Leisure can be hough of as an asse, which would be a funcion of he opporuniy cos, level of funds available, and preferences. Thus, he firs quesion ha arises is: Wha is he opporuniy cos of leisure? The cos of spending hours waching elevision is basically he amoun of money ha he person would receive if i was working. Accordingly, he opporuniy cos of an hour of leisure amouns o he wage paid for a working hour. Funds availabiliy is hen a crucial variable o be aken ino accoun when i comes o he analysis of leisure, and i associaes iself o he variable family income. Preferences deermine he degree a which households will demand more or less leisure, given a change in income or wage (Ehrenberg and Smih, 2000).

10 6 Does governmen spending composiion maer for welfare? The case of Brazil Figure - Welfare analysis: Impulse-Response Funcions are comprised of black curves represening he shock o public invesmen, and of blue curves which represen he shock o income ransfer. Source: Prepared by he auhors. As for he ransfer shock, a higher income promps households o consume more (Figure.c), wih his consumpion level exceeding is seady sae. As a consequence, hey seek o improve heir welfare by demanding more leisure. This is also known as an income effec (Figure.h). These wo effecs are similar, bu differ from he source from which hey arose. The firs one comes from an increased level of wages, while he second one is caused by he shock o income ransfers. Sill on he analysis of households' preferences over changes in wages and income, i proves helpful o use he locus wage-leisure o find ou he poins of occurrence of income and subsiuion effecs. Figure 2 presens he locus wage-leisure for boh shocks. The wo curves are divided ino secions of predominance of income and subsiuion effecs. Poins A and B are he urning poins beween hese effecs. From he far righ on he graphs unil poins A and B, here are sreches wih predominance of subsiuion effec; from hese urning poins up o he far lef, he income effec prevails. Iniially, boh curves behave in he same way: if households are iniially allocaed more leisure,

11 Celso José Cosa Junior; Alejandro C. Garcia-Cinado; Armando Vaz Sampaio 7 increasing wages lead o higher demand for labor (subsiuion effecs). By conras, if households receive less leisure in heir allocaion, so hey have lile, wages and demand for labor will be inversely relaed (income effec). Neverheless, when households are hi by an income ransfer shock, heir demand for labor becomes less sensiive o he increased level of wages. This is due o he fac ha income ransfers bring forh he desired level of consumpion. For his reason, hose wages corresponding o he inflecion poins are around wice as large concerning he shock o income ransfers as hose associaed wih he shock o public invesmen. Figure 2 - Locus wage-leisure. Source: Prepared by he auhors. 5. Conclusions In his sudy we address he effecs of wo alernaives sors of governmen expendiures on he main macroeconomic variables. To his end, wo differen governmen spending shocks in a DSGE model are considered. The firs shock can be hough of as he governmen providing households wih income ransfers. The second one ranslaes ino public invesmen projecs being carried ou. The public invesmen shock curails welfare on impac, bu i also propels oupu growh (and an increased oupu), hus enabling greaer welfare in subsequen periods. By conras, he shock o income ransfers pushes welfare up, bu also causes oupu o decline, which hurs fuure welfare. So if he policymaker chose o encourage public capial accumulaion, i would be faced wih an inergeneraional disribuion of welfare owards he fuure generaions, who would benefi from his new governmen expendiure composiion, and agains he curren generaions, who could consume less. This would be he case of a policymaker placing he same weigh across all generaions. On he conrary, a policymaker who would care more abou curren generaions han fuure ones would find herself deciding o spend more on curren spending han on invesmen projecs. So, as laid ou above, a composiion of governmen expendiures biased owards public invesmen and agains curren expendiure yields greaer reurns o he economy overall. Even hough welfare drops for some ime (en years) unil i

12 8 Does governmen spending composiion maer for welfare? The case of Brazil reaches is iniial seady sae again, fuure generaions will benefi from a larger oupu as far as welfare is concerned. Assuming ha Brazil may be caegorized as an "impaien" sociey, whose represenaive ciizen's discoun rae would supposedly be relaively high by inernaional sandards, individuals would suppor poliical paries which would favor "big governmens" (abundan income ransfers) where here could be lile room for public invesmen in infrasrucure. Welfare would no hen be maximized from an ineremporal poin of view. Those poliicians who would aemp o reverse his everincreasing rend in curren governmen spending would be penalized a he polls, so hese large governmens would somehow perpeuae hemselves. By conras, a benevolen social planner wih a lower discoun rae han he represenaive household would be expeced o pursue a more "opimal" fiscal policy as far as welfare is concerned. I would give prioriy o growh-enhancing invesmens over income ransfers. A he curren conjuncure, Brazil finds iself in a profound fiscal crisis and he new governmen repeaedly announces ha curren public spending growh mus be reduced and mus mach up ha of fiscal revenues as a way o slash public deb and rever is perverse dynamics. A he same ime, hey sress he imporance for public invesmens o be a he cener of heir long-run growh sraegy, alhough a he momen he lousy fiscal siuaion makes i impossible for hese invesmens o be underaken. I is fair o say ha his new fiscal policy mix is proving more difficul o come ino force han expeced. A suggesion for fuure work could be o embed he financial secor ino he model and relax he assumpion of a governmen balanced budge. This would allow one o handle he composiion of he financing sources and deb from an ineremporal perspecive. References AI, Chunrong; and CASSOU, Seven P. A Normaive Analysis of Public Capial. Applied Economics, v. 27, n. 2, p , July AIYAGARI, S. Rao; CHRISTIANO, Lawrence J.; EICHENBAUM, Marin. The Oupu, Employmen, and Ineres Rae Effecs of Governmen Consumpion. Journal of Moneary Economics, v. 30, n., p , Oc AMBLER, Seve; PAQUET, Alain. Fiscal Spending Shocks, Endogenous Governmen Spending and Real Business Cycles. Journal of Economic Dynamics and Conrol, v. 20, Issues -3, p , Jan-March 996. ARAÚJO, Carlos Hamilon Vasconcelos; Ferreira, Pedro Cavalcani Gomes. Reforma ibuária, Efeios Alocaivos e Impacos de Bem-Esar. Revisa Brasileira de Economia. Rio de Janeiro, v. 53, n. 2, p , 999. ARAÚJO, Maria da Glória D.S. e al. The Effec of Adverse Supply Shocks on Moneary Policy and Oupu. Banco Cenral do Brasil, Working Paper Series, Brasília, n. 03, April ARROW, Kenneh Joseph; KURZ, Mordecai. Public Invesmen, he Rae of Reurn and Opimal Fiscal Policy. Balimore: The Johns Hopkins Universiy Press, 970. ASCHAUER, David Alan. Fiscal Policy and Aggregae Demand. American Economic Review, v. 83, n. 3, p , June 993.

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16 22 Does governmen spending composiion maer for welfare? The case of Brazil A. Appendix Figure 3 - Graphics of simulaions in Dynare - Income ansfers. Source: Prepared by he auhors.

17 Celso José Cosa Junior; Alejandro C. Garcia-Cinado; Armando Vaz Sampaio 23 Figure 4 - Graphics of simulaions in Dynare - Public Invesimen. Source: Prepared by he auhors.

18 24 Does governmen spending composiion maer for welfare? The case of Brazil Figure 5 - Disribuions priori and poseriori model. Source: Prepared by he auhors.