Pension System and Fiscal Policy in an Economy with Heterogeneous Agents 1

Transcription

1 Pension Sysem and Fiscal Policy in an Economy wih Heerogeneous Agens 1 Mariam Mamedli 2 Absrac Fiscal disress worsened by demographic rends inensifies he urgency of carrying ou pension reforms in order o insure he susainabiliy of social securiy sysems in he fuure. We deermine an opimal combinaion of fiscal insrumens and compare social welfare in he case of balanced and unbalanced pension sysem. The analysis is based on he overlapping generaions model wih an endogenous ineres rae and he pension fund run wih defici, covered by he governmen, in an economy wih wo ypes of agens: icardian and non- icardian. When all he agens are icardian i is opimal o finance he defici only by an income ax. In he case of an unbalanced pension sysem, he opimal fiscal policy includes a corner soluion wih zero social conribuions and posiive income ax. In heerogeneous economy afer a cerain hreshold level of he share of non-icardian consumers, non-zero social conribuions are opimal wih he lower level of income ax. This resul remains he same when levels of social conribuions differ for icardian and non-icardian agens: wih an increase of he share of non-icardian agens heir social conribuions become posiive, wih zero social conribuions of icardian agens. The opimal choice of governmen expendiure is increasing wih he share of non-icardian consumers, compensaing he decrease of heir welfare a reiremen. JEL Classificaion: E62, H55, H75 Keywords: pension sysem, opimal fiscal policy, overlapping generaions model, reiremen age, non-icardian agens; pension reforms 1 The sudy was implemened in he framework of he Basic esearch Program a he aional esearch Universiy Higher School of Economics. 2 Mmamedli@hse.ru, esearch and Forecasing Deparmen, Bank of ussia; esearcher, Laboraory for Macroeconomic analysis, aional esearch Universiy Higher School of Economics.

2 Inroducion Mos OECD counries have conduced pension reforms recenly in order o ensure boh financial susainabiliy of he pension sysems and adequacy of pensions. This underlines he need for an analysis of he consequences of pension reforms and fuure public expendiure on pension provision. Urgency of hese reforms has been dicaed by: firs, he challenges o financial susainabiliy of he exising pension sysems, puing addiional pressure on public finances (which worsened afer he financial crisis of and sovereign deb crisis); and second, by he longeviy coupled wih sharply decreasing birh raes. Despie underaking pension reforms, public expendiure on pensions as a percenage of GDP is expeced o rise furher in he near fuure in mos OECD counries. According o OECD esimaes, public spending on pensions has increased from 6.7% of GDP in 2000 o 8.2% of GDP in 2013, being he larges par of social expendiure (18% on average of he oal expendiures in 2013). 3 Long-erm OECD forecass for public spending on pensions sugges ha his endency would coninue for mos OECD counries, wih he spending growing in 21 counries and falling in 14. As a resul, pension expendiures are expeced o increase from 8.9% of GDP in o 9.5% of GDP by 2050, reaching 10.9% in The change of pension sysem characerisics such as higher reiremen age or he rae of social conribuions may be considered as an alernaive o sandard consolidaion measures of public finance. Public pension sysems also have a redisribuive role, providing he minimum level of income a he reiremen for low income households who were no able o save during heir working period (minimum pensions are presen in 15 OECD counries). A he same ime, an accoun for he exisence of non-icardian agens (Galí e al., 2007), who consume all heir disposable income and do no make any savings, is crucial in he analysis of fiscal policy (e.g. Almeida e al., 2013). I allows invesigaing more carefully he consequences of opimal fiscal policy and an economic impac i may have. The srucure of he populaion should be aken ino accoun, since fiscal policy direcly affecs he consumpion of non-icardian agens and, as a resul, he oher macroeconomic variables. Inroducion A wide range of pension reforms has been launched in many counries in order o ensure he susainabiliy of he social securiy sysem, which is a risk because of increasing expendiures on pensions. The main drivers of hese dynamics are demographic changes: feriliy raes which are below he replacemen level and increasing life expecancy. These demographic developmens are leading o a significan increase in he old-age dependency raio: he raio is expeced o rise from 29.9 in 2016 o 52.2 in 2070 in he EU-27, while he very old-age dependency raio will increase from 8.4 o 23.0 during his period, according o recen forecass from he European Commission. 5 Despie he implemened reforms, federal 3 Pensions a a Glance (2017), OECD Social Expendiures Daabase (SOCX). 4 The numbers for may differ from he values presened in OECD Social Expendiures Daabase (SOCX) because of he differen range of benefis covered and he definiions used (Pensions a a Glance, 2017). 5 European Commission, The 2018 Ageing epor: Underlying Assumpions and Projecion Mehodologies, ov Very old-age dependency raio refers o 80+/

3 ransfers remain one of he key sources o balance he budge for pension funds. These ransfers are expeced o rise seadily in he fuure: his par of fiscal expendiures will increase in OECD counries from 9.3% of GDP in 2010 o 11.7% of GDP in In ussia, public expendiure on he pension provision is projeced o increase from 6.7% of GDP in 2017 o 7.5% of GDP by Pension reforms can be considered as an alernaive o he radiional measures of fiscal consolidaion. This sudy defines he opimal fiscal insrumens (rae of social conribuions, income ax, governmen expendiure) chosen by he social planner under an unbalanced pension sysem in he economy wih icardian and non-icardian agens (rule-of-humb consumers), 7 who consume all heir disposable income each period. Firs, we specify how opimal social conribuions and income ax change wih he reiremen age, life expecancy, and labor produciviy, and how hey depend on he ype of pension sysem (balanced or unbalanced) in he absence of non-icardian agens. Second, we define he choice of social conribuions, income ax and governmen expendiure by a benevolen governmen in an economy wih boh icardian and non-icardian agens. The focus is on how opimal policy insrumens change wih he share of non-icardian consumers. Models wih non-icardian agens have become common in he analysis of fiscal policy. The inclusion of populaion heerogeneiy via icardian and non-icardian consumers allows us o capure he failure of icardian equivalence. 8 There are several papers ha analyze srucural fiscal reforms and demographic shocks wihin he Global Inegraed Moneary and Fiscal model (GIMF) 9, which incorporaes boh icardian and non-icardian consumers (Almeida e al. 2013a, b; Casro e al., 2015; 10 Karam e al., ). However, as opposed o he curren research hey do no consider he opimal choice of insrumens by a public planner and he impac of he share of non-icardian consumers in his choice. The research on pension reforms can be classified by he ype of pension sysem under consideraion. The firs group consiss of research on PAYG reforms (e.g. ickel e al., 2008; Karam e al., 2010; Kilponen e al., ; Casro e. al., 2017; Almeida e al., 2013 a, b; Pierrard, Snessens, 2009; Marchiori, Pierrard, 2012, ). This research falls ino he firs caegory. Oher research considers he swich from pay-as-you-go (PAYG) o a fully funded 6 OECD, Pensions a glance See Galí e al. (2007). 8 The impac of fiscal policy shocks on privae consumpion can be capured by he inroducion of heerogeneiy in consumers (Galí e al., 2007). 9 The baseline srucure of model is based on GIMF, presened in Kumhof, Laxon (2007, 2009, 2013), Kumhof e al. (2009, 2010). 10 Almeida e al. (2013a) exend he Poruguese Economy Srucural Small Open Analyical model incorporaing financial fricions (as in Bernanke e al., 1999). The model is applied in research on he assessmen of srucural reforms, fiscal simulus and consolidaion (Almeida, Casro, Felix, 2009, 2010; Almeida e al., 2010a, b). 11 Karam e al. (2010) consider hree reforms of he PAYG pension sysem: an increase in he reiremen age, cus in pensions and an increase in social conribuions. They show ha pension reforms can have a posiive effec boh in he shor run, due o an increase in consumpion, and in he long run, due o he lower level of public deb. 12 Kilponen e al. (2006) exend he OLG model of Gerler (1999) inroducing disorionary axaion, imevarying reiremen and deah probabiliies o he model. The model is used for he analysis of demographic changes in a small open economy, using he example of Finland. 13 Pierrard and Snessens (2009) and a series of furher research sudies (Marchiori and Pierrard 2012; 2015) sequenially exend he OLG model of Auerbach and Kolikoff (1987). The model is calibraed for Luxembourg (Luxembourg Overlapping generaion model for policy analysis). 3

4 pension sysem (Borsch-Supan e al., 2006; McGraan, Presco, 2017). Boh ypes of pension sysems were analyzed in Marchiori e al. (2011) and de la Croix e al. (2013). There are also several sudies (Galasso, 2008; 14 Heijdra, omp, ; Beesma e al., 2013) which consider an opimal pension plan or opimal reiremen age. The analysis is based on he overlapping generaions model (OLG) iniially developed by Yaari (1965) and Blanchard (1985) and exended furher by Buier (1988), Giovannini (1988), Weil (1989) and Bovenberg (1993). In order o invesigae he opimal policy mix of social conribuions and income ax rae, we exend he model of Heijdra and Beendorf (2006). They analyzed he economic consequences of lower pensions and a higher reiremen age in an open economy wih raded and non-raded secors (as in Turnovsky, 1997). 16 However, Heijdra and Beendorf (2006) consider an exogenous ineres rae along wih a rudimenary balanced pay-as-you-go (PAYG) pension sysem. 17 While Heijdra and Beendorf (2006) consider he consequences of shocks o he welfare of each generaion, we invesigae he opimal se of measures conduced by a benevolen governmen, which maximizes he social welfare funcion, and how his se of measures is affeced by he share of non-icardian consumers. Their model is exended o invesigae he unbalanced budge of he pension fund in a closed economy wih an endogenous ineres rae. This allows us o accoun for he effec of differen economic characerisics (reiremen age, life expecancy, labor produciviy) on capial accumulaion. The model is exended o incorporae boh icardian and non-icardian consumers in order o invesigae how he share of non- icardian consumers affecs he choice of policy insrumens. Following Heijdra and Beendorf (2006) he model also incorporaes decreasing-wih-age labor produciviy which adds non-icardian characerisics o he model. Heijdra and Beendorf (2006) consider wo ypes of demographic shocks: a proporional decrease of boh birh and deah raes so ha populaion growh remains consan, and a fall of he birh rae accompanied by a growh of he deah rae, which leads o a decreasing populaion size. They consider wo ypes of pension reforms: a decrease in pensions and an increase in he reiremen age. Boh reforms are followed by an adjusmen in social conribuions because Heijdra and Beendorf (2006) consider a balanced pension sysem. If he ineres rae exceeds populaion growh, boh reforms lead o an increase in consumpion and financial asses in he long-run, ye also o a decrease in capial, because here is a higher consumpion of non-radable goods. They also analyze he consequences of reforms on he welfare of differen generaions. A decrease in pensions leads o he sandard resul of a fall in he welfare of he oldes persons living in he period of he shock. 18 An 14 Galasso (2008) wihin a calibraed model of Galasso and Profea (2004) exended i o incorporae an endogenous reiremen age by conducing simulaions up o 2050 for France, Ialy, he Unied Kingdom and he USA, showing ha he reiremen age and social conribuions rae would be increased in all counries considered excep Ialy. 15 Heijdra and omp (2009) analyzed he households reiremen age decisions in he model wih exogenous ineres rae and endogenous labor supply (developed by Heijdra and omp, 2006; 2008). They show ha for pension reform o have an impac on he households decisions, he change needs o be significan. 16 Sudies on populaion aging usually employ dynamic calibraed compuable general equilibrium (CGE) models as Auerbach and Kolikoff (1987). 17 Pension sysem is similar o ielsen (1994). 18 This resul is similar o ha from he sandard wo-generaion Diamond (1965) model. 4

5 increase in he reiremen age does no affec he welfare of reirees and increases he welfare of fuure generaions. The burden of reforms in his case falls on he working generaion. The framework of Heijdra and Beendorf (2006) and ielsen (1994) was exended by ickel e al. (2008), who consider an unbalanced pension sysem. 19 They analyze hree fiscal scenarios in an economy wih a decreasing populaion (Buier, 1988): a suspension of he public pension sysem and a decrease in lump-sum labor ax; he suspension of he public pension sysem and a decrease in disorionary corporae ax; and an increase in he reiremen age. Their resuls sugges ha he adverse consequences of pension reforms can be decreased by appropriae axaion policies. If he ax reform is conduced promply, he negaive effec of reform on consumpion could be offse, while he public deb would reach a lower equilibrium level. 20 While ickel e al. (2008) consider he governmen as a non-maximizing eniy and invesigae how he predeermined changes in policy insrumens would affec he ransiion of he main macroeconomic variables o he new equilibrium in an open economy, we define a socially opimal fiscal policy (social conribuions, governmen expendiure and income ax) and compare he se of policy insrumens in equilibrium wih boh an increasing and decreasing populaion in a closed economy wih an endogenous ineres rae and a heerogeneous populaion. The fac ha he income ax rae and social conribuions are subsiues is illusraed by he comparison of he opimal policy mixes under boh balanced and unbalanced pension sysems. Under a balanced pension sysem social conribuions are sricly posiive and decrease wih populaion growh, while income ax rae is consan and does no depend on i. In he case of an unbalanced pension sysem, on he conrary, he corner soluion is opimal: social conribuions are a zero while he income ax rae decreases wih populaion growh. This policy mix remains opimal in he seady sae regardless of life expecancy and labor produciviy. Under an unbalanced pension sysem he opimal income ax rae changes wih he srucural characerisics of he economy while social conribuions are a zero. Wihin he model which incorporaes icardian and non-icardian consumers we show ha here exiss a hreshold level of he share of non-icardian consumers afer which higher social conribuions and lower income ax are opimal. I is shown ha he opimal share of governmen expendiure is increasing wih he share of non-icardian consumers compensaing heir welfare a reiremen. The paper is organized as follows. Secions 2 presen an exended OLG model of Heijdra and Beendorf (2006) wih an unbalanced pension sysem in a closed economy wih an endogenous ineres rae. Secion 3 presens he comparison of he opimal policy mix and social welfare under balanced and unbalanced pension sysems in an economy populaed by icardian consumers. I is also shown how he opimal policy mix depends on reiremen age, life expecancy and labor produciviy. Secion 4 provides he resuls for he opimal fiscal policy in he economy wih icardian and non-icardian consumers, wih and wihou a 19 They also exend he model by assuming ha firms issue equiies and face adjusmen coss in invesmen. 20 I was shown ha a decrease of pensions o zero, de-faco abolishmen of he pension sysem, is accompanied by he decrease of he disorionary ax on he firms oupu, he negaive effec on he consumpion per capia can be lowered in he shor-run, while in he long-run he oupu and consumpion are higher wih lower levels of privae and public deb. 5

6 pension sysem. I also includes an analysis of he opimal fiscal policy when discriminaion among agens based on heir ype is possible (he case of ype specific social conribuions is considered). Secion 5 concludes he sudy. 2. The model wih icardian and non-icardian consumers The model of Heijdra and Beendorf (2006) is exended by inroducing an unbalanced pension sysem wih he defici covered by a benevolen governmen, which conducs fiscal policy o maximize social welfare. We consider a closed economy wih an endogenous ineres rae. The economy consiss of wo ypes of households, firms, he governmen and he pension fund. Infiniely-lived icardian households maximize he presen value of uiliy from consumpion aking ino accoun life expecancy. on-icardian consumers, whose share is, consume all heir disposable income, do no save, and do no have he abiliy o smooh consumpion over ime. Boh ypes of consumers work and pay income ax hroughou heir lives, pay social conribuions unil he reiremen age and receive pensions a reiremen. Pensions are paid by he pension fund, he defici of which is covered by he governmen. Public deb is financed by bonds held by he households and income ax paymens. In he model upper case variables are aggregaes, lower case variables wih a bar denoe individual variables, and lower case variables wihou any noaion are aggregaes per efficiency unis of labor icardian and non-icardian households The represenaive icardian ype consumer born a ime maximizes a each momen he expeced presen value of insananeous lifeime uiliy of consumpion: where ( )( ) (, ) (1 )ln c (, ) ln d, U g e (1) c is personal consumpion of icardian consumers, g is public spending and 0 is share in he uiliy funcion, 0 is he rae of ime preference and 0 is he probabiliy of deah. Following Beendorf and Heijdra (2006) we consider a pay-as-you-go (PAYG) pension sysem inroduced by ielsen (1994). The households pay income axes hroughou heir lives, pay social conribuions W unil he reiremen age of and receive pensions z a reiremen. The hreshold level can only loosely be considered as a reiremen age because he households coninue o work afer i. icardian consumers can save par of heir disposable income, which can be invesed in G capial goods, k, and governmen bonds, ( a ). They pay income ax on heir labor income and receive an ineres rae r () on heir financial wealh, a(, ). The paymen a(, ) is is he 6

7 acuarially fair annuiy paid by he life insurance company. 21 Ineres and non-ineres ne labor income, WI (, ), are spen on consumpion and saving. Household financial wealh, G herefore, consiss of capial goods, k, and governmen bonds, ( a ), boh denominaed in erms of consumer goods. The budge consrain of a icardian ype consumer in erms of he consumpion good is: 22 (, ) ( ( ) ) (, ) a r a WI (, ) c (, ) (2) WI a(, ) k (, ) a G (, ), (3) (1 ) W (, ) for, (, ) (1 L) W (, ) z for, L W where W (, ) is he wage a ime of he worker born a ime. Labor supply for boh ypes of consumers is non-elasic: each household supplies one uni of labor. 23 Labor produciviy decreases wih he age of he worker. The worker of generaion a ime supplies n(, ) efficiency unis of labor (Beendorf and Heijdra, 2006): n(, ) E( ) l (, ), (5) where l (, ) 1 is he labor hours worked and E ( ) is he so-called efficiency index (Beendorf and Heijdra, 2006), which falls exponenially wih he worker's age as in Blanchard (1985): E (6) ( ) e ( ), 0 where 0, is normalized o 1 and 0 specifies he speed a which produciviy falls wih age. A each momen he household chooses he pahs of consumpion and financial asses o maximize lifeime uiliy (1) subjec o budge consrain (2) and a ransversaliy condiion. The iniial value of he financial asses a(, ) and he governmen consumpion per household are aken as given. The opimal pah of household consumpion is defined by he Euler equaion: c c (4) (, ) r (), (7) (, ) from which i follows ha in each momen consumpion is proporional o oal wealh: Human wealh, c (, ) ( )( a(, ) a (, )). (8) a H, is defined as he presen value of afer-ax labor income: H 21 See Yaari (1965), Blanchard (1985). Yaari (1965) has inroduced a noion of acuarial noe, defined as a noe ha he consumer can buy or sell and which is valid unil he consumer dies, a which ime i is auomaically cancelled. 22 A do above he variable signifies he variable's ime derivaive: a (, ) da (, ) / d. 23 Heijdra and omp (2009) analyze he consequences of demographic shocks and changes in pension sysem on main macroeconomic variables in he OLG model wih endogenous labor supply and endogenous reiremen age. 7

8 where (, ) r( s) ds. (, ) ( ) H (, ) (, )e, a WI d (9) on-icardian households whose share in he oal populaion is, consume all heir disposable income. Their consumpion, herefore, is defined by (10): c (, ) WI (, ). (10) They have he same uiliy funcion as icardian consumers, defined by equaion (1). Their ne labor income is idenical o ha of icardian agens. (1 L) W (, ) W for, WI (, ) (11) (1 L) W (, ) z for. This ype of household consumes all is income, and is unable o save and smooh consumpion over is lifeime. Similar o he human wealh of icardian agens, we can define he human wealh of non-icardian agens. In his case i is equal o he presen value of heir lifeime consumpion. (, ) ( ) (, ) (, ) e H, a WI d (12) 2.2. Demography and aggregae household secor The framework allows us o consider non-zero populaion growh, by disinguishing he probabiliy of deah 0, and he probabiliy of birh, The populaion size L (), which consiss of icardian agens (1 ) and non-icardian agens ( ), and grows proporionally wih he ne growh rae n L : L () nl. (13) L () Taking ino accoun a normalizaion L(0) 1, he populaion size is: L ( ) e n L. (14) The size of he generaion born a is proporional o he curren size of he populaion: L(, ) L( ). (15) The size of each generaion falls exponenially wih he probabiliy of deah : ( ) L(, ) L(, ) e,. (16) The curren size of he generaion born a ime can be obained by subsiuing (14) and (15) ino (16): L(, ) e e. (17) 24 This framework was developed by Buier (1988). 8

9 The aggregae variables are defined as he inegral of he variable values, specific for each living generaion, weighed by he size of ha generaion. Aggregae consumpion can be defined as follows: K C( ) L(, ) c(, ) d C ( ) (1 ) C ( ), (18) where L(, ) and c(, ) are given by (8), (10) and(17), respecively. Aggregaing (8) by generaions of icardian consumers we obain (19) which posulaes ha aggregae consumpion of icardian agens is proporional o heir wealh, where A () is H aggregae financial wealh and A () is aggregae human wealh: C ( ) ( ) A( ) AH ( ). (19) The growh rae of aggregae consumpion is obained from (18), aking ino accoun (7) and (17): where r () ( ) ( ) ( ) (, ) C L c C ( r ), (20) C ( ) C ( ) is he growh of individual consumpion of icardian agens, while he second erm represens he so-called generaional urnover (Beendorf and Heijdra, 2006), which depends on he demographic parameers. Aggregae consumpion of icardian agens increases wih he arrival of new agens and decreases wih he deah of he older generaion. The growh rae of he aggregae consumpion of icardian agens can be simplified o: 25 C ( ) L L( ) ( ) A( ) r( ) n ( ), (21) C ( ) C ( ) r() nl d( ) e z d( ) e e ( ) r( ). L (22) r( ) 1 e r( ) n r( ) The aggregae consumpion growh of icardian agens exceeds he growh of heir individual consumpion ( r () ) if ne populaion growh is posiive ( n 0 ), and labor produciviy decreases over ime ( 0 ). A he same ime, aggregae consumpion growh of icardian agens can be lower han he individual consumpion growh if newborns consume less or if he redisribuion of wealh from he young o he old hrough he pension sysem akes place. In conras o Beendorf and Heijdra (2006), depends on he defici of he pension fund ( d () per capia defici of he pension fund) which is defined below. 26 Beendorf and Heijdra (2006) poin ou ha / ( r ) in an economy wih one ype of consumer can be considered as he per capia defici of he pension sysem. When r n L social conribuions are perceived by working households as a ax on labor income, since hey are forced o save a he rae n L, which is lower han he marke rae r. For reirees he opposie effec akes place. L 25 For more deails see Appendix Defici of he pension fund is defined by he difference beween he sum of pensions paid by he Pension Fund and he sum of social conribuions paid o he Pension Fund (see equaion 39). 9

10 Aggregae financial wealh owned by icardian consumers is defined as follows: A( ) L(, ) a(, ) d. (23) The definiion of aggregae savings can be found by differeniaing equaion (23) for he aggregae financial wealh wih respec o ime and aking ino accoun ha he newborn generaion does no have any financial wealh, a(, ) 0: By subsiuing (2) o (24) we ge: 27 A( ) A( ) L(, ) a(, ) d. (24) A( ) r( ) A( ) WI ( ) C ( ), (25) WI F k L D 0 ( ) (1 L) ( ( ),1)) ( ) ( ), where F ( k ( ),1) is he marginal produc of labor and D () is he defici of he pension sysem, based on he conribuions and pensions of icardian agens. The aggregae labor supply a ime measured in efficiency unis is proporional o he populaion size in he corresponding period. I is obained from (5), (6), (14) and (17): 0 ( ) (, ) (, ) ( ). (26) L n d L (27) 2.3. Firms As opposed o Beendorf and Heijdra (2006), we consider a closed economy wih an endogenous ineres rae, which is imporan in he esimaion of pensions. The oupu is produced according o he Cobb-Douglas echnology: Y F K K 1 (, ), (28) where K and represen capial and effecive unis of labor. Producers maximize profi, choosing he opimal level of capial and labor: K ( ) Y( ) W (, ) L(, ) d W ( ) K( ), (29) K where W () is a capial ren and W (, ) is he wage a ime of he worker of generaion. The firs order condiions are: K W ( ) F ( k ( ),1), (30) K W (, ) W ( ) F( k( ),1), E( ) (31) 27 For more deails see Appendix 2. 10

11 where F F / K and F F /. W () is he wage per uni of effecive labor and K k ( ) ( ) / ( ) K is he capial effecive-labor raio. The produced oupu is allocaed o he oal privae consumpion C, invesmen I and governmen expendiures G. Y( ) C( ) I( ) G( ). (32) The opimal invesmen decision is based on he maximizaion of he ne presen value of cash flows from he invesor's capial sock subjec o he capial accumulaion ideniy: K (, ) ( ) ( ) ( ) ( ) e, where (, ) r( s) ds is he discoun facor. V W K I d (33) K( ) I( ) K( ), (34) The firs order condiion (35), specifies ha he renal rae capial r () aking ino accoun he capial depreciaion rae. K W equals he reurn on K W ( ) r( ). (35) 2.4. Public secor G Governmen budge ideniy defines he accumulaion pah of public deb A (), which depends on he curren governmen expendiures G (), labor ax revenues and addiional expendiures, which we assume come from covering he oal defici of pension fund D (). I can be wrien as follows:. G G L A ( ) r( ) A ( ) G( ) W ( ) ( ) D( ). (36) Taking ino accoun he ransversaliy condiion: he public deb is: (, ) lim G A ( ) e 0, G (, ) ( ) ( ) ( ) ( ) ( ) e L. (37) A W G D d (38) The key difference wih he paper of Heijdra and Beendorf (2006) is he assumpion ha he PAYG pension sysem can be run on an unbalanced-budge basis, wih a defici D (): (1 e ) L( ) ze L( ) D(). (39) W The lef-hand side of (39) represens he oal social conribuions paid by he young generaion, while on he righ-hand side are oal pensions paid o he old and he defici (or surplus) of he pension fund if he sum of social conribuions and pensions do no mach. For easier comparison, we assume ha he governmen deermines he value of social conribuions by seing he value of, which is he share of he median wage ha goes o social conribuions, paid unil reiremen. This makes he value of social conribuions depend on he reiremen age: 11

12 1 1e ln 2 (40) W 0 F( k( ),1) e. The value of pensions can be expressed he same way, as a share of he median wage ha goes o pensions, : 1 1e ln 2 z 0 F ( k( ),1) e. (41) 2.5. Model summary and social welfare Table 1 below summarizes he key equaions of he model in per capia erms, where he endogenous variables are k, y, g, T c, c, c, a, G a, r, W, K W,, n, W, z. The parameers are,, n L,,,, and. The policy insrumens are he reiremen age, he share of he median wage ha goes o social conribuions and pensions, and, public expendiures as a share of oupu,, and income ax L. Table 1. Summary of he Model Descripion Dynamic equaions: Analyical represenaion Capial k( ) ny( ) c T ( ) g( ) ( n ) k( ) (Т1.1) Privae consumpion c ( ) ( r( ) ) c ( ) ( )( ( ) ( ) a( )) (Т1.2) G G Public deb a ( ) ( r( ) n ) a ( ) g( ) n W ( ) d( ) (Т1.3) L Asses a( ) ( r( ) n ) a( ) c ( ) n(1 )(1 ) W ( ) d( ) (Т1.4) Saic equaions: Pension fund enal rae L L L r () n L ( ) ( ) ( ) d e ( ) z d e e r L r ( ) 1 e r( ) n r() where (1 e ) ze d ( ) W K 1 k () W ( ) k ( ) n 1 L, (Т1.5) (Т1.6) K Ineres rae r( ) W ( ) (Т1.7) Wage W ( ) (1 ) y( ) (Т1.8) Oupu Supplied efficiency unis k () y( ) k ( ) n 0 n (Т1.9) (Т1.10) Wealh G a ( ) k( ) a ( ) (Т1.11) Toal consumpion c T ( ) c ( ) c ( ) (Т1.12) Equaion T1.1 corresponds o he accumulaion of per capia capial, and i is obained by combining (34) and (35). Equaion T1.2 represens an opimal pah of consumpion per capia, obained from (21) in per capia erms. Equaion T1.3 is he governmen budge 12

13 consrain expressed in per capia erms, derived from he governmen budge consrain (36). The las dynamic equaion, Equaion T4, represens he accumulaion of per capia asses and is obained from (25), aking ino accoun (26) and (39). Definiion 1. Given he se of policy variables,,,, L ha saisfy he governmen budge consrain, he se W K,,, T,,,,, G r y c c c k a a, d defines equilibrium, if i saisfies he opimal condiions of households and firms, (7) and (30)-(31), and equilibrium condiions for goods and capial markes. However, according o Walras' Law only wo marke equilibrium condiions are needed o ensure equilibrium on hese markes: T y( ) c ( ) i( ) g( ), (41) G a( ) k( ) a ( ). (42) The sysem of dynamic equaions is non-linear and canno be solved analyically, so we are solving he sysem of equaions T1.1-T1.3 numerically, aking ino accoun T To disinguish he socially opimal policy mix of measures (income ax and social conribuions) we check wheher he resuling se of possible equilibria saisfies he sabiliy condiion of he equilibrium. 29 Exending he model furher o incorporae welfare analysis, we define he social welfare funcion as he presen value of he uiliy of all currenly living and fuure generaions weighed by heir share of he populaion. Social welfare is a sum of he welfare of young generaions and reirees. ( )( ) SW ( ) L(, )[(1 )ln c (, ) ln g] e d d ( )( ) L c g e d d (1 ) (, )[(1 )ln (, ) ln ] ( )( ) L(, )[(1 )ln c (, ) ln g] e dd ( )( ) (1 ) L(, )[(1 )ln c (, ) ln g] e dd. Taking ino accoun equaion (8) and (10), individual consumpion of he young and old generaions are expressed as funcions of heir individual human wealh, which depends on he effecive capial. 30 Simplifying equaion (43) he following welfare funcion can be (43) 28 All calculaions were conduced using Malab. Seing k ( ) 0, and a ( ) 0, we use a roo-finding mehod (he bisecion mehod) o define he level of capial per capia o bring he growh of per capia consumpion o zero, c ( ) 0. All possible combinaions of feasible model parameers and policy insrumens are considered o deermine he seady-sae level of * k. 29 The sabiliy condiion ensures ha he deerminan of he Jacobian marix of he log-linearized dynamic sysem of equaions T1.1, T1.2 and T1.4 is negaive. In his case he model is locally saddle-poin sable. The consrain on he public deb ensures ha public deb does no exceed 1.5 imes he oupu. 30 For more deails see Appendix 3. G 13

14 obained, where ypes of consumers: o a H and y a H is he human wealh of he young and old generaions of boh o SW ( ) e (ln(( ) ah ) ( 1) / ) ln g (44) 1 (1 e )(ln(( ) y ah ) ln g) (1 )(1 e e )), n e L, r. n L I is known ha in he OLG model wih icardian agens and a dynamically efficien equilibrium, a PAYG pension sysem worsens social welfare. 31 If he level of pensions is chosen opimally from he maximizaion of social welfare, i would be opimal o se zero pensions and social conribuions. Taking his resul ino accoun in he maximizaion problem he level of pensions and he reiremen age were fixed in order o analyze he opimal choice of income axes and social conribuions. I is worh menioning ha he equilibrium wih diminishing labor produciviy can be dynamically inefficien if he speed of he decrease in produciviy,, is large enough. In his case labor income is high during he youh and falls rapidly wih age, so agens save a lo during youh which makes capial sock oo large, leading o an overaccumulaion of capial. The necessary condiion for dynamic efficiency is, which corresponds o a posiive ineres rae. The calibraion used here saisfies he condiion of dynamic efficiency Calibraion The opimal choice of he reiremen age, social conribuions and pensions illusraes ha he pension sysem is redundan. This resul coincides wih he resuls of neoclassical models, wih forward-looking agens having an incenive o save on heir own in order o smooh heir consumpion. Tha is why we invesigae he opimal mix of income ax and social conribuions wih a fixed level of pensions and a fixed reiremen age. Table 2 conains he parameers used for he baseline calibraion. 31 See Blanchard and Fischer (1989). 14

15 Table 2. Baseline calibraion Variable Symbol Value Source ae of ime preference Heijdra, Lighar (2006) 32 Birh rae Heijdra, Lighar (2006) 33 Probabiliy of deah Heijdra, Lighar (2006) Oupu elasiciy of capial 0.33 Sandard 34 Speed of decline in he labor efficiency ickel e al. (2008) 35 Capial depreciaion rae 0.03 Heijdra, Lighar (2006) 36 eiremen age 60 Beendorf, Heijdra (2006) 37 Share of non-icardian agens [0; 0.9] A range of possible values The share of pensions,, is fixed a 30% of he median lifeime wage, while he opimal size of he mandaory social conribuions,, as a share of he median wage, and income ax are chosen opimally from he maximizaion of social welfare. 38 The share of governmen expendiures,, is fixed a 25% of GDP, a common value for he OECD counries. The produciviy declines wih age a he speed of, which equals 1.25%, meaning ha he worker is half as producive a reiremen age han he was a he beginning of life. For he resuls presened below, he deah rae equals 1.25%, giving a life expecancy of 80 years. The birh rae varies from 1% o 3%. This range allows us o analyze boh negaive and posiive populaion growh. In considered seady saes he endogenous ineres rae is higher han he populaion growh (he so-called Aaron condiion is saisfied). There is no consensus in he lieraure concerning he number of non-icardian agens in he economy. The esimaes vary from 50% in Campbell and Mankiw (1989) for he US o for he Euro area esimaed by Coenen and Sraub (2005). 39 A he same ime Maro (2014) esimaed he share of non-icardian agens as equal o 0.58 for he Poruguese economy. As for ussia, Tiffin and Hauner (2008) assume ha 40% of ussian households are liquidiy-consrained in he GIMF model calibraed for ussia. 40 In he nex wo secions we consider he opimal fiscal insrumens in an economy where all agens are icardian (Secion 3) and in an economy wih wo ypes of agens, icardian and non-icardian (Secion 4). 32 The value belongs o he inerval considered by Heijdra and Lighar (2006): from 0.01 o In Heijdra and Lighar (2006) he birh rae varies from 0.01 o 0.04, while he deah rae varies from 0 o In he baseline calibraion he birh rae equals and he deah rae is In Heijdra and Lighar (2006) elasiciy wih respec o capial equals I is consisen wih he value used in ickel e al. (2008) where his parameer equals 0.014, deah rae a This value is consisen wih he lieraure. Heijdra and Lighar (2006) use depreciaion rae which is equal o 0.06 wih he higher rae of ime preference being equal o In Heijdra e al. (2017) capial depreciaion rae equals o Alhough Beendorf and Heijdra (2006) do no use calibraion, in he numeric example he resricion on he reiremen age posulaes ha i should exceed 48.5 or 56.8 depending on he birh and deah raes considered. 38 The resuls are robus o he change in he share of he median wage paid o pensions. 39 Here he esimaes for poserior means are provided. These esimaes are raher low, aking ino accoun he fac ha Coenen and Sraub (2005) used he value of 0.5 as a mean of he prior disribuion. 40 Global Inegraed Moneary and Fiscal model (GIMF), presened in Kumhof, Laxon (2007, 2009, 2013), Kumhof e al. (2009, 2010). 15

16 3. Opimal fiscal policy insrumens in a homogeneous economy This secion firs shows how opimal social conribuions and income ax rae depend on he reiremen age and populaion growh. We sar by searching for he opimal proporion of he median wage ha goes o social conribuions, and move o he deerminaion of he choice for boh social conribuions and income ax rae. In Subsecion 3.2 he opimal choice of hese wo insrumens is considered under a balanced and unbalanced pension sysem. Subsecion 3.3 provides a robusness check, covering he opimal choice of fiscal insrumens under differen life expecancy and labor produciviy Policy insrumens under unbalanced pension sysem depending on he reiremen age In order o invesigae how he opimal social conribuions depend on he reiremen age we firs consider he case wih a fixed income ax ( L 40% ). Quaniaive resuls sugges ha a higher reiremen age leads o a lower rae of social conribuions (Figure 1). The value of social conribuions W is also affeced by he change in he median wage. Median wage increases wih he higher reiremen age due o he higher per capia capial and decreases wih he higher reiremen age due o he decreasing produciviy of labor. The laer effec is sronger, so median wage decreases wih he higher reiremen age. As a resul, lower pensions correspond o a higher reiremen age. The opimal level of decreases wih higher populaion growh as i leads o a higher share of young generaion members who pay social conribuions. Ψ 35% π = 55 π = 60 π = 65 30% 25% 20% 15% 10% 5% 0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0% n L Figure 1. Opimal social conribuions rae under differen reiremen age Source: esimaes based on he model. 16

17 ex, we consider he opimal choice of wo insrumens: income ax, L, and he rae of social conribuions, W. In his case he corner soluion akes place: he opimal income ax rae is posiive, while he rae of social conribuions equals zero. The corner soluion akes place because zero social conribuions leads o a lower opimal welfare improving income ax rae. Oher seady saes wih zero social conribuions and a higher income ax rae are characerized by lower social welfare. In he neighborhood of opimal insrumen combinaion he same level of capial per effecive uni of labor can be reached wih zero conribuions and posiive income ax as well as wih small posiive conribuions and lower income ax. However, his equilibrium is characerized by higher public deb and a smaller defici of he pension fund. Household savings are invesed in he public deb and no in capial, which leads o inefficiency. As a resul, he opimal combinaion consiss of zero social conribuions and he minimum equilibrium level for he income ax rae. The resuls of welfare maximizaion for 60 and 65 are presened in Table 3 below. 41 Table 3. Opimal income ax under differen populaion growh and reiremen age Income ax rae Pension fund defici o oupu Income ax rae Pension fund defici o oupu nl -0.25% 0% 0.25% 0.5% 0.75% 1.25% 1.75% 60 L 50.3% 48% 46.5% 45.3% 44.2% 42.4% 41.1% d y 8.1% 7% 6% 5.2% 4.4% 3.3% 2.4% 65 L 48.9% 47.2% 45.7% 44.5% 43.4% 41.8% 40.6% d y 7.5% 6.4% 5.4% 4.6% 3.9% 2.8% 2.1% The pension sysem in his case is run wih a defici ( d - he share of he defici in oupu). I decreases wih populaion growh and he reiremen age. Pensions are se a 30% of he median wage, which changes wih he longer working period, so pensions adjus auomaically o he changes in he reiremen age. Figure 2 shows how an opimal income ax depends on he populaion growh. Opimal income ax exhibis he same inverse relaionship as social conribuions (Figure 1). In his case social conribuions are zero, while he income ax rae is decreasing wih higher populaion growh: he defici and pensions can be financed wih lower income axes when he share of he young populaion is high. y 41 Differen level of birh raes are considered wih consan deah rae, 1.25%. This leads o differen levels of populaion growh n L. 17

18 L 52% π = 55 π = 60 π = 65 48% 44% 40% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0% n L Figure 2. Opimal income ax under differen reiremen age Source: esimaes based on he model. Higher income ax and zero social conribuions, when hey boh are chosen opimally, illusrae ha hese insrumens can be considered as subsiues in financing pensions. Addiional calculaions show ha an increase in by 0.5% leads o he decrease in he opimal income ax rae by 0.2%. However, combinaions of lower income ax and posiive social conribuions resul in lower level of capial per capia. Per capia capial is more sensiive o he change in he rae of social conribuions han o he change in he income ax rae. The higher sensiiviy of capial per capia o he income ax rae is explained, firs, by he shorer paymen period of social conribuions (while income ax is paid hroughou he life, social conribuions are paid only up o he reiremen age) and, second, by he fac ha social conribuions are defined by he median wage and paid unil he reiremen age Opimal policy under balanced and unbalanced pension sysem ex, we consider how he opimal policy mix changes depending on wheher he pension sysem is balanced or no. Firs, under he balanced pension sysem he opimal income ax rae is lower han in he case of he unbalanced pension sysem for all growh raes (Figure 3), because in his case pensions are financed by social conribuions and no ou of he governmen budge. Second, under a balanced pension sysem he opimal level of income ax is consan, while he share of social conribuions decreases wih populaion growh. A higher birh rae increases he value of he social conribuions o he pension fund because in his case more members of he young generaion make conribuions. Thus, he lower social conribuion rae is needed o keep he pension fund balanced. 18

19 L 55% d 0 d = 0 50% 45% 40% 35% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0% n L Figure 3. Opimal income ax under balanced and unbalanced pension sysem Source: esimaes based on he model. Therefore, depending on wheher he pension sysem is balanced or no, eiher he opimal income ax or social conribuions change wih he growh rae, while he oher insrumen remains a is opimal level. Figure 4 illusraes he resuls for he opimal level of for a balanced and an unbalanced pension sysem. In he case of a balanced pension sysem, social welfare is lower han in he case of an unbalanced pension sysem. A balanced pension sysem is accompanied by a higher level of per capia capial and herefore, higher social welfare. This finding corresponds o he resuls of he OLG models wih a dynamically efficien seady sae where a PAYG pension sysem leads o lower social welfare. An equilibrium wih an unbalanced pension sysem leads o higher social welfare and o a lower level of public deb due o he lower surpluses. This resul is explained by he comparison of budge surpluses, which serve as a provision of public deb. Under a balanced pension sysem ax revenues are lower. Firs, he opimal ax rae is lower as pensions are financed by social conribuions. Second, he aggregae wage is lower due o he lower capial per capia. Public spending is also lower in he case of a balanced sysem: due o boh lower governmen expendiures and zero defici of he pension fund. 19

20 Ψ 40% d 0 d = 0 30% 20% 10% 0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0% n L Figure 4. Opimal social conribuions under balanced and unbalanced pension sysem Source: esimaes based on he model obusness check: life expecancy and labor produciviy The robusness check includes an analysis of how he opimal policy mix of social conribuions and income ax is affeced by he changes in life expecancy and labor produciviy. We compare seady saes under life expecancy which is equal o 70 and 80 years under he unbalanced pension sysem. These levels of life expecancy correspond o being equal o 1.43% and 1.25%. Income ax and social conribuion raes are chosen opimally o maximize he social welfare. 42 We have considered a fixed reiremen age so ha equilibria under he same birh raes were comparable. The opimal policy mix remains he same: posiive rae of income ax and zero social conribuions (Table 4). 42 To check he robusness of resuls he change in was considered for differen reiremen ages, for from 55 o 70. Since he resuls for differen reiremen ages are similar, we provide here only he resuls for

21 Table 4. Opimal income ax under differen birh raes and life expecancy 1% 1.25% 1.5% 1.75% 2% 2.5% 3% 1.25% Populaion growh Income ax rae aio of pension fund defici o oupu Populaion growh Income ax rae aio of pension fund defici o oupu nl -0.25% 0% 0.25% 0.5% 0.75% 1.25% 1.75% L 50.3% 48% 46.5% 45.3% 44.2% 42.4% 41.1% d y 8.1% 7% 6% 5.2% 4.4% 3.3% 2.4% 1.43% nl -0.43% -0.18% 0.07% 0.32% 0.57% 1.07% 1.57% L 50.3% 48% 46.5% 45.3% 44.2% 42.4% 41.1% d y 8.1% 7% 6% 5.2% 4.4% 3.3% 2.4% Under an unbalanced pension sysem, he higher life expecancy leads o higher level of per capia capial, lower share of per capia privae consumpion in he oupu due o he higher oupu and higher governmen expendiure in he seady sae (defined as a fixed share in he oupu). Public deb is higher under higher life expecancy due o he higher governmen expendiure and lower ineres rae, while he opimal income ax rae is higher in general in he seady saes wih higher. 43 Overall, comparison of he seady saes under he same birh rae and differen deah rae i no generally correc due o he differen populaion growh in he seady saes. The pension sysem is run wih a defici. Is share of GDP is he same under differen because a per capia defici of he pension fund is defined by he raio of pensions o GDP is consan (14.7%), while he opimal share of social conribuions,, is zero. Alhough he absolue value of pensions increases wih higher life expecancy due o a higher level of capial, is change is proporional o he change in he oupu (as boh oupu and median wage are funcions of capial). Tha is why a share per capia defici of he pension fund in he per capia oupu remains unchanged. ex, we consider he case of higher labor produciviy. I is modelled as he lower speed,, wih which he produc of labor decreases wih age. Table 5 shows he resuls for 1.25% and 1.1%. 43 For his case a higher precision was applied for he choice of L (he sep equals 0.01%). 21

22 Table 5. Opimal income ax under differen labor produciviy Income ax rae aio of pension fund defici o oupu Income ax rae aio of pension fund defici o oupu nl -0.25% 0% 0.25% 0.5% 0.75% 1.25% 1.75% 1.25% L 50.3% 47.95% 46.5% 45.25% 44.15% 42.4% 41.1% d y 8.08% 6.95% 5.99% 5.15% 4.42% 3.27% 2.39% 1.1% L 50.4% 48.3% 46.8% 45.45% 44.35% 42.6% 41.2% d y 8.32% 7.17% 6.17% 5.29% 4.55% 3.36% 2.47% Opimal income ax decreases wih populaion growh and increases wih labor produciviy. Higher labor produciviy resuls in a higher capial per capia in he seady sae, leading o higher oupu per capia, governmen expendiures and privae consumpion. Higher produciviy leads o a higher wage, increasing he level of pensions o be equal o 30% of he median wage. I pus higher pressure on he pension sysem and, hus, he governmen budge. However, despie he fac ha he defici of he pension fund is higher under higher labor produciviy, public deb is lower a equilibrium wih he higher produciviy due o he higher income ax paymens (driven by he higher wage), which have increased more han governmen expendiures. 4. Opimal fiscal insrumens: he role of non-icardian agens In his secion we consider he opimal choice of fiscal insrumens under differen condiions. Firs, we consider he opimal choice of income ax in an economy wihou a pension sysem (zero social conribuions and pensions). This case can provide insigh ino how key variables of he model depend on he share of non-icardian agens. We use his seady sae as a benchmark o see he consequences of he inroducion of a pension sysem. The pension sysem is inroduced in Subsecion 3.2, which provides he resuls for he opimal choice of income ax and social conribuions. In Subsecion 3.3 he se of policy insrumens is exended o include opimal governmen expendiures. The se of policy insrumens includes income ax, social conribuions share of he median wage and governmen expendiures share of oal oupu. However, in Subsecions icardian and non- icardian consumers pay he same social conribuions. Subsecion 3.4 provides he resuls for he case of possible discriminaion of agens by heir ype, icardian and non-icardian. This is modelled by seing differen social conribuions depending on he ype of he agen Opimal income ax Firs, le us consider he opimal choice of income ax and he corresponding seady saes. In he absence of a pension sysem, he opimal ax rae, idenical for boh ypes of consumers, does no depend on he share of non-icardian agens. A ax rae of 15.5% is he 22

23 lowes ineres rae in found equilibria under differen parameer combinaions (which saisfies he condiions). 44 Equilibria wih a higher rae of income ax are characerized by lower invesmen in capial per capia, which leads o lower welfare. As a resul, he lowes feasible equilibrium ax rae is opimal. The adjusmen of he ineres rae and public deb ensures he fulfilmen of he governmen budge consrain wih he ax rae saying consan. The higher he share of non- icardian agens, he lower he level of capial in he economy, as fewer agens can hold savings. The lower level of savings is accompanied by a higher ineres rae, which exceeds G he populaion growh. The resuls are provided in Table 3.6, where a is he share of public y deb in oupu. The resuls are calculaed wih a fixed value of governmen expendiures a 10% of he oupu (close o he average opimal level of governmen expendiures for 0.5, see Subsecion 3.3). As a robusness check we compue he resuls for 0.25 (see Appendix). The share of governmen expendiure in he uiliy Oher parameers are equal o he values in baseline calibraion ( 2.5%, 1.25%, 60 ). Table 6. Seady saes wih he opimal choice of income ax rae The share of non-icardian consumers 10% 20% 30% 40% 50% 60% 70% 80% 90% L 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% 15.5% k T c y 60.0% 60.6% 61.3% 62.1% 62.9% 64.0% 65.1% 66.4% 68.0% G a y 70.5% 58.6% 48.8% 40.6% 33.8% 28.0% 23.1% 18.9% 15.3% r 1.7% 1.8% 1.9% 2.1% 2.2% 2.4% 2.7% 3.0% 3.4% T The share of oal consumpion in oupu, c, increases wih he higher share of nony icardian consumers, as fewer resources are direced o savings. Wih he value of per capia consumpion slowly decreasing wih higher, he share of consumpion increases mainly due o lower per capia oupu. For commonly used values of he share of non-icardian consumers, in he range of 40-50%, he model provides an esimae of consumpion a abou 62%, which conforms o he OECD daa. 46 The allocaion of oal consumpion beween he wo ypes of consumers is illusraed by Figure 5. While per capia consumpion of non-icardian consumers is slowly decreasing wih, he wage, which defines heir consumpion, is decreasing wih a fall in capial. The ineres rae on he savings of icardian agens almos doubles wih rising from 10% o 90%, increasing he income of icardian agens. This leads o a significan inequaliy in consumpion of icardian and non-icardian agens wih an increase in he share of non- icardian agens. 44 The choice of ax rae in equilibrium is limied by he equilibrium sabiliy condiion (forms lower consrain) and by he resricion ha public deb should no exceed 1.5 imes GDP, which provides he upper consrain. 45 When 0.25 he opimal level of income ax is higher due o higher public expendiure. 46 According o he OECD esimaes an average share of final household consumpion in GDP for is 61.02%. For 2016 is esimae is a 60.7%. For he USA he corresponding esimaes are 68.36% in and 68.84% in 2016 (OECD, aional Accouns a a Glance, aional accouns daabase). 23