Multiple Objectives in Fiscal Policy: the Case of Taxation

Transcription

1 Muliple Objecives in Fiscal Policy: he Case of axaion Susheng Wang July 27 Insead of a single objecive such as uiliy maximizaion or social welfare maximizaion, his paper discusses he deerminaion of a fiscal policy by several poenial objecives. Besides pure economic facors, poliical and social facors mus affec decisions in fiscal policy. o sudy muliple objecives in fiscal policy, his paper akes axaion as an example. o undersand axaion and o compare differen opions of axaion, we se up an overlappinggeneraions life-cycle model o analyze implicaions of various ax opions on wealh accumulaion, social welfare, poliical suppor, and economic equaliy. Fields: macroeconomics, public economics, poliical economy Keywords: axaion, wealh accumulaion, social welfare, poliical suppor, economic equaliy Address: Deparmen of Economics, Hong Kong Universiy of Science and echnology, Clear Waer Bay, Hong Kong. s.wang@us.hk.

2 . Inroducion Economiss have used o he assumpion ha every economic problem has a single objecive. his single objecive has ypically been uiliy/profi maximizaion or social welfare maximizaion. his paper admis o he fac ha some decisions may no be deermined by a single objecive or even an economic objecive. We discuss he deerminaion of a fiscal policy by several poenial objecives and compare he soluions under differen objecives. here are wo ses of governmen policies: moneary policies and fiscal policies. Moneary policies are ypically independen of governmen inerference; bu, fiscal policies are deermined by he governmen and he parliamen. he reason for his difference is he difference in he objecives of hese wo ses of policies. Being disincively differen from he deerminaion of moneary policy, he deerminaion of fiscal policy is affeced no only by economic facors, bu also by social and poliical facors. In his paper, we ake a governmen-managed pension plan as an example and consider various ax opions ha he governmen can poenially use o finance he pension plan. here are many ways o ax; besides economic consideraions, social issues, such as income inequaliy and poliical sabiliy, influence he adopion and acual implemenaion of a ax policy. o look ino his maer, his paper akes a disinc approach o axaion. Raher han looking a a single economic objecive, we value differen opions of a ax policy in erms of wha we hink are he acual forces ha influence heir adopion and implemenaion. Insead of finding a bes policy based on a single crierion, we discuss he cons and pros of differen opions. Specifically, we invesigae and compare alernaive ax opions in a single framework by four objecives: heir poliical suppor, heir social welfare implicaions, and heir economic impac on wealh disribuion and wealh accumulaion. We also look ino he relaed issues of how changes in reiremen age and changes in he populaion share of reirees affec ax burdens and wealh accumulaion. In an overlapping-generaions (OG) life-syle model, we apply alernaive axes o financing a balanced governmen pension plan. We find ha all axes resul in subsanial social welfare loss and aggregae wealh reducion, while hey may or may no improve equaliy. More specifically, consumpion ax resuls in he leas ax burden and welfare loss, i is medial in wealh reducion and equaliy improvemen, bu i has he leas poliical suppor. Income ax has he mos poliical suppor, i is medial in welfare loss, bu i conribues he leas o equaliy improvemen and resuls in he mos wealh reducion. Lump-sum ax incurs he mos welfare loss, i is medial in poliical suppor, bu i causes he leas in wealh reducion and is he bes in equaliy improvemen. Furhermore, we find ha early reiremen and an increasing populaion share of reirees canno be major causes for he recen increasing srain on pension sysems in indusrialized counries. Page 2 of 9

3 here are wo ineresing observaions from our analysis. Firs, i is ineremporal disorion across periods (he disorion on he behavior of ineremporal subsiuion), raher han price disorion wihin each period, ha is he key driving force in our conclusions. Lump-sum ax has only ineremporal disorion across periods, while ohers have boh ineremporal disorion across periods and price disorion wihin each period. Lump-sum ax can hus reveal he relaive imporance of he wo kinds of disorions. he fac ha lump-sum ax, which has no price disorion bu has ineremporal disorion, creaes as much welfare loss as ohers from our analysis is one indicaion. Second, he exisence and populariy of some ax opions in realiy can be well explained by poliical suppor, bu no by he oher hree facors, especially no by social welfare. his is no surprising, as we have winessed many failures of policy recommendaions ha are sound in erms of economics principles bu are lacking in he undersanding of he poliical economy and insiuional consrains. 2 his paper proceeds as follows. In Secion 2, he model is developed and a closed-form soluion is derived. In Secion 3, he model is numerically simulaed for cerain realisic siuaions, from which we draw conclusions on he four key aspecs of he fiscal policy: wealh accumulaion, social welfare, poliical suppor, and economic equaliy. Secion 4 discusses hree minor issues. Finally, Secion 5 concludes wih a discussion on he robusness of our conclusions. All he derivaions are given in he Appendix, which is available by he Model 2.. he Seup We adop he model from Caballero (99) and Irvine Wang (994), excep ha we have a more general oupu process. Consider an overlapping generaions economy in which each agen may live for infinie periods. 3 Individuals are idenical a birh, wih he same preferences and endowmens (a wealh endowmen A and an income endowmen h ). he chance of surviving hrough a period is p for a working individual and is p for a reiree, where 2 A well-known real-world example is Mrs. Clinon's medicare proposal, which is derived from economics principles bu fails o address poliical concerns and insiuional consrains. Her proposal was buried by he parliamen. 3 Allowing for infinie lifeime drasically reduces he complexiy of our formulas. We will conrol he survival rae so ha he populaion size of hose individuals who live an unreasonably long life is oo small o affec our conclusions. Also, since he probabiliy of living for ha long is very small, individuals will behave as if hey have limied lifeime. Page 3 of 9

4 p, p [, ]. he size of newborns is assumed o be n p p + p p so ha he oal populaion size remains a, where is he reiremen age. 4 here is a pension scheme: while working, each person in each period makes conribuions o he pension plan by paying an income ax τ y, a consumpion ax τ c, a capial ax τ k, and a lump-sum ax x, and afer reiremen, she is given a lump-sum amoun z ou of he pension plan each period. he income process is 5 y b, if, = Bl + h h, if >, () where l is labor, and h is human-capial ha follows a random walk wih a whie noise componen { ε 2 }, where ε N(, σ ), : h = h + ε, + + given h. ha is, he income consiss of a labor income and a random human-capial componen, where h is he iniial human-capial endowmen. 6 he expeced income in each period is E( y )= Bl + h for ; E( y ) = h for >. b Each individual has he same aemporal exponenial uiliy funcion uc ( ) = e θc, wih θ consan absolue risk aversion θ. 7 In our life-cycle model, each person faces a wo-sage problem: a working sage and a reiremen sage. She works in he working sage o earn a labor b income Bl, bu does no work and hence earns no labor income in he reiremen sage. he consumer's lifeime problem is 4 Populaion growh will have imporan implicaions. Our curren seing aims a an economy wih a sable populaion size. 5 We can easily exend he model o allow differen shocks beween pre-reiremen and pos-reiremen periods. his exension, however, will no change our resuls. 6 Exising lieraure on aggregae wealh has been using random-walk shocks for income uncerainy. Inroducing persisency of shocks is sraighforward in our model bu ha will no affec our conclusions. See Wang (2), for example, where persisency of shocks is allowed. 7 A clear advanage of he exponenial emporal uiliy funcion is ha a closed-form soluion can be derived from he model. No oher forms of uiliy funcions can provide a closed-form soluion for a life-cycle model wih income uncerainy. For example, using he CRRA aemporal uiliy funcion, Skinner (988) can only approximae he soluion. Noe ha we have he same conclusions if he aemporal uiliy funcion has he more general form: uc ( ) = ( e θc ). θ Page 4 of 9

5 θ( c ) ( ) ( ) = max λl θ c λl U A E β e + β β e { c}, { l} θ = = + s.. A = RA + I + ( τy) y ( + τc) c x, A = RA + I + ( τ ) y ( + τ ) c + z, > y c lim R ( A+ A) =, a. s. given A, where E is he expecaions operaor condiional on informaion Φ available a ime, c is consumpion, 8 A is individual wealh, I is he inheriance in each period, i is he ineres rae, 9 δ is he rae of ime preference, is he reiremen dae, λ is he marginal rae of subsiuion beween leisure and consumpion, β and β are he effecive dis- p p + δ + δ coun facors ha include boh ime preferences and life uncerainy. he capial ax is levied on capial gains ia, resuling in he afer-ax gross reurn R + ( τk ) i. A is he iniial endowmen of non-human capial and h is he iniial endowmen of human capial. We may hink of h as he iniial endowmen of individual aribues such as alens and being hardworking, and A as he iniial endowmen of moneary wealh. Each individual akes he inheriance as given, bu he economy as a whole will deermine i in equilibrium. he hird consrain in (2) is he so-called ransversaliy condiion. In each period, some people pass away and leave some wealh behind hem. We assume ha inheriances are evenly disribued among all living individuals. Le he oal inheriance in each period be I. Since he populaion size is, each individual receives he inheriance I each period. In paricular, each newborn also receives A = (2) I as an iniial wealh endowmen. Given inheriance I, individuals decide individual wealh profile A in heir problem (2). By he end of a period, he oal wealh lef behind by he dying individuals is he oal inheriance I, i.e., ( ) (3) ( pn ) p A+ p np ( p) A= I. = = + his is he equilibrium condiion ha deermines he equilibrium inheriance I. 8 b Since he compeiive wage rae is bbl b b, he wage income is bbl. he profi is hus π =( bbl ) + ε. he profi can be disribued as bonuses, benefis, and wage increases. A small par of i ha is disribued o share holders may be exemped from he income ax. 9 Here, i can be considered as he real ineres rae for an annuiy or a long-erm indexed bond. he sronger condiion lim R A =, he bounded borrowing condiion, gives he same soluion. Page 5 of 9

6 We adop he following noaion: p p r ( τk ) i, R + r, α, β, β, R + δ + δ τ θ( τy) σ θ( τy) σ c β + τc β Γ ln +, Γ ln +. θ α 2( + τ ) θ α 2( + τ ) he average ages of he working populaion and reirees are, respecively, c p, +. p p p he aggregae income, aggregae consumpion and aggregae wealh are, respecively, = = +, = = + = = + Y n p y + n p p y, C n p c + n p p c W n p A + n p p A, where np and np p are respecively he populaion sizes of age- cohors for he working populaion and for he reirees, and { y } and { c } are respecively he realized income and consumpion across generaions a ha momen of ime, as here represens he age group wih age. If he pension accoun is balanced, Y is also he average per-capia disposable income. c A any momen of ime, he axes are τ Y y, τ C, τ iw and p c k nx, p np paymen o reirees is z p. he pension accoun balance is hus p p P τyy + τcc+ τkiw + n x n z. p p and he pension (4) he pension paymen z, he balanced pension paymen, ha balances he pension accoun ( P = ) is τ c Γ Γ z = ( τy) y ( + τc) λl + ( Γ Γ ) +Γ + τ c r α p p I + τ Y + τ iw + n x + + ( τ )( Y α y) np p np ( p ) τc ( τ ) y k y + c α Γ Γ p x z ( c ) l x n + α τ λ + + Γ r p α. (5) Page 6 of 9

7 2.2. he Soluion Le profiles: l b τ y bb τ λ + l c b and y Bl. Problem (2) implies he opimal labor and income l if, y h, if, + = and y = (6) if > ; h if >. he inheriance is n p I = α Γ Γ Γ Γ α ( τy) y ( + τc) λl x z+ + p n α p r r Γ Γ + ( p ) + p. r r (7) he individual wealh profile is α α Γ Γ Γ A = I + τ y y ( c) l x z r + τ λ + +, r r if, α Γ Γ Γ Γ Γ A = I + τ y y ( τc) λl x z r , r r r if >. (8) he aggregae wealh is ( ) n p Γ np Γ np Γ Γ W = I p r p r p r (9) n Γ Γ p p ( y) y ( c) l x z α α + τ + τ λ + α + p. r r α p p p he individual saving profile is Γ Γ s = α τ y y ( + τc) λl x z+ ri + Γ, r α if, Γ Γ s = ( α ) τ y y ( + τc) λl x z + ( Γ Γ ) ri + Γ, r α if >. Γ and Γ are hus he slopes of savings over ime. he individual consumpion is We ignore he possibiliy of negaive consumpion, in which case he opimal consumpion is zero. For our analysis in Secions 3 and 4, negaive consumpion happens only for a very iny porion of he populaion. For example, even for he case wih a consumpion ax in able 2, negaive consumpion only happens when he oal consumpion from hose who live over = 42 is only np ( p ) c= 5.3, =42 which is oo small an error o affec our conclusions. Page 7 of 9

8 I Γ Γ c = + τ y ( y α y) + α x+ z+ ( + τc) λl + x+ if, Γ, + τ c α r α I Γ Γ c = + τ y y + ( α ) y ( α ) x+ z+ ( + τc) λl + + z + τ c α r + ( Γ Γ ) + Γ, if >. α Finally, he maximum uiliy or he welfare is V ' θ I Γ Γ Γ ( ) λθl α + ( τ y )( α ) y h α x z x τ c α r α = e. () rβθ Several remarks are in order. Firs, consumpion in he working sage is sochasic, ye savings is nonsochasic. his is because consumpion adjuss fully o he income shock in each period. As a resul, aggregae wealh W is nonsochasic. he same conclusion holds in Caballero (99) and Irvine Wang (994). Second, even hough adjusmens of wealh can be passed among all generaions in his ype of model, here is no volunary beques moive. Consequenly, inheriances come solely from involunary bequess. 2 hird, he absence of income insurance in our model is realisic and sandard in his field, due o he moral hazard problems ha would be associaed wih is inroducion. In oher worlds, income uncerainy in our model refers o he uninsurable income risks. Fourh, he absence of an insurance marke for lifeime uncerainy in our model is based on Yaari's (965) resul ha he condiions governing he evoluion of he equaions of moion for savings and consumpion are he same in he no-lifeime uncerainy case as in he case where lifeime is uncerain bu wih an annuiy marke where he rae of ineres is `fair'. hus, if he erminal condiions on he problem were he same in each of hese cases, he acual pah of wealh accumulaion would be he same, and he inclusion of a marke for life insurance would be equivalen o he pah under a cerain lifeime. 3 Fifh, we do no inroduce physical capial in our model. I is a sandard approach in his field, in which an invesmen decision is aken as a given. his can firs be jusified by Fisher's Separaion heorem (Hirshleifer 984), which saes ha, under a perfec capial marke, he invesmen decisions made by a firm and he consumpion decisions made by consumers can be separaed. Second, wih more and more inegraed inernaional rade and capial markes, 2 We argue ha, in he real world, much of bequess is involunary. echnological knowledge, infrasrucure, business links and organizaions, legal and poliical sysems, and educaion, which accoun for he majoriy of inheriances, are mainly in he form of involunary bequess. 3 Kolikoff (988) has, however, argued ha fair annuiies are difficul o supply in pracice because of agen heerogeneiy and self-selecion. Page 8 of 9

9 physical saving (in goods) is no longer an imporan elemen of economic growh. A counry can purchase goods from abroad when is physical saving is in defici; i can expor goods abroad when is physical saving is in surplus. Wha maers is he purchasing power. In he shor run, he purchasing power can be borrowed from domesic and inernaional capial markes. Bu, in he long run, purchasing power mus come from he financial savings, i.e., he aggregae wealh, ha a counry possesses. Sixh, due o an expeced income drop, an individual will have a consumpion drop a reiremen, bu his drop is accompanied by a drop in labor so ha he discouned marginal uiliy of consumpion keeps he same hroughou he individual's enire lifeime. Sevenh, allowing differen survival probabiliies beween reirees and he working populaion is unique in our model, and his feaure is imporan for our resuls. We can easily exend our model o allow differences in discoun raes of ime preferences and random shocks in income, bu hese exensions will no yield subsanially differen resuls. Las, he wage rae is endogenously deermined in our model. We can see from (6) ha he labor income will respond o changes in axes and in parameers b and B ha affec he incenive o work. 3. he Choice of ax 3.. Wealh and Welfare Effecs By he same approach as in Caballero (99) and Irvine Wang (994), we choose he following benchmark parameer values: = 45, Y =, λ =, b =.6, θ =.3, δ = %, i = 4%, p = 98%, p = 9% σ/ Y = %, h / Y = 2%. he real ineres rae i is se a 4%, and he rae of ime preference δ is se a %. he difference i δ represens he degree of preference for a growing consumpion sream (he ineremporal subsiuion moive). he real ineres rae has ypically been chosen o be beween 3% and 5% in he exising lieraure; for example, Skinner (988) chooses 3.7% and Irvine Wang (994) choose 5%. Since he survival probabiliy is par of he discoun facor and is se separaely in our model, we have deliberaely chosen a smaller discoun rae, δ =%, insead of a ypical choice of δ =2% (which implicily includes a survival rae). he survival probabiliy of a working person is se a 98% and he survival probabiliy of a reiree is se a 9%, which give a realisic populaion share of reirees a.9%. he working life is se a 45 years, assuming ha people sar o work a age 2. By he choice of p and p, he average age of he working populaion is 4 years old, and he average age of reirees is () Page 9 of 9

10 75 years old. As Proposiion 6 shows, he value of Y is of no consequence o our conclusions; we will hus choose B such ha Y =, and se he coefficien of absolue risk aversion θ a 3%, which gives rise o a popular choice of relaive risk aversion θ Y =3. he measure of income uncerainy σ /Y is se a %, which is consisen wih he values chosen by many ohers. 4 Since he marginal rae of subsiuion λ has no influence on our conclusions, we arbirarily se i o. he income endowmen h is arbirarily se o 2. In a producion funcion of he ype y = l b k b wih labor inpu l and capial sock k, he labor elasiciy b is known in growh lieraure o be abou.6; we hus choose b =.6. Also, in our benchmark, he sample values of shocks across all generaions a he benchmark are se o be zero, i.e., ε =for all. Our model is in fac quie sable in he sense ha very differen choices of parameer values will no change our main conclusions. Due o his reason, our choices of parameer values are as simple as possible; for example, we se σ / Y = %, bu no 8% or 2%, alhough hey are all permissible in he lieraure. We can now invesigae he impac of alernaive axes on aggregae wealh and social welfare. We will se a pension paymen z a a level and discuss he effecs of differen ax opions ha finance he pension. 5 Specifically, given an arbirary pension paymen of 2% of he average income y, consider four possible balanced pension schemes ha are respecively financed by an income ax, a consumpion ax, a lump-sum ax, or a capial ax. We will look a he wealh-income raio W / Y o see he impac of a ax on wealh accumulaion; we will find he balanced ax rae ha saisfies (5) for a given zy /; and we will also find he cos of ax as he increase in h o compensae he loss of welfare due o he ax. We find: able : Balanced axes for zy / = 2% W / Y No axes 739. balanced ax cos of ax a Income ax %.9% Consumpion ax %.% Lump-sum ax % 5.% Capial ax 489..% 23.% a Lump-sum ax and cos of ax are expressed as percenages of Y. Here and in oher ables, he lump-sum ax and he cos of ax are expressed as percenages of naional income. 4 E.g., MaCurdy (982), Caballero (99), Guiso e al. (99), and Irvine Wang (994). Caballero (99) esimaed i o be abou %. 5 Ohers may rea a real-world pension paymen as an opimal oucome and use i o deermine an opimal ax rae. We prefer o ake he pension paymen as a given, which may be differen from he opimal pension paymen. Imposing he real-world pension paymen o be opimal may be oo srong a requiremen. Page of 9

11 By Summers Carroll (987, able 5), he realisic pension paymen is 4% of he average working income. For his case, we find: No axes 739. able 2: Balanced axes for zy / = 4% W / Y balanced ax cos of ax Income ax % 24.4% Consumpion ax % 22.7% Lump-sum ax % 3.% Since capial ax canno raise enough funds o finance z =.4 y, i is no included in able 2. Noice ha our aggregae wealh figure under he income ax in able 2 is fairly close o he sylized fac ha aggregae wealh is abou hree imes of naional income: W / Y 3 (we refer o income ax since pension is ypically financed by an income ax in realiy). Boh ables and 2 indicae: Proposiion. () All he axes resul in subsanial wealh reducions and welfare losses. 6 (2) Consumpion ax resuls in he lowes ax rae and he leas welfare loss, alhough i is medial in wealh reducion. (3) Income ax resuls in a much larger wealh reducion han consumpion and lump-sum axes, alhough i is medial in welfare loss. (4) Lump-sum ax incurs a significanly larger welfare loss and ax rae han income and consumpion axes, bu i causes he leas wealh reducion. (5) Capial ax has a limied financing capaciy and incurs a subsanially larger welfare loss and wealh reducion han ohers. In shor, by denoing τ wealh τ if ax rae τ resuls in a smaller wealh reducion han ax rae τ, and τ welfare τ if τ resuls in a smaller welfare loss han τ, we have x τ τ τ, τ τ x τ. wealh c wealh y wealh k c welfare y welfare welfare k We end o hink ha lump-sum ransfers are harmless, which is, however, no longer rue in a life-syle model. All forms of axes resul in disorions in ineremporal decisions. his ineremporal disorion may ouweigh he disorions on prices and working behavior. One 6 he welfare loss is a one-ime loss for he whole lifeime of an individual, raher han a repeaed annual loss. Page of 9

12 posiive aspec of income ax is ha i reduces income risk. One posiive aspec of consumpion ax is ha i is a broadly based ax, which resuls in less ax burden and welfare loss for everyone. Lump-sum ax does no have eiher of hese advanages and is herefore economically inferior Economic Equaliy Governmens serve as economic organizaions as well as poliical organizaions. o undersand policy issues, we should also look a he poliical role of governmens. his and he following secions discuss poliical implicaions of fiscal policy. An imporan jusificaion for a paricular social program is is effec on wealh disribuion. Bearing in mind a close relaionship beween social welfare and inequaliy indices, we look a how differen policy opions affec economic equaliy. We firs draw he individual wealh profiles across lifeime for he hree axes in able 2 in he following diagram. A Income ax Lump-sum ax 2 Consumpion ax Figure. Wealh profiles for he cases in able 2 A casual observaion of his figure suggess ha i is reirees' wealh levels ha are mos affeced by he choice of axes. In paricular, lump-sum ax resuls in higher wealh levels for boh he young and he old. Alhough consumpion ax burdens reirees more han income ax does, reirees have much higher wealh levels under a consumpion ax han under an income ax. As he average individual wealh is W, he coefficien variaion is 7 7 See, for example, Lamber (993) for he definiion of CV. Noice ha high values of CV mean high inequaliy. Page 2 of 9

13 CV = n p A W n p p A W. W 2 2 ( ) + ( ) (2) = = + For he cases in able 2, he values of CV for no axes, consumpion ax, income ax, and lump-sum ax are respecively.534,.563,.594, and.527. An ineresing observaion from hese daa is ha pension may or may no improve equaliy, depending on how i is financed. Also, lump-sum ax is effecive in improving equaliy, while income and consumpion axes may worsen i. For he cases in able, he values of CV for no axes, consumpion ax, income ax, lump-sum ax, and capial ax are respecively.534,.5,.5,.494, and.52. In his case, all he axes improve equaliy. However, he capial ax is he leas effecive. Again, lump-sum ax is he bes choice. Noice ha he CV daa are consisen wih he shapes of he wealh profiles in Figure. Proposiion 2. () Pension may or may no improve equaliy, depending on how i is financed and on he amoun of pension paymen. A large pension paymen can worsen equaliy. (2) Lump-sum ax is he bes choice for improving equaliy, and capial ax is he wors choice. In shor, by denoing τ equaliy τ if ax rae τ resuls in beer economic equaliy han ax rae τ, we have x equaliy τc equaliy τy equaliy τk Poliical Suppor Wha are he poliical forces ha suppor or oppose an expansion of a given pension? Wihou he loss of generaliy, assume ha here are no axes a presen, and no one expecs a pension in his/her plan. Now, suppose ha he governmen unexpecedly proposes a balanced pension. Will his pension be suppored? Wihou a pension plan, he welfare of an individual of age wih curren wealh ˆ and income endowmen h is and he welfare of an individual of age > ˆ ˆ ˆ' A ˆ αˆ αˆ yˆ h ˆ Γ Γ ˆ ˆ Γ θ λl yˆ λl αˆ i + Γ i i ˆ V = e, (3) iθβ is ˆ ˆ ˆ' ˆ ˆ' ˆ' A α ˆ h ˆ Γ Γ Γ Γ ˆ Γ θ λl yˆ + + αˆ + Γ i i i i ˆ V = e, (4) iθβ where we use a ha o represen he parameers and variables before he pension is inroduced and where Aˆ is defined in (8) wih no axes. A Page 3 of 9

14 Wih a pension plan, he welfare of an individual of age wih curren wealh and income endowmen h is V θ A α α Γ Γ Γ ( τy)( y h ) x x z ( τy) y ( τc) λl ( τc) λl Γ + τc α r r r = e, (5) rθβ and he welfare of an individual of age > is A V θ A α Γ Γ Γ Γ Γ ( τy) h z x z ( τy) y ( τc) λl τc α r r r r = e Γ, (6) rθβ where A is defined in (8) wih axes. he welfare profiles of he four cases in able 2 are depiced in he following diagram. he curve wihou axes is defined by (3) and (4), and he curves wih axes are defined by (5) and (6). U No axes Lump-sum ax Income ax Consumpion ax Enlargemen Income ax Lump-sum ax Consumpion ax Figure 2. Welfare profiles wih and wihou axes Proposiion 3. Income ax has he mos supporers, consumpion ax has he fewes supporers, and lump-sum ax is in beween. In shor, by denoing τ suppor τ if ax rae τ gains more suppor han ax rae τ, we have τ y suppor x. suppor τc he younger age groups are agains he pension because of he deadweigh loss associaed wih i. he older age groups benefi from no paying he axes in heir early years; and when such benefi is sufficien o cover he deadweigh loss, hey become supporers of he pension. Since an income ax axes reirees less (no labor income o be axed), i wins he mos poliical suppor. Since a consumpion ax evenly axes everyone, i has he leas suppor. Page 4 of 9

15 Le ˆ be he age ha separaes hose who suppor he pension from hose who are agains i. Denoe ˆ as ˆ c, ˆy or x ˆ, respecively, if i is financed by a consumpion ax, an income ax or a lump-sum ax. he hree crossing poins in Figure 2 give he locaions of his ˆ for he hree ax sysems in able 2. We find ˆ c = 4.7, ˆ y =3.5 and x ˆ = 2., by which we find ha 9.% of he populaion suppor an income-ax-financed pension, 62.% suppor a consumpion-ax-financed pension, and 68.3% suppor a lump-sum-ax-financed pension. I is surprising ha he suppor for he pension can be so overwhelming under an income ax in spie of he large welfare loss as indicaed in able 2! Since he pension gains he majoriy suppor no maer how i is financed, i seems o be a poliically ineviable choice in a democracy. 4. Oher Issues 4.. Populaion Share of Reirees Recenly, an increasing populaion share of reirees has been blamed for causing an acue burden on public pensions in indusrialized counries. o invesigae his maer, consider an alernaive survival rae for he reirees. We choose p =.923, by which he populaion share of reirees increases by 3% o 4.9%. We calculae able 2 again using his survival rae: able 3: Balanced axes for p =. 923 No axes 977. W / Y balanced ax cos of ax Income ax %. 26. % Consumpion ax 6. 46% % Lump-sum ax % % We firs noice ha regarding he choice of ax policy, we sill have he same conclusions as in Proposiion, i.e., he policy choice is unaffeced by an increasing populaion share of reirees. Compared o able 2, he axes in able 3 are all higher, which is expeced. he welfare coss are also higher, which is no necessarily expeced. he consumpion ax becomes even more he preferred choice, as ax raes and welfare coss have increased more for he income and lump-sum axes han for he consumpion ax. his is also rue regarding aggregae wealh, i.e., aggregae wealh increases more for he consumpion ax han for he oher wo axes. Page 5 of 9

16 More specifically, for a 3% increase in he populaion share of reirees, we need o increase he income ax by.%, he consumpion ax by.7%, or he lump-sum ax by.5%. hese ax increases are small, while a 3% increase in he populaion share may ake wo o hree decades. We hus conclude: Proposiion 4. An increasing populaion share of reirees will no subsanially increase social and economic burdens on pensions in indusrialized counries Early Reiremen Many counries, especially developing counries, face early reiremen of heir working populaions. his has been claimed o have a desrucive effec on public pension schemes. Le us invesigae his maer by decreasing he number of working years o =4and calculaing able 2 again: able 4: Balanced axes for = 4 No axes 65. W / Y balanced ax cos of ax Income ax % % Consumpion ax %. 24. % Lump-sum ax % % Again, we firs noice ha regarding he choice of ax policy, we sill have he same conclusions as in Proposiion, i.e., he policy choice is unaffeced by a changing reiremen age. Compared o able 2, he axes in able 4 are higher, which is expeced. he welfare coss are also higher, which is no necessarily expeced. he income ax becomes less an inferior choice, as ax raes and welfare coss have increased less for income ax han ohers. his is also rue regarding aggregae wealh. More specifically, for a 5 -year decrease in he reiremen age, we need o increase income ax by.7%, consumpion ax by.9%, or lump-sum ax by.9%. hese ax increases can be considered small, while a 5 -year decrease in he reiremen age is considered o be a major change in indusrialized naions. We hus conclude: Proposiion 5. A changing reiremen age will no cause a grea srain on public pensions in indusrialized naions. 8 According o he World Bank (994), in he Neherlands, Sweden, and he U.S., in he firs 3 years of he esablishmen of heir public pensions, reirees received large posiive lifeime ransfers, so ha laer reirees suffered negaive lifeime ransfers, which may be an imporan cause for he curren srain on many public pensions. Page 6 of 9

17 4.3. High-income vs. Low-income Counries Should policy choice differ beween developed and developing counries? More specifically, when naional income Y increases, wha happens o he financing opions of a governmen? Our soluion indicaes: Proposiion 6. If he (average) relaive risk aversion θ Y, pension burden zy /, income endowmen h /, Y and income variabiliy σ /Y are he same, and ε = for all, hen W / Y, V / Y, balanced ax raes, he coss of axes, and opimal ax raes are independen of naional income Y (and B and λ). 9 his resul suggess ha naional income should no be a facor in he choice of fiscal policy. In oher words, if he only difference beween rich and poor naions is in heir naional incomes, hen hey should face he same choice of fiscal policy. he realiy seems o bear ou his conclusion, as economies in oday's world end o face similar fiscal problems and adop similar fiscal policies. 5. Concluding Remarks Are our resuls robus? o invesigae his, we ried many differen ses of parameer values, and Proposiions 6 always hold. In fac, he working paper version of his paper esablished he same resuls in a quie differen model seing. he fac ha he four differen sysems in ables 4 all suppor Proposiion is an indicaion of robusness. Also, he working paper version of his paper does no have an incenive componen in income. Ye, he wo versions of his paper give he same conclusions on ax policy. his suggess ha he disorion of axes on working behavior is ouweighed by he disorion on an ineremporal decision. he fac ha he lump-sum ax coss as much as oher axes in erms of wealh reducion and welfare loss indicaes ha he disorion on he ineremporal decision mus be he dominan force driving our resuls. References [] Caballero, R. (99): Earnings Uncerainy and Aggregae Wealh Accumulaion, American Economic Review, 8, [2] Deaon, A. (992): Undersanding Consumpion, Oxford: Oxford Universiy Press. 9 For lump-sum ax, define xy / as he ax rae. Page 7 of 9

18 [3] Domeji, D. and P. Klein (2): Accouning for Swedish Wealh Inequaliy, Working Paper, Sockholm Universiy. [4] Guiso, L.,. Jappelli and D. erlizzese (99): Earnings Uncerainy and Precauionary Saving, Journal of Moneary Economics, 3, [5] Hirshleifer, J. (984): Price heory and Applicaions, 3rd ed., Prenice-Hall. [6] Imrohoroglu, A., S. Imrohoroglu and.j. Sargen (995): A Life Cycle Analysis of Social Securiy, Journal of Economic heory, 6, [7] Irvine, I. and S. Wang (994): Earnings Uncerainy and Wealh Accumulaion: Commen, American Economic Review, 84 (5), [8] Irvine, I. and S. Wang (2): Saving Behavior and Wealh Accumulaion in a Pure Life- Cycle Model wih Income Uncerainy, European Economic Review, 45 (2), [9] Kolikoff, L. (988): Inergeneraional ransfers and Saving, Journal of Economic Perspecives, 2, [] Lamber, J.P. (993): he Disribuion and Redisribuion of Income, Mancheser Universiy Press. [] MaCurdy,. (982): he Use of ime Series Processes o Model he Error Srucure of Earnings in a Longiudinal Daa Analysis, Journal of Economerics, 8, [2] Modigliani, F. and R. Brumberg (954): Uiliy Analysis and he Consumpion Funcion: An Inerpreaion of Cross Secion Daa, in K. Kurihara, ed., Pos-Keynesian Economics, Rugers Universiy Press, [3] Shorrocks, A. (975): he Age-Wealh Relaionship, Review of Economics and Saisics, 57, [4] Skinner, J. (988): Risky Income, Life Cycle Consumpion, and Precauionary Savings," Journal of Moneary Economics, 22, [5] Summers, L. and C. Carroll (987): Why is U.S. Naional Saving So Low? Brookings Papers on Economic Aciviy, 2, [6] Wang, S. (2): Deerminans of Aggregae Wealh, Macroeconomic Dynamics, 4 (), [7] Weil, P. (993): Precauionary Savings and he Permanen Income Hypohesis, Review of Economic Sudies, 6, [8] World Bank (994), ed.: World Bank Policy Research Bullein, Augus-Ocober. [9] Yaari, M. (965): Uncerain Lifeime, Life Insurance, and he heory of he Consumer, Review of Economic Sudies, 32, Page 8 of 9

19 [2] Zeldes, S. (989): Opimal Consumpion wih Sochasic Income, Quarerly Journal of Economics, 4, Page 9 of 9