Government Expenditure, Taxation Modes and Economic Growth

Transcription

1 Lne Bastholm Helled and Sgne Høngaard Andersen Unversty of Copenhagen Department of Economcs Supervsor: Carl-Johan Dalgaard Economc Semnar: Productvty Growth, autumn 2005 Handed n: The 28 th of November 2005 Presentaton date: The 5 th of December 2005

2 1. Introducton Turnovsy the model The model Analyss of the model n the form of calbraton by Turnovsy The uncompensated case The compensated case - dfferent fnancng modes Tax substtuton Structure of government expendture Revson of the model Lesure Analyss of the revsed model Level of taxaton Congeston and productve government expendture Negatve externalty Postve externalty Is a hgh tax rate always bad for economc growth? Barro s model Empercal analyss of the sze of governments and growth rates Dscusson of the mpact of government sze on economc growth Bran dran and optmal taxaton Developed Countres versus Newly Industralzng Countres (NIC) The Turnovsy model n relaton to labor ntensve countres Concluson Appendx References

3 1. Introducton In the recent years, one of the man ssues n the poltcal debate n Denmar concerns the effect of taxes on economc growth. The Scandnavan countres have some of the largest tax rates compared to other western world countres. Therefore, the dscusson n Scandnava has been centered on the ssue, whether these hgh tax rates are optmal for the economc growth process. Some of the European countres have lower tax rates and less economc growth. Off course a lot of other factors play a role n the slow economc growth n these countres, but t does ndeed pose the queston: What s the optmal taxaton level n regard to economc growth? And how do changes n the tax rates affect economc growth? The man contrbuton of ths paper s how government expendture fnanced by dfferent taxaton modes affects economc growth. We defne economc growth as the growth n all economc varables. And we defne government sze as the tax rate. The paper s based on Turnovsy (2004), thereby the paper offsets n some of the latest research n ths area. The ssue of taxaton polcy s not adressed. That s, aspects as redstrbuton and nequalty are excluded. The paper contans changes n fscal polces that have an effect on economc growth. Welfare s consdered n the paper as well, but s not the man subject. The paper s organzed as follows: Secton 2 outlnes the central aspects and the analyss of the model n Turnovsy (2004). Secton 3 covers a possble revson of the model by ntroducng dfferent defntons of lesure. Secton 4 s a dscusson about the optmal taxaton level n relaton to the model by Turnovsy (2004) and Barro (1990) and also contans an examnaton of emprc analyses. Secton 5 dscusses whether the results n Turnovsy (2004) dffer, when a Newly Industralzng Country s consdered. Fnally, secton 6 concludes. 3

4 2. Turnovsy the model 2.1 The model The model analyzes effects of fscal polces n a non-scale growng economy wth publc and prvate captal. The author dstngushes between government expendture on nvestment and government expendture on consumpton fnanced by four dfferent taxaton modes. The taxaton modes are: Captal ncome taxaton, labor ncome taxaton, consumpton taxaton. The publc sector allocates resources to a utlty-enhancng consumpton good. Owng to the defnton of the economy as non-scale, the long-run growth effects are unaffected by changes n tax rates. Fscal polcy n ths sense has accumulated effects on the per capta levels of the economc varables. Therefore, the focus les on the transtonal dynamcs, because the growth rates may be affected by polcy changes n perods of tme durng the transton from one equlbrum to another. The model consders a one-sector economy, where output depends on prvate and publc captal and on endogenously suppled labor. Publc captal generates a postve externalty on producton,.e. the producton functon contans ncreasng returns to scale n labor, prvate captal and publc captal. Because of the dstncton between publc and prvate captal, there exst two-dmensonal transtonal paths. The convergence speed can therefore vary over tme and across varables. Note, the producton functon has constant returns to scale n labor and prvate captal. The producton functon: Y = α(1 l ) 1 σ σ σ > 0, η > 0,1 > σ + η K K η G (2.1) where K s the ndvdual s stoc of prvate captal, K s the stoc of government captal, G for example nfrastructure, and l s lesure. Furthermore, t s assumed that government captal s not subject to congeston. Turnovsy consders a representatve agent wth an nfnte lfe horzon and perfect foresght. To measure welfare a utlty functon of the ndvdual s defned. The representatve agent has the followng utlty functon: θ φ γ Ω = (1 γ )( C l H ) e 0 ρt φ > 0, θ > 0; < γ < 1;1 > γ (1 + φ);1 > γ (1 + θ + φ) dt (2.2) 4

5 where C s consumpton of the ndvdual at tme t. H s total consumpton servces receved from the government. θ and φ measure the mpact of lesure and publc consumpton on the ndvdual s welfare. The agent s captal accumulaton equaton: K& [( 1 τ ) r n δ K ] K + (1 τ w ) w(1 l ) (1 + τ c C T = ) (2.3) where τ s captal taxaton, r s the gross return to captal, δ K s the deprecaton rate of prvate captal, [ 1 τ ) r n δ ] ( K denotes thus the after-tax prvate return to captal, w τ s ncome taxaton, and T = T N s the agent s share of lump sum taxes (or transfers). The government captal accumulaton equaton: K& G = G δ K G G where G s the gross rate of government nvestment expendture, and δ G s the deprecaton rate of publc captal. The government fnances ts gross expendture flows from aggregate tax revenues. The government sets the amount of output, whch wll be spent on the consumpton good and the nvestment good: H = hy G = gy where G and H s the gross expendture on government nvestment and government consumpton, respectvely. It s assumed that aggregate output, prvate captal stoc and publc captal stoc grow at the same constant rate n equlbrum, whch means that output-captal rato and the rato of publc captal to prvate captal reman constant. Furthermore, the fracton of tme spent on lesure remans constant as well. Lesure s complementary to consumpton n utlty. Ths ndcates that the consumpton-output rato ncreases wth lesure. The long-run growth rate of output, prvate captal and publc captal: 1 σ ψ = n 1 σ η (2.4) where n s the growth rate of populaton. It s shown that for the dynamcs to be stable σ +η <1, whch mples that ψ > 0. In order to analyze the transtonal dynamcs about the economy s balanced growth path, the scale-adjusted output s defned: y = α 1 σ σ η ( 1 l) g (2.5) 5

6 The equlbrum dynamcs: & y = (1 c g h) δ K & g y = g δ G ψ g ψ ηg l& = F( l){( σ [1 γ (1 + φ)][ σ (1 c g h) + ) + δ η[1 γ (1 + φ)] ([(1 σ )] + γ ] n + ρ)} G g g y δ (1 σ )[1 γ (1 + φ)]) K where 1 σ l 1 τ w c = θ 1 l 1 + τ c C l(1 l) c, F( l) Y (1 γ ) (1 σ )[1 γ (1 + φ)] l θγ (1 l) (2.6) where the parameters θ and φ are the mpact of lesure and publc consumpton on the agent s utlty, respectvely. The steady state equlbrum of the economy: ~ y 1 c ~ K (2.7) ~ y g ~ = δ G +ψ (2.8) ( g h) = δ + ψ g ~ y 1 ~ K (2.9) ( τ ) σ = δ + ρ + [ 1 γ ( 1+ φ) ] ψ + γn The characterzaton of the steady state equlbrum also ncludes equatons (2.5) and (2.6). The system has two state varables, and g, and one jump varable l. In order to analyze the effects of dfferent polces, t s necessary to defne a welfare functon, whch contans both long-run and short-run welfare of the ndvdual: ρt θ φ γ ρt W = Z( t) e dt = (( C N) l H ) e dt 0 0 (2.10) where Z(t) s the short-run welfare and C/N, l and H are on the equlbrum path. W denotes the long-run welfare. 6

7 The amount of taxaton necessary to fnance prmary defct: V = 0 t s( u)(1 τ ) du 0 T ( t) e dt where = 0 τ (2.11) s( u)(1 τ ) du 0 [ g + h σ τ ( 1 σ ) τ ( C Y )] Y ( t) e dt K w s( 1 τ ) r(1 τ ) δ s the equlbrum rate of nterest. c t 2.2 Analyss of the model n the form of calbraton by Turnovsy The calbraton s done n comparson to a benchmar economy. The parameters used are representatve of the US economy. The calbraton analyss s done by nsertng parameter values n equaton (2.5)-(2.11) The uncompensated case The fscal changes are uncompensated (table A1, secton A), whch s reflected n the large changes n the long-run government fscal balance. The comparatve statc s as follows: An ncrease n government consumpton, h, by 0.04 pct., causes long-run prvate and publc captal stoc and output to ncrease proportonately by 6.6 pct., and the long-run prvate consumpton-output rato s crowded out and reduced by Lesure s reduced by 1.29 pct. ponts. Therefore, the margnal productvty of prvate and publc captal s rased and thus output s rased as well. In accordance wth equaton (2.11) the surplus, V, of the long-run government balance s reduced by 49.7 pct. Short-run welfare gans are ncreased by 0.66 pct., and long-run welfare gans are ncreased by 1.98 pct. An ncrease n government nvestment, g, by pct., causes prvate captal and output to ncrease proportonately by 44.6 pct., and publc captal more than doubles by 288 pct., because government nvestments generate publc captal drectly. The larger demand for captal by the government crowds out nvestment n prvate captal. Therefore, the growth rate of prvate captal s reduced n the short run. Because of an ncrease n the relatve scarcty of prvate captal, ts productvty s ncreased. The hgh productvty of prvate captal rases ts growth rate along wth output and consumpton. The consumpton-output rato s reduced by a lttle less than Lesure s reduced by 1.23 pct. ponts. The publc captal-prvate captal rato s ncreased by 199 pct., because of the large ncrease n publc captal. In regard to the long-run government balance, the surplus s also n 7

8 ths case reduced by 51.3 pct. Short-run welfare gans s reduced by 2.90 pct. but s n the long-run rased by a whole 7.87 pct. The reducton of welfare n the short-run s ceters parbus caused by the short-run reducton n the growth rate of prvate captal. An ncrease n the tax on captal ncome from 0.28 pct. to 0.40 pct. reduces publc captal and output proportonately by 16 pct., and reduces prvate captal more than proportonately by 30 pct. The output-prvate captal rato and the publc captal-prvate captal rato are ncreased by 20 pct. The hgher tax rate on captal reduces, on mpact, the growth rate of prvate captal. The reducton n long-run prvate captal reduces productvty of labor and causes agents to choose more lesure and consumpton. Lesure s ncreased by 0.69 pct., and the consumpton-output rato s ncreased by The reducton n labor and prvate captal reduces output and the growth rate of publc captal falls as well. As the prvate captal stoc ncrease n relatve scarcty ts productvty ncreases, whch nduce nvestment n prvate captal. In turn, the relatve scarcty n publc captal ncreases, and lewse, the growth rate s restored through more nvestng. Because of the hgher tax level the surplus, V, n the long-run government balance ncreases by 80.2 pct. Short-run welfare gans are ncreased by 3.98 pct. but are n the long-run rased by 3.56 pct. An ncrease n wage taxaton from 0.28 pct. to pct., causes prvate and publc captal and output to ncrease proportonately by 10 pct. Lesure s n ths case ncreased by 2.02 pct, whle there s no effect on the consumpton-output rato. Wage taxaton has a drect effect on the consumers, such that they ceters parbus wll choose to supply less labor. V n the long-run government balance ncreases by 55.1 pct. Short-run welfare gans are reduced by 1.81 pct. and are n the long-run reduced by 2.88 pct. An ncrease n consumpton taxaton of pct. reduces prvate and publc captal and output proportonately by 6.22 pct. Also consumpton taxaton has a drect effect on the consumers. Lesure s ncreased by 1.25 pct. and thus labor supply s reduced. V n the long-run government balance ncreases by 52.4 pct. Short-run welfare gans s reduced by 0.45 pct. and s n the long-run reduced by 1.73 pct. In concluson, captal ncome taxaton restrans economc growth the most n comparson to the other fnancng modes, n the sense that prvate and publc captal accumulaton and output s more reduced. Furthermore, prmary defct n ths case experence a far larger ncrease. Consumpton taxaton s the most plausble mode of taxaton n ths respect. In the realm of structurng government expendture, t s by far more plausble for a government to place government expendture on nvestments rather than consumpton, all though a myopc government would argue that welfare also n ths case s reduced. 8

9 modes s combned. In the next secton, the structure of government expendture and tax fnancng The compensated case - dfferent fnancng modes In the sequent secton the fscal changes are compensated, n the sense that current government defcts, T n equaton (2.11), reman unchanged (table A1, secton B). The effects lsted below can be compared to the effects of a uncompensated case descrbed n the prevous secton. An ncrease n government consumpton, h, by 0.04 pct. fnanced by a consumpton tax, wll leave the net effect unchanged n the sense that the expansonary effect from the ncreased consumpton wll absorb the contractonary effect from the consumpton tax. On the other hand, f the government consumpton s fnanced by a wage tax, prvate and publc captal decrease proportonately by 3 pct. nstead of an ncrease by 6.6 pct. as n the uncompensated case. Lesure ncreases by 0.61 pct. pont. The surplus n the long-run government balance, V, ncreases by 1.24 pct. Short-run welfare gans are ncreased by 0.16 pct. and are n the long-run reduced by 0.46 pct. Fnally, f the ncrease s fnanced by captal ncome tax, the contractonary effect domnates, and therefore, prvate and publc captal decrease wth a larger fracton than before n the uncompensated case. The surplus, V, ncreases by a whole 16.2 pct. And short-run welfare gans are ncreased by 4.77 pct. and reduced n the long-run by 1.34 pct. An ncrease n government nvestment, by pct. fnanced by a consumpton tax ncreases publc captal by pct., because of the drect effect government nvestments have on publc captal. Prvate captal and output ncreases as well, but at a lower rate at 36.1 pct. Prvate captal temporarly declnes durng the transton, because a crowdng effect. Lesure s n ths case unaffected. The surplus of the government balance, V, reduces by 5.23 pct. Short-run welfare gans are reduced by 3.17 pct. but are n the long-run ncreased by a whole 5.92 pct. Welfare gans n the short run s reduced, because an ncrease n government nvestment has no ntal benefts on welfare. Ths can be seen n relaton to the fact that captal s a state varable,.e. captal s predetermned. On the other hand, f government nvestment s fnanced by a wage tax, lesure ncreases by 0.66 pct. pont. The effect on the other varables s nearly the same as when consumpton taxaton was the fnance mode, although the ncrease n prvate and publc captal and output here s less. Fnancng an ncrease n government nvestment by a captal ncome tax wll ncrease prvate g 9

10 captal by only 2.67 pct. and ncrease publc captal by pct. Prvate captal s n the short run relatvely scarce, whch generates an ncrease n relatve productvty of prvate captal. Therefore, n the long run prvate captal ncreases slghtly. Output ncreases by 22.3 pct. The consumpton-output rato decreases slghtly, and lesure decreases by 0.57 pct. pont. The surplus, V, ncreases by 3.39 pct. Short-run welfare gans are ncreased by 0.69 pct. and are n the long-run ncreased by 3.77 pct. In concluson, government nvestment fnanced by a consumpton tax s most plausble wth regard to economc growth. In ths case, prvate and publc captal and output ncrease by a larger fracton than by the other tax fnancng modes. Also prmary defcts are here decreasng by the largest percentage. In the next secton substtutng one tax mode for another s analyzed. In ths secton, focus les on the tax structure Tax substtuton An ntroducton of a consumpton tax at 6 pct. can replace an ncome tax at pct. and leave T n equaton 2.11 unchanged, that s, reman the ntal government defct. In ths case, output and publc captal ncrease by 5 pct., whereas prvate captal ncreases by 10.8 pct. Lesure s slghtly reduced by 0.14 pct. The prmal surplus, V, s reduced by 3.68 pct. The growth rate of prvate captal ncreases n the short-run by about 2.8 pct., whch n turn stmulate publc captal to accumulate as well, because of a temporary hgher productvty n publc captal. Intally, consumpton drops 1 pct., and labor supply ncreases by 1 pct. Short-run welfare gans s reduced by 1.25 pct. and s n the long-run ncreased by 0.94 pct. In concluson, ths change n the tax structure s evdently postve n vew of economc growth and captal accumulaton, however, ths change does not have sgnfcantly large postve effects on welfare, but n any case, welfare s not reduced n the long-run. In the next secton focus les on the structure of government expendture Structure of government expendture If the government desres an ncrease n government nvestment from 4 to 8 pct. of output whle remanng the ntal defct, T n equaton Ths s possble by reducng publc consumpton expendture from 16 to 11.9 pct. Ths change n the structure of expendture ncreases publc captal by pct., whle output and prvate captal s 10

11 ncreased proportonately by 35.9 pct. On mpact, government nvestment crowds out prvate nvestment and prvate captal declnes, whch enhances the productvty of prvate captal, therefore, nvestment n prvate captal ncreases and the prvate captal stoc ncreases as well. Lesure s slghtly ncreased by 0.03 pct. The prmary surplus, V, s reduced by 4.47 pct. Short-run welfare gans s reduced by 5.09 pct. but s n the long-run ncreased by 3.80 pct. All n all, ths change has large effects on captal accumulaton and hereby economc growth. The change has a postve effect on long-run welfare as well. 11

12 3. Revson of the model 3.1. Lesure In the Turnovsy model, there s no complete defnton of lesure, only that lesure s the tme not spent worng,. In a paper by Mless-Ferrtt and Roubn (1998), lesure s defned n three dfferent ways: Raw tme, home producton and qualty tme. In order to extend the Turnovsy model, publc captal needs a broader defnton also ncludng human captal. Ths seems to be a plausble defnton,.e. publc expendture s allocated to the educaton sector. l The defnton raw tme s dentcal to the defnton of lesure n the Turnovsy model, l. Lesure equals the tme not spent on worng or studyng. In the defnton home producton, lesure s produced wth a CRS technology that has the same nputs as the producton functon 1. In the Turnovsy scenaro, the defnton s: l l = K µ G 1 µ ( l K ) ( l K G ) (3.1) K G where s the fracton of prvate captal not spent on producng maret goods. s the fracton of publc captal not spent on producng maret goods. In the producton functon, lesure s now dvded nto two parts. The ntuton of home producton s that there are two consumpton goods: home-produced goods and maret produced goods. These consumpton goods are substtutes. In the defnton qualty tme 2, lesure only requres human captal, whch means n the Turnovsy model that only publc captal must be ncluded n the defnton: l = l G K λ G l (3.2) where λ 1. Note, that f λ = 1 and µ = 0, then qualty tme and home producton are dentcal defntons of lesure. The ntuton of qualty tme s that lesure tme s spent on vstng theaters and restaurants etc.; therefore n ths defnton human captal s essental. In the subsequent secton the defnton of lesure as home producton s consdered. The model wth the defnton of lesure as qualty tme generates dentcal results as n the Turnovsy model, secton 2.2.1, that s, lesure consdered as raw tme. 1 In the paper of Mless-Ferrt and Roubn (1998) human captal s ncluded n the producton functon. In ths presentaton, wth offset n the Turnovsy model, publc captal and prvate captal are the nputs. 12

13 3.2. Analyss of the revsed model When lesure s defned as home producton, a change n consumpton taxaton has no effect on prvate and publc captal and output but maes the agents choose more lesure and less supply of labor. Lesure s here defned as tme spent on producng goods at home, leavng total output 3 unaffected. An ncrease n consumpton taxaton wll smply affect consumer s choce between maret goods and home-produced goods. The ntuton s that all labor, prvate and publc captal s stll beng used n a productve actvty. The home producton model has two consumpton goods. The consumpton good produced by home producton s not beng taxed, and therefore, wth an ntroducton or an ncrease of consumpton taxaton wll reallocate resources from one sector to another. An ncrease n wage taxaton has the same effect as when lesure s defned as qualty tme or raw tme. Agents wll choose to supply more tme on ther home producton, because ths sector s not tax deductble. However, n ths case, total output wll be unaffected or reduced by less compared to the other defntons of lesure. An alternatve way to defne lesure could be to nclude all three defntons n one model, meanng that when the agent s choosng lesure, he can decde how to dstrbute hs lesure tme between the three alternatves. One could also say that ths would be a more realstc defnton. The overall mpact on output under ths defnton would depend on what share the agents would choose to spend on each type of lesure, when changes n fscal polcy s made. All n all, the results n the Turnovsy model may be affected by changng the defnton of lesure to home producton. In partcular, the effect on output n the model s affected. A defnton of lesure ncludng all three alternatves may be more plausble. 2 For more detals on lesure as qualty tme see: Becer (1965) and Hecman (1976) 3 Total output = maret goods + home-produced goods 13

14 4. Level of taxaton In the Turnovsy model, one of the man conclusons s that n general consumpton taxaton s the most desrable fnancng mode n regard to economc growth. On the other hand, taxaton on captal ncome s the most dstortonary fnancng mode and hampers economc growth the most. Emprcs show that there n fact s captal ncome taxaton and wage ncome taxaton n all OECD countres. The followng fgure shows the structure of taxaton fnancng n dfferent country groups. Fgure 1 Source: Doménech and Garca (2002), fgure 1 The fgure shows that consumpton tax rates are at a relatve low level n comparson to captal ncome tax rates and wage ncome tax rates, whch n some ways contradcts the results of the Turnovsy model. Turnovsy s model s focusng on changes n the taxaton and does not consder the taxaton levels. In ths chapter taxaton levels wll be consdered and dscussed n comparson to the results of the Turnovsy model. 4.1 Congeston and productve government expendture The man purpose of ths secton s to dscuss two effects on the economy, whch are generated by congeston and productve government expendture. In the Turnovsy model, congeston s assumed to be non-exstent, and the effect of productve government expendture needs a more detaled dscusson than what s put forth n the Turnovsy paper. 14

15 4.1.1 Negatve externalty Turnovsy mentons that congeston s dsregarded n the model. In the numercal analyss he taes nto account ths congeston by lowerng the elastcty of publc captal compared to the value suggested by Aschauer (1989). Theoretcally, congeston generates a negatve externalty on producton. In maret equlbrum, t may be Pareto optmal to tax producton, because frms do not tae nto account ths externalty, whch means there s too much captal accumulaton Postve externalty In the Turnovsy model, publc captal generates a postve externalty on producton. Because the government does not charge a fee, ths externalty can create a socalled resdual ncome n producton. 4 Followng ths noton, the rate of return to prvate captal and labor wll therefore not be equal the margnal products. The margnal products n the Turnovsy model are: Y r = K = σ Y K Y Y w = = (1 σ ) N(1 l)) (1 l ) ( When productve publc captal enters the producton functon, the rates of return are hgher than the margnal products. In order to elmnate the resdual ncome n producton, Doménech and Garca (2002) argue that t s necessary to mae an assumpton about the dstrbuton of total ncome between these two prvate factors. In ths sense, an optmal tax on the prvate factors should exactly equal the dfference between the rate of return and the margnal product stemmng from the postve externalty of publc captal. The optmal tax on captal and ncome s, n ths sense, not equal to zero. Hence, taxng these prvate factors has a postve effect on growth and welfare, f the taxes are fnancng publc expendture, whch s spend on nvestments that s growth enhancng. The ntuton s that the frms maxmze profts wthout consderng the externalty and nvest less than what s optmal from a socal planner s vew pont. Captal accumulaton could n ths case be larger, f a socal planner ntervened. In ths sense, the socal planner would be able to ncrease growth by ncreasng captal ncome taxaton and a wage ncome taxaton, such that 4 The dea of a resdual ncome s from Doménech and Garca,

16 the respectve taxaton level s equal to the dfference between the rates of return and the margnal product. Assumng both congeston and productve publc expendture n the Turnovsy model there wll be two contradctory effects at play, a postve externalty and a negatve externalty. These effects may cause captal accumulaton n maret equlbrum to be equal/close to the level of captal accumulaton, whch s socal optmal. In concluson, Turnovsy s model may not be affected f both congeston and productve publc expendture s ncluded. The arguments n ths secton partly explan why most countres do have (postve) taxes on captal ncome and wage ncome, cf. fgure Is a hgh tax rate always bad for economc growth? The man results from the Turnovsy model are that an ncrease n government consumpton wll lead to both a proportonate ncrease n the two captal stoc and output. On the other hand an ncrease n government nvestment leads to proportonate ncreases n prvate captal and output, but to a relatve larger ncrease n publc captal. An ncrease n tax on captal reduces publc captal and output proportonal, and leads to a relatve larger relatve declne n prvate captal. A hgher wage or consumpton tax reduces both types of captal and output proportonal. These results wll n ths secton be dscussed. Most studes on taxaton shows, that lowerng tax on for example ncome and captal have a postve mpact on economc growth. But ths mght not always be the whole story. What happens f the tax revenue s used agan for example government nvestments as educaton, health care systems etc.? Could the mpact of a tax-cut be ambguous? People s state of health and level of educaton s crucal for a country to develop and create growth. Therefore we thn t can be heroc to assume, that a tax-cut wll always have a negatve effect on growth. We thn that t defntely has somethng to do wth what state of development the country s n, on what level the ntal tax rate s on and what the taxes are reused for. In the next secton a model by Barro s consdered to dscuss sze of government n relaton to economc growth. 16

17 4.2.1 Barro s model In Barro (1990) he consders the role of publc servces as an nput to prvate producton, and therefore creates an mportant lnage between government and growth. Barro sets up a model wth nfntely lved households, where the households have a certan amount of tme to spent on wor. Therefore there s no labour-lesure choce n ths model, contrary to Turnovsy s model. Barro ncorporate a publc sector by lettng g be the quantty of publc servces provded to each household producer. The publc servce pr. labor unt g s assumed to be provded wthout user charges and s not subject to congeston 5. He sets up a producton functon. He assumes, that φ g y = φ (3.1) g = A g α. There are constant returns to scale n (prvate captal pr. labor unt) and g together, but dmnshng return to scales n separately. The government expendture s assumed to be fnanced by a flat-rate ncome tax. If we loo at the aggregated economy, ths can be stated n the followng equaton. g = T = τ y (3.2) Ths equaton also tells us, that the government s runnng a balanced budget. From the producton functon we can fnd the margnal product of captal. Ths gves us: y = φ g 1 φ g y = φ g ( 1 η) (3.3) The margnal product of captal s calculated by varyng n (3.1) and holdng g fxed. Ths correspond to the producers belevng that f the amount of hs captal and output changes t doesn t lead to a change n the amount of publc good he receves. η s the elastcty of y wth respect to g, for a gven value of. The part The growth rate of prvate consumpton s gven by the followng equaton: c& 1 y 1 g γ = = (1 τ ) ρ = (1 τ ) φ (1 η) ρ c σ σ (3.4) y ( 1 τ ) s the prvate margnal return to captal, as t wll loo wth a flat ncome tax. As can be seen from equaton (3.4) the ncome tax τ, whch also reflect the sze of government see equaton (3.2), have a negatve mpact on the consumpton growth rate. 5 By excludng congeston t can mean that the productvty of publc captal s hgher than t would be f the model ncluded congeston (cf. secton 4.1). 17

18 Barro states that dfferent szes of governments, whch mean a greater sze of the amount of publc servces and the tax on ncome, have two effects on the growth rate γ. Frst of all, when the ncome tax τ ncreases, the growth rate γ s reduced. Ths s the dsncentve effect, because n ths case an ncrease n τ creates no ncentve for the agents to ncrease nvestments. The second effect s, when there s an ncrease n tax and the amount of publc y servce rse, ths wll have a postve mpact on the margnal product of captal. Ths effect s called the productve effect, because one more unt of prvate producton wll have a postve effect on output and thereby the growth rate. He fnds that the frst effect usually domnates when the government ntally s large, and the second effect domnates when the government s small Empercal analyss of the sze of governments and growth rates In general there s hgh uncertanty about how to test ths relatonshp, and therefore also a lot of dfferent results. Here s a short summary of a few of the results on ths topc. Barro (1991) sets up a cross-secton analyss on 98 countres for the perod , measurng among other thngs how the government consumpton expendture rato affects economc growth. He fnds a sgnfcant negatve relatonshp on 0.12 (s.e. = 0.03) between the government consumpton expendture rato 6 and the real growth rate. When he ncludes the government nvestment raton n the regresson, he fnds a nsgnfcant postve effect fra nvestments to growth on 0.13 (s.e. = 0.10). Fölster and Henreson (2001) fnd a robust negatve relaton between the sze of government, whch they defne as publc expendture, and economc growth. They use a panel dataset to estmates ths effect. In the sample they nclude 23 of the rchest OECD countres and tang the years The robust estmated coeffcents mply that an ncrease n government expendtures by 10 pct. wll lead to a decrease n the growth rate by percentage ponts. OECD members must satsfy certan crteras about growth performance, exstence of democracy etc. Therefore they extend the dataset wth non-opec non-tax haven countres. When they extend the sample wth non-oecd countres, the robust negatve relaton between both tax and growth rate and government consumpton and growth rate remans. 6 averaged over the perod

19 lozdes et.al (2005) uses contegraton to analyze the relatonshp between government expendture and economc growth n Ireland, UK and Greece. They use data from the perod Ther analyss shows no evdence that an ncreasng expendture should lower economc growth. Table 1 summarzes the result of the three analyses. Table 1 Author(s) Countres Data perod Econometrc method Results Barro (1991) Cross-secton Sgnfcant neg. effect from gov. exp. rato on growth. Postve nsgnfcant effect from nv. On growth Fölster and Henreson 23 (OECD) Panel Robust neg. effect from gov. exp. on growth. (2001) Non-OPEC Panel Robust neg. effect from both Countres tax and gov. exp. on growth. Lozdes et. al. (2005) Greece, UK and Ireland Co-ntergraton No sgnfcant effect from gov. exp. on growth. As the latter show there s not a clear emprcal answer to the queston whether government expendture has mpact on economc growth. Ths clearly depends on what econometrc method there s used to answer the queston, and how the data sample s restrcted and selected. One of the reasons that the effect can be very dffcult to measure, s that t s not possble to measure the before and after effects of a change n tax/sze of government. If a country lowers ts tax rate and there s a postve effect on economc growth, t can be dffcult to nterpret whether the postve effect orgns from the tax decrease or another omtted varable. One way to measure an effect caused by fscal changes, could be to use the matchng estmator. Here you need a treatment group, whch n ths case would be countres that have had a change n ther tax rate, and a control group whch would be a group of countres that have not had a change n the tax rate, but have the same characterstcs as the countres that have been "treated". Ths way you would be able to compare two almost smlar 19

20 countres, one that have been treated and one that have not and thereby measure the effect of the treatment. To be realstc t would not be possble to use ths estmator when you loo at countres. It s close to mpossble to fnd two countres that are smlar, and therefore nearly mpossble to measure the actual effects of fscal changes n a country Dscusson of the mpact of government sze on economc growth. 7 It can be dffcult to nterpret how taxes and government expendtures affect economc growth. The negatve effect of government expendtures on growth may especally occur when the expendtures s fnanced by captal and labor taxaton. Dstortonary taxes can have a negatve effect on ncentves to wor and start new busnesses, whch are two of the thngs that are crucal for a country to obtan long run stable growth n the economy. From fgure 1 we can se that all countres are mposng captal tax on ther ctzens, whch does not seem logcal n comparson wth the results from Turnovsy s artcle. Ths could maybe be related to the so-called Wagner's law, whch states that government expendture, as a share of GDP, tends to rse wth lvng standards, reflectng ncomeelastcty demand for government servces. In other words, when the wealth of the populaton ncreases, t wll generate hgher demand for publc servces. To fnance ths hgh demand for publc servces the government must choose a fnancng mode, whch means that n general the taxaton level rses. Therefore, t can be assumed that the dstortonary effects wll mostly occur n hgh-ncome countres. On the other hand, t could be stated that government expendture can have postve effects on economc growth f the tax revenue s nvested n areas that are more closely related to growth such as educaton, nfrastructure, health care and research and development. Ths could especally be assumed to occur at a low level of total government expendtures, Numbers from OECD shows that the member countres spend n the range of pct. of GDP on government expendture. The numbers also show that out of ths, the member countres only use one ffth of the total government expendtures on the areas that s closely related to growth. The above dscusson ndcates that there are two contractonary causaltes between economc growth, taxes and ncome. In turn, economc growth can generate hgher 20

21 ncome, whch wll generate a hgher demand for publc servces and therefore creatng hgher tax rates. On the other hand, hgher taxes can generate a hgher stoc of human captal, whch wll ceters parbus result n hgher economc growth and thereby hgher ncome. All n all the emprcal results on how government sze and economc growth s related seems to be ambguous. It should be remared that n the three artcles we refer to, there s used dfferent econometrc methods. Ths s defntely one reason that the results dffers. We queston f t s at all possble to measure the effect of government sze on economc growth. One way to measure ths could be by usng the matchng estmator, but t could be argued that ths s an unrealstc method to use on countres. 4.3 Bran dran and optmal taxaton In a Developed Country wth hgh levels of taxaton (for nstance Denmar or Canada), t s worth consderng the possblty that there s some upper bound of the level of taxaton. If the ntal taxaton level s very close to ths upper bound, then hgh ncome agents wll ceters parbus choose to mmgrate to another country, where the taxaton level s lower. The loss of human captal could n the long run result n less nnovaton and therefore a reducton n the economc growth. Also the speed of convergence towards the steady state equlbrum may be slower due to lower effcency of labor. In relaton to the Turnovsy model, f the country n queston has a taxaton level very close to ths upper bound, then an ncrease n ether one of the taxaton modes could cause well-educated agents to mmgrate to another country,.e. the country could end up beng bran draned. If the benchmar economy n the model processed very hgh tax levels, the outcome of the analyss may be dfferent. For nstance, an ncrease n government nvestment fnanced by an ncrease n the taxaton of wage ncome may not at all have the postve effect, whch s put forth by Turnovsy. Collns (2004) shows that the effectve tax rate has an mpact on the mgraton pattern. He loos at Canadan and US frst tme unversty graduates. The tax system n Canada and US are very dfferent. The graduates n Canada face a much hgher effectve tax rate than ther counterparts n the US. He shows that the Canadan graduates have greater ncentves to mgrate to the US due to lower effectve tax rates. The Canadan graduates hereby ncrease ther rates of return. 7 OECD (2003) 21

22 In concluson, by determnng the optmal taxaton, the ntal taxaton level n the country s of great mportance. If the tax level s too hgh bran dran s a dstnct possblty. Choosng the optmal tax level dfferentates between countres as the ntal level dffer. 5. Developed Countres versus Newly Industralzng Countres (NIC) 5.1 The Turnovsy model n relaton to labor ntensve countres In the Turnovsy model, one of the man conclusons n secton (the uncompensated case) s that captal ncome taxaton reduces growth more than wage taxaton and consumpton taxaton. The pont of ths secton s to enlghten that for NIC, the result of the analyss could loo dfferent. In the subsequent secton, the conclusve results n the Turnovsy model, secton 2.2.1, wll be dscussed n comparson to a model by Wang and Yp, The model by Wang and Yp dstngushes between a NIC and a Developed Country. It s argued that n NIC most of the producton technologes are hghly laborntensve and labor ncome share s relatve hgher than n developed countres, where the economy generally s captal-ntensve. Moreover, n NIC t s expected that labor s very elastc, and therefore, the labor ncome tax may have greater effect on economc growth. The authors test the hypothess by regressng the growth rates of physcal captal and effectve labor on captal and labor ncome tax rates, respectvely. The regresson s done usng annual data for Tawan n the perod 1954 to The results are as follows: An ncrease n the captal tax by one percent lowers the rate of physcal captal growth by 0.25 pct. However, an ncrease n labor tax lowers the rate of effectve labor by 3.78 pct. These results ndcates that n NIC an ncrease n captal ncome taxaton wll be more growth enhancng than an ncrease n wage ncome taxaton. Ths s certanly not the case n the Turnovsy model. In ths context, t s mportant to bear n mnd that an ncrease n the wage ncome tax ntally reduces labor supply. However, f ths tax ncrease s compensated by a reducton n captal ncome taxaton, labor supply may ncrease. The ntuton s that margnal productvty of labor s ncreased by the ncrease n the prvate captal stoc. However, f labor ntensty s very hgh, the net result on labor supply wll be negatve. 22

23 All n all, t seems to be mportant to tae nto account at whch stage n the developng process the country currently s at. In the Turnovsy model, the analyss s based on data for the US economy. The qualtatve effects of captal and labor taxaton n developed countres and NIC are dentcal, but there exst quanttatve dfferences. In NIC, wage ncome taxaton s more growth dampenng than captal ncome taxaton. And thus, the conclusve results n the Turnovsy model may be qute dfferent, f the model s used to analyze NIC, le Tawan. 6. Concluson In ths paper we have analyzed how government expendture fnanced by dfferent taxaton modes affects economc growth. In the Turnovsy model the conclusve result s that captal ncome tax dampens the economc growth the most, and consumpton taxaton s the most plausble. In regard to the structure of government expendture, government nvestments generate hgher economc growth n comparson to government consumpton. In the short run, choosng government nvestment creates negatve welfare, but n the long run the welfare turns out to be hghly postve. Allocatng government expendture nto publc captal va nvestments generates hgher captal accumulaton, and thereby larger output. Turnovsy fnds that the best soluton for a compensated expendture s nvestment fnanced by consumpton taxaton. In the revson of the Turnovsy model, three dfferent defntons of lesure s ntroduced: raw tme, qualty tme and home producton. It s consdered that Turnovsy regard lesure as raw tme. If the defnton of lesure n the Turnovsy model s home producton nstead of raw tme, t could generate a dfferent result n the analyss. If home producton s ncluded the relatve decrease n output wll be smaller or dsappear n certan nstances. In the model the productve government nvestments generates a postve externalty on the prvate nput factors, labor and captal. Therefore t s concluded that t s optmal to have postve tax rates on these prvate nput factors. Barro (1990) states that government sze s negatvely correlated wth economc growth. Three emprcal analyses usng three dfferent econometrc methods and data samples gve us ambguous results on ths correlaton. Two contractonary causaltes between government sze and economc growth are at play. Economc growth generates hgher ncome levels whch n turn may create a 23

24 hgher demand for publc servces fnanced by hgher taxes. On the other hand hgher taxes create a hgher stoc of human captal, whch n turn may generate hgher economc growth and therefore hgher ncome levels. By determnng the optmal taxaton level t s mportant to consder the ntal taxaton level. If the taxaton level reaches a certan upper bound the possblty for bran dran arses. The conclusve result n the Turnovsy model may be dfferent when loong at NIC. Because of labor ntensve sectors n NIC, wage ncome taxaton can be more dampenng on economc growth compared to captal ncome taxaton. 24

25 Appendx Table A1 Source: Turnovsy (2004), table 3. 25

26 References Aschauer, Davd A., 1989, Is Publc Expendture Productve?, Journal of Monetary Economcs 23, Barro, Robert J., 1990, Government Spendng n a Smple Model of Endogenous Growth, Journal of Poltcal Economy, Vol. 98, No. 5, Part 2: The problem of Development: A Conference of the Insttute for the Study of Free Enterprse Systems (October, 1990), Barro, Robert J., 1991, Economc Growth n a Cross Secton of Countres, Quarterly Journal of Economcs 106(2), Becer, Gary S., 1965, A Theory of the Allocaton of Tme, Economc Journal 75 (September, 1965), Collns, Kr A., 2005, Mgraton Incentves: An Effectve Tax Rate Approach. Dar, Atul A. and Khalhal, Sal Amr, 2002, "Government sze, factor accumulaton, and economc growth: evdence from OECD countres", Journal of Polcy Modelng 24 (2002), Doménech, Rafael and Garca, Jose Ramón, 2002, Optmal Taxaton and Publc Expendture n a Model of Endogenous Growth, Topcs n Macroeconomcs, Vol. 2, Issue 1, Artcle 3. Fölster, Stefan and Henreson, Magnus, 2000, "Growth Effects of Government Expendture and Taxaton n rch countres", European Economc Revew 45 (2001), Hecman, James, 1976, A Lfe-Cycle Model of Earnngs, Learnng and Consumpton, Journal of Poltcal Economy 84 (August, 1976), Lozdes, John and Vanvouas, George, 2004, "Government expendture and economc growth: Evdence from trvarate causalty testng",journal of Appled Economcs, vol. 8 no. 1 (2005), Mless-Ferrtt, Gan Mara and Roubn, Nourel, 1998, Growth Effects of Income and Consumpton Taxes, Journal of Money, Credt and Banng, Vol. 30, No. 4 (November, 1998), OECD, "The sources of economc growth n OECD countres", 2003 Turnovsy, Stephen J., 2004, The Transtonal Dynamcs of Fscal Polcy: Long-run Captal Accumulaton and Growth, Journal of Money, Credt and Banng, Vol. 36, No. 5 (October, 2004). Wang, Png and Yp, Chong K., 1995, Macroeconomc Effects of Factor Taxaton wth Endogenous Human Captal Evoluton: Theory and Evdence, Southern Economc Journal, Vol. 61, No. 3 (January, 1995),