Public Expenditures, Taxes, Federal Transfers, and Endogenous Growth 1

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1 Public Expenditure, Taxe, Federal Traner, and Endogenou Growth Liutang Gong 2 Guanghua School o Management, Peking Univerity, Beijing, China, 0087 and Heng-u Zou CEMA, Central Univerity o Finance and Economic, Beijing, China 0008 Shenzhen Univerity, Wuhan Univerity, and The World Bank ABSTRACT Thi paper extend the Barro (990) model with ingle aggregate government pending and one lat income tax to include public expenditure and taxe by multiple level o government. It derive the rate o endogenou growth and, with both imulation and pecial example, examine how that rate change with repect to ederal income tax, local taxe, and ederal traner. It alo dicue the growth and welare-maximizing choice o taxe and ederal traner. Keyword: Public expenditure; Taxe; Federal traner; Endogenou growth. JEL claiication #: E0, H2, H4, H5, H7, O4, R5. Introduction In an endogenou growth model, Barro (990) ha examined the eect on economic growth o aggregate government pending, including both aggregate public conumption and aggregate public invetment. Subequent work ha extended Barro' analyi by looking into the compoition o government expenditure and economic growth. For example, Eaterly and Rebelo (993) and Devarajan, Swaroop, and Zou (998) have tudied the growth eect o public pending on education, tranportation, deene, and ocial welare. Glomm and Ravikumar (994), Hulten (994), and Devarajan, Xie, and Zou (998), among many other, have paid particular attention to the We are indebted to the Proeor Cuong Le Van and Myrna Wooder or their ueul comment and help in reviing thi paper. Thi reearch wa ponored by the National Science Foundation or Ditinguihed Young Scholar ( ). 2 Mailing addre: Liutang Gong, Guanghua School o Management, Peking Univerity, Beijing, 0087, China. Tel: (860) ; Fax: (860) ; ltgong@gm.pku.edu.cn.

2 aociation between inratructure and output growth. 3 However, the tructure o public expenditure and taxe among dierent level o government ha a undamental impact on economic growth in light o the argument related to ical ederalim; ee Oate (972, 973). In act, the proper aignment o expenditure and taxe among ederal and local government and the proper deign o intergovernmental traner are prerequiite or eicient and equitable public ervice proviion at both the national and local level. One o the mot important goal in etablihing a ound intergovernmental ical relationhip i to promote both local and national economic growth (ee alo Rivlin 992, Bird 993, Gramlich 993, and Oate 973). In view o the important link between the deign o intergovernmental ical relationhip and economic growth, it i natural or u to extend the Barro model and provide an analytical ramework or both theoretical and empirical reearch on the growth eect o public expenditure, taxe, and ederal traner in a ederation or in multiple level o government. Thi i the main tak o our paper. The remainder o thi paper i organized a ollow. Section 2 extend the Barro model with one aggregate government pending and one lat income tax to include: () public expenditure by both the ederal government and local government; (2) variou taxe by both the ederal government and local government; and (3) a ederal traner to a locality 4. Section 3 derive the rate o endogenou growth. With both imulation and pecial example, ection 4 examine the change in the rate o endogenou growth with repect to ederal income tax, local income tax, and ederal traner. Section 5 derive the optimal ederal government income tax rate, local government income tax rate, and the ederal matching traner or the locality. Section 6 preent a more general model with local government conumption tax and property tax. Section 7 conclude the paper. 2. The Model Following Arrow and Kurz (970), Barro (990), and Turnovky (2000), we 3 O coure, the empirical analye in many o thee tudie have ollowed the much-cited work o Achauer (989). 4 The etup o our model i alo very dierent rom the dynamic analyi o Zou (994, 996) in quite a ew repect. Firt, the ocu here i the rate o endogenou growth intead o the traditional long-run analyi o the teady tate; econd, the repreentative agent' utility and production unction are deined on both ederal and local pending intead o only on local pending; third, ederal taxation, ederal traner, and ederal pending are ully integrated into the

3 introduce public expenditure by the ederal government and local government into the repreentative agent' utility unction and production unction. Federal pending i denoted by, local public pending by, and private conumption by c. The intantaneou utility o the repreentative agent i given by uc (,,), which ha the ollowing propertie: u 0, u 0, u 0, u 0, u 0, u 0. () c cc To derive analytical olution or the endogenou growth rate, we extend the utility unction o Barro (990) a ollow c uc (,,) where 0 i the invere o the elaticity o intertemporal ubtitution., (2) The repreentative agent eek to maximize a dicounted utility, a given by where 0 i the contant rate o time preerence. t U u(, c,) e dt, (3) 0 The agent ha acce to the extended Arrow-Kurz-Barro neoclaical production unction where y i output and k i private capital tock. y y( k,, ), (4) The role o government ervice in both the utility unction and the production unction wa introduced to dynamic analyi o public invetment and growth by Arrow and Kurz (970). The approach to endogenou growth model wa popularized by Barro (990). In recent tudie on ical decentralization and growth, the Arrow-Kurz-Barro approach to preerence and technology ha been extended to dierent public expenditure by multiple level o government; ee Brueckner (996), Davoodi and Zou (998), and Zhang and Zou (998) or example. Again, the production unction i aumed to have the ollowing tandard propertie: y 0, y 0, y 0, y 0, y 0, y 0. k kk In thi paper, the production unction take the CES orm, ( ), (5) y k model; and inally, we examine growth-maximizing and welare-maximizing choice o taxe and traner.

4 where,,, and are poitive contant with. The ederal government levie an income tax at the rate o, and a typical local government levie a local income tax 5 (a in the cae o tate income tax in the United State) at the rate o. The ederal government alo make a traner to the local government in the orm o a matching grant or local public pending at the rate o g. I both level o government maintain balanced budget, then their budget contraint can be written a y g (6) and y g, (7) repectively. Hence, ederal public pending,, equal total income tax, y, minu the traner to the local government, g. Local government pending i inanced by it income tax, y and the grant it receive rom the ederal government, g. Given the tax rate o the two level o government, the budget contraint o the repreentative agent can be written a dk ( ) yk (,, ) k c. (8) dt The repreentative agent chooe a conumption path and a capital-accumulation path to maximize hi dicounted utility in equation (3) ubject to contraint (8), and with hi initial capital tock given by k(0) k0. The Hamiltonian aociated with the optimization problem i deined a H u( c,, ) (( ) y( k,, ) k c), where i the cotate variable, and it repreent the marginal utility o wealth. Now, the irt-order condition are uc (,,), c d y( k,, ) [( ) ], dt k and the tranverality condition (TVC) i (9) (0) 5 In the ollowing ection, we extend the model to a more general ramework with conumption tax c and property

5 lim ke t 0. () t Speciically, or the utility unction in equation (2) and the production unction in equation (5), we rewrite equation (9) and (0) a ollow: and c c c (2) {( )( ) k k }. Equation (2) tate that the marginal utility o wealth equal the marginal utility o conumption at an optimum. Equation (3) i the amiliar Euler equation or conumption with multiple government ervice and tax rate. (3) 3. The Balanced Growth Rate Suppoe that the economy i on the balanced growth path where private conumption, private capital, ederal government expenditure, local government expenditure, and output all grow at the ame rate denoted a, i.e, c k y. c k y (4) and Subtituting condition (4) into equation (8) and (3), we obtain c c k k {( ) ( ( ) ( ) ) } k c ( )( ( ) ( ) ). k k k k From equation (5), we have k k ( ) ( ) ( ) ( ). (5) (6) (7) Subtituting equation (7) into equation (6), we derive the conumption-capital ratio a c k ( )( ). ( ) On the other hand, rom government budget contraint (6) and (7), and combining (8) tax k, but we cannot derive the explicit olution or the growth rate.

6 with equation (6), we obtain k ( ) (9) g ( ) and k g ( )( ). (20) g ( ) Uing equation (9) and (20), we have g ( ) ( ) {( )( ) } k k g ( ) { ( ) }. g ( ) (2) Subtituting equation (2) into equation (7) yield the explicit olution or the growth rate : ( ) [ ]. g ( ( ) ( ) ) g g (22) Equation (22) tate that the growth rate i an explicit unction o,,,,, and. For the endogenou growth rate to be poitive in (22), it i required that, g,, ( ) g ( ( ) ( ) ) g g. (23) At the ame time, the TVC () give ( ) g ( ( ) ( ) ) g g ( )[ ]. (24) Equation (23) and (24) preent the condition or endogenou growth. Now, the optimal growth path or capital accumulation, kt (), conumption, ct (), ederal government pending, () t, local government pending, () t, and output, yt () are derived a ollow t t t t t kt () k(0) e, ct () c(0) e, () t (0) e, t () (0) e, yt () y(0) e, (25) where the initial capital tock k (0) i given, but the initial ederal pending (0), local government pending (0), initial conumption c (0), and initial output y (0), will de

7 determined by the model. Firt, rom equation (6) and (7), we obtain (0) (0) y g (26) and g (0) ( ) y(0). (27) g Now, rom equation (5), we have g y(0) k(0) ( ) y(0) ( ) y(0). g g Thu, we obtain the initial output a a unction o the initial capital tock, k (0) a ollow: k(0) y(0). (28) ( ) ( ) g g g With y (0) given in equation (28), (0) and (0) can be determined by equation (26) and (27), repectively; c (0) can be determined by the budget contraint o the agent: c(0) ( ) y(0) ( ) k(0). (29) With the aid o explicit olution or the growth rate, we can analyze the eect on growth o the ederal government' income tax, the local government' income tax, and the ederal government' matching traner. Uing the explicit path o the capital accumulation, conumption, and government' pending, we can derive the ocial welare unction, and then we can derive the optimal tax rate and government traner to maximize the ocial welare. We will proce thee in the next ection. 4. Eect o Taxe and Federal Traner Dierentiating equation (22) with repect to the ederal government income tax rate,, local government' income tax rate,, and the ederal matching grant or locality, g, we have g g ( )( ) ( ) [ ], (30) g g ( ( g) ( g) ) ( ( g) ( g) )

8 g [ ( g) g ( g) ] g g g ( ( g) ( g) ) ( ( g) ( g) ), (3) and g [ ( g) ( g) ] 2 ( g) g ( ( ) ( ) ) g g g. (32) Equation (30), (3), and (32) tate the ambiguou eect on growth o the ederal government income tax rate,, local government' income tax rate,, and the ederal matching grant or locality, g. For the intuition, we preent ome numerical olution. (Inert Figure about here) Figure how the relationhip between the rate o endogenou growth,, and the ederal government' income tax rate,, when the ollowing bae value are ued or the tructure o local government taxation and ederal traner: a local income tax at 0 percent: 0.0, and a ederal matching grant at 50 percent: g 0.5. We aume the ollowing value or preerence and technology parameter: 0.5, 0.05, 0.05, 2, and 0.4. For the parameter o and, which repreent the marginal productivity o ederal government pending and local government pending, repectively, we conider three cae: 0.25 ; 0.35, 0.5; and 0.5, In all three cae, Figure preent typical Laer curve relating the growth rate to ederal income tax. In the cae o equal marginal productivity o ederal government expenditure and local government expenditure, given local tax, ederal traner, and all other parameter in our model, a rie in ederal income tax will increae the growth rate beore the tax rate hit around 3 percent. In act, when the ederal income tax rate rie rom zero to 0 percent, the growth rate rie rom zero percent to almot 4.4 percent. Further increae in the ederal income tax rate above 3 percent will reduce the growth rate. Jut beore the ederal income tax rate reache a high o 60 percent (note that the local income tax rate i aumed to be 0 percent), the growth rate i around zero. The explanation or thi Laer curve i a ollow. A change in ederal income tax ha three eect. Firt, a higher ederal income tax directly reduce the return on private capital and the growth rate directly. Second, a larger tax revenue implie higher ederal

9 expenditure, which i aumed to increae both private utility and private productivity. The riing productivity o private capital raie the growth rate. Third, at the ame time, a larger tax revenue can lead to a larger ederal traner to local government, whoe public ervice are alo utility- and productivity-enhancing. When the ederal income tax rate i initially very mall, the econd and third orce dominate. When the ederal income tax i already high, the irt orce dominate. For the eect o ederal government expenditure and local government expenditure, we ind that a the marginal productivity o local government expenditure increae, the growth rate decreae beore the critical point o ederal government income tax rate The critical point o that rate, which reache the maximum growth rate, decreae. In act, rom equation (22), we have g ( ) (( ) ( ) g g. g ( ( ) ( ) ) g g (33) Thu, when 0, we have g gn( ) gn(( ) ( ) ). g g In thi pecial cae, ( g ) 0.3. Hence, when 0.3, we have 0 ; and when g 0.3, we have 0. Thi i hown in Figure. (Inert Figure 2 about here.) Figure 2 how a imilar picture o the relationhip between the growth rate,, and local income tax rate, uing the ollowing bae value or the tructure o ederal income tax, local taxe other than local income tax, and ederal traner: a ederal income tax at 20 percent: 0.20, and a ederal matching grant at 50 percent: g 0.5. We alo aume the ollowing value or preerence and technology parameter: 0.5, 0.05, 0.05, 2, and 0.4 ; and conider three cae: 0.25 ; 0.35, 0.5 ; and 0.5, We ind Laer curve imilar to thoe in Figure. For the equal marginal productivity o ederal and local government expenditure, a the bae ederal income tax i already at a relatively high rate o 20 percent, the growth

10 rate i riing with local income tax until reache about 5 percent. When the local income tax rate i et at 20 percent, the growth rate i zero. Becaue the local government receive a matching grant rom the ederal government at a rate o 30 percent, and becaue it alo raie tax revenue rom conumption tax and property tax, the local government can till inance it productive public expenditure without reorting to income tax. Thi i why the growth rate in Figure 2 i till above 3 percent even though local income tax i zero. We preent imilar eect o ederal government expenditure and local government expenditure, in thi cae ( g ) We ind that a the marginal productivity o g local government expenditure increae, the growth rate decreae beore the critical point o the government income tax rate The critical point o local government income tax rate, which reache the maximal growth rate, decreae. (Inert Figure 3 about here.) Figure 3 relate the growth rate,, to the ederal matching grant or locality, g, baed on a ederal income tax o 20 percent and a local income tax at 0 percent. Again, we aume the ollowing value or preerence and technology parameter: 0.5, 0.05, 0.05, 2, and 0.4 ; and conider three cae: 0.25; 0.35, 0.5 ; and 0.5, We obtain three dierent eect on growth o a ederal matching grant or the local government: when the marginal productivity o ederal government pending i larger than the marginal productivity local government pending, i.e., the ederal government matching traner will decreae the growth rate. When the two government have the ame marginal productivity, there i a non-evidence eect o the matching traner on growth beore g 0.5. When local government expenditure ha relatively larger marginal productivity, we ind the contrating olution whereby a the ederal matching traner increae, the growth rate increae beore g 0.6. We ind that the eect o a ederal matching traner on growth can be negative when it i too large (ay, g 0.6 ). We have elected the tax bae or the local government income tax rate a 0., and thu the local government ha already

11 obtained an amount o revenue rom it income tax. I the matching traner i too high, then the ederal government hould pay or the major part o local government expenditure, and the local government' income tax will be in urplu. Thi will harm economic growth. Similarly, we can how the eect o the marginal productivity o local government expenditure under the elected parameter, with the critical point g. Thu, 3 when g g g g, the eect o local government expenditure on growth i negative; when,, the eect i poitive. 5. Optimal Taxe and Traner 5. Growth Maximization and Welare Maximization In the lat ection, we numerically preented the relationhip among,, g, and the growth. Recall that Barro (990) how that maximizing ocial welare i equivalent to maximizing the rate o growth, and the optimal tax rate equal the marginal contribution o government expenditure. To compare our olution with that o Barro (990), we reexamine the concluion we have drawn by uing the pecial production unction. In thi ection, we peciy the production unction a the Cobb-Dougla production unction, which amount to et 0 in the CES production unction, namely, where,, and are poitive contant with. y k, (34) Hence, the explicit balanced growth rate expreed in equation (22) ha the ollowing orm, g [( ) ( ) ( ) ] g g. (35) On the other hand, i we ubtitute the growth path (25) or conumption, ederal pending, and local government pending into the utility unction in (2), the agent' welare i given a

12 ( ) t ( ) t ( ) t c(0) e (0) e (0) e t U [ ] e dt 0 c(0) (0) (0) 3, ( ( ) )( ) ( ) (36) where we have ued the TVC () to obtain ( ) 0. Here, (0) and (0) are till determined by equation (26) and (27). y (0) i determined by ubtituting equation (26) and (27) into equation (34), i.e, g y(0) ( ) ( ) k(0) g g Then, c (0) can be determined by equation (29).. (37) (Inert Figure 4 about here!) It i imple to ee that in equation (36) the agent' welare i an increaing unction o the economic growth rate 6,. However 7, becaue c (0), (0), and (0) alo depend on,, and g, welare maximization may not be equivalent to growth maximization. Thi i hown in Figure 4, where we elect the parameter a: 0.5, 0.35, 0.5, 0.05, 0.05,., g 0.5, and We ind that the optimal ederal income tax rate, which maximize growth i around 0.4. However, the optimal ederal income tax rate, which reache the maximum welare, i around 0.5. Thereore, growth- and the welare-maximizing taxe are not equivalent in thi cae. 5.2 The Growth-maximizing Taxe We now ocu on inding the optimal taxe or growth maximization. In act, dierentiating equation (35) with repect to,, and g yield g g g g g ( ) ( ) [ ( ) ( ) ] 0, (38) 6 In act, dierentiating on equation (36) with repect to yield ( ( )) [ ( ) ( )] 2 U ( ( ) ) U Thereore, we have 0 when. 7 We thank the aociate editor very much to point out thi..

13 g g g g g g ( ) ( ) { ( )( ) g g ( )[ ( )( ) ( ) ]} g g g g 0, (39) and g g ( ) ( ) ( ) [ ( ) ( ) ] 0. g g g g g g (40) Thu, we have g ( ) ( ) g g g g ( ) ( )[ ( ) ( )] g g g, (38 ), (39 ) and g ( ) g g. (40 ) Equation (40') yield the ame expreion a equation (38') and (39'). Hence, we know that optimal choice o,, and g are interdependent. The choice o the ederal matching grant i endogenou in the ollowing ene: once g i choen rom the interval (0,), ederal income tax and local income tax are determined by (38') and (39'). From equation (38') and (39'), we obtain the optimal tax rate a 8 and g (4) g or the ederal government and local government, repectively., (42) Once g i given in the interval (0,), the ederal and local income taxe are determined by their productivene and the matching rate multiplied by the productivity o local public pending. The aggregate optimal tax rate i jut the um o the 8 The Jacobian matrix at the optimal taxe can be derived a g ( ) ( ) g. 2 g g ( ) ( 2 ) g ( g ) It i eay to prove that thi matrix i negative deinite. Thereore, the econd-order condition are atiied.

14 productivene o ederal and local expenditure:. (43) With the choice o tax rate and traner peciied in equation (4) and (42), the growth-maximizing growth rate i [ 2 ]. We hould ay omething about the eect o optimal government matching traner and eect o the matching traner on the growth. In the lat ection, we howed the government matching traner can aect growth but the optimal choice o government matching traner and the tax rate are interdependent. Thi occur becaue, rom equation (6) and (7), we have ( ) y. The government traner become an independent variable. We can alo derive the equation with only the ederal government income tax rate and government matching traner; thu, the local government income tax rate become an independent variable. The eect o government matching traner in the lat ection are baed on the elected ederal and local income tax rate. Thu, we obtain the eect hown in Figure 3. In addition, given the local income tax rate, rom equation (38') and (40') we can determine the optimal choice or the government matching traner and ederal income tax rate. 6. A More General Framework We can extend our analytical ramework to a more general one and conider more tax rate. The ame et up i ued or the ederal government but we introduce two more taxe or the typical local government. It now levie three taxe: a local income tax (uch a the cae o tate income tax in the United State) at the rate o, a conumption tax c and a property tax (capital tax in our model) k. The ederal government alo make a traner to the local government in the orm o a matching grant or local public pending at the rate o g. I both level o government maintain balanced budget, then budget contraint (6) and (7) can be written a y g (44)

15 and y k c g, (45) k c repectively. Hence, the ederal government public pending,, i equal to it total income tax, y, minu it traner to the local government, g. The local government' pending i inanced by it income tax, y, it property tax, k k grant it receive rom the ederal government, g., it conumption tax, c c, and the In a imilar way, we derive a highly nonlinear equation or the growth rate : ( ) k ( (,,,,, g,,,,,, )) k c, (46) where (,,, k, c, g,,,,,, ) i given by (,,, k, c, g,,,,,,, ) g g c k {[( ) ]( ) g g c ( ) g k gc k k } { ( ) g g c g ( ) k c k c k ( ) }. g g ( ) g c Note that appear on both ide o equation (46). Thereore, the growth rate i implicitly deined a a unction o,, k, c, g,,,,,, and. For the endogenou growth rate to be poitive, we mut impoe 0, and rom the c TVC ( ) 0, which i alo the condition or a bounded dicounted utility over the ininite horizon. Given uch an extended ramework with government expenditure and taxe by two level o government and intergovernmental traner, we cannot hope that growth-maximizing choice o tax rate and the traner rate will be conitent with the welare-maximizing one. The imple cae in Barro' (990) analyi whereby growth maximization coincide with welare maximization diappear here. In act, when both a local conumption tax and a local property tax are preent, welare i a complicated unction o the growth rate, which in turn i a complicated unction o variou taxe and

16 the ederal traner, a hown in equation (46). 7. Concluion Thi paper ha extended the Barro (990) model with ingle aggregate government pending and one lat income tax to include public expenditure and taxe by multiple level o government. We have derived the rate o endogenou growth under quite general peciication o preerence and production technology. With imulation, we have examined how the rate o endogenou growth change with repect to ederal income tax, local income tax, and ederal traner. We have alo dicued growth-maximizing choice o income taxe and ederal traner. In addition, we extend our model to a more general ramework including a local conumption tax and local property tax. A preliminary imulation analyi ha hown that the local property tax ha the larget negative impact on the rate o economic growth, wherea a local conumption tax i alway growth enhancing. Thi inding contrat with that o Rebelo (99), who how that a conumption tax ha no eect on the growth rate. The model in thi paper et up a poitive ramework or evaluating how the aignment o taxe and expenditure among dierent level o government and intergovernmental traner aect economic growth. Our analyi alo hed light on the role o intergovernmental traner in regional economic growth. I a local government ha uicient revenue bae, ederal traner eem to reduce the growth rate. Even i local revenue i not uicient, the rie in the rate o ederal traner increae the growth rate to a very modet degree. O coure, the model i alo ueul or normative dicuion o the welare- and growth-maximizing choice o taxe, traner, and expenditure in the context o ical ederalim. In uture, we will add two more dimenion: one will be to ollow Arrow and Kurz (970) and introduce public conumption and public capital accumulation at both the ederal and local level into the endogenou growth model; the other will be to ormulate a game-theoretical growth model and allow trategic interaction between the ederal government and multiple local government in the choice o taxe, public expenditure, and intergovernmental traner.

17 Reerence Arrow, K., and M. Kurz (970) Public Invetment, the Rate o Return and Optimal Fical Policy, John Hopkin Univerity Pre. Achauer, D. (989) I government pending productive? Journal o Monetary Economic 23, Barro, R.J. (990) Government pending in a imple model o endogenou growth Journal o Political Economy 98, S03-S25. Bird, R. (993) Threading the ical labyrinth: Some iue in ical decentralization National Tax Journal 46, Brueckner, J. (996) Fical ederalim and capital accumulation Mimeo. Univerity o Illinoi at Urbana-Champaign. Davoodi, H. and H. Zou (998) Fical decentralization and economic growth: A cro-country tudy Journal o Urban Economic 43, Devarajan, S, V. Swaroop, and H. Zou (996) The compoition o government expenditure and economic growth Journal o Monetary Economic 37, Devarajan, S, D. Xie, and H. Zou (998) Should public capital be ubidized or provided? Journal o Monetary Economic 4, Eaterly, W. and S. Rebelo (993) Fical policy and economic growth: An empirical invetigation Journal o Monetary Economic 32, Glomm, G. and B. Ravikumar (994) Public invetment in inratructure in a imple growth model Journal o Economic Dynamic and Control 8,

18 Gramlich, E. (993) A policy maker' guide to ical decentralization National Tax Journal Hulten, C. (994) Optimal growth with inratructure capital: Theory and implication or empirical modeling Mimeo. Univerity o Maryland. King, R.G. and S. Rebelo (990) Public policy and economic growth: Developing neoclaical implication Journal o Political Economy 98, S26-S50. Oate, W. (972) Fical Federalim, New York, Harcourt Brace Jovanovich. Oate, W. (993) Fical decentralization and economic development National Tax Journal 46, Rebelo, S. (99) Long-run policy analyi and long-run growth Journal o Political Economy 99, Rivlin, A. (992) Reviving the American Dream: The Economy, the State, and the Federal Government, Brooking Intitution, Wahington, D.C. Turnovky, S. (2000) Method o Macroeconomic Dynamic, MIT Pre. Zhang, T. and H. Zou (998) Fical decentralization, public pending, and economic growth in China Journal o Public Economic 67, Zou, H. (995) Dynamic eect o ederal grant on local pending Journal o Urban Economic 36, Zou, H. (996) Taxe, ederal grant, local public pending, and growth Journal o Urban Economic 39,

19 Figure : Growth rate veru ederal government income tax rate. The parameter are: 0.5, 0.4, 0.05, 0.05, 2, g 0.5, and 0. : 0.35, 0.5 ; : 0.25, 0.25 ; : 0.5, ; in the cae o Figure 2: Growth rate veru local government income tax rate. The parameter are: 0.5, 0.4, 0.05, 0.05, 2, g 0.5, and 0.2 ; in the cae o 0.35, 0.5 ; : 0.25, 0.25 ; : 0.5, 0.35 :

20 Figure 3: Growth rate veru ederal government matching grant or locality g. The parameter are: 0.5, 0.4, 0.05, 0.05, 2, and 0.; in the, 0.2 cae o : 0.35, 0.5 ; : 0.25, 0.25 ; : 0.5, 0.35

21 Figure 4: Growth maximization and welare maximization. The parameter are: 0.5, 0.35, 0.5, 0.05, 0.05,., g 0.5, and 0.05.