Government Expenditure Financing, Growth, and Factor Intensity

Transcription

1 nternational Journal of Business and Management; Vol., No. 4; 206 SSN E-SSN Published by anadian enter of Science and Education Government Exenditure Financing, Growth, and Factor ntensity Kuo-hao Lee Deartment of nternational Business, Hsing-Wu University, Taiwan orresondence: Kuo-hao Lee, Deartment of nternational Business, Hsing-Wu University, Taiwan. Received: January 29, 206 Acceted: March 8, 206 Online Published: March 5, 206 doi:0.5539/ijbm.vn478 URL: htt://dx.doi.org/0.5539/ijbm.vn478 Abstract By shedding light on the factor intensity, this aer incororates the Romer (986)-tye knowlee sillover technology into the Uzawa (96, 963) two-sector model of consumtion and investment goods and studies the effect of the ratio of government exenditure to total outut on the economic growth rate under three tyes of tax financing schemes: lum-sum tax financing, income tax financing, and consumtion tax financing. We find that a rise in government exenditure with lum-sum tax financing has an ambiguous effect on the balanced growth rate deending on the factor intensity between the sectors. The balanced growth rate decreases (increases) with a rise in government sending if the consumtion (investment) goods sector is caital-intensive. Moreover, the result of consumtion tax financing is equivalent to lum-sum tax financing, while an increase in the government exenditure with income tax financing reduces the balanced growth rate. Our two-sector model with lum-sum tax or consumtion tax financing seems to be able to rovide a channel through which to exlain the mixed emirical findings. Keywords: government exenditure financing, factor intensity, two-sector model, endogenous growth JEL lassification: E62, H6, O4, O38. ntroduction The relationshi between government exenditure and macroeconomic erformances has been extensively exlored within an intertemoral otimizing framework over the last two decades. One strand of the studiesut their emhases on the consequences of government exenditure olicies under alternative financing aroaches [Turnovsky (992), Van der Ploeg and Alogoskoufis (994), Devereux and Love (995), Palivos and Yi (995), Turnovsky (996, 2000), Gokan (2002), and hang et al. (2004), among others]. Deending on model secifications, the multiform methods used to finance a given government exenditure lead to different real effects on relevant economic variables. To enrich the studies in this field, this aer incororates knowlee sillover technology of theromer (986)-tye in the Uzawa (96, 963) two-sector model of consumtion and investment goods to examine the roles of factor intensity and relative rice in evaluating the effects of alternative government exenditure financing scheme.the study of this issue may be justified for three reasons. First, following the remarkable contributions of Romer (986) and Lucas (988), numbers of studies have aid attention to the effects of different government exenditure financing schemes on the economy s growth rate where the steady-state growth rate is endogenously determined in the economy. Most of these studies adot the secification of the one-sector AK technology [Van der Ploeg and Alogoskoufis (994), Palivos and Yi (995), Turnovsky (996, 2000), and Gokan (2002)]. (Note ). With a one-sector growth model and consumtion tax financing, Turnovsky (996) finds that an increase in government consumtionexenditure does not affect the steady-state growth rate (.3), and an increase in government investment exenditure imroves the steady-state growth rate (.39). Moreover, Turnovsky (2000) introduces an endogenous labor-leisure decision into a simle AK growth model and shows that an increase in either government consumtion exenditure or government investment exenditure with lum-sum tax financing imroves the steady-state growth rate. While the one-sector model has the virtue of tractability, it can notroerly cature the fact that the economy consists of a multi-sector environment, such as consumtion goods and investment goods sectors. (Note 2) Second, lenty of studies use the Uzawa (965)-Lucas (988) two-sector model with joint accumulation of hysical caital and human caital to discuss the effect of tax olicies in an endogenous growth framework [King and Rebelo (990), Rebelo (99), Jones et al. (993), Devereux and Love (994), Stokey and Rebelo 78

2 nternational Journal of Business and Management Vol., No. 4; 206 (995), Bond et al. (996), and Mino (996)]. Obviously, the effect of different government exenditure financing schemes is less addressed. To our knowlee, Devereux and Love (995) make a first attemt to examine the imact of government sending financed by either lum-sum or income tax on economic growth rate under a two-sector endogenous growth model with endogenous labor-leisure decision. Their conclusions suggest that a ermanent increase in government exenditure imroves the steady-state growth rate under lum-sum tax financing, but worsens the steady-state growth rate under income tax financing. By contrast, hang et al. (2004) introduce the motive of status-seeking into the two-sector endogenous growth model and show that a negative relationshi exists between government exenditure and the long-run growth rate under lum-sum tax financing. Although the studies have emloyed a two-sector model, the roositions they established does not embody the well-known feature in a two-sector model such as factor intensity between the sectors. As the emirical evidence shown in Jones (2003), the industry-level caital shares are quite discreant in the United States. n addition, the caital shares in investment goods sectors are not necessarily greater than those in consumtion goods sector (we summarize the emirical data of 996 in Jones, 2003 in Table ). Motivated by the emirical evidence, following Uzawa (96, 963), the resent aer construct a two-sector model of consumtion and investment goods in which both sectors use hysical caital and labor as inuts in a Romer (986)-tye technology to highlight the imortant features of factor intensity and relative rice between the sectors in evaluating the growth rate effect of government exenditure olicy under alternative financing schemes. Third, the emirical studies which emhasize the relationshi between government exenditure and the economic growth rate do not enable us to reach a definite conclusion. Kormendi and Mequire (985) use data for forty-seven countries and find that there is no significant cross-sectional relationshi between average government consumtion exenditure and the growth rate of real GDP. Recently, Miller and Russek (997) divided the effects of government exenditure based on alternative financing modes and found that the relationshi between government exenditure and economic growth is emirically mixed. From this ersective, the existing theoretical works clearly can not rovide a general exlanation for the diverse outcomes in the emirical studies. Thus, it is a worthwhile task for us to find a otential vehicle to exlain the emirical evidence. Based on the two-inut two-good model, our findings can be summarized as follows. First, the growth effect of a rise in the government exenditure with lum-sum tax financing deends on the factor intensity between sectors. f the consumtion (investment) goods sector is caital-intensive, then the steady-state growth rate declines (increases). This ambiguous result for the steady-state growth rate sharly contrasts with the results of Devereux and Love (995), Turnovsky (2000) and hang et al. (2004). Second, an increase in government exenditure with income tax financing leads to a deterioration in the steady-state growth rate. The finding is consistent with Devereux and Love (995). Third, in contrast to Turnovsky (996), an exansion in government sending with consumtion tax financing has an ambiguous effect on the steady-state growth rate, which is equivalent to that with lum-sum tax financing. Furthermore, the theoretical outcomes with lum-sum tax or consumtion tax financing are caable of roviding a channel to exlain the diverse emirical results. The rationale for these results is as follows. An increase in the government exenditure through lum-sum tax or consumtion tax financing gives rise to a resources-withdrawal effect which leads to a change in the relative rice between goods and then induces a movement in roduction factors from one sector to another. With the Stoler-Samuelson theorem, an increase in the rice of one sector s outut leads to a more than roortional increase in the rice of the factor used intensively in that sector. As a result, deending on the factor intensities of different sectors, a change in the relative rice leads to an alteration in the caital share-labor ratio. The alteration in the caital share-labor ratio further affects the marginal roductivity of caital which may be beneficial or harmful to economic growth. Therefore, the steady-state growth effect of government exenditure financed by a lum-sum or consumtion tax hinges on the factor intensity between the sectors. With regard to the effects under the income tax financing scheme, there are two channels for the government exenditure to affect the economic growth. The first relates to the induced increase in the income tax rate and the second is due to the alteration in the relative rice. Although the second channel has an ambiguous effect on the economic growth, the growth-retarding effect that arises from the first one always dominates the second one. Therefore, a rise in government sending with income tax financing retards the economic growth rate. The reminder of the aer is organized as follows. n Section 2, we construct the erfect-foresight equilibrium in the Uzawa-Romer endogenous growth framework under a balanced government buet rule in which taxes adjust endogenously to finance a given government exenditure. Section 3 examines the effects of government exenditure on the steady-state relative rice and the economy s balanced growth rate under alternative financing 79

3 nternational Journal of Business and Management Vol., No. 4; 206 schemes. Finally, Section 4resents the main findings of our analysis and concludes. 2. The Analytical Framework We establish a two-sector economy in which one sector roduces investment goods and the other roduces consumtion goods. The economy consists of a continuum of infinitely-lived identical agents and a government. Agents have common references, otimize decisions on the basis of erfect foresight, and emloy a roduction technology of Romer (986)-tye. The government collects taxes (a lum-sum tax, income tax, and consumtion tax) to suort its sending which is a fraction of total outut. The details of this economy are described as follows. 2. The Otimization of Reresentative Agent The objective of a reresentative agent is to maximize the discounted sum of future instantaneous utilities: c e t dt () 0 where c is consumtion, is the inverse of the intertemoral elasticity of substitution, (Note 3) and (0,) is a constant rate of time reference. At each instant of time, the reresentative agent is bounded by two tyes of constraints. First, we assume that the time endowment of the reresentative agent is normalized to unity and l ( l ) is the labor time allocated to the investment (consumtion) goods sector. Thus a time constraint can be exressed as: l l (2) Second, a flow constraint links caital accumulation to any difference between its gross income (the total outut) and its gross exenditure (consumtion, taxes, and caital dereciation). t can be described by: k ( )( y y ) ( c ) k T (3) where an overdot denotes the time derivative, k is the caital stock, y is the outut of investment goods sector, y is the outut of consumtion goods sector, is the relative rice of consumtion goods in terms of investment goods, is the income tax rate, is the rate of consumtion tax, T is the lum-sum tax, and is the dereciation rate of caital. The roduction function of each sector in the economy is the Romer (986)-tye secification of the knowlee sillover effect which is secified as follows: y A ( sk) l k, (4a) y A [( s) k] l k, (4b) where A 0, A 0, 0, 0, k is the average economy-wide level of caital stock, s is the fraction of caital stock allocated to the investment goods sector. By using equations (2), (4a) and (4b), equation (3) can be rewritten as: k ( ){ A ( sk) l k A [( s) k] ( l ) k } ( ) c k T (5) The otimizing roblem for the reresentative agent is to maximize equation () subject to equation (5) and the initial caital holdings k 0 0. Letting be the co-state variable associated with equation (5), the current-value Hamiltonian can be exressed as: c H {( )[ A s k l k A ( s) k ( l ) k ] ( ) c k T} The first-order conditions necessary for this otimizing roblem are: c ( ) (6a) 80

4 nternational Journal of Business and Management Vol., No. 4; 206 l k k A s A ( s) ( l ) k k (6b) l k k ( ) A s ( ) A ( s) ( l ) k k (6c) {( )[ A s l k k A ( s) ( l ) k k ] } (6d) together with equation (5) and the transversality condition of k : t lim ke 0 (6e) t Equation (6a) imlies the equality between the marginal utility of consumtion and the tax-adjusted shadow value of caital stock. Equations (6b) and (6c) resectively determine the otimal allocation of caital and labor between two sectors which requires that the marginal roductivity of caital and labor in terms of investment goods should be equalized across sectors at each oint of time. Equation (6d) is the Keynes-Ramsey rule governing the otimal choice between consumtion and caital accumulation by equating the marginal return on consumtion and the after-tax net rate of returns on caital. Since all agents are assumed to be identical, in a symmetric equilibrium all agents own the same amount of caital, and hence k k is true in equilibrium. Equations (4a), (4b), (5) and (6b)-(6d) are accordingly rewritten as: y A s l k, (7a) y A ( s) l k, (7b) k ( ){ A s l A ( s) ( l ) } k ( ) c k T (7c) s s A ( ) A ( ) (7d) l l s s ( ) A ( ) ( ) A ( ) (7e) l l {( )[ A s l A ( s) ( l ) ] } (7f) 2.2 The Government The government is assumed to imose taxes (a lum-sum tax, income tax, or consumtion tax) to finance its exenditure and maintains a continually balanced buet at each oint in time. Hence, the government s buet constraint can be exressed as: G ( y y ) c T (8) where G is government exenditure. n order to ensure sustained steady-state growth, following Devereux and Love (995) and Palivos and Yi (995), we secify government exenditure to be a fixed ratio of total outut, i.e., G g y y ), 0 g. Equation (8) can thus be rewritten as: ( ( g )( y y ) c T (9) Furthermore, government urchases are assumed to be comosed of investment goods and consumtion goods, i.e., G G G, where G ( G ) denotes government exenditure of investment (consumtion) goods. Without loss of generality, both tyes of government exenditures are set as fixed ratios of the resective outut T 8

5 nternational Journal of Business and Management Vol., No. 4; 206 and both ratios are set equally, that is: G gy and G gy. We then deict our olicy exerience as follows: throughout the aer, the government controls the exenditure ratio g as a olicy instrument and lets the corresonding tax endogenously adjust to maintain the balanced government buet. To be more secific, following Palivos and Yi (995), if the government imlements a lum-sum tax financing scheme, the lum-sum tax T will adjust endogenously to finance the increase in government exenditure and maintain the balanced government buet while the income tax rate and consumtion tax rate are set to be zero. As for the income tax financing scheme or the consumtion tax financing scheme, the method of maniulation is similar to that in the lum-sum tax financing scheme. 2.3 The Equilibrium We turn to derive the equilibrium dynamics of the economy. By combining equations (3) and (9) with equations (7a) and (7b), the consumtion goods and investment goods markets are resectively in their equilibrium through the flexible adjustment of relative rice. That is: c ( g) A ( s) ( l ) k (0a) k k ( g) A s l (0b) Next, from equations (7d) and (7e), we have: s l dv v( ), v v( ) 0 ( ) d, if (a) ds s s( ), s ( ) v( ) 0 (b) 2 d ( ) l l ( ), dl l ( ) ( )( ) 0 (c) 2 d v The rationale of equations (a)-(c) is as follows. When the relative rice of consumtion goods increases, the consumtion (investment) goods sector will increase (decrease) its outut and the roduction factors will move from the investment goods sector to the consumtion goods sector. Hence both s and l will decrease. s However, the effect of the relative rice on the caital share-labor ratio ( )is ambiguous, which in turn is determined by factor intensity. (Note 4) As documented by the Stoler-Samuelson l theorem, if the consumtion goods sector is caital-intensive ( ), then the higher makes caital to be more exensive relative to labor, thereby leading both sectors to use less caital and more labor. Thus the caital share-labor ratio in both sectors declines. By contrast, if the investment goods sector is caital-intensive ( ), then the higher makes labor to be more exensive relative to caital and hence the caital share-labor ratio in both sectors rises. Furthermore, by taking the log derivatives of equation (6a), the otimal change in consumtion is exressed as: c [ c ] (2) Then, taking log derivatives of equation (0a) and substituting the resulting equation into equation (2), the growth rate of the relative rice is obtained as: [( )( k ) ] k (3) 82

6 nternational Journal of Business and Management Vol., No. 4; 206 y where 0 and ] 0 [ s l ( ) y s( ) l ( ). Equation (3) is a generalized equation which governs the movement of the relative rice under alternative government exenditure financingschemes. Moreover, we will show that equation (3) is a one-dimensional differential equation of under the corresonding financing scheme. 3. Long-Run Growth Effects of Alternative Financing Aroaches By using the information mentioned in the former section, the effect of government exenditure under alternative financing aroaches on the steady-state relative rice and growth rate is investigated as follows. 3. Lum-Sum Tax Financing Under a lum-sum tax financing scheme ( 0 ), the endogenous adjustment of T clearly has no direct effect on the otimal behavior of agents and the dynamics of the relative rice. From this ersective, T can be recursively determined by equation (9). onsequently, the system can be exressed by equation (3) with 0 as follows: [( k ) ] k Emloying equations (7f) and (0b) with (7d) and (a)-(c), we have: { A [ v( )] k ( g) A [ s( )] [ l k ( )] } ( ) (, g) (4) (5a) (5b) where ( ) [ ( )] 2 0 A v v, if, g A v )] ( ) [ ( [ s ( ) v( ) l ] 0, and g A [ s( )] [ l ( )] 0 g. Notice that, in equation (5a), A [ v( )] is the marginal roductivity of caital, thus can be regarded as the demand for investment goods. Based on equation (a), when the relative rice of consumtion goods increases, the caital share-labor ratio declines (increases) and thus the after-tax marginal roductivity of caital imroves (deteriorates) if ( ). Accordingly, the demand for investment goods is an increasing (decreasing) function of and the uward-sloing (downward-sloing) locus when ( ) can be illustrated in Figure (Figure 2). n addition, k k in equation (5b) refers to the caital stock which can be used by agents and hence is regarded as the suly of investment goods. According to equations (b) and (c), an increase in makes the roduction factors move from the investment goods sector to the consumtion goods sector and thus decreases the outut of investment goods. As a consequence, the suly of investment goods is 83

7 nternational Journal of Business and Management Vol., No. 4; 206 an increasing function of and the downward-sloing locus k k can be illustrated in Figures and 2. (Note 5). Substituting equations (5a) and (5b) into equation (4), we have a one dimensional differential equation of as follows: [( ( ) (, g)] (6) Equation (6) imlies that the adjustment of deends on the relative strength between the demand for and the suly of investment goods. Given that is a jum variable, the dynamic stability of the system claims that the characteristic root of equation (6) should be ositive to ensure a unique erfect-foresight equilibrium ath, i.e. 0 (7) where 0. When the consumtion goods sector is caital-intensive ( ), 0 is true and equation (7) is obviously satisfied (Figure ). However, when the investment goods sector is caital-intensive k ( ), and are both also negative, and equation (7) claims that k must be steeer than (Figure 2). n the balanced-growth equilibrium, the economy is characterized by 0. Hence is at the steady-state value, namely,, and c and k exhibit a common growth rate,. By substituting 0 into equation (6), can be obtained as follows: ( ) (, g) (8) To ensure the existence and uniqueness of the steady-state equilibrium, by referring to Figures and 2, the following condition is claimed: (Note 6) ( A ) ( g)a (9) Given the conditions in equations (7) and (9), we derive that an increase in the government exenditure ratio will lower by using equation (8) as follows: d g T 0 (20) n Figures and 2, an increase in government sending from g 0 to g gives rise to a decrease in the suly of investment goods [ k ( g 0 ) k k ( g ) ], and thereby decreases accordingly. k Furthermore, with 0 in equation (4), the balanced growth rate is exressed as follows: k ( ) k Thus, by emloying equations (2) and (5a) in the steady state and equation (20), theeffect of an increase in the government exenditure ratio on is derived as follows: (2) 84

8 nternational Journal of Business and Management Vol., No. 4; 206 d T d T 0, if (22) From equation (20), decreases, thus the investment (consumtion) goods sector tends to increase (decrease) its outut and the roduction factors move from the consumtion goods sector to the investment goods sector (both s and l increase). As mentioned before in the Stoler-Samuelson theorem, the decrease in induces an adjustment in the caital share-labor ratio deending on the factor intensity. f the consumtion goods sector is caital-intensive ( ), a decrease in causes labor to be more exensive relative to caital, and hence both roduction sectors enhance the caital share-labor ratios, which in turn deteriorates the marginal roductivity of caital and thus the steady-state growth rate decreases. By contrast, if the investment goods sector is caital-intensive ( ), a decrease in makes caital to be more exensive relative to labor and hence the caital share-labor ratios are reduced in both roduction sectors, which in turn imroves the marginal roductivity of caital and leads to an increase in the steady-state growth rate. This ambiguous result of the steady-state growth rate runs in shar contrast to Devereux and Love (995), Turnovsky (2000) and hang et al. (2004). n addition, it can be viewed as a otential means of exlaining the mixed emirical results [Miller and Russek (997)]. From the above analysis, we obtain the following roosition: Proosition. (The Effect of Lum-Sum Tax Financing) When the government imlements a lum-sum tax financing scheme in a two-sector economy with consumtion goods and investment goods, an increase in the government exenditure ratio lowers the steady-state relative rice of the consumtion good, and has an ambiguous effect on the steady-state growth rate deending on the factor intensity. 3.2 ncome Tax Financing Under income tax k financing ( T 0 ), g can be obtained from equation (9). Here, the suly of investment goods ( ) is still reresented by equation (5b), but the demand for investment goods ( ) with g becomes: k {( g) A [ v( )] } (, g) (23) where ( ) ( ) [ ( )] 2 0 g A v v, if, [ ( )] 0 g A v. g Hence, the dynamic system can also be exressed by substituting equations (23) and (5b) into equation (4) as follows: [( (, g) (, g)] (24) Similar to the analysis for the lum-sum tax financing scheme, the dynamic stability of the system and the uniqueness and existence of the steady-state equilibrium claim that 0 and [( g) A ] ( g)a, resectively. Under the income tax financing scheme, the effect of an increase in the government exenditure ratio on is derived from equation (24) with 0 : d g g [ s( ) ] A [ v( )] 0, if s( ) 0 (25) Now, we go straight to the analysis of the steady-state effect using Figures (3a)-(3b) and (4a)-(4b).Obviously, under the income tax financing scheme, a rise in government exenditure not only gives rise to a 85

9 nternational Journal of Business and Management Vol., No. 4; 206 resource-withdrawal effect which decreases the suly of investment goods [ k ( g 0 ) k k ( g ) ], but also leads k to a deterioration in the after-tax marginal roductivity of caital via an increase in the income tax rate which decreases the demand for investment goods [ ( g 0 ) ( g ) ],as shown in Figures 3a-3b and 4a-4b. As a consequence, the effect of an increase in the government exenditure ratio on the steady-state relative rice of consumtion goods deends on the relative strength between the decreases in the suly of and the demand for the investment goods, i.e., s ( ). When the extent of the decrease in suly is greater (less) than that of the decrease in demand [ s ( ) ( ) ], the relative rice of consumtion goods goes down (u) [Figures 3a and 4a (3b and 4b)]. By using equations (2), (23) and (25) in the steady state, we next obtain: (Note 7) d d g ( g) A 2 [ v( )] 2( ) s 0 (26) Equation (26) indicates that an increase in government exenditure based on income tax financing definitely causes the steady-state growth rate to deteriorate. The rationale is that an increase in government exenditure based on income tax financing affects the after-tax marginal roductivity of caital through two channels. First, due to the increase in the income tax rate, the after-tax marginal roductivity of caital deteriorates. Second, the alteration in further affects the marginal roductivity of caital. f the consumtion goods sector is caital-intensive ( ), the decrease (increase) in leads both sectors to raise (reduce) the caital share-labor ratio and in turn decreases (increases) the marginal roductivity of caital. Obviously, if the marginal roductivity of caital decreases, the second effect reinforces the first growth-retarding effect (Figure 3a). However, if the marginal roductivity of caital increases, the two effects are in conflict with each other and the second one is dominated by the first (Figure 3b). As a result, an increase in the government exenditure ratio using income tax financing always reduces the steady-state growth rate. Nevertheless, if the investment goods sector is caital-intensive ( ), the economic exlanation for the steady-state effects on the relative rice and the growth rate is similar to the case where. To save sace, we only resent the grahical illustrations which are shown in Figures 4a and 4b. This finding is consistent with Devereux and Love (995). Accordingly, we have the following roosition: Proosition 2. (The Effect of ncome Tax Financing) When there is a two-sector economy comosed of consumtion goods and investment goods, an increase in the government exenditure ratio based on income tax financing has an ambiguous effect on the steady-state relative rice of consumtion goods which deends on the relative extent of the difference between s( ) and. Furthermore, it results in a deterioration in the steady-state growth rate. 3.3 onsumtion Tax Financing Under consumtion tax financing scheme ( T 0 ), the endogenous consumtion tax is derived from equation (9) as follows: (Note 8) (, g) (27) y where [ ] 0 y ( ) y and g 0. Based on equation (27), the rate of y y ( g) y change in the consumtion tax rate can be derived as: 86

10 nternational Journal of Business and Management Vol., No. 4; 206 Furthermore, by substituting equation (28) into equation (3), we have: y [ ] (28) y y k [( ) ] k (29) where y k [ ( ) ( )] 0, moreover, ( ) and are ( )( ) y y k still reresented as equations (5a) and (5b). By comaring equation (29) with equation (4), it is clear that the conditions for the dynamic stability and the uniqueness and existence of the steady-state equilibrium under consumtion tax financing are similar to those under lum-sum tax financing, and thus we omit them to save sace. Furthermore, by substituting 0 into equation (29), we can sequentially derive that the steady-state effects of an increase in the government exenditure ratio under consumtion tax financing are equivalent to those under lum-sum tax financing. To be more secific, in referring to Proosition, a consumtion-tax-financed increase in the government exenditure ratio gives rise to an ambiguous effect on the steady-state growth rate that deends on the factor intensity. This result contrasts with Turnovsky (996). Proosition 3. (The Effect of onsumtion Tax Financing) n a two-sector economy with consumtion goods and investment goods, a consumtion-tax-financed increase in the government exenditure ratio gives rise to an ambiguous effect on the steady-state growth rate that hinges on factor intensity. 3.4 Discussion Based on sections , we can summarize that, regardless of the financing scheme, k has to be k satisfied in the steady state. Generally, the above relationshi can be exressed as: {( ) A [ v( )] } ( g) A [ s( )] [ l ( )] (30) furthermore, the steady-state relative rice can be derived with equation (30) as: ( g, ) (3) Obviously, under the lum-sum tax (consumtion tax) financing scheme, the endogenous T ( ) does not affect. Thus, the steady-state effects of an increase in the government exenditure ratio under consumtion tax financing are equivalent to those under lum-sum tax financing, i.e. d d d d T and T (32) However, when the income tax financing is imlemented, an increase in the government exenditure ratio raises d the income tax rate endogenously ( 0 ). By emloying the concet of the Le hatelier Princile and equation (3), we obtain the following equation: (Note 9) d d d d d T T (33) 87

11 nternational Journal of Business and Management Vol., No. 4; 206 furthermore, the effect on the steady-state growth rate is exressed as: (Note 0) d where T 0. (Note ) As a result, the following relationshi is obtained: d d d d d d T T (34) d d T (35) Based on Equations (32) and (35), we have: Proosition 4. (The Policy Recommendation) n the ersective of growth, regardless of the factor intensity, when government attemt to finance a government urchase, a lum-sum tax financing scheme (consumtion tax financing scheme) is always better than the income tax financing scheme. 4. oncluding Remarks By using the Uzawa (96; 963) two-sector model of consumtion and investment goods with a Romer (986)-tye knowlee sillover technology, we examine the growth rate effect of an increase in the government exenditure ratio through three tyes of tax financing: lum-sum tax financing, income tax financing, and consumtion tax financing. The results show that, a rise in the government exenditure ratio based on lum-sum tax financing has an ambiguous effect on the balanced growth rate deending on the factor intensity between the sectors. The balanced growth rate decreases (increases) with a rise in government sending if the consumtion (investment) goods sector is caital-intensive. The outcome for consumtion tax financing is equivalent to that for lum-sum tax financing while an income-tax-financed increase in the government exenditure ratio definitely decreases the economy s long-run growth rate. Since the emirical results reorted by Kormendi and Mequire (985) and Miller and Russek (997) vary quite considerably, our two-sector model that is based on lum-sum tax or consumtion tax financing aears to be able to rovide a channel through which to exlain the mixed emirical findings. Table. aital shares for 2-digit U.S. industries [summarized form Jones (2003)] ndustry aital Share ndustry aital Share onstruction Furniture and Fixture Motor Vehicle Trade Transortation Textile Mill Products Agriculture Electrical Food and Kindred Finance and Petroleum and oal ommunication Machinery Products nsurance Products

12 nternational Journal of Business and Management Vol., No. 4; 206 Figure. The effect of an increase in the government exendituree ratio with a lum-sum tax financing: Figure 2. The effect of an increase in the government exendituree ratio with a lum-sum tax financing: 89

13 nternational Journal of Business and Management Vol., No. 4; 206 Figure 3a. The effect of an increase in the government exenditure ratio with an income tax financing: and s( ) Figure 3b. The effect of an increase in the government exenditure ratio with an income tax financing: and s( ) Figure 4a. The effect of an increase in the government exenditure ratio with an income tax financing: and s( ) 90

14 nternational Journal of Business and Management Vol., No. 4; 206 Figure 4b. The effect of an increase in the government exenditure ratio with an income tax financing: and s( ) References Attanasio, O., Banks, J., & Tanner, S. (2002). Asset Holding and onsumtionn Volatility. Journal of Political Economy, 0(4), htt:/ //dx.doi.org/0.086/ Barro, R. J., & Sala-i-Martin, X. (2004). Economic Growth (2nd ed.). ambrie, MA: MT Press. Bond, E. W., Wang, P., & Yi,. K. (996). A General Two-Sector Model of Endogenous Growth with Human and Physical aital: Balanced Growth and Transitional Dynamics. Journal of Economic Theory, 68(), htt://dx.doi.org/0.006/jeth hang, W. Y., Tsai, H. F., & Lai,.. (2004). Taxation, Growth, and the Sirit of aitalism. Euroean Journal of Political Economy, 20(4), htt://dx.doi.org/0.06/j.ejoleco Devereux, M. B., & Love, D. R. F. (994). The Effects of Factor Taxation in a Two-Sector Model of Endogenous Growth. anadian Journal of Economics, 27(3) ), htt://dx.doi.org/ /0.2307/3578 Devereux, M. B., & Love, D. R. F. (995). The Dynamic Effects of Government Sending Policies in a Two-Sectohtt:/ //dx.doi.org/0.2307/ Gokan, Y. (2002). Alternative Government Financing and Stochastic Endogenous Growth. Journal of Economic Dynamics and ontrol, 26(4), htt://dx.doi.org/0.06/s (00) Hasanov, F. (2005). Housing, Household Portfolio, and ntertemoral Elasticity of Substitution: Evidence from Endogenous Growth Model. Journal of Money, redit, and Banking, 27(), the onsumer Exenditure Survey. Macroeconomics no from EconWPA. Jones,.. (2003). Growth, aital Shares, and a New Persective on Production Function. U.. Berkley, Working Paers. Jones, L. E., Manuelli, R. E., & Rossi, P. E. (993). Otimal Taxation in Models of Endogenous Growth. Journal of Political Economy, 0(3), htt://dx.doi.org/0.086/26884 King, R. G., & Rebelo, S. T. (990). Public Policy and Economic Growth: Develoing Neoclassical mlications. Journal of Politicall Economy, 98( (5), htt://dx.doi.org/0.086/26727 Kormendi, R.. and Mequire, P. G. (985). Macroeconomic Determinants of Growth: ross-ountry Evidence. Journal of Monetary Economics, 6(2), htt://dx.doi.org/0.06/ / (85) Lucas, R. E. Jr. (988). On the Mechanics of Economic Develoment. Journal of Monetary Economics, 22(), htt://dx.doi.org/0.06/ (88) Miller, S. M., & Russek, F. S. (997) Fiscal Structures and Economic Growth: nternational Evidence. Economic nquiry, 35(3), htt://dx.doi.org/0./j tb02036.x Mino, K. (996). Analysis of a Two-Sector Model of Endogenous Growth with aital ncome Taxation. nternational Economic Review, 37(), htt://dx.doi.org/0.2307/

15 nternational Journal of Business and Management Vol., No. 4; 206 Palivos, T., & Yi,. K. (995). Government Exenditure Financing in an Endogenous Growth Model: A omarison. Journal of Money, redit, and Banking, 27(4), htt://dx.doi.org/0.2307/ Rebelo, S. T. (99). Long-Run Policy Analysis and Long-Run Growth. Journal of Political Economy, 99(3), htt://dx.doi.org/0.086/26764 Romer, D. (2005). Advanced Macroeconomics (3rd ed.). New York, NY: McGraw-Hill. Romer, P. M. (986). ncreasing Returns and Long-Run Growth. Journal of Political Economy, 94(5), htt://dx.doi.org/0.086/26420 Samuelson, P. A. (947). Foundation of Economic Analysis. ambrie, MA: Harvard University Press. Silberberg, E., & Suen, W. (200). The Structure of Economics: A Mathematical Analysis (3rd ed.). New York: McGraw Hill. Stokey, N. L., & Rebelo, S. T. (995). Growth Effects of Flat-Rate Taxes. Journal of Political Economy, 03(3), htt://dx.doi.org/0.086/26993 Turnovsky, S. J. (992). Alternative Forms of Government Exenditure Financing: A omarative Welfare Analysis. Economica, 59(234), htt://dx.doi.org/0.2307/ Turnovsky, S. J. (996). Otimal Tax, Debt, and Exenditure Policies in a Growing Economy. Journal of Public Economics, 60(), htt://dx.doi.org/0.06/ (95)059- Turnovsky, S. J. (2000). Fiscal Policy, Elastic Labor Suly, and Endogenous Growth. Journal of Monetary Economics, 45(), htt://dx.doi.org/0.06/s (99) Uzawa, H. (96). On a Two-Sector Model of Economic Growth,. Review of Economic Studies, 29(), htt://dx.doi.org/0.2307/ Uzawa, H. (963). On a Two-Sector Model of Economic Growth,. Review of Economic Studies, 30(2), htt://dx.doi.org/0.2307/ Uzawa, H. (965). Otimum Technical hange in an Aggregative Model of Economic Growth. nternational Economic Review, 6(), 8-3. htt://dx.doi.org/0.2307/ Van der Ploeg, F., & Alogoskoufis, G. S. (994). Money and Endogenous Growth. Journal of Money, redit, and Banking, 26(4), htt://dx.doi.org/0.2307/ Vissing-Jorgensen, A. (2002). Limited Asset Market Particiation and the Elasticity of ntertemoral Substitution. Journal of Political Economy, 0(4), htt://dx.doi.org/0.086/ Notes Note. Van der Ploegand Alogoskoufis (994), Palivos and Yi (995), and Gokan (2002) analyze the relative merits of alternative forms of government exenditure financing under a monetary endogenous growth model. Note 2. The definition of consumtion goods we use here is: the economic goods or services urchased by households to satisfy their wants and desires, such as food, clothing, motor vehicles, communications and finance and insurance. Moreover, the definition of investment goods is: the economic goods or service used by firms as inuts to roduce their roduct, such as construction (lant), electrical machinery, and equiments. Note 3. The setting of imlies that the elasticity of intertemoral substitution is located in the range between 0 and, which is suorted in the emirical studies [Vissing-Jorgensen (2002), and Attanasio et al. (2002)], for a comrehensive survey, see Hasanov (2005). Note 4. From equations (7d) and (7e), s s l l is true. This imlies that the qualitative effect of on the caital share-labor ratio sector. s l in the consumtion goods sector is similar to that in the investment goods Note 5. The concet of the grahical analysis we use here is in the sirit of and in accordance with that in the Solow-Swan growth model. Please refer to Barro and Sala-i-Martin (2004) or Romer (2005) for the detail. 92

16 nternational Journal of Business and Management Vol., No. 4; 206 Note 6. Since lim v, lim s, and lim l, from equations (5a) and (5b), lim ( ) ( A ) 0 and lim (, g) ( g) A 0 is true. Note 7. The relationshi v [ s v( ) l ] is used in deriving equation (26). l Note 8. By substituting equation (0a) into equation (9) with T 0 and using equation (0b), we have: g ( y y ) ( g) y Taking the total differentiation of the above equation and using y y 0 and y 0, we derive equation (27). y Note 9. The Le hatelier Princileis introduced into economics analysis by Samuelson (947), for a detail secification, lease refer to Silberberg and Suen (200). Note 0. This equation is similar to equation (6a) in Turnovsky (2000), d Note. From equations (3) and (5b), T 0 d d and T 0 d can be easily derived. oyrights oyright for this article is retained by the author(s), with first ublication rights granted to the journal. This is an oen-access article distributed under the terms and conditions of the reative ommons Attribution license (htt://creativecommons.org/licenses/by/3.0/). 93