Publicly Financed Education in an Endogenous Growth Model

Creedy, John; Gemmell, Norman Working Paper Publicly Financed Education in an Endogenous Growth Model New Zealand Treasury Working Paper, No. 02/24 Provided in Cooperation with: The Treasury, New Zealand Government Suggested Citation: Creedy, John; Gemmell, Norman (2002) : Publicly Financed Education in an Endogenous Growth Model, New Zealand Treasury Working Paper, No. 02/24, New Zealand Government, The Treasury, Wellington This Version is available at: https://hdl.handle.net/10419/205499 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Publicly Financed Education in an Endogenous Growth Model John Creedy and Norman Gemmell N EW Z EALAND T REASURY W ORKING P APER 02/24 D ECEMBER /2002 473620-1 NZ TREASURY WORKING PAPER 02/24 Publicly Financed Education in an Endogenous Growth Model MONTH / YEAR December/2002 AUTHORS John Creedy New Zealand Treasury 1, The Terrace Wellington New Zealand Email Telephone Fax [email protected] 64 4 471 5009 64 4 473 1151 Norman Gemmell Department of Economics University of Nottingham Nottingham UK Email Telephone Fax [email protected] 44 115 951 5465] 44 115 951 4159 ACKNOWLEDGEMENTS The first draft of this paper was completed while J. Creedy was at the Univeristy of Melbourne. This research was supported by a Visiting Research Scholar award from the University of Melbourne Faculty of Economics and Commerce. We are grateful to seminar participants at the Universities of Nottingham and Sydney for helpful comments. NZ TREASURY New Zealand Treasury PO Box 3724 Wellington 6008 NEW ZEALAND Email Telephone Website [email protected] 64-4-472 2733 www.treasury.govt.nz DISCLAIMER The views expressed in this Working Paper are those of the author(s) and do not necessarily reflect the views of the New Zealand Treasury. The paper is presented not as policy, but with a view to inform and stimulate wider debate. WP 02/24 | Publicly Financed Education in an Endogenous Growth Model i Abstract This paper constructs an endogenous growth model, applicable largely to developing countries, based on human capital accumulation in which education is publicly provided and financed, and schooling is compulsory. Public investment in human and physical capital are financed from taxes on wage and capital income, and consumption. The equilibrium growth properties of the model are examined and the steady-state effects of education and fiscal policy are derived. The specification of the human capital production function and the strength of labour supply effects are shown to be important for the magnitude of steady-state outcomes. Simulations illustrate the model's properties. JEL CLASSIFICATION H52 H2 H4 D5 KEYWORDS Education; Taxation; Endogenous Growth; Labour Supply; General Equilibrium WP 02/24 | Publicly Financed Education in an Endogenous Growth Model ii Table of Contents 1 Introduction 1 2 The Structure of the Model 2 2.1 Production and Investment 3 2.2 Tax Revenue 4 2.3 Consumption and Labour Supply 4 2.4 Basic Properties 5 3 Policy Effects on Equilibrium Growth 6 3.1 Direct and Indirect Effects 7 3.2 Human Capital Investment 7 4 Some Policy Simulations 9 4.1 A Benchmark Case 10 4.2 Time Spent in Education 10 4.3 Changing Expenditure Allocations 11 4.4 Changing Tax Rates 12 4.5 Transitional Dynamics 14 5 Conclusions 15 Appendix: The Dynamics of the Model 16 List of Tables 1. Benchmark Values for Simulations 10 List of Figures 1. Equilibrium Growth and Education Proportion 11 2. Iso-growth Expenditure Proportions 12 3. Equilibrium Growth and Wage Taxation 13 4. A Shift in Public Expenditure Towards Human Capital 15 1 Introduction A central tenet of education policy in developing countries is that expansion of school enrolments is desirable, for reasons of social justice, and because economic prosperity is perceived to be fostered by the accumulation of human capital via education.1This paper examines the growth effects of human capital investment achieved through publicly-provided, compulsory education, financed from income and consumption taxes. The effects on labour supply of higher tax rates, in addition to general equilibrium effects on wages and prices, are examined. Given the aims of the paper, a number of assumptions need to be adopted which differ from those in the growth literature. Since Lucas (1988, 1990) education has been extensively examined in the context of models in which individuals allocate their time to education within an inter-temporal utility-maximising framework.2However, it is not obvious that this framework is the best way to capture education decisions in most developing countries. The theoretical literature on human capital and growth is generally separate from that on fiscal policy and growth. However, any analysis of the growth impact of state-provided education cannot be conducted independently of the financing implications, as dictated by the government budget constraint.3 Section 2 describes the basic structure of the model (with further details regarding dynamics set out in the Appendix). Section 3 examines the effects on equilibrium growth of changes in education policy. Section 4 provides numerical policy simulations to investigate the various policy trade-offs in more detail. Brief conclusions are in Section 5. 1In China for example, where education expansion has been rapid, the government now claims that its nine-year compulsory education programme covers 73% of “opulated area”. A problem with many developing countries is that, despite having compulsory education, participation rates are low. 2Aghion and Howitt (1998) and Topel (1999) provide reviews of much of this literature. 3Models of fiscal policy and growth recognise the government budget constraint, though relatively few examine taxes alongside productivity-enhancing or utility-enhancing public expenditures. Studies include Barro (1990), Barro and Sala-i-Martin (1992), Cashin (1995), Devarajan et al (1996) and Capolupo (2000). With the exception of Capolupo, human capital is either excluded or treated as a private decision in these papers. All these papers assume exogenous labour supply. Models of taxation and growth in which government expenditures have no output or utility effects include King and Rebelo, (1990), Rebelo, (1991), Mendoza et al (1997), Milesi-Ferretti and Roubini (1998). These allow for endogenous labour supply. For example, Milesi-Ferretti and Roubini (1998) demonstrate that the nature of leisure is important for growth predictions, depending on whether leisure requires raw labour time, quality time (time and human capital inputs) or home production (where physical capital inputs are also required). 1 2 The Structure of The Model Modelling fiscal and education policy impacts on growth in an LDC context requires several assumptions that differ from those relevant to a more developed country. The majority of individuals who currently receive education in LDCs do so in public primary or secondary schools, frequently within a compulsory education regime. For those individuals not currently receiving education, this is typically because public education is unavailable rather than because families’ utility-maximising calculus leads them to choose lower levels of education.4 Governments in LDCs also undertake substantial physical capital investment in the form of infrastructure which may be important for private sector productivity. Indeed, in many LDCs, despite recent market-orientated reforms, substantial commercial and especially investment activity is either undertaken, or controlled at the margin, by government, compared with a typical developed country. The allocation of revenues to public physical capital investment therefore needs to be included in the analysis. However, the model abstracts from private sector investment. This allows the analysis to focus on the issues of primary interest, namely the response of growth to publicly funded and provided human capital investment.5It results in a model analogous to Barro (1990) but where output is a function of human capital and public physical capital rather than private and public physical capital. To simplify the exposition, depreciation of human and physical capital is ignored. Unlike Barro (1990) and similar models, labour supply is endogenous. Though choices between income and leisure may seem less relevant in an LDC context, many individuals face choices between income earned in the taxed sector and income (including subsistence activities) from the untaxed sector, or leisure. In analysing output growth, the present model focuses on labour supplied to the taxed sector and labels all other activities as leisure. In this broader sense, endogenous labour supply choices are relevant in LDCs. Since untaxed activities by an individual involve the application of the same human capital, leisure is modelled, following Mendoza et al (1997), as quality time, that is, time augmented by education. It is assumed that individuals maximise their utility within each period but do not maximise inter-temporally. This reflects both the fact that poor individuals with low levels of education are unlikely to make sophisticated inter-temporal calculations and, since there is no private investment or education in the model, there is little to be gained from adopting an inter-temporal utility maximisation 4However, in some LDC contexts, especially in rural agriculture, families demonstrate a preference not to send their children to school, even when available and compulsory, due to preceptions that this reduces family income. 5It is recognised that in some LDCs, education is publicly funded but privately provided, via the use of voucher schemes. 2 framework.6 2.1 Production and Investment The model is a closed-economy general equilibrium model with endogenous labour supply, in which a single individual maximises utility from consumption of asinglefinal good and leisure. The representative individual is initially endowed with raw labour time, N, which may be augmented by education to form human capital, H. In addition, homogeneous physical capital, K, is distributed to the representative individual. This captures the notion that individuals benefit from infrastructure and, as discussed further below, can be taxed on the imputed benefits from that consumption. Private sector production of the final good, Q, in each period can be used for both consumption and investment. The production function takes the CobbDouglas form:7 Q=Aq(uqH)αqK1−αq(1) where uqis the proportion of human capital devoted to production of Q. The government raises revenue from factor and consumption taxes, and spends it on three functions. First, it purchases, at market prices, an amount Qh used as an input into human capital production together with an appropriated fraction of labour time, uh. Adopting the Cobb-Douglas form, the production function for human capital is: dH =AhQαh h(uhH)1−αh(2) The inclusion of Qhin (2) is analogous to the use of physical capital by, for example, King and Rebelo (1990) and Milesi-Ferretti and Roubini (1998).8 The government undertakes physical capital investment in the form of a private (as opposed to public) capital good, whereby the government purchases, again at market prices, an amount of final output equal to Qk.9To capture the 6In this respect the present model is analogous to the Solow-Swan model in which savings are a fixed proportion of income. Although private savings are zero here, the private-good nature of public investment and the compulsory nature of educational time inputs, together with tax-financing, ensure that taxation and education are analogous to a compulsory savings proportion determined by government. There is the additional complication of possible tax disincentive effects on labour supply depending on the form of tax used. 7Throughout the following analysis, time subscripts are suppressed for convenience. 8As in these models, this property (in particular, the value of αh) is important for the growth effects of fiscal policy. However, unlike these models Qis not defined here exclusively as a capital good and can represent educational inputs of a capital or recurrent nature. 9It can be argued that some government investment, for example on infrastructure, should be treated as a public good. However, Barro (1990) and Barro and Sala-i-Martin (1992) argue, with support from empirical evidence, that government expenditures are dominated by goods with quasi-private characteristics and are typically subject to congestion. 3 benefits of this physical capital to the consumer, the model adopts the device of distributing this to the individual at the start of each period. 2.2 Tax Revenue Tax revenue not used in the production of human and physical capital is returned to the individual in the form of an untaxed transfer payment, D. This is designed to reflect the fact that much public expenditure in LDCs is more likely to affect consumption than productivity. Total revenue, R, is divided among the three expenditures in proportions θj,(j=k,h,d)asfollows: Qk=dK =θkR/p Qh=θhR/p D=θdR=(1−θk−θh)R (3) where, pis the tax-inclusive consumer price of Q. The government balances its budget in each period, raising revenue by taxing factor incomes and consumption. As with most education systems in practice, human capital inputs into human capital production are not directly taxed in the model. The implicit income derived from the public capital, distributed to the individual, is taxed. It may be thought more appropriate to treat the private returns from the ownership of such infrastructure capital as untaxed. In practice, however, the consumption of this type of capital, such as road infrastructure, requires the use of private consumption goods (such as vehicles) which are taxed, so that capital is effectively taxed indirectly.10 Total tax revenue is given by: R=trrK +twwuqH+tcp0Q =trrK +twwHq+tcp0Q(4) where tw,t rare the proportional income tax rates on gross wage and rental incomes respectively; tcis the proportional ad valorem tax rate on consumption of Q;andwand rare the pre-tax wage rate and rental per unit respectively. In addition, p0=p/(1+tc)is the tax-exclusive producer price of Q,andHq=uqH is human capital used in the production of Q. For convenience, pis normalised at unity, such that p0=1/(1 + tc). 2.3 Consumption and Labour Supply The representative individual maximises a Cobb-Douglas utility function in each period, expressed in terms of consumption and leisure (the latter defined to 10See Brennan and Buchanan (1980) for explicit modelling of this relationship. They highlight a number of taxes on privately produced consumption goods which de facto tax individuals’ consumption of publicly provided capital. 4 Figure 1: Equilibrium Growth and Education Proportion 0 0.01 0.02 0.03 0.04 0.05 0.06 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 education proportion growth rate E F F: αh =0.5 E: benchmark the benchmark case, giving a steady-state growth rate of just under 2.6%per period. 4.2 Time Spent in Education The above analysis suggested that a Laffer curve effect can be expected as the education proportion, uh, is varied; this is displayed in Figure 1. Using benchmark values for other parameters suggests a growth-maximising human capital allocation of around 30% to education (profile E), rising to around 50% if human capital inputs are more important for human capital accumulation (profile F,whereαh=0.5). These numbers are greater than likely to be observed in practice, though of course policy objectives other than growth maximisation are likely to play a role in determining public education provision. 4.3 Changing Expenditure Allocations The growth trade-offbetween the two productive expenditures on human and physical capital is illustrated in Figure 2 which shows alternative combinations of the proportions, θkand θh, which yield constant growth. Starting with the benchmark values (θk=0.1; θh=0.2), profile Grepresents a form of iso-growth curve, depicting combinations of θkand θhyielding a constant steady-state growth rate 11 Figure 2: Iso-Growth Expenditure Proportions 0 0.2 0.4 0.6 0.8 1 1.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 θh θk and (θk + θh) G H G' H' of 0.026.21 The sum, θk+θh, identifies the remaining public resources available for social transfers, and the minimum point on profile G0indicates that the maximum resources available for social transfers without reducing long-run growth is, by coincidence, close to the benchmark values of θk+θh≈0.3.Theseprofiles are not affected by changes in αh(the elasticity of human capital production with respect to inputs of Q),thoughthevalueofthegrowthratediffers from the benchmark case. Profiles Hand H0show that the θk,θhtrade-offis affected by changes in the importance of human capital in the private sector production function (αq). In particular, profile H(lower αq) is everywhere steeper than profile G(higher αq). This indicates that reallocating a given proportion of expenditure from physical capital towards human capital requires a greater increase in the latter to maintain growth constant if the human capital-output elasticity is lower (profile H). 21These profiles are obtained using an iterative procedure to find the required reductions in θknecessary to maintain constant growth for specified increases in θh. 12 Figure 3: Equilibrium Growth and Wage Taxation 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050.10.150.20.250.30.350.40.450.50.550.60.650.70.750.8 tax rate growth rate C B A D A : tw (benchmark) B: tw (αc = 0.5) C: tw (αc = 0.5; tr = 0) D: tr (benchmark) 13 4.4 Changing Tax Rates Figure 3 shows the relationship between the equilibrium growth rate and the tax rate on wage income.22 These results reveal a similar pattern to those produced by the Barro (1990) model whereby the positive growth effects of productive expenditure enabled by increased tax rates initially dominate the negative growth effects of income taxes via disincentives. However, whereas in the Barro (1990) case disincentive effects operate via disincentives to accumulate physical capital, here it is disincentives to labour supply which eventually cause the profiles to turn down. Profile A, the benchmark case, suggests a growth maximum at around 3.5% associated with a wage tax rate of 0.65. However, lower tax rates do not involve a large growth sacrifice (for example, ˙ Q=2.9%attw=0.35). With a greater leisure preference (profile B;αc=0.5) maximum growth of 2.7% occurs at tw=0.60.Profile C(where tr=0) suggests that the growth effects of allowing for capital income taxation are quite small. Profile Dshows how changes in traffect growth (for tw=0.25), and is approximately linear since there are no disincentive effects here to counteract the positive expenditure-enhancing effects of additional tax revenues.23 4.5 Transitional Dynamics The transitional dynamics are, as shown in the Appendix, determined by tax revenue and labour supply effects. Shocks which generate divergences between the growth rates of tax revenue, and human and physical capital initiate convergent tendencies. Figure 4 shows the dynamic effects of reallocating public expenditures towards human capital by raising θhfrom 0.2 to 0.25. The increase in θh immediately raises the growth rate of human capital above that for physical capital. This in turn causes a rise in the capital growth rate but a fall in the human capital growth rate, re-establishing an equilibrium growth rate around 2.93%, with a half-life of about 36 years. This refers to the time taken for adjustment to a new equilibrium after the change induced by the initial shock. They are similar to the commonly estimated convergence rate of 2% per annum which translates into a half-life of 35 years; see Barro and Sala-i-Martin (1995, pp.26-38). Despite this length of time, the output growth rate is seen to move quickly to a value that is relatively close to its final equilibrium. 22Given the correspondence noted earlier between twand tc/(1 + tc), growth effects from changes in twand tcare similar. 23Some secondary disincentive effects occur with trto the extent that capital income taxes change relative factor prices and hence labour supply decisions. Simulations suggest these are small. 14 Figure 4: A Shift in Public Expenditure Towards Human Capital 0.025 0.026 0.027 0.028 0.029 0.03 0.031 1 112131415161718191101111121131141 Time growth rate Human capital Output Physical capital 5 Conclusions This paper has examined the role of publicly provided and tax-financed human capital accumulation in the context of a general equilibrium endogenous growth model. A key difference from previous models of endogenous human capital accumulation in the Lucas (1988, 1990) tradition is that schooling is compulsory and therefore exogenous to the representative individual.24 Consumption and labour supply choices are based on maximisation of a static (single period) utility function. Arguably these assumptions are more relevant for a developing country seeking to extend compulsory schooling. Education and public physical capital investment are financed from taxes on wage and capital income, and consumption. Direct and indirect effects of increasing both the proportion of time devoted to education, and the proportion of tax revenue used in human capital production, were identified. It was found that, as in the models of Lucas (1988, 1990), Stokey and Rebelo (1995) and Milesi-Feretti and Roubini (1998), the specification of the human capital production function and the strength of labour supply effects are important for the magnitude of steady-state outcomes. In addition, with an endogenous supply of labour, the proportion of time compulsorily devoted to 24The analysis assumed that the compulsion is effective. 15 education acts as a form of distortionary tax on human capital. Numerical analyses found that, for benchmark parameter values, the growth maximising wage tax rate appear to be somewhat higher than those observed in practice, but the growth sacrifice associated with lower tax rates is not large. In the absence of incentives to private accumulation in the model, growthmaximising tax rate predictions should be treated with caution. Nevertheless, the model points to the possibility that, where taxes are used partly to fund growth-enhancing expenditures, growth-maximising tax rates can be quite high, even allowing for strong labour supply responses. Finally it was shown that the model’s transitional dynamics have strong convergence properties in response to fiscal policy changes. These arise essentially because the government budget constraint ensures that tax revenues, and public physical and human capital accumulation, are jointly endogenously determined. As a result, any divergences between their rates of growth are temporary. Simulations using plausible labour supply assumptions suggest typical half-lives of around 30-40 years; that is, similar to empirical regression-based estimates. 16 Appendix: The Dynamics of The Model This appendix examines the dynamic properties of the model. Given the nature of the interdependencies in this general equilibrium framework, it is not possible to solve analytically for the equilibrium output and prices. This also applies to the dynamics. However, output growth can be expressed in terms of what Mendoza et al (1997) refer to as semi-reduced forms. Such equations for output growth yield insights into the influence of fiscal policies on equilibrium growth. As stated above, steady-state growth requires: ˙ Q∗=˙ K∗=˙ H∗=˙ R∗(17) Endogenous steady-state growth also requires ˙ Q∗to be positive and constant. Given the constant returns to reproducible factors, Kand H,in(1),thisis achieved if accumulation functions are linear (non-decreasing), which depends on the relationship between inputs and tax revenue. From the first line of (3): ˙ K=θkR pK (18) and combining (2) with the second line of (3): ˙ H=AhuhµθhR pH ¶αh (19) From the steady-state definition in (17), if an equilibrium growth rate exists, (R/H)∗and (R/K)∗are both positive constants yielding self-sustaining growth. Equating (18) and (19), it can be shown that: ˙ Q∗=˙ K∗=uh·AhµθhK∗ θkH∗¶αh¸1/(1−αh) (20) In equilibrium K∗/H∗is constant and hence, for given technological and fiscal parameters, ˙ Q∗is a positive constant.25 25It was argued above that tax revenue in this model can be expected to display some of the properties of private savings in conventional endogenous growth models. This is shown by substituting in (18), and using (1) to substitute for Q/K, to give ˙ Q∗=Aqθk³R pQ ´³uqH K´αq. Since R/pQ captures the compulsory saving rate, this shows that equilibrium growth is a positive function of the saving rate and the H/K ratio, as in Rebelo (1991). Not all of these compulsory savings are devoted to investment, as the government spends on social transfers. A broader concept of compulsory saving could be employed here, as in Rebelo (1991), to include the compulsory fraction of time, uh,used for educational investment, such that: S/pQ =(R−D+uhwH)/pQ. 17 Substitute for K∗/H∗in (20) to obtain an alternative semi-reduced form in terms of exogenous tax rates and the endogenous labour supply variables, wand uq. Using (10) and (4), equation (12) can be obtained, after some re-arranging. It is also necessary to examine whether the income growth resulting from arbitrarily chosen fiscal parameters converges towards the steady-state rate or whether initial fiscal policy choices display knife-edge properties. First, equating factor marginal products from (1) gives: w r=µαq 1−αq¶K Hq (21) in equilibrium, so that for given αq: ˙w+˙ Hq=˙r+˙ K(22) Differentiating the expression for total tax revenue in (4) gives: ˙ R=β³˙r+˙ K´+γ³˙w+˙ Hq´+(1−β−γ)˙ Q(23) where βand γare the shares of rental and wage income tax revenues in total tax revenue respectively. Hence, in the steady-state, where (22) holds, ˙ R=˙ Q.Out of equilibrium, revenue growth may exceed or fall short of output growth unless uniform income tax rates apply.26 To examine transition properties, consider an initial equilibrium in which ˙ Q∗= ˙ K∗=˙ H∗.Ashocktoafiscal parameter, such as an increase in the proportion of revenues allocated to capital investment, θk,causes: ˙ K> ˙ Q> ˙ H.Forthe case of uniform tax rates, ˙ R=˙ Qand therefore ˙ K> ˙ R> ˙ H, implying that R/K must fall and R/H must rise. Equations (18) and (19) show that this induces a reduction in ˙ Kand an increase in ˙ H, that is, a convergence towards equilibrium. If fiscal policy were to cause both factor inputs to grow more slowly than output (for example ˙ K< ˙ H< ˙ Q=˙ R), R/K and R/H would both rise, restoring equilibrium. In the case of non-uniform income tax rates, a shock away from the steadystate may cause ˙ Rto exceed or fall short of ˙ Q. However, what matters for the transitional dynamics is the relation of ˙ Rto ˙ Kand ˙ H. As with the uniform tax case, if ˙ R< ˙ K, ˙ Hthen R/K and R/H both rise until ˙ R∗=˙ H∗=˙ K∗, restoring equality with ˙ Q∗. A converse equilibrating process occurs if ˙ R> ˙ K, ˙ H. However, if initially, ˙ K< ˙ R< ˙ H,˙ Krises and ˙ Hfalls to restore equilibrium.27 26This can be seen by differentiating (4) for the uniform income tax rate case to give: ˙ R=(β+γ)³˙r+˙ K+˙w+˙ Hq´+(1−(β+γ)) ˙ Q=˙ Q 27Revenue growth does not in general remain constant during the transitional process since ˙ Ris a positive function of ˙ Kand ˙ H. 18 Consider, for example, a case where a fall in θkleads to a reduction in ˙ K from an initial equilibrium in which ˙ R∗=˙ Q∗=˙ K∗=˙ H∗. The reduction in ˙ Kreduces revenue growth but by less than the fall in ˙ K. This is because capital income is only one source of tax revenue and because relative factor price adjustments ensure that the growth of capital income, rK, falls by less than the growth of the capital stock.28 As a result, the higher revenue-to-capital ratio, R/K, generates a temporary increase in capital growth so long as the new investment proportion, θk, remains unchanged. Thus a new steady-state is established in which all variables grow at a lower rate. The transitional dynamics of the model are therefore essentially determined first by the government’s budget which determines the pace of factor accumulation; and secondly labour supply responses to the associated relative factor price changes. 28The shock to capital growth via the reduction in θkhas no effect on human capital growth but affects the human capital used in production of Q, as relative factor price changes (due to reduced ˙ K) induce labour supply changes. 19 References Aghion, P. and Howitt, P. (1998) Endogenous Growth Theory. Cambridge, Mass: MIT Press. Barro, R. (1990) Government spending in a simple model of endogenous growth. Journal of Political Economy, 98, s103-117. Barro, R. and Sala-i-Martin, X. (1992) Public finance in models of economic growth. Review of Economic Studies, 59, 645-661. Baxter, M. and King, R.G. (1993) Fiscal policy in general equilibrium. American Economic Review, 83, 315-335. Bleaney, M., Gemmell, N. and Kneller, R. (2002) Testing the endogenous growth model: public expenditure, taxation and growth over the long-run. Canadian Journal of Economics, 34, 36-57. Brennan, G. and Buchanan, J.M. (1980) The Power to Tax: Analytical Foundations of a Fiscal Constitution. Cambridge: Cambridge University Press. Caballe, J. and Santos, M.S. (1993) On endogenous growth with physical and human capital. Journal of Political Economy, 101, 1042-1067. Capolupo, R. (2000) Output taxation, human capital and growth. Manchester School, 68, 166-183. Devarajan, S., Swaroop, V., and Zou, H. (1996) The composition of public expenditure and economic growth. Journal of Monetary Economics, 37, 313344. Devereaux, M. and Love, D. (1994) The effects of factor income taxation in a two-sector model of endogenous growth. Canadian Journal of Economics,27, 509-536. Devereux, M. and Love, D. (1995) The dynamic effects of government spending policies in a two-sector endogenous growth model. Journal of Money, Credit and Banking, 27, 232-56. Glomm, G. and Ravikumar, B. (1994) Public investment in infrastructure in a simple growth model. Journal of Economic Dynamics and Control, 18, 11731187. Jones, L.E., Rodolfo E.M. and Rossi, P.E. (1993) Optimal taxation in models of endogenous growth. Journal of Political Economy, 101, 485-519. King, R.G., and Rebelo, S. (1990) Public policy and economic growth: developing neoclassical implications. Journal of Political Economy, 98, s126-151. Kneller, R., Bleaney, M.F. and Gemmell, N. (1999) Fiscal policy and growth: evidence from OECD countries. Journal of Public Economics 74, 171-190. 20