Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized WPS4405 P OLICY R ESEARCH W ORKING P APER 4405 Fiscal Policy, Public Expenditure Composition, and Growth Theory and Empirics Willi Semmler Alfred Greiner Bobo Diallo Armon Rezai Anand Rajaram The World Bank Africa Region Public Sector Governance Department November 2007 POLICY RESEARCH WORKING PAPER 4405 Abstract This paper responds to the development policy debate involving the World Bank and the IMF on the use of fiscal policy not only for economic stabilization but also to promote economic growth and increase per capita income. A key issue in this debate relates to the effect of the composition of public expenditure on economic growth. Policy makers and some researchers have argued that expenditure on growth-enhancing functions could enhance future revenue and justify the provision of "fiscal space" in the budget. But there are no simple ways to identify the growth-maximizing composition of public expenditure. The current paper lays out a research strategy to explore the effects of fiscal policy, including the composition of public expenditure, on economic growth, using a time series approach. Based on the modeling strategy of Greiner, Semmler and Gong (2005) we develop a general model that features a government that undertakes public expenditure on (a) education and health facilities which enhance human capital, (b) public infrastructure such as roads and bridges necessary for market activity, (c) public administration to support government functions, (d) transfers and public consumption facilities, and (e) debt service. The proposed model is numerically solved, calibrated and the impact of the composition of public expenditure on the long-run per capita income explored for low-, lower-middle- and upper-middle-income countries. Policy implications and practical policy rules are spelled out, the extension to an estimable model indicated, a debt sustainability test proposed, and the out-of-steady-state dynamics studied. This paper—a product of the Public Sector Governance Department—is part of a larger effort in the Poverty Reduction and Economic Management (PREM) Vice-Presidency to encourage active policy research on fiscal policy and growth issues, with a particular focus on expenditure composition choices and their growth and sustainability implications. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at arajaram@worldbank.org and SemmlerW@newschool.edu. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Fiscal Policy, Public Expenditure Composition, and Growth Theory and Empirics1 Willi Semmler,2 Alfred Greiner,3 Bobo Diallo,4 Armon Rezai,5 and Anand Rajaram6 1 We want to thank Lars Gruene (Univ. of Bielefeld) for extensive help in the numerical part of the paper, David Bevan (Oxford Univ.) and to Shanta Devarajan for valuable guidance, and the audience at the World Bank workshop on "Growth and Fiscal Policy,” June 2006, for useful comments. Financial support from the Bank-Netherlands Partnership Program is gratefully acknowledged. 2 Schwartz Center for Economic Policy Analysis, New School, New York and CEM, Bielefeld 3 Dept. of Economics and CEM, Bielefeld University 4 Schwartz Center for Economic Policy Analysis, New School, New York 5 Schwartz Center for Economic Policy Analysis, New School, New York 6 World Bank, Washington, D.C 1 Introduction Starting from a “production function” view of the growth and development process with a narrow focus on physical capital, labor force, and exogenous technical progress, growth theory has come to acknowledge the role of an economy's endowment and continuing investment in human capital, physical infrastructure, research and knowledge development, institutions, and innovation in explaining its growth trajectory. The implications for policy design are somewhat harder to divine. From the perspective of a government, which policies enhance an economy's growth prospects and how large are policy effects on growth? In part, the answer depends on the empirical approach taken. Studies based on cross-country regressions have explored a large number of forces of growth, but they face methodological perils such as the huge heterogeneity of countries (different technologies, institutions, and preferences across countries), and the uncertainty of presumed underlying models and parameters. Consequently, nonrobustness of the outcomes and ambiguous policy implications are a common criticism of studies based on cross-country regressions.7 Greiner, Semmler and Gong (2005) argue that a time series perspective on economic growth may be more useful to pursue in designing growth and development strategies. Growth models, as advocated by Greiner and colleagues, (1) allow for better specification of microeconomic behavior of economic agents, (2) enable time series study of the forces of growth for a country or a group of countries at particular stages of economic growth, (3) permit analysis using econometric time series methods, and (4) allow us to spell out (though mostly in the context of small-scale models) important implications for growth and development policies. Since such models, which lend themselves to some time series tests, are often difficult to treat when a larger number of forces of growth are introduced, Greiner and colleagues (2005) have suggested identifying the specific forces that are important in a particular country consistent with its particular stage of development. They mainly consider externalities and learning from others, education and human capital, the creation and accumulation of knowledge and public infrastructure as forces of economic growth in a time series context. Overall, this approach allows analysts to better derive the public policy implications for economic growth. The primary interest of this paper is to explore, as the World Bank's papers to the Development Committee (2006, 2007) suggest, whether countries could better use fiscal policy (and in particular, the level and composition of public expenditure) to promote sustainable increases in growth and welfare for low- and middle-income countries. We are encouraged by some recent work by Glomm and Rioja (2006), Agenor and Neanidis (2006), and country studies undertaken by World Bank research.8 Section 2 provides a selective discussion of recent literature and empirical evidence on public investment in infrastructure, health, and education and their effect on growth. In section 3 we sketch a general social planner type model that includes choices regarding the accumulation of physical capital as well as the composition of investment in infrastructure, health, and education. In section 4, the model is calibrated by matching actual differences in per capita income for three groups of countries (for low-income, lower-middle-income and upper-middle-income countries). In addition the effects of a change in foreign aid and other factors that have an impact on growth are explored. Section 5 undertakes a similar calibration exercise; here, however, by considering the growth and welfare effects arising from a change in the composition of the public expenditure. Section 6 discusses sustainability tests of fiscal policy. Section 7 concludes the paper and spells out some practical policy rules. In the appendix the data sources are discussed and the detailed results for the lower-middle-income and upper-middle-income countries are reported. Also, in the appendix the 7 See Rodrik (2005) for a methodological criticism of cross-country regressions in identifying growth effects of policies. See also Easterly (2005) in the Handbook of Economic Growth for a skeptical review of the role of policies in explaining cross-country growth. 8 See the papers by Arestoff and Hurlin (2006), Balonos (2005), Ferreira and Arajo (2006), and Suescun (2005). -2- out-of-steady-state dynamics of a simplified version of the model are explored, and it is shown how that the model can be turned into an estimable model using time series data. 2 Literature and Evidence The scope for policy to influence economic growth depends on the underlying model of growth. So long as the Solow model dominated economists’ view of growth, there was little role for fiscal policy to influence the long term rate of growth, which depended on exogenous technical progress.9 Lucas (1988) and Barro (1990) opened the door to a rich literature on endogenous growth theory and a corresponding attempt to develop our understanding of the implications for fiscal policy. Tanzi and Zee (1997) rovide a relatively early review of the resulting literature on fiscal policy and concluded that despite the lack of robust empirical results, endogenous growth theory provided the basis for confidence that fiscal policy could affect long run growth performance of countries. The theoretical literature on fiscal policy has studied the effect of ‘productive’ and ‘unproductive’ spending and distortionary and non-distortionary taxation on long term growth. This literature generally predicts that productive spending financed by non-distortionary taxes will have a positive effect on long term growth whereas the opposite combination (unproductive spending financed by distortionary taxation) will have a negative effect. The algebraic sign of other spend-tax combinations is more ambiguous since there are opposing effects at work. Barro (1990) suggests that an inverted U-curve relationship would exist between productive government expenditure and economic growth, as the rising cost of distortionary taxation necessary to finance spending overtakes the declining benefits of productive spending. Early models of growth that featured government expenditure used fairly simple characterizations of productive and unproductive spending - public investment was viewed to be productive whereas public consumption was unproductive. Devarajan et al. (1996) developed a model with public investment and consumption expenditure to show that the growth impact of public investment could be negative if there was excessive investment. Glomm and Ravikumar (1997) considered the implications of government expenditure on infrastructure (which influences private production) as well as on education which results in human capital accumulation. More recent literature (Zagler and Durnecker (2003), Glomm and Rioja (2006), Blankenau and Simpson (2004), Agenor and eanidis (2006)) provide a more disaggregated discussion of government expenditure, typically including spending on public infrastructure, health, and education, which are described as providing inputs for private production. Zagler and Durnecker (2003) define an economy where output is produced using labor, private capital and public infrastructure expenditure and consider the effects of government spending and taxation on long term growth rates. Glomm and Rioja (2006) consider the implications of shifting expenditure from transfers to infrastructure or education and conclude, based on empirical evidence from Brazil, that at the margin the growth implications are small. Blankenau and Simpson (2004) focus on education expenditure and growth. Some of the papers take account of the interdependence among these expenditures, with the productivity of health spending depending on education and infrastructure expenditure or stocks, and vice versa. The intuition behind such complementarities is well known - good sanitation and water supply infrastructure has large health benefits, including a reduction in incidence of malaria and gastro-intestinal deseases. This in turn has a positive effect on school attendance rates and on learning outcomes (see Bundy and et al. (2005)) as well as on labor productivity in market activities. While the theoretical models have become more nuanced about public expenditure and their financing, the empirical evidence is often perceived to be ambiguous, reflecting problems of data, differing research methodologies and econometric techniques. Gemmell (2007) provides a useful 9 Temple (2003) argues that the scope for policy to have an influence on the level of output should merit the attention of policy makers and analysts but has been neglected because of a misguided focus on effects on the long term growth rate and an undervaluation of level effects. -3- review of the evidence, and concludes that more recent literature uses more reliable methods (including a clearer specification of the government budget constraint) to derive robust evidence, at least for OECD countries, of long run impacts of fiscal policy on economic growth. Even for developing countries he finds that, consistent with theory, recent studies show a positive medium to long-run growth effect of certain categories of expenditure, such as transport and communication infrastructure, education and health. However, the complementarities between health, education, infrastructure and growth involve trade-offs in the actual development process. Public resources are limited and given the constraints governments often need to weigh the benefits of expenditure on one against the benefits of spending on the other. In the following section a model is formulated to represent both the complementarities and the trade-offs of public investment. 3 A Model of Fiscal Policy and Economic Growth The model to be presented is based on the work by Greiner et al. (2005) but takes into account some of the generalizations that have been put forward by Corsetti and Roubini (1996) and others. The current paper develops a model of growth with a private and a public sector, the latter described by a government that can choose to raise resources through taxation, borrowing, or foreign aid. In our model we assume that the tax rate is chosen optimally and there is a well-defined inter-temporal budget constraint. We allow for foreign debt and spell out fiscal policy rules that ensure sustainability of debt. Besides the accumulation of physical capital by the private sector, the model includes public investment in infrastructure, health and education. In contrast to Agenor and Yilmaz (2006) who work with expenditure flows, we develop a model with stocks: private physical capital, human capital and a broad notion of public capital that includes public infrastructure to support market production as well as facilities for health and education services. The paper attempts to derive some policy insights using empirical techniques to estimate the model. Given that time series models that study forces of growth in a historical context are rather complex and require high quality time series data to be estimated, we adopt a calibration technique to assess the growth impact of fiscal policy on countries identified by levels of income/development. 3.1 The Model The Economy Production in this stylized economy is characterized by a Cobb Douglas function ε ε ε α ( Ak (u1h) β (v1 g )γ for the production of market goods and ((1 − u1 )h) 1 (v2 g ) 2 (v3 g ) 3 for the production of human capital) with private capital k , public capital g , and human capital h . Note that only a part of public capital ( v1 g ) is used to support private market production, while other parts are used to help to build human capital in the form of schools ( v2 g ) and medical centers ( v3 g ) and do not directly influence production.10 This realistically describes the longer gestation lag in creating human capital relative to typical physical infrastructure. The Government Government (represented by a social planner) raises taxes optimally without distortion and can choose four types of public expenditure: (i) public investment to enhance education and health services that increase the stock of human capital, (ii) investment on public infrastructure assets (transport and communication system as well as energy, water supply and sanitation), to support market production and the creation of human capital, (iii) transfers and public consumption representing expenditure with public goods' characteristics which may enter into households' preferences (public parks, civic facilities and consumption transfers), and (iv) public administration necessary for the functioning of the government (including justice, security and tax collection). These four expenditure streams allow us to consider the effect of public expenditure composition on 10 Since the v 's represent shares, v1 + v2 + v3 = 1 . -4- growth. The stylized model developed in this paper focuses on deriving the implications for growth and welfare due to alternative government choices regarding the allocation of the stock and flow of public capital. The government can choose to allocate public investment in infrastructure assets (such as roads) that directly influence market production or in assets relevant for human capital accumulation (such as schools and clinics) that may have a lagged effect on growth. The growth and welfare effects are worth studying since they help us highlight the inter-temporal consequences and trade-offs of policy choices confronting many governments.11 The model enables government to acquire foreign debt and recognizes debt service as a part of the government budget. Foreign transfers to low-income countries are assumed to reflect foreign aid that is earmarked for public investment. The social planner is assumed to maximize a logarithmic welfare function, a form that simplifies preferences. When we define the variables, all variables are in per capita form and we define public capital as non-excludable but subject to congestion in the production of market goods and the creation of human capital, because it is per capita public capital ( g = G/L ) which affects per capita output. Table 1 Variable Overview (all in per capita terms) Variables b c d ep k g h y Description Debt Consumption Debt service Amount of resources absorbed by the public sector Private apital Public capital Human capital GDP Table 2 Parameter Overview (all in per capita terms) Parameters A i pf n r u1 1 − u1 v1 v2 v3 α1 α2 α3 Description Productivity factor Foreign aid Population growth rate Borrowing rate Fraction of h used to support the production of k Fraction of h used to build new h Fraction of g used to support the production of k Fraction of g used to build new h in the form of schools Fraction of g used to build new h in the form of medical centers Share of public resources used for the building of new g Share of public resources used for transfers and public consumption Share of public resources used for the functioning of the administration 11 To focus on the effects of public capital allocation, the model assumes a stylized world where the government decides on the allocation of public capital and the private sector provides the labor to staff the schools and clinics as well as the labor employed in market production. One could imagine an economy where private sector volunteers provide the human capital services but rely on complementary government facilities. Human capital allocation therefore has no direct impact on the government budget. An extension to the current paper could consider the implication of government employment of teachers and doctors and then consider the compositional choice regarding capital and recurrent wage expenditure. -5- α4 α β γ δk δg δh ε1 ε2 ε2 η ρ U Share of public resources used for debt services Elasticity of GDP w.r.t. k Elasticity of GDP w.r.t. h Elasticity of GDP w.r.t. g Depreciation of private capital ( k ) Depreciation of public capital ( g ) Depreciation of human capital ( h ) Elasticity of h w.r.t. existing h Elasticity of h w.r.t. g in the form of schools Elasticity of h w.r.t. g in the form of medical centers Weight of transfers and public consumption in utility Discount rate Utility/welfare The amount of resources absorbed by the public sector, e p , is used for public infrastructure ( i p = α1e p ), transfers and public consumption ( c p = α 2 e p ), and public administration ( tr = α 3e p ). The latter has neither utility nor productive effects, but possesses public goods features and is necessary for the functioning of the state. Finally, for the debt service we have d = (1 − α1 − α 2 − α 3 )e p = α 4 e p . 12 When public investment is turned into public capital, we can think of three uses of the public capital: First, there exists public capital which raises productivity of market production, such as transport systems (roads, bridges, harbors) and utilities (for example water supply). In the model, that part is v1 g . The other fraction of public capital is used for facilitating the formation of human capital via health services, v2 g , and education, v3 g . In our view, the formulation with one public capital stock, which is divided (and subdivided) between use in production and human capital formation, is sufficient to study the composition effect of public expenditure. Note that for the government budget constraint we can write G = i pf + (α1 + α 2 + α 3 + α 4 )e p , with i pf + α1e p earmarked for public investment and α 4 e p for debt service. In the steady state then we have i pf + α1e p = (δ g + n) g . The flow of expenditure should be properly subdivided in spending for infrastructure, health, and education, according to the fractions v1 , v2 and v3 .13 Moreover, note that the government revenue is also T = i pf + e p , but what can be used for domestic spending is only T − α 4 e p , since α 4 e p flows out for debt service. The primary surplus of the government budget is α 4e p . We presume a planner solves the system of equations below to derive the social optimum: 12 b Note that we can allow for net borrowing. If we define net borrowing as i p , earmarked for public investment, we b f will, then, have to add i p in eqns. (4) and (5) as additional borrowing. We can think of i p in eqn. (4) as representing both foreign aid and net borrowing. In the steady state debt, b , and the debt-to-income ratio, b , will correspondingly y fall, since the maximal sustainable debt level will decrease as more debt is taken on. 13 We might think that the annual revenue, earmarked for i p + α1e p , is handed over to a trust fund that manages the f public current and capital expenditure related to infrastructure, health and education. -6- ⎞ ⎛ (c (α 2 e p )η )1−σ −( ρ − n ) t ⎜ e − 1⎟dt max ∫0 ⎟ ⎜ c ,e p ,u1 1−σ ⎠ ⎝ ∞ (1) subject to k& = Ak α (u1h) β (v1 g )γ − c − e p − (δ k + n)k h& = ((1 − u1 )h) (v2 g ) (v3 g ) − δ h h (2) (3) g& (4) ε1 ε2 = i pf + α1e p − (δ g + n) g ε3 b& = (r − n)b − (1 − α1 − α 2 − α 3 )e p (5) Note that for simplicity we assume an additively separable utility function U (⋅) = ln c + η ln (α 2 e p ) . Note also that equations (2) - (5) describe the constraints to the growth of private capital, human capital, public capital and debt. Since we only consider an exogenous growth model in this version, α + β + γ ≤ 1, e.g. α = β = γ = 0.33 . One could introduce here some externalities, as in Greiner et al. (2005, ch.3), to obtain endogenous growth. In a further extension we could allow for foreign borrowing (for public investment) by adding a positive term to eqns. (4) and (5). Since this borrowing will be constant and permanent, the level b of permissible debt level will fall. However, since income will increase, the debt-to-income ratio y 14 will also fall. This is exactly what we expect from a numerical exercise. Our formulation of public debt implies that public debt is foreign public debt. New borrowing from abroad can be allowed for.15 Interest payments on existent foreign debt (for example foreign bonds) is rb (at world interest rate). Repayments and interest payments do not go to the domestic household sector, but go to foreigners. The usual transversality condition is assumed to hold (see section 3.2). Next we explore the stationary state of the model in its form of eqns. (1) - (5). We employ the Hamiltonian to sketch a solution of the model. The Hamiltonian is H (c, e p , k , h, g ) = ln c + ηln(α 2 e p ) + λ1[ Ak α (u1h) β (v1 g )γ − c − e p − (δ k + n)k ] + λ2 [((1 − u1 )h) 1 (v2 g ) 2 (v3 g ) 3 − δ h h] ε ε + λ3 [i pf + α1e p − (δ g + n) g ] ε (6) + λ4 [(r − n)b − (1 − α1 − α 2 − α 3 )e p ] with λ1 , λ2 , λ3 , λ4 the co-state variables. The first order conditions for the two choice variables, c and e p , are: ∂H = 0 ⇒ c −1 = λ1 ∂c 14 15 Note that this term does not have to be constant. It suffices if the term is positive on average for the results to hold. See footnote 3. -7- (7) ∂H = 0 ⇒ ηe −p1 = λ1 − λ3α1 − λ4 (1 − α1 − α 2 − α 3 ) ∂e p (8) For the co-state variables we have λ&1 = λ1 ( ρ − n) − ∂H = λ1 ( ρ − n) − λ1[ Aαk α −1 (u1h) β (v1 g )γ − (δ k + n)] ∂k ∂H = λ2 ( ρ − n) − λ1[ Ak α β (u1h) β −1 u1 (v1 g )γ ] ∂h ε −1 ε − λ2 [ε 1 ((1 − u1 )h) 1 (1 − u1 )((1 − v1 ) g ) 2 − δ h ] λ&2 = λ2 ( ρ − n) − ∂H = λ3 ( ρ − n) − λ1[ Ak α (u1h) β γ (v1 g )γ −1 ⋅ v1 ] ∂g ε ε −1 − λ2 [((1 − u1 )h) 1 ((1 − v1 ) g ) 2 ε 2 (1 − v1 )] + λ3 (δ g + n) λ&3 = λ3 ( ρ − n) − λ&4 = λ4 ( ρ − n) − ∂H = λ4 ( ρ − n ) − λ4 ( r − n ) ∂b (9) (10) (11) (12) Equations (7)-(12), which are derived from the two first order conditions with respect to the choice variables c and e p and the four equations for the co-state variables λ1 , λ2 , λ3 , and λ4 , give us, together with the four state variable equations (2)-(5), a system of ten equations in ten variables {c, e p , k , h, g , b, λ1 , λ2 , λ3 , λ4 } . Writing eqns. (7) and (8) as 0 = λ1 − c −1 (13) 0 = λ1 − λα 1 − ηe −p1 (14) and setting the differential equations (2)-(5) as well as (9)-(12) equal to zero, we can obtain a stationary state {c* , e*p , k * , h* , g * , b*λ1* , λ*2 , λ*3 , λ*4 } . Plugging these into the production function y = Ak α (u1h) β (v1 g )γ , we can also obtain the per capita income, y * , at the stationary state. Given our specification of human capital and its use, we can study the effect of the allocation of human capital on per capita income and the other macroeconomic variables. Furthermore, varying our parameter set v1 , v2 and v3 , we can explore the impact of different public expenditure compositions on the steady-state outcomes of per capita income and the other variables. A further effect on per capita income is predicted to be caused by a change of the parameter A and of foreign aid, if i pf > 0 . Overall, from all of those comparative static studies we expect to obtain information on per capita income, consumption and the other macro variables. Specifying all parameters, the following numerical stationary solution is obtained from necessary optimality conditions using the computer software Mathematica:16 17 18 The parameter values used are: n = 0.015 , ρ = 0.03 , δ k = 0.075 , δ h = 0.075 , δ g = 0.05 , α = β = γ = 0.33 , f u1 = 0.85 , v1 = 0.8 , v2 = 0.1 , v3 = 0.1 , ε1 = ε 2 = 0.2 , ε 3 = 0.25 , α1 = 0.1 , α 2 = 0.7 , α 3 = 0.1 , i p = 0.05 , 16 -8- * b = 0.73 y With this solution technique we can undertake the above described comparative static analyses and some important calibrations, see sects. 4 and 5.19 k * = 86.59, h* = 21.97 , g * = 17.86 , b* = 20.20 , y * = 27.55 , 3.2 Fiscal Policy to Ensure Debt Sustainability20 The model of section 3.1 permits government to borrow from capital markets, in particular to borrow from abroad in order to undertake public investment. In this section, we want to explore the effects and implications of government borrowing from capital markets and briefly discuss the sustainability of fiscal policy when borrowing is allowed for.21 22 Let us assume that the government has borrowed from abroad for undertaking public investment. The implication of this type of expenditure is that along the transition path, this will raise the growth rate of public infrastructure and lead to a higher level of public capital. This higher level brings a distortion into the model by raising the marginal product of private capital. As a consequence, the investment share is increased and the growth rate of consumption rises implying higher welfare after a sufficiently long adjustment period. Note that this also leads to higher growth of physical and human capital. However, in our growth model these growth effects only hold on the transition path. In the long-run, higher public investment leads to higher levels of output and consumption but does not affect the growth rate of endogenous variables. Since here borrowing from abroad equals loans or issuing of bonds to foreigners, the government must pay it back plus interest payments. Debt repayment is represented by α 4 e p . More concretely, the government has to stick to the inter-temporal budget constraint which can be written as b(0) = ∫ e ∞ − ∫ τ 0 (r ( μ )−n)dμ s (τ )dτ ↔ lim e t →∞ − ∫ (r (τ )−n)dτ b(t ) = 0, t 0 (15) where s denotes the primary surplus which, in our model, is given by α 4 e p . The first term in 0 (15) states that per-capita government debt at time zero must equal the discounted stream of future primary surpluses. This implies that the government must run primary surpluses, if it starts with a positive stock of debt. Equivalent to this formulation is the requirement that discounted debt converges to zero asymptotically. It should be mentioned that in theoretical exogenous growth models the inter-temporal budget constraint is met, provided the interest rate exceeds the population growth rate on average, because per-capita debt converges to a finite value. Nevertheless, it is A = 1 , η = 0.1 , r = 0.07 . 17 The Mathematica code is available at www.newschool.edu/gf/cem. Note that these values are dimensionless and are calibrated in such a way as to fit the data. Economic implications are derived in later sections, where the effects of comparative changes are explored. 19 Allowing for additional borrowing by adding a constant in eqns. (4) and (5) and setting this borrowing at the same * * * b size as foreign aid, i p = 0.05 , we obtain the following numerical values: k = 88.67 , h = 22.36 , g = 18.43 , 18 * y = 28.21 , b * = 0.67 y . As one can observe, b and b fall, indicating a fall in permissible debt. y 20 Since this section treats empirical matters, its notation is changed in order to comply with readily available data (e.g. G now refers to primary expenditure and not public capital as in the rest of the paper). 21 f Again, note that in case of net borrowing a constant needs to be added to eqn. ((5)) and the foreign aid parameter i p in eqn. ((4)) is supposed to be corrected for the availability of new investment funds for public capital. In Greiner et al. (2005), ch. 6, more particular model versions are developed with government borrowing for specific government expenditures. 22 -9- important for real world economies to check for rules whether fiscal policies of countries are such that they fulfill the inter-temporal budget constraint or not. One possible rule for sustainability is to require that the government adjusts the primary surplus to GDP ratio to variations in the debt-GDP ratio. To see that a positive linear dependence of the primary surplus ratio23 on the debt ratio can guarantee sustainability, we assume that the primary surplus ratio is given by b(t ) s (t ) , (16) = α + β (t ) y (t ) y (t ) with y (t ) per-capita GDP. β (t ) determines how strongly the primary surplus reacts to changes in the public debt-GDP ratio and α , which is assumed to be constant, can be interpreted as a systematic component determining how the level of the primary surplus reacts to a rise in GDP. α can also be seen as representing other constant variables which affect the primary surplus-GDP ratio. Using equation ((16)), the differential equation describing the evolution of public debt can be rewritten as (17) b&(t ) = (r (t ) − n)b(t ) − s (t ) = (r (t ) − n − β (t ))b(t ) − α y (t ). ∫ (r (τ )−n)dτ e − t 0 Solving this differential equation and multiplying both sides by to get the present value of public debt yields t t τ ⎛ − ( r (τ )−n) dτ − β (τ ) dτ ( β ( μ )−r ( μ )+ n+γ ( μ ))dμ ⎞⎟ t ⎜ ∫ ∫ ∫ 0 0 0 (18) e b(t ) = e dτ ⎟, ⎜ b(0) − α y (0) ∫0e ⎟ ⎜ ⎠ ⎝ with γ the growth rate of GDP. Equation (18) shows that a positive value for β on average, so that ∫ β (τ )dτ t converges to plus infinity asymptotically, is necessary for sustainability. It is also sufficient, if r ( μ ) − n − γ ( μ ) is positive on average.24 It should be noted that a positive value for r − n − γ characterizes a dynamically efficient deterministic economy. If the economy is stochastic, however, this need not necessarily hold for the economy to be dynamically efficient. Nevertheless, testing the reaction of the primary surplus to variations in the debt ratio is reasonable because a positive reaction is necessary for sustainability as mentioned above. Further, this test yields insight as to how governments deal with public debt and, thus, shows how important the goal of stabilizing debt is for the government. One advantage of the sustainability test just presented is to be seen in the fact that it does not depend on the interest rate, in contrast to other tests where the assumed interest rate may be crucial as to the outcome whether a given policy is sustainable or not. In addition, the proposed rule is intuitively plausible from an economic point of view. If a government runs a deficit, it has to run a primary surplus in the future to pay back the deficit. Otherwise, sustainability is not given. In our model economy, this implies a withdrawal of resources from the economy. Therefore, a deficit financed increase in public investment is beneficial for the economy, if the gain in productivity is sufficiently high to cover the interest payments and the loan. A detailed discussion of different types of sustainability tests and how the above suggested sustainability rule can be implemented is undertaken in section 6 of the paper. Next we explore the change of the basic structure of the model and its impact on the macroeconomic variables such as output, consumption, capital stock and debt. 0 23 Note in the subsequent part we solely focus on the sustainability issue and ignore the feedback effects of a changing surplus on the other spending categories. 24 ∫ β (τ )dτ This holds because l'H ô pital gives the limit of the second term in (18) multiplied by e − e − ∫ (r (μ )−n−γ (μ ))dμ /β . t 0 t 0 -10- as 4 Exploring the Basic Structure of the Model We want to explore the effect of foreign aid, i fp , the productivity factor, A , and the fraction of human capital used in market goods production, u1 , on the steady-state variables of three group of countries classified by income level. We follow the World Bank's 2006 paper to the Development Committee in classifying countries in low-income, lower-middle-income, and upper-middle-income groups. Due to the quality of the data, however, only a reduced list of countries is used for the calibration exercise.25 We employ only data for the time period 1994 to 2004. First, we will calibrate the effect of foreign aid, i pf .26 By looking at actual data of foreign aid per capita, we are able to determine a range in which our parameters can vary. Before we can evaluate the effect of foreign aid, productivity factor, and the fraction of human capital used in market goods production on per capita income, we need to calibrate our above-mentioned model (1) to (5) such that we can roughly reproduce the differences in per capita income across the three groups of countries. Since, as discussed above, there are many forces of growth causing the differences in per capita income, we adjust the productivity level of the three groups, the parameter A , such that we roughly obtain the actual differences in per capita income, normalizing the parameter, A , of the lowest per capita income group. Therefore A is set to 1 for the lowest income group. We hereby take the composition of total public expenditure, α1 , α 2 , α 3 , and α 4 , as given for each group as we find them in the data. Now we employ our Mathematica program to obtain stationary state solutions for the three groups of countries.27 This is equivalent to a comparative static analysis for the three country groups. Our exercise consists in keeping the parameter, A , constant for each group of countries and equal to its calibrated value. Then we let foreign aid, i pf , vary during that period and see how such a change affects the steady-state values k , h, g , c, e p , y , b , and U . Such an y exercise was conducted for the low-, lower-middle-, and upper-middle income groups. In the next step we vary the productivity parameter, A , for each group of countries, employing for each country group the A that we used to calibrate the model to obtain the actual differences in per capita income, and increasing it gradually. The parameter, A , is set equal to 1, 1.18, and 1.45 for the low-, lower-middle-, and upper-middle income groups respectively. Finally, we vary u1 , the fraction of human capital used in market goods production, from 0.1 to 0.8, keeping foreign aid equal to its 10-year average, and the other parameters constant. f 4.1 Effects of Foreign Aid per Capita, i p b , and y and there is clearly a positive relationship between the level of foreign aid and The comparative static results for all income groups show that k , h , g , c , e p , y , U are linear in i pf all the variables, except for public resources per capita, e p , and debt per GDP, 25 26 27 b , which show a y See Appendix A.4 for the complete list of countries. f Note that in the following we presume that there is no new borrowing, so that i p is solely foreign aid. The Mathematica code is available at www.newschool.edu/gf/cem. -11- negative relationship with respect to foreign aid, i pf .28 As the foreign aid goes up the public resources per capita falls slightly. The results suggest that any increase in foreign aid per capita would increase k , h, g , c and y but would reduce only very slightly the optimally chosen public resources, e p . Such a negative relationship could be explained by the fact that public resource is a result of a lump-sum taxation and as more aid flows in, there is less and less incentive to tax, and as b a result, a decrease in public resources, e p . A similar argument can be made for debt per GDP, . y As more aid flows in, there is less and less incentive to borrow, and as a result, there would be a fall b in as i pf increases. Actual data for the period 1994-2004 shows that the per capita foreign aid y went from 2 to 4. To conduct our comparative static exercises, we increased i pf by increments of 0.2 from 2 to 4, which is the range provided by the actual data.29 The results of our comparative static exercises for the low-income group are summarized in Table 4 in appendix A.5. The results for the remaining two income groups can also be found in the appendix A.5. Figure 1 below shows b the relationship between i pf and y , U , , and e p respectively for the low-income group. y Similar results are observed for the lower-middle and upper-middle income groups.30 Figure 1: Effects of Foreign Aid ipf on the Steady State Variables (Low-Income Group) 4.2 28 This paper does not address the problems of moral hazard and inefficiency that often characterize aid inflows into poor governance environments. Waste, corruption, and inefficiency would clearly weaken the effects of foreign aid on growth and welfare. 29 Recent literature has studied the effect of foreign aid on per capita income in country by country studies (see Easterly (2006)) or in cross-section studies (see Reddy and Minoiu (2006)). The latter study finds significant and large effects. 30 Note that the effect of an increase of A has rather large effects on output. But also note that an increase of our A by 6% would correspond to an increase in the efficiency of labor by roughly 20%, since we have written A as outside the production function, namely as exogenous technical change affecting total factor productivity. -12- Effect of A , the productivity factor b , and y U are linear in A and there is clearly a positive relationship between the level of foreign aid and all b the variables. The results suggest that any increase in A would increase k , h , g , c , e p , y , , y and U . Because the low-income group is our reference group, A is increased from 1 to 1.06, and the effect on the steady-state variables is observed. As one might predict, results show that there is a positive linear relationship between A and all the steady-state values of the variables, with the fastest increase in k , y , and g , relative to the other variables. The results of our comparative static exercises for the low-income group are summarized in Table 5 in appendix A.5. The results for the other two income groups can also be found in the appendix. Figure 2 below shows the relationship between A and y , and k respectively for the low-income group. Similar results are observed for the lower-middle and upper-middle income groups. The comparative static results for all income groups show that k , h , g , c , e p , y , <<AU: IN FIG. 2, THE RIGHT-HAND GRAPH IS NOT SHOWING UP CORRECTLY:>> Figure 2: Effects of the Productivity Factor A on the Steady State Variables (Low-Income Group) 4.3 Effects of the Fraction of Human Capital Used in Market Goods Production, u1 To analyze the effect of the parameter u1 , it was increased from 0.05 to 0.95 with increments of 0.05, and the steady-state values corresponding to the different values of the parameter were recorded. The comparative static results on u1 for all income groups show a hump-shape, non-linear b relationship, with respect to k , g , h , c , e p , y , , and U . With respect to the hump-shape y relationship, we can make the following observations: First, we observe a positive relationship b between u1 and k , g , c , e p , y , , and U for u1 ≤ 0.8 , and a negative relationship for u1 ≥ 0.8 . y b We observe increasing returns for k , g , c , e p , y , , when u1 ≤ 0.3 and decreasing returns when y b u1 ≥ 0.3 . As for U , and , we always observe decreasing returns for all values of u1 . Second, as to y human capital, h , we observe a positive relationship between 1 − u1 and h when 1 − u1 ≤ 0.3 , and a negative relationship for 1 − u1 ≥ 0.3 . Finally, it was observed in our exercises that the nature, and form of the hump-shape relationship depend on the choice of our parameters. For instance, we chose ε 1 , ε 2 , and ε 3 to sum up to less than 1, indicating decreasing returns. When the above -13- parameters are chosen such that they sum up to more than 1, both the nature of the relationship and the optimal point for u1 change. The results of our comparative static exercise for the low-income group are summarized in Table 6 in appendix . The results for the other two income groups can also be found in the appendix A.5. Figure 3 above shows the relationship between u1 and y , U , h , and b , and between 1 − u1 and h , for the low-income group. Similar results are observed for the lowery middle and upper-middle income groups. Figure 3: Effect of the Fraction of Human Capital Used in Market Goods Production u1 on the Steady State Variables (Low-Income Group) The observation that u1 , has a non-linear, hump-shaped relationship with all the variables suggests a decreasing return effect so that, beyond a point, any increase in the fraction of resources allocated to one area takes away resources from other areas that may indeed contribute more to growth. Furthermore, the hump-shaped form of the effect of 1 − u1 on per capita human capital, h , implies that any increase in the parameters would first increase h , but beyond the 30% threshold, the effect becomes negative. Such a reversal of the relationship could signal the fact that as too much human capital is devoted to human capital production, there is less and less of it available for market goods production. 5 Exploring the Effect of Public Expenditure Composition In this section the model is calibrated for different expenditure structures and the effects of changes in the composition of public investment expenditure are explored for the three country groups. As above, the classification in low-, lower-middle- and upper-middle-income countries is -14- retained.31 Here, again, only the results of the low-income groups are reported. For the results of the other two country groups, see Appendix A.6. The data on public expenditure is obtained from the IMF's Government Finance Statistics. Since these are too detailed for our analysis, the different expenditure categories are summarized to match the following model parameters: public investment in infrastructure, α1v1 , education, α1v2 , and health, α1v3 , public transfers, α 2 , public consumption, α 3 and debt services, α 4 = (1 − α1 − α 2 − α 3 ) .32 Note that the values reflect the averages for all countries of one category. By plugging the obtained numerical values ( α1 = 0.4035 , α 2 = 0.0623 , α 3 = 0.4342 ) into the model, setting ρ = 0.03 , δ k = 0.075 , δ h = 0.075 , δ g = 0.05 , α = β = γ = 0.33 , u1 = 0.85 , ε 1 = ε 2 = 0.2 , ε 3 = 0.25 , r = 0.08 , η = 0.1 , and using the values for A and i pf that were found in the previous section ( A = 1 , n = 0.0195 i pf = 3.361 ), one can simulate the effect of changes in the composition of public expenditure on the stationary states by letting v1 , v2 and v3 vary.33 In the following this is done for the low-income country group.34 Although all graphs are presented in the 3-dimensional space such that the interaction of all three investment expenditure parameters can be observed at the same time, the stationary states for shifts from public investment in health, α1v2 , to public investment in education, α1v3 , are of particular interest.35 Generally, the results suggest that, in order to maximize the growth of per capita income, more than half of public investment expenditure should be on infrastructure while the residual should be roughly equally allocated to investments that support production of human capital. Figures 4 to 12, all of which are hump-shaped, depict the effects of changes in the investment expenditure composition on the various model parameters. Figures 4 to 9 show all possible investment expenditure compositions for income, y , capital, k , public capital, g , public debt, b , consumption, c and total public resource absorption, e p , are qualitatively the same. b , differ in their y behavior. In Figure 12 one can see that human capital can be increased beyond its welfare- and growth-maximizing level by setting v2 = 0.30 and v3 = 0.20 (and v1 = 0.5 ). At this point the maximal h is reached, however, the benefits of its increase do not offset the costs of higher depreciation. Figure 10 depicts the changes in utility over the range of v1 , v2 and v3 . Whilst the curvature of U is less pronounced than in the previous graphs, it is hump-shaped and possesses an interior maximum which lies at general maximum, i.e. v1 = 0.65 , v2 = 0.15 and v3 = 0.20 . The b shape of the debt to income ratio, , differs completely from the other variables as it does not y b possess an interior maximum. As one can see in graph 11, the curvature of is strictly concave y and attains its maximum value at the origin, i.e. v2 = v3 = 0 (and v1 = 1 ). The fact that is, however, more interesting is that the ratio is approximately stable through most of the range of v2 and v3 . Only the graphs for human capital, h , utility, U , and debt/income ratio, 31 See appendix A.4 for the complete list of countries. See appendix A.3 for details. 33 Note that described the numerical values for ρ , δ k , δ h , δ g , α , β , γ , u1 , ε 1 , ε 2 , ε 3 , 32 α1 , α 2 , α 3 and η remain the same for the remainder of this section. Similar results hold for the other two groups. Complete sets of graphs for the other groups are listed in Appendix A.6. 35 Note that v1 + v2 + v3 = 1 always has to hold which restricts the plane to a triangular space. By fixing v2 or v3 the 34 effects of changes in v1 are also always observable. -15- Sustainability problems due to shifts in the investment expenditure composition do not occur in the long run. The aim of this section was to conduct a comparative static exercise for changes in the composition of public investment expenditure. The results show that in the long run the welfareand growth maximum lies at a composition of roughly v1 = 0.65 , v2 = 0.15 and v3 = 0.20 . Debt sustainability problems did not occur throughout the possible range of v1 , v2 and v3 . Yet, overall to the issue of debt sustainability we have presumed here a very passive debt policy as indicated in eqn. ((5)), which assumes that new debt is not issued and the repayment follows a fixed rule, b namely α 4 e p . If we allow for new debt issue, as discussed in section 3.1, the debt to output ratio, y is likely to increase. Figure 4: Effects of Changes on Income y Figure 7: Effects of Changes on Public Capital g Figure 5: Effects of Changes on Capital k Figure 6: Effects of Changes on Public Debt b -16- Figure 8: Effects of Changes on Consumption c Figure 9: Effects of Changes on Public Absorption ep Figure 11: Effects of Changes on Utility U Figure 10: Effects of Changes on Debt to Income Ratio b y Figure 12: Effects of Changes on Human Capital h 6 36 Testing Debt Sustainability36 As in section 3.2 the notation of this section is changed in order to comply with empirically available data. -17- In section 3.2 we modeled the inter-temporal budget constraint in the context of our model but we did not pursue this question further in our calibration studies in section 4 and 5. If one studies particular countries (or country groups) from a time series perspective, it is an important empirical question whether certain public policies for growth stay within the bounds of a sustainable fiscal policy. Here we briefly discuss tests for sustainability of fiscal policies and suggest a version that has been tested for advanced countries. We will then suggest sustainability tests that can be undertaken for specific country studies.37. If one studies the effect of fiscal policy on economic growth, one needs to check, as indicated in section 3.2, whether the government fulfills the inter-temporal budget constraint. As shown in section 3.2, in economic terms, this constraint states that public (net) debt at time zero must equal the expected value of future present-value primary surpluses. In general terms, this requirement is also often referred to as the no-Ponzi game condition. In a general form we can write this as follows. Neglecting stochastic effects and assuming that the interest rate is constant, the intertemporal budget constraint can be written as B (0) = ∫ e − rτ S p (τ ) dτ , ∞ 0 (19) with r the constant interest rate, B(0) public debt at time zero and S p the primary surplus.38 Equivalent to equation (19) is the following equation − rt (20) lim e B(t ) = 0, t →∞ with B(t ) public debt at time t , stating that the present value of public debt converges to zero for t → ∞. In the economic literature numerous studies exist which explore whether (19) and (20) hold in real economies.39 For example, Hamilton and Flavin (1984) suggest testing for the presence of a bubble term in the time series of public net debt which would indicate that a given fiscal policy is not sustainable. Trehan and Walsh (1991) proposed to test whether the budget deficit is stationary or to test whether the primary budget deficit and the public debt series are co-integrated and (1 − λL) Stp is stationary, with 0 ≤ λ < 1 + rt . Another test, proposed by Wilcox (1989), is to test whether the series of undiscounted debt displays an unconditional mean of zero. If this holds the inter-temporal government constraint will be fulfilled, because the inter-temporal budget constraint requires the discounted debt to converge to zero.40 This implies that all government debt will be repaid at some point in time. Moreover, another aspect of these tests which has given rise to criticism is that those tests need strong assumptions, because the transversality condition involves an expectation about states in the future that are difficult to obtain from a single set of time series data and because assumptions about the discount rate have to be made.41 Alternative tests check solely if in the long run some debt-to-income ratio remains stationary. A test procedure which circumvents the problems associated with the above first type of test focuses on the time series of the debt ratio, i.e. on the ratio of public debt-to-GDP. If this series is constant the inter-temporal budget constraint is fulfilled for dynamically efficient economies. To see this let B/Y = c1 be the constant debt ratio, with Y denoting GDP and c1 a positive constant. Inserting B/Y = c1 in ((20)) yields lim c1Y0 e t →∞ (γ − r )t = 0, (21) for γ < r , with γ > 0 the constant growth rate of GDP. The condition γ < r characterizes a 37 For a detailed discussion of sustainability tests see Greiner et al. (2005). For further derivations see e.g. Blanchard and Fischer (1989), ch. 2. 39 See e.g. Hamilton and Flavin (1984), Kremers (1988), Wilcox (1989), and Trehan and Walsh (1991). 40 As to these tests applied to Germany see Greiner and Semmler (1999). 41 See e.g. Bohn (1995,1998). 38 -18- dynamically efficient economy and is likely to hold in real economies. For example, in EU countries this seems to be obvious if one compares interest rates with GDP growth rates. But even the US, where growth rates have exceeded interest rates on safe government bonds since the 1990s, is a dynamically efficient economy.42 Therefore, for advanced countries we may limit our considerations to the case of dynamic efficient economies and assume that the discount rate of government debt exceeds the GDP growth rate.43 For developing countries, like the low- and lowermiddle income countries of this study, this would have to be explored. However, testing for stationarity of the debt-to-GDP ratio is characterized by some shortcomings, too. It is difficult to distinguish between a time series which is stationary about a positive intercept and one that shows a trend. This holds because standard unit root regressions have low power against autoregressive alternatives if the AR coefficient is close to one. As a consequence, the hypothesis that a given fiscal policy is sustainable has been rejected too easily. Therefore, Bohn (1998) suggests to test whether the primary deficit-to-GDP ratio is a positive linear function of the debt-to-GDP ratio. If this holds, a given fiscal policy will be sustainable. As discussed in section 3.2 the intuitive reasoning behind this argument is that if a government raises the primary surplus as the public debt ratio rises, it takes a corrective action which stabilizes the debt ratio and makes public debt sustainable. Before one can undertake empirical tests which apply this concept we need to advance some theoretical considerations about the relevance of this test. We limit our considerations to deterministic economies. Assuming, as in section 3.2, that the primary surplus to GDP ratio depends on a constant and linearly on the debt-to-GDP ratio, this variable can be written as ⎛ B (t ) ⎞ S p (t ) T (t ) − G (t ) ⎟⎟, (22) = α + β ⎜⎜ = Y (t ) Y (t ) ⎝ Y (t ) ⎠ with T (t ) tax revenue at t , G (t ) public spending at t , α and β are constants which can be negative or positive. α is a systematic component which determines how the level of the primary deficit reacts to variations in GDP. α can also be interpreted as other (constant) economic variables which affect the surplus ratio. The coefficient β can be called a reaction coefficient since it gives the response of the primary surplus ratio to an increase in the debt ratio. Inserting (22) in the differential equation, giving the evolution of public debt, the latter equation is then given by (23) B& (t ) = r B(t ) + G (t ) − T (t ) = (r − β ) B(t ) − α Y (t ). Solving this equation we get ⎛ ⎞ α ⎟⎟Y (0)eγ t + e ( r − β ) t C1 , (24) B (t ) = ⎜⎜ − − r γ β ⎝ ⎠ with B(0) > 0 debt at time t = 0 which is assumed to be strictly positive and with C1 a constant given by C1 = B(0) − Y (0)α/(r − γ − β ) . Multiplying both sides of (24) by e − rt leads to ⎛ α e −rt B(t ) = ⎜⎜ ⎝ r −γ − β ⎞ ⎟⎟Y (0)e (γ − r ) t + e − β t C1. ⎠ (25) The first term on the right hand side in (25) converges to zero in dynamically efficient economies and the second term converges for β > 0 and diverges for β < 0. These considerations show that β > 0 guarantees that the inter-temporal budget constraint of the government holds. Further, with equation (22) the debt-to-GDP ratio evolves according to 42 For details of such conditions see Abel et al. (1989). In dynamically inefficient economies the government budget constraint is irrelevant because in that case the government can play a Ponzi game. 43 -19- ⎛ B& Y& ⎞ b& = b⎜⎜ − ⎟⎟ = b(r − β − γ ) − α . ⎝B Y⎠ Solving this differential equation, we obtain the debt-to-GDP ratio b as (26) α + e ( r −γ − β ) t C 2 , (27) (r − β − γ ) where C2 is a constant given by C2 = b(0) − α/(r − β − γ ), with b(0) ≡ B(0)/Y (0) the debtb(t ) = GDP ratio at time t = 0. Equation (27) shows that the debt-to-GDP ratio remains bounded if r − γ − β < 0 holds. This shows that a positive β does not assure boundedness of the debt-GDP ratio although the intertemporal budget constraint of the government is fulfilled in this case. Only if β is larger than the difference between the interest rate and the GDP growth rate the debt ratio remains bounded. These considerations demonstrate that sustainability of debt may be given even if the debt-to-GDP ratio rises over time - a situation which seems to hold for some countries. But it must also be pointed out that for too high a level of public debt the government will probably not be able to raise the primary surplus any further. Then, our rule formulated in equation (27) will break down. This holds because, the present value of future surpluses must equal public debt at any finite point in time. So, if the government is not able to raise the primary surplus as public debt rises any longer from a certain point of time, say t1 , onwards, β is zero or even negative. Then, a fiscal policy is sustainable only if the government has succeeded to reduce public debt to zero up to that point of time t1 . This implies that in the long-run the debt-to-GDP ratio must be constant, although it may well rise transitorily. However, it is ultimately an empirical question what the country specific β will be.44 In this section therefore we suggest some method related to the Bohn method (Bohn(1998)) which allows one to estimate sustainability, but at the same time works, as section 3.2 has indicated, with a time varying reaction of governments to the debt to GDP ratio. This allows one to get some insight using empirical tests about the sustainability of policies. As we have pointed out in section 3.2 our strategy for testing the sustainability of debt has the advantage that the test does not depend on the interest rate which is used to discount public debt as needed in the first type of the above discussed tests. Following our setup in section 3.2, the equation suggested to be tested is as follows: (28) sty = β t bty + α Τ Z t + ε t , where sty and bty are the primary surplus to GDP and the debt-to-GDP ratio, respectively. Z t is a vector which consists of the number 1 and of other factors related to the primary surplus and ε t is an error term which is i.i.d. N (0, σ 2 ). The idea behind estimating (28) is the tax smoothing hypothesis according to which public deficits should be used to finance transitory government spending, for example higher public spending during recessions. Further, the variables contained in Z t may differ depending on which country is analyzed. In the US, for example, military spending is a variable which exerts a strong influence on the primary surplus. In European countries social spending plays an important role affecting the primary surplus. For other countries, for example, low-income countries, other spending categories may be relevant. We want to note, as concerns the primary surplus, one has to distinguish between the primary surplus including the social surplus and the primary surplus exclusive of the social surplus, where social surplus means the surplus of social insurance system. This holds because in some countries deficits of the social insurance system raise the stock of public debt, since the government sector and the social insurance system are not separated, whereas this does not hold for other countries. 44 This could be estimated separately for each country in country studies. -20- So, in some European countries the social insurance systems are autonomous and do not borrow in capital markets. For example, if the social insurance system runs deficits, these deficits are either transitory because they must be paid back in the next period or the deficits are covered by reserves from earlier years. If, on the other hand, the social insurance system has a surplus this does not raise the surplus of the government, but is used as reserve. However, it happens that the government subsidizes the social insurance which leads to a decline in the surplus of the government. This amount, however, is included in the regular surplus or deficit of the government so that taking it into account in the surplus or deficit of the government and adding that of the social insurance would lead to double counting. These considerations demonstrate that institutional regulations determine which concept for the primary surplus should be used. As we noted above, social security and transfer arrangements in countries of different income groups seem to be different. Our suggested test should therefore be adjusted to each type of income group - or country if country specific fiscal policy studies are undertaken. 7 Conclusion The World Bank has argued in two recent policy papers that fiscal policy design should seek to ensure macroeconomic stability as well as promote growth and the long-run welfare of a country. The growth impact of the composition of public expenditure is an important aspect of the design of fiscal policy that is consequently the focus of research interest. In this paper we suggest a general model of fiscal policy and growth in an economy with a government that taxes optimally and undertakes public expenditure on (a) education and health facilities, (b) public infrastructure such as roads and bridges, (c) public administration, (d) transfers and public consumption facilities, and (e) debt service. We use this model to explore the impact of shifts in the composition of expenditure on long-run per capita income and other macroeconomic variables. We also set up the model in a way that allows us to study whether fiscal policy is sustainable. This model is solved, the impact of foreign aid, the allocation of human and public capital and fiscal expenditure on per capita income and other macro variables explored. Foreign aid per capita and the productivity factor both have a positive and linear effect on per capita GDP and welfare. Such a result is clearly what would have been predicted by the theory as inflows of foreign aid are assumed to be used for investment in roads, schools, hospitals, or any other infrastructure that plays an important role in raising productivity. Foreign aid has either no effect, or a slightly negative effect, on the stock of resources absorbed by the public sector.. Such a result could be due to some “crowding-in” effect, reflecting the fact that as foreign aid flows in, more investment and production opportunities open up and resources are used more privately and less publicly. Second, the model suggests that the choice of allocating human capital to market production or to human capital production poses an important trade-off. As the share of human capital that is devoted to human capital production rises (starting from a very low share) income, as well as welfare, initially rises but then falls. In addition, beyond a certain point, the ability to expand the stock of human capital itself is actually diminished. Thus, there exists a growth-maximizing allocation of human capital between final production and the creation of additional human capital. Overall, our model suggests that the larger fraction of human capital should be used for market production.45 The calibration exercise was also undertaken for different compositions of public investment expenditure for the three country groups. The results of this exercise show that the composition of public investment expenditure matters, as the gains of moving to the optimal allocation between 45 Of course, this depends on the assumption in our parameter constellations, in particular on the elasticity parameters in the creation of human capital, which add up to 0.6 , a number far below 1. -21- public infrastructure, and education and health facilities are significant. Based on the model and the calibration exercise, a practical rule of thumb seems to be that about two-thirds of public investment should be directed towards public infrastructure that facilitates market production. The remaining third should be split more or less evenly between public investments in facilities that support the provision of health and education. Such a division of resources would maximize (per capita) income and welfare. This is due to the fact that the facilitation of market good production directly increases the availability of public resources, while the other two expenditure categories first have to permeate the economic system before affecting the availability of public resources and thus growth and utility. This result has relevance for policy debate on the composition of expenditure necessary to achieve the Millenium Development Goals (MDGs), which include an income target (halve the number of people below the poverty line) as well as specific targets related to the achievement of health status and access to educational services. The stylized model in this paper suggests that greater emphasis on the health and educational targets relative to investments that may contribute to expansion of market production may result in slower progress on reducing poverty. During this numerical exercise, attention was also paid to the evolution of public debt. Quite surprisingly, the debt-to-income ratio was almost invariant to all possible investment expenditure compositions. In the considered case the ratio stabilized below 70%. Here the rule of thumb seems to emerge that in the long run debt sustainability does not pose a problem as long as resources for public investments are used in a growth-maximizing way. We conclude with some observations regarding possible extensions of the model described in this paper. One possibility (described in the appendix) is to estimate the model using time series methods. However, this will only be possible for countries where high-quality time series data are available. An important extension of the model would be to develop the revenue side of fiscal policy in order to study the effects of various forms of taxation on per capita income. Another extension would be to consider the growth implications of variations in the balance between recurrent and capital expenditure by allowing government employment of teachers and doctors. Finally, the debt sustainability tests proposed in this paper could be applied to country-specific studies. References Abel, A., G. Mankiw, N. Summers, and R. Zeckhauser (1989). Assessing Dynamic efficiency: Theory and evidence. Review of Economic Studies 56, 1–19. Agénor, P. and K. Neanidis (2006). The allocation of public expenditure and economic growth. Centre for Growth and Business Cycle Research Discussion Paper Series (69). The University of Manchester. Agénor, P. and D. Yilmaz (2006). The tyranny of rules: Fiscal discipline, productive spending and growth. World Bank PREM Conference (April 25-27,2006). Arestoff, F. and C. Hurlin (2006). Estimates of government net capital stocks for 26 developing countries, 1970-2002. World Bank Policy Research Working Paper. Balonos, R. (2005). Public investment, fiscal adjustments and fiscal rules in Costa Rica. World Bank Report, World Bank. Barro, R. (1990). Government spending in a simple model of endogenous growth. Journal of Political Economy 98, 103–125. Blanchard, O. and S. Fischer (1989). Lectures on Macroeconomics. Cambridge, Massachusetts: The MIT Press. -22- Blankenau, W. and N. Simpson (2004). Public education expenditures and growth. Journal of Development Economics 73 (2), 583–605. Bohn, H. (1995). The sustainability of budget deficits in a stochastic economy. Journal of Money, Credit and Banking 27, 257–271. Bohn, H. (1998). The behavior of U.S. public debt and deficits. Quarterly Journal of Economics 113, 949–963. Brock, W., S. Durlauf, and K. West (2003). Policy evaluation in uncertain economic environments. NBER Working Paper Series 10025, NBER. Bundy, D. et al. (2005). School Health and Nutrition Programs, In Jamison, D. et al. (eds.) Disease Control Priorities in Developing Countries. Oxford University Press. Corsetti, G. and N. Roubini (1996). Optimal government spending and taxation in endogenous growth models. NBER Working Paper 5851, NBER. Devarajan, S., V. Swaroop, and H. Zou (1996). The composition of public expenditure and economic growth. Journal of Monetary Economics. Easterly, W. (2005). National economic policies and economic growth: A reappraisal. In P. Aghion and S. Durlauf (Eds.), Handbook of Economic Growth. Amsterdam: North-Holland: Elsevier. Easterly, W. (2006). The White Man’s Burden: Why the West’s Efforts to Aid the Rest Have Done So Much Ill and So Little Good. The Penguin Press. Ferreira, P. and C. Arajo (2006). On the economic and fiscal effects of infrastructure investment in Brazil. Economics Working Papers 613, Graduate School of Economics, Getulio Vargas Foundation (Brazil). Gemmell, N. (2007). The composition of public expenditure and growth. Technical report, Draft World Bank Background Paper. G.F.S. (2005). Government finance statistics. International Monetary Fund, CD-Rom. Glomm, G. and R. Ravikumar (1997). Productive government expenditures and long-run growth. Journal of Economic Dynamics and Control . Glomm, G. and F. Rioja (2006). Fiscal policy and long-run growth in Brazil. Mimeo, Indiana University. Greiner, A., U. Koeller, and W. Semmler (2005). Testing sustainability of German fiscal policy. Evidence for the period 1960 2003. Cesifo Working Paper Series, CESifo GmbH. Greiner, A. and W. Semmler (1999). Staatsverschuldung, wirtschaftswachstum und nachhaltigkeit der finanzpolitik in deutschland. In R. Neck and R. Holzmann (Eds.), Was wird aus Euroland?, pp. 161–180. Vienna. Greiner, A., W. Semmler, and G. Gong (2005). The Forces of Economic Growth - A Time Series Perspective. Princeton University Press. -23- Gruene, L. and W. Semmler (2004). Using dynamic programming with adaptive grid scheme for optimal control problems in economics. Journal of Economic Dynamics and Control 28, 2427– 2456. Hamilton, J. and M. Flavin (1984). On the limitations of government borrowing: A framework for empirical testing. The American Economic Review 76, 808–819. Kremers, J. (1988). Us federal indebtedness and the conduct of fiscal policy. Journal of Monetary Economics 23, 219–238. Lucas, R. (1988). On the mechanics of economic development. Journal of Monetary Economics 22 (1), 3–42. Reddy, S. and C. Minoiu (2006). Development, aid, and economic growth: A positive long-run relation. DESA Working Papers 29, United Nations, Department of Economics and Social Affairs. Rodrik, D. (2005). Why we learn nothing from regressing economic growth on policies. Mimeo, Kennedy School of Government. Suescun, R. (2005). Fiscal space for investment in infrastructure in Colombia. Policy Research Working Paper Series 3629, World Bank. Tanzi, V. and H. Zee (1997). Fiscal policy and long run growth. IMF Staff Papers. Temple, J. (2003). The long-run implications of growth theories. Journal of Economic Surveys 17 (3), 497–510. Trehan, B. and C. Walsh (1991). Testing inter-temporal budget constraints: theory and applications to us federal budget and current account deficits. Journal of Money, Credit and Banking 23, 206– 223. W.D.I. (2005). World development indicators. The World Bank. Wilcox, D. (1989). The sustainability of government deficits: Implications of the present-value borrowing constraint. Journal of Money, Credit and Banking 21, 291–306. World-Bank (2006). Fiscal policy for growth and development: An interim report. Background Paper for the Development Committee Meetings, Development Committee. World-Bank (2007). Fiscal policy for growth and development: Further analysis and lessons from country case studies. Background Paper for the Development Committee Meetings, Development Committee. Zagler, M. and G. Durnecker (2003). Fiscal policy and economic growth. Journal of Economic Surveys. 37 -24- Appendix The appendix begins with the out-of-steady-state solution for a simplified version of the model (A.1) and a suggestion of how to estimate the simpler model using time series analysis (A.2). Appendix A.3 explains how the data used in the calibration was constructed and appendix A.4 lists the countries used. Appendix A.5 lists the data used to compute the graphs shown in section 4 and additional data on the two other country groups which have not been discussed in the paper. Appendix A.6 does the same with graphs on the long run effects of public expenditure composition that have been omitted in the main part of the paper. A.1 Out-of-Steady-State Solutions Since economies are rarely at their steady states, it is, for practical purposes, of great importance to explore what decisions should be taken out of the steady state. There is, however, no analytical solution for our decision variables out of the steady state. Yet, once the parameters have been set and the stationary state of the variables {c, e p , k , h, g , λ1 , λ2 , λ3 } have been computed, the dynamic programming algorithm developed by Gruene and Semmler (2004) can be used to study the out-of-steady-state dynamics not only of consumption, c , and the use of resources by the public, e p , but also the state variables: physical capital stock, human capital and public capital stock.46 Using our parameter set above, next we will compute the out-of-steady-state solutions using a numerical algorithm. This way we can study the following: When, for example, the capital stock of a country is k < k * (and h < h* , g < g * ) the dynamic programming solution allows one to judge whether c should be high or low, how e p behaves, and how the control variables relate to each other out of the steady state. Using the algorithm of Gruene and Semmler (2004) we have solved the model (1)-(4), with u1 fixed, and thus solely with c and e p as control variables and k, h and g as state variables.47 Yet, since the value function (1) is a function of the decision variables c and e p and the state variables k , h and g (the former again depending on k , h and g ) one can only obtain proper graphs by appropriate projections and study the value function and behavior of decision variables in a twodimensional subspace. We have solved the model (1)-(4) in the vicinity of the steady state k * = 65.47, h* = 18.16 , g * = 11.47 which was obtained by solving the equation system arising from the Hamiltonian in section 3.1.48 Next, in the vicinity of the positive steady state we have taken a cube [60,70] × [16,20] × [9,13] for k , u and g , with a subspace for the choice variables [7,8] × [7,8] , for c and e p . Figure 13 shows four sample trajectories in a three dimensional space, with initial conditions for trajectory 1 (T1): (66.2, 18.9, 11.8) which are above the steady state k * , h* , g * . Trajectory 2 (T2) has initial conditions: (67.5, 18.7, 11.4) and is, thus, far to the right of the steady state k * , h* , g * . Trajectory 3 (T3): (63.2, 16.8, 11.1) starts below the steady state k * , h* , g * . Finally, Trajectory 4 (T4) starts with k = 68.2 above, with h = 16.5 below and with g at the steady state. 46 The out of steady state dynamics are analyzed for a simplified version of the model which omits public debt. Note that this simplified version omits the debt equation (5) of the model. 48 There is, however, a second steady state which was neglected because of negative values of some state variables. 47 -25- Figure 13: Out of Steady State Dynamics As one can observe in Figure 13, the correctly taken optimal decisions c and e p make the initial states of state variables converging toward the steady state k * , h* , g * for all four sample trajectories. Note that trajectories (T1), (T2), (T3) and (T4) do not only exhibit some irregular features but also cross each other. This comes from the fact that we follow the trajectories in a 2dim subspace state variables only, namely in the k − h space. For graphical purposes, the third state variable g is fixed in Figure 13. Figure 14: Decision Variable c in the k − h space If one stores the decision variables c and e p at each grid point of the 3-dim cube of k , h and g one can then plot them in a 3-dim space where the height represents the numerical value of the decision variable. In Figure 14, for example, the height stands for the value of c , and the other two axes represent k and h . In Figure 14 it is clearly visible that if k > k * and h > h* the optimal consumption c is required to be high, above its steady state. The reverse holds for the space k < k * and h < h* . Here c has to be below its steady state. This behavior of the optimal c is a result that one would also expect from economic intuition. -26- Figure 15: Decision Variable e p in the k − h space On the other hand as Figure 15 shows the decision variable e p is not so monotonically dependent on k and h . In some regions e p is higher than in others. Note that we have neglected here to study the behavior of c depending on government capital, g . This also can be easily done, but this might not be so relevant in the context of our study. Next, we want to study the dependence of the total use of public resources, e p , on private capital, k , and public capital, g . Figure 16: Decision Variable e p in the k − g space Figure 16 shows how the decision variable e p behaves in the k − g space. We can observe that e p will be high above the steady state, for g > g * , and low below the steady state, for g < g * . The decision variable e p does not seem to depend much on the level of the capital stock, k . Finally, we want to make a comment on the constraints that we have put on the control variables, c and e p . For both the lower constraint is 7 and the upper is 8 so that all optimal c and e p are staying within those constraints. But note that with c* = 7.04 and e*p = 7.53 the decision variables are above the lower constraints of 7. Putting such constraints on the decision variables just means that the decision variables cannot go fast enough down and thus the state variables that are affected by this are not going up fast enough. This is the reason why the trajectory (T4) in Figure 13 -27- first moves far down (to the left) in the state variable k and then rises again moving toward its steady-state value. The above exercise with constraints for the decision variables is nevertheless of great importance for practical economic policy. It basically means that the decision variables do not have to be exactly at their optimal values in order to exhibit convergence dynamics. For actual economies an exact optimal control is indeed hard to achieve, since for actual economies, there is model uncertainty -- which model fits the economy -- as well as data uncertainty (see Brock et al. (2003)). Our computations with constraints for the decision variables then means that the decision variables need to be only above or below their steady-state values in the appropriate state space in order to fulfill the requirement to be roughly optimal. This aspect appears to us of great practical importance, since decisions for c and e p have to be only approximately correct. A.2 The Estimable Form of the Model Next we want to spell out some implications of how to estimate our model with time series methods. Even for our simplified social planner model of eqns. (1) to (4) it could be too ambitious to estimate the model employing Euler equations, derived from the first order conditions for the two control variables for consumption, c , and total use of resources, e p , and the decision variable u1 . As the model is written, it gives us the outcome of the social optimum. We propose to reduce the model further, and treat, for the purpose of a time series estimation, only consumption as decision variable. The other choice variables, e p and u1 are just treated as historical variables, as time series observations. This is also likely to inject some realistic features into the model. For a time series study we thus propose to include only one Euler equation in the time series estimation procedure. We suggest to only use the equations (2)-(4) and the equation for c& , which can be derived from the first order condition of the decision variable c as c& λ& = − 1 → c& = c Aαk α −1 (u1h) β (v1 g )γ − ρ − δ k (29) λ1 c ( ) The model reflects now the fact that it is only optimized with respect to private consumption. The decision making process for all the public variables might be considered too complex to be presumed as the result of some optimization process. Yet, in the normative sense, as we discuss below, we still might consider the other public decision variables as choice variables so as to give us a guidance to welfare improving policies. Above, we have undertaken some calibration and comparative static study in order to explore the impact of fiscal policy decisions on per capita income and welfare. A.3 Data Two different sources were used for gathering the data necessary for the calibration and comparative static exercises. First, information on GDP, population size and foreign aid flows was taken from the World Bank's World Development Indicators (WDI). Second, information on the public expenditure composition was taken from the Government Finance Statistics (GFS). In order to make the data compatible with the model, only category 7 (and its subcategories) of the GFS were used. Public infrastructure investment, v1α1e p , consists of “Economic affairs” (704), “Environmental protection” (705) and “Housing and community amenities” (706). Public expenditure on health, v2α1e p , was taken from “Health” (707). Public expenditure on education, v3α1e p , consists of “Education” (709). “Recreation, culture, and religion” (708) and “Social -28- protection” (710) was subsumed under public transfers, α 2 e p . Public consumption and debt payments, α 3e p and α 4 e p , were defined as the sum of “General public services” (701), “Defense” (702) and “Public order and safety” (703). Since the information on debt service is very spotty, we chose α 4 = 0.10 in a rough approximation and set the accordingly decreased above sum equal to α3 . We follow the IMF Development Committee (2006) in its classification of countries in low, lower-middle and upper-middle income countries. However, due to the bad quality of the data in the GFS, we dropped some countries and reduced the list of countries to the ones listed in appendix A.4. A.4 Country Groups Table 3: Reduced List of Countries Low-Income Bhutan Burundi Ethiopia India Moldova Myanmar Pakistan Yemen Zambia Lower-Middle Income Belarus Bolivia Bulgaria Dominican Republic Egypt El Salvador Iran Jamaica Maldives Morocco Philippines Romania Sri Lanka Thailand Tunisia Upper-Middle Income Argentina Croatia Czech Republic Estonia Hungary Lithuania Mauritius Mongolia Panama Poland Uruguay A.5 Appendix to Section 4 f Table 4: Effect of Foreign Aid, i p , on the Steady-State Variables (Low-Income Group) i fp ep 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 1539.3 1539.1 1538.9 1538.8 1538.6 1538.4 1538.2 1538.0 1537.8 1537.6 1537.5 c 890.4 891.0 891.6 892.1 892.7 893.2 893.8 894.4 894.9 895.5 896.0 k 10848 10850 10851 10853 10855 10856 10858 10860 10861 10863 10865 h 1152.6 1152.8 1152.9 1153.0 1153.2 1153.3 1153.4 1153.6 1153.7 1153.8 1153.9 -29- g 9005 9006 9008 9010 9012 9014 9015 9017 9019 9021 9023 b 2531.8 2531.5 2531.2 2530.8 2530.5 2530.2 2529.9 2529.6 2529.3 25290. 2528.7 y 3451.6 3452.2 3452.7 3453.2 3453.8 3454.3 3454.8 3455.4 3455.9 3456.4 3457.0 U 89.70 89.71 89.72 89.73 89.73 89.74 89.75 89.76 89.80 89.77 89.78 Table 5: Effect of the Productivity Factor, A , on the Steady-State Variables (Low-Income Group) A 1.000 1.005 1.010 1.015 1.020 1.025 1.030 1.035 1.040 1.045 1.050 1.055 1.060 ep c 1538 1589 1641 1694 1749 1805 1863 1923 1984 2047 2111 2177 2245 894 923 953 984 1015 1048 1081 1115 1150 1186 1223 1261 1300 k 10859 11214 11580 11955 12341 12737 13144 13562 13992 14432 14885 15349 15825 h 1153 1175 1196 1218 1240 1262 1284 1307 1330 1354 1377 1401 1425 g 9016 9311 9614 9926 10246 10575 10913 11259 11615 11981 12356 12742 13137 b y 2530 2613 2699 2786 2877 2969 3065 3163 3263 3366 3472 3581 3692 3455 3568 3684 3804 3927 4053 4182 4315 4452 4592 4736 4884 5035 U 89.8 90.2 90.6 91.1 91.5 91.9 92.3 92.8 93.2 93.6 94.0 94.4 94.9 Table 6: Effect of the Fraction of Human Capital Used in Market Goods Production u1 on the Steady-State Variables (Low-Income Group) u1 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 ep 9 39 93 168 263 376 503 642 789 940 1090 1233 1363 1471 1547 1576 1538 1399 1084 c 15 33 64 107 162 227 300 380 464 551 637 719 793 855 899 916 894 814 633 k 104 321 700 1230 1899 2691 3586 4563 5597 6657 7710 8716 9628 10386 10918 11123 10859 9882 7665 h g b y 144 253 383 517 648 774 893 1002 1100 1184 1252 1303 1332 1338 1315 1256 1153 989 721 98 274 588 1028 1582 2239 2982 3793 4650 5530 6404 7239 7995 8624 9065 9236 9016 8206 6366 14 64 152 276 433 618 828 1056 1298 1547 1793 2028 2242 2419 2544 2592 2530 2301 1782 33 102 223 391 604 856 1141 1452 1781 2118 2453 2773 3063 3305 3474 3539 3455 3144 2439 U 32.4 44.4 53.7 60.8 66.4 71.0 74.9 78.1 80.8 83.1 85.1 86.8 88.1 89.2 89.8 90.1 89.8 88.5 85.0 f Table 7: Effects of Foreign Aid, i p , on Steady-State Variables (Lower-Middle-Income Group) i fp 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 ep 5824.8 5824.7 5824.6 5824.5 5824.3 5824.2 5824.1 5823.9 5823.8 5823.7 5823.6 c 4659.7 4660.3 4660.9 4661.4 4662.0 4662.6 4663.1 4663.7 4664.3 4664.8 4665.4 k 45470 45472 45474 45476 45478 45480 45481 45483 45485 45487 45489 h 2742.7 2742.8 2742.9 2743.0 2743.0 2743.1 2743.2 2743.3 2743.4 2743.5 2743.5 -30- g 42050 42052 42055 42057 42059 42061 42064 42066 42068 42071 42073 b 8642.2 8642.0 8641.8 8641.6 8641.4 8641.3 8641.1 8640.9 8640.7 8640.5 8640.3 y 14467.8 14468.4 14469.0 14469.6 14470.2 14470.8 14471.4 14472.0 14472.6 14473.2 14473.8 U 104.38 104.38 104.38 104.38 104.38 104.38 104.38 104.38 104.40 104.39 104.39 Table 8: Effects of the Productivity Factor, A , on the Steady-State Variables (Lower-Middle-Income Group) A 1.180 1.185 1.190 1.195 1.200 1.205 1.210 1.215 1.220 1.225 1.230 1.235 1.240 ep c 5824 5986 6152 6321 6494 6672 6853 7039 7229 7423 7621 7824 8032 4663 4792 4924 5059 5198 5339 5484 5632 5784 5939 6097 6259 6425 k 45481 46742 48034 49355 50707 52091 53506 54953 56434 57948 59496 61079 62698 h 2743 2786 2829 2872 2916 2961 3006 3051 3097 3144 3191 3238 3286 g 42063 43229 44423 45645 46895 48174 49483 50821 52190 53590 55021 56485 57982 b 8641 8881 9127 9378 9636 9899 10168 10443 10725 11013 11308 11609 11917 y 14471 14873 15283 15704 16134 16574 17025 17485 17956 18438 18931 19434 19949 U 104.4 104.7 105.1 105.4 105.7 106.1 106.4 106.8 107.1 107.4 107.8 108.1 108.4 Table 9: Effect of u1 , the Fraction of Human Capital Used in Market Goods Production on the Steady-State Variables (Lower-Middle-Income Group) u1 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 ep c 35 154 359 644 1004 1430 1912 2437 2993 3564 4130 4672 5162 5570 5856 5967 5824 5299 4106 41 137 300 528 815 1155 1540 1959 2403 2859 3311 3743 4134 4460 4688 4777 4663 4243 3291 k 328 1260 2856 5082 7889 11211 14968 19068 23404 27853 32272 36492 40316 43498 45728 46591 45481 41383 32082 h 278 574 894 1217 1532 1835 2119 2380 2613 2813 2977 3097 3168 3181 3126 2988 2743 2351 1713 g 316 1176 2651 4710 7305 10376 13850 17641 21651 25764 29849 33752 37287 40229 42292 43089 42063 38274 29674 b 52 229 532 956 1490 2122 2836 3616 4441 5288 6128 6931 7659 8264 8688 8852 8641 7862 6092 y 104 401 909 1617 2510 3567 4763 6067 7447 8862 10268 11611 12828 13840 14550 14824 14471 13167 10208 U 44.3 59.8 69.8 76.9 82.4 86.8 90.4 93.5 96.0 98.2 100.1 101.6 102.9 103.8 104.5 104.7 104.4 103.2 100.0 f Table 10: Effects of Foreign Aid, i p , on Steady-State Variables (Upper-Middle-Income Group) i fp 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 ep c 10068.2 10068.1 10068.1 10068.0 10067.9 10067.8 10067.7 10067.6 10067.5 10067.4 10067.4 11326.4 11327.3 11328.1 11328.9 11329.8 11330.6 11331.4 11332.3 11333.1 11333.9 11334.8 k 89637 89640 89643 89646 89649 89652 89656 89659 89662 89665 89668 h 3597.5 3597.6 3597.7 3597.8 3597.9 3598.0 3598.0 3598.1 3598.2 3598.3 3598.4 -31- g 68113 68116 68119 68122 68125 68128 68131 68134 68137 68140 68143 b y 13335.4 13335.3 13335.2 13335.1 13334.9 13334.8 13334.7 13334.6 13334.5 13334.4 13334.3 28520.8 28521.8 28522.8 28523.8 28524.8 28525.8 28526.8 28527.7 28528.7 28529.7 28530.7 U 106.26 106.26 106.27 106.27 106.27 106.27 106.27 106.27 106.30 106.27 106.27 Table 11: Effects of the Productivity Factor, A , on the Steady-State Variables (Upper-Middle-Income Group) ep A 1.450 1.455 1.460 1.465 1.470 1.475 1.480 1.485 1.490 1.495 1.500 1.505 1.510 c 10068 10295 10526 10762 11002 11247 11496 11750 12009 12272 12541 12814 13092 k 11331 11586 11846 12111 12381 12656 12936 13221 13512 13808 14110 14417 14729 g h 89654 91674 93733 95830 97967 100145 102363 104622 106924 109268 111656 114088 116564 3598 3643 3689 3735 3782 3829 3876 3924 3973 4021 4071 4120 4170 y b 68130 69664 71228 72822 74446 76100 77785 79502 81251 83032 84846 86693 88574 13335 13636 13942 14254 14572 14897 15227 15563 15906 16255 16610 16972 17341 U 28526 29169 29824 30491 31171 31864 32570 33289 34021 34767 35527 36301 37089 106.3 106.5 106.8 107.0 107.3 107.5 107.8 108.0 108.3 108.5 108.8 109.0 109.3 Table 12: Effect of u1 , the Fraction of Human Capital Used in Market Goods Production on the Steady-State Variables (Upper-Middle-Income Group) u1 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 ep 62 269 623 1116 1738 2474 3307 4215 5176 6162 7141 8076 8923 9629 10123 10314 10068 9160 7099 c 87 319 717 1271 1970 2797 3732 4753 5833 6940 8041 9091 10043 10836 11391 11606 11329 10309 7993 k 623 2465 5610 10000 15534 22083 29491 37575 46124 54894 63606 71927 79465 85739 90136 91837 89648 81569 63232 g h 355 749 1170 1594 2008 2405 2778 3120 3426 3690 3904 4062 4155 4173 4100 3919 3598 3083 2246 488 1886 4276 7611 11815 16791 22419 28561 35056 41719 48338 54660 60387 65153 68494 69787 68123 61985 48054 -32- b 82 356 825 1478 2302 3277 4380 5583 6856 8161 9458 10697 11819 12753 13408 13661 13335 12132 9402 y 198 784 1785 3182 4943 7027 9383 11956 14676 17466 20238 22886 25284 27280 28680 29221 28524 25954 20119 U 49.9 65.1 74.4 81.1 86.1 90.1 93.5 96.3 98.6 100.6 102.3 103.7 104.9 105.8 106.3 106.5 106.3 105.2 102.2 A.6 Appendix to Section 5 Since the calibration exercise for the composition of public expenditure involves too many parameters to list all data in tables, the depiction of the lower-middle- and upper-middle-income cases is limited to graphs. As one can see, these graphs show the same qualitative effects as the low-income group's that were discussed in the main part of the paper. Figure 17: Effects of Expenditure Composition Changes on the per capita Parameters in the Lower-Middle-Income Case -33- Figure 18: Effects of Expenditure Composition Changes on the per capita Parameters in the Upper-Middle-Income Case -34-