metadata: authors: 0: author: Diallo,Mamadou Bobo
1: author: Greiner,Alfred
2: author: Rajaram,Anand
3: author: Rezai,Armon
4: author: Semmler,Willi
count: World
docna: 0: docna: Fiscal policy, public expenditure
            composition, and growth theory and empirics
docty: Policy Research Working Paper
subtopic: Macro-Fiscal Policy,Economic Theory & Research,Economic Adjustment and Lending,Industrial Economics,Health Care Services Industry,Public Sector Economics,Educational Sciences,Infrastructure Regulation,Infrastructure Finance,Economic Growth,Infrastructure Economics,Public Finance Decentralization and
            Poverty Reduction,Infrastructure and Law
teratopic: Public Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: 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.
repnme: repnme: Fiscal policy, public expenditure
            composition, and growth theory and empirics
display_title: Fiscal policy, public expenditure
            composition, and growth theory and empirics
listing_relative_url: /research/2007/11/8736497/fiscal-policy-public-expenditure-composition-growth-theory-empirics
topicv3: Economic Growth m1326241 471,Infrastructure and Growth m1326244 1083,Education m1327048 470,Fiscal Policy m1327144 445,Health m1504661 3480
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Public Sector Development,Macroeconomics and Economic Growth,Finance and Financial Sector Development
no_of_pages: 36
author_keys: 0: author_key: 916851
1: author_key: 903469
2: author_key: 92532
3: author_key: 916850
4: author_key: 903437
model_extractions: WPS4405 Policy ReseaRch WoRking PaPeR 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 Empirics<sup>1</sup>

Willi Semmler,<sup>2</sup> Alfred Greiner,<sup>3</sup> Bobo Diallo,<sup>4</sup> Armon Rezai,<sup>5</sup> and Anand Rajaram<sup>6</sup>

> 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.<sup>7</sup> 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.<sup>8</sup> 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).

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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.<sup>9</sup> 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 ( _Ak_ α ( _u_ 1 _h_ ) β ( _v_ 1 _g_ ) γ for the production of market goods and ((1 − _u_ 1) _h_ ) ε 1 ( _v_ 2 _g_ ) ε 2 ( _v_ 3 _g_ ) ε 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 ( _v_ 1 _g_ ) is used to support private market production, while other parts are used to help to build human capital in the form of schools ( _v_ 2 _g_ ) and medical centers ( _v_ 3 _g_ ) and do not directly influence production.<sup>10</sup> 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, _v_ 1 + _v_ 2 + _v_ 3 = 1 .

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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.<sup>11</sup> 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.

|**T**|**able 1 Variable Overview (all in per capita terms)**|
|---|---|
|Variables|Description|
|_b_|Debt|
|_c_|Consumption|
|_d_|Debt service|
|_p_<sup>_e_</sup>|Amount of resources absorbed by the public sector|
|_k_|Private apital|
|_g_|Public capital|
|_h_|Human capital|
|_y_|GDP|

||**Table 2 Parameter Overview (all in per capita terms)**|
|---|---|
|Parameters|Description|
|_A_|Productivityfactor|
|_f_<br>_p_<sup>_i_</sup>|Foreign aid|
|_n_|Populationgrowth rate|
|_r_|Borrowing rate|
|1<sup>_u_</sup>|Fraction of_h_used to support theproduction of_k_|
|1<br>1 _u_<br>−|Fraction of_h_used to build new_h_|
|1<sup>_v_</sup>|Fraction of_g_used to support the production of_k_|
|2<sup>_v_</sup>|Fraction of_g_used to build new_h_in the form of schools|
|3<sup>_v_</sup>|Fraction of_g_used to build new_h_in the form of medical centers|
|1<br>α|Share of public resources used for the building of new_g_|
|2<br>α|Share ofpublic resources used for transfers andpublic consumption|
|3<br>α|Share ofpublic resources used for the functioningof 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.

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|4<br>α|Share ofpublic resources used for debt services|
|---|---|
|α|Elasticityof GDP w.r.t._k_|
|β|Elasticityof GDP w.r.t._h_|
|γ|Elasticityof GDP w.r.t._g_|
|_k_<br>δ|Depreciation ofprivate capital (_k_)|
|_g_<br>δ|Depreciation of public capital (_g_)|
|_h_<br>δ|Depreciation of human capital (_h_)|
|1<sup>ε</sup>|Elasticityof_h_w.r.t. existing _h_|
|2<br>ε|Elasticity of_h_w.r.t._g_in the form of schools|
|2<br>ε|Elasticity of_h_w.r.t._g_in the form of medical centers|
|~~η~~|Weight of transfers and public consumption in utility|
|~~ρ~~|Discount rate|
|_U_|Utility/welfare|

The amount of resources absorbed by the public sector,<sup>_e_</sup> _p_<sup>, is used for public infrastructure</sup> ( _i p_ = α 1 _e p_ ), transfers and public consumption ( _c p_ = α 2 _e p_ ), and public administration ( _tr_ = α 3<sup>_e_</sup> _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 −α 1 −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 _v_ 1 _g_ . The other fraction of public capital is used for facilitating the formation of human capital via health services, _v_ 2 _g_ , and education, _v_ 3 _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_ + ( α 1 + α 2 + α 3 + α 4 ) _e p_ , _f_ with _i p_ + α 1 _e p_ earmarked for public investment and α 4<sup>_e_</sup> _p_ for debt service. In the steady state then we have _i pf_ + α 1 _e p_ = ( δ _g_ + _n_ ) _g_ . The flow of expenditure should be properly subdivided in spending for infrastructure, health, and education, according to the fractions<sup>_v_</sup> 1<sup>,</sup><sup>_v_</sup> 2<sup>and</sup><sup>_v_</sup> 3<sup>.13 Moreover, note</sup> that the government revenue is also _T_ = _i pf_ + _e p_ , but what can be used for domestic spending is only _T_ −α 4<sup>_e_</sup> _p_ , since α 4<sup>_e_</sup> _p_ flows out for debt service. The primary surplus of the government budget is α 4<sup>_e_</sup> _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<sup>_i_</sup> _p_<sup>, earmarked for public investment, we</sup> _f_

> will, then, have to add<sup>_ib_</sup> _p_<sup>in eqns. (4) and (5) as additional borrowing. We can think of</sup><sup>_i_</sup> _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 _f_ We might think that the annual revenue, earmarked for _i p_ + α 1 _e p_ , is handed over to a trust fund that manages the public current and capital expenditure related to infrastructure, health and education.

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subject to Note that for simplicity we assume an additively separable utility function _U_ ( ⋅ ) = ln _c_ +η ln( α 2<sup>_e_</sup> _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_ will also fall. This is exactly what we expect from a numerical exercise.<sup>14</sup> Our formulation of public debt implies that public debt is foreign public debt. New borrowing from abroad can be allowed for.<sup>15</sup> 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 with λ 1, λ 2, λ 3, λ 4 the co-state variables. The first order conditions for the two choice variables, _c_ and<sup>_e_</sup> _p_<sup>, are:</sup>

> 14 Note that this term does not have to be constant. It suffices if the term is positive on average for the results to hold. 15 See footnote 3.

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For the co-state variables we have Equations (7)-(12), which are derived from the two first order conditions with respect to the choice variables _c_ and<sup>_e_</sup> _p_<sup>and the four equations for the co-state variablesλ</sup> 1, λ 2, λ 3, and λ 4 , 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_ , λ 1, λ 2, λ 3, λ 4} .

Writing eqns. (7) and (8) as 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_ * λ 1*, λ *2, λ *3, λ *4} . Plugging these into the production function _y_ = _Ak_ α ( _u_ 1 _h_ ) β ( _v_ 1 _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<sup>_v_</sup> 1<sup>,</sup><sup>_v_</sup> 2<sup>and</sup><sup>_v_</sup> 3<sup>, we can explore the impact of different public expenditure</sup> 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<sup>_i_</sup> _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_ :<sup>161718</sup>
With this solution technique we can undertake the above described comparative static analyses and some important calibrations, see sects. 4 and 5.<sup>19</sup>

# **_3.2  Fiscal Policy to Ensure Debt Sustainability_**<sup>**_20_**</sup>

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.<sup>2122</sup> 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<sup>_e_</sup> _p_ . More concretely, the government has to stick to the inter-temporal budget constraint which can be written as where _s_ denotes the primary surplus which, in our model, is given by α 4<sup>_e_</sup> _p_ . The first term in (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.

> 18 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,<sup>_i_</sup> _p_ = 0.05 , we obtain the following numerical values: _k_<sup>*</sup> = 88.67 , _h_<sup>*</sup> = 22.36 , _g_<sup>*</sup> = 18.43 ,

> 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<sup>_i_</sup> _p_

> in eqn. ((4)) is supposed to be corrected for the availability of new investment funds for public capital.

22 In Greiner et al. (2005), ch. 6, more particular model versions are developed with government borrowing for specific government expenditures.

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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 ratio<sup>23</sup> on the debt ratio can guarantee sustainability, we assume that the primary surplus ratio is given by 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 with γ the growth rate of GDP. Equation (18) shows that a positive value for β on average, _t_ so that β ( τ ) _d_ τ converges to plus infinity asymptotically, is necessary for sustainability. It is also<sup>∫</sup> 0 sufficient, if _r_ ( μ ) − _n_ −γ ( μ ) is positive on average.<sup>24</sup> 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.

> 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.

> _t_ − β ( τ ) _d_ τ 24<sup>∫</sup> 0 This holds because l'H oˆ pital gives the limit of the second term in (18) multiplied by _e_ as _t_ − ( _r_ ( μ ) − _n_ −γ ( μ )) _d_ μ ∫ 0 _e_ / β .

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# **4  Exploring the Basic Structure of the Model**

We want to explore the effect of foreign aid,<sup>_i_</sup> _fp_<sup>, the productivity factor,</sup><sup>_A_, and the fraction of</sup> human capital used in market goods production,<sup>_u_</sup> 1<sup>, on the steady-state variables of three group of</sup> 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.<sup>25</sup> We employ only data for the time period 1994 to 2004. First, we will _f_ calibrate the effect of foreign aid,<sup>_i_</sup> _p_<sup>.26 By looking at actual data of foreign aid per capita, we are</sup> 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, α 1 , 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.<sup>27</sup> 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,<sup>_i_</sup> _pf_<sup>, vary during that period and</sup> _b_ see how such a change affects the steady-state values , _k_ , _h g_ , , _c_<sup>_e_</sup> _p_ , _y_ , , 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<sup>_u_</sup> 1<sup>, the</sup> 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.

## **_4.1  Effects of Foreign Aid per Capita,_**

### _f_<sup>_i_</sup> _p_

_b_ The comparative static results for all income groups show that _k_ , _h_ , _g_ , _c_ ,<sup>_e_</sup> _p_<sup>,</sup><sup>_y_,</sup> , and _y_

> _U_ are linear in _f_

> <sup>_i_</sup> _p_<sup>and there is clearly a positive relationship between the level of foreign aid and</sup> _b_ all the variables, except for public resources per capita,<sup>_e_</sup> _p_<sup>, and debt per GDP,</sup> , which show a _y_

> 25 See Appendix A.4 for the complete list of countries.

> 26 _f_

> Note that in the following we presume that there is no new borrowing, so that<sup>_i_</sup> _p_ is solely foreign aid.

> 27 The _Mathematica_ code is available at www.newschool.edu/gf/cem.

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retained.<sup>31</sup> 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, α 1<sup>_v_</sup> 1 , education, α 1<sup>_v_</sup> 2 , and health, α 1<sup>_v_</sup> 3 , public transfers, α 2 , public consumption, α 3 and debt services, α 4 = (1 −α 1 −α 2 −α 3) .<sup>32</sup> Note that the values reflect the averages for all countries of one category.

By plugging the obtained numerical values ( α 1 = 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,<sup>_u_</sup> 1 = 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<sup>_i_</sup> _pf_<sup>that were found in</sup> the previous section ( _A_ = 1, _n_ = 0.0195<sup>_i_</sup> _pf_ = 3.361), one can simulate the effect of changes in the composition of public expenditure on the stationary states by letting<sup>_v_</sup> 1<sup>,</sup><sup>_v_</sup> 2<sup>and</sup><sup>_v_</sup> 3<sup>vary.33</sup> In the following this is done for the low-income country group.<sup>34</sup> 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, α 1<sup>_v_</sup> 2 , to public investment in education, α 1<sup>_v_</sup> 3 , are of particular interest.<sup>35</sup> 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,<sup>_e_</sup> _p_<sup>, are qualitatively the same.</sup> _b_ Only the graphs for human capital, _h_ , utility, _U_ , and debt/income ratio, , 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<sup>_v_</sup> 2 = 0.30 and<sup>_v_</sup> 3 = 0.20 (and<sup>_v_</sup> 1 = 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<sup>_v_</sup> 1<sup>,</sup><sup>_v_</sup> 2<sup>and</sup><sup>_v_</sup> 3<sup>. Whilst the</sup> 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.<sup>_v_</sup> 1 = 0.65 ,<sup>_v_</sup> 2 = 0.15 and<sup>_v_</sup> 3 = 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. _v_ 2 = _v_ 3 = 0 (and<sup>_v_</sup> 1 = 1 ). The fact that is, however, more interesting is that the ratio is approximately stable through most of the range of<sup>_v_</sup> 2<sup>and</sup><sup>_v_</sup> 3<sup>.</sup>

> 31 See appendix A.4 for the complete list of countries.

> 32 See appendix A.3 for details.

> 33 Note that described the numerical values for ρ , δ _k_ , δ _h_ , δ _g_ , α , β , γ , _u_ 1, ε 1, ε 2, ε 3, α 1 , α 2 , α 3 and η remain

> the same for the remainder of this section. 34 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 _v_ 1 + _v_ 2 + _v_ 3 = 1 always has to hold which restricts the plane to a triangular space. By fixing<sup>_v_</sup> 2<sup>or</sup><sup>_v_</sup> 3<sup>the</sup>

> effects of changes in<sup>_v_</sup> 1<sup>are also always observable.</sup>

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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.<sup>37</sup> .

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 _p_ with _r_ the constant interest rate, _B_ (0) public debt at time zero and _S_ the primary surplus.<sup>38</sup> Equivalent to equation (19) is the following equation

> 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.<sup>39</sup> 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 − λ _L_ )<sup>_S_</sup> _tp_ is stationary, with 0 ≤ λ < 1 +<sup>_r_</sup> _t_ . 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.<sup>40</sup> 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.<sup>41</sup> 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_ = _c_ 1 be the constant debt ratio, with _Y_ denoting GDP and<sup>_c_</sup> 1<sup>a positive constant.</sup> Inserting _B_ / _Y_ = _c_ 1 in ((20)) yields 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).

> 38 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).

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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.<sup>42</sup> 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.<sup>43</sup> 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 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 & _B_ ( _t_ ) = _r B_ ( _t_ ) + _G_ ( _t_ ) − _T_ ( _t_ ) = ( _r_ − β ) _B_ ( _t_ ) −α _Y_ ( _t_ ). (23) Solving this equation we get with _B_ (0) > 0 debt at time _t_ = 0 which is assumed to be strictly positive and with _C_ 1 a constant given by _C_ 1 = _B_ (0) − _Y_ (0) α /( _r_ −γ − β ) . Multiplying both sides of (24) by _e_<sup>−</sup> _rt_ leads to _e_ − _rt B_ ( _t_ ) = ⎛⎜<sup>⎜</sup> ⎝ _r_ −γα− β⎞⎟<sup>⎟</sup> ⎠ _Y_ (0) _e_ ( γ− _r_ ) _t_ + _e_ −β _t C_ 1. (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).

> 43 In dynamically inefficient economies the government budget constraint is irrelevant because in that case the government can play a Ponzi game.

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Solving this differential equation, we obtain the debt-to-GDP ratio _b_ as 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<sup>_t_</sup> 1<sup>, onwards,βis zero or even</sup> 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 _t_ 1 . 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.<sup>44</sup> 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: _sty_ = β _tbty_ +αΤ _Zt_ + ε _t_ , (28) where<sup>_s_</sup> _ty_<sup>and</sup><sup>_b_</sup> _ty_<sup>are the primary surplus to GDP and the debt-to-GDP ratio, respectively.</sup><sup>_Z_</sup> _t_ is a vector which consists of the number 1 and of other factors related to the primary surplus and<sup>ε</sup> _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<sup>_Z_</sup> _t_<sup>may differ depending on which</sup> 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.

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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.<sup>45</sup> 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.

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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.

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