On National Fiscal Policy and Growth: Searching for Optimality under Externality

ABSTRACT

In this paper, we examine the view of capital fundamentalism claiming that national fiscal policies, with public investment being subject to adjustment costs, can be considered as the primary determinant of economic growth. According to our analysis, a country that experiences a low rate of growth with a relatively low public to private capital ratio can generate and attain a higher long-run rate of economic growth, equivalent to the growth rate of public capital. It is revealed that the after-tax marginal product of capital, hence the rate of return, depends positively on the ratio of private to public capital, something that sharply contradicts the results obtained in the rather traditional strand of research where the rate of return was invariant with that particular ratio. We also reconsider some properties of optimal fiscal policy and conclude that, in accordance to conventional priors, maximisation of the private-sector utility function corresponds to maximisation of the growth rate of the economy.

1. Introduction

It is already well known from the relevant literature that models of economic growth can generate long-run growth without relying on theories of population change, as in Becker and Barro (1988), or exogenous changes in technological progress, due to Romer (1986). A general feature of these models is the presence of constant or increasing returns in the process of accumulating the factors of production; Lucas (1988), and Romer (1989). While exogenous technological change can be ruled out, such models can be viewed as equilibrium models of endogenous technological change in which long-run growth is primarily motivated by the accumulation of knowledge by forward-looking and profit-maximising agents. In contrast to models in which capital exhibits diminishing marginal productivity, the stock of knowledge can endlessly grow. Even in a situation where all inputs of production are held constant, there is no reason why knowledge must also be constant at some steady state and, accordingly, no further research should be undertaken; Barro (1990), and Angelopoulos et al. (2007). Apparently, it is the co-existence of three elements, namely, increasing returns in the production of output, externalities, and decreasing returns in the production of new knowledge that can produce a well-specified competitive and/or equilibrium model of growth; Rodrik (2005).

One strand of the literature on endogenous economic growth is concerned with models in which private and social returns to investment diverge, so that decentralised choices can lead to suboptimal rates of saving and economic growth; Arrow (1962), and Acemoglou et al. (2003). In particular, private returns to scale may be diminishing but social returns reflecting various externalities, such as spillovers of knowledge, can be either constant or increasing. Another strand of the literature is concerned with models without externalities, in which the privately determined choices of saving and growth can be Pareto optimal; Rebelo (1991), and Gale and Orszag (2003). These models rely on constant returns to private capital that is broadly defined to encompass human and physical capital. Still, apart from displaying constant returns to scale technology, these models generate steady-state growth paths, thus being compatible with the stylised facts of economic growth, as described in Kaldor (1961), and enhanced by Arestis (2007).

Unambiguously, one of the most interesting aspects of the recent revival of growth theory is the focus on the long-run effects of economic policy as such are reflected in the wide cross-country dispersion in average rates of growth. Therefore, the role of public policy is central in generating long-run growth; Easterly (2005). King and Rebelo (1993), among others, examine whether national fiscal policies could explain the observed disparity in growth rates across countries by isolating the effects of taxation on long-run growth and, yet, by assuming that government expenditures do not affect private-sector preferences or production technologies. Furthermore, public policy has the feature that either government spending or tax rates are exogenous. There is also a large literature on tax-policy issues in the neoclassical growth model concluding that high income-tax rates end up to lower growth rates; Sato (1967), Feldstein (1974), Stiglitz (1978), Becker (1985), and Easterly et al. (2004). However, in the neoclassical model such an effect can explain the observed cross-country differences in growth rates only during the transition path towards the steady state since it is established that the steady-state rate is given by the rate of exogenous technical progress. According to the traditional theory of “capital fundamentalism”, as surveyed by King and Levine (1994), national fiscal policies can be considered as the main determinant of growth. In essence, it is argued that investment rates are crucially important to economic growth when cross-section estimates are under consideration and, further, that differences in growth rates across countries can be explained by differences in the process of capital accumulation; Levine and Renelt (1992), Mankiw et al (1992), and Rodrik (2005).

Barro and Sala-i-Martin (1992, 1995) have developed a series of models, in which investment in infrastructure affects output through the production function, as a factor along with capital and labour, in order to study the influence of the supply of public goods on growth rates. Clearly, the rate of output growth can be positively related to the share of government purchases, in the form of public services, while examining various policy implications under alternative schemes of the production function. In a similar reasoning, Glomm and Ravikumar (1994) explore the implications for capital accumulation when investment in infrastructure enters into the private-production function as an external input, but with the contribution of infrastructure to private-factor productivity being subject to congestion. Consequently, not only does government expenditure in the form of public investment play a decisive role for the performance of the economy, while strengthening the dynamic character of policy analysis, but also it provides a rationale for empirical studies that establish a strong positive link between investment and output growth rates; Aschauer (1989), Baxter and King (1993), Easterly and Rebelo (1993), Dollar and Svensson (2000), and Bekaert et al. (2005).

In the present context, we introduce a simple open-economy model of endogenous growth in which the production function, apart from labour, consolidates physical and human capital. Following Barro and Sala-i-Martin (1995), and Alogoskoufis and Kalyvitis (1996), the formation of private capital is subject to costs of adjustment so that, the economy’s total (private and public) capital ratio adjusts gradually towards the steady state. Therefore, it remains to see whether, despite any externalities dovetailed with the formation of private capital, an efficient use of government spending in public infrastructure can solely determine the steady-state growth of the economy. Only in this way can the production-enhancing role of government expenditures be underscored, thereby suggesting that policy makers should use public capital in a prudent and effective manner, pointing towards the adoption of “functional finance”, suggested recently by Arestis and Sawyer (2010); for a rather post-Keynesian variant, see Casares and McCallum (2000). Then, in a rather closed-economy version, we extend the analysis by focusing on the issue of financing such expenditures, especially, when the government pursues a balanced budget. Contrary to conventional priors, the after-tax marginal product of capital, therefore the rate of return, depends positively on the ratio of private to public capital. Finally, following Barro (1990), and motivated by Economides et al. (2007), but also Arestis and Sawyer (2010), we examine whether such policies can be optimal regarding both governmental and decentralised choices, in a framework characterised by the familiar externalities implied by public expenditures and taxation. It is shown that private-sector utility maximisation corresponds to maximisation of the economy’s growth rate.

The organisational structure of the paper is the following. Section 2 introduces the basic model, for a small country like Greece, in the presence of adjustment costs on private capital. Section 3 discusses the implications of public investment in infrastructure for the steady-state economic growth. Section 4 examines the issue of financing government expenditure and its impact on both the decentralised economy and the social planner, while exploring the optimality dimension of such policies. Some concluding remarks are offered in the last section, with the stability analysis of the system being displayed in the Appendix.

2. The Model

Assume a small open economy that embraces a large number of competitive firms. Without loss of generality and aggregating across firms, the production function may be given the following expression;

(1)

where: Y denotes output, K is the private-sector capital, and L stands for labour, with α and 1-α being the shares of private capital and labour, respectively. Parameter A reflects the constant technology level, with A>0.

The assumption of constant returns becomes more plausible whenever, as in our case, capital is broadly viewed to encompass both human and physical capital. Indeed, parameter h represents human capital and we consider it to be a function of the existing total (private and public) capital of the economy, denoted by K and G respectively, so that;

(2)

where: ψ>0 stands for an efficiency parameter that captures the degree of the economy’s efficiently used total capital. It becomes evident that, the representative firm’s output is a function of its private capital and of the economy’s total capital. However, human and physical capital need not be perfect substitutes in production.

Therefore, production may exhibit roughly constant returns to scale in the two types of capital taken together, but diminishing returns in either input separately. In other words, even with a broad concept of private capital, production involves decreasing returns to private inputs if the government inputs, acting as a complement, expand in a different fashion. According to the conventional strands of the literature, and assuming full depreciation of public capital, we can refer to government inputs interchangeably as the flow of government purchases or the stock of accumulated public capital. Alternatively, we could think of government spending as the quantity of public services provided to all firms, as a non-rival and non-excludable good. Obviously, the model abstracts from externalities associated with the use of public services such as, various congestion effects which might arise for highways or some other publicly provided services. Furthermore, in our setting, government expenditure in the form of investment in infrastructure leaves the household utility unaltered.

The change in the capital stock of the representative firm is given by;

(3)

where: I clearly shows gross investment, and the dot expresses a derivative with respect to time.

In the presence of adjustment costs during the formation of private capital, the cost in units of output for each unit of investment is an increasing function of I in relation to K, so that;

Cost of investment = (4)

with φ > 0 standing for the sensitivity of the adjustment costs to the total amount invested. It becomes evident that, the costs of adjustment depend on gross rather than net investment.

Therefore, the infinite horizon problem of the representative firm is to maximise the present discounted value of its net cash flow, that is output minus the labour expenses and the cost of investment, taking h as given in order to have;

(5)

subject to (1) and (3), with r being the world real interest rate assuming uncovered parity, w is the real wage rate, and δ shows the rate of depreciation. Now, we can analyse the optimisation problem by setting up the current value Hamiltonian as follows;

(6)

The maximisation entails the standard first-order conditions so that, and , along with the usual transversality condition of

(7)

Hence, the first-order conditions can be expressed as;

(8)

(9)

(10)

If we now substitute (2) into (1), the modified aggregate production function can be presented as;

(11)

Substituting (9) into (10) while rearranging terms, we can get an expression for the modified first-order conditions, so that;

(12)

(13)

(14)

Equation (12) is the usual equation of the marginal product of labour to the wage rate, something that holds because there are no adjustment costs attached to changes in labour input. Equation (13) indicates that the relation between the shadow value of private capital and private investment is monotonically increasing, in terms of contemporaneous output, while the relation between the adjustment-cost parameter and private investment is clearly negative. In addition, equation (13) states that the shadow value of installed capital exceeds unity due to the presence of adjustments costs. Equation (14) offers the change in the shadow value of capital as a positive function of the market rate of return and the rate of depreciation of private capital, minus the return on private capital along with the marginal reduction of the costs of adjustment as private capital increases. Of course, if the costs of adjustment were absent so that the shadow value of capital would equal one, the market rate of return would be given by the difference between the rate of return on private capital and the rate of depreciation.

3. Public Investment in Infrastructure

Let us consider now a situation where the government chooses a growth rate of investment in infrastructure equal to π. It becomes obvious that the change in the capital stock is now turned into;