Since the balanced budget constraint imposes a tax rate of g/y, the steady state growth rate, denoted γ, can be shown to be: It follows that: consider a policy intervention under which d(g/y) > 0 (given any level of k). From equation (3) it follows that γ decreases due to the tax effect in g/y, and increases due to the increase in g/k that is the consequence of the positive effect on the marginal product of k. The net effect depends on which of the two impacts is dominant. Since g/k = (A · g/y)<sup>1/(1−α)</sup> , and hence d(g/k)/d(g/y) > 0, it follows from equation (4) that the net effect of d(g/y) > 0 is conditional on the positive but decreasing ∂y/∂g, with dγ/d(g/y) > 0 for ∂y/∂g > 1, dγ/d(g/y) < 0 for ∂y/∂g < 1, and γmax at ∂y/∂g > 1. Thus the capital productivity effect dominates at low (g/y), and the tax effect at high (g/y).

A clear, theoretical link between output and government infrastructure investment follows. Infrastructure expenditure (g) can prevent diminishing returns to scale in private-sector capital (k), raise the marginal product of private-sector capital (∂y/∂k), and raise the rate of growth of output (γ). An equally important message is that government intervention of this nature can raise economic growth only within limits, and can have both postive and negative impacts on growth. Once the marginal product of government productive expenditure falls below unity, further increases in (g/y) are harmful to economic growth, since the tax effect comes to dominate the capital productivity The following subsections outline the relevant methodologies.

# 3.1 Infrastructure and Productivity

We employ two approaches in establishing the existence of an impact of infrastructure on productivity.

The first examines whether infrastructure has an impact on labor productivity. The specification for this exploration is derived from Bogeti ́c and Sanogo (2005). Though the objective of Bogeti ́c and Sanogo (2005) is to isolate factors influencing regional location decisions by industries intranationally in Côte d’Ivoire, implicit within the model is that infrastructure has an impact on labor productivity, and hence will influence decisions on the regional location of industries. The corollary to this link, which finds confirmation for Côte d’Ivoire, is that infrastructure at the national level should certainly impact output per worker. The general specification estimated in Bogeti ́c and Sanogo (2005) is: where Y denotes real value added of industry i in period t, L the size of the labor force, K the size of the physical capital stock, S a vector of variables measuring scale economies, U urbanization, and I denotes a vector of variables measuring infrastructural capital stock.

The specification provided by equation (5) is explicit in considering public capital stock to be a factor of production that enters directly into the aggregate production function. Not all models of the impact of infrastructural investment on output follow this route. In Barro (1990), for instance, the impact of public capital on output may indeed be direct, or may exercise its influence by raising the marginal product of the private sector capital stock. Under this specification, infrastructure would impact not on output per worker, but on total factor productivity.

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