run growth in Africa. Other studies follow a production function approach. For instance, Ayogu (1999) estimates an infrastructure-augmented production function using regional panel data from Nigeria and finds a strong association between infrastructure and output. Kamara (2006) evaluates the dynamic effects of infrastructure in an aggregate production function for a panel of African countries. Analogously, Boopen (2006) estimates the output contribution of transport infrastructure using panel data.

Among country studies, South Africa and Nigeria have attracted special attention —this partly reflects the better quality of their data when compared to other countries in the region. Perkins and associates (2005) estimated the existence of a long-run relationship between infrastructure (investment and capital stocks) and real economic activity over a span of 100 years. They find two-way causality for most of their monetary measures of infrastructure. Kularatne (2005) examines the impact of infrastructure investment (and also spending on health and education) on output. He also finds bi-directional effects; however, the impact of infrastructure investment is indirect —specifically, it boosts growth by crowding-in private investment. Dykelman (2008) finds a significant impact of household electrification on employment in South Africa’s rural labor markets.

Few papers address the multi-dimensionality of infrastructure and its impact on long-term growth. Calderón and Servén (2010) find that both the quantity and the quality of infrastructure have a positive impact on growth and the distribution of income in Sub-Saharan Africa. Narrowing the infrastructure gap for SSA countries yields significant growth benefits but the costs of financing are also high. More recent evidence for the region shows that there are no short-term growth effects of improved quantity and quality of infrastructure (Kondongo and Ojah 2016).

# **Infrastructure’s effect on growth: A methodology**

Since Aschauer’s (1989) seminal work on infrastructure, more sophisticated techniques have been developed to compute the short- and long-run effects of infrastructure on growth. Researchers have either used monetary measures of public capital and/or investment (e.g. Devajaran et al, 1996) or physical stocks (Calderon & Serven, 2004, 2010). Estimating the impact of infrastructure should address the issues of: (a) multidimensionality at the sectorial level, (b) improving quantity and/or enhancing quality of infrastructure, and (c) ameliorating issues of likely endogeneity and reverse causality.

Computing the growth benefits of narrowing the infrastructure gap in Sub-Saharan Africa is not trivial. It will depend not only on: (a) the infrastructure sectors included in the analysis, (b) the economic approach used to examine this impact, (c) econometric techniques utilized, and (d) the sample of countries. In this context, this section uses the empirical estimation undertaken by Calderón and Servén (2010); that is, a crosscountry panel data regression model that includes synthetic indicators of quantity and quality of infrastructure —and other standard growth determinants as identified by Loayza, Fajnzylber and Calderón (2005); namely, education, financial development, trade openness, lack of price stability, government burden, institutional quality, and terms of trade shocks.

The synthetic measure of infrastructure quantity, _IK1_ , as the first principal component of three variables: (fixed and mobile) phone lines per 1,000 people (Z1/L), electric power generating capacity expressed in MW per 1,000 people (Z2/L), and the length of the road network in km per sq. km of arable land (Z3/A). Each of these variables is expressed in logs and standardized by subtracting its mean and dividing by its standard deviation. All three infrastructure stocks enter the first principal component with roughly similar weights: On the other hand, we compute a synthetic index of infrastructure quality by computing the first principal component of the (arithmetic inverse) of electric power transmission and distribution losses as _Infrastructure in Sub-Saharan Africa - 21_