can indirectly crowd in other inputs owing to the accompanying rise in their marginal productivity, and this indirect effect may take place instantaneously (for variable inputs in elastic supply) or over time (for fixed inputs such as human and non‐infrastructure physical capital). Infrastructure, being a key element of the business environment, conditions individual firms’ transaction and marginal return on investment.<sup>3</sup> Wheeler and Mody (1992) and Richaud et al. (1999) provided evidence that infrastructure can crowd in foreign direct investment, an important element for growth in less developed countries. Eden and Kraay (2014) found that an extra dollar of public investment can raise private investment by roughly two dollars, and output by 1.5 dollars, based on data from 39 low‐income countries.

The magnitude of contribution of infrastructure to productivity and output varies. Various factors are at play. Calderón et al. (2015) found that the long‐run output elasticity of infrastructure ranges from 0.07 to 0.1, using a synthetic index combining power, transport and telecommunications infrastructure as one of the inputs in a production function, based on a large data set covering 88 countries spanning the years 1960–2000. Their results suggest that the marginal productivity of infrastructure is associated with the ratio of aggregate infrastructure to output. Calderón and Servén (2008), drawing from data of 100 countries over 1960‐2005, found that infrastructure development makes, on average, a smaller contribution to growth in Sub‐Saharan Africa than in other regions – just 0.7 percent per annum. This is related to the severe deterioration of the quality of infrastructure services in the region ‐ while the expansion in infrastructure stocks raises the growth rate by 1.2 percent per annum, the deterioration of the quality of infrastructure services reduces the growth rate by 0.5 percent per annum. Bottini et al. (2012) suggested that enhancing service efficiency and supporting innovative technologies adoption can improve the contribution of infrastructure to total factor productivity through better interconnection and stronger complementarities.

The relationship between infrastructure and economic growth is not linear. Hurlin (2006) found that returns to infrastructure exhibit threshold effects and that the highest marginal productivity of investment is found when a network is sufficiently developed but not completely saturated. For example, road construction may have limited effects until it links several locations. After the establishment of a minimum road network, the marginal productivity is high for the new road construction extending the network before congestions kick in (Fernald, 1999). Henckel and McKibbin (2017) pointed out that the economic benefit from transport infrastructure is nonlinear because of network externalities, reflecting the decreasing benefits from additional highway construction to an existing efficient transport network. Telecommunications investment has strong externality. A subscriber’s welfare increases with the increase of the number of people who have access to the network, until reaching the saturation point. Röller and Waverman (2001) found that the impact of telecommunications infrastructure on output is substantially higher in countries where penetration approaches universal coverage.

# **Infrastructure and global value chains**

> 3 See Lin, J. Y. (2011).

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