Early overviews of the empirical literature can be found in Gramlich (1994) and Hakfoort (1996), while Makin and Paul (2003) provide an update.

At least five potential reasons for the contradictory empirical findings on the growth impacts of infrastructure have been advanced in the literature.<sup>8</sup> The first proposes that the relationship between public capital and output may be non-linear, with the corollary that both under- and overinvestment in infrastructure are feasible. Which applies in any given context, then becomes a matter for empirical determination. Thus non-linearity is implicit in the model proposed by Barro (1990). Canning and Pedroni (2004) provide an explicit treatment of this possibility, and find that both under- and over-provision of infrastructure applies across countries. See also Seung and Kraybill (2001) and Nourzad (2001).

A second possible reason for any finding of negative impacts of public capital on output and/or growth, may be the presence of crowd-out effects from public investment. The possibility was identified from the outset in this strand of literature - see Aschauer (1989c). Yakita (2004) theoretically identifies such a possibility where the elasticity of substitution between public and private capital is sufficiently small. Desus and Herrera (1999) report empirical findings in support of a crowd-out effect for a panel of 28 developing countries over the 1981-91 period, while Lachler and Aschauer (1998) find a limited crowd-out present for Mexico.

The possibility of endogeneity of infrastructure measures has been advanced as a third possible reason for contradictory findings on public capital impacts on long run economic development indicators. Bias and inconsistency of standard estimators in the presence of simultaneity in the infrastructure measures would follow where infrastructure provision itself positively responds to productivity gains. Possible reasons for such a feedback would arise under increased reliance on the private sector for the provision of infrastructure services,<sup>9</sup> or under successful lobbying by industry interest groups that experience either positive productivity gains or constraints on performance due to infrastructure provision. Various panel data and country studies tried to address this issue. Thus Röller and Waverman (2001) explicitly model and estimate the impact of telecommunications under simultaneity. In a cross country panel estimation Calderón and Servén (2003, 2005) employ GMM panel estimation methods to control for the possibility of endogeneity, reporting significant improvements in results. And Dessus and Herrera (1999) allow for simultaneity in a panel data set for 28 countries. Country-specific time series studies also confirm the presence of simultaneity between output and infrastructure measures - see Frutos et al (1998) for Spain, and Fedderke, Perkins and Luiz (2005) for South Africa.

A fourth possible explanation of contradictory findings on productivity impacts is that public capital may not exercise its impact on output directly, but rather indirectly by raising the marginal product of private sector capital. Under these circumstances, it becomes critical whether the productivity impact is being investigated with respect to output per worker, or with respect to total factor productivity growth. For instance, Reinikka and Svensson (1999) on microeconomic evidence find that poor public capital in Uganda significantly reduces productive private investment - and see also Reinikka and Svensson (2002). Symmetrically, Delorme et al (1999) find no direct impact of infrastructure capital on labor productivity, but do find an impact on aggregate technical efficiency. By contrast, Fedderke Perkins and Luiz (205) find that infrastructure affects both aggregate labor productivity, as well as growth in total factor productivity - though different forms of infrastructure differ in their impacts.

A final possibility that might drive the ambiguous results obtained from empirical studies on public capital impacts on output might simply be that aggregate measures of infrastructure come to hide the productivity impact of infrastructure at a more disaggregated level. Thus for example Shioji (2001) finds that the positive impact of infrastructure emerges in panels of US and Japanese

> or extremely limited access to electricity, improved water and sanitation, or basic telephone services. See the more extensive discussion of these issues in Bogeti ́c and Fedderke (2006a) for the South African context specifically.

> 8 For the purposes of the present discussion we ignore issues related to data quality.

> 9 See the discussion in Estache, Foster and Wodon (2002) and Calderón and Chong (2004).

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