Such large estimates have often been considered as unrealistic and have triggered a large amount of subsequent research, looking at different samples or refining the techniques used.

As discussed in the theoretical section above, the fact that infrastructure-related capital can be both a public good, an input in the production of other intermediate inputs, and a productivity-shifting force raises a number of additional empirical questions. These include first the disentangling of direct (the first two channels above) versus indirect effects (the third channel), and within these indirect effects the characterization of the part responding strictly to infrastructure. As is apparent from table 3, a very limited amount of research has been devoted to these questions, mostly in the context of growth accounting studies. Notwithstanding the difficulties, already mentioned, involved in attributing a price to infrastructure capital to determine its share of output, Hulten and Schwab (2000) and Hulten et al. (2005) have developed a methodology to overcome that issue and find transport and energy infrastructure to account for an important part of TFP growth in India, while no such effect is found in the US case. Duggall et al. (1999, 2007) develop an alternative methodology based on 29 and 26 years of US data respectively. They find a large infrastructure elasticity, similar to that of Aschauer (1989), and conclude that the effect of infrastructure is partly dependent on the presence of other technologies. Replicating their methodology in the context of developing countries, however, would require data much beyond what is currently available.

An important conclusion of Duggall et al. (2007) is that public capital, through a combination of its direct and indirect effects, has the potential to generate increasing returns to scale at the aggregate level, thereby implying a permanent increase in the growth rate. Setting aside simple cross-country regressions that by nature imply the estimation of the long run growth rate, this issue, of particular policy relevance, has been little addressed in the literature. Canning (1999) and Canning and Pedroni (2004) use unit root and cointegration tests in the context of country level panel data as a way to assess long run effects. Additionally, these contributions highlight the fact that the issue of transitory versus permanent effects is closely linked to the question of identifying optimal infrastructure stocks. Indeed, Canning and Pedroni (2004) conclude that positive (resp. negative) long run effects are characteristic of an aboveoptimal (resp. below-optimal) infrastructure stock. Alternatively, Aschauer (2000) assess the optimality of US states infrastructure stocks by assuming a reference steady-state optimal output elasticity of 0.30. His conclusions, however, are subject to doubt both because this elasticity, in line with his previous results, appears very large and because he fails to account for the potential reverse causation between output and infrastructure.

More fundamentally, it appears that macro-level data on aggregate stocks of infrastructure, be it public capital figures or physical indicators, are by nature not adequate to capture the notion of optimality of infrastructure stocks. Indeed, the spatial nature of infrastructure implies that a given aggregate stock, for example a number of telephone connections or of kilometers of road, can be either optimal or grossly inadequate depending on the way it is distributed across geographical and individual units. We discuss this point further in the next section on the geographical empirical evidence, but an illustration of this is found in Cadot et al. (2005), who 23