_5_ each country to have a different intercept, which combined with the time<sup>dummyallows</sup> us to capture (albeit roughly) the price variable.

Note that our interest is not to establish a causal relationship between infrastructure<sup>stocks</sup> and various economic variables. Instead, since we want to use this regression for projection, our interest is to obtain the best fit possible and the highest explanatory<sup>power.</sup> Thus, since infrastructure stocks tend to change reasonably slowly over<sup>time and havea</sup> long life span, we include lagged value of the dependant variable in the<sup>regressionin</sup> order to increase explanatory power.

We therefore estimate equation 4 as follows: _5._ it, _=a_ + 1 _I aAi,t i,t 4 a5Di 5+ + a 6 Dt + 6i,t_ where all variables are in natural logs to linearize the model, Ii.t<sup>is</sup> demand for infrastructure stock of type j in country i at time t; Pit-i is the lagged<sup>valueofthe</sup> infrastructure stock, y is income per capita; A is share of agriculture value<sup>added inGDP;</sup> M is the share of manufacturing value added in GDP, Di is a country fixed<sup>effect,Dt isa</sup> time dummy; and £ is the error term.<sup>3</sup> Given then that there is no modeling<sup>of the supply</sup> side, equation (5) can be interpreted as a law of motion for infrastructure<sup>stock.</sup> Most infrastructure goods are provided through networks so that the price<sup>of the serviceis</sup> often reduced with higher population density. Urbanization, in particular,<sup>allowseasier</sup> and cheaper access to electricity and telephone. Average costs of<sup>waterandsanitation</sup> tend to be actually higher in urban areas, but this is because the standard<sup>serviceoffered</sup> there is typically much higher. Access is however always much higher<sup>incities,partly</sup> because of the higher income of the population, and partly because<sup>ofpublic health</sup> consideration that make piped water and reasonably sophisticated<sup>sanitation services</sup> necessary. In the case of roads, roads per capita tend to decrease with higher<sup>population</sup> density. We therefore also estimated a version of equation (5) that included<sup>urbanization</sup> and population density to capture the density effect and its impact on<sup>demand(bothdirect</sup> and through price.)

# **_Data_**

The infrastructure variables we use are telephone mainlines<sup>(lines per1000person),</sup> mobile phones (subscribers per 1000 persons), KW of installed electricity<sup>generating</sup> capacity per capita, km of rail per 1000 person, km of paved<sup>road perkm2of landand</sup> percentage of households with access to water and sanitation. The only<sup>reasonforusing</sup> land rather than population as the deflator for roads is that it<sup>yieldedaslightly betterfit.</sup> Annex 1 discusses the variables and their source.

For all but the mobile phone data, our data base is organized as an unbalanced<sup>panelwith</sup> observations every 5 years from 1960 to 2000 and includes all<sup>independentlow,middle</sup> and high income countries with population of more than 500,000 in 2000<sup>for whichdata</sup> was available (113 countries). In the case of mobile phones, this is a more recent

> 3Manufacturing rather than industry was used here because industry includes<sup>mining,whichhasvery</sup> different implications on the demand for infrastructure.