_6_ technology, that appeared in different countries in different years, starting in the eighties. Thus for mobile, we use an annual data base, of different "length" depending on the country (from a minimum of 1 in Sierra Leone to a maximum of 21 in Finland) For these regressions we added a variable called market maturity equal to the number of years the market has existed in a given country.

# _Results_

Using OLS with fixed effects, we ran both the basic model described by equation 5 and an extended model that included density and urbanization on all 5 infrastructure variables. In all cases, we ran regressions both on a full sample of up to 113 countries and then separately for low and middle income as one group and high income countries as another.<sup>4</sup>

> As mentioned, country fixed effects proxy for differences in technology and price across nations. Their use also allow us to obtain consistent parameter estimates. Canning (1998), shows that per capita infrastructure levels are nonstationary, which implies that running the regressions in levels may produce misleading results unless the variable

> variables used in the regressions are cointegrated. Unfortunately, cointegration would not yield an easy system with which to make predictions, leaving us with two possible solutions. One is to run the regressions on first differences, which Canning shows to be stationary. This would reduce our sample size considerably since we only have up to eight time series observations, and the series are often incomplete. The second possibility - which we use- is to include fixed effects. Kao (1997) shows that in this case parameters estimates are consistent even if the estimated relationship is not a cointegrating one.

A Chow test of structural change allows us to determine whether the estimated relationship is the same for developing countries and the high income sample.<sup>5</sup> With the exception of water, sanitation, and mobile we reject the hypothesis that coefficients are equal across samples and therefore present the results separately for developing and high income countries. For water, sanitation and mobile phones however, we cannot reject the hypothesis that they are equal, and therefore run the regression on the world sample.

For mobile phones and rail, we modified the basic regression structure since including a lagged variable or a time dummy resulted in projections that either went to zero (rail) or exploded into infinity (mobile phones.) In the case of mobile, we also found that the sectoral share of GDP did not add any explanatory power so we dropped it.

Table 4 presents the regressions that were subsequently used for the projections. Country fixed effects are not reported. For all but water, we obtain very high R2 (0.95 and above) which is our goal given that we want to predict infrastructure values as best as possible.

> 4When explanatory variables, the variable is set to zero and a dummy variable equal to 1 is included in that regression.

> _5_ Note that the presence of fixed effects somewhat complicated the estimation of Chow test. The hypothesis tested (Ho) was not in fact whether all coefficients were the same across samples, but only whether the coefficients on the explanatory variables other than the country fixed effects and the time dummies.