INFRASTRUCTURE AND GROWTH IN AFRICA that all our indicators of infrastructure quality are rescaled to 0–1 in such a way that higher values indicate better quality of infrastructure services.<sup>8</sup> Our aggregate index of infrastructure service quality, **IQ** , is the first principal component of these indicators of infrastructure quality. It captures approximately 60 percent of their total variation and it shows a high correlation with each of the three individual quality indicators: 0.81 for quality in telecommunications, 0.75 for electricity service quality, and 0.75 for road quality. Using the weights obtained with principal components, the synthetic index of infrastructure quality can be expressed as: where **IQ** represents the first principal component of our measures of infrastructure quality, _Q1_ represents the measure of waiting time for installation of main lines, _Q2_ the share of power output net of transmission and distribution losses in total output, and _Q3_ the share of paved roads in total roads. Again, note that all the variables are rescaled to 0–1 and transformed in such a way that higher values indicate better infrastructure quality. Finally, the indicators of infrastructure quantity and quality share a good deal of common information—that is, the correlation between **IK** 1 and **IQ** is 0.76. Across infrastructure sectors, the respective stocks and their quality measures are also positively correlated: 0.58 for telecommunications, 0.46 for electricity, and 0.59 for roads.

# Econometric methodology<sup>9</sup>

We collect a pooled data set of cross-country and time-series observations for 136 countries (data details are given below), and use an estimation method that is suited to dynamic panel data. This methodology not only controls for unobserved time- and country-specific effects but also accounts for some endogeneity in the explanatory variables. This is the generalized method of moments (GMM) for dynamic models of panel data developed by Arellano and Bond (1991), and Arellano and Bover (1995). For more details on the econometric methodology, see appendix 1.

We run a regression on growth in real output per worker on a standard set of growth determinants, and on aggregate indices of infrastructure stock and infrastructure quality.

Our set of control variables comprises information on the level of human capital, financial depth, trade openness, institutional quality, lack of price stability, government burden, and terms-of-trade shocks.

Estimating our productivity growth-regression equation presents two potential problems: (a) the presence of unobserved effects, and (b) the presence of endogenous regressors. Unobserved time effects are dealt with by the inclusion of period-specific dummies, whereas unobserved country effects are

> 8 The first of these three variables is admittedly not a direct indicator of the quality of telecommunications networks, but is significantly and positively correlated with the conceptually preferable measure (the number of telephone faults per 100 main lines), whose availability is severely limited in our sample. Over the available sample, the correlation coefficient is 0.3. Unfortunately, the coverage of unsuccessful local calls is extremely limited, with information available for only two to three selected years in the 1990s and a maximum cross-section coverage of 68 countries.

> 9 This section draws from appendix II of Calderón and Servén (2004b).

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