We believe that a mildly increasing-returns function (α1 = 0.8; α2 = 0.2; α3 = 0.2) provides a reasonable approximation to road transport quality differentials in SubSaharan Africa.<sup>12,13</sup> Table 2 presents index values by country, normalized to 100 for the highest-quality road transport (in South Africa). Estimated road quality for Botswana (87.5) is over 20 times the quality for the Democratic Republic of the Congo (3.8). We believe that this does not overstate the existing differential in average road speed, vehicle depreciation on bad roads, harassment of truckers, payments at road blocks, and frontier difficulties.<sup>14</sup>

# **4.  Simulating Trade Flows in the Network**

Our objective is to develop a gravity model for inter-city trade that can be used for analysis of road improvement impacts at the country, regional and continental levels. We begin by estimating a gravity model for Sub-Saharan Africa, using recent inter-country 12 The authors’ extensive experience with African roads suggests that “percent paved” alone is an inadequate proxy for road quality. Many stretches of “paved” road in Sub-Saharan Africa are in extremely poor condition, either because government revenues are insufficient to support proper maintenance, or corrupt officials have diverted the maintenance funds. We use per capita income and the CPIA corruption index to incorporate these factors, although we stay relatively close to the Coulibaly-Fontagné index by giving percent paved twice the combined weight of the other two factors in our road quality measure. We have made one adjustment to the published paved-road data, which assign South Africa a paved road percentage of 19.7 (in contrast to Botswana, with 54% and Zimbabwe, with 47.4%). We believe that this grossly misrepresents the relevant road conditions in South Africa, since its components of our primary network are all paved, first-class roads. To ensure a measure that is higher than those for Botswana and Zimbabwe, we have arbitrarily assigned South Africa a paved road percent of 60 for our index. This probably underestimates relative South African road quality. However, it has no effect on our results because we assume that South Africa’s roads (with a continental-maximum index score of 100) do not need improvement in the upgraded network.

13 We have tested our road quality index against current road quality data gathered by the ADB in its assessment of seven potential road corridors in 31 Sub-Saharan African countries. This is a partial view, because the ADB assessment focuses on physical road quality while our index also attempts to incorporate costs and delays at frontiers and internal road barricades. Nevertheless, we find a robust statistical relationship (ρ = -0.57, 99% significance) between our road quality index and the percent of the road network rated poor by the ADB.

14 Arbitrary rescaling of the road quality index in the log-log regression equation (2) does not affect the underlying marginal relationship between log (trade) and log (original road quality index). For example, substituting the square of the original road quality index (which doubles the original log value) will simply halve the regression coefficient. Using the square root of the index (which halves the original log value) will double the regression coefficient.

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