route start/end points using population weights.<sup>8</sup> To approximate this, I compute a global weighted average across routes with weights equal to the product of start/end cell populations divided by their spherical distance.<sup>9</sup> This yields NS of 64.2, RE of 0.68, and TE of 43.9, reflecting greater efficiency on longer routes (Wolfram, 2021). But even the most favorable RE estimate of 0.68 is far below Wolfram (2021)’s estimates of 0.843/0.767 for US/European road networks.

## **2.3 Market Access**

Whereas route and time efficiency are important from a transportation standpoint, the spatial economics literature such as Donaldson & Hornbeck (2016), Jedwab & Storeygard (2022) or Peng & Chen (2021) has used market access (MA), typically defined as an inverse-distance weighted sum of population, or a proxy therefore such as built-up in the case of Peng & Chen (2021), to evaluate economic gains from transport investments. The MA measure for cell _i_ is where _Lj_ is a measure of population and _τ_ a measure of distance, travel time, or transport cost, weighted by an elasticity _θ_ measuring how trade volumes fall as distance/time/costs increase. The value of _θ_ is contentious, for example Jedwab & Storeygard (2022) use _θ_ = 3 _._ 8 whereas Peng & Chen (2021) use _θ_ = 1. In both cases, _τij_ measures travel time.

To appropriately measure continental MA implied by the road network, I incorporate spatial differences in purchasing power into _Lj_ . Kummu et al. (2018) provide a spatial estimate of GDP in 2015 USD PPP terms by distributing national GDP estimates from the World Development Indicators at 5 arc-min (0.0833 degrees or 9.3km at the equator) resolution using subnational value-added estimates from Gennaioli et al. (2013) and population from the HYDE 3.2 database.

Using Eq. 4, I compute MA maps using both measures of economic mass ( _Lj_ ), and trade elasticities of _θ_ = 1 (Peng & Chen, 2021) or _θ_ = 3 _._ 8 (Jedwab & Storeygard, 2022). As Eq. 4 excludes cell _i_ itself, the centers of several large cities have a lower MA measure than adjacent cells. To remedy this, I add _i_ ’s GDP/wealth to the MA measure using a distance _δij_ = 25km/ _κi_ , where _κi_ is cell _i_ ’s RE/TE measure from Figure 4. Figure 5 shows the resulting maps with _σ_ = 1 and Appendix Figure A4 with _σ_ = 3 _._ 8.

Evidently, _θ_ = 3 _._ 8 yields a much stronger concentration of MA around major cities and a high correlation of the MA measure with cell GDP. Both _θ_ values elicit northern Egypt, Nigeria, and, to a lesser extent, greater Johannesburg as high MA areas. Cairo has the greatest MA.

# **3 Barriers to Cross-Border Trade**

Africa has ’thick borders,’ and any evaluation of continental roads should at least be mindful of them. Trade barriers can broadly be distinguished into traditional trade tariffs and regulatory obstacles and frictions at the border. This paper will concentrate on the latter as tariffs and other non-tariff barriers tend to be product- and quantity-specific. But, for the sake of completeness, I begin with a brief overview of tariffs applied by African countries in international comparison.

## **3.1 Trade Tariffs**

The World Development Indicators provide aggregate estimates of the extensive and intensive margins of trade tariffs applied by each country. Table 2 summarizes these indicators for different country groups. While SSA countries only apply specific (non-ad-valorem) rates on 0.1% of tariff lines, 33.9% of African tariffs exceed 15%. When weighted by the product import shares

> 8Concretely, Wolfram (2021) computes the route efficiency of the US road network using OSRM-generated routes between 2000 population-weighted random points in the US and finds a median route efficiency of 0.843 with a standard deviation of 0.045 across 4 million routes.

> 9Following Newton’s Law of Gravity as as operationalized in the empirical trade literature (Head & Mayer, 2014), which finds a distance elasticity around _θ_ = _−_ 1. Inter-city migration gravity models such as Zipf (1946) or Poot et al. (2016) also suggest that migration varies according to the distance rather than the squared distance.

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