The medium-term economic returns to increased MA are very difficult to estimate, especially on such a large scale. The only large-scale analysis I am aware of is Donaldson & Hornbeck (2016). The authors regress changes on the log of land values across 2,327 US counties between 1870 and 1890 on changes in the log of MA, and find an elasticity of 0.5, which is quite robust to different choices of _θ_ . This suggests that in the medium run MA translates into economic activity at a ratio of 2:1. However, present-day Africa may be very different from the historical US.

I thus also run some regression similar to Donaldson & Hornbeck (2016), examining the effect of log(MA) on GDP per capita (Kummu et al., 2018) and the International Wealth Index (Lee & Braithwaite, 2022) using the dataset of 1379 nodes/cities. I control for country fixed effects and also for the log of port outflows in 2020Q1, adding one so that the log is zero in non-port cities. Since MA is endogenous to GDP, I apply the network finding algorithm from Section 4.2 (with EU parameters but not checking against OSM) to generate a hypothetical network with 2869 edges, shown in Appendix Figure A14, and use the MA measure based on this network as an instrument for MA. Table 7 reports the results for MA denominated in both road distance and travel time.

Table 7: Returns to Market Access in Africa ( _N_ = 1379 Nodes)

|Dependent Variable:|log(GDP|/Capita)|I|WI|log(|IWI)|
|---|---|---|---|---|---|---|
|Estimator:|OLS|IV|OLS|IV|OLS|IV|
|_Variables_|||||||
|log(MA): Distance|0.3221<sup>_∗∗_</sup>|0.3250<sup>_∗∗_</sup>|10.44<sup>_∗∗∗_</sup>|10.53<sup>_∗∗∗_</sup>|0.3450<sup>_∗∗∗_</sup>|0.3445<sup>_∗∗∗_</sup>|
||(0.1432)|(0.1451)|(2.258)|(2.425)|(0.0918)|(0.0934)|
|log(Outfows + 1)|0.0103<sup>_∗∗_</sup>|0.0103<sup>_∗∗_</sup>|1.390<sup>_∗∗∗_</sup>|1.390<sup>_∗∗∗_</sup>|0.0370<sup>_∗∗∗_</sup>|0.0370<sup>_∗∗∗_</sup>|
||(0.0042)|(0.0042)|(0.1451)|(0.1456)|(0.0048)|(0.0048)|
|_Fit statistics_|||||||
|R<sup>2</sup>|0.9709|0.9709|0.8079|0.8079|0.7602|0.7602|
|Within R<sup>2</sup>|0.1399|0.1399|0.2465|0.2465|0.1676|0.1676|
|Wu-Hausman, p-value||0.5409||0.6842||0.9508|
|Wald (1st stage), p-value, log(MA)||_<_0_._01||_<_0_._01||_<_0_._01|
|_Variables_|||||||
|log(MA): Travel Time|0.3216<sup>_∗∗_</sup>|0.3147<sup>_∗∗_</sup>|11.33<sup>_∗∗∗_</sup>|10.01<sup>_∗∗∗_</sup>|0.3891<sup>_∗∗∗_</sup>|0.3277<sup>_∗∗∗_</sup>|
||(0.1278)|(0.1379)|(2.044)|(2.177)|(0.0856)|(0.0835)|
|log(Outfows + 1)|0.0100<sup>_∗∗_</sup><br>|0.0100<sup>_∗∗_</sup><br>|1.383<sup>_∗∗∗_</sup><br>|1.378<sup>_∗∗∗_</sup><br>|0.0369<sup>_∗∗∗_</sup><br>|0.0366<sup>_∗∗∗_</sup><br>|
||(0.0041)|(0.0041)|(0.1427)|(0.1421)|(0.0047)|(0.0046)|
|_Fit statistics_|||||||
|R<sup>2</sup>|0.9714|0.9714|0.8140|0.8137|0.7684|0.7678|
|Within R<sup>2</sup>|0.1541|0.1540|0.2703|0.2691|0.1962|0.1940|
|Wu-Hausman, p-value||0.3023||_<_0_._01||_<_0_._01|
|Wald (1st stage), p-value, log(MA)||_<_0_._01||_<_0_._01||_<_0_._01|
|_Fixed-efects_|||||||
|iso3c (49)|Yes|Yes|Yes|Yes|Yes|Yes|

_Clustered (iso3c) standard-errors in parentheses Signif. Codes: ***: 0.01, **: 0.05, *: 0.1_ The coefficients in both MA denominations suggest that in Africa MA translates to GDP/Capita or household wealth with an elasticity of _∼_ 0.33, which is slightly lower than in the US. Using the IWI in level suggests that a doubling of MA raises the IWI [0, 100] by 10 points—a sizeable return.

The failure of the Wu-Hausman test of endogeneity in most cases indicates that the instrument is too strong and possibly itself endogenous. Since the network was constructed by intersecting routes between 453 (port-)cities, 1379 _−_ 453 = 926 nodes/cities were found by intersecting the optimal routes between these cities, and thus already reflect the existing road network.

However, repeating the exercise using just the original 453 (port-)cities and a hypothetical network between them gives the same gdp elasticity (around 0.3), with Wu-Hausman p-values all greater than 0.1, and partly insignificant IWI elasticities around 0.15-0.3. Thus, the cross-sectional IV approach using a hypothetical network in any case does not add much to the exercise.

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