In order to calculate the costs of traveling along the road network, the Highway Development Management Model (HDM-4), a standard model frequently used by road engineers, was applied. This model takes as inputs the road attributes available in the AICD data set, the roughness of terrain along the road, as well as country level information on various factors which can affect the price of transporting goods (i.e. price of fuel, labor costs, etc.). The output is the cost per kilometer of transporting a ton of goods in a heavy truck, for every possible road classification combination.<sup>11</sup> Using this model, the cost of traveling from every location within DRC to the cheapest market is calculated, where a market is defined as a city of 50,000 people.

# **4.2 The Natural-Historical Path instrument**

Recognizing that roads are often placed where they will have the biggest economic impact, leading to a biased OLS estimate, we generate a new instrument for this paper, called the NaturalHistorical path (NHP). As suggested by its name, the NHP takes into consideration historical data on caravan routes from the 19th century, as well as the terrain and historical land cover within DRC to estimate the quickest path, on foot, to and from anywhere within DRC’s borders.

The literature on the economic benefits of roads typically relies on one of two types of IVs; straight line, or “Euclidean distance” IVs, and historical path IVs. Of late, thanks in part to greater access to digitized historical maps and books, the use of historical road IVs has been growing. While these two types of IVs are very different in their formulation, they are both attempts at estimating the same thing; namely, the natural way for humans to travel over land, absent the presence of a road network. Historical paths are useful as IVs, in that they represent the easiest path to travel over land. As these historical paths were constructed with little or no technology, they generally follow a smoother terrain and have been used for hundreds of years, and are thus the most cost effective route to construct a road. At the same time, they are usually not correlated with the current economic benefits that lead to the endogeneity bias, given that in many cases, these routes were constructed well over 100 years ago.<sup>1213</sup> A combination of both the natural path and historical caravan data, represents an improved estimate of how people traveled over land in prior centuries, and thus is the best possible IV for transportation cost. A major problem with only using historical path data is that people now live in areas

> 11 See Appendix II for more information on the inputs and outputs for this model

> 12 While these IVs are desirable, they are not always feasible if data on historical paths are unavailable. In these cases, researchers often rely on straight line IVs. These variables are usually correlated with historical paths, given that the quickest path between two points is usually the path with the shortest length—the straight line. However, they cannot account for the fact that the topography of the land may make traveling in a straight line impossible, or extra costly, making these IVs potentially quite weak.

> 13 Some recent examples of papers employing historical route IVs include: Duranton et al. 2014, which used routes from major exploration expeditions in the US between the 16<sup>th</sup> and 19<sup>th</sup> centuries as instruments for the US interstate highway system;  Garcia-Lopez et al. 2013, which used ancient Roman roads, amongst others, as exogenous sources of variation in Spain’s current highway system; and Martincus et al. 2013, which used the Incan road network to instrument for Peru’s current road infrastructure.

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