From the previous analysis we derived the (shortest) transport time between each pair of cities. As our trade and production data are at the country level, a consistent aggregation approach is required. We address this by considering three essential parameters: location-specific friction, trade elasticity, and trade elasticity with respect to transport time. We aggregate transport time between cities at the country pair level using a theoretically robust iterative method that integrates population weights and a calibrated friction elasticity, as illustrated in Hinz (2017).

The theoretically consistent aggregation for the frictions at the level of the city pairs is as follows: When aggregating at the level of a pair of countries _ij_ , with exporter country _i_ and destination country _j_ , we take into account both the relative population of cities _k_ in _i_ and _l_ in _j_ , as well as the transport time elasticity, denoted as _δθ_ .<sup>12</sup> The transport time elasticity is calibrated using a simple iterative procedure as follows. We start with an arbitrary initial value of the elasticity (i.e. _δθ_ = _−_ 1). Then, we estimate the elasticity in a cross-section gravity equation for the year 2018 with origin and destination fixed effects and controlling for PTAs, language proximity, and shared colonial history (border dummies are not included because border crossing time is already included in transport time).<sup>13</sup> We retrieve the transportation time coefficient and then use it as a parameter in the aggregation equation ( _δθ_ = _β_<sup>_transportation_</sup> ). In the next iteration, this new aggregation parameter is used.<sup>14</sup> Using a network analysis to quantify shipping times and the impact of new and improved transportation infrastructure has advantages and disadvantages. On the plus side, a network analysis can be a useful tool to support modeling of international trade flows. It can enhance the understanding of the impact of changes in infrastructure or other factors on an interconnected system allowing to extract information from spatial data. Specifically, a network analysis enables the measurement of the time it takes to go from one location to another taking into account the overall quality and quantity of infrastructure, physical obstacles (e.g. rough terrain) or other barriers (e.g. border delays), and relative performance measures (e.g. processing time at ports or when crossing a border). As with any modeling exercise, it should be acknowledged that our network is a simplified version of reality and results are affected by the quality of inputs. For example, due to limited data availability, we cannot include some elements that might influence the definition of optimal routes, such as freight service quality, service frequency, conflicts or adverse weather events.

# **1.1.1 Transportation Time Validation**

Before using it as an input in the general equilibrium counterfactual analysis of trade and infrastructure reforms, we validate the transportation time in our dataset using evidence from Hummels & Schaur (2013) and Hummels

> 12The elasticity is a combination of trade elasticity _θ_ and location specific friction elasticity _δ_ .

> 13To retrieve the aggregation parameter we rely on a PPML estimator.

> 14We repeat this process until the estimated coefficient remains unchanged in its 5th digit. We do this separately for transport times with and without the sea route preference assumption. The procedure converges in 7 iterations in both cases. Without sea preference, the estimated _δθ_ is -0.852, with sea preference, the estimated parameter is -0.780.

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