Optimal Transport Networks

Trade costs are a ubiquitous force in international trade and economic geography, generating spatial differences in prices and real incomes. While trade costs result from a diverse set of policies and frictions, transport infrastructure stands out as an important force. How should infrastructure investments be allocated across regions, and how do the aggregate gains depend on the magnitude of the total investment? Infrastructure investments may be sensitive to frictions, local interests or corruption, potentially leading to suboptimal transport networks that may hinder trade and development. How important are these inefficiencies?

Pablo Fajgelbaum

To answer these questions, Pablo Fajgelbaum (UCLA) and Edouard Schaal (CREI) in the working paper “Optimal Transport Networks in Spatial Equilibrium” develop and apply a framework that allows the characterization of optimal transport networks in general-equilibrium spatial models. They solve a global optimization over the space of networks, given any primitive fundamentals, in a general neoclassical framework. Then they apply the framework to European road networks to assess the aggregate and regional impacts of optimal infrastructure growth, the inefficiencies of observed networks, and the optimal placement of roads as a function of observable regional characteristics.

The point of departure for the framework is a neoclassical economy with multiple goods, factors, and locations where labor can be regionally mobile. The key methodological innovation is that locations are arranged on a graph. Goods can only be shipped through connected locations subject to transport costs that depend both on congestion and on how much is invested in infrastructure. The authors tackle the planning problem of simultaneously choosing the optimal transport network, the allocation of production and consumption, and the gross trade flows across the graph. They exploit the fact that the planner’s subproblem of choosing gross trade flows on the network is a well understood and tractable problem in the operations research and optimal transport literatures.  They make assumptions such that the full planner’s problem, involving the general equilibrium allocation and the optimal network investments alongside the optimal transport, inherits that tractability.

The framework has enough flexibility to be matched to real-world data and then used to undertake counterfactuals involving the optimal transport network. The authors discipline the model such that it reproduces the observed population and value added across 50km x 50km cells in 25 European countries. The counterfactuals imply that, across countries, the average welfare gain from an optimal 50% expansion in the resources used to build the observed road networks and the average welfare loss from road misallocation are between 3% and 6%, although these gains are much larger in some specific countries. They also imply larger returns to optimal road expansion and larger losses from road misallocation in poorer economies. Within countries, the optimal expansion or reallocation of roads reduces regional inequalities in real consumption.

The framework could serve as basis for other applications such as political-economy issues associated with infrastructure or spatial competition among planning authorities. It is also well understood that systems of cities and transport networks are highly persistent, and the model could be used to study inefficient network lock-in due to existing investments corresponding to dated economic fundamentals. The framework may also be used to construct instruments for investments in transport infrastructure as function of observable regional characteristics in order to undertake empirical research evaluating the impact of infrastructure investments.