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Optimal Transport Networks in Spatial Equilibrium

Periodic Reporting for period 2 - OPTNETSPACE (Optimal Transport Networks in Spatial Equilibrium)

Reporting period: 2020-07-01 to 2021-12-31

Every year, the world economy invests many resources into the improvement of its transport infrastructure and infrastructure development is one the key tools used by governments and international institutions to foster economic development and international trade. These massive investments have a wide range of impacts on citizens (access to essential goods and services, pollution, migrations) and the economy (the location of economic activity, economic growth, domestic and international trade).

How should infrastructure investments be allocated across space to maximize some notion of social welfare? How should infrastructure networks be designed while taking into account these various trade-offs? This project seeks to provide an answer to these questions.

In a first part, this project develops novel theoretical and quantitative models to analyze the economic impact of infrastructure projects and study their optimal design. The proposed models build on state-of-the-art models of trade and economic geography and are constructed to operate at various scales ranging from the international and domestic scopes to the urban level. The project’s optimal design approach takes into account aspects as varied as how infrastructure affects the flows of goods and people across space, the distribution of economic activity across space, international trade, regional development, migrations, spatial inequalities across and within countries as well as the potential impact on the environment. The objective of the project is to develop tools that can be readily used by researchers and policymakers in charge of infrastructure planning.

In a second part, the project applies these tools to understand real world infrastructure networks. How far are actual and planned infrastructure projects from the social optimum? The second objective of the project is to evaluate to what extent existing infrastructure networks may be a limit to economic growth in developed and developing economies. The project also investigates the potential sources of real-world inefficiencies, considering for instance the role of the political process and international cooperation.
Up to date, the results achieved by the project have been summarized in two articles that were published in leading economic journals.

The first significant result is the development of a new methodology which allows to analyze the optimal design of infrastructure networks in general equilibrium spatial models. The results have been published in “Optimal Transport Networks in Spatial Equilibrium” (Econometrica, 2020), joint with P. Fajgelbaum. The theory builds on a general neoclassical trade model which nests a wide range of international trade, economic geography models and urban models. Locations are arranged on a graph, and goods or people can only travel along the links of the network. The optimal infrastructure planning problem is analyzed through the lens of a planner who chooses how much infrastructure to build in each link, taking into account the private sector’s decisions (where to live/produce, how much/what to produce, optimal shipping/commuting routes and general equilibrium). This novel theory allows the authors to describe the optimal placement of infrastructure taking into account a) the distribution of productivity, resources and amenities, b) the particular geography of a location (availability of land, obstacles like rivers or mountains), c) the characteristics of the transport technology (degree of congestion, economies of scale in transportation). The theory is applied to Europe and is able to quantify the efficiency or suboptimality of the existing road network across countries. The model’s predictions are compared to the EU’s current infrastructure projects. The preliminary results broadly suggest a higher degree of infrastructure misallocation and underinvestment in Eastern European countries. An application to US states is also available on the PI’s website. A MATLAB toolkit that implements the model is available on the PI’s website for the use of other researchers and policymakers.

A second result is an exploration of the project’s optimal network design methodology in an urban environment with an application to COVID-19. The advent of the global pandemic in 2020 has led to a burgeoning of economic research addressing how existing theories could help policymakers in improving their policy response. The article “Optimal Lockdown in a Commuting Network” (American Economic Review: Insights, forthcoming December 2021) joint with P. Fajgelbaum, A. Khandelwal, W. Kim and C. Mantovani, uses elements of the project’s optimal network methodology to study spatially targeted lockdowns at the level of a large metropolitan area in the face of COVID-19. The theory builds on a standard urban framework in which workers choose to live in various districts of a city and must commute to work. The optimal network approach is applied to optimally control population flows in a commuting network in order to balance a trade-off between saving lives and the economic costs implied by lockdown measures. The article applies its methodology to the metropolitan areas of New York and Seoul. The findings suggests great welfare and economic gains from spatially-targeted lockdowns as opposed to uniform lockdowns and recommends generally stricter lockdowns to central locations in comparison to what was implemented in practice.
The development of theoretical and quantitative models to optimally design infrastructure networks in general equilibrium economic models is novel and pushes beyond state-of-the-art methods to evaluate infrastructure projects. The problem of optimizing over networks can be a daunting task using standard optimization techniques, but the methodology developed in the project exploits instead tools from convex optimization and optimal transport, making the computation of optimal networks feasible. The project’s modeling approach also brings the power of modern general equilibrium models of trade and economic geography to infrastructure planning.

The remaining part of the project will keep studying the implications of optimal networks for the understanding of real-world infrastructure networks along three main axes.

The current methodology will be applied to an urban framework, taking into account the specific trade-offs faced by city planners. The focus will be put on residents’ commuting decisions and on the transport of people, allowing for various modes of transportation. The model will also consider the role of negative externalities (noise, pollution) and how infrastructure shapes the availability of land (commercial and residential).

A second line of research article investigates the impact of the political process on the design of existing infrastructure networks and seeks to evaluate how political frictions distort infrastructure investments away from the social optimum.

In a third line of research, the PI will analyze how the hierarchical and fractal features of optimal transport networks in line with empirical evidence can explain the observed distribution of people and economic activity across space. In particular, the PI will seek to understand how optimal network theory may contribute to explain the pervasive empirical observation of the Zipf’s law in the city-size distribution across many countries and over time.