Common power laws for cities and spatial fractal structures.

City-size distributions are known to be well approximated by power laws across a wide range of countries. But such distributions are also meaningful at other spatial scales, such as within certain regions of a country. Using data from China, France, Germany, India, Japan, and the United States, we first document that large cities are significantly more spaced out than would be expected by chance alone. We next construct spatial hierarchies for countries by first partitioning geographic space using a given number of their largest cities as cell centers and then continuing this partitioning procedure within each cell recursively. We find that city-size distributions in different parts of these spatial hierarchies exhibit power laws that are, again, far more similar than would be expected by chance alone-suggesting the existence of a spatial fractal structure.

Between lives and economy: COVID-19 containment policy in open economies.

This paper studies containment policies for combating a pandemic in an open-economy context. It does so via quantitative analyses using a model that incorporates a standard epidemiological compartmental model in a general equilibrium multi-country, multi-sector Ricardian model of international trade with input-output linkages. We quantitatively evaluate the long-run welfare and real-income losses due to the short-run pandemic shocks, and we study the role of trade in these effects. We devise a novel approach to computing national optimal policies. We find that (1) the long-run welfare and real-income losses due to just two years of pandemic shocks are substantial; (2) international trade helps buffer both the welfare and real-income losses, and it also saves lives; (3) the computed optimal policies indicate that most countries should have tightened their containment measures relative to what was done; and (4) compared to the case of autarky, the optimal policy under trade is generally more stringent.