key: cord-0996060-g40fynol
authors: Monte, Ferdinando
title: Mobility Zones
date: 2020-07-18
journal: Econ Lett
DOI: 10.1016/j.econlet.2020.109425
sha: 9e0a6c384d31c9402940d70da31b1f26132636c0
doc_id: 996060
cord_uid: g40fynol

This short note constructs Mobility Zones to facilitate the discussion on the geographic extent of individual mobility restrictions to control the spread of Covid-19. Mobility Zones are disjoint sets of counties where a given level of individual mobility directly or indirectly connects all counties within each set. I compute Mobility Zones for the United States and each state using smartphone-based mobility data between counties. The average area and population of Mobility Zones have sharply shrunk around the onset of the epidemic. Pre-Covid-19 Mobility Zones may be useful in calibrating quantitative studies of targeted restriction policies, or for policymakers deciding on the adoption of specific mobility measures. Two examples suggest the use of Mobility Zones to inform within-state differences and cross-state coordination in mobility restriction policies.

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The current pandemic of Covid-19 has induced a large number of countries to restrict individuals' mobility and production activities to limit the di¤usion of the virus, with massive economic damage. As policymakers consider how to lift and perhaps reimpose these restrictions, it is essential to measure which sets of places are connected by individual mobility in normal, unrestricted circumstances. Widely used SIR models (Kermack and McKendrick, 1927) To construct these zones, we see counties as nodes of a network. Our working assumption is that the infection can travel directly between two counties only when they are linked. An edge links two counties if individuals'mobility between them is above a given threshold t in the interval These indices are based on data from smartphones "pinging" in a given location and date. For a given day d, the data reports, among all the phones active in county g 0 ; the fraction of phones that have also been active in a location g at least once in the previous fourteen days. Each day, from January 20, 2020, the data provide a square matrix of LEX gg 0 d values for 2,018 U.S. counties with a su¢ cient number of active devices. We take these indices as proxies for individual mobility.

There is an already rich literature on the current Covid-19 pandemic. Related to this note, Goldfarb Zones in Tolbert and Sizer (1996) . Commuting zones are aggregates of counties based on commuting patterns; two counties must have commuting ties if they are in the same commuting zone. MZs are based on individual mobility for any purpose; two counties must be connected by a path (but may or may not have direct links) if they are in the same MZ. Counties-to-MZs correspondences are available at any threshold of county-to-county mobility.

Denote with G the set of N locations in the economy. G is left implicit whenever it is not necessary. For a given day d, Couture et al. (2020a) reports, among all the phones active in a geographic unit g 0 ; the fraction of phones that have also been active in a location g at least once in the previous fourteen days, LEX gg 0 ;d . I construct an undirected adjacency matrix M representing the economy as follows.

First, for each pair (g; g 0 ), compute the average

When describing the evolution of MZs over time (Figures 1 and 2 below), D is each day from January 20, 2020 to May 5, 2020, and jDj = 1. When computing the pre-Covid-19 MZs (for the remaining …gures), D is the set of jDj = 21 days in the three weeks from Monday, January 20, 2020, to Sunday, February 9, 2020. Considering all days in a week allows accounting for within-week variation in mobility patterns.

These three weeks are the longest period of data that appears reasonably una¤ected by the Covid-19 outbreak, as discussed below.

Each LEX gg 0 belongs to the interval [0; 1]. As a second step, for a …xed interaction threshold

as an indicator variable equal to 1 if this average share is greater than or equal to t, and 0 otherwise. I say that g and g 0 are linked at level t if m gg 0 (t) = 1 or m g 0 g (t) = 1, or both. As a third step, I construct an N N symmetric matrix M G (t) that indicates if any two counties are linked at level t.

M G (t) represents the adjacency matrix of an undirected network for G. As a fourth step, I identify all the components of this network using readily available computer routines. 

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