key: cord-0798260-xxqxhp9p
authors: Li, Bingjing; Ma, Lin
title: JUE Insight: Migration, Transportation Infrastructure, and the Spatial Transmission of COVID-19 in China()
date: 2021-04-15
journal: J Urban Econ
DOI: 10.1016/j.jue.2021.103351
sha: 4cd3e6b2431b7e82d71107b0c2414bf819c6f0d5
doc_id: 798260
cord_uid: xxqxhp9p

This paper evaluates the impacts of migration flows and transportation infrastructure on the spatial transmission of COVID-19 in China. Prefectures with larger bilateral migration flows and shorter travel distances with Hubei, the epicenter of the outbreak, experienced a wider spread of COVID-19. In addition, richer prefectures with higher incomes were better able to contain the virus at the early stages of community transmission. Using a spatial general equilibrium model, we show that around 28% of the infections outside Hubei province can be explained by the rapid development in transportation infrastructure and the liberalization of migration restrictions in the recent decade.

The spatial transmission of COVID-19 in mainland China is unprecedented. Following the initial report of the novel coronavirus in Wuhan, 262 cities in 30 provinces reported cases of COVID-19 within the next 28 days. By the end of our sample period - The improved transportation infrastructure and liberalized migration policy, among many others, are the potential forces behind the increased mobility of people in the recent decades in China. The transportation infrastructure has expanded rapidly, as dense networks of roads, railways, and airports have significantly reduced travel distance. Ma and Tang (2020a) estimate that the average costs of passenger transportation have declined by around 70 percent between 1995 and 2015. The reduction in commuting costs not only increases the frequency of travel but also lowers the costs of medium-and long-term migrations. Meanwhile, the reform of the household registration system (hukou) has gradually lowered migration barriers in China (Tombe and Zhu, 2019; Fan, 2019) . Many cities have relaxed the requirements to obtain local hukou, which improved the employment prospects of the migrants and, at the same time, elevated their access to public services such as education, healthcare, and social security. The steady decline in migration barriers and the improved transportation infrastructure have induced a phenomenal rise in internal migration. Gross migration flows rose from 64.5 million in 2000 to 129.0 million in 2015; gross flows specific to Hubei more than doubled from 4.2 million to 10.3 million during this period.

The changes in transportation networks and migration patterns could have played important roles in shaping the spread of COVID-19. The onset of the outbreak of was in the run-up to the Spring Festival, the period of travel fest expecting about 3 billion trips (Bloomberg News, 2020) . The population outflow from Wuhan amounted to 4.3 million two weeks before the city-wide lockdown on January 23, 2020. Figure 1 shows the residual scatter plots of a multivariate regression of outflows from Wuhan to different prefectures in the two weeks before the lockdown (January 9-22, 2020). Cities with more emigrants to and more immigrants from Wuhan record greater outflows from Wuhan, reflecting that family reunions are the primary reasons for travel during the Spring Festival. In addition, the partial correlation of population outflow and travel distance is negative, which suggests that in addition to the movement of long-term migrants, short-term population movement, e.g., work-related travel, comprises a significant proportion of all trips.

We evaluate the role of the transportation infrastructure and the reduction in migration barriers in the context of the COVID-19 transmission in China. Specifically, we ask: without the recent changes in the transportation networks and migration policies, how would the transmission of COVID-19 be affected? In these counterfactual experiments, we hold constant the public health measures implemented during the COVID-19 pandemic. Our setting is unique. The spatial spread during our sample period originated from a single epicenter in Hubei (Jia et al., 2020) . Due to the stringent public health measures and travel restrictions, there were few cross-transmissions among the regions outside the epicenter. In light of this pattern, our empirical focus is on the spatial relations specific to Hubei even though our spatial model accounts for all bilateral linkages.

We combine a disease transmission model and a general equilibrium spatial model incorporating trade in goods and migration flows, and conduct the analysis in three steps.

First, guided by the viral transmission model, we find that prefectures with larger bilateral migration flows and shorter travel distances with Hubei experienced a greater spread of COVID-19. However, these factors affected only transmissions in the early stages when most cases were imported, indicating the travel ban's effectiveness and other measures restricting potential social interactions of return-migrants and visitors from Hubei with the local population. Local economic activities also influenced the speed of transmission, with two counteracting mechanisms. Prefectures with greater economic activities received more imported cases; however, higher-income prefectures were better able to contain the virus in the early stages of community transmission.

In the second step, based on the spatial economic model, we quantify the effects of the expanding transportation network and the reduction in migration barriers over the period on migration flows, the spatial distribution of population, and income. The indirect general equilibrium effect on income is part of the total impact of the counterfactual policy shock, affecting both aggregate transmissions and spatial patterns. We find that had the These findings indicate that the swift spatial spread of COVID-19 is partly facilitated by the tighter inter-regional linkages induced by the expanded transportation infrastructure and the reform in migration policies over the past two decades.

Given the low number of infections in China, the healthcare costs of better connectivity are likely to be orders of magnitude smaller than its economic benefits. Under our model, reverting the transportation networks and migration policies to 2005-levels would reduce the aggregate income by 3.60%, which equals to $321 billion, based on the estimates of Chinese GDP from the World Bank. On the other hand, the 28.21% reduction of the incidences from reverting infrastructure and migration policies would lead to 3,517 fewer infections, 132 fewer hospitalizations, and 23 fewer fatalities, based on the estimates of hospitalization and fatality rates in Walker et al. (2020) and Verity et al. (2020) . The costs of these hospitalizations and fatalities are between $35 and $173 million, depending on the estimates of the values of a statistical life as in Ashenfelter and Greenstone (2004) and Viscusi and Aldy (2003) 1 . However, the low costs of better mobility critically depend on the fact that the disease was efficiently controlled in China. Without effective containment policies, the number of infections would have been much higher, and so would the healthcare costs of better connectivity. For example, if China has 100 million cases of COVID-19, the economic costs of a 28.21% change are between $283 billion and $1.40 trillion, which are on par with the estimated benefit of better mobility (see Appendix B for details). One hundred million cases in China is not unimaginable; it puts China at a 7% population infection rate, similar to that in the U.S. in January 2021 (WHO, 2021) . With these cautions in mind, we argue that the unintended and potentially fatal consequences of factor mobility should no longer be overlooked in the long and flourishing literature on transportation economics (Fogel, 1962; Allen and Arkolakis, 2014; Donaldson and Hornbeck, 2016; Donaldson, 2018;  Allen and Arkolakis, 2019).

This study contributes to the literature on the health costs of transportation infrastructure, and more generally, to the long-run economic determinants of the transmission of disease. Adda (2016) employs quasi-experimental variation and a difference-in-differences design to evaluate the role of public transportation and expanding railways in France on viral transmission. We take a different approach by employing a quantitative spatial model that characterizes how transportation costs and migration barriers shape spatial links among prefectures to determine the spread of COVID-19 from Hubei. Our approach enables the computation of the national-level general equilibrium effects of shocks to economic fundamentals while relies more on the model's structure. The literature on COVID-19 also investigates the association between population mobility and spatial spread. Most of these studies focus on projecting the impacts of travel restrictions (Chinazzi et al., 2020) , assessing community transmission risk (Jia et al., 2020) , and evaluating the effectiveness of transmission control 1 Appendix B provides more details on the cost-benefit estimation. measures in containing the spread (Jia et al., 2020; Kraemer et al., 2020; Tian et al., 2020) . In contrast, our study explores the roles of transportation infrastructure and migration policies -the fundamentals that determine population mobility -on disease transmission through the lens of a spatial economic model. 2

Our work is also related to a broader literature that explores the propagation of shocks to economic fundamentals through spatial linkages. Allen and Arkolakis (2014) and Allen et al. (2020) propose a series of spatial general equilibrium models to study the interactions of goods and factor mobility. In the context of the Ricardian models, Caliendo et al. (2018 Caliendo et al. ( , 2019 analyze the transmission of trade and migration shocks in a similar setup to our model. We highlight that in addition to the direct economic impacts usually documented in the literature, the mobility of people has an unintended spatial impact through disease transmission.

The remainder of the paper is organized as follows. Section 2 describes the data. Section 3 examines the roles of migration flows, travel distance, and local economic activities on the spread of COVID-19 outside Hubei. Section 4 lays out a general equilibrium spatial model that computes the aggregate effects of counterfactual changes in transportation networks and migration policies. Section 5 quantifies the model, and Section 6 presents the counterfactual experiments. Section 7 concludes.

Prefecture-level Data on COVID-19 Cases We collected prefecture-level data on reported COVID-19 cases with daily frequency from the Health Commissions of different prefectures. We exclude the data of the epicenter Hubei given that our study focuses on the spatial spread of the disease outside Hubei. 3 Our baseline analysis covers the period from January 28 to February 22, 2020 -30 days after the lockdown of Hubei, when the spread was almost halted, as shown in Figure A .1 in the appendix. By then, there were 12,526 reported cases of infections located across 267 prefectures outside Hubei.

The bilateral migration data come from a 10% subsample of the 1% Population Sampling Survey of China (mini census) in 2015. The mini census data contains information on prefecture of residence and prefecture of hukou registration, based on which we code migration status and calculate bilateral migration flows. We employ the following prefecture-level measures for the empirical analysis: (i) the ratio of emigrants to Hubei to the local population in a particular prefecture, and (ii) the share of immigrants from Hubei in the local population in a particular prefecture. For the quantification analysis, we also employ the data on migration flows in 2005 from a 20% subsample of the 1% Population Sampling Survey of China in 2005.

The transportation network data come from Ma and Tang (2020a) , which constructs the transportation networks from the digitized transportation maps that incorporate roads, railways, high-speed railways, and waterways. The distance is measured as the time required to travel between two points. We use the data from 2005 and 2015 in this paper, which are visualized in Figure A. 2.

Other Data Sources We have used the following datasets in the quantification stage in Section 5. We use the Investment Climate Survey from the World Bank to calibrate the parameters related to internal trade. The Population Census in 2000 and 2010 were used to measure the initial population distribution.

This section lays out an empirical model linking the spatial transmission of COVID-19 to economic fundamentals. Specifically, we consider the number of infections in a locality as a function of bilateral population flows with Hubei, which are determined by the bilateral longterm migration pattern with Hubei, the travel distance, and the size of the local economy.

Guided by the disease transmission model in Appendix C, we estimate the following equation: The time-varying coefficients β ιt represent the cumulative effects of the underlying variables up to period t. We set the starting date t = 0 to January 28, 2020, five days after the lockdown was imposed in Wuhan and other cities in Hubei. At this time, most imported cases would have passed the incubation period, and would have been recorded. Therefore, the estimates β ι0 reveal the effects of the underlying variables on the arrivals of imported cases. For the baseline analysis, we include in the sample the observations from January 28 to February 22, 2020, with time intervals of five days. 5 The differences in the coefficients, β ιt − β ιt−δ , capture the effects of the underlying variables on the local transmission within an incubation period [t − δ, t], which also reflects the effectiveness of the prevention and control policies. For example, when travelers from Hubei are subjected to quarantine orders, β 1t − β 1t−δ and β 2t − β 2t−δ are expected to be zero in the later periods. Figure 2 reports the point estimates of β ιt and their 90% confidence intervals. Appendix E demonstrates that the baseline findings are robust to a variety of alternative specifications.

We find in Panel A that the prefectures with a higher share of Hubei-bound emigrants have on average more cases of COVID-19 infection. However, the cumulative effect remains stable over the sample period. This finding suggests that while cases were imported when Hubei-bound emigrants returned home for the Spring Festival, such imported cases did not engender further community transmissions in the later periods, perhaps due to the effective quarantine measures that were implemented.

As shown in Panel B, a higher share of immigrants from Hubei is also associated with a wider spread of the disease. Additionally, the associated imported cases resulted in local transmissions over an earlier period between January 28 and February 2, 2020, but the effect quickly diminished afterward. Panel C presents the estimates for the distance to Hubei, which reflect the effects of short-term population movement, such as business trips, before the lockdown in Hubei on disease transmission in the subsequent periods. As expected, prefectures closer to the epicenter had more imported cases at the start of the period, but Last but not least, Panel E shows the effects of GDP per capita. Ceteris paribus, prefectures with higher incomes reported more imported cases due to tighter economic relationships with Hubei. Interestingly, as shown in Figure A .3, in an earlier period between January 28 and February 7, 2020, a higher income per capita was associated with a slower spread of the disease, indicating that higher-income regions were more capable of implementing transmission control measures promptly. Lower-income prefectures caught up in the later period, though, and the incidence rate as of February 12, 2020, was no longer correlated with income level.

In Section 6, we take the estimates of the underlying parameters β's as given and quantify the impacts of different counterfactual configurations of transportation networks and migration policies on the transmission of COVID-19. A change in transportation networks alters travel distance and migration flows, as well as spatial distributions of population and income across China through general equilibrium effects. Our regression analysis indicates that all these factors have independent effects on disease transmission. The following section introduces a quantitative spatial model that computes the aggregate effect of counterfactual changes in transportation infrastructure and migration costs.

Our model is drawn from Ma and Tang (2020a) , which extends Tombe and Zhu (2019) to allow for productivity agglomeration. The economy contains a massL > 0 of individuals and J cities indexed by j = 1, 2, ..., J. Individuals can migrate between the J cities within China subject to frictions. Individuals living in city j obtain utilities according to the following CES function:

where ω indexes the goods and η is the elasticity of substitution.

The production side of the model follows Eaton and Kortum (2002) : firms operate in perfectly competitive markets, and every city can produce every variety of ω. The production function for variety ω in city j is:

where j is the labor input. A j is the city-specific productivity that depends on an exogenous component,Ā j , and the population to allow for agglomeration:

where β is the agglomeration elasticity. The city-variety specific productivity, z j (ω), is from an i.i.d. Frechet distribution with parameter θ:

Trade is subject to iceberg costs: for a unit of product to arrive in city i from city j, τ ij > 1 units of goods need to be produced and shipped.

The consumers in city i purchase from the supplier offering the lowest price for every variety ω:

where p ij (ω) is the price of ω from city j at the market in city i.

Individuals decide on migration destinations to maximize utility. Denote V j as the indirect utility of living in city j:

where w j is the nominal wage and P j is the ideal price index in city j:

In addition to the indirect utility, each worker also draws an idiosyncratic location preference for each city {e j } J j=1 from an i.i.d. Frechet distribution with the CDF:

where κ is the shape parameter. Lastly, moving from j to i also incurs a pair-specific cost, λ ij ≥ 1 with λ ii = 1. If a worker moves from city j to i, the utility in the end is the combination of the location preference and the migration costs:

The costs of migration capture the financial costs of moving and commuting, the psychological costs of living in an unfamiliar environment, as well as the policy barriers that deter migration, such as the hukou system.

Considering all the determinants of migration, a worker living in city j will migrate to city i if and only if doing so provides her with the highest utility among all the J locations:

Conditional on V j , the probability of an individual migrating from city j to i is:

This probability is also the fraction of the individuals who migrate from city j to i due to the law of large numbers. Therefore, the migration flow from city j to city i is:

where Π j is the expected utility of a worker who lives initially in j:

Given the parameters of the model, the equilibrium is defined as a vector of prices {w j , p j (ω)}, a vector of quantities {q j (ω)}, and a population distribution {L j } such that:

• Every individual maximizes his utility by choosing the location and the consumption bundle.

• Every firm maximizes its profit.

• The labor market in each location clears.

• Trade is balanced.

Appendix D provides details of the equilibrium conditions.

We quantify the model to 291 prefecture-level cities in China around the year 2015. The sample is determined by data availability, and we focus on the year 2015 as it is the latest year in which the 1% Population Sampling Survey is available. The quantification strategy aims to capture the migration flows into and out of the Hubei province and the broad pattern of migration flows inside China as well. Table 1 summarizes all the parameters.

The following common parameters come from the literature. Following Redding and Turner (2015), we set the agglomeration elasticity, β, to 0.1. We set the elasticity of substitution to, η = 6, which is a value in the middle of plausible ranges. 

We assume that the migration costs from j to i, denoted as λ ij takes the following functional form:

Migration frictions depend on the national migration policy,λ, and the location-specific entry and exit barriers, λ i and λ j . Migration frictions are also related to the underlying passenger transportation networks between the cities, T p ij , up to an elasticity of ξ. We first focus on the transportation network, T p ij ξ .

We use the transportation network, T p ij , in 2015 from Ma and Tang (2020a) . The parameter ξ governs the elasticity of λ ij with respect to the infrastructure, T p ij . We follow the same estimation methods in Ma and Tang (2020a) , with the updated bilateral migration matrix in 2015. The migration flow in equation (6) can be transformed to:

This equation leads to a reduced-form estimation with origin and destination fixed effects.

The two fixed effects, δ i and δ j , absorb all the variables in the expression above except for the last term:

We estimate the equation using OLS, with the migration flow data from the 1% Population

Sampling Survey in 2015. The regression estimates κξ to be 0.40. With the calibrated κ at 2.0, the estimated ξ equals 0.20. We also estimate the equation with an instrumental variable for T p ij to alleviate the concerns of endogenous placements of infrastructure. To do so, we follow Faber (2014) to construct the Minimum-Spanning Tree instruments. The point estimate is only slightly higher at κξ = 0.42 and with corresponding ξ at 0.21. In the baseline model, we use the OLS estimate.

The trade costs matrix is also based on Ma and Tang (2020a) . The trade cost matrix is assumed to be:

whereτ is the overall trade frictions, T g ij is the underlying goods transportation network, and ψ is the elasticity of the iceberg costs to T g ij . We take the values of T g ij ψ directly from Ma and Tang (2020a) and estimateτ in our context.

City-Level Productivity,Ā j We follow the methods in Ma and Tang (2020b) , which implements Donaldson and Hornbeck (2016) in the context of China to estimate the citylevel productivity. The details are explained in Appendix D.

The remaining four parameters call for joint-calibration: the overall migration and trade barriers,λ andτ , and the origin and destination-specific migration barriers, λ i and λ j .

As the COVID-19 outbreak stems from a single epicenter of Hubei, the migration flows between prefectures outside of Hubei are irrelevant to the virus's spatial spread. For this reason, we only impose λ i and λ j on the prefectures within Hubei province, and assume that λ i = λ j = 1.0 for all the migration flows outside of Hubei. To simplify notation, we use λ IN to denote the common migration friction of moving into any prefecture in Hubei, and λ OUT to denote the friction of moving out of Hubei.

We jointly calibrate these four parameters to four moments in the data. The first moment is the internal-trade-to-GDP ratio of 0.625 from the Investment Climate Survey conducted by the World Bank. This moment identifies the overall internal trade barrier,τ . The second moment is the overall stay-rate of 89 percent. This moment is defined as one minus the fraction of migrants in the entire population as computed from the Population Sampling

Survey. This moment pins downλ. The other two moments also come from the same survey:

the outflow rate of all prefectures in Hubei province at 14.7 percent, and the inflow rate at 3.5 percent. The outflow (inflow) rate is defined as the total outflow (inflow) population as a fraction of the initial population of Hubei. The outbound and inbound migration barriers, λ OUT and λ IN , are respectively backed out from these two moments.

Our model is calibrated to match the population flow into and out of the Hubei province in 2015. Moreover, we can also match the bilateral population flows between prefectures in Hubei and prefectures outside Hubei due to the detailed geographic information incorporated in the T p ij matrix. Appendix D discusses the out-of-sample model fit.

In this section, we illustrate the impact of transportation networks and migration policies on disease transmission through the lens of our model. In the model, transportation networks were captured by the T p ij and T g ij matrices, and the migration policies are summarized in the Λ = {λ, λ IN , λ OUT } vector. To counterfactually simulate the population flow, we first need to estimate these objects under the counterfactual scenario.

To back-out the policy parameters, we re-calibrate the model to the state of the Chinese economy around the year 2005. Following the same strategy, we use the data from the 2005 Population Survey, the initial population from the census in 2000, and the T p ij and T g ij matrices in 2005 from Ma and Tang (2020a) to calibrate the counterfactual. We also re-estimate theĀ j vector in the year 2005. All the other parameters are the same as in the 2015 calibration. These parameters are reported in Table 1 .

The migration policy has been substantially liberalized over time, as seen in the table.

Between 2005 and 2015, the national migration multiplier,λ, fell by 54 percent, while the Hubei-specific frictions fell by 11 -43 percent. The decline in these estimated policies is driven by the surge of internal migration in China, as reflected in the two Population Surveys.

In the 2005 survey, the aggregate stay rate was around 94.4 percent, and it declined to 89 percent in 2015. Similarly, the outflow rate of Hubei province doubled from 7.4 percent to 14.7 percent, and the inflow rate more than quadrupled from 0.8 percent to 3.5 percent.

These data patterns are broadly consistent with the reforms in the urbanization policy during that time, as discussed in detail in Hsu and Ma (2021).

In the rest of the section, we present three sets of counterfactual simulations. In the first "constant network" simulation, we use the while the decline in welfare is 7.41%. 8

Given the counterfactual migration flows, travel distance, population, and income per capita, we simulate the incidence of COVID-19 in prefecture i according to:

represents the counterfactual ratio of Hubei-bound emigrants to the local population in prefecture i. Other variables are defined analogously.β ιt 's are the estimates obtained from Section 3.1. The counterfactual total number of infections outside Hubei is computed as The quantitative importance of transportation networks and migration policies is similar in explaining the overall spread of COVID-19 outside Hubei. However, the two factors affect the disease spread through different channels, as revealed by the decomposition exercises in Table 2 . Panel (b.1) finds that under the case of "constant network", the direct effect of an increase in travel distance decreases the number of total reported infections by 11.27%, while the induced decrease in migration flows leads to only a 3.44% reduction. These estimates are consistent with the findings in Section 6.1 that migration flows declines slightly in response to a reversion of the transportation infrastructure to the 2005 configuration. Hence, the rapid expansion of transportation infrastructure in China mainly affects disease transmission by increasing short-term population movement rates rather than altering medium-and longterm migration patterns. Columns (8) and (9) 

We evaluate the impacts of migration flows and transportation infrastructure on the spatial transmission of COVID-19 in China. Using the daily data of reported cases at the prefecture level and the bilateral migration data from the mini census, we show that cities with larger bilateral migration flows and shorter travel distances with Hubei experienced a greater spread of COVID-19. In addition, wealthier prefectures with higher incomes were better able to contain the virus in the early stages. We then evaluate the contribution of the rapid de- to the counterfactual using both the T p ij and T g ij matrices and the Λ parameters in 2005. Panel (a) summarizes the population flows in and out of the Hubei province in the baseline and the counterfactual simulations. Panel (b) reports the actual spread of reported COVID-19 cases over time, and the spreads under three counterfactual scenarios. Columns 4 to 9 decompose the overall counterfactual changes reported in columns 2 and 3 into different components: (i) changes induced by counterfactual changes in bilateral migration flows specific to Hubei (i.e., X i and M i in equation (1)); (ii) changes induced by counterfactual changes in bilateral distance with Hubei (i.e., ln(Dist i ) in equation (1)); (iii) changes induced by counterfactual changes in population and GDP per capita (i.e., ln(P op i ) and ln(GDP pc i ) in equation (1)). J a n 2 3 J a n 2 5 J a n 2 7 J a n 2 9 J a n 3 1 J a n Under each graph two summary statistics are presented. In the first column, the mean is the average counterfactual population growth weighted by the population in the baseline equilibrium. In the middle column (respectively, the last column), the mean change in real wage (respectively, welfare) is the percentage change in the population weighted average of real wage (respectively, welfare) from the baseline to the counterfactual equilibrium, which represents the change in real wage (respectively, welfare) at the national level. All columns report the standard deviation of the counterfactual changes weighted by the population in the baseline equilibrium. 

In this appendix, we lay out a simple model of disease transmission that rationalizes the empirical model in Section 2 and provides structural interpretations of the regression coefficients.

The disease takes two stages to develop. In the first stage, all cases are imported from

Hubei. The number of imported cases, I i (0), follows a Poisson distribution with the arrival rate λ i given by:

where X i denotes the ratio of Hubei-bound emigrants to the local population in prefecture i, and M i is the share of immigrants from Hubei in the local population in prefecture i;

Dist i measures the travel distance between prefecture i and Hubei based on transportation networks in 2015; and P op i and GDP pc i represent population size and GDP per capita in 2015, respectively. The arrival rate takes a gravity form, and is determined by the bilateral migration pattern with Hubei, the travel distance, which affects short-term population movement, and the size of the local economy.

In the second stage, the disease is transmitted locally. We consider the dynamics of the epidemic as follows:

where γ denotes the rate at which new cases develop, which is exogenously determined by We assume that the fraction of susceptible individuals is determined by:

Again, we allow the size of the susceptible population to be affected by bilateral migration patterns and distance with Hubei, reflecting possible interactions such as family gatherings with relatives traveling from Hubei prior to the Spring Festival. Importantly, theα coefficients could vary over time, reflecting the effectiveness of measures to contain the transmission of the disease. For example, when travelers from Hubei are subjected to quarantine orders, the coefficientsα 1t andα 2t are expected to be zero; when the travel ban from and to the epicenter is imposed,α 3t should decrease in magnitude; when prefectures outside Hubei adopt stringent transmission control measures such as social distancing or lockdowns, the coefficientsα 4t andα 5t should shrink. Equation (C.2) is then rewritten as

where α ιt = γα ιt . In the following analysis, we refer to the α coefficients as policy parameters that capture the period-specific prevention and control policies governing the disease transmission at the prefecture level.

In the empirical analysis, we consider a discrete time version of equation (C.4), which is given by

where δ represents the incubation time. Based on the findings in the epidemiological literature on COVID-19, we set the incubation period to five days. As shown in the second line of the equation, the number of infections in time t is determined by the number of initial imported cases and the cumulative increments up to time t. Substituting equation (C.1) into (C.5), we arrive at our estimation equation:

where β ιt = θ ι + τ =δ,...t α ιτ represents the cumulative effects of the underlying variables up to period t, and ν i (t) = ε i (0) + τ =δ,...,t ε i (τ ). With the estimates of β ιt , we can back out the period-specific policy parameters α ιt = β ιt − β ιt−δ , which capture the dynamics of the 

The solution of the model utilizes the equilibrium conditions as specified in Section 4. Conditional on a guess of equilibrium population distribution {L j }, the solution of the model is similar to a standard Eaton-Kortum model. The price charged by the suppliers from city j in city i for variety ω is:

as determined by the profit maximization problem of the firm. The price paid for a particular variety ω in city i is:

The Poisson quasi-maximum likelihood count data model is generally preferred to alternative count data models (such as the negative binomial model), because the Poisson MLE estimator is consistent even when the error distribution is misspecified (i.e., the true distribution is not Poisson), provided that the conditional mean is specified correctly (Cameron and Trivedi, 2013; Wooldridge, 2002) . Despite of this consideration, we demonstrates the robustness of the baseline findings to alternative specifications that estimate the relationship between the number of infections and the economic fundamentals in Appendix E.

Conditional on the Frechet distribution of productivity, the price index in city i is:

is the CDF of prices in city i, and Ψ is the Gamma function evaluated at 1 + (1 − η/θ). The share of total expenditure in city i on the goods from city j is thus:

The expression for the bilateral trade flow from j to i is thus:

From the last equation, it is straightforward to solve for the equilibrium wage rate in city j through a system of non-linear equations. To see this, note that the trade balance condition implies X j = J+1 j=1 X ij = w j L j :

(D.1)

The equation above describes a system of J + 1 non-linear equations where the vector {w j } is the unknown. We solve this with a simple iteration algorithm. All the other endogenous variables are functions of the wage rate. In particular, with the solution of the wage rate, we can compute the indirect utility, V j , followed by the migration probabilities according to equation (5), which we replicate here for completeness:

Note that the equation above is also the solution of the utility maximization problem of the individuals. We don't need to separately solve for the labor market clearing conditions as they are implicitly guaranteed by the trade balance condition per Walras's Law.

The algorithm above depends on a guess of {L j }, and the migration flows from solving equation (5) also imply a new equilibrium vector of population. We iterate on the population distribution until convergence at 1.0E-5.

We estimate the city-level productivity from the residual of the following regression:

where L j is the population of city j and w j is the wage rate that is approximated by per capita GDP. This equation comes from the trade balance condition in equilibrium. One can manipulate equation (D.1) as:

Taking logarithms on both sides of the equation, and approximating the terms in the square bracket as MA j = J+1 j=1 w i L i (τ ij ) −θ following Donaldson and Hornbeck (2016), we arrive at the equation to back-out city-level productivity:

The term, MA j , is the market access from location j that encompasses the physical transportation network and market size distribution in China. 10 Denoting the residual of regressing ln w j on ln L j and ln MA j asν j , it is then straightforward to see thatĀ j = exp ν j θ+1 θ .

We estimate this regression with our sample of 291 cities and use θ = 4 to back out the productivity term.

Our model is calibrated to match the overall population flow into and out of the Hubei province around the year 2015. Consequently, these overall moments are exactly matched in the baseline quantification. Moreover, the T p ij matrix behind the bilateral migration costs captures the underlying geography and the transportation networks. The incorporation of such features allows us to match the bilateral population flows between prefectures in Hubei and prefectures outside Hubei, as shown in the three panels of Figure D .1 in the appendix.

The baseline quantification of the model is able to fit the broad pattern of bilateral migration flows as the model prediction and the data are clustered around the 45-degree line. The popular destination cities among the outbound Hubei migrants in the data, such as Shenzhen, Shanghai, and Beijing, are also the top choices of the Hubei migrants in our model. The predicted outflow is more uniform across destinations compared to the data. This uniformity is mainly because the aggregation elasticity is relatively low (β = 0.1). As a result, the hotspot cities in the data do not attract a sufficiently large population inflow in the baseline model. E Robustness Checks

In the baseline model, we calibrated β, κ, θ, and η using the common values from the literature. In this section, we check the robustness of the quantitative results with respect to these parameters. For each of the parameters listed above, we carry out two robustness checks: one with a value above the baseline level and the other below. In each of the robustness checks, we re-calibrate the four policy parameters (λ,τ , λ IN , and λ OUT ) and

keep the other parameters the same as in the baseline version. We then re-compute the counterfactual results following the same steps as outlined in the paper. The parameter values in the robustness checks are reported in Table E 

In this subsection, we demonstrate the robustness of the baseline findings to alternative empirical models of disease transmission.

Additional controls. We first augment the baseline regression model with additional control variables at the prefecture level, namely, agricultural employment share, manufacturing employment share, share of population aged 60 or above, and the share of male. 11 We consider that these variables are exogenous to the changes in transportation networks and migration policies in the quantitative exercises. Empirically, the question is whether there is evidence in the data that these factors are correlated with the main variables in the baseline 11 These are aggregated variables based on the 1% Population Sampling Survey in 2015, which are assembled and published by the provincial statistics bureau. model, leading to biases in the estimates of β ιt . Figure E .2 reports the regression results.

For the main variables of interest, the baseline estimates (red diamond points) always lie within the 90% confidence intervals of the estimates obtained from the augmented model (blue circle points). For the additional controls, all estimated coefficients are statistically insignificant. In columns (4) and (5) of Table E .2, we conduct the counterfactual simulations using the estimates of the augmented model and obtain very similar results. We take these findings as suggestive evidence that our baseline results are unlikely to be severely biased due to omitted factors that may have independent effects on local transmission.

Negative binomial regression. We adopt the negative binomial model to estimate the relationships between the number of infections and the economic fundamentals. The estimate of β ιt are reported in Figure E .3. Except for the coefficients of ln(P op i ), the baseline Poisson MLE estimates are always within the 90% confidence intervals of the negative binomial estimates. We then employ the negative binomial estimates to conduct counterfactual simulations. Columns (6) and (7) in Table E Linear regression model with logarithm transformation. We also estimate the following linear model by the OLS regression ln(1+I i (t)) = β 0t +β 1t X i +β 2t M i +β 3t ln(Dist i )+β 4t ln(P op i )+β 5t ln(GDP pc i )+ε i (t). (E.1)

The consistency of OLS estimates does not depend on the assumption of the error distribution. Figure (8) and (9). 13 Compared to the baseline results, the linear specification with log transformation generates larger counterfactual changes in the earlier period. But the gap across different specifications diminishes over time.

Instrumentation strategy. One may concern that the travel distance to Hubei could be correlated with unobserved local socioeconomic factors that have independent effects on disease transmission. To address this potential problem, we follow Faber (2014) (12) and (13) repeat the exercise based on the linear IV model, and obtain similar results.

The stability of the estimated coefficients obtained from the IV regression in Figure   E .5 and the augmented model in E.2 suggests that, conditional on local income level and 13 Using the OLS estimates, the counterfactual number of cases is calculated according to I i (t) CF = 1 + I i (t) exp β 1t ∆X i +β 2τ ∆M i +β 3t ∆ ln(Dist i ) +β 4t ∆ ln(P op i ) +β 5t ∆ ln(GDP pc i ) − 1, population size, the travel distance with Hubei based on the pre-determined transportation networks could be exogenous to other unobserved determinants of local transmission. It is very challenging to find a valid instrument for GDP per capita. Therefore, the causal interpretation of the local income coefficient should be taken with caution. Although the potential confounding effects of the omitted variables are a priori ambiguous, we argue that they are unlikely to severely bias the quantitative results for the following reason. We find that the real income would have declined by 3.60% on average in the counterfactual scenario where the transportation networks and migration policy remained the same as in 2005. Based on the baseline estimate, this translates to a decline in the number of cases by 1.14% at the end of the sample period. This is gauged against the overall counterfactual change of 28.21% (column (3) of Table 2 ). Therefore, quantitatively, the baseline findings of the counterfactual experiments may not be too sensitive to the bias induced by the omitted variables that are correlated with local income, unless the bias is an order of magnitude larger than the baseline estimate. As is discussed above, the estimated coefficients of ln(GDP pc) remain stable at least to the additional controls such as local demographics and industry structure.

Additional robustness checks. In Figure E .7, we augment equation (1) with province × day fixed effects, which necessarily account for unobserved province-specific factors (e.g., local institutional quality, stringency of control measures) that may be correlated with the variables of interest and may have independent effects on the spread of the virus. Our baseline findings remain robust to this more stringent specification. To confirm that it is the migration flows specific to Hubei rather than migration flows per se that induced the propagation of COVID-19 in the early stages, we introduce additional controls of bilateral migrations with regions outside Hubei. The results are reported in Figure E 

Routes of Infection: Exports and HIV Incidence in Sub-Saharan Africa

Note: This table reports the actual spread of reported COVID-19 cases over time, and the spreads under the counterfactual scenario

The remaining columns repeat the counterfactual simulation, but replacê β ιt with the estimates from alternative regression models, namely: (i) the augmented model with additional controls in Figure E.2 (columns 4 and 5); (ii) the negative binomial model in Figure E.3 (columns 6 and 7); (iii) the linear model with dependent variable ln(1 + Case)

Credit Author Statement Li, Conceptualization; Methodology and formal analysis (empirical analysis); writing

Conceptualization; Methodology and formal analysis (quantitative model)