JUE insight: Migration, transportation infrastructure, and the spatial transmission of COVID-19 in China

Abstract

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.

1. Introduction

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 — February 22, 2020 — the number of infections outside Hubei province had reached 12,526. Part of the high transmissibility of COVID-19 is undeniably due to biological reasons (Petersen et al., 2020); nevertheless, it remains an open question as to what extent have socioeconomic factors, i.e., the unprecedented ease at which people travel and commute over long distances in China, contributed to the spread of the disease. Recognizing the links between connectivity and disease transmission broadens our understanding of the impacts of factor mobility, one of the central topics of interest in spatial economics. In this paper, we set out to answer this question.

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% 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, 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 COVID-19 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. Fig. 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.

Fig. 1.

Residual Scatter Plots. Note: The residual scatter plots are of the multivariate regression $\ln OutFlo{w}_i={\gamma }_0+{\gamma }_1\ln X_i+{\gamma }_2\ln M_i+{\gamma }_3\ln Dis{t}_i+{\nu }_i,$ where $\mathit{OutF}\mathit{lo}{w}_i$ denotes the share of population outflows from Wuhan to prefecture $i$ in the two weeks before the lockdown (January 9–22, 2020); $X_i$ denotes the ratio of emigrants to Hubei to the population in prefecture $i$ in 2015; $M_i$ is the share of immigrants from Hubei in the local population in prefecture $i$ in 2015; $Dis{t}_i$ measures the travel distance between prefecture $i$ and Hubei based on transportation networks in 2015. We discuss the data sources in Section 1. The green straight line is the best-fitted line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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 2005–15 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 transportation network reverted to the 2005 configuration, the travel distance with Hubei would increase by nearly 90% for the average prefecture, while the total population flow in and out of Hubei would decline by 14 percent. The reversion of the migration policy to the 2005 configuration would reduce the Hubei-related migration flow by 57%.

In the third and final step, we bring together the counterfactual changes in migration flows, population distribution, and income with the elasticities of incidence to these underlying variables, and simulate the counterfactual changes in the spread of COVID-19 outside Hubei. We find that the number of infections would have been lower by 15.31% by February 22, 2020, had there been no expansions in transportation networks between 2005 and 2015. The transportation infrastructure affects the spread of COVID-19 mainly by altering migration flows related to Hubei and short-term population movement; the quantitative effect of migration flows is around one-fourth that of short-term population movement. The counterfactual change in migration policies had a similar quantitative effect. On its own, the reversion of migration barriers to the 2005 configuration would have lowered the number of infections by 17.82%. If both transportation networks and migration policies had reverted to their 2005 configurations, the spread of COVID-19 would have been reduced by 28.21%. 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 3517 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, Arkolakis, 2014, Donaldson, Hornbeck, 2016, Donaldson, 2018, Allen, 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 measures in containing the spread (Jia, Lu, Yuan, Xu, Jia, Christakis, 2020, Kraemer, Yang, Gutierrez, Wu, Klein, Pigott, du Plessis, Faria, Li, Hanage, et al., 2020, Tian, Liu, Li, Wu, Chen, Kraemer, Li, Cai, Xu, Yang, 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, Parro, Rossi-Hansberg, Sarte, 2018, Caliendo, Dvorkin, Parro, 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.

2. Data

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.

Migration Flows 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.

Transportation Networks 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 4. 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.

3. Empirical framework and results

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 long-term 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:

$$\begin{array}{ccc}\hfill I_i\left(t\right)& =& \exp ({\beta }_{0t}+{\beta }_{1t}{X}_i+{\beta }_{2\tau }{M}_i+{\beta }_{3t}\ln \left(Dis{t}_i\right)\hfill \\ & & +{\beta }_{4t}\ln \left(Po{p}_i\right)+{\beta }_{5t}\ln \left(GDPp{c}_i\right)+{\nu }_i\left(t\right)),\hfill \end{array}$$ (1)

where $I_i\left(t\right)$ is the number of infections at time $t$; $X_i$ 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 $i$; $Dis{t}_i$ measures the travel distance between prefecture $i$ and Hubei based on transportation networks in 2015;4 and $Po{p}_i$ and $GDPp{c}_i$ represent population size and GDP per capita in 2015, respectively. Eq. (1) is estimated by a Poisson quasi-maximum likelihood count model (Wooldridge, 1999), with robust standard errors clustered by prefecture.

The time-varying coefficients ${\beta }_{\iota t}$ 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 ${\beta }_{\iota 0}$ 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, ${\beta }_{\iota t}-{\beta }_{\iota t-\delta },$ capture the effects of the underlying variables on the local transmission within an incubation period $[t-\delta ,t],$ which also reflects the effectiveness of the prevention and control policies. For example, when travelers from Hubei are subjected to quarantine orders, ${\beta }_{1t}-{\beta }_{1t-\delta }$ and ${\beta }_{2t}-{\beta }_{2t-\delta }$ are expected to be zero in the later periods.

3.1. Empirical results

Fig. 2 reports the point estimates of ${\beta }_{\iota t}$ and their 90% confidence intervals. Appendix E demonstrates that the baseline findings are robust to a variety of alternative specifications.

Fig. 2.

Estimates of Cumulative Effects: ${\beta }_{\iota t}$. Note: This figure plots the point estimates and the corresponding 90% confidence intervals of the ${\beta }_{\iota t}$ coefficients in Eq. (1).

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 the distance does not affect subsequent transmissions, consistent with the travel restrictions from and to Hubei. We observe a similar pattern for population size in Panel D. The lack of correlation between population size and the number of local transmissions indicates the effectiveness of a range of public health interventions aimed at minimizing interpersonal contact (Jia, Lu, Yuan, Xu, Jia, Christakis, 2020, Kraemer, Yang, Gutierrez, Wu, Klein, Pigott, du Plessis, Faria, Li, Hanage, et al., 2020, Tian, Liu, Li, Wu, Chen, Kraemer, Li, Cai, Xu, Yang, et al., 2020).

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 5, we take the estimates of the underlying parameters $\beta$’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.

4. The model

Our model is drawn from Ma and Tang (2020a), which extends Tombe and Zhu (2019) to allow for productivity agglomeration. The economy contains a mass $\overline{L}>0$ of individuals and $J$ cities indexed by $j=1,2,\dots ,J$. 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:

$$U_j={\left({\int }_0^1{\left(q_j\left(\omega \right)\right)}^{\frac{\eta -1}{\eta }}d\omega \right)}^{\frac{\eta }{\eta -1}},$$ (2)

where $\omega$ indexes the goods and $\eta$ 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 $\omega$. The production function for variety $\omega$ in city $j$ is:

$$q_j\left(\omega \right)=A_j·z_j\left(\omega \right)·{\ell }_j,$$

where ${\ell }_j$ is the labor input. $A_j$ is the city-specific productivity that depends on an exogenous component, ${\overline{A}}_j,$ and the population to allow for agglomeration:

$$A_j={\overline{A}}_j·{\left(L_j\right)}^{\beta },$$ (3)

where $\beta$ is the agglomeration elasticity. The city-variety specific productivity, $z_j\left(\omega \right),$ is from an i.i.d. Frechet distribution with parameter $\theta$:

$$F\left(z\right)=\exp [-{\left(z\right)}^{-\theta }].$$

Trade is subject to iceberg costs: for a unit of product to arrive in city $i$ from city $j,$ ${\tau }_{ij}>1$ 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 $\omega$:

$$p_i\left(\omega \right)=\underset{j=1,\cdots ,J}{\min }\left\{p_{\mathit{ij}}\left(\omega \right)\right\},$$

where $p_{ij}\left(\omega \right)$ is the price of $\omega$ from city $j$ at the market in city $i$.

4.1. Migration

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

$$V_j=\frac{w_j}{P_j},$$ (4)

where $w_j$ is the nominal wage and $P_j$ is the ideal price index in city $j$:

$$P_j={\left({\int }_0^1{\left(p_j\left(\omega \right)\right)}^{1-\eta }d\omega \right)}^{\frac{1}{1-\eta }}.$$

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

$$F\left(e_j\right)=\exp [-{\left(e_j\right)}^{-\kappa }],$$

where $\kappa$ is the shape parameter. Lastly, moving from $j$ to $i$ also incurs a pair-specific cost, ${\lambda }_{ij}\ge 1$ with ${\lambda }_{ii}=1$. 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:

$$\frac{V_i·e_i}{{\lambda }_{ij}}.$$

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:

$$\frac{V_i·e_i}{{\lambda }_{ij}}\ge \frac{V_k·e_k}{{\lambda }_{kj}},\forall k=1,2,\dots ,J.$$

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

$$m_{ij}=\frac{{\left(V_i\right)}^{\kappa }{\left({\lambda }_{ij}\right)}^{-\kappa }}{{\sum }_{m=1}^J{\left(V_m\right)}^{\kappa }{\left({\lambda }_{mj}\right)}^{-\kappa }}.$$ (5)

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:

$$L_{ij}={\left(V_i\right)}^{\kappa }{\left({\lambda }_{ij}\right)}^{-\kappa }{\left({\Pi }_j\right)}^{-\kappa }{\overline{L}}_j,$$ (6)

where ${\Pi }_j$ is the expected utility of a worker who lives initially in $j$:

$${\Pi }_j={\left[\sum _{m=1}^J{\left(V_m\right)}^{\kappa }{\left({\lambda }_{mj}\right)}^{-\kappa }\right]}^{\frac{1}{\kappa }}.$$

4.2. The equilibrium

Given the parameters of the model, the equilibrium is defined as a vector of prices $\{w_j,p_j\left(\omega \right)\},$ a vector of quantities $\left\{q_j\left(\omega \right)\right\},$ and a population distribution $\left\{L_j\right\}$ 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.

5. Quantification

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.

Table 1.

Calibration results.

(a) Fixed Parameters
Name	Value	Source	Note
$\beta$	0.1	Redding and Turner (2015)	The agglomeration elasticity
$\theta$	4.0	Simonovska and Waugh (2014)	Trade elasticity
$\kappa$	2.0	Hsieh and Moretti (2019)	Migration elasticity
$\eta$	6.0	Anderson and van Wincoop (2004)	Elasticity of substitution
${\overline{A}}_j$	-	Ma and Tang (2020b)	City-level productivity

(b) Calibrated Parameters
Name	2005	2015	Note
$\overline{\lambda }$	1415.24	645.24	Overall Migration Barrier
${\lambda }_{\text{IN}}$	7.77	4.41	Entry Barrier, Hubei
${\lambda }_{\text{OUT}}$	0.85	0.76	Exit Barrier, Hubei
$\overline{\tau }$	10.65	13.46	Overall Trade Barrier

Note: This table summarizes the calibrated model parameters. Panel (a) presents the parameters that come from the literature. Panels (b) presents the jointly calibrated parameters.

Common Parameters The following common parameters come from the literature. Following Redding and Turner (2015), we set the agglomeration elasticity, $\beta ,$ to 0.1. We set the elasticity of substitution to, $\eta =6,$ which is a value in the middle of plausible ranges.6 The trade elasticity is $\theta =4$ as in Simonovska and Waugh (2014). The elasticity of migration, $\kappa ,$ varies between 1.4 and 3.3 in the literature; we set $\kappa =2.0$ following Hsieh and Moretti (2019).7 Appendix E provides robustness checks and shows that the quantitative results are robust to the alternative parameter values.

Initial Population Distribution The initial population distribution comes from the Population Census in the year 2010. We use the total population, including the urban and rural populations in each prefecture, as the initial population.

Migration and Trade Costs We assume that the migration costs from $j$ to $i,$ denoted as ${\lambda }_{ij}$ takes the following functional form:

$${\lambda }_{ij}=\overline{\lambda }·{\lambda }_i·{\lambda }_j·{\left(T_{ij}^p\right)}^{\xi }.$$ (7)

Migration frictions depend on the national migration policy, $\overline{\lambda },$ and the location-specific entry and exit barriers, ${\lambda }_i$ and ${\lambda }_j$. Migration frictions are also related to the underlying passenger transportation networks between the cities, $T_{ij}^p,$ up to an elasticity of $\xi$. We first focus on the transportation network, ${\left(T_{ij}^p\right)}^{\xi }$.

We use the transportation network, $T_{ij}^p,$ in 2015 from Ma and Tang (2020a). The parameter $\xi$ governs the elasticity of ${\lambda }_{ij}$ with respect to the infrastructure, $T_{ij}^p$. We follow the same estimation methods in Ma and Tang (2020a), with the updated bilateral migration matrix in 2015. The migration flow in Eq. (6) can be transformed to:

$$\begin{array}{cc}\hfill \log \left(L_{ij}\right)& =\kappa \log \left(V_i\right)-\kappa \log \left({\Pi }_j\right)+\log \left({\overline{L}}_j\right)-\kappa \log \overline{\lambda }-\kappa \log {\lambda }_i\hfill \\ & -\kappa \log {\lambda }_j-\kappa \xi \log \left(T_{ij}^p\right).\hfill \end{array}$$

This equation leads to a reduced-form estimation with origin and destination fixed effects. The two fixed effects, ${\delta }_i$ and ${\delta }_j,$ absorb all the variables in the expression above except for the last term:

$$\log \left(L_{ij}\right)={\delta }_i+{\delta }_j-\kappa \xi \log \left(T_{ij}^p\right).$$

We estimate the equation using OLS, with the migration flow data from the 1% Population Sampling Survey in 2015. The regression estimates $\kappa \xi$ to be 0.40. With the calibrated $\kappa$ at 2.0, the estimated $\xi$ equals 0.20. We also estimate the equation with an instrumental variable for $T_{ij}^p$ 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 $\kappa \xi =0.42$ and with corresponding $\xi$ 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:

$${\tau }_{ij}=\overline{\tau }·{\left(T_{ij}^g\right)}^{\psi },$$

where $\overline{\tau }$ is the overall trade frictions, $T_{ij}^g$ is the underlying goods transportation network, and $\psi$ is the elasticity of the iceberg costs to $T_{ij}^g$. We take the values of ${\left(T_{ij}^g\right)}^{\psi }$ directly from Ma and Tang (2020a) and estimate $\overline{\tau }$ in our context.

City-Level Productivity,${\overline{A}}_j$ We follow the methods in Ma and Tang (2020b), which implements Donaldson and Hornbeck (2016) in the context of China to estimate the city-level productivity. The details are explained in Appendix D.

5.1. Joint calibration

The remaining four parameters call for joint-calibration: the overall migration and trade barriers, $\overline{\lambda }$ and $\overline{\tau },$ and the origin and destination-specific migration barriers, ${\lambda }_i$ and ${\lambda }_j$. 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 ${\lambda }_i$ and ${\lambda }_j$ on the prefectures within Hubei province, and assume that ${\lambda }_i={\lambda }_j=1.0$ for all the migration flows outside of Hubei. To simplify notation, we use ${\lambda }_{\text{IN}}$ to denote the common migration friction of moving into any prefecture in Hubei, and ${\lambda }_{\text{OUT}}$ 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, $\overline{\tau }$. The second moment is the overall stay-rate of 89%. 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 down $\overline{\lambda }$. The other two moments also come from the same survey: the outflow rate of all prefectures in Hubei province at 14.7%, and the inflow rate at 3.5%. 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, ${\lambda }_{\text{OUT}}$ and ${\lambda }_{\text{IN}},$ 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 $T_{ij}^p$ matrix. Appendix D discusses the out-of-sample model fit.

6. Quantitative results

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 $T_{ij}^p$ and $T_{ij}^g$ matrices, and the migration policies are summarized in the $\Lambda =\{\overline{\lambda },{\lambda }_{\text{IN}},{\lambda }_{\text{OUT}}\}$ 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 $T_{ij}^p$ and $T_{ij}^g$ matrices in 2005 from Ma and Tang (2020a) to calibrate the counterfactual. We also re-estimate the ${\overline{A}}_j$ 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, $\overline{\lambda },$ fell by 54%, while the Hubei-specific frictions fell by 11–43%. 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%, and it declined to 89% in 2015. Similarly, the outflow rate of Hubei province doubled from 7.4% o 14.7%, and the inflow rate more than quadrupled from 0.8% to 3.5%. 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).

6.1. Counterfactuals: migration flows, population, real income and welfare

In the rest of the section, we present three sets of counterfactual simulations. In the first “constant network” simulation, we use the $T_{ij}^p$ and $T_{ij}^g$ matrix in the year 2005 and keep all the other parameters the same as in the 2015 baseline. In the second counterfactual, “constant policy”, we use the $\Lambda$ vector in 2005. In the third simulation, “constant network and policy”, we revert $T_{ij}^p,$ $T_{ij}^g,$ and $\Lambda$ back to 2005. The counterfactual results, together with the baseline model, are presented in Table 2 . With the older transportation network, the total population flow in and out of Hubei province declines by 13%. The mild response of migration flow is expected because distance-related costs are a minor obstacle for migrants (Morten and Oliveira, 2016). The tightening of migration policies, on the other hand, induces a sharp decline in population flow. Reverting the policy vector to the year 2005 reduces the Hubei-related population flow by 57%. Lastly, combining both changes leads to a 63% reduction in population flow.

Table 2.

Counterfactual Experiments.

(a) Population Flow: Baseline v.s. Counterfactual Simulations (Thousands)
Case	Total Flow	Outflow	Inflow	Fraction of Baseline
	(1)	(2)	(3)	(4)
Baseline	10253.11	8247.61	2005.50	1.00
Constant Network	8971.20	7339.09	1632.11	0.87
Constant Policy	4359.36	3797.87	561.49	0.43
Constant Network & Policy	3779.17	3325.76	453.41	0.37

(b) Incidence of COVID-19 Outside Hubei: Actual v.s. Counterfactual Simulations
	Actual	Counterfactual
		All Factors		Migration Flows		Travel Distance		GDP and Pop
	Cases	Cases	Decline %	Cases	Decline %	Cases	Decline %	Cases	Decline %
Date	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Panel b.1: Constant Network (Transportation Networks Same as 2005)
28/Jan/2020	2349	1975	15.94	2267	3.47	2078	11.53	2311	1.64
02/Feb/2020	5873	4794	18.37	5656	3.69	5055	13.93	5777	1.63
07/Feb/2020	9368	7829	16.43	9024	3.67	8228	12.17	9245	1.31
12/Feb/2020	11,266	9468	15.96	10,863	3.58	9937	11.79	11,124	1.26
17/Feb/2020	12,068	10,263	14.95	11,637	3.57	10,767	10.78	11,921	1.22
22/Feb/2020	12,464	10,556	15.31	12,035	3.44	11,059	11.27	12,313	1.21
Panel b.2: Constant Policy (Migration Policies Same as 2005)
28/Jan/2020	2349	1953	16.85	1983	15.58	2349	0.00	2315	1.43
02/Feb/2020	5873	4748	19.15	4829	17.77	5873	0.00	5776	1.65
07/Feb/2020	9368	7564	19.25	7685	17.97	9368	0.00	9226	1.52
12/Feb/2020	11,266	9156	18.73	9297	17.47	11,266	0.00	11,101	1.47
17/Feb/2020	12,068	9817	18.65	9969	17.39	12,068	0.00	11,890	1.47
22/Feb/2020	12,464	10,243	17.82	10,397	16.59	12,464	0.00	12,285	1.44
Panel b.3: Constant Network & Policy
28/Jan/2020	2349	1695	27.83	1978	15.81	2078	11.53	2279	2.99
02/Feb/2020	5873	4005	31.81	4809	18.12	5055	13.93	5688	3.14
07/Feb/2020	9368	6532	30.28	7652	18.31	8228	12.17	9114	2.71
12/Feb/2020	11,266	7946	29.47	9261	17.79	9937	11.79	10,971	2.62
17/Feb/2020	12,068	8622	28.55	9931	17.71	10,767	10.78	11,757	2.58
22/Feb/2020	12,464	8947	28.21	10,359	16.89	11,059	11.27	12,148	2.54

Note: This table reports the results of three counterfactual experiments: “Constant Network” refers to the counterfactual using the $T_{ij}^p$ and $T_{ij}^g$ matrices in 2005; “Constant Policy” refers to the counterfactual using the $\Lambda$ parameters in 2005; “Constant Network & Policy” refers to the counterfactual using both the $T_{ij}^p$ and $T_{ij}^g$ matrices and the $\Lambda$ 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., $\ln \left(Dis{t}_i\right)$ in equation (1)); (iii) changes induced by counterfactual changes in population and GDP per capita (i.e., $\ln \left(Po{p}_i\right)$ and $\ln \left(GDPp{c}_i\right)$ in equation (1)).

When transport network and migration policies are altered, spatial distributions of population and income change as well. Figure A.4 in the appendix shows the distribution of changes in population and wage rates in different counterfactual scenarios. The induced change in welfare is significantly larger than that in real income. For example, the population-weighted average decline in real wage under the case of “constant network & policy” is 3.60%, while the decline in welfare is 7.41%.8

6.2. Counterfactuals: disease transmission

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

$$\begin{array}{ccc}\hfill I_i{\left(t\right)}^{CF}& =& I_i\left(t\right)\exp ({\widehat{\beta }}_{1t}\Delta X_i+{\widehat{\beta }}_{2\tau }\Delta M_i+{\widehat{\beta }}_{3t}\Delta \ln \left(Dis{t}_i\right)\hfill \\ & & +{\widehat{\beta }}_{4t}\Delta \ln \left(Po{p}_i\right)+{\widehat{\beta }}_{5t}\Delta \ln \left(GDPp{c}_i\right)),\hfill \end{array}$$

where $\Delta X_i=X_i^{CF}-X_i$ and $X_i^{CF}$ represents the counterfactual ratio of Hubei-bound emigrants to the local population in prefecture $i$. Other variables are defined analogously. ${\widehat{\beta }}_{\iota t}$’s are the estimates obtained from Section 2.1. The counterfactual total number of infections outside Hubei is computed as $I{\left(t\right)}^{CF}={\sum }_i{I}_i{\left(t\right)}^{CF}$.

Panel (b) in Table 2 presents the counterfactual trends of COVID-19 under the three scenarios discussed above and contrasts them with the actual data. For brevity, we focus on the actual and counterfactual spreads by February 22, 2020. We find that had the transportation networks been the same as in 2005, the total number of reported infections would have been lower by 1908, amounting to 15.31% of the total reported infections. In the counterfactual scenario where the migration policy remained the same as in 2005, the number of reported infections would have been lower by 2221, which is 17.82% of the total reported infections. Lastly, had both transportation networks and migration policies reverted to their 2005 configurations, the number of infections would have been lower by 3517, which is 28.21% of the total reported infections. Figure A.5 in the appendix presents the spatial distribution of the counterfactual declines in the number of infections across prefectures. We find that the spread could have been reduced more in the coastal areas and in the regions that are geographically closer to Hubei in the counterfactuals.

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 5.1 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 long-term migration patterns. Columns (8) and (9) reveal the roles of changes in income and population distributions induced by the changing transportation network. We find that such general equilibrium effects lower the reported number of COVID-19 cases by 1.21%. Panel (b.2) shows that the counterfactual changes in migration policies mainly affect the disease spread through changing migration flows, while the general equilibrium effects lead to a moderate reduction of 1.44%. Lastly, as shown in Panel (b.3), under the case of “constant network and policy”, the induced changes in migration flows, travel distance, and income and population reduce the reported number of infections by 16.89%, 11.27%, and 2.54%, respectively.

7. Conclusion

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 development in transportation infrastructure and the liberalization of migration restrictions in the recent decade using a general equilibrium spatial model. We show that the increased mobility of people following the expansion of transportation networks and easing migration policies explain around 28% of the infections outside Hubei province. The strong link between disease transmission, migration policy, and transportation networks documented in this paper highlights the need to incorporate epidemiological elements in the models of the spatial economy in future research.

CRediT authorship contribution statement

Bingjing Li: Conceptualization, Methodology, Formal analysis, Writing - original draft. Lin Ma: Conceptualization, Methodology, Formal analysis, Writing - original draft.

Appendix A. Supplementary materials

Supplementary Data S1

The replication package can be downloaded at http://dx.doi.org/10.17632/tdy2dkyrbv.1. Supplementary Raw Research Data. This is open data under the CC BY license http://creativecommons.org/licenses/by/4.0/