Cities in a pandemic: Evidence from China

Abstract This paper studies the impact of urban density, city government efficiency, and medical resources on COVID‐19 infection and death outcomes in China. We adopt a simultaneous spatial dynamic panel data model to account for (i) the simultaneity of infection and death outcomes, (ii) the spatial pattern of the transmission, (iii) the intertemporal dynamics of the disease, and (iv) the unobserved city‐specific and time‐specific effects. We find that, while population density increases the level of infections, government efficiency significantly mitigates the negative impact of urban density. We also find that the availability of medical resources improves public health outcomes conditional on lagged infections. Moreover, there exists significant heterogeneity at different phases of the epidemiological cycle.

In this paper, we study the roles of city density, city government efficiency, and medical resources in the context of early COVID-19 transmissions in China. The analysis draws on panel data of infections and subsequent deaths in 330 cities in China. The sample spans the period of the first epidemiological cycle between January 20, 2020, and March 31, 2020. We adopt a spatial dynamic panel data model to account for the nature of the spatial transmission and intertemporal dynamics of the disease. We also account for correlations between infections and deaths by estimating a simultaneous spatial dynamic panel data model. By interacting lagged prevalence of the disease with time-invariant city characteristics, we uncover the role of city-specific features in altering the transmission speed at different phases of the epidemiological cycle. We find a large and significant role of urban density in contributing to high infections, especially at the early stage of the transmission cycle. We also document an important counteracting role of government efficiency and medical resources in reducing infections and mortality.
The findings in this paper contribute to the understanding of the "demons of density" manifested through issues related to public health (Glaeser, 2011). Urban economists have long been concerned with the easy spread of contagious diseases in cities as a type of urban cost. In the past, Plague, Cholera, and AIDS have caused several serious episodes of epidemics that affected urban areas more than rural areas. With the development of new technology and improved livelihood infrastructure, the urban population now in general enjoys higher life expectancy than their rural counterparts. 1 However, these technologies do not immune cities from new outbreaks and the spread of new contagious air-borne diseases. Despite the intuition on the role of urban density in the transmission of these diseases, we lack rigorous evidence on the magnitude to which density and urbanization cause severe disease outbreaks and direct economic losses. This article contributes to this literature.
It is equally important to study the role of city government capacity and efficiency in fighting against the pandemic. A similar but broader notion of state capacity has been well recognized in the literature, especially in its role in driving nationwide economic prosperity (Acemoglu et al., 2015(Acemoglu et al., , 2016. How government capacity matters for cities, in particular, becomes critical, especially in a state of declared disaster with massive negative externalities, such as a pandemic. 2 How quickly public health measures are taken, how fast COVID-19 testing is adopted, how well contact tracing is administered, and how efficiently medical resources and vaccinations are deployed all matter critically in deterring rapid virus transmissions and reducing death tolls. 3 The effective enforcement of these control measures depends on government efficiency, which echoes the notion of state capacity in the economics literature and the call for "a strong state" in combating the crisis in media coverage. 4 We demonstrate that there are significantly fewer COVID-19 cases in cities with more effective governments, which highlights the importance of city government capacity in combating the epidemic. We also study the role of medical resources to provide a fuller picture of cities fighting against the pandemic. It is widely documented that medical resources are highly concentrated in large cities (Li, 2014). The availability of medical services allows sick patients to receive necessary medical treatment and improves their chances of survival.
In other words, although city density imposes a high risk of infection due to intimate social contact and interactions, abundant medical resources available in large cities help mitigate the cost of infection by improving the chance of survival. This aspect is also crucial in assessing the net cost of urban density amid the global pandemic. 1 Improved water sanitation systems in cities are believed to be a key factor in improving urban health (Ashraf et al., 2016;Cutler & Miller, 2005); Troesken, 2002. 2 All 50 states in the United States were under a major disaster declaration by April 13, 2020 due to the failure in containing early-stage  transmissions. 3 For instance, Lee and Lee (2021) and Argente et al. (2022) demonstrate that effective public disclosure of COVID-19 cases' residences and their mobility paths dramatically affects location-specific mobility patterns and the subsequent infection and death outcomes. We consider this as one of the channels through which government efficiency impacts public health outcomes. 4 Studying these issues in the context of early COVID-19 transmissions in China yields several advantages for our empirical design. First, China completed the full cycle of its first-round anti-corona virus campaign during our sample period. Since the middle of March 2020, daily new cases in China have been reduced to near-zero levels.
The completion of a cycle allows us to trace the full dynamics of the outbreak. Second, the early stage of the COVID-19 is associated with a high death rate with no effective vaccination and treatment. This feature led to a strong emphasis on curbing disease transmissions. In addition, China's pandemic management follows a top-down approach in which the central government declares the zero-COVID policy and local government must treat the policy as a primary political task and a top objective of the country. Such a political regime, combined with the nature of the early phase of the COVID-19, ensures the homogeneity in local government objectives and leaves the efficiency of management a key political factor driving the variation in the anti-corona virus campaign. 5 Third, China imposed a lockdown on Wuhan on January 23, 2020, to quarantine the epicenter of COVID-19. The lockdown effectively reduced infection cases outside Wuhan and allowed for local government measures to take effect (Fang et al., 2020).
We adopt a simultaneous spatial dynamic panel data model to account for various features associated with disease transmissions. The simultaneous structure of the infection and death equations allows us to model the death tolls conditional on lagged infections and address potential correlations in the corresponding error terms to achieve estimation efficiency. We also include a spatial autoregressive term to account for the cross-city transmission of the disease in our model. The spatial weight matrix is specified in various ways to capture the varying natures of cross-sectional dependence and to ensure the robustness of our estimates. The dynamic structure of the model further captures the intertemporal dynamics of the virus transmission.
Despite the richness of the model, the system of equations suffers from three sources of endogeneity. First, there may exist city-specific or time-specific unobserved characteristics that are correlated with our key regressors.
Second, the presence of time-dynamic effects may induce endogeneity if the unobserved city-specific effects exist (random or fixed), see Baltagi (2021). Third, a reflection problem arises from the contemporaneous spatial lag effect.
To address the first endogeneity concern, we take advantage of the panel structure and control for two-way fixed effects which account for unobserved city-specific and time-specific characteristics. The second and third endogeneity concerns are addressed via an instrumental variables approach. The instruments for the time-lagged dependent variables are obtained within the system as explained in Section 3 in detail. In brief, we adopt a forward orthogonal deviations (FODs) transformation which conveniently leaves out the past values of the dependent variable as ideal sources of exogeneity in constructing instruments. 6 Meanwhile, the exogenous time-lagged dependent variables also serve as the source of exogeneity in constructing instruments for the contemporaneous spatial lag effect.
We obtain three main findings. First, we find strong correlations in the error terms of both infection and death equations, especially for the prepeak period. The presence of correlations between infections and deaths calls for the estimation of a system of two equations to improve efficiency. Second, we document strong spatial dependence in the prevalence of COVID-19 infections. Direct and indirect effects are similarly strong in magnitude for the prepeak period, but the direct effect dominates in the postpeak period. The evidence demonstrates the importance of cross-city collaboration in fighting against the pandemic, especially in the early phase of transmission.
Third, we find that population density plays an important role in contributing to the level of new infections, but government efficiency significantly reduces the number of new infections. Both effects are strikingly more pronounced during the prepeak period. We also find that the availability of medical resources improves public health outcomes conditional on lagged infection cases. This effect is slightly increased for the postpeak period, 5 This feature allows us to identify the impact of government efficiency from various confounding factors related to ideology and formal or informal institutions, such as laws, forms of organization, social norms, trust in political institutions, and so forth, that impact human behaviors during a pandemic (Bottasso et  | 3 compared to the prepeak period, showing improvement in medical effectiveness over time. The key findings are robust to a variety of specification checks that we perform in the paper.
The remainder of the paper is organized as follows. In Section 2, we discuss burgeoning literature linking city characteristics and other factors to within-city COVID-19 prevalence and cross-city virus transmission. Section 3 lays out our conceptual framework and empirical methodology. Section 4 presents data and variables. Section 5 shows the empirical results and robustness checks. Section 6 concludes.

| LITERATURE
There is an emerging literature studying the relationship between population density and the prevalence of COVID-19 or pandemics in general. Wheaton and Kinsella Thompson (2020a) study 372 CBSAs and 628 counties in the United States and find a significantly positive correlation between population density and the incidence of the disease. Wheaton and Kinsella Thompson (2020b) further explore more-refined data at the level of municipalities and towns in Massachusetts, and document that greater density is associated with a significantly higher per capita incidence of the disease. Almagro and Orane-Hutchinson (2020) also find a positive relationship between population density and confirmed cases across New York City zip code areas and Desmet and Wacziarg (2020) show similar patterns across US counties. Carozzi et al. (2020) use instrumental variables based on historical information to address the potential endogeneity of urban density and obtain similar patterns. 7 Overall, the evidence seems to suggest that high population density in urban areas impose inherent public health risks during a pandemic. Does this mean that cities unavoidably suffer from the spread of contagious diseases and there is no cure? To answer this question, we seek to understand the role of various other city-specific features that are either exogenously shaped or endogenously determined in general equilibrium but before the threat of a global pandemic. As the current pandemic is unprecedented in recent history and is unforeseen, we argue that other city-specific features that we observed before the pandemic are not developed in response to the potential threat of a large-scale spread of a contagious disease. Hence, the nature and the scale of the current pandemic allow us to causally evaluate the impact of various city-specific characteristics on the ongoing coronavirus spread.
Several papers study the severity of COVID-19 in relation to other aspects of cities. For example, Wheaton and Kinsella Thompson (2020a) show that the share of land use in commercial-industrial categories is positively associated with high infection rates. Almagro and Orane-Hutchinson (2020) look into the roles of city demographics, such as race, income, and occupation. Desmet and Wacziarg (2020) examine the link between the severity of the outbreak and the roles of public transportation and political preference. Adda (2016) shows that the expansion of transportation networks increases the spread of the virus and has significant health costs. Glaeser et al. (2020) highlight the importance of urban mobility in the spread of COVID-19. 8 Xie et al. (2021) document a negative relationship between the availability of public health resources and the mortality rate of the disease. In sum, the direct impact of urban density could be either aggravated or mitigated by other important city-specific features.
Besides focusing on city-specific features in driving the spread of COVID-19 within a city, existing studies also highlight the importance of cross-city contagion and its contributing factors. Li and Ma (2020) use a spatial general equilibrium model to evaluate the impacts of migration flows and transportation infrastructure on the cross-city 7 Qiu et al. (2020) control for population density in explaining cross-city transmissions of COVID-19 in China. They instrument lagged infections with weather conditions and document a negative and close to zero effect of population density. Li and Ma (2020) also document a lack of correlation between population size and the number of local transmissions. However, both findings could be confounded by the omitted role of government efficiency emphasized in our paper. This point is also highlighted on Page 4 of Li and Ma (2020) that "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." 8 Linking cell phone data to COVID-19 cases per capita and applying an instrumental variable approach, the paper documents a 20% decrease of total COVID-19 cases for every 10-percentage point fall in mobility.
transmission of COVID-19 in China. Kuchler et al. (2021) use aggregate data from Facebook to show that COVID-19 is more likely to spread between regions with stronger social network connections. Mangrum and Niekamp (2020) suggest that college student travel also contributed to the cross-city COVID-19 spread. It is, therefore, important to model cross-city transmissions when explaining the variation in the severity of city-specific outbreaks.
Recognizing the association between social mobility and the spatial spread of the disease both within and between cities, the literature on COVID-19 also evaluates the effectiveness of the policies imposing mobility and travel restrictions. For example, Greenstone and Nigam (2020), Dave et al. (2020), and Maloney and Taskin (2020) highlight the importance of social distancing. Brzezinski et al. (2020) evaluate the impact of government-ordered lockdowns. Chinazzi et al. (2020aChinazzi et al. ( , 2020b use a global metapopulation disease transmission model to show that the travel quarantine of Wuhan had a marked effect on virus transmission on an international scale. Fang et al. (2020) employ a difference-in-differences strategy to show that the lockdown of Wuhan contributes significantly to reducing the total infection cases outside of Wuhan.
Our paper contributes to the literature by highlighting the role of a previously overlooked fundamental institutional force that governs the effectiveness of implementing relevant policies in combating COVID-19. We document the role of government efficiency in counteracting the negative impact of urban density on COVID-19 prevalence in China. The focus differs from Narita and Sudo (2021) that highlight the role of different political regimes. The paper also highlights the cross-city contagion of infections at different phases of the epidemiological cycle which provides empirical justification for a broad theoretical literature modeling the spatial diffusion of COVID-19 across countries or locations, see Antras et al. (2020), Bisin and Moro (2020), and Cunat and Zymek (2020).

| METHODOLOGY
Given the nature of the pandemic, we follow a spatial dynamic econometric modeling approach to model cross-city variation in infection and death outcomes in simultaneous equations setting while controlling for potential spatial interactions and cross-sectional dependence. 9 The model is specified as follows:

∑
where subscript i n = 1, 2, …, represents the city and subscript t T = 1, 2, …, represents the time. We simplify notation in Equations (3.1) and (3.2) by stacking observations over the city index, i, for each time period, t, and consider the following vector form for t T = 1, 2, …, , are time-invariant n × 1 vectors that represent city population density, government efficiency, and available medical resources; ⊙ represents the Hadamard product (also known as the element wise product); α α α = ( , …, )′ n 1 1 1 1 and α α α = ( , …, )′ n 2 2 1 2 are n × 1 vectors of city fixed effects; W is a row-normalized n n × spatial weight matrix with the i j ( , )th element represented by w ij . λ t 1 and λ t 2 are the time fixed effects with l n being an n × 1 vector of ones; u u u = ( , …, )′ t t n t 1 1 , 1 1 , and u u u = ( , …, )′ t t n t 2 2 , 1 2 , are the n × 1 vectors of remainder error terms.
The spatial structure is defined as follows. We start by capturing the spatial relationship based on the travel intensity between two cities. In the baseline specification, the pairwise travel intensity between two cities is calculated as the average travel intensity 2 weeks before the start of the sample. This is before the date when a top Chinese medical expert, Dr. Zhong Nanshan, announced on state television that the virus is transmissible between people and, hence, captures the original mobility linkages between cities unaffected by potential fear to travel. As the spatial transmission of the disease is directly affected by mobility, the travel intensity before the Wuhan lockdown serves as an exogenous but relevant measure to capture inherent spatial interactions between cities. In this case, a typical element w ij of W is defined as the proportion of inbound travels into city i that come from city j. 10 Next, we specify the error structure in the model. Note that u t 1 is the error term for the infection equation and u t 2 is that for the death equation. Their elements, u u ( , ) it it 1, 2, , are allowed to be correlated within each pair (simultaneity) and are assumed to be independent and identically distributed iid ( ) across all pairs. Specifically, with σ 1 2 and σ 2 2 being the variances of u it 1, and u it 2, , and ρ being the correlation coefficient between u it 1, and u it 2, . While it is important to have the three effects (unobserved city and time heterogeneity, spatial interaction, and time dynamics) under control when studying the factors impacting the infection and death outcomes, these three effects are also the sources of endogeneity, making the model estimation and inference difficult. First, the unobserved city-specific or time-specific effects may be correlated with the key regressors arbitrarily. Hence, they must be treated as fixed parameters (or fixed effects). Joint estimation of these fixed effects together with the model's common parameters makes the estimates of (some) common parameters inconsistent or asymptotically biased, giving rise to the incidental parameters problem of Neyman and Scott (1948). The standard way of handling the fixed effects is to transform the model to wipe out these effects and then run an ordinary least squares (OLS) on the transformed model. This method produces consistent estimates for regression coefficients for panel data models with strictly exogenous regressors but not for models with weakly exogenous or endogenous regressors.
Second, the presence of time-lagged terms in addition to the city-specific effects introduces weak exogeneity (with respect to idiosyncratic errors) and endogeneity (with respect to the city-specific effects). This makes the standard panel estimation methods invalid whether the city-specific effects are treated as random or fixed effects. 11 To see this, consider the OLS estimation when city-specific effects are treated as random effects. The compound error term α u + i i t 1 1 , is correlated with the lagged dependent variable Infection i t , −1 since Infection i t , −1 also contains city-specific effects α i 1 . This renders the OLS estimator inconsistent. When the within estimator is applied, the within transformation is employed to eliminate city fixed effects and then an OLS regression is run on the transformed model. The within transformation, however, introduces correlations between the demeaned lag 1, , leading to the inconsistency of the within estimator, which is the well-known Nickell (1981) bias. 10 We experiment with alternative ways of defining the spatial weight matrix in our robustness checks. 11 The presence of time-lagged term and its interaction with time-invariant variables rule out the use of (quasi) likelihood type approach due to the unavailability of a proper likelihood function. 6 | Third, the inclusion of the contemporaneous spatial lag effect as a regressor induces endogeneity. That is, for city i, its neighbor's (say, city j s ′ ) infection outcome, Infection jt , is adversely affected by city i s ′ outcome, is correlated with the error term u , it 1, causing standard panel estimation methods to be invalid.
From the above, one sees that the three types of endogeneity problems are not isolated and must be dealt with collectively. We rely on an instrumental variable approach following an FOD (forward orthogonal deviation) transformation. In particular, we obtain instruments that are based on exogenous regressors in previous periods through an FOD transformation as opposed to a within transformation to eliminate the city fixed effects. The difference between an FOD transformation and a within transformation is that the FOD transformation subtracts the mean of future values only, leaving out the current and past values, in computing the mean. This convenient feature provides an opportunity for the lagged values of the dependent variable to be used as instruments for the time-dynamic terms (Lee & Yu, 2014).
The FOD transformation of a variable, say Infection t , is defined simply as follows: The transformed errors are thus for r = 1, 2. Death* t is defined similarly. Due to the time-invariant nature of the variables Density, Efficiency, and Beds, the transformed interaction terms are The advantages of the FOD transformation are seen immediately. First, it wipes out the unobserved city-specific effects and automatically adjusts the loss of degrees of freedom (the effective sample size is now n T ( − 1)). 13 Second, the transformed error pairs ( ) remain independent across i and uncorrelated over t with the same mean and variance as the original error pairs (as seen below). 14 Third, Infection t−1 is correlated with Infection* t−1 , but uncorrelated with u* t 1 , implying that Infection t−1 is a valid instrument for Infection* t−1 . 15 Interestingly, the FOD transformation is related to the within transformation and is a special case of the general , and the general orthonormal transformed variables are obtained 12 The FOD transformation is often referred to as Helmert's transformation in the literature. See for details Arellano and Bover (1995, p. 41), and Cameron and Trivedi (2005, p. 759). 13 The first difference (FD) transformation shares the same property, but the within transformation does not. The time-specific effects can be removed by another transformation but given the fact that our time dimension is not big and that the analyses are done separately before and after the peak of the pandemic, we simply control the time effects by adding the time dummies in the model. 14 Under both FD and within transformations, the transformed error pairs remain independent across i but become correlated over t. 15 The FD transformation can achieve the same goal as does the FOD transformation as far as finding instruments is concerned. Intuitively, FOD may perform better than FD as, for example, Infectiont−1 may be "stronger" when instrumenting for Infection* t−1 than for △Infectiont as in the former Infectiont−1 is the main term but in the latter the two terms have equal weights. Indeed, Hayakawa (2009)  T TT 1 2 , −1 . The former is n T × and the latter is n T × ( − 1). If we write is a special choice of F T T , −1 . An important property of the eigenvectors is that they are orthonormal, that is, In this new system of equations, the city fixed effects α 1 and α 2 are eliminated. The time fixed effects λ* t 1 and λ* t 2 are captured by time dummies. Because u* t and Infection* t−1 involves 1 , Infection* t−1 and u* t 1 are correlated. More generally, all the right-hand-side regressors of Equation (3.6) are correlated with their own error term u* t 1 . If u* t 1 and u* t 2 are correlated, the right-hand-side regressors of Equation (3.7) are correlated with the error term u* t 2 as well. This renders the OLS estimator biased and inconsistent.
Conveniently, the endogeneity in the transformed system of equations can be addressed by obtaining instruments within the system. The idea is that the original lagged outcome variables are not correlated with the transformed error terms but predict our key regressors. Therefore, they serve as ideal exogenous sources to help construct instruments. For example, we use Infection t−1 as an instrument for The proposed instruments are also relevant when it comes to addressing the endogeneity problem arising from the contemporaneous spatial effect. The conventional instruments for the spatial lagged dependent variable are the spatial lags of the exogenous regressors. According to Kelejian and Prucha (1998), the ideal instrument for We undertake a three-stage least squares (3SLS) approach suggested by Yang and Lee (2019) to estimate Equations (3.6) and (3.7). In the first stage, we regress each endogenous variable on all the proposed instruments to obtain its fitted value. In the second stage, we run an OLS with all the endogenous variables replaced by their fitted values from the first stage and generate 2SLS residuals. In the third stage, we run a GLS based on the variance-covariance matrix of the error terms estimated based on the 2SLS residuals to obtain 3SLS estimates for Equations (3.6) and (3.7).

| DATA AND VARIABLES
We rely on a variety of data sources for our analysis. We first obtain daily city-level COVID-19 transmission records from the National Health Commission of China. The data cover 330 cities within mainland China for the period between January 20 and March 31, 2020. across all cities which exhibit a similar pattern. Panel C displays average infections for each city throughout the sample period, where the darker colors denote cities with higher levels of infections and lighter colors denote cities with lower levels of infections. Significant spatial correlations presented in the map justify our approach of incorporating spatial dependence in the model. 18 We obtain city-specific measures of population density and government efficiency from the 2019 Global Urban Competitiveness Yearbook. The extent of city agglomeration is measured by the population density in our baseline estimation. We further take into consideration both city area size and population density in various robustness checks to reflect agglomeration effects manifested through both the extensive margin and the intensive margin (Combes & Gobillon, 2015). 19 Government efficiency measure is based on comprehensive survey questions and reflects the city's management capacity to utilize limited resources to generate wealth. We also obtain city-specific measures of gross domestic product (GDP), income per capita, employment, transportation infrastructure, and human capital from this yearbook to support a set of robustness checks. 20 The third data source is the 2019 Statistical Yearbook of China from which we collect the number of hospital beds per 1000 people as a proxy for city-specific medical resources in our baseline specification. As a robustness check, we also use the number of medical staff from the same data as an alternative proxy.
Summary statistics are given in Table A1. Figure 2 plots the correlation between city population and the three key measures used in our empirical analysis: population density, government efficiency, and the amount of medical resources. Cities with a larger population size are associated with higher population density, higher city efficiency, and more abundant medical resources. Figure 3 reports the kernel density estimates for city characteristics.
The last data set contains information on the intensity of travel between city pairs which is provided by Baidu (https://qianxi.baidu.com). This information allows us to construct two versions of the spatial weight matrix, one of which is used in our baseline specification and the other in robustness checks. 21 Although the data set provides time variation in travel flows between city pairs, we do not explore this time variation in capturing the extent of cross-city contagion as timely travel flows are adversely affected by the infection and death outcomes. Instead, we collapse the pairwise inflow travel intensity for 2 weeks either before the sample starts (baseline) or at the beginning of the sample (robustness check) and use this cross-sectional variation to construct the spatial weight matrix. Compared to the classic spatial weight matrix computed based on either spatial contiguity or geographic distance, the travel information is more economically relevant. 17 Manski and Molinari (2020) note that the infection rate might be substantially higher than reported based on data from Illinois state and New York state in the United States and Italy. 18 We remove Wuhan, the epicenter of the COVID-19 outbreak, in our regression sample to avoid issues related to extreme centrality and measurement errors. In the setting of SAR models with social interactions, the unit associated with an extremely high Bonacich (1987) measure may dominate in its own spatial effect on neighbors but is less subject to the feedback spatial effect (Liu and Lee, 2010). Moreover, Wuhan followed especially stringent lockdown orders and received a vast amount of centrally deplored resources in fighting against the virus transmission. Those aspects are not accurately and consistently measured in our data. To avoid potential estimation bias, we incorporate Wuhan's spatial effect on its neighbors when constructing the spatial weight matrices but remove Wuhan from the final regression sample when estimating the spatial effect in equilibrium. 19 In the extensive literature assessing the benefits and costs of city agglomeration, employment is generally preferred to population in measuring the city scale as it better reflects the magnitude of local economic activities. In our context, population measure is more appropriate because our sample period covers the Chinese Spring Festival when the majority of migrant workers travel back home to celebrate the festive season. 20 The appendix of this paper provides detailed explanations on the construction of city-level indexes to measure various aspects of cities' competitiveness. One caveat is that the government efficiency measure based on the information before COVID-19 may not reflect the true government efficiency during COVID-19. If such measurement error occurs randomly, we suffer from the standard attenuation bias. In such a scenario, we claim that the estimated impact of government efficiency on infection and death outcomes is understated. However, such measurement errors may not be random.
A likely scenario is that cities short of effective management in combating the pandemic suddenly receive additional central government support/ resources and experience an increase in their effectiveness in coping with COVID-19. This scenario again would lead to a downward bias in the magnitude of the estimated coefficients. 21 One caveat of this data is that only the shares of the top 100 destinations are reported. However, this amounts to about 95% of the total travel intensity.
(3)  Note: Columns (1)-(4) are coefficients for single equations and a system of equations before the peak. Columns (5)-(8) are coefficients for single equations and a system of equations after the peak. We control for city and time fixed effects.

BALTAGI ET AL.
| 13 correlation is expected due to the simultaneity of infections and deaths. However, the correlation between infections and deaths in the postpeak period is small. It is possible that, during the postpeak period, public health measures and medical treatments are more standardized across cities in reducing social contacts and treating the infected. Hence, the time-lagged infections and city-specific controls that we include in the death equation explain a larger variation in the data for the postpeak period than the prepeak period, leaving a small residual correlation in the errors.
Second, both the spatial and the temporal dynamic effects are strong and statistically significant. The significant spatial effect is consistent with prevalent cross-city transmissions. It highlights the importance of incorporating city-to-city spatial dependence in modeling infections. This effect is stronger in the prepeak period than in the postpeak period, suggesting that necessary measures to prevent cross-city transmission in the early phase of The findings that the urban density and government efficiency present opposite impacts with similar magnitudes help to reconcile the findings in the literature on the small and insignificant impact of city size and population density (Li & Ma, 2020;Qiu et al., 2020). Given that there exists a high correlation between urban density and government efficiency, as highlighted in Figure 2, failing to control for government efficiency may lead to a small and insignificant impact of urban density on infection and death outcomes. In other words, large cities did not experience widespread outbreaks in the early phase of the pandemic in China because their highly efficient government management mitigates the potential high transmission risk induced by high population density.
As to the determinants of death counts, we find that previous infections significantly contribute to the current death. In addition, the availability of medical resources reduces the number of deaths, holding previous infections fixed. The impact of medical resources is slightly stronger for the postpeak period than the prepeak period, suggesting an improvement in the effectiveness of medical interventions over time.
(3)  Note: Columns (1) and (2) are marginal effects for the regression of column (1) in Table 1. Columns (3) and (4) are marginal effects for the regression of column (3) in Table 1. Columns (5) and (6) are marginal effects for the regression of column (5) in Table 1. Columns (7) and (8) are marginal effects for the regression of column (7) in Table 1. We control for city and time fixed effects. ρ represents cross-equation correlations between u 1,it and u 2,it . *p < 0.10, **p < 0.05, and ***p < 0.01. t We calculate and report the marginal effects separately for the direct effects and the indirect effects in Table 2.
Columns (1)-(4) show the marginals for the prepeak estimates and Columns (5)-(8) report the marginals for the postpeak estimates. Patterns are similar to Table 1 but there exist varying degrees of the effect coming through either the direct channel or the indirect channel. For the prepeak period, a larger impact is driven by the direct channel, but the indirect channel is also quantitatively important. For the postpeak period, the majority of the impact is coming through the direct channel and the indirect channel is quantitatively small despite its significance.
The strong indirect spatial channel reflects the importance of intercity collaboration in curbing the virus transmission, especially in the early phase of the outbreak.
Controlling for lagged infections, the estimated marginal effects in Columns (3) and (4) demonstrate the extent to which population density and government efficiency affect the city-specific infection outcomes in a dynamic structure. Specifically, in the prepeak period and conditional on lagged infections, a city with population density in the 75th percentile has 29% more infections through the direct channel and 20% more infections through the indirect channel, compared to a city with population density in the 25th percentile. 23 In the prepeak period and conditional on lagged infections, a city with government efficiency in the 75th percentile has 27% fewer new infection cases through the direct channel and 18% fewer new infection cases through the indirect channel, compared to a city with government efficiency in the 25th percentile. 24 Evidence suggests that the impact of government efficiency is strong enough to almost mitigate all potential negative impacts of urban density. We also find that both effects become smaller in magnitude but quantitatively important for the postpeak period.
In Table 3, we report the average effect throughout the full cycle. We report the estimated coefficients in Columns (1)-(4) and the marginal effects on infections in Columns (5)-(8). Taken together, we find that the urban density positively increases the current infections, and that government efficiency decreases the incidence of infections. The majority of the impact takes place through the direct channel, but the indirect channel is also quantitatively important and significant. We also find a similar impact of medical resources in reducing the number of deaths, conditional on previous infections.

| Robustness checks
We embark on a collection of additional empirical exercises to check for robustness of our estimates to alternative spatial weight matrices, alternative specifications for the infection and death equations, including lagged spatial effect, an alternative proxy for medical resources, and death count dynamics, additional controls for efficiency, medical resources and economic development, alternative approaches to account for connectivity of the epicenter, additional controls for the role of the city area size as well as the role of other city characteristics. 23 The city with a population density measured at the 25th percentile is Liaoyuan in Jilin province, and the corresponding density index is 0.2346. The city with a population density measure at the 75th percentile is Guiyang in Guizhou province, and the corresponding density index is 0.3464. On the basis of the estimated marginal effect of 2.6103 in Column (3) of Table 2 Note: Columns (1) and (2) are coefficients for single equations of Infections and Deaths. Columns (3) and (4) are coefficients for a system of equations. Columns (5) and (6) are marginal effects for regression in column (1). Columns (7) and (8) Table 4 reports the estimated coefficients for three alternative spatial weight matrices. The first spatial weight matrix is an alternative weight matrix based on the travel intensity averaged across the first 2 weeks at the beginning of the sample period. Two other spatial weight matrices are based on contiguity and geographic distance.
For the contiguity-based spatial weight matrix, the element w ij of W takes value 1 if cities i and j share the same border and 0 otherwise. As cities are not considered as neighbors to themselves, the diagonal elements w ii are set equal to 0 for i n = 1,2, …, . Then, we row-normalize all elements to obtain the spatial weight matrix, W. For the distance-based spatial weight matrix, we take the inverse distance as the element before row-normalizing the elements. Given the setup, the spatial lag of the dependent variable WInfections t captures a weighted average of infections in the neighboring cities and the ith element of WInfections t is expressed as Infections jt represents the number of new cases in city j at time t.
The estimated coefficients are largely consistent across different spatial weight matrix specifications, with albeit small differences. The first noticeable difference is that the spatial effects are most pronounced when we use the inverse distance-based spatial weight matrix. This is largely driven by the fact that the inverse distancebased spatial weight matrix is less sparse and allows for more, albeit heavily diluted, interactions between cities. The second noticeable difference is that the spatial effect is the smallest, but the impact of government  (1) and (2) are coefficients for a system of equations based on an alternative travel intensity weighted spatial weight matrix. Columns (3) and (4) are coefficients for a system of equations based on the contiguity spatial weight matrix.

T A B L E 4 Impact of city characteristics on number of infections and deaths based on different weight matrices
Columns (5) and (6) are coefficients for a system of equations based on distance weighted spatial weight matrix. We control for city and time fixed effects. ρ represents cross-equation correlations between u 1,it and u 2,it . *p < 0.10, **p < 0.05, and ***p < 0.01. t stats are reported in parentheses.
efficiency is most pronounced when the spatial weight matrix is defined based on contiguity. This could be because contiguous cities are more likely to cooperate which minimizes spatial transmission and maximizes the effectiveness of local anti-corona virus measures.

| Lagged spatial effect
Despite the justifications for the contemporaneous spatial effect in classic spatial dynamic panel data models, one might also be interested in a lagged spatial effect that incorporates not only equilibrium spatial patterns but also time dynamics associated with the spatial term. We present evidence of this in Columns (1) and (2)  Note: Columns (1) and (2) consider the temporal lag of spatial dependence. Columns (3) and (4) replace a number of beds with a number of medical staff. Columns (5) and (6) consider the dynamics of death equation. All regressions control for city and time fixed effects. ρ represents cross-equation correlations between u 1,it and u 2,it . *p < 0.10, **p < 0.05, and ***p < 0.01. t stats are reported in parentheses.
cities are less correlated with the current infections of a target city, leaving more unexplained variations in infections to be explained by lagged infections. However, we still obtain clear evidence on the impact of urban density and government efficiency.

| Alternative proxy for medical resources
In Columns (3) and (4) of Table 5, we examine the robustness of the proxy for the abundance of medical resources. In the baseline regression, we use the number of hospital beds to proxy for medical resources.
However, temporary medical facilities are built quickly during this period to treat and quarantine infected patients. To alleviate this concern, we experiment with using the number of medical staff, as opposed to the number of hospital beds, as a proxy for the availability of medical resources. Although medical staff are also mobile and can be dispatched to facilitate the treatment in other cities, the combined and consistent evidence on the number of hospital beds and the number of medical staff help alleviate potential concerns on whether those proxies are working as intended. Once again, the results are fairly robust to the measure of medical resources used.

| Death count dynamics
In our baseline specification, we assume away any potential dynamics associated with the death outcomes. This assumption could be violated if previous death outcomes affect the current availability of medical resources, the current effectiveness of medical treatment, and also the mental status of current patients. Therefore, we alleviate this restriction by allowing for the time series dynamics for the death outcomes. We present the findings in Columns (5) and (6) of Table 5. We find that lagged death outcomes are positively correlated with current death counts. This effect dilutes some of the impact previously absorbed in the coefficient associated with lagged infections. The magnitude of the impact of medical resources also becomes smaller. However, the key evidence on the impact of urban density and government efficiency on infections remains largely unchanged.

| Impact of efficiency on deaths
In Columns (1) and (2) of Table 6, we experiment with adding government efficiency interactions to the death equation. The underlying rationale is that the ability of the local government in managing medical resources may directly affect how efficiently the infected receive medical treatment and how likely they subsequently recover from the disease. We find that government efficiency does play a significant role in reducing death tolls while maintaining its significant impact on reducing infections.

| Impact of hospital beds on infections
In our baseline specification, we consider that medical resources mainly work through impacting the death outcomes. However, better and timely treatments of the infected may reduce future infections. In Columns (3) and (4) of  Note: Columns (1) and (2) control for government efficiency in the death equation. Columns (3) and (4) control for a number of hospital beds in the infection equation. Columns (5) and (6) control for gross domestic product (GDP) and disposable income per capita in both equations. Columns (7) and (8) include all controls of models in Columns (1)-(6). All regressions control for city and time fixed effects. ρ represents cross-equation correlations between u 1,it and u 2,it . *p < 0.10, **p < 0.05, and ***p < 0.01. t stats are reported in parentheses.

| Role of GDP and income per capita
The level of economic development could matter in the dynamics of the infection and death outcomes because residents in more developed cities have more resources to cope with adverse shocks. In Columns (5) and (6), we further control for the interaction of lagged infections with city-specific GDP and the interaction of lagged infections with city-specific income per capita. We observe a significant positive impact of GDP on infections. This could be because measures of economic development are highly correlated with the population density and, hence, capture a part of the variations in population density. The income per capita plays a significant role in reducing death tolls, while the role of medical resources is muted in the death equation, which could be driven by the high correlation between the number of hospital beds and measures of economic development. In Columns (7) and (8), we adopt a specification that includes the full set of controls presented in Columns (1)-(6), the findings remain robust.

| Connectivity to the epicenter
One concern on the potential misspecification of our baseline model is that the initial values for the dynamics of infections are not sufficient to capture the impact of a city's connectivity to the epicenter of the pandemic. As the city's infection and death outcomes are significantly affected by its population inflows from the city experiencing the initial outbreak, failing to properly account for the connectivity to the epicenter could result in biased estimates of our explanatory variables.
To address this concern, we adopt two approaches. First, we remove the first week of the sample in which cities may continue receiving a significant share of the population inflows from the epicenter. Such continuous shocks may change the dynamics that we modeled in the baseline specification because the dynamics of the current infections driven by the lagged infections of own cities and nearby cities could vary at the beginning versus at the later phase of the transmission. Focusing on the period of the sample in which the lockdown of the epicenter has already taken effect helps to mitigate such concerns. We report the corresponding results in Columns (1) and (2) of Table 7.
Second, to account for the possibility of breakage to the lock-down policy or a prolonged incubation period of Wuhan infected travelers, we directly control for daily population inflows from Wuhan provided by the Baidu migration database. We report the corresponding estimates in Columns (3)-(6) of Table 7. In Columns (3) and (4), we report findings after adding this additional control to our baseline specification. In Columns (5) and (6), we report these findings after adding this additional control to the specification presented in Columns (7) and (8) of Table 6.
Note that in both cases, the sample size becomes smaller than that for the baseline specification because the information on daily population inflows from Wuhan is only available between January 20, 2020, and March 13, 2020. Despite the smaller sample size, the main findings on the role of city population density and government efficiency remain robust.

| Extensive margin of city size
To preserve the power of identification, we choose to only focus on the intensive margin of city size and the role of government efficiency in our baseline model. As a robustness check, we control for the role of the city area size to understand the extensive margin of the city effect. We report the estimated coefficients in Columns (1) and (2) of Table 8. Not surprisingly, larger cities have more infections conditional on the population density and government efficiency. More importantly, the additional control of the interactive effect of the city area size does not dramatically change the magnitudes of the impacts of population density and government efficiency.
5.2.10 | Role of employment, transport infrastructure, and human capital One concern with the interpretation of the impact of government efficiency is that this proxy might be correlated with other city-level characteristics, and it could be mainly those other characteristics that drive the change in the prevalence of infections. To alleviate these concerns, we further control for three key city-specific features-the employment size, the extent of the transportation infrastructure build-up, and the level of city-specific human capital-in a different set of robustness checks. Results are reported in Columns (3)-(8) of  (1) and (2) drop observations of the first week. Columns (3) and (4) control for daily inflow from Wuhan based on the model in Columns (1) and (2). Columns (5) and (6) include additional controls of gross domestic product (GDP) and disposable income per capita in both equations while controlling for daily outflow from Wuhan. All regressions control for city and time fixed effects. ρ represents cross-equation correlations between u 1,it and u 2,it . *p < 0.10, **p < 0.05, and ***p < 0.01. t stats are reported in parentheses.  (3) and (4) include additional control variable for the total employment to the previous model in Columns (1) and (2). Columns (5) and (6) include additional control variable for the intracity mobility to the previous model in Columns (3) and (4). Columns (7) and (8) include additional control variable for higher education to the previous model in Columns (5) and (6). All regressions control for city and time fixed effects.

| CONCLUSION
Urban density brings in significant benefits manifested through improved access to goods and services, enhanced productivity, and reduced travel costs. It also comes with various costs in the form of congestion, concentrated crimes, pollution, as well as propagation of contagious diseases (Duranton & Puga, 2020). We focus on highlighting the cost of cities in the context of the COVID-19 pandemic and potential counteracting forces that may mitigate the cost. By fitting a simultaneous spatial dynamic panel data model with information on early COVID-19 transmissions in China, we show that population density plays a significant role in contributing to the wide prevalence of infected cases and resulting deaths across Chinese cities. Despite the significant cost of urban density measured in terms of infections and deaths, we also find that effective city government management mitigates the potential cost through possible effective implementations of public health measures. In addition, conditional on the number of lagged infections, medical resources that are more abundant in larger cities effectively reduce the number of deaths in those cities.
We acknowledge that this aspect of the urban cost that we highlight in this paper operates at a very different intertemporal scale than that related to most considerations on urban benefits, so they are not directly comparable. However, with significant uncertainty associated with how long the current pandemic may last and the possibility of future re-current outbreaks, it is essential to factor in the public health costs that density entails to better understand the trade-off between the cost and benefit of cities. 25 Moreover, the evidence on the importance of the city government efficiency in a pandemic provides broad implications for the potential role of government practices in mitigating widely documented costs of big cities, such as pollution and congestion.
As a final note, our analysis does not speak directly to the policy debate on whether to adopt stringent controls to clear out the virus or mitigating measures to flatten the curve of virus transmissions. However, in the context of early COVID-19 transmissions in China in which knowledge about the COVID-19 virus was sparse and no effective treatment or vaccination for the disease was available, it was sensible to adopt a zero COVID policy with the aim to curb disease transmissions as effectively as possible. This context provides a credible opportunity to study the role of government efficiency as it ensures that our government efficiency measure accurately reflects the effectiveness of local government in achieving a clearly specified and nationwide homogeneous objective.

ACKNOWLEDGMENTS
We would like to thank the coeditor, professor Edward Coulson, and two anonymous referees for their insightful and constructive comments, which led to significant improvements in the paper. We thank conference participants at the 2021 European Meeting of the Urban Economics Association for their helpful comments. Jing Li gratefully acknowledges the financial support from Singapore Management University under the Lee Kong Chian Fellowship.
The remaining errors are our own.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.

APPENDIX
This section provides additional information on city-level indexes used in our empirical analysis. We obtain city-level measures from the 2019 Global Urban Competitiveness Yearbook. This yearbook was jointly published by Chinese and Foreign Institute of City Competitiveness, Hong Kong Gui Qiang Fang Institute of Global Competitiveness, and World Organization for City Cooperation and Development.
We rely on this data source for our analysis because researchers compiling this yearbook set their main theme as assessing Chinese cities' competitiveness, and one of the key aspects is the government efficiency. The government efficiency index measure is designed to reflect many key aspects of cities in a holistic way. Those aspects include the ability of city residents to generate wealth, the ability of the city government to produce wealth by adjusting for the area of the city, and the ability of the city government to manage the city's daily operations efficiently. Overall, it is designed to assess cities' effectiveness in utilizing their resources to maximize wealth. which are not included in our sample. Other key indicators published in the same yearbook and used in our analysis are city density, city size, GDP, income per capita, employment size, transport infrastructure index, and human capital index (a city's labor scale and stock adjusted for education). We summarize those measures used in our empirical analysis in Table A1 and report the kernel density estimates for city characteristics in Figure 3.
More details can be found in the yearbook. 26 Researchers designing the indexation of the measures prefer to differentiate the minimal value of a measure from 0. This monotonic transformation does not impact the estimated coefficients as the additional constant will be absorbed by the dummy variables included in the regression model.