| Id |
Subject |
Object |
Predicate |
Lexical cue |
| T77 |
0-15 |
Sentence |
denotes |
Empirical model |
| T78 |
16-82 |
Sentence |
denotes |
Our analysis sample includes 304 prefecture-level cities in China. |
| T79 |
83-171 |
Sentence |
denotes |
We exclude Wuhan, the capital city of Hubei province, from our analysis for two reasons. |
| T80 |
172-265 |
Sentence |
denotes |
First, the epidemic patterns in Wuhan are significantly different from those in other cities. |
| T81 |
266-425 |
Sentence |
denotes |
Some confirmed cases in Wuhan contracted the virus through direct exposure to Huanan Seafood Wholesale Market, which is the most probable origin of the virus6. |
| T82 |
426-494 |
Sentence |
denotes |
In other cities, infections arise from human-to-human transmissions. |
| T83 |
495-754 |
Sentence |
denotes |
Second, COVID-19 cases were still pneumonia of previously unknown virus infections in people’s perception until early January so that Wuhan’s health care system became overwhelmed as the number of new confirmed cases increased exponentially since mid-January. |
| T84 |
755-912 |
Sentence |
denotes |
This may have caused severe delay and measurement errors in the number of cases reported in Wuhan, and to a lesser extent, in other cities in Hubei province. |
| T85 |
913-1020 |
Sentence |
denotes |
To alleviate this concern, we also conduct analyses excluding all cities in Hubei province from our sample. |
| T86 |
1021-1144 |
Sentence |
denotes |
To model the spread of the virus, we consider within-city spread and between-city transmissions simultaneously (Adda 2016). |
| T87 |
1145-1361 |
Sentence |
denotes |
Our starting point is yct=∑s=114αwithin,syc,t−s+∑s=114αbetween,s∑r≠cdcr−1yr,t−s+∑s=114ρszt−s+xctβ+𝜖ct, where c is a city other than Wuhan, and yct is the number of new confirmed cases of COVID-19 in city c on date t. |
| T88 |
1362-1543 |
Sentence |
denotes |
Regarding between-city transmissions, dcr is the log of the distance between cities c and r, and ∑r≠cdcr−1yrt is the inverse distance weighted sum of new infections in other cities. |
| T89 |
1544-1844 |
Sentence |
denotes |
Considering that COVID-19 epidemic originated from one city (Wuhan) and that most of the early cases outside Wuhan can be traced to previous contacts with persons in Wuhan, we also include the number of new confirmed cases in Wuhan (zt) to model how the virus spreads to other cities from its source. |
| T90 |
1845-2108 |
Sentence |
denotes |
We may include lagged yct, yrt, and zt up to 14 days based on the estimates of the durations of the infectious period and the incubation period in the literature7. xct includes contemporaneous weather controls, city, and day fixed effects8. 𝜖ct is the error term. |
| T91 |
2109-2151 |
Sentence |
denotes |
Standard errors are clustered by province. |
| T92 |
2152-2366 |
Sentence |
denotes |
To make it easier to interpret the coefficients, we assume that the transmission dynamics (αwithin,s, αbetween,s, ρs) are the same within s = 1,⋯ ,7 and s = 8,⋯ ,14, respectively, but can be different across weeks. |
| T93 |
2367-2568 |
Sentence |
denotes |
Specifically, we take averages of lagged yct, yrt, and zt by week, as y¯ctτ=17∑s=17yct−7τ−1−s, y¯rtτ=17∑s=17yrt−7τ−1−s, and z¯tτ=17∑s=17zt−7τ−1−s, in which τ denotes the preceding first or second week. |
| T94 |
2569-2671 |
Sentence |
denotes |
Our main model is 1 yct=∑τ=12αwithin,τy¯ctτ+∑τ=12αbetween,τ∑r≠cdcr−1y¯rtτ+∑τ=12ρτz¯tτ+xctβ+𝜖ct.Model A |
| T95 |
2672-3007 |
Sentence |
denotes |
We also consider more parsimonious model specifications, such as the model that only considers within-city transmissions, 2 yct=∑τ=12αwithin,τy¯ctτ+xctβ+𝜖ct,and the model where the time lagged variables are averages over the preceding 2 weeks, yct=αwithin114∑s=114yc,t−s+αbetween114∑s=114∑r≠cdcr−1yr,t−s+ρ114∑s=114zt−s+xctβ+𝜖ct.Model B |
| T96 |
3008-3104 |
Sentence |
denotes |
There are several reasons that y¯ctτ, y¯rtτ, and z¯tτ may be correlated with the error term 𝜖ct. |
| T97 |
3105-3323 |
Sentence |
denotes |
The unobserved determinants of new infections such as local residents’ and government’s preparedness are likely correlated over time, which causes correlations between the error term and the lagged dependent variables. |
| T98 |
3324-3463 |
Sentence |
denotes |
As noted by the World Health Organization (2020b), most cases that were locally generated outside Hubei occurred in households or clusters. |
| T99 |
3464-3701 |
Sentence |
denotes |
The fact that big clusters give rise to a large number of cases within a short period of time may still be compatible with a general low rate of community transmissions, especially when measures such as social distancing are implemented. |
| T100 |
3702-3855 |
Sentence |
denotes |
Therefore, the coefficients are estimated by two-stage least squares in order to obtain consistent estimates on the transmission rates in the population. |
| T101 |
3856-4090 |
Sentence |
denotes |
In Eq. 2, the instrumental variables include averages of daily maximum temperature, total precipitation, average wind speed, and the interaction between precipitation and wind speed, for city c in the preceding third and fourth weeks. |
| T102 |
4091-4188 |
Sentence |
denotes |
Detailed discussion of the selection of weather characteristics as instruments is in Section 3.2. |
| T103 |
4189-4243 |
Sentence |
denotes |
The timeline of key variables are displayed in Fig. 1. |
| T104 |
4244-4525 |
Sentence |
denotes |
The primary assumption on the instrumental variables is that weather conditions before 2 weeks do not affect the likelihood that a person susceptible to the virus contracts the disease, conditional on weather conditions and the number of infectious people within the 2-week window. |
| T105 |
4526-4702 |
Sentence |
denotes |
On the other hand, they affect the number of other persons who have become infectious within the 2-week window, because they may have contracted the virus earlier than 2 weeks. |
| T106 |
4703-4861 |
Sentence |
denotes |
These weather variables are exogenous to the error term and affect the spread of the virus, which have been used by Adda (2016) to instrument flu infections9. |
| T107 |
4862-4894 |
Sentence |
denotes |
Fig. 1 Timeline of key variables |
| T108 |
4895-5122 |
Sentence |
denotes |
Another objective of this paper is to quantify the effect of various socioeconomic factors in mediating the transmission rates of the virus, which may identify potential behavioral and socioeconomic risk factors for infections. |
| T109 |
5123-5408 |
Sentence |
denotes |
For within-city transmissions, we consider the effects of local public health measures (see Section 5 for details) and the mediating effects of population density, level of economic development, number of doctors, and environmental factors such as temperature, wind, and precipitation. |
| T110 |
5409-5589 |
Sentence |
denotes |
For between-city transmissions, apart from proximity measures based on geographic distance, we also consider similarity in population density and the level of economic development. |
| T111 |
5590-5695 |
Sentence |
denotes |
To measure the spread of the virus from Wuhan, we also include the number of people traveling from Wuhan. |
| T112 |
5696-5735 |
Sentence |
denotes |
The full empirical model is as follows: |
| T113 |
5736-6097 |
Sentence |
denotes |
3 yct=∑τ=12∑k=1Kwithinαwithin,τkh¯ctkτy¯ctτ+∑τ=12∑k=1Kbetween∑r≠cαbetween,τkm¯crtkτy¯rtτ+∑τ=12∑k=1KWuhanρτkm¯c,Wuhan,tkτz¯tτ+xctβ+𝜖ct,where h¯ctkτ includes dummies for local public health measures and the mediating factors for local transmissions. m¯crtkτ and m¯c,Wuhan,tkτ are the mediating factors for between-city transmissions and imported cases from Wuhan. |
