Appendix
The Appendix consists of three sections. Section A provides details on the first stage of the IV regressions and the selection of the instrumental variables for the local public health policies. Section B shows that our main findings are not sensitive to the adjustment in COVID-19 case definitions in Hubei province in February. Section A contains details on the computation of the counterfactuals.

Appendix A. First stage regressions
Weather conditions affect disease transmissions either directly if the virus can more easily survive and spread in certain environment, or indirectly by changing human behavior. Table 9 reports results of the first stage of the IV regressions (Table 4) using the full sample. In columns (1) and (2), the dependent variables are the numbers of newly confirmed COVID-19 cases in the own city in the preceding first and second weeks, respectively. In columns (3) and (4), the dependent variables are the sum of inverse log distance weighted numbers of newly confirmed COVID-19 cases in other cities in the preceding first and second weeks, respectively. These are the endogenous variables in the IV regressions. The weather variables in the preceding first and second weeks are included in the control variables. The weather variables in the preceding third and fourth weeks are the excluded instruments, and their coefficients are reported in the table. Because the variables are averages in 7-day moving windows, the error term may be serially correlated, and we include city by week fixed effects. Also included in the control variables are the average numbers of new cases in Wuhan in the preceding first and second weeks, interacted with the inverse log distance or the population flow.
Table 9 First stage regressions
Dependent variable Average # of new cases
Own city Other cities
1-week lag 2-week lag 1-week lag 2-week lag
(1) (2) (3) (4)
Own City
Maximum temperature, 3-week lag 0.200*** − 0.0431 0.564 − 2.022***
(0.0579) (0.0503) (0.424) (0.417)
Precipitation, 3-week lag − 0.685 − 0.865* 4.516 − 1.998
(0.552) (0.480) (4.045) (3.982)
Wind speed, 3-week lag 0.508** 0.299 − 0.827 3.247*
(0.256) (0.223) (1.878) (1.849)
Precipitation × wind speed, 3-week lag − 0.412** 0.122 − 1.129 − 2.091
(0.199) (0.173) (1.460) (1.437)
Maximum temperature, 4-week lag 0.162*** 0.125** 1.379*** 1.181***
(0.0560) (0.0487) (0.410) (0.404)
Precipitation, 4-week lag 0.0250 − 0.503 2.667 8.952***
(0.440) (0.383) (3.224) (3.174)
Wind speed, 4-week lag 0.179 0.214 − 1.839 1.658
(0.199) (0.173) (1.458) (1.435)
Precipitation × wind speed, 4-week lag − 0.354** − 0.0270 1.107 − 2.159**
(0.145) (0.126) (1.059) (1.043)
Other cities, weight = inverse distance
Maximum temperature, 3-week lag − 0.0809*** − 0.00633 0.0520 1.152***
(0.0203) (0.0176) (0.149) (0.146)
Precipitation, 3-week lag 4.366*** − 2.370*** 17.99*** − 72.68***
(0.639) (0.556) (4.684) (4.611)
Wind speed, 3-week lag 0.326*** − 0.222** − 1.456 − 11.02***
(0.126) (0.110) (0.926) (0.912)
Precipitation × wind speed, 3-week lag − 1.780*** 0.724*** − 6.750*** 27.73***
(0.227) (0.197) (1.663) (1.637)
Maximum temperature, 4-week lag − 0.0929*** − 0.0346* − 0.518*** 0.0407
(0.0220) (0.0191) (0.161) (0.159)
Precipitation, 4-week lag 3.357*** − 0.578 46.57*** − 25.31***
(0.504) (0.438) (3.691) (3.633)
Wind speed, 4-week lag 0.499*** 0.214** 4.660*** − 4.639***
(0.107) (0.0934) (0.787) (0.774)
Precipitation × wind speed, 4-week lag − 1.358*** − 0.0416 − 17.26*** 8.967***
(0.178) (0.155) (1.303) (1.282)
F statistic 11.41 8.46 19.10 36.32
p value 0.0000 0.0000 0.0000 0.0000
Observations 12,768 12,768 12,768 12,768
Number of cities 304 304 304 304
# cases in Wuhan Yes Yes Yes Yes
Contemporaneous weather controls Yes Yes Yes Yes
City FE Yes Yes Yes Yes
Date FE Yes Yes Yes Yes
City by week FE Yes Yes Yes Yes
This table shows the results of the first stage IV regressions. The weather variables are weekly averages of daily weather readings. Coefficients of the weather variables which are used as excluded instrumental variables are reported. *** p < 0.01, ** p < 0.05, * p < 0.1
Because the spread of the virus depends on both the number of infectious people and the weather conditions, the coefficients in the first stage regressions do not have structural interpretations. The Wald tests on the joint significance of the excluded instruments are conducted and their F statistics are reported. The excluded instruments have good predictive power.
The implementation of local public health measures is likely correlated with the extent of the virus spread, so weather conditions that affect virus transmissions may also affect the likelihood that the policy is adopted. The influence of weather conditions on policy adoption may be complicated, so we use the Cluster-Lasso method of Belloni et al. (2016) to select the weather variables that have good predictive power on the adoption of closed management of communities or family outdoor restrictions. Let dct be the dummy variable of the adoption of the local public health measure, i.e., dct = 1 if the policy is in place in city c at day t. qct is a vector of candidate weather variables, including weekly averages of daily mean temperature, maximum temperature, minimum temperature, dew point, station-level pressure, sea-level pressure, visibility, wind speed, maximum wind speed, snow depth, precipitation, dummy for adverse weather conditions, squared terms of these variables, and interactions among them. First, city and day fixed effects are removed. d¨ct=dct−1n∑cdct−1T∑tdct+1nT∑ctdct and q¨ct is defined similarly. The Cluster-Lasso method solves the following minimization problem: 1nT∑ctd¨ct−q¨ct′b2+λnT∑kϕk|bk|.λ and ϕ are penalty parameters. A larger penalty value forces more coefficients to zero. The penalty parameters are picked using the theoretical result of Belloni et al. (2016). The estimation uses the Stata package by Ahrens et al. (2019). Table 10 lists the selected weather variables, which are used as the instruments in Table 8.
Table 10 Variables selected
Dependent variable: closed management of communities
Dew point 1-week lag
Diurnal temperature range 1-week lag
Dew point 2-week lag
Sea-level pressure 2-week lag
Dew point 3-week lag
Visibility 4-week lag
Precipitation 4-week lag
Dependent variable: family outdoor restrictions
Station pressure 1-week lag
Dummy for adverse weather conditions such as fog, rain, and drizzle 1-week lag
Maximum temperature 2-week lag
Sea-level pressure 2-week lag
Average temperature 3-week lag
Minimum temperature 3-week lag
Visibility 3-week lag
This table shows the weather variables selected by lassopack (Ahrens et al. 2019), which implements the Cluster-Lasso method of Belloni et al. (2016). City and date fixed effects are included. Candidate variables include weekly averages of daily mean temperature, maximum temperature, minimum temperature, dew point, station-level pressure, sea-level pressure, visibility, wind speed, maximum wind speed, snow depth, precipitation, dummy for adverse weather conditions, squared terms of these variables, and interactions among them

Appendix B. Exclude clinically diagnosed cases in Hubei
COVID-19 case definitions were changed in Hubei province on February 12 and February 20. Starting on February 12, COVID-19 cases could also be confirmed based on clinical diagnosis in Hubei province, in addition to molecular diagnostic tests. This resulted in a sharp increase in the number of daily new cases reported in Hubei, and in particular Wuhan (Fig. 2). The use of clinical diagnosis in confirming cases ended on February 20. The numbers of cases that are confirmed based on clinical diagnosis for February 12, 13, and 14 are reported by the Health Commission of Hubei Province and are displayed in Table 11. As a robustness check, we re-estimate the model after removing these cases from the daily case counts (Fig. 8). Our main findings still hold (Table 12). The transmission rates are significantly lower in February compared with January. Population flow from the epidemic source increases the infections in destinations, and this effect is slightly delayed in February.
Fig. 8 Number of daily new confirmed cases of COVID-19 in mainland China and revised case counts in Hubei Province
Table 11 Number of cumulative clinically diagnosed cases in Hubei
City Feb 12 Feb 13 Feb 14
Ezhou 155 168 189
Enshi 19 21 27
Huanggang 221 306 306
Huangshi 12 26 42
Jingmen 202 155‡ 150‡
Jingzhou 287 269‡ 257‡
Qianjiang 0 9 19
Shiyan 3 4 3‡
Suizhou 0 6 4‡
Tianmen 26 67 65‡
Wuhan 12364 14031 14953
Xiantao 2 2 2
Xianning 6 189 286
Xiangyang 0 0 4
Xiaogan 35 80 148
Yichang 0 51 67
‡The reductions in cumulative case counts are due to revised diagnosis from further tests
Table 12 Within- and between-city transmission of COVID-19, revised case counts in Hubei Province
Jan 19–Feb 29 Jan 19–Feb 1 Feb 2–Feb 29
(1) (2) (3) (4) (5) (6)
OLS IV OLS IV OLS IV
Model A: lagged variables are averages over the preceding first and second week separately
Average # of new cases, 1-week lag
Own city 0.747*** 0.840*** 0.939*** 2.456*** 0.790*** 1.199***
(0.0182) (0.0431) (0.102) (0.638) (0.0211) (0.0904)
Other cities 0.00631** 0.0124 0.0889 0.0412 − 0.00333 − 0.0328
wt. = inv. dist. (0.00289) (0.00897) (0.0714) (0.0787) (0.00601) (0.0230)
Wuhan 0.0331*** 0.0277 − 0.879 − 0.957 0.0543* 0.0840
wt. = inv. dist. (0.0116) (0.0284) (0.745) (0.955) (0.0271) (0.0684)
Wuhan 0.00365*** 0.00408*** 0.00462*** 0.00471*** − 0.000882 − 0.00880***
wt. = pop. flow (0.000282) (0.000287) (0.000326) (0.000696) (0.000797) (0.00252)
Average # of new cases, 2-week lag
Own city − 0.519*** − 0.673*** 2.558 − 1.633 − 0.286*** − 0.141
(0.0138) (0.0532) (2.350) (2.951) (0.0361) (0.0899)
Other cities − 0.00466 − 0.0208 − 0.361 − 0.0404 − 0.00291 − 0.0235**
wt. = inv. dist. (0.00350) (0.0143) (0.371) (0.496) (0.00566) (0.0113)
Wuhan − 0.0914* 0.0308 3.053 3.031 − 0.154 0.0110
wt. = inv. dist. (0.0465) (0.0438) (2.834) (3.559) (0.0965) (0.0244)
Wuhan 0.00827*** 0.00807*** 0.00711*** − 0.00632 0.0119*** 0.0112***
wt. = pop. flow (0.000264) (0.000185) (0.00213) (0.00741) (0.000523) (0.000627)
Model B: lagged variables are averages over the preceding 2 weeks
Own city 0.235*** 0.983*** 1.564*** 2.992*** 0.391*** 0.725***
(0.0355) (0.158) (0.174) (0.892) (0.0114) (0.101)
Other cities 0.00812 − 0.0925* 0.0414 0.0704 0.0181 − 0.00494
wt. = inv. dist. (0.00899) (0.0480) (0.0305) (0.0523) (0.0172) (0.0228)
Wuhan − 0.172* − 0.114** − 0.309 − 0.608 − 0.262 − 0.299*
wt. = inv. dist. (0.101) (0.0472) (0.251) (0.460) (0.161) (0.169)
Wuhan 0.0133*** 0.0107*** 0.00779*** 0.00316 0.0152*** 0.0143***
wt. = pop. flow (0.000226) (0.000509) (0.000518) (0.00276) (0.000155) (0.000447)
Observations 12,768 12,768 4,256 4,256 8,512 8,512
Number of cities 304 304 304 304 304 304
Weather controls Yes Yes Yes Yes Yes Yes
City FE Yes Yes Yes Yes Yes Yes
Date FE Yes Yes Yes Yes Yes Yes
The dependent variable is the number of daily new cases. The endogenous explanatory variables include the average numbers of new confirmed cases in the own city and nearby cities in the preceding first and second weeks (model A) and averages in the preceding 14 days (model B). Weekly averages of daily maximum temperature, precipitation, wind speed, the interaction between precipitation and wind speed, and the inverse log distance weighted sum of these variables in other cities, during the preceding third and fourth weeks, are used as instrumental variables in the IV regressions. Weather controls include contemporaneous weather variables in the preceding first and second weeks. Standard errors in parentheses are clustered by provinces. *** p < 0.01, ** p < 0.05, * p < 0.1

Appendix C. Computation of counterfactuals
Our main model is
4 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.
It is convenient to write it in vector form, 5 Ynt=∑s=114Hnt,s(αwithin)+Mnt,s(αbetween)Yn,t−s+∑τ=12Zntτρτ+Xntβ+𝜖nt,
where Ynt=y1t⋯ynt′ and 𝜖nt are n × 1 vectors. Assuming that Yns = 0 if s ≤ 0, because our sample starts on January 19, and no laboratory confirmed case was reported before January 19 in cities outside Wuhan. Xnt=x1t′⋯xnt′′ is an n × k matrix of the control variables. Hnt,s(αwithin) is an n × n diagonal matrix corresponding to the s-day time lag, with parameters αwithin={αwithin,τk}k=1,⋯,Kwithin,τ=1,2. For example, for s = 1,⋯ , 7, the i th diagonal element of Hnt,s(αwithin) is 17∑k=1Kwithinαwithin,1kh¯ct,ik1, and for s = 8,⋯ , 14, the i th diagonal element of Hnt,s(αwithin) is 17∑k=1Kwithinαwithin,2kh¯ct,ik2. Mnt,s(αbetween) is constructed similarly. For example, for s = 1,⋯ , 7 and i≠j, the ij th element of Mnt,s(αbetween) is 17∑k=1Kbetweenαbetween,1km¯ijtk1. Zntτ is an n × KWuhan matrix corresponding to the transmission from Wuhan. For example, the ik th element of Znt1 is m¯i,Wuhan,tk1z¯t1.
We first estimate the parameters in Eq. 4 by 2SLS and obtain the residuals 𝜖^n1,⋯,𝜖^nT. Let ⋅^ denote the estimated value of parameters and ⋅~ denote the counterfactual changes. The counterfactual value of Ynt is computed recursively, Y~n1=∑τ=12Z~n1τρ^τ+Xn1β^+𝜖^n1,Y~n2=∑s=11H~n2,s(α^within)+M~n2,s(α^between)Y~n,2−s+∑τ=12Z~n2τρ^τ+Xn2β^+𝜖^n2,Y~n3=∑s=12H~n3,s(α^within)+M~n3,s(α^between)Y~n,3−s+∑τ=12Z~n3τρ^τ+Xn3β^+𝜖^n3,⋮
The counterfactual change for date t is ΔYnt=Y~nt−Ynt. The standard error of ΔYnt is obtained from 1000 bootstrap iterations. In each bootstrap iteration, cities are sampled with replacement and the model is estimated to obtain the parameters. The counterfactual predictions are obtained using the above equations with the estimated parameters and the counterfactual scenario (e.g., no cities adopted lockdown). 1  COVID-19 is also known as novel coronavirus pneumonia or 2019-nCoV acute respiratory disease.
2  In 2020, the Lunar New Year was on January 25.
3  Coronavirus COVID-19 Global Cases by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (https://gisanddata.maps.arcgis.com/apps/opsdashboard/index.html#/bda7594740fd40299423467b48e9ecf6).
4  For instance, using data on the first 425 COVID-19 patients by January 22, Li et al. (2020) estimate a basic reproduction number of 2.2. Based on time-series data on the number of COVID-19 cases in mainland China from January 10 to January 24, Zhao et al. (2020) estimate that the mean reproduction number ranges from 2.24 to 3.58.
5  We assume a case fatality rate of 4%, the same as China’s current average level. Of course, the eventual case fatality rate may be different from the current value, and it depends on many key factors, such as the preparedness of health care systems and the demographic structure of the population outside Hubei province in comparison to China as a whole. Also importantly, among patients who have died from COVID-19, the time from symptom onset to outcome ranges from 2 to 8 weeks (World Health Organization 2020b), which is partially beyond the time window of this analysis. Therefore, we defer more rigorous estimates about avoided fatality to future studies.
6  Li et al. (2020) document the exposure history of the first 425 cases. It is suspected that the initial cases were linked to the Huanan Seafood Wholesale Market in Wuhan.
7  The COVID-19 epidemic is still ongoing at the time of writing, and the estimates are revised from time to time in the literature as new data become available. The current estimates include the following. The incubation period is estimated to be between 2 and 10 days (World Health Organization 2020a), 5.2 days (Li et al. 2020), or 3 days (median, Guan et al. (2020)). The average infectious period is estimated to be 1.4 days (Wu et al. 2020a).
8  On February 12, cities in Hubei province include clinically diagnosed cases in the confirmed cases, in addition to cases that are confirmed by nucleic acid tests, which results in a sharp increase in the number of confirmed cases for cities in Hubei on February 12. The common effect on other cities is controlled for by the day fixed effect.
9  Flu viruses are easier to survive in cold weather. Adverse weather conditions also limit outdoor activities which can decrease the chance of contracting the virus. For details, see Adda (2016) and Section 3.2.
10  Hong Kong and Macao are excluded from our analysis due to the lack of some socioeconomic variables.
11  Baidu migration (https://qianxi.baidu.com).
12  The 100-km circle is consistent with the existing literature. Most studies on the socioeconomic impacts of climate change have found that estimation results are insensitive to the choice of the cutoff distance (Zhang et al. 2017).
13  These cities are Xiaogan, Huanggang, Jingzhou, Suizhou, Ezhou, and Xiangyang.
14  The shares of top 100 destinations are available. The starting and ending dates of the average shares released by Baidu do not precisely match the period of the analysis sample.
15  It is estimated that 14,925,000 people traveled out of Wuhan in 2019 during the Lunar New Year holiday (http://www.whtv.com.cn/p/17571.html). The sum of Baidu’s migration index for population flow out of Wuhan during the 40 days around the 2019 Lunar New Year is 203.3, which means one index unit represents 0.000013621 travelers. The destination share is in percentage. With one more case in Wuhan, the effect on a city receiving 10,000 travelers from Wuhan is 0.00471 × 0.000013621 × 100 × 10000 = 0.064.
16  http://www.whtv.com.cn/p/17571.html
17  From mid February, individual specific health codes such as Alipay Health Code and WeChat Health Code are being used in many cities to aid quarantine efforts.
18  Disease prevalence can also affect economic development. One channel is the fertility decision which leads to changes in the demographic structure (e.g., Durevall and Lindskog 2011; Chin and Wilson 2018). Fogli and Veldkamp (forthcoming) show that because a dense network spreads diseases faster and higher income is positively correlated with more closely connected social network, infectious diseases can reduce long-run economic growth by limiting the size of social networks.
19  There was insufficient hospital capacity in Hubei (and Wuhan in particular) in late January. Most patients in Wuhan were hospitalized and isolated around mid February with the completion of new hospitals, makeshift health facilities, and increased testing capacity. See Section 5.1 for details.
20  We should note that the summary of China’s policy responses here is not a comprehensive list. Other entities have also made efforts to help curtail the spread of COVID-19. For example, on January 27, the State Grid Corporation of China declared that it would continue supplying electricity to resident users even if payment was not received on time. School and universities were closed already because of Lunar New Year holidays.
21  According to Law of the People’s Republic of China on Prevention and Treatment of Infectious Diseases, class A infectious diseases only include plague and cholera.
22  For a list of quarantine measures, see 2020 Hubei lockdowns (https://en.wikipedia.org/w/index.php?title=2020_Hubei_lockdowns&oldid=946423465), last visited April 2, 2020.
23  Wenzhou, Zhengzhou, Hangzhou, Zhumadian, Ningbo, Harbin, Fuzhou
24  This restriction varies from 1 to 5 days across cities. In most cities, such restrictions are once every 2 days. “Closed management of communities” and “family outdoor restrictions” were mostly announced in city-level government documents. There are some cities in which only part of their counties declared to implement “closed management of communities” or “family outdoor restriction” policy. However, other counties in the same city may have quickly learned from them. Thus, as long as one county in a city has implemented “closed management of communities” or “family outdoor restrictions,” we treat the whole city as having the policy in place.
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We are grateful to Editor Klaus Zimmermann and three anonymous referees for valuable comments and suggestions which have helped greatly improve the paper. We received helpful comments and suggestions from Hanming Fang and seminar participants at Institute for Economic and Social Research of Jinan University and VoxChina Covid-19 Public Health and Public Policy Virtual Forum. Pei Yu and Wenjie Wu provided excellent research assistance. All errors are our own.

Funding Information
Qiu and Shi acknowledge the support from the 111 Project of China (Grant No.B18026). Chen thanks the following funding sources: US PEPPER Center Scholar Award (P30AG021342) and NIH/NIA grants (R03AG048920; K01AG053408). Shi thanks the National Natural Science Foundation of China (Grant No.71803062) and the Ministry of Education of China (Grant No.18YJC790138) for financial support.

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Conflict of interests
The authors declare that they have no conflict of interest.