PMC:7210464 / 78514-92260 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/7210464","sourcedb":"PMC","sourceid":"7210464","source_url":"https://www.ncbi.nlm.nih.gov/pmc/7210464","text":"Appendix\nThe 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.\n\nAppendix A. First stage regressions\nWeather 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.\nTable 9 First stage regressions\nDependent variable Average # of new cases\nOwn city Other cities\n1-week lag 2-week lag 1-week lag 2-week lag\n(1) (2) (3) (4)\nOwn City\nMaximum temperature, 3-week lag 0.200*** − 0.0431 0.564 − 2.022***\n(0.0579) (0.0503) (0.424) (0.417)\nPrecipitation, 3-week lag − 0.685 − 0.865* 4.516 − 1.998\n(0.552) (0.480) (4.045) (3.982)\nWind speed, 3-week lag 0.508** 0.299 − 0.827 3.247*\n(0.256) (0.223) (1.878) (1.849)\nPrecipitation × wind speed, 3-week lag − 0.412** 0.122 − 1.129 − 2.091\n(0.199) (0.173) (1.460) (1.437)\nMaximum temperature, 4-week lag 0.162*** 0.125** 1.379*** 1.181***\n(0.0560) (0.0487) (0.410) (0.404)\nPrecipitation, 4-week lag 0.0250 − 0.503 2.667 8.952***\n(0.440) (0.383) (3.224) (3.174)\nWind speed, 4-week lag 0.179 0.214 − 1.839 1.658\n(0.199) (0.173) (1.458) (1.435)\nPrecipitation × wind speed, 4-week lag − 0.354** − 0.0270 1.107 − 2.159**\n(0.145) (0.126) (1.059) (1.043)\nOther cities, weight = inverse distance\nMaximum temperature, 3-week lag − 0.0809*** − 0.00633 0.0520 1.152***\n(0.0203) (0.0176) (0.149) (0.146)\nPrecipitation, 3-week lag 4.366*** − 2.370*** 17.99*** − 72.68***\n(0.639) (0.556) (4.684) (4.611)\nWind speed, 3-week lag 0.326*** − 0.222** − 1.456 − 11.02***\n(0.126) (0.110) (0.926) (0.912)\nPrecipitation × wind speed, 3-week lag − 1.780*** 0.724*** − 6.750*** 27.73***\n(0.227) (0.197) (1.663) (1.637)\nMaximum temperature, 4-week lag − 0.0929*** − 0.0346* − 0.518*** 0.0407\n(0.0220) (0.0191) (0.161) (0.159)\nPrecipitation, 4-week lag 3.357*** − 0.578 46.57*** − 25.31***\n(0.504) (0.438) (3.691) (3.633)\nWind speed, 4-week lag 0.499*** 0.214** 4.660*** − 4.639***\n(0.107) (0.0934) (0.787) (0.774)\nPrecipitation × wind speed, 4-week lag − 1.358*** − 0.0416 − 17.26*** 8.967***\n(0.178) (0.155) (1.303) (1.282)\nF statistic 11.41 8.46 19.10 36.32\np value 0.0000 0.0000 0.0000 0.0000\nObservations 12,768 12,768 12,768 12,768\nNumber of cities 304 304 304 304\n# cases in Wuhan Yes Yes Yes Yes\nContemporaneous weather controls Yes Yes Yes Yes\nCity FE Yes Yes Yes Yes\nDate FE Yes Yes Yes Yes\nCity by week FE Yes Yes Yes Yes\nThis 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 \u003c 0.01, ** p \u003c 0.05, * p \u003c 0.1\nBecause 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.\nThe 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.\nTable 10 Variables selected\nDependent variable: closed management of communities\nDew point 1-week lag\nDiurnal temperature range 1-week lag\nDew point 2-week lag\nSea-level pressure 2-week lag\nDew point 3-week lag\nVisibility 4-week lag\nPrecipitation 4-week lag\nDependent variable: family outdoor restrictions\nStation pressure 1-week lag\nDummy for adverse weather conditions such as fog, rain, and drizzle 1-week lag\nMaximum temperature 2-week lag\nSea-level pressure 2-week lag\nAverage temperature 3-week lag\nMinimum temperature 3-week lag\nVisibility 3-week lag\nThis 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\n\nAppendix B. Exclude clinically diagnosed cases in Hubei\nCOVID-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.\nFig. 8 Number of daily new confirmed cases of COVID-19 in mainland China and revised case counts in Hubei Province\nTable 11 Number of cumulative clinically diagnosed cases in Hubei\nCity Feb 12 Feb 13 Feb 14\nEzhou 155 168 189\nEnshi 19 21 27\nHuanggang 221 306 306\nHuangshi 12 26 42\nJingmen 202 155‡ 150‡\nJingzhou 287 269‡ 257‡\nQianjiang 0 9 19\nShiyan 3 4 3‡\nSuizhou 0 6 4‡\nTianmen 26 67 65‡\nWuhan 12364 14031 14953\nXiantao 2 2 2\nXianning 6 189 286\nXiangyang 0 0 4\nXiaogan 35 80 148\nYichang 0 51 67\n‡The reductions in cumulative case counts are due to revised diagnosis from further tests\nTable 12 Within- and between-city transmission of COVID-19, revised case counts in Hubei Province\nJan 19–Feb 29 Jan 19–Feb 1 Feb 2–Feb 29\n(1) (2) (3) (4) (5) (6)\nOLS IV OLS IV OLS IV\nModel A: lagged variables are averages over the preceding first and second week separately\nAverage # of new cases, 1-week lag\nOwn city 0.747*** 0.840*** 0.939*** 2.456*** 0.790*** 1.199***\n(0.0182) (0.0431) (0.102) (0.638) (0.0211) (0.0904)\nOther cities 0.00631** 0.0124 0.0889 0.0412 − 0.00333 − 0.0328\nwt. = inv. dist. (0.00289) (0.00897) (0.0714) (0.0787) (0.00601) (0.0230)\nWuhan 0.0331*** 0.0277 − 0.879 − 0.957 0.0543* 0.0840\nwt. = inv. dist. (0.0116) (0.0284) (0.745) (0.955) (0.0271) (0.0684)\nWuhan 0.00365*** 0.00408*** 0.00462*** 0.00471*** − 0.000882 − 0.00880***\nwt. = pop. flow (0.000282) (0.000287) (0.000326) (0.000696) (0.000797) (0.00252)\nAverage # of new cases, 2-week lag\nOwn city − 0.519*** − 0.673*** 2.558 − 1.633 − 0.286*** − 0.141\n(0.0138) (0.0532) (2.350) (2.951) (0.0361) (0.0899)\nOther cities − 0.00466 − 0.0208 − 0.361 − 0.0404 − 0.00291 − 0.0235**\nwt. = inv. dist. (0.00350) (0.0143) (0.371) (0.496) (0.00566) (0.0113)\nWuhan − 0.0914* 0.0308 3.053 3.031 − 0.154 0.0110\nwt. = inv. dist. (0.0465) (0.0438) (2.834) (3.559) (0.0965) (0.0244)\nWuhan 0.00827*** 0.00807*** 0.00711*** − 0.00632 0.0119*** 0.0112***\nwt. = pop. flow (0.000264) (0.000185) (0.00213) (0.00741) (0.000523) (0.000627)\nModel B: lagged variables are averages over the preceding 2 weeks\nOwn city 0.235*** 0.983*** 1.564*** 2.992*** 0.391*** 0.725***\n(0.0355) (0.158) (0.174) (0.892) (0.0114) (0.101)\nOther cities 0.00812 − 0.0925* 0.0414 0.0704 0.0181 − 0.00494\nwt. = inv. dist. (0.00899) (0.0480) (0.0305) (0.0523) (0.0172) (0.0228)\nWuhan − 0.172* − 0.114** − 0.309 − 0.608 − 0.262 − 0.299*\nwt. = inv. dist. (0.101) (0.0472) (0.251) (0.460) (0.161) (0.169)\nWuhan 0.0133*** 0.0107*** 0.00779*** 0.00316 0.0152*** 0.0143***\nwt. = pop. flow (0.000226) (0.000509) (0.000518) (0.00276) (0.000155) (0.000447)\nObservations 12,768 12,768 4,256 4,256 8,512 8,512\nNumber of cities 304 304 304 304 304 304\nWeather controls Yes Yes Yes Yes Yes Yes\nCity FE Yes Yes Yes Yes Yes Yes\nDate FE Yes Yes Yes Yes Yes Yes\nThe 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 \u003c 0.01, ** p \u003c 0.05, * p \u003c 0.1\n\nAppendix C. Computation of counterfactuals\nOur main model is\n4 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.\nIt is convenient to write it in vector form, 5 Ynt=∑s=114Hnt,s(αwithin)+Mnt,s(αbetween)Yn,t−s+∑τ=12Zntτρτ+Xntβ+𝜖nt,\nwhere 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.\nWe 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,⋮\nThe 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 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