Does Lockdown Improve Air Quality? Evidence from the blockade policy of county-level units in Hubei Province, China

Background: The COVID-19 posed a great threat to the health of people all over the world. In response to the outbreak of COVID-19, Wuhan implemented the blockade policy on January 23, 2020. Subsequently, other cities in Hubei responded one after another. The flow of people, production and consumption activities were greatly reduced, and air pollution in some cities was obviously improved. Method We used the daily air pollution and weather data of 103 county-level units in Hubei Province from 2019 to 2020 to test whether the blockade policy affected the air quality. The method of regression discontinuity designs is adopted. And the blockade policy implemented by the government during COVID-19 is regarded as exogenous policy impact, so as to investigate whether the blockade policy will affect the air quality. Results (1) Lockdown has indeed brought about an improvement in air quality. During the lockdown period, the AQI decreased by 15.316%, and the concentrations of four air pollutants (PM10, NO2, PM2.5 and SO2) decreased by 19.607%, 12.395%, 11.448% and 1.278% respectively. (2) The improvement of air quality brought about by the blockade policy is not sustainable, and every index rebounded again about 30 days after lockdown. (3) RD estimation found that the concentrations of AQI, PM2.5, PM10 and NO2 decreased by 35.402%, 29.207%, 14.809% and 7.751% respectively. This is consistent with the change trend of the above results, but the change range is obviously larger than the previous one. Conclusion Although the study confirmed that most pollutant indexes decreased during the lockdown period, the blockade policy is not applicable to the prevention and improvement of air pollution. We put forward the policy suggestions from the following two aspects: Firstly, promote green travel and reduce traffic emission sources. Secondly, promote end-of-pipe governance and improve emission reduction efficiency.


Introduction
Looking back at the process of Reform and Opening Up, China's rapid economic growth is accompanied by serious environmental pollution. The economic development mode is too extensive, which leads to the continuous widening of the "scissors difference" between economic growth rate and environmental quality. In recent years, serious air pollution has caused great economic losses and health consequences, which has aroused widespread concern in academic circles and society (Chen et al. 2016, Shuai et al. 2019, Xu et al., 2015. At present, China's economy has changed from high-speed growth stage to high-quality development stage. In order to promote the coordinated development of ecological environment and economy and society, it is required to resolutely ght a tough battle against pollution. It is extremely urgent to strengthen the effective control of air pollution, which is related to the successful transformation of China's economic growth mode in the new period and the effective satisfaction of people's needs for a better life. The outbreak of COVID-19 in early 2020 posed a great threat to the health of people all over the world. On January 23, the Wuhan government issued the blockade policy [1]. A few days later, other municipal governments in Hubei Province also announced lockdown one after another. In the next two weeks, 80 cities in 15 provinces of China were blocked and closed management was implemented in urban residential areas. Many enterprises have stopped production, and unless they get permission from the local epidemic prevention department, the company may not resume production, and almost all avoidable outdoor activities are prohibited.
During this period, will the air quality be improved because of lockdown? Therefore, based on the fact of lockdown in Hubei province during COVID-19 period, this paper discusses the impact of the blockade policy on air environment.
Studies have shown that in some special periods, air pollution can be reduced by arti cially controlling emissions. Some local governments have improved air quality by taking temporary control measures. Scholars found that AQI, PM 2.5 , PM 10 and other indicators in Wuhan were signi cantly reduced during the Military games, but this improvement was not sustainable (Fu et al. 2021). Some scholars collected the regional emission data during the parade in Beijing, and identi ed the main pollution sources and their temporal and spatial variation characteristics by using the positive matrix factorization (PMF). They found that the air pollution in Beijing was well controlled during the temporary control period. Collaborative emission reduction and meteorological conditions had a positive impact on environmental improvement in surrounding areas (Xue et al. 2018). Speci cally, the local government controls the concentration of pollutants by temporarily closing the factory sites in the surrounding areas and prohibiting the operation of vehicles . The daily concentration of PM 2.5 in Beijing was 47.53 g/m 3 during the "APEC Blue" period, and it dropped to 17.07 g/m 3 during the "Parade Blue" period (Lin et al. 2017). Therefore, we think the problem that will COVID-19 lockdown also improve the air quality. Through case studies in speci c countries, scholars compared the changes of air quality indicators before and after lockdown, and con rmed that the blockade policy led to a signi cant improvement in air quality (Dantas et al. 2020). Mahato (2020) pointed out that during the lockdown period, the decline of PM 10 and PM 2.5 reached 60% and 39% respectively in Delhi, and the air quality was improved by 40%-50%. However, a few studies believed that the impact of COVID-19 was unclear, and may even reduce the air quality in Hubei Province, the center of China's epidemic situation (Almond et al. 2020). found that serious air pollution incidents still occurred in the North China Plain during the COVID-19 period. Studies have shown that much transportation emission reductions and a small amount of industrial emission reductions cannot avoid serious air pollution in China, especially in unfavorable meteorological conditions. In addition, some scholars have investigated the global in uence of COVID-19 by collecting global data (Dang and Trinh 2021). It was believed that the PM 2.5 of major cities in the world (New York, Los Angeles, Zaragoza, Rome, Dubai, Delhi, Mumbai, Beijing and Shanghai) has been reduced to a certain extent due to the reduction of personnel mobility during the lockdown period (Akshansha and Ramesh 2020) At present, most of the related achievements are case studies of speci c countries, which directly show the overall changes of air quality before and after the epidemic through data and charts., there are few results to verify the relationship between the blockade policy and the change of air quality by using the measurement method. However, it is worth noting that before the outbreak of COVID-19, China's air quality has been improving due to the government's continuous environmental governance policy (Greenstone andSchwarz 2018, Qiang et al. 2019). Studies have shown that during the Lunar New Year, China's air pollution will be greatly reduced (Q. et al. 2015). Therefore, directly comparing the changes of air quality data before and after the epidemic may exaggerate the in uence of COVID-19 in reducing pollution (He et al. 2020). Also, most of the existing studies only consider the impact of COVID-19 on air quality, but ignore the reverse causal relationship that air pollution will aggravate the epidemic. The innovations of this paper are as follows: First, we study the change of air quality in county-level units and collect the daily average data of 103 county-level units in Hubei Province from 2019 to 2020. Second, the method of regression discontinuity (RD) designs is adopted. And the blockade policy implemented by the government during COVID-19 is regarded as exogenous policy impact, to investigate whether the blockade policy will affect the air quality. The research results can provide an important empirical reference for the formulation of relevant policies, and provide a basis for how to balance economic bene ts and environmental losses in the post-epidemic era.
The remaining structure of this paper is as follows: the second part introduces the research methods and data sources. The third part is the empirical results. The fourth part further discusses the empirical results. And the fth part is the conclusion.
[1] Notice of the Prevention and Control Command of Pneumonia Infected by novel coronavirus in Wuhan City (No.1): Since 10: 00 on January 23, 2020, the city's urban public transport, subway, ferry, and long-distance passenger transport have been suspended; For no special reason, citizens should not leave Wuhan, and the access roads from the airport and railway station to Han are temporarily closed.

Methods
At present, many methods can be used to test the impact of the blockade policy on air quality. For example, the single difference method can simply compare the changes of air quality before and after COVID-19 lockdown (Sahraei et al. 2021).
Double difference method selects other cities as the control group (He et al. 2020). And RD method is to study whether the air quality changes suddenly during the lockdown period (Bao and Zhang 2020). Simply using single difference method is too rough. On the one hand, it cannot distinguish the effects of the blockade policy and other policies, on the other hand, it cannot strip away the inherent trend of urban air quality change. And the double difference method can partially control the common air quality change trend in different regions, but it is di cult to solve the difference problem in different regions except the COVID-19 lockdown. In addition, the double difference method cannot distinguish the impact of the blockade policy and other policies on air quality. The RD method can better solve the identi cation problem of the blockade policy, and analyze whether the air quality is suddenly impacted by the blockade policy in the gradual change with the date. RD analysis is considered as the closest test method to random experiment, which can alleviate the endogenous problem of parameter estimation, and has been used in more and more researches recently. Therefore, this paper uses RD method to estimate and analyze the air quality and its differences before and after the implementation of the blockade policy in sample areas.
First, we set the following panel xing effect model: In the Equation (1), subscripts and represent the region and date respectively, A it represents the air quality. L it is a dummy variable, and its value is 1 when the blockade policy that it is implemented, otherwise it is 0.
is a group of weather control variables, including the highest temperature, the lowest temperature, precipitation, snowfall, and wind etc. Its coefficient reflects the influence of weather factors on air quality.
The coefficient is the focus of this article. and represent the regional fixed effect and the time fixed effect respectively. is the regional fixed effect of area, is the time fixed effect of t time. Also, we control the year, month, and Spring Festival respectively, to avoid the seasonal factors and the influence of Spring Festival holiday.
The Equation (1) cannot include the characteristic factors of sample areas that changed with time before COVID-19 outbreak, such as the degree of environment regulation and the public preference for environmental protection. At the same time, some studies pointed out that the higher the concentration of air pollutants, the higher the risk of infection with COVID-19 ). This condition has led the government to implement a stricter blockade policy. If these possible reverse causal relationships are not controlled, the estimation results will be biased. Therefore, we use RD Design to treat the blockade policy against COVID-19 as exogenous policy impact.
Where is a function of running variable , and running variable is set as the number of days after the blockade policy which it was implemented. Other settings are the same as Equation (1). Coefficient reflects the impact of the blockade policy on air quality. Coefficient reflects the influence of weather factors on air quality. are regional fixed effect and time fixed effect.

Data sources
As of December 31, 2020, Hubei Province has 12 prefecture-level cities, 1 autonomous prefecture (13 prefecture-level administrative regions in total), 39 municipal districts, 26 county-level cities, 35 counties, 2 autonomous counties and 1 forest region (103 county-level units in total). This paper collects the data of 103 county-level units in Hubei Province from 2019 to 2020 [2]. Where, the air pollution data include AQI, PM 2.5 , PM 10 , SO 2 , CO, O 3 and NO 2 , which are often used to evaluate air quality (Kuang et al. 2018). Weather conditions can affect the formation and diffusion of air pollutants (Bao and Zhang 2020). Therefore, we collect the weather data of 2345 weather network, including the highest temperature (TEMP_H), the lowest temperature (TEMP_L), precipitation (RAIN), snowfall (SNOW), and wind (WIND) to control the impact of weather changes on air quality. The main explanatory variable of this paper is the blockade policy and the implementation date data of lockdown is from the o cial websites of local governments. We encoded a binary variable, which records the lockdown restrictions of 103 county-level units. If the government adopts the blockade policy, it is 1, otherwise it is 0. Figure 1 shows the detailed lockdown schedule of 103 county-level units. Table 1 reports descriptive statistics of these variables. As shown in the table, during the lockdown period, the concentrations of AQI, PM 10 , O 3 , NO 2 and SO 2 were signi cantly lower than normal. For example, the average concentration of AQI is 72.815, lockdown period is 62.951, and normal days is 73.737. Moreover, the results of T-test also con rmed that there were signi cant differences between the values of all indexes during the lockdown and those at normal days. However, through the standard deviation, maximum value, and minimum value of each air index, it can be seen that the mean value conceals the huge difference of air quality in different areas and at different times. Therefore, it is necessary to further control the regional and time effects.

Event study analysis
In order to verify the conclusion, this paper selects event study method and uses air quality variables to carry out regression analysis on control variables, regional xed effect, time xed effect and a series of "event occurrence time". Speci c practices are as follows. First, we divide the samples into a group every 10 days. B1, B2 and B3 represents 10 days, 20 days, and 30 days before lockdown. A1, A2 and A3 represents 10 days, 20 days, and 30 days after lockdown. The regression estimation results of air quality and various variables within 100 days before and after the implementation of the blockade policy are presented by grouping method.
The results are shown in Figure 3. The AQI, PM 2.5 , PM 10 , and NO 2 decreased obviously 10 days after lockdown (A1). The variation range of SO 2 , CO and O 3 is small, which is roughly consistent with the estimated result of Figure 2. However, it is worth noting that after the COVID-19 lockdown for about 30 days, almost all indicators showed a rebound trend, which indicated that the blockade policy could not bring about continuous improvement of air quality. In addition, except for O 3 , the values of all other pollutants in B2-A3 period (from January to February) are lower than those in other periods, which may be related to seasonal changes. Therefore, we added the monthly variable to control the in uence of seasonal changes on air quality in this paper.

RD design
As the RD design needs to select the appropriate bandwidth to delimit the research window period, this paper takes the best bandwidth of AQI, PM 2.5 , PM 10 , O 3 , NO 2 , SO 2 and CO as the benchmark bandwidth for regression. According to Figure Table 2 shows the speci c RD estimation results, and the regression controls the weather variables, time xed effect and regional xed effect. At the same time, parameter estimation will face the problems of bandwidth selection, tting polynomial function setting and missing variables, and nonlinear tting method can make up for its defects. Therefore, this paper selects three different forms of functions to estimate the air index. According to the results, AQI, PM 2.5 , PM 10 , NO 2 , and CO are signi cantly negative no matter which running variable function is set. Among them, AQI, PM 2.5 , PM 10 and NO 2 changed greatly, reaching -35.402, -29.207, -14.809 and -7.751 respectively, while SO 2 and CO did not change signi cantly, reaching -0.393 and -0.099 respectively. While O 3 has a positive correlation with the blockade policy of 4.916. The change trend of RD is consistent with the above results, but the change range is larger than that of event study results. The reason may be due to the sample bandwidth selected by RD, which leads to the more obvious change trend of results.

Robustness analysis
(1) Placebo test. This paper continues to set the placebo test to verify the robustness of the above estimation results, by arti cially assuming the lockdown date. That is, selecting a value different from the discontinuity as the placebo discontinuity, and estimating it separately. In this paper, 5, 10, 15, 30 and 45 days before the real discontinuity are selected as breakpoints respectively. The results of placebo discontinuity are not the same as above, and the signi cance is not as good as above, which proves the robustness of above results. (2) Sensitivity test of sample selection. The closer the sample is to the discontinuity, the more motivated it is to manipulate arti cially, which is also called doughnut effect. Therefore, this paper deleted the samples of 1, 2, 3, 4 and 5 days before and after the discontinuity respectively and tested the robustness. The results showed that the regression results of all indexes except SO 2 remained signi cant. It shows that even if there is arti cial manipulation, the discontinuity effect still exists. (3) Bandwidth sensitivity analysis. The bandwidth will affect the result of RD. Small bandwidth can effectively t the distribution of samples near discontinuity, but too small bandwidth will lead to excessive sample loss and biased estimation results. A robust result requires that the bandwidth length cannot be too sensitive. Therefore, this paper manually sets the bandwidth to 25%, 50%, 75%, 150% and 200% of the optimal bandwidth for regression. According to the results, within the optimal bandwidth range of 25%-200%, all indexes except SO 2 show remarkable results, which shows that the above results are reliable.

Discussion
In China, many studies have shown that air pollution has negative effects on health outcomes, such as life expectancy, mortality, and morbidity. It has also been found that air pollution can affect mental health, cognitive ability, productivity, and defense ability (He et al. 2020). Therefore, air pollution has obviously caused a considerable burden, and the improvement of environmental quality during COVID-19 lockdown may bring huge potential health bene ts. According to the above results, we nd that different air indexes have different changes during the lockdown period. The AQI, PM 2.5 , PM 10 , and NO 2 showed a signi cant downward trend after lockdown, while SO 2 and CO changed slightly, while O 3 showed an upward trend. Therefore, we further discuss the causes of different results.
As one of the main sources of air pollution is tra c mobility (Viard and Fu 2015), stricter policies may lead to lower mobility, thus improving air quality. According to the structural rules of AQI and the characteristics of air pollution in China, PM 2.5 and PM 10 are the main factors affecting the change trend of AQI. The main sources of PM 2.5 and PM 10 are burning smoke, industrial dust, building dust, ground dust and secondary pollutants produced by chemical reaction of other pollutants. NO 2 mainly comes from motor vehicle exhaust emissions, high temperature combustion (boiler, furnace) emissions, etc.
Inhalable particulate matter and nitrogen oxides were all affected by tra c interruption and industrial activity reduction during the lockdown period, so AQI, PM 2.5 , PM 10 and NO 2 all showed a signi cant decline.
And SO 2 is often produced by the combustion of fossil fuels in power generation and heating furnaces. Therefore, its response to the blockade policy may be different. Apart from automobile exhaust, a large proportion of CO comes from various incomplete combustion products (such as boilers, industrial furnaces, internal combustion engines, household stoves, etc.). O 3 is a kind of secondary pollutants, mainly nitrogen oxides, volatile organic compounds, and other pollutants in the air, which produce photochemical reactions under the action of sunlight. According to the US Environmental Protection Agency (EPA), SO 2 , CO and O 3 are "standard air pollutants", which will affect human health and the labor market (Hanna and Oliva 2015), and harm people's health(Deschênes and Shapiro 2017, Lleras-Muney 2010). To some extent, residents staying at home have increased the demand for residential electricity and heating resources, especially high-sulfur carbon. Therefore, the increase in residential demand offsets the decrease in industrial demand to a certain extent, resulting in a small change in SO 2 and CO during the lockdown period. The amount of O 3 is inversely proportional to the concentration of nitrogen oxides (Shi and Brasseur 2020). Therefore, when other variables remain unchanged, the reduction of nitrogen oxides leads to the increase of ozone concentration.
Studies have shown that human-related activities are closely related to air quality. However, the blockade policy is not applicable to the prevention and control of air pollution. The reduction of AQI, PM 2.5 , PM 10 and NO 2 is not enough to avoid serious air pollution. Although urban blockade has greatly reduced the air pollution level, the high economic cost of lockdown makes it an unsustainable choice to solve the pollution problem. Compared with other environmental laws and regulations implemented in China, we nd that similar air quality improvement can be achieved at much lower cost. For example, the limitation of gasoline fuel standard alone may reduce the air quality index value by about 13% (Li et al. 2020). The regulations during the Beijing Olympic Games can reduce the concentration of PM 10 in the host city by about 30% (He et al. 2016). In other words, it is very ine cient to use lockdown to reduce pollution, and there are many other more convenient ways to achieve the same environmental goals. The results also con rm that the decline of these indicators is only temporary and not sustainable. After the unsealing, the labor force gradually returned to work, and this temporary improvement is di cult to maintain. As far as China, especially Hubei, it is still too early to think that COVID-19 lockdown can improve the air weather and bene t people's health. However, it is feasible to reduce unnecessary personal trips and improve air quality by emphasizing the importance of green transportation and green production and life.
Our research still has the following limitations: due to the lack of some data, we cannot investigate the in uence of all factors and the subtle reaction mechanism of air quality during the lockdown period. In the follow-up, we can also compare the air quality under the blockade policy in other middle and high-risk areas, such as Pudong in Shanghai and Hebei Province. In addition, we can also consider the in uence of the local government's decision-making autonomy on the blockade policy under the Chinese political system.

Main conclusions
In response to the impact of COVID-19, Hubei Province has adopted unprecedented blockade measures, including closing factories and suspending internal tra c in cities, which may bring about improvement in air quality. The exogenous impact of the epidemic enables us to test the impact of blockade restrictions on air pollution. By controlling the in uence of a series of weather indicators, the effects of the blockade policy on reducing air pollution were systematically evaluated by using linear regression, event study and RD design.
Empirical analysis shows that the restriction measures adopted by 103 county-level units in Hubei have signi cantly reduced air pollution emissions. The AQI decreased by 15.316%, and the concentrations of four air pollutants (PM 10 , NO 2 , PM 2.5 and SO 2 ) decreased by 19.607%, 12.395%, 11.448% and 1.278% respectively. For further study, we analyzed the events study by incorporating a series of "event occurrence times" into regression equation. The results showed that AQI, PM 2.5 , PM 10 and NO 2 all showed a rebound trend about 30 days after the implementation of the blockade policy, which indicated that the temporary lockdown could not bring about continuous improvement of air quality. We also made RD estimation, and found that the concentrations of AQI, PM 2.5 , PM 10 and NO 2 decreased by 35.402%, 29.207%, 14.809% and 7.751% respectively. This is consistent with the change trend of the above results, but the change range is obviously larger than the previous one. We conducted placebo test, sensitivity test of sample selection and different bandwidth estimation to ensure the robustness of the results all of which con rmed the above results. In addition, we further discussed the causes of different pollutants' varying degrees and the inapplicability of using the blockade policy to improve air quality.

Policy Suggestions
According to the above analysis, the lockdown policy adopted by 103 county-level units in Hubei province has signi cantly reduced air pollution emissions, but the improvement in air quality is not sustainable. Based on the research results, this paper puts forward the policy suggestions from the following two aspects:

Promote green travel and reduce tra c emission sources
The emission reduction effect is very signi cant in the case of tra c shutdown during the epidemic, but the high-intensity tra c restriction will cause great economic cost, and the tra c ow restriction policy is not sustainable. Even in the face of COVID-19, a major public health event, travel patterns will not change substantially in the short term. However, as one of the main sources of air pollution, it is necessary to strengthen the effective prevention and control of exhaust pollution. Therefore, this paper proposes to improve air quality by strengthening automobile exhaust emission reduction technology in the following aspects.
First of all, strengthen relevant policy constraints. In view of the environmental pollution caused by automobile exhaust, a simple driving restriction policy cannot bring about sustainable environmental improvement. It is necessary to promulgate relevant policies to restrict the entry into the market of vehicles that do not meet the emission standards of exhaust pollution, and to scrap the vehicles that exceed the standards in an orderly manner, so as to reduce the emission of toxic gases from exhaust gas. Capacity building of vehicle exhaust testing, meanwhile, should keep pace with the market demand, the construction way can draw lessons from foreign advanced I/M management mode, the government set up the regulation of the professional team in the eld of motor vehicle exhaust testing, vehicles for routine testing of the city, to detect unquali ed cases should be given a ne processing.
Secondly, improve fuel quality and cleanliness. With the proposal of China's dual carbon target, the development of new energy vehicles will be an inevitable trend. The research and development of new energy is imminent. At present, the most mainstream new energy technology is electric drive, such as pure electricity and hybrid electricity. In terms of electric energy acquisition, there are lithium batteries, fuel cells, solar cells and so on. New energy vehicles have the characteristics of strong power, low pollution, energy saving and emission reduction. Remove bring new types of new energy solutions, the current mainstream models for diesel locomotives, the market's relatively large, so to solve a lot of fuel engine exhaust emissions is one of the most important way, through the fuel quality improvement to reduce exhaust emissions, can effective implementation in the actual operation level.
Finally, the promotion of public transport vehicles. Despite the high economic cost of tra c restrictions, the air quality improvement brought by tra c restrictions during the lockdown period is obvious to all. Therefore, in the context of the explosive growth of motor vehicles, this paper suggests to improve the relevant policies of vehicle purchase restriction, prevent excessive growth of cars, take appropriate measures to limit the number of vehicles, regularly limit the number of vehicles, improve public transport travel supporting measures, and guide the new trend of green and energy-saving travel. Under certain conditions, the construction of a new way of urban railway travel, on the premise of meeting the emergence of convenience, fast travel will greatly increase people's choice of public transport as the main way of travel.

Promote end-of-pipe governance and improve emission reduction e ciency
The effect of reducing emissions by adjusting industrial structure and limiting production scale is limited. In the context of dual carbon targets, some polluting industries may be reduced in size. However, some of these industries, as essential sectors of national economy, will not only affect the development of local economy, but also may have negative radiating effects through the national division of labor network. Therefore, one-size-ts-all limits on production scale cannot bring good pollution reduction effects.
In order to achieve the goal of "carbon peak" and "carbon neutral", it is necessary to steadily promote the adjustment of industrial structure, especially the internal adjustment of the secondary industry. The key to the green development of the secondary industry and internal energy and chemical industry lies in the transformation and upgrading of the production process. Reducing the dependence on labor force through technological upgrading is the main direction of carbon reduction in light industry. Strengthening the prevention and control of industry, especially light industry, energy and chemical industry and other manufacturing polluters, can signi cantly improve air quality. In the manufacturing industry, there are also high-tech industries such as medicine and polymer materials, whose heavy pollution means that their development mode is still extensive, and it is urgent to realize the dual transformation and upgrading of structure and technology. To realize e cient development in the adjustment of industrial structure is an important direction for these industries in the future. This paper suggests that in the short term, we should give priority to promoting the end treatment of polluting industries mentioned above, and stabilize the cost through corresponding incentive and subsidy mechanism. In the long term, the development of emission reduction technology of polluting industries should be included in local assessment targets to improve e ciency. Figure 1 Dates of lockdown timeline of cities in Hubei Province Note: The unsealing time in Wuhan is April 8th, while in other areas it is March 25th.

Figure 2
Full Sample Regression Results Note *, **, and *** respectively indicate signi cance levels of 10%, 5%, and 1%, All regressions control weather factors, regional and time effects. Coef. is the estimated coe cient value, the vertical line is 95% CI of the estimated coe cient (Coef.) Page 16/17