Did Road Space Rationing Reduce Air Pollution?Evidence from China

Wenbo Li∗

University of Notre Dame

December 3, 2019

The latest version: Click here

Abstract

Road space rationing policies keep cars off the street on the basis of the last digit

of the license plate number. This paper evaluates how different road space rationing

policies affected the air quality of cities in a Chinese province from 2017 to 2019.

I offer the length of the policy as a novel way to categorize road space rationing.

Using a variety of methods including difference-in-differences, event study, and the

synthetic control method, I find significant heterogeneity in policy effectiveness. In

cities where road space rationing was implemented permanently, the policy reduced air

pollution, while in cities where road space rationing was implemented temporarily, I

cannot reject that the policy had zero impact. Furthermore, denser roads experienced a

larger decline in air pollution, and policies that restricted more cars were more effective,

confirming that traffic reduction was the mechanism behind the air pollution effect of

road space rationing. I suggest the intuition behind how permanent and temporary

road space rationing policies can induce different behaviors among people and have

different implications for air quality.

Keywords: Road space rationing; Air pollution; Traffic restriction; China.

JEL Classification Numbers: Q52, Q53, Q58.

∗I thank my advisors Abigail Wozniak, Daniel Hungerman, and Christopher Cronin for their guidance andsupport; and participants of the Notre Dame Micro Brown Bag Seminar for useful comments. This researchis made possible in part by support from the Liu Institute for Asia and Asian Studies at the University ofNotre Dame. All mistakes are my own.

1

1 Introduction

Air pollution plagues cities in developing countries around the world. According to the

World Bank (2003), the 10 cities with the highest airborne particulates are all located in

developing countries. Air pollution affects people’s cardiopulmonary health. A 10 µg/m3

increase in particulate matter concentration has been shown to decrease life expectancy by

0.6 year (Pope III et al., 2009), increase heart failure by 1.3% (Dominici et al., 2006), and

lead to 4-7 more infant deaths per 10,000 live births (Chay and Greenstone, 2003). The 2010

Global Burden of Disease Study (Lim et al., 2010) concludes that air pollution is among the

top 10 health risk factors worldwide and among the top 6 in the developing countries in Asia.

In addition to health outcomes, air pollution has also been shown to incur other short-term

costs to workers’ productivity (Zivin and Neidell, 2012; Li et al., 2015), test scores (Currie

et al., 2009; Stafford, 2015), and happiness (Zheng et al., 2019).

Among other sources, air pollution originates from motor vehicles. The mechanisms

behind motor vehicles as a pollution source include motor vehicle exhaust, which emits par-

ticulate matter, carbon monoxide (CO), unburned hydrocarbon (HC), and nitrogen oxides

(NOx) as well as brake wear, tire wear, and dust raised from the road, all of which also

contribute to particulate matter. The share of particulate matter with diameter less than

2.5 micrometers attributed to motor vehicles in China has been estimated to be around 16%

(Che et al., 2011), and this number can be as high as 41% in major cities in other developing

countries such as India.1

Thus, cities in many countries in Latin America and Asia target private vehicles as

a relatively inexpensive way to curb air pollution. One of the most commonly adopted

measures is road space rationing, which keeps private vehicles off the road on the basis of

the last digit of the license plate number. Compared to other measures that target industrial

sources, road space rationing has the most direct impact on the lives of all residents living

1https://timesofindia.indiatimes.com/city/delhi/usual-suspects-vehicles-industrial-em

issions-behind-foul-play-all-year/articleshow/66228517.cms

2

in urban centers. In China, the people affected by the policy amount to 86 million in more

than 30 Chinese cities.

Other cities around the world that have adopted road space rationing include Mexico City,

Mexico; Sao Paolo, Brazil; Bogota, Columbia; Santiago, Chile; San Jose, Costa Rica; Quito,

Ecuador; and Delhi, India. Intuitively, the effect of road space rationing on air pollution is

unclear. The policy might have induced drivers to carpool or use public transportation more

often; in this case, the amount of air pollution should have decreased. It is also possible

that drivers intertemporally substituted trips on restricted days with trips on non-restricted

days, or that less traffic congestion induced drivers to drive more on non-restricted days; in

these cases, the reduction in air pollution would not be as substantial. In fact, the policy

might have induced some drivers to drive around the restricted area, so that the total miles

driven and the amount of air pollution would have increased.

Previous studies that examine the air quality effect of road space rationing find mixed

results. Eskeland and Feyzioglu (1997), Davis (2008), and Gallego et al. (2013) find that

road space rationing did not improve air quality in Mexico City; they find evidence that

families bought a second car, which was older and more polluting, in response to the policy.

Bonilla (2019) does not find any air quality effect of the policy in Bogota, either. In contrast,

Troncoso et al. (2012) and Carrillo et al. (2016) find that road space rationing in Santiago

and Quito reduced air pollution. Similarly, Viard and Fu (2015) and Chen et al. (2013) find

that road space rationing in Beijing reduced air pollution. Viard and Fu (2015) particularly

finds a surprising result that a more restrictive policy in Beijing was less effective than a less

restrictive policy in the same city.

In this paper, I evaluate road space rationing in Chinese cities and address the following

two questions. First, did road space rationing successfully curb air pollution? Given the

mixed findings in the existing literature and the ambiguity in the direction of potential

effects, the link between road space rationing and air pollution merits further empirical

investigation. In my setting, the 17 cities I study are all located in the same province, and

3

thus are similar in culture and policy enforcement, making these cities comparable. Second,

what feature of a road space rationing policy could make it more effective? I propose that

the length of the policy mattered for the effectiveness of the policy. The restrictiveness and

the length of the policies varied both within and across the 17 cities I study. This variation

allows me to study the heterogeneous effects of the policies along these dimensions. The

existing literature focuses on the restrictiveness as the main way to categorize a policy, but

other sources of heterogeneity might contribute to the wide range of effects I observe.

I collect each road space rationing policy in my sample of cities by examining government

announcements and news articles. The policies of the 17 cities in my sample varied from

4 weeks to 2 years in length, creating significant differences in policy adoption dates and

end dates. Employing a difference-in-differences design, my main approach exploits these

differences, and uses the 17 cities as control groups for each other. Since these cities are all

located in the same province, this strategy controls for policies and meteorological conditions

common to the province. The strategy also controls for any city-specific time-invariant

characteristics such as geographic location and long-run growth rate. In an event study, I

show that there are no underlying trends in the cities that are correlated with the adoption of

the policy, lending validity to this approach. In addition, I also construct synthetic controls

for cities with the policy using cities without the policy across China as an alternative

data-driven approach to form credible control groups. This approach broadens the scope

of potential control groups and avoids local factors such as wind from contaminating the

control group. In forming the synthetic control, I also explicitly include socio-economic

characteristics among the air pollution predictors, which have the potential to better capture

the long-run trend. Furthermore, I also employ data on road density to show that traffic

reduction was the mechanism behind the air pollution effect of road space rationing.

I divide the cities in my sample into two categories on the basis of whether an end

date was announced upon the announcement of the policy. I find significant heterogeneity

in the policy effects. In particular, in cities where road space rationing was implemented

4

permanently, the policy reduced air pollution by 6 percent, while in cities where road space

rationing was implemented temporarily, I cannot reject that the policy had zero impact. I

also find a larger air pollution effect when more vehicles were restricted, further confirming

that traffic reduction was the mechanism behind the effects I observe.

My paper contributes to the existing literature in two ways. First, I offer an addi-

tional way to categorize road space rationing policies, particularly by whether the policy

was adopted permanently or temporarily. I show that the duration of the policy affected its

effectiveness both conceptually and empirically. I suggest three theoretical explanations as

to how permanent and temporary road space rationing policies can induce different behav-

iors among people and have different implications for air quality. In particular, a permanent

policy is more likely to induce people to purchase electric cars, less likely to lead people to

choose non-compliance, and less likely to cause people to stay at home. In this way, I pro-

vide an explanation for the surprising result in Viard and Fu (2015) that a more restrictive

policy was less effective than a less restrictive policy in Beijing, by pointing out that the

more restrictive policy was adopted temporarily while the less restrictive policy was adopted

permanently.

Second, my multi-city setting allows me to separately identify the heterogeneity that

originates from the restrictiveness of the policy and the length of the policy. The existing

literature analyzes one city with road space rationing at a time, and thus it is hard to

disentangle the heterogeneous effect by the restrictiveness of the policy from other features

of the policy, such as the length of the policy, as well as the environment in which the policy

took place, such as people’s readiness for the policy, car purchase limit policies, and other

measures the government implemented to control air pollution. Since, in my setting, the

restrictiveness and the length of the policies varied both within and across cities, I can more

firmly establish the heterogeneous effects along both these dimensions.

5

2 Background

Starting from 2008, a number of cities in China have adopted road space rationing policies.

Beijing, one of the first to adopt such policies, restricted motor vehicles to be off the road

every other day during the two months around the 2008 Summer Olympics; the days a vehicle

was restricted was based on the last digit of the license plate number. For example, vehicles

with a license plate number that ends with an odd number could only be driven on odd

dates, and those with a license plate number that ends with an even number could only be

driven on even dates. I hereafter refer to this policy as the “odd-even policy”, or “OE”. After

the Olympics, Beijing reinstated driving restrictions on Oct. 11, 2008, this time restricting

motor vehicles to be off the road one day per week; the days a vehicle was restricted was

also based on the last digit of the license plate number. For example, vehicles with a license

plate number that ends with 1 or 6 could not be driven on Mondays; those with a license

plate number that ends with 2 or 7 could not be driven on Tuesdays, etc.; there were no

restrictions during the weekend. I hereafter refer to this policy as the “one-day-per-week

policy”, or “OD”. The government of Beijing renewed the one-day-per-week policy for a

few times, essentially making it permanent. Viard and Fu (2015) show that the odd-even

policy reduced the particulate matter in Beijing during the 2008 Summer Olympics by 18

percent, and the less restrictive one-day-per-week policy that ensued the Olympics reduced

particulate matter in Beijing by an even larger 21 percent.

Several Chinese cities have followed the footstep of Beijing, and have adopted the one-

day-per-week policy permanently. Many more have chosen to implement short-term road

space rationing policies to combat air pollution in the winter, when air pollution in China

was particularly severe. In the winter of 2018, ten years following the Beijing Olympics,

more than 30 cities in China adopted road space rationing. Most of these cities are situated

in Henan, Hebei, Shanxi, and Shaanxi, four adjacent provinces in central, northern, and

western China. Among them, Henan is the only province in which both the type and the

length of road space rationing policies varied both within and across cities. Thus, I focus

6

my analysis on Henan in this paper. Figure 1 shows where Henan situates in China, and

Figure 2 shows a map of the 17 cities in Henan. These 17 cities consist of an exhaustive list

of cities in Henan Province.

Why did cities in Henan adopt road space rationing? Although three cities in Henan,

Xinxiang, Anyang, and Puyang, did adopt road space rationing earlier, all other 14 cities in

Henan implemented road space rationing for the first time in Dec. 2017. Such a sweeping

policy change was not a coincidence, even though the decision to adopt a road space rationing

policy was made at the city level. In fact, the State Council of China released the Air

Pollution Prevention and Control Action Plan in 2013. The Plan specified that all cities in

China were required to reduce their particulate matter concentration by at least 10 percent

by 2017 on the basis of its respective 2012 level. 2017 marked the deadline for this assessment,

and, realizing that its cities were a bit behind in hitting the targets, Henan had a last-minute

scramble to encourage them to adopt road space rationing to hit the targets. Indeed, on

Nov. 30, 2017, a Henan standing committee member stated “the average PM10 (particulate

matter with diameter less than 10 micrometers) concentration target for Henan in 2017 is 108

µg/m3”, but by Nov. 28, 2017, the year-to-date average PM10 concentration was 111 µg/m3,

i.e. 3 µg/m3 above the target.2 For this reason, the adoption of road space rationing among

cities in Henan can be seen as exogenous. In the U.S. context, Chay and Greenstone (2005)

similarly use the attainment status of U.S. counties under the Clean Air Act as exogenous

variation in changes in future air quality, under the assumption that the attainment status

is unlikely to be correlated with other time-varying city characteristics.

Figure 3 shows each road space rationing episode in each city in Henan during my sample

period from Jan. 1, 2017 to May 11, 2019. The policies varied from 4 weeks to a couple of

years in length. The solid line represents the odd-even policy and the short dash represents

the one-day-per-week policy. The odd-even policy was widely adopted in the winter of both

2017 and 2018, but the one-day-per-week policy was more common in other seasons, partic-

2http://other.caixin.com/2017-12-05/101180801.html (in Chinese)

7

ularly among cities that made the policy permanent. I define a road space rationing policy

as permanent if, upon announcing the start date, the city government did not announce the

end date. The policies adopted by 9 cities satisfy this definition, and the policies adopted by

the other 8 cities, which “toggled” between having the policy and not having the policy, do

not. I thus categorize the former set of cities as “permanent adopters” and the latter set of

cities as “togglers”. There was much variation in the policy adoption dates and end dates,

both for permanent adopters and togglers, and this fact forms the basis of my empirical

strategy.

Cities in Henan also undertook measures that targeted air pollution from industrial

sources, for example rectifying coal-fired boilers, moving production away from highly pol-

luted seasons, and shutting down construction sites, but it is likely that the start dates

and end dates of these measures do not coincide with those of road space rationing. Thus,

given that my data are at the daily frequency, my empirical specification, to be explained in

Section 5, should still be able to identify the effect of road space rationing alone.

As mentioned in Section 1, the mixed findings in the existing literature on the effect

of road space rationing on air pollution suggest that the policy effect can be very context

specific. In particular, China has replaced its emission standards three times over the past

decade and rapidly scrapped cars that did not meet these standards. This fact rules out the

possibility that families bought a second car that was more polluting when facing road space

rationing, and implies that the policy might not have increased air pollution as Mexico City

experienced.

The restriction applies to both gasoline cars and more polluting diesel trucks. Violations

of traffic restriction were detected by both police officers on the street and cameras installed

throughout the cities. Violators were fined 100-200 Yuan (approximately 16-32 USD), which

was 2-4 percent of Henan residents’ mean monthly income.3 In addition, violators were also

commonly given penalty points on the drivers’ licenses. Viard and Fu (2015) find high levels

3Henan Statistical Yearbook 2018.

8

of compliance in Beijing. Given the government approach in China, it may be reasonable to

assume similar compliance in my setting, but I will allow for non-compliance in my conceptual

framework, which I turn to next.

3 Conceptual Framework

In this section, I build a model to illustrate how the length of a road space rationing

policy can have different implications for people’s behavior and thus air pollution. I offer

three channels through which this might hold: 1) an individual only purchases an electric

car, a type of car not restricted by road space rationing, when the policy is long enough;

2) a high-income individual only chooses not to comply with road space rationing when the

policy is short enough; and 3) an individual might stay at home when the policy is short,

but choose a new way to travel when the policy is long. In particular, a representative driver

solves the following problem in partial equilibrium:

max{xt,lt},b,N

T∑t=1

xαt l1−αt

s.t. bE +T∑t=1

xt = A0 + wT∑t=1

(24− lt − zt)− pfT

2N

(3.1)

I assume the above preferences for convenience, but, as I show in Appendix A, the

intuition does not rely on this assumption. I also assume no discounting and perfect foresight.

The driver maximizes life-long utility from Period 1 to Period T by choosing a consumption

good x, leisure l, whether or not to purchase an electric car, and whether to comply with road

space rationing. b is a dummy variable that equals 1 if the individual purchases an electric

car and 0 if not. The price of the electric car is E. N is a dummy variable that equals 1

if the individual chooses non-compliance, i.e. to drive on restricted days and to risk being

fined. p is the probability of being caught on a single day if he/she chooses non-compliance;

f is the fine if he/she gets caught. A0 is an exogenous initial non-wage income, and w is an

9

exogenous hourly wage. zt is the transit time, which is equal to a) z if the individual travels

by public transit, b) z if the individual travels by (electric or gasoline) car, with z > z, or

c) 0 if the individual does not go to work. Assume that an odd-even policy is in effect from

Period 1 to Period T (where T is an even number), and that the individual’s gasoline car is

restricted in the even periods, thus Period 2, 4, . . . , T . Assume that the individual has to

work every period. Then,

Implication 1: The individual purchases an electric car if and only if the road space ra-

tioning policy lasts long enough.

(See Appendix A for a formal proof.)

Intuitively, purchasing an electric car represents paying a high fixed cost. If the individual

is willing to pay this fixed cost, he/she can later enjoy more periods with low transit time.

Even though electric cars consume electricity and electricity generation may create air

pollution, road space rationing did not restrict electric cars. This is because the air pollution

created from power plants are meant to be carried far away, and thus the impact electric cars

have on ground-level air pollution is less than 1/10 of that by gasoline cars. Furthermore,

once a driver purchases an electric car, he/she is likely to only drive the electric car from

then on, including on days his/her gasoline car is not restricted. Thus, the purchase of an

electric car reduces air pollution compared to the case in which the individual takes public

transportation on restricted days.

Even though the purchase of an electric car in this case can be generalized into the

purchase of another gasoline car, the latter does not change the individual’s contribution

to air pollution on a potentially restricted day compared to his/her contribution absent the

policy. On the other hand, any individual who purchases an electric car reduces his/her air

pollution input on a potentially restricted day. Thus, this model still implies that only the

road space rationing policies that are long enough can reduce air pollution.

More broadly, the purchase of an electric car can be generalized to the choice of other

modes of transportation that involve a high fixed cost. For example, drivers who want to

10

carpool need to find a person to carpool with. Given this fixed cost, a longer road space

rationing policy will drive down the average cost and thus make these drivers to more likely

to opt to these alternative modes of transportation.

Implication 2: A high-income individual only refuses to comply with road space rationing

when the policy is short.

(See Appendix A for a formal proof.)

A model allowing for non-compliance implies that a high-income individual chooses non-

compliance, i.e. to drive on restricted days and to risk being fined, when the policy is short,

and purchases an electric car when the policy is long. Intuitively, if the individual chooses

non-compliance, his/her probability of getting caught increases as the road space rationing

policy gets longer; this makes the option of buying an electric car more attractive if the

policy lasts long enough. Since the individual’s contribution to air pollution remains high if

he/she chooses non-compliance, this implication means that non-compliance can be another

channel through which a longer road space rationing policy can be more effective.

Of course, sometimes an individual might choose not to work, so now I will consider a

setting where that is their choice.

Implication 3: An individual under a flexible work schedule might not work on restricted

days.

(See Appendix A for a formal proof.)

The model shows, unsurprisingly, that an individual is more likely to stay at home if the

opportunity cost of doing so is small. A potential implication of this is that, if policies (such

as short-term policies) create relatively small costs for those who choose to stay at home,

they could induce many individuals to stay at home, but this response would be purely

temporary in nature.

The upshot is that, even if road space rationing is effective in keeping cars off of the road

during the period of the policy, the effect could be driven either by short-term (stay at home)

or long term (find a new way to travel) behavior, and the implications of these for air quality

11

are different, because it is possible that those who find a new way to travel may form a habit

of choosing this new way even in periods when they are no longer restricted. Lastly, the

model shows that long-term solutions are more likely to be observed for long-term policies.

This model has implications for applied work. First, it shows that variation in the

duration of policy can matter empirically. Second, Davis (2008) on Mexico City and Viard

and Fu (2015) on Beijing both implement the regression discontinuity design, which focuses

on the few days and the few weeks before and after policy adoption. My model shows

that interpretation of a policy’s effectiveness could require studying a policy over months

or more, rather than just focusing on the days and the weeks immediately after a policy

is introduced. Finally, the effects of a policy could vary depending upon the context. For

example, countries differ in the probability an individual gets caught if he/she refuses to

comply. In this case, a policy in Mexico could have different impacts than policies in China.

This paper will attempt to bring all of these ideas to bear in its empirical analysis; I discuss

the data and the empirical set up next.

4 Data

4.1 PM2.5 Concentration and Air Pollution Measure

Cities in China are required by law to build monitoring stations to monitor air quality.

The locations of the monitoring stations have been chosen to cover all of the built-up area

within a city. The readings from the monitoring stations are published on the China National

Environmental Monitoring Center (CNEMC) website and updated hourly. These readings

include pollutant concentrations for particulate matter with diameter less than 2.5 microm-

eters (PM2.5), particulate matter with diameter less than 10 micrometers (PM10), nitrogen

dioxide (NO2), carbon monoxide (CO), sulfur dioxide (SO2), and ozone (O3). In addition

to pollutant concentrations, the CNEMC also reports the Air Quality Index (AQI), which is

12

calculated based on concentrations of all pollutants observed by the monitors.4 The index

ranges from 0-500, with a higher number indicating worse air quality. It is classified into

six levels of air quality: excellent for AQI≤50, good for 51≤AQI≤100, lightly polluted for

101≤AQI≤150, moderately polluted for 151≤AQI≤200, heavily polluted for 201≤AQI≤300,

and severely polluted for 301≤AQI≤500. In China, a “blue sky day” is defined as a day

with the AQI not exceeding 100; the number of blue sky days in a year often factors into

the cadre evaluation of local government officials, and raising this number is seen as a major

government objective.

I choose PM2.5, one of the primary pollutants of motor vehicles, to be the focus of this

study to be consistent with Chen et al. (2013) and Viard and Fu (2015), who use the Air

Pollution Index, which is similar to the AQI and is mostly driven by particulate matter

concentration, as their main outcome. Another reason for choosing PM2.5 as the focus of

this paper is that a significant portion of ambient particulate matter originates from motor

vehicles. In fact, the share of PM2.5 attributed to motor vehicles in Henan is estimated to be

10-15 percent on a day with good air quality and 22-38 percent on a heavily polluted day.5

The hourly data published by the CNEMC since 2014 were web-scraped and made avail-

able by a third party.6 My data include readings from 1605 monitoring stations in 369 cities

in China, and cover the period from Jan. 1, 2017 to May 11, 2019. For my main analysis, I

aggregate these data to the city-date level, and thus my full sample is a panel of PM2.5 con-

centrations and the AQI for 369 cities over a span of two and a half years. Table 1 reports the

summary statistics for a subsample of the 17 cities in Henan only. The air quality guideline

of the World Health Organization (WHO) stipulates that the annual mean of PM2.5 does

not exceed 10 µg/m3, which is substantially lower than the mean PM2.5 concentration (66.8

µg/m3) of the cities in Henan during the sample period. The daily PM2.5 concentration 1

standard deviation above the mean is 115.7 µg/m3, and the daily PM2.5 concentration 1

4To calculate the AQI, CNEMC performs a non-linear transformation of each pollutant concentration tocalculate the individual AQI’s. The AQI is then the maximum of these individual AQI’s across all pollutants.

5http://www.xinhuanet.com/local/2017-12/15/c 1122113564.htm?baike (in Chinese)6http://beijingair.sinaapp.com/ (in Chinese)

13

standard deviation below the mean is 17.9 µg/m3. Although these numbers suggest that

most cities in Henan qualified for the blue sky days most of the time, a significant frac-

tion of cities experienced many highly-polluted days with PM2.5 concentration above 100

µg/m3 during the winter. The between-city standard deviation and the within-city stan-

dard deviation reported in Table 1 capture this strong seasonality of air pollution and its

significant day-to-day variation: around 90 percent of the variation in PM2.5 concentration

is within-city.

I decide to choose readings from land-based monitoring stations over satellite data, be-

cause the aerosol optical depth (AOD) data employed by Chen et al. (2013) are shown to

lag behind actual air pollution levels by up to 4 months, making satellite data unsuitable

for high-frequency observations required for this study. In addition to providing accurate

air pollution measure and pollutant concentrations, the data from land-based monitoring

stations also have another advantage over remote sensing satellite data, because monitoring

stations in China are only meant to cover the built-up area, but not the rural area. Road

space rationing in Henan typically only affects the urban center within the built-up area,

making the changes in air pollution levels in this area particularly relevant.

4.2 Weather

The weather data, which I use as controls in a robustness check and as air pollution

predictors in forming the synthetic control, are made available by the National Oceanic and

Atmospheric Administration (NOAA), and are daily readings from land-based monitoring

stations. The observed measures include average, minimum, and maximum temperature,

dew point, precipitation, and wind speed. All these measures are known to predict the

amount of air pollution: higher temperature speed up chemical reactions in the air; moisture

worsens the smoggy conditions; rain washes out water-soluble pollutants and particulate

matter; wind affects the dispersion and dilution of pollutants.

Since the cities in my sample do not completely overlap with the locations of the NOAA

14

monitoring stations, I follow Qin and Zhu (2018) and search for the closest monitoring

station for each city. In sum, I match the 369 cities in my sample with 240 different NOAA

monitoring stations. For dates when the weather data from the NOAA website were not

available for any city, I collect the same weather measures from a third party that also

publishes historical weather readings of NOAA monitoring stations.7 For dates when the

weather data for only certain cities were unavailable, I perform linear interpolation for the

weather measures of these cities. Panel A of Table 1 also reports the summary statistics of

these weather controls in Henan. There is little variation in weather measures within Henan

on any single day, so I leave out weather controls in my main specifications and instead

include them in a robustness check.

4.3 Other City-level and Monitor-level Characteristics

Panel A of Table 1 also reports the summary statistics of some city-specific characteris-

tics. I use car ownership, collected from the Henan Statistical Yearbook 2018, in a robustness

check to determine whether the heterogeneous effects by permanent adopters and togglers are

confounded by this variable. Population, per-capita GDP, industrial output, dust emission,

and unemployment rate can potentially determine air pollution, and are used as additional

predictors in forming the synthetic control. These measures come from the China City Sta-

tistical Yearbook 2017, and capture the pre-treatment conditions in demographics, industrial

composition, industrial waste, and labor market.

Panel B of Table 1 reports the summary statistics of road density on a cross-section of

monitoring stations. There were on average around 5 monitoring stations in each city. Road

density is measured by 1km resolution, and values exist for the entire Henan Province. I

assign a road density value to each monitoring station by locating its longitude and latitude.

The road density data are based on OpenStreetMap, and are collected by Niu et al. (2017).

The standard deviations of car ownership, population, industrial output, and road den-

7http://www.meteomanz.com/

15

sity are relatively small compared to the differences between the respective maximum and

minimum, indicating that the variation across cities is mostly driven by the extreme values

created by a megacity, namely Zhengzhou.

5 Empirical Strategy

5.1 Difference-In-Differences Using Local Area Controls

The identification strategy exploits the differences in policy adoption dates and end dates

across cities. The effect of road space rationing is then identified by taking two differences,

across cities and across dates. Thus, following the program introduction literature (Hoynes

and Schanzenbach, 2009, for example), I categorize this empirical strategy as difference-

in-differences (DiD). This strategy controls for any shock that affected the air pollution

levels in cities with and without road space rationing at the same time, such as policies or

meteorological conditions common to the province. It also controls for any city-specific time-

invariant characteristics, such as geographic location and long-run growth rate. In addition,

as described in Section 2, I categorize the 17 cities in Henan into 9 permanent adopters and

8 togglers based on whether the end date was announced upon the adoption of the policy. In

estimating the following equation, I determine the air pollution effects of road space rationing

for permanent adopters and togglers separately on a sample that includes daily observations

of the 17 cities in Henan Province from 2017 to 2019:

AirPollutionct = β0 + β1RSRinPermanentct + β2RSRinTogglerct + δc + µt + εct (5.1)

Where c denotes city, and t denotes date; AirPollutionct is the PM2.5 concentration of

city c on date t; RSRinPermanentct is an indicator variable that takes the value of 1 if city

c is a permanent adopter and if city c had road space rationing in place on date t; similarly,

RSRinTogglerct is an indicator variable that takes the value of 1 if city c is a toggler and if

16

city c had road space rationing in place on date t; δc is the city fixed effect; µt is the date

fixed effect; εct is the error term. To allow the error terms to be correlated within a city, I

cluster the standard errors at the city level.

As I mentioned in Section 4.1, another policy-relevant outcome is whether a city qualified

for a blue sky day or not, so I also estimate Equation 5.1 with having a blue sky day (i.e.

with AQI≤100) as the dependent variable to determine whether road space rationing had

the potential to impact cadre evaluation.

The control group of this two-way fixed effects DiD estimator is an average of the following

two types of observations: 1) for a city/day with a policy, the control group consists of own

city in the past without the policy and other cities without the policy on the same date; 2)

for a city/day without a policy, the control group consists of own city in the future with the

policy and other cities with the policy on the same date. That is, the control group consists

of cities that were untreated for a longer period compared to other cities as well as cities that

were treated for a longer period compared to other cities. The DiD estimator places more

weight on the city-by-city comparisons that involve a city that made road space rationing

permanent relatively early, i.e. in the middle of my sample period (Goodman-Bacon, 2018).

The identifying assumptions are two-fold. First, there are no underlying trends in the

cities that are correlated with the adoption of the policy, i.e. road space rationing episodes

can be seen as being quasi-randomly assigned. Second, no city-specific characteristic is

correlated with both the air pollution effect of road space rationing and whether a city was a

permanent adopter, i.e. the permanent adopter status can be seen as being quasi-randomly

assigned.

To explicitly test the validy of the first identifying assumption, I conduct an event study,

following Hoynes and Schanzenbach (2009). In particular, I estimate the following equation:

AirPollutionct = c0 +19∑

j=−18

τj1(EventWeekct = j) + δc + µt + εct (5.2)

Where 1 is an indicator function; EventWeekct takes the value of j if date t fell in the

17

j’s week since the road space rationing policy was introduced in city c; i.e. EventWeekct is

0 if date t fell in the last week before the policy took effect in city c; the omitted reference

group is j = −1. Thus, τj measures the difference in mean air pollution levels j weeks after

road space rationing took effect and the week before the policy took effect. I estimate this

equation separately for permanent adopters and for togglers. In estimating this equation, I

let δc again be the city fixed effect, and µt the date fixed effect. Standard errors are again

clustered at the city level. In Section 6.1, I discuss additional tests that probe the validity

of the second assumption.

5.2 Synthetic Control Method

So far, I have used cities in the same province as control groups for each other (hereafter

“local area controls”, or “LAC”). As an alternative approach to construct credible control

groups, I construct a synthetic control for each permanent adopter from cities across China,

following Abadie and Gardeazabal (2003) and Abadie et al. (2010) (hereafter “synthetic

control method”, or “SCM”). A potential disadvantage of the LAC is that wind might carry

pollutants from one city to another, and thus making a treated city untreated and vice versa.

This will attenuate the effects estimated by the LAC, but the SCM avoids this problem by

extending the pool of available controls to cities that are farther away. Another advantage

of the SCM is that, in forming the synthetic control, I employ air pollution predictors such

as population, per-capita GDP, gross industrial output, dust emission, and unemployment

rate. I believe that these socio-economic characteristics may better capture the long-run

trend in air pollution. For example, if the central government implement an environmental

policy that only affects the real estate industry of cities of certain sizes, a far-away city of

similar size may form a better control group than a nearby city of disparate size.

In order to construct a valid synthetic control, the characteristics of the treated city

must lie within the convex hull of those of the untreated cities, or the “donor pool”. This

assumption can be visually inspected by comparing the pre-trend of a treated city and

18

its synthetic control as well as quantitatively verified by checking the pre-treatment mean

squared prediction error (PMSPE). In applying the SCM, I examine the adoption of road

space rationing policies among all 9 permanent adopters in Henan in the winter of 2017.

To fix ideas, first assume that there is only one treated city, denoted by city 1. Let J

be the total number of available control cities in the donor pool, and denote each available

control city j ∈ {2, . . . , J + 1}. I exclude from the donor pool cities with road space ra-

tioning.8 Let Y1 be a (T × 1) vector whose elements are the PM2.5 concentration for the

treated city on date t, denoted by Y1t. Let Y0 be a (T × J) matrix which contains the values

of the same variables for control city j on date t, denoted by Yjt. Let T0 be the number of

pre-treatment periods, with 1 < T0 < T . Let W = (w2, . . . , wJ+1)′ be a (J × 1) vector of

non-negative weights which sum to one. The scalar wj, (j = 2, . . . , J + 1), represents the

weight of city j in the synthetic city. Let X1 be a (33× 1) vector of pre-treatment values of

33 air pollution predictors for the treated city. These predictors include the annual average

of average temperature, maximum temperature, minimum temperature, dew point, precipi-

tation, wind speed, the PM2.5 concentrations of every other day for the 24 days immediately

preceding policy adoption, and of every 30 days in 2017 before policy adoption, as well as

population, per-capita GDP, gross industrial output, dust emission, and unemployment rate.

Let X0 be a (33 × J) matrix which contains the values of these same variables for the J

possible control cities. Let V be a diagonal matrix with non-negative components. The

values of the diagonal elements of V indicate the relative importance of the 33 air pollu-

tion predictors. Following Abadie and Gardeazabal (2003) and Abadie et al. (2010), I use a

nested structure to determine W ∗ and V . The vector of weights W ∗ is chosen to minimize

(X1 −X0W )′V (X1 −X0W ) subject to wj ≥ 0, (j = 2, ..., J + 1), and w2 + ... + wJ+1 = 1.

The vector W ∗(V ) determines the combination of control cities which best resembled the

treated city given a chosen set of relative importance of air pollution predictors, V . Then, I

8I exclude from the donor pool Beijing, Nanchang, Guiyang, Hangzhou, Chengdu, Lanzhou, Tianjin,Xi’an, Xianyang, Tongchuan, Baoji, Weinan, Shijiazhuang, Handan, Baoding, Langfang, Zhangjiakou, Tang-shan, Cangzhou, Xingtai, Qinhuangdao, Yangquan, Jincheng, Yuncheng, Xinzhou, Linfen, Changzhi, andJinzhong.

19

choose V to minimize the PMSPE, i.e.∑T0−14

t=1 (Y1t −∑J+1

j=2 wjYjt)2. To avoid pre-treatment

dates close to the treatment from contaminating the construction of the synthetic control, I

exclude the two weeks prior to the treatment when minimizing the PMSPE. After obtaining

W ∗, the treatment effect of post-treatment day t is given by α1t = Y1t −∑J+1

j=2 wjYjt with

t = T0 + 1, . . . , T .

I then aggregate the outcomes of the treated cities and their synthetic controls across

cities. To save computation time, I limit the available control cities to be within the 7

provinces adjacent to Henan that never adopted road space rationing policies.9 There are

a total of 63 such cities. The advantage of aggregating the treatment effect is that, besides

ease of interpretation, it eliminates some noise in day-to-day air pollution changes. To do

so, I need to allow the treatment time to vary across cities. I follow Cavallo et al. (2013)

and aggregate the effect for each post-treatment day t by taking a simple average across all

treated cities t days after road space rationing was introduced. I denote each treated city g =

1, . . . , 9. Then, the estimated average effect for the 9 road space rationing policies is given by

α = (αT0+1, ..., αT ) = 19

∑9g=1 (αg,T0+1, ..., αg,T ). To conduct inference, I again follow Cavallo

et al. (2013) and calculate the p-values that measure the probability that an observed effect

happened by chance. I choose 9 cities among the 63 available control cities and assign placebo

road space rationing episodes to them corresponding to the road space rationing episodes of

the actually treated 9 cities. I obtain the placebo treatment effect for each post-treatment

day l as αpl(np)l , where np represents all 639 possible placebo averages. Then, the p-value

for post-treatment day l is given by P(|αl| < |αPL(np)l |) = 1

639

∑639

np=1 1(|αl| < |αPL(np)l |). In

practice, to save computation time, I randomly draw 1,000,000 placebo averages to calculate

the p-values.

9These provinces are Hebei, Shandong, Jiangsu, Anhui, Hubei, Shaanxi, and Shanxi.

20

6 Results

6.1 Baseline

I first show results that probe the validity of the first identifying assumption: the adoption

of road space rationing can be seen as being quasi-randomly assigned. Figure 4 shows the

results from the event study. The top panel reports the estimates of τj as well as the 95-

percent confidence intervals for the road space rationing episodes in permanent adopters.

The pre-trend is very close to 0 and stays constant. The coefficient estimates post-treatment

are mostly negative, albeit only statistically significant in Weeks 10, 13, and 15. The bottom

panel reports the results for the road space rationing episodes in togglers. The pre-trend

is again not discernable from 0. The coefficient estimates post-treatment are also mostly

statistically insignificant. I take these as evidence that there are no underlying trends in

cities that are correlated with the adoption of the policy.

I now show results that probe the validity of the second identifying assumption: whether

a city was a permanent adopter can be seen as being quasi-randomly assigned. Table 2 dis-

plays results from a logit regression that tests if car ownership, population, per-capita GDP,

and dust emission can independently or jointly determine whether a city was a permanent

adopter. These four characteristics are chosen to capture the size (population), the wealth

(car ownership and per-capita GDP), as well as the cleanliness (dust emission) of the 17 cities

in Henan. Given that the regression is run on a sample of 17 cities, it is no surprise that

no coefficient estimate is statistically significant. Nevertheless, conversations with officials

at the Department of Ecology and Environment of Henan Province suggest that the most

relevant variable of interest is car ownership. In particular, I wish to address the concern

that perhaps only the cities with many cars implemented road space rationing permanently.

In Figure 5, I plot car ownership by city, which in turn is grouped into permanent adopters

and togglers. I fit a red line to all the observations, and the red line is slightly sloping up-

wards, but an outlier, Zhengzhou, which had close to three times as many cars as the second

21

most car-rich city, seems to be driving the fitted line. Thus, I exclude Zhengzhou, and fit

a green line, which barely slopes upwards. I take this as evidence that permanent adopters

and togglers do not differ much in car ownership. I thus conclude that whether a city was a

permanent adopter can be seen as being random.

Table 3 reports the baseline results from estimating Equations 5.1. Road space rationing

in permanent adopters reduced PM2.5 concentration by 4 µg/m3, which translates into a

6-percent decline. The policy in togglers raised PM2.5 concentration by 10 µg/m3, which

translates into a 15-percent increase, but this latter result is not robust to alternative specifi-

cations in Section 6.2. Meanwhile, for permanent adopters, a day when road space rationing

was in effect was 3 percentage point (5 percent) more likely to be a blue sky day; for togglers,

a day when the policy was in effect was 7 percentage points (11 percent) less likely to be a

blue sky day. I take these results as evidence that in cities where road space rationing was

implemented permanently, the policy reduced air pollution, while in cities where road space

rationing was implemented temporarily, I cannot reject that the policy had zero impact.

As mentioned in Section 4.1, the share of PM2.5 attributed to motor vehicles in Henan is

estimated to be 10-15 percent on a day with good air quality and 22-38 percent on a heavily

polluted day. Since road space rationing restricts 1/5 or half of the motor vehicles, a simple

back-of-the-envelope calculation suggests the policy should reduce PM2.5 concentration by

2-19 percent. The 6-percent decline I find in permanent adopters falls within this range. In

comparison, the existing literature finds that road space rationing reduced air pollution by

13-29 percent in Beijing (Viard and Fu, 2015; Chen et al., 2013). The 6-percent decline I

find is smaller, but this difference can be due to the fact that there are many more motor

vehicles in Beijing than in Henan. The effects found for cities in other countries include a

decline of air pollution by 5-12 percent in Santiago (Troncoso et al., 2012) and a decline in

air pollution by 9-11 percent in Quito (Carrillo et al., 2016). The effect I find is similar in

magnitude to these numbers.

22

6.2 Robustness of the LAC

Table 4 shows the results from estimating Equation 5.1 while using other pollution mea-

sure and pollutant concentrations as the dependent variable. The coefficient estimates for

the AQI, PM2.5, PM10, NO2, and CO are all negative and statistically significant. The

effects range from 4 percent for PM10 to 6 percent for PM2.5. The fact that the percentage

reduction of PM2.5 is larger than that of PM10 may indicate that the policy had the largest

impact on the finest particulate matter. Furthermore, since car exhaust does not include

SO2, road space rationing should not have any effect on SO2 concentration. Indeed, Column

(6) shows that the coefficient estimate for SO2 is not statistically significant.

An alternative to estimating Equation 5.1 is categorizing each road space rationing

episode as either an open-ended episode or a short-term episode. An open-ended episode

is defined as one upon whose announcement no end date was announced, and a short-term

episode is defined as one upon whose announcement an end date was announced. This

alternative specification differs from Equation 5.1 in that it groups the initial episodes of

permanent adopters in Dec. 2017 together with the episodes of togglers. In particular, I

estimate the following equation:

AirPollutionct = γ0 + γ1OpenEndedRSRct + γ2ShortTermRSRct + δc + µt + ξct (6.1)

Where OpenEndedRSRct is an indicator variable that takes the value of 1 if city c had an

open-ended episode in effect on date t; similarly, ShortTermRSRct is an indicator variable

that takes the value of 1 if city c had a short-term episode in effect on date t. δc is again the

city fixed effect, and µt the date fixed effect. Standard errors are again clustered at the city

level.

If people in permanent adopters did not expect the road space rationing policies to be

made permanent during the initial episodes in Dec. 2017, then Equation 6.1 should be

a preferred specification to Equation 5.1. This is because the later open-ended episodes

23

in permanent adopters should be treated as being independent from the initial short-term

episodes in Dec. 2017 in the same cities. On the other hand, if people in permanent adopters

did expect the policies to be made permanent during the initial episodes in Dec. 2017, then

Equation 5.1 should be preferred. In this case, the later open-ended episodes in permanent

adopters were merely a continuation of the initial short-term episodes in Dec. 2017 in the

same cities.

Table 5 shows the results from estimating Equation 6.1. Open-ended episodes reduced

PM2.5 concentration by 3 µg/m3, which translates into a 5-percent decline. A day during

an open-ended episode was 2 percentage points (3 percent) more likely to be a blue sky day.

The coefficient estimates for short-term episodes are not statistically significant. Thus, the

results are robust to grouping the initial episodes of permanent adopters with the episodes

of togglers.

Additional evidence suggests that Equation 5.1 should be preferred to Equation 6.1, that

is, people in permanent adopters during the initial episodes in Dec. 2017 did expect the

policy to be made permanent later. 5 news articles in two permanent adopters and one

toggler discuss whether people expected the policy to be made permanent in the future: 1)

an article in Zhengzhou (a permanent adopter) compares Zhengzhou in 2017 to Beijing in

2008, implying that road space rationing was going to be made permanent in Zhengzhou

as it had been in Beijing;10 2) an article in Zhengzhou cites the potential of road space

rationing being made permanent as the reason why a person bought an electric car;11 3) an

article quotes an provincial official and says that whether the decision of making road space

rationing permanent across Henan was inconclusive by that time, but road space rationing

would be implemented in highly polluted days in the future;12 4) an article in Kaifeng

(another permanent adopter) lays out the government objectives, which include formulating

the rules of a permanent road space rationing policy, implicitly taking a future permanent

10http://www.hnr.cn/news/snxw/201712/t20171214 3045557.html (in Chinese)11https://4g.dahe.cn/news/20171207233055 (in Chinese)12https://new.qq.com/omn/20171223/20171223A048RZ.html (in Chinese)

24

road space rationing policy as given;13 5) an article in Shangqiu (a toggler) quotes a local

official who said that the odd-even policy that Shangqiu adopted in Dec. 2017 could only

be short-term and was not sustainable.14 I take these articles as evidence that people in

permanent adopters expected the policy to be made permanent in the months following

Dec. 2017, while people in togglers did not. Table A.2 provides further evidence showing

that this is the case.

Table 6 shows the results from alternative specifications of Equation 5.1. Column (1)

shows the baseline results. I include the weather controls in Column (2). To avoid highly

polluted days from driving my results, in Column (3), I use logged PM2.5 concentration as the

dependent variable. In Column (4), I explicitly only include days with PM2.5 concentration

less than 350 µg/m3. Since more cities adopted road space rationing toward the end of my

sample, and since air pollution was on the decline over my sample period, in Column (5), I

include variable-specific time trend, where the variables include population, per-capita GDP,

and gross industrial output. In Table A.1, I show that the results are robust to including

quadratic time trends. Since most cities adopted road space rationing at the end of a calendar

year, when major holidays took place, to avoid the concern that there might be a slowdown

in economic activities during these holidays, in Column (6) of Table 6, I drop Chinese New

Year, New Year’s Day, and Christmas. In Column (7) of Table 6, I weight the regression by

city population to give the coefficients a per-capita interpretation. The results are robust to

these alternative specifications.

Cluster-robust t-statistics can lead to severe overrejection when the number of clusters is

small (Djogbenou et al., 2019; MacKinnon and Webb, 2017; MacKinnon and Webb, 2018),

but the wild cluster bootstrap adjusts for this bias (Cameron et al., 2008; Djogbenou et al.,

2019). P-values calculated from the wild cluster bootstrap are 0.007 for RSRinPermanentct

and 0.100 forRSRinTogglerct, suggesting that the coefficient estimate of the former covariate

is statistically significant. Alternatively, to address the concern that the sample size may

13http://www.kfhb.gov.cn/index.php/Home/News/view/id/2945.html (in Chinese)14http://k.sina.com.cn/article 5062856580 12dc50f840340061mz.html (in Chinese)

25

not be large enough and that the errors may not be normally distributed, I conduct a

permutation test, where I collect the set of real policies of the 17 cities and randomize these

policies within the 17 cities. This allows me to draw a set of placebo coefficient estimates. I

draw 1000 sets of such placebo coefficient estimates, whose distribution I show in the yellow

bars of Figure 6. The red lines represent the values of the real coefficient estimates. From

this test, the coefficient estimate of RSRinPermanentct is significant at the 5 percent level,

and that of RSRinTogglerct is significant at the 1 percent level.

To avoid any single city from driving my results, I estimate Equation 5.1 while dropping

one city at a time. Figure 7 shows the coefficient estimates of RSRinPermanentct in the

top panel and those of RSRinTogglerct in the bottom panel. The city name on the vertical

axis represents the city that is being dropped. The coefficient estimates and the 95-percent

confidence intervals are consistent throughout dropping any city. I take this as evidence that

the results are not driven by any single city alone.

Furthermore, the Beijing-Tianjin-Hebei and Surrounding Areas may be subject to tighter

environmental regulations to protect the air quality of Beijing. 7 cities in Henan, Zhengzhou,

Kaifeng, Anyang, Hebi, Xinxiang, Jiaozuo, and Puyang, are located in these Areas. These

7 cities, in addition to three other cities, Luoyang, Pingdingshan, and Sanmenxia, may be

the target for more restrictive air pollution control policies in Henan. 8 out of 9 permanent

adopters are among these 10 cities, and are all located in north and west Henan, which

has more heavy industry and worse natural endowment compared to south and east Henan.

To test whether permanent adopters and togglers still followed the same trend absent the

policy, I conduct an event study where I identify the difference between the air pollution

in permanent adopters and in togglers over time. Figure 8 plots the coefficient estimates

of the interaction terms between the dummy for permanent adopters and weeks before and

after Dec. 4, 2017, when most cities in Henan first adopted road space rationing. This

figure differs from Figure 4 in that Figure 8 plots the difference between permanent adopters

and togglers while Figure 4 compares the city-days within permanent adopters and within

26

togglers. The pre-trend in Figure 8 is not statistically significantly different from 0. Thus, I

conclude that permanent adopters and togglers are still comparable.

6.3 SCM Results

Recall that two limitations of the LAC approach are that 1) wind might contaminate the

policy treatment status, and that 2) cities in the same province might not have comparable

long-run trends in air pollution. The SCM overcomes these limitations under the assumption

that air pollution in a treated city lies within the convex hull of that in the donor pool. Fig-

ure 9 plots the daily PM2.5 concentration of each city along with its synthetic control. The

dotted line represents the date road space rationing was implemented. Compared to the syn-

thetic control, 7 out of 9 permanent adopters (Zhengzhou, Kaifeng, Luoyang, Pingdingshan,

Xinxiang, Jiaozuo, and Zhumadian) experienced a decline in air pollution after road space

rationing was implemented. Figure 10 displays the results from aggregating the outcomes

of the 9 cities. The top-left panel presents the aggregated treated group and the aggregated

synthetic control by week, and the top-right panel presents their difference over time. The

red line represents the last week before road space rationing took effect. There was a sharp

drop in air pollution in the 4 weeks when the policy was in effect. The bottom-left panel

conducts statistical inference, and reports the p-value by each post-treatment day. The p-

values stand for the probability that the effect was only observed by chance, and are small for

most post-treatment days. This is evidence that the observed effects are mostly statistically

significant. In Table A.1, I show that the results from estimating Equation 5.1 are robust to

excluding days with high p-values.

7 Mechanisms

In this section, I test whether traffic reduction was the mechanism behind the air pollution

effect of road space rationing. I also assess whether policy restrictiveness (OD versus OE) is

27

associated with differences in impacts. First, Chen et al. (2013) document that areas with

denser roads in Beijing experienced a larger drop in air pollution when road space rationing

was implemented, since areas with denser roads presumably experienced a larger reduction

in traffic on policy days. I implement this idea in my multi-city setting, but adopt a finer

road density dataset by 1km resolution, compared to the road density dataset by 2.5 km

resolution used in Chen et al. (2013). In particular, I estimate the following equation on a

panel of monitors in Henan:

AirPollutionmt = π0 + π1RoadDensitym + π2RSRinPermanentmt

+ π3RSRinPermanentmt ×RoadDensitym + π4RSRinTogglermt

+ π5RSRinTogglermt ×RoadDensitym + δc + µt + εmt (7.1)

Where m stands for monitor and t stands for date. RoadDensitym is the road density,

measured in km/km2, where monitor m is located. I include city fixed effect, so I exclude

the variation in road density between cities. Table 7 shows the result. In Column (1), I

estimate Equation 7.1 on the sample of all monitors in Henan including both the permanent

adopters and the togglers. The coefficient estimate of RoadDensitym is positive and signifi-

cant, suggesting that, within a city, areas with denser roads did have higher traffic volume.

The coefficient estimate of the interaction term, RSRinPermanentmt × RoadDensitym, is

negative and significant, indicating that areas with denser roads in permanent adopters did

experience a larger reduction in traffic when road space rationing was in effect. In particular,

an area with 1 km/km2 higher road density in a permanent adopter experienced a 1-percent

sharper drop in air pollution when road space rationing was in effect. The air pollution

effect of road space rationing in permanent adopters seems to be entirely driven by areas

with denser roads. Once again, to avoid the concern that permanent adopters and togglers

may not be comparable, in Columns (2) and (3), I estimate Equation 7.1 on the sample of

monitors in permanent adopters and the sample of monitors in togglers separately to only use

28

permanent adopters as controls for permanent adopters and togglers as controls for togglers.

Under this cleaner set-up, the coefficient estimate for RSRinPermanentmt×RoadDensitym

is still negative and significant. I take this as evidence that the reduction in traffic is the

mechanism behind the air pollution effect of road space rationing.

Finally, I follow Viard and Fu (2015) to determine whether the more restrictive odd-

even policy was more effective than the less restrictive one-day-per-week policy. In the

existing literature, only one city is treated, so the type of the policy and the length of

the policy are perfectly collinear. In contrast, my setting in which both the type and the

length of the policies varied both within and across cities makes it possible to identify

each source of heterogeneity. To see more clearly where the variation comes from, Table

8 shows the number of city-days and the number of episodes in each group formed by the

two types of classification: permanent adopters vs. togglers and odd-even vs. one-day-

per-week. Although the treated days in permanent adopters tend to be predominantly

one-day-per-week, each intersection is represented by some treated city-days and road space

rationing episodes. To determine whether the effect of road space rationing differed by policy

restrictiveness, Column (1) of Table 9 estimates the following equation:

AirPollutionct = α0 + α1OEct + α2ODct + α3ODct ×Weekendt + δc + µt + νct (7.2)

Where OEct is an indicator variable that takes the value of 1 if city c had the odd-even

policy in effect on date t; ODct is an indicator variable that takes the value of 1 if city c

had the one-day-per-week policy in effect on date t; Weekendt is an indicator variable that

takes the value of 1 if date t fell on a weekend, since the one-day-per-week policy had no

restrictions on the weekends. δc is again the city fixed effect, and µt the date fixed effect.

Standard errors are again clustered at the city level. The coefficients of interest are α1 and

α2.

Odd-even days had 7 µg/m3 lower PM2.5 concentration, while the coefficient estimate for

29

one-day-per-week days is not statistically significant. Compared with a base of 67 µg/m3,

the reduction on odd-even days translates into a 10-percent decline. As mentioned in Section

4.1, the share of PM2.5 attributed to motor vehicles in Henan is estimated to be 10-15 percent

on a day with good air quality and 22-38 percent on a heavily polluted day. Since odd-even

policies mostly occurred during heavily polluted winter days, and one-day-per-week policies

might occur in other less polluted seasons, a simple back-of-the-envelope calculation suggests

that the odd-even policy should reduce PM2.5 concentration by 11-19 percent, and the one-

day-per-week policy could reduce PM2.5 concentration by 2-3 percent. These numbers are

comparable to the 10-percent decline I find for odd-even days and the null effect I find for

one-day-per-week days.

In Column (2), the dependent variable is being qualified for a blue sky day, i.e. with

AQI≤100. On average, odd-even days were 6 percentage points more likely to be a blue sky

day. This increase is against a mean of 0.65, and thus represents a 11-percent increase, on

par with the decline in PM2.5 concentrations. One-day-per-week days again did not have a

statistically significant effect on the probability of having a blue sky day.

In Columns (3) and (4) of Table 9, the regressors are all four groups created by the two

types of classifications seen in Table 8. The coefficient estimates for permanent adopters are

negative and significant, with that for odd-even days in permanet adopters being larger in

magnitude. The results for togglers are not robust to the restrictiveness of the policy.

Furthermore, it is possible that particulate matter stayed in the air for up to a few weeks

from creation (Textor et al., 2006). If traffic reduction is indeed the mechanism behind the

air pollution effect of road space rationing, the air pollution effect should lag behind the

policy for up to a few weeks. Figure 11 shows the coefficient estimates and the 95-percent

confidence intervals of lagged odd-even days terms, i.e. estimating Equation 7.2 instead

with OEc,t−7k as the regressor, where k ranges from -10 weeks to 10 weeks. OEc,t−7k with

negative k’s represents the leads. The coefficient estimates are statistically significant when

the policy variable is lagged by 0, 1, 3, 4, 5 weeks, suggesting that particulate matter might

30

have stayed in the air for up to 5 weeks before dispersion.

8 Conclusions

High levels of air pollution plague cities in developing countries, and have high health

and non-health impacts. In this paper, I have studied the effect of road space rationing that

cities in China’s Henan Province adopted from 2017 to 2019 on their air pollution levels.

I have collected information on the policies at the city level, and have identified the effect

through a difference-in-differences design, an event study, and the synthetic control method.

I have found that, in cities where road space rationing was implemented permanently, the

policy reduced air pollution by 6 percent, while in cities where road space rationing was

implemented temporarily, I cannot reject that the policy had zero impact. Thus, my paper

points to adopting road space rationing permanently as a potential way to curb air pollution.

A back-of-the-envelope calculation suggests that, in Henan alone, road space rationing

policies adopted permanently increased life expectancy by 0.4 year, decreased heart failure

by 0.8%, and avoided 62-109 infant deaths per year. Since more than 30 cities in China have

adopted road space rationing, these numbers can only be larger for China as a whole.

In conclusion, my paper shows how a long-term policy can induce long-term behavioral

changes that a short-term policy cannot, and thus has different implications for air quality.

The extent this pattern holds for other government policies deserves further investigation by

researchers and policy makers.

31

References

Alberto Abadie and Javier Gardeazabal. The economic costs of conflict: A case study of the

basque country. American economic review, 93(1):113–132, 2003.

Alberto Abadie, Alexis Diamond, and Jens Hainmueller. Synthetic control methods for

comparative case studies: Estimating the effect of california’s tobacco control program.

Journal of the American statistical Association, 105(490):493–505, 2010.

Jorge A Bonilla. The more stringent, the better? rationing car use in bogota with moderate

and drastic restrictions. The World Bank Economic Review, 33(2):516–534, 2019.

A Colin Cameron, Jonah B Gelbach, and Douglas L Miller. Bootstrap-based improvements

for inference with clustered errors. The Review of Economics and Statistics, 90(3):414–427,

2008.

Paul E Carrillo, Arun S Malik, and Yiseon Yoo. Driving restrictions that work? quito’s pico

y placa program. Canadian Journal of Economics/Revue canadienne d’economique, 49

(4):1536–1568, 2016.

Eduardo Cavallo, Sebastian Galiani, Ilan Noy, and Juan Pantano. Catastrophic natural

disasters and economic growth. Review of Economics and Statistics, 95(5):1549–1561,

2013.

Kenneth Y Chay and Michael Greenstone. The impact of air pollution on infant mortal-

ity: evidence from geographic variation in pollution shocks induced by a recession. The

quarterly journal of economics, 118(3):1121–1167, 2003.

Kenneth Y Chay and Michael Greenstone. Does air quality matter? evidence from the

housing market. Journal of political Economy, 113(2):376–424, 2005.

Wenwei Che, Junyu Zheng, Shuisheng Wang, Liuju Zhong, and Alexis Lau. Assessment of

32

motor vehicle emission control policies using model-3/cmaq model for the pearl river delta

region, china. Atmospheric Environment, 45(9):1740–1751, 2011.

Yuyu Chen, Ginger Zhe Jin, Naresh Kumar, and Guang Shi. The promise of beijing: Eval-

uating the impact of the 2008 olympic games on air quality. Journal of Environmental

Economics and Management, 66(3):424–443, 2013.

Janet Currie, Eric A Hanushek, E Megan Kahn, Matthew Neidell, and Steven G Rivkin.

Does pollution increase school absences? The Review of Economics and Statistics, 91(4):

682–694, 2009.

Lucas W Davis. The effect of driving restrictions on air quality in mexico city. Journal of

Political Economy, 116(1):38–81, 2008.

Antoine A Djogbenou, James G MacKinnon, and Morten Ørregaard Nielsen. Asymptotic

theory and wild bootstrap inference with clustered errors. Journal of Econometrics, 2019.

Francesca Dominici, Roger D Peng, Michelle L Bell, Luu Pham, Aidan McDermott, Scott L

Zeger, and Jonathan M Samet. Fine particulate air pollution and hospital admission for

cardiovascular and respiratory diseases. Jama, 295(10):1127–1134, 2006.

Gunnar S Eskeland and Tarhan Feyzioglu. Rationing can backfire: the “day without a car”

in mexico city. The World Bank Economic Review, 11(3):383–408, 1997.

Francisco Gallego, Juan-Pablo Montero, and Christian Salas. The effect of transport policies

on car use: Evidence from latin american cities. Journal of Public Economics, 107:47–62,

2013.

Andrew Goodman-Bacon. Difference-in-differences with variation in treatment timing. Tech-

nical report, National Bureau of Economic Research, 2018.

Hilary W Hoynes and Diane Whitmore Schanzenbach. Consumption responses to in-kind

33

transfers: Evidence from the introduction of the food stamp program. American Economic

Journal: Applied Economics, 1(4):109–39, 2009.

Teng Li, Haoming Liu, and Alberto Salvo. Severe air pollution and labor productivity. IZA

Discussion Papers, 2015.

Stephen S Lim, Theo Vos, Abraham D Flaxman, Goodarz Danaei, Kenji Shibuya, Heather

Adair-Rohani, et al. al, e.(2012). a comparative risk assessment of burden of disease and

injury attributable to 67 risk factors and risk factor clusters in 21 regions, 1990–2010: A

systematic analysis for the global burden of disease study 2010. The Lancet, 380(9859):

2224–2260, 2010.

James G MacKinnon and Matthew D Webb. Wild bootstrap inference for wildly different

cluster sizes. Journal of Applied Econometrics, 32(2):233–254, 2017.

James G MacKinnon and Matthew D Webb. The wild bootstrap for few (treated) clusters.

The Econometrics Journal, 21(2):114–135, 2018.

Zheng Niu, Peiying Kou, Zhengjia Liu, Kaiyi Bi, and Meng Meng. Yidaiyilu jiqi bilin quyu

1km fenbianlv daoluwang miji shujuji [one belt one road and its neighboring regions 1km

resolution road density data]. Journal of Global Change Data & Discovery, 2017.

C Arden Pope III, Majid Ezzati, and Douglas W Dockery. Fine-particulate air pollution and

life expectancy in the united states. New England Journal of Medicine, 360(4):376–386,

2009.

Yu Qin and Hongjia Zhu. Run away? air pollution and emigration interests in china. Journal

of Population Economics, 31(1):235–266, 2018.

Tess M Stafford. Indoor air quality and academic performance. Journal of Environmental

Economics and Management, 70:34–50, 2015.

34

C Textor, M Schulz, S Guibert, Stefan Kinne, Y Balkanski, S Bauer, T Berntsen, T Berglen,

Olivier Boucher, M Chin, et al. Analysis and quantification of the diversities of aerosol

life cycles within aerocom. Atmospheric Chemistry and Physics, 6(7):1777–1813, 2006.

Rodrigo Troncoso, Louis De Grange, and Luis A Cifuentes. Effects of environmental alerts

and pre-emergencies on pollutant concentrations in santiago, chile. Atmospheric environ-

ment, 61:550–557, 2012.

V Brian Viard and Shihe Fu. The effect of beijing’s driving restrictions on pollution and

economic activity. Journal of Public Economics, 125:98–115, 2015.

World Bank. World development indicators. Washington, DC: World Bank., 2003.

Fenggang Yang and J. E. E. Pettit. South-Central China, pages 147 – 172. Brill, Leiden,

The Netherlands, 2018. ISBN 9789004358850.

Siqi Zheng, Jianghao Wang, Cong Sun, Xiaonan Zhang, and Matthew E Kahn. Air pollution

lowers chinese urbanites’ expressed happiness on social media. Nature Human Behaviour,

3(3):237, 2019.

J. G. Zivin and M Neidell. The impact of pollution on worker productivity. Am Econ Rev,

102(7):3652–3673, 2012.

35

Figure 1: Henan Province In China

Notes: Wikimedia Commons.

36

Figure 2: Cities In Henan Province

Notes: Yang and Pettit (2018).

37

Figure 3: RSR by City

Notes: I collect the dates and the restrictiveness of each road space rationing episode by examining government announcements and news articles

over a period from Jan. 1, 2017 to May 11, 2019. The dates before Nov. 2017 were omitted from this figure because no city in Henan had road

space rationing during that time. I define a road space rationing policy as permanent if, upon announcing the start date, the city government did not

announce the end date. “Permanent adopters” are the cities that have adopted a permanent policy, and “togglers” are the cities that have not.

38

Figure 4: Event Study of Permanent Adopters vs Togglers

-15

-10

-50

510

PM2.

5 co

ncen

tratio

n

-16 -12 -8 -4 0 4 8 12 16 Weeks since RSR adoption

RSR in permanent Adopters (Weeks Since Treatment)

-20

-10

010

2030

PM2.

5 co

ncen

tratio

n

-16 -12 -8 -4 0 4 8 12 16 Weeks since RSR adoption

RSR in togglers (Weeks Since Treatment)

Notes: Week 0 is the last week before treatment. Each dot represents the difference in average PM2.5

concentrations between each week following the adoption of a road space rationing episode and the week

before the adoption of the policy. The solid lines represent the 95-percent confidence intervals.

39

Figure 5: Civil Vehicle Ownership per 100 People by Treatment Status

Zhengzhou0

1020

3040

Car

ow

ners

hip

(per

100

peo

ple)

0 1Permanent Adopter

Fitted line including Zhengzhou Fitted line excluding Zhengzhou

Notes: The data are from the Henan Statistical Yearbook 2018. Each dot represents one of the 17 cities in Henan. The horizontal axis categorizes a

city by whether it is a permanent adopter, with a value of 1 if the city is a permanent adopter and 0 if the city is a toggler.

40

Figure 6: Permutation Tests

0.0

5.1

.15

Frac

tion

-5 0 5 10

Placebo Estimates Real Estimate

RSR in permanent adopters

0.0

2.0

4.0

6.0

8Fr

actio

n

-10 -5 0 5 10

Placebo Estimates Real Estimate

RSR in togglers

Notes: The yellow bars represent the distribution of 1000 sets of placebo coefficient estimates, where each

placebo coefficient estimate is obtained by randomizing the set of real policies within the 17 cities and

estimating the main specification, Equation 5.1. The red lines represent the values of the real coefficient

estimates.41

Figure 7: LAC - Dropping a City at a Time

Zhengzhou

Kaifeng

Luoyang

Pingdingshan

Anyang

Hebi

Xinxiang

Jiaozuo

Puyang

Xuchang

Luohe

Sanmenxia

Nanyang

Shangqiu

Xinyang

Zhoukou

Zhumadian

-8 -6 -4 -2 0

RSR in permanent adoptersZhengzhou

Kaifeng

Luoyang

Pingdingshan

Anyang

Hebi

Xinxiang

Jiaozuo

Puyang

Xuchang

Luohe

Sanmenxia

Nanyang

Shangqiu

Xinyang

Zhoukou

Zhumadian

0 5 10 15 20 25

RSR in togglers

Notes: This figure displays the coefficient estimates and the 95-percent confidence intervals from estimating the main specification, Equation 5.1,

dropping one city at a time. The label of each coefficient represents the city that is dropped.

42

Figure 8: Interaction Terms Between Permanent Adopters Dummy and Weeks Since Treatment

-60

-40

-20

020

PM2.

5 co

ncen

tratio

n

-40 -36 -32 -28 -24 -20 -16 -12 -8 -4 0 4 Weeks since RSR adoption

Notes: This figure displays the coefficient estimates and the 95-percent confidence intervals from an event study of the effect of being a permanent

adopter on PM2.5 concentrations. Each dot represents the coefficient estimate of an interaction term between the permanent adopter dummy and

the number of weeks since Dec. 4, 2017, when cities in Henan first introduced road space rationing. Week 0 is the last week before treatment.

43

Figure 9: SCM for PM2.5 of Each Permanent Adopter in 2017

010

020

030

040

0PM

25

01jan2017 01apr2017 01jul2017 01oct2017 01jan2018date

Zhengzhou synthetic Zhengzhou

010

020

030

040

0PM

25

01jan2017 01apr2017 01jul2017 01oct2017 01jan2018date

Kaifeng synthetic Kaifeng

010

020

030

040

0PM

25

01jan2017 01apr2017 01jul2017 01oct2017 01jan2018date

Luoyang synthetic Luoyang

Notes: This figure displays the PM2.5 concentrations in each permanent adopter and its synthetic control

at the daily frequency. The reference line represents Dec. 4, 2017, the first day RSR was in effect.

44

Figure 9: SCM for PM2.5 of Each Permanent Adopter in 2017 (Continued)

010

020

030

0PM

25

01jan2017 01apr2017 01jul2017 01oct2017 01jan2018date

Pingdingshan synthetic Pingdingshan

010

020

030

040

0PM

25

01jan2017 01apr2017 01jul2017 01oct2017 01jan2018date

Anyang synthetic Anyang

010

020

030

0PM

25

01jan2017 01apr2017 01jul2017 01oct2017 01jan2018date

Hebi synthetic Hebi

Notes: This figure displays the PM2.5 concentrations in each permanent adopter and its synthetic control

at the daily frequency. The reference line represents Dec. 4, 2017, the first day RSR was in effect.

45

Figure 9: SCM for PM2.5 of Each Permanent Adopter in 2017 (Continued)

010

020

030

0PM

25

01jan2017 01apr2017 01jul2017 01oct2017 01jan2018date

Xinxiang synthetic Xinxiang

010

020

030

040

0PM

25

01jan2017 01apr2017 01jul2017 01oct2017 01jan2018date

Jiaozuo synthetic Jiaozuo

010

020

030

0PM

25

01jan2017 01apr2017 01jul2017 01oct2017 01jan2018date

Zhumadian synthetic Zhumadian

Notes: This figure displays the PM2.5 concentrations in each permanent adopter and its synthetic control

at the daily frequency. The reference line represents Dec. 4, 2017, the first day RSR was in effect.

46

Figure 10: Aggregated Effects for SCM Among Permanent Adopters Around Dec. 2017

050

100

150

PM2.

5

-40 -30 -20 -10 0Weeks since treatment

Treated Synthetic Control

Averages of treatment group and of control group

-30

-20

-10

010

20Ef

fect

- PM

2.5

-40 -30 -20 -10 0 10Weeks since treatment

Weekly Average Fitted Line Fitted Line

Difference between averaged treatment group and control group

0.1

.2.3

.4.5

.6.7

.8.9

1Pr

obab

ility

that

this

wou

ld h

appe

n by

cha

nce

1 6 11 16 21 26 31Days since treatment

P-values

Notes: The top-left panel displays the PM2.5 concentrations of the treated cities and their synthetic controls averaged across all 9 permanent adopters

at the weekly frequency. The averages of the treated cities and of their synthetic controls are weighted by population. The top-right panel displays

their difference also at the weekly frequency. The red lines in both panels represent the week before Dec. 4, 2017 (Period 0), the last week before

RSR took effect. The fitted line is calculated while excluding Period 0. The bottom panel displays the p-values, i.e. the probability that the effect is

observed by chance, at the daily frequency for each day following Dec. 4, 2017.

47

Figure 11: Effect of Lagged Odd-even (by Weeks) on PM2.5

-15

-10

-50

5PM

2.5

Con

cent

ratio

n

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10Weeks Lagged

Notes: This figure displays the coefficient estimates and the 95-percent confidence intervals of odd-even days from a regression of PM2.5 concentration

on lagged policies. Each dot is a separate regression, with the number on the horizontal axis representing the number of weeks lagged.

48

Table 1: Summary Statistics

N. Obs. N. Days Mean Std.Dev.

BetweenStd.Dev.

WithinStd.Dev.

Min Max

Panel A:PM2.5 (µg/m3) 14552 856 66.8 48.9 5.6 48.6 3.9 414.9AQI 14552 856 101.8 56.8 7.3 56.3 13.9 456.7Avg Temperature (°C) 14552 856 14.9 10.0 0.7 9.9 -7.7 33.6Dew Point (°C) 14552 856 43.8 20.6 3.3 20.4 -26.5 81.6Max Temperature (°C) 14552 856 19.6 10.4 0.5 10.4 -6.2 40.3Min Temperature (°C) 14552 856 9.6 9.8 1.0 9.8 -14.5 29.7Precipitation (mm) 14552 856 2.4 8.6 0.6 8.6 0.0 185.4Wind Speed (km/h) 14552 856 9.2 3.5 1.2 3.3 2.0 27.8Car Ownership (per 100 people) 17 1 12.0 7.3 - - 5.9 38.9Population (in million) 17 1 6.3 3.0 - - 1.6 11.9Per-capita GDP (in 1000) 17 1 48.5 14.2 - - 24.3 82.8Cumulative PM2.5 (in 1000) 17 1 19.1 2.5 - - 14.8 23.9Ind. Output (in 1000) 17 1 1.3e+08 1.2e+08 - - 4.2e+07 5.7e+08Dust Emission (ton) 17 1 15256.1 12425.6 - - 1114.0 51644.0Unemployment Rate (%) 17 1 4.5 2.8 - - 0.2 9.8

Panel B:Road Density (km/km2) 83 1 5.1 4.5 - - 0.0 24.6

Notes: Panel A represents daily observations for a panel of 17 cities in Henan from Jan. 1, 2017 to May 11, 2019. The dataon PM2.5 concentrations are from the China National Environmental Monitoring Center. The weather data are from theNational Oceanic and Atmospheric Administration. Other city-level controls are from the Henan Statistical Yearbook 2018and the China City Statistical Yearbook 2017. Panel B represents a cross-section of 83 monitoring stations in Henan. Theroad density data are from Niu et al. (2017).

49

Table 2: Testing the Endogeneity of Whether a City Was a Permanent Adopter

(1) (2) (3) (4) (5)Dependent Var.: Perma-

nentadopter

Perma-nent

adopter

Perma-nent

adopter

Perma-nent

adopter

Perma-nent

adopterCar ownership (per 100people)

0.24 0.26(0.19) (0.43)

Population (in million) -0.13 -0.03(0.17) (0.28)

Per-capita GDP (in 1000) 0.07 -0.01(0.04) (0.09)

Dust emission (in 1000ton)

0.10 0.09(0.07) (0.07)

pseudo R2 0.13 0.03 0.12 0.16 0.25Mean of Dep. Var. 0.53 0.53 0.53 0.53 0.53N 17 17 17 17 17

Notes: This table shows the results of logit regressions of the permanent adopterstatus on city characteristics on a sample of 17 cities in Henan. The city characteristicsare from the Henan Statistical Yearbook 2018 and the China City Statistical Yearbook2017. Standard errors in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.

50

Table 3: Difference-in-differences for Permanent Adopters vs. Togglers - Baseline

(1) (2)Dependent Var.: PM2.5 Blue

Sky DayRSR in permanentadopters

-4.24∗∗ 0.03∗∗∗

(1.49) (0.01)

RSR in togglers 9.82∗∗ -0.07∗∗

(3.70) (0.02)R2 0.81 0.65Mean of Dep. Var. 66.82 0.65N 14552 14552

Notes: PM2.5 concentrations are collectedfrom the China National EnvironmentalMonitoring Center, and a day qualifies for ablue sky day if the Air Quality Index is below100. All regressions control for city fixed ef-fects and date fixed effects. Standard errorsclustered at the city level. Standard errorsin parentheses. * p < 0.1, ** p < 0.05, ***p < 0.01.

51

Table 4: LAC by Permanent Adopters vs. Togglers - Other Pollutants

(1) (2) (3) (4) (5) (6)Dependent Var.: AQI PM2.5 PM10 NO2 CO SO2

RSR in permanentadopters

-4.20∗∗ -4.24∗∗ -4.50∗ -2.18∗∗ -0.07∗ -1.56(1.73) (1.49) (2.34) (0.83) (0.03) (0.92)

RSR in togglers 11.49∗∗∗ 9.82∗∗ 11.77∗∗∗ 1.71∗∗∗ 0.00 0.22(3.44) (3.70) (3.84) (0.58) (0.03) (1.02)

R2 0.81 0.81 0.81 0.80 0.75 0.71Mean of Dep. Var. 101.83 66.82 116.58 38.04 1.15 17.02N 14552 14552 14549 14552 14552 14552

Notes: All pollutant concentrations and air pollution measure are collected from the ChinaNational Environmental Monitoring Center. All regressions control for city fixed effectsand date fixed effects. Standard errors clustered at the city level. Standard errors inparentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.

52

Table 5: Difference-in-differences for Open-Ended vs. Short-term Episodes

(1) (2)Dependent Var.: PM2.5 Blue

Sky DayOpen-ended RSR -3.80∗∗∗ 0.03∗∗

(1.23) (0.01)

Short-term RSR 6.38∗∗ -0.03(2.41) (0.02)

R2 0.81 0.65Mean of Dep. Var. 66.82 0.65N 14552 14552

Notes: An open-ended RSR episode is de-fined as an episode upon whose announce-ment no end date was announced. A short-term RSR episode is defined as an episodeupon whose announcement an end date wasannounced. PM2.5 concentrations are col-lected from the China National Environmen-tal Monitoring Center, and a day qualifies fora blue sky day if the Air Quality Index is be-low 100. All regressions control for city fixedeffects and date fixed effects. Standard errorsclustered at the city level. Standard errors inparentheses. * p < 0.1, ** p < 0.05, ***p < 0.01.

53

Table 6: LAC by Permanent Adopters vs. Togglers - Other Specifications

(1) (2) (3) (4) (5) (6) (7)Dependent Var.: PM2.5 PM2.5 logPM2.5 PM2.5 PM2.5 PM2.5 PM2.5

RSR in permanentadopters

-4.24∗∗ -3.69∗∗ -0.06∗∗∗ -4.33∗∗∗ -2.87∗ -4.34∗∗∗ -4.22∗∗

(1.49) (1.72) (0.02) (1.46) (1.50) (1.48) (1.57)

RSR in togglers 9.82∗∗ 9.53∗∗∗ 0.14∗∗ 9.25∗∗ 10.79∗∗ 9.64∗∗ 12.39∗∗∗

(3.70) (2.96) (0.05) (3.65) (3.76) (3.80) (3.07)

Weather controls YExclude extreme values YTime trend×variables YExclude holidays YWeighted by population Y

R2 0.81 0.82 0.82 0.81 0.81 0.81 0.83Mean of Dep. Var. 66.82 66.82 3.99 66.65 66.82 66.44 67.22N 14552 14552 14552 14544 14552 14467 14552

Notes: Weather controls include average, maximum, and minimum temperature, dew point, precipitation, wind speed,and pressure, and are from the National Oceanic and Atmospheric Administration. Column (4) only includes days withPM2.5 concentrations less than 350 µg/m3. Variables interacted with time trend in Column (5) include population,per-capita GDP, and gross industrial output, and are from the China City Statistical Yearbook 2017. The excludedholidays in Column (6) include Chinese New Year, New Year’s Day, and Christmas. Column (7) is weighted by citypopulation in 2016. PM2.5 concentrations are collected from the China National Environmental Monitoring Center. Allregressions control for city fixed effects and date fixed effects. Standard errors clustered at the city level. Standard errorsin parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.

54

Table 7: Heterogeneous Effect by Road Density

(1) (2) (3)Dependent Var.: PM2.5 PM2.5 PM2.5

Road density 0.35∗∗∗ 0.41∗∗∗ 0.06(0.07) (0.11) (0.16)

RSR in permanentadopters

-1.66 2.60(1.53) (2.00)

RSR in permanentadopters×Road density

-0.46∗∗∗ -0.52∗∗∗

(0.14) (0.13)

RSR in togglers 13.05∗∗ 5.08(5.56) (5.18)

RSR in togglers×Roaddensity

-0.53 0.03(0.77) (0.67)

R2 0.80 0.86 0.79Mean of Dep. Var. 67.54 70.18 63.96N 63310 36382 26928

Notes: All three columns are the results from monitor-levelregressions. Column (2) is on the subsample of permanentadopters; Column (3) is on the subsample of togglers. Roaddensity is measured by km/km2, and the data are from Niuet al. (2017). PM2.5 concentrations are collected from theChina National Environmental Monitoring Center. All regres-sions control for city fixed effects and date fixed effects. Stan-dard errors clustered at the city level. Standard errors in paren-theses. * p < 0.1, ** p < 0.05, *** p < 0.01.

55

Table 8: Number of City-Days/Episodes by Type and Length

Panel A: Number of city-daysOdd-even One-day-

per-weekPermanent adopters 516 2616

Togglers 218 478

Panel B: Number of episodesOdd-even One-day-

per-weekPermanent adopters 15 21

Togglers 10 11

Notes: Panel A shows the number of city-days with RSRby policy type and whether a city is a permanent adopter.Panel B shows the number of RSR episodes by the sameclassification.

56

Table 9: Difference-in-differences for Odd-Even vs. One-Day-Per-Week

(1) (2) (3) (4)Dependent Var.: PM2.5 Blue

Sky DayPM2.5 Blue

Sky DayOdd-even days -6.68∗∗ 0.06∗∗∗

(2.86) (0.02)

One-day-per-week days -0.26 0.01(1.63) (0.01)

One-day-per-weekdays×Weekend

-0.96 -0.01(1.35) (0.01)

Odd-even days inpermanent adopters

-10.02∗∗ 0.08∗∗∗

(3.50) (0.02)

One-day-per-week days inpermanent adopters

-3.54∗∗ 0.03∗∗∗

(1.32) (0.01)

Odd-even days in togglers 7.69 -0.03(5.26) (0.04)

One-day-per-week days intogglers

8.61∗∗ -0.06∗∗

(3.66) (0.02)R2 0.81 0.65 0.81 0.65Mean of Dep. Var. 66.82 0.65 66.82 0.65N 14552 14552 14552 14552

Notes: Columns (1) and (2) categorize each RSR episode by policy restric-tiveness. Odd-even days are a dummy variable that takes the value of 1 ifa city had an odd-even policy in effect on a certain day. One-day-per-weekdays are similarly defined for the one-day-per-week policy. Columns (3)and (4) categorize each RSR episode by policy restrictiveness and whetherthe city is a permanent adopter. PM2.5 concentrations are collected fromthe China National Environmental Monitoring Center, and a day qualifiesfor a blue sky day if the Air Quality Index is below 100. All regressionscontrol for city fixed effects and date fixed effects. Standard errors clus-tered at the city level. Standard errors in parentheses. * p < 0.1, **p < 0.05, *** p < 0.01.

57

A Theory Appendix

A.1 Proof of Implications from the Model

Implication 1: The individual purchases an electric car if and only if the road space ra-

tioning policy lasts long enough.

Proof: For now, assume that the individual always complies, and that the individual works in

every period. If the individual does not purchase an electric car, under road space rationing,

he/she is restricted for a total of T2

periods, in which he/she faces transit time z; he/she

is not restricted for a total of T − T2

periods, in which he/she faces transit time z. If the

individual purchases an electric car, he/she faces transit time z for all T periods. Thus,

problem 3.1 is equivalent to

max{xt,lt},b

T∑t=1

xαt l1−αt

s.t. bE +T∑t=1

xt = A0 + 24wT − wT∑t=1

lt − w[T

2z + (T − T

2)z](1− b)− wTzb

(A.1)

Since b only enters the budget constraint and not the utility function, b = 1 if and only

if E − w T2z + w T

2z < 0, i.e. T > 2E

w(z−z) .

Implication 2: A high-income individual only refuses to comply with road space rationing

when the policy is short.

Proof: Now, I allow for non-compliance. The individual’s budget constraint becomes

bE +T∑t=1

xt = A0 + 24wT − wT∑t=1

lt − w(T − T

2)z

−wzT2

[1− (1− b)(1−N)]− wzT2

(1− b)(1−N)− pf T2N

(A.2)

58

which simplifies to

bE +T∑t=1

xt = A0 + 24wT − wT∑t=1

lt − w(T − T

2)z

−wzT2

+ w(z − z)[1− (1− b)(1−N)]T

2− pf T

2N

(A.3)

Move the terms that involve b andN to the RHS: w(z−z)[1−(1−b)(1−N)]T2−pf T

2N−bE.

Since it only makes sense for the individual to choose non-compliance if he/she does not

purchase the electric car, I only need to compare the budget constraint in three cases: 1)

b = 1, N = 0, 2) b = 0, N = 0, and 3) b = 0, N = 1. The respective values for

w(z− z)[1− (1− b)(1−N)]T2− pf T

2N − bE in these three cases are 1) w(z− z)T

2−E, 2) 0,

and 3) w(z − z)T2− pf T

2. The top panel of Figure A.1 shows these three values as functions

of the policy length, T , for low-income individuals, particularly with w(z − z) − pf < 0.

These people comply with the policy on restricted days. The three values are shown as g, j,

and f . In particular, since w(z − z) − pf < 0, f slopes downward. The upper envelope of

these three functions are shown in red. This indicates that the low-income individual does

not purchase the electric car and complies to road space rationing when the policy is short;

he/she purchases an electric car when the policy is long.

The bottom panel of Figure A.1 shows the three values as functions of T for high-income

individuals, particularly with w(z − z) − pf ≥ 0. These people find it profitable not to

comply with road space rationing. Since w(z− z)− pf < 0, f slopes upwards, but its slope,

w(z− z)− pf , is lower than that of g, w(z− z). The upper envelope of these three functions

are shown in red. This indicates that the high-income individual chooses non-compliance

when the policy is short; he/she purchases an electric car when the policy is long.

Implication 3: An individual under a flexible work schedule might not work on restricted

days.

Proof: First, I show that it may be optimal for the individual not to work on restricted days

if he/she does not purchase an electric car. If the individual does not purchase an electric

59

car, in a period in which he/she is restricted by road space rationing, then he/she solves the

problem

maxxt,lt,At+1

xαt l1−αt

s.t. xt + At+1 = At + 24w − wlt − wz1(lt < 24)

(A.4)

Where 1 is an indicator function, and At is the non-wage income carried from Period

t− 1 to Period t. At+1 is the optimal non-wage income carried from Period t to Period t+ 1.

In the remainder of the proof, I am characterizing part of the solution while holding the rest

of the solution, namely At+1, constant. Figure A.2 illustrates a sufficient condition under

which the individual would not work on restricted days. The individual’s budget set is given

by CD and KB, and his/her indifference curves are given by g and p. The indifference

curve g is tangent to KB at point L(x∗t , l∗t ). Nevertheless, bundle L is not optimal since the

individual can choose not to work, and thus staying on CD. The optimal bundle is given by

D. The sufficient condition I will establish is that x∗t < At−At+1, that is point L lies to the

left of point D.

Suppose the individual does not have the option not to work. Let the optimal bundle be

(x∗t , l∗t ) (illustrated by point L). Then, the first-order conditions of A.4 give l∗t = 1

w1−ααx∗t .

Plugging into the budget constraint gives x∗t = α(At − At+1 + 24w − wz). Consider the

situation in which At − At+1 and z are large enough and w and α are small enough such

that α(At − At+1 + 24w − wz) = x∗t < At − At+1. Then, since the upper contour set of the

indifference curves is convex, the individual must prefer the corner solution (point D) than

the interior solution (point L). An example of parameters that satisfy this requirement is

w = 10, z = 1, α = 0.5, At − At+1 = 500.

Similarly, if the individual purchases an electric car, a sufficient condition under which

he/she chooses not to work on restricted days is that α(At−At+1 + 24w−wz) < At−At+1.

Note that not working on restricted days does not necessarily imply that the individual

also does not work on unrestricted days. In a period in which the individual is not restricted

60

by road space rationing, he/she solves the problem

maxxt,lt,At+1

xαt l1−αt

s.t. xt + At+1 = At + 24w − wlt − wz1(lt < 24)

(A.5)

Budget constraint A.5 is the same as budget constraint A.4 except that the individual

faces transit time z if he/she chooses to work. In Figure A.3, I illustrate how not working

(lt = 24) can be a solution under budget constraint A.4, but working (lt < 24) can be a

solution under budget constraint A.5. CD and KB represent budget constraint A.4, and

CD and EF represent budget constraint A.5. g and p are the respective indifference curves

that result in a) a corner solution at D, and b) an interior solution at G. Thus, with an

appropriate α, large enough A0 and z, and small enough z, it is possible that the individual

does not work on restricted days but works on unrestricted days.

61

Figure A.1: Implication 2 - Budget Constraints for Low- and High-Income Individuals

Case 1 (low-income individual): suppose w(z − z)− pf < 0

Case 2 (high-income individual): suppose w(z − z)− pf ≥ 0

Notes: This figure shows values of the terms in the budget constraint that involve b and N over the duration

of the policy separately for low-income individuals and high-income individuals.62

Figure A.2: Implication 3 - Not Work on Restricted Days

xxtt

lltt gg

DDCC KK

BB

pp

LL

Notes: This figure illustrates a sufficient condition under which the individual would not work on restricted days.

63

Figure A.3: Implication 3 - Not Work on Restricted Days but Work on Unrestricted Days

xxtt

lltt gg pp

hh

iiff

CC DDEE

FF

KK

BB

GG

Notes: This figure illustrates how not working can be a solution on restricted days, but working can be a solution on unrestricted days.

64

Table A.1: Additional Robustness Checks

(1) (2) (3) (4)Dependent Var.: PM2.5 PM2.5 PM2.5 PM2.5

RSR in permanentadopters

-4.24∗∗ -2.65∗ -4.15∗∗ -4.37∗∗

(1.49) (1.47) (1.47) (1.63)

RSR in togglers 9.82∗∗ 10.66∗∗ 9.49∗∗ 10.79∗∗∗

(3.70) (3.75) (3.66) (3.47)

Quadratic time trend YExclude high p-values YMonitor-level sample Y

R2 0.81 0.82 0.81 0.80Mean of Dep. Var. 66.82 66.82 66.50 67.54N 14552 14552 14399 63310

Notes: Column (1) reports the baseline results. Column (2) includes quadratictime trend interacted with population, per-capita GDP, and gross industrial out-put, which are from the China City Statistical Yearbook 2017. Column (3) ex-cludes dates with p-value greater than 0.1 as reported in Figure 10. Column (4)estimates the main specification, Equation 5.1, on a monitor-level panel. PM2.5

concentrations are collected from the China National Environmental MonitoringCenter. All regressions control for city fixed effects and date fixed effects. Stan-dard errors clustered at the city level. Standard errors in parentheses. * p < 0.1,** p < 0.05, *** p < 0.01.

65

Table A.2: LAC - with Intermediate Periods Dummy for Permanent Adopters

(1) (2)Dependent Var.: PM2.5 PM2.5

RSR in permanentadopters

-4.24∗∗ -6.28∗∗∗

(1.49) (1.85)

RSR in togglers 9.82∗∗ 9.28∗∗

(3.70) (3.56)

Interim periods inpermanent adopters

-4.22∗

(2.06)R2 0.81 0.81Mean of Dep. Var. 66.82 66.82N 14552 14552

Notes: An intermediate period is defined as dayswithout RSR for permanent adopters after Jan.1, 2018. PM2.5 concentrations are collected fromthe China National Environmental MonitoringCenter. All regressions control for city fixed ef-fects and date fixed effects. Standard errors clus-tered at the city level. Standard errors in paren-theses. * p < 0.1, ** p < 0.05, *** p < 0.01.

66