Going Fast or Going Green? Evidence from Environmental Speed Limits in Norway

This paper studies the impact of speed limits on local air pollution using a series of datespecific speed limit reductions in Oslo over the 2004-2011 period. We find that lowering the speed limit from 80 to 60 km/h reduces travel speed by 5.8 km/h. However, we find no evidence of reduced air pollution as measured next to the treated roads. Our estimates suggest an annual time loss of the speed limit reductions of 55 USD per affected vehicle. Our findings imply that policy makers need to consider other actions than speed limit reductions to improve local air quality. JEL classification: H23, Q53, Q58, R41


Introduction
Policy makers increasingly search for new ways to reduce air pollution, as projections suggest air pollution to be the top environmental cause of mortality worldwide by 2050 (OECD 2012).
Transport is the only major sector in the EU where greenhouse gas emissions are still rising (European Commission 2017). As a new policy tool, cities like Amsterdam, Barcelona and Oslo have lowered speed limits to improve local air quality. 1 Speed limits have the desirable properties of being easy to enforce and difficult to circumvent, and their effects would be immediate.
Yet, the scientific evidence on the effect of lower speed limits on local air pollution is mixed.
Engineering simulation models tend to find that reduced speed should improve air quality (EEA 2011a, UK Government 2017, while existing empirical studies offer mixed conclusions (van Benthem 2015, Bel and Rosell 2013). The effect of speed limit reductions on local air quality is hard to predict, as it depends on the behavioural responses of drivers as well as on the technical relationship between speed and pollution for the affected vehicle fleet and roads. Ex-ante, there is considerable uncertainty about these aspects, calling for ex-post policy evaluation.
In this paper, we take advantage of speed limit reductions in Oslo to estimate the effect of speed on local pollution. In 2004, Oslo lowered the maximum speed limit from 80 km/h to 60 km/h on National Road 4 during the winter. The aim was to improve local air quality by reducing the level of Particulate Matter. Oslo later expanded the Environmental Speed Limit policy (ESL) to include additional roads, before national regulation halted the use of the policy in 2012-2015. In 2016, Oslo reintroduced the policy.
The date-specific introduction of the policy every year creates a series of natural experiments.
High quality hourly data on the population of traffic and air pollution in the immediate vicinity of the highways allow us to utilize these experiments in a regression discontinuity design (RDD). We estimate the effect of the ESL on air quality in terms of Nitrogen Oxides (NO2 and NOX) and Particulate Matter (PM2.5 and PM10). We also estimate the effects on travel speed and traffic volume, and we use the estimates to undertake a cost-benefit analysis of the policy.
This study adds to the existing literature by its use of real-world data, which allows for behavioural responses among drivers and other real-world aspects influencing the link between speed and air quality. The RDD, utilizing a series of natural experiment to isolate confounding factors, generates plausibly causal estimates.
The paper proceeds as follows. Section 2 presents a literature review, section 3 contains background information about the ESL-policy in Oslo and section 4 describes the data. Section 5 explains our empirical strategy. Section 6 presents the results and the cost-benefit analysis.
Section 7 discusses threats to identification, robustness checks and external validity. The final section concludes. An online appendix provides supplementary material.

Literature review
Traffic is an important source of air pollution, as wear of brakes, tires and asphalt is a source of Particulate Matter, and exhaust fumes is a source of NO2 and NOX. 2 The relationship between average speed and vehicle emissions has been held to be U-shaped for stable speed (Bel and Rosell 2013). However, acceleration, decelerations and congestion make the relationship more complicated and recent work has put emphasis on the importance of traffic Recent empirical evidence has uncovered increasing emissions as speed decreases, related to congestion and acceleration. Gately et al. (2017) study emissions of carbon monoxide (CO), NO2, NOx, PM2.5 and carbon dioxide (CO2) from vehicles on 280,000 road segments in Massachusetts, using mobile phone and vehicle GPS data on speed. They find that PM2.5 emission rates from heavy trucks increase markedly when speed falls below 55 km/h, while NOX emission rates increase more smoothly as speed falls. They also find that congestion The literature that has investigated the effect of actual speed limit changes on real-world air pollution has reached mixed conclusions. van Benthem (2015), studying rural areas in western U.S. states, finds that higher speed limits are associated with a 15% increase in concentrations of NO2 and no statistically significant change in the concentration of PM10. Bel and Rosell (2013) study the effect of two separate policies implemented by the regional government of Catalonia (Spain) on concentrations of NOX and PM10. They find that lowering the fixed speed limits to 80 km/h increases the level of NO2 by 2-3% and PM10 by 5-6%. In contrast, the introduction of variable speed limits reduces the level of NO2 by 8-17% and PM10 by 14-17%.  analyse the consequences of a similar reduction in the maximum speed limit in Amsterdam on NOX, PM1 and PM10. Their findings suggest that the policy lead to a decrease in PM10 of about 7%. However, they find no evidence of an improvement in the level of NO2. Some of these results were disputed by , who look at the effect of the same speed limit policy on a sample of roads with a strict enforcement of the new speed limit. The findings of  suggest that a reduction in the maximum speed coupled with "strict enforcemet" lead to a reduction of 5-30% for NOX and 5-25% for PM10. Table 1 in summarizes the previous research evaluating the impact of speed management policies on air quality using statistical methods and real-world data. The previous papers using statistical methods to unocver the effects of speed limits have relied on difference-in-difference estimators (Ashenfelter andGreenstone 2004, Bel andRosell 2013;Benthem 2015) or simple difference regressions comparing before vs. after a speed limit change (Bel, et al. 2015;. These identifiation strategies are prone to omitted variable bias, e.g., speed limits are not set randomly but depend on, for the researcher, unobserved characteristics. 3 The studies reviewed above indicate a complex relationship between traffic dynamics and vehicle emissions. This paper adds to the litearture by providing plaubily causal estimates of the effect of speed on emissions based on natural experiments and real-world behaviour. Notes: Summary of previous research on the effects of changes in maximum speed limits on air quality. The columns labelled NO (nitrogen oxides) and PM (particle matter) indicates whether the speed management policy improved air quality or not. (-) indicates no change.

Figure 1. Timeline of Environmental Speed Limits in Oslo
Notes: Timeline describing the development of environmental speed limits in Oslo for National Road 4, Ring Road 3 and European Route 18.

Monitoring stations and sample
We combine hourly data from separate sources for traffic, air pollution and weather. We focus on three monitoring stations for air pollution and three monitoring stations for traffic, located at four different locations in Oslo. The monitoring stations Smestad, Manglerud and Nydalen are all located roadside to Ring Road 3 while the location for Aker Hospital is roadside to National Road 4. 5 We match our air pollutant observations and traffic observations on each road and pool the roads together. In our main analyses, we use this pooled dataset for the period 2006-2011. As a placebo location for air pollutants, we use Kirkeveien. The monitoring station for weather is located at Blindern, i.e. within 7 km from all of the monitoring stations for air pollution. The height difference between the weather monitoring station and the lowest and highest monitoring station for air pollution is no more than 50 meters. We link the same weather observations to all the monitoring stations for air pollution. Figure 2 shows the location of each monitoring station for traffic (solid circle), air pollution (hollow circle) and weather (star). 6 5 We have excluded European Route 18 from our analysis because of many missing observations and because the policy there differs slightly from the policy implemented on National Road 4 and Ring Road 3. The differences would complicate the interpretation of the results and obscure the clean cut-off in the regression discontinuity design. 6 For both Manglerud and Aker Hospital, the monitoring station for traffic and air pollution are located close to each other, less than 1 km apart. For the air pollution monitoring station located at Smestad, the nearest traffic monitoring station is located in Nydalen, 8 km to the northeast of the air pollution monitoring station. This

Figure 2. Map Over Monitoring Stations and Roadways in Oslo
Notes: Map showing the location of the Monitoting stations. The monitoring stations Smestad, Nydalen and Manglerud are all located roadside to Ring Road 3 while the location for Aker Hospital is roadside to National Road 4. European Road 18 is excluded from our analysis. Marienlyst located roadside to Kirkeveien, a part of Ring Road 2, is used as a placebo station. The weather station is located at Blindern. For reference, the distance between Manglerud and Smestad along the treated road in the map is about 13 km. Source: Modified map from Elvik (2013). Table A.5 in the online appendix presents a summary of the main characteristics for each monitoring station.

Traffic data
The Norwegian Public Road Administration monitors the traffic in Oslo and records hourly speed and the number of passing vehicles each hour for each lane. 7 Actual speed is based on all vehicles passing the monitoring station the last hour. In our analysis, we have treated observations with no passing vehicles and speed observations lower or equal to 0 as missing. column states a simple t-test for differences in means between October and November. From column 6 and 8, we observe that the average speed was approximately 5 km/h below the posted speed limit before the implementation of the environmental speed limits, and approximately 8 km/h above the posted speed limit after the implementation. About 2,400 vehicles passes each monitoring station every hour, on average. This adds up to almost 58,000 vehicles every day.

Air pollution data
The Norwegian Public Road Administration in collaboration with The Norwegian Institute for Air Research operates the automated monitoring stations for air pollution. The monitoring stations are located close to the roads with the purpose of measuring pollution related to traffic.
The Norwegian Institute for Air Research validates all air pollution data by automatic as well as manual procedures, i.e. they correct measurement errors and manually calibrate the levels of air pollution. The dataset includes hourly observations for NO2, NOX, PM2.5 and PM10 . Speed is measured in kilometres per hour (km/h), Vehicles measures the number of passing vehicles per hour across all lanes. NO2, NOX, PM10 and PM2.5 is measured in parts per billion (g/m 3 ), Temperature (Temp.) is measured in degrees Celsius, Precipitation (Rain) is measured in millimetres (mm) and wind speed is measured in meters per second (m/s). Column (10) state the difference in means between October and November. The asterisk indicates the pvalue for the hypothesis that the means in October and November do not differ. * p < 0.05, ** p < 0.01, *** p < 0.001. measured in g/m 3 . 8 In our analysis, we have treated entries with zero or negative concentrations as missing. Table 2, Panel B summarises the descriptive statistics for each of the individual air pollutants, NO2, NOX, PM10 and PM2.5. The variance in hourly concentration levels is high across all air pollutants, and all air pollutants have maximum observations with worse air quality than what is legal according to Norwegian law. 9 The simple t-test suggests that the air pollution levels are significantly higher in November compared to October, reflecting that air pollution is seasonal and tend to increase during the winter.

Weather data
Data on temperature, precipitation, wind speed and wind direction are from the Norwegian Metrological Institute. Temperature is measured in Celsius Degree, two meters above the ground level. Precipitation is measured in millimetres and includes both snow and rain. It is included because of its ability to interact with existing air pollutants to create secondary ones and because of its ability to wash away particles from the air and minimise their formation (Viard and Fu 2015). We set entries with negative values of precipitation as missing. Minuteobservations of precipitation are aggregated to hourly observations. To reduce the number of missing observations, we have imputed values based on observations that record the total precipitation in the last 7 hours. Wind speed is measured in metre per second (m/s) and is measured as the mean value for last 10 minutes, 10 m above ground level. Higher wind speeds may remove air particles; however, it may also import air particles from nearby areas. Wind direction has been simplified into a Northern, Southern, Eastern and Western wind and is based on the general wind direction the last 10 minutes. 10 Descriptive statistics for temperature, precipitation and wind speed are presented in Table 2, Panel C. We observe a small decrease in wind speed between October and November. Furthermore, the temperature is 4.3 degrees Celsius lower in November compared to October. All these differences are statistically significant at conventional significance level. We observe no significant change in precipitation between October and November.

Empirical Strategy
The key identifying assumption in our regression discontinuity design (RDD) is that all characteristics relevant for speed and air pollution, other than the policy change, are continuous across the threshold, i.e. from October 31 st to November 1 st . As long as agents do not have precise control to sort themselves around the threshold date (e.g., move driving from the ESL-period to the earlier non-ESL-period), the variation in the treatment is as good as random and the RDD mimics a locally randomized experiment (Hahn et al. 2001;Lee and Lemieux 2010). Several similar applications, with time as the running variable, have used RDD (Hausman and Rapson 2018).
We estimate the effect of introducing the ESL on speed and traffic as well as on the four air quality outcomes NO2, NOX, PM10 and PM2.5 by the following econometric model: 11 Where y is a placeholder for speed, number of passing vehicles or one of the four air-quality outcomes. 1( ) is an indicator variable that equals 1 in the environmental speed limit period and 0 otherwise. When y is speed or traffic, 1 expresses the compliance with the ESL.
When y is one of the air quality outcomes, 1 is the intention to treat (ITT) effect of implementing environmental speed limits (the reduced form effect of the policy). is a set of control variables (temperature, current and 1-hour lags of precipitation, wind speed and wind direction). We include a large set of fixed effects: station, year, day of the week and hour, in addition to interactions between the hour and day of the week fixed effects and between station and wind direction fixed effects. The assignment variable is time ( ) and the date of introduction of the environmental speed limit policy is . (•) is a polynomial in time, and the interaction with 1( ) allows it to differ on either side of the cut-off date.
To estimate the effect of a reduction in speed on the air quality outcomes, we scale the effect on the air quality outcomes with the effect on speed. We do this by standard two stage least squares estimation (2SLS), where the first stage is equation (1) with speed as the dependent variable y and 1( ) as the instrument. The second stage is as follows: ̂ is the fitted values from the 1 st stage. 2 is the coefficient of interest and gives an unbiased estimate of the effect of speed, s, on pollution, y, given that the relevance criteria and exclusion restriction hold. We use the same control variables in (2) as in (1). In both, we cluster the standard errors by year (we provide a robustness check to this choice in the online appendix).

The first stage: The effects on speed and traffic volume
The purpose of the environmental speed limit policy was to improve local air quality by reducing travel speed. Figure  As explained in section 7.2, we use simple linear trends on each side of the cut-off and find the optimal bandwidth to be approximately 15 days for speed and traffic volume.
In the left-hand panel of Figure 3, there is a clear discontinuity in speed at the cut-off date, which indicates that the environmental speed limit did influence the choice of speed. However, the reduction in travel speed is much lower than the reduction in the maximum speed limit, in line with imperfect compliance to the new speed limit. There are no indications of jumps at other points than the cut-off date, providing support for a valid RDD and a causal interpretation of the jump at the cut-off date.
The right-hand panel of Figure 3 presents the number of passing vehicles, for which we observe little or no change at the cut-off date. This observation indicates that drivers did not substitute away from roads with the ESL to other roads. We confirm this finding in regressions in the online appendix and treat the number of vehicles as a control variable in the rest of the paper. 13 12 For the graphical presentation of the data, we have chosen daily bins based on comparing different bin-sizes and visual examination of the data. We average across all stations and years (2006)(2007)(2008)(2009)(2010)(2011) to construct the daily means. Thus, each bin contains a maximum of 6 ( ) × 3 ( ) × 24 (ℎ ) = 432 observations. 13 We show in the online appendix that our results are robust to the exclusion of control variables, and the issue of endogenous controls (Angrist and Pischke 2009) should therefore not be a big concern for our estimates. Table 3, Panel A, Column (1), reports our baseline estimate of the ESL on speed, which indicates a reduction of 5.8 km/h. Thus, a 1 km/h reduction in the maximum speed limit is associated with a 0.3 km/h reduction in travel speed. The estimates are considerably below 20 km/h. However, this might not be surprising as factors other than the posted speed limit may affect speed, such as congestion, weather and individual preferences. The modest effect could also be because of weak incentives to comply to the new speed limit, as the police would not ticket exceedances. Our finding of 0.3 km/h reduction in speed for a 1 km reduction in the speed limit is in line with Benthem (2015), who found that a 1 km/h increase in the maximum speed limit in the U.S. was associated with a 0.3-0.4 km/h increase in travel speed.  estimated that the pilot project on National Road 4 led to a decrease in travel speed of about 0.5 km/h per 1 km/h reduction in the speed limit.

Figure 3. Graphical Evidence on the Effect of the ESL on Traffic (a) (b)
Notes: The figure shows the effect of lowering the posted speed limit with 20 km/h on travel speed and traffic volume (number of passing vehicles). We see a clear discontinuity at the cut-off (November 1 st ) for speed, but no visible discontinuity for Traffic Volume. These findings indicate that the environmental speed limit did influence the choice of speed, but not the choice of roadway (i.e. no traffic substitution effects). To illustrate the noise in the underlying data, the scale of the y-axis in Figure 3 (b) have been set to equal the 25 th and 75 th percentile for the hourly observations of the number of passing vehicle.

The effects on air pollution
We first present Intention-to-Treat (ITT) estimates of the ESL on the four air pollutants. Figure   4 plots the residuals from estimating equation (1) excluding the ESL-dummy. 14 As we did for speed, we average over all monitoring stations and years into daily bins. We note that the linear time trends fit the data well. They are almost horizontal, indicating little variation between October and November in the air pollution, conditional on controls. The figure provides no indications of a discontinuity at the cut-off date, except for NO2, which shows slightly higher levels in the ESL-period. There is also no indication of jumps at points away

Figure 4. Graphical Evidence on the Effect of the ESL on Air Pollution
Notes: The figure shows the effect of lowering the posted speed limit with 20 km/h on four pollutants. We do not see a discontinuity at the cut-off at any air pollutants. The lack of a clear discontinuity at the cut-off suggests that the environmental speed limit did not influence air pollution concentrations levels.
from the cutoff-date. The data show substantial variation and some cyclical patterns common to all the four air pollutants.
We obtain the ITT-estimates by estimating equation (1) with the four air pollutants as the dependent variable. We use a 20-day symmetric window around the cut-off date, as justified in section 7.2. Table 3, Panel A, columns (2) through (5) present the ITT-coefficients. They all take an unexpected positive sign, but only for NO2 is the coefficient statistically significant at the 5%level. Thus, we find no evidence that the ESL-policy improves the air quality. The estimate for NO2, suggests instead a deterioration of 11.75%. These results are consistent with the  (2) on each air pollutant. All pollutants measured in logs. All models include control variables for current traffic volume (number of passing vehicles), wind direction, current and 1-hour lags of weather (precipitation, temperature and wind speed), in addition to station fixed effects, year, day of the week and hour fixed effects, interactions between hour and weekday fixed effects and interactions between station and wind direction fixed effects. The data are hourly observations from a pooled sample of the monitoring stations Manglerud, Smestad, Nydalen and Aker Hospital. Sample years are 2006 -2011. The F-statistics of about 110 indicate that our estimation should not suffer from weak instrument problems (Staiger and Stock 1997). Column (1) in Panel A based on a bandwidth of 15 days, the remaining columns on a bandwidth of 20 days. Standard errors in parentheses clustered by year. * p < 0.05, ** p < 0.01, *** p < 0.001. graphical evidence in Figure 4. Results for each individual station, presented in Table A.5 in the online appendix, show that all estimates are statistically insignificant.
To estimate the effect of a 1 km/h-reduction in speed on the four air pollutants, we scale the jump in air pollution with the jump in speed. We do this by using the ESL-dummy as an instrument for speed in a 2SLS-estimation. Columns (2) through (5), Table 3, Panel B, present the results. As the scaled estimate is simply the ratio between the ITT-coefficient for the air pollutant and the first stage coefficient on speed, we find that all the second stage coefficients take a negative sign. 15 Higher speed is associated with lower level of air pollution. Only the estimate for NOX is statistically significant, but this result is not robust to estimating for each station separately (results not presented to save space). 16 We illustrate our estimates in Figure 5. The thin red bars show the Norwegian legal limits. For NOX, the composite of NO and NO2, there is no stated legal limit. The thick grey bars show the observed levels in our sample under treatment (the weeks in November). The blue circles show estimated counterfactual levels together with their 95% confidence bands. The counterfactual means of NO2 and NOX would have been the same or lower in absence of the policy than the observed levels with the policy, as the effect is borderline significant at the 95%-level. At the lower end of the confidence interval for NO2, we can exclude that the air quality would have been within the legal limit without the policy.
For PM10, we estimate insignificant coefficients, in line with the results of Bel et al. (2015) and Benthem (2015). Our findings differ from the results of . They had data only for one road and one season of the ESL, as they studied the pilot project. When we now use data for several roads and several seasons, we find their results not to be robust. Our estimated counterfactual mean of 26 μg/m3 is 1 μg/m3 below the observed mean and 1 μg/m3 above the legal limit. From the estimated 95% confidence interval, we cannot rule out that the counterfactual value would have been 20 μg/m3 or 32 μg/m3. These +/-6 μg/m3 correspond to 25% of the standard deviation in the treated weeks in our sample. 15 The second stage estimate is numerically identical to the ratio of the reduced form coefficients for pollution and speed, in our case = ⁄ (Lee & Lemieux, 2010). E.g., −0.0178 = 0.1053 −5.8994 ⁄ for NOX. 16 The results for each individual station are similar to the results for the pooled sample, with statistically insignificant coefficients across all air pollutants and stations. For PM2.5, both the observed and the estimated counterfactual levels are below the legal limit, i.e. the legal limit is 15 μg/m3, the observed mean is 11 μg/m3 and the estimated counterfactual just below 11 μg/m3. The 95% confidence interval is +\-3.5 μg/m3.
In conclusion, we find no evidence that the ESL-policy improves air quality in Oslo. If anything, there is some weak evidence that the ESL-policy increases the concentrations of Nitrogen Oxides (NO2 and NOX). The estimates for PM10 and PM2.5 are uncertain. The expected effect of the policy is about zero, with about the same probability of worsening as improving air pollution in terms of PM10 and PM2.5.

Figure 5. Estimated Counterfactual Levels of Air Pollution
Notes: The figure presents the levels of the four air pollutants, as regulated by the Norwegian law (thin red) and as observed in our sample under treatment (thick grey). The blue circles indicate the estimated counterfactual level of air pollution, had the policy not been implemented. These estimates are our baseline reduced-form estimates presented in the upper panel of Table 3, and the 95% confidence intervals are based on standard errors clustered at the year-level. Note that clustering affects the standard errors as well as the critical t-values on which the confidence intervals are based. Figure A.8 in the online appendix includes also confidence intervals based on clustering on day or week. The level of clustering does not affect the conclusions of this study. Table 4 presents a simple cost benefit calculation of the ESL-policy, which indicates a time loss of about 30 MNOK each ESL-period (3.8 million USD). In addition comes potential saving in terms of fuel, noise and accidents of 4.7, 5.7 and 3 MNOK, respectively, adding up to a total social cost of 17 MNOK (2.1 million USD). We now explain how we have calculated these numbers. We present figures in local currency (NOK). The exchange rate between NOK and USD is about 8 NOK/USD. We provide more details in the online appendix.

Cost-Benefit Analysis
The value of time is based on the average salary in Norway and the time loss associated with the implementation of the ESL for a ten-kilometre distance, adjusted for average vehicle occupancy. We stipulate an average hourly salary after tax of 199 NOK, 1.5 persons per vehicle, 40 seconds lost time for every vehicle and about 57 600 vehicles using National Road 4 or Ring Road 3 each day. 17 The average length of the ESL-periods is about 160 days. The 17 We discuss these assumptions in online appendix C. In short, we arrive at these assumptions by the following: Our traffic data gives the mean number of cars per day. Data from Statistics Norway in combination with an assumed 25% tax rate give the after tax hourly wage. Research by  motivates 1.5 passengers per car. 40 seconds time-loss per vehicle is based on an assumed distance of 10 km travelled on the ESL-road. For reference, the distance between Manglerud and Smestad along the treated road in the map in Figure 2 is about 13 km. In terms of the levels of the four air pollutants, we cannot reject that the ESL-policy had zero effect. We therefore set the value of these potential benefits to zero.

Discussion regarding identification, specification and external validity
In this section, we provide an overview of checks we have undertaken regarding potential threats to identification and with respect to our specification choices. We also discuss robustness checks regarding maximum compliance and potential time-varying and non-linear effects. We conclude that none of the checks changes the conclusions of this study.

Potential threats to identification
Strategic driving shifts in driving around the cutoff could in principle be a threat to our identification. Our primary identifying assumption is that, absent of the ESL-policy, the air and Table A.2 in the online appendix). Our conclusion is that the coincidence between the implementation of environmental speed limits on November 1 st and the end date for the restrictions on the use of studded tires should not be a big concern. One likely reason is that weather conditions, which we find to be continuous across the cutoff-date, influence the timing of the tire change. Another likely reason is that the convenient time for changing tires, i.e. free time for drivers to do it themselves or capacity of professional tire changers, is unlikely to occur at November 1 st for everyone every year.
Other measures implemented by the city of Oslo to improve air quality are sweeping, road washing and road dust treatment with magnesium chloride (salt) to reduce the spread of PM.
These efforts should not be a threat to our identification, as there is no reason why they should change discontinuously on the cut-off date November 1 st . Instead, their use is likely to correlate with weather variables. 20 The share of diesel cars in Norway increased from 18.5% suggests that the spread of road dust from studded tires is about one hundred times larger than from studdless winter tires. Because of the adverse effects on road surfaces and air quality, Norwegian law restricts the use of studded tires: the use of studded tires is illegal from the second Monday after Easter Sunday up to and including October 31 st (Lovdata 1990), unless the weather requires the use of winter tires for safe driving. This exception applies also if one is travelling to a place where safety requires winter tires. in 2005 to 42% in 2012 (Statistics Norway, 2017). 21 As long as the share of diesel cars does not change discontinuously around November 1 st , our RD design is robust to the changing share of diesel cars.
To investigate whether our identifying assumption of smooth variation in relevant characteristics around the cut-off is likely to hold, we test for discontinuities in weather variables (see Table A.4 in the online appendix). We also conduct placebo tests by using observations from years and locations without ESLs to investigate whether there are jumps in our outcomes around November 1 st in absence of the ESL-policy (see Table A.2 in the online appendix). We do not find any indications of discontinuous changes around November 1 st , other than those plausibly caused by the ESL-policy.

Specification checks
To estimate the jump at the cut-off, we need to specify the order of the polynomial time trend In the online appendix (Table B.1-B5), we vary our RD specification along four dimensions: bandwidth (number of days around the cut-off), the order of the polynomial trend, the inclusion of covariates and the role of outliers. We do also run a robustness check with alternative clustering.
As a final robustness check, we run our analysis for the years with the largest change in speed, to get an "upper bound" for the effect of the policy (see Table A.2 in the online appendix). We focus on the first stage estimates and the ITT-estimates. For completeness, we include a section with OLS-estimates in the online appendix (section D).

External validity
Although our RD design helps us to achieve high internal valitidy, local circumstances, such as the car fleet and road quality, may affect the relationship between speed and air pollution.
For example, diesel cars have relatively high emissions of NOX (ICCT 2017) and newer roads typically have less spread of PM than older roads, due to less wear and tear on the asphalt (Norwegian Directorate for the Environment 2016). The level of speed is also likely to matter, as the relationship between speed and emissions is U-shaped Rosell 2013, van Benthem 2015). These are not concerns for our results for Oslo, as we have directly tested the policy on outcomes of interests, but they may affect the generalizability of our findings.

Conclusion
Authorities increasingly consider lowering speed limits in the hope of improving air quality, as road transport is an important contributor to air pollutants such as NOX and PM2.5. In this paper, we studied the environmental speed limit policy in Oslo, which the city has implemented to various degrees since 2004. The reduction of the maximum speed limit from 80 km/h to 60 km/h reduces travel speed by 5.8 km/h. However, we found no evidence that the policy improves air quality. We also calculated a net social loss from the policy. We conclude that policymakers should focus on other actions to improve local air quality and thereby reduce the adverse health effects of air pollution.

References
Aldrin     Effect of ESL on Air Quality Trimmed Sample RD Table B.5 Effect of ESL on Air Quality S.E. Robustness RD           (2) and (3) describes the concentration levels and the number of permitted exceedances per year required by Norwegian Law. Columns (4) and (5)   main results for the effect of ESL on NOX, NO2, PM10 and PM2.5 using different samples. All air pollutants are measured in logs. All models include control variables for current traffic density (number of passing vehicles) and wind direction; current and 1-hour lags of weather (precipitation, temperature and wind speed); in addition to, traffic density, school holiday fixed effects, station fixed effects, day of the week and hour fixed effects and a full set of interactions between hour and day of the weekday fixed effects; and station and wind direction. The models in Panel A and C are estimated by using hourly observation from the monitoring stations Manglerud, Smestad, Aker Hospital. Panel B uses hourly observations from the monitoring station located at Marienlyst. Column (2) through (5) in Panel A, B and C has been estimated using a bandwidth of 20 days. Column (1) has been estimated using a bandwidth of 15 days. Standard errors in parentheses are clustered by year. * p < 0.05, ** p < 0.01, *** p < 0.001  (2) through (5) include control variables for station fixed effects, the day of the week and hour fixed effects and a full set of interactions between the hour and day of the weekday fixed effects. The results in column (1) include control variables for current and 1-hour lags of weather (precipitation, temperature, wind speed and wind direction), in addition to, station fixed effects, year, day of the week and hour fixed effects and a full set of interactions between hour and day of the week fixed effects; and station and wind direction. The models are estimated by using hourly observation from a pooled sample of the monitoring stations Manglerud, Smestad, Nydalen. Sample years are 2006 -2011. All models have been estimated by using a bandwidth of 20 days. Standard errors in parentheses are clustered by year. * p < 0.05, ** p < 0.01, *** p < 0.001 and travel speed for each individual monitoring station. All pollutants are measured in logs. The models are estimated by using hourly observation and the same specifications as in Table B.2. * p < 0.05, ** p < 0.01, *** p < 0.001

B. Robustness
As mentioned in the main text, we undertake a host of different robustness checks. First, we examine the robustness of our result along four dimensions of our RD specification: bandwidth (number of days around the cut-off), the order of the polynomial trend, the inclusion of covariates and the role of outliers. We do also run a robustness check with alternative clustering. Finally, we run our analysis for the years with the largest change in speed, to get an "upper bound" for the effect of the policy. We focus on the first stage estimates and the ITT-estimates. Table B.1 reports the estimates of the effect of the ESL on speed and traffic volume using different combinations of order of the polynomial and bandwidths. For speed, all the point estimates are negative. The magnitude is also stable, except for the smallest bandwidth in combination with fifth-order polynomials. All the coefficients are statistically significant at the 5%-level, except for two with fifth-order polynomials. Even though the optimal order of polynomial given by Akaike´s information criteria suggests a polynomial of fifth order, we use a linear trend in our baseline specification to keep the model as simple as possible. 1  find that specifications with high order polynomials (higher than second order) can be misleading and should not be used. 1 We calculate AIC as = ln(̂2) + 2 where is the number of observations used in the regression, ̂2 is the mean squared error of the regression, and is the number of parameters in the regression model (Lee & Lemieux, 2010).

B.1 Choice of bandwidth and polynomial in the assignment variable
For traffic volume, we maintain our conclusion of no effect on traffic volume, as most of the estimates are statistically insignificant and the magnitudes are relatively small compared to the average number of passing vehicles (2588 in October). Although 5 out of 18 estimates are statistically significant at the 5%-level, 3 of them are based on a zero-order polynomial. This is equivalent to a simple mean comparison before and after the cut-off date (Lee and Lemieux 2010). The estimates simply pick up a decreasing trend over the cut-off, reflecting that the number of cars gradually decreases as winter is coming. The optimal order of the polynomial based on Akiake's Information Criterion (AIC). The note of Table 3 provides further description. Table B.2 presents the estimated treatment effect of the ESL on NOX, NO2, PM10 and PM2.5 for different order of polynomials and bandwidths. Only 3 out of the 48 point estimates are statistically significant using a 5% significance level. The 3 statistically significant point estimates are positive and are for NO2 and NOX. Only 8 of the 48 point estimates takes the expected negative sign. The robustness of the positive signs underpins our previous conclusion that the implementation of the ESL did not improve local air quality in Oslo. 2

B.2 Controls
Inclusion of covariates should not affect the estimated jump at the cutoff-date, no matter how correlated they are with the outcome, if the "no-manipulation" assumption holds (Lee and 2 The cross-validation function for NOX, NO2 and PM10 suggest that using a bandwidth of about 40 days is optimal, whereas the cross-validation function for PM2.5 suggests that using a bandwidth of about 20 days is optimal. In robustness checks not shown to save space, we use the optimal bandwidth suggested by the cross-validation function and it does not change the sign for any of the air pollutants. Furthermore, the point estimates are all statistically insignificant at the 5%-level. These checks and figures plotting the values of the Cross-Validation function over a range of bandwidths are available on request from the authors. 40 days 20 days  40 days 20 days  40 days 20 days  40 days 20 days (1) (2)  (3) (4)  (5) (6)  (7) Observations  22211  12420  22124  12371  22605  12482  22362 12555 Notes: The optimal order of the polynomial based on Akiake's Information Criterion (AIC). The note of Table 3 provides further description.
Lemieux 2010). Table B.3 in this online appendix repeats baseline Table 3, excluding control variables. The point estimate for speed is similar to our baseline estimate and is still statistically significant at the 5%-level. Also for the air pollutants, our baseline results hold.
All the coefficients take the same sign and are statistically insignificant at the 5%-level. As expected, the precision of the point estimates is reduced compared to our baseline estimates, since the main reason for including control variables in a well-specified RD is to reduce sampling variability (Lee and Lemieux 2010).

B.3 Outliers
We now exclude outliers by only including values that lie below the 95 th percentile and above the 5 th percentile for each separate air pollutant. Table B.4 in this online appendix presents the results and we find no substantial changes in magnitude, sign or statistical significance. Thus, excluding outliers does not alter the conclusions from our baseline results.

B.4 Clustering of standard errors
Our observations are likely to be correlated across time and space and we therefore cluster the standard errors. Since too few clusters may lead to an underestimation of the standard errors (Angrist and Pischke 2009), we now cluster the standard errors at the weekly [or daily] level, rather than the yearly level (see Table B.5). 3 This increases the number of clusters from 6 to 40 [or 213] for the air pollutants and from 6 to 29 [or 164] for speed. 4 The choice of clustering does not alter the conclusion of this study. The only notable difference is that the effect on NO2 is statistically insignificant with weekly clusters, which underlines that the statistically significant estimate for NO2 in our baseline estimation is not robust. Figure A.8 in the appendix illustrates graphically the differences in confidence bands due to different levels of clustering.

B.5 Maximum observed compliance
As the ESL-policy in Oslo was active, it became increasingly clear that the Police was hesitant to enforce it. 5 Compliance may therefore have decreased over time. Figure A.3 shows that the drop in speed at November 1 st is smaller for later years. Perhaps the drop in speed was simply too small to make a detectable improvement in air quality? As our estimates take the unexpected positive sign, this is unlikely to be essential. However, we now estimate the ITTeffect of the ESL on the four air pollutants on the sub-sample of years with the greatest estimated changes in speed, i.e. 2007speed, i.e. -2008 Table A.2 reports the results from this estimation. The estimates for NOX, NO2, and PM2.5 are similar to our baseline estimates, with positive and statistically insignificant coefficients. The coefficient for PM10 now takes a negative sign, but is still statistically insignificant.  (2) through (5) use a bandwidth of 20 days, column (1) a bandwidth of 15 days. Standard errors in parentheses are clustered by year. * p < 0.05, ** p < 0.01, *** p < 0.001. .5 by using a trimmed sample. The trimmed sample have been constructed by excluding outliers, defined as observations above the 95 th percentile and below the 5 th percentile for each separate pollutant. All pollutants are measured in logs. All models include control variables for current traffic density (number of vehicles) and wind speed; current and 1-hour lags of weather (precipitation, temperature and wind speed), in addition to, station fixed effects, year, day of the week and hour fixed effects and a full set of interactions between hour and day of the weekday fixed effects; and station and wind direction. The models are estimated by using hourly observation from a pooled sample of the monitoring stations Manglerud, Smestad, and Aker Hospital. Sample years are 2006-2011. Standard errors in parentheses are clustered by year. All columns have been estimated by using a bandwidth of 20 days. * p < 0.05, ** p < 0.01, *** p < 0.001  (5) on speed, NOX, NO2, PM10 and PM2.5. All models include control variables for current wind direction; current and 1-hour lags of weather (precipitation, temperature and wind speed), in addition to, station fixed effects, year, day of the week and hour fixed effects and a full set of interactions between hour and day of the weekday fixed effects; and station and wind direction. Columns (2) through (5) also include a control variable for current traffic density (number of passing vehicles). The models are estimated by using hourly observation from a pooled sample of the monitoring stations Manglerud, Smestad, Nydalen and Aker Hospital. Sample years are 2006 -2011. Columns (2) through (5) use a bandwidth of 20 days, column (1) a bandwidth of 15 days. Standard errors in parentheses are clustered by year. Standard errors in curly braces are clustered by week. Standard errors in brackets are clustered by date. * p < 0.05, ** p < 0.01, *** p < 0.001

C. Cost -Benefit Analysis
In the following section, we quantify the monetary costs and benefits of implementing ESL based on our estimates of the effects of the policy. The key aspects are time costs and the benefits of cleaner air. We start out with a thorough discussion of time costs. Because our analysis indicates no changes in air quality, we assume that the implementation of ESL has no impact on health outcomes. All numbers are adjusted for inflation, reported in 2017 NOK, except for the alternative time costs calculations provided by Directorate of Public Roads (2018), which are in 2016 NOK. As any cost-benefit analysis, the analysis is not complete but based on previous literature and assumptions.

Time costs
We first estimate the cost of travel time by the time loss associated with the implementation of ESL for a ten-kilometre distance, adjusted for average vehicle occupancy. For reference, the distance between Manglerud and Smestad along the treated road in the map in Figure 2 in the main text is about 13 km. We assume on average 1.5 persons per vehicle, based on research published by . To estimate the number of affected vehicles each period we use the average number of passing vehicles per hour from Table 2 in the main text. Thus, 57 576 vehicles use National Road 4 or Ring Road 3 each day. 6 The average length of an ESLperiod is 159.2 days. Table 2 in the main text of the paper reports the average speed before ESL-implementation to be 74.6 km/h. The estimated average speed after ESL-implementation is 68.8 km/h, based on the estimated 5.8 km/h speed reduction in section 5.1. Consequently, each vehicle loses 40 seconds every day in the environmental speed limit period for a tenkilometre drive, which is 1.77 hours (1 Hour and 46 minutes) for the entire environmental speed limit period.
As a simple benchmark for the value of time, we use the average salary in Norway. Based on Statistics Norway (2016), we assume the average monthly salary before tax measured in 2017 NOK to be 42,400 NOK. We assume average working hours to be 40 hours per week and end up with an estimate of the average hourly salary, after tax, of 199 NOK. 7 With this value of time, the time cost related to the estimated speed reduction is 352 NOK 8 per person and 528 6 Passing vehicles environmental speed limit period: 2399 vehicles hourly x 24 hours per day = 57 576 vehicles per day 7 Hourly salary after tax: 40,300 NOK x 1.052 x 0.75 tax / (40 hours x 4 weeks) = 199 NOK 8 Total time loss per person each environmental speed limit period: 1.77 hours x 199 NOK per hour = 352 NOK NOK per vehicle. This implies a total cost of 30 million NOK in each environmental speed limit period. 9 Table C.1 presents the details of our benchmark time cost calculation. We also refer to this calculation as "simple wage" in Table C.2 (the second column).   We use our data to estimate the share of light versus heavy vehicles (about 9% of the traffic is by heavy vehicles, as shown in table C.2). We assume that 50% of the heavy traffic are busses and 50% are trucks.
In the right part of  Time cost estimates are debatable due to the many required assumptions, including assumptions about preference, productivity and wage variations across the country. The national estimates may not be entirely representative for the road users in Oslo. Furthermore, the composition of long and short travel and the purpose of the travels on the ESL-roads in Oslo may also differ from the assumptions made by the public road authorities. One insight from the above, however, is that the heavy traffic is a relatively important part of the costs, in spite of counting for less than 10% of the traffic. 10 The public figures allow us to assign different costs to light and heavy vehicles. We use traffic data broken down on light and heavy vehicles and find that heavy vehicles account for 20% of the costs of 27 million NOK, although they account for only about 9% of the traffic. The reason is that an hour with a heavy vehicle is valued at 582 NOK (assuming 50% trucks and 50% busses) and an hour with a light vehicle is valued at 233 NOK (based on the national average of travelling distance and type of travel).

Fuel consumption
A speed reduction from 80 km/h to 60 km/h is also associated with a reduction in fuel consumption. Research suggests that the most efficient speed in terms of fuel consumption, is between 50 -90 km/h, as the fuel consumption curve is relatively flat within this window (Strand, et al. 2009). Strand et al. (2009) suggest a 22% fuel consumption reduction for private vehicles when the speed reduces from 90 km/h to 70 km/h. The decrease is somewhat smaller for larger vehicles. We assume this effect to be linear as the fuel consumption curve is relatively flat. Thus, in our private benefit calculation, we use a 5% reduction to calculate the change in fuel costs related to the 5.8 km/h speed reduction. The average fuel consumption for the current vehicles fleet is assumed to be 0.074 l/km (Tempo 2017). The average fuel price in the period 2006 -2011, measured in 2017 NOK, was 13.8 NOK/l (The Norwegian Petroleum Industry Association 2009) 11 . We assume, as we did above, a ten-kilometre drive each day in the environmental speed limit period, which adds up to 1600 km for each vehicle.
Thus, the total private benefit related to a reduction in fuel consumption is 759 MNOK each environmental speed limit period. 12 This implies a benefit of 83 NOK per vehicle.

Accidents and noise
We now consider social benefits associated with a reduction in travel speed. Because of the lack of evidence of an improvement in air quality, we have only calculated the social benefits related to a reduction in accidents and noise pollution. 13 Higher speed is usually associated with an increased risk of accidents, but the rate depends on the initial speed and road type (European Comission 2017). The Norwegian Public Road Administration records the number of injury accidents. These records include fatal, serious and slight injuries. Using these records, we calculate that the average number of injury accidents on National Road 4 and Ring Road 3 to be on average 39 injury accidents each year, during the period 2002-2015. 14 This implies a likelihood of being involved in an accident of 0.00019%. 15 We also calculate that 95% of these accidents included only slight injuries, 4.8% of the accidents included serious injuries and only 0.2% were fatal accidents. Figure A.6 illustrates the development in the number of 11 Average cost based on both diesel and gasoline 12 Total fuel benefit: (1600 km x 0.074 l/km x 13.8 NOK x 9,166,099 vehicles) x 0. 05 = 758,952,997 NOK 13 Because out crash records do not distinguish single vehicle accidents from accidents that also involve other parties, we assume that all accidents also have an external effect (e.g., all accidents are assumed to also include other vehicles or cyclists). Thus, we consider all costs related to accidents to be social costs. 14 These estimates are based on data obtained from Norwegian Public Road Administration. This estimate is conservative as it only includes accidents with reported injuries. From Figure A.6 we see that the number of accidents vary greatly across the different years. To mitigate the problem of statistical variance biasing our estimated number of accidents per year we choose to look at an extended time-period of 13 years. 15 Yearly number of vehicles is 57,576 x 365 = 21 024 000. Likelihood of accident: 39/21 024 000 = 0.0000019 = 0.00019% accidents during the period 2002-2015 for National Road 4 and Ring Road 3. Even though the likelihood of an accident is small, a study by Elvik (2013) suggests that the implementation of ESL reduced the number of accidents by 25%. This is a conservative estimate as it constitutes the lower bound of the estimates by Elvik (2013). We assume this reduction equal for all environmental speed limit roadways and across all accident types. We value the cost of a fatal accident to be approximately 35.4 MNOK; the cost of an accident involving a serious injury to be 12.4 MNOK; and the cost of an accident involving a slight injury to be 0.7 MNOK.
All valuations are measured in 2017 MNOK. These estimates are conservative and recommended by the Institute of Transport Economics in Norway . 16 Thus, the social benefit from a reduction in the number of accidents is estimated to be 5.7 MNOK each environmental speed limit period, implying a social benefit of 0.6 NOK per vehicle. 17 This estimate includes reported injury accidents and not purely materialistic accidents. The social benefit related to accidents is approximately equal to the value of saving one life every fifth year, if the value a statistical life is 30.5 MNOK. 18 The last social benefit we relate to lower travel speed is the value of a reduction in noise pollution. The value depends on the initial speed as speeds above 30 -40 km/h is dominated by rolling noise while speeds below 30 -40 km/h is dominated by engine noise (Kable 2011, Amundsen and Klaeboe 2005, Jongens 2008). There are about 392,400 citizens in Oslo exposed to at least 55 dB from the 1310 kilometres of public roads (Agency for Urban Environment, City of Oslo 2013). Thus, we assume there are about 300 vulnerable citizens per km. 19 The length of Ring Road 3 and National Road 4 is approximately 29 km. Thus, we assume there are 8,687 vulnerable citizens close to the environmental speed limit roadways that are exposed to at least 55 dB. 20 Meland et al. (2005) estimate that the reduction in traffic noise related to the implementation of ESL is 2 dB. We assume that this result is generalizable to all environmental speed limit roadways. The value of one dB reduction in noise is most often based on either hedonic pricing methods or contingent valuation. The estimated value of a 1 dB reduction in noise pollution depends on the method employed and varies from 20 NOK to 900 NOK (Navrud 2002, Navrud 2004, Boer and Schroten 2007. In our calculation, we

D. OLS estimates
For completeness, we present OLS-estimates of the association between speed and air pollution in Panel A, Table G.1. Only for PM10 do we estimate a statistically significant and positive coefficient on Speed, suggesting that a decrease in speed of 6 km/h is associated with a decrease in the concentration of PM10 of about 3.9%. The estimated coefficients on speed are negative and statistically insignificant for the three other pollutants. The OLS-estimated coefficient on the ESL-dummy, presented in Panel B, Table G.1, is negative for all pollutants and statistically significant for three of them. The coefficients suggest that the ESL-period was associated with better air quality, by 13.46% for NO2, 20.91% for NOX and 12.92% for PM10.
However, the divergence between the RDD and the OLS estimates when it comes to PM10 are no longer present when we estimate with OLS for each station (results not presented to save space). The OLS estimate for PM10 on speed is statistically insignificant across all stations and the estimates for the ESL-coefficient are statistically insignificant across all air pollutants and stations.
Trending omitted variables may explain the divergences between the RDD-and OLSestimates, as the RDD provides an unbiased estimate as long as the omitted variables are trending smoothly across the cutoff-date. One case in point is traffic volume and the ESLdummy. In Table G.1, we include traffic volume as a control, whereas omitting traffic volume creates a negative bias in the ESL-coefficients (results not presented to save space). This is consistent with the ESL-dummy correlating negatively with traffic volume, and traffic volume having a positive effect on the levels of the air pollutants. The descriptive statistics in Table 2 show that traffic volume is lower in November than in October. This may be due to for example more challenging driving conditions in November. The OLS-estimates may then mistakenly assign the downward trend in traffic volume to the ESL-policy active in November, whereas other factors are in reality explaining the fall in traffic volume. This example illustrates how trending omitted variables create a bias in the OLS-estimates and can lead researcher to draw the wrong conclusions.  1.b) on NOX, NO2, PM10 and PM2.5. All pollutants are measured in logs. All models include control variables for current traffic density (number of vehicles) and wind direction; current and 1-hour lags of weather (precipitation, temperature and wind speed); in addition to, station, year, month, day of the week and hour fixed effects and a full set of interactions between hour and day of the weekday fixed effects; and between station and wind direction. The models are estimated by using hourly observation from a pooled sample of the monitoring stations Manglerud, Smestad, Nydalen and Aker Hospital. Sample years are 2006 -2011. Standard errors in parentheses are clustered at the monthly level. * p < 0.05, ** p < 0.01, *** p < 0.001