## Abstract

In this paper, we analyze the effect of light conditions on road accidents and estimate the long-run consequences of different time regimes for road safety. Identification is based on variation in light conditions induced by differences in sunrise and sunset times across space and time. We estimate that darkness causes annual costs of more than £500 million in Great Britain. By setting daylight saving time year-round, 8% of these costs could be saved. Thus, focusing solely on the short-run costs related to the transition itself underestimates the total costs of the current time regime.

## I. Introduction

DAYLIGHT saving time (DST), also summer time, refers to the practice of moving clocks forward by one hour from standard winter time in spring and backward by one hour to winter time in the fall. It was introduced in Germany, followed by Great Britain, France, and the United States during World War I, in an attempt to conserve energy by shifting daylight from morning to evening hours. Currently, around seventy countries (e.g., including those in Europe and large parts of the United States and Canada), covering about one-quarter of the world's population, adopt DST regimes, yet concerns about the usefulness of DST are growing. In March 2019, the Sunshine Protection Act, a bill that would introduce year-round DST in most areas of the United States, was brought to U.S. Congress (2019). At about the same time, the European Parliament (2019) voted for a resolution to scrap the biannual clock change from 2021 onward. Although neither bill has been approved yet, they mirror the rising concerns about whether the harms of changing the clocks twice a year potentially outweigh the intended benefits of this policy regulation.

Recent literature provides empirical evidence that DST does not have the originally intended effect on energy conservation. To the contrary, it may even increase total energy consumption, since energy savings in lighting are at least offset by increased energy use in other areas such as heating or air-conditioning (Kellogg & Wolff, 2008; Momani, Yatim, & Ali, 2009; Krarti & Hajiah, 2011; Kotchen & Grant, 2011; Sexton & Beatty, 2014).1 In addition, several studies indicate that the transition in and out of DST causes disruptions in the circadian rhythm and adversely affects the duration and quality of sleep (Lahti et al., 2006; Kantermann et al., 2007), which in turn may have unintended negative side effects in various (economic) dimensions other than energy saving. These negative short-term effects range from lower general well-being (Kountouris & Remoundou, 2014) and life satisfaction (Kuehnle & Wunder, 2016), decreases in stock market returns (Kamstra, Kramer, & Levi, 2000) and students' performance (Gaski & Sagarin, 2011) to higher risk of work injuries (Barnes & Wagner, 2009; Lahti et al., 2011), acute myocardial infarction (Janszky & Ljung, 2008; Jiddou et al., 2013; Toro, Tigre, & Sampaio, 2015), suicides (Berk et al., 2008), and fatal road accidents (Varughese & Allen, 2001; Sullivan & Flannagan, 2002; Sood & Ghosh, 2007; Smith, 2016).2

While this literature provides evidence in favor of abolishing the yearly ritual of changing the clocks twice, at least from a short-term perspective, it is less clear for which time regime, DST or standard winter time, a society eventually should adopt. From an economist's point of view, this decision should be based on the long-term costs and benefits of establishing one of these time regimes instead of the other. One area in which permanent costs and benefits might arise is road safety. This is mainly because choosing one time regime instead of the other affects the distribution of natural light across hours of the day. Since traffic density also differs by time of the day, shifting light from the morning hours to the evening hours or the other way a round might have consequences for annual road accident counts if light levels affect road safety. It is the aim of this paper to empirically assess to what extent this is indeed the case and how different time regimes affect road safety.

To estimate the effect of darkness on accident counts, we make use of large, administrative data from England, Scotland, and Wales covering all accidents on public roads that resulted in a personal injury and were reported to the police. Our identification strategy exploits arguably exogenous variation in darkness stemming from three sources of variation in sunrise and sunset times: day-by-day variation for a given region and hour, east-west variation for a given day of the year and hour, and north-south variation for a given day of the year and hour. The resulting estimates are used to simulate the number of fatal, serious, and slight accidents under two different time regimes: setting the clocks permanently to DST versus permanent standard winter time.

Our contribution to the literature is twofold. First, we extend the literature on the effects of DST on road safety by looking at the long-run consequences for accident counts of different time regimes. This allows us to assess whether year-round DST or all-year standard winter time should be implemented, at least from a road safety perspective. Most of the related literature on the effect of DST on traffic accidents exploits the abrupt transition from standard winter time to DST in spring and vice versa in fall (e.g., Smith, 2016). This approach allows for credible identification of the effects of the transition into and out of DST under plausible assumptions; however, the resulting estimates cannot easily be used to assess the effects of DST over the entire year, as they are valid only locally (around the dates of transition into and out of DST). Only a few early papers have investigated the long-run consequences of time regime choice for road safety (e.g., Ferguson et al., 1995; Coate & Markowitz, 2004).3 Yet as these papers essentially compare accident counts during the morning and evening hours across weeks, strong assumptions have to be imposed to give their estimation results a causal interpretation.4 Second, exploiting information about all individuals involved in each accident, we shed some light on potential mechanisms through which darkness might affect road safety. Given that light levels not only affect vision but might also influence concentration and fatigue due to adjustments of the circadian rhythm, it is unclear whether measures that aim at increasing visibility such as more road lighting can be effective in reducing road casualties.

We find that darkness increases accident counts by around 7% per hour, which translates into annual costs of more than £500 million caused by darkness. As the estimated effects are larger for fatal and serious accidents than for slight accidents, our results indicate that light conditions increase not only accident risk but also accident severity. Simulations based on these estimates suggest that shifting light from the morning to the evening by setting the clocks permanently to DST could save lives and costs. Compared to an all-year standard winter time regime, setting the clocks to DST during the entire year could avoid at least £40 million per year across England, Scotland, and Wales. This indicates that the literature on the effects of the transition itself underestimates the total costs of the current time regime. Our heterogeneity analyses indicate that the positive effects of darkness on accident counts are likely due to a reduction in vision during darkness.

The remainder of the paper is structured as follows. Section II describes the data and the empirical approach. In section III we present our main results, as well as the results from heterogeneity and sensitivity analyses. Section IV concludes and discusses policy implications.

## II. Empirical Framework

### A. Data and Measurement

Our accident data come from the STATS19 database (Department for Transport, 2018b). It covers all accidents on public roads in England, Scotland, and Wales that resulted in a personal injury and were reported to the police between 1996 and 2017. The data are collected by the police using a nationally standardized form for the collection of data on each road accident, each casualty, the vehicles involved in the accident, and drivers and passengers.5

Three properties make the STATS19 data especially suitable to study the effects of ambient light condition on road safety. First, the data provide detailed information on the level of individual accidents. For each accident we not only have information on the location and the exact date and time of the accident, but also on the type of accident; the number of slightly, seriously, and fatally injured casualties; and the age of all drivers. Thus, we can assign each accident to a geographic region and distinguish among certain types of accidents; for example, we can distinguish car accidents from accidents involving pedestrians. Second, the coverage of the STATS19 data is exceptionally large. As our identification strategy is based on variation in sunrise and sunset time across latitude, longitude, and day of the year, we are reliant on data covering a sufficiently large area and time span. Our sample comprises information on more than 4.1 million accidents from all across England, Scotland, and Wales between 1996 and 2017. Finally, the data can be considered to be highly reliable. According to our sample, a police officer attended the accident scene to obtain the details for the report in almost 80% of all accidents. The information for another 20% of accidents were gathered in questionings at the police station, while the details about the accidents were obtained using a self-completion form only in less than 0.2% of all accidents.

The individual-level data are aggregated in order to yield hourly accident counts for a panel of 265 regions. We use a grid reference system based on longitude and latitude to define regions. This system divides Great Britain into 265 regions, each spanning an area of the size $0.5∘$ longitude $×$$0.5∘$ latitude.6 Using information about the type and severity of the accident as well as the age of the drivers,7 we distinguish among the following accident categories: all accidents; accidents involving pedestrians; accidents involving drivers younger than 25, between 25 and 45, between 45 and 65, or above the age of 65; and accidents with only slightly injured casualties, accidents with seriously injured casualties, and fatal accidents. The left panel of figure 1 illustrates the grid reference approach and shows how accidents are distributed across regions.
Figure 1.

Distribution of Accidents and Weather Stations across GB

Own calculations and illustration based on STATS19 and MIDAS data. Left: Grid-based regions and the distribution of accidents during the year 2017 across these regions. Darker shading indicates more accidents. Right: The distribution of weather stations across Great Britain.

Figure 1.

Distribution of Accidents and Weather Stations across GB

Own calculations and illustration based on STATS19 and MIDAS data. Left: Grid-based regions and the distribution of accidents during the year 2017 across these regions. Darker shading indicates more accidents. Right: The distribution of weather stations across Great Britain.

As one might worry that changes in light intensity are systematically related to changes in weather conditions, we amend the accident data with information about weather conditions at site. Hourly weather data come from the Met Office's MIDAS database (Met Office, 2006a, 2006b) and include information on wind speed, precipitation, and temperature. In order to make the weather data compatible with the accident data, we first calculate simple averages of all stations within each region and hour for all weather variables. These regional averages are then used to generate three variables with four (wind speed), two (precipitation), and six (temperature) categories.8 Furthermore, we include a dummy variable to capture icy road conditions (positive precipitation and temperature below 2$∘$C). As there are regions without operating weather stations during all or some time periods, the sample clearly decreases in size when we include weather information (see the right panel of figure 1 for an overview about the distribution of relevant weather stations across Great Britain). In the following, we thus present results for both samples: the sample covering all observations from all regions during the whole observation period, as well as the sample covering only those observations for which weather data are available.

Although the STATS19 data provide some information about lighting conditions at accident sites, we cannot use those data to derive a measure for darkness, since the raw data naturally provide such information only for regions (and hours) with at least one accident. Thus, if we decided to make use of the information about lighting conditions, we would have had to discard a large share of potentially informative observations (i.e., observations with a zero accident count) and run our estimations on the truncated sample. Instead, we treat a region-hour as a dark or light hour based on information about the position of the sun relative to the horizon in this region and at this date and time. For each region and date, we first calculate the times when the sun's position is 6 degrees below the horizon as seen by an observer who is located in the center of the region. This happens twice a day, once in the morning before sunrise and once in the evening after sunset, and marks the beginning or ending, respectively, of civil twilight. (For a detailed description of the procedure used here to calculate the position of the sun based on longitude, latitude, date, and time, see Cornwall, Horiuchi, & Lehman, 2015.) During civil twilight, no ray of sunlight touches the ground. Yet higher air layers are still directly illuminated by the sun and diffract a relevant part of the sunlight to the ground. This indirect lighting during civil twilight is sufficient for the human eye to clearly distinguish objects. We thus make use of a definition of darkness that is based on the onset and offset of civil twilight rather than on sunrise and sunset. Similar definition of darkness have been used in the related literature (Sullivan & Flannagan, 2002) but also became part of U.K. law. The Road Vehicles Lighting Regulations 1984, for example, also refer to the beginning and ending of civil twilight when it defines the daytime hours as the time between half an hour before sunrise and half an hour after sunset and require drivers to keep headlights lit during the hours of darkness (Department for Transport, 1984).

Based on the exact information about the beginning and ending of twilight at the center of each region, day, and hour, we are able to define our main treatment variable for darkness: dark gives the fraction of the hour that is dark. Thus, it takes the value 1 if the hour of observation is before the hour of transition from nautical twilight (dark) into civil twilight (light) in the morning or after the hour of transition from civil twilight into nautical twilight in the evening and the value 0 if the hour of observation is after the hour of transition into civil twilight in the morning and before the hour of transition out of civil twilight in the evening. If the hour of observation is instead the same as the hour of transition from or into civil twilight, $dark$ can take on some value between 0 and 1, which depends on the minute of transition out of or into civil twilight.9

### B. Identification and Estimation

The basic intuition of our main empirical strategy is to make use of variation in darkness induced by variation in sunrise and sunset times across time and space to estimate the effect of darkness on road safety and then to simulate road safety under alternative time regimes. In order to be able to put the results of our main analysis into perspective, we follow the related literature and also present results based on a regression discontinuity (RD) design. The RD exploits the discrete change from standard winter time to DST in spring and vice versa in autumn and has been used (Smith, 2016) to directly estimate the effect of DST on road safety. The intuition behind this approach is that one might expect to see a sharp increase (decrease) in the number of accidents around the date of DST transition if DST affects road safety. Specifically, we estimate regressions based on equation (1):
$lnaccidentsdt=f(daysdt)+πpostdt+f(postdt×daysdt)+ηdt,$
(1)

where $accidentsdt$ is the total number of accidents (of a certain type and net of day of the week and year fixed effects)10 at day $d$ in year $t$, $daysdt$ is the running variable and denotes the number of days from DST transition (either in spring or in autumn), $postdt$ is a dummy equal to 1 for days after DST transition, and $ηdt$ is an error term. The interaction between post and days is included to allow for different slopes at both sides of the cutoff. The parameter of interest in this setting is $π$ and gives the effect of the transition into or out of DST on accident counts. To account for the fact that the length of the day is 23 instead of 24 hours on the day of DST transition in spring, we follow Smith (2016) and count accidents during 3:00 a.m. hour twice. Correspondingly, we drop half of the accidents during 2:00 a.m. hour on the day of DST transition in autumn. To further increase the comparability of daily accident counts, we drop holidays11 from the estimation sample.

The assumption required for $π$ being consistently estimated is that in the absence of DST transition, $ln$accidents would change continuously in days around the transition date. If this assumption holds, comparing accident counts just before with accident counts just after the cutoff date yields a reasonable estimate of the short-run effect of DST on road safety. Note that this assumption is likely to hold if people cannot manipulate treatment, as in this setting where the whole country is treated, and if there are no other rules that might affect the outcome differently at both sides of the cutoff. To our knowledge, there are no other discontinuities around the DST transition dates that might have an effect on road safety. To determine the number of days to be used at both sides of the cutoff, we make use of mean squared error optimal bandwidth selectors (see Calonico et al., 2017).

While the RD provides causal estimates of the effect of DST transition on road safety under plausible assumptions and thus can be used to assess the costs of DST transition, its use is rather limited when it comes to the main goal of this paper: assessing the costs of alternative time regimes throughout the entire year. This is because the RD estimates are valid only very locally, namely, just a few days around the date of transition into and out of DST, and cannot be used easily to extrapolate the number of accidents under DST far away from the transition date, for example, in January. Our main approach, which aims at assessing the long-run consequences of different time regimes, is therefore to estimate the effect of darkness on accident counts and then using these estimates to simulate the number of accidents under the different time regimes. This approach uses variation in darkness and accident counts throughout the entire year and thus is more suitable to assess the relative costs of establishing one time regime instead of the other.

Figure 2.

Distribution of Accidents by Year, Week, Hour, and Day of Week

Own calculations and illustration based on STATS19 data. The figure shows the total number of accidents in thousands by year (upper left), the total number of accidents in thousands during the year 2017 by week (upper right), day of the week (lower left), and hour (lower right).

Figure 2.

Distribution of Accidents by Year, Week, Hour, and Day of Week

Own calculations and illustration based on STATS19 data. The figure shows the total number of accidents in thousands by year (upper left), the total number of accidents in thousands during the year 2017 by week (upper right), day of the week (lower left), and hour (lower right).

To identify the effect of darkness on accident counts, we estimate regressions based on the following equation:
$accidentsihdt=f(βdarkihdt+Xihdt'γ+αi+ρh+δd+λt+ɛihdt),$
(2)

where $accidentsihdt$ denotes the number of accidents (of a certain type) in region $i$ during hour $h$ on day $d$ of year $t$, $darkihdt$ is the dark share in hour $h$ in region $i$ on day $d$ of year $t$ (see above), $αi$ are region, $ρh$ hour of the day, $δd$ day of the year, and $λt$ year fixed effects. Finally, $Xihdt$ includes weather variables and indicator variables for the day of week, and $ɛihdt$ is an error term.

The parameter $β$ is the parameter of interest and gives the causal effect of darkness on hourly accident counts. To estimate $β$ consistently, the necessary assumptions have to hold; most important, $dark$ has to be conditionally exogenous. We argue that there are good reasons to assume that $dark$ is exogenous conditional on the fixed effects and the weather controls included in $X$. First, by including hour of the day fixed effects ($ρh$), we account for the fact that both darkness and accidents are distributed unevenly across hours. Darkness concentrates on some hours during night when people are at home and road traffic, and thus accident counts, are quite low (see figure 2), while daylight concentrates on hours when people go about their daily tasks and streets are rather crowded. Second, by including day of the year fixed effects ($δd$), we avoid bias due to correlated changes in road and light conditions in the course of the year. While most hours are dark and road conditions can be hazardous due to snow, ice, and fog during winter, the opposite is true for the summer months. Third, to capture that differences in the number of accidents might be related to differences in the share of dark hours between regions (northern versus southern regions), we include region fixed effects ($αi$). Finally, as changes in light conditions might be directly related to changes in weather conditions, we also estimate variations of equation (2) where we control for weather conditions at the accident site.

The variation in $dark$ that is not captured by one of the fixed effects is used to identify $β$. It comes, as will be shown in the following figures, from variation in the offset and onset of darkness across time and space. Figure 3 shows the timing of transition from darkness to daylight in the morning (upper two panels) and from daylight to darkness in the evening (lower two panels) over the course of the year. In the left two panels, we distinguish between two places on the same line of latitude: one in the very east of Great Britain (dashed line) and one in the very west (solid line). Similarly, in the right panels, we differentiate between two places on the same line of longitude: one in the very north (dashed line) and one in the very south (solid line). What can be seen immediately are three sources of variation in darkness: changes in the timing of onset and offset of darkness throughout the year and by longitude (east-west comparison) as well as latitude (north-south comparison).
Figure 3.

Variation in Offset and Onset of Darkness

Own calculations and illustration. The figure shows the timing of offset (upper panels) and onset (lower panels) of darkness at four different places in Great Britain and over the course of the year (2017). The panels on the left side differentiate between two places on the same line of latitude (52.25$∘$ latitude), a place in the very west ($-5.25∘$ longitude, solid line), and a place in the very east (1.25$∘$ longitude, dashed line) of the country. Correspondingly, the panels on the right side differentiate between two places on the same line of longitude ($-4.25∘$ longitude); a place in the very south (50.25$∘$ latitude, solid line) and a place in the very north (58.25$∘$ latitude, dashed line).

Figure 3.

Variation in Offset and Onset of Darkness

Own calculations and illustration. The figure shows the timing of offset (upper panels) and onset (lower panels) of darkness at four different places in Great Britain and over the course of the year (2017). The panels on the left side differentiate between two places on the same line of latitude (52.25$∘$ latitude), a place in the very west ($-5.25∘$ longitude, solid line), and a place in the very east (1.25$∘$ longitude, dashed line) of the country. Correspondingly, the panels on the right side differentiate between two places on the same line of longitude ($-4.25∘$ longitude); a place in the very south (50.25$∘$ latitude, solid line) and a place in the very north (58.25$∘$ latitude, dashed line).

Figure 4 shows for selected hours of the day, days of the year, and regions how this variation in the timing of onset and offset of darkness translates into variation in darkness. The shaded areas in each panel give the proportion of the respective hour that is dark. The 5:00 a.m. hour in the morning, for example, is completely dark until the end of February. Then the dark proportion of this hours starts to decrease such that by March 25, at least 30% of this hour is light all across Great Britain. As all clocks are then set one hour ahead due to daylight saving time transition,12 the dark proportion of 5:00 a.m. jumps back to 100% but then decreases again. Similar variation in darkness across time can be found for other hours of the day but at different days of the year, for example, during October, November, and December, for the 4:00 p.m. hour.

Aside from variation in darkness for a given hour and region across day of the year, there is also variation in darkness for a given hour and day of the year across regions. As can be seen in the left part of figure 4, the dark proportion of an hour is 0 to 50 percentage points higher in the morning in regions of the very west of Great Britain compared to regions (on the same line of latitude) in the very east. The opposite is true for hours in the evening. The left panel of the graph shows that the dark proportion of an hour varies also by latitude. By isolating these three parts of variation in darkness to estimate $β$ and additionally controlling for weather conditions, we are confident of giving our estimation results a causal interpretation.

Figure 4.

Variation in Darkness used for Identification

Own calculations and illustration. The figure shows the dark proportion of an hour by day of the year and for selected hours and places. The four panels on the left side differentiate among six places on the same line of latitude but on different lines of longitude (the darker the color, the more in the west. The four panels on the right differentiate among six places on the same line of longitude but different lines of latitude (the darker the color, the more in the south).

Figure 4.

Variation in Darkness used for Identification

Own calculations and illustration. The figure shows the dark proportion of an hour by day of the year and for selected hours and places. The four panels on the left side differentiate among six places on the same line of latitude but on different lines of longitude (the darker the color, the more in the west. The four panels on the right differentiate among six places on the same line of longitude but different lines of latitude (the darker the color, the more in the south).

Equation (2) is estimated using a negative binomial (NB) model, as our outcome variables are count variables with a large proportion of 0s and show signs of overdispersion. In order to avoid the well-known incidental parameter bias problem, we estimate the NB fixed-effects models by including full sets of dummies for regions, hours, days of the years, and years. Although there is no formal proof available that this approach rules out inconsistencies due to the incidental parameter bias problem, simulations by Allison and Waterman (2002) and Greene (2004) suggest that the bias should be small even if the number of time periods is small (Cameron & Trivedi, 2015). Given that the number of time periods is rather high in our application, the incidental parameter bias problem should not pose a threat here. Nevertheless, we also estimated OLS regressions. The OLS results are mostly quite similar to the NB results but less precisely estimated. We thus focus in the following on the NB results and present OLS estimates in the online appendix.

## III. Results

### A. Main Results

Before turning to the results of our main analysis, we show the results from the replication part of our analysis in table 1. The corresponding graphical representation to the RD estimates can be found in figure B1 in the online appendix. The first two columns of table 1 report the estimates for the spring transition, while columns 3 and 4 show the results for the fall transition. We do not find clear evidence that the transition into or out of DST increases accident counts. Only the RD estimates and graphs for fatal accidents consistently suggest that DST transition adversely affects road safety. According to the point estimates, entering DST increases the number of fatal accidents by 8% to 10%. While both estimates are of considerable size and in line with the results of Smith (2016), who finds that entering DST increases the number of fatal crashes in the United States by around 6%, only one of them is marginally significantly different from 0 ($p<0.1$). The results for the other accident types, as well as the results for the total number of accidents, rather point to small or 0 effects of DST transition on road safety.

Table 2 shows the baseline results of our main analysis. The first column gives the estimated coefficients of darkness on the total number of accidents and the number of accidents by accident severity for all regions. Columns 2 and 3 present the estimates for the same outcomes, but the sample includes only observations for which weather information is available. While column 2 gives the estimates from the regression including the standard controls, column 3 shows the results for our preferred specification in which we additionally control for weather conditions at accident site.

The results from our preferred specification, shown in column 3, suggest that darkness increases the total number of accidents for a given hour by 7.2%. As the effect of darkness is larger for the number of fatal ($+$31.8%) and serious ($+$11.3%) than for the number of slight accidents ($+$6.2%), darkness seems to affect not only accident frequency considerably but also accident severity. The corresponding estimates derived from OLS regressions, though less precisely estimated and partly smaller, point in the same direction and are shown in table B3 in the online appendix.

Table 1.
RD Estimates of DST Transition on Accidents
Spring TransitionFall Transition
Bandwidth SelectorOneTwoOneTwo
ln # all accidents −0.028 (0.022) −0.012 (0.017) 0.037* (0.021) 0.013 (0.020)
Observations 466 990 638 638
ln # slight accidents −0.043* (0.022) −0.004 (0.018) 0.031 (0.022) 0.011 (0.021)
Observations 544 1,034 682 638
ln # serious accidents 0.025 (0.030) 0.016 (0.025) 0.021 (0.027) 0.034 (0.025)
Observations 754 1,100 770 792
ln # fatal accidents 0.083 (0.055) 0.099* (0.056) 0.013 (0.055) 0.051 (0.052)
Observations 1,830 1,659 1,071 1,441
Spring TransitionFall Transition
Bandwidth SelectorOneTwoOneTwo
ln # all accidents −0.028 (0.022) −0.012 (0.017) 0.037* (0.021) 0.013 (0.020)
Observations 466 990 638 638
ln # slight accidents −0.043* (0.022) −0.004 (0.018) 0.031 (0.022) 0.011 (0.021)
Observations 544 1,034 682 638
ln # serious accidents 0.025 (0.030) 0.016 (0.025) 0.021 (0.027) 0.034 (0.025)
Observations 754 1,100 770 792
ln # fatal accidents 0.083 (0.055) 0.099* (0.056) 0.013 (0.055) 0.051 (0.052)
Observations 1,830 1,659 1,071 1,441

Own calculations based on STATS19 data. Each estimate gives the effect (semielasticity) of DST transition on the number of accidents in the respective category and comes from a separate local linear regression based on Equation (1). Bandwidth selectors are either a common mean squared error (MSE)-optimal bandwidth selector (denoted by one) or two different MSE-optimal bandwidth selectors below and above the cut-off (denoted by two). Robust standard errors are in parentheses. Significance levels: *$p<0.1$; **$p<0.05$; and ***$p<0.01$.

Table 2.
NB Estimates of the Effects of Darkness on Accidents
All RegionsRegions with Weather Data
Weather ControlsNoNoYes
# all accidents 0.071*** (0.006) 0.072*** (0.006) 0.072*** (0.007)
# slight accidents 0.062*** (0.006) 0.063*** (0.007) 0.062*** (0.007)
# serious accidents 0.108*** (0.007) 0.111*** (0.008) 0.113*** (0.008)
# fatal accidents 0.339*** (0.018) 0.315*** (0.021) 0.318*** (0.022)
Observations 51,103,130 21,352,015 21,352,015
All RegionsRegions with Weather Data
Weather ControlsNoNoYes
# all accidents 0.071*** (0.006) 0.072*** (0.006) 0.072*** (0.007)
# slight accidents 0.062*** (0.006) 0.063*** (0.007) 0.062*** (0.007)
# serious accidents 0.108*** (0.007) 0.111*** (0.008) 0.113*** (0.008)
# fatal accidents 0.339*** (0.018) 0.315*** (0.021) 0.318*** (0.022)
Observations 51,103,130 21,352,015 21,352,015

Own calculations based on STATS19 and MIDAS data. Each estimate gives the effect (semielasticity) of darkness on the number of accidents of the respective category and comes from a separate negative binomial regression. All regressions include region, year, day of the year, day of the week, and hour fixed effects. Standard errors clustered at region level are in parentheses. Significance levels: *$p<0.1$; **$p<0.05$; and ***$p<0.01$.

Our results are robust to the inclusion of weather controls. There are no relevant differences with respect to size or statistical significance between the estimates presented in columns 2 and 3. For both specifications and all outcomes, we find relatively large, positive, and significant effects of darkness on accident counts. This finding also holds when we use the entire sample (column 1), with observations for which weather information is not available.

Using simulations based on the results for all regions, we can now address two questions. First, how many accidents per year have been caused by darkness in England, Scotland, and Wales under the current regime with Greenwich Mean Time (GMT) during winter and DST during summer? This number shows how many accidents could potentially be avoided if darkness-related accidents could be brought to 0. The second question is, does having more light in the evening than in the morning help to bring down accident counts, that is, does setting the clocks permanently to DST prevent at least some accidents that would happen under an all-year GMT regime? Our approach to answer these questions is to predict the number of accidents in the hypothetical situations without darkness as well as under an all-year GMT and an all-year DST regime by adjusting the darkness variable accordingly.13 The resulting accident counts are then multiplied with the following average accident costs for 2017 as provided by the Department for Transport (2018a) to broadly assess the social costs: £25,451 for a slight accident, £243,635 for a serious accident and £2,130,922 for a fatal accident. Because these costs are quite low compared to estimates used in the related literature,14 our results for the social costs represent lower bounds of the true costs.

The credibility of this simulation approach mainly rests on the assumption that darkness has a uniform impact over the course of the day. This assumption, however, might be violated, for example, if darkness interacts with fatigue or traffic density. We thus not only present simulation results for the baseline models allowing only for one uniform effect of darkness, but also present results where we relax this assumption. Specifically, we also show simulated accident counts based on regressions that allow for different effects during early morning (midnight–4:59 a.m.), late morning (5–8:59 a.m.), early evening (3–6:59 p.m.), and late evening (7–11:59 p.m.).15 The underlying regression results for this more flexible specification are shown in table 3 and indicate that the effect of darkness is larger during busy hours in late morning and early evening. For slight and serious but not for fatal accidents, the effect also seems to be larger on average during morning hours than evening hours.

Table 3.
NB Estimates of the Effects of Darkness on Accidents by Time of Day
Morning HoursEvening Hours
Midnight–4 a.m.5–8 a.m.3–6 p.m.7–11 p.m.
# slight accidents 0.078*** (0.028) 0.274*** (0.017) 0.064*** (0.005) 0.013 (0.013)
# serious accidents 0.136*** (0.040) 0.351*** (0.021) 0.138*** (0.010) 0.022 (0.014)
# fatal accidents −0.053 (0.097) 0.428*** (0.044) 0.472*** (0.028) 0.214*** (0.027)
Morning HoursEvening Hours
Midnight–4 a.m.5–8 a.m.3–6 p.m.7–11 p.m.
# slight accidents 0.078*** (0.028) 0.274*** (0.017) 0.064*** (0.005) 0.013 (0.013)
# serious accidents 0.136*** (0.040) 0.351*** (0.021) 0.138*** (0.010) 0.022 (0.014)
# fatal accidents −0.053 (0.097) 0.428*** (0.044) 0.472*** (0.028) 0.214*** (0.027)

Own calculations based on STATS19 data. Each estimate gives the effect (semielasticity) of darkness on the number of accidents of the respective category at the particular hours. All three regressions are based on 51,103,130 observations and include region, year, day of the year, day of the week, and hour fixed effects. To allow the effect of darkness to vary over the course of the day, we interact darkness with time of day. Standard errors clustered at region level are in parentheses. Significance levels: *$p<0.1$; **$p<0.05$; and ***$p<0.01$.

Table 4.
Annual Accident Counts and Simulated Preventable Accidents
Preventable Accidents
AllDST
Current GMT/DSTHours Lightversus GMT
ObservedPredictedM1M2M1M2
Slight 157,542 157,641 2,202 1,887 358 −487
Serious 26,246 26,247 768 646 109 −46
Fatal 2,490 2,490 275 149 26 30
Preventable Accidents
AllDST
Current GMT/DSTHours Lightversus GMT
ObservedPredictedM1M2M1M2
Slight 157,542 157,641 2,202 1,887 358 −487
Serious 26,246 26,247 768 646 109 −46
Fatal 2,490 2,490 275 149 26 30

Own calculations based on STATS19 data. The table shows the average annual (preventable) number of accidents by time regime. The first column (Observed) gives the observed number of accidents by accident severity, and the following column (Predicted) gives the predicted number of accidents under the status quo, with GMT during winter and DST during summer. The remaining columns show the estimated number of accidents that could be prevented if all hours were light (columns All Hours Light) and by setting the clocks to DST during the entire year instead of setting them to GMT year-round (columns DST versus GMT), where the column heading M1 marks the results based on the baseline model and M2 those based on the model allowing the effect of darkness to vary by time of the day. Positive and negative numbers in the last two columns indicate more/ less preventable accidents under an all-year DST, then under an all-year GMT.

The first two columns of table 4 show the observed and predicted number of accidents by accident class for the status quo with GMT during winter and DST during summer. In columns 3 to 6, we distinguish between two cases: results from the baseline model are marked by M1 in the column heading and results from the more flexible model allowing for different effects of darkness over the course of the day are marked by M2. Columns 3 and 4 report how many accidents could be prevented in the hypothetical situation where none of the hours is dark. The remaining results of the simulation shown in columns 5 and 6 address the question of whether setting the clocks permanently to DST instead of to GMT for the whole year can save lives and prevent injuries.

Depending on the underlying model, we estimate that darkness causes around 150 to 275 fatal, 650 to 750 serious, and 1,900 to 2,200 slight accidents per year, for annual total costs of £520 to £830 million. Thus, measures that can reduce accidents due to darkness (almost) to 0 would have a positive net value only if the costs to implement these measures would not exceed around £500 to £800 million per year. Our results provide evidence supporting the view that setting the clocks permanently to DST instead of to GMT for the whole year can save lives and reduce costs. While there is some ambiguity with respect to the predicted number of slight and serious accidents, the results for fatal accidents, which cause the bulk of accident-related costs, are clear-cut. We find that by setting DST instead of GMT year-round, at least 25 fatal accidents could be prevented. Multiplying the estimated number of preventable accidents of each severity type with the average costs of the respective type, we arrive at an estimated annual cost savings potential of £40 to £90 million under the all-year DST regime compared to the GMT regime, representing 7.7% to 11% of all accident costs caused by darkness.

Given that the simulation results based on the model including the interaction term require less restrictive assumptions, we refer to these results and thus the more conservative cost saving potential of £40 million in the following. Although this seems to be not too much, one has to bear in mind that this £40 million is only due to the long-term effects of DST on road safety, that is, are the consequence of shifting light from the quiet morning hours to the rather busy afternoon hours. Abolishing the yearly transition into and out of DST has the potential to prevent additional road casualties due to low concentration and fatigue following the clock change.

### B. Mechanisms

While the simulation reveals that establishing DST as the standard time throughout the year could prevent a considerable number of fatal accidents, the general mechanisms of the effect of darkness on accident counts are unknown. Although we cannot disentangle these mechanisms unambiguously with the data at hand, we exploit some features of the data to provide suggestive evidence in favor of one or the other channel. Theoretically, there are at least three potential channels through which ambient light conditions might affect road safety. First, darkness might influence vision and thus the ability to recognize other road users early enough to prevent a collision. Second, natural light conditions influence the circadian rhythm. Thus, darkness might increase accident risk by increasing fatigue and reducing concentration. Third, people might expect driving to be more dangerous during darkness than during daylight. Consequently, they avoid driving during darkness, especially if they are insecure drivers, which in turn might reduce accident counts during darkness.16 As we find positive effects of darkness on accident counts, we can rule out that such behavioral responses are the main channel through which the effect operates.

Table 5.
RD Estimates of DST Transition on Accidents during Affected Hours
Spring TransitionFall Transition
MorningEveningMorningEvening
ln # all accidents 0.091* (0.054) −0.115*** (0.032) 0.038 (0.043) 0.136*** (0.028)
Observations 1,042 832 814 682
ln # slight accidents 0.129** (0.065) −0.104*** (0.037) 0.070 (0.044) 0.212*** (0.019)
Observations 1,084 793 858 1,386
ln # serious accidents −0.057 (0.064) −0.082 (0.052) −0.145** (0.070) 0.254*** (0.044)
Observations 1,508 1,670 1,029 1,209
ln # fatal accidents −0.033 (0.058) 0.037 (0.055) 0.006 (0.056) 0.076 (0.060)
Observations 614 834 794 1184
Spring TransitionFall Transition
MorningEveningMorningEvening
ln # all accidents 0.091* (0.054) −0.115*** (0.032) 0.038 (0.043) 0.136*** (0.028)
Observations 1,042 832 814 682
ln # slight accidents 0.129** (0.065) −0.104*** (0.037) 0.070 (0.044) 0.212*** (0.019)
Observations 1,084 793 858 1,386
ln # serious accidents −0.057 (0.064) −0.082 (0.052) −0.145** (0.070) 0.254*** (0.044)
Observations 1,508 1,670 1,029 1,209
ln # fatal accidents −0.033 (0.058) 0.037 (0.055) 0.006 (0.056) 0.076 (0.060)
Observations 614 834 794 1184

Own calculations based on STATS19 data. Each estimate gives the effect (semielasticity) of DST transition on the number of accidents of the respective category during those hours in the morning/evening that turn light/dark due to the DST transition and comes from a separate local linear regression based on equation (1). Bandwidth selected using common mean squared error (MSE)-optimal bandwidth selector. Robust standard errors are in parentheses. Significance levels: *$p<0.1$; **$p<0.05$; and ***$p<0.01$.

Depending on the underlying mechanism, politicians might want to establish different measures to avoid at least some of the accidents that are due to poor light conditions. If, for example, darkness decreases road safety due to reduced vision of every driver during night, an option to reduce accidents might be to increase road lighting. However, it might also be that the risk of poor night vision is not the same for everybody but starts to increase at the age of 45, as the medical literature suggests (Darius et al., 2018). In case that this is the main driver of the effect, a more cost-efficient way to reduce road casualties might then be to identify drivers with impaired night vision, for example, by establishing compulsory night vision screenings for older drivers. If, instead, the main driver of the effect is an increase in fatigue and poor concentration during darkness, neither an expensive expansion of road lighting nor vision screenings would help to reduce road casualties.

We cannot provide direct evidence for any of the mechanisms proposed above, as we have no information about the vision of road users or about their physical and mental constitution. However, we can use the information on the timing and about those involved in the accident to see whether one of the mechanisms is likely to be more important than others. Our first approach is the following: We again estimate the effect of DST transition on accident counts using an RD, but now look only at hours that were light/dark before DST transition and turned dark/light due to the transition. For the spring transition into DST, this is from 5:00 a.m. to 6:59 a.m. and 7:00 p.m. to 8:59 p.m. For the autumn transition back to standard time this is 6:00 a.m. to 7:59 a.m. and, at the end of the day, 6:00 p.m. to 7:59 p.m. If vision is a key mechanism, we would expect a positive effect of DST transition in spring for the morning hours that turn dark (again) due to the transition and a negative effect for the evening hours that turn light. For the autumn transition back to standard time, we would expect exactly the opposite: a decrease in accidents for morning hours and an increase for evening hours. Table 5 gives the results of this analysis. While all significant estimates show the expected signs, those pointing in the wrong direction are statistically not different from 0. Thus, the general impression is pretty much in line with our expectations and indicates that vision is an important mechanism.

Table 6.
NB Estimates of the Effects of Darkness on Additional Accident Categories
 # accidents involving pedestrians 0.118*** (0.015) # accidents by age of oldest driver $0<$age$≤25$ −0.040*** (0.011) $25<$age$≤45$ 0.001 (0.010) $45<$age$≤65$ 0.143*** (0.007) $65<$age 0.210*** (0.017) # accidents involving pedestrians and age of oldest driver $<45$ 0.028* (0.016) # accidents involving pedestrians and age of oldest driver $>45$ 0.251*** (0.016)
 # accidents involving pedestrians 0.118*** (0.015) # accidents by age of oldest driver $0<$age$≤25$ −0.040*** (0.011) $25<$age$≤45$ 0.001 (0.010) $45<$age$≤65$ 0.143*** (0.007) $65<$age 0.210*** (0.017) # accidents involving pedestrians and age of oldest driver $<45$ 0.028* (0.016) # accidents involving pedestrians and age of oldest driver $>45$ 0.251*** (0.016)

Own calculations based on STATS19 and MIDAS data. Each estimate gives the effect (semielasticity) of darkness on the number of accidents of the respective category and comes from a separate negative binomial regression. All regressions use 21,352,015 observations and include region, year, day of the year, day of the week, and hour fixed effects as well as weather controls. Standard errors clustered at region level are in parentheses. Significance levels: *$p<0.1$; **$p<0.05$; and ***$p<0.01$.

This impression is also supported by the results of a series of regressions (see table 6), where we estimate the effect of darkness on the number of accidents involving pedestrians and the number of accidents differentiated by age of the driver. The intuition behind this second approach is the following: If vision is an important mechanism, one would expect that darkness has a larger effect on the number of pedestrian accidents, as especially small and unlit objects are difficult to spot during night, and on the number of accidents involving older drivers, as the risk of poor night vision increases in age. Indeed, compared to the baseline effect (7%), we find quite large effects for pedestrian accidents (12%) and accidents involving drivers above the age of 45 (between 14, and 21%). The estimates for accidents involving only younger drivers, on the other hand, are either rather small and negative or not significant.17 The results of interaction-like regressions show that the effect on pedestrian accidents is mainly driven by accidents that feature both “risk types,” older drivers and pedestrians (25%), while the effect for accidents also involving pedestrian but only younger drivers is quite small (3%).18

### C. Sensitivity Analyses

We provide sensitivity analyses in the online appendix. By employing different aggregation schemes, we show that our results are not sensitive to the sources of variation in darkness (north-south, east-west, and over the year) used for identification. We also present estimates from specifications where we interact darkness with weather conditions. The results reveal that the effect of darkness is not driven by the coincidence of darkness and hazardous road conditions.

## IV. Conclusion

In a time when the political debate about the usefulness of DST flares up again, a thorough knowledge of all potential costs and benefits associated with the alternative time regimes is essential for policymakers who consider abolishing the biannual clock change. Since the choice of the time regime affects the distribution of light and darkness throughout the day, it has been hypothesized that establishing an all-year DST regime could prevent road casualties because this would shift light from the morning hours to the afternoon hours when streets are crowded and accident risk is high. To quantify the number of accidents and the associated costs under the alternative time regimes, we estimated how darkness affects accident counts and used the resulting estimates to simulate the number of accidents under the two time regimes.

We find that darkness considerably affects road safety. Our results show that darkness increases accident counts for a given hour on average by around 7%. This implies that darkness causes around 150 fatal, 600 serious, and 1,800 slight accidents per year, for total annual costs of at least £500 million in England, Scotland, and Wales. Comparing the simulated accident counts under the different time regimes, our results suggest that road safety is indeed somewhat higher under an all-year DST than under an all-year standard time. According to our estimates, establishing DST throughout the year could reduce social costs related to darkness by around 8% per year compared to a situation with all-year standard time. These numbers result only from shifting daylight from the morning hours to the evening hours and do not include the number of prevented accidents that are due to the abolishment of the transitions, especially the spring transition. The latter has been reported to be quite substantial, at least for fatal accidents, with an increase of 6% for the United States (Smith, 2016) and 8% or Great Britain.

To put the effect size into perspective, we apply the same back-of-the-envelope calculation as Smith (2016).19 Assuming that the estimated effect of the transition into DST on fatal accidents persists for six days—until the circadian rhythm has adjusted after the clock change—one would expect that abolishing the clock change would prevent around three fatal accidents each year. Compared to the estimated annual saving potential due to changes in light conditions (around 25 fatal accidents), the absolute number of prevented accidents due to disruptions of the circadian rhythm seems rather low, indicating that, other than hypothesized by Smith (2016), the distribution of natural light across hours of the day still seems to matter for road safety. This interpretation is also consistent with the results from the heterogeneity analysis, where we found that the effect of darkness on accident counts likely operates through a reduction in vision during darkness. Consequently, by solely focusing on the (spring) clock change, one runs the risk of significantly underestimating the total costs of the current time regime.

We acknowledge that our analysis covers only one, though, as we believe, important aspect of time regime choice and emphasize that an informed decision must take into account all potential benefits and side effects of time regime choice. For example, it is often argued that setting DST year-round leads to an increase in mental illnesses and learning difficulties in school. Furthermore, we acknowledge that the simulation results do not necessarily hold for other countries, especially if these countries are not at the same latitudes and thus have different sunrise and sunset times or if, for example, say, peak traffic times and road conditions differ fundamentally. Finally, people might adjust to the new sunrise and sunset times under permanent DST or permanent GMT. We cannot rule out such behavioral responses in the long run, however, this should if anything, alleviate but not reverse our main results.

Against the ongoing debate about which time regime should be implemented, our results challenge the notion of an all-year GMT standard time, at least from a road safety perspective. This is in line with results from previous empirical research that emphasizes the benefits of having more light during afternoon and evening hours, such as increased physical activity (Wolff & Makino, 2012) and reduced crime (Doleac & Sanders, 2015), and thus support the call for an all-year DST regime. Finally, adverse effects in various dimensions caused by the biannual transitions could be avoided.

## Notes

1

See Aries and Newsham (2008) and Havranek, Herman, and Irsova (2018) for a literature review covering earlier studies on the relationship between DST and lighting energy usage.

2

There are also studies finding no effect of the transition into DST on stock market returns (Gregory-Allen, Jacobsen, & Marquering, 2010), students' performance (Herber, Quis, & Heineck, 2017), myocardial infarction (Sandhu, Seth, & Gurm, 2014), hospital admissions (Jin & Ziebarth, 2020), and fatal accidents (Lahti et al., 2010).

3

For a broader overview about the previous literature, see Carey and Sarma (2017).

4

These studies assume that gradual changes in accident counts in the course of the year are only the result of gradual changes in the number of light hours and not influenced by other factors, such as road conditions, traffic composition, or the number of road users.

5

Although the local police forces are not obliged to use the standardized form to collect the relevant data, a great majority of forces use the precise form or a minor variation (Department for Transport, 2013).

6

0.5 degrees longitude corresponds to approximately 36 kilometers in the very south of Great Britain and 27 kilometers in the very north; 0.5 degrees latitude corresponds to approximately 55.5 kilometers. With respect to the grid size, there is a trade-off between spatial precision and computational feasibility. Increasing spatial precision, for instance, by a factor of four ($0.25∘$ longitude $×$$0.25∘$ latitude), quadruples the number of observations and increases the computational burden by a multiple of four.

7

The term driver includes all active road users, that is, car drivers, pedestrians, cyclists, and so on, but no passengers.

8

As shown in table B1 in the online appendix, using alternative cutoffs (quintiles and deciles) does not alter the results.

9

Descriptive statistics are shown in table B2 in the online appendix.

10

To get rid of differences in accident counts by day of the week and year, we follow Smith (2016) and use the residuals from a regression of (logged) daily accident counts on day of the week and year fixed effects as the dependent variable.

11

January 1, Easter holidays (Good Friday until Easter Monday), Early May and Spring Bank holidays, as well as Christmas holidays (December 25 and 26).

12

Note that our estimates are not sensitive to the exclusion of observations from two weeks after DST transition and thus do not reflect effects of this transition.

13

For example, to get the predicted accident count under an all-year DST regime, we determine sunrise and sunset times in this hypothetical situation, adjust the value of dark accordingly, and then predict accident counts based on the regression results presented in column 1 of tables 2 and 3.

14

Smith (2016), for example, assumes average social costs of $4–$10 million per fatality.

15

We abstain from presenting simulation results from even more flexible models (e.g., where darkness is interacted with individual hours), as it is not clear what some of the resulting coefficients—namely, those for the very early/late morning/evening hours—identify. This is because the whole variation in darkness during these hours comes from regions in the very north, which is problematic here for several reasons. First, because these regions are located on rather small islands, there is neither east-west nor north-south variation in darkness for these hours. Second, given that these hours turn light/dark only during a few days in June/December, there is also very little day-by-day variation. Finally, these islands are located far away from the mainland, are sparsely populated, and thus might exhibit very different traffic conditions. Thus, using these estimates in the simulation and applying them to other regions (with quite different traffic situations) might yield misleading results. Nevertheless, differentiating only between morning and evening hours seems to be too restrictive (compare figure B2 in the online appendix).

16

Note that this does not imply any kind of selection that renders our results inconsistent, but would be a mechanism and thus a part of the effect.

17

We cannot provide an unambiguous explanation for the negative and significant estimate for drivers younger than 25. Note that this is a very specific subgroup since every actively involved person must be 25 or younger. One speculative explanation could be that this group of drivers is less frequent on the streets during darkness. Although this might not be the case on weekend days, it is conceivable that young drivers are less frequent on the streets during darkness on the remaining weekdays.

18

Figure B3 in the online appendix shows the estimated effects of darkness on accident counts differentiated by year. Although there have been advances in vehicle lighting and vehicle safety technology, we do not find evidence that the effect of darkness on accident risk has diminished over time.

19

To calculate the number of fatal accidents that are due to the clock change in spring, we multiply the estimated coefficient of the spring transition (0.08) with the average number of fatal accidents per day on Sundays and weekdays in March and April (6.2) and the number of days (6). We look at fatal accidents only, since costs due to fatal accidents constitute the largest part of total costs.

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## Author notes

We thank the editor and an anonymous referee for very helpful comments and suggestions. We also thank Daniel Kamhöfer, Irene Palnau, Hendrik Schmitz, Harald Tauchmann, Matthias Westphal and Ansgar Wübker for valuable comments and Diana Freise for research assistance. Moreover, we are grateful for comments at the Quantitative Economics Days in Soest, the German Health Economics Association conference in Hamburg, the European Health Economics Association conference in Maastricht, the European Conference on Data Analysis in Paderborn and the annual conference of the International Association for Applied Econometrics in Nicosia. This study uses road accident data from the STATS19 data base gathered by the UK Department for Transport. Access to weather data from the MET Office's MIDAS database was provided by the Centre for Environmental Data Analysis.

A supplemental appendix is available online at https://doi.org/10.1162/rest_a_00873.