DISCUSSION PAPER
Ma y 2015; revised April 2016

RFF DP 15-19-REV
Weather, Traffic
Accidents, and
Exposure to
Climate Change
Benjamin Leard and Kevin Roth
1616 P St. NW
Washington, DC 20036
202-328-5000 www.rff.org
Weather, Traffic Accidents, and Exposure to Climate
Change
Benjamin Leard and Kevin Roth∗
April 8, 2016
Abstract
Quantifying the costs of climate change requires measurement of direct effects as well
as behavioral responses. While behavioral responses have been shown to increase costs,
we identify responses that reduce costs, which we define as “voluntary exposure.” We
quantify the response of the transportation sector in terms of traffic accidents and
travel demand to daily variation in weather. We find warmer temperatures and reduced
snowfall are associated with a significant increase in fatal accidents. We find, however,
that almost all of the estimated effect of temperature on fatalities is due to changes in
exposure for pedestrians, bicyclists, and motorcyclists. While the application of these
results to middle-of-the-road climate predictions suggests that weather patterns for the
end of the century would lead to 397 additional fatalities per year, the associated welfare
losses are almost completely offset by voluntary exposure benefits from increased
travel by walking, biking, and motorcycling. To facilitate more accurate estimates
of climate change impacts, we also introduce the empirical cumulative distribution
function method to the economics literature for correcting baseline weather errors from
climate simulations.
Key Words: Traffic Accidents, Exposure, Climate Change
JEL Classification Numbers: Q58, Q52, H23, R41
∗
Leard: Resources for the Future, 1616 P St. NW, Washington, D.C. 20036, e-mail: leard@rff.org. Roth:
University of California, Irvine 3297 Social Science Plaza, Irvine, CA 92697, e-mail: kroth1@uci.edu. The
authors thank Edson Severnini and Sol Hsiang for useful suggestions and are grateful to seminar participants
at 2016 AEA AERE session, UC-Irvine, and USC for helpful comments.
1
1
Introduction
Understanding the channels by which climate change will affect the economy is required to
estimate the costs of climate change and to develop adaptation strategies. Extreme heat may
result in direct costs such as increased mortality from heat stress and lower productivity.
Economists have also made clear that individuals are likely to engage in costly defensive
activities to mitigate these outcomes (Harrington and Portney, 1987). For example, where
heat aggravates respiratory illness, individuals may use medication and air conditioning to
reduce exposure to risk (Deschênes, Greenstone and Shapiro, 2013; Graff Zivin and Neidell,
2014). In such cases, measuring direct costs is a lower bound of the true welfare effects
because it omits these defensive expenditures.
Less attention has been paid to situations where climate change generates costs that
are, at least partially, explained by voluntary exposure to risk. Warmer weather facilitates
spending time outdoors. Choosing to spend time outdoors provides many benefits, but it
also exposes individuals to potential risks from air pollution, crime, UV radiation, and traffic.
Where costs from these risks occur as part of a utility maximizing decision to spend time
outside, these costs must be offset with the welfare gain from spending time outside. But
the costs of time spent outside in terms of illness, injury, or death are often much easier to
measure than the benefits.
To understand the welfare consequences of climate change, it is important to examine
exposure to risk. Where climate change aggravates an existing risk, individuals will engage
in costly behavior to avoid exposure to that risk, but when climate change increases the
utility of an activity with an associated risk, individuals will voluntarily increase exposure
to that risk. We define the resulting welfare effects of the latter case as voluntary exposure
benefits. Under the extreme assumption where an entire observed change in risk is due to
voluntary exposure, the net welfare costs of climate change would be zero. Whether or not
an observed increase in risk is accompanied by additional costs from defensive expenditure
or offsetting benefits can be ascertained by examining exposure. Where individuals avoid
risk, there are additional costs; where individuals engage in more risky activity, there are
offsetting welfare benefits. Problematically, in many empirical settings there is almost no
information on exposure to determine which effect generates the direct cost.
In this paper we analyze these issues in the context of the transportation sector by
estimating the relationship among weather, traffic accidents, and travel demand. We choose
to focus on the transportation sector because even small changes to traffic fatalities are
likely to carry large costs. Worldwide, nearly 1.24 million people die in traffic accidents
annually (WHO, 2013).1 To quantify the effects of climate change on traffic accidents,
we examine the effect of weather on accidents and generate future outcomes with climate
change using simulated future weather. By exploiting plausibly random daily variation
in temperature, rainfall, and snowfall, we are able to estimate the effect of weather on
transportation outcomes.
We find a large and statistically significant relationship between weather and traffic
fatalities. Unsurprisingly, we find precipitation plays a role in fatal car crashes. But we also
1
In 2006, traffic fatalities were the leading cause of death in the United States for individuals between
the ages of 4 and 35 (Subramanian, 2009).
2
find large effects for temperature. As temperatures rise, an increasing number of fatalities
involve pedestrians, bicycles, and motorcycles, or ultra-light duty (ULD) accidents. Warmer
weather is intuitively linked to more exposure as people will derive utility from spending
leisure time outside or from traveling by bicycle or motorcycle for transportation or leisure
purposes. We are also able to measure exposure directly by estimating the demand for ULD
trips as a function of weather.
To estimate these effects, we use detailed data on police-reported accidents, daily travel
logs of households, weather, and climate change prediction data. We find that for a day
with temperature above 80◦ F there is a 9.5 percent increase in fatality rates compared with
a day at 50-60◦ F. Our estimates indicate that the majority, but not all, of this effect is
due to fatalities involving individuals traveling by ULD modes. We also find evidence that
individuals avoid ULD travel on cold days, while estimates for demand on hot days are
positive but imprecise. We cannot rule out the possibility that reduced cognitive ability
brought on by heat is responsible for some of the estimated effect particularly for light-duty
travel on hot days, and we find some evidence on the hottest days that drivers avoid trips
by light-duty vehicles, consistent with defensive behavior.
We estimate that the discounted costs of additional traffic fatalities caused by climate
change are $40 billion from 2015 to 2099, an amount on the same order of magnitude as
others such as profit changes to the agriculture industry (Deschênes and Greenstone, 2007;
Fisher et al., 2012) and social welfare effects from criminal activity (Ranson, 2014). But
we find that welfare gains from increased ULD travel reduces these costs by at least $34
billion. Under the extreme assumption that the entire observed change in traffic fatalities
is due to voluntary ULD exposure, the marginal costs of climate change stemming from the
increase in traffic fatalities are less than $9 billion and not statistically distinguishable from
zero. Including reduced injuries and property damage only (PDO) accidents suggests that
net welfare effects may even be positive. In sum, we find that omitting voluntary exposure
behavior from welfare analysis may lead to a significant overestimate of climate change costs.
Methodologically, we also introduce a new technique for using predicted weather from
climate models when simulating future outcomes derived from an approach used in the
climate science literature. It is well known that climate prediction models can forecast
baseline weather that is different from the weather actually observed (Auffhammer et al.,
2013). Various methods to correct baselines have been used in prior papers, but none are able
to align the full distribution of baseline outcomes with observed weather, while also allowing
the variance of events to change. This is particularly important for studies that seek to
understand how economic outcomes respond to a change in climate variability. We show
that prior methods may yield unintuitive results. Furthermore, these methods are often not
well suited to predict precipitation changes, which are important in our setting. We make use
of a quantile-mapping method inspired by techniques used in the climate science literature.
This technique allows us to avoid the baseline climate modeling error that can generate
spurious results in areas with complex geography, while also applying the full distributional
changes predicted by climate models.
The rest of the paper proceeds as follows. Section 2 reviews the economic, transportation,
and medical literature relevant to our study. Section 3 develops a framework for estimating
how much households are willing to pay to avoid climate change. Section 4 describes the
data and Section 5 develops the econometric framework for our outcomes and the results of
3
our estimation. Section 6 details our simulation of future weather outcomes and Section 7
concludes.
2
Literature Review
Several papers from the traffic safety literature explore the relationships between weather
outcomes and traffic accidents. This literature has primarily estimated the impact of rainfall
or snowfall on accident frequency (Eisenberg, 2004; Eisenberg and Warner, 2005), but does
not examine the relationship with temperature or the impact of climate change. An exception
is Froom et al. (1993), who show that high temperatures are associated with higher rates of
helicopter pilot errors.
In the medical literature there is extensive research that suggests plausible physiological
reasons that accidents and fatalities may be affected by temperature. While prior work has
documented effects of temperature on ability to perform a task, the relationship is complex
(Hancock and Vasmatzidis, 2003).2 In a laboratory setting, Broadbent (1963) show that heat
in excess of 85◦ F did not affect the speed of task completion but did result in a higher error
rate. Heat has been found to primarily affect vigilance, tracking, and multitasking but simple
perception and reaction time remain unaffected (Grether, 1973). While air conditioning may
mitigate these effects, many effects from heat are due to prolonged exposure that increases
core temperature (Hancock and Vasmatzidis, 2003).
The economics literature has studied the impact of climate change using temperature
and occasionally precipitation data in a variety of areas such as agriculture (Deschênes and
Greenstone, 2007; Fisher et al., 2012), economic growth (Dell, Jones and Olken, 2014), and
health (Neidell, 2004). Graff Zivin and Neidell (2014) examine how weather influences time
allocation showing that warmer weather draws individuals outdoors, possibly exposing them
to extreme pollution events (Bäck et al., 2013). Graff Zivin, Hsiang and Neidell (2015)
find that heat is associated with more errors on cognitive assessment exams but these
transitory shocks do not affect long-run human capital formation. Our study is also related
to work on crime and conflict (Jacob, Lefgren and Moretti, 2007; Hsiang, Burke and Miguel,
2013; Ranson, 2014) that has found a strong relationship between heat and violent activity.
Deschênes and Moretti (2009) use mortality data from the Multiple Causes of Death files
and include regressions for motor vehicle deaths. They find some evidence for a decrease in
fatalities from cold weather, which they conjecture is due to avoided travel.
Finally, this work contributes to a literature that attempts to incorporate behavior into
welfare calculations when health and safety risks change. Harrington and Portney (1987)
and Graff Zivin and Neidell (2013) emphasize that defensive behavioral adjustments to an
environmental risk can be crucial for providing a comprehensive welfare assessment, and
prior literature has attempted to empirically estimate these expenditures in environmental
settings (e.g., Deschênes and Greenstone (2011), Deschênes, Greenstone and Shapiro (2013)
and Barreca et al. (2013)).3 We expand this literature by identifying and quantifying a new
2
This is because many factors influence the effect of heat stress on cognitive performance, such as task
type, exposure duration, skill and acclimatization level of the individual.
3
See Auffhammer and Mansur (2014) for a review of the economics literature on how climate change
affects energy expenditures.
4
direction of individual response to climate change. Our research contributes to this literature
by showing that exposure is an important consideration in the interpretation of these costs
and shows that excluding voluntary exposure behavior can overstate welfare costs.
3
Framework for
Climate Change
Estimating
Welfare
Effects
of
In this section, we present a simple analytical framework for characterizing the welfare effects
of climate change on traffic accidents building on Harrington and Portney (1987). Subsection
3.1 presents the model assumptions and subsection 3.2 includes a derived welfare formula
that we use for estimating the welfare effects of climate change on traffic accidents.
3.1
Assumptions
Suppose that a representative household is endowed with a light-duty vehicle (LDV) and
decides how to spend income to maximize utility. The household decides how many miles
to travel by LDV and by walking, biking, or motorcycling, or any other ultra-light duty
(ULD) mode. We examine ULD travel separately from automobile travel because the utility
of traveling by this mode is likely to be strongly influenced by weather and is subject to a
higher fatality rate per collision, all other crash characteristics equal. The household chooses
a number of LDV miles, denoted by m, ULD miles, denoted by b, and consumption of a
composite good x. It faces a fixed LDV operating cost per mile denoted by pm , a fixed permile cost of ULD travel denoted by pb , and a price of the composite good that we normalize
to one. The household then maximizes utility subject to a budget constraint with endowed
income I.
Utility is a function of LDV and ULD miles, consumption of the composite good, and
the probability that traveling causes a traffic accident. The likelihood of a traffic accident is
a function of the household’s LDV miles, ULD miles, and weather conditions, denote by W .
We characterize weather conditions with measured temperature, rainfall, and snowfall. We
assume that the probability of an accident, a = am (m, W ) + ab (b, W ), is additively separable
in the probability of getting into an accident while driving (represented by the function am (·))
and the probability of getting into an accident while walking/bicycling/riding a motorcycle
(represented by the function ab (·)).
The probability of an accident is assumed to increase in LDV or ULD miles, so that
∂a
∂a
> 0 and ∂a
> 0. We leave the sign of ∂W
for our empirical analysis.
∂m
∂b
The household makes choices based on the following problem:
V = max {U (m, b, x, a)} subject to
(1)
a = am (m, W ) + ab (b, W ),
(2)
pm m + pb b + x = I.
(3)
m,b,x
∂U
The household’s utility function, U (·), is assumed to satisfy ∂m
> 0, ∂U
> 0, ∂U
> 0, ∂U
> 0,
∂b
∂x
∂l
∂U
< 0, and sufficient second-order derivative properties to ensure an interior solution.
∂a
5
3.2
Expressions for WTP/WTA for a Change in Weather
For a change in a weather variable, the household must be compensated with income I for
changes in W to hold utility constant. This implies that we can define income as a function
of W :
I = I ∗ (W ).
(4)
The function I ∗ (W ) keeps utility constant in response to change in a weather outcome.
Holding fixed all other exogenous parameters, we can express indirect utility as
V = V (I ∗ (W ), W ).
(5)
Differentiating Equation 5 with respect to W yields
∂V dI ∗
∂V
dV
= ∗
+
= 0.
dW
∂I dW
∂W
(6)
Rearranging terms yields a general expression for WTP/WTA for a change in weather
conditions:
∂V
dI ∗
= − ∂W
.
(7)
∂V
dW
∗
∂I
In Appendix A, we show that Equation (7) can be expressed as
∂U
∂U
∂U
dI ∗
dam ∂U
dab
∂am
∂ab
= − ∂a
+ ∂a
mεm + ∂a
bεb .
− ∂a
dW
dW} |λ {z
dW} |λ ∂m
∂b }
|λ {z
{z
} |λ {z
a
W T Pm
W T Pba
WTPm
(8)
WTPb
The first and second terms, W T Pma and W T Pba , are the welfare effect from a change in the
probability of an LDV accident and ULD accident, respectively, resulting from a change in
weather. Each term is the product of the monetary value from a change in the probability of
an accident and the effect of a change in a weather variable on the probability of an accident.4
The third term, W T P m , is the welfare effect from a change in miles driven induced by a
change in weather. The fourth term, W T P b , is the welfare effect from a change in ULD miles
traveled induced by a change in weather. Each term is the product of the price of travel,
in terms of accidents per mile, and the change in travel induced by weather. The change in
∂m
, and the
automobile miles from weather is given by the LDV trip semi-elasticity, εm = m1 ∂W
1 ∂b
change in ULD miles from weather is given by εb = b ∂W .
The third and fourth terms are central to our analysis and measure the welfare effect of
households reacting to climate change in potentially two distinct ways. If households respond
in a defensive manner by reducing exposure to negative outcomes, such as reduced driving to
avoid accidents when conditions are rainy, these terms will represent costly defensive activity
(Harrington and Portney, 1987). This behavior is calculated as a welfare cost; studies
omitting this component underestimate the welfare costs of climate change. The second
potential reaction is that households may expose themselves more to negative outcomes
4
An increase in the fatality rate from more snow, for example, lowers household welfare, implying that
m
the household is willing to pay to avoid this weather change. This term will be positive when da
dW > 0
because ∂U
∂a < 0 and λ > 0.
6
if the private benefits of doing so exceed the costs. We define this behavior as voluntary
exposure. Where these terms are positive, voluntary exposure is calculated as a welfare
benefit and omitting this component will overestimate the welfare costs of climate change.
As an example, assume warmer weather increases fatal motorcycle accidents. If this
∂b
< 0 and W T P b
increase is accompanied by households avoiding motorcycle travel, then ∂W
5
will be a defensive expenditure cost. If, however, warmer weather encourages voluntary
∂b
exposure so that ∂W
> 0, then W T P b will be positive. Such an outcome occurs if individuals
engage in more motorcycle driving in warmer weather leading to more motorcycle accidents.
At an extreme, if the entire change in accidents is due to voluntary exposure, the envelope
dI ∗
theorem implies that W T Pba = W T P b and W T Pma = W T P m , and dW
in Equation (8) is
6
equal to zero. In our empirical analysis we will mostly focus on fatal accidents but we will
also consider PDO accidents and injuries. For fatal crashes we also examine two subcases
where all LDV fatalities are due to exposure or where all ULD fatalities are due to exposure
by setting the welfare effect of each group to zero to give a sense of the relative contribution
of each mode to the final welfare cost.
3.3
Implications for Measuring Welfare Effects of Climate Change
Equation (8) is valuable because empirical estimates for all terms are available from our
own estimates, the literature, or existing datasets for fatalities. In our empirical model, we
m
, the marginal effect of the change of a weather variable
estimate the following terms: da
dW
dab
, the marginal effect of the change of a weather
on the probability of an LDV accident; dW
variable on the probability of a ULD accident; εm , the LDV mile semi-elasticity with respect
to a change in weather; and εb , the ULD mile semi-elasticity with respect to a change in
weather.
Estimates for the remaining terms in Equation (8) are available from our data or
/λ, the monetary value from the change in the
additional sources. These include ∂U
∂a
∂a
probability of a accident, which is the value of a statistical life (VSL) for fatal accidents; ∂m
and ∂a
, the marginal effect of a change in miles on the probability of an LDV fatality or
∂b
ULD fatality respectively, which can be approximated by the per mile fatality rate; m, the
number of LDV miles; and b, the number of ULD miles.7
It is important to note that a change in the number of miles is not the only behavioral
adjustment drivers may make. Warmer weather may allow other channels of voluntary
exposure, such as driving faster, or more scenic but dangerous routes. Although we examine
some of these voluntary exposure channels in the appendix, such as speed, there will be
5
At the optimum, the household is equating the monetary value of the marginal disutility from the
increased likelihood of an accident stemming from driving one more mile to the marginal value of driving
that is unrelated to accidents.
6
A similar assumption underlies the calculation of the value of a statistical life where individuals consume
risk that is compensated with benefit. Our framework also assumes they understand and properly value
these risks when engaging in travel.
7
For PDO accidents and injuries we do not have some elements of this calculation as national level
statistics are not collected. Although we believe accidents and injuries are consistently collected within a
state-year in our SDS data, they vary across years and states, creating ambiguity on which injury or accident
rate is most appropriate.
7
some adjustments we cannot measure.8 Similarly, we do not observe defensive expenditures
such as using air conditioning or purchasing safety helmets, implying that the cost of climate
change is higher than what we report.9
Equation (8) also does not include long-run margins of adjustment that households or
governments may adopt in response to changes in climate.10 We think there are three key
types of long-run adjustment that could occur. First, there may be a private adaptation
to local conditions. Such adaptation includes purchasing a different vehicle that is safer
to drive or making changes in behavior to adapt to local conditions. To some degree we
are able to empirically test for this type of adaptation by separately estimating our results
across regions, which we do in the appendix.11 Second, migration may occur if individuals,
for example, move farther north in response to climate change. This is another type of private
adaptation but one that we cannot examine with our data. Both of these forms of private
adaptation imply that the true costs of climate change are lower than what we report. The
third type is public adaptation through infrastructure or institutional changes that attempt
to address these costs. Estimating these changes is beyond the scope of our paper, but our
welfare calculation serves as a component in determining the amount of spending warranted
in a public response to traffic fatalities from climate change. It is also important to note that
if the primary mechanism for our observed effects is voluntary exposure, we may see private
or public adaptation but not migration. If warmer weather increases the amount of biking,
helmet sales may increase and bike lanes may pass a cost-benefit test whe they would not
have earlier, but we would not expect people to flee northward.
4
Data and Summary Statistics
4.1
4.1.1
Data Sources
Accident, Injury, and Fatality Data
We obtain the population of police-reported accidents for 20 states from the State
Data System (SDS) maintained by the National Highway Traffic Safety Administration
(NHTSA). These data are collected and used by the NHTSA to provide analysis and policy
recommendations for U.S. DOT. The benefit of these data is that they include not only
fatalities, as recorded in other sources, but also non-fatal accidents.
8
See Appendix Table H17 for speed regressions.
Another possible welfare consideration in our context is the external cost of traffic accidents. Although
we do not explicitly model external costs of traffic accidents, our empirical estimate of the direct effect of
a
climate change on traffic accidents (W T Pm
and W T Pba in Equation (8)) incorporates the entire social cost
of the change in accidents.
10
This equation also omits welfare effects from the marginal impact of climate change on travel quality. For
example, taking a trip to the beach on a warm and sunny day is more valuable than taking the same trip on
a cold day, even if the accident probability is the same. To model the value of a trip taken by the household
that is independent of the accident probability as a function of weather conditions, we could incorporate
comfort into the choice problem by defining quality-adjusted miles traveled functions for LDV and ULD
travel, qm = q(m, W ) and qb = q(b, W ), that enter directly in the household’s utility function. Poor weather
conditions (e.g., heavy rain or extreme temperature) lowers quality-adjusted miles traveled. Leaving this
component out of our empirical evaluation of welfare will understate the welfare effects of climate change.
11
See Appendix Table H10.
9
8
Accident reports, completed by police officers, are administered at the state level. These
files are requested annually by the NHTSA from the state agencies that computerize the
data, which are then formatted for consistency and compiled into the SDS.12 We obtained
permission to use SDS data from Arkansas, California, Florida, Georgia, Iowa, Illinois,
Kansas, Michigan, Minnesota, Missouri, Montana, Nebraska, New Mexico, New York, North
Carolina, Ohio, Pennsylvania, South Carolina, Washington, and Wyoming.13
While there is considerable variation in what each state records, all states in our sample
provide a record of each police reported accident, the day when the accident occurred, the
county where the incident occurred, the types of parties involved (e.g., light-duty vehicle,
motorcycle, bicycle, pedestrian) and the number of fatalities involved. Others variables such
as vehicle information or factors contributing to the accident are subject to considerable
state-level variation in the manner and detail with which they are recorded. Our main
regressions focus on fatalities, PDO accidents, and injuries. Thus we are able to largely
avoid variables that are inconsistently recorded.14 We also make use of fields that record
whether or not the accident involved any ULD parties, which is almost universally recorded.15
However, in some robustness checks in the appendix we use a subset of states with intoxicated
or young operators, which are subject to more variation among states and years.16
We note that an accident appears in our dataset only if the police file a report. PDO
accidents may not always be reported, and reporting rates could be subject to weather
changes. For minor accidents, police may have different reporting thresholds by state, and
policy changes may affect reporting rates over time, which we can control for with countyyear-month fixed effects. There is, however, some concern that weather may influence the
likelihood that a report gets filed. In particular when bad weather results in more accidents,
departments may become overwhelmed, resulting in higher threshold for filing. If this is the
case then we underestimate the effect of weather on accidents. This concern is less important
for fatalities, which form our primary analysis, because they will always be reported (Blincoe
et al., 2014).
4.1.2
NHTS Daily Travel Data
We construct household vehicle miles traveled (VMT) and trip count from the 1990 National
Personal Transportation Survey and the 1995, 2001, and 2009 National Household Travel
12
The agencies that usually collect the data are state police, state highway safety department, or the
state’s Department of Transportation.
13
Years of coverage in the SDS data include AR 1998-2010, CA 1995-2008, FL 1995-2008, GA 1995-2008,
IA 2001-2005, IL 1995-2009, KS 1994-2008, MI 1995-2009, MN 1995-2007, MO 1995-2008, MT 1995-2008,
NE 2002-2008, NM 1991-2010, NY 2002-2010, NC 1999-2008, OH 2000-2010, PA 1991-1999 and 2003-2010,
SC 1997-2008, WA 1994-1996 and 2002-2010, and WY 1998-2007.
14
Injuries are often but not always recorded as five levels of severity including fatality, incapacitation,
injury, possible injury and property damage only. Incapacitation, injury, and possible injury are included in
‘crashes with an injury.’ There are two state-year combinations where injuries cannot be discerned and are
dropped from the analysis.
15
Besides pedestrian, motorcycle, and bicycle, we also include mopeds, motorized scooters, pedalcycles,
unicycles, and tricycles.
16
See Appendix Table H11. Because some states do not disaggregate drugs from alcohol use, we consider
drivers to be intoxicated if they are tested to be beyond the legal limit for alcohol or if they are reported to
have taken any illicit drug.
9
Surveys (NHTS). Administered by the U.S. DOT Federal Highway Administration, these
surveys are representative cross sections of randomly selected U.S. households.17
The NHTS has several data files available to researchers, one of which includes data on
household daily travel diaries. Travel diaries are trip-by-trip travel logs for a single individual.
Each trip reports where the respondent went (name of place), what time the trip started
and ended, why the respondent made the trip, how the respondent traveled, and the travel
distance of the trip, in miles.18
Staff at the Federal Highway Administration and Oak Ridge National Laboratory helped
us acquire the confidential version of the NHTS data files that contain either zip code or
county of residence for all households in each sample.19 The restricted files that we acquired
include the day, month, and year of the household’s assigned day of travel, which is required
to merge the travel data with our daily weather data.20
We take several steps to clean and merge the travel diary data. Since our unit of analysis
is the household, we aggregate trip count and VMT to the household level for three categories
of trips: light-duty, ULD, and public transit. After minor data cleaning, we arrive at a final
sample of 283,857 household by travel day observations.21
4.1.3
Historical Weather Data
Daily weather data come from the National Climatic Data Center (NCDC) Global Historical
Climatology Network-daily, which provides daily minimum and maximum temperature and
total daily rainfall and snowfall for weather stations in the United States. This database
collects and performs quality control for weather data from land based weather stations
around the globe and is archived by the National Oceanic and Atmospheric Administration.
We use data from 2,607 stations located in all 50 states and the District of Columbia.22
Weather stations are used to calculate county-level weather. Prior literature has
documented that missing weather station data can account for a substantial portion of the
variation in weather measures if naively averaged (Auffhammer et al., 2013). Therefore we
impute data using a regression of temperature or precipitation for a detector on its nearest
neighbor (Auffhammer and Kellogg, 2011; Schlenker and Roberts, 2009). The coefficients
from this regression are then used to predict missing values to correct for systematic
17
Each wave is a survey of the non-institutionalized population of the United States using ComputerAssistant Telephone Interviewing (CATI) Technology. The 2009 survey had an average response rate of 19.8
percent.
18
The NHTS specifies that the beginning of a travel day is 4:00 a.m. An example of a recorded trip taken
from the 2001 User Guide is the following: “from 7:14 p.m. to 7:22 p.m., return home, by car, 1 mile.”
19
The 2001 confidential file includes zip codes for most households but has limited county information.
We assign households to counties using the 2000 U.S. Census zip code to county cross walk. In a few cases,
the zip codes reported in the NHTS data do not match any zip codes in the 2000 U.S. Census cross walk. In
these cases, we use the 2010 U.S. Census zip code to county cross walk or the U.S. Department of Housing
and Urban Development zip code to county cross walk.
20
The public files include the month and year of the travel day.
21
See Appendix B for more details.
22
For more information see Peterson and Vose (1997). We also perform some additional minor quality
control. In some instances outliers cannot be confirmed through other sources and appear to be misplaced
decimals. As a rule, we impute all observations with snow or rain greater than 1000 cm. We also drop a
detector in Nevada that reported several temperatures above 5000◦ C.
10
differences in levels among stations. For the case of missing rain and snowfall, to ensure
positive predicted values, we restrict the regression to have a zero intercept. Where the
weather data for the next closest detector is missing the imputation is done using the
following detector, up to a maximum distance of 200 km.
These stations are then averaged to predict daily, county-level weather using inverse
distance weighting to the county centroid. This average uses all detectors within 200 km
of the county centroid, and where no detectors are within this distance, the county is
dropped.23 Because the creation of county-level weather often predicts extremely small
levels of precipitation whenever any station has rain or snow, any value less than 0.01 cm is
rounded to 0 cm. This results in a balanced panel of 3,140 counties with weather data from
1991 to 2010. Of these counties, 1,474 are then matched to SDS data and 2,944 are matched
to NHTS trip data.
4.1.4
Weather Prediction Data
CCSM4 is the model used in the Fifth Assessment of the International Panel on Climate
Change to predict future climate and weather under a variety of scenarios. We use scenario
RCP6.0, which represents a middle-of-the-road prediction of future warming and changes in
precipitation. It represents a future with a balanced development of (fossil fuel and non fossil
fuel) energy technology.24 Although it is less carbon development than the CCSM4 RCP8.5
scenario, it still entails 2.3◦ C (4.2◦ F) of warming in the United States. In the appendix, we
examine outcomes for other climate change scenarios and an alternative model and find that
our broad conclusions are unchanged.25
We obtained the CCSM4 RCP6.0 scenario daily weather predictions from the Centre for
Environmental Data archival website, made available through the British Atmospheric Data
Centre.26 The data include predictions from January 1, 2006, to December 31, 2100 for 0.94
degree latitude by 1.25 degree longitude grid points throughout the entire world.27 Available
weather variables include average, minimum, and maximum daily temperatures and rainfall
and snowfall rates.28
23
This drops seven counties from the total sample: Aleutians East, Aleutians West, Bethel Census Area,
Dillingham, Nome, Northwest Arctic, and Yakutat City all of which are located in Alaska.
24
Other scenarios represent extreme predictions. For example, the RCP8.5 scenario represents a fossil-fuel
intensive future, while RCP4.5 represents a predominantly non fossil fuel future.
25
We examine outcomes from climate scenarios RCP4.5 and RCP8.5 using CCSM4 output. We also report
outcomes using prediction data from the A1B middle-of-the-road warming scenario presented in the Fourth
IPCC Report using the Hadley 3 climate prediction model, which has been used in prior economics literature.
See Appendix Table H20 and Figure H.1 for the results from these models.
26
We use the CCSM4 model exclusively for future weather predictions because CCSM4 is one of the few
models that report separate outputs for rainfall and snowfall. In contrast, most models report a single
precipitation variable that combines rainfall and snowfall. Since we expect rainfall and snowfall to have
different impacts on accidents and travel demand, it is crucial to use climate predictions that report separate
values for each precipitation type.
27
CCSM4 predictions provide 365 days per year of weather predictions.
28
We convert temperature, reported in Kelvins, to degrees Fahrenheit and precipitation rates, reported in
kilograms per meter squared per second to centimeters of precipitation. To convert the rainfall predictions to
centimeters per day, we multiply the reported value by 8,640 (http://www.cpc.ncep.noaa.gov/products/
outreach/research_papers/ncep_cpc_atlas/2/cont_data.html). For snowfall, about 1 centimeter of
snowfall represents 1 millimeter of water. To make our prediction data consistent with our observed weather
11
To assign predicted weather outcomes to counties, we use the same method that was
used to assign observed weather to counties based on weather station locations. Here, for
every county, we locate every CCSM4 grid point that is within 200 kilometers of the county’s
centroid. The weather predictions at these grid points are then averaged to predict daily
county-level weather using inverse distance weighting to the county centroid.
4.1.5
Other Data Sources
To predict the change in fatalities nationwide, we require the average daily fatality rate
by county, which the accident files provide for 20 states. The Fatality Analysis Reporting
System (FARS) tracks annual automobile fatalities for all states and provides information on
the county in which the fatality occurred. This allows us to calculate average daily fatality
rates from which to project changes in future fatalities. We sum the fatalities recorded by
FARS data from 2000-2009 for each county and divide by the number of days to calculate
this baseline fatality rate. We also use the FARS data from 1975 to 2013 in the appendix as
a check on our main fatality results.29 Finally, in regressions run on urban, suburban, and
rural samples, we use the classification system of the National Center for Health Statistics
generated by the CDC.
4.2
Summary Statistics
Our analysis uses weather data matched to accidents and travel demand for our primary
estimation. For our simulation we use daily observed and predicted weather data to generate
county-day measures of future weather. Table 1 presents summary statistics for our two
primary datasets used in the estimation. Panel A gives key summary statistics on the
matched accident data. These data consist of observations of county-day weather matched
to counts of accidents and fatalities. Panel B gives statistics on the NHTS travel demand
data. These data consist of daily weather matched to aggregate household VMT and trips
in that 24 hour period.
Panel A describes some key statistics of the SDS data by Census Region. Of the 46
million accidents in our data, 267,984 record a fatality, the vast majority of which do not
involve a ULD mode. Additionally, there are 15 million recorded accidents with injuries,
but not all states record injuries in all years. When aggregated by county-day, our unit of
observation, we record the count of incidents for 6.69 million county-day observations, and
where no incidents occur, the day is assigned a count of zero.30 In the average county there
are 7.2 accidents per day per 100, 000 people, and 0.07 fatalities per day per 100, 000.
The summary statistics by census region reveal that there is considerable variation in
temperature, rainfall, and snowfall among regions. We display the 5th, 50th, and 95th
quantiles of temperature and the 75th and 95th quantiles of rainfall and snowfall. The
station data, which do not report water equivalent snowfall, we must scale the predicted snowfall values.
Therefore, we multiply predicted snowfall by 8,640*10 to convert the snowfall predictions to centimeters per
day.
29
See Section C for more detail and Appendix Table H8 for results.
30
We assume that if a county has observations in a given year, all days where no accidents are recorded
are assigned a zero.
12
Northeast is the snowiest region with 1.91 cm of snowfall at the 95th quantile. It also has the
lowest accident rate, 3.6 per 100, 000, and fatality rate, 0.04 per 100, 000. The Midwest has
the largest temperature fluctuations with 61 degrees between the 5th and 95th quantiles. The
South is generally warmer and rainier than other regions and has little snowfall, with a high
accident rate of 8.8 per 100, 000 and fatality rate of 0.08 per 100, 000. The West is drier with
less variation in temperature than other regions. This regional variation without location
based fixed effects may be cause for concern if, for example, colder climate is correlated with
public transportation in cities like New York, Philadelphia, and Chicago, while low-density
car oriented cities like Los Angeles and Atlanta are located in warm regions.
Panel B describes the NHTS household travel survey data. Because the trip data are a
random sample, they do not capture the total number of trips or miles driven in a county but
has the benefit of wider coverage with observations in the majority of counties in all 50 states
and the District of Columbia and are collected through the course of a year. These data
provide information on 283,857 households in 2,944 counties. The data record 1.3 million
trips with a total distance of 11.5 million miles. The average household in our sample drives
52.5 miles per day with a total of 6.2 trips. Households in the South take the fewest trips, 6.0
daily, but for the greatest number of miles, 55.2 miles. The Midwest takes the most trips, 6.5
per household, and the Northeast, with 49.3 miles per household per day, travels the fewest
miles. The weather observed for these households is generally similar to the accident data,
although the West is hotter and less snowy than in the accident data, due to the inclusion
of additional states.31
Table 2 presents weather statistics used in our simulation. The sample includes all countyday measures in all states. Panel A depicts the observed weather data for 2000-2009, Panel B
shows CCSM4 RCP6.0 predictions for 2006-2009, and Panel C has CCSM4 RCP6.0 scenario
for 2090-2099.32 Comparing Panels A and B we can see that CCSM4 generally predicts 5th
quantiles and median temperatures in 2006-2009 that are colder than observed in the actual
weather data from 2006-2009, while the 95th quantile is predicted to be slightly hotter than
actually observed. This indicates that the baseline CCSM4 data display excessive dispersion
and that an error correction method targeting the mean may not adequately correct the
extreme events. The table indicates that the baseline CCSM4 predicts rainfall well; however,
it over-predicts snowfall, both in frequency and in amount. Comparing Panel B with Panel
C we note that CCSM4 predicts warmer temperatures, an increase in rainfall (0.11 cm at the
95th quantile), and much lower snowfall. Table 2 also demonstrates why error correction is
important. Without error correction, one might conclude that global warming would change
temperatures less than CCSM4 predicts, because CCSM4 2006-2009 is a colder baseline than
the observed data. In our application where snowfall is important, without error correction
the naive comparison of observed data with CCSM4 2090-2099 would suggest that climate
change will increase snowfall for all regions except the Northeast.
31
We show in Appendix Table H1 that all regions have some observations in each of the weather bins used
in the specification.
32
In Appendix Table H3 we report disaggregated statistics by state for our observed weather station data
for 2000-2009.
13
5
5.1
Estimating the Effect of Weather on Accidents and
Travel Demand
Estimation Methodology
This section details the econometric framework we use to determine the effects of weather on
accidents and travel demand. Our main analysis uses a Poisson regression model because the
distributions of our dependent variables are nonnegative and skewed. We first describe the
estimation of accidents that is the framework used for fatalities, injuries, and PDO accidents.
Next we describe the estimation of travel demand in terms of daily trip count and miles per
trip for LDVs, ULD modes, and public transit.
5.1.1
Accidents
We chose a Poisson model for our initial analysis based on several aspects of our
data. Accident counts are all non-negative, integer-valued random variables. For data
characterized as a counting process, the Poisson distribution is the benchmark model
(Cameron and Trivedi, 2013). Poisson regression will yield consistent estimates provided
the conditional mean is correctly specified.33
We assume that the count of accidents on date d in county c given xd,c is Poisson
distributed with density
f (yd,c |xd,c ) =
e−µ µyd,c
,
yd,c !
yd,c = 0, 1, 2, ...
(9)
We specify the mean µ using the conventional exponential mean function:
E[yd,c |xd,c ] = µ = exp
8
X
j
αj Td,c
+
j=1
8
X
j=1
j
j
α−1
Td−1,c
+
5
X
5
X
j=1
j
j
β−1
Rd−1,c
+
j=1
5
X
j
β j Rd,c
+
5
X
j
γ j Sd,c
+
j=1
j
j
γ−1
Sd−1,c
+ θscym + z0d,c δ
(10)
j=1
j
where Td,c
is an indicator for mean daily temperature on date d in county c lying within
j
j
j
j
j
the bounds of bin j, Rd,c
is for rain, Sd,c
is snow, Td−1,c
, Rd−1,c
, and Sd−1,c
indicate lagged
weather, θscym is a state-county-year-month fixed effect, and zd,c includes other possible
covariates.
The appropriate functional form of the daily weather variables is unknown and we
adopt the semi-parametric approach of Deschênes and Greenstone (2011). This concern
is particularly relevant here, where even after controlling for precipitation, there may be
33
Cameron and Trivedi (2013) note that for many common negative binomial models, consistency requires
not only correct specification of the mean and variance but also that the data have a negative binomial
distribution. A violation of the assumed Poisson distribution will allow for valid inference only if the
standard errors are appropriately computed, which requires correction particularly when there is over- or
under-dispersion.
14
differential effects above and below freezing that could be difficult to capture using a
parametric specification.34 We assume that the impact of temperature is constant within
10◦ F intervals, and constant for rain or snow falls between 0.0 cm< x ≤ 0.1 cm, 0.1
cm< x ≤0.5 cm, 0.5 cm< x ≤1.5 cm, 1.5 cm< x ≤ 3.0 cm, and 3.0 cm< x.35 Because
drivers who are unaccustomed to snow may face an elevated risk, we also create an indicator
variable for snow of more than 0.1 cm following a month without any recorded snow.36
Our preferred empirical estimates include lagged variables of weather. The motivation
for including these lags is that unfavorable travel conditions may cause individuals to delay
travel. We therefore include lags of temperature and precipitation by one day, or one week,
to account for this inter-temporal displacement.37 In our setting we include shorter lags than
are typical in this literature because it is unlikely that weather is bringing forward accidents
that were bound to happen at a later date, but weather may defer trips increasing rates at
a later date, although the time-span for such deferment is unlikely to be longer than a week.
Consistent estimation of Equation (10) requires that we control for unmeasured shocks
that covary with weather. Both regressions include a set of state-county-year-month fixed
effects to capture all unobserved determinants of incidents that vary at the county and
monthly levels.38 These fixed effects absorb both temporal and spatial changes related to
population, employment, and gasoline prices, as well as policy changes such as drunk driving
laws and graduated drivers licenses. Conditioning on these fixed effects, we identify αj , β j ,
and γ j from weather deviations within a county in a given month. Once controlling for these
factors, it seems plausible, due to the random nature of weather, that weather is orthogonal
to unobserved determinants of accidents and travel demand.
The first two moments of the Poisson distribution, E[Y ] = µ and V [Y ] = µ show the
equidispersion property that is often violated. The presence of overdispersion, while still
providing consistent estimates, will inflate the t-ratios in a Poisson model. To correct the
standard errors we block bootstrap at the annual level.
34
For example, even after several days without snow, melting and refreezing may create slick roads.
The primary restriction of bin choice lies in the NHTS household survey data, which are more limited
than the SDS data for observations on days with extreme weather conditions. We have run specifications
with more weather bins for our non-fatal accident and fatality regressions (see Appendix Table H9) and find
nearly identical results to those estimated here.
36
In robustness tests included in Appendix H, we also create a variable for infrequent rainfall after one
month of no rain. This variable will also capture the effect of oil or debris that may be dislodged by infrequent
rainfall.
37
In many other fatality settings, for example, respiratory illness, there is a concern that inclement weather
may harm only those who were likely to die shortly thereafter and this literature has stressed the inclusion
of lags sufficiently long to capture the net effect (Deschênes and Moretti, 2009). In the main text we report
the sum of coefficients from the contemporaneous and lagged weather. Appendix Table H6 gives the full
disaggregated set of coefficients. We also include specifications with longer lag periods and more weather
bins. In Appendix Table H14 we also examine aggregation of our data to the monthly level.
38
In Appendix Tables H8, H12, and H13 we report estimation results for models that include state-month,
county-year fixed effects, which are often used in studies with more aggregate data, and find results that are
similar in sign and magnitude.
35
15
5.1.2
VMT and Trips
To model travel demand we fit the following equation:
E[yi |xd,c ] = exp
8
X
α
j
j
Td,c
+
j=1
8
X
j=1
j
j
α−1
Td−1,c
+
5
X
j
j
β−1
Rd−1,c
5
X
β
j
j
Rd,c
+
j=1
+
j=1
5
X
j
j
γ−1
Sd−1,c
5
X
j
γ j Sd,c
+
j=1
+ θscym +
(11)
z0d,c δ
j=1
We avoid log-linearizing and then estimating the equation using ordinary least squares for
several reasons. First, there are some households that have zero daily trips or miles for which
log-linearization is infeasible. Second, as shown by Santos Silva and Tenreyro (2006), Jensen’s
inequality implies that interpreting the coefficients from such an estimate as an elasticity can
be incorrect in the presence of heteroskedasticity. Instead, we estimate Equation (11) using
Poisson regression.39 The covariates include county-year-month fixed effects, first snowfall,
and controls for household characteristics. These controls include the household size, the
number of adults, vehicles, and workers in the household, the NHTS defined life-cycle stratum
and income group, race, and the day of the week on which the household was followed.40
The estimation procedure is identical to that of Equation (10) except that we now bootstrap
the standard errors at the state-by-survey-year level.
5.2
5.2.1
Results
Estimates of the Impact of Weather on Accidents
We estimate Equation (10) for three mutually exclusive and collectively exhaustive types
of accidents: accidents involving a fatality, (PDO) accidents, and accidents involving an
injury. Table 3 presents the estimates of the impact of temperature, rainfall, and snowfall
on these three types of accidents. We present the sum of the current and lagged coefficients
to account for any inter-temporal offsetting that may occur for a given weather fluctuation.
In each regression, the temperature bin of 50–60◦ F is omitted, implying that each estimated
coefficient is the percent change in accidents compared to a day at 50–60◦ F. Bins for rainfall
of 0 cm and snowfall of 0 cm are also omitted.
The initial set of columns, (1) through (5), display point estimates associated with
weather variables on fatalities. In column (1), our central specification, we find that
temperature has a strong and statistically significant effect on fatalities. Compared with
a day at 50◦ F, fatality risk rises from -14.3 percent at <20◦ F to 9.5 percent for a day
at >80◦ F. The estimated effects for precipitation are somewhat complex. While snowfall
increases fatalities, rainfall decreases total fatalities. We suspect this is because drivers
avoid trips or drive cautiously enough to reduce overall fatality risks on rainy days, which
we will confirm with our PDO accident and travel demand regressions.41
39
In Appendix Table H15 we examine other functional forms of our trip demand model, including the
Inverse Hyperbolic Sine Function.
40
Specifications excluding controls given in Appendix Table H16.
41
Note that the number of observations changes between regressions and is larger than the total count of
16
The following columns examine the source of these effects and test the robustness of our
fatality result. In column (2) we estimate the daily count of fatalities, omitting fatalities
where any party involved was a ULD mode, leaving only fatalities where all parties were
LDVs.42 The estimated coefficients are small and generally insignificant, with one potentially
important exception being the >80◦ F bin with a 5.4 percent increase in fatalities. If this
increase was due to more drivers on the road, we could attribute this effect to exposure. But,
as we will show in the travel demand estimates, the hottest days are associated with less
travel, which is consistent with heat aggravating an existing risk. The effects from rainfall
are also largely removed but snowfall effects remain positive.
Column (3) uses only the sample of fatalities where at least one party traveled by a ULD
mode. The effects are extremely large. Compared with a day at 50◦ F, a day below 20◦ F sees
a 61 percent decrease in fatalities, while a day above 80◦ F sees an 18 percent increase. These
magnitudes are large because ULD accidents are a relatively small share of fatalities. With
a small base, a change of a few fatalities will result in a large percentage change. Together
columns (2) and (3) suggest that ULD fatalities may be a minority of total fatalities but
they are the primary mechanism of the temperature-fatality relationship found in column
(1). Although it is possible that heat somehow makes an existing set of ULD trips more
at risk, this seems unlikely. If cognition were the primary factor, one would expect the
minimum number of fatalities to occur between 60◦ F and 80◦ F when comfort is highest, but
instead we find the minimum at days when temperatures are below freezing.43
In column (4) we consider the possibility that weather may affect behavior beyond
the one-day lag of our main specification in column (1). In this specification we include
additional lags for the entire week and find that the sum of the contemporaneous and all
lagged coefficients is nearly identical to that with only a single lag.44 Column (5) examines
only the set of counties considered large or medium metro counties by the National Center for
Health Statistics 2006 Urban-Rural Classification Scheme. The gradient of point estimates
from coldest to hottest temperature bins remains as strong as when estimated from the entire
sample, suggesting that our results are not driven by counties with low population.45
fatalities in our dataset. This is because all days within a county-year-month are included, many of which
are zero. Whenever a county-year-month group has only zero outcomes, the group is omitted, reducing the
sample size for regressions such as that in column (3) because ULD crashes are relatively rare. In Appendix
Table H8 under the column titled FARS, we also estimate our fatality model, Equation (10), using the FARS
records of fatal accidents between 1975 and 2013, finding results are nearly identical to those that we find
with the SDS data. See Appendix C for a detailed description of FARS. These data cover only fatal crashes
but in all states.
42
We also include heavy-duty vehicles over 4,000 lbs.
43
In Appendix D we estimate models of compositional changes to hold fixed the number of daily accidents.
We find that given an accident the likelihood that it involves a ULD vehicle increases with temperature.
We also find that fatalities are no more likely to involve alcohol, young drivers, or males as temperatures
increase.
44
This specification also removes the possibility our effects are individuals simply picking the warmest day
of the week for discretionary travel or ULD travel as exercise, helping to differentiate between relative and
absolute effects.
45
Because the fixed effect specification removes all county-year-month groups without any variation, the
central specification will generally contain more urban counties. We also estimate models of adaptation in
the appendix to identify whether safety technology or driver behavior has altered the relationship between
weather and traffic accidents. We find little evidence that the relationship has changed in the past 20 years.
17
In column (6) we examine the daily PDO accident count as a function of weather. We find
that heat does not increase accidents over 50◦ F. If the mechanism for increased fatalities were
cognition or aggression, it would be surprising that small crashes follow a different pattern.
We mostly find effects of temperatures below freezing, which could be due to persistent ice.
We also find that rainfall or snowfall increases PDO accidents. Our largest rainfall coefficient
is associated with the ¿3 cm bin, indicating that PDO accidents increase by 18.8 percent
over a day without rainfall. The effect of snowfall is more than two times larger, with a day
of ¿3 cm snowfall increasing PDO accidents by 43.3 percent. This suggests that precipitation
generates more accidents but drivers, through either reduced trips or careful driving, reduce
the per accident fatality rate. In the case of rainfall these behavioral changes lower the total
fatalities, but for snowfall the increase in accidents is so large that the total fatality rate
increases, albeit less than the accident rate.
Finally, column (7) reports the effect of weather on accidents with at least one injury
but no fatalities. There is a slight positive association between temperature and accidents
with injuries. The precipitation effects display a similar pattern as that for accidents but
of a smaller magnitude. For example a day with snowfall of > 3 cm is associated with an
increase in injuries of only 25.9 percent. Broadly these results are a transition between PDO
accidents and fatalities.
5.2.2
Estimates of the Impact of Weather on Travel Demand
The estimated effects of weather on daily fatalities are suggestive of an exposure mechanism
for ULD accidents but the mechanism for the remaining LDV effects is unclear. In this
section we further explore these mechanisms using the NHTS logs of daily household travel.
Table 4 gives the point estimates and standard errors for a regression of weather on several
aspects of travel demand. Our coefficient estimates are again the sum of contemporaneous
and lagged effects.46 Given the limited amount of data, statistical precision is lower than in
the prior section, but some broad patterns are found in these results.
The estimates in column (1) indicate that mean daily temperatures below 20◦ F see 7.6
percent fewer LDV miles per household. Warmer days do not show evidence of a statistically
significant change in demand but the bin above 80◦ F does have a negative point estimate.
This provides some evidence that the increase in LDV fatalities above 80◦ F cannot be
attributed to additional driving and exposure as a mechanism. Similarly the point estimates
for precipitation are marginally significant but consistently negative. For LDVs it appears
possible that precipitation and possibly hot weather aggravate an existing risk and avoided
trips are an additional defensive expenditure.
Because our travel demand estimates are based on a self-reported survey, we believe
households record trip count with more precision than miles. While miles are a complete
measure of adjustment, distance can be difficult to judge and is often rounded. In column
(2), we examine the total trip as a function of weather. We find similar patterns as the total
miles regression but the bin above 80◦ F finds a larger effect and greater precision, again
showing avoided travel.47
See Appendix E for details.
46
See Appendix Table H7 for the disaggregated results.
47
In the appendix, we combine distance with the duration of the trip to generate speed. Speed can be a
18
In columns (3) and (4) we present results with only ULD travel by households. In
column (3) we document a positive correlation between temperature and ULD miles below
50◦ F. Above this temperature the point estimates continue to grow but are not precisely
estimated. Comparing these estimates with those in column (1), we can see that the changes
in demand are an order of magnitude larger than for LDV travel. On days below 20◦ F
demand decreases by 76 percent. As might be expected these exposed modes of transit are
also unpopular on days with precipitation. The ULD trip count, estimated in column (4),
shows that cold temperatures and rainfall also decrease the trip demand. The general pattern
confirms our earlier fatality results that ULD demand is closely linked to temperature.
The final column, (5), examines only trips taken with public transit options such as bus
and subway. Our strongest results come from cold days when users reduce trip demand.
Although not measured with precision, the point estimates are negative for hot days when
waiting for buses and subways is more unpleasant.
Several general observations can be made from these estimates. In Table 4 we find no
evidence that ULD travel is reduced as temperature and fatality risk increase. This suggests
an exposure mechanism. For LDV travel a different picture emerges where elevated fatality
risk on days above 80◦ F (or accident risks on cold, rainy, or snowy days) reduces demand,
suggesting reduced LDV travel is a defensive action against aggravated risk due to weather.48
6
Simulation of Future Outcomes
The estimates above present a mixed picture of the effect of climate change on traffic
accidents. While our estimates suggest warmer temperatures will result in more fatalities,
a transition from snow to rain will reduce fatalities. It is also possible that changes in
travel demand will offset or exacerbate these costs. In this section we use predicted future
weather data to examine the welfare changes from each of these weather changes. Simulating
these changes requires a baseline and a predicted future outcome. It is natural to use
observed weather as the baseline and the output from climate forecasting models as the
future. A common problem arising with this setup is that the current observed weather
can be very different from the current weather predicted from the model. Failure to correct
for this discrepancy will lead to biased estimates. Prior correction methods typically adjust
either the current observed weather or prediction data by adjusting mean outcomes. This is
problematic because, as noted in our summary statistics, global warming involves not only
shifting mean values, but also increased variability in weather.
In this section we initially describe the framework of how our estimates from above are
applied to a new distribution of weather outcomes generated by climate change. Then we
examine in depth how that new weather distribution is developed from climate models taking
account of the baseline error inherent in these models. We first describe the existing methods
function of driver choice but also of congestion, complicating interpretation of the speed estimates. But one
might be concerned that deadly crashes were generated by higher intensity crashes. In Appendix Table H17
we do not find any evidence that fatalities are due to speed effects. If anything, drivers reduce speed on days
with temperatures over 80◦ F and when there is snowfall, again suggesting defensive behavior.
48
These results are robust to alternative functional form assumptions. We estimate an alternative model
that can handle zero values, the Inverse Hyperbolic Sine, in Appendix Table H15 and find that our results
are broadly consistent with those reported using the Poisson model.
19
and discuss cases where they may result in counterintuitive results. We also illustrate some
of these concerns with an example. Finally, we provide an improved methodology inspired
by techniques used by climate scientists.
To calculate the change in accidents we sum the daily changes to each county:
XX
∆y =
∆yd,c ,
(12)
c
d
where ∆yd,c is the predicted change in accidents on day d in county c.
To calculate the daily changes in accidents, we multiply the baseline accident rate in the
county with the percent change in accident rate for each weather measure:
" 8
#
X
j
j
j
∆yd,c =
α
bj + α
b−1
· Tbd,c
− Td,c
yd,c +
j=1
" 5
X
j
b j − Rj
(βbj + βb−1
)· R
d,c
d,c
#
yd,c +
(13)
j=1
"
#
5
X
j
j
j
yd,c .
(b
γj + γ
b−1
) · Sbd,c
− Sd,c
j=1
j
j
j
The α
bj , βbj , γ
bj and α
b−1
, βb−1
,γ
b−1
terms denote our estimated contemporaneous and lagged
coefficients from Equation (10), respectively, which are summed to give the net effect of a
j
bj and Sbj represent indicators for future
day with particular weather conditions. The Tbd,c
,R
d,c
d,c
weather on date d in county c within bin j. Equation (13) generates the percent change in
accidents by multiplying the number of bin changes by the marginal effect of a bin change.
This percent change is then multiplied by the baseline daily level of accidents in the county
yd,c .49
Because our SDS data have fatality rates, yd,c , for only 20 states, we use FARS data
to generate average daily fatality rates at the county level.50 For simulations of LDV and
ULD fatalities, injuries, and PDO accidents, we project the county baseline using a Poisson
model by regressing the outcome variable (e.g., LDV fatalities) on the fatality rate and
population by county for the counties in the SDS data and use the estimated coefficients
to impute missing counties. For our trip demand simulations we use the observed average
per household in each county in our NHTS sample, and where no NHTS data is given in a
county, we apply the national average.51 This daily household value is then multiplied by
365 days and the number of households in the county as taken from the census.
Evaluating Equation (12) requires obtaining estimates of future weather predictions.
We base our weather predictions on the CCSM4 RCP6.0 Scenario, which includes daily
(minimum, maximum, and average) temperature and precipitation throughout the United
States. Problematically, these models do not predict weather at a county level but rather at
49
As an example, suppose α
b7 = 0.05, α
b8 = 0.08. If future predicted values indicate that one day will move
th
th
7
8
from the 7 bin to the 8 bin, then Td,c = 1 and Tbd,c
= 1. If the baseline level of accidents yd,c = 2, then
∆yd,c = [0.08 − 0.05] 2 = 0.06, interpreted as a predicted increase of 0.06 accidents in county c on day d.
50
We use FARS data averaged from 2000 to 2010 for these baseline estimates.
51
These averages are generated across all of our NHTS data.
20
equally spaced grid points. This implies that what the model predicts in the baseline years
from 2006 to 2009 will not match observed weather outcomes particularly in areas with
complex terrain (Wilcke, Mendlik and Goblet, 2013). If these baseline discrepancies are not
adjusted, the simulation will generate changes that are the result of this baseline discrepancy
as opposed to changes in weather. In the next section we detail the shortcomings of prior
methods used to correct this discrepancy and compare them with quantile-based methods,
based on methods developed in the climate science literature.
6.1
Prior Calibration Methods
Traditionally, economists have corrected biases between the baseline observed data and the
baseline predicted data from models like CCSM4 with an additive term or a multiplicative
factor to match means (Deschênes and Greenstone, 2011; Ranson, 2014). We characterize
these methods as four unique corrections: predicted additive, predicted multiplicative,
observed additive, and observed multiplicative. Although in theory any method can be
used, additive methods tend to be used on temperature, while multiplicative methods tend
to be used on precipitation.
A predicted additive correction adds a value to each future prediction (CCSM4 20902099), where the correction is defined by
ξτ,c =
1 X
(xd,c − xd,c ) .
Nτ d∈τ
(14)
The value of the correction term is the average of the difference between the baseline CCSM4
prediction (2006-2009), denoted by xd,c , and the observed weather station data, denoted by
xd,c , for a given weather variable and predefined time period τ . The term Nτ represents the
number of days observed in the time period τ . The time period τ can be as short as a single
day to as long as an entire decade.52 The correction term is then added to the CCSM4 future
prediction, denoted by x
ed,c , to obtain a corrected future prediction:
x
bd,c = x
ed,c + ξτ,c .
(15)
A predicted multiplicative correction takes the product of the CCSM4 future prediction and
a multiplicative factor:
x
bd,c = x
ed,c ντ,c .
(16)
The term ντ,c is defined as
ντ,c =
1
Nd
1
Nd
P
xd,c
P
xd,c
d∈τ
d∈τ
.
(17)
The term ντ,c is the ratio of the average observed weather station data and the average
CCSM4 baseline data for a given month and county.
52
The choice of the time period varies across studies. For example, Deschênes and Greenstone (2011)
calculate errors for each county by day of year by computing the difference between county by day of year
specific average temperature from observed weather data and CCSM4 predictions during the baseline period.
Ranson (2014) calculates errors for each county by month of year.
21
Another class of correction method uses the current observed distribution as its base and
adds or multiplies the change observed in the CCSM4 prediction. For the additive observed
correction a projected change is added to each outcome in the observed weather. The change
is defined by
1 X
(18)
(e
xd,c − xd,c ) .
ψτ,c =
Nd d∈τ
The correction term is then added to the observed weather data, xd,c , to obtain a corrected
future prediction:
x
bd,c = xd,c + ψτ,c .
(19)
The multiplicative observed correction scales each outcome in the observed weather, where
the scaling factor is defined by
P
1
ed,c
d∈τ x
Nd
.
(20)
ζτ,c = 1 P
d∈τ xd,c
Nd
The correction term can be multiplied by the observed weather data, xd,c , to obtain a
corrected future prediction:
x
bd,c = xd,c ζτ,c .
(21)
Our concerns with existing methods fall into two categories. First, they can correct biases
only in the mean and not other moments of the distribution. Failing to match higher order
moments may lead to unrealistic weather changes. One benefit of the observed additive
correction, which has been used in recent work (e.g., Schlenker and Roberts (2009); Ranson
(2014)), is that corrected future data will not have dispersion or compression of weather
values that is purely the result of baseline modeling error. The drawback is that where
CCSM4 predicts a change in weather variability, it will be omitted from the simulation.53
Second, existing correction methods often imply unreasonable corrections to daily
precipitation variables, which have many zeros. Although additive methods are generally
not used for precipitation, if ξτ,c > 0 or ψτ,c > 0, then the corrected rainfall prediction
will shift all days with zero precipitation to a positive value. Prior studies have instead
corrected precipitation
with a multiplicative method. This correction can, nevertheless, be
P
problematic. If
xd,c = 0, which is likely to be the case for snowfall in many places or
d∈τ
rainfall in dry counties, ντ,c is undefined.54 Thus any correction method must be performed at
a highly aggregate level and is sensitive to trace precipitation.55 The multiplicative correction
method also has no ability to generate or remove trace precipitation days and can only scale
up or down already existing precipitation.
In Panels (a) and (b) of Figure 1 we illustrate these concerns using a temperature
distribution from a representative county.56 Panel (a) depicts the PDF of observed daily
53
Changes in weather variability are of particular interest for projecting crop yield changes (Schlenker,
2006).
P
54
xd,c is slightly greater than zero, ντ,c can be large, which is unrealistic as most
In some cases when
d∈τ
climate models predict modest changes in precipitation.
55
Trace precipitation is defined as daily rainfall or snowfall less than 0.01 inch or 0.0254 cm.
56
The data that we used to generate these distribution functions are taken from Orange County, CA;
however, we have shifted and enhanced some features to aid in exposition.
22
mean temperature data, the CCSM4 2006-2009 baseline prediction, and the CCSM4 20902099 future prediction. CCSM4 predicts a baseline mean temperature of 40.0◦ F, which in
this particular county is nearly equal to the observed mean temperature of 41.0◦ F. Crucially,
the dispersion of the baseline CCSM4 data is much higher and it predicts more extreme
temperatures in 2006-2009 than were actually observed. The future CCSM4 prediction of
mean temperature is 48◦ F, which is an 8◦ F increase. While CCSM4 predicts that all days
increase in temperature, this increase is disproportionately large for days that were already
warm. In this example, the CCSM4 predictions suggest that the hottest days are nearly
20◦ F warmer, while the coldest are only 5◦ F warmer.
In Panel (b) we demonstrate the additive mean-matching correction methods used in
prior papers for temperature. Because the initial means are nearly identical, the predicted
additive method does not substantially transform future CCSM4 weather outcomes. This
method implies that there will be an increase in the frequency of days below 20◦ F, even
though it is obvious from Panel (a) that all days become warmer. The implications for hot
days are also somewhat unrealistic. The hottest days increase by more than 40◦ F. No shift
of this magnitude is seen between the CCSM4 baseline and future predictions.
For the observed additive method, all days are shifted up by 8◦ F. While this method
does not spuriously generate colder days, all days warm by an equal amount; this translation
omits the change in dispersion that characterized the CCSM4 prediction. In Appendix G
we produce a similar figure illustrating the outcomes of the multiplicative methods. The
concerns, however, are similar.57 When matching only the mean, broader changes in the
distribution are forced and are often unrealistic.
6.2
Calibration Using a Quantile-Mapping Method
To correct these biases with more intuitive outcomes, we draw on quantile-based methods
used by atmospheric and climate scientists (Wilcke, Mendlik and Goblet, 2013). The major
advantage of this method is that it corrects all moments of the distribution, not just the
mean. With these methods, it is possible to have positive corrections to some parts of
the distribution and negative corrections to others. Our method consists of three steps:
defining the Empirical Cumulative Distribution Function, solving for and applying the error
correction, and correcting for any wet bias.
Quantile-mapping methods generate a corrected prediction by comparing Empirical
Cumulative Distribution Functions (ECDFs) for each weather measure X ∈ {T, R, S}. The
researcher must pick the relevant geographic area and time window from which to generate
these functions. In our simulation, we construct these for the average year at the county
level, c, based on 10 years of data. Once the ECDF is generated, we take the inverse.
This generates three inverse ECDFs: the observed baseline, Φ−1
X,τ,c (·), the CCSM4 baseline
−1
e −1 (·).
prediction, ΦX,τ,c (·), and the CCSM4 future (uncorrected) prediction, Φ
X,τ,c
These three functions allow us to solve for the error correction. For a given observed
weather outcome xd,c , we compute the cumulative probability of achieving that outcome in
57
Appendix Figure H.2 uses a different CCSM4 2090-2100 distributional change (an upward translation)
and shows how multiplicative methods can generate spurious effects.
23
the observed baseline data, denoted by p:
p = ΦX,τ,c (xd,c ).
(22)
Next, we evaluate the difference between the baseline CCSM4 ECDF and the future
prediction CCSM4 ECDF at the probability p:
e −1 (p) − Φ−1 (p).
∆xd,c = Φ
X,τ,c
X,τ,c
(23)
We then add the difference to the current weather outcome to generate an error-corrected
weather prediction:58
x
bd,c = xd,c + ∆xd,c .
(24)
The method is illustrated in Panels (c) and (d) of Figure 1 for temperatures in our
representative county. In Panel (c) we show the inverse ECDFs for all three functions
and the final corrected outcomes. Take an observed temperature of 33◦ F. The ECDF of the
observed temperatures indicates that 20 percent of all days have temperatures below 33◦ F.
e −1 (0.2) − Φ−1 (0.2) = 5◦ F. This correction
The correction applied to this temperature is Φ
T,τ,c
T,τ,c
increases the temperature to 38◦ F in the future corrected outcomes. This non-parametric
correction is applied to each quantile, generating the inverse ECDF denoted by the dotted red
line. Panel (d) shows the final corrected PDF, which indicates both increasing temperatures
and increasing dispersion, mirroring the changes predicted by CCSM4.
For precipitation measures, a few other corrections must be made. First, the correction
must be bound from below by zero:
x
bd,c = max{xd,c + ∆xd,c , 0}.
(25)
Second, when precipitation in the observed baseline is less frequent than the predicted
baseline, and the future prediction indicates more precipitation, the “wet bias” must be
corrected.59 This set of circumstances is illustrated in Panels (e) and (f) for a hypothetical
county where we exaggerate outcomes to aid in exposition. In this county, 20 percent of all
days currently receive no rainfall. For this county CCSM4 predicts an increase in rainfall.
Without wet bias correction, any dry day will be mapped to a positive precipitation amount
e −1 (0.175)−Φ−1 (0.175) = ∆xd,c = 0.1 cm. To reduce the number of days with rainfall,
of Φ
X,τ,c
X,τ,c
we randomly draw precipitation days from the future predicted ECDF below the point where
e −1 (p ≤ ΦX,τ,c (0)).
the baseline predicted ECDF is 0. Specifically, we randomly draw from Φ
X,τ,c
This reduces the number of days with trace rainfall to match the CCSM4 model prediction.
6.3
6.3.1
Results
Simulation Results using Quantile Mapping
Table 5 summarizes the results of our simulation and welfare calculations using our quantile
mapping method. Each simulation in Panel A details the changes in accidents or travel
58
See Appendix G for a slightly modified version of the quantile-mapping correction method that uses
the CCSM4 baseline weather data to establish the probability p. The two methods generally give nearly
identical results.
59
Wet bias is a common phenomenon in climate prediction research and occurs when quantile mapping
methods are applied in settings where dry day frequency in prediction models is higher than in the observed
weather data. See Wilcke, Mendlik and Goblet (2013) for more details.
24
demand from each weather component as well as the 95 percent confidence intervals.60
Column (1) reports the effect of weather from 2090 on fatalities using our estimates
from Table 3 column (1). The reduction in snowfall and increase in rainfall result in
reduced fatalities. These effects are more than offset by the increased fatalities due to
temperature. The net change in fatalities is an increase of 397. Applying the Department
of Transportation’s (DOT) VSL at $9.1 million, these fatalities have a cost of $3.6 billion.
When discounted using a 3 percent rate, this has a present value of $360 million.61
Columns (2) and (3) attribute these costs to LDV and ULD crashes using the estimates
of columns (2) and (3) from Table 3. These results suggest that LDV fatalities will increase
by 63 annually but these estimates are not distinguishable from zero, while ULD fatalities
will increase by 298.62 Therefore, we cannot reject the possibility that the entire increase in
fatalities will be due to ULD crashes.
We estimate welfare changes stemming from changes in demand for LDV and ULD travel
using terms W T P m and W T P b in Equation (8).63 Column (4) applies the estimated LDV
mile demand effects estimated in column (1) of Table 4 to future weather outcomes. The
increase in miles generates a benefit of $48 million although the 95 percent confidence interval
overlaps with zero and we cannot reject the possibility there are defensive expenditures that
carry additional costs.
Column (5) uses the ULD mile demand estimates from column (3) of Table 4. ULD
miles will be expected to increase by 0.98 billion by 2090 carrying a benefit of $315 million.
This value is statistically different from zero and would offset 88 percent of the total fatality
costs.64
Column (6) uses our accident regressions from Table 3, column (6). Because PDO
accidents are negatively correlated with temperature, weather from 2090 would decrease
the number of PDO accidents by 22,485. We evaluate these costs using a value per PDO
accident of $10,633 with a total benefit of $18 million.65
60
These confidence intervals incorporate the uncertainty of our point estimates but not the uncertainty
across various climate change models. These are generated by drawing from a normal distribution with the
mean and standard deviation of coefficient estimates given in Table 3. These draws are then applied to the
predicted weather effects in each decade. From these values the mean and 95 percent confidence interval are
calculated. When summing across decades, the mean and 95 percent confidence interval are assigned to the
midpoint of the decade and linear interpolation is used between those years.
61
We do not adjust the VSL amount for future changes in income. We use a 3 percent discount rate to be
consistent with DOT assumed rates (Blincoe et al., 2014).
62
Because these are taken from the estimates in Table 3 they do not sum to 397 but are not inconsistent
with this value.
63
To calculate the change in demand from our estimates, we multiply the estimated percent change in
demand times the number of miles taken daily in the county. To generate the daily number of miles, we use
the average number of miles across households in the county in the NHTS data, which is multiplied by the
number of households in the county. Miles are priced based on the average fatalities per LDV or ULD mile
times the VSL.
64
We reiterate that these terms are derived from a stylized framework that leaves out several features
that may influence travel demand and thus alter the welfare calculation. For example, due to the lack of
appropriate data we cannot measure the welfare gains from improvements in trip quality as temperature
increases from cold to warm. These effects are likely positive for both travel modes, implying that we are
underestimating the welfare gains from increases in travel demand stemming from climate change.
65
We use the per vehicle value of PDO crashes from Blincoe et al. (2014) and multiply this by the average
number of vehicles per crash of 1.75.
25
The net effect on injuries, given in column (7), is an additional 4,909 in 2090. Because
the relationship between temperature and injuries is flatter than fatalities, the 95 percent
confidence interval overlaps with zero and in many near-term intermediate years there is
a decrease of injuries. We evaluate these at $141,677 per injury, which is the frequency
weighted average of the five injury levels recognized by the DOT’s Maximum Abbreviated
Injury Scale.66 This generates an additional cost of $94 million.
Panel B aggregates results from 2015 through 2099. The total net present cost of an
additional 18,603 fatalities is $39.9 billion.67 We find that the benefits of ULD travel are
$34.1 billion. These benefits would offset more than 85 percent of the fatality damages and
we cannot reject full offsetting.68 Taken together, our results suggest that excluding exposure
benefits from cost-benefit analysis can dramatically overestimate the expected net costs from
climate change.
Figure 2 illustrates the effect of end-of-the-century climate change on traffic accidents
by plotting impacts for each county in the United States. Panels (a), (b), and (c) map the
net effects of climate change on traffic fatalities, injuries, and PDO accidents, respectively.
Counties colored red are predicted to see an increase in fatalities, while blue colored counties
are predicted to see a decrease in fatalities. The deeper the color, the larger the magnitude
of the effect. The ranges for each color are in terms of average annual fatalities per 100,000
people. Panel (a) shows that nearly all counties are predicted to see an increase in the rate of
fatalities per person except some interior regions in the North-West. For injuries that appear
in Panel (b), much of the country will experience an increase in injuries, except for a swath
from Michigan and Ohio through Oklahoma, northern regions bordering Canada, and south
Florida. In contrast, we see in Panel (c) that a majority of counties will experience a reduction
in PDO accidents, although a significant number of counties in the South and South-West
experience an increase. The effect of climate change on PDO accidents is dominated by the
transition of days with snowfall to rainfall, as the temperature coefficients are small and the
heavy snowfall coefficients are much larger than the corresponding heavy rainfall coefficients.
6.3.2
Comparison of Weather Correction Methodologies
Table 6 presents the comparison between our quantile-mapping method and the methods
common in the literature that are based on the mean. Column (1) repeats our predicted
change in fatalities for the decade 2090-2099 with 95 percent confidence intervals given in
brackets. We note that our earlier summary statistics from Table 2 showed that future
66
This standardized scale was developed by the Association for the Advancement of Automotive Medicine.
We use the weights of police reported injury levels from Blincoe et al. (2014). These include costs for quality
of life, medical, property damage, congestion, insurance, market and household productivity, and legal costs.
67
In Appendix H, we present net present cost estimates under several other warming scenarios and
prediction models. Table H20 shows that under the RCP4.5 scenario, there would be 18,115 fatalities
from 2015 to 2099 with a total net present cost of $44.7 billion. The RCP8.5 scenario would generate 33,376
fatalities and costs of $73.5 billion during that time span. The Hadley 3 A1B scenario generates 27,493
fatalities for a total cost of $62.6 billion.
68
It is important to note that offsetting can be sensitive to the climate scenario used because there can
be substantial variation in the timing and location of weather changes. These additional trips are evaluated
by their price, which only incorporates the risk of a fatality. We do not incorporate accident or injury costs
because FARS does not track these and the SDS data only track crashes involving LDVs. We also evaluate
LDV trips only using fatality costs, excluding other costs such as time and gasoline for consistency.
26
weather was broadly characterized by higher temperatures, increased rainfall, and decreased
snowfall. While population is not evenly divided among all counties, intuition suggests
that our results should broadly align with these national trends where temperature changes
increase fatalities while snow and rainfall effects are negative.
First we examine columns (2) and (3) with CCSM4 2090 predicted data as future weather,
but correct that prediction based on the baseline discrepancy between observed weather and
CCSM4 2006-2009 predicted weather. This is accomplished with either an additive term
in column (2) following Equation (15), or a multiplicative term in column (3) following
Equation (16). Examining snowfall for both methods we find an increase in fatalities by
406 and 307 annually. This result is counterintuitive given our positive point estimates for
snowfall in Table 3. A decrease in snowfall should reduce snow-related fatalities.
In columns (4) and (5) we simulate fatalities using the additive observed method given
in Equation (19), and multiplicative observed method given in Equation (21), respectively.
These methods generate future weather outcomes by adjusting the current distribution of
weather such that the mean changes by the amount predicted by the CCSM4 simulation
between 2006-2009 and 2090-2099. Here we focus on rainfall. Nationally we expect rainfall
to increase, and with negative point estimates for rainfall effects in Table 3, there should be a
decrease in fatalities. Therefore, it is unsurprising that fatalities decease. What is surprising
about the additive method shown in column (4) is the magnitude, which indicates a decrease
of 433 fatalities. This large result is likely due to counties with a predicted increase in rainfall
where a common additive term will change all zero events to positive events, resulting in
hundreds of days with trace rainfall. By contrast a multiplicative correction, such as that
demonstrated in column (5), can only adjust rainfall by changing the quantity on preexisting
nonzero events. This implies that frequency will never adjust and that most of the adjustment
will occur on extreme events.69 This could explain the small change in fatalities of -12.
While the comparison given in this table does not prove our method is correct, we find our
results to be intuitive given the summary statistics of weather changes predicted by CCSM4.
Many of the discrepancies among methods seem likely due to the mechanics of matching
only the mean. Most prior work in this literature has focused on temperature where we find
that the confidence intervals generally overlap among all methods, but it is unclear whether
this result will hold more generally. Where rainfall and snowfall are important, as in our
context, the quantile-mapping method overcomes drawbacks of prior methods.
6.4
Discussion
There are several relevant caveats to our predictions of future fatalities. First, there are many
aspects of automobile demand that may change given the time scale involved. Car ownership
rates in the United States are among the highest in the world and may change substantially.
Public attitudes, city structure, congestion levels, and energy prices could change driving
behavior in unexpected ways. As an example, in 2008 the number of fatalities was 34,172,
but one year later fatalities were 30,862 due to reduced driving from the recession.
Second, even if all 397 additional deaths are due to voluntary exposure, this is not an
69
For example, if a location has only 1 rainfall event of 10 cm, a 0.5 adjustment will reduce this amount
to 5 cm, which remains in the top bin.
27
argument against public policy to reduce this number. Increased fatalities may change the
cost-benefit analysis of a particular policy. There is also a lot of room for policy to reduce
fatalities. A gasoline tax of roughly $0.17 would reduce miles sufficiently to remove these
fatalities.70
Another limitation of our welfare calculations is that they do not incorporate adaptation.
Adaptation may come in the form of private or public adaptation to warmer, rainier weather.
Although regressions shown in the appendix do not find evidence that the marginal effect
of weather on fatalities is different between cold and hot locations or has changed over the
past 20 years,71 it is possible that individuals will invest in adaptation. Driver-assistance
technology (e.g., automatic lane changing) and autonomous vehicle technology are two key
examples of technology that may help to avoid fatal interactions with ULD vehicles. Leaving
these potential technologies out of our welfare calculations imply that our estimates overstate
the long-run impacts of climate change.
But there is also reason to worry that the role of private adaptation is limited. Any
optimal private response to changing fatality rates requires that accident costs be internalized
(White, 2004). Most states use “contributory negligence” whereby damages are assigned in
proportion to fault. But provided the driver is not negligent, there is no incentive to avoid
heavy pedestrian areas, maintain larger distances from bicycles and motorcycles, or avoid
automobile travel altogether on warm days when these risks are high.
Finally, our estimates do not account for the possibility that individuals could migrate
away from affected areas, as a form of private adaptation. If the fatalities we estimate are
due to voluntary exposure, migration should not be expected because they would not be
associated with lower utility. Because our measure of voluntary exposure does not offset all
costs, some of our estimates may be due to aggravated risk, which would encourage migration.
Previous estimates of migration in response to climate change suggest that migration from
hot to cool regions will be modest (Albouy et al., 2016). Migration and other forms of private
adaptation reduce the costs of climate change, so including them in our framework would
lower our computed costs.
7
Conclusion
This paper estimates the impact of weather on traffic fatalities, injuries, and PDO accidents
as well as total trip demand. We exploit plausibly random day-to-day variation in weather
to show that fatalities increase with snowfall, decrease with rainfall, and are positively
correlated with temperature. The evidence suggests that these effects are primarily due
to interactions with pedestrians, bicycles, and motorcycles. We apply these estimates to a
climate change scenario RCP6.0, a balanced growth scenario of fossil and non-fossil energy
sources resulting in 2.3◦ C (4.2◦ F) of warming by the end of the century across the United
States. The climate data are corrected for use in our simulation using a quantile-mapping
methodology that allows us to account for baseline modeling error while allowing for changes
in the distribution beyond the mean. We find that while the shift from snow to rain will save
roughly 72 lives annually, temperature increases will cause 468 additional fatalities. The
70
71
This calculation assumes no change in vehicle characteristics, and a rebound effect of 20 percent.
See Appendix Table H10.
28
net annual increase will be 397 fatalities by 2090. But when deaths involving pedestrians,
bicyclists, and motorcyclists are removed, the increase is no longer statistically different
from zero. It is possible that some fatalities are due to psychological effects or changes in
aggression but most evidence points to voluntary exposure as the primary mechanism of
increase. We find that these fatalities carry a total net present cost of $40 billion by the
end of the century. Increased benefits from travel that capture the benefits of voluntary
exposure, however, offset more than 85 percent of these costs. Accounting for these benefits
more broadly may help to explain why, despite the numerous documented negative outcomes
associated with heat, the predominant migration pattern within the United States in recent
decades has been towards warmer climates.
One broader implication of this research is that voluntary exposure is an important
mechanism for understanding the welfare implications of climate change. Our estimated
effects appear to be the result of individuals being drawn outdoors and using forms of
transportation that will not protect them in a crash. It is possible that individuals spending
time outdoors will also be exposed to street crime or air pollution. In the agriculture sector
farmers may choose riskier but higher-profit crops. Maize, with a longer time to maturity,
has higher yield but is also riskier to grow.72 It is plausible that warm locations may be
susceptible to large profit losses from weather shocks because farmers choose high-risk, highreward crops. Voluntary decisions may also be important for broader economic measures.
Warmer climate may allow for outdoor leisure time in activities like biking, for which the
welfare benefits may or may not be captured by GDP. It may also increase the opportunity
cost of working. A priori it is difficult to ascertain what fraction of GDP loss during warm
weather is due to an aggravated cost and what has an offsetting voluntary benefit. In other
domains, such as health effects of temperature for infants and elderly, a voluntary exposure
mechanism seems less plausible.
Finally, it is important to note that the exposure mechanism will vary across countries,
particularly for transportation. The United States, with highly developed infrastructure,
limited access highways, and urban areas designed to channel high speed traffic away
from residential areas, provides significant separation between vehicles and pedestrians, and
bicycles. By contrast, developing nations, and even some middle income countries, have
larger fatality rates per capita, largely due to vehicles colliding with pedestrians (Kopitis
and Cropper, 2005). It should also be noted that our results do not indicate that reliance on
walking, biking, and motorcycling imply large fatality rates, as other English-speaking and
western European nations have per capita fatality rates that are often less than half that of
the United States.73 Some countries like Sweden with extraordinarily low fatality rates have
pursued a variety of urban design and legislative changes to reduce fatalities with policies
such as replacing intersections with roundabouts to slow vehicles where they are likely to
72
For example, a hybrid with a relative maturity rating of 100 days may produce 210 bu/A, while one with
a 101 day rating may produce 212 bu/A. An extra day of maturation requires a warmer climate but also
exposes the crop to a higher possibility of an extreme weather event. Generally, perennial crops such as citrus,
and wine have high dollar value but are restricted to warm climates as they require a long, uninterrupted
growing season and can suffer for many years from short-run shocks, while commodity crops such as wheat
are annual, hardy, and can be grown in northern Alberta.
73
Per capita rates in the United States are 11.4 per 100,000. The rate for Australia is 6.1, Canada 6.8,
Germany 4.7, Norway 4.3, Sweden 3.0, Switzerland 4.3, and the UK 3.7 (World Health Organization, 2013).
29
encounter pedestrians.74 Relatively simple changes like these may prove to be effective,
although unglamorous, adaption strategies to climate change.
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32
Table 1: Summary Statistics, Accidents and Travel Demand Data
Panel A. State Accident Data, 1991-2010
Census Region (States
Included)
Accidents
Fatalities
per 100,000 per 100,000
Temperature (◦ F)
5th
50th
95th
Quantile Quantile Quantile
(3)
(4)
(5)
Rainfall (cm)
75th
95th
Quantile Quantile
(6)
(7)
Snowfall (cm)
75th
95th
Quantile Quantile
(8)
(9)
(1)
(2)
Northeast
(NY, PA)
3.6
0.04
20.0
50.9
75.3
0.34
1.32
0.01
1.91
Midwest
(IA, IL, KS, MI, MN, MO,
NE, OH)
7.6
0.06
17.2
53.0
79.0
0.23
1.25
0.00
0.94
South
(AR, FL, GA, NC, SC)
8.8
0.08
37.2
65.9
82.6
0.33
1.68
0.00
0.00
West
(CA, MT, NM, WA, WY)
5.6
0.08
23.3
53.1
76.6
0.10
0.75
0.00
0.93
All 20 States
7.2
0.07
21.2
56.4
80.4
0.24
1.30
0.00
0.70
Panel B. NHTS Daily Travel Data, 1990-1991, 1995-1996, 2001-2002, and 2008-2009
Temperature (◦ F)
Census Region (States
Household Household
5th
50th
95th
Included)
Miles
Trip Count
Quantile Quantile Quantile
(1)
(2)
(3)
(4)
(5)
Rainfall (cm)
75th
95th
Quantile Quantile
(6)
(7)
Snowfall (cm)
75th
95th
Quantile Quantile
(8)
(9)
Northeast
(CT, MA, ME, NH, NJ, NY,
PA, RI, VT)
49.3
6.2
21.4
50.4
74.8
0.30
1.13
0.00
1.75
Midwest
(IA, IL, IN, KS, MI, MN, MO,
ND, NE, OH, SD, WI)
51.9
6.5
14.4
46.6
75.6
0.24
1.21
0.00
1.39
South
(AL, AR, DC, DE, FL, GA,
KY, LA, MD, MS, NC, OK,
SC, TN, TX, VA, WV)
55.2
6.0
34.8
65.1
83.3
0.22
1.40
0.00
0.00
West
(AK, AZ, CA, CO, HI, ID,
MT, NM, NV, OR, UT, WA
WY)
49.8
6.3
41.1
64.4
81.8
0.02
0.61
0.00
0.00
All States
52.5
6.2
25.5
60.1
82.0
0.20
1.19
0.00
0.36
Notes: Panel A details the state accident data for 20 states grouped by census region. States with available data are listed below
each region. Panel A statistics are based on 6,698,935 county-by-day observations of accidents, fatalities, and weather. Columns
(1) and (2) give average daily accidents and fatalities per 100,000 residents. Columns (3) through (5) give temperature, (6) and
(7) rainfall, and (8) and (9) snowfall for the listed quantiles. Panel B describes the National Household Transportation Survey
data grouped by census region with included states listed. The statistics detail 283,857 households and their driving behavior for
a 24 hour period. Columns (1) and (2) detail the average household’s daily vehicle miles traveled, and trip count. Columns (3)
through (9) detail weather statistics as in Panel A.
33
Table 2: Observed Weather and CCSM4 RCP6.0 Prediction Data
Daily Temperature (◦ F)
Daily Rainfall (cm)
5th
50th
95th
75th
95th
Census Region
Quantile Quantile Quantile Quantile Quantile
(1)
(2)
(3)
(4)
(5)
Panel A. Observed Weather Station Data, 2000-2009
Northeast
21.0
54.6
79.5
0.32
1.48
Midwest
14.4
51.8
78.0
0.22
1.20
South
33.4
63.6
82.7
0.30
1.54
West
20.9
51.0
76.1
0.11
0.71
All Regions
21.9
57.3
81.0
0.24
1.32
Daily Snowfall (cm)
75th
95th
Quantile Quantile
(6)
(7)
0.00
0.00
0.00
0.00
0.00
1.43
1.04
0.00
1.12
0.55
Panel B. Baseline Predicted CCSM4, 2006-2009
Northeast
21.0
57.3
80.0
0.34
Midwest
13.7
55.2
84.3
0.23
South
32.2
65.3
84.0
0.38
West
14.6
48.2
77.7
0.17
All Regions
21.4
59.4
83.1
0.30
1.33
1.08
1.32
0.90
1.19
0.00
0.00
0.00
0.02
0.00
0.57
0.67
0.01
2.34
0.46
Panel C. Predicted Future
Northeast
25.9
Midwest
20.6
South
35.9
West
22.6
All Regions
26.9
1.45
1.10
1.44
1.11
1.30
0.00
0.00
0.00
0.00
0.00
0.28
0.41
0.00
1.69
0.22
CCSM4, 2090-2099
61.2
84.2
59.2
88.9
69.3
88.1
52.2
81.8
63.3
87.5
0.37
0.23
0.40
0.24
0.31
Notes: The table details the 11,429,977 county-by-date observations used in the simulation.
Each panel presents temperature, rainfall, and snowfall for the listed quantile by census
region. Panel A describes the observed weather data from the National Climatic Data
Center’s Global Historical Climatology Network-daily. Panels B and C describe the data
from the CCSM4 RCP6.0 scenario predicting daily weather.
34
Table 3: Poisson Regression of Accidents on Weather Variables
Fatalities
Current + Lag
Mean Temp.
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80 ◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Controls
Restrictions
LDV Crashesa
ULD Crashesb
Urban Countiesc
Controls
Week of Lagsd
County-year-monthe
First Snowfallf
Num. Obs.
PDO
Accidents
Injuries
(1)
LDV
Crashesa
(2)
ULD
Crashesb
(3)
Week of
Lagsd
(4)
Urban
Countiesc
(5)
(6)
(7)
-0.143***
(0.029)
-0.117***
(0.026)
-0.089***
(0.019)
-0.063***
(0.014)
0.055***
(0.009)
0.069***
(0.015)
0.095***
(0.015)
0.014
(0.055)
0.007
(0.026)
0.005
(0.015)
-0.012
(0.016)
0.021**
(0.009)
0.015
(0.014)
0.054***
(0.020)
-0.605***
(0.117)
-0.632***
(0.074)
-0.413***
(0.077)
-0.143***
(0.031)
0.128***
(0.018)
0.176***
(0.030)
0.177***
(0.027)
-0.098***
(0.047)
-0.112***
(0.024)
-0.085***
(0.017)
-0.058***
(0.013)
0.053***
(0.009)
0.064***
(0.014)
0.090***
(0.016)
-0.114**
(0.054)
-0.128***
(0.033)
-0.078**
(0.034)
-0.033*
(0.018)
0.058***
(0.010)
0.069***
(0.018)
0.087***
(0.026)
0.097***
(0.022)
0.028*
(0.017)
-0.031***
(0.009)
-0.023***
(0.005)
-0.005
(0.005)
-0.011*
(0.006)
-0.010
(0.008)
0.000
(0.022)
-0.041***
(0.015)
-0.070***
(0.007)
-0.044***
(0.004)
0.020***
(0.004)
0.022***
(0.005)
0.016**
(0.007)
-0.029***
(0.009)
-0.049***
(0.011)
-0.059***
(0.015)
-0.086***
(0.016)
-0.048
(0.032)
-0.001
(0.010)
-0.006
(0.012)
0.006
(0.015)
-0.040**
(0.020)
0.024
(0.044)
-0.080***
(0.029)
-0.176***
(0.023)
-0.201***
(0.035)
-0.302***
(0.052)
-0.227**
(0.096)
-0.028***
(0.010)
-0.054***
(0.011)
-0.062***
(0.015)
-0.114***
(0.019)
-0.052
(0.033)
-0.027*
(0.015)
-0.047***
(0.015)
-0.039**
(0.018)
-0.012
(0.020)
-0.018
(0.049)
0.023***
(0.004)
0.071***
(0.005)
0.107***
(0.007)
0.147***
(0.011)
0.188***
(0.015)
0.014***
(0.005)
0.058***
(0.005)
0.088***
(0.007)
0.119***
(0.010)
0.144***
(0.017)
0.027*
(0.016)
0.073***
(0.020)
0.130***
(0.028)
0.155***
(0.023)
0.040
(0.044)
0.054***
(0.020)
0.083***
(0.023)
0.158***
(0.029)
0.143***
(0.042)
-0.032
(0.047)
-0.017
(0.062)
-0.170***
(0.060)
0.028
(0.073)
-0.032
(0.104)
-0.117
(0.094)
0.032*
(0.017)
0.069***
(0.020)
0.143***
(0.030)
0.165***
(0.031)
-0.002
(0.043)
-0.002
(0.023)
0.017
(0.025)
0.070***
(0.026)
0.094**
(0.040)
-0.085
(0.055)
0.022***
(0.007)
0.098***
(0.010)
0.230***
(0.010)
0.354***
(0.012)
0.433***
(0.014)
0.007
(0.008)
0.078***
(0.007)
0.189***
(0.010)
0.281***
(0.010)
0.259***
(0.022)
N
N
N
Y
N
N
N
Y
N
N
N
N
N
N
Y
N
N
N
N
N
N
N
Y
Y
3,117,797
N
Y
Y
2,829,908
N
Y
Y
406,051
Y
Y
Y
3,117,797
N
Y
Y
767,735
N
Y
Y
6,665,499
N
Y
Y
5,067,561
Notes: The estimates are from a Poisson regression of the daily count of fatalities, property-damage-only (PDO)
accidents, or injuries by county on weather and other covariates as indicated. Standard errors, in parentheses, are
block bootstrapped by year. Reported coefficients and standard errors are the linear combination of the current and
lagged estimates. Disaggregate results presented in Appendix Table H6. * significant at 10% level, ** significant
at 5% level, *** significant at 1% level.
a Includes only fatality counts where all participant were light-duty vehicles (also includes heavy duty vehicles).
b Includes only fatality counts where one participant was an ultra-light duty mode.
c Includes only counties classified as large or medium urban and suburban counties as classified by the National
Center for Health Statistics 2006 Urban-Rural Classification Scheme.
d Includes controls for 6 additional days of lags for each weather bin. Coefficients and standard errors include the
sum of all current and lagged weather controls.
e Fixed effects for county by year by month.
f Indicator for first snowfall after 1 month without snow.
35
Table 4: Poisson Regression of Travel Demand
Household
Miles
(1)
Trip
Count
(2)
Household
Miles
(3)
Trip
Count
(4)
Public
Transit
Trip
Count
(5)
-0.076**
(0.031)
-0.063**
(0.024)
-0.011
(0.015)
-0.026**
(0.011)
0.001
(0.011)
0.002
(0.016)
-0.015
(0.030)
-0.051**
(0.023)
-0.037**
(0.016)
-0.026**
(0.010)
-0.003
(0.007)
-0.007
(0.009)
-0.009
(0.008)
-0.037**
(0.016)
-0.760***
(0.154)
-0.489***
(0.109)
-0.343***
(0.088)
-0.129*
(0.072)
0.061
(0.051)
0.068
(0.087)
0.129
(0.106)
-0.292***
(0.060)
-0.144***
(0.039)
-0.095***
(0.033)
-0.033
(0.022)
0.027
(0.020)
0.006
(0.031)
0.021
(0.042)
-0.281**
(0.125)
-0.199**
(0.101)
-0.036
(0.051)
-0.066
(0.046)
0.048
(0.060)
0.028
(0.063)
-0.144
(0.103)
-0.004
(0.010)
-0.026**
(0.010)
-0.015
(0.014)
0.010
(0.021)
-0.023
(0.037)
-0.012*
(0.006)
-0.005
(0.008)
-0.007
(0.007)
-0.031**
(0.012)
-0.034*
(0.020)
-0.115**
(0.052)
-0.224***
(0.046)
-0.281***
(0.059)
-0.571***
(0.114)
-0.326
(0.238)
-0.007
(0.019)
-0.067***
(0.019)
-0.091***
(0.018)
-0.144***
(0.040)
-0.087
(0.059)
0.001
(0.051)
0.027
(0.039)
0.010
(0.060)
0.036
(0.062)
0.214*
(0.124)
0.026
(0.024)
-0.007
(0.024)
-0.014
(0.030)
-0.090**
(0.045)
-0.156***
(0.058)
-0.003
(0.015)
-0.017
(0.013)
-0.012
(0.020)
-0.075**
(0.030)
-0.160***
(0.035)
0.117
(0.087)
-0.057
(0.087)
-0.100
(0.108)
-0.065
(0.160)
-0.089
(0.115)
0.025
(0.044)
-0.127***
(0.037)
-0.151***
(0.044)
-0.105
(0.068)
-0.104
(0.077)
0.068
(0.055)
-0.054
(0.090)
-0.155
(0.079)
-0.034
(0.114)
0.005
(0.141)
Y
Y
Y
261,667
Y
Y
Y
261,667
Y
Y
Y
228,144
Y
Y
Y
228,144
Y
Y
Y
177,987
Light-Duty Vehicles
Current + Lag
Mean Temp.
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Controls
County-year-montha
First snowfallb
Household Controlsc
Num. Obs.
Ultra-Light Duty
Notes: The estimates are from a Poisson regression of the daily count of trips and miles
per trip for Light-Duty Vehicles, Ultra-LightDuty Modes, and Public Transit by household
on weather and other covariates as indicated. Standard errors, in parentheses, are block
bootstrapped by year. * significant at 10% level, ** significant at 5% level, *** significant
at 1% level
a Fixed effects for county by year by month.
b Indicator for first snowfall after 1 month without snow.
c Includes controls for count of vehicles in household, household size, number of workers in
household, number of adults in household, NHTS life cycle stratum, race, NHTS defined
income group, and day of week. Specifications excluding controls given in Appendix
Table H16.
36
Table 5: Estimates of the Change in Accidents and the Present Discount Value Costs of Climate Change
Panel A. Outcomes in 2090
Fatalities
Change in 2090 due to
Temperature
Change in 2090 due to
Rainfall
Change in 2090 due to
Snowfall
Net Change in 2090
Net Present Cost
($2015 Million)
(3)
LDV Tripsb
(in billions)
(4)
ULD Tripsb
(in billions)
(5)
98
316
4.33
[387, 547]
[49, 469]
[276, 257]
-27
-2
-24
[-34, -19]
[-9, 4]
-45
-33
[-57, -33]
Full Sample
LDVa
ULDa
37
Accidentsa
Injuriesa
(1)
(2)
(6)
(7)
468
1.15
-10,369
7,716
[-5.83, 14.60]
[0.72, 1.60]
[-16,562, -3,861]
[5,426, 10,094]
-0.55
-0.20
7,887
2,745
[-28, -20]
[-1.07, 0.13]
[-0.25, -0.15]
[7,431, 8,366]
[2,543, 2,956]
7
2.68
0.03
-20,003
-5,552
[-43, -22]
[0, 13]
[1.34, 3.92]
[-0.01, 0.07]
[-20,692, -19,350,]
[-5,893, -5,226,425]
397
[310, 476]
63
[-25, 144]
298
[259, 341]
6.45
[-3.81, 16.90]
0.98
[0.59, 1.42]
-22,485
[-28,949, -15,748]
4,909
[2,399, 7,386]
$360c
$60c
$261c
-$48d
-$315e
-$18f
$94g
[$276, $438]
[-$21, $140]
[$225, $300]
[-$151, $51]
[-$171, -$472]
[-$25, -$10]
[$58, $130]
ULD Tripsb
(in billions)
(5)
Accidentsa
Injuriesa
Panel B. Outcomes from 2015 to 2099
Fatalities
(1)
(2)
(3)
LDV Tripsb
(in billions)
(4)
(6)
(7)
18,603
3,290
13,501
247.90
45.1
-1,056,915
220,672
[14,240, 22,802]
[-1,149, 7,571]
[11,451, 15,631]
[-285.31, 787.86]
[23.29, 68.19]
[-1,385,121, -712,150]
[95,091, 348,906]
$39.9c
$8.3c
$27.4c
-$4.7d
-$34.1e
-$3.0f
$5.7g
[$29.4, $50.1]
[-$2.5, $18.8]
[$22.4, $32.6]
[-$18.0, $8.5]
[-$14.0, -$55.1]
[-$4.0, -$2.0]
[$0.9, $10.5]
Full Sample
Sum of Net Changes
2015-2099
Sum of Costs
($2015 Billion)
LDVa
ULDa
Notes: Net Present Cost estimates are reported in 2015 dollars. The net change estimates are the sum of county-level changes in weather on the listed outcome. All future
weather simulations use quantile mapping to adjust current weather to the changes predicted by the CCSM4 RCP6.0 scenario. Values given in brackets indicate the 95%
confidence interval. See text for further details of calculations. All costs assume a discount rate of 3%.
a For counties with missing daily average LDV, ULD, injuries, and accidents, rather than applying a national average, we impute using a Poisson regression of the daily count
of incidents for states with SDS data on county population and fatalities.
b For counties without NHTS data we are missing LDV trips and ULD trips and we apply the national average.
c Assumes the value of a statistical life is $9.1 million (Blincoe et al., 2014).
d The cost of LDV miles is evaluated with total cost of nationwide LDV fatalities divided by the annual number of LDV miles. This cost is on average $.09 per mile.
e The cost of ULD miles is evaluated with total cost of nationwide ULD fatalities divided by the number of ULD miles per household per day (0.59), as taken from the NHTS
data, multiplied by 365 days and the number of households in the census. This cost is on average $3.36 per mile.
f Assumes the cost per accident is $10,633 (Blincoe et al., 2014).
g Assumes the value of a statistical injury of $141,677. Calculated based on the observed frequency of 5 severity levels recognized by the DOT (Blincoe et al., 2014).
Table 6: 2090 Fatality Changes, Comparison of Correction Methods
(1)
Additive
Predictedb
(2)
Multiplicative
Predictedc
(3)
Additive
Observedd
(4)
Multiplicative
Observedd
(5)
468
464
457
478
-1196
[387, 547]
[368, 552]
[370, 536]
[396, 555]
[-1,529, -857]
-27
-297
-507
-433
-12
[-34, -19]
[-375, -234]
[-727, -318]
[-615, -271]
[-19, -4]
ECDFa
Change in 2090 due to
Temperature
Change in 2090 due to
Rainfall
Change in 2090 due to
Snowfall
Net Change in 2090
-45
406
307
59
-28
[-57, -33]
397
[310, 476]
[122, 687]
573
[255, 862]
[-99, 752]
253
[-232, 587]
[-24, 150]
103
[-112, 308]
[-45, -11]
-1235
[-1,567, -891]
Notes: All simulations predict the change in fatalities based on weather changes using the 2090 decade of the CCSM4
RCP6.0 scenario. Values given in brackets indicate the 95% confidence interval. See section for further details of various
methodologies.
a Adjusts current weather to 2090-2099 weather using our nonparametric quantile-mapping detailed in section 6.2.
b Adjusts CCSM4 2090-2099 with an additive correction based on the mean difference between observed 2006-2009 data
and CCSM4 2006-2009 predictions.
c Adjusts CCSM4 2090 with a multiplicative correction based on the mean difference between observed 2006-2009 data and
CCSM 2006-2009 predictions.
d Adjusts 2006-2009 mean observed weather with an additive factor base on the change between CCSM4’s 2006-2009 and
2090-2099 predictions.
e Adjusts 2006-2009 mean observed weather with a multiplicative factor base on the change between CCSM4’s 2006-2009
and 2090-2099 predictions.
38
CCSM 4 2090-2099
Observed Weather
Predicted Additive
Observed Additive
40
70
Smoothed Density
.02
.03
.04
Smoothed Density
.02
.03
.04
.05
CCSM 4 2006-2009
.05
Observed Weather
41.0° F
.01
.01
40.0° F
0
0
48.0° F
0
10
20
30
40
50
60
70
80
90
100
0
10
20
30
50
60
80
90
100
Temperature
Panel (c): Inverse ECDF: Quantile-based Method
Panel (d): Quantile-based Correction Methods
.06
Temperature
100
90
CCSM 4 2006-2009
CCSM 4 2090-2099
QM
Observed Weather
Quantile-based Method
.05
Observed Weather
80
Smoothed Density
.02
.04
.03
70
60
50
38
33
28
23
.01
Temperature
Panel (b): Traditional Correction Methods
.06
.06
Panel (a): PDF of Hypothetical Temperature Profile
10
0
0
0
.2
.4
.6
.8
1
0
10
20
30
40
50
60
70
80
90
100
Temperature
Panel (e): Inverse ECDF: Wet Bias Uncorrected
Panel (f): Inverse ECDF: Wet Bias Correction
.8
.8
Probability
CCSM 4 2090-2099
QM
Observed Weather
CCSM 4 2006-2009
CCSM 4 2090-2099
QM
.2
0
0
.2
Rainfall in CM
.4
Rainfall in CM
.4
.6
CCSM 4 2006-2009
.6
Observed Weather
.1
.15 0.1650.175
.2
.25
.3
.1
Probability
.15 0.1650.175
.2
Probability
Figure 1: Demonstration of Error Correction Methods
39
.25
.3
(a) Average Annual Predicted Change in Fatalities per 100,000 People
(b) Average Annual Predicted Change in Injuries per 100,000 People
(c) Average Annual Change in PDO Accidents per 100,000 People
Figure 2: County-Level Predictions, 2090-2099
40
Appendix for Weather, Traffic Accidents, and
Exposure to Climate Change
Benjamin Leard and Kevin Roth∗
April 8, 2016
∗
Leard: Resources for the Future, 1616 P St. NW, Washington, D.C. 20036, e-mail: leard@rff.org. Roth:
University of California, Irvine 3297 Social Science Plaza, Irvine, CA 92697, e-mail: kroth1@uci.edu. The
authors are grateful to seminar participants at UC-Irvine for helpful comments.
1
A
Proof of Equation (8)
In this section we present a proof of the welfare formula (8). Partially differentiating the
indirect utility function (1) with respect to I yields
∂V
= λ.
∂I
(A.1)
Partially differentiating the indirect utility function (1) with respect to W yields
∂U ∂am ∂U ∂ab
∂V
=
+
.
∂W
∂a ∂W
∂a ∂W
(A.2)
Substituting (A.1) and (A.2) into Equation (7) yields
∂U
∂U
dI ∗
∂am
∂ab
= − ∂a
− ∂a
.
dW
λ ∂W
λ ∂W
(A.3)
Totally differentiating am (·) and ab (·) with respect to W and rearranging terms yields
dam ∂am ∂m
∂am
=
−
,
∂W
dW
∂m ∂W
dab
∂ab ∂b
∂ab
=
−
.
∂W
dW
∂b ∂W
Substituting (A.4) and (A.5) into (A.3) and rearranging terms gives
∂U
∂U
∂U
∂U
dI ∗
dam
dab
∂am ∂m
∂ab ∂b
= − ∂a
− ∂a
+ ∂a
+ ∂a
.
dW
λ dW
λ dW
λ ∂m ∂W
λ ∂b ∂W
(A.4)
(A.5)
(A.6)
Defining semi-elasticities for miles traveled by automobile and by ULD modes with respect
∂m
∂b
to weather as εm = m1 ∂W
and εb = 1b ∂W
, respectively, and substituting these terms into
(A.6) yields Equation (8).
B
NHTS Data Description
Our travel demand data come from the 1990, 1995, 2001, and 2009 waves of the National
Household Travel Survey (NHTS). We provide an overview of these data in the main paper
and further details on the data here. Although the surveys follow a similar sampling strategy,
there are subtle differences. One difference is the sample size. In total, there are 22,317,
42,033, 69,817, and 150,147 usable household observations in the 1990, 1995, 2001, and 2009
surveys, respectively, for a total of 284,314 households.1 There is also some variation in the
months that the surveys were administered: the 1990 survey lasted from March 1990 until
March 1991; the 1995 survey lasted from May 1995 until July 1996; the 2001 survey lasted
1
Occasionally these samples are supplemented by add-on surveys requested by state and metropolitan
transportation planning organizations. In the 2009 survey, the add-on partners with the largest samples
included California (18,000 household target), Texas (14,342 household target), New York (14,000 household
target), and Florida (14,000 household target).
2
from March 2001 through May 2002; and the 2009 survey lasted from March 2008 through
May 2009. In each survey, households were randomly assigned a travel date. The NHTS
balanced the variation in travel by day of the week by assigning travel days for one-seventh
of the sample telephone numbers to each day of the week.2 Seventy-one percent and seventytwo percent of individuals who completed a survey filled out a travel diary in the 2001 and
2009 NHTS, respectively.
The original restricted day travel data files include 149,546, 409,025, 642,292, and
1,167,321 trips in the 1990, 1995, 2001, and 2009 surveys, respectively, for a total of 2,368,184
trips. We took several measures to clean the travel diary and household data. We dropped
trips with missing travel distance, start time, or end time. Some trips showed unrealistically
high distances. We restricted all distances to be at most the distance implied by reported
travel time moving at a speed of 100 mph.
To create household measures of daily travel decisions, we aggregated the trip level data
to the household level. Because the travel data are reported at the respondent level, a trip
taken by two household members is reported twice, once per individual that was involved
in the trip. To avoid double-counting these trips, we included only one trip per household
with the same transportation mode, vehicle identification number, trip start time and miles
traveled.3 This yielded 1,909,488 unique household trips.4 We then summed the number of
trips, the total number of miles, and averaged the miles per trip for each household. We
separate trips into three groups: light duty (e.g., automobile) trips, ULD trips, and public
transit trips. For households that reported no trips of a particular type, we assign them
zero total trips and miles traveled. From the initial set of 284,314 households, we drop 447
households with missing county or date information and 10 households that we could not
match to weather data, yielding 283,857 household by travel day observations.5
C
FARS Data Description
Our alternative dataset for traffic fatalities comes from the Fatal Accidents Reporting System
(FARS), a nationwide census administered by the National Highway Traffic and Safety
Administration (NHTSA). It contains the universe of police reported accidents involving
traffic fatalities from 1975 to 2013 and is updated annually.6
The data are collected and recorded by representatives of each state plus the District of
Columbia and Puerto Rico. While FARS observations include detail about fatal accidents,
2
When a household was successfully recruited to the survey, the computer-assisted telephone interviewing
system assigned the household’s travel date on the selected day of the week 10 to 14 days in the future.
3
About 10 percent of automobiles have a missing identification number. We assigned a new identification
number to these vehicles based on observing that the trips taken in vehicles with missing identification
numbers appeared to be non-overlapping trips with different miles traveled among all trips taken by a given
household.
4
This is 129,708, 324,006, 492,444, and 963,330 unique household trips in the 1990, 1995, 2001, and 2009
surveys, respectively.
5
The households that we could not match all were located in Alaska, where a weather station was not
located within 200 km of the households’ county centroid.
6
FARS was created to help NHTSA and other federal agencies evaluate the effectiveness of motor vehicle
safety policies.
3
there are no records for non-fatal accidents. Relevant for our requirements, the date and
county of each fatal accident are recorded.
The FARS data requires little cleaning to convert the raw data to the final sample
that we use for estimation. We drop a small number of observations that have missing
or unidentifiable day/month/year or county information. Appendix Table H4 demonstrates
that we use almost the entire original sample for estimation and that there are no years in
particular where we drop a substantial number of fatal accident observations. We match
fatal accidents to our weather data using county and day/month/year variables.
D
Compositional Changes
In this section we present a model that allows us to estimate how weather changes the
relative composition of the types of accidents that occur. Taking the example of accidents
that are fatal, if fatalities increase under particular weather conditions, our count models in
section 5 cannot tell if this increase is because total accidents increase while the fatalities
per accident remain constant, or if accidents remain constant but become more deadly. We
examine the possibility that weather changes the likelihood that an accident will be fatal or
that a fatality will involve a particular set of circumstances using a linear probability model.
D.1
Estimation Methodology for the Impact of Weather on
Accident Composition
First we estimate the conditional expectation of a fatality in accident i as a function of
weather and the covariates.
E[f atalityi |xd,c , accidenti ] =
8
X
5
X
j
αj Td,c
+
j=1
8
X
j
j
α−1
Td−1,c
+
j=1
5
X
j
β j Rd,c
+
j=1
j
j
β−1
Rd−1,c
+
j=1
5
X
5
X
j
γ j Sd,c
+
j=1
j
j
γ−1
Sd−1,c
(D.1)
+ θscym + z0d,c δ
j=1
where f atalityi is an indicator for accident i involving a fatality.
We also estimate the conditional expectation that fatality i will involve an individual
traveling by a ULD mode, an intoxicated or young driver, or a single vehicle crash as a
function of weather and the covariates
E[attributei |xd,c , f atalityi ] =
8
X
α
j
j
Td,c
+
j=1
8
X
j=1
j
j
α−1
Td−1,c
+
5
X
j
j
Rd−1,c
+
β−1
5
X
j=1
5
X
β
j
j
Rd,c
+
5
X
j
γ j Sd,c
+
j=1
(D.2)
j
j
+ θscym + z0d,c δ
γ−1
Sd−1,c
j=1
j=1
where attributei is an indicator for fatality i involving a particular type of crash.
For both models, all covariates, including fixed effects, are identical to that of Equation
(10). Because an observation is a particular accident or fatality as opposed to a count of
4
incidents, the observations are no longer aggregated by county and day but weather variables
are matched at the county-day level. For these regressions we cluster standard errors at the
year level.
D.2
Estimation Results for the Impact of Weather on Accident
Composition
Table H5 presents the estimates of the impact of weather on the composition of accidents
and fatalities. Column (1) estimates Equation (D.1), examining the probability that an
accident is fatal as a function of temperature and precipitation. This regression helps to
distinguish the possibility that fatalities increase because accidents are more severe from the
possibility that they are equally severe, but accidents are more frequent. The negative and
statistically significant coefficients on cold temperatures and both precipitation measures
indicate that if an accident occurs, it is less likely to be deadly. This result is important
because it is evidence that drivers behaviorally adjust to changes in accident risk to reduce
fatality risk. Given the results in the main paper for fatalities in Table 3, column 1, it
appears that when there is snowfall, accidents are less likely to be deadly, but the frequency
increases enough to generate more total fatalities. One remaining puzzle is why drivers are
successful in reducing the probability of a fatality for precipitation and cold but not for heat.
It is possible that accidents from cold and precipitation involve different channels from heat,
with cold and precipitation accidents originating from an inability to control the vehicle,
while heat involves a cognitive component, but we suspect the most likely explanation is
that heat increases LDV-ULD interactions and when an LDV and a pedestrian or ultra-light
duty vehicle collide, there may be no behavioral adjustment that can reduce the probability
of a fatality.7
Columns (2) through (6) estimate Equation (D.2) using only fatal crashes. These
regressions examine the probability that a participant in a fatal accident changes with the
weather. The dependent variable in column (2) is an indicator for fatal crashes involving
a pedestrian, bicycle, or motorcycle. This regression indicates that these ULD modes are
increasingly involved in fatal accidents as temperature increases. The maximum of point
estimates across temperature bins indicates that they are 3.6% more likely to be involved
in a fatal crash on a day with mean temperature of 70 to 80◦ F than a day of 50 to 60◦ .
Column (3) considers the possibility that changes in drunk driving may explain our result,
if, for example, people used alcohol as a coping mechanism for hot or cold weather. We
find no evidence that this explains any of the temperature related fatalities.8 Column (4)
tests for changes in the number of accidents involving a driver less than 21 years old. The
concern is that young, inexperienced drivers may change travel patterns around weather,
or that our fixed effects are not properly controlling for temporal patterns such as school
attendance. We see no evidence that young drivers substantially contribute to our findings.
The results in column (5) illustrate that changes in the frequency of male drivers, who are
7
We provide further robustness tests to explain the effect of temperature on fatalities in Appendix
Table H11. In this table we report coefficient estimates from models where we omit accidents involving
intoxication and young drivers. The results for these specifications are close to our benchmark specification.
8
There is some evidence that accidents involving alcohol decrease with snowfall. A potential explanation
is that drivers avoid intoxication when they anticipate that driving will be difficult.
5
known to be at higher risk of accidents and possibly more aggressive drivers, do not appear
to explain our result. Column (6) examines the possibility that our results are due to single
vehicle crashes, which may indicate that weather affects a driver’s control of a vehicle. The
results here indicate that this dynamic may occur around the freezing point, where we see
some statistically significant effects between 20 and 40◦ F. At these temperatures melting and
refreezing may cause unexpected ice, resulting in vehicles sliding off the road. We do not see
any evidence that such explanations extend beyond this narrow range.
In summary, Table H5 presents evidence that exposure to pedestrians, bicycles, and
motorcycles is one of the key mechanisms for the temperature effect. To the extent that
a psychological mechanism exists, it must act equally across age groups, genders, and the
number of involved parties.
E
Examining the Evidence for Adaptation
We return to our count model to examine the capacity for adaptation. We present adaptation
results in Table H10. First we examine the possibility that technological change has weakened
this relationship over time. Next we consider the possibility that there may be private or
public adaptation to the local climate.
There have been many safety innovations over the 20 year time period encompassed
by our data including dual front airbags and anti-lock brakes. To the extent that this
technology would reduce the effects of weather on fatalities, we might see evidence of a
reduced gradient in 2000-2009 compared with 1990-1999. Columns (1) and (2) show that no
such reduction has occurred for temperature. The number of states reporting to the state
data system has grown over time and consequently the precision of our estimates is greater in
the later time period, but if anything the relationship between temperature and fatalities has
grown stronger.9 Increased automobile air conditioning also seems to have minimally affected
this relationship. This may not be entirely surprising as ULD exposure is not affected by
vehicle air conditioning. For rainfall there may be some support that these technologies have
improved safety, although most changes are not statistically different between the two time
periods, and the same improvement cannot be found for snowfall.
Columns (3) and (4) examine the possibility that drivers or cities may be adapted to local
conditions. Drivers in warmer locations may know how to avoid heat or be more attentive
to features such as air conditioning in vehicles. Cities might adapt through policing, bike
lanes, or insurance rates that mitigate these risks. Alternatively, residents in locations with
frequent hot weather may not avoid hot days if they suspect the following day is unlikely to
see improved conditions and a warm climate may facilitate choosing a bike or motorcycle over
a light duty vehicle. Columns (3) and (4) show the results estimated from the coldest quartile
of counties and the hottest quartile of counties. We do not find evidence that these two sets
of counties have statistically different responses to temperature. If anything, the hottest
quartile of counties has a larger increase in fatalities on hot days than the coldest counties.
One potential explanation for this lack of evidence for adaptation is that a significant share
9
We present robustness checks for this result in Appendix Table H11 by estimating models with early
time period data (1990-1995) and later time period data (2005-2010). Our results presented in Table H10
are robust to these alternative specifications.
6
of accident costs is external (Parry, Walls and Harrington, 2007), suggesting that agents will
not privately choose the optimal level of adaptation. Together these results suggest that
adaptation would need to take the form of either migration or dramatically new technology,
such as driverless cars, that some hope will remove human error.
F
Comparison of Quantile-Mapping Method with
Multiplicative Methods
Figure H.2 demonstrates a change in temperature profile that cannot be captured by
multiplicative methods. Unlike the comparable figure in the text (Figure 1), temperatures
in this location increase by a uniform 10◦ F.10
Panel (a) shows that the baseline observed weather has a mean of 41◦ F, while the baseline
simulated CCSM4 data has a mean of 40◦ F. With global warming the entire distribution
would shift up by 10◦ F such that the new mean is 50◦ F. Crucially, the observed data have
a much smaller variance than the simulated data. Panel (b) first illustrates the distribution
of outcomes generated by applying a multiplicative correction factor to the predicted 2090
data using Equation (16) from the main text. Because the observed and predicted baseline
data have very similar means, the correction changes the CCSM4 2090 data little under the
predicted multiplicative factor. The second correction is generated by changing the baseline
data with a multiplicative factor based on the change in CCSM4 between 2010 and 2090
using Equation (21) from the main text. Applying a multiplicative change to the observed
baseline data increases all temperatures but to a greater degree for warm days than cold
days. Mechanically, warmer days will always warm by more than 10◦ F, while cold days will
warm by less.
Panels (c) and (d) show the correction generated by the quantile-based method. In
Panel (c) the figure shows that all points in the distribution increase by 10◦ F between
the CCSM4 predictions in 2010 and 2090. This correction is then applied in Panel (d)
uniformly translating the observed data up by 10◦ F. This illustrates the flexibility of the
quantile-mapping method. Because the correction is non-parametric, it can capture both
multiplicative and additive changes to the distribution.
G
Modified Quantile-Mapping Correction Method
A slight variant of the quantile mapping correction method involves changing how one defines
the probability p. In the original method, we define the probability p by
p = ΦW,τ,c (xd,c ),
(G.1)
which is the cumulative probability of achieving the observed weather outcome xd,c in the
observed weather data. Alternatively, we can define p as
p = ΦW,τ,c (xd,c ),
10
(G.2)
Because the figure in the main text was generated with a multiplicative increase, it could be captured
with a multiplicative method; however, as noted in the text, multiplicative methods are generally not applied
to temperature data.
7
which is the cumulative probability of achieving the observed weather outcome xd,c in the
CCSM4 baseline prediction. This requires creating an ECDF for each weather variable,
county, and month in the CCSM4 baseline data. The remaining steps to compute the errorcorrected prediction are identical to those described in the text. Results using this method
for fatalities are given in Table H19, column (6), and generally produce similar but slightly
larger numbers of lives lost than with the primary method used in the main text.
8
H
Further Tables and Figures
9
Table H1: Count of Observations by Bin
Panel A. State Data
Total Observations
Rainfall
0 cm
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0 cm
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Temperature
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
50-60◦ F
60-70◦ F
70-80◦ F
>80◦ F
Northeast
644,252
Midwest
3,325,021
South
1,664,548
West
1,065,114
All Regions
6,698,935
182,395
165,783
175,670
95,852
21,290
3,262
1,419,930
727,732
681,449
377,398
99,396
19,116
698,950
301,974
340,543
222,392
77,150
23,539
587,227
215,994
175,820
68,579
14,151
3,343
2,888,502
1,411,483
1,373,482
764,221
211,987
49,260
480,996
38,621
47,999
36,781
20,054
19,801
2,793,250
143,488
157,499
110,686
58,802
61,296
1,625,472
15,642
13,489
6,000
2,065
1,880
893,746
33,393
59,819
42,521
19,853
15,782
5,793,464
231,144
278,806
195,988
100,774
98,759
32,055
69,249
105,173
106,243
104,301
128,689
93,824
4,718
223,391
315,508
488,899
490,963
493,730
598,647
586,654
127,229
1,345
19,864
105,654
229,797
284,596
337,611
463,170
222,511
37,907
62,780
142,433
219,773
221,618
215,618
142,024
22,961
294,698
467,401
842,159
1,046,776
1,104,245
1,280,565
1,285,672
377,419
Northeast
180,151
Midwest
22,546
South
48,505
West
31,924
All Regions
283,126
77,081
38,057
37,613
20,911
5,128
1,361
9,039
4,933
4,930
2,873
652
119
20,529
9,747
9,666
5,935
1,907
721
24,240
2,857
2,495
1,769
458
105
130,889
55,594
54,704
31,488
8,145
2,306
153,545
7,164
7,785
5,228
2,955
3,474
17,710
1,371
1,406
1,059
507
493
47,212
601
447
176
40
29
30,342
305
584
391
169
133
248,809
9,441
10,222
6,854
3,671
4,129
6,711
12,479
22,925
26,887
29,714
35,418
32,521
13,496
2,162
2,530
3,699
3,580
3,260
3,672
3,241
402
57
639
2,770
5,475
8,042
10,979
13,514
7,029
119
205
893
4,680
9,428
8,435
6,994
1,170
9,049
15,853
30,287
40,622
50,444
58,504
56,270
22,097
Panel B. NHTS Data
Total Observations
Rainfall
0 cm
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0 cm
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Temperature
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
50-60◦ F
60-70◦ F
70-80◦ F
>80◦ F
Notes: Each observation represents a day-month-year in a given region. In our Accidents (upper
panel) and NHTS (lower panel) data, we have 6,698,935 and 283,126 day-month-year observations,
respectively. In our State Data, states in the Northeast include New York and Pennsylvania; states
in the Midwest include Iowa, Illinois, Kansas, Michigan, Minnesota, Missouri, Nebraska, and Ohio;
states in the South include Arkansas, Florida, Georgia, North Carolina, and South Carolina; states in
the West include California, Montana, New Mexico, Washington, and Wyoming. In our NHTS Data,
states in the Northeast include Connecticut, Massachusetts, Maine, New Hampshire, New Jersey,
New York, Pennsylvania, Rhode Island, and Vermont; states in the Midwest include Iowa, Illinois,
Indiana, Kansas, Michigan, Minnesota, Missouri, North Dakota, Nebraska, Ohio, South Dakota,
and Wisconsin; states in the South include Alabama, Arkansas, District of Columbia, Delaware,
Florida, Georgia, Kentucky, Louisiana, Maryland, Mississippi, North Carolina, Oklahoma, South
Carolina, Tennessee, Texas, Virginia, and West Virginia; states in the West include Alaska, Arizona,
California, Colorado, Hawaii, Idaho, Montana, New Mexico, Nevada, Oregon, Utah, Washington,
and Wyoming.
10
Table H2:
Statistics
State
Extended Accident Summary
CountyDaily
Day
Accidents
Observations per 100,000
Daily
Fatalities
per 100,000
Northeast
New York
Pennsylvania
203,794
440,458
4.67
3.05
0.03
0.04
Midwest
Iowa
Illinois
Kansas
Michigan
Minnesota
Missouri
Nebraska
Ohio
180,774
558,858
575,295
449,278
381,321
588,110
237,801
353,584
4.94
7.47
8.05
12.81
4.19
6.34
7.20
8.18
0.05
0.05
0.08
0.05
0.05
0.07
0.08
0.05
South
Arkansas
Florida
Georgia
North Carolina
South Carolina
356,100
337,524
404,006
365,300
201,618
4.79
2.87
20.57
6.80
5.77
0.07
0.06
0.12
0.05
0.07
West
California
Montana
New Mexico
Washington
Wyoming
286,384
286,384
241,065
170,937
80,344
4.22
6.38
6.30
4.71
7.58
0.06
0.11
0.11
0.04
0.09
Notes: States reported in this table are those that are
contained in our accidents State Data. In the column titled
County-Day Observations, we report the total number of
county-day-month-year observations appearing in each state.
Note that these observations are not conditional on having at
least one accident; an observation is recorded as having no
accidents if there were no reported accidents in the county on a
given day. We compute Daily Accidents per 100,000 by taking
the daily average of the number of accidents in a county across
all years in our sample and dividing by the 2010 population size
of the county and then averaging these rates over a given state.
Our computed accident rate includes PDO accidents, accidents
involving an injury, and accidents involving a fatality.
11
Table H3: Extended Weather Summary Statistics
State
Daily Temperature (◦ F)
5th
50th
95th
Quantile Quantile Quantile
Daily Rainfall (in cm)
75th
95th
99th
Quantile Quantile Quantile
Daily Snowfall (in cm)
75th
95th
99th
Quantile Quantile Quantile
Northeast
New York
Pennsylvania
17.0
21.7
49.1
51.6
74.4
75.7
0.36
0.34
1.34
1.31
2.53
2.44
0.06
0.00
2.61
1.51
7.43
5.75
Midwest
Iowa
Illinois
Kansas
Michigan
Minnesota
Missouri
Nebraska
Ohio
13.4
20.2
23.4
14.5
4.8
23.6
16.6
20.4
51.1
54.8
56.4
47.4
46.2
57.2
51.5
53.1
77.7
78.8
82.4
73.8
74.5
80.8
79.2
76.3
0.18
0.29
0.14
0.26
0.18
0.26
0.12
0.34
1.21
1.39
1.18
1.07
1.03
1.54
0.96
1.27
2.50
2.70
2.61
1.99
2.10
3.09
2.17
2.28
0.00
0.00
0.00
0.01
0.00
0.00
0.00
0.00
0.65
0.51
0.30
2.62
1.71
0.20
0.64
1.05
4.86
3.57
3.24
7.17
6.05
2.64
4.80
3.94
South
Arkansas
Florida
Georgia
North Carolina
South Carolina
33.5
49.1
38.7
34.7
38.8
63.1
73.0
65.0
61.0
64.1
83.8
83.3
81.9
80.4
82.1
0.29
0.39
0.34
0.32
0.31
1.82
1.74
1.65
1.63
1.53
3.66
3.54
3.43
3.14
3.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.00
0.42
0.00
0.08
0.69
0.12
West
California
Montana
New Mexico
Washington
Wyoming
41.1
12.3
30.1
29.6
15.8
59.5
45.0
56.3
49.5
45.7
79.1
72.6
79.0
70.8
73.6
0.04
0.09
0.07
0.29
0.07
1.10
0.49
0.52
1.14
0.43
2.71
1.17
1.24
2.36
1.02
0.00
0.00
0.00
0.00
0.02
0.31
1.59
0.51
0.86
1.78
2.29
4.79
3.49
3.34
5.14
Notes: The table displays temperature, rainfall, and snowfall for the listed quartile by state in our observed
weather station data from 2000 to 2009. These statistics are derived from observed weather data from the
National Climatic Data Center’s Global Historical Climatology Network-daily.
12
Table H4: FARS Sample, by Calendar Year
Year
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
Total
Original
Sample
Observation
Count
44,522
45,522
47,877
50,330
51,090
51,089
49,282
43,945
42,587
44,250
43,823
46,086
46,388
47,087
45,582
44,597
41,507
39,250
40,146
40,711
41,816
42,065
42,010
41,498
41,716
41,944
42,193
43,004
42,881
42,834
43,510
42,708
41,259
37,423
33,883
32,999
32,479
33,782
32,719
1,658,394
Observations
Dropped
Remaining
Observations
40
3
4
3
10
7
185
15
9
15
13
9
12
10
9
13
21
8
12
17
13
22
24
17
5
5
21
12
21
18
14
0
0
1
1
0
3
1
2
595
44,482
45,519
47,873
50,327
51,080
51,082
49,097
43,930
42,578
44,235
43,810
46,077
46,376
47,077
45,573
44,584
41,486
39,242
40,134
40,694
41,803
42,043
41,986
41,481
41,711
41,939
42,172
42,992
42,860
42,816
43,496
42,708
41,259
37,422
33,882
32,999
32,476
33,781
32,717
1,657,799
Percent of
Original
Sample
Retained
99.91
99.99
99.99
99.99
99.98
99.99
99.62
99.97
99.98
99.97
99.97
99.98
99.97
99.98
99.98
99.97
99.95
99.98
99.97
99.96
99.97
99.95
99.94
99.96
99.99
99.99
99.95
99.97
99.95
99.96
99.97
100.00
100.00
100.00
100.00
100.00
99.99
100.00
99.99
99.96
Notes: The table displays counts of fatalities and dropped observations for FARS
data (see Appendix C) used in the national-level projections and auxiliary regressions
in Table H8.
13
Table H5: Linear Probability Model, Compositional Changes
Given an
Accident
Given a Fatality
(1)
Ultralight
Duty
(2)
Intoxicated
Driver
(3)
Young
Driver
(4)
Male
Driver
(5)
Single
Vehicle
(6)
-0.0010***
(0.0002)
-0.0007***
(0.0001)
-0.0004***
(0.0001)
-0.0002**
(0.0001)
0.0003***
(0.0001)
0.0004***
(0.0001)
0.0006***
(0.0001)
-0.119***
(0.015)
-0.114***
(0.009)
-0.085***
(0.007)
-0.045***
(0.008)
0.023***
(0.005)
0.036***
(0.005)
0.024***
(0.008)
0.000
(0.017)
0.017
(0.012)
0.010
(0.011)
0.006
(0.009)
0.007
(0.005)
0.002
(0.008)
-0.005
(0.009)
0.037
(0.013)
0.017
(0.016)
0.016
(0.010)
0.015
(0.005)
-0.002
(0.005)
-0.006
(0.007)
-0.015
(0.009)
0.019**
(0.007)
0.002
(0.009)
0.004
(0.007)
0.007
(0.005)
0.000
(0.003)
0.002
(0.004)
0.000
(0.008)
0.019
(0.015)
0.034**
(0.014)
0.027***
(0.007)
0.009
(0.007)
0.000
(0.007)
0.007
(0.007)
0.005
(0.012)
0.0003***
(0.0000)
-0.0006***
(0.0000)
-0.0009***
(0.0001)
-0.0013***
(0.0001)
-0.0013***
(0.0002)
-0.023***
(0.005)
-0.039***
(0.005)
-0.053***
(0.006)
-0.074***
(0.011)
-0.081***
(0.015)
0.003
(0.006)
0.004
(0.005)
-0.002
(0.007)
-0.017
(0.010)
0.009
(0.028)
0.003
(0.003)
0.010***
(0.003)
0.011**
(0.005)
0.006
(0.007)
0.008
(0.015)
-0.001
(0.004)
0.002
(0.004)
-0.008
(0.006)
-0.004
(0.006)
0.003
(0.018)
-0.006
(0.005)
-0.007
(0.006)
-0.003
(0.007)
-0.017*
(0.010)
0.015
(0.023)
0.0001
(0.0001)
-0.0001
(0.0001)
-0.0005***
(0.0001)
-0.0008***
(0.0001)
-0.0012***
(0.0001)
-0.011
(0.012)
-0.001
(0.012)
0.003
(0.010)
0.019
(0.016)
0.040***
(0.012)
0.007
(0.014)
-0.009
(0.015)
-0.029***
(0.016)
-0.087***
(0.023)
-0.113***
(0.028)
0.003
(0.011)
-0.008
(0.013)
-0.005
(0.011)
0.000
(0.013)
-0.041**
(0.018)
-0.003
(0.010)
-0.008
(0.011)
-0.004
(0.012)
0.007
(0.014)
0.033*
(0.017)
0.009
(0.015)
0.015
(0.014)
-0.004
(0.015)
-0.092***
(0.016)
-0.085***
(0.023)
Fixed Effects
County-year-montha
Y
Y
First snowfallb
Num. Obs.
46,570,970
Y
Y
222,613
Y
Y
222,613
Y
Y
222,613
Y
Y
222,613
Y
Y
222,613
Fatality
Current + Lag
Mean Temp.
<20 ◦ F
20-30 ◦ F
30-40 ◦ F
40-50 ◦ F
60-70 ◦ F
70-80 ◦ F
>80 ◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Notes: The estimates are from a linear probability regression of the listed indicator on weather and other
covariates. Dependent variable is a 1 where any participant had the characteristic listed and a 0 otherwise.
Column 1 is the probability that a fatality occurred in any party given that an accident occurred. Columns
2 through 6 limit the sample to fatal collisions. Standard errors, in parentheses, are clustered by year. *
significant at 10% level, ** significant at 5% level, *** significant at 1% level
a Fixed effects for county by year by month.
b Indicator for first snowfall after 1 month without snow.
14
Table H6:
Estimates
Poisson Regression of Accidents on Weather Variables—Full
PDO Accidents
Contemporaneous
Temperature
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Lagged
Temperature
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
First Snowfall
Fixed Effects
State-county-year-month
Num. Obs.
Injuries
Fatalities
0.027
0.014
-0.033***
-0.026***
0.010**
0.010*
0.017**
(0.028)
(0.019)
(0.009)
(0.005)
(0.004)
(0.006)
(0.007)
-0.046
-0.041**
-0.064***
-0.045***
0.025***
0.030***
0.027***
(0.029)
(0.018)
(0.008)
(0.005)
(0.004)
(0.004)
(0.007)
0.028***
0.100***
0.162***
0.216***
0.271***
(0.004)
(0.006)
(0.008)
(0.012)
(0.017)
0.020***
0.088***
0.144***
0.190***
0.230***
(0.005) -0.015** (0.007)
0.007
(0.006)
(0.006) -0.027*** (0.009) 0.017** (0.007)
(0.009) -0.028* (0.015) 0.029*** (0.010)
(0.011) -0.043** (0.017) 0.028** (0.012)
(0.017)
-0.022 (0.029) 0.059** (0.024)
0.023***
0.111***
0.265***
0.402***
0.483***
(0.004)
(0.009)
(0.008)
(0.010)
(0.013)
0.011**
0.086***
0.210***
0.316***
0.325***
(0.005)
(0.006)
(0.012)
(0.013)
(0.017)
0.035***
0.081***
0.195***
0.253***
0.225***
(0.010)
(0.011)
(0.014)
(0.021)
(0.027)
0.070***
0.014
0.002
0.003
-0.015***
-0.021***
-0.028***
(0.017) 0.046*** (0.018)
(0.011)
0.000
(0.010)
(0.006)
-0.006 (0.005)
(0.003)
0.002
(0.004)
(0.003)
-0.005 (0.003)
(0.006)
-0.008 (0.006)
(0.007) -0.011* (0.006)
0.033
0.000
-0.004
-0.006
0.018**
0.008
0.026
(0.031)
-0.014 (0.029)
(0.023)
-0.023 (0.021)
(0.015)
-0.022 (0.014)
(0.014)
-0.015 (0.011)
(0.007) 0.019*** (0.007)
(0.011)
0.005
(0.010)
(0.016)
0.006
(0.016)
-0.005**
-0.029***
-0.056***
-0.069***
-0.083***
(0.002)
(0.003)
(0.003)
(0.006)
(0.007)
-0.001
-0.012***
-0.035***
-0.048***
-0.050***
(0.005)
-0.004 (0.004)
-0.007
(0.005) -0.008** (0.003)
-0.007
(0.007) -0.021*** (0.005) -0.065***
(0.011) -0.035*** (0.012) -0.099***
(0.013) -0.066*** (0.014) -0.185***
(0.015)
-0.003 (0.015)
(0.014)
-0.020 (0.016)
(0.020) -0.055*** (0.020)
(0.020) -0.108*** (0.020)
(0.030) -0.177*** (0.029)
(0.049)
(0.052)
0.022
Y
6,665,499
-0.006***
-0.030***
-0.056***
-0.071***
-0.086***
0.010
Y
5,067,561
-0.175***
-0.117***
-0.085***
-0.058***
0.037***
0.061***
0.069***
(0.032)
(0.021)
(0.014)
(0.009)
(0.009)
(0.013)
(0.024)
Fatalities, Omit ULD
-0.043
0.011
0.013
0.001
0.007
0.018
0.040*
0.043***
0.065***
0.150***
0.174***
0.119***
(0.029)
(0.019)
(0.011)
(0.009)
(0.008)
(0.013)
(0.024)
(0.009)
(0.012)
(0.017)
(0.017)
(0.027)
(0.002) -0.014** (0.006) -0.012* (0.007)
(0.003) -0.022*** (0.005) -0.024*** (0.005)
(0.004) -0.030*** (0.009) -0.032*** (0.010)
(0.006) -0.043*** (0.012) -0.055*** (0.014)
(0.008)
-0.027 (0.026) -0.048* (0.027)
(0.038)
0.093*
Y
3,117,797
0.077*
(0.046)
Y
2,860,068
Notes: The estimates are from a Poisson regression of the daily count of PDO accidents, injuries, or
fatalities by county on weather and other covariates as indicated. The reported coefficient estimates include
both contemporaneous and lagged variables for each weather category. The final column reports estimates
of our fatalities model with omitting fatalities involving ultra-light duty fatal accidents. Because countymonth groups with zero incidents are automatically excluded from the regression, regressions for injuries
and fatalities have fewer observations. Standard errors, in parentheses, are block bootstrapped by year. *
significant at 10% level, ** significant at 5% level, *** significant at 1% level
15
Table H7: Poisson Regression of Trip Counts on
Weather Variables—Full Estimates
Contemporaneous
Temperature
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Lagged
Temperature
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
First Snowfall
Fixed Effects
State-county-year-month
Num. Obs.
LDV Trip Count
ULD Trip Count
-0.039*
-0.015
-0.016
-0.011
-0.007
-0.015
-0.044***
(0.022)
(0.015)
(0.012)
(0.007)
(0.008)
(0.012)
(0.015)
-0.333***
-0.206***
-0.116***
-0.055***
0.041**
0.010
0.033
(0.052)
(0.040)
(0.031)
(0.018)
(0.018)
(0.029)
(0.043)
-0.008
-0.012**
-0.017***
-0.054***
-0.038
(0.005)
(0.006)
(0.006)
(0.014)
(0.024)
-0.034**
-0.091***
-0.129***
-0.253***
-0.168***
(0.015)
(0.019)
(0.026)
(0.031)
(0.041)
0.002
-0.005
-0.016
-0.076***
-0.154***
(0.011)
0.023
(0.035)
(0.015) -0.104*** (0.037)
(0.018) -0.082** (0.037)
(0.024)
-0.044 (0.044)
(0.017)
-0.083 (0.064)
0.020
0.005
-0.005
0.003
-0.003
-0.003
0.004
(0.018)
(0.013)
(0.013)
(0.008)
(0.006)
(0.012)
(0.014)
-0.010
0.047
0.017
0.029
-0.007
-0.009
0.002
(0.049)
(0.036)
(0.036)
(0.026)
(0.019)
(0.022)
(0.034)
-0.004
0.008
0.011
-0.007
-0.002
(0.006)
(0.007)
(0.008)
(0.014)
(0.018)
0.026
0.024
0.029
0.058*
-0.024
(0.019)
(0.018)
(0.021)
(0.031)
(0.047)
-0.002
-0.011
0.025
0.020
0.000
(0.009)
(0.015)
(0.017)
(0.019)
(0.026)
0.018
-0.005
-0.022
-0.046
-0.017
(0.033)
(0.037)
(0.030)
(0.053)
(0.039)
-0.107** (0.048)
0.003
(0.143)
Y
270,121
Y
241,577
Notes: The estimates are from a Poisson regression of the daily
count of trips taken on weather and other covariates as indicated.
The reported coefficient estimates include both contemporaneous and
lagged variables for each weather category. The last column reports
estimates of our trip count model with ultra-light duty trips only.
Standard errors, in parentheses, are block bootstrapped by year. *
10% level, ** 5% level, *** 1% level
16
Table H8: Additional Specifications for Fatalities Model, FARS, Fixed
Effects, and NHTS Months
FARS Data
Temperature
quad <20◦ F
quad 20-30◦ F
quad 30-40◦ F
quad 40-50◦ F
quad 60-70◦ F
quad 70-80◦ F
quad >80◦ F
Rainfall
quad 0-0.1 cm
quad 0.1-0.5 cm
quad 0.5-1.5 cm
quad 1.5-3 cm
quad >3 cm
Snowfall
quad 0-0.1 cm
quad 0.1-0.5 cm
quad 0.5-1.5 cm
quad 1.5-3 cm
quad >3 cm
Model
Fixed Effects
State FE
State-county-year-month
State-month, County-year
Other Regressors
First Snowfall
First Rainfall
Num. Obs.
Same
Months as
NHTS
Changing Fixed Effects
-0.190***
(0.019)
-0.121***
(0.013)
-0.081***
(0.007)
-0.051***
(0.005)
0.047***
(0.005)
0.061***
(0.006)
0.078***
(0.008)
-1.217***
(0.077)
-0.901***
(0.070)
-0.720***
(0.045)
-0.383***
(0.037)
0.067***
(0.022)
0.131***
(0.031)
0.348***
(0.042)
-0.301***
(0.032)
-0.182***
(0.034)
-0.177***
(0.020)
-0.237***
(0.019)
0.068***
(0.016)
0.162***
(0.016)
0.261***
(0.014)
-0.169***
(0.027)
-0.149***
(0.025)
-0.106***
(0.015)
-0.076***
(0.012)
0.066***
(0.009)
0.073***
(0.013)
0.097***
(0.016)
-0.113**
(0.055)
-0.162***
(0.047)
-0.161***
(0.037)
-0.100***
(0.013)
0.047
(0.037)
0.057
(0.052)
0.094
(0.067)
-0.017***
(0.003)
-0.028***
(0.006)
-0.052***
(0.007)
-0.073***
(0.008)
-0.021
(0.020)
-0.360***
(0.026)
-0.360***
(0.030)
-0.323***
(0.027)
-0.329***
(0.034)
-0.141***
(0.050)
-0.099***
(0.009)
-0.149***
(0.014)
-0.178***
(0.016)
-0.179***
(0.017)
-0.047
(0.029)
-0.034***
(0.009)
-0.053***
(0.011)
-0.070***
(0.014)
-0.104***
(0.016)
-0.068**
(0.030)
-0.052**
(0.021)
-0.064***
(0.012)
-0.069***
(0.014)
-0.103***
(0.026)
-0.095*
(0.057)
0.000
(0.010)
0.038***
(0.009)
0.063***
(0.012)
0.104***
(0.015)
-0.059***
(0.022)
Poisson
0.287***
(0.046)
0.534***
(0.042)
0.710***
(0.064)
0.686***
(0.055)
0.474***
(0.068)
Poisson
0.001
(0.022)
-0.046*
(0.026)
-0.009
(0.039)
-0.040
(0.039)
-0.188***
(0.050)
Poisson
0.029**
(0.014)
0.069***
(0.019)
0.123***
(0.029)
0.135***
(0.026)
0.006
(0.043)
Poisson
0.104***
(0.032)
0.107***
(0.033)
0.087
(0.104)
0.120***
(0.037)
0.050
(0.073)
Poisson
N
Y
N
N
N
N
Y
N
N
N
N
Y
N
Y
N
Y
N
19,200,000
Y
N
6,698,935
Y
N
6,698,935
Y
N
6,321,916
Y
N
489,714
Notes: The estimates are from a Poisson regression of the daily count of fatalities by county on
weather and other covariates as indicated. Standard errors, in parentheses, are block bootstrapped
by year. Reported coefficients and standard errors are the sum of the current and lagged estimates.
The first column reports coefficient estimates from our fatalities model using FARS data for all
counties in the United States from 1975 to 2013. In the next three columns we report coefficient
estimates without fixed effects, with state, and finally with state-month, county-year fixed effects. *
10% level, ** 5% level, *** 1% level
17
Table H9: Additional Specifications for Fatalities Model, More Weather
Bins, and Negative Binomial Model
Temperature
<0◦ F
0-10◦ F
10-20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
80-90◦ F
>90◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Fixed Effects
Model
State FE
State-county-year-month
State-month, County-year
Other Regressors
First Snowfall
First Rainfall
Num. Obs.
More Weather
Variables
(1)
Maximum Daily
Temperature
(2)
-0.187**
(0.088)
-0.114**
(0.051)
-0.152***
(0.034)
-0.118***
(0.026)
-0.090***
(0.019)
-0.063***
(0.014)
0.055***
(0.009)
0.069***
(0.015)
0.096***
(0.015)
0.066
(0.077)
-0.469*
(0.248)
-0.051
(0.088)
0.154**
(0.069)
-0.080**
(0.034)
-0.042*
(0.024)
-0.028
(0.018)
0.055***
(0.014)
0.113***
(0.014)
0.140***
(0.014)
0.171***
(0.019)
-0.190**
(0.081)
-0.118**
(0.050)
-0.155***
(0.034)
-0.120***
(0.026)
-0.091***
(0.017)
-0.064***
(0.013)
0.056***
(0.009)
0.070***
(0.015)
0.096***
(0.016)
0.067
(0.073)
-0.029***
(0.009)
-0.049***
(0.011)
-0.059***
(0.015)
-0.086***
(0.016)
-0.049
(0.032)
-0.019**
(0.009)
-0.034***
(0.011)
-0.038**
(0.015)
-0.062***
(0.016)
-0.021
(0.031)
-0.029***
(0.009)
-0.050***
(0.012)
-0.060***
(0.015)
-0.087***
(0.015)
-0.050
(0.037)
0.027*
(0.016)
0.074***
(0.020)
0.131***
(0.029)
0.155***
(0.023)
0.042
(0.044)
0.028**
(0.014)
0.070***
(0.020)
0.123***
(0.029)
0.146***
(0.024)
0.030
(0.044)
0.027*
(0.016)
0.074***
(0.021)
0.132***
(0.027)
0.157***
(0.023)
0.046
(0.042)
Poisson
N
Y
N
Poisson
N
Y
N
Neg. Binomial
N
Y
N
Y
Y
3,117,797
Y
N
3,117,797
Y
N
3,117,797
Negative Binomial
(3)
Notes: The estimates are from a Poisson regression of the daily count of fatalities by county on weather
and other covariates as indicated. Standard errors, in parentheses, are block bootstrapped by year.
Reported coefficients and standard errors are the sum of the current and lagged estimates. In column 1,
we disaggregate the endpoints into more temperature bins and include the first rainfall event after 1 month.
The final two columns keep these additional temperature bins. Column 2 replaces average temperature
with the maximum daily temperature. Column 3 reports estimates from a Negative Binomial model. *
10% level, ** 5% level, *** 1% level
18
Table H10: Poisson Regression of Fatality Count,
Adaptation
Current + Lag
Temperature
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Sample Restriction
Controls
County-year-montha
First Snowfallb
Num. Obs.
Time Period Changes
(1)
(2)
Regional Sorting
(3)
(4)
-0.089*
(0.045)
-0.075
(0.053)
-0.029
(0.025)
-0.063***
(0.018)
0.055***
(0.020)
0.068**
(0.027)
0.096***
(0.034)
-0.166***
(0.033)
-0.136***
(0.025)
-0.114***
(0.019)
-0.063***
(0.017)
0.056***
(0.010)
0.070***
(0.019)
0.095***
(0.016)
-0.210***
(0.046)
-0.170***
(0.057)
-0.113***
(0.036)
-0.085*
(0.046)
0.124***
(0.029)
0.130***
(0.033)
0.105
(0.084)
-0.048
(0.335)
-0.072
(0.078)
-0.062**
(0.030)
-0.039**
(0.016)
0.062***
(0.014)
0.088***
(0.020)
0.131***
(0.021)
0.001
(0.018)
-0.005
(0.014)
-0.027
(0.028)
-0.051**
(0.024)
-0.013
(0.046)
-0.042***
(0.007)
-0.068***
(0.009)
-0.073***
(0.015)
-0.101***
(0.021)
-0.066
(0.046)
-0.050***
(0.022)
-0.095***
(0.025)
-0.116***
(0.033)
-0.295***
(0.058)
-0.341
(0.214)
-0.036**
(0.016)
-0.023
(0.016)
-0.016
(0.016)
-0.040**
(0.019)
0.008
(0.043)
0.019
(0.046)
0.048
(0.039)
0.099***
(0.031)
0.088**
(0.050)
0.046
(0.071)
0.032**
(0.012)
0.084***
(0.022)
0.144***
(0.033)
0.183***
(0.022)
0.036
(0.053)
0.072**
(0.031)
0.163***
(0.038)
0.201***
(0.044)
0.319***
(0.054)
0.321***
(0.058)
-0.005
(0.071)
0.096
(0.064)
0.076
(0.062)
0.058
(0.118)
-0.259
(0.204)
1990-1999
2000-2010
County in
Coldest
Quartile
County in
Hottest
Quartile
Y
Y
907,028
Y
Y
2,210,769
Y
Y
576,079
Y
Y
1,040,523
Notes: The estimates are from a Poisson regression of the daily count of
fatalities for a county on weather and other covariates. Standard errors, in
parentheses, are block bootstrapped by year. * significant at 10% level, **
significant at 5% level, *** significant at 1% level
a Fixed effects for county by year by month.
b Indicator for first snowfall after 1 month without snow.
19
Table H11: Additional Specifications for Fatalities Model—Explaining
Fatalities and Time Period Changes
Explaining Fatalities
Omit
Omit
UltraOmit
Young
light
Intoxicated
Driver
Duty
Accidents
Accidents
Accidents
Temperature
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Fixed Effects
State-county-yearmonth
Num. Obs.
Time Period Changes
1990-1999
2000-2010
1990-1995
2005-2010
-0.057**
(0.027)
-0.012
(0.026)
-0.009
(0.016)
-0.014
(0.015)
0.027***
(0.008)
0.023*
(0.013)
0.046**
(0.021)
-0.117***
(0.044)
-0.126***
(0.024)
-0.083***
(0.027)
-0.055***
(0.016)
0.059***
(0.011)
0.076***
(0.018)
0.106***
(0.018)
-0.131***
(0.039)
-0.094**
(0.038)
-0.109***
(0.037)
-0.071***
(0.024)
0.035*
(0.021)
0.033
(0.023)
0.120***
(0.043)
-0.089*
(0.045)
-0.075
(0.053)
-0.029
(0.025)
-0.063***
(0.018)
0.055***
(0.020)
0.068**
(0.027)
0.096***
(0.034)
-0.166***
(0.033)
-0.136***
(0.025)
-0.114***
(0.019)
-0.063***
(0.017)
0.056***
(0.010)
0.070***
(0.019)
0.095***
(0.016)
-0.111
(0.122)
-0.077
(0.105)
-0.029
(0.077)
-0.058
(0.051)
0.022
(0.034)
0.047
(0.050)
0.057
(0.105)
-0.181***
(0.061)
-0.107***
(0.032)
-0.134***
(0.022)
-0.058**
(0.024)
0.081***
(0.013)
0.111***
(0.023)
0.109***
(0.034)
-0.005
(0.010)
-0.007
(0.009)
-0.003
(0.013)
-0.028*
(0.016)
0.010
(0.033)
-0.023***
(0.008)
-0.033***
(0.012)
-0.034**
(0.016)
-0.037
(0.026)
0.005
(0.034)
-0.017
(0.023)
-0.062***
(0.018)
-0.041**
(0.021)
-0.073*
(0.038)
-0.102
(0.081)
0.001
(0.018)
-0.005
(0.014)
-0.027
(0.028)
-0.051**
(0.024)
-0.013
(0.046)
-0.042***
(0.007)
-0.068***
(0.009)
-0.073***
(0.015)
-0.101***
(0.021)
-0.066
(0.046)
-0.060
(0.042)
-0.039
(0.031)
-0.063
(0.078)
0.011
(0.058)
-0.197*
(0.114)
-0.052***
(0.007)
-0.080***
(0.015)
-0.103***
(0.024)
-0.130***
(0.026)
-0.132**
(0.058)
0.040**
(0.018)
0.045*
(0.024)
0.095***
(0.031)
0.066**
(0.026)
-0.059
(0.043)
0.025
(0.027)
0.083**
(0.036)
0.155***
(0.036)
0.246***
(0.038)
0.205***
(0.055)
0.057
(0.041)
0.032
(0.037)
0.105*
(0.060)
-0.046
(0.061)
-0.271***
(0.063)
0.019
(0.046)
0.048
(0.039)
0.099***
(0.031)
0.088**
(0.050)
0.046
(0.071)
0.032**
(0.012)
0.084***
(0.022)
0.144***
(0.033)
0.183***
(0.022)
0.036
(0.053)
0.035
(0.046)
0.079
(0.046)
0.103
(0.071)
0.145
(0.103)
-0.120
(0.086)
0.016
(0.012)
0.079**
(0.031)
0.127**
(0.055)
0.148***
(0.021)
0.034
(0.065)
Y
Y
Y
Y
Y
Y
Y
2,860,068
1,846,940
1,046,954
907,028
2,210,769
254,147
1,093,558
Notes: The estimates are from a Poisson regression of the daily count of fatalities by county on weather
and other covariates as indicated. Standard errors, in parentheses, are block bootstrapped by year.
Reported coefficients and standard errors are the sum of the current and lagged estimates. Under the
first three columns we restrict the sample to different subsets of fatal accidents by omitting those that
share particular characteristics. Under the next group of columns, we restrict the sample to different
time periods to determine whether our estimated effects of weather on fatalities change over time. The
first two columns under Time Period Changes, titled 1990-1999 and 2000-2010, split the sample in half
by decade. The next two columns titled 1990-1995 and 2005-2010, further restrict the split subsample
into the earliest and latest six years of our full sample. * significant at 10% level, ** significant at 5%
level, *** significant at 1% level
20
Table H12: Additional Specifications for PDO Accidents Model
Urban
Counties
Changing Fixed Effects
NHTS
Sample
Temperature
<0◦ F
0-10◦ F
10-20◦ F
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80◦ F
-0.596***
(0.068)
-0.455***
(0.045)
-0.467***
(0.032)
-0.275***
(0.033)
-0.034**
(0.016)
-0.063***
(0.018)
-0.142***
(0.035)
-0.005
(0.024)
0.005
(0.022)
-0.095***
(0.018)
-0.188***
(0.021)
-0.021*
(0.012)
0.021**
(0.010)
0.017
(0.015)
0.119***
(0.020)
0.029*
(0.015)
-0.038***
(0.008)
-0.030***
(0.005)
-0.004
(0.005)
-0.012**
(0.006)
-0.021***
(0.008)
0.106***
(0.022)
0.014
(0.018)
-0.039***
(0.009)
-0.022***
(0.005)
0.001
(0.004)
-0.002
(0.006)
0.003
(0.008)
0.063
(0.088)
-0.006
(0.040)
-0.020
(0.014)
-0.022***
(0.006)
0.007
(0.007)
0.015
(0.019)
0.026
(0.023)
80-90◦ F
>90◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Model
State FE
State-month, County-year
State-county-year-month
First Snowfall
First Rainfall
Num. Obs.
More Temp. Max. Daily
Bins
Temp.
Negative
Binomial
0.403***
(0.051)
0.203***
(0.030)
0.056**
(0.023)
0.516***
(0.052)
0.396***
(0.049)
-0.090
(0.062)
0.208***
(0.034)
0.042
(0.028)
-0.077***
(0.024)
0.034**
(0.016)
-0.031***
(0.009)
-0.023***
(0.005)
-0.005
(0.005)
-0.011*
(0.006)
0.077***
(0.020)
0.047***
(0.012)
-0.010
(0.007)
0.013***
(0.004)
0.013***
(0.005)
-0.075***
(0.016)
-0.107***
(0.008)
-0.061***
(0.005)
0.025***
(0.003)
0.035***
(0.004)
-0.010
(0.008)
-0.005
(0.008)
0.012*
(0.007)
0.015**
(0.007)
0.048***
(0.007)
0.076***
(0.012)
-0.144***
(0.024)
-0.042*
(0.022)
0.039
(0.027)
-0.024
(0.037)
0.053
(0.055)
-0.017**
(0.008)
0.030***
(0.010)
0.066***
(0.012)
0.059**
(0.023)
0.194***
(0.031)
0.021***
(0.004)
0.071***
(0.004)
0.108***
(0.007)
0.148***
(0.010)
0.186***
(0.014)
0.024***
(0.005)
0.077***
(0.005)
0.120***
(0.008)
0.170***
(0.013)
0.206***
(0.019)
0.007
(0.006)
0.063***
(0.005)
0.079***
(0.005)
0.112***
(0.012)
0.161***
(0.018)
0.023***
(0.004)
0.071***
(0.005)
0.107***
(0.007)
0.147***
(0.011)
0.188***
(0.015)
0.023***
(0.004)
0.071***
(0.005)
0.107***
(0.007)
0.148***
(0.011)
0.190***
(0.015)
0.012***
(0.003)
0.049***
(0.004)
0.073***
(0.005)
0.102***
(0.008)
0.154***
(0.012)
0.227***
(0.033)
0.454***
(0.034)
0.702***
(0.048)
0.735***
(0.043)
0.687***
(0.059)
-0.014
(0.028)
0.046**
(0.022)
0.162***
(0.028)
0.168***
(0.035)
0.185***
(0.043)
0.020***
(0.007)
0.097***
(0.010)
0.223***
(0.010)
0.351***
(0.012)
0.446***
(0.014)
0.015*
(0.008)
0.070***
(0.012)
0.177***
(0.014)
0.291***
(0.016)
0.372***
(0.014)
0.025***
(0.005)
0.086***
(0.011)
0.222***
(0.009)
0.361***
(0.017)
0.445***
(0.063)
0.022***
(0.007)
0.098***
(0.010)
0.228***
(0.010)
0.352***
(0.011)
0.436***
(0.014)
0.016**
(0.007)
0.092***
(0.010)
0.220***
(0.010)
0.343***
(0.012)
0.426***
(0.014)
Poisson
Poisson
Poisson
Poisson
Poisson
Poisson
Poisson
N
N
N
Y
N
6,698,935
Y
N
N
Y
N
6,698,935
N
N
Y
Y
N
1,014,853
N
N
Y
Y
N
1,067,616
N
N
Y
Y
Y
6,665,499
N
N
Y
Y
N
6,665,499
0.012*
(0.006)
0.106***
(0.008)
0.258***
(0.008)
0.396***
(0.010)
0.466***
(0.017)
Neg.
Binomial
N
N
Y
Y
N
6,665,499
N
Y
N
Y
N
6,694,960
Notes: The estimates are from a Poisson regression of the daily count of PDO accidents by county on weather and other covariates
as indicated. Standard errors, in parentheses, are block bootstrapped by year. Reported coefficients and standard errors are
the sum of the current and lagged estimates. In the first three columns we report coefficient estimates without fixed effects,
with state, and finally with state-month, county-year fixed effects. Next we report coefficient estimates for a model restricted to
counties that are defined as urban using the classification system of the National Center for Health Statistics generated by the
CDC. In the next column we restrict our sample to the county-year-months that appear in the NHTS travel diary data. Under
the header More Temp. Bins, we desegregate the endpoints into more temperature bins and include the first rainfall event after
1 month. The final two columns keep these additional temperature bins. The column titled Max. Daily Temp. replaces average
temperature with the daily maximum temperature. The last column of the table reports estimates from a Negative Binomial
model. * 10% level, ** 5% level, *** 1% level
21
Table H13: Additional Specifications for Injuries Model
Urban
Counties
Changing Fixed Effects
NHTS
Sample
Temperature
<0◦ F
0-10◦ F
10-20◦ F
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80◦ F
-1.230***
(0.078)
-0.923***
(0.066)
-0.748***
(0.047)
-0.385***
(0.042)
-0.009
(0.013)
0.055*
(0.030)
0.213***
(0.042)
-0.143***
(0.030)
-0.097***
(0.017)
-0.151***
(0.017)
-0.245***
(0.026)
0.007
(0.013)
0.094***
(0.010)
0.125***
(0.016)
-0.001
(0.018)
-0.047***
(0.013)
-0.070***
(0.007)
-0.047***
(0.003)
0.023***
(0.003)
0.024***
(0.004)
0.010*
-0.006
0.025
(0.021)
-0.051***
(0.017)
-0.074***
(0.007)
-0.035***
(0.004)
0.020***
(0.004)
0.022***
(0.005)
0.020***
(0.007)
-0.032
(0.080)
-0.054
(0.038)
-0.066***
(0.024)
-0.040***
(0.003)
0.023***
(0.007)
0.041***
(0.013)
0.045***
(0.014)
80-90◦ F
>90◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Model
State FE
State-county-year-month
State-month, County-year
First Snowfall
First Rainfall
Num. Obs.
More Temp. Max. Daily
Bins
Temp.
Negative
Binomial
0.209***
(0.048)
0.071**
(0.029)
-0.029
(0.022)
0.248***
(0.059)
0.235***
(0.047)
-0.059
(0.053)
0.098**
(0.041)
-0.006
(0.033)
-0.092***
(0.025)
-0.038**
(0.015)
-0.070***
(0.007)
-0.044***
(0.004)
0.020***
(0.004)
0.023***
(0.005)
0.018
(0.019)
-0.001
(0.014)
-0.023***
(0.006)
0.034***
(0.003)
0.057***
(0.005)
-0.089***
(0.015)
-0.107***
(0.008)
-0.067***
(0.004)
0.036***
(0.003)
0.048***
(0.004)
0.017**
(0.007)
0.018
(0.013)
0.065***
(0.007)
0.063***
(0.006)
0.049***
(0.006)
0.067***
(0.015)
-0.316***
(0.029)
-0.225***
(0.030)
-0.092***
(0.034)
0.024
(0.049)
0.383***
(0.062)
-0.098***
(0.010)
-0.083***
(0.012)
-0.033**
(0.013)
0.053**
(0.024)
0.287***
(0.034)
0.010***
(0.004)
0.050***
(0.004)
0.077***
(0.005)
0.104***
(0.009)
0.129***
(0.015)
0.015***
(0.005)
0.060***
(0.005)
0.101***
(0.008)
0.138***
(0.012)
0.157***
(0.020)
-0.001
(0.010)
0.041***
(0.011)
0.063***
(0.009)
0.091***
(0.010)
0.136***
(0.021)
0.014***
(0.005)
0.058***
(0.005)
0.088***
(0.007)
0.119***
(0.010)
0.144***
(0.017)
0.018***
(0.005)
0.063***
(0.005)
0.095***
(0.007)
0.128***
(0.010)
0.156***
(0.017)
0.008**
(0.004)
0.047***
(0.004)
0.068***
(0.006)
0.092***
(0.009)
0.120***
(0.015)
0.254***
(0.065)
0.458***
(0.041)
0.655***
(0.046)
0.763***
(0.028)
0.757***
(0.052)
-0.037
(0.026)
-0.102***
(0.025)
-0.082**
(0.039)
-0.018
(0.044)
0.061
(0.047)
-0.001
(0.006)
0.066***
(0.007)
0.160***
(0.010)
0.236***
(0.013)
0.211***
(0.020)
-0.002
(0.008)
0.052***
(0.008)
0.140***
(0.013)
0.203***
(0.013)
0.180***
(0.021)
0.025***
(0.005)
0.075***
(0.014)
0.207***
(0.007)
0.294***
(0.023)
0.307***
(0.085)
0.007
(0.008)
0.078***
(0.007)
0.189***
(0.010)
0.281***
(0.010)
0.260***
(0.022)
0.005
(0.007)
0.074***
(0.007)
0.183***
(0.010)
0.273***
(0.011)
0.252***
(0.022)
Poisson
Poisson
Poisson
Poisson
Poisson
Poisson
Poisson
N
N
N
Y
N
5,489,551
Y
N
N
Y
N
5,489,551
N
N
Y
Y
N
5,247,345
N
Y
N
Y
N
810,928
N
Y
N
Y
N
807,775
N
Y
N
Y
Y
5,067,561
N
Y
N
Y
N
5,067,561
0.008
(0.007)
0.086***
(0.007)
0.211***
(0.009)
0.315***
(0.010)
0.302***
(0.022)
Neg.
Binomial
N
Y
N
Y
N
5,067,561
Notes: The estimates are from a Poisson regression of the daily count of injuries by county on weather and other covariates as
indicated. Standard errors, in parentheses, are block bootstrapped by year. Reported coefficients and standard errors are the sum
of the current and lagged estimates. In the first three columns we report coefficient estimates without fixed effects, with state, and
finally with state-month, county-year fixed effects. Next we report coefficient estimates for a model restricted to counties that are
defined as urban using the classification system of the National Center for Health Statistics generated by the CDC. In the next
column we restrict our sample the county-year-months that appear in the NHTS travel diary data. Under the header More Temp.
Bins, we desegregate the endpoints into more temperature bins and include the first rainfall event after 1 month. The final two
columns keep these additional temperature bins. The column titled Max. Daily Temp. replaces average temperature with the daily
maximum temperature. The last column of the table reports estimates from a Negative Binomial model. * 10% level, ** 5% level,
*** 1% level
22
Table H14: Aggregation of Data to Monthly Level
Temperature
<20◦ F
1-day effect
20-30◦ F
1-day effect
30-40◦ F
1-day effect
40-50◦ F
1-day effect
60-70◦ F
1-day effect
70-80◦ F
1-day effect
>80◦ F
1-day effect
Rainfall
0-0.1 cm
1-day effect
0.1-0.5 cm
1-day effect
0.5-1.5 cm
1-day effect
1.5-3 cm
1-day effect
>3 cm
1-day effect
Snowfall
0-0.1 cm
1-day effect
0.1-0.5 cm
1-day effect
0.5-1.5 cm
1-day effect
1.5-3 cm
1-day effect
>3 cm
1-day effect
Fixed Effects
State-month, county-year
Num. Obs.
PDO Accidents
Injuries
Fatalities
0.004
(0.004)
0.120
-0.006
(0.005)
-0.180
-0.002
(0.002)
-0.060
-0.005*
(0.002)
-0.150
-0.001
(0.001)
-0.030
0.000
(0.002)
0.000
-0.001
(0.002)
-0.030
0.004
(0.005)
0.120
-0.009
(0.005)
-0.270
0.001
(0.003)
0.030
-0.004**
(0.002)
-0.120
-0.001
(0.002)
-0.030
-0.002
(0.003)
-0.060
-0.002
(0.003)
-0.060
-0.010**
(0.004)
-0.300
-0.012***
(0.003)
-0.360
-0.005**
(0.003)
-0.150
-0.007***
(0.002)
-0.210
0.001
(0.001)
0.030
0.003*
(0.001)
0.090
0.005***
(0.002)
0.15
0.002
(0.002)
0.060
0.002*
(0.001)
0.060
0.004*
(0.002)
0.120
0.002
(0.003)
0.060
-0.001
(0.005)
-0.030
-0.002
(0.002)
-0.060
-0.002
(0.002)
-0.060
0.001
(0.002)
0.030
0.000
(0.004)
0.000
0.006
(0.006)
0.180
-0.002
(0.002)
-0.060
-0.006**
(0.003)
-0.180
-0.010***
(0.003)
-0.300
-0.008**
(0.004)
-0.240
-0.017***
(0.006)
-0.510
-0.004
(0.003)
-0.120
0.004
(0.004)
0.120
0.008***
(0.003)
0.240
0.006
(0.006)
0.180
0.015***
(0.005)
0.450
-0.007*
(0.004)
-0.210
0.001
(0.003)
0.030
0.006*
(0.003)
0.180
0.010**
(0.005)
0.300
0.013*
(0.007)
0.390
-0.003
(0.003)
-0.090
0.001
(0.003)
0.030
0.009**
(0.004)
0.270
-0.003
(0.005)
-0.090
-0.011
(0.009)
-0.330
Y
218,607
Y
179,111
Y
218,524
Notes: The estimates are from a Poisson regression of the month count of fatalities, PDO accidents,
and injuries by county on weather and other covariates as indicated. Standard errors, in parentheses,
are block bootstrapped by year. Reported coefficients and standard errors are the sum of the current
and lagged estimates. * 10% level, ** 5% level, *** 1% level
23
Table H15: Travel Demand Robustness: Inverse Hyperbolic Sine
Inverse Hyperbolic Sine
LDV Trip
LDV
ULD Trip
ULD
Count
Miles
Count
Miles
Temperature
<20◦ F
20-30◦ F
30-40◦ F
40-50◦ F
60-70◦ F
70-80◦ F
>80◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Fixed Effects
State-month, county-year
State-county-year-month
Num. Obs.
-0.069** -0.117*** -0.078*** -0.087***
(0.030)
(0.042)
(0.018)
(0.016)
-0.042** -0.070** -0.048*** -0.063***
(0.021)
(0.035)
(0.013)
(0.012)
-0.031**
-0.030
-0.035*** -0.040***
(0.015)
(0.025)
(0.009)
(0.008)
-0.008
-0.012
-0.011* -0.016***
(0.010)
(0.017)
(0.006)
(0.006)
-0.014
-0.003
0.014**
0.012*
(0.012)
(0.018)
(0.007)
(0.007)
-0.026**
-0.025
0.008
0.006
(0.013)
(0.021)
(0.011)
(0.012)
-0.065*** -0.098***
0.004
0.009
(0.021)
(0.036)
(0.015)
(0.014)
-0.010
(0.009)
-0.008
(0.012)
-0.004
(0.010)
-0.045***
(0.013)
-0.055**
(0.028)
-0.010
(0.016)
-0.027
(0.021)
-0.018
(0.020)
-0.059**
(0.024)
-0.077
(0.047)
0.000
(0.007)
-0.020***
(0.007)
-0.031***
(0.007)
-0.045***
(0.013)
-0.041**
(0.018)
Weighted Inverse Hyperbolic Sinea
LDV Trip
LDV
ULD Trip
ULD
Count
Miles
Count
Miles
-0.089*
(0.046)
-0.072**
(0.034)
-0.050**
(0.024)
-0.004
(0.014)
-0.010
(0.019)
-0.019
(0.020)
-0.043
(0.028)
-0.136**
(0.062)
-0.099*
(0.051)
-0.052
(0.042)
-0.010
(0.024)
0.015
(0.033)
0.006
(0.036)
-0.035
(0.053)
-0.058*** -0.070***
(0.020)
(0.019)
-0.034** -0.050***
(0.014)
(0.015)
-0.019* -0.026***
(0.011)
(0.009)
-0.008
-0.010
(0.010)
(0.007)
0.015
0.015
(0.011)
(0.010)
0.004
0.002
(0.011)
(0.010)
-0.003
-0.006
(0.016)
(0.014)
-0.005
-0.009
0.003
0.006
0.001
(0.006)
(0.013)
(0.020)
(0.007)
(0.007)
-0.029***
-0.001
-0.012
-0.011
-0.021***
(0.007)
(0.015)
(0.026)
(0.008)
(0.007)
-0.041***
0.014
0.017
-0.021** -0.033***
(0.006)
(0.017)
(0.032)
(0.008)
(0.007)
-0.065*** -0.090*** -0.121*** -0.053*** -0.066***
(0.009)
(0.026)
(0.044)
(0.013)
(0.012)
-0.042***
-0.052
-0.103
-0.015
-0.017
(0.016)
(0.042)
(0.071)
(0.036)
(0.030)
-0.017
-0.018
0.001
-0.009
-0.043
-0.066
-0.004
-0.015
(0.021)
(0.034)
(0.014)
(0.012)
(0.028)
(0.044)
(0.015)
(0.013)
-0.015
-0.021
-0.038*** -0.025***
-0.027
-0.049
-0.046*** -0.032***
(0.019)
(0.035)
(0.011)
(0.008)
(0.037)
(0.060)
(0.014)
(0.011)
-0.025
-0.063** -0.040*** -0.038***
-0.001
-0.035
-0.033** -0.041***
(0.026)
(0.030)
(0.012)
(0.011)
(0.037)
(0.048)
(0.014)
(0.012)
-0.105** -0.168**
-0.031*
-0.034*
-0.109** -0.182**
-0.017
-0.017
(0.043)
(0.067)
(0.018)
(0.019)
(0.045)
(0.076)
(0.014)
(0.020)
-0.223*** -0.377***
-0.030
-0.022
-0.245*** -0.423***
-0.025
-0.019
(0.045)
(0.074)
(0.025)
(0.019)
(0.062)
(0.104)
(0.016)
(0.013)
N
Y
283,657
N
Y
283,657
N
Y
283,657
N
Y
283,657
N
Y
283,657
N
Y
283,657
N
Y
283,657
N
Y
283,657
Notes: The estimates are from Inverse Hyperbolic Sine of the daily count of trips taken, total miles, ultra-light
duty trip count, and ultra-light duty miles on weather. Other covariates include household size, number of vehicles,
number of workers, number of adults, family structure, race, income, day of week, and fixed effects as indicated.
Inverse Hyperbolic Sine has been suggested as a transformation for a skewed dependent variable that is defined
for zero but approaches the log transformation for larger values (Burbidge, Magee and Robb, 1988). The reported
coefficient estimates include both contemporaneous and lagged variables for each weather category. Standard errors,
in parentheses, are block bootstrapped by year. Reported coefficients and standard errors are the sum of the current
and lagged estimates. In the first four columns we report coefficient estimates of unweighted Inverse Hyperbolic Sine
models. In the last four columns we report coefficient estimates of weighted Inverse Hyperbolic Sine models, where
observations are weighted by the inverse frequency of households in each survey wave. Since the NHTS significantly
increases in size over time–from about 20,000 households in 1990 to about 150,000 households in 2009–the weights for
households in the earlier surveys are much larger than the weights for households in the later surveys. * significant
at 10% level, ** significant at 5% level, *** significant at 1% level.
a Weighted based on survey size to account for the fact that earlier surveys are smaller.
24
Table H16: Poisson Regression of Travel Demand without
Household Controls
Trip
Count
(1)
-0.047*
(0.028)
-0.029*
(0.017)
-0.025*
(0.013)
-0.006
(0.008)
-0.009
(0.010)
-0.017
(0.011)
-0.035*
(0.020)
Miles per
Trip
(2)
-0.017
(0.070)
-0.039
(0.051)
0.011
(0.027)
-0.051***
(0.017)
0.033*
(0.020)
0.043
(0.034)
0.022
(0.054)
Trip
Count
(3)
-0.254***
(0.065)
-0.112**
(0.043)
-0.079**
(0.032)
-0.029
(0.025)
0.025
(0.021)
-0.009
(0.033)
0.017
(0.047)
Miles per
Trip
(4)
-0.730***
(0.159)
-0.456***
(0.119)
-0.333***
(0.096)
-0.127
(0.088)
0.074
(0.053)
0.100
(0.082)
0.121
(0.110)
Public
Transit
Trip
Count
(5)
-0.207
(0.134)
-0.126
(0.092)
0.010
(0.046)
0.002
(0.042)
0.061
(0.053)
-0.015
(0.076)
-0.072
(0.134)
-0.013
(0.010)
-0.005
(0.009)
-0.002
(0.011)
-0.058***
(0.019)
-0.039
(0.033)
0.002
(0.017)
-0.051***
(0.017)
-0.012
(0.029)
0.092**
(0.041)
0.061
(0.100)
-0.012
(0.020)
-0.064***
(0.018)
-0.089***
(0.021)
-0.169***
(0.037)
-0.134**
(0.060)
-0.090*
(0.048)
-0.226***
(0.048)
-0.291***
(0.068)
-0.538***
(0.112)
-0.363
(0.239)
-0.054
(0.053)
-0.008
(0.056)
0.001
(0.057)
-0.214***
(0.078)
0.000
(0.168)
-0.009
(0.015)
-0.028
(0.022)
-0.008
(0.024)
-0.071**
(0.032)
-0.169***
(0.038)
0.030
(0.047)
0.017
(0.043)
-0.030
(0.062)
0.047
(0.104)
0.061
(0.088)
0.034
(0.044)
-0.126***
(0.036)
-0.144***
(0.042)
-0.095
(0.060)
-0.099
(0.064)
0.078
(0.078)
-0.078
(0.089)
-0.159
(0.104)
-0.090
(0.165)
-0.049
(0.110)
0.121*
(0.071)
-0.007
(0.103)
-0.011
(0.088)
-0.007
(0.114)
-0.017
(0.107)
Y
Y
N
261,748
Y
Y
N
223,766
Y
Y
N
228,712
Y
Y
N
228,210
Y
Y
N
177,659
Light-Duty Vehicles
Current + Lag
<20 ◦ F
20-30 ◦ F
30-40 ◦ F
40-50 ◦ F
60-70 ◦ F
70-80 ◦ F
>80 ◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Controls
County-year-montha
First Snowfallb
Household Controlsc
Num. Obs.
Ultra-Light Duty
Notes: The estimates are from a Poisson regression of the daily count of trips and
miles per trip for Light-Duty Vehicles, Ultra-Light Duty Modes, and Public Transit by
household on weather and other covariates as indicated. Standard errors, in parentheses,
are block bootstrapped by year. * significant at 10% level, ** significant at 5% level,
*** significant at 1% level
a Fixed effects for county by year by month.
b Indicator for first snowfall after 1 month without snow.
c Excludes controls for count of vehicles in household, household size, number of workers
in household, number of adults in household, NHTS life-cycle stratum, race, NHTS
defined income group, and day of week.
25
Table H17: Extended Poisson Regression of Travel Demand
with Household Controls
Current + Lag
<20 ◦ F
20-30 ◦ F
30-40 ◦ F
40-50 ◦ F
60-70 ◦ F
70-80 ◦ F
>80 ◦ F
Rainfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Snowfall
0-0.1 cm
0.1-0.5 cm
0.5-1.5 cm
1.5-3 cm
>3 cm
Controls
County-year-montha
First Snowfallb
Household Controlsc
Num. Obs.
LDV
Total
Miles
(1)
-0.076**
(0.031)
-0.063**
(0.024)
-0.011
(0.015)
-0.026**
(0.011)
0.001
(0.011)
0.002
(0.016)
-0.015
(0.030)
(2)
0.008
(0.018)
0.017
(0.011)
0.021***
(0.006)
0.005
(0.006)
0.002
(0.005)
0.007
(0.006)
-0.001
(0.012)
LDV
Travel
Time
(3)
-0.053**
(0.021)
-0.055***
(0.019)
-0.026**
(0.012)
-0.018**
(0.008)
0.001
(0.008)
-0.005
(0.011)
-0.027
(0.022)
ULD
Total
Miles
(4)
-0.760***
(0.154)
-0.489***
(0.109)
-0.343***
(0.088)
-0.129*
(0.072)
0.061
(0.051)
0.068
(0.087)
0.129
(0.106)
Public
Transit
Miles
(5)
-0.122
(0.224)
-0.173
(0.170)
0.059
(0.106)
-0.018
(0.064)
0.101
(0.075)
0.118
(0.097)
-0.073
(0.246)
-0.004
(0.010)
-0.026**
(0.010)
-0.015
(0.014)
0.010
(0.021)
-0.023
(0.037)
0.000
(0.005)
0.000
(0.004)
-0.003
(0.007)
0.029***
(0.008)
-0.008
(0.018)
-0.003
(0.006)
-0.018
(0.009)
-0.006
(0.008)
-0.016
(0.016)
0.000
(0.027)
-0.115**
(0.052)
-0.224***
(0.046)
-0.281***
(0.059)
-0.571***
(0.114)
-0.326
(0.238)
-0.024
(0.099)
0.018
(0.075)
-0.030
(0.094)
0.208*
(0.115)
-0.246
(0.197)
0.026
(0.024)
-0.007
(0.024)
-0.014
(0.030)
-0.090**
(0.045)
-0.156***
(0.058)
0.000
(0.009)
-0.005
(0.014)
-0.006
(0.013)
-0.030*
(0.017)
-0.067***
(0.018)
0.015
(0.017)
-0.001
(0.019)
-0.014
(0.019)
-0.058
(0.040)
-0.105***
(0.040)
0.117
(0.087)
-0.057
(0.087)
-0.100
(0.108)
-0.065
(0.160)
-0.089
(0.115)
0.170
(0.114)
-0.079
(0.142)
-0.464**
(0.215)
0.004
(0.210)
0.101
(0.287)
Y
Y
Y
261,667
Y
Y
Y
223,676
Y
Y
Y
261,627
Y
Y
Y
228,144
Y
Y
Y
177,987
LDV
Speed
Notes: The estimates are from a Poisson regression of the daily count of trips and
miles per trip for Light-Duty Vehicles, Ultra-Light Duty Modes, and Public Transit by
household on weather and other covariates as indicated. Standard errors, in parentheses,
are block bootstrapped by year. * significant at 10% level, ** significant at 5% level,
*** significant at 1% level
a Fixed effects for county by year by month.
b Indicator for first snowfall after 1 month without snow.
c Includes controls for count of vehicles in household, household size, number of workers
in household, number of adults in household, NHTS lifecycle stratum, race, NHTS
defined income group, and day of week.
26
Table H18: Change in Fatalities with Climate Change: Intermediate Dates Using
CCSM4 RCP6.0
Fatalities
2045
(2)
2025
(1)
Annual Change due to
Temperature
Annual Change due to Rainfall
Annual Change due to Snowfall
Annual Net Change
Net Present Cost ($2015 Million)
Annual Change due to
Temperature
Annual Change due to Rainfall
Annual Change due to Snowfall
Annual Net Change
Net Present Cost ($2015 Million)
Annual Change due to
Temperature
Annual Change due to Rainfall
Annual Change due to Snowfall
Annual Net Change
Net Present Cost ($2015 Million)
2065
(3)
73
220
383
[54, 91]
10
[4, 17]
-8
[-11, -64]
76
[56, 95]
[173, 263]
-3
[-7, 3]
-24
[-31, -18]
192
[147, 238]
[319, 442]
0
[-4, 5]
-34
[-41, -25]
349
[285, 410]
$511.37
$718.36
$724.43
2025
(1)
LDV Fatalities
2045
(2)
2065
(3)
17
51
76
[-4, 36]
-1
[-6, 6]
-3
[-6, 1]
14
[-8, 34]
[6, 96]
1
[-3, 5]
-18
[-24, -12]
34
[-15, 80]
[17, 135]
-1
[-5, 4]
-26
[-33, -19]
49
[-13, 109]
$92.20
$127.56
$101.78
2025
(1)
ULD Fatalities
2045
(2)
2065
(3)
48
149
261
[38, 59]
-3
[-2, 7]
1
[-1, 3]
51
[40, 63]
[117, 171]
-6
[-9, -3]
3
[-1, 7]
146
[124, 168]
[230, 291]
0
[-3, 3]
4
[0, 6]
265
[235, 298]
$347.42
$545
$550
Notes: The estimates are the sum of county-level changes in weather on the listed outcome. All future weather
simulations use quantile-mapping to adjust current weather to the changes predicted by the CCSM4 RCP6.0
scenario. Values given in brackets indicate the 95% confidence interval.
27
Table H19: Fatality Change Using Prior Correction Methods 2090-2099
Temperature
Rainfall
Snowfall
Additive
Predicted
(1)
464
[368, 552]
-297
[-375, -234]
406
[122, 687]
Multiplicative
Predicted
(2)
457
[370, 536]
-507
[-727, -318]
307
[-99, 752]
Additive
Observed
(3)
478
[396, 555]
-433
[-615, -271]
59
[-24, 150]
Multiplicative
Observed
(4)
-1196
[-1,529, -857]
-12
[-19, -4]
-28
[-45, -11]
ECDF 1
ECDF 2
(5)
468
[387, 547]
-27
[-34, -19]
-45
[-57, -33]
(6)
485
[416, 581]
-102
[-142, -55]
-55
[-81, -30]
573
253
103
-1235
397
340
[255, 862]
[-232, 587]
[-112, 308]
[-1,567, -891]
[310, 476]
[265, 439]
Annual Net
Change
Notes: The estimates are the sum of county level changes in weather on the listed outcome. All future weather simulations
use quantile-mapping to adjust current weather to the changes predicted by CCSM4 RCP6.0 scenario. Values given in
brackets indicate the 95% confidence interval. The Additive Predicted model adjusts the 2090 CCSM4 prediction data
using an additive correction of the baseline discrepancy. The Multiplicative Predicted model adjusts the 2090 CCSM4
prediction data using a multiplicative correction of the baseline discrepancy. The Additive Observed method adds the mean
shift in weather between the baseline and future CCSM4 to the current observed weather. The Multiplicative Observed
method adjusts the current observed weather through multiplication of a common term that matches the baseline CCSM4
to the future CCSM4 data. ECDF 1 repeats Table 6 column 1, which is the Empirical Cumulative Distribution Function
outlined in the main text. ECDF 2 uses the Empirical Cumulative Distribution Function outlined in Appendix G. See
text for further details of calculations.
Table H20: Predicted Changes in Accidents and Net Present Costs under Various Future
Weather Scenarios
CCSM 4.5
(1)
353
[282, 420]
CCSM 6
(2)
397
[310, 476]
CCSM 8.5
(3)
701
[541, 857]
Hadley 3 A1B
(4)
603
[402, 796]
Present Cost ($2015 Mil.)
$302
[$241, $359]
$339
[$265, $408]
$695
[$537, $850]
$511.49
[$344, $681]
Sum of Changes 2015-2099
18,115
[13,910, 22,342]
18,603
[14,240, 22,802]
33,376
[25,419, 41,225]
27,493
[17,964, 37,179]
Sum of Costs ($2015 Mil.)
$44,743
[$33,982, $55,484]
$39,882
[$29,409, $50,134]
$73,482
[$55,569, $91,262]
$62,603
[$38,688, $86,883]
Net Change in 2090
Notes: This table shows net present cost estimates for fatal accidents under the various levels of warming and for various climate
model scenarios and models. For each traffic accident category, we report predicted changes in annual accident frequency stemming
from changes in temperature, rain and snow caused by climate change in 2090 and summed between 2015 and 2099. The Sum of
Costs estimates in the bottom row are the discounted value of costs from 2010 to 2099, using a discount rate of 3 percent and a
VSL of $9,100,000 (Blincoe et al., 2014).
28
(a) Average Annual Predicted Change in Fatalities per 100,000 People
(b) Average Annual Predicted Change in Injuries per 100,000 People
(c) Average Annual Change in PDO Accidents per 100,000 People
Figure H.1: County-Level Predictions, 2090-2099, under the RCP8.0 Future Weather
Scenario
29
.06
Panel (b): Traditional Correction Methods
.06
Panel (a): PDF of Hypothetical Temperature Profile
CCSM 4 2090-2099
Observed Weather
Observed Multiplicative
Smoothed Density
.03
.04
.02
Smoothed Density
.02
.03
.04
41.0° F
0
.01
50.0° F
0
.01
40.0° F
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
Temperature
Temperature
Panel (c): Inverse ECDF: Quantile-based Method
Panel (d): Quantile-based Correction Methods
100
.06
0
100
90
CCSM 4 2006-2009
CCSM 4 2090-2099
QM
Observed Weather
Quantile-based Method
.05
Observed Weather
80
Smoothed Density
.02
.03
.04
70
60
50
40
30
.01
20
10
0
0
Temperature
Predicted Multiplicative
.05
CCSM 4 2006-2009
.05
Observed Weather
0
.2
.4
.6
.8
1
0
Probability
10
20
30
40
50
60
Temperature
Figure H.2: Demonstration of Error Correction Methods
30
70
80
90
100
Appendix References
Blincoe, Lawrence, Ted R. Miller, Eduard Zaloshnja, and Bruce A. Lawrence.
2014. “The economic and societal impact of motor vehicle crashes, 2010.” National
Highway Traffic Safety Administration, Washington, DC.
Burbidge, John B., Lonnie Magee, and A. Leslie Robb. 1988. “Alternative
transformations to handle extreme values of the dependent variable.” Journal of the
American Statistical Association, 83(401): 123–127.
Parry, Ian, Margaret Walls, and Winston Harrington. 2007. “Automobile
externalities and policies.” Journal of Economic Literature, 373–399.
31