The Effect of Urban and Rural Interstate Speed Limits On Automobile Fatality Rates Abstract Since the beginning of time, people have taken risks. Why? – Perhaps for the inevitable thrill, and exhilaration. This is why people speed, and why speed-deaths account for nearly 30% of all fatal automobile crashes. Yet what is the role of speed limits? Do interstate speed limits actually curb auto fatalities? In the following paper, using panel data, I analyze the general effect of both urban and rural interstate speed limits on fatal automobile crashes within the United States over the years 1994 to 2008. The final results include an empirical model and show an average increase of 0.81% in auto fatalities for every one mile per hour increase in urban interstate speed limits. However, the results of the dummy variables which indicate the change to higher speed limits in both urban and rural interstates are both statistically insignificant. Brian Koralewski Master’s Thesis, Fall 2010 Final Draft (12/9/2010) SUNY Binghamton
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The Effect of Urban and Rural Interstate Speed
Limits On Automobile Fatality Rates
Abstract
Since the beginning of time, people have taken risks. Why? – Perhaps for the inevitable thrill,
and exhilaration. This is why people speed, and why speed-deaths account for nearly 30% of all
fatal automobile crashes. Yet what is the role of speed limits? Do interstate speed limits actually
curb auto fatalities? In the following paper, using panel data, I analyze the general effect of both
urban and rural interstate speed limits on fatal automobile crashes within the United States over
the years 1994 to 2008. The final results include an empirical model and show an average
increase of 0.81% in auto fatalities for every one mile per hour increase in urban interstate speed
limits. However, the results of the dummy variables which indicate the change to higher speed
limits in both urban and rural interstates are both statistically insignificant.
Brian Koralewski
Master’s Thesis, Fall 2010
Final Draft (12/9/2010)
SUNY Binghamton
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I. Introduction
Ever since the introduction of the automobile into American society in the early 1900s,
crashes and the subsequent fatalities have been an unfortunate side effect of this otherwise
pivotal invention. It was not until the late 1960s and early 1970s when the U.S. government
began taking the initiative in preventing auto crashes. Regulation laws mandating three-point
seat belts, airbags, and rear/side-view mirrors in all U.S. manufactured automobiles were
authorized over the years1. In 1974, Congress passed the Emergency Highway Conservation
Act, in which the National Maximum Speed Law was included. This maximum speed law
required all national interstate speed limits to be set at no higher than 55 miles per hour.
Interestingly enough, this federally mandated 55 mph speed limit was instigated not only for the
purpose of reducing automobile crashes and fatalities, but to also limit the country’s gas usage,
as the world was in a critical energy crisis at the time2.
In 1994, however with building pressure from the National Motorists Association,
Congress repealed the National Maximum Speed Law, leaving state governments to dictate their
own interstate speed limits. In 1995, the National Highway Designation Act was passed. This
act removed all federal control of interstate speed limits. Since then, a good number of states
have reverted back to their pre-1974 speed laws, raising their interstate speed limits twenty mph
higher in some cases. Although several studies have been conducted examining the effect of the
repeal of the National Maximum Speed Law, the results have largely been varied. A 1999 study
by Stephen Moore of the Cato Institute proposed that “Speed Doesn’t Kill” which attributed the
repeal to an actual decline in automobile fatalities as well as auto insurance premiums in the
1 Peltzman, Sam. "The Effects of Automobile Safety Regulation." The Journal of Political Economy, 1975. 2 Statement on Signing the Emergency Highway Energy Conservation Act, Richard Nixon, 1974.
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following years3. A contrary study done by the Insurance Institute for Highway Safety (IIHS) a
year earlier proposed the opposite: that increased speed limits lead to more accidents and deaths4.
The study done by the IIHS was criticized by Moore for analyzing simply a sample of states that
had raised their speed limits, as opposed to studying all of the states that had done so. Although
the study conducted by the Insurance Institute for Highway Safety surely had its flaws, the
evidence certainly does not indicate Moore’s study as being in the right. His study does not
utilize any statistical analysis; rather, he observes only percent changes in auto fatality rates and
crashes from the years 1995 through 1997. His sample size of only two years of data is also
quite meager. Thus the question remains: do higher speed limits indeed cause more or less auto
fatalities?
II. The Models
The true effect of the repeal of the National Maximum Speed Limit Law in late
1995 would surely be an interesting outcome to measure. However, since the data on individual
state fatality rates are for some reason severely limited in their history (see following paragraph),
and that data on the FARS website (Fatality Accident Reporting System – the data source of the
analysis), despite its extensiveness, goes back only to 1994 for automobile death rates, a before-
after comparison would have yielded biased, not to mention flawed, statistical results. To go
back as far as 1994 is certainly not enough time before the law to observe an accurate effect of
the repeal. Thus consequently, I will simply look at the general effect of speed limits on
automobile fatality rates (controlled for density of traffic). Though the Maximum Speed Limit
Law was repealed in ’95, many states did not change their interstate speed limits until a few
years later. Hence up until at least 1995, all states were at the federally mandated 55 mph speed
3 Speed Doesn't Kill: The Repeal of the 55-MPH Speed Limit; The Cato Institute, Stephen Moore 1999. 4 Insurance Institute for Highway Safety, 1999.
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limit. My study therefore, will show if there are any positive, statistically significant speed limit-
coefficients after regressing on auto fatality rates. Three different models will be used. The first
model will be a simple panel regression using fixed-effects and controlling for the
heteroscedasticity using robust standard errors. The second model will be a panel regression
model with AR(1) disturbances (also with fixed-effects and robust standard errors). And the last
model will be a recent technique imposed by Driscoll and Kraay some ten years back, using a
Driscoll-Kraay standard error and a fixed-effects MA(1) process to control for trend and any
cross-sectional dependence within the panel.
The data consist of a panel, with 49 states over fifteen years (1994-2008), for a total of
735 observations5. I decided to analyze the effect of speed limits over the whole country, rather
than just individual states, due to the lack of data in certain state’s Department of Transportation
websites. In some states such as New York for example, the data on auto fatalities went back
only as far as 1987, and any data presented after the year 2000 was noted to be “incomparable”
to the previous years due to changes in “data collection.”6 Also there were no quarterly data
readily available.7 Thus I was inclined to rely on the Fatality Accident Reporting Statistics
website, a statistical research group under the heading of the government-regulated National
Highway Traffic and Safety Administration (NHTSA). Data given by FARS included the
automobile fatality rate per one hundred million Vehicle Miles Traveled for each state. This
allowed me to combine all states into a panel, bringing the final number of observations to: 49 x
15 = 735. The dependent variable is the annual number of fatalities divided by annual Vehicle
Miles Traveled, multiplied by one hundred million and then logged. The independent variables
5 D.C. and Maine were left out of the panel due to missing data (i.e. no rural interstates in D.C. and no urban interstates in Maine) 6 New York State Department of Motor Vehicles; Statistical Summaries, Archives. 7 When I inquired by email for quarterly data reports I received a response that requested I fill out a Freedom of Information Law form (FOIL), and was told that this still did not guarantee the availability of quarterly data regarding automobile fatality rates for New York State.
(reference*). Thus to account for this apparent negative trend I use a fixed-effects panel
regression with AR(1) disturbances. An MA(1) or moving average process on the other hand
also accounts for trend, calculating the current value of the dependent variable using current and
lagged disturbances, as opposed to lagged values of the actual dependent variable (which is AR).
The MA model has been criticized for calculating only unobservable shocks as opposed
to actual observed values, as the autoregressive process demonstrates. This is the main reason
why the AR process is a better controller of trend than the MA model (reference*). Furthermore
AR models use a current shock and all the lagged values of the dependent variables in the entire
dataset, where as MA uses simply a current shock and a lagged shock that goes back only one
time period. Despites its given short-comings however, the moving-average process is still quite
a well-rounded estimator of general trend in any observed variable of interest, and is in fact used
widely today in the financial world to forecast stock prices. For my final model in order to
12 “Fixed Effects Models.” David Dranove, Northwestern University.
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account for cross-sectional dependence within the panel, I use specific standard errors by
Driscoll and Kraay. In estimating these specific errors, an MA(1) process is used.
After running a Pesaran test and uncovering cross-sectional dependence within the data
(i.e. one state affects another states fatality rates), I account for this by using Driscoll-Kraay
standard errors13
. This model also uses a regular fixed-effects panel regression, however with an
MA process. The reasoning behind the Driscoll-Kraay standard errors is that, although in many
microeconomic panel data sets (such as the one in the current study) the standard errors are
adjusted for heteroscedasticity and autocorrelation, they do not in fact account for cross-sectional
(i.e. spatial) dependence across the panel. Although it is easy to say that there should be cross-
sectional independence within data containing states, and/or countries, recent empirical analysis
has proved otherwise, stating there to be “…complex patterns of mutual dependence between the
cross-sectional units.” (Hoechle) The Pesaran Cross-Dependence test positively testifies to this
statement, in regards to the current panel dataset at hand. Thus the standard errors of commonly
used regression methods (i.e. OLS, White, clustered standard errors) that do not account for
spatial correlation will ultimately be biased. Originally, robust and clustered standard errors
remain statistically valid if the residuals are correlated within the entities, but not between them.
Hence, this is where Driscoll and Kraay came in. Driscoll and Kraay ten years earlier formulated
an estimator that calculated heteroscedastic standard errors and also controlled for “spatial and
temporal dependence.”14
Initially in 1967, a paper by Parks proposed the feasible generalized
least squares approach (FGLS) to deal with the problem of cross-sectional dependence within
microeconomic panel data sets. Yet this method turned out to produce only valid results if the
number of years was greater than the number of entities (i.e. T>N), as is rarely the case for many
13 Robust Standard Errors For Panel Regressions With Cross–Sectional Dependence; Daniel Hoechle, 2007. 14 John Dricoll and Aart Kraay, 1998. “Consistent Covariance Matrix Estimation With Spatially Dependent Panel Data," The Review of Economics and Statistics, MIT Press.
within 4.323436 1994 2008 T = 15 between 0 2001 2001 n = 49year overall 2001 4.323436 1994 2008 N = 735 within 170.9397 284.4449 3359.912 T = 15 between 643.1654 0 2001 n = 49andupy~r overall 1753.312 659.5393 0 2008 N = 735 within 945.8071 -.0027211 2008.131 T = 15 between .0190476 668.2 668.3333 n = 49avgyear overall 668.3306 945.8071 0 2008 N = 735 within 845.6532 -772.3102 2702.356 T = 15 between 535.06 401.4 2001 n = 49lyear overall 1095.756 997.9769 0 2008 N = 735 within 692.5299 -519.9592 2955.441 T = 15 between 698.3936 0 1735.067 n = 49ryear overall 1215.107 978.7993 0 2008 N = 735 within 644.4479 -628.9769 2445.423 T = 15 between 767.2528 0 1735.067 n = 49uyear overall 1106.09 996.3743 0 2008 N = 735 within .0852415 .1428571 1.67619 T = 15 between .321455 0 1 n = 49drive1~p overall .8761905 .3295884 0 1 N = 735 within .4717255 0 1 T = 15 between 0 .3333333 .3333333 n = 49dummya~e overall .3333333 .4717255 0 1 N = 735 within 62.0412 209.785 822.785 T = 15 between 110.4745 233.7333 766.2 n = 49justic~s overall 402.785 125.7813 146 906 N = 735 within .4217088 -.3863946 1.346939 T = 15 between .2676992 .2 1 n = 49baclaw overall .5469388 .4981309 0 1 N = 735 within .3457278 -.2598639 1.473469 T = 15 between .3488725 0 .8666667 n = 49change~l overall .6068027 .4887926 0 1 N = 735 within .3217798 -.3142857 1.219048 T = 15 between .3832125 0 .8666667 n = 49change~n overall .552381 .4975873 0 1 N = 735 within 5.511115 48.40136 81.73469 T = 15 between 4.663679 55 72.33333 n = 49rural overall 65.73469 7.190789 55 75 N = 735 within 4.09388 43.99592 74.66259 T = 15 between 5.27054 50 72.33333 n = 49urban overall 61.32925 6.633899 50 75 N = 735 within .1186906 -.1873605 .8073061 T = 15 between .2520267 -.1753333 .8873333 n = 49y overall .4293061 .2763935 -.4 1.08 N = 735 Variable Mean Std. Dev. Min Max Observations
overall = 0.0995 max = 15 between = 0.0098 avg = 15.0R-sq: within = 0.4967 Obs per group: min = 15
Group variable: state1 Number of groups = 49Fixed-effects (within) regression Number of obs = 735
> verage drive16andup uyear ryear lyear avgyear andupyear year, fe robust. xtreg y urban rural changeurban changerural baclaw justiceexpenditures dummya
Key: Y = Annual automobile fatalities per state divided by annual Vehicle Miles Traveled, multiplied by 100
million, and then logged
urban = urban interstate speed limits (i.e. within an urbanized area holding a population of 50,000 people
or greater)
rural = rural interstate speed limits
changeurban = dummy variable accounting for the change in urban interstate speed limits by state
changerural = dummy variable accounting for the change in rural interstate speed limits by state
baclaw = dummy variable indicating the .08 BAC illegal per se law, per state
justiceexpenditures = Justice expenditures per capita by state (includes police protection, judicial and legal
expenditures and corrections)
dummyaverage = dummy variable indicating years when state averages were filled in for missing data years
in justice expenditures (i.e. 2001, 2003, 2006-2008) drive16andup = dummy variable indicating whether or not the earliest age to acquire a regular license per
state is at least 16
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uyear = interaction term; changeurban * year
ryear = interaction term; changerural* year
lyear = interaction term; baclaw * year
avgyear = interaction term; dummyaverage * year
andupyear = interaction term; drive16andup * year
year = trend
The coefficient on urban implies a partial effect of 0.67%. This indicates a 0.67%
increase in the auto fatality rate for every one mile per hour increase on urban speed limits, even
though the resulting t-statistic is insignificant. The other coefficient with a high t-statistic (in
context of the model) is baclaw. The partial effect on baclaw is measured as b5 + b11*year,
which numerically equals approximately 14.8 - .0074*year. Thus as time increases, the partial
effect of the coefficient baclaw on auto fatality rates decreases. The trend variable is also
negative, implying that for every one-year increase, fatalities decrease by about 0.69%. This
decrease is undoubtedly attributed to increased safety regulations on automobiles, and improved
roadways across the nation21
.
21 Chan, K.S., and Johannes Ledolter. "Evaluating the Impact of the 65 mph Maximum Speed Limit on Iowa Rural Interstates." American Statistician, 1996.
within R-squared = 0.4967maximum lag: 2 Prob > F = 0.0000Group variable (i): state1 F( 14, 48) = 1377.80Method: Fixed-effects regression Number of groups = 49Regression with Driscoll-Kraay standard errors Number of obs = 735
Key: Y = Annual automobile fatalities per state divided by annual Vehicle Miles Traveled, multiplied by 100
million, and then logged
urban = urban interstate speed limits (i.e. within an urbanized area holding a population of 50,000 people
or greater)
rural = rural interstate speed limits
changeurban = dummy variable accounting for the change in urban interstate speed limits by state
changerural = dummy variable accounting for the change in rural interstate speed limits by state baclaw = dummy variable indicating the .08 BAC illegal per se law, per state
justiceexpenditures = Justice expenditures per capita by state (includes police protection, judicial and legal
expenditures and corrections)
dummyaverage = dummy variable indicating years when state averages are filled in for missing data of
justice expenditures (i.e. 2001, 2003, 2006-2008)
drive16andup = dummy variable indicating whether or not the earliest age to acquire a regular license per
state is at least 16
uyear = interaction term; changeurban * year
ryear = interaction term; changerural* year
lyear = interaction term; baclaw * year
avgyear = interaction term; dummyaverage * year
andupyear = interaction term; drive16andup * year year = trend
The final model uses Driscoll-Kraay standard errors, to account for cross-sectional
dependence within the data. Driscoll-Kraay estimation also uses a moving average process,
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which benefits the model since there is certainly presence of a decreasing trend in auto fatalities
in our years of interest. Once again we assume fixed effects between states. The coefficients are
identical to the initial model, in which a regular fixed-effects panel regression is used, but the
Driscoll-Kraay standard errors are much lower, thus several variables now hold statistically
significant t-statistics at the 95% level. The coefficient on urban implies a significant 0.67%
increase in the fatality rate with every one mile per hour increase on urban interstates. baclaw
also boasts a relevant t-statistic, with its partial effect equaling 14.8 - .0074*year. Again as
mentioned in the first model, baclaw has a negative effect on fatalities over time. Interestingly,
the coefficients on changerural and its interaction term ryear are almost relevant at the 90%
level. The partial effect of changerural equals 4.33 - .002*year, indicating that over time, the
change to higher rural interstate speed limits caused a slight decline in auto fatalities. As
mentioned earlier, this decline is undoubtedly due to safer cars and improved roadways across
the nation.
IV. Discussion
Urban interstate speed limits had a significant positive effect on fatalities in the last two
models, indicating an average increase of 0.81% in fatalities for every one mph rise in the urban
speed limit. Likewise, the dummy variable baclaw was significant, as was its interaction term.
However, in contrast to the positive effect of urban, the partial effect of this alcohol-related
driving law signified a consequential relevant decline in auto fatalities over time. Also
interestingly, in the final model which used Driscoll-Kraay standard errors to account for cross-
sectional dependence in the panel, the coefficient on changerural boasted an almost significant t-
statistic at the 90% level, as did its interaction term with the trend variable. The partial effect of
changerural indicated that over time, the change to higher rural speed limits actually lowered
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auto fatalities. This decreasing trend is most likely due in part to an increase of safer cars, and
improved highway conditions across the country. Furthermore, the variable dummyaverage was
significant at the 95% level in the autoregressive model, that seemingly implies that increasing
police and legal action funding may indeed have an inverse effect on auto fatalities (although
interpreting this variable is rather difficult, since dummyaverage does not exactly signify justice
expenditures, but simply the specified years). Lastly, it must be mentioned that although urban
speed limits indeed possessed a positive significant effect on fatalities within the latter models,
the dummy variable changeurban, which accounted for the change to higher urban interstate
speed limits nationwide, happened to be quite insignificant within all three results. Therefore,
the effect on urban must not be misinterpreted – as we can see from this study, higher speeds do
not necessarily indicate more deaths. The variable justiceexpenditures was insignificant in all
three models, perhaps implying the minimal effect of police protection on auto fatalities. Also
insignificant was the variable rural.
V. Conclusion
What is the ultimate effect of speed limits on auto deaths? Does speed really kill?
According to the current analysis, the answer is still partly ambiguous. Certainly, driving faster
will increase the probability of crashing, therefore the probability of death increases as well. Yet
in the last two decades an increase in automobile safety regulation, mandating safer cars on the
roads, has greatly reduced this probability. Further reducing the chances of death on the road
include improved highway and road conditions across states, also enabling cars to drive faster by
decreasing the risk of a probable fatal crash. Another factor has been increased legislation on
traffic safety, such as imposing harsher penalties for violating traffic laws, and instituting new
laws within each state such as the BAC illegal per se law. In order to discreetly analyze the
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effect of speed limits on auto fatalities, one would have to include all traffic and automobile
regulations that were passed between the years 1994-2008, as well as any interstates with
improved road conditions (i.e. all time-variant variables left outside of the fixed-effects model).
However, would the findings be very different than those found in the current study? I think not
– the effect would certainly perhaps be less; most likely very close to zero, yet still positive.
Which goes to show that speed, no matter how safe our vehicle, still ups the chances of us
crashing and possibly dying. Therefore, for any individual behind the wheel, it is key to
remember that our lives are worth enough surely, to slow down.