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Econometrics
“Speed Thrills but Kills!”
Econ 330
Group 2
Ahsan Ahmad
Muhammad Ovais Siddiqui
Sarmad Alam
Shan e Ahmad

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Table of Contents
Abstract 3
Introduction 4
Literature review 5
Econometric Analysis 7
Conclusion (Limitations) 14
Works Cited 15

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Does an increase in the speed limit
increase the total number of accidents
on rural roads?
Abstract

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Introduction
A sound policy question which we would like to investigate from the data of amount of
accidents from 1981-1989 presented to us is: Will the increase in the speed limit from 55 mph to
65 mph affects the total number of accidents on the rural roads positively or negatively ?
The governmental intervention and regulation of speed limit laws in the U.S have
experienced variation with time. At times of fuel shortages stringent speed limits are enforced
aimed at reducing the maximum speed limit. This is the reason why in 1974 due to the severe oil
crisis a minimum speed limit of 55 mph was applied that remained in force till 1987. The
recovery of U.S economy from recession in 1987 allowed the government at first to amend the
National Maximum Speed Law and raise the maximum limit to 65 mph (as shown in the data
set) and later to repeal it in 1996 by transferring the regulatory authority to the states. Since then
many states like Kentucky (2007), Utah (2009), Ohio (2011) and Texas (2012) have decided to
increase their posted maximum speed, with similar proposals underway in Illinois and South
Carolina1
. However, there is a need of drawing a distinction between two sets of Highways:
statewide rural interstate highways and urban non-interstate highways. Speed limit was raised in
rural interstate highways in 1987 speed laws amendment because these highways had less traffic
congestion as compared to urban non-interstate highways. Our concern in this study will only be
regarding the highways in the rural states.
1
Do We Need Speed Limits on Freeways?
Arthur van Benthem

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Literature Review
The effect of speed limits on accidents has been a subject of particular interest to
economists since the very beginning. The study of these two variables is an important
economical and social concept and a great deal of research has been done in this regard. A few
researchers have tried to answer this question directly, whereas other have tried to relate the
effects of speed limits to accidents through different measures like traffic, or the characteristics
of rural or urban areas.
Arthur Van Benthem of The Wharton School, University of Pennsylvania, in his research
paper on the effects of Speed Limit changes on the number of accidents, found out that a 10 mph
speed limit increase on highways leads to a 3-4 mph increase in travel speed which leads to
9-15 % increase in the road accidents and 34-60% more fatal accidents. He found out that
the social costs of raising the speed limit from 55 to 65 mph are three to ten times larger than the
social benefits.2
This is in coherence with our model which shows that increasing the speed limit
to 65 mph leads to 16.3% increase in the total accidents on the rural roads.
2
Do We Need Speed Limits on Freeways?
Arthur van Benthem

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The government of U.S seems to be pursuing the policy of saving time to cater the fast pace of
its capitalist economy. In the time versus fatality cost-benefit analysis U.S government has
preferred to weigh the notion of saving travel time more than fatality caused by accidents. In
their research, Orley Ashenfelter and Michael Greenstone found out that the 65 mph limit increased
speeds by approximately 3.5% (i.e., 2 mph), and increased fatality rates by roughly 35%.3
Thus,
there are several researches showing the same kind of relationship between the changes in speeds
and resulting increase in the number of accidents.
One of the exogenous variables in our regression analysis is seat belt law. Interestingly
seat belt law shows a positive impact on the number of accidents in the U.S between 1981-1989
i.e. instead of the conventional perception that seat belts reduce accidents we find that seat belt
law actually cause an increment in the accident rate. Our model verifies the views of Peltzman
(1975), who argued that drivers wearing the seatbelts feel more secure, they drive less carefully,
leading to more traffic accidents. Thus, although the use of seat belts decrease fatalities among
drivers wearing them, fatalities among other individuals go up, offsetting the beneficial effects of
seat belts. Findings similar to our findings have been reported by McCarthy (1999) who found
that a mandatory seat belt law increases the number of fatal accidents, whereas Derrig et al.
(2002) found no statistically significant effect of the implementation of seat belt law on road
accidents.
Moreover, the findings of Alexander C. Wagenaar in his paper, Effects of
Macroeconomic Conditions on the Incidence of Motor Vehicle, show that there has been an
inverse relation between unemployment and road accidents. An increase in unemployment in
1974 and 1975 was associated with a decrease road crashes and a decrease in unemployment in
1976 to 1978 was associated with an increase in road crashes. This inverse relation between
these two variables is explained by the fact that higher unemployment would result in lesser road
travel which leads to lesser road crashes. Moreover, high unemployment, which is associated
with a fall in income, would reduce the discretionary driving and unemployed people would
prefer to save their cost of traveling which, again, leads to lesser number of road accidents.
3
Orley Ashenfelter and Michael Greenstone, September 2002. Using Mandated Speed Limits to Measure
the Value of a Statistical Life

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Econometric Analysis
Data Description:
The data provided about road accidents of US was recorded over a period of 108 months from
1981-1989. The variables used in our model are listed below.
The data was sorted in a time series framework where t is the time variable.
Name of variable Description
rtotacc Total accidents on rural 65 mph roads
spdlaw =1 after 65 mph in effect
unem State unemployment rate
beltlaw =1 after seat belt law
feb =1 if month is Feb.
mar =1 if month is Mar.
apr =1 if month is Apr.
may =1 if month is May.
jun =1 if month is Jun.
jul =1 if month is Jul.
aug =1 if month is Aug.
sep =1 if month is Sep.
oct =1 if month is Oct.
nov =1 if month is Nov.
dec =1 if month is Dec.
lrtotacc Log(rtotacc)

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Model Specification and Modification:
The data we are taking is about the speed limit which, as explained earlier, was increased
from 55 mph to 65 mph in May 1987. Our hypothesis is to see the general association of this
increase in speed limit on the number of accidents on these rural roads. For that we run the
regression of our basic model.
After the regression, the Beta coefficient of spdlaw turns out to be positive. This shows
that the modification in the law i.e. the increase of speed limit from 55 mph to 65 mph is
associated with an increase in the total number of accidents on the rural roads by 133.5 accidents
on average.
This increase in total accidents (rural) can be attributed to the increase in speed limit.
After allowing the people to drive at a higher speed, they are more likely to have accidents.
However, this simple equation needs to incorporate the omitted variables and needs to be
checked for several other requirements that should be fulfilled.
200300400500600
tot.acc.onrural65mphroads
0 20 40 60 80 100
time trend

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Firstly, since time-series data generally follows a seasonal trend, it needs to be de-
seasonalised. To do so we added the seasonal months’ dummy variables to the equation keeping
January as the base group. In our particular example the effect of seasonality on the number of
cars can be such that in different seasons the road conditions may affect the probability of the
occurrence of an accident. This means that from our starting equation we have accounted for the
effect of seasonality among different months that was formerly showing in the coefficient
of spdlaw, thus the coefficient of spdlaw decreases as expected.
The high coefficients for the months of June, July, August and September might be
because people travel more often during this season which automatically increases the chance of
an accident occurring.
Further we performed the omitted variable test so as to determine whether the model
suffers from any omitted variable bias. Since we get the p-value 0.3616 we conclude that there is
no omitted variable bias.
However we still add unemployment (unem) variable to the equation because it is a
significant variable (according to prior research in the field) and adding it to the equation
increases our R2
(the percentage of the total accidents explained by the several independent
factors). Adding unem also brings down the coefficient of spdlaw by a significant amount.

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Unem is highly correlated with total accidents and the relationship is negative. The
negative relationship shows that an increase in unemployment rate is associated with a decrease
in the total number of accidents. This may be because, as we discussed earlier, as the rate of
unemployment increases more people are likely to stay at home and there will lesser road
traveling thus less travelling would take place, thereby reducing the chances of accidents.
To check for functional form misspecification we carry out the Regression Specific Error
Test (RESET). The p-value for this equation’s RESET Test is 0.0432 which shows that
functional for misspecification exists. To remove this functional form misspecification we take
the log of rtotacc and repeat the RESET. Following this change the RESET shows that there is
no more functional form misspecification.

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Now, our interpretation also changes; the implementation of the policy is now associated
with a 23.6% increase in total accidents on rural roads when speed law is implemented
comparatively.
Our data includes information on another legislation; the belt-law. The use of seat-belt,
according to our data, was made mandatory in January 1986. We would like to include this
variable as well into the equation so as to gauge the association of the use of belt law and the
number of accidents. After the belt-law was implemented, the number of accidents increased on
average by about 17.9% (keeping other independent variables fixed). A related explanation was
5
5.5
6
6.5
log(rtotacc)
0 20 40 60 80 100
time trend

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recently offered by the British Psychological Society. This proposes that during narrow escapes
while driving, the actual physical restraint experienced by seatbelt wearers leads to a reduced
sense of threat to life. A reduced sense of threat may then lead to the adoption of a more
dangerous driving style which increases the accidents. 4
Since we have added variables to our original equation we need to see if the standard
errors are high due to multi-collinearity amongst the independent variables. For this we make use
of Variance Inflation Factors (VIF). Our mean VIF is 2.07 and the maximum VIF among the
independent variables is 2.93. Since these VIFs are well below the benchmark of 4 then this is
good news for our model.
Durbin-watson statistic (measure of serial correlation in a time-series model) comes out
to be 0.996. To cure serial correlation we add lag variables for unemployment rate. This results
in a decreased dwstat contributing to serial correlation.
4
The Puzzle of Seat Belts Explained, Press Release of the Annual Conference of the British
Psychological Society, April 1999

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To check for homoskedasticity we use archlm command since the data is time-series. The
p-value comes out to be 0.7066 thus we fail to reject our null hypothesis that is no
Autoregressive Conditional Heteroskedasticity. Hence our model is homoskedastic.
To check if the error term follows a normal distribution or not we use sktest command in
Stata. The null hypothesis, that there is no difference between the normal distribution and the
distribution of the error term. Since we fail to reject our null hypothesis then we conclude that
our error term follows the normal distribution.

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Conclusion (limitations)
Through our econometrics analysis we came to the conclusion that the increase in speed
limit in 1987 was quite substantially related with the number of accidents on the rural roads. Our
final model estimates that after the imposition of the new speed limit, the total rural accidents
went up by 16.3%. The report by Arthur Van Benthem also claims that a 9-15% increase in the
total number of accidents due to the increase in the speed limit.
We also incorporated ‘The seat belt law’ (beltlaw) and ‘Unemployment’ (unem) variables
in our regression model to purify the effect of speed law (spdlaw) on our dependent variable
(lrtotacc).
There were some limitations with respect to the data provided, for instance, if other
driving laws statistics, eyesight laws of driving, other information regarding the condition of
roads like frequency of street lights, sign boards, traffic signals and information about drivers for
example, age of drivers, alcohol consumption level, experience and education of driving etc.
The unemployment information used in our regression model is statewide whereas, the
data we have taken into account for total accidents is for the rural roads only.
Our model suffers from serial correlation which is the major drawback of our model.
Even after incorporating the lag unemployment variables, the dwstat remained close to 0.98. This
problem could be attributed to the lack of further available variables as mentioned.

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Works cited
Wagenaar, Alenadaer C. EFFECTS OF MACROECONOMIC CONDITIONS ON. Rep. U.S.A:
Pergamon, 1984. Web. 11 Dec. 2012.
<http://deepblue.lib.umich.edu/bitstream/2027.42/24788/1/0000214.pdf>.
Cohen, Alma, and Liran Einav. THE EFFECTS OF MANDATORY SEAT BELT LAWS ON
DRIVING. Rep. N.p.: n.p., n.d. Web. 11 Dec. 2012.
<http://econweb.umd.edu/~vegh/courses/Econ396-397/Econ396/Computer-lab-
material/Cohen.pdf>.
Ashenfelter, Orley, and Michael Greenstone. "Using Mandated Speed Limits to Measure the
Value of a Statistical Life." N.p., Nov. 2002. Web. 11 Dec. 2012.
<http://papers.ssrn.com/sol3/papers.cfm?abstract_id=331463>.
Balkin, Sandy, and Keith Ord. "The Impact of Speed Limit Increases on Fatal Interstate
Crashes." N.p., n.d. Web. 11 Dec. 2012.
<http://www.consumersunion.org/other/speedlimits/speed031500a4.htm>
Wagenaar, Alexander C. UNEMPLOYMENT ANDMOTOR VEHICLE ACCIDENTS IN
MICHIGAN. Rep. U.S.A: n.p., 1983. Web. 11 Dec. 2012.
<http://deepblue.lib.umich.edu/bitstream/2027.42/208/2/48596.0001.001.pdf>.