1. Factors that Affect the Drunk-driving Crashes
DPU ID: 414796
Prof. Goma
2013/5/8
Abstract
This paper answers the question, what factors affect drunk-driving crashes
between 1994 and 2010, in the U.S through the analysis of previous related
literature as well as through regression analysis. According to the model
constructed in this paper, macroeconomic conditions such as unemployment rate
and per capita personal income combined with microeconomic variables,
including gasoline prices and alcohol taxes altogether have a significant impact
on drunk-driving crashes.
2. Index
1. Introduction……………………………………………………………………... 3
2. Literature Review………………………………………………………………...5
3. Model and Data…………………………………………………………………..7
4. Results…………………………………………………………………………...13
5. Conclusion……………………………………………………………………….16
6. Appendix………………………………………………………………………...17
7. References……………………………………………………………………….22
3. I. Introduction
Although great efforts have been made to control alcohol-impaired driving
since the release of new legislation in 1980s, nearly ten thousands fatal crashes
were defined as alcohol-impaired driving1
according to the FARS database, which
accounted more than 30% of the total fatal crashes in 2011. However, these
numbers only covered the case of fatal crash in which at least one person dies
within 30 days of the time and date of the accident. In fact, nearly 1.2 million
drivers were arrested for driving under the influence of alcohol and more than 160
million people self-reported that they had once drunk driven in 2011. Even though
a set of new alcohol control policies2
such as minimum legal drinking age (MLD)
have been implemented several years ago, little progress has been seen by the
public. For example, the fatalities in alcohol related crashes per million miles
traveled changed little in the past ten years. After a dramatic decline between 1982
and 1989, the alcohol-impaired fatalities have been fluctuating around the level of
56 per million miles traveled. A chart, which illustrates the past trend of
alcohol-impaired fatalities, is listed in Appendix A. Meanwhile, the percentage of
total traffic fatalities that are alcohol related has maintained around 30% since
1994. Unfortunately, the number of people who were killed on our nation’s
highways due to the alcohol-impaired driving steadily increased these years
(Appendix B).
1
Alcohol-impaired driving is defined as at least one driver or motorcycle rider had a BAC of .08 or
higher.
2
Other policies include laws focused on the distribution and consumption of alcohol. In addition,
community programs such as Mothers against Drunk Driving (MADD) and Students against Drunk
Driving (SADD) have been developed to reduce drinking sentiment.
4. Among all age groups of drivers in fatal crashes with BAC levels 0.08 or
higher, 21 to 24-year-old drivers are considered to be the most intoxicated.3
Male
drivers are expected to be twice as likely (26%) as female drivers (13%) to be
intoxicated in fatal crashes based on the fact that more than 80% of all drunk
drivers with BAC .08 or greater are males.
The last but the most important fact about impaired driving is its highly
economic cost to the society, which makes it the focus of a large number of
economic researches. In 2011, alcohol related crashes cost an estimated $120
billion in total, $57.8 billion in direct monetary costs and $ 62.2 billion in quality
of life losses, including but not limited to medical costs, work loss, public services
costs for police, fire, ambulance, and helicopter services, property damage, and
court costs. Alcohol-impaired driving also has a huge impact on the insurance
industry, which is considered as the major private sector to undertake the
considerate cost of the destructive consequences of alcohol-involved car accidents.
According to Miller and Zaloshnja (2011), alcohol-related crashes accounted for
an estimated 18 percent of the $110 billion in U.S. auto insurance payments in
2011. Moreover, alcohol-impaired driving poses a significant pressure on the
nation’s employers. A recent survey done by National Highway Traffic Safety
Administration pointed out that alcohol involved crash injuries on and off the job
cost employers almost $62 billion annually during 2009-2011.
In order to help policy makers find better ways to reduce alcohol-impaired
3
Appendix C
5. driving, this paper try to determine major factors that are highly correlated to
alcohol-impaired crashes with an emphasis on macro and micro economic
variables such as price level, unemployment rate, and per capita personal income
rather than previously implemented policies. A multiple-variable model is going to
be developed to examine the relationship among drunk-driving crashes and macro
and micro economic variables, using the annual data between 1994 and 2011, in
the U.S. Thus, the paper is arranged in the following way. In section II, we review
the previous research on this topic. In section III, we present our model and briefly
discuss the sources of our data. Section IV contains different regression results.
Section V is the conclusion and suggestion for further study.
II. Literature Review
Although a great deal of research about alcohol-impaired driving existed,
most work focused on the impacts of public policies. For example, Eisenberg
(2003) compares the time-series results of states with different alcohol control
policies in reducing the number of fatal crashes and found that the 0.08 Law4
was
the most effective one. The second most effective policy is found to be the
graduated licensing programs, which gradually grant young drivers more
privileges over time. Based on Eisenberg’s finding, Thomas S. Dee (2001) extends
the research by including state and fixed year effects in a simple regression model.
The associated coefficient is found significant at 5% significance level, implying
that 0.08 limit reduces the alcohol-involved crash rate by approximately 1200
4
The 0.08 Law is signed by President Clinton in October 2000, which encourages states to adopt a 0.08 Blood
Alcohol Content standard. Otherwise, states gradually loose federal highway funding over several years.
6. people annually, in consistence with the previous estimation of Eisenberg. In
another study discussed the proper amount of alcohol allowed in a driving
person’s blood, Carpenter (2004) concludes that Zero Tolerance laws5
reduces the
overall amount of alcohol-impaired driving 20%-30% by directly reducing the
alcohol consumption behavior. Other studied policies include BAC levels, Dram
Shop Laws,6
open container laws, and mandatory jail sentence for first time
offenders, and seatbelt enforcement. Though, the logic behind this cause
relationship is obscure, the study conducted by Eisenberg indicates that a lower
BAC limit is significant at the five percent level in reducing the amount of fatal
crashes involved alcohol, especially during the period of six years after policy
enactment. In addition, seatbelt laws and open container laws are found as
contributors to the decline of alcohol-involved crash rate in different regressions.
However, little has been done to examine the correlation between
macroeconomic conditions and alcohol-impaired driving. Up to date, one of the
most comprehensive literature reviews is given by Chad and Nathan (2010), in
which he listed several major outcomes from Evans, Graham, Wagenaar, Leigh
and Waldon. For example, Evans and Graham (1998) find a procyclical
relationship between unemployment and fatalities in alcohol related by controlling
VMT. Slightly different from Evans and Graham who use cross-sectional data for
all states in U.S., Wagenaar (2004) finds a negative but small in magnitude
relationship between unemployment and alcohol-related fatalities using
5
Laws which made it a crime to be an underage driver and have any noticeable amount of alcohol in one’s blood.
6
Persons injured by drunk drivers can take legal action against establishments frequented by the intoxicated
person.
7. time-series data extracted from Michigan between 1994 and 2004. In addition,
Leigh and Waldon (2001) find the sign of raw correlation between unemployment
and alcohol-related fatalities change from negative to positive, after relaxing the
control of VMT7
in estimating random-effects regression models. Yet, this result
is contradictory to Wagenaar’s finding that VMT doesn’t have a significant
intervening effect on the unemployment-alcohol-related fatalities relationship.
Other than the unemployment rate, per capita personal income is another
explanatory variable frequently included in the previous models. For example, a
case study by Traynor (2008) using the data of Ohio finds a nonlinear relationship
between per capita personal income and alcohol-related fatalities per VMT when
an interaction term is included.
While past research comprehensively examined the relationship between
economic conditions and alcohol-related fatalities as well as the effectiveness of
public policies on reducing the alcohol-impaired driving, no studies have
integrated macro and micro economic variables with public policies together to
study their combined impacts on reducing drunk drivers. Our paper is going to fill
this gap by constructing a multi-variable model including but not limited to
variables mentioned above but with a focus on macro and micro economic
variables.
III. Model and Data
This paper uses the time series and regression based approach to quantify the
7
Vehicle miles travelled
8. strength of relationship between drunk-driving crashes and selected macro and
micro economic variables. To apply the method of generalized linear regression in
a multi-variable model, we assume the linearity based on the findings of most
previous researches. For example, Mast et al. (1999) develops a simple linear
regression to describe the relationship between alcohol-related fatalities and
alcohol taxes. Joseph (2006) analyzes the influences of drunken driving laws and
demographics on incidents of drunk driving, using cross-section data and
multi-variable regression. Although all independent variables selected in this
paper have been mentioned in previous research, no one before has combined
these factors together in one model to study their aggregating impacts due to the
challenges of Multicollinearity among independent variables and the stationarity
of time series data. Thus, a large portion of models developed in the past times
tend to overestimate the power of independent variables due to the exclusion of
other potential variables. In order to fix the problem of over-simplification,
following explanatory variables are chosen and their impact on the magnitude of
drunk driving is estimated using the following model
1. : is defined as drunk-driving crashes per vehicle million miles traveled in
year t8
considering that increasing amount of traffic through time will result
more crashes. Since the increasing trend of drunk-driving crashes violates the
stationary requirement of OLS regression, we divide the total number of
8
From now on, the lower subscript “t” represents year t, indicating that the data is time-series. For this
study, we take the time period from 1994-2011. All data are annual data or calculated as the average of
12 monthly data.
9. drunk-driving crashes by total vehicle miles travelled. Different from previous
researchers, who used crash rates generated from data provided by the Fatal
Accident Reporting System of the National Highway Traffic Safety
Administration, this paper uses data of fatal, injury, and property damage only
drunk-driving crashes to represent each year’s total amount of
alcohol-impaired driving. Although we only obtained annual data at national
level for the past eighteen years, it is still an improvement compared to the
previous sources of data because the Fatal Accident Reporting System only
released the numbers of the fatal crashes in the U.S. but did not provide
information on injury and PDO crashes. However, the majority of
alcohol-impaired driving results in nonfatal driving crashes. Thus, it’s
important to include all types of drunk-driving crashes.
2. : is defined as the unemployment rate. We use each year’s average number,
obtained from the U.S. Bureau of Labor Statistics for the past eighteen years.
Found by most researches, which link the alcohol-impaired driving with the
quantity of driving and changes in behaviors associated with driving risk
during a recession, higher unemployment rate means lower drunk-driving
crashes. Nevertheless, debate over this negative relationship between
unemployment rate and drunk-driving crashes never stops. People like Cotti
(2011) who agree with this statement, hypothesize that families used to
traveling by air to vacation destinations may shift to driving to less expensive,
relatively nearby destinations when the economy is in the downturn.
10. Following the logic described above, more miles driven cause more
drunk-driving crashes. On the other hand, it’s possible that people who lost
jobs or reduced work hours will commute less to and from work. Moreover,
even individuals who remain employed may have less disposable income,
which results in less driving. Thus, drunk-driving crashes tend to decrease with
a decline in the total driving. In the past twenty years, unemployment rate of
U.S. experienced several ups and downs, while drunk-driving crashes declined
rapidly for the first ten years but remained unchanged for the second ten years,
which implies that other variables such as per capita personal income may
greatly offset the impacts of unemployment.
3. : is defined as per capita personal income as drunk-driving is an individual
behavior. Again, we use the average number for each year posted by the U.S.
Bureau of Labor Statistics. Here, personal income per capita is not only
included as a major macroeconomic variable but also a factor of alcohol
consumption. It’s no doubt that alcohol consumption is the key to the problem
of alcohol-impaired driving. In order to simplify the discussion, we assume
that the equilibrium in the alcohol market has been achieved. Thus, alcohol
consumption is determined by the interaction of supply and demand. Variables
such as income, price, and laws affect availability determine the quantity
demanded of alcohol. On the other hand, price, transportation costs, taxes, and
level of competition affect the quantity supplied of alcohol. After running
regressions on various variables, Mast et al.(1999) define the function of
11. alcohol consumption as following:
In order to avoid the problem of Multicollinearity, we can’t directly include the
alcohol consumption as a dependent variable. Therefore, income, availability
laws and taxes are picked from Mast et al.’s model as most significant
determinants of alcohol consumption.
4. : is defined as the average value of federal excise rates for both beer and
wine using weighted calculation method. The number is calculated and posted
by the Beer Institute. Debate involving the effect of alcohol taxes on
drunk-driving crashes started forty years ago. Early research between the mid
1970s to the early 1980s finds that beer taxes had a negative and significant
relationship to alcohol-related fatalities. In contrast, economists using recent
data argue that this relationship is insignificant. Motivated by the diversity of
empirical results among different studies, this paper tests the impacts of
alcohol taxes using the most recent data as well as including wine taxes that
often ignored in previous studies.
5. : is defined as average annual per-gallon prices for regular-grade
unleaded gasoline from the U.S. Department of Energy’s Energy Information
Administration (EIA) for the period 1994 – 2011. Moreover, we adjust the
gasoline prices for inflation using January 2012 dollars.
According to the previous research, the impacts of gasoline price changes
on drunk-driving crashes are found in two possible directions - positive and
12. negative. On one hand, higher gasoline prices reduce drunk-driving crashes by
lowering people’s consumption of alcohol. As people’s need of gasoline is
greater than that of alcohol, increasing gasoline price causes driving people to
decrease the quantity of alcohol consumed, given all other factors are constant.
Moreover, the rise of gasoline prices may directly reduce gasoline
consumption and travel demand, which in turn reduces people’s exposure to all
types of crashes, including drunk-driving crashes. In order to save the gasoline
fees, people may choose to have a drink at home or nearby bars. Some people
may also change to use public transportation, which is the substitute of driving.
Empirical evidence found by Nelson (1997), Ruhm (1995), and Sloan et al.
(1995) shows that alcohol consumption levels tend to be lower when gasoline
prices are higher. Berger and Snortum (2006) later concluded that lower
alcohol consumption levels resulted in fewer drunk-driving crashes. Dahl
(1979) also points out that rising gasoline prices could cause drivers to drive
more slowly and cautiously in order to save additional fuel occurred during
sudden speeding and braking.
On the other hand, higher gasoline prices may lead to more drunk-driving
crashes as people rely on alcohol to relieve stress when facing personal
economic strain, which is proved by Pearlin and Radabaugh (1994) using
cross-sectional data at state level. The contradiction between these two
hypotheses, which are all well-supported by empirical data and reasoning
encourages us to include gasoline price as an independent variable and run the
13. regression test again with the latest data.
6. : is defined as a dummy variable measures the strength of public policies
implemented with values of 0 and1. We extracted these numbers from a study
by Kenkel (2012), which sets the scales of the effectiveness of powers based
on a comprehensive survey. There are two reasons why we use a dummy
variable to represent the impacts of public policies. First, the effectiveness of
public policies is a qualitative aspect. Second, the focus of our paper is not
about policies as many studies have contributed to this topic. However, we
include it in order to have a more accurate result.
IV. Result
First, all the explanatory variables and dependent variable are confirmed
to be stationary by Augmented Dickey-Fuller test. No Multicollinearity exists
based on the results of the Variance Inflation Factor test9
(Appendix D).
Secondly, we use the OLS10
procedure to get the estimation of the explanatory
coefficients for the value of drunk-driving crashes per vehicle million miles in
the original multiple-variable model (Appendix E). Two (unemployment rate
and per capita personal income) of five estimated coefficients are significant at
5% level. However, we reject the Durbin-Watson test and have the serial
correlation problem. 11
Because the Durbin-Watson statistic (1.34) is
9
“In statistics, the variance inflation factor (VIF) quantifies the severity of Multicollinearity in an
ordinary least squares regression analysis. It provides an index that measures how much the variance
(the square of the estimate’s standard deviation) of an estimated regression coefficient is increased
because of collinearity” (Wikipedia).
10
Abbreviation for Ordinary Least Squares, which is “a method for estimating the unknown
parameters in a linear regression model” (Wikipedia).
11
“In statistics, the Durbin-Watson statistic is a test statistic used to detect the presence of
14. substantially less than 2, there is evidence of positive serial correlation. Thus,
we have to use GLS12
to correct the fifth order serial correlation, which is
consistent with our previous findings about the significant positive serial
correlation of the drunk-driving crashes per vehicle million miles at five lags
(Appendix F). After applying GLS, the Durbin-Watson statistic is back to the
level of 2.04. Finally Newey-West procedure is used to obtain both
Hetroskedasticity and serial correlation corrected standard errors of the
parameter estimates (Appendix G). All t-statistics are adjusted accordingly.
The results are presented as following.
Estimate Prob. Variable
Coefficient
34.57671 0.0021 Intercept
0.171772 0.0027 Unemployment rate
-3.072728 0.0024 Per capita personal income (dollar)
0.004875 0.0246 Alcohol Taxes (dollar)
0.302043 0.0049 Gasoline Prices (cents)
0.061646 0.0021 Dummy variable for the effectiveness of
public policies
From the results above, the individual impacts of all explanatory variables on
autocorrelation (a relationship between values separated from each other by a given time lag) in the
residuals (prediction errors) from a regression analysis” (Wikipedia).
12
Abbreviation for Generalized Least Squares, which “is a technique for estimating the unknown
parameters in a linear regressional model. Different from OLS, the GLS is applied when the variances
of the observations are unequal (Hetroskedasticity), or when there is a certain degree of correlation
between the observations. We choose GLS because in these cases ordinary least squares can be
statistically inefficient, or even give misleading inferences” (Wikipedia).
15. drunk-driving crashes are statistically significant.13
All of them are statistically
significant at 1% level. Although the t-test result of alcohol taxes is significant at 1%
level, the coefficient of alcohol taxes is extremely small in value, only around 0.005,
indicating that a change in the money price of alcohol brought by a change in taxes
has a extreme small effect on the number of drunk-driving crashes, which is
consistent with the results of most previous studies. In addition, we find a
significant negative relationship between per capita personal income and
drunk-driving crashes. This result actually matches most previous assumptions. For
instance, alcohol is a normal good for which demand decreases when income
decreases. Also, this negative relationship agrees with most previous research
regarding the impacts of macroeconomic conditions. In general, the regression
results are same as our hypotheses. The only violation is the positive relationship
between drunk-driving crashes and effectiveness of public policy, which should be
negative. Again, this shows the difficulty of including the qualitative aspect of an
explanatory variable into a quantative econometric model, which requires more
complicated work to combine both qualitative and quantative measurements in
further study. In general, the aggregating impacts of those factors discussed above
are statistically significant, indicating by the extreme small p-value of F-statistic,
0.000213.
V. Conclusion
13
Determined by their p-values, which are far less than 0.05 and 0.01.
16. This paper has two primary functions. First, it answers the question, what are
significant determinants of the drunk-driving crashes between 1994 and 2011
in the U.S.? Based on earlier research, we include both macroeconomic and
microeconomic explanatory variables in our model to examine their combined
impacts on drunk-driving crashes. Secondly, this paper tests the previous
hypotheses about two-direction relationship between drunk-driving crashes
and major explanatory variables within one model. The overall impact of
selected explanatory variables in our model is significant and consistent with
previous study. In addition, we find that gasoline prices, alcohol taxes, and
unemployment rate all have positive impacts on drunk-driving crashes. In
contrast, per capita personal income is negatively related to drunk-driving
crashes. However, we get an unexpected sign of the relationship between
drunk-driving crashes and effectiveness of public policies. Possible solutions
to this problem for the future research are increasing the number of
observations such as using monthly data or adding cross-section data. A better
measure of the effectiveness of alcohol control policies is necessary and very
important.
Appendix A: Alcohol Related Crashes per MMT
19. Dependent Variable: Y
Method: Least Squares
Date: 05/08/13 Time: 02:18
Sample: 1 18
Included observations: 18
Variable Coefficient Std. Error t-Statistic Prob.
C 70.17273 18.05886 3.885779 0.0022
G -0.252564 0.144807 -1.744143 0.1067
I -6.253683 1.647101 -3.796781 0.0025
TAX -0.011846 0.037249 -0.318021 0.7559
U -0.206424 0.036170 -5.707053 0.0001
DUMMY -0.079682 0.082539 -0.965380 0.3534
R-squared 0.933428 Mean dependent var 4.066163
Adjusted R-squared 0.905690 S.D. dependent var 0.554919
S.E. of regression 0.170415 Akaike info criterion -0.439960
Sum squared resid 0.348495 Schwarz criterion -0.143170
Log likelihood 9.959643 Hannan-Quinn criter. -0.399037
F-statistic 33.65146 Durbin-Watson stat 1.344639
Prob(F-statistic) 0.000001
Appendix F: GLS Regression Results
Dependent Variable: Y
Method: Least Squares
Date: 05/08/13 Time: 02:34
Sample (adjusted): 6 18
Included observations: 13 after adjustments
Convergence achieved after 18 iterations
Variable Coefficient Std. Error t-Statistic Prob.
C 34.57671 1.204052 28.71697 0.0012
G 0.302043 0.014831 20.36505 0.0024
I -3.072728 0.112705 -27.26343 0.0013
TAX 0.004875 0.001046 4.658722 0.0431
U 0.171772 0.007046 24.37949 0.0017
DUMMY 0.061646 0.004266 14.45151 0.0048
AR(1) 0.038334 0.025616 1.496480 0.2732
AR(2) 0.397945 0.019706 20.19459 0.0024
20. AR(3) -0.376219 0.018647 -20.17586 0.0024
AR(4) -0.242159 0.020859 -11.60943 0.0073
AR(5) 0.544500 0.014593 37.31245 0.0007
R-squared 0.999957 Mean dependent var 4.328430
Adjusted R-squared 0.999744 S.D. dependent var 0.358285
S.E. of regression 0.005732 Akaike info criterion -7.664900
Sum squared resid 6.57E-05 Schwarz criterion -7.186866
Log likelihood 60.82185 Hannan-Quinn criter. -7.763158
F-statistic 4687.745 Durbin-Watson stat 2.045196
Prob(F-statistic) 0.000213
Inverted AR Roots .80 .44-.77i .44+.77i -.82-.43i
-.82+.43i
Appendix G: Final Results
Dependent Variable: Y
Method: Least Squares
Date: 05/05/13 Time: 23:43
Sample (adjusted): 6 18
Included observations: 13 after adjustments
Convergence achieved after 18 iterations
HAC standard errors & covariance (Bartlett kernel, Newey-West fixed
bandwidth = 3.0000)
Variable Coefficient Std. Error t-Statistic Prob.
C 34.57671 1.595898 21.66598 0.0021
G 0.302043 0.021168 14.26876 0.0049
I -3.072728 0.150456 -20.42277 0.0024
TAX 0.004875 0.000779 6.258830 0.0246
U 0.171772 0.008896 19.30929 0.0027
DUMMY 0.061646 0.002849 21.63899 0.0021
AR(1) 0.038334 0.028317 1.353744 0.3085
AR(2) 0.397945 0.015517 25.64504 0.0015
AR(3) -0.376219 0.015232 -24.69866 0.0016
AR(4) -0.242159 0.024774 -9.774733 0.0103
AR(5) 0.544500 0.016356 33.28983 0.0009
R-squared 0.999957 Mean dependent var 4.328430
Adjusted R-squared 0.999744 S.D. dependent var 0.358285
S.E. of regression 0.005732 Akaike info criterion -7.664900
21. Sum squared resid 6.57E-05 Schwarz criterion -7.186866
Log likelihood 60.82185 Hannan-Quinn criter. -7.763158
F-statistic 4687.745 Durbin-Watson stat 2.045196
Prob(F-statistic) 0.000213
Inverted AR Roots .80 .44-.77i .44+.77i -.82-.43i
-.82+.43i
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