Seminar paper 5

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.

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

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.

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

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.

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.

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

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.

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.

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

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

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

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

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).

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.

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

Appendix B: Total Alcohol-Related Fatalities by Year

Appendix C

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Appendix D: Variance Inflation Factor

Variance Inflation Factors

Date: 05/08/13 Time: 02:20

Sample: 1 18

Included observations: 13

Coefficient Uncentered Centered

Variable Variance VIF VIF

C 2.546892 12662779 NA

G 0.000448 5836.047 501.9272

I 0.022637 11723603 493.8233

TAX 6.07E-07 4057.957 64.29543

U 7.91E-05 8815.213 325.1791

DUMMY 8.12E-06 22.69258 18.68807

AR(1) 0.000802 3067.326 893.8483

AR(2) 0.000241 1376.566 282.3623

AR(3) 0.000232 2829.209 605.0411

AR(4) 0.000614 12996.94 3455.025

AR(5) 0.000268 8065.128 2076.655

Appendix E: OLS Regression Results

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16-20 21-24 25-34 35-44 45-54 55-64 76-74 75+

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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



Date: 05/08/13 Time: 02:34

Sample (adjusted): 6 18

Included observations: 13 after adjustments

Convergence achieved after 18 iterations


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

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




Sum squared resid 6.57E-05 Schwarz criterion -7.186866




Inverted AR Roots .80 .44-.77i .44+.77i -.82-.43i

-.82+.43i

Appendix G: Final Results



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)


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




Sum squared resid 6.57E-05 Schwarz criterion -7.186866




Inverted AR Roots .80 .44-.77i .44+.77i -.82-.43i

-.82+.43i

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Seminar paper 5

Health & Medicine

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