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Seminar paper 5

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
  17. 17. Appendix B: Total Alcohol-Related Fatalities by Year Appendix C 0 20 40 60 80 100 120 140 160 180 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
  18. 18. 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 0 5 10 15 20 25 30 35 16-20 21-24 25-34 35-44 45-54 55-64 76-74 75+ Percentage Age of Drivers
  19. 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. 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. 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 References:
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