Objective of this project is to estimate the impact of drunk driving laws on traffic deaths

1. BUAN/MECO 6312
Group Project
Spring 2017
Team Members
Andrea Brewerton Aab151230
Keerthana Ashok Kumar Kxa163230
Lakshmi Durga Panguluri Ldp160030
Vishvajeet Singh Rathore Vsr160030

2. Objective:
The objective of this project is to estimate the impact of drunk driving laws on traffic deaths.
Dataset Description:
The dataset contains balanced panel data from the “lower 48” U.S. states (excluding Alaska and
Hawaii), annually from 1982 through 1988. Each state has the same number of observations.
Dependent Variable:
The traffic fatality rate is the number of traffic deaths per 10,000 people for a given state in a given year.
By looking at the variables in the dataset, “mrall”, which is the Vehicle Fatality Rate (VFR), would
represent this number best when compared to other variables in the dataset. Additionally, “mralln”,
which is the night-time VFR, will be used as a dependent variable to test the effect of alcohol laws on
changes in night-time VFR.
Independent Variables:
Our objective is to estimate the impact of the drinking-and-driving laws on traffic deaths. The variables
“jaild” and “comserd” describe the states’ way of dealing with drinking-and-driving cases and are
therefore considered essential to include in the model. Additionally, there are other factors we must
consider that may or may not have a significant effect on the VFR. These are listed below.
Variable Descriptions
jaild Mandatory Jail Sentence: one if state requires jail time.
comserd Mandatory Community Service: one if state requires community service
spircons Per Capita Pure Alcohol Consumption (Annual, Gallons)
unrate State Unemployment Rate (%)
perinc Per Capita Personal Income ($)
beertax Tax on Case of Beer ($)
sobapt % Southern Baptist
mormon % Mormon
mlda Minimum Legal Drinking Age (years)
dry % Residing in Dry Counties: A dry county is a county whose government
forbids the sale of any kind of alcoholic beverages. Some prohibit off-premises
sale, some prohibit on-premises sale, and some prohibit both.
yngdrv % of Drivers Aged 15-24
vmiles Ave. Mile per Driver
pop Population
pop1517 Population, 15-17 year olds
pop1820 Population, 18-20 year olds
pop2124 Population, 21-24 year olds
miles total vehicle miles (millions)
gspch GSP Rate of Change: This is a measure of economic growth

3. Data Visualization:
Vehicle Fatality Rate
The following map shows the overall vehicle fatality rate on a state-by-state basis. From the graph, we
can see that New Mexico has the highest average VFR of 3.653 per 10,000 people and Massachusetts
has the lowest average VFR of 1.110 per 10,000 people. States such as New Mexico, Wyoming,
Montana, Nevada, Idaho and Arizona have high VFRs whereas states such as Massachusetts, Minnesota,
New York, and Illinois have low VFRs.
Correlation Matrix:
As we can see from the above correlation matrix, the variables for population and total vehicle miles (in
millions) are highly correlated which is expected: as the population increases the number of people
driving also increases which leads to higher total vehicle miles. Also from the matrix, per capita income

4. and unemployment are negatively correlated, which aligns with economic theory in that as the per capita
income increases, unemployment goes down. Lastly, it appears that either states with high populations
of Southern Baptists tend to have higher beer taxes or that states with higher beer taxes tend to have high
populations of Southern Baptists as is evidenced by the high correlation between the two variables.
VFR and Night-Time VFR and Alcohol-Involved VFR vs Beer Tax:
The above graph represents the effect of beer taxes on overall VFR (Steel Gray), Night-time VFR
(Green) and Alcohol-Involved VFR (Blue). Based on our analysis of the graph, it appears that beer taxes
have no effect on night-time VFR as night-time VFR is almost constant despite increases in beer tax. On
the other hand, overall VFR and Alcohol-Involved VRF depict similar behavior that is seemingly
quadratic. If beer taxes increase up to a certain point, the VFR and Alcohol-Involved VFR will also
increase up to a certain point. Once that point is reached however, both will begin to decrease. To cite
economic theory, the reason for this behavior could be due to the inelasticity of alcohol especially when
taking into consideration its addictive properties for some people. This can be illustrated by the fact
that, unless the increase in beer tax is significant, light drinkers may not notice an increase in beer taxes
since they don’t drink very often to begin with and heavy drinkers may already be addicted, in which
case an increase in the beer tax would need to be highly significant to deter them. An alternative
explanation for the data’s quadratic behavior could be that the vehicle fatality rate is increasing every
year and the state governments are reacting to the higher vehicle fatality rate by imposing higher beer
taxes.

5. VFR vs Per Capita Income:
Based on our knowledge of economic theory and cultural attitude, we hypothesize that the relationship
between the vehicle fatality rate and the per capita income is quadratic due to the quadratic nature of per
capita income and alcohol consumption. With regards to the low per capita income, despite having less
money to spend on alcohol, we assume that alcohol consumption is high due to the lower economic
status experienced by this group of people which includes general frustration and higher levels of stress.
It is then easy to see that as the per capita income increases, people tend to have lower consumption of
alcohol as we assume that higher per capita income suggests people that are more educated, responsible,
and generally less stressed than those with low per capita income. What may be less evident is the idea
that once per capita income reaches a certain point, alcohol consumption begins again to increase and
we assume this is due to the fact that the people on this end of the spectrum are experiencing overly high
levels of occupational and potentially familial stress. As they say, “More money, more problems”! The
graph presented below appears to prove our theory correct; it is possible that additional data points with
higher per capita income will add more concrete proof to our theory.

6. VFR vs Unemployment Rate:
Again, using our knowledge of economic theory and cultural attitude, we hypothesize that as the
unemployment rate increases people tend to consume more alcohol due to more stress including, but not
limited to, family pressure to provide and personal emotional stress due to feelings of failure.
Additionally, people who are unemployed now have more idle time in which they can drink and are
more prone to depression. This has been proven by the graph below.
% Residing in Dry Counties vs VFR
According to our assumptions, as the % Residing in Dry Counties increases the VFR should also
increase. This is because people living in dry counties still drink but since there is no alcohol available
to them within their respective counties, they now must drive to the nearest county that allows the sale
and consumption of alcohol. It is highly possible that, in returning to their homes after obtaining and
consuming alcohol, these same people may in fact be driving while intoxicated thereby increasing the
chances for accidents which in turn will increase the Vehicle Fatality Rate. As shown in the graph
below, we see an increasing trend in VFR as the % Residing in Dry Counties increases.

7. Mandatory Jail Sentence and Mandatory Community Service vs VFR:

8. For states that have enacted mandatory jail sentences and/or mandatory community service as a means
to deter drinking and driving, we would expect the effect of these laws to be a decrease in VFR.
However, from the above graphs, the effect appears to be completely opposite. This could be due to
reverse causality where mandatory jail sentencing and mandatory community service are not causing the
VFR to increase but instead a higher VFR causes the states to impose mandatory jail sentencing and
mandatory community service.
Other variables such as population, average miles per driver, minimum drinking age, % Southern
Baptist, and % Mormon have little to no visual effect on vehicle fatality rate but in theory, we would
expect the following effects. Higher percentages of Southern Baptists and Mormons should result in a
reduction of the overall alcohol consumption which in turn should decrease VFR. Reducing the
minimum drinking age should result in an increase in alcohol consumption since there are now more
people who are legally allowed to consume alcohol and therefore should cause an increase the VFR.
Finally, increases in population should also increase the VFR since there is potential for more people to
drink however, that may not always be the case.
Regression Models:
Pooled Least Square Model:
Running a pooled model corresponding to given data gives following output.

9. From the output above it is clear that many of the variables are insignificant. Unemployment rate should
have good contribution towards VFR but it is insignificant according to this model. Removing all the
highly insignificant variables and rerunning the regression gives following results.
Since this is panel data, there is a possibility that same-state errors may be correlated over time (serially
correlated errors). The variance may also be different in different time periods (heteroskedasticity). As
we know, if serially correlated errors and heteroskedasticity exist, the least squares estimator is still a
linear unbiased estimator, but it is no longer best. Also, the formulas for the standard errors typically
computed for the least squares estimator are no longer correct. Hence, the statistical test and confidence
intervals thus calculated would be wrong.
Pooled Least Square Model with Cluster Robust Standard Errors:
In response to the incorrect standard errors, we are able to address the issue by running a regression
using robust standard errors as seen on the following page. As we can see, using robust standard errors,
although now correct, yield standard errors that almost double in value compared to the original standard
errors. This suggests that the model is inefficient and therefore still not best. In addition to the higher
standard errors, we now see that some of the coefficients have surprising/switching signs and most of
the variables are no longer significant.

10. The issues mentioned earlier for the pooled least square model without cluster robust standard errors,
serially correlated errors and heteroskedasticity, would still be present in the pooled least square model
with cluster robust standard errors. Furthermore, one other issue that both models have is that of
omitted variable bias. In both cases, we could say that the omission of the variable speed limit is
resulting in a less efficient model since we know that speed limit has a major impact on accidents.
If for example the maximum speed limit is high, then there are more chances for accidents and thus an
increasing vehicle fatality rate. Below is the average speed limit representation for every state in the
United States. Comparing this map to that of the vehicle fatality rate map on page 3, we can see that they
are almost identical in that the states with the higher speed limits are the same states with the higher
vehicle fatality rates thus proving our hypothesis.

11. In the end, we determine that this model cannot be used for further analysis since statistical tests such as
a t-test or F-test and confidence intervals would yield wrong results.
The Fixed Effects Model:
In an attempt to address the issue of serial correlation, we run a regression using fixed entity effects.
The output is shown below.
After reviewing the output, we see that the results are not as we expected as it appears that a majority of
the explanatory variables are insignificant. We begin to drop insignificant variables one by one based
on t- and p- values. Using trial and error, we come across the output shown on the following page. In
this model, the least squares estimator is still linear and unbiased, but it is not best as the standard errors
are once again incorrect.

12. Fixed Effect model with Robust Standard Error:

13. The above model yields good results as all variables are significant and the standard errors have been
corrected, although still not efficient. While the results yielded are good, we would still like to look at
the regression model with time fixed effects since is helpful when an omitted variable varies over time
but not across states. An example of this would be national laws that are changed or updated after so
many years but would affect all states equally.
Entity and Time Fixed Effect Model:
Using only the significant variables from the previous regression, we run the entity and time fixed effect
model.
Upon reviewing the output, we realize that while the model does include time variation, it fails to yield
significant results. The sign of the variable “gspch” switched from negative to positive and other

14. variables became even smaller. Hence, this model can no longer be used and we can conclude that there
are no omitted variables that vary over time but not across states. We will be using Fixed Effect model
with robust standard errors.
The Random Effect Model:
Because the fixed effect model does not work well with data that are slow changing or that remain
constant within states, we decide we need to consider the random effect model as well despite the fact
that the random effect model works better for data in which observations are randomly selected and our
data set did not involve any sort of random selection process. The output of random effect model is
given below.
Upon inspection, the variables “beertax” and “perinc” have become insignificant which is completely
opposite to what we considered in our statistical analysis. This leads us to question the effectiveness of
the random effect model as compared with the fixed effect model. Additionally, it is possible that the
random effect model may suffer from the problem of endogeneity wherein one of the explanatory
variables may be highly correlated with an omitted variable that is part of the error term. If this is in fact
the case, we should opt to settle with the fixed effect model and its estimators. To determine if there is
the presence of endogeneity in the random effect model, we perform a Hausman test.

15. Hausman Test:
Based on the results of the Hausman test below, we can reject the null hypothesis at any significance
level that there is no endogeneity and instead choose the alternate hypothesis that an explanatory
variable may be correlated with an omitted variable in the error term. Because of this, we decide that
the fixed effect model with robust standard errors and its estimators are the most suitable for the given
data.
Summary:
Without recognizing the existence of serial correlation or testing for heteroskedasticity, our initial
pooled least square estimator was a linear unbiased estimator but not best. By introducing the cluster
robust standard errors in our regression, we corrected the standard errors. However, our model was still
inefficient. In order to improve our model, we introduced fixed effects using an estimator with entity and
time fixed effects.
Since a random effects model exposes our model to possible endogenous regressors, we decided to
compare the coefficient estimates from both the fixed effects and random effects models. From the
Hausman test, we conclude the random effects estimator is inconsistent and we should stick to the fixed
effects estimator for our model.
Conclusion:
The fixed effect estimators indicate that increasing beer tax will reduce the vehicle fatality rate in states
whereas state laws against drinking and driving are ineffective due to reverse causality. We need to
come up with different ways to cope with this problem for example by running several awareness

16. programs to bring down the alcohol consumption and educate people on the consequences of drinking
and driving. Other factors such as the unemployment rate, GSP, and per capita income cannot be
controlled immediately, so they just indicate how they affect vehicle fatality rate. We saw that
unemployment is a major factor and states’ policies to reduce unemployment will help reduce the stress
and depression among people which in turn will decrease vehicle fatality rate.
Limitations:
 Data related to natural hazards, speed limits and over speeding cases would help to analyze the
case even better.
 Adding more variables that are directly related to drunk driving laws would improve the model.
 Variables related to drunk driving laws should have higher variance across the states.
 Including data for a longer time period would definitely help in estimating the coefficients more
accurately.