Analysis of The Minimum Legal Drinking Age With The Use Of A Regression Discontinuity Design and Two-Stage Least Squares Instrumental Variable Approach By Christopher David Christensen This article’s global purpose is to analyze and review some of the practical issues dealing with the usefulness and implementation of Regression Discontinuity Designs (RDDs). We will be doing so in the context of the minimum legal drinking age (MLDA). This RDD allows for causal inferences of the effect that drinking (when it becomes legal to do so) has on mortality rates to be evaluated. An analysis of the MLDA’s effectiveness in reducing both the mortality rate and the proportion of people who consume alcohol will be presented. These RDD estimates will then be used to compute an estimate of the effect that the MLDA has on mortality in terms of increased alcohol consumption at age 21 by exploiting an instrumental variables approach. It is found that after no longer being legally bound by the MLDA, there is a significant increase in alcohol consumption and the mortality rate. Persuasive evidence in support of our current MLDA in the U.S. is documented in this article. The adverse impacts borne onto society from young adults who decide to drink when it is no longer illegal are proved to be substantial. I. Introduction This paper’s main focus is on the minimum legal drinking age (MLDA) in the U.S and the effects that the current minimum drinking age of 21 has on the individual and society as a whole. The CDC reports that in the United States alone, excessive alcohol consumption is a contributing factor to an estimated 4,300 deaths each year for persons under age 21. This statistic and the other countless non-fatal harm’s associated with drinking is not enough evidence to some that the current MLDA is effective. In 2008, more than 100 college presidents and officials signed the Amethyst Initiative which aimed to re-
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Analysis of The Minimum Legal Drinking Age With The Use Of A Regression Discontinuity
Design and Two-Stage Least Squares Instrumental Variable Approach
By Christopher David Christensen
This article’s global purpose is to analyze and review some of the practical issues dealing with the
usefulness and implementation of Regression Discontinuity Designs (RDDs). We will be doing so in the context of
the minimum legal drinking age (MLDA). This RDD allows for causal inferences of the effect that drinking (when it
becomes legal to do so) has on mortality rates to be evaluated. An analysis of the MLDA’s effectiveness in reducing
both the mortality rate and the proportion of people who consume alcohol will be presented. These RDD estimates
will then be used to compute an estimate of the effect that the MLDA has on mortality in terms of increased alcohol
consumption at age 21 by exploiting an instrumental variables approach. It is found that after no longer being
legally bound by the MLDA, there is a significant increase in alcohol consumption and the mortality rate.
Persuasive evidence in support of our current MLDA in the U.S. is documented in this article. The adverse impacts
borne onto society from young adults who decide to drink when it is no longer illegal are proved to be substantial.
I. Introduction
This paper’s main focus is on the minimum legal drinking age (MLDA) in the U.S and
the effects that the current minimum drinking age of 21 has on the individual and society as a
whole. The CDC reports that in the United States alone, excessive alcohol consumption is a
contributing factor to an estimated 4,300 deaths each year for persons under age 21. This statistic
and the other countless non-fatal harm’s associated with drinking is not enough evidence to some
that the current MLDA is effective. In 2008, more than 100 college presidents and officials
signed the Amethyst Initiative which aimed to re-examine the effectiveness of the MLDA. The
participants of this initiative contend that the MLDA causes irregular and more dangerous
drinking activities than a lower drinking age which aligns with much other age limited activities
(ex. 18 being the legal age to vote, enter the army etc.). This paper ultimately provides
statistically significant evidence that the current MLDA is effective in decreasing the proportion
of young adults who drink and in turn the mortality rate for this group.
The data in the first part of this analysis comes from the National Health Interview
Survey. This data is used to show that the people just above and just below the threshold of being
21 years old are very similar with respect to their observable characteristics recorded in the home
interviews. The second data set comes from death certificate information stored in the
government’s vital statistics database. Vital statistics are records of births, deaths, fetal deaths,
marriages and divorces, which are collected through an administrative system run by the
government known as civil registration. Both data sets contain the most accurate and
comprehensive statistics in the U.S and are both provided through contracts with the National
Center for Health Statistics (NCHS), which is an agency of the U.S. Federal Statistical
System. This statistical information is used to guide policies that aim to improve the health of the
American population.
The Regression Discontinuity Design (RDD) is at the heart of the framework for this
analysis. This design shows how to estimate the treatment effect by running linear regressions on
both sides of the threshold. In order to measure the jump at the threshold, a binary variable
“Over21” was created which takes on a value of 1 if the respondent is 21 or older and 0
otherwise. So when there is a 1 unit increase in Over21 (going from 0 to 1), there is an effect on
the dependent variable in the regression equal to the estimated coefficient on Over21. Several
regression specifications are used with the covariate Over21 in order to measure the change in
alcohol consumption, mortality rates and other observable characteristics at the threshold.
After conducting a careful analysis of the MLDA with the use of a precisely implemented
RDD, it is found that there is statistically significant evidence in support of the current MLDA.
First it is shown that there is a significant increase in alcohol consumption at the threshold or in
other words our sample population sees an increase in alcohol consumption after their 21st
birthday. It is found that the proportion of people who drink alcohol in the past month increases
by an estimated 8-9% at the threshold. Even when controlling for celebration effects occurring
near peoples birthdays, the overall increase in alcohol consumption is significant and about the
same regardless of celebration effects. The standard error on our variable “over 21” is .014,
which supports our estimate of a 9% increase in alcohol consumption after age 21.
Then an in depth analysis of the mortality rate is conducted where it is found that there is
a significant increase in overall deaths at the threshold accompanied by an increase in most other
causes of death after age 21. Our results estimate that there is an increase in the mortality rate of
about 8 additional deaths per 100,000 people with a standard error of 2.167. In the final sections
a two-stage least squares instrumental variables approach is used to estimate a causal relationship
between the increased alcohol consumption at the threshold and the mortality rate within the
same time frame for our sample population. Due to the nature of this analysis whereby a
controlled experiment is not feasible, the random occurrence of turning 21 years old is used as
Note: P values *,**,***represent statistical significance at the 10, 5 and 1 percent levels respectively. Each column represents a differentregression specification with their own unique estimates.
With the age variable centered at 21 and fully interacted with the binary variable Over21
that is activated when over age 21, we have an estimated increase in alcohol consumption at the
threshold of about 8%. This is a statistically significant increase in alcohol consumption. Even
though this is a well implemented RDD, every model has its limitations. Two very important
aspect of this analysis that could potentially affect our estimates of alcohol consumption pertain
to celebration effects and misreporting. Our interest is in the permanent effect of legal and easy
access to alcohol, therefore the celebration effects resulting from birthday parties may lead to
bias. The logic behind this is that on peoples birthdays they tend to put themselves in potentially
riskier situations when celebrating. Changing behavioral patterns during celebrations leads to
higher intoxication rates, DUI’s, and other alcohol related externalities. The potential bias was
controlled for with the celebration effects covariate which we defined earlier as a binary variable
called birthday which takes on a value of 1 if the days to ones 21st birthday equals 0 and takes on
a value of 0 otherwise. This allows the birthday variable to absorb unwanted distortions of our
estimates that in fact result from celebrating and not just being able to legally consume alcohol.
Before moving on to the effects that the MLDA has on mortality rates I want to address
the limitation that is imposed on the quality of our data due to misreporting during interviews in
the context of alcohol consumption. Previously touched upon was the issue of under or over
reporting when answering interview questions, but here it could become a particularly relevant
source of bias. It is true that people may report their drinking habits inaccurately due to memory
issues but there is a more important underlying incentive for respondents to under report their
alcohol consumption. People are less likely to report that they drink alcohol when it is illegal to
do so therefore respondents under 21 years of age are more than likely under reporting their
alcohol consumption. A good way to visualize the upward bias being introduced by this is to
refer to figure 2 which shows the effect of turning 21 on drinking. If under reporting is
significant, then the pre-threshold best-fit-line on the left is artificially low, thus creating a false
sense of the jump from the pre-threshold best-fit-line on the left to the post-threshold best-fit-line
on the right.
Now that we have a plausible estimate for the increased alcohol consumption at the
threshold, let’s review our findings on the relationship between the MLDA and mortality rates.
Recall that these estimates were produced using mortality data from death certificates collected
by the NVSS. The observations are no longer demographic characteristics in this part of the
analysis but instead there is a variable for all causes of death and the different cause of death sub-
categories. Figure 5 on the next page shows the age profile of mortality for all causes on a per
100,000 person scale. It is visible that there is a very sharp increase in all deaths at age 21,
leading to the conclusion that the MLDA is effective in not only reducing alcohol consumption
but the mortality rate.
Earlier we proved that the treatment group was very similar to the counter factual group
by verifying that there were no sharp increases in their observable characteristics at the
threshold. This supports our finding that the MLDA reduces the mortality rate because other than
suddenly being able to legally drink the two groups are almost identical. Even more compelling
visual evidence in support of the MLDA reducing mortality is show in figure 6 below, where the
age profile of mortality is presented with only the motor vehicle accident (MVA) and alcohol
related deaths plotted.
Note: Deaths due to MVA and Alcohol are represented by the top and bottom plots respectively.
These causes of death have high correlation with increased alcohol consumption and both
causes of death show a sharp increase in mortality rates at the threshold. In figure 6 you can see
that deaths due to MVAs begin a downward trend possibly due to increased maturity levels and
driving ability as people get older before making a turn for the worst and making a sharp jump at
age 21. Figure 6 shows an opposite trend for deaths due to alcohol poisoning starting at age 19.
The amount of deaths start to increase possibly due to people coming of age and being exposed
to riskier situations where alcohol is present although again we see a sharp increase in mortality
at age 21.
We have now established strong visual evidence that the MLDA reduces the mortality
rate in all causes and ones highly correlated with increased alcohol consumption, but a more
important question is by how much has the mortality rate been reduced. You can get a sense of
the effectiveness of the MLDA in reducing the mortality rate from figures 5 and 6 but to provide
an actual estimate we will refer to table 3 located at the end of the article, which provides a
summary of estimates for the overall increase in deaths at age 21 and each cause of death sub
category. As shown in row1, column1, of table 3 there is an estimated overall increase of about 8
deaths per 100,000 people. According to the standard error of 2.167 listed under the coefficient
on Over21, this estimate is statistically significant and is evidence that the MLDA reduces
overall deaths for young adults while it is still illegal for them to consume alcohol.
The estimated difference between the pre and post-threshold groups for the MVAs,
alcohol related deaths and suicides are also presented in Table 3. For the next few cause of death
estimates, we will be referring to Table 3, row 1, which presents our estimates for the Over21
variable. In column 7, you can see that there is an estimated 3.6 additional deaths per 100,000
people for those over 21 due to MVAs. Column 4 shows an increase in alcohol poisoning deaths
of an estimated .37 per 100,000. Lastly, column 6 shows that suicides increase at the threshold
by an estimated 2.4 per 100,000 people. The standard errors on these few cause of death sub
categories are all in the range of supporting the statistical significance of our estimates, and are
listed below their respective coefficients.
The p-value’s for these cause of death estimates are also worth commenting on and are
denoted by the number of asterisks on their coefficients. MVAs, suicide, and All causes of death
have a p-value that is less than .01 which represents a strong statistical significance for these
estimates. Specifically, this means that these estimates are within the 99% confidence interval
and are statistically significant at the 1% level. The estimate for our alcohol coefficient is still
within the range of statistical significance although only at the 10% level. Overall, this section
has provided compelling visual evidence and regression estimates showing that the easing of
access to alcohol increases mortality rates significantly through MVAs, alcohol poisoning and
suicides.
Evidence of a potential downward bias in our results has been documented by a study
conducted by the CDC analyzing the underreporting of alcohol-related mortality on death
certificates. Death certificates based on the underlying cause of death alone are shown in this
study to underestimate alcohol-related mortality because they do not reflect contributing factors
that are related to alcohol. “As shown in this study, even when a multiple-cause analysis is
applied to official cause-of-death records, alcohol-related deaths are still grossly underestimated.
There are shortcomings in official mortality reporting that are more fundamental than the failure
to take into account all listed conditions. Among the problems are the apparent omission of
diagnostic information available at the time of death or obtained after death. The frequent
omission of excessive blood alcohol levels was a major shortcoming in the death certificates
analyzed by CDC.”
Conclusion
Evidence from our analysis which shows a strong relationship between increased alcohol
consumption and mortality rates at the threshold can be estimated through the use of a two-
staged-least squares instrumental variable approach (2SLSIV). The framework for this approach
has been carefully set up throughout this article. The first stage estimate was derived when we
showed that at the threshold there was a significant increase in alcohol consumption.
Alternatively our first stage can be thought of as the causal effect of becoming 21 on drinking,
which we found to be an increase of about 8%-9% depending on if we controlled for the
celebration effects and what order polynomials were used. The process for obtaining the reduced
form in our 2SLSIV approach was estimating the effects that the MLDA has on mortality. We
found that at the threshold there was an increase of about 8 deaths per 100,000 which serves as
our reduced form. Our 2SLSIV estimate which we will return to after this short digression is
defined as βIV = π 1α 1
In order to highlight a subtle but very important aspect of the results we will soon arrive
at with the 2SLSIV approach, a comparison should be made between the changes in internal and
external causes of death at the threshold. In row 1, column 2 and 3 of Table 3, you can see the
extreme difference between the external and internal cause of death increase when the
respondents are no longer legally bound by the MLDA. External causes of death increase by
about 7.4 per 100,000, with internal causes at a much lower .66 deaths per 100,000. If this
comparisons importance doesn’t immediately lend itself to you, think about the overall health of
people considered in our age range in this analysis and what is most likely to be the cause of
death for these individuals. People between the ages of 19-22 tend to be fairly healthy and
usually are not dying of internal causes such as cancer or other health related issues. For this
reason it is safe to assume that almost all of the 7.4 per 100,000 additional deaths are due to
external causes resulting from increased alcohol consumption at the threshold.
Instrumental variable (IV) estimates can be viewed as the average treatment effect for
those who comply with assignment. Complying with assignment in this analysis would be going
from not drinking to drinking at the threshold. In order to get the estimate of the IV we need to
compute the ratio of our two causal effects which are both intent to treat estimates presented in
this article. In other words we need to divide our reduced form by the first stage to get an
estimate for this chain of causation. Our 2SLSIV estimate is then 8.06/.092=87.6, with a standard
error of 20.3 which was calculated with the delta method. This means that scaled to the type of
people who began drinking at the threshold or “complied with assignment”, there is a statistically
significant increase in the mortality rate of an estimated 87.6 per 100,000 people instead of our
original estimate of 8 deaths. The reason for rescaling the estimate is because only 9% change
their alcohol intake at the threshold. With our data showing that virtually all the increase in
deaths are due to external alcohol related causes, it becomes evident that only the 9% who began
drinking at the threshold are causing the increase in mortality of 8 per 100,000. In other words,
the increase in mortality is driven by those who change their drinking behavior after age 21 and
not the entire portion of the sample who are over 21. The IV estimate gives us a sense of the
causal relationship between alcohol consumption and mortality if everyone complied with
treatment instead of the observed 9%. The actual impact that drinking has on dying and
ultimately the true effectiveness of the MLDA is presented with the 2SLSIV estimate.
This method is the most widely used IV in econometrics although it is conceptually
complex and easily misused. For this reason I would like to discuss the validity of our results and
see whether the assumptions under which it is sensible to estimate the IV in this context are
satisfied. The instrument that we use is a random occurrence which is a good start because
without this assumption met, your experiment should stop there. The threshold of turning 21 is
the instrument that we used to show the actual estimated effect that turning 21 has on drinking
alcohol and in turn on mortality rates. Turning 21 is a random event in one’s life and because of
this people above and below the threshold are very similar in respect to their observable
characteristics. This allows for consistent estimates of the reduced form to be obtained.
For the most part, the instrument also affects the causes of death independent of other
endogenous factors that have some effect on mortality. Turning 21 doesn’t have some effect on
someone’s life that is going to increase their chances of dying other than suddenly increasing
their alcohol consumption because it is now legal to do so. One could argue that being in bars or
other venues where alcohol is served could be inherently dangerous but this is still directly
related to being able to legally consume alcohol. Also, in support of our IV estimate, we saw a
substantial increase in suicides which is not directly correlated with bar attendance.
Convincing evidence is shown here that irresponsible acts ensue causing the proportion
of people dying from external causes to increase. This satisfies the exogeneity assumption for
our instrumental variable. Lastly, since we estimated the change in alcohol consumption to be
9%, the assumption stating that our first stage cannot be 0 is met. Note that the reason for this
assumption lies in the fact that there would be no difference between the treatment and control
group if our first stage was 0.
Overall it is safe to infer that the reduction in mortality rates (due to people abiding by
the MLDA) is definitely effected by the curbing of alcohol consumption. The increase in the
proportion of people being killed by these various causes at the threshold undoubtedly has a
correlation with alcohol consumption. For example, when people consume alcohol and become
impaired, they make poor and often irrational choices. This increases the likelihood of someone
acting on suicidal thoughts, getting into car accidents or any number of external causes of death.
This claim is supported by the coefficients on Over21 for Suicide, MVA and External in table 3.
These estimates show an increase in deaths of 2.4, 3.6 and 7.4 per 100,000 respectively. It is true
that these estimates alone do not constitute a causal relationship between the MLDA reducing
mortality although we showed earlier that at the same threshold there is a sharp increase for both
alcohol consumption and the mortality rate. Recall that the only observable statistically
significant difference between the treatment and counterfactual groups was that people in the
treatment group could all of a sudden drink legally. With that in mind deducing that the MLDA
reduces both alcohol consumption and in turn mortality is a logical conclusion.
This article has documented persuasive evidence in support of our current MLDA in the
U.S. The adverse impacts borne onto society from young adults who decide to drink when it is
no longer illegal are substantial. This analysis of the MLDA is by no means based on an
exhaustive study of this policy and is not inclusive of the spill-over effects we briefly touched
upon but did not include in our calculations. Due to this our conclusions regarding the MLDA’s
effectiveness should serve as a downward biased estimate. Other studies are encouraged and if
possible should include the negative externalities such as reduced productivity, increased suicide
rates and the many other alcohol related negative externalities in their estimates.