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

the instrumental variable to infer this causal relationship. It is found that for the population who

increase their alcohol consumption at the threshold, about 8 more people per 100,000 die in what

seems to be alcohol related incidents. With this in mind, any changes to the MLDA should be

subject to a strenuous process that provides extremely strong evidence to prove the findings in

this paper to be incorrect or insignificant.

Data

The NHIS data set used in this analysis is a sample drawn from the 1997-2007 record of

the National Health Interview Adult Files. This data set is composed of 61,784 observations of

14 different variables. The NHIS has been conducted since 1957 although the content of the

survey has been updated every 10-15 years. These statistics were collected through cross-

sectional household interviews where sampling is continuous year round in each state. Due to the

nature of this survey being of self-reported behavior, there may be inaccuracies in the data. The

quality of the data relies on the accuracy of what is reported. Some respondents may under or

over report certain behavior on purpose but in some cases human error may be the cause of

certain biases. For the most part there is little incentive to misreport when answering the

questions about the demographic characteristics we are interested in, besides this is the best data

available for an analysis of this type.

The demographic data generated by the NHIS was first used in this analysis to document

that with respect to their observable characteristics, the people just under 21 in our sample are

very similar to those just over 21. This data was then used to estimate the change in alcohol

consumption at the threshold. The demographic variables used in this data set originally

consisted of 11 binary and 3 numeric variables. Before providing a better understanding of the

initial variables used in this data set, I believe it would be advantageous to list them with the 11

binary preceding the 3 numeric: drinks alcohol (Reports they drink alcohol), high school

diploma, hispanic, white, black, uninsured, employed, married, working last week, going to

school, male, days_21 (Days to 21st birthday), AGE_yrs, and perc_days_drink (Percent of days

on which they report drinking). The binary covariates are either activated and take on a value of

1 if the given characteristic applies to the respondent or takes on a value of 0 otherwise. For

example, let’s say we have a regression model with “drinks alcohol” as the response variable and

all the other demographic characteristics as the explanatory variables. Once this regression is ran

and the estimates obtained, it is interpreted that for each binary variable associated with a given

person, the average effect pertaining to alcohol consumption is equal to the estimated coefficient

on that given variable.

Our second data set is mortality data from the National Vital Statistics System (NVSS)

which documents demographic, geographic and cause-of-death information via death

certificates. The NVSS is a fundamental source of health related data and is one of the few

records available of this type for long periods of time. The NVSS is the longest lasting and most

thriving inter-governmental data sharing system in public health. This data set contains 10

variables, one of which is Age and the other 9 being different causes-of-death with some minor

overlaps. The mortality rates in this data set are on a per 100,000 persons scale by age and

encompass all the primary causes of death. The variables in this data set are all continuous

numeric observations and are as follows: Age, All (causes of death), Internal, External, Alcohol,

Homicide, Suicide, Motor Vehicle Accidents, Drugs and External.Other (causes of death). We

will use this data set to show how the MLDA reduces the mortality rate. Then using this estimate

along with the alcohol consumption increase at the threshold, we will be able to estimate the

effects of drinking behavior after age 21 on overall deaths and each cause-of-death sub-category,

with the use of a two-stage least squares instrumental variables approach.

Before transitioning into the methods section of this analysis I want to provide some

background information on the MLDA. After prohibition ended in 1933, states were granted

permission to make their own laws regarding alcohol. The most common law across the states

was the MLDA and at the time it was set at 21 years of age. In the early 1970’s the MLDA was

lowered to ages ranging between18-20 depending on the state. This trend was heavily influenced

by the passage of the 16th amendment which lowered the voting age to 18. By the early 1980’s

only 14 states still had a MLDA of 21. Lasting over a decade, this decrease in the MLDA was

quickly reversed when the National Minimum Drinking Age Act was implemented in 1984.

This act prompted states to raise their MLDA in order to avoid losing millions in federal

highway funds and by the late 1980’s all 50 states had raised their MLDA back to 21.

Methods

Some other variables were added to the initial data set in order to aid the graphical

representation of the RDD and to provide regression flexibility with the use of higher order

polynomials. Arguably the most important covariate which we touched upon in the introduction

is the Over21 variable, which takes on a value of 1 if the respondent is over 21 years old and 0

otherwise. Another useful binary variable in our analysis was created and used to shed some light

on certain trends occurring on people’s 21st birthdays. This “birthday” variable takes on a value

of 1 if the amount of days to ones 21st birthday is equal to 0 and 0 otherwise. A new “Age”

variable is also defined as 21+ (days to 21/365) and is used to create the “age-centered” variable

which is defined as Age-21. Denoted as AgeC, the age-centered variable allows the x axis in our

plots to be centered with ages just below 21 to the left of the threshold and ages over 21 being to

the right of the threshold. The age centered variable is then used to create linear, quadratic and

cubic age centered variables for pre and post threshold periods. The quadratic and cubic age

centered variables are simply defined as the age centered variable (AgeC) raised to the 2nd and 3rd

powers respectively. The post threshold versions of these variables are then created by

interacting the pre threshold variables with the Over21 variable which is only activated after age

21 (our threshold).

Graphical representation in regression discontinuity analysis is imperative to the visual

aspect of presenting the local average treatment effect. For this reason we will spend some time

on how the decisions were made pertaining to the scales, bin widths and ranges of the plots used

in this analysis. Well start with data binning since the process is not as transparent and will need

a little more explanation than choosing the ranges for the x and y axis. I was torn between the 50

and 65 day bin, although after much deliberation I ended up picking the 50 day bin. The smaller

bins leading up to the 50 day bin are just way too noisy although at the 50 day bin the data

begins to become clearer. It is noteworthy that the 128 day bin has too large of gaps between the

data points to be useful. I almost picked the 65 day bin because the trend was clear and the jump

at 21 in the data was visible without too much noise but chose the 50 day bin for two reasons.

First, the trend was clear without a bunch of overlapping data points but more importantly the

jump in the data at age 21 is more visible and was representative of the findings, which we will

discuss in later sections.

For a better understanding of why we bin the data, you can refer to figure 1 above. Figure

1 is what the data spread looks like before using the bins and averaging the data. This is due to

using a binary variable representing the answer to a yes or no question, thus creating two parallel

lines representing respondent answers with similar ages and different answers to whether they

drink alcohol or not. Our goal here is to cut the age variable into pieces that are equally spaced

and contain the amount of days specified before averaging the respondents answers to whether

they drink or not. This will allow the plot to clearly represent the change in alcohol consumption

at the threshold. Different examples of bin widths are presented in Figure 2, which is the panel of

plots below, with the bottom left being the 50 day bin.

Another important task was determining what range of age to include in the age profile of

whether or not people drink alcohol. Since the proportion of people who drink alcohol at very

young ages is relatively small, the lower bound of the age range is important in creating a plot

with pertinent information. The upper bound is equally important because people tend to change

their drinking habits after a few years when the excitement wears off from being able to legally

drink. Besides these two reasons for selecting the correct age range, we are analyzing the MLDA

which is 21 so we should naturally focus on an age range that is not too far above or below 21.

For a visual aid of the following descriptions you may refer to the panel of plots below in Figure

3, which shows the different age ranges that were considered before choosing to cut off ages

below 19 and above 23 for our analysis. The bottom left plot shows the 19-23 range.

The 19-23 range did not have too large of gaps between the data points, as did the 20-22

range. I believe that the 19-23 also provides a sufficient amount of data before and after 21

which is where our focus is when examining this data. The jump at 21 is still also prevalent

unlike the 20-22 range where it is barely noticeable. It’s not that with the 20-22 age range the

jump is any smaller but it visually seems to be because at this small range we are too zoomed in,

thus skewing the visual representation of the results. Lastly, the 19-23 range provides a

continuous plot without the data stopping at 18 like with the 17-25 range.

Now to complete the framework for the age profile on alcohol consumption and mortality

rates let’s now address the range for the alcohol consumption levels in the age profile of whether

or not people drink alcohol. I chose the .35-.75 alcohol range for the y axis which represents

alcohol consumption levels for the respondents. This is because our data set does not observe

levels above or below this range. This allows us to zoom in on our observed data points, thus

giving us a better view of the observed data. This range also makes the jump at 21 more

noticeable because we are focusing on the drinking levels we have data recorded for, thus giving

a better picture of the effects on alcohol consumption at age 21.

Now that we have a better idea of the visual aids in our analysis, let’s now review the

econometric methods used to create our estimates and findings. Before eliciting the causal effects

from our RDDs intervention, the control and treatment groups were compared. This was done to

verify that people just under and just over the threshold of being 21 years old were very similar

besides the fact that the people over 21 were now allowed to legally drink as per the MLDA.

Table 1 presents the level estimates for each of the demographic variables for people just under

21 and how they change at 21. This is similar to a balance table in a controlled experiment. A

controlled experiment is not feasible due to the nature of this analysis; therefore this is how we

are able to conclude that our average local treatment effect is a valid estimate. This method was

performed by running individual regressions on the variables Over21, AgeC, and AgeCpost with

the observable characteristics as the response variable in each regression. Each of the 10

regression models had a different response variable but an example using Table 1, column 1 as a

reference is:

uninsuredi = βo + β1*Over21i + β2*AgeCi + β3* AgeCi*Over21i + ui

The Over21 variable is very important throughout this analysis which will soon become

apparent. With each of these 10 regressions, the coefficient on Over21 is the estimated difference

between the pre and post-threshold groups. Ideally to prove that the two groups are almost

identical, we want the coefficient on Over21 to be close to 0. Recall that Over21 is a binary

variable designed to take on a value of 1 for a respondent over 21 years old and 0 otherwise. This

functionality allows Over21 to absorb the difference between each demographic response

variable for the people above and below the threshold.

With the framework for the visual representation solid, the treatment and counter-factual

groups documented as very similar, the core of our RDD was then employed. A very important

aspect of the MLDA is whether or not it is effective in reducing alcohol consumption. This

concern was answered with another RDD with whether the person drinks as the response

variable. The celebration effect variable we call “birthday” and the higher order age-centered

polynomials come into to play in this specification as explanatory variables along with Over21,

AgeC and AgeC*Over21. The birthday variable serves to absorb the effects that birthday

celebrations have on behavioral patterns that may affect alcohol consumption or mortality. The

higher order age-centered-polynomials are added into the regressions from least to most flexible

so we could create a plot with the regression lines superimposed over the data points in order to

assess which model best fits the age profile. The specification process ultimately yielded these

regression models with the quadratic and cubic age-centered covariates added to them for the

higher order polynomial versions:

(1) drinks_alcoholi =αo + α1 *Over21i+ α2*AgeCi + α3* AgeCi*Over21i+ ui

(1a) drinks_alcoholi = αo + α1 * Over21i+ α2*AgeCi + α3* AgeCi*Over21i + α4*birthdayi +ui

I chose the linear regression specification. This specification makes the most sense to

me because it seems to be the best fit to the data unlike the higher order polynomial

specifications that skew the data and either over or under estimate the jump at the threshold.

With higher order polynomials, it is less likely to have biases although it comes at the cost of less

precision which is quite obvious by the superimposed lines resulting from the squared and cubed

regressions being pretty far away from being a best-fit-line for the data at some points. My main

goal in choosing the right polynomial order was to make the line pass through the middle of the

data points as well as possible while having an obvious threshold jump. The linear specification

not only follows the trend of the data properly but also makes the jump at the threshold

noticeable without making it more extreme than the raw data points show without the

superimposed lines.

The most important statistic related to increased alcohol consumption for those no longer

affected by the MLDA is arguably the mortality rate, which we will focus on in this section.

Specifically, we will provide the framework for estimating the effect on mortality at the

threshold. Once again, the Over21 variable is exploited to estimate the average treatment effect

although this time we will be estimating the effect of turning 21 on all causes of mortality and

each primary cause-of-death. In order to derive these estimates we utilize another RDD model,

but this time using the mortality data set. For this model the different causes of death will serve

as the response variables for each of the 9 specifications. The same method for choosing the

appropriate polynomial order was used here as with the different regressions ran when estimating

the pre vs.post threshold alcohol consumption levels. I believed the best-fit-line was with the use

of the quadratic age-centered variable which resulted in this general form with table 3, row 1 as a

reference:

AllCausesi = πo + π1 * Over21i+ π2*AgeCi + π3* AgeCi *Over21i + π4*( AgeCi)2 +

π5* (AgeCi *Over21i) 2 + π6birthday i+ ui

Before presenting the results it is worth noting that the local average treatment effect

found for the regression specification with all causes of death as the response variable will be

used as the reduced form in our instrumental variables approach. This reduced form along with

the first stage will be used to estimate the effect of drinking on mortality in later sections.

Results

As noted earlier a series of regressions were conducted with the demographic

characteristic as the response variable for each of the 10 specifications. The table of regression

estimates are presented in Table 1 located at the end of the article. Extra attention should be

given to the coefficients on the Over21 variable, as they measure the difference between each of

the treatment and control group’s observable characteristics. It was found that the two groups

were very similar with the standard errors and coefficients on the Over21 variable being very

small. The difference between people just above and just below 21 proved to be insignificant for

nearly all observable characteristics. Being married had the largest difference between the two

groups and this estimate was still only about a 3 %.

With the thorough documentation of the control and treatment groups being similar, we

can now begin discussing the core results in our analysis with confidence that the estimates of

this particular intervention are causal.

As shown in Figure 4 there is a discontinuity in the best-fit regression line which

represents the increase in alcohol consumption at the threshold. The sharp increase shown by the

jump at 21 presents compelling visual evidence that the MLDA is effective in reducing alcohol

consumption.

More support in favor of this argument is shown in table 2. The regression estimates

summarized in this table are from the model specified to measure the MLDA’s effectiveness in

reducing alcohol consumption. As shown by the coefficients on Over21 in this table, the MLDA

does decrease alcohol consumption for people bound by the law. The estimates vary depending

on the order of the polynomial and whether or not the birthday variable was included.

Nonetheless all the coefficients on Over21 are positive and range from 7.8% to 9.2%. The

different ordered polynomials could be a contributing factor to the fluctuations in the coefficient

on Over21. The lowest estimated increase in alcohol consumption is observed with the cubic

AgeC coefficients.

(Table 2)Drinking Profile================================================================== Dependent variable: ----------------------------------------------------- drinks_alcohol (1) (2) (3) (4) (5) (6) ------------------------------------------------------------------Over 21 0.086*** 0.086*** 0.092*** 0.091*** 0.081*** 0.078*** (0.014) (0.014) (0.021) (0.021) (0.029) (0.029) AgeC 0.044*** 0.044*** -0.024 -0.024 -0.051 -0.051 (0.009) (0.009) (0.036) (0.036) (0.090) (0.090) AgeC*Over21 -0.024* -0.024* 0.094* 0.095* 0.214* 0.222* (0.012) (0.012) (0.049) (0.050) (0.124) (0.125) birthday 0.002 0.020 0.037 (0.084) (0.085) (0.086) AgeC2 -0.034* -0.034* -0.068 -0.068 (0.017) (0.017) (0.104) (0.104) AgeC2*Over21 0.009 0.009 -0.072 -0.080 (0.024) (0.024) (0.143) (0.145) AgeC3 -0.011 -0.011 (0.034) (0.034) AgeC3*Over21 0.050 0.052 (0.047) (0.047) Constant 0.559*** 0.559*** 0.536*** 0.536*** 0.532*** 0.532*** (0.010) (0.010) (0.015) (0.015) (0.021) (0.021) ------------------------------------------------------------------Observations 18,824 18,824 18,824 18,824 18,824 18,824 R2 0.025 0.025 0.025 0.025 0.025 0.025 ==================================================================Note: *p<0.1; **p<0.05; ***p<0.01================================================================== *p<0.1; **p<0.05; ***p<0.01

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.