Purpose

Guidelines

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• Your responses should be professionally formatted and written.
• The due date is Monday, April 1st, at 10 pm EDT. (Note that this is the week of your 48-hour project, so you may not want to spend all your monday on it)

Tips

• Clean your desk, get a bottle of water, pick your favorite beverage, turn on “do not disturb,” set a timer for 45 min (then take breaks), put on some work tunes, and dive into the fun of learning.
• Tackle the homework by doing a rough draft, reading it, noticing what you must do to answer questions, and then assessing how long it could take. Then, plan for your week and when you’ll tackle it.
• Start early!

Understanding the paper: The Minimum Legal Drinking Age and Crime

1. What is the research question?
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What is the effect of legal access to alcohol on crime?
2. What ages does the analytic sample contain?
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The sample contains young adults age 19-22,inclusive.
3. What is the running variable?
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The running variable is age.
4. Who should be considered the “treated” group?
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People who were at least 21 years old form the treated group
5. Who should be considered the “control” group?
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The control group contains people who were not yet 21.
6. What must we be willing to assume if we want to believe that this analysis captures the causal effect of legal alcohol access on arrests? Use the context, not general words that could be applied to any context.
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This analysis rests on the assumption that legal access to alcohol is the only systematic difference between people who have just turned 21 and those who are slightly younger. This is a safe assumption because people don't have any control over when they turn 21, so it's not easy to manipulate the running variable, age. The MLDA is also a relatively arbitrary cutoff in the United States. This means that units right above and right below are similar in observable and unobservable characteristics. Legal rights, like driving and tobacco, kick in at earlier ages, so it's unlikely that another major contributor to crime shares this eligibility cutoff.
7. Interpret the results from Table 1 in words. What is the total arrest rate for the control group in this analysis? Be sure to specify the units for arrest rates in your answer. Is the arrest rate larger or smaller than you anticipated?
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There were 1,543 arrests per 10,000 person-years in the control group. Person-years are tricky units to interpret. The control group contained people at least 19 years old but not yet 21. If everyone who lives to be 19 also survives to age 21, then a sample of 10,000 person-years contains 5,000 distinct people: each person contributes two years between his/her 19th and 21st birthdays. In reality, some people die between age 19 and 21, which the researchers adjust for, but it's not a bad approximation to think of 10,000 person-years as roughly 5,000 people in this sample. Given that approximation, 1,543 arrests should probably sound pretty high. It's nearly one arrest for every three people. That said, some people were likely arrested more than once. We can't tell from these data whether the 1,543 arrests came from 1,543 distinct people or from 400 people who each had three or four arrests. (You didn't have to say all of this to get full credit for your answer, but let this be a reminder that we must take time to understand the units before we know whether a number is big or small.)
8. How does legal alcohol access affect the total arrest rate? Present your answer as a percent change relative to the control group's arrest rate.
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Legal alcohol access increased the total arrest rate by 90.3 arrests per 10,000 person-years or roughly six percent $\frac{90.3}{1543.1}=0.059$)
9. Repeat steps (7)-(8) for the violent crime results in Table 1. Specify the control mean, calculate the treatment effect in percentage terms, and interpret the magnitudes, and assess statistical significance.
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Legal alcohol access increased the violent crime arrest rate by 10.9 arrests per 10,000 person-years, or roughly seven percent relative to the control mean of 151.4. This effect is highly significant ($t=\frac{10.9}{1.1}\approx10$) and similar in magnitude to the effect on total arrests.
10. What category of crime accounts for the largest share of the change in crime rates at the MLDA discontinuity? Give three examples of crimes from this category.
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Increased arrests for “other” crimes account for more than half of the effect on total arrests. $(\frac{50.7}{90.3})$. The “other” crimes results are plotted in Figure 4 and detailed in footnote 10. County ordinance violations are the primary contributor. These crimes include public urination, social host liability, and alcohol possession in public parks.
11. Figures 1-4 reveal some interesting trends in arrest rates for young adults.
1. Give two examples of crimes for which arrest rates are pretty stable as teenagers enter their early twenties.
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Murder and manslaughter rates are both low and quite stable as young adults age.
2. Give two examples of crimes for which arrest rates vary dramatically with age.
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Property crimes fall steadily as young adults age: arrest rates are nearly 50 percent higher at 19 than 23. DUIs rise steadily between age 19 and 21 and then jump dramatically at the MLDA.

Policy Implications & Robustness of Results

13. Carpenter and Dobkin analyze the effect of legal alcohol access on arrest rates, but they're interested in the effects on crime. Good crime data are hard to come by since many crimes don't result in arrests.
1. Why might arrests increase at age 21 even if legal access to alcohol doesn't increase crime? Give two distinct reasons.
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People who can legally drink in public spaces, like concerts, bars, and sporting events, may, therefore, be closer to police when they commit crimes and be more likely to get caught. Drunk criminals could also be more careless. If drunk burglars trip alarms more often than sober thieves, we might expect burglars who can buy alcohol to get arrested more often than those who can't. Both factors might cause an uptick in arrests at age 21, even if the number of crimes committed doesn't change.
2. What evidence do Carpenter and Dobkin provide to bolster the case that their findings capture effects on crimes committed and not just arrests?
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The authors address the first critique by showing that arrests also increase for crimes that mostly take place in private residences (e.g., assaults). These effects aren't likely driven by drinking in public spaces. To address the second concern, they identify many crimes for which arrests don't change at age 21, like drug possession and murder. It's not clear why we'd expect criminals to be sloppy about committing assault but not about making drug deals, so the careless factor probably isn't driving most of these results.
14. Each US state gets to set its legal drinking age, but the federal government strongly incentivizes states to choose 21. According to the National Minimum Legal Drinking Act, states that set the drinking age below 21 risks losing up to 10 percent of their federal highway funding. Mothers Against Drunk Driving (MADD) was a major political player in lobbying for the Act's passage in 1984. What do Carpenter and Dobkin's findings suggest about the effects of this federal act on young adult crime? Would crime rates be lower if state MLDAs went back to 18? What caveats would you offer in drawing policy conclusions from these results? (Pass or fail)
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These findings suggest that raising the MLDA did, indeed, reduce crime among young adults. It shows that there are people under the age of 21 who commit more crimes as soon as they have legal access to alcohol. We must be cautious in extrapolating these results from the age 21 cutoff. It's not clear that alcohol effects are the same for 18 and 21-year-olds. Teens could be somewhat more or less sensitive to alcohol access. Still, it seems unlikely that the alcohol effect is ever negative over this range, so the net effect of raising the MLDA from 18 to 21 should be less crime. However, these results don't necessarily imply that we should raise the MLDA further (say, from 21 to 25). We have to weigh the reduction in alcohol-related harms against the consumer surplus that people derive from consuming alcohol.
15. The United States is one of only four developed countries in the world with a nationwide drinking age above 18. Iceland, Japan, and South Korea are the other three. Why should we be cautious in generalizing MLDA results from the US to countries like France and Italy, which permit alcohol purchasing at younger ages? (Pass or fail)
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We should always be cautious when generalizing results across countries. Children who grow up in cultures that encourage social drinking at younger ages may be less affected by legal alcohol access later in life. Other countries may also have different standards for criminal behavior and law enforcement.

Estimating the results

17. The goal is to recreate Figure 1. For that, we’ll start by plotting violent crimes. Then, a similar process was used to create the rest of the figure. The commands that will be super helpful are collapse ,twoway, scatter and the option lfit.
1. Step 1: Open the data and understand its layout.
2. Step 2: type twoway (scatter violent_r days_to_21, sort). What this graph shows you is, for every day away from one’s 21st bday, what is the rate of violent crime per 10,000 person-years. We can start seeing the discontinuity there, but it is not as clear as in Figure 1. The main difference is how the information is “binned.” The x-axis is not every single day, but it’s binning days together and telling us the average violent crime rate for a given bin of days. So we need to create the bins. The graph bins the data into bins of 14-days. Therefore, each point is the average violent crime rate for 14 days. See if you can create a set of bins and then use the collapse command on your own, but if that’s taking too much time, jump to step 3.
3. Step 3: Create the 14-day bins: gen age_fortnight = 21 + (14*floor(days_to_21/14))/365. We are creating the bins of 14 days for you on this variable. Browse the data so that you understand better what this is doing: br days_to_21 age_fortnight
4. Step 4: Now that we’ve created the bins, use the collapse command to transform the data into means of violent crime per each bin
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use "$hw/hw4_carpenter_dobkin.dta", clear 

gen age_fortnight = 21 + (14*floor(days_to_21/14))/365 

collapse violent_r, by(age_f)

5. Step 5: Now, we are ready to plot! Use the two-way command with scatter and the lfit options. Here are a couple of hints:
1. Use the point-and-click feature to get the code!
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Video

2. Do things one by one, and add things as you go.
3. Label your axis!
4. Notice that Figure 1 only uses data for 2 years before 21 and 2 years after 21. not the whole span.
5. Notice that the violent crime rate range in Figure 1 is on the right y-axis, not the left one. So you should compare your results with those numbers.
6. Turn the legend off in your graphs that you produce.
7. Change the y-axis range so it’s similar to the one from the paper rather than the one STATA gives you.
6. Step 6: Once you’ve created the graph, submit a screenshot of your figure in Gradescope and the code as well.
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use "$hw/hw4_carpenter_dobkin.dta", clear 

gen age_fortnight = 21 + (14*floor(days_to_21/14))/365 

collapse violent_r, by(age_f)


twoway (scatter violent_r age_fortnight, sort) ///
(lfit violent_r age_fortnight if age_fortnight<21, lcolor(black)) ///
(lfit violent_r age_fortnight if age_fortnight>=21, lcolor(black)) ///
if age_fortnight >= 19 & age_fortnight < 23, ///
ytitle(`"Violent Crime rate "') ylabel(100(100)300) ///
xtitle(`"Age at Time of Arrest"') ///
title(`"ARREST RATES PER 10,000 PERSON-YEARS"') ///
 legend(off)

graph export "$hw/violentcrime.png", replace 

18. Now that you’ve created “one” of those lines from the graph, to get closer to Figure 1, we need to add lines for the following outcomes: violent crimes, property crimes, alcohol-related, drug possession (ill_drugs_r), and other crimes. Follow a similar process as above to create the figure.
1. The only tricky thing is to label the two axes - which is not essential, but if you want to figure out how to do it, here are some tips:
1. Make property the first variable you plot, and in the options of anything property related, add yscale(range(200,600) axis(1)), and right before the title option (after the main “,”) add ylabel(#3)
2. Then, for the variables on the second-axis, violent crimes and drug possession have the following code after their respective “,” yaxis(2) yscale(range(100,300) axis(2)) ylabel(#3, axis(2))
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use "$hw/hw4_carpenter_dobkin.dta", clear 

local vars  = "violent_r property_r ill_drugs_r alcohol_r other_r"

keep `vars'  days_to_21

gen age_fortnight = 21 + (14*floor(days_to_21/14))/365 

collapse (mean) `vars', by(age_f)


twoway ///
(scatter property_r age_fortnight , yscale(range(200,600) axis(1))  sort) ///
(lfit property_r age_fortnight if age_fortnight<21, lcolor(black) yscale(range(200,600) axis(1))) ///
(lfit property_r age_fortnight if age_fortnight>=21, lcolor(black) yscale(range(200,600) axis(1))) ///
(scatter violent_r age_fortnight, yaxis(2) yscale(range(100,300) axis(2)) sort) ///
(lfit violent_r age_fortnight if age_fortnight<21, yaxis(2) yscale(range(100,300) axis(2)) ylabel(#3, axis(2)) lcolor(black)) ///
(lfit violent_r age_fortnight if age_fortnight>=21,  yaxis(2) yscale(range(100,300) axis(2)) lcolor(black)) ///
(scatter ill_drugs_r age_fortnight, yaxis(2) sort) ///
(lfit ill_drugs_r age_fortnight if age_fortnight<21, yaxis(2) lcolor(black)) ///
(lfit ill_drugs_r age_fortnight if age_fortnight>=21, yaxis(2) lcolor(black)) ///
(scatter alcohol_r age_fortnight, sort) ///
(lfit alcohol_r age_fortnight if age_fortnight<21, lcolor(black)) ///
(lfit alcohol_r age_fortnight if age_fortnight>=21, lcolor(black)) ///
(scatter other_r age_fortnight, sort) ///
(lfit other_r age_fortnight if age_fortnight<21, lcolor(black)) ///
(lfit other_r age_fortnight if age_fortnight>=21, lcolor(black)) ///
if age_fortnight >= 19 & age_fortnight < 23, ///
xtitle(`"Age at Time of Arrest"') /// 
ylabel(#3) ///
 title(`"ARREST RATES PER 10,000 PERSON-YEARS"') legend(off)

 graph export "$hw/fig1.png", replace 

19. Using binscatterNow that you’ve figured out how to graph things using Collapse and twoway, let’s do something similar with binscatter. Install binscatter (if you haven’t already installed it by using ssc install binscatter.
1. Open the original data again. Learn on how to use the binscatter command; try binscatter dui_r days_to_21 . Notice what binscatter is doing: it automatically creates bins for you and does the collapse plus the fit-line, an all-in-one command.
2. Change the graph to include two different fit lines before and after the cutoff (hint: look at the by option or at the rd option) and use only information from 19 to 23.
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use "$hw/hw4_carpenter_dobkin.dta", clear 

gen post=0
replace post=1 if days_to_21>=0

 gen square_post2=(post*days_to_21)^2

binscatter dui_r days_to_21 if days_to_21 >=-2*365 & days_to_21<= 2*365 -1, by(post)
binscatter dui_r days_to_21 if days_to_21 >=-2*365 & days_to_21<= 2*365 -1, by(post) legend(off) ytitle("DUI") xtitle("Days from 21") xscale(range(-730 730)) xlabel(-730(100)730) title("Arrest per 10,000 Person-year")
 graph export "$hw/fig2.png", replace 

20. Replicating Table 1. Finally, we’ll get to replicating Table 1. The following steps will help you get the first estimate, but you’ll have to do the final table yourself.
1. Step 1: Run the most basic RD regression using “all” arrest as your main outcome. (Save this as regression 1.) Add the option “, robust” at the end of each regression in all of your following regressions. This is a great place to use eststo and esttab.
2. Step 2: Run the same regression, but now only use data from ages 19 to 23. This is regression 2.
3. Step 3: Run the same regression as step 2, but now add an interaction between your cutoff variable and the “running variable - cutoff” variable, allowing for different slopes. This is regression 3.
4. Step 4: Now run the same regression as step 3, but allow for both slopes (before and after the cutoff) to be quadratic and to differ between each other.
5. Step 5: Finally, add the birthday covariates. Read the table notes of Table 1, which we write here: “The first line contains the estimate of the discrete increase at age 21 in arrest rates for each crime type. The regressions include a quadratic polynomial in age fully interacted with an indicator variable for age over 21 and indicator variables for 19th, 20th, 21st, and 22nd birthdays and the days immediately after. The regressions are estimated based on arrests of people 19 to 22 years old. Each observation is the arrest rate per 10,000 person-years days from a person’s 21st birthday. Standard errors are in parentheses. The codes that comprise each crime category are in online appendix A.” The only thing left is adding indicator variables for 19th, 20th, 21st, and 22nd birthdays and the days immediately after; these are dummies you can create, but these have already been created for you called birthday_19 and birthday_19_1 and so on.
6. Answer the following question: Why must we add the birthday covariates?
7. Now that you’ve run the 5 regressions output them in a table with their standard error and significant stars. Your results should look like this:

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estimates clear 
qui eststo: reg all_r post days_to_21  , robust 
qui eststo: reg all_r post days_to_21  if days_to_21 >= -2*365 & days_to_21 <= 2*365 -1, robust 
qui eststo: reg all_r post days_to_21 i.post#c.days_to_21  if days_to_21 >= -2*365 & days_to_21 <= 2*365 -1, robust 
qui eststo: reg all_r post days_to_21 c.days_to_21#c.days_to_21 i.post#c.days_to_21 square_post2 if days_to_21 >= -2*365 & days_to_21 <= 2*365 -1, robust 
qui eststo: reg all_r post days_to_21 c.days_to_21#c.days_to_21 i.post#c.days_to_21 square_post2 birthday_19  birthday_19_1 birthday_20  birthday_20_1 birthday_21  birthday_21_1 birthday_22 birthday_22_1 birthday_23 birthday_23_1 if days_to_21 >= -2*365 & days_to_21 <= 2*365 -1, robust 

esttab, keep(post) se

21. Now replicate fully table 1, including adding: “Rate just under 21”. Present your screenshot and code.
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* ###### Replicate all of table 1
estimates clear 
eststo: reg all_r 		post days_to_21 c.days_to_21#c.days_to_21 i.post#c.days_to_21 square_post2 birthday_19  birthday_19_1 birthday_20  birthday_20_1 birthday_21  birthday_21_1 birthday_22 birthday_22_1 birthday_23 birthday_23_1 if days_to_21 >= -2*365 & days_to_21 <= 2*365 -1, robust 
eststo: reg violent_r  	post days_to_21 c.days_to_21#c.days_to_21 i.post#c.days_to_21 square_post2 birthday_19  birthday_19_1 birthday_20  birthday_20_1 birthday_21  birthday_21_1 birthday_22 birthday_22_1 birthday_23 birthday_23_1 if days_to_21 >= -2*365 & days_to_21 <= 2*365 -1, robust 
eststo: reg property_r 	post days_to_21 c.days_to_21#c.days_to_21 i.post#c.days_to_21 square_post2 birthday_19  birthday_19_1 birthday_20  birthday_20_1 birthday_21  birthday_21_1 birthday_22 birthday_22_1 birthday_23 birthday_23_1 if days_to_21 >= -2*365 & days_to_21 <= 2*365 -1, robust 
eststo: reg ill_drugs_r post days_to_21 c.days_to_21#c.days_to_21 i.post#c.days_to_21 square_post2 birthday_19  birthday_19_1 birthday_20  birthday_20_1 birthday_21  birthday_21_1 birthday_22 birthday_22_1 birthday_23 birthday_23_1 if days_to_21 >= -2*365 & days_to_21 <= 2*365 -1, robust 
eststo: reg alcohol_r 	post days_to_21 c.days_to_21#c.days_to_21 i.post#c.days_to_21 square_post2 birthday_19  birthday_19_1 birthday_20  birthday_20_1 birthday_21  birthday_21_1 birthday_22 birthday_22_1 birthday_23 birthday_23_1 if days_to_21 >= -2*365 & days_to_21 <= 2*365 -1, robust 
eststo: reg other_r  	post days_to_21 c.days_to_21#c.days_to_21 i.post#c.days_to_21 square_post2 birthday_19  birthday_19_1 birthday_20  birthday_20_1 birthday_21  birthday_21_1 birthday_22 birthday_22_1 birthday_23 birthday_23_1 if days_to_21 >= -2*365 & days_to_21 <= 2*365 -1, robust 

esttab, keep(post _cons) se coeflabel(post "Increase at 21" _cons "Rate just under 21")

References

• Christopher Carpenter and Carlos Dobkin. The effect of alcohol consumption on mortality: Regression discontinuity evidence from the minimum drinking age. American Economic Journal: Applied Economics, 1(1):164–182, 2009.
• Christopher Carpenter and Carlos Dobkin. The minimum legal drinking age and public health. The Journal of Economic Perspectives, 25(2):133–156, 2011.
• Christopher Carpenter and Carlos Dobkin. The minimum legal drinking age and crime. Review of Economics and Statistics, 97(2):521–524, 2015.
• Scott E Carrell, Mark Hoekstra, and James E West. Does drinking impair college performance? evidence from a regression discontinuity approach. Journal of Public Economics, 95(1):54–62, 2011.
• Benjamin Crost and Santiago Guerrero. The effect of alcohol availability on marijuana use: Evidence from the minimum legal drinking age. Journal of Health Economics, 31(1):112–121, 2012.