Going to College to Avoid the Draft
Going to College to Avoid the Draft: The Unintended Legacy of the Vietnam War
Authors: David Card and Thomas Lemieux
The Vietnam War was fought between the communist North Vietnamese government and the non-communist South Vietnamese government. The United States allied with South Vietnam to prevent the spread of communism. Fearing the unique brutality of the front lines of that war and morally opposed to its existence, young American men of the time were reluctant to enlist in the army.
The United States began drafting soldiers through two methods. For most of the war, the government required men to report to the draft office when they turned 18, and if deemed eligible, they were registered for the draft. The local draft board would then fill a quota of draftees from the registered men, starting with delinquents and volunteers and then, when necessary, the other men deemed eligible for the draft.
As the war dragged on, the government changed to a random birthday lottery to appear less partial. Under the lottery, men of drafting age were split into cohorts by birth year (for example, men born between 1944 and 1950 are a cohort). Each cohort was only at risk for one year of the draft. A man was only drafted by the lottery if his birthday was randomly selected and he was born in the relevant cohort for the year. Across both draft strategies, it was possible to obtain a deferment (effectively avoiding the war altogether) by attending college.
Card and Lemieux broadly want to determine whether college deferments were really a prevalent method of avoiding the draft. Because only men were eligible for the draft, they look at changes in the ratio of men to women enrolled in college during the Vietnam War. They also take into account that different age cohorts faced different levels of risk.
After assuming a smooth trend in gender ratio of college graduates and that draft-avoidant behavior increases for age cohorts eligible for the draft, Card and Lemieux run a regression. They regress education of men and women in a cohort on the risk of that cohort being drafted and an inter-cohort trend function.* They look for a positive and significant coefficient on the risk variable and find such a coefficient for all three outcomes in the regression.
To test this regression, Card and Lemieux try changing parts of the model. They rerun the regression with a quadratic inter-cohort trend and after removing the log from the gender ratio. They also tried distinguishing between before and after people realized how grave the front lines were in their measure of draft avoidance. The last thing they try is a dummy variable for the 1942-1950 cohort. None of these changes changed the results in any major way, so the model is likely working properly. They also address spikes in college attendance that could be attributed to high-risk draftees returning and going to college on the GI Bill. The number of people who followed that path is very small and it can be ruled out as a cause of the variation.
Counterfactual Assumption In a natural experiment, nobody knows what would have happened to the population under different conditions. So, the counterfactual assumption is just an educated guess at what might have happened without the intervention being observed.
Regress To regress y on x means to see whether x causes y. So, if you regress y on x, you're trying to find the best m and b such that y = b + mx + e (where e is everything besides x that causes y/the error term). This is a simple linear regression.
Difference in Differences Difference in differences compares the difference between two groups before and after a treatment. One group (in this case, women) is unaffected by the treatment and one group (men) is affected by the treatment. If the difference between the groups changes, it is called an intervention effect.
What exactly is happening with the inter-cohort trend function? When would you use a function like that in a regression and when would you omit it?
How do they account for societal changes that might allow more women to go to college and change the rate? What if more women go to college because men are getting drafted? Is this included in the fact that this is a diff in diff? Is it accounted for in the inter-cohort trend?
I think the way they test the robustness of the regression is really cool. How do they decide what to test? Is it just other things that they find interesting/viable or is there a standard way of doing that?
What are dummy variables and when do you use them?
*They regress education of men and women in a cohort on the risk of that cohort being drafted and an inter-cohort trend function.
There are three dependent variables representing education. The three outcomes are enrollment rate of 20-21-year-olds, graduation rate, and percentage with some college. Card and Lemieux use the log of the gender ratio for each of these outcomes for their dependent variables. Because the log of the ratio of each outcome follows a linear pattern over time, they use a linear inter-cohort trend.
The risk of induction for a cohort is the average number of inductions when that cohort is between 19 and 22 years old divided by the size of the cohort. They also include an inter-cohort trend function. This is a way of reducing error. A trend between the cohorts, that would likely create a similar pattern in college attendance that would be misleading. So, regressing on that trend accounts for those patterns.
The American Economic Review, Vol. 91, No. 2, Papers and Proceedings of the Hundred Thirteenth Annual Meeting of the American Economic Association. (May, 2001), pp. 97-102.
