Now, new research suggests that the draft did more than dim the prospects of that earlier generation: The children of men with unlucky draft numbers are also worse off today. They earn less and are less likely to have jobs, according to a draft of a report from Sarena F. Goodman, an economist with the Federal Reserve Board of Governors, and Adam Isen, an economist at the Treasury Department. (A copy was released by the Fed in December, but research does not reflect the opinions of the government.)

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The researchers have not nailed down how, exactly, any of this is happening, nor why the disadvantage appears to be over twice as potent for sons than for daughters. But the work is valuable for showing how the circumstances of one’s parents can have lasting repercussions. This is one way that inequality persists through the generations.

“I think it is a very important illustration of the importance of family background in determining people’s life outcomes,” Jesse Rothstein, Berkeley professor and former chief economist of the Department of Labor, said in an e-mail. (Rothstein was not involved in the research, but Goodman is a former student.)

Studies like this are exceedingly hard to come by. You cannot force men or women into a certain profession just to see how it would affect their future lives and children. Except, in the case of the Vietnam draft, that’s kind of exactly what happened.

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How they did the research

Goodman and Isen used confidential tax data from the IRS to look at fathers born specifically in 1951-1952, as well as their children. These men came of age toward the end of the Vietnam war, so few were actually conscripted, and even fewer saw combat. In fact, these fathers were just as likely to be alive in 1996 as men whose draft numbers were never called.

One hitch is that the researchers didn’t know which fathers actually served in Vietnam. They only knew who were draft-eligible — whose draft numbers got called — because people’s draft numbers were based on their birthdays, and that information was available.

Being draft-eligible didn’t mean you were conscripted automatically. It just meant that you were called up for review. People were excused from military service for all kinds of reasons. Men could get deferments to go to college, or to take care of their families. Some men had disqualifying medical conditions. And conversely, plenty of men who weren’t draft-eligible — whose numbers weren’t called up — volunteered to join the military.

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So even if the researchers could compare the veterans to the non-veterans, it wouldn’t make sense to do that. The men who ended up in the military — whether by draft or by choice — were systematically different than the ones who remained civilians.

In their analysis, Goodman and Isen sidestepped the question of military service. Their paper compares fathers who were draft-eligible to fathers who weren’t. This is fair because the lottery itself was random, even if the subsequent conscription process was not.

That’s what so interesting about their main finding, which is pictured in the charts below:

What these charts show is the effect of having a draft-eligible father on a son’s earnings in 2013. There is a small but significant hit, with greater impacts falling on older sons. On average, the sons of draft-eligible dads were earning about $268 less in 2013 than the sons of draft-ineligible dads.

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That doesn’t seem like a lot at first — $268 is only 0.72 percent of average annual incomes for these sons.

But remember: This is the impact of having a dad whose draft number was called, whether or not he actually served. And not that many served. In the latter years of the war, draft-eligible men were only about 13 percentage points more likely to join the military because of the draft.

Of course, it’s probably those 13 percent of men that are making the difference here. The economists can’t prove it, but it’s reasonable to suspect that if your dad didn’t enlist via the draft, your life was pretty much unaffected. Likewise, if your dad was always going to volunteer, the draft lottery probably wouldn't have changed your life one way or the other.

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(There are caveats here: Draft dodging was real, and the threat of the draft may have compelled some men to apply to college to avoid military service. But in general, economists don’t find that these practices were widespread enough to make a difference in the data.)

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How did the draft hurt the children of the Vietnam generation?

If all this seems a little circumspect, that’s because Goodman and Isen are very cautious economists. But let’s invoke common sense for a second. If the draft lottery had any effect on later generations, it’s probably through the unlucky men were pressed, involuntarily, into service.

If you want to know the effect of having a dad who went through Vietnam, not just a dad who was draft-eligible, Goodman and Isen’s data suggest that the disadvantages were pretty huge.

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The math works like this: If sons of all draft-eligible fathers earn $268 less on average, but draft-eligible fathers were only 13 percentage points more likely to serve, then the sons of conscripted veteran fathers are probably earning $2,000 less. That's assuming the entire effect of the draft is contained to those compelled by the draft to serve in the war.

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To repeat: A man who enlisted because of the Vietnam draft probably caused his sons to earn $2,000 less a year in 2013. That’s a difference of 5 percent of average incomes. That’s a big deal. These sons were also about 25 percent more likely to join the military. Daughters were affected too, to a much lesser extent.

Those are the facts. Now here come the theories. What about having an veteran father was holding these children back? The economists went through the possible reasons.

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First they wondered if there was something to do with the mothers. Maybe the men who were draft-eligible married different kinds of women. But the data showed that these mothers were basically the same in terms of their careers and their disability rates.

Next, the researchers wondered if the differences in earnings had to do with military service. The children of draft-eligible dads were more likely to enlist themselves — and maybe they could be earning more in the private-sector. But that’s not a plausible explanation either, because the military pays fairly well. And only a gigantic difference in salaries would cause the differences that Goodman and Isen found in the data.

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The only remaining explanations have to do with how these children of the Vietnam war were raised, and in what kinds of environments. Psychological studies have shown that PTSD, which many Vietnam combat veterans suffered from, affects the whole family and can cause behavioral problems in children.

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Men returned from Vietnam at a disadvantage. What the draft represented was the government taking away their time — time they could have spent in school or training for a job. Of course, people learn skills in the military too, and there were other benefits of enlistment: money to go to college, preferential hiring for veterans, and the VA healthcare system.

But on balance, economists have found that men who enlisted because of the Vietnam draft started from behind, and took decades to catch up to their peers in terms of wages. During that time, not only were they were earning less, but they also tended to settle in neighborhoods that were less nice. These factors affected how their children were brought up.

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That, at least the best guess that the economists have come up with. And it explains why older children were affected more by the draft. They grew up at a time when their veteran fathers hadn’t yet built their lives back up. As for why boys were affected more than girls, it may be that boys are more sensitive to the environment where they grow up.

This research has implication beyond veterans and Vietnam.“We’ve known for a while that there’s a strong (and probably growing) correlation between parents’ circumstances and kids’ outcomes,” Rothstein, the Berkeley professor said.