Even most opponents of immigration concede that immigration has a positive effect on native wages overall. But opponents insist that immigration hurts specific groups of American workers, in particular low-skilled workers who lack high school diplomas. By far the most vocal economist making this argument is Harvard's George Borjas, who has for years produced research claiming substantial harms to poor Americans from immigration.

But there's a lot of research contradicting Borjas's findings. One influential study by Berkeley economist David Card found that the Mariel boatlift — in which 125,000 Cubans suddenly immigrated to Florida in 1980 — didn't cost jobs or reduce wages for people already in Florida, including existing Cuban immigrants. Last month, Borjas released a reanalysis of the boatlift claiming that Miamians with less than a high school diploma saw wages fall dramatically: by 10 to 30 percent. Immigration opponents were thrilled:

The big pro-immigration data point--that the Mariel boatlift didn't suppress wages--has seemingly been destroyed http://t.co/Mrt1W1Ed0K — Mickey Kaus (@kausmickey) September 17, 2015

Does the reanalysis hold up? Researcher David Roodman delved into Borjas's paper and concluded that it doesn't. He argues that Borjas makes a number of inappropriate analytical choices that make it look like the boatlift caused a decline in wages. But if you do a more rigorous analysis, Card's finding that nothing much changed is validated.

Borjas ignores women entirely, and argues that immigration hurt wages years later

First off, Borjas can't claim to show that the influx of Cubans hurt low-skilled workers in Miami in general, because he didn't look at all low-skilled workers. He just looked at men. "It is tempting to increase sample size by including working women," Borjas writes. "But female labor force participation was increasing very rapidly in the 1980s, so that wage trends are likely to be affected by the selection that obviously marks women’s entry into the labor market."

This is a rather odd reason to exclude women, Roodman argues:

The idea seems to be that forces unrelated to the Cuban influx were driving trends in women’s earnings, and these could mask the effect of that influx. But similar things might be said for low-education men, whose earnings would have been influenced by broad events such as recessions and de-industrialization. Analytical devices such benchmarking against control groups and focussing on changes immediately after the immigration influx should seemingly work as well for women as for men.

Note that last point — focusing on changes immediately after the influx. Borjas doesn't do that, either. While Card looked at year-by-year figures, Borjas grouped multiple years together. For example, he compares 1977-'79 to 1981-'83, or looks at 1981-'86 as a single "short run" period following the boatlift. Roodman believes this is a bad practice that makes it harder to isolate the effects of the boatlift: "Borjas appears readier than Card (or me) to attribute changes 3–5 years after the boatlift to the boatlift. I am unready because many forces buffeted the Miami economy circa 1980 — an oil shock, extreme interest rates, two recessions, and a debt crisis in Latin America. To be fair, they affected cities in the control group too, but perhaps not equally. A relative wage drop 3–5 years after the boatlift seems to admit many explanations."

Borjas used a second, smaller data set

Borjas also uses two different data sets: the Outgoing Rotation Group (ORG) survey from the US Census Bureau (which is conducted monthly and produces the data on unemployment rates and job growth you hear on the news on the first Friday of each month), and the Annual Social and Economic Supplement (ASEC), which asks people how much they made the previous year. ORG reached twice as many people in Miami during the period in question, and because it records how much respondents made in the week prior, it is potentially more accurate (though noisier, due to week-to-week variation in earnings). Card used ORG data only for this reason, but Borjas uses both — and his most dramatic findings rely on ASEC. That's where the 30 percent wage drop figure comes from.

But this is based on a pretty small sample. In 1980, the year of the boatlift, ASEC reached only 17 male, non-Hispanic Miami workers with less than a high school education; in 1981, the year after, it reached 19. ORG, by contrast, reached 55 and 51, respectively. Borjas tries to get around this problem by lumping multiple years together, but as Roodman notes, that makes it harder to attribute changes to the boatlift as opposed to other factors.

Once you add it all up, the harm to Miami workers disappears

So Roodman looked at the data again. He used ORG, rather than ASEC. He included all non-Hispanic high school dropouts ages 25 to 59 in Miami, be they male or female.

The blue line below shows how average inflation-adjusted annual earnings changed for this group, relative to 1977 (so if a data point is at 90 percent, that implies a 10 percent drop in wages since 1977). The red line takes that data and adjusts it for changing age composition and benchmarks it against a control group of cities/urban areas that Borjas chose (Anaheim, Rochester, Long Island, and San Jose). The green line averages effects over three years — which Borjas likes, though Roodman notes it hurts the analysis:

There is no decline in wages between 1980 and 1981, when you'd expect to see one if the boatlift had hurt these workers. There is a decline in the following years — but the US also entered a recession then.

Breaking it down further, women actually saw wages increase over the period in question. It's doubtful that had much to do with the boatlift — but if the boatlift had a large negative effect on wages, you wouldn't expect to see a boost at all. Wages for men did fall over the period in question, but the decline began in 1977 and kept steady. Even for men, Roodman finds, there was no "sharp, statistically significant drop immediately after the boatlift."

Borjas: "He didn’t seem to find any errors in my analysis"

Via email, Borjas says that he hasn't had time to read Roodman's analysis in detail. But he doesn't find it compelling. "Glancing at the short writeup that you linked me to, he didn’t seem to find any errors in my analysis. So pretty much my data stands, regardless of interpretation," Borjas says. He also repeated his argument that the fast growth in the population of women workers means that the sample is "changing radically over time" and thus is best excluded: "I suspect few economists would have trouble with leaving them out."

Borjas concludes by quoting a line of Roodman's, analyzing effects on men: "The telling quote in the link you sent me is: 'Borjas’s finding of a wage decline after the 1980 boatlift still looks reasonable.'" Roodman does say this — but he's also clear that he's unsure we can attribute that wage decline to the boatlift itself.

Borjas's raw data seems quite solid. He's a widely respected economist, as even people who disagree with his stand on immigration would acknowledge. But the Roodman response does raise some questions about whether Borjas is interpreting the raw data correctly.