Republican presidential front-runner Donald Trump says he wants to stop immigration into the US in order to increase American wages. The only problem? Immigration already raises American wages.

Trump’s decision to seize immigration as the major issue of his campaign has been a key factor in his rise to prominence; foreign job seekers have proven to be a suitable villain for America’s economic anxieties overall. It’s not a surprise that many white power groups see Trump as a spokesperson for their agenda, as the New Yorker reports in a conversation with Matthew Heinbach, a white nationalist who has met with Greece’s fascist Golden Dawn party:

“Even if you play the game, even if you do everything right, then the future, when it comes to your income, when it comes to benefits, when it comes to everything, we are going to be the first generation in American history to be living worse than our parents.” He went on, “My own parents tell me, ‘Well, you should just shut up, you should go get a normal job, and get a two-car garage, and then you’ll be happy.’ ” On the economics, Heimbach’s narrative is not wrong. During a half-century of change in the American labor market—the rise of technology and trade, the decline of manual labor—nobody has been hit harder than low-skilled, poorly educated men. …

Actually, Heimbach’s narrative is wrong, as is the New Yorker’s assessment of it. Heimbach is 24. Over the course of his lifetime, real median household income has actually risen 3.3%. Comparing young adults in 2013 to young adults in 1989 (pdf), average net worth is slightly lower—thanks to the largest recession since the Great Depression—but today’s young adults are more likely to own homes, hold stock, and save for retirement, and less likely to carry a high share of their income in debt versus predecessor cohorts.

But more importantly, while the New Yorker notes that wages for unskilled male workers have fallen by 23% between 1979 and 2013, it doesn’t mention that immigration has nothing to do with it—and that Heimbach, a college graduate, isn’t part of this demographic to begin with.

The effect of immigration on US native wages

Here are estimates from two separate studies—one from the Economic Policy Institute (EPI), and the other by economics professors Gianmarco Ottaviano and Giovanni Peri, of the London School of Economics and the University of California, Davis, respectively, of how immigration to the US has changed native workers average wages. Both focus on periods spanning the 1990s tech bubble and the 2000s housing bubble, when many immigrants came to the US in search of jobs:

Education 1994-2007, EPI 1990-2006, OP Less than HS 0.30% 1.50% High School 0.30% 0.70% Some College 0.70% 0.10% College 0.40% 0% All 0.40% 0.60%

You’ll notice they are all positive: Almost everyone has seen wages rise thanks to immigrants in the economy, even though they are pretty marginal effects.

Economists have been arguing about how to measure the impact of immigration on native workers for a long time now, but consensus seems to be settling on the idea that they are complementary to US workers.

How do more people entering the economy lead to higher wages? They made the economic pie bigger by helping produce more, they are consumers of goods and services themselves, and their new ideas can unlock entire new industries, whether that’s California nail salons or ethnic restaurants.

Some earlier estimates found major reductions in wages from immigration, but newer work has identified a flaw in those estimates: They tended to assume that the amount of capital in the US was fixed and that immigrants can easily substitute for native workers.

But US capital stocks continue to increase, and empirical data suggests that native workers actually tend to be pretty different from immigrants. Native workers tend to have better language and cultural skills, and immigrants tend to bring knowledge and experience that the US is lacking.

Examining those assumptions led to the kind of estimates in the table above, which suggest that native wages increased between 0.4 and 0.6% because of the last big immigration boom.

What about unskilled men?

But when we think about immigrants substituting for native workers, manual labor is one where they should be able to do so pretty easily. And the main area where economists find problems for native US workers is, unsurprisingly, in the demographic composed of men without much in the way of skills. Here’s one breakdown of that effect:

Male workers, by education 1994-2007, EPI Less than HS -0.20% HS -0.20% Some College 0.90% College 0.70% All 0.40%

So you might think here that, at last, The Donald has a point. But remember that big statistic—wages for unskilled male workers have fallen by 23% between 1979 and 2013?

For 14 years of that 34-year time period, we know that immigration barely contributed to that dramatic change. Even in the unlikely case that the effect was doubled or tripled during the other 20 years in the sample, immigration just isn’t what’s getting at unskilled male workers wages.

Instead, it appears that the reason unskilled men have seen their wages fall so dramatically is trade—specifically because foreign workers abroad have outbid them for economic activity. And unlike foreign workers who come to the US, none of the benefits of their work accrue to the US economy.

The other culprit eyed is for hurting low-skill wages is automation—that is, robots—but there appears to be more evidence that it’s trade behind the unskilled US worker’s woes. Stemming low-skilled immigration won’t change that.

Where does this leave us?

There are two other groups of people to consider when talking about jobs and immigration.

The first are other recent immigrants. Economists tend to estimate that increasing immigration tends to hit them the hardest. The reason: Again, substitution, as recent cohorts of immigrants create direct competition for one another when it comes to wages. In that EPI study from 1994-2007, foreign-born workers in the US saw their wages decrease by an average of 4.7% because of the effect of immigration.

The other group to consider is the one causing the decrease: the newest of the newcomers. These are the biggest winners in the wage game. By shifting their labor to a new milieu, they have massively increased their earnings power, even if their wages remain low by US standards. The increase in living standards affects these new immigrants and their home countries; as migration experts are fond of noting, remittances from immigrants vastly exceed foreign aid from governments, leading to theories that increasing immigration is a smart way to increase global economic development and avoid leaving trillion-dollar bills on the sidewalk (pdf).

Arguments for immigration as an anti-poverty program have not yet been able to surmount the kind of deep-set suspicion that Trump’s campaign is exploiting. But at the very least, we can establish that however much he or anyone else claims immigration is hurting US wages, the latest research just doesn’t support the argument.

Podcast break!

We recently talked about a bunch of these issues on our podcast, Actuality, digging into the particularly thorny case of unskilled farm laborers:

Actuality is a podcast jointly produced by Quartz and Marketplace, hosted by Tim Fernholz (that’s me) and Sabri Ben-Achour. You can listen and subscribe to the podcast on iTunes or use this RSS feed with any podcast application.