Americans think immigrants used to pull themselves up by their bootstraps. That’s wrong.

If your ancestors came to the US in the late 1800s or early 1900s (or if you’ve talked to someone whose ancestors came then), you probably think of them this way: they came to the US with nothing but the clothes on their backs, worked hard in low-paying jobs, learned English, moved up the income ladder, and made sure their children could do just as well in life as anyone else’s children.

But data from UCLA and Stanford researchers — with a big assist from Ancestry.com — shows the reality that many immigrants experienced might have been much more complicated, and much less in line with the American dream.

The researchers looked at the occupations immigrants held in 1900, versus the occupations natives had. (Natives were a lot more likely to be farmers, for example; immigrants were more likely to work as laborers, but also as managers.) They then compared the average incomes for each set of occupations. The result: as of 1900, immigrants were actually in higher-paying positions than natives in most states. In some states, immigrants were in occupations that paid as much as 20 percent (or even, in New Mexico, 40 percent) more than the occupations natives held:

This doesn’t necessarily mean immigrants were getting paid more than natives. The researchers didn’t know the income an individual immigrant (or native) made — the census didn’t ask about income in 1900. That’s why they looked at the average incomes for the occupations each group had. So it’s possible that immigrants in a certain industry were discriminated against, and made less than the average income for someone in their position. On the other hand, it’s also possible that as an immigrant stayed in the same job for years or decades, he started earning more — and the data doesn’t capture that, either.

Here’s what the map does show: the kinds of work immigrants were doing in 1900 weren’t necessarily less skilled than the work natives were doing at that time. That goes against the idea that immigrants of the late 1800s usually came to the US with nothing but a work ethic and worked their way up from there. Instead, what the data shows is that how well an immigrant did usually depended on where he came from — and his background in his home country — to begin with.

Immigrants from countries that were more developed in the late 1800s (like Great Britain or Belgium) went straight into jobs with a higher-than-average income: the average immigrant from a high-income country in 1900 was in a position that made $800 more than the average for native-born workers. Immigrants from less-developed countries (say, Norway) went into low-paying jobs: the average immigrant from a low-income country in 1900 was in a job that paid $1,700 less than the average for all natives.

Of course, over the late 1800s and early 1900s, where immigrants came from changed a great deal: Italians and Eastern European Jews started coming in far greater numbers. Overall, immigrants who came in the 1890s were much more likely to be in unskilled occupations than those who came in the 1880s. And even within individual countries, the immigrants who came in the 1890s were likely to be in jobs that paid less than jobs their predecessors held.

But how much an immigrant made at one point in time doesn’t really tell the whole story. That’s where the Ancestry.com data comes in: the researchers were able to track immigrants over time as they aged, and even track the occupations their children and grandchildren went into.

But what they found was profoundly worrisome. Not only did less-educated immigrants from less-developed countries work in low-paying occupations when they got to the US, but their children also were likely to work in jobs that paid less than the average for natives. This chart shows some of that (though it also combines many countries’ more-skilled 1880s immigrants with their less-skilled 1890s ones):

The data suggests that there have always been two different types of immigrants: immigrants who came to the US with the skills to go into high-paying occupations, and immigrants who came from backgrounds that didn’t give them those skills. And those distinctions don’t appear to disappear among children born to immigrant parents (though they could disappear in future generations).

On one level, this is an extremely depressing finding. The US has been extremely good at integrating immigrants in some respects, like giving them the chance to learn English. But it appears it was never as good at economic assimilation as the myth of immigrants pulling themselves up by their bootstraps implies.

On the other hand, the data is just another sign that today’s immigrants — who overwhelmingly are in lower-paying occupations — aren’t less hardworking or less willing to assimilate than the immigrants of a hundred or more years ago. Many of them just haven’t been given the tools to succeed.