The job news is increasingly good: 321,000 jobs created in November. Yet the national economic mood remains grimly bleak.

Many Americans feel a sharp distinction between what’s said about “the” economy and what they experience in “their” economy. At the top of the income distribution, wages are rising. In the middle and bottom, wages stagnate. Jobs are created, yes—but native-born Americans are not hired for them.

Last month, the Center for Immigration Studies released its latest jobs study. CIS, a research organization that tends to favor tight immigration policies, found that even now, almost seven years after the collapse of Lehman Brothers, 1.5 million fewer native-born Americans are working than in November 2007, the peak of the prior economic cycle. Balancing the 1.5 million fewer native-born Americans at work, there are 2 million more immigrants—legal and illegal—working in the United States today than in November 2007. All the net new jobs created since November 2007 have gone to immigrants. Meanwhile, millions of native-born Americans, especially men, have abandoned the job market altogether. The percentage of men aged 25 to 54 who are working or looking for work has dropped to the lowest point in recorded history.

Labor Force Participation Rate Among Men Aged 25 to 54, 2004-2014

                                                                                     Bureau of Labor Statistics    

It's said again and again that immigrants do not take jobs from natives. Here’s National Journal, reporting just last year, under the headline "Left and Right Agree: Immigrants Don't Take American Jobs":

That immigrants take the jobs of American-born citizens is “something that virtually no learned person believes in,” Alex Nowrasteh, an immigration expert at the libertarian Cato Institute, said at a Thursday panel. “It’s sort of a silly thing.”

Most economists don’t find immigrants driving down wages or jobs, the Brookings Institution’s Michael Greenstone and Adam Looney wrote in May. In fact, “on average, immigrant workers increase the opportunities and incomes of Americans,” they write. Foreign-born workers don’t affect the employment rate positively or negatively, according to a 2011 analysis from the conservative American Enterprise Institute. And a study released Wednesday by the liberal Center for American Progress suggests that granting legal status to undocumented workers might even create jobs.

So there you have it. Experts say it’s impossible. Can’t be happening. And if actual observed data from the real economy seem to suggest that the impossible is happening—well, Albert Einstein himself answered that one. If the material universe doesn’t support the theory: “Then I’d feel sorry for the good Lord. The theory is correct."

Before deciding whom to trust on this issue, the economists or your lying eyes, it helps to understand how the economists reached their conclusion.

Since the time of Adam Smith, economists have agreed that the secret of economic growth is specialization. Rather than everyone baking his or her own bread and sewing his or her own clothes, everyone chooses one occupation and then trades for the products others make. The more individuals specialize, the more productive everyone becomes. The more people trade, the more widely the benefits of productivity are shared.

Immigration economists apply this insight to the domestic labor market. One of the most eminent specialists in the field of immigration economics, Giovanni Peri of the University of California at Davis, offers this homely analogy:

An extreme example of this would be if you have an engineer and you add a construction worker. With the engineer by himself you’re not going to do much. But with an engineer plus a construction worker, you can build a building. Therefore, the productivity of the engineer goes up a lot. And the wages for both workers increase.

The technical term for the situation Peri is describing is “complementarity.” The labor of the engineer and the labor of the construction worker each complement the other. Immigration economists argue that immigrant labor likewise complements native-born labor. As Peri assured readers in a 2010 paper for the San Francisco Federal Reserve, "Immigrants expand the U.S. economy’s productive capacity, stimulate investment, and promote specialization that in the long run boosts productivity. Consistent with previous research, there is no evidence that these effects take place at the expense of jobs for workers born in the United States.”

So long as everyone imagines that low-wage immigrant workers are paired off with high-wage natives, such assurances seem credible. The foreign-born nanny enables her college-educated employer to return to the workforce earlier, raising wages for both nanny and employer. The foreign-born gardener mows the lawn, freeing his accountant employer to spend Saturday morning billing clients.

Even as the encounter between low-paid immigrants and highly paid natives becomes more distant and abstract, the complementary relationship of their labor seems to hold. Immigrant labor enables middle-class Americans to buy a roasted chicken and pre-washed salad at the supermarket or to check a box and have their holiday presents arrive at their door already gift-wrapped. Upper-income Americans live easier and more efficient lives thanks to millions of low-paid immigrant workers they never see and whose names they never know.

But what about everybody else? The promise of the immigration economists is not that some Americans, the already successful, would be enriched even further. The promise is that all Americans would be made better off, even if they don’t employ nannies, even if they mow their own lawns, even if they can't afford the rotisserie chicken, even if they shop at the thrift store rather than Amazon. How can that be possibly be true?

The answer embedded in the economic models is that immigration prods even less affluent natives to shift away from immigrant-dominated economic niches and find new work that pays better. The immigrant groundskeeper can’t speak English very well, so the lawn service hires a bilingual Mexican-American to supervise him. The rising numbers of immigrant nannies call forth specialized payroll firms that hire native-born workers to process checks and pay taxes. More supermarkets operating more chicken rotisseries causes local governments to hire more health officers to confirm the chicken meets sanitary standards. More immigrants wrapping presents in L.L.Bean’s warehouses mean more native-born UPS drivers delivering presents.

Everybody wins!

Yet three things have to be said about the above story.

First: The story about immigration benefiting all (or almost all) native workers could be true. But that doesn’t mean it is true. Economists prove their claims about immigrant law by drawing regression curves that compare ratios between data sets based upon the number and the pay of immigrant and native workers. Have they drawn their data sets correctly? Did they choose the correct basis for comparison?

These technical decisions at the beginning of the calculation have huge impacts on the final conclusion at the end. Between 1990 and 2006, the wages of non-college-educated Americans declined. The less education the worker had, the steeper the decline. How much was immigration responsible? The data the economist chooses to look at will determine the answer.

Let’s go to the fine print, relying on a critique of Giovanni Peri’s work by George Borjas, of Harvard’s Kennedy School. Aggregate high-school dropout and high-school graduates together, and immigrant labor accounted for 13.2 percent of the increase in hours worked between 1990 and the onset of the Great Recession: big, but not cataclysmic. But if you take more care to compare like with like, you begin to see huge supply shocks. Among high-school dropouts only, immigrants accounted for 23 percent of the increase in hours worked between 1990 and 2006. Among high school dropouts in their 30s and 40s, immigrants accounted for over one-third of the increase in hours worked.

Here’s what that means for economic modeling. If you assume that all low-education workers are potential substitutes for each other—the 23-year-old recent arrival from Guatemala with the 53-year-old who proceeded from high school to the Army—then your model will show a less dramatic effect of immigration on wages. If, however, you assume that the 23-year-old Guatemalan is competing with 20- and 30-something native-born workers who lack diplomas, then your model will show a very big effect.

A model based on unrealistic assumptions can still achieve perfect internal consistency. It just won’t describe the real world very accurately. Which seems to be precisely what is happening with immigration economics.

Second: If the economists are right about the complementarity of immigrant and native labor, it’s important to understand how and why. Back in the 20th century, there were presumably many accountants who would have preferred to spend Saturday mornings finishing their work rather than mowing the lawn. There were many new mothers who would have returned to work if nanny services had been more widely available. What changed between, say, 1970 and 2005? The short answer is that the cost of employing people in these immigrant-dominated niches plummeted, in real terms. Because the cost plummeted, more hiring occurred in those niches, enabling the mothers to return to work, the accountants to spend Saturday mornings at the office.

Economic popularizers passionately deny that immigration causes wage declines and job displacement. From the point of view of several actual economists, however, these reassurances are so much uninformed propaganda. As the technical economists understand, wage cuts and job displacement are the exact and only ways that immigration confers any benefits on native workers at all. It is wage decline and job displacement that drives natives to shift to higher-paid sectors. No wage cuts, no job displacement. No jobs displaced, no benefit to natives. Here’s Peri saying just that: "Large inflows of less educated immigrants may reduce wages paid to comparably-educated, native-born workers. However, if less educated foreign- and native-born workers specialize in different production tasks, because of different abilities, immigration will cause natives to reallocate their task supply, thereby reducing downward wage pressure.”

When economists minimize the impact of immigration on wages, they aren’t denying that immigration pushes wages down in the jobs that immigrants take. They concede that immigration does do that. They celebrate that immigration does that. Instead, they join their celebration of immigration’s wage-cutting effects with a prediction about the way that the natives will respond.

But what if the prediction is wrong? What if natives respond to immigrant competition by shifting out of the labor market entirely, by qualifying for disability pensions? The proportion of the population receiving disability pensions doubled between 1985 and 2005 and jumped by another 20 percent during the Great Recession. 14 million Americans now receive disability pensions. The evidence is compelling that disability applications rise when the job market weakens.

Why? Economists talk too blithely about natives shifting to more skilled and remunerative work. Up-skilling costs time, effort, and money. It can oblige a worker to move away from family and friends. It forces older workers to begin again at a time in their lives when they felt settled, to risk failure at a time in life when risk is not appreciated. It’s not highly surprising that many displaced workers would opt to give up on work altogether instead.

The exit of native-born men from the workforce—at least arguably because of immigration—has the curious side effect of tilting the immigration models in a pro-immigration direction. Remember, the models are based on ratios of hours worked and wages paid. If a native-born janitor earning $18 an hour is displaced by an immigrant and then shifts to a $12 an hour retail job, the models capture that change as a harm to native-born workers. But if the displaced native-born janitor exits the labor force, he disappears from the model altogether, and with him, the evidence of the harm. It may seem crazy, but it’s the way the model is built.

Third: Economists habitually regard the free movement of investment, goods, and people as the natural order of things. They don’t feel much need to explain such movements, any more than lawyers ask why people violate contracts or doctors ask why people fall off ladders.

Yet immigration is inescapably a political act. Nations can regulate immigration, can make choices about which immigrants they allow and how many, about how strictly labor laws will be policed and what will be done with lawbreakers.

Theoretically, a nation could determine that high-skill labor is complementary to low-skilled labor and make decisions such as the following:

“If we admit a lot of foreign-born surgeons, we could hugely drive down the cost of major medical operations. American-born doctors would shift their labor to fields where their language facility gave them a competitive advantage: away from surgery to general practice. This policy would hugely enhance the relative purchasing power of plumbers and mechanics, enabling them to eat out more often and buy more American-made entertainment, increasing GDP and creating jobs.”

Or: “The ratio of CEO pay to other workers has skyrocketed. Obviously we are suffering from a glut of workers and massive CEO scarcity. We should issue work permits automatically to any executive with a job offer that pays more than $500,000 a year. Americans with organizational skills will be pressed to shift to the public sector, improving the quality and lowering the cost to taxpayers of government services.”

But that’s not how things are done. In the United States, the hypothesis of native-immigrant complementarity is deployed to justify policies that intensify competition for the lower and middle echelons of the society, rarely near the top. Perhaps it doesn’t have to be that way, yet somehow it always is.