In The Big Short, one of the characters explains how he discovered the worthlessness of the mortgages that supposedly undergirded Wall Street’s triple-A securities: “I read them.”

The political equivalent of Wall Street’s mortgage-backed securities are the economic models invoked to support this policy or that one. Everybody cites them. Too few look inside them. And the results are the same: Trusted products turn out to be junk.

One of the most influential such modeling exercises was a paper published by the University of California’s David Card in 1990. Card studied the economy of Miami after an influx of 125,000 Cuban migrants between April and October 1980, the “Mariel boat lift.” Under American law, Cuban migrants become almost immediately eligible to work in the U.S. The result: In bare weeks, the greater Miami workforce jumped by 8 percent—and the stock of workers without a high-school diploma spiked a startling 20 percent. Yet—according to David Card—even this large and sudden supply shock had no negative effect on the wage trend for low-skilled workers. (Wages did decline, he finds, but no more for those workers he regarded as competing with Marielitos than for those he regards as not competing.)

This finding, if true, carried enormous implications. The United States in the 1990s would experience a vast surge of very low-skilled migration, legal and illegal, from Mexico and Central America. Simple economic logic predicted that competition from these migrants should depress the wages of native-born Americans. Card reassured policymakers that simple logic was wrong: They could welcome the newcomers at no cost to the settled population. Here at last was the free lunch that Milton Friedman had so obstinately insisted could not exist.

How was it possible that immigration could stand as the sole exception to the usual laws of supply and demand?

A 2010 paper by another eminent California economist, Giovanni Peri, answered the question with—of course—another economic model.  

According to Peri, what happened was this: As new workers arrived, wages did fall for the jobs they took. Declining wages for existing jobs prodded native-born workers to improve their skills and shift to better paid work. So, while the wages for particular job categories might drop, the incomes of the people who formerly held jobs would paradoxically rise. Or, translated into econo-speak:

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.

Anyway, that was the theory.

But was the theory true?

I laid out the reasons for disbelieving it in a post for The Atlantic earlier this year.

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.

However, this reply to Peri is as theoretical as Peri’s own modeling. Over this whole debate loomed the great fact of David Card’s work, seemingly proving that so long as migrants arrived into a reasonably healthy job market—South Florida in the early 1980s, not the depressed U.S.A. of the Great Recession—native workers need fear no ill effect.

But how good was that work? What went into David Card's model? Over the past year, the economic profession has witnessed a series of autopsies and counter-autopsies upon Card’s data, sparking a debate that has rapidly grown both intensely ideological and vituperatively personal.

In October 2015, Harvard’s George Borjas—academia’s leading immigration skeptic—returned to the original data sets that supported David Card’s famous paper. Borjas insisted that Card had chosen his comparisons wrong. Borjas redid the 1990 paper’s math and hurled a defiant criticism:

In fact, the absolute wage of high school dropouts in Miami dropped dramatically, as did the wage of high school dropouts relative to that of either high school graduates or college graduates. The drop in the low-skill wage between 1979 and 1985 was substantial, perhaps as much as 30 percent. …

At least in the short run, the labor market responded precisely in the way that the “textbook” model predicts: an increase in the number of potential workers lowered the wage of those workers who faced the most competition from the new immigrants.  

Here’s where things get testy. David Card’s 1990 paper has been unusually influential, cited again and again as a “classic” of immigration economics. It exerts its influence in large part because it purports to be based on close study of real-world effects, not blackboard computations. As Princeton’s Alan Kreuger—formerly the chair of President Obama’s Council of Economic Advisers—wrote in 2006: "Studies that claim to find a deleterious effect of immigration on natives’ wages are typically based on theoretical predictions, not actual experience.” Card, by apparent contrast, had exited the ivory tower to discover facts in the marketplace. And now a critic dared claim that Card had got his math wrong? Impossible. Intolerable.

In short order, a rebuttal to Borjas’ criticism of Card was published by Giovanni Peri and a University of California graduate student, Vasil Yasenov.

Their answer in their winter 2015 paper was scorching:

We point out that the very different conclusions in a recent reappraisal by George Borjas (2015) stem from the use of a small sub-sample of high school dropouts in the already very small March-CPS sample. That sample is subject to substantial measurement error and no other sample provides the same findings. Being imprecise about the timing of the data and the choice and validation of the control sample further contribute to the impression of an effect from the boatlift in Borjas.

In a December 18 op-ed at Bloomberg View, the columnist Noah Smith cited the Peri-Yasenov paper to pour even more scorn on Borjas’s work and reputation.

Not only was Borjas’s sample too small, but—contended Smith—it was downright manipulated.

Even more damning, Peri and Yasenov find that Borjas only got the result that he did by choosing a very narrow, specific set of Miami workers. Borjas ignores young workers and non-Cuban Hispanics -- two groups of workers who should have been among the most affected by competition from the Mariel immigrants. When these workers are added back in, the negative impact that Borjas finds disappears.

Smith’s column concluded by attempting to excommunicate Borjas from all future participation in immigration debates.

All of this leaves Borjas’ result looking very fishy. He would have had to have searched hard to find the one small group of workers who seemed to suffer from the Mariel influx. Borjas could well have been subject to heavy confirmation bias—he might have been so fundamentally certain that immigration was bad for native workers that he searched and searched until he found one group that seemed to confirm his pre-existing beliefs. In science terms, that is called data mining; it's a big no-no.

In debates about immigration, the anti-immigrant side inevitably cites Borjas. He has gained fame and notoriety for being the most prestigious economist who thinks that immigration is a disaster for native workers. All of Borjas’ papers seem to arrive at this same conclusion. Participants in immigration debates really should stop citing Borjas’ research so much.

As one of those who cites Borjas’s work often, I suppose I was supposed to share the burn of this hot take. Soon after it appeared, I called Borjas for comment. He had just finished a reply, he said, and it would be a doozy. And so it is.

To understand what the economists are arguing about, you need to understand their methods. When economists compare wages, they must begin by deciding which wages to compare. You wouldn’t prove much, one way or the other, by studying wages of Miami-area stockbrokers before and after the Mariel migration: The Marielitos did not compete with stockbrokers.

Well, who should the Marielitos be compared with?

You want to compare them to similarly situated workers. But that creates two statistical problems.

The first is: How do you define a similarly situated worker?

The second is: Remember, all this happened some time in the past. The only way we know what anybody was making in 1980 is by looking at Department of Labor samples, often collected for other reasons. Suppose we wanted to say something about Miami-area stockbrokers in 1980. The Department of Labor would have an average wage—but that average would be aggregated from a certain number of persons chosen to answer a government questionnaire. If we wanted to know about women stockbrokers, the number of answers would be smaller, and if we wanted to know about women stockbrokers in their 40s, it would be smaller again.

When Borjas did his work on the Mariel Cubans, he defined a “similarly situated worker” quite precisely. He counted only men. He counted only native-born workers. And he counted only workers who’d dropped out of high school. That meant he was looking at the wages of only about two dozen people. He tried to compensate by looking at that small control group over three different year periods … but still, a small control group times three remains a small control group.

So that’s a problem.

But now look at what Peri and Yasenov did to make their control groups bigger. They included women. They included other recent Hispanic immigrants. And instead of counting only high school “dropouts,” they included everyone in the Department of Labor samples who had not yet finished high school—including people still currently enrolled in school!

That generated a big sample all right, but a big, worthless sample.

Men and women have different labor-market experiences. Would you expect an influx of men without high-school diplomas to affect the wages of nannies?

Inserting other immigrants into the control group was also distorting, in work intended to discern the effects of immigration on wages. It might, conceivably, have led to comparing some people who are driving wages down to other people who are also driving wages down.

And as for treating people who have not yet completed high school as the equivalent of high-school dropouts—that’s the most intensely dubious comparison of all.

Data mining is indeed bad. But this kind of data dredging seems far, far worse. Yet data dredging on an industrial scale seems to be the only way to rescue the Card paper from the withering criticism Borjas has offered. That’s not very reassuring from an academic point of view. And if the most important immigration-doesn’t-hurt-the-unskilled research of the past quarter-century must be rejected as hopelessly contaminated by its own sampling errors, then what is left? It’s famously said that economic science represents the triumph of pure reason over common sense. But in this case, what has triumphed over common sense is not reason, but massaged and manipulated data.