At last night’s Republican presidential debate, Texas Senator Ted Cruz disagreed with his rivals about immigration, arguing that practical fixes to recognize undocumented immigrants would be a political loser because they hurt ordinary American’s wages.

But he’s wrong—and in a surprisingly personal way. Here’s what he had to say:

I understand that when the mainstream media covers immigration, it doesn’t often see it as an economic issue. But, I can tell you for millions–of Americans at home watching this, it is a very personal economic issue. And, I will say the politics of it will be very, very different if a bunch of lawyers or bankers were crossing the Rio Grande. Or if a bunch of people with journalism degrees were coming over and driving down the wages in the press. Then, we would see stories about the economic calamity that is befalling our nation. And, I will say for those of us who believe people ‘ought to come to this country legally, and we should enforce the law, we’re tired of being told it’s anti-immigrant. It’s offensive. I am the son of an immigrant who came legally from Cuba to seek the American dream. And, we can embrace legal immigration while believing in the rule of law—and I would note, try going illegally to another country. Try going to China, or Japan. Try going to Mexico. See what they do. Every sovereign nation secures its borders, and it is not compassionate to say we’re not going to enforce the laws. And we’re going to drive down the wages for millions of hardworking men and women.

So let’s get this out of the way: Immigrants have not driven down native wages in the US, as we’ve discussed in the context of Donald Trump’s similar claims. Two different multi-year studies show that new immigrants in the US economy have led to small net wage increases to people all over the skill spectrum, or at worst, no change:

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%

The reality is that the US economy is dynamic, and can grow in response to new labor and capital.

Then there is the hypocrisy charge: Are journalists biased against toward high-skilled immigration? Not that I can see. The economic benefits of bringing in high-skilled workers are generally presented in the same light as low-skilled workers—positively. Many professionals already work in globalized labor markets and compete against people from other nations. Look, for example, at the medical field: More than a quarter of US doctors are foreign born, offering trained immigrants higher wages and lessening the US physician shortage.

Finally, there’s the matter of family history. While the extent of his participation in Fidel Castro’s revolution is under question, Cruz’s father emigrated legally from Cuba to the US (though he does admit a family friend bribed an official for an exit permit) in 1957 to attend the University of Texas.

When his student visa ran out, he received political asylum from the US, a policy widely applied to Cubans in an effort to combat Castro’s socialist regime—soon, any Cuban who could get to the US and stay one year would receive permanent residency. Today, there is a major debate over whether foreign students who earn four-year degrees at US institutions should be allowed even temporary visa extensions.

One assumes that when Cruz discusses his father’s legal immigration, he’s not in favor of a regime that would extend permanent residency to anyone who can make it to the US—but that’s the case for Cubans. And that special treatment has given some empirical ammunition to arguments that immigration hurts workers. In 1980, more than 100,000 Cubans fled to Florida in the “Mariel boatlift,” and were granted residency.

This is a far larger and more concentrated influx of immigrants to a small area, so it would likely have a much larger effect on wages. Sure enough, a recent study (pdf) by economist George Borjas found that in Miami, low-skilled wages for men fell between 10% and 30% in the years after the influx. But even the study of this extreme case has been criticized for conflating the effects of immigration with an oil shock and recession that followed. Economists attempting to replicate Borjas’ findings say there was no decline in wages in the year after the boatlift.

To offer a little more comparison: In 1980, Miami had a population of about 1.6 million people, so the influx of new unskilled immigrants was equal to almost eight percent of the population in just a few months. Under the comprehensive immigration reform passed by the US Senate in 2013, the US would have awarded permanent residency to 10.4 million immigrants over the next decade, many of whom already live in the US and many with valuable skills, equal to just 3% of the total US population.