What to do? The author of the UCLA study recommends an amnesty to give new immigrants more rights, on the theory that that will increase their bargaining power with employers. But an amnesty will only draw even more new immigrants, further flooding the labor pool and depressing wages.
The real answer is to scale back legal immigration and control the nation's borders, so low-income workers don't have to compete against new immigrants, especially people who have no right to be here. That's why the late Barbara Jordan, one of the great liberal voices of the past three decades, called for cutting back on immigration in the 1990s. She was demonstrating a traditional liberal solicitude for low-income workers, particularly blacks.
The fact is that societies have always sought to exploit cheap labor with no or few rights, from ancient Greece with its Helots to the antebellum South with its slaves. Our reliance on immigrant labor is nowhere near as odious as those prior systems, but it is morally corrupting. Certain jobs are now considered unfit for natives, and employers are benefiting from illegality to wiggle out of paying native workers what they otherwise would make.
It's time to tell middle-class families across the country, from California to the suburbs of New York: Mow your own damn lawns. And to tell employers: Stop cheating your fellow citizens.
As a practical political matter, that won't happen until liberals rediscover their overriding concern for low-wage workers. Don't count on it. On the left today, multiculturalism trumps all, and instead of higher wages, liberals prefer to give low-income Americans political correctness.