People with similar skills and similar levels of education make a lot more money in New York and San Francisco than they do in St. Louis or Cleveland. You might expect these differences to even out over time, as workers relocate from low-income areas to high-income areas to take advantages of the opportunities there.

High housing costs make it hard for companies in high-cost areas to attract workers

But that hasn't been happening. Over the last half-century, income differences between metropolitan areas have actually been increasing. One study estimated that this effect is costing the country hundreds of billions of dollars in lost income every year.

It's not hard to figure out why people aren't moving. While the wage difference between St. Louis and San Francisco is large, the difference in housing costs is even bigger. A programmer in St. Louis might get a big raise by moving to San Francisco to take a job at a technology company there, but he might still be left worse off thanks to the much higher rents there. High housing costs make it hard for companies in high-cost areas to attract workers, stunting the growth of some of America's most dynamic industries.

Why lower housing costs could add billions to the economy

How much does this cost the economy? In a study released as a discussion draft last year, economists Chang-Tai Hsieh and Enrico Moretti tried to figure that out. They imagine a world where the housing markets in America's most productive cities became more elastic, meaning that increasing demand led to more construction rather than higher rents.

If housing wasn't so expensive in coastal cities, a lot more people would move to New York, Washington, Boston, Seattle, and the San Francisco Bay Area. The data suggests that — even after controlling for factors such as education — workers in these cities are more productive than in other metropolitan areas. The study doesn't try to explain these productivity differences, but possible explanations include better infrastructure, opportunities to learn new skills, and a culture that encourages entrepreneurship.

Hsieh and Moretti estimate that moving American workers to higher-productivity cities could increase the income of Americans by a stunning amount: more than $1 trillion. That amounts to a raise of several thousand dollars for every American worker.

America's biggest cities could get even bigger

That's a huge number, and unfortunately, achieving it would require drastic — and totally implausible — changes in where we work and live. Hsieh and Moretti envision the New York metropolitan area becoming 9 times its current size, meaning that more than half the country would live there. The Austin metropolitan area would quadruple in size, as would the San Francisco Bay Area. Half the cities in America would lose 80 percent or more of their population. The population of Flint, MI, would shrink from 102,000 people to fewer than 2000.

Housing restrictions cost the American economy tens of billions of dollars per year

Obviously, this won't — and shouldn't — happen. But the huge potential gains from this admittedly implausible thought experiment is a helpful reminder that less dramatic population changes could still produce significant economic gains. New York isn't going to get nine times bigger overnight, but it could double in size over the next generation. The Tokyo metropolitan area today has almost twice the population of the New York metropolitan area on a lot less land. Adding millions of people to the New York metro area would add tens of billions of dollars to the output of the US economy.

The same is true in the San Francisco Bay Area and in the Boston region. Strict regulations limit the supply of housing in these areas, limiting the growth of some of America's most dynamic companies.

Hsieh and Moretti's analysis suggests that housing restrictions — and the Not In My Backyard (NIMBY) activists who lobby for them — are costing the American economy tens — perhaps hundreds — of billions of dollars per year. If we want to ensure the American economy grows robustly in the coming decades, a high priority should be figuring out ways to allow more people to live in America's most productive metropolitan areas.