Limited housing is keeping workers away from the cities where they could be most productive, and that's costing the U.S. economy. 

Reducing land-use constraints in high-productivity New York, San Francisco and San Jose to the level of the median city would expand their labor forces, boosting U.S. gross domestic product by 9.5 percent, according to estimates from a new study by the University of California at Berkeley's Enrico Morettiand the University of Chicago's Chang-Tai Hsieh. 

"A limited number of American workers can have access to these very high-productivity cities,'' Moretti said in an interview. A more efficient distribution would be "a general benefit for the entire economy."

The researchers used data for 220 U.S. cities to assess how much each added to national output growth between 1964 and 2009, relative to how much the metro itself expanded.

Labor productivity and demand grew very quickly in San Francisco, New York and San Jose over that 45-year period, owing to their human capital-intensive industries including technology and finance, the researchers find. Yet those cities weren't America's growth engine: Their local economies grew a collective 19.3 percent, yet they only contributed 6.1 percent to aggregate growth. 

"The reason is that the main effect of the fast productivity growth in New York, San Francisco, and San Jose was an increase in local housing prices and local wages, not in employment," they write. "Despite the large difference in local GDP growth between New York, San Jose, and San Francisco and the Rust Belt cities, both groups of cities had roughly the same contribution to aggregate output growth."

By contrast, about three-quarters of all U.S. output gains between 1964 and 2009 came from growth in Southern U.S. cities and a group of 19 other large cities. In some, such as Boston, Portland and Salt Lake City, local growth almost exactly matches the national contribution. In others, such as Chicago and Los Angeles, the overall contribution was even higher than local growth would suggest. For a final subset, including Phoenix, the national gain was small compared with the city's expansion.

"Phoenix, Las Vegas and Riverside have attracted many residents because of good weather and abundant supply of cheap housing,'' according to the study. The reallocation leads to a loss in national output, because it brings workers to cities "where the marginal product of labor is low."

The takeaway is that a short supply of apartments isn't just a drag for Manhattan renters and Bay Area denizens. It also comes at a broader cost to the nation. 

"The places that are delivering the most output are unaffordable, and I think that is an issue,''  said Aaron Renn, a senior fellow at the Manhattan Institute for Policy Research in New York and author of the blog The Urbanophile. At the same time, he said, housing supply isn't the sole driver of where people live, and building restrictions exist for a reason: They help cities to retain their attractive features.