Only a crazy pilot would be exempt from flying missions, but only a sane man would ask to be removed from duty. That’s how you keep flying missions you know are insane—it’s Catch-22, as the classic 1960s novel by Joseph Heller phrased it. The antiwar classic became a baby-boomer byword for a dilemma or a trap where you’re damned if you do and damned if you don’t—and it’s looking more and more like it applies to the relationship in America between employment and homeownership.

Only a crazy homebuyer would move to a place where there aren’t high-paying jobs—but only a sane one would insist on buying an affordable house. In the American economy of the 2020s, the highest-paying jobs are where the affordable houses aren’t—and vice versa. It’s housing’s Catch-22.

With mortgage rates at 8%—a 21st-century high— homebuyers are struggling to keep up with the rising cost of housing in the U.S. In fact, many buyers are facing the challenge of becoming house-poor with associated costs accounting for up to 60% of their monthly income.

Those hoping that finding a higher-paying job is the answer may be in for a surprise. Research by labor economists Jesse Rothstein, David Card, and Moises Yi, published by the National Bureau of Economic Research, shows how wage differences affect home purchasing power and what that means for housing demand, thus addressing the age-old question of whether it’s possible to both be both job- and house-rich. The NBER research suggests that moving to higher-income areas can effectively be a wash because subsequent housing prices are so high.

“We find that housing costs more or less fully offset the extra weight that you can get from moving to big cities or to high-wage places,” Rothstein, a labor economist with the University of California–Berkeley, tells Fortune. “You’ll get higher wages, but then you have to pay enough in extra housing costs. You lose all of those extra earnings that you get. Whether that’s worthwhile or not depends on how much you value being in a big city.”

New York, San Francisco, and Chicago have some of the lowest building activity

The median weekly earnings for the 121.5 million full-time workers in the U.S. was $1,110 per week, or about $57,200 per year, as of July 18, according to the U.S. Bureau of Labor Statistics. However, workers in LA, D.C., and NYC make a median wage of more than $60,000.

Indeed, the cost of housing in NYC is 230% higher than the national average, according to RentCafe, an internet-based listing service.

Despite the higher salary-to-housing cost ratio, migration trends show that people are still continuing to move to some of the biggest cities. Some cities with the largest population growth include San Antonio and Las Vegas. However, these cities are also among those with the lowest housing stock and lowest number of building permits issued this year, according to research by Bank of America.

Large metro areas including New York City, Boston, San Francisco, and Chicago had the lowest percentage of building permits issued as a share of the local population, the BofA data shows. This serves as evidence that the best job markets in the U.S. also have the biggest housing shortgages.

The migration problem

“We have many more people going into the biggest cities, which are the highest-wage places,” Rothstein says. “Those places do have more housing, but they don’t have enough more housing to accommodate all the people who want to move there. They tend to have pretty high housing prices.”

BofA data tells a slightly different story, though. In light of high housing prices, its data shows, some workers are actually starting to move away from the larger and more expensive cities—likely due to housing shortages and the strain of higher housing costs. Cities including New York City, Baltimore, San Diego, and Los Angeles each saw population decreases within the past year and relatively lower housing-to-population ratios at less than 43%.

“It’s clear that if it were as easy to build in big cities as small cities, we’d be building a lot more, and a lot more of our people would be living in those big places,” says Rothstein.

“It really is a big problem for the economy”

Overall, the study points to the dire need for more affordable housing in larger cities, agrees Adam Ozimek, chief economist at Economic Innovation Group.

“The report really highlights this longer-standing issue of housing affordability, and it really is a big problem for the economy,” Ozimek tells Fortune.

In the meantime, he suggests, remote work can help to combat this issue by letting people access higher-paying labor markets while living in lower-cost areas.

“I am optimistic that we at least have the opportunity to have better trends in housing affordability in this country,” he says. “But it will take policymakers to do the right thing and embrace an attitude of building and better regulation.” Until that day comes, the housing Catch-22 will remain, except unlike the sane pilot who was forced to keep flying crazy missions, the economy will be grounded.