A diminished supply of available homes is swelling prices in large United States metro areas from New York to Miami to Los Angeles, squeezing out would-be buyers and pushing up rents as more people are forced to remain tenants.

The trend is pressuring Americans' budgets, with about one-third of households spending more than 30 percent of their gross income on housing as of 2015, according to a report being released Friday by Harvard University's Joint Center for Housing Studies.

Homeownership rates have stagnated in part because high rents have made it difficult for many prospective buyers to amass a down payment for a house.

At the same time, the sparse supply of available properties is benefiting existing homeowners, many of whose home values have recovered from the housing bust a decade ago.

The tight supply of homes and a shortage of affordable rental housing have improved little in recent years for a variety of reasons. Among the key factors is that construction has yet to regain the pace of homebuilding that predated the bust.

"As the economy continues to recover, as income picks up as household formations pick up, it's not spurring a supply response," said Chris Herbert, managing director of Harvard's Joint Center for Housing Studies. "It's a worsening of the situation that was evident last year."

Here are some major findings documented in the report:

Housing affordability

The government considers people who spend over 30 percent of their income on housing to be "cost-burdened." Those who spend more than 50 percent are considered "severely" burdened.

About one-third of households – 38.9 million – were considered cost-burdened in 2015, down from 39.8 million a year earlier. This was the fifth straight annual decline.

Still, roughly 16 percent of households, or about 18.8 million, paid more than half their income on housing. The share of renters paying more than they can afford varies from city to city. In Miami, it's 35.4 percent. In El Paso, Texas, it's just 18.4 percent. Other cities where households were deemed to be cost-burdened include Daytona Beach, Fla.; Riverside, Calif.; and Honolulu.

Ryan Welch of Santa Monica, Calif., is among those feeling stuck between rising rents and home prices. Mr. Welch, 32, pays about $1,500 a month for a rent-controlled one-bedroom apartment he shares with his wife. That works out to about a quarter of their monthly income, an affordable portion.

Welch, who works in advertising sales, would like a bigger place with more amenities. But he's reluctant to leave their apartment.

"I'm nervous to move to a place that's not rent-controlled," he said.

Saving to own a home, something he wants to do, has had to take a back seat to making payments on student loans and his car, among other expenses.

"I'd much rather buy, but I can't come up with the down payment," Welch said.

Home supply and prices

The availability of homes for sale has fallen short of demand. Last year, the typical new home for sale was on the market for just 3.3 months, according to the report – well below the average of 5.1 months dating to the 1980s.

All told, 1.65 million homes were on the market last year, the fewest in 16 years, the report said.

The supply is worse for lower-priced homes that would be affordable to typical first-time buyers. Builders have been constructing fewer homes for that segment of buyers.

Between 2004 and 2015, construction of single-family homes of less than 1,800 square feet fell to 136,000 from nearly 500,000, according to the report.

The trends helped boost national home prices 5.6 percent last year, above their housing boom peak. (Prices remained nearly 15 percent below their peak, when adjusted for inflation.)

"Builders are starting to turn more attention to the entry-level market," Mr. Herbert said. "My guess is we'll see some increase in our supply of smaller, more moderate-cost new housing on the single-family side."

Widening cost gap

One striking finding in the Harvard report is the gap in home values that's widened since 2000, well before the market hit its boom-era highs. When adjusted for inflation, prices in markets along the East and West coasts have vaulted more than 40 percent since 2000. By contrast, values in the Midwest and South have declined.

Among the markets where prices remain well below their housing-boom peaks: Las Vegas; Chicago; Detroit; and Tampa, Fla. By contrast, home values have risen far above their previous highs in Denver, San Francisco, and Austin, among other markets.

"If you go back to, say, 1970 and you look at the differences in house prices across market areas, they were not nearly as extreme as they are now," Herbert said. "It's a function of income inequality and how much the differences in income have grown."

In addition, regulatory constraints and a shortage of available land limit construction in many areas.

Rental prices and supply

Though apartment construction surged in the years after the housing bust, demand for rental housing has grown even more. The rental vacancy rate fell last year to 6.9 percent, a three-decade low, according to the Harvard report. That's the seventh straight annual decline.

Much of the apartment construction in recent years has been made up of luxury developments catering to affluent renters rather than to households of modest means.

The number of rental units available for under $800 fell by 261,000 between 2005 and 2015, according to the report. By comparison, the number of units for $2,000 or more climbed by 1.5 million in the same period.

Homeownership rate

The nation's homeownership rate has been falling since peaking around 69 percent in 2004. Last year, it hit 63.4 percent, just above the low set in 1965. But the rate appears to be stabilizing, according to the report.

"Even if it is no longer falling, it's settling in at a rate that's low by historic standards," Herbert said.

The rate has grown notably worse for African-Americans, the report found. Homeownership among African-Americans is now at its lowest point since the 1960s and nearly 30 percentage points below the rate for whites, Herbert said.

Homebuilding up, but still low

Construction increased in 2016 for the seventh year in a row, adding 1.17 million houses and apartments. But that was still the lowest growth rate since 2011, the report noted.

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Building of single-family homes has been rising faster, up 9.4 percent last year to 781,600 units. Even so, residential construction still trails the 1.4-1.5 million annual rate that prevailed in the 1980s and 1990s, the report notes.

"We're still not yet at 1.2 million starts," Herbert said. "Back in the day, it would have been a bad year during a recession, and we're still trying to get back up there. We're certainly not back to normal in terms of supply."