America’s housing market has grown so overheated as demand outpaces supply that prices keep hitting record highs — and roughly half of all U.S. houses are now selling above their list price.

Two years ago, before the pandemic struck, just a quarter of homes were selling above the sellers’ asking price, according to data from the real estate brokerage Redfin.

On Tuesday, new data further illuminated the red-hot nature of the housing market: Prices rose in March at the fastest pace in more than seven years. The S&P CoreLogic Case-Shiller 20-city home price index jumped 13.3% that month compared with a year earlier — the biggest such gain since December 2013. That price surge followed a 12% year-over-year jump in February.

And mortgage rates remain at historically low levels, with the average rate on a 30-year fixed mortgage around 3%. A year ago, the average was nearly 3.25%.

Investors, including individuals buying second houses and wealthy Wall Street firms, are also buying more homes, intensifying the competition. Investors bought 17% of homes in April, up from 10% a year earlier, according to the National Association of Realtors. The large millennial generation is also increasingly turning toward home-buying.

Daryl Fairweather, chief economist at Redfin, said that demand had been outstripping supply even before the pandemic as developers struggled to build enough new homes. Builders now say that shortages of workers and lumber are limiting their ability to build.

New home construction fell in April after reaching a 15-year high a month earlier.

“All told, there is little, if any, indication that home prices will slow their appreciation anytime soon,” said Matthew Speakman, an economist at real estate website Zillow.

The number of homes for sale fell 21% in April compared with a year earlier, to just 1.16 million, near a record low in figures that date to 1982, according to the National Association of Realtors. The plummeting supply has pushed buyers into a near-frenzy. Properties were on the market for just 17 days in April, and 88% of homes sold were on the market for less than a month, the NAR said.

The ensuing bidding wars raised the price of the typical, or median, house to $341,600 last month, the NAR said, a record high.

Glenn Kelman, CEO of Redfin, said Tuesday on Twitter that one desperate home buyer in Bethesda, Maryland, offered — perhaps partly tongue-in-cheek — to name her first-born child after the seller. (She still lost out to another buyer.)

Kelman also noted that there are now more real estate agents than there are homes listed for sale. According to the Labor Department, 1.7 million Americans were working in real estate in April.

Some of the year-over-year price gain likely reflects the slower sales and reduced demand a year ago at the onset of the pandemic. All 20 cities in the Case-Shiller index reported faster price increases in March than in February.

The largest increase was in Phoenix for the 22nd straight month; prices there rose 20% compared with a year ago. San Diego experienced the next-largest gain, at 19.1%, followed by Seattle, with 18.3%.

Fairweather, the Redfin economist, said the housing market may cool off in the coming months. With vaccinations spreading and COVID-19 waning, more sellers may be willing to list their homes.

Fairweather suggested that many Americans are likely to start spending more money on services, such as vacations, dining out and other entertainment, and focus less on new homes.

Indeed, the number of people signing contracts to buy homes dropped in May, and fewer people are applying for mortgages. Sales of newly-built homes dropped nearly 6% in April, likely because of spiraling prices.

“At a certain point,” Fairweather said, “buyers just back off, and you get more stable price growth. I think this is the peak, but it’s going to be hot for a long time. It’s more like a plateau.”