The median Bay Area home price surged to an all-time high of $820,000 in March, up 9.3 percent from February and up 14.7 percent from March of last year, research firm CoreLogic reported Tuesday.

The previous peak was $784,000 in November. The report includes newly built and existing homes and condos sold in all nine counties. For the past six months, the median price has risen 12.8 percent year over year on average.

For the fourth consecutive month, Santa Clara and San Mateo counties showed the steepest year over year gains: 33.6 and 25.7 percent, respectively.

New home construction in Silicon Valley hasn’t come close to keeping up with the growth in high-paying jobs. Facebook, based in Menlo Park, disclosed in an April 13 filing that its employees earned a median pay package of $240,430 last year.

Rising mortgage rates and shrinking tax breaks for mortgages were expected to put a damper on home prices, but so far that has not proved to be true in the Bay Area.

The yield on the 10-year Treasury note, which serves as a benchmark for mortgage rates, surpassed 3 percent Tuesday for the first time since January 2014. Coincidentally, Freddie Mac reported on Thursday that the average 30-year fixed mortgage rate increased 0.05 percentage points to 4.47 percent last week, its highest level since January 2014.

The federal tax law passed in December was expected to discourage home buying. It limited the itemized deduction for all state and local property and income tax combined to $10,000 per year (previously there was no cap) and reduced the basic mortgage-interest deduction to interest on up to $750,000 in debt, from $1 million previously.

People “are trying to desperately buy something before it becomes completely unaffordable,” said Scott Anderson, chief economist with Bank of the West. “Six months, a year from now, you will see more of the downside from rising rates.”

A 650-square-foot home in South San Francisco with no garage that fronts an alley went on the market this month for $599,000, or nearly $1,000 per square foot. After a busy open house last weekend, listing agent Kent Flinn expects it to sell for much more.

South San Francisco, the erstwhile “industrial city,” and neighboring San Bruno have traditionally been two of the more affordable cities in San Mateo County, but like everywhere else in the Bay Area, “demand is heavy and supply is limited,” Flinn said.

As demand has grown in those cities, it also has changed. “It used to be a three-bedroom, two-bath home in a certain district would sell better in one area than another,” Flinn said. Today buyers “are less concerned about neighborhood and more about size.” They want enough space for their family or a spare room to rent out.

In the past, people didn’t want to live near Caltrain in those cities. Now it’s a draw. People want to be able to walk to BART or Caltrain, said Flinn’s wife and business partner, Beverly Flinn.

March’s 14.7 percent increase in median home prices across the region “was the highest year over year for any month since last September, when it was also 14.7 percent,” CoreLogic analyst Andrew LePage said.

That increase “is significant, and it stands out statewide and nationally, but there is a mix issue,” he said. The median price is the halfway point between the highest and lowest prices homes sold for in a particular month. In recent months, “there has been a shift toward more mid- to high-price homes selling and less in the lower end,” LePage said. That tends to raise the median price.

The number of homes and condos sold last month was 7,122, up 43.9 percent from February but down 3.3 percent from last March. An increase between February and March is typical, as the spring selling season heats up. Since 1988, the average increase between those months is 39.8 percent, CoreLogic said.

But last month’s sales were 17.1 percent below the March average of 8,590 sales since 1988.

The Bay Area has been sheltered from rising rates and the new tax law because its housing market “is chronically undersupplied,” Anderson said.

The California Association of Realtors reported this week that the median time a home in the Bay Area sat on the market before an offer was accepted was just 12 days in March, down from 13 in February and 14 a year ago. At the current pace of sales, it would take just 1.9 months to sell every Bay Area home on the market, down from 2.6 months in February and 2.2 last March.

Home prices haven’t been hurt by rising mortgage rates because at 4.5 percent, they are still low by historical standards, said Aaron Terrazas, chief economist with Zillow, a real estate website. He expects mortgage rates will peak at 5.5 to 6 percent in a year or two.

“We think mortgage rates can go up to 5 percent or a little above before we see any headwind on the housing market,” Terrazas said. When that happens, “I don’t think it will cause a decline in prices; it will cause a slowdown (nationwide). The risks are bigger in the Bay Area because home prices are so high.”

On a $650,000 mortgage, going to 5 percent from 4 percent would add $386 to the monthly payment.

Anderson predicts that the new tax law eventually will depress home prices — by about 4 percent nationwide over two years — by raising the after-tax cost of homeownership. “In higher cost areas, the impact would be greater,” he said.

People have been leaving California for other states, but its population has continued to grow thanks to immigration from other countries and the natural increase from births minus deaths. But “we expect more out-migration from the Bay Area and the state as a result of high housing costs,” Anderson said. “I think by the end of this year,” the state’s population will decline for this first time in this economic expansion.

Kathleen Pender is a San Francisco Chronicle columnist. Email: kpender@sfchronicle.com Twitter: @kathpender