Housing construction in the United States declined 0.7 percent last month to the lowest level since the end of the recession, and more Americans were behind on their mortgage payments during the summer than at any time in the past 30 years, according to data released yesterday.

At the same time, however, the nation's personal income rose 0.7 percent in November, and consumer spending jumped an even stronger 0.9 percent.

The data, though mixed, evoked optimism from the Reagan administration, with Commerce Secretary Malcolm Baldrige pointing to recent declines in interest rates and predicting "gains in new housing activity and higher sales of new and existing homes in the months ahead."

His views were echoed by Peter D. Herder, president of the National Association of Home Builders, who said he believes "the decline in interest rates could boost housing construction modestly . . . during the first half of 1985."

The news came as interest rates dipped again, apparently as a result of easier monetary policy by the Federal Reserve. Bankers Trust Co., the nation's ninth-largest bank, cut its prime lending rate a full half-point, to 10.75 percent -- matching Manufacturers Hanover's reduction on Monday. The rest of the banking industry is expected to follow suit in the next few days. The decline touched off a massive stock market rally. Details on Page B1

The prime rate is now at its lowest level since August 1983, and further softening of interest rates is predicted. Many analysts said they expect the Federal Reserve to cut its discount rate -- the rate it charges when it lends to its member banks -- later this week.

Today the government will release its "flash" estimate of economic growth for the last three months of the year. Many economists expect it to be in the 2.5 percent-to-3 percent range, up from the 1.9 percent rate of the previous quarter but still well below the very brisk rates of the first half of the year.

Economists also expect further increases in growth early in 1985, but several expressed caution about the outlook for later in the year.

"The economy has sort of moved sideways ever since perhaps July or early summer, and clearly some of the November numbers . . . were somewhat better," said Lawrence Chimerine, chairman of Chase Econometrics and president of the Monetary Forum, a group of economists and business leaders.

But he added, "I still think that it's premature to conclude that the economy has begun to pick up again. . . .When you put it together, we may be moving up slightly, but in my judgment . . . at best we're picking up slowly from the stagnation we've had over the past four or five months."

Indeed, Chimerine noted that a recent survey of Monetary Forum members gave the economy a 35 percent chance of sliding into recession in the next six months, and a 60 percent chance of such a downturn within a year.

A major factor in these analysts' caution is the massive federal deficit, which many said shows no sign of coming down. Chimerine said that "the unanimous opinion of the Monetary Policy Forum is that the deficit outlook is horrendous. . . . Without new policy actions, deficits are likely to begin rising again in the current fiscal year, and rise for the remainder of the decade."

The best news in the housing construction report issued by the Commerce Department was in building permits. These, often regarded as a barometer of future activity, rose 11 percent from October. But housing starts declined 0.7 percent to a seasonally adjusted annual rate of 1.528 million, the lowest level since December 1982.

Michael Sumichrast, chief economist of the home builders association, said he was "not very happy" with the November figures, but added that because of the improved interest rate picture, the NAHB is revising its forecast for 1985 up slightly to about 1.6 million starts. The November rise in incomes and spending, also announced by the Commerce Department, put personal income at an annual rate of $3.0998 trillion, and spending at $2.4829 trillion. The income rise was almost twice that of the month before, and the spending increase reversed a 0.2 percent decline in October.

The mortgage delinquency and foreclosure data, collected by the Mortgage Bankers Association of America, showed that 5.86 percent of home loans were 30 days or more overdue, the highest level since the trade group began keeping such statistics in 1953.

Thomas R. Harter, chief of the MBA's economics department, noted that unemployment compensation is running out on some people, and that there are "pockets," such as western Colorado, where the collapse of the oil boom left "ghost towns like the Old West . . . where there is no alternative employment and no one to sell the houses to."

But the "good news," Harter said, is that the largest share of the delinquencies is in the 30-days-overdue category, "and a lot of that could get corrected" by the end of the year.