Stocks fell in a volatile session Tuesday, with a sharp decline in General Motors dragging down the Dow Jones industrial average, while...

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NEW YORK — Stocks fell in a volatile session Tuesday, with a sharp decline in General Motors dragging down the Dow Jones industrial average, while broader indexes fell slightly in an end-of-year malaise.

The Dow Jones industrial average fell 30.98 to 10,805.55.

Microsoft, one of the 30 Dow stocks, added 3 cents to close at $26.86 a share. Boeing, also a Dow stock, gained 77 cents to $70.74.

Broader stock indicators were slightly lower. The Standard & Poor’s 500 index fell 0.30 to 1,259.62, and the Nasdaq composite index fell 0.32 to 2,222.42.

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General Motors fell to its lowest level since the crash of 1987 after a report by J.D. Power and Associates said it was losing market share to its Asian rivals.

Broader indexes moved lower, despite a bullish report on wholesale inflation, an uptick in home construction for November and a strong earnings report by Wall Street firm Morgan Stanley.

“There’s a lot of uncertainty going into the end of the year,” said Ralph Acampora, managing director of technical research at Knight Capital Group, an asset-management firm.

Traders are especially concerned about future Federal Reserve interest-rate increases and oil prices. Those “crosscurrents” have led to choppy trading this month, a sharp change from the market’s gains last month, Acampora said.

A strike by New York City transit workers had little effect on volume, which was slightly lower than Monday’s shares traded.

Crude-oil futures edged higher ahead of Wednesday’s weekly inventory data, with a barrel of light crude quoted at $57.98, up 64 cents, on the New York Mercantile Exchange.

In economic news, a jump in home construction last month helped ease worries about the cooling housing market. Housing starts rose to an annualized rate of 2.123 million homes last month, up from October’s rate of 2.014, according to the Commerce Department. The number of permits issued also rose to an annualized rate of 2.155 million last month, up from 2.103 million in the month prior.

The increase may have been due to last month’s warm weather, UBS economist Maury N. Harris wrote in a research note.

The Labor Department’s producer price index (PPI) for November, which measures inflation, showed overall producer prices fell 0.7 percent for the month as energy prices declined. Economists had expected a 0.5 percent drop.

Even with energy prices removed, so-called “core” PPI rose just 0.1 percent, versus the 0.2 percent increase expected on Wall Street. With inflation remaining relatively tame, the Federal Reserve is considered more likely to halt its current regime of rate hikes soon.

In company news, General Motors stock fell $1.20, or 5.7 percent, to $19.85, its lowest level since October 1987. Along with the report saying the company was losing market share, GM also recalled more than 400,000 vans because of faulty seatbelts.

Morgan Stanley’s record quarter sent its shares up $1.04 to $57.71. The company’s quarterly earnings surpassed Wall Street’s forecasts by 34 cents per share before a one-time tax benefit.