WASHINGTON — The U.S. economy grew more slowly over the summer than the government had earlier estimated because businesses cut back more sharply on restocking of shelves.

The Commerce Department said Tuesday that the economy expanded at an annual rate of 2 percent in the July-September quarter, lower than an initial 2.5 percent estimate made last month. The government also said after-tax incomes fell by the largest amount in two years, reflecting high unemployment and lower pay raises.

The downward revision was largely because weaker data on inventory building came in after the government’s first estimate. Many businesses reduced their stockpiles over the summer, probably because they didn’t anticipate the strength consumer and business spending.

A decline in inventories is not always a bad sign. Economists believe this could lead to stronger growth in the current quarter, if businesses foresee more demand and restock their shelves.

Economists predict growth will strengthen to around 3 percent in the October-December quarter. Many raised their estimates after seeing encouraging October reports on retail sales and factory output.

“While this report is disappointing, it is a look back in time,” said Jennifer Lee, senior economist at BMO Capital Markets. “It is encouraging, to say the least, to see the October data coming in stronger, which is good news for the current quarter.”

Still, growth could be slowed if consumers continue to earn less. After-tax, inflation-adjusted incomes fell at a 2.1 percent rate. That’s steeper than the 1.7 percent decline initially estimated and the biggest drop since the third quarter of 2009, just as the recession was ending. It also marked the second straight quarterly decline.

Incomes are primarily wages and salaries, but they also include dividend and interest payments and government benefits. While the decline doesn’t directly affect economic growth, income fuels consumer spending and that makes up 70 percent of economic activity. So if income continues to decline, consumers will likely spend less and slow growth.

And many Americans could take home even less next year if Congress doesn’t extend a Social Security tax cut and emergency unemployment benefits. Both expire at the end of this year.

“For now the U.S. economy looks to be moving in the right direction,” said Paul Ashworth, chief U.S. economist at Capital Economics, who predicts growth of more than 3 percent in the fourth quarter.

But the January-March quarter “could be a different story, particularly if the payroll tax cut isn’t extended,” Ashworth said.

The modest third-quarter growth is not nearly enough to lower the unemployment rate, which has been stuck near 9 percent for more than two years. And economists caution that their brighter outlook hinges on Europe’s financial crisis, which could trigger a recession in that region and slow U.S. growth next year.

The government makes three estimates of the gross domestic product, the economy’s total output of goods and services, each quarter with the revisions based on more complete economic data.

In the first six months of the year, the economy grew at an annual rate of just 0.9 percent. It was the weakest growth since the recession officially ended, which stocked fears over the summer that the economy could be on the verge of another downturn.

The stronger growth in the July-September quarter helped calm those worries. Still, Americans spent more while earning less, and they dipped into their savings to make up the difference. At the same time, businesses invested more in machines and computers, not workers.

Without more jobs and higher pay raises, consumers are unlikely to be able to sustain those gains.

In October, the economy added a net total of 80,000 jobs. It was the 13th straight month of gains. Still, the additional jobs were fewer than the roughly 125,000 that are needed each month just to keep up with population growth.

There have been signs that the economy and job market are both getting better.

Last week, the government reported further improvement in the number of people seeking unemployment benefits for the first time. The number fell to 388,000, the fewest since April.

Retail sales and factory production both increased in October. While U.S. builders started slightly fewer homes, building permits, a gauge of future construction, surged nearly 11 percent. That gain was led by a 30 percent increase in apartment permits, to their highest level in three years.

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