President Obama and Vice President Joseph R. Biden Jr. spoke about the economy, energy policy, Medicare and Afghanistan on Thursday night as they accepted their nominations at the Democratic National Convention in Charlotte, N.C. Here is a closer look at some of their assertions:

Manufacturing

Mr. Obama, in his acceptance speech, said, “We can help big factories and small businesses double their exports, and if we choose this path, we can create a million new manufacturing jobs in the next four years.”

Looking at current trends, it is certainly possible: the nation has added about 222,000 manufacturing jobs in the past year. Moreover, the Obama campaign has several proposals to encourage manufacturers to add workers.

But there is a bigger economic story behind the gains in manufacturing.

For three decades, manufacturers had cut jobs, and then when the recession hit, they slashed hundreds of thousands more. Now, some economists say, they might be adding workers to simply regain some lost capacity.

American workers’ wages have also been stagnant for more than a decade, and in many cases have declined during the recession. Over the same period, pay climbed in many other countries, making American workers’ wages more competitive. Strong blue-collar wage growth here or lower wages in foreign countries would send more jobs back overseas, economists say.