Many Americans believe the unemployment rate remains stubbornly high because U.S. multinational companies have been outsourcing and offshoring jobs to low-wage countries at the expense of jobs at home. And they believe this in part because politicians and the media tell them it’s so, even though it isn’t.

Consider this story today from the Associated Press under the provocative headline, “Where are the jobs? For many companies, overseas.”

Corporate profits are up. Stock prices are up. So why isn’t anyone hiring?

Actually, many American companies are–just maybe not in your town. They’re hiring overseas, where sales are surging and the pipeline of orders is fat.

More than half of the 15,000 people that Caterpillar Inc. has hired this year were outside the U.S. UPS is also hiring at a faster clip overseas. For both companies, sales in international markets are growing at least twice as fast as domestically.

The trend helps explain why unemployment remains high in the United States, edging up to 9.8 percent last month, even though companies are performing well: All but 4 percent of the top 500 U.S. corporations reported profits this year, and the stock market is close to its highest point since the 2008 financial meltdown.

But the jobs are going elsewhere. The Economic Policy Institute, a Washington think tank, says American companies have created 1.4 million jobs overseas this year, compared with less than 1 million in the U.S. The additional 1.4 million jobs would have lowered the U.S. unemployment rate to 8.9 percent, says Robert Scott, the institute’s senior international economist.

Where to start? First, look back at the reference to Caterpillar, the quintessential U.S. multinational company. If more than half of the employees the company has hired this year are outside the United States, doesn’t that imply that the company also hired workers within the United States, perhaps several thousand?

In fact, as I noted on p. 101 of my Cato book Mad about Trade, Caterpillar and other U.S. multinationals tend to hire workers at home when they are hiring workers abroad. When global business is good, employment tends to ramp up throughout a multinational company’s operations, whether in the United States or abroad. (Earlier this month the Dayton (Ohio) Daily News ran a story about Caterpillar hiring 600 new workers at a local distribution center.)

It is simply false to argue that, if U.S. multinationals did not add jobs to their operations abroad, those jobs would be created at home. The opposite is much closer to the truth. Over the past 30 years, the change in employment of U.S. multinationals in their U.S. parent operations and in their affiliates abroad has been positively and strongly correlated. When hiring grows abroad, it grows at home, and when it lags at home, it lags abroad.

And when U.S. companies do hire abroad, their aim is not typically to cut wage costs but to reach new customers (as I explained in an earlier op-ed). That’s why U.S. multinationals employ far more workers in high-wage Europe than in low-wage countries such as India and China. In fact, according to the most recent numbers from the U.S. Commerce Department, U.S. multinationals employed five times as many workers in Europe (4.82 million) in 2008 than they did in China (950,000).

If U.S. companies are forced to reduce their operations abroad in the name of fighting unemployment at home, they will be less able to compete in global markets and less able to expand production and employment in their domestic operations.