The U.S. is slowly working towards free trade agreements with Colombia, Panama, and South Korea. After years of wrangling, they might even pass this summer. President Obama is making the agreements a priority. But it won’t be easy. Some people prefer protection to competition, and they have the ear of many politicians.

Politico, for example, reports that “Labor groups and other critics . . . have labeled the pacts ‘job-killing, NAFTA-style trade agreements.’” That’s quite a claim. Did NAFTA really kill jobs? If it did, then maybe this year’s free trade agreements are a bad idea.

Let’s look at the data and find out. The St. Louis Fed’s FRED database has exactly what we’re looking for, which is the size of the civilian labor force over time. You can view and download the raw data here, and you can view it in graph form here.

NAFTA passed in 1993 but didn’t take effect until January 1, 1994. So let’s take December 1993 as our pre-NAFTA job total. At that time, there were 129,941,000 people in the labor force. As of this writing, the most recent data is from March 2011. In that month, the labor force was 153,406,000 people strong.

That means that there are 23,465,000 more jobs in America now than there were before NAFTA. This despite the last few years of hard economic times! So when someone claims that free trade agreements are job killers, they are either uninformed or lying. Neither option speaks well of the accuser.

Of course, 23 million new jobs don’t mean that NAFTA and other trade agreements are job-creators, either. They aren’t. Most labor force growth comes from population growth. International trade has almost zero long-term effect on the number of jobs. What it affects are the types of jobs. In the long run this is a very good thing. That’s why Congress and President Obama should pass the pending trade agreements with Colombia, Panama, and South Korea.

When governments lower trade barriers, they allow more people to exchange and to work together. In economics jargon, the size of the relevant market gets bigger. And the bigger the relevant market, the more people can specialize.

Readers familiar with Adam Smith will recognize this as his division of labor. Everyone knows that specialized workers are more productive than jacks of all trades. That’s why Henry Ford’s assembly lines were so much more productive than his competitors’. The same number of people could suddenly produce more cars in less time, because they had a more specialized division of labor.

Workers didn’t have to waste time switching from one task to another. They got very good at their tasks. And because they knew their jobs so well, they were better able to come up with new, better ways of doing them. Rising productivity is how an economy grows. Prosperity doesn’t depend on the number of jobs. It depends on how much stuff workers can create.

In ancient times, farmers were so unproductive that most of the population was stuck on farms. As they specialized and innovated, it took fewer and fewer people to feed everyone. Today, it takes less than two percent of America’s population to feed the rest.

That frees up the other 98 percent of us to specialize as doctors, engineers, artists, software designers, almost anything. Division of labor and the productivity it allows are what drive the modern economy. And none of it would be possible without trade. One of the reasons that America is rich is that Illinois can’t charge tariffs on goods from Indiana. The whole country was set up as a free-trade zone. When we move in that direction with other countries, as with NAFTA and the Panama, Colombia, and South Korea agreements, we open up new possibilities for specialization and wealth creation.

Low trade barriers allow the world to come together. Imagine having nearly 7 billion specialists instead of 300 million. The upcoming trade agreements won’t open up the whole world to trade, obviously. But they are a small step in the right direction, and deserve to be passed. Critics need not worry: if NAFTA is any guide, they won’t throw millions of people out of work.

Ryan Young is Fellow in Regulatory Studies at the Competitive Enterprise Institute.