REUTERS/Kevin Lamarque

The recession created millions of long-term and shadow unemployed, and the question is whether the recovery will bring them back.

Now, as Fed Chair Janet Yellen testified before Congress, there are still plenty of reasons to think there's plenty of slack left in the labor market. There are the part-time unemployed, who have jobs but can't find the full-time ones they want. Then there are the long-term unemployed, who have been looking for work for six months or longer and have trouble getting companies to even read their resumés anymore. And finally, there are the shadow unemployed, who have given up looking but would take a job if they could find one. This all adds up to a much weaker economy than the headline 6.1 percent unemployment rate suggests. And it's why wage growth has stayed so weak even though things have started to pick up a bit.

The hope, of course, is that a stronger recovery will suck in more of these marginalized workers. But how realistic is that? Well, it's not clear. On the one hand, there is evidence that a better job market does help the long-term unemployed, despite the discrimination they face in the hiring process. You can see that in the chart below from a recent Fed study. It shows each state's short-term and long-term unemployment rates compared to their pre-recession averages. In general, the more a state's short-term unemployment rate has fallen, the more its long-term one has too—and that's mostly because of people finding jobs, not dropping out.

But, on the other hand, there isn't much—or any, really—evidence that a better job market brings back more of the shadow unemployed. As you can see in the chart I made from FRED, there's basically no relationship between the unemployment rate and the percent of people not in the labor force who either get or start looking for a job. And by "basically no relationship," I mean an R-squared of 0.00099.

It doesn't matter if unemployment is 5 or 6 or 7—or even 10 percent. The percent of people entering the labor force doesn't really change: it's always somewhere between 7 and 8 percent. Now, that doesn't mean nothing changes. When unemployment is low, more people move from out of the labor force into jobs. And when it's high, more of them move into unemployment—they start looking for work, but can't find it. You can see that in the chart below that former CEA Chair Alan Krueger has highlighted.

What explains this? Well, during the good times, the people entering the labor force are probably students looking for and finding jobs. But during the bad times, kids stay in school as long as they can to hide out from the recession, and the people entering the labor force are ones who didn't expect to work but need to now. Maybe their spouse got laid off, or maybe their 401(k) got vaporized—in either case, they start looking for jobs that aren't there.

You might expect this time to be different—with more discouraged people returning—because this recession was different. But there's no sign of that yet. In fact, people are entering the labor force at a lower rate today than at any other time in the past 25 years. Part of that might be because more of the people not in the labor force are retired, but still, there's been no bounceback.

The depressing lesson might be that there's a high cost to letting the short-term unemployed become long-term unemployed and then shadow unemployed. That cost is careers lost, forever.