Here's former President Bill Clinton last week on The Daily Show With Jon Stewart:

For the first time in my lifetime, literally in my lifetime, when coming out of a recession, posted job openings -- that means they'll hire you tomorrow morning if you can do the job ... are going up at twice the rate of job hires. ...

There are two reasons for this. One is more than 10% of us are living in houses where the mortgage is worth more than the home, so we can't move. And that's cutting down on labor mobility, which has always been a big strength of America. But that's way the smaller problem.

By far the bigger problem is the jobs that are open don't have applicants that are qualified to do them. There's this huge skills mismatch. [There was a] huge college dropout in the last decade because costs went up 75% after inflation, and because the economy went down people had to drop out to work, and they cut back on a lot of intensive skills training.

We ought to have a list of every job that's been vacant for more than three weeks, by state, and just give 'em the money to train people immediately. And they ought to be able to do it while they're on unemployment. Give it to the employers if the community colleges and the vocational programs won't do it. ... You know how many jobs that is? Five million. The unemployment rate could go down under 7% if no bank made a single loan [and] if no corporation invested any of their surplus cash -- if we just made sure that tomorrow we had qualified applicants to go fill every posted job opening.

I think Clinton is on the right track here. There are a few indisputable facts about this recession. One is that the job market is strangely bad given the rebound in gross domestic product and corporate profits. Another is that the burden of joblessness has fallen disproportionally on the less educated. In 2007, the unemployment rate for those with bachelor's degrees was about 2 percentage points lower than for those that only had high school diplomas. Today, it's roughly 6 percentage points lower.

Another detail you may accept or reject as you wish: The government doesn't focus enough on education and training. Out of 19 major line items in the federal budget, just one department (besides interest payments) had its budget cut in 2009: education and training. Just the annual increase in 2009's defense spending amounted to almost two-thirds of what the federal government spends on education and training. (Although to be fair, states pull most of the education weight).

So I think Clinton's proposal is entirely laudable. But I'm not sure it's the cure-all he makes it out to be. First, college dropout rates may be rising. Costs certainly are soaring. But the fact is that more people have degrees today than ever before. The percentage of workers with bachelor's degrees or higher has been on an unabated surge since the 1940s:

Source: Bureau of Labor Statistics, author's calculations.

Why the skills mismatch Clinton mentions if degree-attainment is at an all-time high? One reason is that education isn't what employers look for. It's experience. That's why the negative correlation between age and unemployment is so strong. The more experienced you are, the more valuable you are. Another reason is that the degrees people are attaining might not be training them for anything useful. The hard reality is that a degree in 18th-century German literature increases your marketable job skills by roughly nothing. That's also one of the big gripes about degrees at for-profit schools like those owned by Apollo Group (Nasdaq: APOL) and Career Education (Nasdaq: CECO). They make you minimally, at best, more attractive to employers.

So then we move to the details of Clinton's proposal: Skip the schools and just give the money to employers. Let them do the training. Cut out the middle man and let those actually hiring permanent workers -- the current ranks include companies such as UnitedHealth (NYSE: UNH) General Dynamics (NYSE: GD), and Amazon (Nasdaq: AMZN) -- do the dirty work. But the problem with this argument is that corporations are holding record amounts of cash, and corporate profits are at an all-time high. Companies have plenty of money to train workers on their own. They're just choosing not to.

Why? Maybe because the workers can't come to them. This is what Clinton pointed out yet pooh-poohed: labor mobility. With 10% of homes underwater (so Clinton says; other statistics put it at more like 22% of mortgages), the ability to move to where the jobs are is hindered. How much this affects unemployment, no one really knows. No study I've seen has even attempted to answer the question. One comparative example, though, is to look at our neighbors to the north. Due to structural differences, Canada's unemployment rate is typically a few percentage points higher than ours. Today, it's almost 2 percentage points lower. Why? Perhaps because they basically had no housing bust, and thus aren't drowning in the labor mobility constraints we are.

I do like Clinton's proposal, if only because it's the rare idea to come from a politician (or former one) that's slightly pragmatic and acknowledges our problems are structural, not cyclical. Still, as we're now keenly aware, there is only so much stimulus can do. And it's usually not much. Well-thought-out stimulus plans can help move a recovery along, but the only thing that actually heals a recession is letting the damn thing work itself out.

Check back every Tuesday and Friday for Morgan Housel's columns on finance and economics.

Fool contributor Morgan Housel doesn't own shares in any of the companies mentioned in this article. Apollo Group, General Dynamics, and UnitedHealth Group are Motley Fool Inside Value recommendations. and UnitedHealth Group are Motley Fool Stock Advisor picks .Motley Fool Options has recommended a diagonal call position on UnitedHealth Group. The Fool owns shares of UnitedHealth Group. Try any of our Foolish newsletter services free for 30 days. True to its name, The Motley Fool is made up of a motley assortment of writers and analysts, each with a unique perspective; sometimes we agree, sometimes we disagree, but we all believe in the power of learning from each other through our Foolish community. The Motley Fool has a disclosure policy.