Consider it the Fed’s chicken-or-the-egg dilemma: Do rising stocks drive down unemployment or does lower unemployment drive up stocks?

One view of the relationship between the two suggests that it is the former and not the latter, hence the continuation of the central bank’s easy-money policies.

Nick Colas, chief investment strategist at BNY ConvergEx, has run a comparison and found an interesting relationship that often sees unemployment fall when stocks go up.

The upshot: If the economy does get to Fed Chairman Ben Bernanke’s target of 8 percent unemployment by 2012, that would mean the Standard & Poor’s 500 would have to rise to 1,755—a stunning 35 percent gain from current levels and beyond even the already-bullish prognostications for this year.

“That’s not our price target, but it may just be the Fed’s,” Colas wrote in a note to clients.

On average, a 15 to 20 percent drop in stock prices leads to an increase of 1.2 percentage points in unemployment; a rise of 30-35 percent in stocks usually leads to a 0.4-point drop in unemployment.

If the analysis holds up—and Colas admits that recent history suggests it may not—the implications are staggering, particularly for the central bank’s quantitative easing program.

For one, it would mean that not only is QE3 on the table but also that QE4 and even QE5 are somewhere on the horizon if the Fed wants to keep the recovery rolling. It would mean that Bernanke’s “wealth effect” is in full gear, and that the road to recovery runs straight through the debt markets.

On the other side, the implications for debt- and deficit-cutters aren’t pretty. It would mean that the path to finally driving down unemployment is through the inflated asset prices that low-interest easy-money policies have paved.

But before we get too breathless, let’s look at some caveats.

For one, the relationship between stock market and employment gains has been absent since the recovery from the March 2009 stock market lows and the initial wave of Fed QE. As the Fed expanded its balance sheet by $2 trillion, unemployment has risen from 8.6 percent to Friday’s suspect number of 9.0 percent, while stock prices have nearly doubled.

Also, Colas points out that the correlation to the downside is much stronger than the upside. That is, a drop in stock prices has cut employment more than a rise has seen creation of jobs.

Yet another thing to remember is that for the past five years trying to rely on the Fed to forecast job trends has been like asking a sugar cane farmer in Peru to predict the final score in the Super Bowl. He might get it right, but it likely will be just a lucky guess. So all this talk about 8 percent could end up being little more than throwing darts at a map.

Still, the correlation between the two numbers is about 28 percent—not exactly a lead-pipe cinch but something to consider. The trend does better, though, in more extreme, or “tail” circumstances, such as would be required to get unemployment down to 8 percent in a year.

“[W]e are talking about a 40-year time frame, after all, with everything from wars to tech and housing bubbles in the mix,” Colas notes. “So it is close enough for ‘government work,’ which is, after all, what we’re doing anyway.”