The Fed’s magic jobs number by Stephen Gandel @FortuneMagazine July 2, 2013, 1:39 PM EST E-mail Tweet Facebook Google Plus Linkedin Share icons FORTUNE — 220,957 jobs a month. I think. Maybe. Ever since Ben Bernanke raised the possibility last month that the Federal Reserve would pull back on bond purchases as early as later this year, people have been wondering just how likely that is. The bond market seems to think it’s pretty likely. A parade of Fed governors have been saying not so much. In a perfect world, we would get a better sense of what’s going to happen on Friday, when the government releases its number of how many jobs were added in June. Bernanke said the Fed would stop buying bonds if the unemployment rate hits 7% in mid-2014. At the end of May, the unemployment rate was 7.6%. So if the June report shows the economy added enough jobs to get us to 7% in 13 months, then it is time for the Fed to start “tapering” its bond buying. If it adds fewer, the Fed keeps buying. Figuring out that number is tricky stuff. According to CNNMoney’s current survey of economists, the median estimate is for job growth of 155,000 in June. That might not do it, but it could be close, perhaps. Hamilton Place Strategies, a Washington-based PR firm/pseudo think tank that counts a number of the big banks among its clients, says the number we need to get to 7% is 169,000 a month. So we may come up a little short in June. But since we had been averaging gains of about 187,000 jobs up until June, we are still well within the range of job growth the Fed is looking for, according to the HPS’s estimate. HPS did not respond to a request for information about how they arrived at their figure. MORE: Uncle Sam ahead on the Ally bailout But that number is most certainly wrong. Citigroup’s main Fed strategist Nathan Sheets’ back-of-the-envelopes the number at 200,000. So that means the economy needs to pick up a little before the Fed can pull back. But even that number could be low. The rub has to do with something called the labor force participation rate, which has been a hotly-debated topic in the last year or so among economists. Right now we have about 156 million people in the civilian labor force, of which about 11.8 million are unemployed. Based on those numbers, the economy needs to add 846,000 jobs by next June, or 65,000 jobs a month, to get to 7%. Piece of cake. But that calculation doesn’t factor all the new workers who enter the market every month looking for work, especially now. The growth of the labor force hasn’t been as strong as it typically is (it’s even shrunk some months) because of the economy, and some say because of baby boomers retiring. Nonetheless, in the past two and a half years, the labor force has grown an average of 69,000 workers a month. And those people end up employed or unemployed as well. Factor that in and the economy needs to add 1.7 million jobs, or 134,000 a month, to get to the magical 7%. It also doesn’t factor all the workers who have given up looking for work, but who will presumably try again when the economy improves. That’s the labor force participation rate, which slumped to a three and a half decade low of 63.3% in March. It has averaged 66% in the past 20 years. If we were to gain back half of the drop-outs in the next year, the economy would have to create 4.9 million jobs, or 381,000 a month. MORE: Only the wealthy feel economic recovery But if history is right, worker participation won’t rise that fast. And retiring baby boomers, which make up a good portion of that drop, are unlikely to go back to work, even if things improve dramatically. In the 1990s, the labor force participation rate grew by a half a percentage point in the year after it bottomed. If that were to happen today, we would need 256,000 jobs a month to hit 7% unemployment by June 2014. In the early 2000s recovery, the participation rate jumped by a smaller one-third of a percentage point. Repeat that performance, and the economy would have to add just fewer than 221,000 jobs a month, which is the number I’m going with. So to recap, in order for us to know that the Fed will start to end its bond buying program later this year, the economy would have to add at least 134,000 jobs in June, but probably more like 200,000, and maybe as many as 381,000, but probably not that much. The Fed, for its part, doesn’t say how many workers it expects to re-enter the workforce. It did recently lower its estimate for GDP growth. At the same time, it said it thought the unemployment rate would fall faster than expected. That, I guess, means the Fed is predicting participation rates to stay low, or even drop further, though no one at the Fed is explicitly saying that. In the past few weeks, as the bond yields have risen relatively quickly following Bernanke’s 7% talk, a number of commentators have wondered whether the Fed is revealing too much these days. And yet, despite all that talk, even after the jobs number comes out on Friday, the market is likely to be just as confused about what the Fed will do next as it was on Thursday. So much for clarity.