Will the Fed "Taper" in September if the August unemployment rate is 7.6%?

Short answer: No.

The BLS will release two more employment reports before the September 17-18 FOMC meeting (employment reports for July and August).  The current unemployment rate is 7.6% (as of June), and the Fed's forecast is for the unemployment rate to decline to an average of 7.2% to 7.3% in Q4 of this year.

A significant portion of the decline in the unemployment rate from 10.0% in October 2009 to 7.6% in June 2013 was related to a decline in the participation rate from 65.0% in Oct 2009 to 63.5% in June 2013.  If the participation rate had held steady, the unemployment rate would be 9.7% (assuming an increase in the participation rate with the same employment level).

Of course a large portion of the decline in the participation rate was expected and was due to demographics (both the aging of the population, and more young Americans staying in school).  There has been an ongoing debate about how much of the decline in the participation rate has been due to demographics and how much due to economic weakness (I think more demographics, other have attributed more of the decline to economic weakness).

However just about every analyst expects 1) a continued long term decline in the participation rate, 2) some short term bounce back in the participation rate as the economy recovers.  The bounce back could be just a flattening of the participation rate (the short term bounce back just offsetting the long term decline) or the participation rate could increase 0.5% or so in the next year or two.  (I think somewhat flat is likely)

The participation rate could be very important regarding the timing of when the Fed starts tapering QE3 asset purchases.  We can use the Atlanta Fed's Jobs Calculator tool to estimate how many jobs per month will be needed to reach a certain unemployment level based on the participation rate.

As an example,  if the participation rate holds steady over the next two months, it would take 114 thousand jobs added per month to keep the unemployment rate at 7.6%.  The economy has added 202 per month so far in 2013, and at that pace - with the participation rate steady at 63.5% - the unemployment rate would decline to 7.4% to 7.5% in August.

However, if the participation rate increases slightly to 63.6% (more people returning to the labor force), then the economy would need to add 220 thousand jobs per month to just keep the unemployment rate steady at 7.6%.

The participation rate was probably one of the factors Fed Chairman Ben Bernanke was referring to yesterday when he said the June unemployment rate of 7.6% "probably understates the weakness of the labor market."   I've seen a number of analysts point to recent job gains as the key to the Fed tightening in September; I think the unemployment rate and participation rate are more important indicators for the Fed.

Note: You can put in your own assumptions to the calculator. Another frequent question is when will the unemployment rate fall to 6.5% (the Fed's threshold, but not trigger, for raising the Fed's funds rate). If the participation rate stays steady, the unemployment rate will fall to 6.5% in December 2014 if the economy adds around 200,000 jobs per month. This is consistent with the Fed not raising rates until 2015 or later.