AirBnB has, at best, a $56 million impact on the SF economy. Ben Bernanke is printing $85 billion per month to buy mortgage backed securities via QE3/4:

http://www.forbes.com/sites/afontevecchia/2012/12/12/qe4-is-...

  QE4 is here.  Only a few months after announcing what had 
  been dubbed QE3, an open-ended $40 billion a month program 
  to buy up mortgage backed securities (MBS), the FOMC 
  decided to extend its asset purchases in 2013 as Operation 
  Twist expires. Combined with QE3, the Fed will be taking 
  $85 billion in bonds, both Treasuries and MBS

It is likely that Bernanke's $85B/month has a far bigger impact on housing price inflation, and hence rent.