So, I'm going to take the opposite side of this argument.
I think things like 'interest rates are so low that it is causing crazy high prices....etc' arguments miss the mark.
If I asked you, if Gas prices were $4.00 a gallon of if they were $2.00 a Gallon, which scenario would people buy more gas? Most people immediately say that at $2.00 a Gallon, people would buy more. The classic, price effect on demand equation from Econ 101. However, in practical terms, it's usually an opposite observed effect. The reason is that it's BECAUSE people are using more gasoline that the price is $4.00 and it's BECAUSE people are using less that it's $2.00.
The reason I mention this is it relates to interest rates directly. The common theme is that when interest rates are low people borrow more than when the interest rates are high is observably false. In every cycle interest rates are not inversely related to the actual demand for credit they are directly related (i.e. high interest rates = high demand, and vice versa).
Interest rates are not controlled by the FED. The FED controls only the short end of the curve, and to some extent mid curve rates on T-Notes. However, central banks do not control consumer lending and business lending rates directly. Those rates are actually LOWER today than 2 years ago. The reason is the aggregate demand for credit is much much lower than in 2006 era lending.
In fact, global demand for credit is arguably at 30 year low. Hence the negative interest rates (something economists long thought practically impossible) in Europe.
Interest rates are likely to be almost permanently (if you define that as say, the next 10-20 years) lower than historical norms.
In addition to that, as of December 2014 US Household formation was at 2Million per year. As of March 2015 US Housing starts are at an annual rate of 1Million per year. Compare that to 2000-2006 annual Household formation average of 1.35 million per year and the 2004-2006 annual Housing Start rate of 2.2Million.
Put simply, we way over built for a decade in housing, and we're way underbuilding (and have been) for the last 5 years. Rents therefore almost assuredly going to continue to rise because they have to.