The NYT had an interesting piece on how a rapidly growing number of people are finding rents unaffordable (defined as more than 30 percent of gross income. There are two reasons that rents can rise in price. The first is that the same units cost more money. The second reason is that the mix of rental units change so that the the typical unit costs more.
It is clear that the main cause of higher rents is the latter, as shown below.
This graph shows that the owner equivalent rent index from the Consumer Price Index (CPI) has almost exactly tracked the overall rate of inflation since the start of the century. (I used owner equivalent rent since this excludes the cost of utilities. The cost of utilities has likely outpaced inflation, but that is a somewhat different story.)
If this index from the CPI, which is effectively a quality adjusted price index, is not outpacing inflation, then it implies that the problem must be the quality is getting better. In other words, the units added to the rental housing stock (either by new construction or conversion of ownership units) are either bigger or better in some way than the average rental unit in 2000.
The other factor that could explain a rise in the ratio of the median rental price to income is a decline in real income, which we have seen to some extent in this century. In that case the problem is not really high housing prices, but low wages.