"econometrics of rent control" brings here. The fairly consistent econ 101 conclusion about rent control is that it never works. If you're talking about another conclusion, what is it?
We don't need to argue about this. Rent control has been removed from many communities, and the rent becomes much more volatile without the stabilization control.
There's lots of actual case study literature on this.
These things aren't mere untested hypothesis where our personal politics come in to play - they are well studied.
I really think you should look into the research. There's a lot of tested hypothesis and survey analysis in them.
We tend to not treat economics like a science - as if our general education is enough to have an informed opinion. We certainly don't do that with psychology, chemistry, biology, or even softer sciences like sociology and anthropology.
But yet, when it comes to economics, we all have a pretty solid opinion and think we are all fairly well informed.
I encourage you to look deeper into the topic. Attend proseminars at your local university. Watch some graduate level lectures online. And, this is just an encouragement, revisit statistics and calculus --- you'll find out why if you look into 21st century econ.
As far as your other claims ... those are harder to measure really.
Rent amounts is a pretty easy number but things like lower quality (how much lower, what kind, where, is it predominant) and higher competition (amongst whom, using what process, which strategies aren't in play any more) ... well those are much harder questions. The microeconomic topic here is called Welfare economics: http://en.wikipedia.org/wiki/Welfare_economics and in economic theory is the social welfare function: http://en.wikipedia.org/wiki/Social_welfare_function
I'm not saying those broad ideas don't hold ... but defining things like quality and competition can be a much trickier business than price.
And unfortunately, if you are going to approach it as a science, you can't really go off anything other than definition, observation, and measurement.