If you have statistics, i'm interested, but to my knowledge there is no housing shortage in Berlin. If anything, there's more housing than ever before, it's just trapped in the hands of landlords who want to speculate on it.
The point is, it wouldn't matter if it is trapped in the hands of landlords who want to speculate, if there is enough housing to go around, because they couldn't determine the market.
It is illegal to keep an apartment empty for more then three months. So if you are aware of any empty housing, feel free to denounce it (https://www.stadtentwicklung.berlin.de/wohnen/zweckentfremdu...). In 2018, 1,9% of the flats in Mitte were subject to an ongoing official procedure on those grounds. The owner can simply claim, they are reforming, but I presume there are limits to that too.
How many flats are really empty is unclear.
I've read that according to the Senat,
- there is an estimated 0.8%-2% of the flats unoccupied