Hard to say. My guess is yes, the rental market will decline. Of course if we magically return to where we were then we will be where we were, but I don't see that happening.
Owning still makes a ton of sense. Rates will likely never go back to a place where renting is the better option, so this will continue to hold the rental market down. Prices could fall if rates go up, but again I don't see that happening to a degree where it causes people not to buy, just to pay less. I think the days of earning from a savings account are over and we have traded them for lower mortgage rates. I think new starts will likely fall as more stock becomes available, due to reasons explained next.
I think the higher earners are not as safe as they think, and that will probably help the rental market.
However the lower earners are all screwed so any gains from the higher peeps stepping down is going to be lost here and then some.
I think we are likely looking at a lot of doubling up in housing / moving in with relatives / roommates / etc - so that will hurt the rentals. Though the folks that rent per bedroom might do great. This is what will cause stock for owner-occupied to increase and therefore hurt new starts.
Unless we see hyperinflation where prices increase and wages do too, we will probably see rents flatten or even decrease as demand goes down.
No money means no demand - don't need to be a Pulitzer winner or possess a crystal ball to see that coming.
So the answer will be the hustle. Those with better marketing and better units will win, while those with junk units and no marketing will fail. I think this hurts a bigger operator more than it might a small guy who knows how to hustle.
For me I plan to make things worse (and better) on myself by requiring first/last/damage up front in all cases. This will decrease my renter pool significantly but that's actually the goal, believe it or not. It's how I plan to survive long-term in the hood. But I can do that, because I'm small and don't have 100/1000 units to fill. My strategy is long-term, financially stable, property preserving tenants - they are out there and I intend to go get them. I intend to offer emergency credit with respect to the last months rent I hold, so a renter can access that money if they hit a bump. I expect that service to offset the pain of paying last months up front. A bit of a hard sell, but frankly I hope it catches on. The damage deposit insurance companies that are coming around might be game changers too.