I think it greatly depends.  With the new rent control laws Gov. Nusiance passed and with the talks of vacancy taxes (in the Bay area), there may be incentive for landlords to sell and move their properties out of state. 

I think whatever happens in the sales market will be duplicated in the rental market. 

If I had a vacant property, I'd either rush to get it rented or I'd pull it off the market until this blows over.  Really all depends on what the rents are now, what direction they're going and where they are likely to be in 3 months time.  I'd hold it off if rents were dropping and I thought I could get more in June/July (which typically I can in the summer/school moving months).

There is seemingly no end to predictions,  questions about predictions as well as implications and more beyond forecasting.

I have no idea, and all I want is for this to be over!  

Rentals are in strong, unrelenting demand as people need a place to stay

if it's priced properly, it never lingers on the market..... rentals, homes, condos or multi's.... price them for the current market.

People need to move, they move. I have a rental on the market right now it's slow, but I have client needing to short term rent so I have time to help her find a home and she's actively searching. I'm experiencing both sides of the coin. Ultimately, only the landlords or an NAR survey can share that data, hard to track otherwise.

Rentals will continue to grow in popularity as people lose faith in the market.

Our local Halifax-Dartmouth hasn't seen such low vacancies rates in decades ( under 1% over the past year ) driving rents up and more appartment buildings being built. 

I live in the bay area ... only time will tell how this all plays out and impacts the bottom line in real estate in general. 

honestly, I prefer to sell homes so I don't care about rentals. Maybe in your neck of the woods it's important but not here.

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