If you are talking about Manhattan, they won't really go down as a whole. The vacancy rate here is way too low. Rents won't increase as much, but they don't typically go down significantly. It is a bit slower right now so some landlords will do the following:
Offer one month free rent, Offer to pay the broker fee (or part of it), be more lenient on rules (such as pets), negotiate a little on the rent.
They are more about incentives, so they aren't lowering the actual rent, thus de-valuing their product.
Brooklyn & Queens may be different though. I only focus on Manhattan.
Let me know if you need assistance.
Scott
646 637 6377