Rodenticide is probably cheaper. Dogs have to be fed, watered and cared for.
Or cats. That seems to be the age-old solution to the problem. Barn cats are wildly efficient vermin murder machines.
Some of the rats in NYC are quite big, I'm not sure cats would go for them.
Oh our old barn cat would come out of the barn door carrying a dead rat so large she couldn't hold it off the ground.
Yeah, my cat's literally dug up moles before. I know NYC has mutant rats, but I'm sure it's not difficult to find a cat adventurous enough.
I have seen a junivile cat do the same she was hardly out of kittenhood and took a rat bigger than her.
Yeah, at the right age, a juvenile cat is a pound and a half of death, and it isn't shy about showing you. I think later on in their lives cats are a bit more secretive, especially about prey they want to eat.
If you don't feed a cat much, it'll go after just about anything rodent-like that it thinks it can sink its teeth into.
[Edit: also bird-like, which is why a number of eco-friendly people aren't too fond of free range domestic cats in many different parts of the world]
Our old barncat just hunted the ratlings. Tenderer meat, you know.
You will need a lot of dogs. Rats can breed like crazy if they have enough food.