This week, New York City started enforcing new rules cracking down on short-term rentals — think Airbnb, Vrbo and other booking platforms. The law ramps up regulations for anyone hosting a short-term rental in New York, including a requirement that hosts register their listing with the city.

That means hosts will also have to adhere to strict rules. They’ll have to stay on site during each booking. They’ll have to keep the entire apartment or house accessible to guests.

Airbnb has called the move a “de-facto ban.”

City officials have argued that short-term rentals like Airbnb listings reduce the amount of available long-term housing. And less rental supply means higher rents. But the link between the amount of short-term rentals and housing affordability isn’t exactly clear.

A few years ago, Davide Proserpio, a marketing professor at USC, looked into how an increase in short-term rental listings can affect housing costs overall.

“We basically look at most of the United States and try to link the growth in Airbnb listings with both house prices and rental rates,” Proserpio said.

Proserpio and his co-authors found that yes, there is a relationship between an increase in Airbnb listings and rising rents.

“Basically, we find that Airbnb contributes to a fifth of the actual rent growth, in a zip code, in a year,” he said.

But the only way that an increase in short-term rentals might reduce the supply of longer-term housing “is if someone is taking a unit off the long-term rental market, and running it purely as an Airbnb,” said Arun Sundararajan, a professor at New York University and the author of “The Sharing Economy.”

He said in many cases, especially in New York City, listings on sites like Airbnb are posted by people who live in the same unit. “They’re just renting it out on the side during the days that they’re not there, or they’re renting out a spare room.”

Sundararajan said cracking down on short-term rentals like that might not have a big impact on the supply of long-term rental units. “Because it’s not like there’s some special stock of housing that is running exclusively on Airbnb that will suddenly be released to the market,” he said.

Sundararajan said if cities want some other ways to increase the supply of long-term rental housing?

All those empty commercial offices would be one place to start.