It’s a costly pied-in-the-sky.

Mayor Zohran Mamdani and Gov. Kathy Hochul’s proposed pied-à-terre tax on luxury second homes could generate nearly $200 million less than promised – and cost New York City roughly $40 million a year in part due to an exodus of wealthy residents, according to a study released Thursday.

The eye-opening report from Democratic City Comptroller Mark Levine’s office cast doubt on the proposal’s much-trumpeted projected $500 million in revenue, noting a similar tax in Vancouver, Canada, prompted property owners to rent, sell or even live full-time in their second homes.

Levine found that the proposed policy — framed as a needed revenue booster for the city — would likely bring in closer to $340 to $380 million. He warned the loss could be even greater over time. 

“Behavioral responses to the tax — conversions to rental, primary-residence claims by relatives, sales, and possible legal challenges — introduce further variability that will only become observable after implementation,” Levine’s study states.

The findings add another complication to the affluent-targeting proposal pitched by Hochul amid a push by Mamdani to broadly “tax the rich” amid what he has called “a budget crisis of historic magnitude.”

The moderate governor and socialist mayor argued taxing luxury second homes worth $5 million or more – or roughly 13,000 across the city – would help close the Big Apple’s reputed $5.4 billion budget shortfall.

But the comptroller’s audit warned that the political odd couple’s rosy revenue estimates were based heavily on unknown factors.

Many of the pricey pads are rented to tenants by the owners, which may exclude them from the tax, and it was unclear how the levy would treat homes owned by trusts, LLCs or family members, the study noted.

Another giant question mark was how peevish well-to-do would respond to having the taxman go after their swanky Big Apple pads, according to the study.

The answer may well be found in Vancouver, which implemented a similar tax during 2017, the study argued.

Vancouver’s “Empty Homes Tax” was designed to increase the supply of rental homes by adding a levy on homes that remained largely vacant. 

The British Columbian city had roughly 2,500 homes when the tax was enacted, but the number steadily fell to fewer than 1,000 by last year, or a 60% reduction, the study noted.

Canadian officials have touted the tax’s positive affect on curbing housing speculation, increasing rental stock and raising revenue, Business in Vancouver reported. 

But Levine’s study argued the experience, along with that of a second home tax in England, showed it was prudent to assume a similar scramble to sell homes would take place in New York City – estimating a 10% revenue loss.

“The revenue loss from behavioral changes could compound over time,” he added.

Behavorial changes such as moving from the city could slash $38 million to $42 million from the tax’s expected revenue, the study found.

Turning the properties into rentals could lead to an $88 million to $133 million loss in projected revenue, according to the report.

Fears that an added wealth-targeted tax could trigger an exodus of rich New Yorkers predated even the most recent push by Mamdani and Hochul.

The mayor further stoked the anxiety after he filmed one of his trademark slick social media videos outside Florida-based billionaire Ken Griffin’s $238 million Central Park South penthouse, declaring “Today we’re taxing the rich.”

The stunt infuriated executives at Griffin’s Citadel hedge fund, who threatened to yank a $6 billion project from Park Avenue.

Frantic business leaders quickly pressed Hochul and Mamdani to craft a luxury home tax exemption for property owners who create 100 or more jobs.

The proposed tax’s well-heeled opponents quickly seized on the study’s conclusions.

“Comptroller Levine’s analysis is yet another confirmation that a tax on second homes would not deliver the tax revenue expected,” said James Whelan, president of the powerful Real Estate Board of New York, in a statement.

“This proposed tax also presents significant logistical issues as to how you identify second homes, value co-ops and condos, and account for changes in taxpayer behavior. If implemented haphazardly, this tax would result in less investment, less housing and less revenue for the City, State and MTA.”

Representatives for Hochul and Mamdani largely brushed off the comptroller’s findings.

“While details of the policy are still being negotiated, the governor’s proposal will generate at least $500 million for New York City,” insisted Jen Goodman, a spokeswoman for Hochul, in a statement.

Mamdani’s senior spokeswoman Dora Pekec likewise double-downed on the $500 million estimate.

“The comptroller’s report makes one thing very clear: thoughtfully crafting and implementing this legislation will do exactly that,” she said.