fwiw the housing price index in New York has actually seen lower increase since 2000 than the rest of the country

https://fred.stlouisfed.org/series/NYXRSA

https://fred.stlouisfed.org/series/CSUSHPINSA

The same is also true if you use 2005 or 2009 as your start date. I agree there is variance in theory, but in practice it has been about the same as the national.