This happens in the UK, to an extent. Council tax (For a 3 bed flat in a good location, £2000/year) goes up, though not exponentially.

> You can be charged an extra amount of Council Tax (a ‘premium’) if your home has been empty for 2 years or more.

> You can be charged up to 4 times your normal Council Tax bill if your home has been empty for 10 years or more.