Italy calls it la dolce visa.
If you are interested in moving to Italy and you would be bringing a ton of money with you, then the Italian government has an offer that might be appealing to some very high-income expatriates: a maximum flat tax of 100,000 euros per year, irrespective of income, so long as that income is not earned by working a job in Italy. Earn 1 million euros? Pay 100,000. Earn 100 million euros? Pay 100,000. Italy here is making a bid for the sort of affluent taxpayer who might be interested in Switzerland’s “forfait” system, in which noncitizens residing in Switzerland have the option of using their annual housing expenditures rather than their income as their basis of taxation — an attractive option for thrifty billionaires."
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