You could live in Panama tax-free, even as a U.S. citizen (that is to say, paying no income tax either in Panama or in the United States).
However, some work and preparation are required. You have to set yourself up properly.
If you’re retired, you won’t pay taxes on retirement income you bring into Panama or on any dividends or interest income earned outside the country. But, you would still pay taxes in the United States on the dividends and interest income.
And, depending on the source of the retirement income, you’d pay the same tax to the IRS as you would if you lived in the States (although, if you live in a state that taxes retirement income, you’d avoid that tax by moving to Panama).
To live completely income tax free in Panama as a U.S. citizen, you must have a business generating earned income for you as an individual and that income must be derived from outside Panama.
Panama taxes residents on income earned in the country only, so your non-Panama business would pay no taxes in Panama.
And, assuming it is a business where you can legitimately claim that you are earning your income outside the country, your individual income wouldn’t be taxed there.
Typically, this means a consulting or an Internet-based business.
If you start an active business in Panama, with sales in Panama to Panama residents, then that income would be taxable in Panama, as would any related personal compensation you receive.
In either case, your salary up to the annual Foreign Earned Income Exclusion limit (US$101,300 for 2016) can be excluded for U.S. income tax purposes. The key is that it be truly earned income.