How to Reform Social Security To the Chilean Model

Here's how they do social security in Chile according to Cato.org. Workers are given the choice as to whether they would like to stay in a pay-as-you-go plan (like we have in the U.S.) or a new system in which they can put their entire payroll tax into a retirement account. That way, they can benefit from compound interest.
93% of Chileans elect to participate in the new system. It's run by 15 private companies.
Here's how the country's former Secretary of Labor, Jose Pinera explains what has happened:
We guaranteed benefits for the elderly -- we told those people who had already retired that they had nothing to fear from this reform. We also told people entering the labor force for the first time that they had to go to the new system.
Today, all workers in Chile are capitalists, because their money is invested in the stock market. And they also understand that if government tomorrow were to create the conditions for inflation, they would be damaged because some of the money is also invested in bonds -- around 60%. So the whole working population of Chile has a vested interest in sound economic policies and a pro-market, pro-private-enterprise environment.
Not only that, but the savings rate in Chile went up from 10% to 27% of GNP. There's no payroll tax, and with full employment and that great savings rate, the economy has blossomed.
The graphic below represents the Chilean Model: