Chile is an exception. What Chile did was quite ingenious. While retaining government's role in the supervision of the system, and assurance of its solvency and stability, all funds were diverted to private, individual investment accounts. In other words, money does not flow to the government, the people invest it in their own special retirement accounts. But suitable investments are chosen by the people, and by investment companies chosen by them.
Participants are free to switch investment companies.
As a result, the recipients of people's money know that they must earn good rate of return on these funds. And they have. Indeed, Chile has become an example for the rest of the continent. Similar reforms have been introduced by Argentina, Colombia, Peru, and recently Mexico, Bolivia, and El Salvador. One may indeed wonder if the next zone of economic miracle will not be Latin America, in contrast to the current admiration for the achievements of Southeast Asia.