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In contrast to a Ponzi scheme, dependent upon an unsustainable progression, a common financial arrangement is the so-called "pay-as-you-go" system. Some private pension systems, as well as Social Security, have used this design. A pay-as-you-go system can be visualized as a pipeline, with money from current contributors coming in the front end and money to current beneficiaries paid out the back end.
If the demographics of the population were stable, then a pay-as-you-go system would not have demographically-driven financing ups and downs and no thoughtful person would be tempted to compare it to a Ponzi arrangement. However, since population demographics tend to rise and fall, the balance in pay-as-you-go systems tends to rise and fall as well. During periods when more new participants are entering the system than are receiving benefits there tends to be a surplus in funding (as in the early years of Social Security). During periods when beneficiaries are growing faster than new entrants (as will happen when the baby boomers retire), there tends to be a deficit. This vulnerability to demographic ups and downs is one of the problems with pay-as-you-go financing. But this problem has nothing to do with Ponzi schemes, or any other fraudulent form of financing, it is simply the nature of pay-as-you-go systems.
Social Security is and always has been either a "pay-as-you-go" system or one that was partially advance-funded. Its structure, logic, and mode of operation have nothing in common with Ponzi schemes or chain letters or pyramid schemes.
Superficially, these critics have a point, and there is a parallel between Social Security and a Ponzi scheme. But on a fundamental level, they are very wrong, and it's worth explaining why.
First, the parallel. Social Security taxes current workers to pay Social Security benefits for current retirees. In other words, the new entrants into the Social Security system, the young workers, pay off the previous entrants, the older workers. And despite the fact you have a Social Security "account", there is no necessary link between what you paid into the system in taxes, and what you receive.
That's very similar to the structure of a Ponzi scheme, where new investors pay off the original investors. As long as enough new 'victims' are brought into the scheme, it keeps growing and growing. But when the new investors runs out, the Ponzi collapses. Analogously, the slowdown in population growth puts pressure on Social Security finances.
But there is one enormous difference between Social Security and a Ponzi scheme: Technological change. Over the past century, new technologies have enabled the output of the country to grow much faster than its population. To be more precise, the U.S. population has more than tripled since the early 1900s, while the U.S. economic output has gone up by more than 20 times.
This long track record of technology-powered growth has enabled the enormous rise in living standards in the U.S. and other developed countries. In fact, this increase in productivity -- output per worker -- is the key fact which gives us our way of life today.