With a 3% payroll deduction, someone with $50,000 of real annual earnings during his working years could accumulate enough to fund an annual payout of about $22,000 after age 67, essentially doubling the current Social Security benefit. That assumes a real rate of return of 5.5%, less than the historic average return on a balanced portfolio of stock and bond mutual funds.
Mark Thoma points, but indicates skepticism with a (???). My skepticism runs to 4 question marks. I wrote in 2004 in an essay in favor of privatizing Social Security that what I called the "stock market scenario" is bogus.
The stock market scenario assumes that the stock prices will grow faster than the economy forever. This violates Stein's Law, which says that anything that can't go on forever, stops.
As I explained in the essay, the ratio of stock prices to GDP can be thought of as the product of the price/earnings ratio times the ratio of earnings to GDP. At least one of those ratios has to rise in order for the ratio of stock prices to GDP to rise.
The ratio of earnings to GDP varies depending on the state of the business cycle and on the tax and regulatory environment, which can affect the extent to which people use public corporations as an investment vehicle. (I mention that because some economists think that the public corporation is in decline, due to Sarbanes-Oxley and other assaults.) In any case, the ratio of earnings to GDP certainly has an upper limit.
The main reason that stock prices have risen faster than GDP historically is that the price-earnings ratio was at very low levels a hundred years ago. It has risen gradually since then, although the rise in P/E suffered major interruptions in 1929, 2000, and 2008. In any event, this ratio, too, has a limit.
This means that the growth in stock prices has an asymptote, which is the growth rate of GDP. Unless we approach the technological rapture known as the Singularity (and if we do approach the Singularity, that in itself will eliminate all worries about Social Security, Medicare, and much else), real GDP growth will be closer to 3 percent than to 5.5 percent. In which case, it would be safer to assume stock returns closer to 3 percent than closer to 5.5 percent.