That's pretty much the definition of a Ponzi scheme. About the only difference is that the Government doesn't even pretend to invest in anything. They just count on being able to take enough taxes from this generation of workers to pay the last. From http://www.smithsonianmag.si.edu/smithsonian/issues98/dec98/ponzi.html:
[Charles] Ponzi claimed to have found a way to profit by speculating in international postal reply coupons — a form of prepaid return postage for use in foreign correspondence. After he had paid off his first round of investors, Darby relates, he scarcely had to repeat his story. All that anyone cared about was that he paid 50 percent interest in 90 days. Later, he shortened the investment period to 45 days.
In no time, the money was rolling in. "At the height of his success, Ponzi had offices from Maine to New Jersey." The problem, Darby explains, was that there was no actual investment going on; the only activity was the shuffling of money from new investors to old ones. This kind of swindle, borrowing from Peter to pay Paul, is also known as a pyramid scheme or — since 1920 — a Ponzi scheme.
"Half-a-dozen banks crashed in the aftermath of Ponzi's fall," reports Darby, who is currently working on a screenplay about the charming con artist. "His note holders received less than 30 cents on the dollar." But, she asks, was Ponzi's proposition, which snared nearly 40,000 would-be millionaires, "any more absurd than the promise of a $59,000 loan in exchange for $20 sent to a post office in Las Vegas?" Pitches like this one, says Darby, are now popping up on the Internet, and as long as people are more worried about their profits than their principal, Ponzi schemes will continue to part fools and their money.