When interest rates get quite low, the normal basic tool of monetary policy — lowering a targeted interest rate — becomes less effective. At low enough interest rates, simply hoarding any new money put into the system becomes inexpensive; this is the liquidity trap, where the central bank tries to flood the system with more currency and that extra currency heads promptly to mattresses.
Even injecting extra money into the system, once short-term interest rates are zero, requires something other than an interest rate target, but, as Milton Friedman noted and Ben Bernanke quoted, dropping enough money from helicopters ought to eventually trigger inflationary expectations. More fuel efficient and orderly is a process of quantitative easing, or simply a partial monetization of the national debt; these should have similar monetary repercussions. Once inflation is expected, the cost of putting money under a mattress instead of looking to purchase real goods (possibly investment goods) becomes higher.
Part of the problem is that real investments lock up resources for long periods of time; if short-term rates go to zero, leaving normal monetary policy feckless, long-term rates may still be high enough that investors are insufficiently confident that they can produce real returns in excess of the opportunity cost of capital. The mattress may be a less interesting destination for long-term savings than treasury bonds are; monetary authorities would rather neither be as attractive as real investment. Very long term real interest rates should not go negative; one can imagine fantastic projects — an oft-cited example would be to fill in some patch of water with land — that ought, given enough time, to produce returns that exceed the cost. If long-term nominal yields on treasury debt can be pushed down, and inflation expectations can be pushed up, such projects — or more likely ones — should start to attract investors.
One simple way to do this would be for the federal reserve to go about its quantitative easing by purchasing long-dated treasury debt, inflating the currency supply while reducing the relative attractiveness, even in nominal terms, of those modes of saving. The Federal Reserve (in the United States) could do this; alternatively, the same result should come from the Treasury simply shortening the duration of its debt issuances, effectively — relative to its previous policies — selling short term debt (which the fed has pinned to a zero yield) to buy up its own long-term debt. Much of the federal government's recent emergency borrowing for the recent programs to shore up the banking sector has taken the form of bills maturing in the next year, with most of it considerably shorter than that. I wonder, if one looks at the usual impact of monetary policy, whether including the duration of the federal debt, or something like that, adds any predictive value, particularly in times of low interest rates.