The intuitive answer is no, right? I mean, who would consign himself to an investment that underperforms socking money away in the mattress? And furthermore, what possible incentive could there be to holding such an investment until it matures? Think about it: you cash out the t-bill before it fully vests, and you avoid a blunt-force trauma. Whereas at month 11, you disinvest without realising a negative-interest sting, at month 12, tough luck, hombre.
But that sort of misses the point, I think. The fed's current positive interest rates aren't horribly attractive to consumers either—there are much better deals out there than our 3-year treasuries presently underperforming inflation by half a percent. And they aren't meant to be: they exist to give investors a fail-safe—a fail-safe which, in this economy, is the least stimulative thing an investor can do with his money. So, they're not priced to sell. They're not meant to sell. They're priced to be there for you if, in your starkest throws of desperation, you're absolutely forced to seal your money in a vault. They provide safety, security. They are, essentially, an asset-of-last-resort. If t-bills with negative interest rates would still serve this function, they become at least a theoretical possibility.
Thus, a couple of contexts in which you could see negative interest rates:
First, the obvious: in a different world, where, say, the face value of fiat currency actually deteriorates by a predictable amount, a negative interest rate would be the equivalent of, well, a non-negative interest rate.
Second, more titillating: say there were non-negligible costs associated with keeping money in savings accounts. This could owe to any number of things. Maybe the government imposes a tax on savings. Maybe the maintenance of savings accounts becomes unduly expensive, with banks ending up having to charge mandatory fees. Maybe savings accounts suddenly involve risk (like in a world without FDIC insurance). It really doesn't matter. What's important is that, suddenly, the mattress scenario becomes all too real. You literally have to stuff your mattress to retain your currency at face value. In that scenario, you might elect for a safe—because, after all, mattress-lining itself would involve risk. In fact, it'd involve a lot of risk in that world! If everyone's incentivised to do it, and a good number are, that's a lot of hot action for petty thieves! And there we have the rub. Safes, closed-circuit TV, ADT home-invasion deterrence—none of those are free. In fact, it might end up being economic to just bite the bullet and use the bank anyway. Or, you could buy a government note! And in this alter-world, government notes could easily sell at subzero rates.
Third, most titillating of all: it's not inconceivable that in some alter-world, government bonds themselves could end up becoming the preferred medium of exchange. It's true that this is a conceptually difficult world to envision. Let's face it, bonds are always nonetheless denominated in the base currency. But let's dig deeper: could we not appraise dollars by their purchasing power in bonds in the same way we appraise bonds by their FMV in dollars? That perception shift is key, I think. Because, once we cross that rubicon, we find worlds that permit what's otherwise truly counterintuitive. In this example–where we have bonds that are our main instruments of transaction–their originator (the government) would presumably have some degree of freedom in pegging them at an ever-diminishing rate against the dollar. “But wait,” you say, “that can't be! Why wouldn't they be immediately converted back to dollars every time they're earned? Today's single bond could buy me two through the conduit of a dollar! Why wouldn't there be an instantaneous transition back to the dollar economy we began with?!”
I told you this world would be counterintuitive.
Basically, this world would be peculiar in one very key respect: something would be stigmatising the dollar. And this is where the hypo veers into the world of sci-fi. To take one possibility, maybe the government begins implanting dollars with RFIDs. Since apparently triangulation to pinpoint the location of cell-phone users doesn't require a warrant, that move, which would expose bearers everywhere to a higher risk of intrusion, would definitely decrease their value. And taking that as a starting point, the dollar's fall off in use would be precipitous. Since some vendors would outright refuse to use them in trade, no one would know how fungible their dollars truly were. That would plunge demand; that plunge would decrease dollars in circulation; that decrease would spawn an ersatz currency (like bonds); that ersatz would then dominate everyday transactions; and eventually you would get the dollar ending up relegated to a niche commodity. That dollar, in such a world, ends up being a government dividend to agree to be surveilled. Creepy. Very creepy. But also a cool illustration of my medium-of-exchange-shift scenario.
And here ends another instalment of our quirkiness.
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