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Zero percent interest rates forever


Noah Smith asks what would happen if the Fed kept interest rates at zero forever. Specifically:
Suppose that the Fed targets only one interest rate, a short-term nominal interest rate, and that its only tool is Open Market Operations (it cannot provide any "forward guidance" or communicate with the public at all). Suppose that at date T, the Fed decides to keep the interest rate at zero in perpetuity, and remains unwaveringly committed to this decision for all time > T.
He asks this because Nayarana Kocherlakota, head of the Minneapolis Fed, once said, somewhat counter-intuitively, that over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation. This seems odd at first blush because we've been conditioned to assume that low interest rates lead to inflation, not deflation.

I'm going to try and give an answer that financial types will understand. The spoiler is... over the short term we'd have inflation, but Kocherlakota is probably right that after some time passes, an artificially low federal funds rate will lead to a steady deflation.

Imagine that you're an investor who can hold either deposits at the central bank or units of some durable good. In order for these two assets to be willingly held by both you and your fellow investors, each must provide attractive returns. If one of these assets provides excess returns, arbitrage dictates that you'll all try to switch to that asset until those excess returns cease to exist.

A bank deposit's return can be decomposed into an interest component, expected capital appreciation (or depreciation), and a liquidity yield. Liquidity is a special benefit that a deposit provides since it more marketable than most assets. The durable good, assume it costs nothing to store, provides a return in the form of capital appreciation (or depreciation), but no interest and a liquidity yield that is so minimal that it may as well be nothing.

At the outset, the returns on the two assets are already equal. But the central bank suddenly lowers the interest component of the return it pays on deposits to nothing, catching the investment community by surprise. As an investor you're distraught. The deposit you held just prior to the announcement yielded, say, 5%, and now it yields just 0%. You'd like to sell it for the durable good, since the return on the durable good (which is composed, say, of expectations of 10% price appreciation) is superior. But investors holding the durable good won't sell to you, simply because the return they require on the 0% deposit must be similar to the return on the durable good they already own. And it isn't.

To convince them to accept your 0% deposit for their good, you must increase its return. You can do this by increasing the expected capital appreciation provided by the deposit. By marking down the current price of the deposit relative to its expected future price, you provide your trading partner with the necessary potential capital appreciation. Whoever buys the deposit can be sure that even though it yields an interest rate of 0%, it will provide a commensurate capital return of 5% or so.

In knocking down the market price of the deposit, you've caused immediate inflation. The purchasing power of money (the deposit) has fallen such that you can't buy as many durable goods with it as you could before. At the same time, you've cleared the stage for future expectations of deflation. That's because in low-balling the offer price for your deposit to attract buyers, you've increased the expected capital appreciation provided by the deposit. You've caused inflation in order to promise deflation.

Maybe the entire process happens immediately. But economists like to divide things into the short and long run. In the short run, all you'll see is inflation as the market gropes for a new and lower clearing price for deposits. At first, perhaps, most investors think that the central bank will only keep rates at 0% for a year and then set them back at their normal rate. But when the next year comes and the bank surprises the market by keeping those rates at zero, once again you'll have to rapidly lower the price of your deposit so as to provide potential deposit buyers with enough capital appreciation to compensate for the disappointing yield on deposits.

This yearly pattern of lowering the price you offer on your deposits continues until the market is no longer surprised by the central bank's intentions to keep rates at 0% for eternity. Only then will the inflation end. Deposits, which by now have been bid down to some terminally low level, will slowly and steadily appreciate. This is the "consistent deflation" that Kocherlakota describes.

There is one interesting caveat here. I started out the example by pointing out that one component of a deposit's return is its liquidity yield. Because the market puts a premium on liquid assets —a liquidity premium, so to say —deposits and other liquid assets can provide lower interest rates than not-so-liquid assets.


But if deposits (or any other money-like object) are constantly plunging in value, they cease to be attractive as medium of exchange. In general, people prefer to transact with relatively stable monies. Thus each time you mark down the deposit's value, its liquidity premium deteriorates as the market searches out for other assets that can serve as better mediums of exchange. With the decline in its liquidity yield, the overall return from holding deposits declines even further. This inferior return can only be compensated by a promise of more capital appreciation ie. yet another fall in today's market price relative to expected future prices. This process feeds on itself as the falling value of a liquid assets renders it less liquid which causes it to fall further in price. At some point, the deposit risks being demonetized.

What comes first? Will the deposits reach a terminally low price from which they commense their rise? Or will they become demonetised and valueless? What about the assets that back deposits... might these provide some lower limit for the price of a deposit, even if it pays 0% loses its entire liquidity premium? Fun questions, but I'll leave those for someone else.


Related blog posts:
Karl Smith here and here, and Andy Harless here.
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