Evan Soltas
Mar 2, 2015

What's the Actual Lower Bound?

Economists had believed that it was effectively impossible for nominal interest rates to fall below zero. Hence the idea of the "zero lower bound." And they had a good reason for believing that. Currency pays a zero nominal interest rate -- that is, a dollar bill today is a dollar bill tomorrow, no more and no less --  and therefore any attempt to lower interest rates on bank deposits below zero will merely result in depositors withdrawing their money and putting it into currency.

Well, so much for that theory. Interest rates are going negative all around the world. And not by small amounts, either. $1.9 trillion dollars of European debt now carries negative nominal yields, and the overnight interest rate in Swiss franc is around -1 percent annually.

How can we make sense of that? If people aren't converting deposits to currency, one explanation is that it's just expensive to carry or to store any significant amount of it. Therefore, the true lower bound is some negative number: zero minus the cost of currency storage.

You're only better off cashing out your bank deposits when the deposit rate is larger than the cost of storage.  For example, if it costs you 2 percent annually to store your money in currency, you'll keep your money in the bank even if the bank charges you 1 percent annually.

That's what Greg Mankiw was getting at when he said this great line about the effects of negative nominal interest rates: "[T]he only thing you’ll generate is a demand for safe assets — and by that I mean...they’re going to be buying a bunch of safes so people can put their money in their safes rather than in the bank."

But nobody really seems to have a good handle on what the new, negative lower bound might be. So how much would it actually cost, I wondered, to store $10,000 in currency for a year?

This seems to me a decent, and admittedly entertaining, way of getting a rough estimate of a lower bound. I picked $10,000 because it's about twice the average balance of a savings account in the U.S., giving me a conservative estimate of the average percentage cost.

A safe deposit box at a bank seems to cost around $100 a year after insurance. Then the average cost of storing currency is about 1 percent annually -- maybe a bit more if you buy a safe.

Yet, rather obviously, having $10,000 in a deposit box is not the same thing as having $10,000 in a bank account. You can spend from your bank account using a credit card, or you can go to an ATM and withdraw cash. You can't do the same with a safety deposit box.

How much is that convenience worth? It seems like a hard question, but we have a decent proxy for that: credit card fees, counting both those to merchants and to cardholders. That's because the credit-card company is making exactly the same calculus as we are trying to make -- how much can we charge before we make people indifferent between currency and credit cards? The data here suggest a conservative estimate is 2 percent annually.

So my rough guess is that the average depositor is probably better off keeping their money at a bank up to a nominal interest rate of -3 percent annually. (This is also what other people said, in an extremely informal poll, would be the most they would accept.) But, from an economic perspective, what we really care about is the marginal depositor -- that is, who has the lowest cost of currency storage?

And here, I am at a loss. Are there are efficiencies of scale in currency storage? What does the marginal cost curve for currency storage look like?

Would banks, in response to persistently negative nominal interest rates on deposits, increase the amount they keep in currency in vaults? Or would investors start bidding up the price of any asset that can function as a store of value and try to find ways to make their holdings function more like liquid deposits? Do companies start doing weird things with inventories and working capital?'


Further reading:

Paul Krugman and David Keohane have both weighed in. Krugman argues that, since the marginal holder of currency is only doing it as a store of value, the convenience doesn't matter to finding the true lower bound. Keohane reviews some useful ECB numbers and discussion from Barclays -- we're all ending up in the same range of numbers.

Update (2/24/16): I would recommend Matt Rognlie's job market paper, "What Lower Bound? Monetary Policy With Negative Interest Rates" on this topic. I think it much better characterizes the economics of negative interest rates -- semi-elasticities! -- than the "bound" discussion of this post.