Is there a zero bound? The “mysterious” world of negative nominal interest rates.

By Eric Tymoigne

Yesterday I attended a Federal Open Market Committee (FOMC) simulation at Reed College in Portland, OR. At the beginning of the simulation the President of the College jokingly asked participants to find a way to make the policy rate negative, so that we (the FOMC members) could pay banks who borrow reserves. Of course everybody in the audience laughed but let’s take a look at this more carefully: Could the Federal Reserve set the nominal federal funds rate and the nominal discount rate in negative territory?


The discount rate is the most straightforward to grasp: the Board of Governor has perfect control over the discount rate and can set it wherever it wants whenever it wants. There is no operational constraint that prevents the Board from setting a discount rate at -1%, -10% or even -100%, it just needs to announce tomorrow that this is what it is and that is it.

The federal funds rate is slightly more complicated but not that much. To set a negative fed fund rate, the Fed just has to do overnight repos on securities at a premium. If one applies this to zero-coupon securities like T-bills, the present value of a T-bill is:

P = F/(1 + d)t

P is the present value, F is the face value, d is the discount factor, and t is time to maturity (let’s set t = 1 to simplify). Usually, d is positive meaning that the Fed buys T-bills at $90 and bankers agree to buy back the next day at $95 (d = 5%). Currently, for practical purposes one can assume that d = 0%, i.e. if bankers want reserves from the Fed, they sell T-bills at $90 and promise to buy them back at $90 the next day. To set d negative, the only thing the Fed has to do is to buy at $95 and resell at $90; stated differently, the Fed just has to agree to accept T-bills as collateral at a value of $95 and bankers have to agree to buy them back at $90 the next day. In this case the federal funds rate target will be negative 5%: 90/95 – 1. If the Fed performs enough of these kinds of operations, the federal funds rate will reach the -5% target.

So there is no operational constraint on setting negative nominal interest rates.

Once one passes this first hurdle a second question that usually comes is: is it “moral,” or does it make sense, to get paid by the person who lent you money?

First, negative interest rates on borrowed money are not new. Take checking accounts, for decades you and I have been willing to deposit our funds at a bank while earning 0% and paying a fee to maintain our checking account. This still applies today if you do not maintain a certain amount of funds in your account. The same has been going on T-bills and T-bonds. For example, “from mid-1932 through mid-1942, the vast majority of coupon-bearing U.S. government securities bore negative nominal yields as they neared maturity” (Cechetti 1988: 1112). The bid price of newly issued short-term US Treasuries slightly exceeded par during some weeks in the 1930s and the 1940s (Board of Governors of the Federal Reserve System 1943: 460, 462; Clouse et al. 2000), which resulted in very small negative yields (averaging -0.05% (Cechetti 1988)). Similarly, Treasury bonds with less than a year to maturity reached a magnitude as low as -1.7%. More recently, Japanese short-term treasuries had a slightly negative yield in 1998. It also happened in 2001 and 2003 (repos) and again in 2008 (T-bills) in the US (e.g. Fleming and Garbade 2004). Those peculiar cases can all be explained relatively simply by technical aspects specific to those securities and/or the circumstances of the moment. And those rates would have gone more negative if the overnight inter-bank lending rate had been set negative.

Second, currently the Fed is advancing reserves at 0-0.25% and paying 0.25% on reserves, effectively having a negative carry on its reserve account. That’s negative interest rate by another name right there: banks can borrow reserves at a lower rate than what they get paid to hold them.

Third, does it make sense to set a negative interest rate? What makes sense is what satisfies the needs and financial considerations of borrowers and lenders. Does it make sense for you and I to pay a fee on our checking account even though the reward is negative (0% – fee) ? Yes it does because of the convenience of having a checking account. Did it make sense for financial market participants to agree on negative interest rates on T-bills and T-bonds? Yes it did given the considerations at the time. So IF the Federal Reserve thinks that it makes sense to set its policy rates in negative territory, it can do it. Not tomorrow, not with the help of others; now, and at its discretion. And it could do so not by injecting any excess reserves, but just by operating in a way it has been operating since 1914 as explained previously here.

Board of Governors of the Federal Reserve System (1943) Banking and Monetary Statistics: 1914-1941. Washington D. C.: Federal Reserve System.

Cecchetti, S.G. (1988) “The Case of the negative nominal interest Rates: New estimates of the term structure of interest rates during the Great Depression.” Journal of Political Economy, 96 (6): 1111-1141.

Clouse, J., Henderson, D., Orphanides, A., Small, D. and Tinsley, P. (2000) “Monetary policy when the nominal short-term interest rate is zero.” FEDS paper 2000-51.

Fleming, M.J. and Garbade, K.D. (2004) “Repurchase agreements with negative interest rates.” Federal Reserve Bank of New York Current Issues in Economics And Finance, 10 (5): 1-7.

6 Responses to Is there a zero bound? The “mysterious” world of negative nominal interest rates.

  1. Thank you for anwering the question I asked on Paul Krugman's piece about "shibboleths," i.e. things that everybody knows that are not founded in reality: is the zero lower bound a shibboleth?So the answer is yes, the zero lower bound is a shibboleth. Or is it? The fourth question, after "can we do it?", "is it right?", and "does it make sense?", is "how will people respond?".Will the response be smooth and proportionate, or will it be completely non-linear this time?Does anyone have an answer to that question?

  2. Thank you for the post. How is it accounted for when the Fed takes a loss? Using your example where the Fed uses a repo to pay 95 for a T-Bill and sell it for 90 the next day, wouldn't such a situation extended indefinitely would lead to a negative net-worth on the Fed's balance sheet? In an accounting sense, who takes the loss here? I know that the Fed must remit all of its profits to the Treasury, so would the Treasury have to "take the loss"?This makes sense to a degree and is an idea which dates back to the Depression. I think it was Irving Fischer who advocated a money stamp — akin to a vehicle license sticker where people would have to pay periodically to get a stamp validating their money as legal tender.The problem I have with these ideas is that they work out of the is-lm framework where the liquidity preference of money is just a function of interest rates. Making the interest rate negative doesn't remove fundamental uncertainty and I worry that penalizing money holders would just cause a run on metals and commodities without any other real effect. I can't see this having any real effect on longer-term yields since no one would believe the Fed would do this indefinitely.I am in favor of zero rates but I think negative rates is stretching it. Fiscal policy would make much more sense. And as bad as it is politically for fiscal policy, the political case for negative rates is even worse.

  3. awsome! we now have a way to give banks more free money! instead of lowering rates further the fed needs to raise them. they need to put an end to the uncertainty as to when rates will go up and do it. banks are not the only ones holding large cash reserves, google, insurance companies and others are just sitting on cash. lets move away from zero in the positive direction. the money is out there now us it. eventually firms will start to expand because if they don't someone else will and market position and strength will be lost. Rip the band aid and get back to work!

  4. No operational constraint…..but there is a practical constraint. What's to stop banks from taking their cash and sticking it in a vault? The way to bring nominal interest rates into significantly negative territory is to tax money (e.g., Silvio Gessell's century old stamped money idea).Nick R Kyto

  5. @Greg, in terms of yield curve nothing will change conceptually. If positive, the yield curve will shift down so other assets will have a negative yield through arbitrages.@de yes the NW of the fed would go down given everything else. For the board it is not a problem because it is not a for-profit institution. For the federal reserve banks, shareholders may complain and sue (one would have to look have the legal documents to get a clear idea).

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