Wednesday, December 31, 2008

Zero Is Not A Lower Bound For Interest Rates

In recent days Paul Krugman has been flailing a model of the term structure of interest rates and the liquidity trap based on the idea that there is an absolute lower bound of zero percent for nominal interest rates. This may have been true in the distant past, but it is not true anymore. We have seen numerous episodes of negative interest rates, with several outbreaks in the last few months, including on the actual federal funds rate and on 90 US Treasury bills, as well as on Japanese interbank rates in the late 1990s, when their target rate was at 0%. A not widely known episode that went on off and on between August and November of 2003 was in the repo market, which used to be used by the Fed for open market operations, as reported in a New York Fed study from April 2004 by Fleming and Garbade, accessible at It has only been convention and a left over belief like the old religious view that negative numbers did not exist that has led so many economists and others to think that zero is some absolute lower bound on interest rates. We may well see that bound breached more seriously and frequently in the months ahead, if the economic crisis continues to deepen.

The prejudice against believing in negative interest rates, sometimes viewed as the "price of time," is not unrelated to the long-held opposition to the idea of negative prices. We see them regularly in real life, but they often get assumed away by defining paying for the removal of something (such as excess water) as a different market with a positive price from providing the same good when we want more of it (water for irrigation), even when the same activity does both things (building a dam with an irrigation system). Negative real estate prices often are associated with environmental problems, such as kaput coal mines leaking toxic waste that the owner is responsible for paying the cleanup of. In some countries, brides have a positive price while in some grooms do, although as Michael Perelman recently reported, Herodotus tells us of bride auctions in ancient Babylon where some are sold for positive and some for negative prices in the same auction. The great efforts by the general equilibrium theorists to avoid negative prices (not a problem for Walras) were a waste of time, as were all the huffings about negative surplus value in the Sraffian debates. Time to get over it, especially if we start seeing widespread negative interest rates.

Hidden conclusion here.


Anonymous said...

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David Beckworth said...


Just to be clear, are you saying nominal interest rates do not have a lower bound of zero?

Also, the link to the NY Fed does not seem to work.

Martin Klein said...

Adding to the previous comment: you are not making a clear distinction between nominal & real interest rates. Real interest rates have of course been negative before (in the US & elsewhere), with generally negative consequences for resource allocation. Nominal interest rates are widely thought to be be bounded at zero (because of the obvious alternative of holding currency at zero interest) but the New York Fed article that you are citing shows that this need not hold true for certain repo deals. said...

I apologize for having put up a bad link and thank Martin Klein for getting it properly done.

To all of you, I am talking about negative nominal interest rates, not negative real ones, which are trivial, and have clearly existed frequently, although I note that in theory they are not supposed to exist. If they are not supposed to exist, but do, why should not negative nominal ones also?

In the case of Japan in the late 1990s, those were positive real rates, but negative nominal ones. It is a bit unclear what the rate of inflation in the US is right now, so the negative nominal ones in November might well have been positive real ones, but I think that in September we still had a positive rate of inflation, so the negative nominal ones then were negative real ones also, as were the ones in the repo market in 2003 reported in the linked study.

I also note that I know through a private source that during the day on December 31, 1986, the last day of the old tax code, that the federal funds rate varied during the between -1/2% and 18% nominally, although it ended the day about where it started at some boringly positive single digit rate. It was hearing of that over 20 years ago that made me first aware of this possibility, and it may be that this event was the first time that it ever happened.

Regarding the cash alternative, I note that we are already in a weird situation, given that the Fed is paying 1% on deposits in it. Why on earth are we seeing any interest rates below 1%? Jim Hamilton at econbrowser has provided some possible explanations, but I must say that I find them pretty tortured and complicated.

Regarding the cash question, I note two aspects of this. One is "cash in the bank." Well, the bank can fail, and if the FDIC is ultimately backed up increasingly shakey looking US Treasury securities, although the argument for their rates being negative is their supposed relative safety, then "cash in the bank" may be viewed as riskier than holding US Treasuries, even at negative yields.

The other matter is "cash in hand." Well, obviously there are costs of maintaining that securely, a good vault or lockbox or whatever. Heck, the dangers of holding cash in hand is one of the more primitive reasons for why banks arose in the first place.

The bottom line argument is that in a world where virtually all assets appear to be sharply declining in value, or threatening to do so, then one may well be willing to pay a bond issuer who is more certain of repaying the principal than others to promise to do so. Perfectly rational.

Again, I think much of what is involved with getting all bent out by the idea of negative interest rates or prices is a primordial prejudice, much like those church fathers who alternated between denying the reality of negative numbers and declaring them to be demonic. In the end it was accounting and economics pressures that changed their minds, as the rise of double entry accounting in Northern Italy also brought in the Arabic numerals, and the reality of negative balances in accounting made negative numbers seem more real, if not always all that pleasant.

knzn said...

I quite disagree with the substance of what you're saying, although it is of course true that slightly negative nominal interest rates have existed.

First of all, the analogy between negative prices and negative interest rates is a bad one. Of course there are negative prices, because there are things we would rather not have, and we are willing to pay not to have them. And there are things we would really, really prefer not to have, and we are willing to pay a lot not to have them. The price of a beating is quite negative, and that's how thugs are able to extort money: by selling beatings for a negative price. And of course there are some things that some people would rather have and others would rather not, and the price can be either positive or negative depending on supply and demand.

Can the use of money be one of those things that people would prefer not to have? To a tiny extent, yes. There are certain risks and inconveniences associated with holding large quantities of wealth in the form of money, so the use of money can have a negative price (a negative nominal interest rate).

But this leads to two questions. First, can the risks and inconveniences associated with holding money be large enough to make the interest rate significantly negative, rather than just slightly negative? Second, even if the interest rate does become significantly negative, does that make any economic difference outside the specific money market?

If the money that we're talking about consists only of bank reserves, the answer to the the first question is clearly "no." The risk and inconvenience of holding a deposit at the Fed, relative to holding a treasury bill, is insignificant. If the money includes currency, then it is conceivable that the rate could go significantly negative, but I rather doubt it. Currency can be held under lock and key -- many locks with many keys, for diversification -- and the cost, while high perhaps in absolute terms, will be small relative to the amount of money involved, unless that is also small, in which case FDIC-insured bank accounts are available that are not much more risky, and clearly are more convenient, that Treasury bills. In any case, the Fed is not in the business of creating currency, except to the extent that the market demands it. It is the policy of the Fed to accommodate changes in the quantity of currency demanded. Ordinary monetary policy operates by changing the quantity of bank reserves, which cannot have a significantly negative interest rate.

But suppose the rate did go significantly negative. Would that be any different, in terms of economic implications, than having a zero interest rate? I submit that it would not. The option of holding wealth in the form of money is still available, as it has been all along. When the T-bill rate is zero, risky assets, such as commercial paper, pay a certain premium over money, which reflects the higher risk associated with such assets.

Although the (hypothetical) market interest rate is negative, the vast majority of market participants are people who would still prefer money to T-bills even if the interest rate were slightly positive. The rate becomes negative only because we have moved so far down the money demand curve that the few who prefer T-bills have become the marginal demanders of money. Those people have an extreme preference for safety and are unlikely to have held any risky assets (let's say, commercial paper) in the first place. For those who were actually demanding commercial paper, the choice is still between a safe, zero return asset (which used to be called T-bills and is now called money) and a risky asset. Since the quantity of neither asset has changed (money replaced T-bills, leaving the total quantity of that safe asset constant), the change has no effect on the market for commercial paper. The only market that is affected is the T-bill market, and the only effect is that the government gets a slight subsidy for borrowing -- which might encourage fiscal policy but has little direct effect. said...


It may be that the most important effect is the one I opened my post with, that all the multifarious stories about financial markets and the term structure that rely on an absolute zero bound on nominal interest rates is hogwash, and it is a huge literature. I think we have not seen negative rates in the past because of this primordial belief they are impossible. But that is now clearly not the case. So, we may indeed see more of this.

I do not think it is necessarily a bad thing. You are probably right that it will be hard to maintain deeply negative rates for a long time, given cash, but the possibility is there. A real breakthrough would be the Fed, or some other central bank, actually setting a negative rate target. The Japanese central bank could have done this, probably, for awhile in the late 1990s, and gotten away with it. It would accommodate an easier fiscal policy, if it could be pulled off.

Regarding switching to holding cash, I think there are severe limits to this in our current economy. After all, M0 is less than 5% of M2. For people to switch to cash would involve a major headache.

Again, I note that although you began with "I quite disagree," in the end you admit that negative nominal interest rates are quite possible, even if you think there are serious limits to how negative they can get.

Happy new year, everybody!

Anonymous said...

There is a difference between what is possible and what is sane. There is nothing that prevents the Fed from setting a negative interest rate. However it is also INSANE for the Feb to set a negative interest rate because everyone will be taking their cash out. The Fed does not have enough paper money in circulation for this to happen.

If you want to see what a 'Negative Interest rate' banking system looks like, look up Zimbabwe.

Barkley Rosser said...


Interest rates in Zimbabwe are in the millions or billions of percents, somewhere behind the latest something quadrillion percent or whatever inflation rate, with the real interest rate at, as if it meant anything, oh, a hundred or maybe a thousand percent. Not relevant, a.

I am not forecasting or expecting any central bank to actually do what I just suggested. However, I note that the recent Fed move to lower its target rate to 0-.25% could easily be described as insane, given that the Fed itself is paying well above that for people to put money in the Fed. This is indeed insane, much worse than anything I am talking about.

Why did the Fed move the target rate to an insanely low level? Because the actual rate has been sitting down there for some time. If the actual rate not only goes negative, as it has on occasion, but stays there, well, that will be the setup for a central bank to set a negative target rate. It can happen, and maybe this year.

Happy new year, everybody...

Anonymous said...

I believe you may be out of date with respect to the interest rate the Fed is paying on reserves.

Sorry, I don't have an immediate source.

Anonymous said...

After a little digging, here it is:

Press Release
Release Date: December 16, 2008

For immediate release

The Federal Reserve on Tuesday issued a technical note concerning the calculation of interest rates on required reserve balances and excess balances for reserve maintenance periods ending December 17.

On Tuesday, the Federal Open Market Committee (FOMC) established a target range for the effective federal funds rate of 0 to 1/4 percent, and the Federal Reserve Board established the interest rates on required reserve balances and excess balances at 1/4 percent for reserve maintenance periods beginning December 18.

Previously, the interest rate on required reserve balances had been set as the average target federal funds rate over the reserve maintenance period, and the interest rate on excess balances had been set at the lowest target federal funds rate over the reserve maintenance period. For the reserve maintenance periods ending December 17, the interest rates on required reserve balances and excess balances will be set based upon these previously existing formulas and will use the 1/4 percent upper bound of the FOMC's current target range in the calculations for the last two days of the period. As a result, the rate paid on required reserve balances for the maintenance periods ending December 17 will be based on the 1 percent target rate that prevailed through December 15 and a 1/4 percent rate for December 16 and 17. The rate of interest on excess balances for the reserve maintenance periods ending December 17 will be 1/4 percent.

Barkley Rosser said...

OK, so the Fed's interest rate is now .25%, which remains above the target fed funds rate, which is zero to .25. The more important point is that before the last change both the target rate and the Fed's own interest rate were 1%. However, their hand has been forced by the fact that the actual federal funds rate was running around .25%. So, this is not a matter of the Fed controlling any of this. This is the Fed catching up with what the markets have been doing.

I predict that if we ever see a negative target rate, it will be because the actual rate has gone negative and stayed there.

Michael Perelman said...

Brooke-Rose, Christine. 1971. AZBC of Ezra Pound (Berkeley: University of California Press, 1971).

227: says that Silvio Gesell's idea of Schwundgeld or perishable currency was used in the small Austrian town of Wo"rgl in 1932. The town printed work certificates to use as script money. Holders of the currency had to affix a stamp worth 1% of its value each month. The local economy revived. The French Prime Minister, Daladier, and Irving Fisher commended the experiment. The government forced an end to the experiment because the Austrian National Bank feared that the experiment would spread.

Reino Ruusu said...

I didn't know that the Fed is only paying interest on required reserves. Paying a high interest on required reserves is, I guess, a way of creating incentives for banks to generate more demand deposits, which is the only way to increase their required reserves.

I guess a company with a large monthly payroll could by treasuries with negative rates rather than risk freezing their payroll accounts at a failed bank.

Negative rates in treasuries might also have been triggered by traders that had been shorting them and would then be forced to by them back at any price at all. Widespread failures to deliver in the treasury market provides some evidence for the role of short-sellers.

knzn said...

My point is that, even though negative interest rates are possible, it is still reasonable to use the assumption of a zero floor for analysis purposes. Just as, for example, we assume that the market for exchange-traded stocks clears continuously, even though prices are actually set by specialists who can vary the size of their inventories.

As for negative targets, I don't think that would be possible for the Fed, targeting the federal funds rate. Interbank loans are clearly riskier, and probably less convenient, than deposits at the Fed. I doubt there are any lenders in the federal funds market who would be willing to lend at a negative federal funds rate.

Barkley Rosser said...


I would agree that there is a lot of resistance to negative target rates, part of due to people thinking that negative rates are "impossible," even though we have seen them, including negative actual federal funds rate in September. Much of this is sheer prejudice and superstition.

I remain amused at how much effort was spent intellectually by general equilibrium theorists to get around the possibiity of negative prices, even though we have unequivocally seen plenty of those as well. A recent curious case has been Texas wind farms paying people to take their power. Even now, grad students are taught GE as being a non-positive price solution. Hah! (Of course, I realize that negative interest rates imply very high prices of the associated assets, although that depends on the rate of inflation, and, heck, we have seen negative real interest rates for extended periods in many places, so this issue is not a problem, although the idea of the rate of interest rate as the "price of time" runs into the prejudice against negative prices).

YouNotSneaky! said...

"Currency can be held under lock and key -- many locks with many keys, for diversification"

I'm stealing that joke for my class.

But like knzn I'm not quite sure what the problem with negative prices would be in GE since the definition of "good" in the model is arbitrary. When I pay to get my driveway shoveled am I paying a positive price for clean driveway or a negative price for snow? When I buy an orange is that a positive price for food or a negative price for hunger?
A guess based on my limited knowledge would be that what matters is not actually whether prices are positive or negative but whether the set of possible prices is compact, or bounded or something. In other words some of those funkier theorems are easier to prove if a certain technical condition about boundary behavior of some function is satisfied. So what would matter is not whether it's + or - but whether, for a consistently defined good, there's some min (or max) or maybe just an inf (or sup). That's a guess, since I'm not familiar with what the actual controversy's about.

Barkley Rosser said...


Ah, a more technical discussion. So, you are right that usually this matter is dealt with by simply defining the activity of removing an undesirable something, such as garbage or pollution, or too much water in the basement, is to label it a different good with its own market, with a positive priice (the price of snow removal). That is why I like these examples where we are clearly talking about the same good that shows both positive and negative prices, the Babylonian wife auction where the desirable women get sold off for a positive price while the less desirable ones end up having their families paying a groom to take them off their hands, or the Texas wind farms that mostly sell power at a positive price, but at some points do so for a negative price.

In terms of the formal mathematical aspect, allowing for negative prices should ease things up. After all, Walras's initial stab allowed for a solution with negative prices, which was viewed as one of the things wrong with his approach. Go read Roy Weintraub's history of GET in the JEL from some years ago. He makes it very clear that a number of GE theorists, including von Neumann, spent a lot of time and effort to come up with all sorts of tricks or methods to get rid of these troublesome negative prices. They are not a problem for compactification as one gets the necessary compact price simplex by a transformation of putting everything in relative terms mapped into the unit simplex. What really cannot be allowed are infinite prices, but negative prices are no problem for this exercise.

Regarding the business about cash, theory usually assumes that it is costless and riskless to hold it, but this is clearly not the case. I remember a former colleague who was a randy bastard, who was married but had a much younger girlfriend in very poor Moldova. He gave her a bunch of US dollars to help her out. Given the lousy banking system there, she put it in a jar and buried it in her backyard. Some time later when she went to retrieve it, her dollars had gone all moldy and rotten and were unusable.

It even strikes me that the argument about cash as the source of a zero bound on interest rates may work in an economy where there is still a lot of use of cash. This may be why in the Great Depression we never saw negative nominal interest rates. But today, well, cash is less than 5 percent of M2. It is essentially irrelevant, not a real alternative in a serious way, especially for the wealthy.

Barkley Rosser said...

Speaking of technical matters, I am now at the ASSA/AEA meetings in San Francisco. About two hours ago I had a conversation with Kenneth Arrow. I asked him about the status of negative prices in general equilibrium theory. He told me that Gerard Debreu wrote a paper about the matter that appeared in some collection of papers of his. The trick was to put the price space onto a sphere for normalizing into a compact space rather than on a plane. I need to check this out further.

YouNotSneaky! said...

Ay, you've piqued my interest in this now. I've tried to track down the Weintraub article you mention but the search engine at JEL site is sort of crappy.
But yes, I think my intuition was that negative prices aren't as much of a problem as infinite prices (or -infinite prices) (or an unbounded price space) since GE determines relative prices and with infinity you can't normalize - w/ 2 goods, if the price of one is infinite and the other finite, and you normalize, the finite one is going to be indeterminate. Also, what Arrow said sort of makes sense (though obviously I'm just guessing here). If you're mapping it to a sphere you're more or less squaring things, so you're 'killing' the minus signs, but that's not the case with mapping it to a plane.

Argh, I got official work to do but I know I'm gonna keep thinking about it.

Barkley Rosser said...


Interested in working on a paper on this? I think you know how to reach me off this blog. Not sure how to get at you. Best regards.

YouNotSneaky! said...

Barkley, thanks. I'll send you an email via the address on your webpage.

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