### Bryan Caplan

...seems to think that nominal interest rates can fall below 0%. Think about this for a minute. A one-period nominal interest rate is based on the price on a one-period bond. Let's say that the government will pay you

Of course it is quite common to push the

*H*in the next period if you purchase a bond in this one. We'll call the price of bonds in this period*p*. Then the nominal interest rate is**defined**as*i = (H/p) - 1*. Now assume*i < 0*. What would need to be true for this to happen? We would need*(H/p) - 1 < 0*which simplifies to*H < p*. So, the price of a bond in this period would have to be greater than the amount you will get for owning the bond in the next period. In this situation, why would you buy a bond? If you just kept your*p*under your mattress you'd have*p*in the next period instead of*H*and*H < p*.Of course it is quite common to push the

**real**interest rate below 0%. The real interest rate is defined as*r = i - ne*, where*ne*is the expected rate of inflation from this period to the next. Then for*r < 0*we must have*i < ne*which is certainly possible. If we substitute for*i*we get*(H/p) - 1 < ne*which simplifies to*H/(1 + ne) < p*. This means that the real amount you spend on the bond today is greater than the real amount you'll receive in the next period. Now, why is this OK and*H < p*is not? Well, while there is a guaranteed way to maintain your money's nominal value (just holding on to it) there is no guaranteed way to maintain your money's**real**value. If you just hold on to it, it will be inflated away. It may be that there are no investments with a positive real rate of return. In these cases, there can be a negative real interest rate. But it is crazy to think that**nominal**interest rates could be negative!
## 1 Comments:

Negative interest rates have intrigued me for a good while. As you correctly point out the problem to solve is the zero boundary on short-term nominal interest rates. In a world with coins and bank notes, like our own, one cannot simply introduce negative interest rates, as people would simply start holding their money in cash. The floor for nominal interest rates is always formed by the nominal interest rate on currency. At any given time, the demand for currency becomes infinite the moment nominal interest rates for other types of assets drop below that of currency. After all why would anyone want to hold a 10-year government bond if it pays less yield than cash?

Admittedly the above abstracts from holding costs of currency, which tend to be fairly significant in real life, yet even when taking those into account it would be hard-pushed to expect them to mount up to more than 50bps or so.

I didn't see it mentioned in your blog, but an interesting concept was offered by Silvio Gesell's idea of currency taxes, the so-called stamp scrip. A modified concept of his original idea could very well suit the purpose of avoiding the zero boundary problem. In practice it will be very hard to make it work. In the distant future Gesell taxation would not even be necessary if cash is abolished in favor of an e-money only - charging negative interest rates won't be an issue then, at least not in terms of practical administration.

I wrote a brief paper about this 2 years ago, if you are interested let me know and I can forward it to you.

Good reading material includes:

* Buiter W.H. and Panigirtzoglou, N. "Liquidity Traps: How to Avoid Them and How to Escape Them", NBER Working Paper No. 7245, July, 1999 - revised version of this paper as of June 2001 and October 2002

Coincidentally I just got two new papers on my desk about this topic as well:

* Buiter W.H., "Overcoming the Zero Bound on Nominal Interest Rates: Gesell's Currency Carry Tax vs Eisler's Parallel Virtual Currency", Hi-Stat Discussion Paper Series, No 96, June 2005

* Mitsuhiro Fukao, "The Effects of Gesell (Currency) Taxes in Promoting Japan's Economic Recovery", Hi-Stat Discussion Paper Series, No. 94, June 2005

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