Brain twisters

Can the real interest rate be negative in a world where some but not all goods can be stored costlessly? Consider for illustration an economy with two goods, immortal potatoes and transient haircuts, with both items currently selling for $1 and both given equal weights in the CPI. If you put $2 into a 1-year TIPS with a real interest rate of -1% in that world, next year you’d have the ability to purchase 0.99 potatoes and 0.99 haircuts.

Why buy the TIPS when you could simply save the $2 in the form of 2 potatoes and still have those same 2 potatoes a year from now? If nothing else changes, and 2 potatoes were still worth 2 haircuts a year from now, everybody would want to do just that. If we were in long-run equilibrium before the real rate went negative, in response to a negative real interest rate, everybody would want to buy potatoes today as an investment vehicle. The price of potatoes today would have to be bid up to a point above the long-run equilibrium so that from here, potato prices are expected to rise less quickly than the price of hair cuts. Your 2 potatoes might be worth 2 haircuts today, but if they’re only worth 1.96 haircuts next year, you might be just indifferent between an investment in TIPS or physically storing the commodity.

Here is much more.  Greg Mankiw, among others, has pointed out that we are seeing negative real rates of return in some credit markets.  I don’t read this as a reflection of intertemporal preferences and constraints.  I read this as a (scary) sign of how segmented some credit markets have become.  More concretely, lots of people are running to Treasuries but out of a general sense of fear rather than from rational calculation.  Right now rational calculation is very difficult, agency problems are causing people to avoid the possible blame that can result from risky assets, and credit market arbitrage isn’t much working.  It’s no longer clear how much information prices are reflecting.

Comments

This of course assumes that potatoes will be worth the same amount in following time periods. I don't think this assumption makes much sense in the real world. Especially if hoarding today leads to price drops later.

Put another way, if we think investors are fearful of losing principle then it makes sense that they would flock to T-Bills, as well as other 'perpetual' stores of value such as immortal potatoes, gold, toilet paper etc.

In the case of T'bills they accept a clearly negative real rate because principle-return is guaranteed. Investors often have liabilities denominated in dollars (life insurance, pension obligations, debts, etc), which make treasuries even better than any other store of value.

I would argue that for one with a low risk appetite and future obligations denominated in dollars, there is no better investment than a T-bill.

N, I'm not sure, but I think you may be missing something. TIPS aren't the same as T'bills. TIPS are T'bills that pay a fixed rate of interest (normally less than T'bills) plus inflation. What's happened lately is that people have bid down the interest rate on TIPS to zero! They are willing to loan money to the government for free, as long as they get inflation protection. They might as well just buy dozens of washing machines, or some other item they can sell in the future.

The fed seems to be more focused on growth than reducing extreme inflation/deflation. What's happening with TIPS could be a sign that the fed's strategy is flawed. People will start making seemingly weird valuations because of inflation fears and thus destroy any chance of growth.

I suppose the good news is that people are buying TIPS and not dozens of washing machines, but when you look at the price of gold (and oil?) you have to wonder if maybe we aren't already there.

To me, the main difference between the brain teaser and reality--other than having only 2 goods :)--is that you can't store many things costlessly in the real world. In fact, the only costlessly storable commodities that come quickly to mind are financial instruments. Almost anything else--even immortal potatoes--would require storage space, possibly insurance against theft or fire, et cetera. Another cost for more mortal items would be degradation/obsolesence.

Suppose these storage costs are 2% for non-financial commodities. Then someone determined to save for the future would be willing to accept real interest rates as low as -2% on financials. You'd still need to explain why they wanted to save (expecting less income in the future?), but you wouldn't need to invoke a lack of of rationality or information. I'm not saying those other things couldn't be factors, but that's not an inescapable conclusion.

For N, you say:

"Investors often have liabilities denominated in dollars (life insurance, pension obligations, debts, etc), which make treasuries even better than any other store of value...I would argue that for one with a low risk appetite and future obligations denominated in dollars, there is no better investment than a T-bill."

I'd argue that if the investors can buy down their future obligations, that option would be a better investment than T-bills whenever T-bill interest is negative and the implicit rates of their obligations are positive (or even merely "less negative").

"It's no longer clear how much information prices are reflecting."

Where is the market whose prices convey information on how informative market prices are?

Brain twisters indeed.

Jason / Jack - Thanks for the responses these are both helpful for my understanding of the issue.

Jason - with regards to your comment: "TIPS aren't the same as T'bills. TIPS are T'bills that pay a fixed rate of interest (normally less than T'bills) plus inflation. What's happened lately is that people have bid down the interest rate on TIPS to zero!"

I am still not sure whether the difference is relevant for the point I was making about guaranteed returns. I would suppose that whenever TIPS is offering negative interest rates that T-bills would be offering negative real rates. Is there really a divergence here which is relevant? Would appreciate your additional thoughts on this.

I am surprised that the commenters are actually discussing questions that are not asked in the setup.

The question is: Suppose that we have a two good economy as described above. Is it possible that _in this two-good economy_, the real interest rate may be negative? I know that the setup is very much incomplete, but we should not deviate from the stated setup much.

For starters, we should ask what real interest rate are we talking about. There is not _one_ real interest rate. From micro 101 we know that each (investment) good carries it's own real rate of interest. Do _all_ real interest rates above have to be positive, or just some of them? If they can be negative, is the discount factor a lower bound? Etc.

N,

Guaranteed returns don't mean you will see negative real interest rates. All you need is a return that is less than inflation.

Since we don't know what the rate of inflation will be it's hard to say T'bills are yielding negative real interest rates. You can only do that with TIPS, which is why I brought them up.

I kind of agree with your advice, if I owed someone money in the future and had all the money I owed them I should theoretically put that money in some sort of government security.

Theoretically, if I invested in T'bills or TIPS I should get the same rate of return.

Funny thing though, my savings account yields more than a two year treasury, taxes included. Both are backed by the same government. That's where my money would go. Although I might take Jake's advice and try buying my debt back on the cheap.

"Immortal potatoes and transient haircuts..." In what science but economics could one find such wonderfully surreal analogies?

we should pay more attention on these people

Comments for this post are closed