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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.
Posted by Tyler Cowen on March 8, 2008 at 06:52 AM in Economics | Permalink
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.
Posted by: N at Mar 8, 2008 7:18:23 AM
These "real rates" are deduced from inflation-indexed T-bills. Could the negative "real rates" be the sign of an underlying bias in the CPI?
Posted by: Stephane at Mar 8, 2008 7:57:51 AM
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.
Posted by: Jason at Mar 8, 2008 8:26:21 AM
You get negative short-term real interest rates when the Fed starts pumping out money.
You get negative long-term interest rates when there's speculation that any inflation will abate soon enough (and so there's a good chance of a capital gain in the future).
You also get negative short term interest rates in a deflation, when the central bank loses control of the money supply. Massive amounts of new money gets stuffed into mattresses instead. Why buy today when it will be cheaper tomorrow.
Posted by: Ron Hardin at Mar 8, 2008 12:08:27 PM
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").
Posted by: Jack Schieffer at Mar 8, 2008 12:25:24 PM
My advice at getting through this financial crisis: Liquidate all your assets, purchase gold, put it in a suitcase, and run for the mountains.
Posted by: thehova at Mar 8, 2008 1:17:12 PM
"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.
Posted by: Steve Waldman at Mar 8, 2008 4:28:50 PM
"It's no longer clear how much information prices are reflecting." - yeah well when you don't now what the assets on a bank's balance sheet are you can quit making lemonade from the lemos and just smile as best you can while you suck on them.
Posted by: oops at Mar 8, 2008 5:17:53 PM
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.
Posted by: N at Mar 9, 2008 5:17:06 AM
"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."
Commodities would be the most likely choice for that "item they can sell in the future". In fact, the concept of buying large quantities of goods to store cheaply and to sell in the future almost demands "commodities" by definition. But the price of commodities has risen incredibly in recent periods (in many cases over 100% annualized), and some are even talking about a "commodities bubble". So commodities are not a safe investment. Even if the overall economy experiences inflation, commodities might still fall in value.
Moreover, TIPS pay for inflation based on the CPI, which is based on a particular basket of goods. So it's perfectly reasonable for one to believe that the particular basket of goods measured by the CPI will experience inflation, but that the overall economy will not.
Please note that I don't actually agree with this bet. But it does seem like one that could be rationally made.
Posted by: Anthony at Mar 9, 2008 11:18:35 AM
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.
Posted by: pinus at Mar 9, 2008 12:51:54 PM
For commodities, articles like this one seem to indicate that the ETF tail is wagging the commodities dog: so much money has flowed into one particular fund that it has hit its position limits. "The commodity exchanges and the Commodity Futures Trading Commission set maximum amounts that certain investors can hold in individual commodities." ... and the PowerShares DB Agriculture ETF has now hit those limits.
Perhaps speculation rather than demand is behind the magnitude of the latest recent price increases.
Posted by: at Mar 9, 2008 1:56:58 PM
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.
Posted by: Jason at Mar 9, 2008 2:53:58 PM
Has anyone actually seen significant numbers of professional investors act mainly on fear? I'm really curious, because I've never seen it. Most of the professional investors I've spoken to seem, well, professional. The most bearish one I've spoken to didn't seem at all fearful or panicked; he appeared (to me, at least) to have rational reasons for his expectations.
Just because market prices are reflecting uncertainty doesn't mean rational calculation isn't taking place, it just means that rational calculation is harder. In such an environment, what is irrational about moving to T-bills? Given the uncertain worth of many assets, and whatever unknown actions the feds and the Fed might take, I don't think there is much information out there for markets prices to reflect.
Posted by: Grant at Mar 9, 2008 11:53:42 PM
"Immortal potatoes and transient haircuts..." In what science but economics could one find such wonderfully surreal analogies?
Posted by: Crash at Mar 10, 2008 5:55:55 PM
OK, I'll give my CPI idea another try :
The CPI is imperfect because it rests on a given basket of goods, and cannot be used as a reliable value-measuring stick over time. Let's assume that the CPI basket of goods has been temporarily undervalued relatively to other goods. When prices adjust the other way, the basket's value will increase relative to other goods. Having a slightly smaller basket will be compensated by the increased purchasing power of this basket in terms of other goods.
Why is this relevant? Housing, stocks, and possibly commodities have been significantly overvalued relative to consumer goods included in the CPI basket. If the market expects them to go down, it could consider that 99.5 CPI baskets in 1 year are a better deal than 100 CPI baskets today. Hence the slightly negative TIPS rate.
Am I wrong?
Posted by: Stephane at Mar 22, 2008 6:56:56 AM
