Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Thursday, November 3, 2011

Negative real interest rates

The nominal interest rate is a relative price. It is the price of a dollar today measured in units of (the promise of) future dollars. For example, if the risk-free annual interest rate on a U.S. treasury is currently 5%, then one dollar today is valued at 1.05 future (one year from now) dollars.

Current dollars usually trade at a premium relative to future dollars; the degree of this "impatience" is reflected in the nominal interest rate. The higher the nominal interest rate, the more money is valued today vis-a-vis future money. A high nominal interest rate reflects the market's strong desire to have you part with your money today (in exchange for a promise of future money). Conversely, a low nominal interest rate reflects the market's ambivalence about where to allocate dollars across time. A zero nominal interest rate means that the market values current and future dollars equally. To the extent that it is costless to store cash over time, the nominal interest rate is bounded below by zero. This "fact" is sometimes referred to as the zero lower bound.

In macroeconomic theory, the nominal interest rate plays second-fiddle to the so-called real interest rate. The real rate of interest is also a relative price. It is the price of output today measured in units of future output (think of "output" as consisting of an expenditure-weighted basket of commonly purchased consumer goods and services.) So, if the risk-free annual interest rate on an inflation-indexed U.S. treasury is 2%, then one unit of output today is valued at 1.02 units of output in the future.

In the same way that the nominal interest rate measures the relative scarcity of money across time, one can think of the real interest rate as reflecting the relative scarcity of output across time. Economists typically focus on the real interest rate because people presumably care about output and not money (they care about money only to the extent that it may be used to purchase output).

Current output usually trades at a premium relative to future output; that is, the real interest rate is usually positive. The higher the real interest rate, the more output is valued today vis-a-vis future output. A high real interest rate reflects the market's strong desire to have you part with your output today (in exchange for a promise of future output). Unlike the nominal interest rate, however, there is nothing that naturally prevents the real interest rate from becoming negative; see Nick Rowe. And indeed, this appears to have happened recently in the U.S. The following diagram plots the real interest rate as measured by the n-year treasury inflation-indexed security (constant maturity) for n = 5, 10, 20; see FRED.

Prior to the Great Recession, real interest rates are hovering around 2% p.a. and the yield curve is upward sloping (long rates higher than short rates), at least until early 2006 (when it flattens). Following the violent spike up in real interest rates (associated with the Lehman event), real interest rates have for the most part declined steadily since then. The 20 year rate is below 1%, the 10 year rate is basically zero, and the 5 year rate is significantly negative. What does this mean?

The decline in real rates that has taken place, especially since the beginning of 2011, is a troubling sign. A negative 5-year rate implies that current output is now less valuable than future (5 year) output. In other words, (claims to) future output are now trading at a premium. This premium may be signalling an expected scarcity of future output. If so, then this is a bearish signal.

The decline in market real interest rates is consistent with a collapse (and anemic recovery) of investment spending (broadly defined to include investments in job recruiting). For whatever reason, the future does not look as bright as it normally does at the end of a recession. To some observers, this looks like a "deficient aggregate demand" phenomenon. To others, it is the outcome of a rational pessimism reflecting a flow of new regulatory burdens and a potentially punitive tax regime. Both  hypotheses are consistent with the observed "flight to safety" phenomenon and the consequent decline in real treasury yields.

Unfortunately, the two hypotheses yield very different policy implications. The former calls for increased government purchases to "stimulate demand," while the latter calls for removing whatever barriers are inhibiting private investment expenditure. There seems to be room for compromise though. Surely there are public infrastructure projects that can be expected to yield a real return higher than zero? This is a great time for the U.S. treasury to borrow (assuming that borrowed funds are not squandered, of course).

In the event of an impasse, can the Fed save the day? It is hard to see how. The Fed's influence on real economic activity is usually thought to flow through the influence it has (or is supposed to have) on the real interest rate. One could make the case that real interest rates are presently low in part owing to the Fed's easing policies. But this would be ignoring the fact that the Fed's easing policies were/are largely driven by the collapse in investment spending. (I am suggesting that in a world without the Fed, these real interest rates would be behaving in more or less the same way.)

In any case, real interest rates are already unusually low. How much lower should they go? Is it really the case that our economic ills, even some of them, might be solved in any significant manner by driving these real rates any lower? My own view is probably not. If there is something the Fed can do, it is likely to operate through some other mechanism. The problem is not that real interest rates are too high. The problem is that they are not high enough (the robust economic prospects that push real rates higher appear to be absent).

Most Fed types probably hold the view that the main goal of monetary policy is to keep inflation low and stable so as to "anchor" inflation expectations; see James Hamilton on Ben Bernanke's 2007 inflation expectations speech. Bernanke defines well-anchored inflation expectations as being "relatively insensitive to incoming data."

We can compute a market-based measure of inflation expectations using a no-arbitrage-condition which states the the real rate of return on nominal and inflation-indexed treasuries should be roughly equal (the Fisher equation). The relevant nominal interest rates are plotted here:

Next, take the nominal interest rate above (at a given horizon) and subtract the corresponding real interest rate from the first diagram to get:

According to this data, the sharp spike up in real interest rates in the depths of the financial crisis stemmed entirely from a precipitous decline in longer-horizon inflation expectations. While inflation expectations appear to have rebounded to their more normal range of 2-3%, they continue to be more volatile than before the recession.

On the other hand, there is no evidence to suggest that inflation expectations are whirling out of control, one way or the other. I'm not sure to what extent this constitutes success. At the very least it is not utter failure.

Am off to Vancouver now for the 25th Annual CMSG


  1. Given the extent to which interest rates are manipulated by central banks (and manipulated downwards in recessions), I’d question whether the current “low” rates are much of a guide as to how best to allocate resources.

  2. Just want to mention Lars E.O. Svensson have done some major work in this area (actually the Swedish central bank was the first in the world to introduce negative interest rate in 2009).

    By the way, where do you get the data from and what program do you use to plot the graphs? Just wondering.

  3. CL,

    David was clearly sitting in on my bonds lecture the other day... those graphs look suspiciously like my own. If he's anything like me, the data is from or the St. Louis Fed: and the program is Excel (2007, prob).


    When you say 'real' interest rate, how similar is your understanding of the 'real' interest rate to a Wicksellian 'natural' interest rate? Do you think they are the same thing?

  4. Prof J, I´ve been searching your graphs so similar to these of David, and I did not see them.
    On the other hand, it is not so hard to do in Saint Louis Fed FRED. BTW, A GREAT and useful system to manage data.
    The post is very nice, beutiful, and very clear. I agree, but I have a doubt: is not so important that the spread between risk free bonds (Treasury) and private bonds is in one of its highest level?

  5. Luis,

    It was a joke - my bonds lecture was in class to my private students. I didn't do a post about this issue on my by blog.

    I agree, St Louis Fred is wonderful.

  6. "When you say 'real' interest rate, how similar is your understanding of the 'real' interest rate to a Wicksellian 'natural' interest rate? Do you think they are the same thing?"

    Yes, I second that question.

    Also: "The nominal interest rate is a relative price."

    This is an own-rate, right?

  7. "So, if the risk-free annual interest rate on an inflation-indexed U.S. treasury is 2%, then one unit of output today is valued at 1.02 units of output in the future."

    There is something mythical about the real rate, right? First, there is no abstract unit of output with a unique real rate, only a number of goods, each with its own relative price (differential between its own spot and future price). And most of these relative prices are unobservable since futures markets exist for only a few commodities.

    We can pretend that the TIPS rate measures the real rate, but there is a specific non-zero risk of default built into the price of TIPS, and also some sort of liquidity premium. So TIPS are by no means an ideal abstraction of the real rate.

  8. i will third the question on the natural rate as a precursor to a question on negative natural rates! (c.f.

  9. Ralph Musgrave: How do you think the real interest rates plotted above might have evolved absent Fed intervention, and why?

    CL, the data is from FRED and Haver (gathered by my RA, Constanza Liborio). The graphics are constructed with Excel.

    Prof J, the Wicksellian "natural" rate of interest is a theoretical object, not an empirical object. I'm not sure how this measure of the real rate corresponds to Wicksell's natural rate. If I had to guess, I'd say that the two do not correspond. As per Ralph's comment above, some might hold the view that the real rate is currently below the natural rate, owing to Fed intervention.

    JP Koning, I'm not sure if "mythical" is the right word. But you are basically right. The problem is evident whenever we aggregate. What is one unit of real GDP, for example? Having said this, I have no problem in interpreting this measure of real interest rate as a weighted average of the own-rates that exist in the CPI basket of goods. Perhaps not an ideal abstraction of the real rate, as you say, but then, what do you recommend instead?

  10. "Perhaps not an ideal abstraction of the real rate, as you say, but then, what do you recommend instead?"

    Why do we even need to have a variable that represent the "real rate"? I am having difficulty getting my head around this stuff.

    Your post was linked to at interfluidity:

  11. JP Koning:

    I mentioned in my post that the real rate plays second-fiddle to the nominal rate. It is for the same reason that real variables are more important than nominal variables.

    Think of the real rate as measuring the relative scarcity of purchasing power across time. "Purchasing power" can be measured in any number of ways, but whichever way it is done, it is probably more meaningful than a measure of the relative scarcity of dollars across time.

  12. I strongly, strongly suspect that the rise in real yields and associated decline inflation breakevens in the depths of the financial crisis is entirely explained by investors madly selling out of TIPS to buy nominal Treasuries. There is really very little information about inflation or economic expectations contained therein. Even though TIPS and Treasuries are both backed by the exact same full-faith and credit, TIPS are by magnitudes less liquid than nominal bonds. Thus, when liquidity became extremely prized, investors sold out of TIPS and bought nominal bonds. Hence, real rates spiked, nominal rates collapsed, and inflation expectations seemed to crash. Further evidence of this can be seen by looking at the on-the-run / off-the-run spreads of nominal bonds (again suggesting that liquidity was highly valued). In short - do not believe anything from the TIPS market in late 2008.

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