# The yield curve and predicting recessions

Jonathan Wright, a brilliant research economist at the Federal Reserve Board, recently completed a very interesting paper titled The Yield Curve and Predicting Recessions. Wright’s research seems to have been influential in Fed Chair Ben Bernanke’s recent assessment that the current very flat yield curve does not signify a coming significant economic slowdown.

###### Probability of recession within the next 4 quarters (in percent) as a function of the spread between 10-year and 3-month yields only.
Spread Probability

1.00 32%

0.75 39%

0.50 46%

0.25 54%

0.00 61%

-0.25 68%

-0.50 74%

-0.75 80%

-1.00 85%

Wright used a probit model to describe the probability of an economic recession sometime during the next four quarters as a function of the spread between the yields on 10-year and 3-month U.S. Treasury securities. Unlike some other researchers, Wright found little evidence that the relation has been unstable over time, though he acknowledged that, given the relatively low number of recessions we have observed, it might be difficult to detect any changes that might have occurred.

Wright’s base model (which he called “Model A”) describes the probability of a recession sometime within the next year as a function of S, the spread between the 10-year and 3-month bond yield,

Prob = F(0.28 – 0.74 x S),

where F denotes the cumulative distribution function for a standard Normal variable with mean zero and unit variance. The probabilities implied by different values of S are summarized in the table on the left. According to this simple model, one might have started to become concerned last summer when the spread fell below 100 basis points. Note that with the spread now below 25 basis points, Wright’s Model A would judge that we are more likely than not to see a recession within the next year. The probabilities as calculated from this model at any historical date are compared with actual recessions in the figure below.

###### Probability of recession within the next 4 quarters (in percent) as a function of both the spread between 10-year and 3-month yields and the level of the fed funds rate.
Spread FF = 3.5 FF = 4.0 FF = 4.5 FF = 5.0 FF = 5.5

1.00 4% 6% 9% 12% 16%

0.75 6% 9% 12% 16% 21%

0.50 9% 13% 16% 21% 27%

0.25 13% 17% 22% 27% 33%

0.00 17% 22% 28% 34% 40%

-0.25 23% 28% 34% 41% 48%

-0.50 29% 35% 41% 48% 55%

-0.75 35% 42% 49% 56% 63%

-1.00 43% 50% 57% 63% 70%

However, Wright and other researchers (such as Andrew Ang, Monika Piazzesi and Min Wei in a research paper that appeared in the most recent issue of the Journal of Econometrics) suggest that in addition to the spread it is helpful to look at the overall level of short term interest rates. Wright’s Model B uses both the spread (S) and the funds rate (R) to calculate the probability:

Prob = F(-2.17 – 0.76 x S + 0.35 x R).

According to Model B, the low values for the spread that we saw last summer were not a source of concern for future economic activity because a fed funds rate below 4% was so low by historical standards. Research like this seems to have played a role in Fed Chair Ben Bernanke’s assessment that

I would not interpret the currently very flat yield curve as indicating a significant economic slowdown to come, for several reasons. First, in previous episodes when an inverted yield curve was followed by recession, the level of interest rates was quite high, consistent with considerable financial restraint. This time, both short- and long-term interest rates–in nominal and real terms–are relatively low by historical standards

Of course, one would expect that the real fed funds rate, rather than the nominal fed funds rate, is the variable that should matter for such calculations, though Wright did not find any statistical evidence that adding inflation helped improve the predictions generated by Model B. And although it is true that the level of the nominal fed funds rate remains low relative to the historical average, I don’t agree with Bernanke’s assessment that the short-term real interest rate is still low in comparison with the historical average.

Even so, if we accept Model B at face value, a couple more 25-basis point bumps by the Fed would put the funds rate at 5.25% and likely push the spread into negative territory. From the table above, that starts to make a recession look like a pretty good possibility.

Think Bernanke wants to take that gamble? I’m betting he won’t.

UPDATE: Political Calculations has created a neat tool that lets you input values for the different yields to calculate the probabilities from Wright’s Model B.

## 22 thoughts on “The yield curve and predicting recessions”

1. schimpfermann

If its true that the relatively low long term yields are due to a drop in term premiums, as indicated by Bernanke, the implied probabilities of recession are currently much lower. I’d take on the bet.

2. MrQuant

I have spent a considerable amount of time studying probit recession models as well, and there are a few small points which are worth noting.
First, I’m very confused about some of Bernanke’s conflicting comments. eg: in his March 20, 2006 speech, he said
“Other indicators that have had empirical success in the past, including corporate risk spreads, would seem to be consistent with continuing solid economic growth”
Yet, Bernanke was also one of the first authors to apply yield curve/interest rate spreads to forecast macro econ activity, in a papter in 1988 (if I remember correctly). In that article, he said (paraphrasing) that “the predictive capacity of the corporate spread appears to have diminished in recent years”.
Secondly, and much more importantly, very few probit studies focus on out of sample performance, which is important if we plan on using forecasts “in realtime”. Most probit recession models have considerably lower out of sample forecast performance. If you look at section 4 of his paper, it appears that he only considered out of sample performance in the post 1980’s period. This is questionable, in my opinion, for a few reasons:
1. It coincides almost perfectly with the peak in and subsequent secular downward trend in interest rates – a much longer period would be desireable, eg: back to the 1950s at a minimum
2. Macro economic volatility also decreased considerably in this period – obviously this is somewhat related to #1 but more care is required to differentate between the two
3. There are only 4 recessions in this period, and given the biases from the previous two points, I am not a huge fan of drawing conclusions from such a small sample size
4. It sounds as though he computes out-of-sample performance using a regression window that grows over time. It would also be advantageous to use a rolling regression with a fixed lookback, as this allows more flexibility for parameter instability.

3. Hal

You mentioned a few days ago that ten year yields were up 50 basis points this year. It sounds like they’re rising almost as fast as the FF rate. If so, then the spread won’t necessarily narrow even if the Fed continues to raise rates.

4. algernon

calmo, my bet it that the Asian central banks are starting to restrain themselves.
This instance highlights the futility of this kind of modeling. The recent flatness of the curve has resulted from the unique situation of the Fed tightening while the Asian central banks supply us with liquidity via buying primarily our long bonds. Very different from previous tightenings/flat curves.

5. jf

The reason the dollar took a hit midweek is that some Chinese government official made an offhand remark about possibly investigating whether or not there is an asset in the world that could also be a good investment in addition to the hundreds of billions of dollars they own in the form of U.S. Treasury paper. The squeeze has been felt finally, as everybody and their mother who have been leaning on China’s appetite got a reminder.

6. jim miller

Who’s to say which yield curve? Here we discuss the difference between the 10-year and the three month.
If you look at the difference between the 3-month and the 30-year,the spread has widened.
On the other hand, M2 has been decelerating steadily since early February. MZM has basically stalled at no growth in the most recent reporting period. If the monetary aggregates don’t show some life soon,the equity markets will weaken and a recession will occur. No matter what interest rates do.

7. Don Persons

Your report shows considerable analytical ambiguity. However, I appreciate your work and efforts.

8. DF

Given that the oncoming recession will be of the 30’s king, any model based only on postwar data is irrelevant.
The major indicator of an oncoming crash is not the level of interest rate, but the Debt/GDP ratio. That debt/GDP ratio is now higher than in the 20’s, higher than ever in past history. THere’s nothing economic policy can do to fight cycles in the debt/GDP ratio. That ratio is about to fall right now because it has never been so high and because it can’t rise forever.
It is going to fall, whatever the yeld curve is, it is going to fall, and this is precisely why the yelds are so low and starting to get negative, the causality flows from debt/gdp ratio to the yeld curve to a major recession ahead of us, not the other way round.
The only choice the econmic planners face is : do we inflate debt away or do we allow debt deflation ?

9. Ironman

DF,

Some perspective might be in order regarding debt-to-GDP history. First, here’s the the debt-to-GDP ratio (expressed as a percentage) over the last 105 years, and here’s the national debt-per-capita to GDP index over the same period. Basically, the debt levels with respect to GDP have been sitting at or near their present levels for some time (about a decade.)

JDH,

I couldn’t resist – Political Calculations now features a tool that does the recession odds math you presented!

10. ADP

Wouldn’t you expect the Fed Chair to say it is different this time? I’d be surprised if Bernanke came out and said something to the effect of, “If longer rates don’t back up faster than the pace of tightening, we’re going into recession.” He’s not going to want to take political blame for a recession. There is always a case to be made for why it is different this time, but, the curve has continued to be important. Banks still have less room for error with a flat curve. Lending standards become a lot more sensitive in a flat/inverted curve enviornment raising contraction probabilities.

11. Roberto

As a naive brazilian economist, I am trying to grasp your thoughts. I can?t understand how the US economy will lower the current account deficit (my understanding is that the current dinamycs is unsustainable) if not by lowering GDP growth pace (at least in the short-term). So when you get worried about a recession in the US, it seems to me something unreasonable, because sooner or later I understand that will happen anyway. And in my point of view, it rather occur sooner than later. If you could shed some light on this issue, I would be glad.
Tks and rds
Roberto

12. kharris

Calmo and Algernon,
The rise to and through 4.80% seems to coincide with a shift in the funds strip, suggesting that the odds of a 5.25% funds rate had grown more likely. On the break of 4.80% (plus a bit, apparently), mortgage portfolios began shifting their hedges, which involved shedding long-dated Treasuries. That will tend to be the response whenever a range of interest rates not explored in some time is entered. So a good bit of the distance from 4.80%+ to 4.957% probably was due to a purely technical, and inevitable, event.
Of course, once that move gets started, events like the jobs report can carry a good bit of scare value.
Commitment of traders data show a reduction in net spec longs at tens years, so the fuel for another quick rise in long rates may – may – be somewhat dissipated.

13. ADP

Roberto, Although the Fed is supposed to be independent, they are still important politically. The stated goal of the Fed is full employment and low inflation; the size of deficits are secondary. Since recessions have come with less frequency, many believe that a day or reconing can be put off for years. Meanwhile, it is possible that a lower dollar or other factors could slow the imbalance. And, not all agree a day of reconing is inevitable. Also, if Bernanke were to indicate a recession is an acceptable price for balancing the current account, there would be a cry for protectionism that would be economically counterproductive.

14. calmo

Thanks as always for your careful thoughts kharris,
Now to get my head around that “inevitable technical event”, the shedding of long-dated treasuries by hedge funds as they weighed the liklihood of a FF rate of 5.25%.
It does sound like you have resolved this matter and that you expect the ~50bp spread to remain should the FF rate go even higher than 5.25%.
So the near zero margin before could be sustained only so long as foreign cbs were willing to buy the notes at the non-profitable price? [The last tbill sale was 5yr and was very light on fcb participation, no?] If the fcbs are looking at better yielding paper now, is that enough to send the long rates up?
jim miller, M3 is no longer being pulished so money supply is not publicly known, yes?
The spread we are interested in is the one that captures the banks attention who lend to the mortgage market which used to be the 10yr term but maybe that should be scoped down. Is that your suggestion?

15. calmo

This view from Machael Panzer sheds some light:
Over the past five years, whenever we have seen a sharp decline in the 13-week cumulative total of Japanese net investment in medium and long-term foreign bonds, as reported by Japan’s Ministry of Finance, it has been accompanied by a parallel rise in the 5-year U.S. treasury bond yield (among others).
Since December 30th, we have seen such a move, with a cumulative measure of net investment falling by 8.39 trillion yen, or more than \$70 billion dollars. That suggests we could be due for even more of a slide in bond prices than we have seen already.

(International Perspective)
http://www.prudentbear.com/

16. Notes from Japan

The Yield Curve

The yield curve is an importand graph when doing investments. It basically describes the yield you get for bonds, for different durations. From an investor’s point of view, it is natural that for a 10 year bond, you get a…

17. Alex Grey

Much higher debt levels today make the lower risk of recession as predicted by Model B questionable. I think that the model, which includes the level of nominal interest rates, predicts a lower risk of recession because of past periods of low nominal fed funds rates, which are different from today’s. Over the sampling period previous instances of low nominal interest rates (1960s, pre-1973 1970s) were associated with much lower consumer debt (mortgage and consumer credit) levels. Consequently a low nominal rate would lead to strong deband for loans, reducing the risk of recession. Now individual debt levels have risen to the extent that the consumer debt service burden is higher than it was in the early 1980s when nominal rates were much higher. One cause of this is financial deregulation/innovation which has allowed indivuals to borrow much more heavily, in particular using short-term or adjustable rates. Thus a persistently low Fed Funds rate post-2000 has resulted in a much larger build-up of debt than would have been the case in the 1960s-early-1970s. This serves to weaken the effect of a low nominal Fed Funds rate.

18. Allan Fisher

I must pick a serious bone with the way Political Calculations does their calculations of the Wright paper. A close reading of his paper shows that he is NOT using the daily values of the Fed Funds, 90 day bill and 10 year note, but rather a quarter average (66 business days) of the effective fed funds rate and a quarter average (66 business days) of the spread. This is a huge difference from using daily values. This paper then closely matches the previous fed paper which also used the quarter average of the spread. If you use just a daily reading, you are not going to receive a correct reading on the recession risk, and you will not really be following the Wright paper results.

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