Some new studies suggest that the yield curve inversion might not be quite as ominous as some of us have been assuming.
The yield spread is the gap between a long-term interest rate Rt (such as the ten-year Treasury rate) and a short-term rate rt (such as the 3-month Tbill rate). The spread Rt – rt is usually positive, reflecting a preference of lenders for short-term liquidity. But when the spread as recently becomes small or turns negative, that is often a harbinger of slower economic growth or even a recession.
One way of describing the determinants of the yield spread comes from reasoning as follows. Suppose that instead of buying the 10-year bond and earning return Rt each year, you purchased a 3-month bill paying rt. Then 3 months from now you buy a new bill paying rt+1, 3 months after that you buy a bill paying rt+2, and so on until n = 40 the number of quarters spanned by a 10-year bond. Let Xt,n denote your average return from the latter strategy:
rt+2 + … + rt+n-1).
If Xt,n turns out to be bigger than Rt, then to a first approximation, you’d be better off with the Tbills than the bond. If Xt,n < Rt, the bond is better. We don’t know at date t which of these will be the case, but investors have some expectation, denoted Et(Xt,n), of what Xt,n will be. The expectations hypothesis of the term structure of interest rates holds that the long-term bond will be priced such that Rt = Et(Xt,n).
Although it’s an attractive theory, the expectations hypothesis is certainly not a perfect description of long-term yields. We can define the term premium Tt to be the amount by which the long yield Rt differs from the quantity predicted by the expectations hypothesis:
Tt = Rt – Et(Xt,n).
It then follows as a matter of definition that the yield spread can be decomposed into an expectations component and the term premium:
Rt – rt = [Et(Xt,n) - rt] + Tt.
We might then ask, to what extent is the observed correlation between the yield spread (Rt – rt) and subsequent GDP growth coming from the expectations component (Et(Xt,n) – rt) and to what extent from the term premium (Tt).
The problem is that we don’t have any direct observations on the subjective beliefs of bond-holders, and therefore don’t get to observe Et(Xt,n) directly. One way to get around this is to posit that, whatever investors believe, they form their opinions rationally. From this assumption it would follow that any components of Rt – Xt,n that were predictable at time t would be interpreted as part of the term premium. My 2002 paper published in the Journal of Money, Credit and Banking (coauthored with Professor Dong Heon Kim whom I am visiting this week at Korea University) uses this fact to estimate separately the contribution of the term premium to the predictability of GDP growth. We found that it makes a similar, though smaller, contribution as the expectations component. A later paper by Professors Carlo Favero, Iryna Kaminska, and Ulf Soderstrom, all of the University of Bocconi, reached a similar conclusion.
A more structured approach was suggested in a research paper by Andrew Ang of Columbia University, Monika Piazzesi of the University of Chicago, and Min Wei of the Federal Reserve Board that appeared in the Journal of Econometrics last March. One can try to calculate forecasts of future short rates on the basis of the most recent GDP growth, short rate, and yield spread as a function of those three variables, and then calculate what the current yield on any maturity should be (again as a function of these 3 variables) if the expectations hypothesis were true. This predicted relation for the yield can be compared with what appears to be the actual empirical relation, with the deviation between the predicted and actual then fit to a particular parametric function that is interpreted as the term premium. Using this decomposition, Ang and coauthors found that it seemed to be the expectations component rather than the term premium that helps to forecast GDP.
new study on this question has just been completed by Glenn Rudebusch and Eric Swanson, two very accomplished and widely respected researchers at the Federal Reserve Bank of San Francisco, and former Fed star Brian Sack, now at Macroeconomic Advisers. Their paper reviews these and a number of other approaches to measuring the term premium, and comes out in favor of an approach developed by Don Kim and Jonathan Wright (two other excellent Fed researchers familiar to Econbrowser readers). The Kim-Wright model is similar in spirit to the Ang-Piazzesi-Wei approach, positing that the interest rate at any maturity could be described as a linear function of three unobserved factors. The expectations component is again inferred by extrapolating the behavior of these factors forward, and any deviation between the actual pricing relation and that predicted by the expectations hypothesis is again interpreted to be the term premium.
The figure above, taken from Rudebusch and coauthors’ paper, plots the Kim-Wright term premium over the last half century, along with the deviation of output from the level believed by the Congressional Budget Office to be associated with full employment. This measure of the term premium appears to be countercyclical, rising when output is low. This is the opposite of the relation found by myself and other previous researchers, and suggests that it is only the expectations component that accounts for the anticipatory procyclical behavior of the yield spread.
The Kim-Wright measure of the term premium has declined substantially over the last four years. In terms of the statistical procedure, this reflects the fact that a reasonable forecast of future short rates has increased over this period, while the long rate has declined. Possible explanations for this decline in the term premium offered by Kim and Wright include reduced variability of inflation and output, greater interest in U.S. securities from foreigners, and modest business capital spending. To the extent that the decline in the yield spread does represent a fall in the term premium, and if indeed a fall in the term premium itself does not signal an economic slowdown, it means that the current negative yield spread does not have quite as bearish a connotation as the historical correlation between the yield spread and output might otherwise suggest.
Notwithstanding, it is clear that recent week-to-week moves in the yield spread do not represent fluctuations in the term premium, but instead have been dominated by news about the real economic outlook, with prospects for slower economic growth translating into lower expectations for future short rates and a lower yield spread. Insofar as that’s the case, the recent pitch into negative territory must still be regarded as worrisome.
But just how worrisome? Slower than normal growth still looks to me like a safe bet. On the other hand, the negative growth characteristic of a recession is a little less likely than I regarded it before studying the latest research.