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May 17, 2021

Sovereign Markets, Global Factors

Remarks by
Richard H. Clarida
Vice Chair
Board of Governors of the Federal Reserve System
at
“Fostering a Resilient Economy and Financial System: The Role of Central Banks”
25th Annual Financial Markets Conference, sponsored by
the Center for Financial Innovation and Stability, Federal Reserve Bank of Atlanta
Amelia Island, Florida
(via webcast)

May 17, 2021

Good morning, and thank you, Raphael. I am delighted to participate in the 25th
Financial Markets Conference, sponsored by the Federal Reserve Bank of Atlanta, which
this year focuses on the role of central banks in fostering a resilient economy and
financial system. 1
Central banks can indeed make important contributions to the resilience of the
economy and the financial system. In the case of the Federal Reserve, our
responsibilities include ensuring that banks are well supervised and regulated, working
with other government agencies through the Financial Stability Oversight Council to
promote financial stability, and, of course, conducting a U.S. monetary policy that aims
to achieve our dual-mandate goals of maximum employment and price stability. As the
title of my talk suggests, my remarks today will focus on the importance of some specific
global financial linkages that are relevant to the execution and communication of U.S.
monetary policy aimed at achieving our domestic mandates.
Signs of financial globalization are abundant and evident across markets for many
asset classes. But why and in what possible ways is financial globalization relevant for
national monetary policies charged with achieving domestic mandates? A
comprehensive and complete answer to this fundamental question is, of course, beyond
the scope of a single speech, and so in my remarks today, I will focus specifically on two

On May 27, 2021, this speech was updated to add a sentence to footnote 10 and add the following to the
“References” section: Gospodinov, Nikolay (2020). “Global Factors in U.S. Yield Curve,” working paper,
July, available at https://sites.google.com/site/gospodinovfed.
The views expressed are my own and not necessarily those of other Federal Reserve Board members or
Federal Open Market Committee participants. I am grateful to Antulio Bomfim for assistance in drafting
these remarks, to Canlin Li for contributing the empirical work, and to Hannah Firestone for preparing the
figures.

1

-2ways in which the integration and globalization of sovereign bond markets is relevant to
the execution and communication of national monetary policies.
Central banks rightly pay a lot of attention to domestic sovereign bond yields
“across the curve” for at least two reasons. First, yield curves for nominal and inflationindexed bonds provide useful—if also noisy—information about the expected future path
of the policy rate, inflation, the business cycle, and the term premium required to hold
sovereign bonds. Second, yields on long-maturity bonds represent, generally, a key
channel in the transmission of monetary policy to the real economy and, specifically, are
a fundamental building block markets use to discount cash flows relevant for valuing
financial assets. To anticipate my bottom line, the message of this speech is that global
integration of sovereign bond markets has important implications not only for how
central banks extract relevant signals from observed yields on bonds issued by the
domestic sovereign, but also for how central banks calibrate the transmission of policy
and policy guidance to the real economy via the yields on long-maturity bonds that are
relevant for saving, investment, and asset valuation.
Sovereign Yields Embed Global Factors
There is a rich academic and practitioner literature devoted to modeling and
interpreting fluctuations in domestic sovereign yield curves. A fundamental empirical
regularity that motivates much of this research is that, across time and geography, yields
along any given sovereign curve tend to rise and fall—and steepen and flatten—together
over time. This empirical regularity led Litterman and Scheinkman (1991) to
hypothesize and demonstrate that in the market for U.S. Treasury securities, a very small
number of common factors—two or, at most, three—are able to account not only for

-3most of the time-series variation, but also for the cross-sectional dispersion in yields
across the entire Treasury curve. Moreover, the two most empirically important factors
extracted statistically from the Treasury yield curve have intuitive geometric
interpretations as “level” and “slope.” The “level” factor has approximately an equal
effect on yields across the maturity spectrum—thus, changes in the level factor are often
referred to as “parallel shifts” in the yield curve—and accounts for most of the variance
in yields across the full range of maturities. The “slope” factor has an effect that is
increasing (monotonically) in maturity—thus, changes in the slope factor are often
referred to as “steepening” or “flattening” pivots in the yield curve.
The original Litterman and Scheinkman (1991) factor model, with its geometric
interpretation of level and slope factors, has held up remarkably well over the ensuing
three decades and has been replicated for sovereign yield curves across scores of
countries around the world, revealing similar regularities. Indeed, many, if not most,
major central banks—and certainly their central bank watchers—estimate yield curve
models and extract the factors that are reflected in their domestic sovereign yield curves.
So, for example, for the three major economies included in figure 1, one can easily
extract—using the methodology developed in Diebold and Li (2006)—on a country-bycountry basis, U.S., U.K., and German level factors as well as U.S., U.K., and German
slope factors. As is clear from figure 1, level and slope factors extracted from these
individual sovereign yield curves are highly correlated across these major sovereign bond
markets.
Economic theory suggests at least two reasons why the factors embedded in
sovereign yield curves may be correlated across countries. First, this correlation will be

-4present if the underlying macro fundamentals—for example, productivity growth,
saving–investment imbalances, and longer-term inflation expectations—that drive the
factors are correlated across countries. 2 Second, as is emphasized in Clarida (2019c) and
Obstfeld (2020), this correlation will also be present if countries are tightly financially
integrated even if fundamentals themselves are independent across countries. 3
Interpreting the Global Level Factor
From any set of level and slope factors extracted across a collection of sovereign
yield curves, one can in turn extract a global level factor and a global slope factor that
account for the correlation among the country-specific level and slope factors. 4 As can
be seen in figure 1, the global level factor (the blue line) accounts for most of the evident
downward trend and much of the variation relative to that trend in the estimated U.S.,
U.K., and German level factors. But what is this global level factor? Plausibly, the
global level factor embedded in these three sovereign yield curves reflects the
contribution of possibly several global macro fundamental drivers—including global
productivity growth, the balance between global saving and investment, and longer-term
inflation expectations—and likely also other “market” or “technical” factors specific to
the trading of these sovereigns in the global bond market.
As can be seen in figure 2, however, most of the trend and variation in the global
level factor about this trend can be accounted for by the evolution of estimates of the

For instance, Clarida (2019b) discusses the role of falling neutral real rates and longer-term inflation
expectations worldwide in the decline in global sovereign bond yields.
3
See Ferreira and Shousha (2021) for a rigorous econometric study of the fundamental determinants of real
interest rates in global general equilibrium.
4
Diebold, Li, and Yue (2008) extended the single-country model developed by Diebold and Li (2006) to a
multicountry framework that allows for both global and country-specific factors to affect domestic yield
curves. In these remarks, for ease of exposition, I define the global level factor as the simple average of the
Diebold-Li country level factors (renormalized as discussed in the notes to figure 1).
2

-5neutral real interest rates in these countries. 5 Figure 2 plots the global level factor against
a simple average of the Holston, Laubach, and Williams (2017, henceforth HLW) timeseries estimates of r*—the neutral real interest rate consistent with trend growth and
stable inflation—for the United States, the United Kingdom, and Germany. Now, while
it is certainly intuitive that an r* index for these countries would be correlated with the
global level factor extracted from their yield curves, the degree to which this simple
index can account for the trend and variation in the global level factor around this trend is
striking. And because central banks, including the Federal Reserve, typically channel
Milton Friedman (1968) and believe that the evolution of r* primarily reflects
nonmonetary factors that are beyond the central bank’s control, an “r* theory” of the
level factor—if true—has important implications for how central banks extract signal
from noise from sovereign yield curves as well as for how they calibrate the stance of
monetary policy consistent with a credible inflation target. Under this interpretation, and
as was anticipated years ago by Greenspan (2005), Bernanke (2005), Clarida (2005), and
others, credible inflation-targeting central banks operating in an integrated global capital
market—at least when they are operating away from their effective lower bound (ELB)—
are primarily in the yield curve “slope” business, but much less so in the yield curve
“level” business. 6
Figure 3 shows the relationship between the yield on a 10-year Treasury note and
an estimate of the neutral nominal U.S. policy rate, which I set equal to the HLW
Recent work by Bauer and Rudebusch (2020) highlights the role of movements in neutral real interest
rates in the dynamics of the yield curve.
6
Interestingly, it was the success of credible inflation targeting, in addition to financial globalization, that
has put central banks in the “slope” business. In a world in which inflation expectations are not well
anchored, monetary policy can have a major effect on the level of interest rates by shifting, for better or
worse, longer-term inflation expectations, as was the case in the United States from the 1960s through the
early 1990s (Clarida, Galí, and Gertler, 2000).
5

-6estimate of r* for the United States plus a 2 percent inflation objective, a proxy for the
neutral nominal interest rate when longer-term inflation expectations are anchored at the
2 percent target. As is evident from the figure and as can be verified econometrically,
there has been since at least the 1990s a stable, mean-reverting dynamic relationship
between the benchmark nominal Treasury yield and a neutral nominal interest rate proxy
derived from the HLW time-series estimates for r* in the United States.
Interpreting the Slope Factor
I would now like to illustrate what I mean when I say that the slope of the yield
curve is an important channel through which monetary policy is transmitted. Figure 4
plots the Diebold-Li (DL) slope factor for the United States—which is included in
figure 1—against the spread between the HLW estimate of the U.S. neutral nominal
policy rate and the actual federal funds rate (hereafter the “policy rate spread”). As is
evident from figure 4, most of the variation in the DL slope factor for the Treasury yield
curve can be accounted for by changes in the U.S. policy rate spread. 7 A simple
regression over the 1999:Q1 to 2019:Q4 sample of the slope factor on the policy rate
spread shown in figure 4 yields an R2 of 0.84 with a coefficient on the policy rate spread
of 1.23. In other words, over the past 20 years, more than three-fourths of the variance of
the Treasury slope factor can be accounted for by the policy rate spread, which is
obviously something the Federal Reserve can control when it sets the federal funds rate.
The remaining variance of the benchmark Treasury slope factor is, by construction,
accounted for by factors that are uncorrelated with the U.S. policy rate spread. A similar

See Bomfim (1997) for an early exploration of the “policy rate spread” as a factor embedded in the
Treasury yield curve as well as an early effort to obtain an estimate of r* consistent with medium-term
macroeconomic equilibrium. See also the appendix for a simple model linking the neutral nominal interest
rate, the yield curve, the policy rate spread, and the term premium.
7

-7empirical relationship between the policy rate spread and the slope factor embedded in
gilt and bund yield curves is also evident in the data, although there is some evidence in
these markets of a structural break in these relationships between the slope factor and the
policy rate spread sometime after the Global Financial Crisis. 8 In the interest of time, I
shall not put forward a theory of what accounts for the residual variance of yield curve
slope factors after accounting for the policy rate spread itself, but obvious candidates
(certainly at the ELB) would include forward guidance about the path of the future policy
rate as well as actual and prospective large-scale asset purchase (LSAP) programs.
Identifying Causation from Bond Yield Correlations
It is a truism that “correlation is not causation,” and this is especially the case
when trying to interpret contemporaneous correlation among asset prices generally and
among bond yields in particular. Having identified one possible, parsimonious set of
economic fundamentals that can help account for yield curve fluctuations in three major
sovereign markets, I will now review what the empirical evidence has to say about the
direction of causality reflected in observed correlations among sovereign yields. 9 I will
explore two possibilities. The first possibility is that, in reality, there are no latent
“global” factors whatsoever, but rather there are just U.S. factors that exogenously

For example, over the subsample 1999:Q1–2014:Q1, a regression of the DL slope factor embedded in the
gilt (bund) yield curve on the U.K. (euro area) policy rate spread yields an R2 of 0.83 (0.61) with a
coefficient on the policy rate spread of 0.91 (0.96), results that are comparable with the estimates for the
Treasury curve discussed earlier. However, in the remaining subsample 2014:Q2 to 2019:Q4, the slope
factor in these two countries is much flatter than predicted by the empirical relationship with the policy rate
spread that holds in the earlier subsample.
9
I think of r* and the policy rate spread as mapping a potentially large set of macroeconomic fundamentals
into two scalars and thus enabling dimension reduction compatible with a factor model structure. For
example, the Ferreira and Sousha (2021) specification for r* includes six explanatory variables, one of
which is a trade-weighted index of global productivity and demographic trends. Likewise, one can always
write the policy rate spread as r* + π* - {r* + π* + 1.5(π - π*) + 0.5(gap) + dev} = 1.5(π - π*) - 0.5(gap)
- dev, where dev is the deviation from a Taylor rule with a time-varying intercept equal to r* + π*.
8

-8fluctuate and cause the global correlations in bond yields we observe in the data. There is
a vast literature (Claessens, Stracca, and Warnock, 2016, provide an overview) that
documents the existence of spillovers from U.S. monetary policy, especially to emerging
market (EM) financial conditions, although the recent paper by Hoek, Kamin, and
Yoldas (2020) suggests that the degree of those spillovers depends importantly on the
source of the shock that triggers changes in Federal Open Market Committee (FOMC)
policy. In particular, as summarized in figure 5.1, they identified FOMC actions
associated with “growth news” as those that were immediately followed by changes in
the 10-year Treasury yield and the S&P 500 index in the same direction, whereas actions
associated with “monetary news” elicited changes in yields and equity prices in opposite
directions. Their key finding, illustrated in figure 5.2, was that FOMC policy rate
surprises attributed to stronger U.S. growth generally have only moderate spillovers to
EM financial conditions, whereas FOMC policy rate surprises attributed to U.S.
inflationary pressures trigger more substantial spillovers to EM financial conditions.
Regardless of the type of FOMC policy action, Hoek, Kamin, and Yoldas (2020) also
found compelling evidence that the size of the spillover effects from the United States
depends importantly on the degree of macroeconomic vulnerability of each emerging
market economy (EME), with more vulnerable EMEs experiencing larger spillovers.
While I certainly believe that both fundamental and financial shocks originating
in the United States propagate throughout the global financial system and likely account
for a significant share of the asset price correlations across global markets that we
observe in the data, the evidence—and introspection—suggests to me that causality can

-9and often does run both ways. 10 Anecdotally, it is not difficult to recall events—
plausibly exogenous to the United States—that have triggered spillovers from foreign
sovereign markets to the U.S. Treasury market. A prominent example would be the
surprise Brexit vote of June 23, 2016. As the news of the Brexit vote filtered through
global markets that day, sovereign yields plunged in both Germany and the United States.
Indeed, as is shown in figure 6, on that day, the 10-year Treasury yield fell almost 20
basis points, the single largest one-day decline in the eight years—and over 2,000 trading
days—between January 2012 and March 2020. 11
The evidence that two-way causality is reflected in sovereign bond yield
correlations is not limited to one-off geopolitical events such as Brexit. For instance,
Curcuru, De Pooter, and Eckerd (2018) examined 12 years of monetary policy
announcements by the FOMC and the European Central Bank (ECB)—a combined total
of 266 monetary policy communications—focusing on how sovereign yields in one
jurisdiction responded to monetary policy announcements made in the other. Their main
findings are summarized in the two panels in figure 7. The left panel presents some of
the evidence of the well-known, statistically significant spillovers from FOMC policy
announcements to euro-area bond markets. But, as is shown in the right panel, the

For example, Ferreira and Sousha (2021) attribute 85 basis points of the decline in U.S. neutral real
interest rates since 2000 to global spillovers. Moreover, in their model, foreign central bank purchases of
U.S. Treasury securities are a significant contributor to fluctuations in the supply of safe assets, which in
turn empirically account for much of the variation in global real interest rates in their model. The notion of
two-way causality was also examined empirically by Gospodinov (2020), who added a global factor to an
otherwise standard affine term structure model of the U.S. Treasury curve.
11
Also note from figure 6 that in the weeks before and after the Brexit vote, the 10-year Treasury yield and
the dollar–pound exchange rate were rising and falling together as the market assessed the likelihood of a
Brexit vote (before) and the implications of a Brexit vote (after).
10

- 10 authors found that the spillover effect from ECB policy announcements to U.S. yields is
roughly as large as that from the FOMC announcements to bund yields. 12
In another influential study using a very different identification methodology,
Ehrmann, Fratzscher, and Rigobon (2011) estimated significant and approximately equal
spillovers from U.S. bond market shocks to EU bond markets, and from EU bond market
shocks to the U.S. Treasury market. 13 They attributed their findings to significant
incipient and anticipated portfolio allocation flows across the two jurisdictions that
respond elastically to expected rate-of-return differentials. 14
Concluding Remarks
To sum up, I believe that in extracting signal from noise from the Treasury yield
curve, it is essential to incorporate the fact that observed yields in the United States and
other major sovereign markets are determined in a global general equilibrium that is
reflected, at least in part, in the global level of neutral policy rates and the state of longerterm global inflation expectations. 15 Conditional on neutral policy rates and longer-term
inflation expectations, the Federal Reserve and other major central banks can be thought
of as calibrating and conducting the transmission of policy—be it through rates, forward

The finding of two-way causality suggests that major central banks (not just the Federal Reserve) still
retain a fair amount of “monetary autonomy,” as discussed recently by Panetta (2021).
13
Ehrmann, Fratzscher, and Rigobon (2011) also examined potential spillovers between the United States
and the euro area in the money and equity markets, finding that, particularly in the latter, spillovers from
the euro area to the United States were very small, whereas those from the United States to the euro area
were quite sizable. They attributed this asymmetry to the central role that U.S. equity markets play in
world equity markets. Ehrmann, Fratzscher, and Rigobon (2011) used Rigobon’s (2003) identificationthrough-heteroskedasticity methodology to estimate a structural model where various asset prices are
determined simultaneously in the United States and the euro area.
14
The evidence of two-way causality is also consistent with the U.S. economy’s increasing integration with
the rest of the world, which has made it more exposed to foreign shocks (Clarida, 2019a).
15
Of course, there are very likely other fundamentals—such as equilibrium term premiums required to hold
long-duration sovereign bonds and, in many countries, default and illiquidity premiums required to hold
riskier sovereign debt—that are embedded in yield curve level and slope factors in addition to neutral
policy rates and longer-term inflation expectations.
12

- 11 guidance, or LSAPs—primarily through the slopes of their yield curves and much less so
via their levels. 16 Thank you very much for your time and attention. I look forward to
my conversation with Raphael.

The focus of these remarks has been on sovereign bond markets and monetary policy, but monetary
policy is, of course, also transmitted through the foreign exchange market. See Clarida (2019c) for a global
model of monetary policy, exchange rates, and neutral real interest rates.

16

- 12 References
Bauer, Michael D., and Glenn D. Rudebusch (2020). “Interest Rates under Falling
Stars,” American Economic Review, vol. 110 (May), pp. 1316–54.
Bernanke, Ben S. (2005). “The Global Saving Glut and the U.S. Current Account
Deficit,” speech delivered at the Sandridge Lecture, Virginia Association of
Economists, Richmond, Va., March 10,
https://www.federalreserve.gov/boarddocs/speeches/2005/200503102/default.htm.
Bomfim, Antulio N. (1997). “The Equilibrium Fed Funds Rate and the Indicator
Properties of Term-Structure Spreads,” Economic Inquiry, vol. 35 (October),
pp. 830–46.
Clarida, Richard H. (2005). “Our Post-Bubble World,” Wall Street Journal, April 11.
——— (2019a). “Global Shocks and the U.S. Economy,” speech delivered at “The Euro
Area: Staying the Course through Uncertainties,” BDF Symposium and 34th
SUERF Colloquium, sponsored by Banque de France and the European Money
and Finance Forum, Paris, March 28,
https://www.federalreserve.gov/newsevents/speech/clarida20190328a.htm.
——— (2019b). “Monetary Policy, Price Stability, and Equilibrium Bond Yields:
Success and Consequences,” speech delivered at the High-Level Conference on
Global Risk, Uncertainty, and Volatility, cosponsored by the Bank for
International Settlements, the Board of Governors of the Federal Reserve System,
and the Swiss National Bank, Zurich, November 12,
https://www.federalreserve.gov/newsevents/speech/clarida20191112a.htm.
——— (2019c). “The Global Factor in Neutral Policy Rates: Some Implications for
Exchange Rates, Monetary Policy, and Policy Coordination,” International
Finance, vol. 22 (Spring), pp. 2–19.
Clarida, Richard H., Jordi Galí, and Mark Gertler (2000). “Monetary Policy Rules and
Macroeconomic Stability: Evidence and Some Theory,” Quarterly Journal of
Economics, vol. 115 (February), pp 147–80.
Claessens, Stijn, Livio Stracca, and Francis E. Warnock (2016). “International
Dimensions of Conventional and Unconventional Monetary Policy,” Journal of
International Money and Finance, vol. 67 (October), pp 1–7.
Curcuru, Stephanie E., Michiel De Pooter, and George Eckerd (2018). “Measuring
Monetary Policy Spillovers between U.S. and German Bond Yields,”
International Finance Discussion Papers 1226. Washington: Board of Governors
of the Federal Reserve System, April, https://doi.org/10.17016/IFDP.2018.1226.
Diebold, Francis X., and Canlin Li (2006). “Forecasting the Term Structure of
Government Bond Yields,” Journal of Econometrics, vol. 130 (February),
pp. 337–64.

- 13 Diebold, Francis X., Canlin Li, and Vivian Z. Yue (2008). “Global Yield Curve
Dynamics and Interactions: A Dynamic Nelson-Siegel Approach,” Journal of
Econometrics, vol. 146 (October), pp. 351–63.
Ehrmann, Michael, Marcel Fratzscher, and Roberto Rigobon (2011). “Stocks, Bonds,
Money Markets and Exchange Rates: Measuring International Financial
Transmission,” Journal of Applied Econometrics, vol. 26 (September-October),
pp. 948–74.
Ferreira, Thiago, and Samer Shousha (2021). “Supply of Sovereign Safe Assets and
Global Interest Rates,” International Finance Discussion Papers 1315.
Washington: Board of Governors of the Federal Reserve System, April,
https://doi.org/10.17016/IFDP.2021.1315.
Friedman, Milton (1968). “The Role of Monetary Policy,” American Economic Review,
vol. 58 (March) pp. 1–17.
Gospodinov, Nikolay (2020). “Global Factors in U.S. Yield Curve,” working paper,
July, available at https://sites.google.com/site/gospodinovfed.
Greenspan, Alan (2005). “Testimony of Chairman Alan Greenspan,” statement before
the Committee on Banking, Housing, and Urban Affairs, U.S. Senate,
February 16,
https://www.federalreserve.gov/boarddocs/hh/2005/february/testimony.htm.
Hoek, Jasper, Steve Kamin, and Emre Yoldas (2020). “When Is Bad News Good News?
U.S. Monetary Policy, Macroeconomic News, and Financial Conditions in
Emerging Markets,” International Finance Discussion Papers 1269. Washington:
Board of Governors of the Federal Reserve System, January,
https://doi.org/10.17016/IFDP.2020.1269.
Holston, Kathryn, Thomas Laubach, and John C. Williams (2017). “Measuring the
Natural Rate of Interest: International Trends and Determinants,” Journal of
International Economics, vol. 108 (May, S1), pp. S59–75.
Laubach, Thomas, and John C. Williams (2003). “Measuring the Natural Rate of
Interest,” Review of Economics and Statistics, vol. 85 (November), pp. 1063–
1070.
Litterman, Robert B., and Josè Scheinkman (1991). “Common Factors Affecting Bond
Returns,” Journal of Fixed Income, vol. 1 (Summer), pp. 54–61.
Obstfeld, Maurice (2020). “Global Dimensions of U.S. Monetary Policy,” International
Journal of Central Banking, vol. 16 (February), pp. 73–132.
Panetta, Fabio (2021). “Monetary Autonomy in a Globalised World,” welcome address
delivered at the joint BIS, BOE, ECB, and IMF conference “Spillovers in a ‘PostPandemic, Low-for-Long’ World,” Frankfurt, April 26,
https://www.ecb.europa.eu/press/key/date/2021/html/ecb.sp210426~0ac9c74462.
en.html.
Rigobon, Roberto (2003). “Identification through Heteroskedasticity,” Review of
Economics and Statistics, vol. 85 (November), pp. 777–92.

- 15 Appendix
We derive in this appendix a simple model that can be used to interpret the empirical
relationship between Treasury yields, the neutral real interest rate, and the policy rate
spread. Begin with the identity that the policy rate spread equals the difference between
the neutral interest rate (𝑟𝑟𝑡𝑡∗ + 𝜋𝜋 ∗ ) and the current policy rate:
𝑠𝑠𝑡𝑡 = 𝑟𝑟𝑡𝑡∗ + 𝜋𝜋 ∗ − 𝑅𝑅𝑡𝑡,1 .

Now define the n-period term premium 𝜏𝜏𝑡𝑡,𝑛𝑛 through the long-term rate definition:
1

𝑅𝑅𝑡𝑡,𝑛𝑛 = 𝐸𝐸𝑡𝑡 � � ∑𝑛𝑛−1
𝑖𝑖=0 𝑅𝑅𝑡𝑡+𝑖𝑖,1 + 𝜏𝜏𝑡𝑡,𝑛𝑛 .
𝑛𝑛

Consider a simple data-generating process consistent with Laubach and Williams (2003)
for the neutral real interest rate
∗
𝑟𝑟𝑡𝑡∗ = 𝑟𝑟𝑡𝑡−1
+ 𝑤𝑤𝑡𝑡

and a simple first-order autoregression for the policy rate spread
𝑠𝑠𝑡𝑡 = 𝜌𝜌 𝑠𝑠𝑡𝑡−1 + 𝑒𝑒𝑡𝑡 ,

where 𝑤𝑤𝑡𝑡 and 𝑒𝑒𝑡𝑡 are assumed to be some unforecastable disturbances.
Then at any horizon 𝑛𝑛 we have
𝑅𝑅𝑡𝑡,𝑛𝑛 = 𝑟𝑟𝑡𝑡∗ + 𝜋𝜋 ∗ −

Regress 𝜏𝜏𝑡𝑡,𝑛𝑛 on the policy rate spread

1 (1−𝜌𝜌𝑛𝑛 )

𝑠𝑠
𝑛𝑛 �1−𝜌𝜌 � 𝑡𝑡

+ 𝜏𝜏𝑡𝑡,𝑛𝑛 .

𝜏𝜏𝑡𝑡,𝑛𝑛 = 𝜏𝜏0,𝑛𝑛 + 𝛽𝛽𝑛𝑛 𝑠𝑠𝑡𝑡 + 𝑣𝑣𝑡𝑡,𝑛𝑛,
where 𝜏𝜏0,𝑛𝑛 and 𝛽𝛽𝑛𝑛 are regression parameters and 𝑣𝑣𝑡𝑡,𝑛𝑛 is the residual, and we have (cf.
figure 3)
𝑅𝑅𝑡𝑡,𝑛𝑛 =

𝑟𝑟𝑡𝑡∗

1 (1 − 𝜌𝜌𝑛𝑛 )
+ 𝜋𝜋 + 𝜏𝜏0,𝑛𝑛 + �𝛽𝛽𝑛𝑛 −
� 𝑠𝑠 + 𝑣𝑣𝑡𝑡,𝑛𝑛 .
𝑛𝑛 (1 − 𝜌𝜌) 𝑡𝑡
∗

So yields at each maturity are anchored by the common neutral nominal rate 𝑟𝑟𝑡𝑡∗ +
𝜋𝜋 (Bauer and Rudebusch, 2020). The difference between the long rates 𝑅𝑅𝑡𝑡,𝑛𝑛 and the
neutral interest rate (𝑟𝑟𝑡𝑡∗ + 𝜋𝜋 ∗ ) is a linear function of the policy rate spread with a loading
that depends on the dynamics of the policy rate spread as well as the covariance between
the spread and the term premium.
∗

Figure 1: Diebold−Li Country Level and Slope Factors
Level factor

Weekly

Percent

Slope factor

Weekly
8
6

United Kingdom
United States

10

Germany

Global level factor
Germany

Percent

United Kingdom

8

United States

6

4

4

2

2
0

0

Feb. 26

Feb. 26

1999

2002

2005

2008

2011

2014

2017

−2
2020

1999

2002

2005

2008

2011

2014

2017

−2

−4
2020

Note: Country level factors are average of yields across all maturities from 3 months to 10 years at 3−month increments. They are the level factor from a renormalized
Diebold−Li level−slope two−factor model. This renormalization subtracts from the original Diebold−Li slope loading function a constant that is equal to the cross−sectional
average of the original Diebold−Li slope loadings at all included maturities (0.34 in our case). The sign of their slope loading function is flipped so that the renormalized
slope factor is positively related to the yield curve slope. The global level factor is a simple average of the plotted country level factors.
Source: Diebold and Li (2006); Bloomberg; staff calculations.

Figure 2: R* and the Global Level Factor
Percent

Percent
3

6
Global level factor (right scale)
Average r* (left scale)
4

2

2
1

Q4
Feb. 26
0

0

1999

2002

2005

2008

2011

2014

2017

2020

Note: The data for the global level factor are weekly, and the data for average r* are quarterly. The global level factor is a simple average of the country level
factors plotted in figure 1. The average r* is a simple average of the Holston, Laubach, and Williams (2017) estimated r* for the same three countries.
Source: Holston, Laubach, and Williams (2017); Diebold and Li (2006); Bloomberg; staff calculations.

Figure 3: 10−Year U.S. Treasury Yield and Neutral Nominal Policy Rate
Percent
8
Neutral nominal U.S. policy rate
10−year U.S. Treasury yield

6

4
Q4
2
Feb. 26
1999

2002

2005

2008

2011

2014

2017

2020

Note: The data for the neutral nominal U.S. policy rate are quarterly, and the data for the 10−year U.S. Treasury yield are weekly. Neutral nominal policy rate is
the Holston, Laubach, and Williams (2017) estimated U.S. r* plus 2 percent.
Source: Holston, Laubach, and Williams (2017); Bloomberg.

0

Figure 4: U.S. Slope Factor and Policy Rate Spread
Percent

Percent
4

6

Policy rate spread (left scale)
U.S. slope factor (right scale)

4
2
Q4
2
Feb. 26

0

0

−2

1999

2002

2005

2008

2011

2014

2017

2020

−2

Note: The data for the policy rate spread are quarterly, and the data for the U.S. slope factor are weekly. Policy rate spread is the Holston, Laubach, and Williams (2017)
estimated U.S. r* plus 2 percent (the neutral nominal policy rate) minus the federal funds rate. The U.S. slope factor is calculated from the Diebold and Li (2006) model.
Source: Holston, Laubach, and Williams (2017); Diebold and Li (2006); Bloomberg; staff calculations.

Figure 5.1: Growth and Monetary News around FOMC Meetings
Monetary news
2

1

1

0

0

−1

−1

−2

−2
−15

−10

−5

0

5

10

15

Change in 10−year U.S. Treasury yield (basis points)

Change in S&P 500 (percentage points)

Change in S&P 500 (percentage points)

Growth news
2

2

2

1

1

0

0

−1

−1

−2

−2
−15

−10

−5

0

5

10

15

Change in 10−year U.S. Treasury yield (basis points)

Note: Growth (monetary) news represents cases where the 10−year U.S. Treasury yield and S&P 500 index move in the same (opposite) direction. FOMC is Federal
Open Market Committee.
Source: Hoek, Kamin, and Yoldas (2020); Bloomberg; Federal Reserve Bank of New York.

Figure 5.2: Effect of a 100 Basis Point Increase in 10−Year U.S. Treasury Yield on EME Local Currency Bond Yields
Basis points
250
Growth news
Monetary news

200
150
100
50

High vulnerability

Low vulnerability

0

Note: Growth (monetary) news represents cases where the 10−year U.S. Treasury yield and S&P 500 index move in the same (opposite) direction. Countries are placed
in high or low vulnerability buckets based on six macroeconomic indicators: inflation, current account deficit, international reserves, government debt, external debt, and
private−sector credit growth. EME is emerging market economy.
Source: Hoek, Kamin, and Yoldas (2020); Bloomberg; Federal Reserve Bank of New York; Haver Analytics; International Monetary Fund; Federal Reserve Board staff
calculations.

Figure 6: 10−Year U.S. Treasury Yield and GBP Exchange Rate around 2016 Brexit Vote
USD/GBP exchange rate

Percent
1.75

1.50
GBP−USD exchange rate (right scale)

1.65

1.45

10−year U.S. Treasury yield (left scale)

1.55

1.40

1.45

1.35

1.35

1.30

1.25

June 12

June 15

June 18

June 21

June 24

June 27

June 30

July 3

July 6

July 9

July 12

1.25

2016
Note: Data are daily. Vertical dashed line indicates the Brexit referendum on June 23, 2016. GBP is British pound sterling; USD is U.S. dollar.
Source: Bloomberg.

Figure 7: Futures−Based Yields' Reaction to FOMC and ECB Events
FOMC events, 2−hr. event window change

ECB events, 2−hr. event window change

Basis points

Basis points

30
20

0
−10

Bund futures yield

10

30

y = 0.48 + 0.53x
(0.16***) (0.07***)
R−squared = 0.46

20
10
0
−10

−20

−20

−30
−50

−40

−30

−20

−10

0

UST futures yield

10

20

30

UST futures yield

y = 0.15 + 0.45x
(0.13) (0.02***)
R−squared = 0.88

−30
−50

−40

−30

−20

−10

0

10

20

30

Bund futures yield

Note: Horizontal and vertical lines are marked at 0. Black lines are the estimated linear regression lines, and the shaded areas around the regression lines show the
95 percent confidence interval. The inset box in the left (right) panel shows the results of the estimated ordinary least squares regressions where changes in 10−year
German (U.S) futures yields are regressed on changes in 10−year U.S. (German) futures yields in a two−hour window around FOMC (ECB) announcements. FOMC is
Federal Open Market Committee; ECB is European Central Bank; UST is U.S. Treasury.
Source: Curcuru, De Pooter, and Eckerd (2018).