Macroeconomics and the Term Structure

TLDR: The authors provides an overview of the analysis of the term structure of interest rates with a special emphasis on recent developments at the intersection of macroeconomics and finance, and shows that many features of the configuration of interest rate are puzzling from the perspective of the expectations hypothesis.

Abstract: This paper provides an overview of the analysis of the term structure of interest rates with a special emphasis on recent developments at the intersection of macroeconomics and finance. The topic is important to investors and also to policymakers, who wish to extract macroeconomic expectations from longer-term interest rates, and take actions to influence those rates. The simplest model of the term structure is the expectations hypothesis, which posits that long-term interest rates are expectations of future aver- age short-term rates. In this paper, we show that many features of the configuration of interest rates are puzzling from the perspective of the expectations hypothesis. We review models that explain these anomalies using time-varying risk premia. Although the quest for the fundamental macroeconomic explanations of these risk premia is ongoing, inflation uncertainty seems to play a large role. Finally, while modern finance theory prices bonds and other assets in a single unified framework, we also consider an earlier approach based on segmented markets. Market segmentation seems important to understand the term structure of interest rates during the recent financial crisis. ( JEL E31, E43, E52, E58)

Figures

Figure 7: Yields on Treasury coupon securities on selected dates

Figure 3: Bond Yields and Forward Rates Since 1984

Figure 4: One-year Excess holding period returns of the ten-year over the one-year bonds

Figure 5: Slope of Nominal and TIPS Yield curves

Table 2: Slope Coe¢ cient from Estimation of Equation (8)

Figure 1: Selected Interest Rates in Recent Years

Full text

Macroeconomics and the Term Structure

Refet S. Gürkaynak
y
Jonathan H. Wright
z
First Draft: April 2010
This version: September 12, 2010
Abstract
This paper provides an overview of the analysis of the term structure
of interest rates wi th a special emphasis on recent developments at the
inter sectio n of macroecon omics an d …nance. The topic is important to
investors and also to policymakers, who wish to extract macroeconomic
expectations from longer-term interest rates, and take actions to in‡uence
those rates. The si mplest model of the term structur e is the expectatio ns
hypothesis, wh ich posits that long-term interest rate s are expectat ions
of future average sh ort-te rm rates. In this pape r, we show that many
featu res of the con…gu ration of interest rates are puz zling from the per-
spective of the expectations hypothesis. We review models that explain
these anomalies usi ng time-vary ing risk premia. Although the quest for
the funda mental macroecon omic explanations of thes e risk premia is ongo-
ing, in‡ation uncertainty seems to play a large role. F inally, while modern
…nance theory prices bonds and other assets in a single uni…ed framework,
we also consider an earlier approach based on segmented markets. Mar-
ket segmentation seems important to understa nd the term structure of
inter est rates during the recent …nan cial crisis.
JEL Classi…cation: C32, E43, E44, E58, G12.
Keywords: Term structure, interest rates, expectations hypothesis,
a¢ ne models, in‡ation, …nancial crisis, segmented markets.

We are very gratef ul to Roger Go rdon and three anonymous reviewers for their very helpful
comments on various draft s of this paper. All er rors and omiss ions are our own responsbility
alone.
y
Department of Economics, Bilkent University, 06800 Ankara, Turkey and CEPR.
ref et@bilkent.edu.tr.
z
Department of Economics, J ohns Hopkins University, Baltimore MD 21218.
wrightj@jhu.edu.

1 Introduction
On Jun e 29, 2004, the day before the Federal Open Market Committee (FOMC)
began its most recent tightening cycle, the overnight interest rate, the federal
funds target, was one percent and the ten-year yield was 4.97 percent. On June
29, 2005, the corresponding rates were three percent and 4.07 percent. Over
the course of a year when the Fed was tightening monetary policy, increas-
ing the overnight rate by 2 percentage points, longer-term yields had inste ad
fallen. The ten-year rate decreased by 90 basis points. Fixed mortgage rates
and longer-term corporate bond yields fell even more. This rotation of the yield
curve surprised then Fed Chairman Greenspan. In his oft-quoted February 2005
testimony to Congress, he stated:
“This development contrasts with most experience, which sug-
gests that ...increasing short-term interest rates are normally ac-
companied by a rise in longer-term yields. . . For the moment, the
broadly unanticipated behavior of world bond markets remains a
conun drum.”
But similar patterns in the con…guration of interest rates have happe ned before—
and since. Figure 1 shows the federal funds rate, three-month Treasury bill
yields, and ten-year Treasury yields over the last seven years. The federal funds
rate and three-month yields moved closely together, but ten-year (and other
long-term) yields were often uncoupled from short-term rates. Greenspan’s co-
nund rum is one example. Another is that in the early fall of 2008, as the FOMC
was cutting the federal funds rate sharply, long-term interest rates actually rose,
peaking in early November of that year. This could be called the “conundrum
in reverse.” Later on, long-term yields declined sharply, around the time that
the Fed announced the start of large-scale asset purchases.
1

The object of this paper is to discuss work on the mac roeconomic forces that
shape the term structure of interest rates. Broadly, the explanations fall into
two categories. The …rst is that long-term interest rates re‡ect expectations
of future short-term interest rates. This is the expectations hypothesis of the
term structure of interest rates. If short-term interest rates are in turn driven
by in‡ation and the output gap, as in the Taylor rule, then the term structure
of interest rates ought to re‡ect expectations of future in‡ation and the output
gap. For example, if the FOMC lowers policy rates today bu t, because of higher
expected in‡ation, this leads agents to anticipate higher short-term interest rates
in the future, then long-term interest rates could actually increase. The second
category of explanations argues that long-term interest rates are also a¤ected
by risk premia, or by the e¤ects of market segmentation, which can break the
link between long-term interest rates and expectations of future short rates.
The literature on term structure modeling is vast. This paper portrays the
state of that literature by presenting di¤erent theories in a uni…e d framework.
We look at which aspects of the data are explained by di¤erent models using
term structure data from 1971 to the present, and discuss the macroeconomic
foundations and implications of the di¤erent models. Our aim is to focus on
interactions between macroeconomics, monetary policy, and the term structure,
rather than to consider term structure models from a more technical …nance
perspective. Comprehensive reviews of the latter variety are already available
in Du¢ e (2001), Singleton (2006) and Piazzesi (2008).
There are many reasons why policy-makers, investors and academic econo-
mists should and do care about the forces that a¤ect the term structure of
interest rates. First, economists routinely attempt to reverse-engineer mar-
ket expectations of future interest rates, in‡ation, and other macroeconomic
variables from the yield curve, but accomplishing this task also requires us to
2

separate out any e¤ects of risk premia. For example, in early 2010, the yield-
curve slope was quite steep. Some commentators suggested that this steep yield
curve represented concerns about a potential pickup in in‡ation, but without
more formal models, it is hard to know if this was right, or if other forces were
at work instead. Second, analysis of the term structure has implications for
how monetary policy ought to respond to changes in long-term interest rates.
If long-term rates were to f all because of an exogenous fall in risk premia, then
it seems natural that policy-makers ought to lean against the wind
1
by tighten-
ing the stance of monetary policy to o¤set the additional stimulus to aggregate
demand (McCallum (1994)). However the models that we shall discuss in this
paper attempt to endogenize risk premia, and in this case the appropriate policy
response is ambiguous and depends on the source of the change in risk premia
(Rudebusch, Sack an d Swanson (2007)). Third, at present, the federal funds
rate is stuck at the zero bound. Monetary policy-makers may wish to pro-
vide additional stimulus to the economy. Unde r the expectations hypothesis,
the only way that they can do this is by in‡uencing market expectations of
future monetary policy, perhaps by committing to keep the federal funds rate
at zero for an extended period. On the other hand, if long-term interest rates
are also bu¤eted by risk premia, then measures to alter those risk premia, per-
haps through large-scale asset purchases, may be e¤ective as well. The Federal
Reserve and some other central banks have recently tried this. Fourthly, under-
standing the evolution of the term structure of rates is important for predicting
asset returns and for determining the portfolio allocation choices of investors
and their strategies for hedging interest rate risk. Finally, governments around
the world borrow by issuing b oth short- and long-term debt, and debt that is
1
The whole term structure of interest rates should be relevant for aggregate demand. For
example, business …nanc ing involves a mix of short-term commercial paper and long-term
corpo rat e bonds. In the U.S.— though not in foreign countries— most mortgages are …xed-
rate.
3

both nominal and index-linked (in‡ation protected). Understanding the market
pricing of these di¤erent instruments is important in helping governments de-
termine the bes t mix of securities to issue in order to keep debt servicing costs
low and predictable.
The plan for the remainder of this paper is as follows. Section 2 describes
basic yield curve concepts and gives some empirical facts about the term s truc-
ture of interest rates. Section 3 discusses the evidenc e on the e xpectations
hypothesis of the term structure. Section 4 introduces a¢ ne term structure
models, which the …nance literature has been developing over the last ten years
or so as a potential alternative to the expectations hypothesis. Progress has
been rapid, and these models provide an alternative in which long-term interest
rates represent both expectations of future short term interest rates and a time
varying risk premium, or term premium, to compensate risk-averse investors for
the risk of capital loss on selling a long-term bond before maturity and/or the
risk of the bond’s value being eroded by in‡ation. The models that are dis-
cussed span a spectrum from reduced form statistical mod els to fully speci…ed
structural dynamic stochastic general equilibrium (DSGE) models, and many
intermediate cases. Section 5 examines the implications of structural breaks
and learning for these models. Section 6 discusses term structure models with
market segmentation, and section 7 concludes.
2 Basic Yield Curve Concepts and Stylized Facts
This section …rst introduces the basic bond pricing terminology that will be
used in the remainder of the paper, and then presents the most salient stylized
facts of the term structure of interest rates.
4

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Macroeconomics and the term structure" ?

This paper provides an overview of the analysis of the term structure of interest rates with a special emphasis on recent developments at the intersection of macroeconomics and nance. In this paper, the authors show that many features of the con guration of interest rates are puzzling from the perspective of the expectations hypothesis. The authors review models that explain these anomalies using time-varying risk premia. Finally, while modern nance theory prices bonds and other assets in a single uni ed framework, the authors also consider an earlier approach based on segmented markets. The authors are very grateful to Roger Gordon and three anonymous reviewers for their very helpful comments on various drafts of this paper. 

Q2. What future works have the authors mentioned in the paper "Macroeconomics and the term structure" ?

FOMC members were discussing the possibility of expanding the size of its balance sheet further, should the economic recovery falter. But the evidence from the macro- nance term structure literature suggests that if that were to happen in the future, then it would lead to a large rebound in term premia Notes: Estimates of the slope coe¢ cient in equation ( 7 ) for selected choices of m and n, in months. Both expected short rates and term premia can be tied to ( observable or latent ) economic fundamentals within this framework and the yields can be decomposed into expected rates and term premia to make policy relevant inferences. But the potential for market segmentation has been highlighted by the recent nancial crisis, and preferred habitat models are enjoying a renaissance. 

Q3. What can be done to make policy relevant inferences?

Both expected short rates and term premia can be tied to (observable or latent) economic fundamentals within this framework and the yields can be decomposed into expected rates and term premia to make policy relevant inferences. 

Q4. What is the importance of understanding the term structure of rates?

understanding the evolution of the term structure of rates is important for predicting asset returns and for determining the portfolio allocation choices of investors and their strategies for hedging interest rate risk. 

Q5. What is the problem with a structural model for both the pricing kernel and the factor dynamics?

A general problem with a structural model for both the pricing kernel and the factor dynamics is that it is challenging to maintain computational tractability and yet obtain timevariation in term premia. 

Q6. What is the reason why the regressions are subject to peso problems?

the regressions are subject to the possibility of peso problems in which yields are priced allowing for the possibility of a regime shift that was not actually observed in the short sample. 

Q7. how many principal components are used to account for nearly all of the variation in bond yields?

As three principal components are su¢ cient to account for nearly all of the crosssectional variation in bond yields (Litterman and Scheinkman (1991)), most of these papers use three yield-curve factors in Xt, which can be interpreted as the level, slope, and curvature of yields. 

Q8. What is the key to having lower and more stable risk premia?

It would be hard to tell a policymaker that the key to having lower and more stable risk premia is to change the law of motion of some latent factor. 

Q9. What would the rebounds in forward rates represent?

It would also imply that the rebounds in forward rates during the early fall of 2008 and again in late 2009 represent increases in long-term expectations of in ation and/or real rates. 

Q10. What is the way to explain the fty-year indexed government bond yield?

Long-term bond yields have been especially low in the United Kingdom since these rules came into force, with the real yield on fty-year indexed government bonds in the U.K. falling below half a percentage point at one time. 

Q11. What is the logical conclusion of a progression from atheoretical to structural models?

But recently some authors have used structural models for both the factor dynamics and the pricing kernel, and this is the logical conclusion of a progression from atheoretical to structural models. 

Q12. What would mean that the net supply of bonds would have larger eects?

That would mean that shifts in the net supply of bonds would have larger e¤ects on yields at times of market stress than at times of more normal market functioning. 

Q13. What is the difference between the resale value of a bond before maturity and?

That is, the resale value of the bond before maturity (or the opportunity cost of funding the bond position) depends on the uncertain trajectory of future short term interest rates. 

Q14. Why is the a ne model popular?

Although other assumptions on the functional form of the pricing kernel and short-term interest rate are of course possible, the a¢ ne model is most popular in part because of its tractability. 

Q15. What is the difference between the pricing kernel and the utility maximization problem?

In this subsection, the authors now turn to discussing papers that have instead derived the pricing kernel from an explicit utility maximization problem, while going back to having unrestricted reduced form dynamics for the factors. 

Q16. What is the way to re-estimate the term structure?

One simple approach is to take any standard term structure model, but to re-estimate it in each period using a rolling window of data (such as the last ten years, or using some pattern of declining weights).