Expected Inflation and Other Determinants of Treasury Yields

• DOI: http://doi.org/10.1111/jofi.12700
• Author: GREGORY R. DUFFEE
• Date: 01 October 2018
• Published date: 01 October 2018

THE JOURNAL OF FINANCE •VOL. LXXIII, NO. 5 •OCTOBER 2018

Expected Inflation and Other Determinants

of Treasury Yields

GREGORY R. DUFFEE∗

ABSTRACT

Shocks to nominal bond yields consist of news about expected future inflation, ex-

pected future real short rates, and expected excess returns—all over the bond’s life. I

estimate the magnitude of the first component for short- and long-maturity Treasury

bonds. At a quarterly frequency, variances of news about expected inflation account

for between 10% to 20% of variances of yield shocks. Standard dynamic models with

long-run risk imply variance ratios close to 1. Habit formation models fare somewhat

better. The magnitudes of shocks to real rates and expected excess returns cannot be

determined reliably.

ALARGE AND EXPANDING LITERATURE explores the relation between nominal bond

yields and inflation. In a particularly important contribution, Ang and Piazzesi

(2003) introduce Gaussian macro-finance dynamic term structure models to

determine the compensation investors require to face shocks to inflation and

macroeconomic activity. Subsequent studies have branched out to include un-

spanned macro risks, non-Gaussian dynamics, and fundamental explanations

for inflation risk premia that are grounded in investor preferences and New

Keynesian macro models. Yet it is difficult to uncover from this literature any

widely accepted conclusions about the joint dynamics of inflation and the nom-

inal term structure. Motivated by this point, Ang, Bekaert, and Wei (2008)

attempt to produce some basic facts. More recent research does not converge

on their conclusions or any other set of core results. Thus, it remains unclear

which branches of the macro-finance literature are likely to be fruitful and

which should be abandoned.

In this paper, I make an additional attempt to identify a robust empirical

property that can be used to guide future research. I focus on the question

“How large are shocks to expected inflation relative to shocks to nominal bond

yields?” Embedded in this question is an accounting identity. Campbell and

Ammer (1993) show that the shock to a nominal bond’s yield equals the sum

of news about expected inflation, expected short-term real rates, and expected

excess returns, all over the life of the bond. The “inflation variance ratio,” as

∗Gregory R. Duffee is with Johns Hopkins University. I thank seminar participants at many

schools and conferences, Ravi Bansal, Mike Chernov, Anna Cieslak, George Constantinides, Lars

Lochstoer,Kenneth Singleton (Editor), Jonathan Wright, and three anonymous referees for helpful

comments. I thank especially the discussants Anh Le and Scott Joslin. I have read the Journal of

Finance’s disclosure policy and have no conflicts of interest to disclose.

DOI: 10.1111/jofi.12700

2139

2140 The Journal of Finance R

defined here, is the variance of expected inflation news relative to the variance

of the yield shock.

Three observations motivate a focus on this ratio. First, it can be estimated

without much structure, using survey forecasts of inflation to identify revisions

in inflation expectations. Second, ratios based on quarterly U.S. data are reli-

able, in the sense that standard errors are tight and estimates are reasonably

stable over time. Third, ratios inferred from these data are strongly at odds

with corresponding values from both endowment economy long-run risk models

and standard New Keynesian dynamic models.

Results for the 10-year horizon are representative. During the past 35 years,

the standard deviation of quarterly shocks to 10-year average expected in-

flation is in the neighborhood of 20 basis points. The standard deviation of

quarterly shocks to the 10-year bond yield is much larger—around 60 basis

points. Squaring and dividing produces a variance ratio estimate close to 10%.

The challenge for economists is easier to see when viewing the result from

a different angle. In the data, shocks to nominal yields are large and driven

primarily by a combination of news about expected short-term real rates and

expected excess returns. In our benchmark macro-finance models, channels for

both types of news are small.

Bansal and Yaron (2004) develop one of these benchmark models, combining

a representative agent, recursive utility preferences, and persistent fluctua-

tions in the endowment growth rate. Short-term real rates are driven largely

by fluctuations in expected consumption growth. The long-run risk literature

follows Bansal and Yaron (2004) by relying on a high elasticity of intertempo-

ral substitution and fairly small shocks to expected growth. The combination

of these properties results in low volatility of news about expected short-term

real rates.

These conditionally log-normal models generate news about expected excess

returns only through shocks to conditional volatilities of macroeconomic shocks.

The amount of news this mechanism produces depends on the average level of

bond risk premia, which are much too small to allow for sizable volatilities of

news about expected excess returns.

Dynamic New Keynesian models also produce low volatilities of real rate

news because the dynamics are not sufficiently persistent. Since these models

do not have conditional log-normal dynamics, nonlinearities can potentially

create more news about expected excess returns than can models in the tradi-

tion of Bansal and Yaron(2004). But for parameterized models in the literature,

the nonlinearities are not sufficient to generate realistic volatilities of shocks

to yields.

Habit formation preferences in the spirit of Campbell and Cochrane (1999)

break the link between expected consumption growth and short-term real rates,

creating another mechanism for generating real rate news. In addition, the

models’ nonlinearities can create substantial news about expected excess re-

turns. We can therefore choose parameterizations of these models that are

consistent with observed inflation variance ratios. However, the evidence is

much too tentative to warrant the conclusion that nominal bond dynamics are

Expected Inflation and Treasury Yields 2141

best understood through the lens of habit formation. In particular, parame-

terizations that are successful in reproducing inflation variance ratios exhibit

other properties that appear implausible.

Empirically, innovations to expected short-term real rates and expected ex-

cess returns are the primary drivers of yield shocks. Unfortunately, there is

insufficient information in the data to disentangle the relative contributions of

these two components, at least without imposing restrictive assumptions. The

relevant properties of the data are easy to summarize. Shocks to short-term

real rates are large, and long-term nominal yields covary strongly with them.

If short-term real rates are highly persistent, then the variation in long-term

yields is explained by shocks to average expected future short-term real rates.

If short-term real rates die out quickly, the variation is explained by shocks

to expected excess returns—also called shocks to term premia—that positively

covary with short-term real rates. Point estimates of the persistence are con-

sistent with the latter version, but statistical uncertainty in these estimates

cannot rule out the former version.

The paper is organized as follows. Section Idescribes how I measure inflation

variance ratios and discusses the data used to construct shocks to inflation

expectations. Section II documents the low level of the ratio in the data. Section

III discusses volatilities of components of yield shocks in various macro-finance

equilibrium models. Section IV attempts to determine the relative roles of news

about expected future short rates and expected future returns. An Internet

Appendix, available in the online version of the article on the Journal of Finance

website, contains detailed discussions of various issues.

I. Inflation Variance Ratios

“Inflation news” is not a clear-cut concept—there is no unique or best way to

measure how shocks associated with an inflation process affect nominal bond

yields. The New Keynesian model examined by Rudebusch and Swanson (2012;

hereafter R/S) helps illustrate the ambiguity. In the model, there are no exoge-

nous shocks to inflation. Thus, in a narrow sense, there is no inflation news.

However, shocks to productivity, monetary policy, and government spending

each affect the paths of expected inflation, real rates, and nominal bond risk

premia. Thus, in a broad sense, all news is inflation news, as every shock con-

veys information about expected future inflation. Models in which a monetary

authority follows a Taylor rule typically have the same property. Outside the

special cases, a shock to any variable that appears in the Taylor rule affects

both yields and expected future inflation.

Rather than adopt a specific model’s interpretation of inflation shocks, in

this paper I measure the magnitude of inflation news using an accounting

approach that has its roots in the dividend/price decomposition of Campbell

and Shiller (1988), as extended to returns by Campbell (1991). The measure

is straightforward to estimate with available data. Any dynamic model of both

inflation and bond yields—a class of which includes a wide variety of dynamic

macro models—implies a value of a bond’s inflation variance ratio.