The Term Structure of Uncertainty: New Evidence from Survey Expectations

• Published date: 01 February 2022
• Author: CAROLA BINDER,TUCKER S. MCELROY,XUGUANG S. SHENG
• Date: 01 February 2022
• DOI: http://doi.org/10.1111/jmcb.12811

DOI: 10.1111/jmcb.12811

CAROLA BINDER

TUCKER S. MCELROY

XUGUANG S. SHENG

The Term Structure of Uncertainty: New Evidence

from Survey Expectations

We construct measures of forecasters’ subjective uncertainty at horizons

from 1 to 5 years, using the European Central Bank’s Survey of Profes-

sional Forecasters. The uncertainty curve is more linear than the disagree-

ment curve. We document heterogeneity across forecasters in the leveland

the term structure of uncertainty,and show that the difference between long-

run and short-run uncertainty is procyclical. Wedevelop a signal extraction

model that features (i) Kalman lter updating, (ii) time-varying uncertainty,

and (iii) assessment of multistep ahead uncertainty. Heterogeneous patterns

of uncertainty over different horizons depend on perceived persistence and

variability of the signal and the noise.

JEL codes: D84, E31, E32, E37

Keywords: density forecasts, perceived persistence, term structure,

subjective uncertainty

H    G Recession has

prompted renewed efforts to investigate the sources and consequences of uncer-

tainty (Bloom 2009, Leduc and Liu 2016, Kozeniauskas, Orlik, and Veldkamp 2018).

Survey forecasts provide valuable information about the expectation formation pro-

cess and the associated subjective uncertainty (Coibion and Gorodnichenko 2012,

Ben-David, Graham, and Harvey 2013).

This paper was presented at University of Chicago Conference on “Developing and Using Business

Expectations Data,” the third “Forecasting at Central Banks Conference” at the Bank of Canada, and

the 27th Annual Symposium of the Society for Nonlinear Dynamics and Econometrics at the Federal

Reserve Bank of Dallas. Wethank Pok-Sang Lam (the editor), two anonymous referees, and the conference

participants for very useful comments. The views expressed herein are those of the authors and do not

necessarily reect the views of U.S. Census Bureau.

C B is an Assistant Professor of Economics at Haverford College (E-

mail: cbinder1@haverford.edu). T S. M is at U.S. Census Bureau (E-mail:

tucker.s.mcelroy@census.gov). X S. Sis an Associate Professor of Economics at

American University (E-mail: sheng@american.edu ).

Received August 7, 2019; and accepted in revised form February 16, 2021.

Journal of Money, Credit and Banking, Vol. 54, No. 1 (February 2022)

© 2021 The Ohio State University

40 :MONEY,CREDIT AND BANKING

In this paper, we construct measures of individual forecasters’ subjective uncer-

tainty at horizons ranging from 1 to 5 years, using density (histogram) forecasts

from the European Central Bank’s Survey of Professional Forecasters (ECB SPF).

Uncertainty refers to the spread (e.g., variance) of an individual agent’s probability

distribution about an outcome. We also construct measures of disagreement, or dis-

persion of expectations across forecasters, at each horizon. We explorethe properties

of uncertainty and disagreement over shorter and longer horizons, documenting four

stylized facts.

First, the term structure of uncertainty is highly linear—that is, uncertainty at

the 1- and 2-year horizons can almost perfectly predict uncertainty at the 5-year

horizon. This is true for both aggregate uncertainty and at the individual forecaster

level.

Second, the slope of the term structure of uncertainty is time-varying. We con-

rm that uncertainty is countercyclical, but also show that the slope is procyclical.In

recessions, short-run uncertainty rises signicantly more than long-run uncertainty.

Third, forecasters are overcondent at all horizons, in the sense that ex post uncer-

tainty is higher than ex ante uncertainty. For unemployment, the forecasters are most

overcondent at the longest horizon.

Fourth, we document substantial heterogeneity across forecasters in both the level

and term structure of uncertainty. While average uncertainty increases with forecast

horizon, a sizeable minority of forecasters have higher uncertainty at shorter horizons.

This heterogeneity is persistent. That is, particular forecasters tend to have particu-

larly wide or narrow (or even inverted) term structures of uncertainty.

Guided by our stylized facts, we model forecasters’ signal extraction process under

an information structure with private and public channels of information. We adopt

the framework of Baker, McElroy, and Sheng (2020) that features Kalman lter up-

dating and state-dependent information processing. Wegeneralize their framework by

allowing for time-varying uncertainty in both the signal and the noise and by study-

ing uncertainty and disagreement across multiple forecast horizons. The interplay

between signal and noise that is metrized through signal-to-noise ratio (SNR) plays

an essential role in establishing the last three stylized facts. The sticky information

model àlaMankiw and Reis (2002) cannot explain the linear term structure of un-

certainty. Classical noisy information model àlaSims (2003) can account for this

linearity, but cannot explainthe procyclical term structure of uncertainty. While a ba-

sic VAR model alone can also explain this linearity, it cannot account for the other

empirically observed phenomena.

Our theory emphasizes that perceived persistence is the keyto understanding multi-

step ahead expectation formation. When the signal is perceived as being more persis-

tent, the term structure of uncertainty takes on an increasingly linear pattern. For the

less persistent signal, uncertainty increases at all horizons, but the increase is sharper

at shorter horizons, leading to a procyclical term structure. This result supports

CAROLA BINDER, TUCKER S. MCELROYAND XUGUANG S. SHENG :41

intrinsic expectations persistence in Fuhrer (2017, 2018).1Perceived variability also

plays an important role. When the perceived noise variability is substantially lower

than the actual noise variability, agents lower their forecast uncertainty uniformly

across horizons, resulting in overcondence. In contrast, when the signal variabil-

ity is perceived by some agents to be higher at shorter horizons, but lower at longer

horizons, the regular ordering of uncertainty might be inverted across horizons for

these agents.

Our paper contributes to several strands of a broad literature using survey data to

study expectations formation, information frictions, and uncertainty (Mankiw, Reis,

and Wolfers 2004, Armantier et al. 2015, Coibion and Gorodnichenko 2015, Abel

et al. 2016, Kozeniauskas, Orlik, and Veldkamp 2018). A subset of this literature

makes use of the multiple-horizon forecasts that are available from some surveys

to extract additional information (Andrade et al. 2016, Binder 2018). For example,

Aruoba (2020) combines ination forecasts at various horizons from several surveys

to obtain a term structure of ination expectations, and combines this with nominal

interest data to obtain a term structure of ex ante real interest rates.

Several papers examine disagreement at various forecast horizons. Lahiri and

Sheng (2008) use multihorizon data to estimate the relative importance of three com-

ponents of disagreement: (i) differences in prior beliefs, (ii) different weights attached

on priors, and (iii) differential interpretation of public information. In a similar vein,

Patton and Timmermann (2010) show that the term structure of disagreement can be

used to determine the relative importance of differences in priors versus differences

in private information. Andrade and Le-Bihan (2013) emphasize two sources of het-

erogeneity: inattention and noisy signals, while Giacomini, Skreta, and Turén (2020)

nd that in normal times heterogeneous priors and inattention are enough to generate

persistent disagreement, but not during the crisis.

Other papers examine uncertainty at multiple horizons. Ination uncertainty at dif-

ferent horizons is of particular interest to monetary policymakers. Ball and Cecchetti

(1990) nd that the level of ination has a stronger effecton the variance of permanent

than of temporary shocks, and therefore has a greater effect on longer horizon than

on shorter-horizon ination uncertainty. These authors do not use a direct measure of

ination uncertainty, but rather use ination variability as a proxy. Using data from

the Michigan Survey of Consumers, Binder (2017) constructs an index of consumer

ination uncertainty and documents that the uncertainty was higher for the longer

than shorter horizon until the mid-1990s. Since then, longer-run ination uncertainty

declined more than shorter-run uncertainty, inverting the term structure.

Barrero, Bloom, and Wright (2017) study uncertainty at short and long horizons

using rm and macro implied volatility as proxies for uncertainty. As with our un-

certainty measures, the term structure of implied volatility is linear, so they fo-

cus on just the 30-day and 1-year horizons as proxies for short-run and long-run

1. Fuhrer(2017) shows that intrinsic persistence in expectations, rather than price indexation or habit

formation, is a keysource of macro-economic persistence. Fuhrer (2018) further explores howexpectations

might exhibit such inertia and nds that agents smooth their expectations’ response to news.