CORRIGENDUM: MEASURING UNCERTAINTY
AND ITS IMPACT ON THE ECONOMY

Andrea Carriero, Todd E. Clark, and Massimiliano Marcellino*

Original article: Carriero, Andrea, Todd E. Clark, and Massimiliano Marcellino, “Measuring Uncertainty and Its Impact on
the Economy,” this REVIEW 100:5 (2018), 799–815. 10.1162/rest_a_00693

Abstract—Carriero, Clark, and Marcellino (2018, CCM2018) used a large
BVAR model with a factor structure to stochastic volatility to produce an
estimate of time-varying macroeconomic and financial uncertainty and as-
sess the effects of uncertainty on the economy. The results in CCM2018
were based on an estimation algorithm that has recently been shown to be
incorrect by Bognanni (2022) and fixed by Carriero et al. (2022). In this
corrigendum we use the algorithm correction of Carriero et al. (2022) A
correct the estimates of CCM2018. Although the correction has some im-
pact on the original results, the changes are small and the key findings of
CCM2018 are upheld.

IO.

introduzione

TO make tractable the estimation of the large model of

Carriero, Clark, and Marcellino (2018, hereafter denoted
CCM2018), we used an equation-by-equation approach to the
vector autoregression (VAR) based on a triangularization of
the conditional posterior distribution of the coefficient vector
developed in Carriero, Clark, and Marcellino (2019, here-
after CCM2019). Tuttavia, Bognanni (2022) recently iden-
tified a conceptual problem with the triangular algorithm of
CCM2019: the triangularization does not deliver the intended
posterior of the VAR’s coefficients. The same problem afflicts
the estimation algorithm used in CCM2018.

In response, Carriero et al. (2022) have developed a cor-
rected triangular algorithm for Bayesian VARs that does
yield the intended posterior. This new algorithm permits an
equation-by-equation approach to the VAR and offers the
same basic computational advantages of the original triangu-
lar algorithm. Inoltre, the new algorithm can be used to
properly estimate the uncertainty model of CCM2018.

In this corrigendum, we provide corrected versions of
the published results of CCM2018. Drawing from Carriero
et al. (2022), Section II briefly explains the problem with
the original triangular algorithm and the correction. Sezione
III presents corrected versions of the results of CCM2018.
Although the correction has some impact on results, these
impacts are small, and the key findings of CCM2018 are
upheld.

II. Original Algorithm and Correction

For convenience, we briefly detail the model used in
CCM2018. Let yt denote the n × 1 vector of variables of
interesse, split into nm macroeconomic and n f = n − nm fi-
nancial variables. Let vt be the corresponding n × 1 vector
of reduced-form shocks to these variables, also split into two
groups of nm and n f components. The reduced-form shocks
are

vt = A−1(cid:2)0.5

T

(cid:3)T , (cid:3)t ∼ iid N (0, IO ),

(1)

where A is an n × n lower triangular matrix with ones on the
main diagonal, E (cid:2)t is a diagonal matrix of volatilities,
with the log volatilities following a linear factor model:

(cid:2)

ln λ jt =

βm, j ln mt + ln h j,T ,
β f , j ln ft + ln h j,T ,

j = 1, . . . , nm
j = nm + 1, . . . , N.

(2)

The variables h j,T , which do not enter the conditional mean
of the VAR, specified below, capture idiosyncratic volatility
components associated with the jth variable in the VAR and
are assumed to follow (in logs) an autoregressive process,

ln h j,t = γ j,0 + γ j,1 ln h j,t−1 + e j,T , j = 1, . . . , N,

(3)

with νt = (e1,t , . . . , en,T )(cid:4) jointly distributed as iid N (0, (cid:4)ν)
and independent among themselves, so that (cid:4)ν = diag(φ1,
. . . , φn). These shocks are also independent of the conditional
errors (cid:3)T . The reduced-form error covariance matrix is (cid:5)t =
A−1(cid:2)t A−1(cid:4).

The variable mt is our measure of (unobservable) aggre-
gate macroeconomic uncertainty, and the variable ft is our
measure of (unobservable) aggregate financial uncertainty.
Together, the two measures of uncertainty (in logs) follow an
augmented VAR process,
(cid:3)

(cid:3)

(cid:4)

(cid:3)

(cid:3)

(cid:4)

(cid:4)

(cid:4)

ln mt
ln ft

= D(l)

ln mt−1
ln ft−1

+

δ(cid:4)
M
δ(cid:4)
F

yt−1 +

um,T
u f ,T

,

(4)

∗Carriero: Queen Mary University of London and University of Bologna;
Clark: Federal Reserve Bank of Cleveland; Marcellino: Bocconi University,
IGIER, and CEPR.

The views expressed here are solely our own and do not necessarily reflect
the views of the Federal Reserve Bank of Cleveland or the Federal Reserve
System. We are grateful to Mark Bognanni for identifying a problem in the
triangular estimation algorithm of Carriero, Clark, and Marcellino (2019),
later corrected in Carriero et al. (2022). Todd E. Clark is the corresponding
author.

where D(l) is a lag-matrix polynomial of order d. The shocks
to the uncertainty factors um,t and u f ,t are independent of the
shocks to the idiosyncratic volatilities e j,t and the conditional
errors (cid:3)T , and they are jointly normal with mean 0 and variance
var(ut ) = var((um,T , u f ,T )(cid:4)) = (cid:4)tu.

The uncertainty variables mt and ft can also affect the
levels of the macro and finance variables contained in yt ,

The Review of Economics and Statistics, May 2022, 104(3): 619a–619k
© 2022 The President and Fellows of Harvard College and the Massachusetts Institute of Technology
https://doi.org/10.1162/rest_e_01172

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619B

THE REVIEW OF ECONOMICS AND STATISTICS

contemporaneously and with lags. In particular, yt is assumed
to follow

yt = (cid:6)(l)yt−1 + (cid:6)M(l) ln mt + (cid:6) F (l) ln ft + vt ,

(5)

where p denotes the number of yt
lags in the VAR,
(cid:6)(l) = (cid:6)1 − (cid:6)2L − · · · − (cid:6)pL p−1, con (cid:6)i an n × n ma-
trix, i = 1, . . . , P, E (cid:6)M(l) E (cid:6) F (l) are n × 1 lag-matrix
polynomials of order pm and p f . In explaining estimation, Esso
will be helpful to collect the coefficients of (cid:6)(l), (cid:6)M(l),
E (cid:6) F (l) in a k × n matrix (cid:6) and the regressors of each
equation in the k × 1 vector xt and write the VAR system as

yt = (cid:6)(cid:4)xt + vt .

(6)

Estimating the model with a Gibbs sampler requires the
conditional posterior for the matrix of VAR coefficients (cid:6).
With smaller models, it is common to rely on a GLS solution
for the posterior mean of the coefficient vector of the sys-
tem of equations. Tuttavia, such a system-of-equations ap-
proach slows considerably with larger models. In CCM2018,
we instead estimated the VAR coefficients on an equation-
by-equation basis, following a factorization of the posterior
developed in CCM2019. Specifically, let π( j) denote the jth
column of the matrix (cid:6), and let π(1: j−1) denote all of the
previous columns. For each equation j, we drew π( j) from
a multivariate Gaussian distribution with mean and variance
come segue,

μπ( j) = (cid:7)π( j)

(cid:7)−1

π( j) = (cid:7)−1
π( j)

(cid:5)

t=1xt λ−1
(cid:5)T

j,t y∗(cid:4)
j,T

+ (cid:5)T

j,t x(cid:4)
t=1xt λ−1

T

+ (cid:7)−1

π( j) (μ

π( j) )

(cid:6)

,

,

j−1,t

j, j−1

λ0.5

λ0.5
1,T

π( j) and μ

(cid:3)1,T + · · · + a∗

= y j,t − (a∗
j,1

where y∗
(cid:3) j−1,t ),
j,T
j,i denoting the generic element of the matrix A−1 and
with a∗
(cid:7)−1
π( j) denoting the prior moments of the jth equa-
zione, given by the jth column of μ
(cid:6) and the jth block on
the diagonal of (cid:7)−1
(cid:6) . Based on CCM2019, we intended for
this approach to yield draws from the (correct) conditional
posterior,

π( j)|π(1: j−1), UN, β, f1:T , m1:T , h1:T , y1:T ∼ N (μπ( j), (cid:7)π( j) ).
(7)

Tuttavia, as follows from the results in Bognanni (2022),
drawing the VAR’s coefficients in this way does not deliver
the intended posterior distribution of the coefficient matrix.
Questo è, drawing the coefficients as was done in CCM2018
does not actually sample from the density (7). As explained
in more detail in Carriero et al. (2022), the actual density
associated with the original algorithm is missing a term,
involving the information about π( j) contained in the most
recent observations of the dependent variables of equations
j + 1, . . . , N.

To correctly use the information in question in an algorithm
for sampling from the conditional posterior for the VAR’s

coefficients, Carriero et al. (2022) propose using a sequence
of Gibbs sampler draws. Specifically, in the model setting of
CCM2018, one can correctly sample from the joint distribu-
zione (cid:6)|UN, β, f1:T , m1:T , h1:T , y1:T by cycling through the full
conditional distributions

π( j) | π(− j), UN, β, f1:T , m1:T , h1:T , y1:T

(8)

j = 1, . . . , N, where π( j)

is the jth column of the
for
k × n matrix (cid:6)—that is, the vector of coefficients appear-
ing in equation j—and π(− j) = (π(1)(cid:4), . . . , π( j−1)(cid:4), π( j+1)(cid:4),
. . . , π(N)(cid:4)
)(cid:4) collects all the coefficients in the remaining equa-
zioni.

To establish this corrected approach, consider the triangu-

lar representation of the system

˜yt = Ayt = A(cid:6)(cid:4)xt + (cid:2)0.5

T

(cid:3)t = A(X(cid:4)

T

(cid:6))(cid:4) + (cid:2)0.5

T

(cid:3)T ,

(9)

which can be expressed as the following system of equations:

(cid:3)1,T ,

π(1) + λ0.5
1,T
π(1) + X(cid:4)
T
π(1) + a3,2x(cid:4)

T

(cid:3)2,T ,

π(2) + λ0.5
2,T
π(2) + X(cid:4)
T

T

π(3) + λ0.5
3,T

(cid:3)3,T ,

T

˜y1,t = x(cid:4)
˜y2,t = a2,1x(cid:4)
˜y3,t = a3,1x(cid:4)
…
˜yn,t = an,1X(cid:4)

T

T

π(1) + · · · + an,n−1x(cid:4)

(cid:3)N,T ,
(10)
with ˜yt = Ayt a vector with generic jth element ˜y j,t = y j,T +
a j,1y1,t + · · · + a j, j−1y j−1,t .

π(n−1) + X(cid:4)
T

π(N) + λ0.5
N,T

T

With this recursive system (10), it is evident that the
coefficients π( j) of equation j
influence not only equa-
tion j but also the following equations j + 1, . . . , N, Quale
is yet another way of seeing that these equations have
some extra information about π( j) that the old algorithm
missed. Importantly, Anche se, it remains true that the previ-
ous equations 1, . . . , j − 1 have no information about the
coefficients of equation j. With coefficient priors π( j) ∼
j = 1, . . . , N, that are independent across
N (μ
equations (as is the case in all common VAR implementa-
zioni), the first j − 1 elements in the quadratic term above do
not contain π( j). It follows that the conditional distribution
P(π( j) | π(− j), UN, β, f1:T , m1:T , h1:T , y1:T ) can be obtained us-
ing the subsystem composed of the last n − j + 1 equations
Di (10).

, (cid:7)π( j) ),

π( j)

In implementation, for drawing the coefficients of equa-
tion j, we use only equations j and higher to sample
P(π( j) | π(− j), UN, β, f1:T , m1:T , h1:T , y1:T ):

π( j) + λ0.5
j,T

(cid:3) j,T ,
π( j) + λ0.5

j+1, jx(cid:4)

T

j+1,t

(cid:3) j+1,t ,

T

z j,t = x(cid:4)
z j+1,t = a(cid:4)
…
zn,t = an, jx(cid:4)

π( j) + λ0.5
N,T

(cid:3)N,T ,

T

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CORRIGENDUM: MEASURING UNCERTAINTY AND ITS IMPACT ON THE ECONOMY

619C

where z j+l,t = ˜y j+l,t −
n − j, and ai,i = 1.

(cid:7)

j+l
io(cid:5)= j,i=1 a j+l,ix(cid:4)

T

π(io), for l = 0, . . . ,

Then, using the above triangular representation, the full
conditional distribution (π( j) | π(− j), UN, β, f1:T , m1:T , h1:T ,
y1:T ) È

(π( j) | π(− j), UN, β, f1:T , m1:T , h1:T , y1:T ) ∼ N (μπ( j), (cid:7)π( j) ),

Dove

(cid:7)−1

π( j) = (cid:7)−1
π( j)

T(cid:8)

N(cid:8)

a2
io, j

i= j

t=1

1
λi,T

xt x(cid:4)

T

,

+

⎛

μπ( j) = (cid:7)π( j)

⎝(cid:7)−1
π( j)

μ

π( j)

+

N(cid:8)

T(cid:8)

ai, j

i= j

t=1

1
λi,T

(11)

⎞

⎠ .

xt zi,T

(12)

As documented in Carriero et al. (2022), this approach pre-
serves the gains in computational complexity described in
CCM2019. Although the use of additional information (dati)
for all but the nth equation makes this algorithm empirically
slower than that originally used in the paper, in application
the computational time is comparable. Accordingly, in this
note, we use this approach to sampling the VAR’s coefficients
to correct and update the results of CCM2018.1

III. Corrected Results

Generalmente, the correction of the estimation algorithm has
proven to make it somewhat more difficult to disentangle
measures of macroeconomic and financial uncertainty. Ab-
stracting from algorithm considerations, some challenges are
to be expected, given the comovement of forecast error vari-
ances across the variables of the model, the countercyclical-
ity of uncertainty, the nonlinear features of the model, E
the large size of the model. The algorithm correction seems
to have made these challenges steeper, for reasons not easy
to pinpoint. Per esempio, with some of the loose prior set-
tings of CCM2018, estimates with the new algorithm showed
more issues with mixing and convergence of the MCMC
chain.

Accordingly, to be able to reliably estimate the model with
the corrected algorithm, we have made two changes relative
to the settings of CCM2018. Primo, we have tightened a few
prior settings. We lowered the hyperparameter θ3 governing
shrinkage of the factor coefficients in the VAR’s conditional
mean from the paper’s uninformative setting of 1,000 ad a
more modestly informative setting of 1. We also lowered the
prior variance on the elements of the A matrix from the pa-
per’s largely uninformative setting of 10 to a more modestly
informative setting of 1. Secondo, we have shortened the esti-
mation sample, so that it starts in January 1985 instead of July

1See Carriero et al. (2022) for an implementation of computations that
makes use of a data-matrix type of notation that is easy to implement and
computationally efficient in programming languages such as Matlab.

1960 as in the paper. With the shorter sample, there are fewer
concerns with potential sample instabilities owing to various
structural shifts in the economy, monetary policy in partic-
ular. Some other work in the uncertainty literature (Baker,
Bloom, & Davis, 2016, and Basu & Bundick, 2017) also
focuses on samples starting in the mid-1980s. Since some
other studies on uncertainty, such as Alessandri and Mumtaz
(2019) and Shin and Zhong (2020), started estimation in the
1970S, we have repeated our analysis with a sample start-
ing in 1975, finding results qualitatively very similar to those
reported below.

In the remainder of this corrigendum, we provide results for
the 1985–2014 sample corresponding to those in CCM2018,
but using the corrected algorithm for VAR estimation de-
scribed above. Generalmente, the corrected results are qualita-
tively the same as those provided in CCM2018.

Figura 1 displays the posterior distribution of the updated
measures of macro (top panel) and financial uncertainty (bot-
tom panel). The updated estimates are very similar to those of
the paper, with correlations (paper with corrected algorithm)
of about 0.9 for the macro factor and 0.98 for the financial
factor. It continues to be the case that the macro and financial
factors are modestly correlated, with a correlation of about
0.3 for the 1985–2014 period in both the original and up-
dated estimates. Relative to the paper, the main difference
in the uncertainty estimates is that the new macro factor is
a little more variable than the paper’s estimate. But in gen-
eral, the new estimates display the same features as did the
original estimates. Per esempio, the financial uncertainty fac-
tor increases not only during recessions, as does the macro
uncertainty factor, but also in other periods of financial tur-
moil. As indicated in figure 1, our estimates of uncertainty
show significant increases around some of the political and
economic events that Bloom (2009) highlights as periods of
uncertainty, as in the case of financial uncertainty around the
Black Monday event of 1987.

T

Figura 2 reports the updated estimates of the reduced-form
volatilities of the variables in our model, questo è, the diagonal
elements of (cid:5)0.5
, which reflect both the common uncertainty
factors and idiosyncratic components, along with the esti-
mated idiosyncratic volatilities (reported in the chart as h0.5
io,T ).
In broad terms, these results are comparable to the paper’s
original estimates. Per esempio, the volatility of the funds
rate declines sharply in the 1980s. As another, for some vari-
ables (per esempio., industrial production), most variability appears
to be driven by the common factors, whereas for a few oth-
ers (per esempio., real consumer spending, the PPI for finished goods,
and the Federal funds rate), the idiosyncratic variation is pre-
ponderant, explaining most of the overall variation in the
volatility.

Tavolo 2 (we preserve the numbering of the paper for ease
of reference) provides correlations of our updated estimates
of macroeconomic and financial uncertainty shocks with
some well-known macro shocks. In most cases, the uncer-
tainty shocks continue to show little correlation with “known”
macroeconomic shocks. Per esempio, the correlations of

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619D

THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 1.—UNCERTAINTY ESTIMATES: POSTERIOR MEDIAN (SOLID BLACK LINE) AND 15%/85% QUANTILES (DOTTED LINES), WITH MACRO UNCERTAINTY (m0.5
THE TOP PANEL AND FINANCIAL UNCERTAINTY ( F 0.5
) IN THE BOTTOM PANEL. THE GRAY SHADING INDICATES PERIODS OF NBER RECESSIONS. THE PERIODS INDICATED
BY BLACK VERTICAL LINES OR REGIONS CORRESPOND TO THE UNCERTAINTY EVENTS HIGHLIGHTED IN BLOOM (2009). LABELS FOR THESE EVENTS ARE INDICATED IN
TEXT HORIZONTALLY CENTERED ON THE EVENT’S START DATE

) IN

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uncertainty shocks with productivity shocks are small and
insignificant in these updated estimates, as they were in the
paper’s reported results. Tuttavia, with the shorter sample
and updates, there are a few instances of small, significant cor-
relations of the uncertainty shocks with “known” macroeco-
nomic shocks. Per esempio, the monetary policy shocks have
a small, statistically significant correlation with the shock to
financial uncertainty. Some of the shift in these results seems
to be due just to the shortening of the sample; in a few cases,
with the sample starting in 1985, the uncertainty shocks of
the paper’s original estimates show similarly significant cor-
relations with “known” macroeconomic shocks.

Figura 3 provides the impulse response estimates of a 1
standard deviation shock to log macro uncertainty (ln mt ).
These estimates are qualitatively the same as those reported
in the paper. The shock to log macro uncertainty produces a
rise in uncertainty that gradually dies out over the course of
about one year. Financial uncertainty rises in response, also
for about a year, although the response of financial uncer-
tainty is estimated less precisely than the response of macro
uncertainty. Activity measures including consumption, real
M&T (manufacturing and trade) sales, industrial production,
and capacity utilization decline significantly. The labor mar-
ket also deteriorates, with employment and hours falling and

CORRIGENDUM: MEASURING UNCERTAINTY AND ITS IMPACT ON THE ECONOMY

619e

FIGURE 2.—REDUCED-FORM (BLACK LINE) AND IDIOSYNCRATIC VOLATILITIES (h0.5

io,T , GRAY LINE), SELECTED VARIABLES, POSTERIOR MEDIANS

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TABLE 2.—CORRELATIONS OF UNCERTAINTY SHOCKS WITH OTHER SHOCKS

Known
Shock

Productivity: Fernald TFP
(1985:Q1–2014:Q2)

Oil supply: Hamilton (2003)

(1985:Q1–2014:Q2)
Oil supply: Kilian (2008)
(1985:Q1–2004:Q3)

Monetary policy: Gürkaynak et al. (2005)

(1990:Q1–2004:Q4)

Monetary policy: Coibion et al. (2016)

(1985:Q1–2008:Q4)

Fiscal policy: Ramey (2011)

(1985:Q1–2008:Q4)

Fiscal policy: Mertens and Ravn (2012)

(1985:Q1–2006:Q4)

Macro
Uncertainty
Shock
−0.065
(0.406)
0.144
(0.039)
−0.123
(0.236)
−0.054
(0.570)
−0.143
(0.173)
0.076
(0.343)
0.079
(0.101)

Financial
Uncertainty
Shock

0.137
(0.164)
0.150
(0.009)
0.064
(0.651)
0.159
(0.029)
−0.332
(0.000)
0.093
(0.036)
−0.033
(0.248)

The table provides the correlations of the orthogonalized shocks to uncertainty (measured as the posterior medians of C

−1
(cid:4) ut , where C(cid:4) denotes the Choleski decomposition of (cid:4)) with selected macroeconomic
shocks. The monthly shocks from the model are averaged to the quarterly frequency. The Fernald TFP shocks are updates of estimates in Basu, Fernald, and Kimball (2006). Entries in parentheses provide the sample
period of the correlation estimate (column 1) and the p-values of t-statistics of the coefficient obtained by regressing the uncertainty shock on the macroeconomic shock (and a constant). The variances underlying the
t-statistics are computed with the prewhitened quadratic spectral estimator of Andrews and Monaghan (1992).

the unemployment rate rising. Despite the significant decline
of economic activity in response to the macro uncertainty
shock, there doesn’t appear to be evidence of a broad de-
cline in prices. Although the PPI for finished goods declines
steadily (with an imprecise estimate), overall consumer prices
as captured by the PCE price index fail to display a signifi-
cant change. In the face of this sizable deterioration in the real
economy and in the absence of much movement in prices, IL
Federal funds rate gradually falls. The responses of financial
indicators to the shock to macro uncertainty are somewhat
mixed, often muted, and sometimes imprecisely estimated.
Tuttavia, in these corrected estimates as compared to the
paper’s original results, the shock to uncertainty produces a
larger and more precisely estimated falloff in the S&P 500
and excess return.

Figura 4 provides the impulse response estimates of a 1
standard deviation shock to log financial uncertainty (ln ft ).
These updated estimates are also comparable to those re-
ported in the published paper, although in this case of a fi-
nancial uncertainty shock, the corrected responses tend to be
a little smaller than those reported in CCM2018. The shock
to log financial uncertainty produces a rise in uncertainty that
only gradually dies out over the course of almost two years.
In response, macro uncertainty slightly declines (whereas in
the paper’s estimates, it slightly rose), although by an amount
that would not be significant at confidence levels modestly
greater than 70% (as they are barely significant at 70%). As
to broader effects of financial uncertainty, when compared to
a macro uncertainty shock, a financial uncertainty shock has
similar macroeconomic effects, but often modestly smaller or
sometimes less precisely estimated. Tuttavia, in these esti-
mates, as in the paper’s results, a financial uncertainty shock
does not have significant effects on the housing sector (starts
and permits). Inoltre, as in the paper’s results, the shock
to financial uncertainty produces a persistent and significant
rise in the credit spread, with a hump-shaped pattern. It also

produces a sizable falloff in aggregate stock prices and re-
turns, but the responses of the risk factors included in the
model are insignificant.

Figura 5 provides corrected historical decomposition re-
sults for the period from 2003 through 2014. The charts
show the standardized data series, a baseline path correspond-
ing to the unconditional forecast, the direct contributions of
shocks to (separately) macroeconomic and financial uncer-
tainty, and the direct contributions of the VAR’s shocks. IL
reported estimates are posterior medians of decompositions
computed for each draw from the posterior. These updated re-
sults are also qualitatively similar to those provided in the pa-
per. Around the Great Recession, shocks to uncertainty con-
tribute to fluctuations in economic activity, the Federal funds
rate, the credit spread, and uncertainty itself, but not much to
inflation or stock prices (or other financial indicators). How-
ever, for the macroeconomic and financial variables of the
modello, the effects of uncertainty shocks are generally dom-
inated by the contributions of the VAR’s shocks. One qual-
itative difference with the corrected results compared to the
estimates originally reported is that the contribution of shocks
to financial uncertainty is smaller in the new estimates.

Figura 6 shows the effects of uncertainty shocks on the
predictive distributions of selected variables. The solid black
line and gray shading report the predictive density of a base-
line path for the variables. The alternative path denoted by the
dotted (median) and dashed lines (15% E 85% quantiles)
instead shows the predictive density with additional uncer-
tainty shocks (for December 2007 through June 2009) corre-
sponding to those obtained with our estimated model. These
corrected results are very similar to the original estimates
provided in CCM2018. Consistent with the simple impulse
responses, the shocks to uncertainty cause the path of eco-
nomic activity to shift down. For many variables, the shocks
also have a distributional effect beyond just moving the center
of the distribution: they also cause the distribution to rotate

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CORRIGENDUM: MEASURING UNCERTAINTY AND ITS IMPACT ON THE ECONOMY

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FIGURE 3.—IMPULSE RESPONSES FOR 1 STANDARD DEVIATION SHOCK TO MACRO UNCERTAINTY, SELECTED VARIABLES, POSTERIOR MEDIAN (BLACK LINE), AND
15%/85% QUANTILES (GRAY SHADING)

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THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 4.—IMPULSE RESPONSES FOR 1 STANDARD DEVIATION SHOCK TO FINANCIAL UNCERTAINTY, SELECTED VARIABLES, POSTERIOR MEDIAN (BLACK LINE), AND
15%/85% QUANTILES (GRAY SHADING)

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CORRIGENDUM: MEASURING UNCERTAINTY AND ITS IMPACT ON THE ECONOMY

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FIGURE 5.—HISTORICAL DECOMPOSITION FOR 2003–2014, SELECTED VARIABLES, POSTERIOR MEDIANS, WITH ACTUAL DATA SERIES IN SOLID BLACK LINE

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619j

THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 6.—EFFECTS OF UNCERTAINTY SHOCKS ON PREDICTIVE DISTRIBUTIONS, DECEMBER 2007 THROUGH DECEMBER 2012, SELECTED VARIABLES. THE BASELINE
PATH IS REPORTED AS THE SOLID BLACK LINE (MEDIAN) WITH GRAY SHADING (15%/85% QUANTILES). THE PATH WITH THE EFFECTS OF THE ESTIMATED UNCERTAINTY
SHOCKS OVER THE PERIOD IS REPORTED AS THE DOTTED LINE (MEDIAN) WITH DASHED LINES (15%/85% QUANTILES)

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CORRIGENDUM: MEASURING UNCERTAINTY AND ITS IMPACT ON THE ECONOMY

619k

downward. The 15th percentile of the 70% credible set ap-
pears to fall more than does the 85th percentile. These effects
are most evident for those variables for which an uncertainty
shock affects the median of the distribution, particularly for
measures of economic activity (per esempio., employment, industrial
production), the Federal funds rate, and the credit spread. For
variables for which the median responses are smaller (per esempio.,
for the PCE price index), there are no obvious distributional
effects.

REFERENCES
Alessandri, Piergiorgio, and Haroon Mumtaz, “Financial Regimes and Un-
certainty Shocks,” Journal of Monetary Economics 101 (2019), 31–
46. 10.1016/j.jmoneco.2018.05.001

Andrews, Donald W. K., and J. Christopher Monahan, “An Improved Het-
eroskedasticity and Autocorrelation Consistent Covariance Matrix
Estimator,” Econometrica 60 (1992), 953–966. 10.2307/2951574

Baker, Scott R., Nicholas Bloom, and Steven J. Davis, “Measuring Eco-
nomic Policy Uncertainty,” Quarterly Journal of Economics 131
(2018), 1593–1636. 10.1093/qje/qjw024

Basu, Susanto, and Brent Bundick, “Uncertainty Shocks in a Model of
Effective Demand,” Econometrica 85 (2017), 937–958. 10.3982/
ECTA13960

Basu, Susanto, John G. Fernald, and Miles S. Kimball, “Are Technol-
ogy Improvements Contractionary?” American Economic Review
96 (2006), 1418–1448. 10.1257/aer.96.5.1418

Bloom, Nicholas, “The Impact of Uncertainty Shocks,” Econometrica 77

(2009), 623–685. 10.3982/ECTA6248

Bognanni, Segno, “Comment on ‘Large Bayesian Vector Autoregressions
with Stochastic Volatility and Non-Conjugate Priors’,” Journal
of Econometrics 227 (2022), 498–505. 10.1016/j.jeconom.2021
.10.008

Carriero, Andrea, Joshua Chan, Todd E. Clark, and Massimiliano Mar-
cellino, “Corrigendum to: Large Bayesian Vector Autoregressions
with Stochastic Volatility and Non-Conjugate Priors,” Journal
of Econometrics 227 (2022), 506–512. 10.1016/j.jeconom.2021
.11.010

Carriero, Andrea, Todd E. Clark, and Massimiliano Marcellino, “Measur-
ing Uncertainty and Its Impact on the Economy,” this REVIEW 100
(2018), 799–815. 10.1162/rest_a_00693, PubMed: 30344046
——— “Large Bayesian Vector Autoregressions with Stochastic Volatility
and Non-Conjugate Priors,” Journal of Econometrics 212 (2019),
pag. 137–154. 10.1016/j.jeconom.2019.04.024

Coibion, Olivier, Yuriy Gorodnichenko, Lorenz Kueng, and John Silvia,
“Innocent Bystanders? Monetary Policy and Inequality in the U.S.,”
manuscript (2016).

Gürkaynak, Refet S., Brian Sack, and Eric T. Swanson, “Do Actions Speak
Louder Than Words? The Response of Asset Prices to Monetary
Policy Actions and Statements,” International Journal of Central
Banking 1 (2005), 55–93.

Hamilton, James D., “What Is an Oil Shock?” Journal of Econometrics 113

(2003), 363–398. 10.1016/S0304-4076(02)00207-5

Kilian, Lutz, “Exogenous Oil Supply Shocks: How Big Are They and How
Much Do They Matter for the U.S. Economy?” this REVIEW 90
(2008), 216–240. 10.1162/rest.90.2.216

Mertens, Karel, and Morten O. Ravn, “Empirical Evidence on the Aggregate
Effects of Anticipated and Unanticipated U.S. Tax Policy Shocks,"
American Economic Journal: Economic Policy 4 (2012), 145–181.
10.1257/pol.4.2.145

Ramey, Valerie A., “Identifying Government Spending Shocks: It’s All in
the Timing,” Quarterly Journal of Economics 126 (2011), 1–50.
10.1093/qje/qjq008

Shin, Minchul, and Molin Zhong, “A New Approach to Identifying the Real
Effects of Uncertainty Shocks,” Journal of Business and Economics
Statistics 38 (2020), 367–379. 10.1080/07350015.2018.1506342

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