# Agreed and Disagreed Uncertainty111We would like to thank Philippe Andrade,
George-Marios Angeletos, Fabio Canova, Joshua Chan, Eric Eisenstat, Laura
Gáti, Yuriy Gorodnichenko, Refet Gürkaynak, Luigi Iovino, George Kapetanios,
Riccardo Masolo, Franck Portier, Barbara Rossi, Ozge Senay, Ulf Söderström,
participants to the Bank of Finland “2018 Workshop on Empirical
Macroeconomics,” “2022 Workshop on Heterogeneity” at the University of Exeter,
and seminar participants at the Banque de France, EDHEC Business School,
European Central Bank, King’s College London, Shanghai University of Finance
and Economics (SUFE), Sveriges Riksbank, Sveriges Riksbank, and Universities
of Birmingham, Glasgow, Oxford and St. Andrews for valuable comments.

Luca Gambetti  Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona,
Spain Universitá di Torino, 10134, Torino, Italy Dimitris Korobilis
University of Glasgow, Adam Smith Business School, Glasgow, G12 8QQ, U.K. John
D. Tsoukalas  University of Glasgow, Adam Smith Business School, Glasgow, G12
8QQ, U.K. Francesco Zanetti  University of Oxford, Department of Economics,
Oxford, OX1 3UQ, U.K.

(February 2023)

###### Abstract

When agents’ information is imperfect and dispersed, existing measures of
macroeconomic uncertainty based on the forecast error variance have two
distinct drivers: the variance of the economic shock and the variance of the
information dispersion. The former driver increases uncertainty and reduces
agents’ disagreement (agreed uncertainty). The latter increases both
uncertainty and disagreement (disagreed uncertainty). We use these
implications to identify empirically the effects of agreed and disagreed
uncertainty shocks, based on a novel measure of consumer disagreement derived
from survey expectations. Disagreed uncertainty has no discernible economic
effects and is benign for economic activity, but agreed uncertainty exerts
significant depressing effects on a broad spectrum of macroeconomic
indicators.

Keywords: uncertainty, information frictions, disagreement, Bayesian vector
autoregression (VAR), sign restrictions.

JEL Classification: E20, E32, E43, E52.

##  1 Introduction

Since the seminal work of Bloom, (2009), a large body of research shows that
uncertainty has powerful recessionary effects on a broad spectrum of activity
indicators.222See Bloom, (2014) for a survey. However, although recessions do
coincide with heightened uncertainty, protracted and elevated uncertainty is
not always associated with recessions. Examples include the stock market crash
of October 1987, which resulted in enormous losses in stock returns, and the
2011 debt-ceiling crisis, which resulted in increase in U.S. government credit
default swaps of 46 basis points without generating a contraction in real
activity.333In November 1998, the Russian crisis and near collapse of the
hedge fund LTCM lead various uncertainty proxies to spike above their levels
in the 2001 recession without a concomitant slowdown in economic activity.
This paper argues that the dispersion in consumer views about the state of the
economy (thereafter consumer disagreement) conveys important information about
the systematic effect of uncertainty on economic activity. By developing a new
index of consumer disagreement about current and future economic conditions
from survey data, we show that spikes in uncertainty during periods of high
consumer agreement (“agreed uncertainty”) have the standard depressing effects
on activity indicators found in numerous studies (e.g., Bloom,, 2009; Jurado
et al.,, 2015; Caldara et al.,, 2016); however, equivalent spikes in
uncertainty in periods of high consumer disagreement (“disagreed
uncertainty”), have no discernible effects on economic activity.

The starting point of our analysis is a dispersed (and noisy) information
framework. Mankiw and Reis, (2002), Woodford, (2003), Sims, (2003), Mackowiak
and Wiederholt, (2009), Mankiw et al., (2004), and Okuda et al., (2021) argue
in favour of information frictions manifested in models of sticky and noisy
information. Coibion and Gorodnichenko, (2012) and Coibion and Gorodnichenko,
(2015) (see Coibion et al.,, 2018 for a comprehensive survey) establish robust
evidence in favor of information rigidities in agents’ expectation formation,
with the bulk of evidence supporting noisy information models. This framework
allows us to formalize the distinction between agreed and disagreed
uncertainty. In this framework, the observed uncertainty – measured by the
conditional volatility of the forecast error – is a function of both
innovations in the volatility of fundamental disturbances and innovations in
the volatility of idiosyncratic noise, inherent in the noisy signals that
agents process. This finding opens up the possibility that innovations in both
types of volatility may drive changes in the observed uncertainty. More
precisely, the premise of our study is that innovations in the volatility of
idiosyncratic noise may increase measured uncertainty, without a change in the
volatility of exogenous fundamental disturbances, and the spike in uncertainty
may not necessarily exert depressing effects on economic activity.

We provide new evidence from the Michigan Survey of Consumers on the
prevalence of dispersion of information manifested in our new index that
captures the disparity of consumers’ opinions about current and future
economic conditions.444The empirical literature cited above on information
frictions focuses primarily on consumer inflation expectations. We document
several new facts. First, consumer disagreement is pervasive and applies to
both _current_ and _future_ economic conditions. Second, it is pro-cyclical
and negatively correlated with widely used measures of economic uncertainty.
Third, the procyclicality of disagreement is time-varying: it increases in
recessions and weakens in periods of robust economic activity. This result
evinces the widening in the dispersion of consumer views during economic
expansions that diminishes during recessions, leading to more homogeneous
views concomitant to the decline in economic activity. In other words,
consumers disagree less strongly about current and future conditions (low
disagreement) when then economy is in a recession.

The core analysis proceeds in two steps. First, we develop a simple model with
noisy and dispersed information that sheds light on the interplay between
disagreement and uncertainty. We then use the predictions of the model to
formulate simple sign restrictions in a Bayesian VAR model to identify shocks
to agreed and disagreed uncertainty in the data. The empirical analysis based
on our novel index of consumer disagreement sheds lights on important
differences in the effects of agreed and disagreed uncertainty shocks in the
data.

In our simple model, agents receive idiosyncratic signals about a fundamental
shock and form forecasts about the path of the latter by solving a signal
extraction problem. The resulting dispersion of forecasts is proportional to
the variance of the noise in the signal. We derive measures of uncertainty and
disagreement in the model that are consistent with their empirical
counterparts. Specifically, uncertainty in the model is the variance of the
forecast errors made by the agents (the standard measure of uncertainty in
Jurado et al.,, 2015 and several other studies). We show that the measure of
uncertainty in the model is an increasing function of both the variance of the
fundamental shock and the variance of the idiosyncratic noise.555The variance
of the idiosyncratic shock affects uncertainty in the model because the
forecast error itself is a function of a key parameter – the signal-to-noise
ratio – that controls the updating of forecasts agents make. The latter is
inversely related to the variance of idiosyncratic noise. At the same time,
the model disagreement index is an increasing function of the variance of
noise, but a decreasing function of the variance of the fundamental shock.
Therefore, an increase in either the variance of fundamental shock or the
variance of the noise can increase uncertainty, but with _opposite_ shifts in
the index of disagreement. More concretely, a rise in the variance of the
fundamental shock increases uncertainty and _decreases_ the index of
disagreement, but a rise in the variance of the noise increases both
uncertainty and the index of disagreement. Thus, although uncertainty always
raises when the variances of the fundamental shock or the noise rise, the
opposite response of the index of disagreement allows us to identify shocks to
agreed and disagreed uncertainty. These distinct predictions provide a set of
minimal sign restrictions we use in a medium-scale VAR model, with U.S.
monthly data from 1977 to 2020, to estimate the dynamic effects of agreed and
disagreed uncertainty shocks.

The baseline empirical results can be summarized as follows. _Agreed
uncertainty_ shocks, identified by a concomitant fall in disagreement and rise
in uncertainty indicators, generates large, protracted, contractionary
economic effects consistent with the standard negative impact of economic
uncertainty on real activity, as reported in seminal studies by Bloom, (2009),
Jurado et al., (2015), and Ludvigson et al., (2021). Specifically, a positive
innovation in agreed uncertainty is associated with large and persistent
declines in industrial production, and employment. By contrast, _disagreed
uncertainty_ shocks identified by the joint increase in disagreement and
uncertainty indicators exhibit qualitatively different dynamic effects.
Although the rise in uncertainty is strong, significant, and persistent, as in
the case of agreed uncertainty shocks, economic activity indicators do not
exhibit any depressing effects. A positive innovation in disagreed uncertainty
generates a short-lived positive response of industrial production and
employment, after which both activity indicators return to the pre-shock
level. Finally, the contrasting dynamic effects of agreed and disagreed
uncertainty shocks are robust to using various measures of consumer
disagreement, uncertainty, and they are robust to VAR models that encompass a
broader spectrum of macroeconomic activity indicators, as well as to VAR
models that distinguish consumer disagreement by education and age cohorts.

These empirical findings contribute to the growing literature on the
macroeconomic effects of economic uncertainty, and we are the first study to
link uncertainty and consumer disagreement. Our evidence sheds light on a new
channel in the propagation of uncertainty to economic activity, showing that
high consumer disagreement is a relevant indicator for the dampened effect of
uncertainty in the economy. Bloom, (2009), Jurado et al., (2015), and
Ludvigson et al., (2021) show that uncertainty shocks are strongly
contractionary on economic activity. Baker et al., (2016) develop an index of
economic policy uncertainty and show that innovations in policy uncertainty
exert a negative effect on employment, industrial production, and investment.
Bachmann et al., (2013) use uncertainty measures from U.S. and German business
survey data and find a significant negative effect of uncertainty in
production and employment. Caldara et al., (2016) and Alessandri and Mumtaz,
(2019), stress the interaction between financial conditions and uncertainty,
providing evidence that the negative impact of uncertainty shocks is amplified
when financial conditions worsen. Fernàndez-Villaverde et al., (2011),
Fernàndez-Villaverde et al., (2015), Fernàndez-Villaverde et al., (2019,
2021), Fernàndez-Villaverde et al., (2023), Mumtaz and Zanetti, (2013), Born
and Pfeifer, (2014), Basu and Bundick, (2017), Cascaldi-Garcia et al., (2022),
Melosi et al., (2022), and several others show that uncertainty from different
sources, such as fiscal and monetary policy, costs of borrowing, and future
perceived uncertainty, results in reduced economic activity. We also relate to
Caggiano et al., (2014), Leduc and Liu, (2016), Theodoridis and Zanetti,
(2016), Schaal, (2017), and Cascaldi-Garcia and Galvao, (2021) which show a
tight link between uncertainty, labor, and production markets. Earlier
literature studies the cyclical effects of first moment noise shocks (e.g.,
Lorenzoni,, 2009; Blanchard et al.,, 2013; Forni et al.,, 2017). Our work
contributes to this literature by identifying potential cyclical effects of
second-moment noise shocks. Recent work also shows that episodes of high
uncertainty may not have adverse economic effects. For example, Segal et al.,
(2015) distinguish between bad and good uncertainty, and their good
uncertainty measure is benign for production and consumption.666Using measures
of low and high uncertainty from quantile factor models, Korobilis and
Schröder, (2022) show that only high-uncertainty shocks cause a significant
fall in industrial production. Aastveit et al., (2017) show that in periods of
high uncertainty, monetary policy effects to output are dampened. Berger et
al., (2020) separate contemporaneous shocks in realized stock market
volatility from news shocks that they interpret as forward-looking
uncertainty, which are benign for economic activity.

The remainder of the paper is organized as follows. Section 2 derives our
measures of consumer disagreement and studies the time-series properties of
our index. Section 3 develops a stylized model to study the links between
uncertainty and consumer disagreement. Section 4 uses predictions from the
model that disentangle the dynamic effects of agreed and disagreed
uncertainty. Section 5 explores robustness of the empirical results to
alternative modeling assumptions. Section 6 concludes the paper.

##  2 Measuring consumer disagreement

In this section we construct a new index of consumer disagreement using the
University of Michigan Survey of Consumers. It is a parsimonious index that
encapsulates the cross-sectional dispersion of consumer views from different
survey questions, and it reveals consumers’ information and beliefs on current
and future economic conditions. We then study the cyclical properties of our
disagreement index and focus on the link with economic activity and
alternative measures of uncertainty.

###  2.1 Consumer survey data

The Michigan Survey of Consumers (hereafter MSC), is produced by the Survey
Research Center at the University of Michigan. Each month, it conducts a
minimum of 500 interviews, and consumers answer a questionnaire that contains
28 core questions and several subquestions. Survey questions are aggregated
over respondents (consumers) to produce approximately 45 monthly and quarterly
categorical time series.777The only exception is the question that asks
consumers to forecast a value for inflation one year and five years ahead,
which results in a continuous variable. The samples for the Surveys of
Consumers are statistically designed to be representative of all American
households. For a detailed description of the survey, including
questionnaires, see: https://data.sca.isr.umich.edu/survey-info.php. To
formulate our index, we select questions that capture the views of consumers
about current and future economic conditions, summarized in Table 1.

Table 1: Questions from the Michigan Survey of Consumers Question | Mnemonic | Topic
---|---|---
Q23 | NEWS | News Heard of Recent Changes in Business Conditions
Q25 | BAGO | Current Business Conditions Compared with a Year Ago
Q26 | BEXP | Expected Change in Business Conditions in a Year
Q28 | BUS12 | Business Conditions Expected During the Next Year
Q29 | BUS5 | Business Conditions Expected During the Next 5 Years

Consumer responses to the survey questions consist of three qualitative
categories (“better/about the same/worse,”); the associated time-series
measures the proportion of respondents in each category.888Depending on the
question, these answers can also take the form “favorable/no
mention/unfavorable,” “good time/uncertain/bad time,” or “more/about the
same/less.” Our benchmark measure is an index of _tail disagreement_ , which
reflects disagreement between the two polar categories in the distribution of
responses. That is, the _tail disagreement_ index extracts disagreement from
the “better/worse” (or “good time/bad time,” or “favorable/unfavorable”)
responses. Formally, the definition of the disagreement index is:

$\displaystyle T_{t}^{(j)}=1-\frac{|b_{t}^{(j)}-w_{t}^{(j)}|}{100},$ (1)

where $j=\text{NEWS, BAGO, BEXP, BUS12, BUS5}$ indexes each of the five survey
questions, $b_{t}^{j}$ is the percentage of respondents in question $j$ with a
positive/optimistic answer, and $w_{t}^{j}$ is the percentage of respondents
with a negative/pessimistic answer. The disagreement index $T_{t}^{(j)}$ takes
values of 0 and 1 by construction. A value equal to zero, which occurs if
either $b_{t}^{(j)}$ or $w_{t}^{(j)}$ is equal to 100, indicates all
respondents have the same opinion or view about the current and future
economic outlook and therefore no disagreement. On the other hand, a value
equal to 1 indicates that consumers are evenly split between the two polar
responses, reflecting sharp differences in opinions or views and consequently
maximal disagreement. This indicator is intuitive but ignores information from
the middle category of responses (e.g., “no mention,” “same”). In section 5 we
compute the Shannons’ entropy (Shannon,, 1948) measure of disagreement, which
considers both the polar and “middle” category responses. The entropy can be a
measure of uncertainty: consumers are more uncertain about economic conditions
when the “middle” category has a non zero chance of occurring. We show that
results are robust to this consideration. It is important to stress that the
qualitative approach in the reporting of views suggests our measure of
consumer disagreement refers to what we can loosely call “directional”
disagreement. Thus, our concept of disagreement is different from disagreement
among professional forecasters. In other words, our index does not convey
information about the intensity of the responses (e.g., how much better
relative to how much worse). The index also cannot capture disagreement within
the proportion of consumers that report better (or worse) economic prospects.

###  2.2 Time-series properties of consumer disagreement

We use monthly data spanning the period 1978M1 to 2020M12, and we derive
distinct measures of disagreement by applying the formula in equation (1) to
each of the five survey questions. We denote the singular disagreement
measures related to each survey question in Table Table 1 by $T^{NEWS}$,
$T^{BAGO}$, $T^{BEXP}$, $T^{BUS12}$, and $T^{BUS5}$. The measures of
disagreement based on the mnemonics “NEWS” and “BAGO” in Table 1 (i.e.,
$T^{NEWS}$ and $T^{BAGO}$, respectively) refer to _current_ business
conditions and thus directly relate to the information that consumers receive
and process about the past and present economic conditions. If all agents
could perfectly access all information relevant for assessing current
conditions, the degree of disagreement on _past and present_ conditions would
be absent. The degree of disagreement on _future_ economic conditions will
still be present, as agents need to make forecasts conditional on potentially
different models of the economy. Thus, a good check to ascertain the degree of
information dispersion is to focus on disagreement about _current_ economic
conditions that would be absent if agents have full information on the state
of the economy. Our indices $T^{NEWS}$ and $T^{BAGO}$ record substantial
disagreement on present and past economic conditions, suggesting substantial
disparity of views across consumers and evincing imperfect information about
the state of the economy.

To develop a parsimonious indicator of disagreement, we summarize the
information in the five different measures by formulating a single, latent,
consumer disagreement index using principal component analysis. In line with
the literature on macroeconomic diffusion indexes (see for example, Stock and
Watson,, 2002), our latent index is the first principal component of the five
individual disagreement series. The first principal component is a weighted
average of all five series, where the weights (loadings) are such that the
latent index maximizes the variance explained for each series.999In order to
ensure that the first principal component describes the direction of maximum
variance, we standardize the individual disagreement measures (and the index)
to have a mean equal to zero and a variance equal to 1. This transformation
does not affect the informational content of each series; rather, it affects
the scale. However, disagreement as a concept is not an ordinal measure in the
sense that an index value of, say, 0.5 implies that consumers disagree “twice
as much” compared to a value of 0.25. For that reason, we prefer to work with
an index that is standardized. We refer to our latent index as DISAG, and we
use it as the benchmark measure of consumer disagreement for the rest of the
analysis.

The top four panels and the bottom left panel of Figure 1 show the estimate of
the disagreement index (DISAG) against the individual measures of
disagreement. A first finding is the large and significant time variation in
the disagreement index that also characterizes the individual disagreement
series.101010The variability in consumer disagreement remains broadly
unchanged across the full sample period, without displaying a reduction in
volatility during the Great Moderation period of 1984-2007 that characterizes
several macroeconomic activity indicators. See Liu et al., (2019) for a
discussion of the changes in time-series properties of macroeconomic variables
since the 1960s. The figure shows that the comovement of the disagreement
index with each individual series is high. The bottom right panel of Figure 1
shows the loadings of each series on the principal component. The values in
the figure are the weights with which each individual series contributes to
the estimate of our latent disagreement index. The values show that the DISAG
index is evenly and strongly correlated with the individual disagreement
indexes NEWS, BAGO, BUS12, BUS5, and it is less strongly correlated with the
BEXP measure of disagreement.

Figure 1: Measures of disagreement and loading factors

_Notes: The top four panels and bottom left panel show individual tails
disagreement measures using the Michigan survey questions (solid line) against
the aggregate index of consumer disagreement (variable DISAG, dashed line).
The bottom right panel shows the estimated weights of each individual series
on the principal component. All series are standardized to have a mean of zero
and variance of 1._

We proceed to study the cyclical properties of DISAG by focusing on the
comovement of the disagreement index with two representative measures of
economic activity: the monthly Industrial Production Index and Real Personal
Consumption Expenditure. Over the entire sample period, DISAG is very weakly
correlated with either industrial production (0.19) and real personal
consumption growth (0.04); however, the correlation displays significant time
variation. Figure 2 shows a rolling correlation between the disagreement
index, industrial production, and real personal consumption growth: It
demonstrates that the correlation coefficient is time varying, covering a wide
range of values between -0.65 to 0.85 over the sample period.111111The
conditional correlation is obtained from a trivariate BEKK-GARCH(1,1)
specification on disagreement and the growth rates of industrial production
and consumption. We use Kevin Sheppard’s MFE Toolbox for MATLAB
(https://www.kevinsheppard.com/code/matlab/mfe-toolbox/ for the estimation of
the BEKK-GARCH(1,1)). The results are qualitatively similar when estimating
other multivariate GARCH models, such as the so-called CCC and DCC models. The
multivariate GARCH approach is superior to estimating sample correlations in
rolling windows of the data sample, because the latter approach discards
valuable information in the data and the former uses information in all of the
sample when estimating time-varying correlations. Starting from the 1981
recession, the correlation between disagreement and either measure of real
activity becomes predominantly positive and peaks during the five subsequent
recessions (shown in shaded areas). In other words, the positive correlation
between disagreement with economic activity indicators increases significantly
during recessions, implying that disagreement falls sharply with declines in
real activity.

Figure 2: Time-varying correlations of DISAG with industrial production and
real personal consumption growth

_Notes: IP-Industrial production growth. CONS-real personal consumption
growth. The correlation estimates are from a multivariate GARCH model (see
footnote 11 for details)._

Figure 3: Index of consumer disagreement and uncertainty indicators

_Notes: The figure plots in a clockwise manner a) consumer disagreement
(DISAG) (solid red line) against the 12-month macroeconomic (JLN12) and
financial (JLNF12) uncertainty indicators from Jurado et al., (2015), b) DISAG
(solid red line) against the Business Forecast Dispersion Index (BOS) from
Bachmann et al., (2013) (updated to 2019 by the authors), c) DISAG (solid red
line) against stock market volatility (CBOE S&P 100 volatility index (VXO)),
and d) DISAG (solid red line) against Economic Policy Uncertainty (EPU)
developed by Baker et al., (2016). The series are standardized to have mean
zero and unitary variance._

We next compare the disagreement index with empirical measures of uncertainty
and measures of disagreement derived from business surveys. Jurado et al.,
(2015) develop uncertainty indicators from a large set of macroeconomic and
financial time-series data using factor-augmented VAR methods. The top left
panel of Figure 3 displays our disagreement index (solid line) together with
the Jurado et al., (2015) measures of macroeconomic and financial uncertainty
(JLN12 and JLNF12, respectively) obtained from a 12-month forecast horizon
(dotted and dashed line). The uncertainty indicators are highly
countercyclical and exhibit a strong negative comovement with our index of
disagreement; the correlations of JLN12 and JLNF12 with the index of consumer
disagreement are -0.62 and -0.57, respectively.

The top right panel of Figure 3 compares our disagreement index with the
business-level uncertainty index from the Philadelphia Fed Business Outlook
Survey (BOS) that encapsulates the cross-sectional-forecast dispersion about
six-month-ahead business activity in the manufacturing sector. Bachmann et
al., (2013) shows that this index is a good proxy for uncertainty. The
correlation of our index with the business dispersion index exhibits a
negative yet weak correlation equal to -0.1.121212The survey question in the
FED BOS is: General Business Conditions: What is your evaluation of the level
of general business activity six months from now vs. [CURRENT MONTH]:
decrease, no change, increase? To preserve comparability, we compute the BOS
forecast dispersion index identically to Bachmann et al., (2013). The bottom
left panel of Figure 3 compares our index with the CBOE S&P 100 volatility
index (VXO) measure, the latter being a measure of uncertainty in many
previous studies. VXO exhibits strong negative comovement with our
disagreement index, with a correlation coefficient equal to -0.55. Last, the
bottom right panel of Figure 3 compares our index with the measure of Economic
Policy Uncertainty developed by Baker et al., (2016). As in the case of
business dispersion, this indicator, capturing a different dimension of
uncertainty, is not strongly negatively correlated with our disagreement
indicator with a correlation coefficient equal to -0.36. The key finding from
these comparisons is the _negative_ comovement of the different uncertainty
indicators with consumer disagreement. In sum, consumer disagreement has
fundamentally different cyclical properties compared to indicators of
business-level uncertainty, stock market volatility, or uncertainty indicators
from forecasts of financial and macroeconomic indicators and economic policy
uncertainty.

##  3 A simple model of information dispersion

We develop a simple model with disagreement arising from imperfect and
dispersed information, and uncertainty stemming from changes in the variance
of a fundamental shock. We study the effect of information dispersion and the
volatility of the fundamental shock on i) the variance of the forecast errors,
the empirical proxy for uncertainty, and ii) the model index of disagreement
congruous with our empirical measure of disagreement. The model allows us to
separately identify shocks to information dispersion and shocks to
uncertainty, and it provides simple sign restrictions that enable us to
illustrate how disagreement is associated with the different concepts of
uncertainty, which we use to identify the effect of agreed and disagreed
uncertainty in the data (see Section 4).

The economy is populated by a continuum, large number of $N$ agents defined
over the unit interval, indexed by $i$. In each period $t=1,2,...$, the
economy experiences the realization of an exogenous process $a_{t}$ (expressed
in logs) whose growth rate ($\Delta a_{t}=a_{t}-a_{t-1}$) follows the
invertible moving average (MA) process:

$\displaystyle
a_{t}-a_{t-1}=\psi_{0}\varepsilon_{t}+\psi_{1}\varepsilon_{t-1}+\psi_{2}\varepsilon_{t-2}+...+\psi_{n}\varepsilon_{t-n},$
(2)

where, $\psi_{0}$, $\psi_{1}$, …, $\psi_{n}$ are the MA coefficients and
$\varepsilon_{t}\sim N(0,\sigma_{\varepsilon}^{2})$ is an i.i.d. fundamental
shock with known variance $\sigma_{\varepsilon}^{2}$.131313The exogenous
fundamental process can adopt a variety of interpretations (e.g., productivity
or demand shocks that are relevant sources of macroeconomic fluctuations).

Information is imperfect and dispersed. It is imperfect because agents cannot
observe the current fundamental shock $\varepsilon_{t}$ and the current
exogenous process $a_{t}$ during each period $t$, while they observe the
history $\varepsilon_{t-1}$, …, $\varepsilon_{t-n}$, and the past exogenous
process $a_{t-1}$.

Information is dispersed because each agent $i$ receives a different
idiosyncratic signal about the fundamental shock:

$\displaystyle s_{it}=\varepsilon_{t}+v_{it},$ (3)

where $v_{it}\sim N(0,\sigma_{v_{i}}^{2})$ is an idiosyncratic, i.i.d. shock
with known variance $\sigma_{v_{i}}^{2}$. The idiosyncratic shock $v_{it}$
blurs the realization of the fundamental shock and generates cross-sectional
dispersion in the signals across agents. This formulation implies an
innovation to the volatility of the idiosyncratic shock, $\sigma_{v_{i}}^{2}$,
which leads to a greater dispersion of information across agents. Agents care
about the path of the fundamental shock $\varepsilon_{t}$, and they solve a
signal extraction problem to infer the fundamental shock from the signal
$s_{i}$. Each agent $i$ solves this problem by conditioning on the history and
volatilities as follows:
$\mathcal{I}_{it}\equiv\\{a_{t-1-j},\varepsilon_{t-1-j},s_{it-j},\sigma_{\varepsilon}^{2},\sigma_{v}^{2}\\}_{j=0}^{\infty}$,
where $\mathcal{I}_{it}$ is the agent specific information set.

Formally, each agent $i$ uses equation (2) to form expectations about the
growth rate of the exogenous process $a$ in future periods $t+1,...,t+n$,
which yields:

$\displaystyle E\left(\Delta a_{t+k}|\mathcal{I}_{it}\right)$ $\displaystyle=$
$\displaystyle\psi_{k}E\left(\varepsilon_{t}|\mathcal{I}_{it}\right)+\psi_{k+1}\varepsilon_{t-1}+...+\psi_{n}\varepsilon_{t+k-n},\quad\text{for}\quad
k=1,2,...,$ (4)

as well as in the current period,

$\displaystyle E\left(\Delta a_{t}|\mathcal{I}_{it}\right)$ $\displaystyle=$
$\displaystyle\psi_{0}E\left(\varepsilon_{t}|\mathcal{I}_{it}\right)+\psi_{1}\varepsilon_{t-1}+...+\psi_{n}\varepsilon_{t-n},\quad$
(5)

where $E$ is the rational expectations operator, and
$E\left(\varepsilon_{t}|\mathcal{I}_{it}\right)$ is the expectation on the
current fundamental shock $\varepsilon_{t}$ conditional on the information set
$\mathcal{I}_{it}$, which can be represented as the linear projection of
$\varepsilon_{t}$ on $s_{t}$ by solving the signal extraction problem.
Equations (4) and (5) show that the presence of the idiosyncratic signal
generates cross-sectional dispersion on current and future growth expectations
of the exogenous process $a$, reflected by the dependency of the conditional
expectations $E\left(\varepsilon_{t}|\mathcal{I}_{it}\right)$ on the agent-
specific information set. By solving the signal extraction problem for agent
$i$, we rewrite equation (4) as:

$\displaystyle E\left(\Delta a_{t+k}|\mathcal{I}_{it}\right)$ $\displaystyle=$
$\displaystyle\psi_{k}\gamma_{i}s_{it}+\psi_{k+1}\varepsilon_{t-1}+...+\psi_{n}\varepsilon_{t+k-n}$
$\displaystyle=$
$\displaystyle\psi_{k}\gamma_{i}(\varepsilon_{t}+v_{it})+\psi_{k+1}\varepsilon_{t-1}+...+\psi_{n}\varepsilon_{t+k-n}\quad
k=1,2,...$

and equation (5) as:

$\displaystyle E\left(\Delta a_{t}|\mathcal{I}_{it}\right)$ $\displaystyle=$
$\displaystyle\psi_{0}\gamma_{i}s_{it}+\psi_{1}\varepsilon_{t-1}+...+\psi_{n}\varepsilon_{t-n}$
$\displaystyle=$
$\displaystyle\psi_{0}\gamma_{i}(\varepsilon_{t}+v_{it})+\psi_{1}\varepsilon_{t-1}+...+\psi_{n}\varepsilon_{t-n}\quad
k=1,2,...$

where

$\gamma_{i}=\frac{\sigma_{\varepsilon}^{2}}{\sigma_{\varepsilon}^{2}+\sigma_{v_{i}}^{2}}$
(8)

is the agent-specific linear projection coefficient. Equations (3) and (3)
show that the future and current expected growth rate of the exogenous process
$a$ depends on the agent-specific reaction to the signal, controlled by the
coefficient $\gamma_{i}$. The response of these expectations to the signal
falls with the dispersion of information encapsulated by the variance of the
idiosyncratic shock, $\sigma_{v_{i}}^{2}$, and it increases with the variance
of the fundamental shock, $\sigma_{\varepsilon}^{2}$, as implied by equation
(8). The dispersion of information decreases the content of information
contained in the signal received by each agent $i$, and it makes the
conditional expectations in equations (3) and (3) less responsive to the
signal. In the rest of the analysis, we simplify the analytical derivation of
the system without loss of generality by assuming an identical variance of the
idiosyncratic shock across agents (i.e., $\sigma_{v_{i}}^{2}=\sigma_{v}^{2}$).

###  3.1 Interplay between uncertainty and information dispersion

In this section, we study the interplay between uncertainty and information
dispersion. We proxy uncertainty with the variance of the $k$-periods-ahead
forecast errors for $\Delta a_{t+k}$, and disagreement with an index derived
from simulations of the model that is consistent with our measure of
disagreement in Section 2. Our aim is to map the effect of dispersed
information and the spread of the fundamental shock into the empirical proxies
for disagreement and uncertainty.

As a preliminary step, we derive the $k$-periods-ahead _aggregate
expectations_ by averaging the different expectations of the single agents in
equation (3) across the $N$ agents in the economy:

$\displaystyle E\left(\Delta a_{t+k}|\mathcal{I}_{t}\right)$ $\displaystyle=$
$\displaystyle\frac{1}{N}\sum_{i=1}^{N}E\left(\Delta
a_{t+k}|\mathcal{I}_{it}\right)$ (9) $\displaystyle=$
$\displaystyle\psi_{k}\gamma\frac{1}{N}\sum_{i=1}^{N}(\varepsilon_{t}+v_{it})+\frac{1}{n}\sum_{i=1}^{n}\left(\psi_{k+1}\varepsilon_{t-1}+...+\psi_{n}\varepsilon_{t+k-n}\right)$
$\displaystyle=$
$\displaystyle\psi_{k}\gamma\varepsilon_{t}+\frac{1}{N}\sum_{i=1}^{N}\left(\psi_{k+1}\varepsilon_{t-1}+...+\psi_{n}\varepsilon_{t+k-n}\right),$

where $\frac{1}{N}\sum_{i=1}^{N}v_{it}$ converges to zero by the law of large
numbers, and the average projection coefficient is equal to:

$\displaystyle\gamma=\frac{\sigma_{\varepsilon}^{2}}{\sigma_{\varepsilon}^{2}+\sigma_{v}^{2}}.$
(10)

####  3.1.1 Variance of forecast error

Our proxy for uncertainty is the variance of the forecast error $k$-periods
ahead, which is equal to:

$\displaystyle var[\Delta a_{t+k}-E(\Delta a_{t+k}|\mathcal{I}_{t})]$
$\displaystyle=$ $\displaystyle
var[\psi_{0}\varepsilon_{t+k}+\psi_{1}\varepsilon_{t+k-1}+\psi_{2}\varepsilon_{t+k-2}+...+\psi_{k}(1-\gamma_{t})\varepsilon_{t}]$
(11) $\displaystyle=$
$\displaystyle\left[\psi_{0}^{2}+\psi_{1}^{2}+\psi_{2}^{2}+...+\psi_{k}^{2}\left(\frac{\sigma_{v}^{2}}{\sigma_{\varepsilon}^{2}+\sigma_{t}^{2}}\right)^{2}\right]\sigma_{\varepsilon}^{2}$
$\displaystyle+2\psi_{0}\sum_{j=1}^{k-1}\psi_{j}cov(\varepsilon_{t+k},\varepsilon_{t+k-j})+2\psi_{1}\sum_{j=2}^{k-1}\psi_{j}cov(\varepsilon_{t+k-1},\varepsilon_{t+k-j})+...$
$\displaystyle+2\psi_{k-2}\sum_{j=1}^{k-1}\psi_{j}cov(\varepsilon_{t+2},\varepsilon_{t+k-j})+2\psi_{k}(1-\gamma)\sum_{j=0}^{k-1}\psi_{j}cov(\varepsilon_{t},\varepsilon_{t+j+1})$
$\displaystyle=$
$\displaystyle\left[\psi_{0}^{2}+\psi_{1}^{2}+\psi_{2}^{2}+...+\psi_{k}^{2}\left(\frac{\sigma_{v}^{2}}{\sigma_{\varepsilon}^{2}+\sigma_{v}^{2}}\right)^{2}\right]\sigma_{\varepsilon}^{2},$

where the covariance terms are equal to zero because the shock
$\varepsilon_{t}$ is i.i.d. Equation (11) shows two important properties of
the effect of uncertainty and information dispersion on the variance of the
forecast error. First, the effect of a unitary change in uncertainty on the
variance of the forecast error at time $t+k$ is equal to:141414Appendix A
shows that, for an invertible MA process, the sign of equation (12) is always
positive.

$\frac{\partial var[\Delta a_{t+k}-E(\Delta
a_{t+k}|\mathcal{I}_{t})]}{\partial\sigma_{\varepsilon}^{2}}=\psi_{0}^{2}+\psi_{1}^{2}+\psi_{2}^{2}+...+\psi_{k}^{2}\left(\frac{\sigma_{v}^{2}}{\sigma_{v}^{2}+\sigma_{\varepsilon}^{2}}\right)\left(\frac{\sigma^{2}_{v}-\sigma_{\varepsilon}^{2}}{\sigma_{v}^{2}+\sigma_{\varepsilon}^{2}}\right)>0.$
(12)

This positive derivative underpins and supports the prevalent adoption of the
variance of the forecast error as a proxy for uncertainty. Second, the
variance of the forecast error increases with a unitary change in information
dispersion:151515This finding is consistent with the positive relationship
between dispersion in beliefs and aggregate uncertainty, as outlined in
Bianchi and Melosi, (2016).

$\frac{\partial var[\Delta a_{t+k}-E(\Delta
a_{t+k}|\mathcal{I}_{t})]}{\partial\sigma_{v}^{2}}=2\psi_{0}^{2}\sigma_{\varepsilon}\left(\frac{\sigma_{v}^{2}}{\sigma_{\varepsilon}^{2}+\sigma_{v}^{2}}\right)\left(\frac{\sigma_{\varepsilon}^{2}}{(\sigma_{\varepsilon}^{2}+\sigma_{v}^{2})^{2}}\right)>0.$
(13)

Our model shows that the empirical proxy for uncertainty, measured by the
variance of the forecast error, increases in _both_ innovations in the
variance of the fundamental uncertainty shock, and in the variance of the
idiosyncratic noise. These comovements, complemented by two further
restrictions we derive in the next section, allow us to disentangle
innovations to the variance of fundamental shocks (agreed uncertainty) and
innovations to information dispersion (disagreed uncertainty).

####  3.1.2 Mapping information dispersion and volatility of fundamental
shocks on disagreement

We use the model to study the mapping from information dispersion to
disagreement, and investigate the relation between disagreement and
uncertainty. Because we cannot derive an analytical solution that shows the
effect of information dispersion and the variance of fundamental shocks on
disagreement, we compute the disagreement index from numerical simulations of
the model consistent with our empirical index.

In the model, the cross-sectional expectations of consumers about economic
conditions are represented by:

$\displaystyle E(\Delta a_{t+k}|\mathcal{I}_{it})$ $\displaystyle=$
$\displaystyle\psi_{k}\gamma_{it}(\varepsilon_{t}+v_{it})+\psi_{k+1}\varepsilon_{t-1}+...+\psi_{n}\varepsilon_{t+k-n}.$
(14)

In the MSC, the consumer responses to several questions about _future_
business conditions is the natural empirical concept corresponding to the
forecast captured by equation (14). We therefore use the equation to generate
artificial survey data consistent with the qualitative responses in MSC by
defining the following indexes for individual answers:

$\text{Expected
Conditions}:\left\\{\begin{array}[]{ll}b_{it}^{\text{Expected}}=1\;\;\;\mbox{if}\;\;\;E(\Delta
a_{t+k}|\mathcal{I}_{it})>0,\\\
w_{it}^{\text{Expected}}=-1\;\;\;\mbox{if}\;\;\;E(\Delta
a_{t+k}|\mathcal{I}_{it})<0.\end{array}\right.$ (15)

We apply the standard quantification method for qualitative survey data and
code with $b_{it}=1$ a positive forecast, and $w_{it}=-1$ a negative forecast.
This coding is equivalent to the responses (“better or worse,” “good times or
bad times”) reported for the survey questions in the MSC summarized in Table
1. Consistent with the empirical disagreement index described in Section 2, we
compute the index of tail disagreement as:

$\tilde{T}_{t}=1-\frac{1}{N}\left|\sum_{i=1}^{n}b_{it}-w_{it}\right|$ (16)

We simulate the model as follows. We assume a monthly time period consistent
with the frequency in the MSC. We set the order of the MA process that governs
$\Delta a_{t}$ equal to $n=12$, and we set $k=12$, which corresponds to a
forecast one year ahead.161616For robustness we repeat this simulation
exercise assuming an annual frequency and changing the order of the MA process
to equal 5. It is well known that the condition for invertibility of an MA
process is the counterpart to the stationarity condition for an AR process.
Thus, taking a stationary AR(1) process with AR coefficient equal to $\beta$,
we write the MA coefficients as $\psi_{k}=\beta^{k}$. The variances of the
idiosyncratic component, $\sigma^{2}_{v}$, and of the fundamental shock,
$\sigma^{2}_{\varepsilon}$, are both allowed to vary in a discrete manner in
the set $[1,5]$.171717For each value in the set $[1,5]$ we generate random
draws from a normal distribution to compute the forecast in (14) for each
economic agent. We set the AR coefficient $\beta=0.5$, although the results
are quantitatively very similar to alternative values to this parameter. We
set the number of agents to $N=10000$. Using this calibration of the model, we
compute the tail disagreement index $\tilde{T}_{t}$ in equation (16).

Figure 4: Disagreement index in the model

_Notes_ : The disagreement index is obtained from
$\tilde{T}_{t}=1-\frac{1}{N}\left|\sum_{i=1}^{n}b_{it}-w_{it}\right|$ and
plotted as a function of $\sigma^{2}_{v}$. The Figure shows the disagreement
index corresponding 12-months-ahead economic conditions. To ease exposition,
the figure plots the index for five alternative values of
$\sigma^{2}_{\varepsilon}$ equal to $1,2,3,4$, and $5$. The disagreement index
increases with information dispersion ($\sigma^{2}_{v}$), but it falls with
the increase in the variance of the fundamental shock
($\sigma^{2}_{\varepsilon}$).

Each dashed line in Figure 4 shows the tail disagreement index from simulating
the model (y-axes) as a function of the variance of the idiosyncratic shock
$\sigma^{2}_{v}$ (x-axes), and we compute it for different values for the
variance of the fundamental shock $\sigma^{2}_{\varepsilon}$ equal to
$1,2,3,4$, and $5$ (blue-dashed line). The figure illustrates that the
disagreement index is an increasing function of information dispersion but
decreases with the variance of the fundamental shock
$\sigma^{2}_{\varepsilon}$ for any given level of $\sigma^{2}_{v}$. The
intuition from our model is that the signal becomes more precise and agents
downplay the idiosyncratic information content of the signal when
$\sigma^{2}_{\varepsilon}$ increases, thus agents update expectations more
strongly in the direction of the signal and agree more (i.e., agents disagree
less). Important to our analysis, the model establishes an inverse comovement
between disagreement and uncertainty, consistent with the strong negative
correlation between those indicators in the data, as documented in Section 2.

##  4 Empirical model

##### VAR inference and shock identification.

Our starting point is a Bayesian vector autoregressive (VAR) in the tradition
of several recent studies on uncertainty (Jurado et al.,, 2015, Gilchrist et
al.,, 2014). We use the identifying sign restrictions extracted from the
simple model of information dispersion in order to disentangle the dynamic
effects of agreed uncertainty and disagreed uncertainty shocks in the data
using the VARs. The restrictions are (i) those in equations (12) and (13), and
(ii) those implied by Figure 4. Table 2 summarizes our identifying
restrictions, showing the response of the observed variables (i.e.,
uncertainty and disagreement) to agreed and disagreed uncertainty, in columns
(1) and (2), respectively.

Table 2: Identifying restrictions |  | Shock
---|---|---
|  | (1) | (2)
Observed variable |  | $\sigma_{\varepsilon}$ | $\sigma_{v}$
|  | Agreed Uncertainty | Disagreed Uncertainty
Variance of the forecast error |  | + | +
Index of disagreement |  | $-$ | $+$

Column (1) in the table shows that an innovation to the fundamental shock
$\sigma^{2}_{\varepsilon}$ is associated with an increase in observed
uncertainty (represented by the variance of the forecast error) and a decrease
in the index of disagreement. This is our concept of _agreed uncertainty_.
Instead, column (2) in the table shows that an innovation to information
dispersion $\sigma^{2}_{v}$ is associated with a simultaneous increase in
observed uncertainty and the index of disagreement. This is our concept of
_disagreed uncertainty_.181818To rule out the autonomous effect of uncertainty
shocks on economic activity that results in overstating the impact economic
effects of agreed or disagreed uncertainty shocks, we impose a zero-impact
response of activity indicators to the identified shocks. Using these distinct
comovements in observed uncertainty and the index of disagreement, we identify
the two distinct concepts of uncertainty shocks in the data.

We tackle estimation of the VAR under these restrictions using the Bayesian
Markov chain Monte Carlo (MCMC) algorithm developed in Korobilis, (2022),
which allows us to sample sign and zero restrictions in arbitrarily large VARs
with high computational efficiency. For the $n\times 1$ vector of time-series
variables $\bm{y}_{t}$, the VAR takes the multivariate regression form:

$\mathbf{y}_{t}=\mathbf{\Phi}\mathbf{x}_{t}+\bm{\varepsilon}_{t},$ (17)

where $\mathbf{y}_{t}$ is a $\left(n\times 1\right)$ vector of observed
variables,
$\mathbf{x}_{t}=\left(1,\mathbf{y}_{t-1}^{\prime},...,\mathbf{y}_{t-p}^{\prime}\right)^{\prime}$
a $\left(k\times 1\right)$ vector (with $k=np+1$) containing a constant and
$p$ lags of $\mathbf{y}$, $\mathbf{\Phi}$ is an $(n\times k)$ matrix of
coefficients, and $\bm{\varepsilon}_{t}$ is a $\left(n\times 1\right)$ vector
of disturbances distributed as $N\left(\mathbf{0}_{n\times
1},\mathbf{\Omega}\right)$ with $\mathbf{\Omega}$ an $n\times n$ covariance
matrix. We further assume the following factor decomposition of
$\bm{\varepsilon}_{t}$:

$\bm{\varepsilon}_{t}=\mathbf{\Lambda}\mathbf{f}_{t}+\mathbf{v}_{t},$ (18)

where $\mathbf{\Lambda}$ is an $n\times r$ matrix of factor loadings,
$\mathbf{f}_{t}\sim N(\bm{0},\bm{I}_{r})$ is an $r\times 1$ vector of factors,
and $\mathbf{v}_{t}\sim N(\bm{0},\bm{\Sigma})$ is an $n\times 1$ vector of
idiosyncratic shocks with $\bm{\Sigma}$ an $n\times n$ diagonal matrix.

The rationale behind the VAR in equations (17)-(18) is that the
$n$-dimensional vector of VAR disturbances is decomposed into $r$ common
shocks $\mathbf{f}_{t}$ ($r<n$) and $n$ idiosyncratic shocks
$\mathbf{v}_{t}$.191919Gorodnichenko, (2005) also exploits this formulation of
the VAR for the identification of monetary policy shocks. Because
$\bm{\Sigma}$ is diagonal, we consider only the $r$ common shocks as
structural and the $n$ idiosyncratic shocks as nuisance shocks (e.g., due to
measurement error or asymmetric information). Indeed, by left-multiplying the
VAR using the generalized inverse of $\mathbf{\Lambda}$, the implied
structural VAR form is:

$\displaystyle\mathbf{y}_{t}$ $\displaystyle=$
$\displaystyle\mathbf{\Phi}\mathbf{x}_{t}+\mathbf{\Lambda}\mathbf{f}_{t}+\mathbf{v}_{t}$
(19)
$\displaystyle\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}\mathbf{y}_{t}$
$\displaystyle=$
$\displaystyle\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}\mathbf{\Phi}\mathbf{x}_{t}+\mathbf{f}_{t}+\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}\mathbf{v}_{t}$
(20) $\displaystyle\mathbf{A}_{1}\mathbf{y}_{t}$ $\displaystyle=$
$\displaystyle\mathbf{B}_{1}\mathbf{x}_{t}+\mathbf{f}_{t}+\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}\mathbf{v}_{t},$
(21)

where
$\mathbf{A}_{1}=\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}$
and $\mathbf{B}_{1}=\mathbf{A}_{1}\mathbf{\Phi}$. As long as $\bm{\Sigma}$ is
diagonal the term
$\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}\mathbf{v}_{t}$
vanishes asymptotically, meaning that $\mathbf{f}_{t}$ retains the
interpretation of structural shocks. Therefore, the desired sign and zero
restrictions required for identifying agreed and disagreed uncertainty can
take the form of simple parametric restrictions imposed on the respective
elements of $\mathbf{\Lambda}$.

Bayesian inference requires specification and tuning of prior distributions
for all parameters, and estimation with iterative MCMC algorithms requires
further assumptions and tuning parameters. Without dismissing the significance
of such choices, we use default, automatic prior choices justified in detail
in Korobilis, (2022).202020Our default choice is to iterate the algorithm
600,000 times, discard the first 100,000 iterations, and save every 100th draw
from the parameter posterior. In all VARs of different sizes we estimate, this
setting ensures low autocorrelation of posterior samples, as well as their
good numerical properties. We provide further technical details in the
Appendix.

##### Data and specifications.

Because fluctuations in measures of uncertainty and disagreement are short-
lived, following Bloom, (2009), Jurado et al., (2015), and Berger et al.,
(2020) our benchmark results rely on monthly U.S. macroeconomic data. The
sample runs from 1978M1 to 2020M12, where the earliest date is dictated by the
availability of the MSC data. Consumer disagreement is measured by our
disagreement index DISAG described in Section 2. We adopt the 12-month-ahead
macro uncertainty indicator developed by Jurado et al., (2015) as the
benchmark measure of uncertainty. We compute this indicator from estimates of
conditional volatilities of $h$-step ahead forecast errors using a monthly
dataset of 134 macroeconomic time series and captures broad-based
macroeconomic uncertainty.212121Methodologically, the indicator captures
broad-based movements in economic uncertainty while filtering out variations
in the conditional volatilities of the forecast errors. This procedure avoids
accounting predictable movements in the economy as uncertainty, as shown in
Ludvigson et al., (2021). This indicator, being a conditional variance of a
forecast error, is therefore the natural counterpart of the model concept.
Moreover, because macro-uncertainty is about broad-based future economic
conditions, it links more naturally to the concept of information dispersion
we use in this paper, which is about dispersion of consumer views about
economy-wide business conditions. The remaining monthly variables in our
benchmark VAR specification are: real industrial production index (IP), real
personal consumption expenditure index (CONS), total non-farm employment
(EMPL), inflation rate based on the personal consumption expenditure price
index (INFL), the S&P 500 index (SP500), and the federal funds effective rate
(FEDFUNDS). We discuss robustness of our results in Section 5. The VAR models
are estimated with 13 lags, and Appendix C describes the econometric
methodology in detail. To conserve space we report IRFs to four key variables
from the VAR specification, and the Appendix reports the remaining IRFs.

##### Benchmark specification.

The left panel in Figure 5 shows IRFs to a positive innovation in the variance
of the fundamental shock $\sigma_{\epsilon}$ – agreed uncertainty – identified
by imposing the sign restrictions in column (1) of Table 2 on the response of
uncertainty and disagreement indicators in the first period after the shock.
The JLN-12 uncertainty indicator rises immediately on impact and remains
persistently elevated for approximately 15 months, but the DISAG indicator
declines persistently in the short run and remains depressed for approximately
20 months. Beyond the initial period (where the response of activity
indicators are restricted to zero), industrial production, and employment
decline sharply and remain depressed even at the sixty month horizon. Our
results echo recent findings in the literature (e.g., Jurado et al.,, 2015,
Gilchrist et al.,, 2014, Ludvigson et al.,, 2021) using similar empirical
methods; they emphasize a significant depressing effect of economic
uncertainty on real activity indicators.

Figure 5: Benchmark model. Agreed $\sigma_{\varepsilon}$ (left) versus
disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses to the JLN 12-months-ahead
uncertainty indicator (JLN12), the disagreement index (DISAG), industrial
production (IP), and employment (EMPL). IRFs from an eight-variable VAR system
as described in the text. The shaded gray areas are the 16% and 84% posterior
bands generated from the posterior distribution of VAR parameters. The units
of the vertical axes are percentage deviations, and the horizontal axes report
time measured in months.

The right panel in Figure 5 shows IRFs to a positive innovation in the
variance of idiosyncratic noise, $\sigma_{v}$ – disagreed uncertainty. It is
identified by imposing the sign restrictions in column (2) of Table 2 on the
response of uncertainty and disagreement indicators in the first period after
the shock. The JLN-12 indicator shows a persistent rise that extends beyond
the 30-month horizon, while disagreement displays a short-lived, persistent
rise and stays elevated for about 10-months after the shock. Note that the
increase in the JLN-12 indicator is stronger and more persistent than the
increase in JLN-12 estimated in the left panel of the figure. Despite a
stronger and more persistent rise in uncertainty, the responses of real
activity indicators are qualitatively different than the responses under the
agreed uncertainty shock. Specifically, industrial production exhibits a small
positive and statistically significant short-lived response, in contrast to
the persistent negative response estimated in the left panel; it then quickly
reverts to the pre-shock level. Similarly, employment exhibits a small
positive and statistically significant response that persists until month 30,
in contrast to the negative persistent response estimated in the left panel.
Thus, disagreed uncertainty shocks are characterized by dynamic effects that
are broadly benign for economic activity in the short run, and they differ
qualitatively from the strong, adverse, and long-lasting effects on economic
activity in the aftermath of shocks to agreed uncertainty. Appendix D reports
the complete set of IRFs.

To summarize, identified innovations in _agreed uncertainty_ and _disagreed
uncertainty_ display sharp qualitative differences in the dynamic responses of
real activity indicators. _Agreed uncertainty_ shocks are robustly
contractionary and generate a sustained decline in industrial production and
employment. By contrast, _disagreed uncertainty_ shocks are broadly benign;
they are associated with a small and statistically significant positive
response of real activity in the short run. We are the first study to show
that disagreement in household views about current and future economic
conditions that characterizes disagreed uncertainty is critical for the benign
effects of uncertainty on real activity, but agreed uncertainty retains the
standard adverse effect on real activity.

Forecast error variance decomposition. We decompose the share of forecast
error variance (FEVD) of the benchmark VAR variables into the two identified
shocks. This is a useful check to ascertain whether these shocks are important
drivers of the empirical indicators of uncertainty and disagreement.

Figure 6 below shows the variance decomposition to the identified shocks of
agreed uncertainty (green) and disagreed uncertainty (blue); we also report
the residual variation, which is not attributed to any identified shock
(yellow). Two important findings emerge. First, the share of FEVD in JLN-12
explained by the two shocks is significant, rising to over 70% after the
seven-month horizon. Interestingly, the share of FEVD in JLN-12 accounted for
by the innovation in disagreed uncertainty alone exceeds the share of FEVD
accounted for by the agreed uncertainty shock at all horizons, suggesting that
the former is a significant driver of the variance in JLN-12. The disagreed
uncertainty innovation accounts for 50% of FEVD in JLN-12 after the seven-
month horizon and never drops below 20% of the same FEVD. Second, the two
shocks combined account for the majority of the FEVD in disagreement,
approximately 70% at all horizons. For disagreement, the share in FEVD
accounted for by the agreed uncertainty shock exceeds the FEVD share accounted
for by the disagreed uncertainty shock by a large margin. These findings
establish that our two different uncertainty shocks jointly explain a
significant share of the variation in the indexes of uncertainty and
disagreement. Taken together, the results show the key role of innovations to
the dispersion of information to explain movements in the different types of
uncertainty, supporting the insight from our simple model in Section 3. Our
exercise also suggests that the combination of two uncertainty shocks accounts
for a large share of FEVDs in industrial production, rising from approximately
20% at the 10-month horizon to 40% at the 60-month horizon, and innovations to
agreed uncertainty account for the majority of this total. These shocks,
however, account for a relatively small share, which is approximately 10%
after 10-months in the FEVD of employment, suggesting that other unidentified
shocks are the major drivers of the variation in this variable.222222Even
though our sample period and VAR identification is different, the FEVD in IP
accounted for by the two uncertainty shocks combined is broadly consistent
with estimates of FEVD accounted by macro uncertainty shocks identified via
JLN-12 reported in Jurado et al., (2015). The FEVD in employment accounted for
by the two shocks displayed earlier is somewhat smaller in comparison to
estimates of FEVD accounted by the macro uncertainty shocks reported in the
same study.

Figure 6: Variance Decomposition: Agreed ($\sigma_{\varepsilon}$, green) vs.
disagreed ($\sigma_{v}$, blue) uncertainty.

_Notes_ : The figure shows the variance decomposition of the variables from
the benchmark VAR specification to $\sigma_{\varepsilon}$ (green),
$\sigma_{v}$ (blue), and the residual variance not attributed to any other
shocks (yellow). The units of the vertical axes are percent, and the
horizontal axes reports monthly horizons.

##  5 Robustness analysis

In this section we briefly discuss the robustness analysis intended to check
the sensitivity of our results to alternative measures of consumer
disagreement. We investigate the robustness of our findings when we control
for different demographic characteristics of consumers, namely, age and
education. In Appendix D we examine the robustness to alternative proxies to
uncertainty used in related studies.232323Specifically, we examine VAR
specifications where we switch our benchmark uncertainty indicator to one of
the following: the Jurado et al., (2015) 12-months-ahead financial uncertainty
indicator (henceforth JLNF-12), the business dispersion measure (BOS-
dispersion) developed in Bachmann et al., (2013), stock market volatility
(CBOE S&P 100 volatility index VXO), or the Economic Policy Uncertainty index
(EPU) developed by Baker et al., (2016). We also consider VAR specifications
that i) estimate the dynamic effects of the two shocks on a broad spectrum of
macroeconomic (including labor market) and survey indicators, ii) replace the
DISAG index with individual disagreement indices from specific survey
questions, iii) estimate a VAR specification using a quarterly macro dataset.
These results are also described in Appendix D.

Alternative disagreement indicators. The tails disagreement employed in our
benchmark specification is simple and intuitive, but does not fully utilize
all the responses from MSC. Specifically, it only considers the two polar
categories of responses (better/worse), while ignoring the middle category
(depending on the question, this category relates to past/future conditions
that are either the “same” or “uncertain”). For that reason we recompute the
disagreement index using two alternative measures: “Entropy disagreement”
using Shannon’s (Shannon,, 1948) entropy measure, and “Lacy disagreement”
using the transformation proposed by Lacy, (2006). These exploit all possible
answers from consumers.

The entropy disagreement is defined as242424This measure we define as
disagreement is called the “Shannon Index” in ecology and related sciences,
and it is used to measure the diversity and distribution of types of species
in a community; see Hill, (1973).

$H_{t}^{j}=-\sum_{i=1}^{n}p(x^{j}_{i})\log{p(x^{j}_{i})}$

where $x_{i}^{j}$ is option $i$ of $n$ possible answers for question $j$, and
$p(x^{j}_{i})$ is the proportion of individuals answering $x_{i}^{j}$. This
index gives a measure of the cross-sectional uncertainty of consumers about
the possible business outcomes that may occur, where $p(x^{j}_{i})$ has an
interpretation of probabilities.252525We assume that consumers who have the
same view about business conditions do so because they also agree on the
probabilities about observing a specific outcome. The higher the index the
higher the uncertainty and the higher the disagreement. For example, if all
consumers shared the same view about the prospects of the economy, the value
of the index will be zero, which reflects a situation of zero uncertainty and
disagreement. By contrast if consumers are equally divided between the three
outcome categories (“better,” “worse,” “same”), the value of the index attains
the maximum value. The second alternative disagreement measure, from Lacy,
(2006), describes how dispersed or concentrated ordinal data is without
requiring further assumptions about inter-category distances. The Lacy
disagreement is defined using,

$D_{j}^{2}=\sum_{i=1}^{n-1}F_{i}\left(1-F_{i}\right),$

where $F_{i}$ is the cumulative relative frequency for the $i$th category.
Note that the sum excludes the last category, because $F_{n}$ is always 1.
This $D_{j}^{2}$ measure ranges from $0$ to $\left(n-1\right)/4$. When the
value of this measure is zero, all responses fall in the same category. The
maximum value of $\left(n-1\right)/4$ denotes completely polarized
distribution in which half of the responses are in category $1$ and half are
in category $n$. Values between the minimum and the maximum indicate
intermediate levels of dispersion.

We re-estimate the VAR after replacing the disagreement indicator DISAG with
the two alternative indicators one at a time, retaining all other variables in
the benchmark specification. The results are reported in Figure 7 below.
First, we note that the median IRFs displayed following a shock to agreed
uncertainty (left panel) and disagreed uncertainty (right panel) are
qualitatively and quantitatively similar when we use either the Lacy (DISAG-L,
dashed-green line) or Entropy (DISAG-E, dashed-blue line) concept of
disagreement in the VAR, and they are broadly similar to the IRFs we estimate
from the benchmark specification (also plotted in the same figure). This
result shows that the different VAR specifications identify the same shocks to
agreed and disagreed uncertainty. Moreover, the VAR specifications with the
DISAG-L and DISAG-E indicators suggest that the short-run positive response of
industrial production and employment following an innovation to disagreed
uncertainty are stronger in comparison to the responses in the same variables
estimated in the benchmark specification. Overall, this exercise ensures that
the DISAG indicator used in the benchmark VAR is robust to including
information from those consumers that are more uncertain about the strength or
weakness of current and future economic conditions.

Figure 7: Alternative disagreement indexes. Agreed ($\sigma_{\varepsilon}$,
left) vs. disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows (median) impulse responses for alternative
disagreement indexes: Tail disagreement (DISAG-T) as used in the benchmark
VAR, Entropy disagreement (DISAG-E), and Lacy disagreement (DISAG-L). The
units of the vertical axes are percentage deviations, and the horizontal axes
reports time measured in months.

Whose disagreement: Education and age. In addition to the overall aggregate
response to the survey questions, the MSC collects demographic responses from
consumers of different education and age status. They collect responses from
three education categories, namely: high-school, some college, and college
degree. They also collect responses from three age groups: 18-34, 35-54, and
55 and above. In this section we compute disagreement indicators for each of
these education and age groups – six in total – using the tails concept of
disagreement. We then, re-estimate the benchmark VAR using these indicators
one at a time. Figures 8, 9, and 10 display dynamic effects from the VARs that
condition on the disagreement indicators based on the different education
groups. The dynamic effects of agreed and disagreed uncertainty shocks, when
we condition on disagreement of the least educated group (high school
education, Figure 8), are very similar quantitatively to those dynamic effects
reported for the baseline specification. Interestingly, the IRFs from the
specifications that condition on disagreement of the some college and college
degree groups do not exhibit the sharp differences in the estimated real
effects following agreed and disagreed uncertainty shocks. Industrial
production is the only variable that appears to respond statistically
significantly following an agreed uncertainty shock. Figures 9 and 10 suggest
industrial production and employment do not respond statistically
significantly following a disagreed uncertainty shock. It appears that
disagreement from those consumers with high school educations matters the most
for the real activity effects we estimate in the benchmark specification. We
report results from the VAR specifications conditioned on disagreement
indicators based on the three age groups. When we condition the VAR on
disagreement from the age groups, 18-34, and 35-54 age groups (see Figures 11,
12), the responses to industrial production and employment following agreed
and disagreed uncertainty shocks are not statistically different from zero
(with the exception of industrial production after the 40-month horizon in
Figure 11). By contrast, when we condition on disagreement of the 55-and-over
age group, the responses to the real activity indicators following agreed and
disagreed uncertainty innovations (Figure 13) are strong and statistically
significant and very similar to the dynamic effects displayed in 5. Moreover,
the dynamic responses of the real activity indicators to agreed and disagreed
innovations display the systematic differences we estimate in the benchmark
specification. These results suggest that disagreement from the 55-and-over
age group appears to be the most relevant driver behind our benchmark results,
which are based on the aggregate responses.

Figure 8: Benchmark model–education: High school. Agreed
$\sigma_{\varepsilon}$ (left) versus disagreed $\sigma_{v}$ (right)
uncertainty.

_Notes_ : The figure shows impulse responses to the JLN 12-months-ahead
uncertainty indicator (JLN12), the disagreement index for high school
education level (DISAG-EDU1), industrial production (IP), and employment
(EMPL). We compute IRFs from an eight-variable VAR system as described in the
text. The shaded gray areas are the 16% and 84% posterior bands generated from
the posterior distribution of VAR parameters. The units of the vertical axes
are percentage deviations, and the horizontal axes report time measured in
months.

Figure 9: Benchmark model–education: some college. Agreed
$\sigma_{\varepsilon}$ (left) versus disagreed $\sigma_{v}$ (right)
uncertainty.

_Notes_ : The figure shows impulse responses to the JLN 12-months-ahead
uncertainty indicator (JLN12), the disagreement index for college educational
level (DISAG-EDU2), industrial production (IP), and employment (EMPL). We
compute the IRFs from an eight-variable VAR system as described in the text.
The shaded gray areas are the 16% and 84% posterior bands generated from the
posterior distribution of VAR parameters. The units of the vertical axes are
percentage deviations, and the horizontal axes report time measured in months.

Figure 10: Benchmark model–education: College or higher. Agreed
$\sigma_{\varepsilon}$ (left) versus disagreed $\sigma_{v}$ (right)
uncertainty.

_Notes_ : The figure shows impulse responses to the JLN 12-months-ahead
uncertainty indicator (JLN12), the disagreement index for college-or-higher
education level (DISAG-EDU3), industrial production (IP), and employment
(EMPL). We compute IRFs from an eight-variable VAR system as described in the
text. The shaded gray areas are the 16% and 84% posterior bands generated from
the posterior distribution of VAR parameters. The units of the vertical axes
are percentage deviations, and the horizontal axes report time measured in
months.

Figure 11: Benchmark model–age: 18-34. Agreed $\sigma_{\varepsilon}$ (left)
versus disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses to the JLN 12-months-ahead
uncertainty indicator (JLN12), the disagreement index for 18-34 age group
(DISAG-AGE1), industrial production (IP), and employment (EMPL). We compute
IRFs from an eight-variable VAR system as described in the text. The shaded
gray areas are the 16% and 84% posterior bands generated from the posterior
distribution of VAR parameters. The units of the vertical axes are percentage
deviations, and the horizontal axes report time measured in months.

Figure 12: Benchmark model–age: 35-54. Agreed $\sigma_{\varepsilon}$ (left)
versus disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses to the JLN 12-months-ahead
uncertainty indicator (JLN12), the disagreement index for age 35-54 (DISAG-
AGE2), industrial production (IP), and employment (EMPL). We compute the IRFs
from an eight-variable VAR system as described in the text. The shaded gray
areas are the 16% and 84% posterior bands generated from the posterior
distribution of VAR parameters. The units of the vertical axes are percentage
deviations, and the horizontal axes report time measured in months.

Figure 13: Benchmark model–age: 55 and above. Agreed $\sigma_{\varepsilon}$
(left) versus disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses to the JLN 12-months-ahead
uncertainty indicator (JLN12), the disagreement index for age 55 and above
(DISAG-AGE3), industrial production (IP), and employment (EMPL). We compute
the IRFs from an eight-variable VAR system as described in the text. The
shaded gray areas are the 16% and 84% posterior bands generated from the
posterior distribution of VAR parameters. The units of the vertical axes are
percentage deviations, and the horizontal axes report time measured in months.

##  6 Conclusion

In this paper we establish two new, distinct concepts of uncertainty shocks,
namely, _agreed_ and _disagreed_ uncertainty shocks. We show that the
dispersion of consumer views about current and future economic conditions,
measured by consumer disagreement, is an important conditioning factor for the
effect of uncertainty on economic activity. We present a dispersed and noisy
information model where agents form expectations by processing idiosyncratic
signals about an economic fundamental. We use the model to illustrate the
connection between consumer disagreement, which is a manifestation of
information dispersion, and uncertainty. The model shows that the change in
observed uncertainty, measured by the variance of a forecast error, is a
function of both the variance of the fundamental shock and the variance of the
idiosyncratic noise. Thus, a larger dispersion of views on economic conditions
(i.e., higher consumer disagreement) may increase the variance of the forecast
error without involving any change in the volatility of exogenous fundamental
forces in the economy.

We use the model to formulate simple sign restrictions that disentangle the
dynamic effects of innovations to _agreed_ and _disagreed_ uncertainty on U.S.
economic indicators in a medium-scale Bayesian VAR model. In our benchmark
specification, innovations in agreed uncertainty foreshadow significant and
often long-lasting, depressing effects on economic activity, namely,
industrial production and employment, corroborating the evidence from numerous
studies. By contrast, innovations in disagreed uncertainty (a rise in
uncertainty in periods of high consumer disagreement) are benign for economic
activity indicators, and they often lead to a short-run, positive responses in
those indicators. Our analysis suggests that shocks to disagreed uncertainty
are non-recessionary. Our results imply it is important to distinguish between
the two types of uncertainty shocks to study the link between uncertainty and
economic activity.

Our study opens up interesting avenues for future research. The analysis
implies that the disclosure of information that reduces disagreement may
increase the adverse effect of uncertainty. A straightforward extension of our
analysis is to study how policy announcements that convey information about
the economy may result in lower disagreement and exacerbate the negative
effect of uncertainty. It would be interesting to study whether a strategic
diffusion of information that maintains a wide range of views could alleviate,
or even overturn, the adverse effect of uncertainty. Finally, our results show
that the heterogeneity of views is critical for the aggregate effect of
uncertainty on output, suggesting that models with heterogenous agents may
prove fruitful for the study of expectations and the interplay between
uncertainty and economic activity. We plan to pursue some of these ideas in
future work.

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## Appendix

##  Appendix A Proof of inequality (12)

We can write equation (12) as

$\psi_{0}^{2}+\psi_{1}^{2}+\psi_{2}^{2}+...+\psi_{k-1}^{2}>-\psi_{k}^{2}\left(\frac{\sigma_{v}^{2}}{\sigma_{v}^{2}+\sigma_{\varepsilon}^{2}}\right)\left(\frac{\sigma^{2}_{v}-\sigma_{\varepsilon}^{2}}{\sigma_{v}^{2}+\sigma_{\varepsilon}^{2}}\right).$
(A.1)

All variance parameters are positive, hence, the term
$A=\left(\frac{\sigma_{v}^{2}}{\sigma_{v}^{2}+\sigma_{\varepsilon}^{2}}\right)$
can take values in the support $[0,1]$ and the term
$B=\left(\frac{\sigma^{2}_{v}-\sigma_{\varepsilon}^{2}}{\sigma_{v}^{2}+\sigma_{\varepsilon}^{2}}\right)$
in the support $[-1,1]$. Consequently, the term on the RHS of equation (A.1)
attains a maximum when $A=1$ and $B=-1$, and it is sufficient to prove that

$\psi_{0}^{2}+\psi_{1}^{2}+\psi_{2}^{2}+...+\psi_{k-1}^{2}>\psi_{k}^{2}.$
(A.2)

As all $\psi_{i}^{2}$ are non-negative for $i=1,...,k$, it suffices to show
that

$\psi_{0}^{2}>\psi_{k}^{2}.$ (A.3)

An MA($k$) process is invertible if the associated polynomial equation

$\psi(z)=\psi_{0}z^{k}+\psi_{1}z^{k-1}+...+\psi_{k-1}z+\psi_{k},$ (A.4)

has $k$ real or complex-valued roots $z^{\star}_{j}$, $j=1,...,k$, that are
inside the unit circle, that is, $|z^{\star}_{j}|<1$. By Vieta’s formulas we
have that

$\prod_{j=1}^{k}z^{\star}_{j}=(-1)^{k}\frac{\psi_{k}}{\psi_{0}}.$ (A.5)

If we take squares on both sides, and we use the fact that
$\prod_{j=1}^{k}\left(z^{\star}_{j}\right)^{2}<1$ because $|z^{\star}_{j}|<1$,
we have that

$\displaystyle\left((-1)^{k}\frac{\psi_{k}}{\psi_{0}}\right)^{2}$
$\displaystyle<$ $\displaystyle 1\Rightarrow$ (A.6)
$\displaystyle\frac{\psi_{k}^{2}}{\psi_{0}^{2}}$ $\displaystyle<$
$\displaystyle 1\Rightarrow$ (A.7) $\displaystyle\psi_{0}^{2}$
$\displaystyle>$ $\displaystyle\psi_{k}^{2},$ (A.8)

which means that inequalities (A.1) and (12) hold.

##  Appendix B Data Appendix

Our benchmark results are based on a VAR with eight monthly time series, but
overall we test the robustness of our results using multiple measures of
disagreement (based on different statistical measures of qualitative
variation, different measures of current and future expectations, and
different demographic groupings), multiple measures of uncertainty proposed in
the literature, and multiple combinations of macroeconomic variables. All
series are presented in Table B.1 below. There are four main sources indicated
in the third column of this table, FRED (Federal Reserve Economic Data,
https://fred.stlouisfed.org/), UofM (University of Michigan Survey of
consumers, https://data.sca.isr.umich.edu/), JLN2015 (data from Jurado et al.,
(2015), available at https://www.sydneyludvigson.com/macro-and-financial-
uncertainty-indexes) and Philly Fed (Federal Reserve Bank of Philadelphia,
Business Outlook Survey, https://www.philadelphiafed.org/surveys-and-
data/regional-economic-analysis/manufacturing-business-outlook-
survey).262626The Business Outlook Survey (BOS) data are used to extract the
uncertainty index of Bachmann et al., (2013) based on question 4 of the survey
(expectations about shipments from six months from now). As the authors do not
provide updates on this index, we use the raw BOS data and apply the
transformation $FDISP_{t}$ (see Bachmann et al.,, 2013, page 7) to compute its
values. All data were downloaded in different dates throughout July 2021. The
fourth column of Table B.1 shows the stationarity transformations applied to
the series, where Tcode = 1 is for levels and Tcode = 5 is for first
differences of the natural logarithm. Series that are originally observed at
daily or weekly frequencies (e.g. FEDFUNDS) are converted into monthly by
taking simple arithmetic averages over the calendar month.

We also estimate a VAR on quarterly data to test the robustness of our
findings. This is particularly important as the MSC data are available at
quarterly frequency from 1960, instead of 1978 for monthly data. Additionally,
at the quarterly frequency we are able to use GDP as the proxy for output,
plus we have other important series not available at the monthly frequency
(for example, investment). The uncertainty measure is again JLN12 and for
disagreement we use our primary tails index (both averaged over the quarter to
produce quarterly frequencies). The additional quarterly variables are (FRED
mnemonics, followed by Tcode, in parenthesis): GDP (GDPC1, 5), real personal
consumption (PCECC96 , 5), GDP deflator (GDPDEF, 5), real gross private
domestic investment (GPDIC1 ), employment (PAYEMS, 5), Federal funds rate
(FEDFUNDS, 1). Data on the S&P 500 index are quarterly averages of the same
monthly series presented in Table B.1. We also use a measure of stock market
variance, but because the popular VIX index is available only since 1985, we
use instead variable SVAR obtained from Amit Goyal’s webpage.272727See Ivo
Welch and Amit Goyal (2008), A Comprehensive Look at The Empirical Performance
of Equity Premium Prediction, The Review of Financial Studies, Volume 21,
Issue 4, Pages 1455-1508. All quarterly series are available for the period
1960Q1 - 2020Q4.

Table B.1: Monthly dataset, 1978M1 - 2020M12

Mnemonic | Description | Source | Tcode
---|---|---|---
Variables in benchmark VAR
JLN12 | JLN Macroeconomic Uncertainty, 12 months | JLN2015 | 1
DISAG | Tails disagreement total index | UofM | 1
INDPRO | Industrial Production: Total Index | FRED | 5
PCEPI | Personal Consumption Expenditures (Price Index) | FRED | 5
DPCERA3M086SBEA | Real personal consumption expenditures | FRED | 5
PAYEMS | All Employees, Total Nonfarm | FRED | 5
SP500 | S&P 500 | Yahoo! Finance | 5
FEDFUNDS | Federal Funds Effective Rate | FRED | 1
Other macroeconomic variables
DDURRA3M086SBEA | Real personal consumption expenditures: Durable goods | FRED | 5
DNDGRA3M086SBEA | Real personal consumption expenditures: Nondurable goods | FRED | 5
DSERRA3M086SBEA | Real personal consumption expenditures: Services | FRED | 5
AHETPI | Total Average Hourly Earnings of Production and Nonsupervisory Employees | FRED | 5
AWHNONAG | Total Average Weekly Hours of Production and Nonsupervisory Employees | FRED | 5
FLTOTALSL | Total Consumer Credit Owned and Securitized, Flow | FRED | 1
TERMCBPER24NS | Finance Rate on Personal Loans at Commercial Banks | FRED | 1
HWI | Composite help-wanted index | FRED | 1
PAGO | Current Financial Situation Compared with a Year Ago | UofM | 1
PEXP | Expected Change in Financial Situation in a Year | UofM | 1
RINC | Expected Change in Real Household Income During Next Year | UofM | 1
UMEX | Expected Change in Unemployment During the Next Year | UofM | 1
DUR-ALL | Buying Conditions for Large Household Durables | UofM | 1
VEH-ALL | Buying Conditions for Vehicles | UofM | 1
Alternative measures of uncertainty
JLNF12 | JLN Financial Uncertainty, 12 months | JLN2015 | 1
BOS DISP | Business Outlook Survey uncertainty index (expectations about shipments) | Philly Fed | 1
VXO | CBOE S&P 100 Volatility Index: VXO, Index, Monthly | FRED | 1
USEPUINDXM | Economic Policy Uncertainty Index for United States | FRED | 1
Alternative measures of disagreement
DISAG-E | Entropy disagreement total index | UofM | 1
DISAG-L | Lacey disagreement index | UofM | 1
DISAG_HS | Tails disagreement total index, High-school | UofM | 1
DISAG_SC | Tails disagreement total index, Some college | UofM | 1
DISAG_CD | Tails disagreement total index, College degree | UofM | 1
DISAG_A18-34 | Tails disagreement total index, Age group 18-34 | UofM | 1
DISAG_A35-54 | Tails disagreement total index, Age group 35-54 | UofM | 1
DISAG_A55+ | Tails disagreement total index, Age group 55+ | UofM | 1

##  Appendix C Econometric Methodology

This appendix describes the structural vector autoregression methodology for
identifying $\sigma_{e}$ and $\sigma_{v}$ shocks via sign restrictions. The
core VAR formulation follows Korobilis, (2022), who develops an efficient
algorithm for posterior inference in VARs with sign restrictions. This
algorithm allows for estimating VARs of arbitrarily large dimensions, and is
particularly suited for the monthly medium-scale VAR models with 13 lags we
use in this paper. For the $n\times 1$ vector of time series variables
$\bm{y}_{t}$ the VAR takes the multivariate regression form

$\mathbf{y}_{t}=\mathbf{\Phi}\mathbf{x}_{t}+\bm{\varepsilon}_{t},$ (C.1)

where $\mathbf{y}_{t}$ is a $\left(n\times 1\right)$ vector of observed
variables,
$\mathbf{x}_{t}=\left(1,\mathbf{y}_{t-1}^{\prime},...,\mathbf{y}_{t-p}^{\prime}\right)^{\prime}$
a $\left(k\times 1\right)$ vector (with $k=np+1$) containing a constant and
$p$ lags of $\mathbf{y}$, $\mathbf{\Phi}$ is an $(n\times k)$ matrix of
coefficients, and $\bm{\varepsilon}_{t}$ a $\left(n\times 1\right)$ vector of
disturbances distributed as $N\left(\mathbf{0}_{n\times
1},\mathbf{\Omega}\right)$ with $\mathbf{\Omega}$ an $n\times n$ covariance
matrix. We further assume the following factor decomposition of
$\bm{\varepsilon}_{t}$

$\bm{\varepsilon}_{t}=\mathbf{\Lambda}\mathbf{f}_{t}+\mathbf{v}_{t},$ (C.2)

where $\mathbf{\Lambda}$ is an $n\times r$ matrix of factor loadings,
$\mathbf{f}_{t}\sim N(\bm{0},\bm{I}_{r})$ is an $r\times 1$ vector of factors,
and $\mathbf{v}_{t}\sim N(\bm{0},\bm{\Sigma})$ is an $n\times 1$ vector of
idiosyncratic shocks with $\bm{\Sigma}$ an $n\times n$ diagonal matrix.

The rationale behind the VAR model in equations (C.1)-(C.2) is that the
$n$-dimensional vector of VAR disturbances is decomposed into $r$ common
shocks $\mathbf{f}_{t}$ ($r<n$) and $n$ idiosyncratic shocks $\mathbf{v}_{t}$.
Because $\bm{\Sigma}$ is diagonal, we consider only the $r$ common shocks to
be structural while the $n$ idiosyncratic shocks can be considered as nuisance
shocks e.g. due to measurement error or asymmetric information. Indeed, by
left-multiplying the VAR using the generalized inverse of $\mathbf{\Lambda}$,
the implied structural VAR form is

$\displaystyle\mathbf{y}_{t}$ $\displaystyle=$
$\displaystyle\mathbf{\Phi}\mathbf{x}_{t}+\mathbf{\Lambda}\mathbf{f}_{t}+\mathbf{v}_{t}$
(C.3)
$\displaystyle\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}\mathbf{y}_{t}$
$\displaystyle=$
$\displaystyle\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}\mathbf{\Phi}\mathbf{x}_{t}+\mathbf{f}_{t}+\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}\mathbf{v}_{t}$
(C.4) $\displaystyle\mathbf{A}_{1}\mathbf{y}_{t}$ $\displaystyle=$
$\displaystyle\mathbf{B}_{1}\mathbf{x}_{t}+\mathbf{f}_{t}+\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}\mathbf{v}_{t}.$
(C.5)

As long as $\bm{\Sigma}$ is diagonal the term
$\left(\mathbf{\Lambda}^{\prime}\mathbf{\Lambda}\right)^{-1}\mathbf{\Lambda}^{\prime}\mathbf{v}_{t}$
vanishes asymptotically, meaning that $\mathbf{f}_{t}$ retains the
interpretation of structural shocks. Korobilis, (2022) shows that structural
identifying restrictions are identical to parametric restrictions on
$\mathbf{\Lambda}$, and provides an efficient Markov chain Monte Carlo (MCMC)
scheme for sampling such restrictions in high-dimensional VARs.282828A VAR can
be high-dimensional due to the large number of time series $T$, large number
of endogenous variables $n$, large number of identified shocks $r$, large
number of lags $p$, or combinations of these.

Based on the model in equations (C.1)-(C.2) the joint likelihood function can
be written as

$\left(\bm{y}|\bm{x},\bm{\Phi},\bm{\Lambda},\bm{f},\bm{\Sigma}\right)\sim\prod_{t=1}^{T}N\left(\mathbf{\Phi}\mathbf{x}_{t},\mathbf{\Lambda}\mathbf{\Lambda}^{\prime}+\bm{\Sigma}\right)$
(C.6)

and we define the following prior distributions

$\displaystyle\bm{\phi}_{i}\equiv vec\left(\mathbf{\Phi}_{i}\right)$
$\displaystyle\sim$ $\displaystyle
N_{k}\left(\mathbf{0},\underline{\mathbf{V}}_{i}\right),$ (C.7)
$\displaystyle\underline{\mathbf{V}}_{i,(jj)}$ $\displaystyle=$
$\displaystyle\sigma^{2}_{i}\tau_{i}^{2}\psi_{i,j}^{2},$ (C.8)
$\displaystyle\psi_{i,j}$ $\displaystyle\sim$ $\displaystyle
Cauchy^{+}\left(0,1\right),$ (C.9) $\displaystyle\tau_{i}$ $\displaystyle\sim$
$\displaystyle Cauchy^{+}\left(0,1\right),$ (C.10)
$\displaystyle\mathbf{f}_{t}$ $\displaystyle\sim$ $\displaystyle
N_{r}\left(\mathbf{0},\mathbf{I}\right),$ (C.11)
$\displaystyle\mathbf{\Lambda}_{ij}$ $\displaystyle\sim$
$\displaystyle\left\\{\begin{array}[]{ll}N\left(0,\underline{h}_{ij}\right)I(\Lambda_{ij}>0),&\text{if
$S_{ij}=1$},\\\ N\left(0,\underline{h}_{ij}\right)I(\Lambda_{ij}<0),&\text{if
$S_{ij}=-1$},\\\ \delta_{0}\left(\mathbf{\Lambda}_{ij}\right),&\text{if
$S_{ij}=0$},\\\
N\left(0,\underline{h}_{ij}\right),&\text{otherwise},\end{array}\right.$
(C.16) $\displaystyle\sigma^{2}_{i}$ $\displaystyle\sim$ $\displaystyle inv-
Gamma\left(\underline{\rho}_{i},\underline{\kappa}_{i}\right),$ (C.17)

for $i=1,...,n$, $j=1,...,r$, where $\mathbf{\Phi}_{i}$ is the $i^{th}$ row of
$\mathbf{\Phi}$, $\sigma_{i}^{2}$ is the $i^{th}$ diagonal element of the
matrix $\mathbf{\Sigma}$, and $\delta_{0}\left(\mathbf{\Lambda}_{ij}\right)$
is the Dirac delta function for $\mathbf{\Lambda}_{ij}$ at zero (i.e. a point
mass function with all mass concentrated at zero). The hyperparameters
$\psi_{i,j}$ and $\tau_{i}$ are components of a Horseshoe prior, which is a
tuning-free shrinkage priors with excellent statistical properties (see
Korobilis,, 2022, for explanation and references to the statistics literature
justifying the excellent theoretical properties of this prior). Therefore, we
only need to select parameters with an underline, namely
$\underline{h}_{ij},\underline{\rho}_{i},\underline{\kappa}_{i}$. As we
typically do not have substantial prior information on these hyperparameters,
it is fairly trivial to choose noninformative values. Following standard norms
in Bayesian inference, we set $\underline{h}_{ij}=10$ and
$\underline{\rho}_{i},\underline{\kappa}_{i}=0.01$ such that the priors in
equations (C.16) and (C.17) become locally Uniform. Posterior computation and
impulse response inference follows Korobilis, (2022) and the reader should
refer to this paper for technical details.

##  Appendix D Additional results

In this Appendix we report i), the complete set of IRFs estimated from the VAR
specifications in the main body of the paper and ii), results from VAR
specifications that use various economic, financial, and survey indicators,
iii), results from VAR specifications that use alternative proxies for
uncertainty, iv) VAR specifications with disagreement indices derived from
specific questions. These VAR specifications serve to examine the robustness
of the main finding in the main body of the paper, namely, the different
dynamic effects of agreed and disagreed uncertainty shocks.

##### Complete IRFs from benchmark model.

Figure D.1 below displays the complete set of IRFs from the benchmark
specification. Private consumption displays a negative effect following an
agreed uncertainty innovation consistent with the negative responses estimated
for industrial production and employment. Following a disagreed uncertainty
innovation private consumption exhibits a small short run increase that is
nevertheless not statistically significant. There are also systematic
differences in the responses of S&P 500, Federal Funds rate and consumer price
inflation following agreed and disagreed uncertainty innovations, suggesting
that the qualitatively different dynamic responses following the two shocks
are broad based.

Figure D.1: Benchmark model. Agreed $\sigma_{\varepsilon}$ (left) versus
disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses from a eight-variable VAR system
on JLN 12-month ahead uncertainty indicator (JLN12), disagreement index
(DISAG), Industrial production (IP), private consumption (CONS), Consumer
price inflation (INFL), employment (EMPL), S&P 500 index (SP500), Federal
funds rate (FEDFUNDS). The shaded gray areas are the 16% and 84% posterior
bands generated from the posterior distribution of VAR parameters. The units
of the vertical axes are percentage deviations, while the horizontal axes
reports time measured in months.

The benchmark specification in section 4 used the macro uncertainty measure
(JLN-12) as the baseline measure of uncertainty. In this section we replace
JLN-12 in the benchmark VAR with four alternative uncertainty measures used in
earlier work. Jurado et al., (2015) developed the 12-month ahead financial
uncertainty indicator (henceforth JLNF-12) using estimates of conditional
volatilities of $h$-step ahead forecast errors from 147 financial time series.
Ludvigson et al., (2021) suggest this indicator is a preferable measure of
uncertainty as it is less likely to be confounded by exogenous shocks –and
hence can be treated as an exogenous source of variation in uncertainty– in
comparison to JLN-12. Beyond this measure we also use the business dispersion
measure (BOS-dispersion), developed in Bachmann et al., (2013), and a popular
measure of stock market volatility (CBOE S&P 100 volatility index VXO) used in
several important studies as a proxy for uncertainty (Bloom,, 2009, Gilchrist
et al.,, 2014, Basu and Bundick,, 2017). Finally, we use the Economic Policy
Uncertainty index (EPU) developed by Baker et al., (2016). The latter is
developed using text mining methods and captures uncertainty, broadly
speaking, about future fiscal, monetary, trade, regulatory policy actions.

##### Complete IRFs from VAR model with JLNF-12.

Figure D.2 below displays the complete set of IRFs from the VAR specification
with JLNF-12 used as the uncertainty indicator discussed in section 5 of the
main body. The IRFs are broadly consistent with the IRFs displayed in the
Figure D.1 above. The left panel which plots the IRFs to the agreed
uncertainty shock displays very similar –qualitatively– depressing effects on
industrial production and employment in comparison to the effects estimated
when JLN12 is used as the uncertainty proxy. The negative effects on
industrial production and employment are however significantly smaller in
magnitude (evaluated at the peak median response) in comparison to the
negative effects estimated in the benchmark specification displayed in Figure
D.1. This appears to be a consequence of the smaller increase of the JLNF-12
uncertainty indicator in comparison to the response of the JLN-12 indicator
displayed in Figure D.1. The depressive effects on economic activity are
consistent with the evidence in Ludvigson et al., (2021) who also use JLNF-12
as the uncertainty indicator in their empirical analysis. The right panel
displays the IRFs following an innovation to the disagreed uncertainty shock.
Qualitatively the dynamic effects estimated are very much in line with those
displayed in D.1. Both industrial production and employment exhibit a short
run positive and statistically significant response. Thus, both the benchmark
and this alternative specification suggest that innovations to disagreed
uncertainty display a benign effect on economic activity, strikingly different
from the strong depressing effect on activity estimated under agreed
uncertainty.

Figure D.2: JLNF-12 measure. Agreed $\sigma_{\varepsilon}$ (left) versus
disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses from a eight-variable VAR system
on JLNF 12-month ahead uncertainty indicator (JLNF12), disagreement index
(DISAG), Industrial production (IP), private consumption (CONS), Consumer
price inflation (INFL), employment (EMPL), S&P 500 index (SP500), Federal
funds rate (FEDFUNDS). The shaded gray areas are the 16% and 84% posterior
bands generated from the posterior distribution of VAR parameters. The units
of the vertical axes are percentage deviations, while the horizontal axes
reports time measured in months.

##### Complete IRFs from VAR model with BOS-DISPERSION.

Figure D.3 below displays the complete set of IRFs from a VAR specification
with the BOS-DISPERSION used as the uncertainty indicator. A key difference in
this Figure in comparison to Figure is the different dynamic response of
uncertainty: while uncertainty rises under both agreed and disagreed shocks,
the business dispersion measure displays more short-lived and non-persistence
dynamics in comparison to JLN-12 or JLNF-12. This may not be surprising given
this dispersion measure is based on a very different information set –firms in
the manufacturing sector, in comparison to the broad spectrum of variables
considered in JLN-12 aand JLNF-12. Nevertheless the dynamic effects following
an agreed uncertainty shock identified from this alternative indicator suggest
a strong and long lasting period of depressed activity, very much in line with
conventional wisdom and our findings above. Focussing on the dynamic effects
following a disagreed uncertainty shock, broadly speaking, real activity
indicators do not respond in a statistically significant manner. This suggests
the response of real activity indicators is non-contractionary under disagreed
uncertainty shocks, identified from this uncertainty proxy, and importantly
there is a distinct quantitative difference between the dynamic effects
estimated under disagreed and agreed uncertainty shocks.

Figure D.3: Business Dispersion measure. Agreed $\sigma_{\varepsilon}$ (left)
versus disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses from a eight-variable VAR system
on Business dispersion indicator (BOS-DISPERSION), disagreement index (DISAG),
Industrial production (IP), private consumption (CONS), Consumer price
inflation (INFL), employment (EMPL), S&P 500 index (SP500), Federal funds rate
(FEDFUNDS). The shaded gray areas are the 16% and 84% posterior bands
generated from the posterior distribution of VAR parameters. The units of the
vertical axes are percentage deviations, while the horizontal axes reports
time measured in months.

##### Complete IRFs from VAR model with VXO.

Figure D.4 below displays the complete set of IRFs from the VAR specification
with VXO used as the uncertainty indicator. Uncertainty responds sharply and
it is short-lived. The IRFs to an agreed uncertainty innovation are consistent
with a depressing and long lasting effect on real activity –this very similar
to what we have estimated in all other specifications. The dynamic effects
estimated following a disagreed uncertainty shock suggest an initial short run
but barely statistically significant depressing effect on industrial
production which reverts very quickly to the pre-shock level. The employment
response suggests a statistically significant decline. The response of
employment is qualitatively different to the findings reported so far. We do
however emphasize two important caveats with this specification. First, the
sample period is different, due to the availability of the VXO indicator,
beginning in 1986M1. Second, and more importantly the IRFs suggest that the
identification of the disagreed uncertainty shock is potentially problematic.
The positive sign restriction on disagreement that identifies this shock is
not satisfied in a statistical sense. Specifically, note that the response of
disagreement is not statistically significant different from zero following an
innovation to disagreed uncertainty. We therefore, do not consider this joint
response of uncertainty and disagreement, strictly speaking, as genuinely
identifying a disagreed uncertainty shock. Because we want to be as
conservative as possible, our sign restrictions put very minimal constraints
on the dynamics. This suggests that more identifying restrictions may be
fruitful in order to clearly separate the two types of uncertainty shocks,
when using this uncertainty indicator. Nevertheless, there are some
quantitative differences in the responses of the real activity indicators; the
economic effects following this type of innovation are significantly smaller
in magnitude in comparison to the economic effects estimated following an
agreed uncertainty innovation.

Figure D.4: Stock market implied volatility (VXO) measure. Agreed
$\sigma_{\varepsilon}$ (left) versus disagreed $\sigma_{v}$ (right)
uncertainty.

_Notes_ : The figure shows impulse responses from a eight-variable VAR system
on CBOE S&P 100 volatility index (VXO), disagreement index (DISAG), Industrial
production (IP), private consumption (CONS), Consumer price inflation (INFL),
employment (EMPL), S&P 500 index (SP500), Federal funds rate (FEDFUNDS). The
shaded gray areas are the 16% and 84% posterior bands generated from the
posterior distribution of VAR parameters. The units of the vertical axes are
percentage deviations, while the horizontal axes reports time measured in
months.

##### Complete IRFs from VAR model with EPU.

Figure D.5 below displays the complete set of IRFs from the VAR specification
with EPU used as the uncertainty indicator. Its not straightforward to map the
connection of this concept of uncertainty to the broad based macro or
financial uncertainty indicators examined above. Moreover, the EPU indicator
is not clearly related to our central measure of consumer disagreement as the
latter refers to business conditions and the former is focussed on economic
policy. Therefore its not straightforward to relate a change in information
dispersion to the volatility of this indicator which is derived from text
mining methods. The sample period, 1985M1 to 2020M12, for this specification
is different to the benchmark due to the availability of the EPU index. We
nevertheless wanted to examine the behavior of the real activity indicators
using the concepts of agreed and disagreed uncertainty identified via this
measure. Figure D.5 suggests a broad similarity to our findings when
considering the dynamic effects following the agreed uncertainty shock –both
industrial production and employment exhibit long lasting and depressing
effects. While the response of industrial production is negative following
both agreed and disagreed shocks, the response of employment is not
statistically significant in the case of disagreed uncertainty shock (except
barely so in month two only). We suggest this may be partly due to the fact
that, similar to the VXO specification above, the identification of disagreed
uncertainty shocks appears to be problematic since the disagreement index
barely moves in a statistically significant manner in the case of the
disagreed uncertainty shock.

Figure D.5: EPU measure. Agreed $\sigma_{\varepsilon}$ (left) versus disagreed
$\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses from a eight-variable VAR system
on Economic Policy Uncertainty (EPU), disagreement index (DISAG), Industrial
production (IP), private consumption (CONS), Consumer Inflation (INFL),
employment (EMPL), S&P 500 index (SP500), Federal funds rate (FEDFUNDS). The
shaded gray areas are the 16% and 84% posterior bands generated from the
posterior distribution of VAR parameters. The units of the vertical axes are
percentage deviations, while the horizontal axes reports time measured in
months.

##### Complete IRFs from VAR model with DISAG-E.

Figure D.6 below displays the complete set of IRFs from the VAR specification
with the entropy measure, DISAG-E, used as the disagreement indicator and
discussed in section 5 of the main body.

Figure D.6: Disagreement entropy measure. Agreed $\sigma_{\varepsilon}$ (left)
versus disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses from a eight-variable VAR system
on JLN 12-month ahead uncertainty indicator (JLN12), disagreement index
(DISAG-E), Industrial production (IP), private consumption (CONS), Consumer
price inflation (INFL), employment (EMPL), S&P 500 index (SP500), Federal
funds rate (FEDFUNDS). The shaded gray areas are the 16% and 84% posterior
bands generated from the posterior distribution of VAR parameters. The units
of the vertical axes are percentage deviations, while the horizontal axes
reports time measured in months.

##### Complete IRFs from VAR model with DISAG-L.

Figure D.7 below displays the complete set of IRFs from the VAR specification
with Lacy measure, DISAG-L, used as the disagreement indicator and discussed
in section 5 of the main body.

Figure D.7: Disagreement Lacy measure. Agreed $\sigma_{\varepsilon}$ (left)
versus disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses from a eight-variable VAR system
on JLN 12-month ahead uncertainty indicator (JLN12),disagreement index
(DISAG-L), Industrial production (IP), private consumption (CONS), Consumer
price inflation (INFL), employment (EMPL), S&P 500 index (SP500), Federal
funds rate (FEDFUNDS). The shaded gray areas are the 16% and 84% posterior
bands generated from the posterior distribution of VAR parameters. The units
of the vertical axes are percentage deviations, while the horizontal axes
reports time measured in months.

##### Individual disagreement (BUS5 and NEWS).

Our benchmark DISAG index is the first principal component of the five
individual disagreement series, described in section 2. This aggregate index
captures dispersed consumer views about current and future business
conditions. We examine the robustness of our findings when we instead focus on
individual disagreement indices. Figures D.8 and D.9 display complete set of
IRFs estimated from two specifications where we replace the DISAG indicator in
the benchmark VAR with disagreement about NEWS (News Heard of Recent Changes
in Business Conditions) and BUS5 (Business Conditions Expected During the Next
5 Years ), one at a time. The estimated IRFs from those specifications are
broadly similar to the those from the benchmark and we do not discuss them
further.

Figure D.8: Disagreement NEWS. Agreed $\sigma_{\varepsilon}$ (left) versus
disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses from a eight-variable VAR system
on JLN 12-month ahead uncertainty indicator (JLN12),disagreement index about
NEWS (NEWS-T), Industrial production (IP), private consumption (CONS),
Consumer price inflation (INFL), employment (EMPL), S&P 500 index (SP500),
Federal funds rate (FEDFUNDS). The shaded gray areas are the 16% and 84%
posterior bands generated from the posterior distribution of VAR parameters.
The units of the vertical axes are percentage deviations, while the horizontal
axes reports time measured in months.

Figure D.9: Disagreement BUS5. Agreed $\sigma_{\varepsilon}$ (left) versus
disagreed $\sigma_{v}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses from a eight-variable VAR system
on JLN 12-month ahead uncertainty indicator (JLN12),disagreement index about
BUS5 (BUS5-T), Industrial production (IP), private consumption (CONS),
Consumer price inflation (INFL), employment (EMPL), S&P 500 index (SP500),
Federal funds rate (FEDFUNDS). The shaded gray areas are the 16% and 84%
posterior bands generated from the posterior distribution of VAR parameters.
The units of the vertical axes are percentage deviations, while the horizontal
axes reports time measured in months.

##### Labor market conditions and unemployment expectations.

We enrich our benchmark specification with the following indicators of labor
market conditions in addition to employment: the help wanted index –a proxy
for labor market tightness, average hourly earnings, and the Michigan consumer
expectations about unemployment in the next twelve months. The left panel in
Figure D.12 shows the IRFs of the enriched VAR model following an innovation
to agreed uncertainty. The response of the variables is similar to our
benchmark specification, evinced by the significant fall in industrial
production and employment; the responses of the additional labor market
variables show that following an agreed uncertainty shock depresses the help
wanted index for more than sixty months. Total private consumption displays a
depressing effect with an estimated effect which becomes statistically
significant in the ten month horizon –this is slightly weaker in comparison to
the benchmark specification. The strong positive response of unemployment
expectations over the next twelve months signal weak employment prospects
expected by households. Despite the adverse labor market conditions and
depressed expectations on labor market prospects, the response of earnings
remains statistically insignificant.

The right panel in Figure D.12 shows that IRFs from an innovation in disagreed
uncertainty. The responses of real activity indicators, industrial production,
employment and consumption, are statistically insignificant. The dynamic
responses of the remaining labor market variables are also statistically
insignificant, suggesting this shock has a muted effect on the labor market.
Thus, accounting for labor market dynamics in the propagation of uncertainty
does not alter our central finding: agreed uncertainty innovations retain the
standard adverse effect on economic activity, while disagreed uncertainty
innovations remains non-contractionary for economic activity.

Figure D.10: VAR model with additional labor market variables. Agreed
$\sigma_{v}$ (left) versus disagreed $\sigma_{\varepsilon}$ (right)
uncertainty.

_Notes_ : The figure shows impulse responses from a eight-variable VAR system
on JLN 12-month ahead uncertainty indicator (JLN12), disagreement index
(DISAG), Industrial production (IP), private consumption (CONS), employment
(EMPL), hourly earnings (EARNINGS), 12 month ahead unemployment expectations
(UNEXP12), Help wanted index (HWI). The shaded gray areas are the 16% and 84%
posterior bands generated from the posterior distribution of VAR parameters.
The units of the vertical axes are percentage deviations, while the horizontal
axes reports time measured in months.

##### Disaggregated consumption.

Our benchmark specification includes total private consumption. It is
interesting to examine the dynamic responses of different consumption
components. To this end we estimate a VAR specification which builds on the
one estimated with the additional labor market variables above, where we
introduce real services, non-durables and durables consumption. One would
expect that uncertainty would mostly impact large durables purchases. For
example, Eberly, (1994) emphasizes the option to delay purchases of durable
goods in an environment of elevated uncertainty, which in theory would depress
durables spending, although the effects on non-durables and services might be
weaker. Similarly, Bernanke, (1983) and Romer, (1990) show that uncertainty
significantly delays consumer spending on durable purchases by increasing the
option value of waiting. Bertola et al., (2005) provide extensive evidence on
the sensitivity of durable goods spending to uncertainty. Figure D.11 displays
the IRFs from this specification. Consumption non-durables and durables
display a significant depressing effect following an innovation in agreed
uncertainty. By contrast, the response of consumer services does not display
any negative effects, but interestingly a positive response which becomes
statistically significant after the forty month horizon. Thus, it appears
services consumption mitigates the depressing effects on total consumption
following an agreed uncertainty shock. By contrast the responses of the
disaggregated consumption components are not statistically significant
following a disagreed uncertainty innovation.

Figure D.11: Benchmark model. Agreed $\sigma_{\varepsilon}$ (left) versus
disagreed $\sigma_{v}$(right) uncertainty.

_Notes_ : The figure shows impulse responses from a ten-variable VAR system on
JLN 12-month ahead uncertainty indicator (JLN12), disagreement index (DISAG),
Industrial production (IP), consumption durables (CONS DUR), consumption non-
durables (CONS NDUR), consumption services (CONS S), employment (EMPL), hourly
earnings (EARNINGS), 12 month ahead unemployment expectations (UNEXP12), Help
wanted index (HWI). The shaded gray areas are the 16% and 84% posterior bands
generated from the posterior distribution of VAR parameters. The units of the
vertical axes are percentage deviations, while the horizontal axes reports
time measured in months.

##### Results based on a VAR specification using quarterly data.

We estimate a VAR specification using a sample with a quarterly frequency.
This allows to examine the dynamic responses to GDP and investment that are
only available in this frequency. The quarterly sample is 1960Q1 to 2020Q4.
The results from this specification are broadly consistent with our benchmark
results which are based on a monthly sample. A shock to agreed uncertainty
depresses the economic activity indicators, namely real GDP, consumption,
employment and private non residential investment. By contrast, real GDP,
consumption and employment, do not respond in a statistically significant
manner following a disagreed uncertainty shock. Private non residential
investment does not respond in the short term but responds negatively after
the six month horizon.

Figure D.12: Benchmark model. Agreed $\sigma_{v}$ (left) versus disagreed
$\sigma_{\varepsilon}$ (right) uncertainty.

_Notes_ : The figure shows impulse responses from a quarterly ten-variable VAR
system using JLN 12-month ahead uncertainty indicator (JLN12), disagreement
index (DISAG), GDP, private consumption (CONS), inflation based on the GDP
deflator (INFL), private non residential fixed investment (INV), employment
(EMPL), S&P 500 index, Federal funds rate (FEDFUNDS), and the stock market
variance from the S&P Index (SVAR) computed as the sum of squared daily
returns on S&P 500. Sample period 1960Q1 to 2020Q4. The shaded gray areas are
the 16% and 84% posterior bands generated from the posterior distribution of
VAR parameters. The units of the vertical axes are percentage deviations,
while the horizontal axes reports time measured in quarters.