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Working Paper Series

Learning About Informational Rigidities
from Sectoral Data and Diffusion Indices

WP 10-09

This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/

Pierre-Daniel Sarte
Federal Reserve Bank of Richmond

Learning About Informational Rigidities from Sectoral
Data and Di¤usion Indices
Pierre-Daniel Sarte
Federal Reserve Bank of Richmond
May 2010
Working Paper No. 10-09

Abstract
This paper uses sectoral data to study survey-based di¤usion indices designed to
capture changes in the business cycle in real time. The empirical framework recognizes
that when answering survey questions regarding their …rm’s output, respondents potentially rely on infrequently updated information. The analysis then suggests that their
answers re‡ect considerable information lags, on the order of 16 months on average.
Moreover, because information stickiness leads respondents to …lter out noisy output
‡uctuations when answering surveys, it helps explain why di¤usion indices successfully
track business cycles and their consequent widespread use. Conversely, the analysis
shows that in a world populated by fully informed identical …rms, as in the standard
RBC framework for example, di¤usion indices would instead be degenerate. Finally,
the data suggest that information regarding changes in aggregate output tends to be
sectorally concentrated. The paper, therefore, is able to o¤er basic guidelines for the
design of surveys used to construct di¤usion indices.
JEL classi…cation: E32, C42, C43
Keywords: Information Stickiness, Di¤usion Indices, Approximate Factor Model

I want to thank, without implicating them in any way, Adrian Pagan, Ricardo Reis, and Mark Watson
for helpful discussions and comments. I am also indebted to Nadezhda Malysheva for outstanding research
assistance. The views expressed in this paper are those of the author and do not necessarily re‡ect those of
the Federal Reserve Bank of Richmond or the Federal Reserve System. All errors are my own.

1

1

Introduction

Data provided by statistical agencies regarding the state of the economy typically lag current
conditions. For example, manufacturing data are released with a one month lag by the
Federal Reserve Board, revised up to three months after their initial release, and further
subject to an annual revision. At the monthly frequency, this data is also quite noisy in
a way that partially masks underlying business cycle conditions. Thus, in an alternative
attempt to track the business cycle in real time, and to con…rm initial Board data releases,
information is also compiled by many institutions and government agencies from qualitative
data. The Institute for Supply Management (ISM), for example, constructs a widely used
monthly di¤usion index of manufacturing production, based on nationwide surveys, that will
be the focus of the analysis. In addition, several Federal Reserve Banks including Atlanta,
Dallas, Kansas City, New York, Philadelphia, and Richmond, produce similar indices that
are meant to capture real time changes in economic activity at a more regional level.1
A central issue pertaining to these surveys is that gathering information on a large number
of sectors in a timely fashion is costly and, given time and resource constraints, the scope
of the questions must necessarily be limited. Thus, di¤usion indices constructed by the ISM
and Federal Reserve Banks rely on simple trichotomous classi…cations whereby respondents
are asked whether a variable, say production for that respondent’s …rm, is “up,”“the same,”
or “down” relative to the previous period. The number of respondents can vary over time
and the respondents themselves need not be the same from survey to survey. Individual
responses are aggregated into proportions of respondents reporting a rise, no change, or a
fall in output. Di¤usion indices are then constructed by further converting these proportions
into aggregate time series meant to track economic activity. The methods typically used in
performing these conversions are discussed in detail in Section 2.
While various properties of di¤usion indices, sometimes also referred to as balance statistics, have been studied in some detail, this work has been limited because …rm-level data
underlying individual survey responses are either not systematically recorded or not publicly available. It has proven challenging, therefore, to say much about the nature of survey
responses, and whether they re‡ect informational rigidities. It has also been di¢ cult to
explain why converting qualitative answers in the way suggested by di¤usion indices has
proven useful in following economic activity in real time.2
1

Other examples of popular national di¤usion indices include the Employment Di¤usion index constructed
by the Bureau of Labor Statistics, and the Di¤usion Index for Industrial Production constructed by the Board
of Governors.
2
Di¤usion indices, however, have been used to investigate the extent to which expectations can be considered rational as well as to help forecast economic activity. See Pesaran and Weale (2006) for a comprehensive

2

In this paper, I use sectoral manufacturing data to construct an empirical framework
composed of hypothetical survey respondents. Each respondent acts as a spokesperson for
a …rm whose output re‡ects both aggregate conditions and conditions speci…c to the sector
in which it operates. Methods used to construct di¤usion indices are then applied to these
hypothetical respondents to create a synthetic di¤usion index of manufacturing production
that can be directly compared to that published by the Institute for Supply Management.
The analysis makes two key assumptions. First, information is costly to acquire so
that survey respondents are not necessarily aware of their …rm’s exact output at each date.
Speci…cally, I allow respondents to update their information set infrequently in the manner
suggested by Mankiw and Reis (2002, 2006). Second, as noted in Pesaran and Weale (2006),
respondents recognize that some changes in their …rm’s output are not necessarily meaningful
so that increases or decreases are reported only when exceeding given thresholds. Under the
maintained assumptions, a primary objective of the analysis is to provide estimates of i) the
degree of information stickiness, and ii) the thresholds that de…ne perceptions of rises and
falls in output, that best describe the ISM manufacturing production index.
Using data on manufacturing production in 124 sectors over the period 1972-2009, I
estimate that survey respondents update their expectations on average every 16 months.
Furthermore, the data also suggest that the degree of information stickiness has fallen over
time. Thus, using the onset of the Great Moderation to split the sample, the empirical work
estimates an average information lag of 20 months prior to the Great Moderation compared
to 13 months during the latter period. These …ndings, therefore, are consistent with a fall in
the cost of acquiring information over time. For comparison, previous studies relying on nontruncated surveys and aggregate data have found average information stickiness of roughly
12 months, as presented in Carroll (2003) based on data from the Michigan Survey of Consumers and the Survey of Professional Forecasters (SPF), and 12:5 months, as calculated in
Mankiw, Reis and Wolfers (2003) using similar information as well as the Livingston Survey.
In a di¤erent vein, Mankiw and Reis (2006), and Reis (2009), use quantitative models to
calibrate the degree of information stickiness by targeting di¤erent aspects of the cyclicality
of aggregate variables or their responses to shocks. This work …nds that information lags
of 6 to 16 months are generally most consistent with salient features of the data. Most
recently, Coibion and Gorodnichenko (2009) present evidence against the hypothesis of full
information based on a variety of survey forecasts. Their …ndings suggest that forecast errors
are persistent with a half-life of up to 16 months. More important, the dynamics of these
forecast errors are consistent with predictions of models with informational rigidities. None
treatment of survey expectations. See also Ivaldi (1992), as well as Jeong and Maddala (1996), for studies
of the rationality of survey data:

3

of these studies, however, include the detailed level of disaggregation exploited here.
A key implication of this paper is that informational rigidities provide a foundation
for the widespread use of di¤usion indices as contemporaneous economic indicators. In
particular, these rigidities mean that a considerable fraction of respondents answer surveys
based on what they expect their …rm’s output to be given their most recent information rather
than actual production. Therefore, high frequency output ‡uctuations that are unrelated to
business cycles tend to be …ltered out. Accordingly, around 60 percent of the variation in the
monthly ISM production di¤usion index is located at business cycle frequencies compared to
just 23 percent of the variance in monthly aggregate manufacturing. Information stickiness,
therefore, in e¤ect lets respondents abstract from “noisy”movements in sectoral production.
The analysis further shows that in a world populated by identical …rms that are always fully
informed, as in the standard Real Business Cycle (RBC) environment for example, di¤usion
indices become degenerate and thus cease to be useful.3
As mentioned earlier, information on individual survey responses that underlie the construction of di¤usion indices is either not recorded systematically or not made publicly available. In contrast, because the empirical framework involves the modeling of hypothetical
survey respondents, it allows for the tracking, as a counterfactual of sort, of the proportions of “up,”“same,”and “down”responses over past business cycles. The empirical work
then shows some notable di¤erences in the historical behavior of these proportions. Prior
to the Great Moderation, the proportion of “optimists” (those reporting expected output
increases) and “pessimists” (those reporting expected output decreases) play an equal role
in driving the di¤usion index. Hence, recessions and expansions are re‡ected by corresponding spikes in the measure of “optimists” and “pessimists.’ However, after the onset of the
Great Moderation, while recessions are still marked by sharp increases in the proportion of
“pessimists,” movements in the proportion of “optimists” are considerably more subdued.
Therefore, from this standpoint, the Great Moderation period is not only associated with a
noticeable decline in volatility but also with an asymmetry in sectoral output ‡uctuations.
Finally, drawing on previous work in Foerster, Sarte and Watson (2008), the analysis suggests that information regarding changes in overall manufacturing tends to be concentrated
in relatively few sectors. Hence, taking as given the methods by which qualitative survey
responses are converted into a quantitative di¤usion index, the empirical framework o¤ers
3

There is also a large literature that examines the pitfalls associated with ignoring the distinction between
real time and revised data. These problems motivate in part the interest in creating di¤usion indices. See
Croushore (2009) for a recent and comprehensive survey of real-time data analysis. See also Runkle (1998),
Croushore and Stark (2001), and Fernald and Wang (2005), for the challenges posed by data revisions to
the making of policy in real time.

4

some basic lessons regarding the design of surveys that underlie these indices. First, contrary
to standard practice at some Federal Reserve Banks, it is not necessary for surveys to try
to capture a representative sample of all manufacturing. The intuition is straightforward.
In some sectors, variations in output are driven almost entirely by aggregate factors while,
in other sectors, output movements re‡ect mostly sector-speci…c considerations. Therefore,
to gain insight into current aggregate business cycle conditions, surveys should emphasize
the former sectors and largely disregard the latter sectors. Second, having identi…ed sectors
whose variations re‡ect mostly factors driving aggregate changes, I show that a useful di¤usion index may be produced using as few as 15 sectors instead of all 124 sectors in the data
set.
The rest of this paper is organized as follows. Section 2 describes the methods typically
used to construct the ISM and other di¤usion indices based on qualitative surveys. Section
3 highlights key di¤erences between sectoral manufacturing production data and the ISM
manufacturing production index. Section 4 then presents an empirical framework aimed
at reconciling these di¤erences under the assumption that survey respondents update their
expectations only infrequently. The estimation methods and …ndings are reviewed in section
5. Section 6 performs a series of counterfactuals that illustrate how the usefulness of di¤usion
indices relates to di¤erent aspects of the economic environment. Section 7 o¤ers concluding
remarks.

2

Description of the ISM and other Production Di¤usion Indices

The Institute for Supply Management is a large U.S. trade association comprising approximately 40,000 supply management professionals. As part of a broader mandate, it compiles
a monthly Manufacturing Report on Business based on questions asked of purchasing executives. To keep the survey process straightforward, and to limit the burden on respondents,
questions are posed in a format such that they reply with only one of three answers to
indicate a change relative to the previous month. The spirit of the survey, therefore, is
very much to capture some notion of changes in output otherwise re‡ected more formally in
growth rates. In this case, answers regarding production are limited to “up,” “the same,”
or “down,”and an index is then constructed from the responses. Because this simpli…cation
lets respondents answer more quickly than if a precise answer regarding production changes
(rather than a general assessment) were required, it is crucial to the timeliness of the index.
The ISM calculates its index by adding the percentage of positive responses to half of the
5

percentage of “same”responses.
Formally, let M represent the number of manufacturing sectors that make up total manufacturing as classi…ed by the U.S. Census Bureau. Let xij
t denote the output of a given …rm
i working in a sector j at date t, and

xij
t denote its growth rate relative to the previous

period. Consider a survey that asks a sample of N respondents in each of these M manufacij
ij
turing sectors whether their …rm’s output is “up” (uij
t ), “the same” (st ), or “down” (dt ),

relative to the previous period. Following Pesaran and Weale (2006), the ISM surveying
process would then typically be described as cataloging respondents’perception of changes
in their …rm’s output at t relative to t
if

ij
ij
ij
xij
t > ; respondent i reports “up”; ut ( ) = 1; st ( ) = dt ( ) = 0;

xij
t

if
if

1 in the following manner:

xij
t

<

ij
ij
; respondent i reports “same”; sij
t ( ) = 1; ut ( ) = dt ( ) = 0;

; respondent i reports “down”;

The interval [

dij
t (

) = 1;

uij
t (

)=

sij
t (

(1)

) = 0:

; ] de…nes an indi¤erence region that represents respondents’ latent

perceptions of rises and falls in output. It captures the idea that changes in output may not
always be substantive enough to convey meaningful information, or that respondents may
not be certain that they are, and therefore may not worth reporting as “up” or “down.”
An immediate implication is that whether an output change is considered “up,”“same,”or
“down,” depends intrinsically on the threshold that de…nes the bounds of the indi¤erence
ij
ij
interval. This dependence is made explicit by writing uij
t ( ), st ( ), and dt ( ) in equation

(1).
Given the structure of the surveys, the fraction of “optimists”in the sample is given by
Ut = M

1

N

1

M X
N
X

uij
t ( ):

(2)

j=1 i=1

Similarly, the fractions of “same”respondents and “pessimists”are given by
St = M

1

N

1

M X
N
X

sij
t ( )

(3)

dij
t ( );

(4)

j=1 i=1

and
Dt = M

1

N

1

M X
N
X
j=1 i=1

respectively. The value of the ISM di¤usion index at t, denoted It , is then de…ned as
1
100
Ut + S t
2
M X
N
X
1 ij
1
1
= M N
uij
t ( ) + st ( )
2
j=1 i=1

It =

6

100:

(5)

The resulting index values range from 0 to 100, with numbers above 50 generally indicating
an expansion of economic activity.
In the case of the Federal Reserve Banks (FRB) surveys, the respondents are also asked
to report only “increases,” “decreases,” and “no change” in output relative to the previous
month, but the form of the index varies slightly relative to the ISM index. The FRB Richmond survey, for example, calculates its index by subtracting the percentage of negative
responses from the percentage of positive responses, producing the so-called “balance statistic” motivated by the probability approach of Carlson and Parkin (1975). Hence, in this
case, we have that
It = (Ut

Dt ) 100
M X
N
X
1
1
= M N
uij
t ( )

dij
t ( )

100;

(6)

j=1 i=1

which is bounded between

100 and 100 and takes on a value of zero when an equal number

of respondents reports increases and decreases.
It is useful to note that actual changes in aggregate manufacturing output, denoted

xt ,

are given by
xt =
where

xjt

=

P

ij
i wt

M
X

wtj xjt ;

(7)

j=1

xij
t

represents output growth in sector j, wtij is the share (or weight) of

…rm i’s production in sector j, and wtj is the share of sector j’s output in aggregate production. Foerster, Sarte and Watson (2008) show that movements in

xt are relatively invariant

to the exact sectoral weighting scheme so that the expression in (7) is well approximated
P P ij ij
P
xt . Therefore, if the sample of respondents, N , is
xjt = M 1 M
by M 1 M
j=1
i wt
j=1
large enough, the di¤usion indices in (5) and (6) rely on approximately the same aggrega-

tion used to arrive at manufacturing output growth. A key di¤erence, of course, is that the
variables being aggregated in the di¤usion indices are truncated reports of individual …rm
output changes (in the sense of being translated to 0s and 1s) rather than actual output
growth.
Some key questions that the analysis will address are: i) How well does the ISM di¤usion
index of manufacturing production capture variations at business cycle frequencies and,
moreover, how does it compare to actual manufacturing output growth? ii) How is the
di¤usion index’s ability to track movements at business cycle frequencies related to various
features of the environment, in particular the degree of information stickiness characterizing
survey respondents? iii) Given an upper bound on the number of sectors that can feasibly be
surveyed in a given period, how does one choose which sectors to survey? Put another way,
7

how does one distinguish between sectors that are informative about the state of aggregate
manufacturing and those that are not?

3

Basic Properties of Sectoral Manufacturing Data and
the ISM Di¤usion Index

Because Federal Reserve Banks’di¤usion indices re‡ect regional rather than national conditions, and given that manufacturing data is unavailable at the state level, the analysis uses
nation-wide sectoral manufacturing data and the corresponding ISM manufacturing production di¤usion index. As explained above, the di¤usion index is a monthly series obtained
from the Institute for Supply Management constructed as in equation (5). Monthly data on
manufacturing production are obtained from the Board of Governors over the period 19722009. The manufacturing sector is disaggregated into 124 industries according to the North
American Industry Classi…cation System (NAICS), which corresponds roughly to a six-digit
level of disaggregation. The raw output data are used to compute sectoral growth rates as
well as the relative shares of di¤erent sectors in aggregate manufacturing. Monthly growth
rates (in percentage points) in sectoral output are computed as

xjt = ln(Xtj =Xtj 1 )

1200,

where Xtj denotes production in the j th sector at date t. The main properties of the data
are described in Table A1.
Figures 1A and 1B show the behavior of manufacturing production growth, computed
according to equation (7), and that of the monthly ISM manufacturing production index
over the period 1972-2009. The intervals de…ned by the dashed vertical lines depict recessions dated by the National Bureau of Economic Research (NBER). Looking at Figure 1A,
monthly growth rates in manufacturing productions are quite volatile, exceeding 8 percentage points (at an annual rate) over the whole sample period. The fall in volatility associated
with the Great Moderation is also evident in Figure 1A; the standard deviation of manufacturing production growth declines essentially by half after 1984. Aside from having a
large standard deviation, observe also that the manufacturing production series is relatively
“choppy,”with growth in a given month bearing little relationship to growth in the previous
or subsequent months. In stark contrast, despite also re‡ecting monthly reported changes,
the ISM manufacturing production di¤usion index shown in Figure 1B is much smoother
with high frequency ‡uctuations that are much less apparent. At the same time, the ISM
series evidently picks up recessions quite well, with the index falling considerably below 50,
the neutral threshold in equation (5), in each recession since that of 1973. Given that the
ISM manufacturing di¤usion index is meant to capture economic activity in real time, Figure
8

1B makes clear why it is a popular contemporaneous economic indicator.4
To gain additional insight into the two measures of manufacturing production illustrated
in Figures 1A and 1B, Figures 2A and 2B show the power spectra of manufacturing output
growth and the di¤usion index (up to frequency =2). On the whole, the spectral shapes
shown in Figure 2 are typical of growth rate spectra for real macroeconomic variables, as
documented for example in King and Watson (1996); the spectra are low at low frequencies,
increase to a peak at a cycle length of approximately 50 months, and then decline sharply at
high frequencies. King and Watson (1996) refer to this shape as the “typical spectral shape
for growth rates” and it is noteworthy that, despite being based on truncated qualitative
responses, the spectral shape of the di¤usion index conforms closely to that benchmark.
To interpret the shapes shown in Figures 2A and 2B more speci…cally, it is helpful to
recall some key concepts of frequency domain analysis. The Spectral Representation Theorem
states than any covariance-stationary series, for example

xt in this case, can be expressed

as a weighted sum of periodic functions of the form cos(!t) and sin(!t),
Z
Z
xt = +
(!) cos(!t)d! +
(!) sin(!t)d!;
0

(8)

0

where ! denotes a particular frequency and the weights (!) and (!) are random variables
with zero means. The variance of

xt can then be subsequently decomposed as
Z
f (!)d!;
var( xt ) = 2

(9)

0

where the power spectrum, f (!), gives the extent of frequency !’s contribution to the total
variance of the series. Each frequency, !, is in turn associated with cycles of period p =
2 =!.
Following King and Watson (1996), business cycle frequencies are de…ned in this paper
as those associated with cycles of periods ranging from 24 to 96 months.5 Thus, the dashed
vertical lines in Figures 2A and 2B correspond to frequencies, !, ranging from 0:065 =
(2 )=96 to 0:26 = (2 )=24.
Two observations stand out in Figures 2A and 2B. First, the business cycle interval
indeed contains the peak of the spectrum of manufacturing output growth and, remarkably,
that of the ISM manufacturing production index as well. More importantly, consistent
with Figures 1A and 1B, it is unmistakable that business cycle frequencies explain a much
4

The ISM series, however, is subject to a minor adjustment each year to re‡ect changes in seasonal factors
used to construct the index.
5
This de…nition is in turn based on earlier work by NBER researchers using the methods described in
Burns and Mitchell (1947).

9

larger fraction of the variance in the di¤usion index than in manufacturing output growth. In
particular, compared to the manufacturing di¤usion index, a substantially greater fraction of
the variation in manufacturing output growth is located at high frequencies, thus accounting
for the “noisy” aspect of output growth relative to the di¤usion index. The power spectra
in Figure 2 imply that the business cycle interval contains close to 60 percent of the overall
variance in the di¤usion index compared to just 23 percent of the variance in monthly
manufacturing output growth. In that sense, month to month, the manufacturing di¤usion
index performs considerably better than actual manufacturing output growth in tracking
variations at business cycle frequencies.
Of course, it is always possible to use quarterly growth rates of manufacturing output,
or …lter the series in some other way, to follow its movements at business cycle frequencies.
However, the question then is: why does this issue not arise with the di¤usion index which,
similarly to output growth, is based on monthly aggregated reports of individual changes in
output?6 The next sections will argue that the answer lies not in the truncating and averaging
used in equation (5), but follows from having di¤erentially informed survey respondents.
While month-to-month variations in manufacturing output growth shown in Figure 1A
are large, variations in growth rates at the sectoral level are even more pronounced. This
follows from the fact that, in equation (7), some of the sectoral variation “averages out” in
aggregation. Figure 3A indeed shows that, at the six-digit level of disaggregation, the standard deviations of sectoral growth rates can easily exceed 100 percent and, on average, are
on the order 43 percent compared to a standard deviation of 8:5 percent in aggregate manufacturing growth. Although …rm-level data are not available, the same reasoning suggests
that …rm-level variations in output might be even larger. From that standpoint, therefore,
it is unclear that surveying individual …rms in the way carried out by the ISM would produce a useful economic indicator. In fact, the ISM production index not only performs well
in capturing downturns and upturns in manufacturing generally, but the magnitude of the
di¤usion index is also suggestive of the strength in these cyclical swings. Thus, looking at
Figure 3B, most index values are clustered between 45 and 55 as expected, but index values
of 35 and below are clearly associated with the most signi…cant falls in output growth in
Figures 1A and 1B (i.e. the recessions in the 1970s and 1980s as well as the most recent
recession).
Tables 1 and 2 summarize the main observations made in this section. Table 1 gives the
6

In addition, since monthly manufacturing output is released with a lag and subject to several revisions,
the problem of not having the information available for real time analysis persists. This problem is compounded by the fact that, even if an output measure were available in real time, conventional …lters that
successfully isolate business cycle frequencies are two-sided.

10

standard deviations of manufacturing output growth and of the ISM index, as well as the
fractions of variance explained by business cycle and higher frequencies in the two series.
Table 2 shows the autocorrelations in output growth and the di¤usion index, as well as the
cross correlations between the two series at di¤erent leads and lags. Observe the distinct
di¤erence between the …rst and second row of Table 2. Consistent with the “choppiness”of
the manufacturing series shown in Figure 1A, manufacturing output growth in a given month
bears little relationship to growth in previous months. In contrast, this is clearly not so for
the manufacturing di¤usion index, whose index values in a given month are highly correlated
with index values in previous months. In addition, observe also that manufacturing output
growth leads the manufacturing di¤usion index in that the correlations between output
growth and the di¤usion index are larger for future values, rather than past values, of the
index. An objective of the paper will be in part to explain all of these observations.
Given the nature of sectoral output growth in manufacturing, the next section sets up
an empirical framework that helps explain the key di¤erences between aggregate manufacturing output growth and the manufacturing di¤usion index discussed in Figures 1 through
3 and Tables 1 and 2. The framework exploits the fact that the di¤usion index derives from
aggregated reports of monthly manufacturing output changes. Thus, one of its a central
assumption is to allow for a distribution of hypothetical respondents with di¤erentially updated information. The paper then explores what degree of information stickiness helps best
reconcile the two series.

4

The Empirical Framework

Let output growth of a …rm i operating in a sector j evolve according to
xij
t =

xjt + uit ;

(10)

where Et 1 (uit ) = 0 8i . In other words, changes in output for a …rm working in sector j

re‡ect in part changes in that sector’s conditions and in part …rm-level idiosyncratic disturbances that have zero mean. Each …rm is associated with a spokesperson who reports on
changes in her …rm’s output. As in Mankiw and Reis (2002), however, I assume that at any
given date, it is costly to determine exactly what a …rm’s production changes are, or for the
purpose of the surveys, what portion of a …rm’s production changes are actually informative
about the current state. The presumption is that information ‡ows from the factory ‡oor,
production process, and other relevant sectoral considerations are imperfect and that the
…rm representative responding to the surveys is only infrequently apprised of the exact state

11

of output growth. Formally, at each date and in each sector, a fraction

2 (0; 1) of repre-

sentatives are able to update their information set. This implies that in each time period,
a fraction

of spokepersons have current information, a fraction (1

) of spokepersons

2

have one-period old information, a fraction (1

) of spokepersons have two-period old

information, and so on.7
As discussed above, survey designers ask a sample of N representatives in each of M
sectors whether their …rm’s output increased, decreased, or stayed the same at t relative to
1. Because of informational rigidities, respondents’answers cannot always re‡ect their

t

…rm’s current output growth. Instead, for respondents who do not have current information,
answers to the surveys are based on what they expect current output changes to be conditional on their most recent information, Et k ( xij
t ), where t

k is the date at which they

last updated their information set.
Because some respondents base their answers on expected output changes, Et k ( xij
t ),
rather than actual output changes,

xij
t , a basic element of the empirical framework concerns

their perceptions of sectoral output growth,

xjt , in equation (10). To this end, I model

changes in sectoral output as
xjt =

j

Ft + ejt ; j = 1; :::; M;

Ft =

(L)Ft

1

+

(11)

t;

where Ft represents a set of latent dynamic factors common to all manufacturing sectors,
is a common disturbance such that Et 1 ( t ) = 0,
and

ejt

is a sector-speci…c shock such that

Et 1 (ejt )

factor model in (11) can be expressed as

j

is a factor loading speci…c to sector j,

= 0 8j. In vector notation, the dynamic
(12)

Xt = Ft + et ;
where Xt is an M

0
1 vector of sectoral growth rates, ( x1t ; :::; xM
t ),

matrix of factor loadings, Ft is an r
1 vector of sectoral shocks,

M

variance-covariance matrix

ee .

t

is an M

r

1 vector of manufacturing-wide factors, and et is an

0
(e1t ; :::; eM
t ),

that are cross-sectionally weakly correlated with

The number of time series observations is denoted by T .

As discussed in Stock and Watson (2010), the dynamic factor model in (12) has proven
a valuable approach to handling, and modeling simultaneously, large data sets where the
number of series approaches or exceeds the number of time series observations, as in this
paper’s application. Aside from this strict statistical interpretation, however, Foerster, Sarte,
and Watson (2008) also show that equation (12) can be derived as the reduced form solution
7

See Reis (2006) for the microfoundations of this approach to modeling information stickiness.

12

to a canonical multisector growth model of the type …rst developed in Long and Plosser
(1983), and further studied in Horvath (1998, 2000), Dupor (1999), and Carvalho (2007).
Because these models explicitly take into account input-output linkages across sectors, the
“uniquenesses,”et , may not satisfy weak cross-sectional dependence. In particular, while Ft
in (12) can generally be identi…ed with common shocks to sectoral total factor productivity
(TFP), the et ’s re‡ect linear combinations of the underlying structural sector-speci…c shocks.
By ignoring the comovement in “uniquenesses,”the factor model (12) can then overstate the
degree of comovement in sectoral output that is attributed to common TFP shocks. Using
sectoral data on U.S. industrial production and matching input-output tables, Foerster et al.
(2008) show that the internal comovement stemming from input-output linkages is relatively
small. Therefore, for the remainder of the analysis, I interpret Ft as re‡ecting aggregate
sources of variation in sectoral TFP.
With the dynamic factor model (12) in hand, it is now possible to create a “synthetic”
manufacturing production di¤usion index. The synthetic index is analogous to that discussed
in section 2 but makes explicit that not all respondents have up-to-date information when
answering surveys.
As a simple example, suppose that Ft =

Ft

1

+

t,

< 1. Then, in each sector j,

N respondents know their …rm’s current production change exactly, Et ( xij
t ) =
j

Ft + ejt + uit . Furthermore, under the maintained assumptions,

(1

xij
t =

)N respondents

last updated their information set in the previous period and, for these respondents, survey
answers re‡ect what they expect current output growth to be given that period’s information,
Et 1 ( xij
t ) =
j 2

j

Ft 1 . Similarly, (1

)2 N respondents’answers will re‡ect Et 2 ( xij
t ) =

Ft 2 , and so on.

Observe that, except for the respondents who have current information, only …xed sectorspeci…c characteristics and aggregate factors end up playing a role in the construction of the
synthetic index. This is because Et k ( xij
t ) =
so that only the sector-speci…c factor loadings,
lags,

k

j k
j

Ft k , j = 1; :::; M , and k = 1; 2; :::

, and the factor components and their

Ft k , are ultimately relevant. Thus, for the majority of …rms (assuming that

is

small), variability arising either from …rm-level shocks or from sectoral shocks tends to be
…ltered out as Et k (uit ) = 0 and Et k (ejt ) = 0 8i; j and k = 1; 2; ::: . Put another way, as a
result of information stickiness, some …rm representatives can only report what they expect
output growth to be instead of actual output growth. It follows that for these respondents,
month to month shocks a¤ecting changes in …rm output will not be fully re‡ected in the
di¤usion index. However, since the goal of di¤usion indices is precisely to capture aggregate
business cycles, this implication of infrequent updating turns out to be particularly useful
for this purpose. In addition, because answers based on expected output growth re‡ects past
13

information through

j k

Ft k , information stickiness may help explain not only the smooth

nature of the di¤usion index in Figure 1B, but also why manufacturing output growth leads
the index in Table 2.
Since individual …rm level data is not available,

xij
t cannot be computed for the fraction

of …rms whose respondents have current information. In that case, I assume that
xjt =

j

xij
t =

Ft + ejt . In other words, currently informed respondents are assumed to represent

…rms whose output growth mimics the sector in which they operate. This allows the empirical
framework to abstract from individual …rm variability entirely. However, as made clear by
Figure 2A, sectoral output remains quite volatile. Therefore, if …rm-level output volatility
is considerably more pronounced than sectoral volatility, then the empirical framework only
provides a lower bound for the degree of information stickiness. Put another way, more
informational rigidity would then be necessary to …lter out high frequency ‡uctuations in
output growth in order to obtain the smooth di¤usion index shown in Figure 1B.
Analogously to equation (1), the synthetic ISM surveying process described in this section
can be characterized as recording, for each sector j, di¤erentially informed perceptions of
changes in output according to the following conditions:
kj
kj
kj
if Et k ( xij
t ) > , then ut ( ) = 1; st ( ) = dt ( ) = 0; k = 0; 1; :::

if
if Et k (

Et k ( xij
t )
xij
t )

<

kj
kj
, then skj
t ( ) = 1; ut ( ) = dt ( ) = 0; k = 0; 1; :::

, then

dkj
t (

) = 1;

ukj
t (

)=

skj
t (

where, at each date t and in each sector j, Et k ( xij
t ) =

(13)

) = 0; k = 0; 1; :::;

j k

Ft

k

for (1

)k N respondents.

The proportions of “up,”“down,”and “same”respondents now depend not only on the
threshold that de…nes perceptions of rises and falls in output, , but also on the degree of
information stickiness, . Given the empirical set-up, the number of “optimists”and “same”
respondents in the survey is given by
Ut ( ; ) = M

1

M X
1
X

(1

)k ukj
t ( )

(14)

(1

)k skj
t ( );

(15)

j=1 k=0

and
St ( ; ) = M

1

M X
1
X
j=1 k=0

respectively. Therefore, similarly to equation (5), the synthetic di¤usion index for manufacturing production, denoted Iet ( ; ), takes the form
14

Iet ( ; ) =

1
100
Ut ( ; ) + St ( ; )
2
M X
1
X
1 kj
(1
)k ukj
M 1
t ( ) + st ( )
2
j=1 k=0

100:

(16)

Given this synthetic di¤usion index, the natural question is: what degree of information
stickiness, , and indi¤erence threshold, , best describe the actual manufacturing production index created by the ISM? Thus, a and
min S( ; ) =
;

are chosen to satisfy

T
X
t=1

It Iet ( ; )

2

(17)

:

Before moving on to the estimation and …ndings, it is worth summarizing the two key
elements of the empirical framework set out in this section. First, respondents who do
not have current information answer survey questions based on expected output growth,
conditional on their most recent information, rather than actual output growth. Hence,
since Et k (uit ) = 0 and Et k (ejt ) = 0 8i; j; and k = 1; 2::: , this feature of information
stickiness helps …lter out high frequency ‡uctuations that arise through shocks. Second, to
the extent that respondents’answers re‡ect past information through

j k

Ft k , and because

equation (17) is a weighted sum of these information lags, one expects the resulting di¤usion
index to be smoother than manufacturing output growth. It is also precisely this mechanism
that may allow manufacturing output growth to lead the ISM di¤usion index as shown in
Table 2.

5

Estimation and Empirical Findings

The estimation of the empirical framework described in the previous section proceeds in
two steps. The …rst step involves estimation of the dynamic factor model (12). The second
step uses the resulting model estimates to construct a synthetic di¤usion index according to
equations (13) through (16) and solves equation (17).
In the …rst step, the number of factors in (12) are estimated using the Bai and Ng (2002)
ICP1 and ICP2 estimators. The factors themselves and the loadings are then estimated by
principle component methods. When M and T are large, as they are in this paper’s application, Stock and Watson (2002) show that principle components provide consistent estimates
of the factors. In addition, the estimation error in the estimated factors is su¢ ciently small
15

that it can be ignored when carrying out variance decompositions or conducting inference
about . In other words, Fbt , can be treated as data in a second-stage regression or subsequent investigation. In the second step, therefore, estimates of the factors obtained in this
way are used in the construction of the synthetic di¤usion index, Iet ( ; ), according to the
rules given by (13). Equation (17) is then solved for the degree of informational rigidity, ,

and the indi¤erence threshold, , that best characterize the actual manufacturing di¤usion
index.
The Bai and Ng (2002) ICP1 and ICP2 estimators yield 2 factors in the full sample

(1972-2009), and the …ndings in this section are based on this 2-factor model. However, for
robustness, the analysis was also carried out using 1 and 3-factor models with similar results
(not shown).
Given equation (12), the factor analysis centers on two main results that will help develop
intuition for the behavior of the di¤usion index. First, I denote by R2 (F ) the fraction of
aggregate manufacturing variability that is explained by common shocks. In particular,
letting w denote the M
R2 (F ) = w0

FF

0

w=

1 vector of constant mean shares,
2

x,

where

2
x

xt = w0 Ft + w0 et so that

is the variance of aggregate manufacturing output

growth. Second, I also highlight the extent to which the common factors explain output
growth variability in individual sectors, Rj2 (F ) =

j

FF

j0

=

2

xj ,

where

2
xj

is the variance

of sector j’s output growth. The purpose of this last calculation is to show that in some
sectors, ‡uctuations in output growth re‡ect in part aggregate factors while, in other sectors,
changes in output result mostly from idiosyncratic considerations. This feature of sectoral
data will be key in providing guidelines regarding which sectors to survey in the construction
of a manufacturing di¤usion index.
The factor model implies a volatility of aggregate manufacturing output growth that
is nearly identical to that found in the data, 8:47 percent. More important, the common
factors explain 85 percent or the bulk of the variability in aggregate manufacturing output
growth: Figure 4A further illustrates this point by plotting manufacturing output growth,
xt , and the model’s …tted values of the factor component, w0 Ft . Consistent with the
factors’dominant role in driving aggregate variability, the two series track each other closely
over the full sample period. It immediately follows that, in order to build a di¤usion index
that re‡ects aggregate manufacturing output growth, a practical step involves focusing on
particular sectors whose output variability is largely driven by the common factors.
To help distinguish sectors along this dimension, Figure 4B depicts the distribution of
Rj2 (F ) statistics. The …gure shows that, in fact, common factors typically account for a small
fraction of the variability in sectoral output growth (the mean and median Rj2 (F ) are 0:17
and 0:13 respectively). Simply put, sector-speci…c shocks tend to drive sectoral variability.
16

However, Figure 4B also shows that this is not the case of all sectors. The factor component
explains more than 40 percent of the variations in output growth in approximately 15 sectors,
and Rj2 (F ) is as high as 0:65 in this exercise. It is those sectors, therefore, that are likely to be
most informative to surveys used to construct a di¤usion index of manufacturing production.
Given these …ndings, equation (17) yields estimates of 0:06 for

and 3:04 for .8 In other

words, respondents update their information set every 16 and a half months on average, and
changes in output are reported as “up” or “down” if they exceed 3 percent. Recall that
Figure 2 implied a median standard deviation of 31:7 percent for monthly sectoral output
growth. Therefore, relative to that benchmark, the indi¤erence interval for which respondents report “no change”appears remarkably narrow, approximately one tenth of the median
sectoral standard deviation. In addition, the extent of information stickiness suggested by
this experiment is somewhat longer than that found in previous work, mainly with aggregate in‡ation data. For instance, Carroll (2003) uses the Michigan Survey, a quarterly series
on households’in‡ation expectations, as well as the Survey of Professional Forecasters over
the period 1981

2000, to estimate individuals’degree of information stickiness in forming

in‡ation expectations. He …nds that on average, individuals update their expectations once
a year. Similarly, Mankiw, Reis and Wolfers (2003) use the Livingston Survey and the
Michigan Survey to estimate the rate of information updating that maximizes the correlation between the interquartile range of in‡ation expectations from the survey data with that
predicted by the model in Mankiw and Reis (2002). In this exercise, a vector autoregression
(VAR) is estimated using monthly aggregate U.S. data to generate forecasts of future annual
in‡ation. The authors then …nd that on average, the general public updates their expectations once every 12:5 months. In other work, Mankiw and Reis (2006), as well Mankiw
and Reis (2007), estimate that a rate of information updating that generally ranges from 6
to 16 months helps best match key aspects of business cycle ‡uctuations. Finally, Coibion
and Gorodnichenko (2009) use various macroeconomic survey forecasts to show that forecast
errors are persistent, with a half-life of up to 16 months, and are consistent with predictions
of models with informational rigidities.
8

Since the number of time series observations is …nite in practice, the horizon for k in equation (16)
must be truncated at some value, kmax . In this case, kmax is set to 35 which can be thought of as an upper
bound on information lags. That is, respondents with potentially older information in (13) form expectations
ij
according to the information set de…ned by kmax , Et k ( xij
t ) = Et kmax ( xt ) 8k > kmax . However, note
that when = 0:06, only 10 percent of respondents have information lags that excced 35 months. Thus,
increasing kmax does not materially a¤ect the …ndings, although this can only be checked to a point since
observations are lost as kmax increases. Finally, the number of lags, L, used in equation (11) to model
respondents’ expectations is folded into problem (17). Solving this problem gives that L = 2 helps best
decribe the ISM di¤usion index in the sense of minimizing the overall sum of squares, S.

17

Tables 3 and 4 describe basic properties of the synthetic di¤usion index estimated from
sectoral data. Looking at Table 3, the synthetic index is not quite as volatile as that actually
produced by the Institute for Supply Management. However, the proportions of variance
of the synthetic index explained by business cycles and higher frequencies almost exactly
match those of the ISM di¤usion index. Recall that the monthly sectoral data at the base
of the empirical work re‡ect mainly high frequency, or “noisy,” ‡uctuations (Table 2 and
Figure 3A). Therefore, information stickiness in essence …lters out these ‡uctuations to
produce an index that instead moves mostly with the business cycle. As indicated in Table
4, the autocorrelations of the synthetic di¤usion index at di¤erent lags, (Iet ; Iet k ), closely

match those of the actual index created by the ISM, (It ; It k ). Furthermore, because

some survey respondents rely on expectations of output changes conditional on information
that has not been updated, information stickiness also helps explain why manufacturing
output growth leads the ISM di¤usion index. Thus, Table 4 shows that the cross-correlations
between manufacturing output growth and the synthetic index at di¤erent leads and lags,
( xt ; Iet+k ), are generally quite close to those between manufacturing output growth and
the actual ISM index, ( xt ; It+k ).

Figure 5 summarizes these …ndings graphically. Looking at Figure 5A, the synthetic

di¤usion index moves relatively closely with the actual ISM index apart from two notable
exceptions. First, the synthetic di¤usion index mostly misses the depth of the recessions of
the early 1980s. In contrast, the fall in economic activity associated with these recessions
is re‡ected in a large decline in the ISM index. Second, the economic expansion that followed the 1991 recession is marked by particularly large values of the ISM index by historical
standards, but is more subdued according to the synthetic index. These two key di¤erences
between the synthetic and actual ISM indices explain in large part the lower volatility of the
synthetic di¤usion index. Comparing Figures 3B and 5B, the distributions of the synthetic
and ISM index values are remarkably alike although, as just indicated, the synthetic index
does not quite reproduce extreme values of the actual index at either end of the support.
Finally, note that the shape of the synthetic di¤usion index’s power spectrum in Figure 5C
closely resembles that of the ISM index in Figure 2B. Not surprisingly, therefore, the proportions of variance in the two series that are explained by speci…c frequencies are remarkably
close (as in Table 3).
Di¤usion indices, in practice, do not systematically record or make public individual
survey responses on which they are based. However, as indicated earlier, the proportions
of “optimists” (those reporting expected production increases), and “pessimists,” (those
reporting expected production decreases) in the empirical framework are simply given by
P P1
PM P1
k kj
1
Ut ( ; ) = M 1 M
(1
)
u
(
)
and
D
(
;
)
=
M
)k dkj
t
t
t ( ),
j=1
k=0
j=1
k=0 (1
18

respectively.

Similarly, the proportion of respondents reporting no change is given by
P P1
St ( ; ) = M 1 M
)k skj
t ( ). Figures 6A and 6B show the model-implied
j=1
k=0 (1
behavior of these proportions over past business cycles. Two features are worth highlight-

ing. First, at any given time, most respondents typically report no change. Second, the
proportions of “optimists” and “pessimists” behave di¤erently before and after the Great
Moderation. Thus, prior to 1984, recessions are marked by spikes in the proportion of “pessimists” while expansions are marked by similar spikes in the proportion of “optimists.”
However, after the onset of the Great Moderation, while the recessions of 1991, 2001, as well
as the current recession, are still marked by sharp increases in the fraction of respondents
reporting expected output declines, increases in the proportion of respondents reporting an
expected rise in output is more subdued. From this standpoint, therefore, the Great Moderation period is not only associated with a sharp decline in volatility (Figure 1A) but also an
asymmetry in sectoral output ‡uctuations. A conjecture that would be interesting to explore
is whether this reduction in “optimism”post 1984 may be indirectly to the slow employment
recoveries that followed the 1991 and 2001 recessions, or other notable changes in business
cycles.

6

Deconstructing the ISM Di¤usion Index

Having described the ISM index and its implications for the degree of information stickiness
characterizing survey respondents, this section further deconstructs the index according to
various components of the empirical framework. In particular, it asks four questions related
to the construction of di¤usion indices: i) how does the extent of informational rigidity
among survey respondents a¤ect the behavior of the ISM di¤usion index? ii) how important
is the degree of heterogeneity across sectors in producing a qualitative index that helps track
the business cycle? iii) is it possible to more e¢ ciently construct a di¤usion index by steering
the underlying survey’s e¤orts towards key relevant sectors? iv) Does the Great Moderation
have implications for potential changes in the types of sectors that are most informative
about aggregate manufacturing and the degree of informational rigidity inferred from the
ISM index?

6.1

Fully Informed Survey Respondents

Figure 7 shows how changes in the degree of informational rigidity, , and the indi¤erence
threshold, , a¤ect the behavior of the synthetic di¤usion index relative to that produced by
the ISM. Looking at Figure 7A, assuming that
19

is as estimated in section 5 but that

= 0,

the synthetic di¤usion index becomes considerably more volatile than that estimated in the
previous section. Its standard deviation is now 16:8, more than twice as volatile as that
of the actual ISM. This …nding re‡ects the fact that all changes in output, no matter how
immaterial, are now always reported as “up”or “down.”Moreover, in this case, the synthetic
index with

= 0 is considerably less correlated with manufacturing production growth, with

a correlation of 0:25, compared to the actual correlation of 0:45 which the synthetic index
was able to match in section 5.
More interesting is the e¤ect of relaxing the information stickiness assumption. Figure
7B illustrates the estimated synthetic index that obtains when
respondents are always fully informed,
if

= 1. In that case, equations (13) and (16) become

xjt > , then ujt ( ) = 1; sjt ( ) = djt ( ) = 0
xjt

if
if

is set as in section 5 but all

xjt

<

, then sjt ( ) = 1; ujt ( ) = djt ( ) = 0;

, then

djt (

and
Iet (1; ) = M

1

) = 1;

M
X
j=1

ujt (

)=

sjt (

1
ujt ( ) + sjt ( )
2

(18)

) = 0;

100;

(19)

respectively. When all respondents are fully informed, the empirical framework is one where
answers of “up,” ujt ( ), and “same,” sjt ( ), are independent of information lags, k. In
essence, the synthetic di¤usion index (19) now re‡ects contemporaneous sectoral output
changes up to the truncation rules described by equation (18). One e¤ect of these truncation rules is to transform what would be an overall measure of manufacturing output growth,
P
xjt , into an index bounded between 0 and 100.
M 1 M
j=1

Figure 7B depicts the di¤usion index that obtains under this scenario. Two observations

are worth noting. First, the synthetic di¤usion index is considerably more volatile than that
produced by the ISM. More striking, the time series properties of this synthetic index now
more closely match those of manufacturing output growth instead of the ISM index. The
correlation between the synthetic index and changes in manufacturing production is 0:85
instead of 0:45. Furthermore, as indicated in Table 5, the proportions of variance of Iet (1; )

that are attributable to business cycles (as well as shorter frequency ‡uctuations) are essentially identical to those of manufacturing output growth. Finally, Table 6 shows that the
autocorrelation properties of Iet (1; ) are now much closer to those of manufacturing output

growth than those of the ISM index (as shown in Table 4). In sum, without information
stickiness, movements in the synthetic di¤usion index essentially mimic those of manufactur-

ing output growth despite the truncation rules de…ned by (18). This …nding is reminiscent
of the work in Kashyap and Gourio (2007) who show that it is not necessary to keep track
20

of exact changes in a series, in their case aggregate investment, to capture some of its most
salient features. Given the di¤erences between Figures 1A and 1B, I interpret this …nding as
prima facie evidence that survey respondents do not report current actual changes in output
but rather some notion of changes that incorporates past information.9
Figure 8 illustrates the role of sectoral heterogeneity in the construction of di¤usion
indices. In particular, it asks: is it important for sectors to behave di¤erently in order to
construct meaningful di¤usion indices? Thus, Figure 8A re‡ects a scenario where all sectors
have the same factor loadings, equal to the mean factor loading, and sectoral shocks are shut
P
j
down. In terms of the notation introduced earlier, j = = M 1 M
8j. 10 Therefore,
j=1

expectations of current output changes, Et k ( xij
t ), are no longer sector dependent and the
only source of di¤erences across respondents resides in information lags,
Et k ( xij
t ) =

k

Ft k 8 i; j and k = 1; 2; ::::

(20)

By and large, Figure 8A shows that heterogeneity in information lags alone goes a long way
towards producing a synthetic di¤usion index that is close to the actual ISM index. This
is in spite of what essentially amounts to a representative …rm assumption. In that sense,
informational heterogeneity appears at least as important as heterogeneity in production.
The fraction of the synthetic di¤usion index variance explained by business cycle frequencies
is now somewhat lower than that of the ISM index, 0:45 instead of 0:58, but still considerably
higher than that of manufacturing output growth, 0:23. In addition, the autocorrelation
structure of the synthetic index series shown in Figure 8A resembles more closely that of the
ISM index than that of manufacturing output growth (not shown).
Suppose now that, in addition to …rms behaving identically across sectors, respondents
are always fully apprised of current conditions and always able to report changes as either
“up”or “down.”In this frictionless environment with a representative …rm, typical of many
RBC models for example, we have that either ujt = 1 and djt = 0 8j or vice versa so that, at

any date, everyone simultaneously reports “up” or “down.” Hence, the ISM di¤usion index
can now only take on two values, 100 or

100, and thus becomes degenerate. As shown

in Figure 8B, without heterogeneity of any kind, the standard di¤usion index described in
section 2 ceases to be useful. Given that the nature of production is the same in Figures 8A
and 8B, the contrast between the two …gures only serves to underscore the importance of
heterogeneous information lags across respondents.
9

In addition, to the extent that …rm level output growth is even more idiosyncratic than sectoral output
growth, a di¤usion index that re‡ects real time output changes would be even less useful.
10
Under this assumption, the factor component becomes an exact proxy for aggregate output growth in
PM
manufacturing, Ft = M 1 j=1 xjt .

21

6.2

Choosing Which Sectors to Survey in Creating Di¤usion Indices

Section 5 presented estimates from the factor model such that i) the factor component,
w0 Ft , accounted for most of the variation in manufacturing output growth,

xt , (recall

Figure 4A), and ii) sectors di¤ered in the degree to which they were driven by common
factors rather than idiosyncratic considerations, (recall Figure 5B). These two observations
suggest that information regarding the state of overall manufacturing is likely to be located
in some sectors more than others. In fact, Figure 5B suggests that many sectors in the
data set likely contribute very little information to a di¤usion index meant to track overall
changes in manufacturing in real time. To explore this notion further, it is useful to rank
sectors according to their Rj2 (F ) statistic. Output variations in sectors where Rj2 (F ) is close
to zero are almost entirely driven by idiosyncratic considerations while those with higher
Rj2 (F ) re‡ect in part the e¤ects of common factors. Figure 9 then plots di¤usion indices
constructed as in section 5 (i.e. with

= 0:06 and

= 3:04) but using only the top and

bottom 15 sectors ranked by Rj2 (F ).
Remarkably, Figure 9A shows that surveying only 15 sectors where the common factors
have the greatest role is enough to produce a di¤usion index that is nearly identical to that
constructed using all sectors in section 5. This …nding re‡ects the fact that information
regarding changes in aggregate manufacturing tends to be concentrated in relatively few
sectors.11 Conversely, Figure 9B indicates that a di¤usion index constructed using 15 sectors
where the common factors are least important would have a noticeably more di¢ cult time
tracking expansions and contractions in economic activity. Because the factor component
does not dominate variations in sectoral output in this case, the implied di¤usion index is
relatively uniform and varies little over time. That said, even in this scenario, information
stickiness remains useful in …ltering out high frequency ‡uctuations resulting from idiosyncratic shocks. Therefore, whatever variation is left in the di¤usion index still tends to move
with the business cycle.
Tables 7 and 8 give the 15 sectors with highest and lowest Rj2 (F ) statistics used to construct the synthetic di¤usion indices in Figures 9A and 9B, as well as their share or weight
in overall manufacturing. Interestingly, Table 7 suggests that a fairly large proportion of
the most informative sectors involve metal work in one way or another (e.g. Metal Valves,
Architectural and Structural Metal Products, Fabricated Metals: Forging and Stamping,
Foundries, Metalworking Machinery, Coating and Engraving, etc.). At the opposite ex11

See Foerster, Sarte, and Watson (2008) for alternative calculations that highlight this feature of sectoral
data.

22

treme, Table 8 indicates that many of the least useful sectors in the di¤usion index involve
food-related industries (e.g. Fluid Milk, Co¤ee and Tea, Animal Food, Seafood Product
and Preparation, Wineries and Distilleries, Soft Drinks and Ice, etc.). That said, one should
be cautious in interpreting Figure 9A. While it suggests that using only 15 sectors, chosen
according to their Rj2 (F ) statistic, is enough to replicate the di¤usion index created using
all sectors in section 5, the empirical framework assumes that enough …rms are surveyed in
each sector to recover the entire distribution of information lags across respondents. Given
time and resource constraints in the surveying process, this is potentially far from the case.
Finally, Tables 7 and 8 indicate that sectors that may be most informative in the construction of a di¤usion manufacturing index tend to represent a larger share of manufacturing.
However, this relationship is far from tight so that some of the most informative sectors, such
Metalworking Machinery or Coating, Engraving, and Allied Activities, have small weights
at 0:05 and 0:08, respectively. In fact, virtually all of the least informative sectors in Table
8 have larger weights. This observation points to the pitfall of assuming that sectors that
represent a small share of overall manufacturing must necessarily be uninformative about its
state.

6.3

The ISM Manufacturing Production Di¤usion Index and The
Great Moderation

Of course, the sectoral rankings shown in Tables 7 and 8 are not exact and will change somewhat as the estimation is carried out over di¤erent sample periods. One of the most studied
aspects of Figure 1 is the break in the volatility of aggregate manufacturing output growth
around 1984, and it is natural to ask whether structural changes in U.S. manufacturing over
time have led to changes in the way that information is concentrated across sectors. In fact,
when the factor model (12) is estimated before and after the Great Moderation, in particular
over the periods 1972 1983 and 1984 2009, the sectors that are most and least informative
about aggregate manufacturing tend not to change much. Speci…cally, out of the 30 sectors
with the highest Rj2 (F ) statistics over the full sample period, 22 of those sectors can be found
in the pre Great Moderation period while 23 are found in the post 1984 sample. Similarly,
of the bottom 30 least informative sectors, 18 are found in the pre 1984 period while 25 of
those sectors are found post Great Moderation.
Finally, section 5 pointed out that the rate of information updating estimated in this
paper, around 16 months, is somewhat higher than that estimated in other studies using more
aggregated survey work, for instance around 12 months in Carroll (2003). Because the latter
paper relies on in‡ation and employment expectations measured by the Michigan Survey
23

of Consumers, the sample period in that work re‡ects mostly the post Great Moderation
period, in particular 1981

2000 for in‡ation expectations. Now, observe that the ISM

manufacturing di¤usion index in Figure 1B does not experience the dramatic decline in
volatility that characterizes manufacturing output growth around 1984. It follows that after
that date, all else equal, less information stickiness is needed in order to smooth out high
frequency output ‡uctuations (since those are less pronounced) and match the di¤usion index
in Figure 1B. Consistent with this observation, estimating the empirical model in section 5
over the 1972

1983 period yields

= 0:05 compared to

= 0:076 over the 1984

2009

period. In other words, the rate of information updating averages approximately 20 months
prior to the Great Moderation and falls to around 13 months after 1984. Because the
variability of the ISM index remains approximately unchanged throughout the entire sample,
this …nding follows almost mechanically from having to smooth larger manufacturing output
growth ‡uctuations in the 1970s which are mostly absent starting in the early 1980s (apart
from the most recent recession). Therefore, when estimated over separate subsamples, the
empirical model suggests, somewhat intuitively, that the cost of acquiring information has
fallen over time.

7

Concluding Remarks

This paper has used disaggregated manufacturing data to study survey-based di¤usion indices that aim to capture changes in the business cycle in real time. To keep surveys straightforward, and to limit the burden on respondents, these di¤usion indices are generally constructed from questions that require only one of three qualitative answers to indicate changes
in a variable relative to the previous month. The empirical framework then recognizes that
in answering these survey questions, respondents potentially use infrequently updated information.
The analysis suggests that survey answers underlying the ISM manufacturing production
di¤usion index re‡ect considerable information lags, on the order of 16 months on average.
Furthermore, it underscores that informational rigidities, in essence, lead respondents to
…lter out high frequency output ‡uctuations when answering surveys. The resulting index,
therefore, is better able to isolate variations at business cycle frequencies. In that sense,
informational rigidities provide a foundation for the widespread use of di¤usion indices as a
contemporaneous economic indicators. The analysis further shows that in a world populated
by fully informed identical …rms, as in the standard RBC environment for instance, di¤usion
indices become degenerate.
24

Finally, the empirical work highlights the fact that information regarding changes in
aggregate manufacturing output tends to be concentrated in relatively few sectors. Hence,
contrary to standard practice, it is not necessary for surveys to try to capture a representative
sample of all manufacturing sectors in order to track changes in aggregate activity. The
intuition is straightforward. In some sectors, changes in output re‡ect to a signi…cant extent
factors that drive aggregate changes while, in other sectors, output variations are mostly
explained by idiosyncratic considerations. The analysis then uses factor analytic methods to
provide a ranking of the most and least informative sectors in constructing a di¤usion index
of manufacturing production. In particular, it shows that a useful index may be produced
using as few as 15 sectors instead of all 124 sectors that make up U.S. manufacturing.

25

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26

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1295-1328.
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27

Table A1
Summary Statistics of Sectoral Growth Rates by NAICS Industry
Classi…cation, 124 Sectors
Sector
Animal Food
Grain and Oilseed Milling
Sugar and Confectionery Products
Fruit and Vegetable Preserving and Specialty Foods
Fluid Milk
Creamery Butter
Cheese
Dry, Condensed, and Evaporated Dairy Products
Ice Cream and Frozen Desserts
Animal Slaughtering and Meat Processing Ex Poultry
Poultry Processing
Seafood Product Preparation and Packaging
Bakeries and Tortilla
Coffee and Tea
Other Food Except Coffee and Tea
Soft Drinks and Ice
Breweries
Wineries and Distilleries
Tobacco
Fiber, Yarn, and Thread Mills
Fabric Mills
Textile and Fabric Finishing and Fabric Coating Mills
Textile Furnishings Mills
Other Textile Product Mills
Apparel
Leather and Allied Products
Sawmills and Wood Preservation
Veneer and Plywood
Engineered Wood Member and Truss
Reconstituted Wood Products
Millwork
Wood Containers and Pallets
Manufactured Homes [Mobile Homes]
Prefabricated Wood Building and All Other Miscellaneous Wood Products
Pulp Mills
Paper and Paperboard Mill
Paperboard Containers
Paper Bags and Coated and Treated Paper
Other Converted Paper Products
Printing and Related Support Activities
Petroleum Refineries
Paving, Roofing, and Other Petroleum and Coal Products
Organic Chemicals
Industrial Gas
Synthetic Dyes and Pigments
Other Basic Inorganic Chemicals

28

Weight
0.42
0.77
0.55
1.03
0.38
0.01
0.17
0.16
0.11
0.88
0.45
0.14
1.23
0.18
0.98
0.59
0.45
0.27
1.07
0.22
0.67
0.30
0.35
0.20
1.76
0.33
0.43
0.16
0.07
0.09
0.34
0.09
0.13
0.15
0.08
1.58
0.71
0.38
0.37
2.28
1.79
0.34
1.43
0.21
0.15
0.57

St. Dev.
20.34
24.63
42.61
30.45
7.08
59.67
19.99
52.57
36.50
24.45
24.69
64.90
10.99
67.55
18.70
23.06
50.06
85.54
56.86
47.96
19.04
25.15
43.20
21.38
16.98
23.46
59.18
61.58
42.19
47.19
24.25
21.81
57.06
26.65
29.73
25.73
22.66
35.37
25.59
13.66
26.00
27.19
37.32
31.99
77.57
54.49

Min
‐77.95
‐102.10
‐164.10
‐105.55
‐26.48
‐267.00
‐82.90
‐231.36
‐138.26
‐102.78
‐89.13
‐183.23
‐46.35
‐482.59
‐70.06
‐84.53
‐263.55
‐341.73
‐193.63
‐243.22
‐78.45
‐113.25
‐186.23
‐92.27
‐80.86
‐147.29
‐360.33
‐439.26
‐216.46
‐207.97
‐119.46
‐76.67
‐217.45
‐117.69
‐198.33
‐93.49
‐124.69
‐156.42
‐104.31
‐42.62
‐144.77
‐158.31
‐396.50
‐187.49
‐297.87
‐448.42

Max
73.41
97.04
218.06
126.93
21.94
214.20
97.03
193.13
160.08
157.19
109.23
194.39
46.64
256.91
79.24
147.10
161.54
487.06
240.72
173.63
83.48
75.18
126.54
122.51
60.69
72.74
244.06
292.12
140.13
144.84
72.95
105.69
392.50
68.15
126.75
98.47
119.40
141.08
113.58
50.30
177.58
89.93
243.72
151.15
295.62
337.87

Sector
Plastics Materials and Resins
Synthetic Rubber
Artificial and Synthetic Fibers and Filaments
Pesticides, Fertilizers, and Other Agricultural Chemicals
Pharmaceuticals and Medicines
Paints and Coatings
Adhesives
Soap, Cleaning Compounds, and Toilet Preparation
Other Chemical Product and Preparation
Plastics Products
Tires
Rubber Products Ex Tires
Pottery, Ceramics, and Plumbing Fixtures
Clay Building Materials and Refractories
Flat and Brown Glass and Other Glass Manufacturing
Glass Container
Cement
Concrete and Products
Lime and Gypsum Products
Other Nonmetallic Mineral Products
Iron and Steel Products
Alumina Refining
Primary Aluminum Production
Secondary Smelting and Alloying of Aluminum
Miscellaneous Aluminum Materials
Aluminum Extruded Products
Primary Smelting and Refining of Copper
Primary Smelting/Refining of Nonferrous Metal [Ex Cu and Al]
Copper and Nonferrous Metal Rolling, Drawing, Extruding, and Alloying
Foundries
Fabricated Metals: Forging and Stamping
Fabricated Metals: Cutlery and Handtools
Architectural and Structural Metal Products
Boiler, Tank, and Shipping Containers
Fabricated Metals: Hardware
Fabricated Metals: Spring and Wire Products
Machine Shops; Turned Products; and Screws, Nuts, and Bolts
Coating, Engraving, Heat Treating, and Allied Activities
Metal Valves Except Ball and Roller Bearings
Ball and Roller Bearings
Farm Machinery and Equipment
Lawn and Garden Tractor and Home Lawn and Garden Equipment
Construction Machinery
Mining and Oil and Gas Field Machinery
Industrial Machinery
Commercial and Service Industry Mach/Other Gen Purpose Mach

29

Weight
0.70
0.10
0.33
0.50
2.63
0.40
0.13
1.41
0.93
2.29
0.43
0.40
0.11
0.15
0.44
0.18
0.19
0.68
0.12
0.37
1.67
0.05
0.14
0.04
0.19
0.09
0.06
0.07
0.35
0.77
0.50
0.34
1.16
0.58
0.29
0.20
1.05
0.41
1.15
0.17
0.39
0.10
0.44
0.29
0.73
2.17

St. Dev.
Min
48.01 ‐405.72
65.28 ‐243.86
55.83 ‐326.64
28.60 ‐121.31
14.88
‐64.87
40.25 ‐217.57
31.46 ‐113.83
25.74
‐72.81
25.69
‐99.87
16.00 ‐102.16
72.31 ‐458.82
26.67 ‐177.39
26.62 ‐178.58
40.23 ‐238.86
23.55
‐92.92
48.81 ‐226.22
53.02 ‐292.85
28.01 ‐103.06
71.19 ‐448.70
31.89 ‐111.52
63.15 ‐311.12
34.00 ‐234.00
24.54 ‐192.40
71.18 ‐217.41
93.97 ‐699.29
95.80 ‐715.36
135.37 ‐1285.13
84.11 ‐405.04
71.67 ‐327.73
24.05 ‐122.17
19.59
‐89.44
19.44
‐83.68
13.70
‐54.41
24.56
‐79.38
26.47
‐89.19
20.49
‐95.10
22.07
‐79.57
17.86 ‐138.55
13.18
‐57.14
32.17 ‐190.44
100.40 ‐808.88
70.30 ‐281.26
112.71 ‐696.01
35.46 ‐137.09
26.89 ‐147.88
13.04
‐55.75

Max
367.90
287.58
215.32
171.54
48.83
147.49
167.52
98.71
88.83
68.43
730.97
132.57
76.15
173.10
94.66
236.17
236.65
84.81
247.56
125.19
232.73
216.92
68.39
566.08
517.89
528.85
743.14
394.53
269.51
72.36
62.80
103.95
43.04
111.19
91.05
57.73
77.58
48.19
38.84
147.70
543.35
249.34
704.18
133.41
73.05
42.24

Sector
Ventilation, Heating, Air‐cond & Commercial Refrigeration eq
Metalworking Machinery
Engine, Turbine, and Power Transmission Equipment
Computer and Peripheral Equipment
Communications Equipment
Audio and Video Equipment
Semiconductors and Other Electronic Components
Navigational/Measuring/Electromedical/Control Instruments
Magnetic and Optical Medi
Electric Lighting Equipment
Small Electrical Household Appliances
Major Electrical Household Appliances
Electrical Equipment
Batteries
Communication and Energy Wires and Cables
Other Electrical Equipment
Automobiles and Light Duty Motor Vehicles
Heavy Duty Trucks
Motor Vehicle Bodies
Truck Trailers
Motor Homes
Travel Trailers and Campers
Motor Vehicle Parts
Aircraft and Parts
Guided Missile and Space Vehicles and Propulsion
Railroad Rolling Stock
Ship and Boat Building
Other Transportation Equipment
Household and Institutional Furniture and Kitchen Cabinets
Office and Other Furniture
Medical Equipment and Supplies
Other Miscellaneous Manufacturing

30

Weight
0.71
0.84
0.78
1.50
1.54
0.18
2.32
2.34
0.19
0.33
0.15
0.36
0.88
0.16
0.21
0.47
2.28
0.15
0.21
0.08
0.05
0.08
3.04
2.40
0.76
0.23
0.51
0.16
0.86
0.62
1.22
1.36

St. Dev.
Min
58.57 ‐161.66
18.21
‐97.69
36.79 ‐164.35
23.36
‐51.56
26.44 ‐208.02
143.23 ‐538.96
27.57 ‐159.64
12.95
‐37.83
41.36 ‐133.44
28.23 ‐157.19
42.18 ‐194.91
70.30 ‐500.84
21.65
‐62.60
59.40 ‐213.32
27.62 ‐107.21
21.28
‐82.05
96.68 ‐667.76
187.80 ‐1736.24
64.98 ‐417.67
98.98 ‐627.44
133.18 ‐857.31
96.89 ‐687.25
36.06 ‐196.79
36.34 ‐306.70
36.14 ‐187.51
42.62 ‐161.57
31.09 ‐151.82
50.94 ‐309.80
19.70
‐81.92
21.73
‐67.72
11.99
‐39.71
13.66
‐54.00

Max
251.32
38.33
153.17
76.46
205.26
782.25
83.97
56.63
161.54
115.86
218.19
428.10
58.28
268.63
99.73
79.85
628.14
1509.01
212.83
550.81
650.42
374.34
191.45
241.50
229.34
151.64
127.32
248.16
65.33
77.00
59.57
49.97

Figure 1. Aggregate Variations in Manufacturing

31

Figure 2. Frequency Decomposition of Manufacturing Variations

32

Figuer 3. Individual Sector Variations and the Distribution of ISM indices

33

Figure 4. Accounting for Manufacturing Variations Using Common Factors

34

Figure 5. Properties of the Synthetic Di¤usion Index

35

Figure 6. Historical Behvavior of the Proportions of “Optimists”and “Pessimists”

36

Figure 7. Removing Informational Rigidities with Heterogenous Sectors

37

Figure 8. Removing Informational Rigidities with Homogenous Sectors

38

Figure 9. Information Concentration and the Construction of Di¤usion Indices

39

Table 1
Volatility of Output Growth and the ISM Di¤usion Index in Manufacturing
1972-2009
Fraction of Variance at
Standard Deviation Business Cycle Frequencies
2 years

p

Fraction of Variance
at High Frequencies

8 years

p < 2 years

Output Growth

8.48

23.39

69.37

Di¤usion Index

6.91

57.91

19.27

Table 2
Autocorrelation and Cross-correlation Structure of
Output Growth and the ISM index
Autocorrelations (1972-2009)
0

k

1

( xt ; xt k ) 1.00 0.35
(It ; It k )

2
032

3

4

5

6

0.27 0.15 0.10 0.10

1.00 0.92 0.85 0.77 0.68 0.60 0.51
Cross-Correlations (1972-2009)
-3

k
( xt ; It+k )

-2

-1

0

1

2

3

0.15 0.22 0.31 0.45 0.51 0.50 0.48

Table 3
Volatility of the Manufacturing ISM Di¤usion and Synthetic Di¤usion Indices
1972-2009
Fraction of Variance at
Standard Deviation Business Cycle Frequencies
2 years

p

8 years

Fraction of Variance
at High Frequencies
p < 2 years

Di¤usion Index

6.91

57.91

19.27

Pseudo Di¤usion Index

4.79

54.10

21.66

40

Table 4
Autocorrelation and Cross-correlation Structure of
the ISM Di¤usion and Synthetic Di¤usion indices
Autocorrelations (1972-2009)
0

k
(It ; It k )
(Iet ; Iet k )

k

1

2

3

4

5

6

1.00 0.92 0.85 0.77 0.68 0.60 0.51
1.00 0.95 0.88 0.78 0.67 0.56 0.47
Cross-Correlations (1972-2009)
-3

-2

-1

0

1

2

3

( xt ; It+k ) 0.15 0.22 0.31 0.45 0.51 0.50 0.48
( xt ; Iet+k ) 0.24 0.25 0.30 0.45 0.52 0.64 0.64

Table 5
Volatility of Manufacturing Output Growth and the Synthetic
=1

Di¤usion Index with Fully Informed Respondents,
1972-2009
Fraction of Variance at

Standard Deviation Business Cycle Frequencies
2 years

p

8 years

Fraction of Variance
at High Frequencies
p < 2 years

Output Growth

8.48

23.39

69.37

Pseudo Di¤usion Index

11.60

25.74

63.88

Table 6
Autocorrelations of Manufacturing Output
Growth and the Synthetic Di¤usion Index with Fully
Informed Respondents,

=1

Autocorrelations (1972-2009)
k

0

1

2

3

4

5

6

( xt ; xt k ) 1.00 0.35 032 0.27 0.15 0.10 0.10
(Iet ; Iet k )
1.00 0.39 0.38 0.41 0.21 0.17 0.21
41

Table 7
Most Informative Sectors Ranked According to Rj2 (F )
Rj2 (F ) Weight

Sector
1. Plastic Products

0.65

1.36

2. Household and Institutional Furniture

0.52

1.22

3. Metal Vales Except Balls and Roller Bearings

0.49

0.62

4. Architectural and Structural Metal Products

0.47

0.86

5. Commercial and Service Industry Machinery

0.45

0.17

6. Other Miscellaneous Manufacturing

0.45

0.51

7. Reconstituted Wood Products

0.45

0.23

8. Fabricated Metals: Forging and Stamping

0.45

0.76

9. Foundries

0.43

2.40

10. Fabricated Metals: Spring and Wire

0.43

3.04

11. Sawmills and Wood Preservation

0.42

0.08

12. Metalworking Machinery

0.41

0.05

13. Coating, Engraving, and Allied Activities

0.39

0.08

14. Textile Furnishings Mills

0.37

0.21

15. Other Electrical Equipment

0.37

0.15

42

Table 8
Least Informative Sectors Ranked According to Rj2 (F )
Rj2 (F ) Weight

Sector
1. Aircraft and Parts

0.00

0.42

2. Guided Missile and Space Vehicles

0.00

0.77

3. Fluid Milk

0.00

0.55

4. Co¤ee and Tea

0.01

1.03

5. Dry, Condensed, and Evaporated Dairy Products

0.01

0.38

6. Primary Smelting/Re…ning of Nonferrous Metals

0.01

0.01

7. Farm Machinery and Equipment

0.01

0.17

8. Animal Food

0.01

0.16

9. Seafood Product Preparation and Packaging

0.01

0.11

10. Heavy Duty Trucks

0.01

0.88

11. Wineries and Distilleries

0.01

0.45

12. Soft Drinks and Ice

0.02

0.14

13. Copper and Nonferrous Metal Rolling

0.02

1.23

14. Grain and Oilseed Milling

0.02

0.18

15. Mining and Oil and Gas Field Machinery

0.02

0.98

43