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Home / Publications / Research / Economic Brief / 2025
Understanding Di usion Indexes: Insights and
Applications
By Santiago Pinto
Economic Brief
February 2025, No. 25-05
Key T akeaways
Di usion indexes (DIs) are commonly used to analyze economic trends. T hey o er
timely insights into economic activity and are valuable for assessing employment
trends, consumer sentiment and sectoral shifts.
While DIs capture the prevalence of change ("how many"), they do not necessarily
account for the intensity ("how much"). Misinterpreting their values can lead to
inaccurate conclusions. Adding con dence intervals and polarization indicators
improves their reliability.
T he relevance of DIs shifts in di erent economic contexts. For instance, during the
pandemic-induced recession, the intensity of change outweighed the breadth,
emphasizing the need to consider both "how many" and "how much" dynamics for
a better understanding of economic shifts.
Di usion indexes (DIs) are statistics that o er timely glimpses into the state of the
economy.1 Frequently constructed from responses to qualitative surveys, these indexes
provide a snapshot of the direction and breadth of change in key economic variables.
T ypically, these surveys ask participants to report whether a speci c variable — such as
employment or business conditions — improved, declined or remained unchanged
compared to a previous period. T he responses are then aggregated to calculate a DI, often
expressed as a percentage. A DI above a certain threshold — which varies depending on
the weighting method — typically signi es an expansionary scenario, while a DI below the
threshold indicates a contractionary one.
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T he appeal of DIs generally lies in their timeliness, simplicity and relatively low cost of
participation. T hey o er insights into economic conditions more rapidly than traditional
economic data releases, making them valuable tools for policymakers, analysts and market
participants.
T his article explores various uses and interpretations of DIs using data from three
sources:2
Sectoral employment growth from the Bureau of Labor Statistics (BLS)
T he Federal Reserve Bank of Richmond's manufacturing survey
Consumer sentiment from the University of Michigan's Surveys of Consumers
Measuring the Breadth of Change
T he actual change of an aggregate economic series can be broken down into "how much,"
or the intensity of the change, and "how many," or the breadth of the change. One of the
strengths of DIs is their ability to measure the "how many" aspect of economic activity. A DI
shows how many entities within a particular sector or economy are experiencing a change
in a speci c variable.
For instance, a DI for employment can reveal how many rms are increasing hiring, while a
DI for consumer sentiment can indicate how many consumers are optimistic about the
economy's future. T his information is valuable for gauging the overall direction of
economic activity, as it highlights the prevalence of speci c trends across a wide range of
participants and sectors.
Decomposing Employment Growth
T he BLS publishes an employment DI, monitoring changes across roughly 260 sectors.
T hese indexes help determine if employment shifts are widespread or concentrated in
speci c industries. T o evaluate the "how much" and "how many" aspects, we decompose
BLS employment growth and analyze the evolution of these components over time.
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T his analysis suggests that DIs could be reliable indicators of economic activity, especially
when analyzing employment trends — in other words, changes in "how many" explain an
important part of changes in aggregate employment growth — but there are some
important caveats.
Prepandemic Trends
Until 2020, changes in the breadth of employment growth ("how many") as measured by
DIs accounted for a substantial portion of the uctuations in aggregate employment
growth. T his implies that, during periods of relative economic stability, employment
growth is often driven more by the number of rms adding or losing jobs than by extreme
changes in employment levels within individual sectors.
Recessions
During recessions, a distinct pattern emerges. T he intensity of change ("how much")
becomes more in uential in shaping employment trends. In these downturns, both the
"how much" and "how many" components (along with their interaction) play signi cant
roles in driving the decline in employment. T his suggests a potential asymmetry in how
employment dynamics unfold during expansions and contractions.
Pandemic E ects
T he pandemic further highlighted the importance of the intensity of change ("how much").
During the pandemic-induced recession, the "how many" margin (typically captured by DIs)
played a relatively smaller role, while the "how much" margin became dominant, both
during the steep decline and the subsequent recovery. T his unusual pattern re ects the
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unique nature of the pandemic shock, which led to widespread and simultaneous job losses
across numerous sectors and emphasized the intensity of the change rather than the
breadth.
Usefulness and Limitations of DIs
T hese ndings underscore the value of DIs in understanding employment dynamics. By
providing insights into the "how many" component, DIs help to disentangle the underlying
forces driving employment trends and reveal important asymmetries in how employment
responds to di erent economic conditions.
Other applications of DIs indicate that they can serve as reliable indicators of economic
activity in various settings. One example comes from my 2017 article "Using the Richmond
Fed Manufacturing Survey to Gauge National and Regional Economic Conditions," coauthored with Nika Lazaryan. In that article, we evaluate the Richmond Fed's
manufacturing survey of business conditions and assess the survey's ability to explain
national and regional economic conditions. We nd that the DIs reported by the survey
perform reasonably well in explaining both national and regional economies. T he analysis
also suggests that the predictive power of these indexes can be improved by considering
models with richer dynamic structures and by adjusting the weights used in the calculation
of the composite DI.
Despite their usefulness, DIs come with limitations that need to be carefully considered.
DIs are most e ective when analyzing variables where the breadth of change ("how many")
is the primary driver of aggregate changes. However, they might not be as informative
when dealing with variables heavily in uenced by the intensity of change ("how much").
A prime example is average wages. Wage movements often re ect the magnitude of wage
adjustments within rms or sectors rather than the number of rms increasing or
decreasing wages. A company might implement substantial pay raises for its entire
workforce, leading to a signi cant shift in average wages even if the proportion of rms
raising wages remains relatively stable. In such cases, a DI based on the number of rms
adjusting wages would not accurately capture the true dynamics of wage changes.
Another crucial limitation is that DIs cannot be directly interpreted as measures of
disagreement. A DI value of zero can arise from two very distinct scenarios, both leading to
the same numerical outcome but re ecting di erent underlying economic realities.
Scenario 1 (high polarization): Half of the survey respondents report an increase, and
the other half report a decrease. T his situation suggests a high degree of polarization
or disagreement within the economy, as rms or sectors hold opposing views on the
direction of change.
Scenario 2 (uniform stagnation): All respondents report no change. T his scenario
implies greater consensus and stability, with rms or sectors experiencing similar
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conditions.
Misinterpreting a DI of zero as simply indicating no change without considering the
underlying distribution of responses can lead to awed conclusions about the state of the
economy. While a DI might suggest stability at the aggregate level, a high degree of
polarization beneath the surface could signal potential volatility or uncertainty.
Recognizing this distinction is key for policymakers, analysts and anyone else using DIs to
gauge economic conditions.
Enhancing DI Interpretation: Con dence Intervals and
the Disagreement Indicator
T he interpretation of DIs can be improved by reporting — along with the DI itself — the
indexes' con dence intervals and an indicator of polarization or disagreement (PI), which is
based on the variance of the DI.
Con dence Intervals
Con dence intervals can be constructed to address the inherent uncertainty associated
with DIs as estimates. T hese intervals provide a range within which the true value of the
underlying economic variable is likely to fall, given the DI's statistical properties. For
example, consider the Richmond Fed's manufacturing employment DI, which tracks
employment trends in the Fifth Federal Reserve District.
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Historical data indicate that the DI is not statistically di erent from zero when its value lies
between -4 and 4. T his means that when the DI falls within this range, it is statistically
indistinguishable from zero, making it di cult to draw rm conclusions about whether
employment is expanding or contracting based solely on the DI. Using con dence intervals
helps to contextualize the DI and to prevent overinterpretation of small uctuations that
might not be statistically signi cant.
Capturing Polarization: Leveraging the Variance of DIs
Instead of relying on the DI itself as a measure of disagreement, my 2020 paper "T he
Information Content and Statistical Properties of Di usion Indexes" — co-authored with
Pierre-Daniel Sarte and Robert Sharp — proposed a more nuanced approach: using the
variance of the DI as an indicator of polarization or disagreement. T his method
acknowledges that a DI of zero can mask varying levels of disagreement among
respondents. For example:
A high variance around a DI of zero suggests greater polarization and diverse views
on the direction of economic change. T his might indicate uncertainty about the future
path of the economy, as di erent rms or sectors experience varying conditions.
A low variance around a DI of zero implies more agreement among respondents,
which suggests a greater degree of consensus and a potentially more stable economic
outlook.
Once again, consider the Richmond Fed's employment DI and the index's PI. T he gure
below compares the trends of the two indicators.
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T he graph shows that DI and PI uctuated in opposite directions until 2010. However, they
experienced a period of concurrent increase from 2010 to 2018, and they have both been
declining since 2020. T herefore, incorporating DI variance into the analysis provides a
more comprehensive understanding of the underlying dynamics driving the DI and avoids
misinterpreting a seemingly stable DI that conceals a high degree of polarization.
Composite Di usion Indexes
Many DIs are composite DIs, in the sense that they are weighted sums of individual DIs.
Widely recognized examples of composite DIs include the University of Michigan's Survey
of Consumers, the ISM Manufacturing Index and the Richmond Fed's Manufacturing
Composite DI.
When working with composite DIs, the interpretation of polarization becomes more
intricate, since it aggregates information contained in individual DIs that may uctuate in
di erent (and possibly con icting) ways. T herefore, the overall level of disagreement
re ected in a composite DI is in uenced by not only the variance of each individual DI but
also the covariance between them. T his means that the extent to which disagreement
across di erent individual DIs coincides plays a role in shaping the polarization of the
composite DI.
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Consider the case of a composite DI that combines three individual DIs and two possible
situations.
High Polarization, Coincident Disagreement
If all three individual DIs exhibit high polarization, and the polarization tends to move in
the same direction (high positive covariance), the composite DI will re ect a heightened
level of overall polarization. T his scenario suggests a widespread lack of consensus across
di erent aspects of the economy, potentially signaling economic uncertainty.
High Polarization, O set Disagreement
Conversely, if the individual DIs show high polarization but tend to o set each other (low
or negative covariance), the composite DI might exhibit a lower level of overall polarization.
T his situation implies that while there might be disagreement within speci c areas of the
economy, these disagreements balance each other out at the aggregate level, potentially
leading to a more stable overall outlook.
T herefore, analyzing the covariance between individual DIs is crucial for understanding
how polarization manifests in composite DIs and for drawing accurate conclusions about
the level of agreement or disagreement within the economy.
Di usion Indexes and Consumer Sentiment
T he Survey Research Center at the University of Michigan publishes three composite DIs:
T he Index of Current Economic Conditions (ICC)
T he Index of Consumer Expectations (ICE)
T he Index of Consumer Sentiment (ICS)
T hese indexes are key indicators of consumer behavior, which drives a signi cant portion
of economic activity. Each monthly survey contains several core questions that track
di erent aspects of consumer attitudes and expectations. Each month, a minimum of 500
interviews are conducted by telephone, with data available since 1978. T he samples for the
Surveys of Consumers are statistically designed to represent all American households.
T he indexes emphasize distinct aspects of how consumers perceive economic conditions.
T he ICC emphasizes current household nancial conditions and views on purchasing
conditions for durable goods and other big-ticket items. T he ICE examines how households
perceive their nancial prospects, the general economy over the short term and the
general economy over the long term. T he ICS aggregates information from both indexes
and serves as an overall measure of consumer con dence.3
Figure 4 shows several readings based on the ICC: We construct con dence intervals for
each individual DI and develop an index of polarization for each DI. We also construct
con dence intervals and a PI for the composite ICC.
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Enlarge
Notably, the individual DIs evolve similarly over time, while PIs behaved di erently during
the period 2003-2014. Since 2022, all of the DIs and PIs based on the Survey of Consumers
have been increasing. T he main driver of polarization in the ICC is the variance of the
survey question that tracks consumer attitudes towards buying durable goods and bigticket items. Recently, polarization has been at its highest levels, characterized by the high
variance of the DI associated with that question (which is typical after recessions) and a
higher covariance between the DI that tracks changes in consumers' current nancial
conditions and the DI that tracks consumer attitudes toward buying durable goods and
big-ticket items.
We also construct con dence intervals and PIs for the ICE and ICS, and we examine their
respective trajectories, as seen in Figure 5.
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Enlarge
Focusing on the recent period, we can discern several key insights from these graphs.
Before the pandemic, both ICE and ICS were on the rise, while the PI remained steady. ICE
and ICS initially declined during the pandemic, but they have been rising since 2022, this
time accompanied by an increase in the PI.
T he table below compares the con dence intervals for ICC, ICE and ICS across di erent
periods to analyze changes in their variability or uncertainty.
Table 1: ICC, ICE and ICS 95% Con dence Intervals
Series
January 1978-February 2020
March 2020-March 2024
January 1978-March 2024
ICC
±4.29
±4.41$
±4.30$
ICE
±4.22$
±4.08$
±4.21$
ICS
±3.47$
±3.47$
±3.47$
Source: The University of Michigan's Survey of Consumers and author's calculations.
T he table shows that the con dence intervals for ICC and ICE experienced some variation
between the two periods. T he con dence interval for the ICC increases slightly in the most
recent period, indicating potentially greater variability or uncertainty during this time. T he
ICE con dence interval decreases slightly during the most recent period, suggesting a
minor reduction in variability or uncertainty. T he ICS con dence interval remains constant
across all periods, indicating stable levels of consumer sentiment. T his suggests that while
some indexes have experienced changes in uncertainty, overall consumer sentiment (ICS)
has remained steady.
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Finally, we compare our PI to existing measures of uncertainty, nancial volatility and
political polarization:
Economic policy uncertainty — measured by the Economic Policy Uncertainty Index —
experienced a similar evolution to that of ICC, with di erent behavior since 2020.
Macroeconomic uncertainty — represented by the JLN uncertainty measurement —
and ICC polarization behave similarly.4
Movement in the Partisan Con ict Index is closely related to movements in ICE and ICS
polarization: Indicators increased between 2008 and 2014, moved in opposite
directions between 2014 and 2020 and have shown an increasing trend since 2020.
Our polarization indicators and the Chicago Board Options Exchange Market Volatility
Index (commonly referred to as VIX) do not seem to move closely together.
Conclusion: DIs as Powerful Tools With Essential Caveats
DIs are widely used as tools for analyzing economic trends and understanding the breadth
of change across various economic variables. T heir ability to measure the "how many"
aspect of economic activity o ers valuable insights into the direction and prevalence of
speci c trends. However, DIs alone can present an incomplete and potentially misleading
picture, particularly when analyzing variables primarily driven by the "how much" margin or
when interpreting the information content of a given value of the DI.
By incorporating con dence intervals and PIs into DI analysis, we can address these
limitations and gain a more comprehensive understanding of economic trends and the
uncertainty surrounding them. Con dence intervals provide a measure of statistical
signi cance, helping to avoid misinterpretations of small uctuations in the DI. PIs, in turn,
reveal the level of disagreement or polarization among survey respondents, o ering
crucial insights into potential vulnerabilities or divergent trends even when the DI
suggests stability.
T his enhanced approach to DI analysis has signi cant implications for policymakers,
analysts and market participants. By considering the statistical properties of DIs and the
potential for variability, we can make more informed decisions based on a more accurate
assessment of the data. As we navigate an increasingly complex and uncertain economic
landscape, the ability to understand and interpret DIs e ectively will be crucial for making
sound judgments and promoting sustainable economic growth.
Santiago Pinto is a senior economist and policy advisor in the Research Department at the
Federal Reserve Bank of Richmond.
To cite this Economic Brief, please use the following format: Pinto, Santiago. (February 2025)
"Understanding Di usion Indexes: Insights and Applications." Federal Reserve Bank of
Richmond Economic Brief, No. 25-05.
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1 They are used by organizations around the world, including many central banks (such as the
Federal Reserve), government agencies (such as the Bureau of Labor Statistics and Census
Bureau) and trade groups (such as the National Association of Home Builders and the Institute
for Supply Management).
2 DIs are also used to track changes in business conditions. The ISM Manufacturing Index, for
instance, is one of the most closely watched indicators of manufacturing activity and is often
used as a leading indicator of overall economic performance.
3 The core questions contained in the survey cover household nancial conditions (changes from
the previous year and expected change a year from now), current state of the economy
(business conditions better or worse than a year ago), expected state of the economy (business
conditions for next ve years) and household's perceptions of buying conditions for durable
goods and other big items. The answers are aggregated into ve individual DIs: D1 (household
nancial conditions change from previous year), D2 (household nancial conditions expected
change in one year), D3 (current state of the economy), D4 (expected state of the economy)
and D5 (household perceptions of buying conditions). The composite indexes are constructed
based on these individual DIs as follows: ICC = (D1 + D5)/2.6424 + 2, ICC = (D2 + D3 +
D4)/4.1134 + 2, and ICC = (D1 + D2)/6.7558 + 2.
4 The construction of the JLN uncertainty measurement is discussed in the 2015 paper
"Measuring Uncertainty" by Kyle Jurado, Sydney Ludvigson and Serena Ng.
T his article may be photocopied or reprinted in its entirety. Please credit the author,
source, and the Federal Reserve Bank of Richmond and include the italicized statement
below.
Views expressed in this article are those of the author and not necessarily those of the Federal
Reserve Bank of Richmond or the Federal Reserve System.
Topics
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