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SEPTEMBER/OCTOBER 1992

ECONOMIC PERSPECTIVES
A review from the
Federal Reserve Bank
of Chicago

Making sense of economic indicators:
a consumer's guide to indicators
of real economic activity
Conference announcement:
Shaping the Great Lakes Economy

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Contents
Making sense of economic indicators:
a consumer's guide to indicators
of real economic activity..........................................................................2
Francesca Eugeni, Charles Evans,
and Steven Strongin

Policymakers and business analysts face a
daunting array of economic indicators; which
indicators are useful in a given situation depends
on the question and the time frame. The authors
evaluate a number of different indicators and
discuss their use in a variety of contexts.

Conference announcement:
Shaping the Great Lakes Economy....................................................... 32

ECONOMIC PERSPEC I IVES
Karl A. Scheld, S e n io r V ic e P r e s id e n t a n d
D ir e c to r o f R e s e a rc h
Editorial direction

Carolyn McMullen, e d ito r , David R. Allardice, r e g io n a l
Herbert Baer, f in a n c ia l s tr u c tu r e a n d re g u la tio n ,
Steven Strongin, m o n e ta r y p o lic y ,
Anne Weaver, a d m in is tr a tio n

s tu d ie s,

Production

Nancy Ahlstrom, ty p e s e ttin g c o o r d in a to r ,
Rita Molloy, Yvonne Peeples, ty p e s e tte r s ,
Kathleen Solotroff, g r a p h ic s c o o r d in a to r
Roger Thryselius, Thomas O’Connell,
Lynn Busby-Ward, John Dixon, g r a p h ic s
Kathryn Moran, a s s is ta n t e d ito r

Septem ber/O ctober 1992 V olum e XVI, Issue 5

ECONOMIC PERSPECTIVES is published by
the Research Department of the Federal Reserve
Bank of Chicago. The views expressed are the
authors’ and do not necessarily reflect the views
of the management of the Federal Reserve Bank.
Single-copy subscriptions are available free of
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Articles may be reprinted provided source is
credited and The Public Information Center is
provided with a copy of the published material.
ISSN 0164-0682

M aking sense of econom ic indicators:
a consum er's guide to indicators
of real econom ic activity

Francesca Eugeni, Charles Evans,
and Steven Strongin

Economic data arc used prima
rily in two ways. Academic
| economists typically use data to
build models of the economy in
I order to understand how the
economy works. Business analysts, on the other
hand, use economic data to forecast future eco
nomic activity. These two activities and groups
of people are not truly distinct groups, neverthe
less the two activities do involve some substan
tive differences. The problem facing the busi
ness analyst, and to a large extent the policy
maker or businessman who has to make deci
sions based on the economic outlook, is how
each piece of new information should be as
sessed. Does it portend higher growth or lower,
a recession or a boom, slow growth or stasis?
Such assessments are crucial to running a suc
cessful business and to the proper ongoing evalu
ation of economic policy. Yet economic analy
sis rarely focuses on precisely these questions.
In the current article, we develop an organized
structure for evaluating economic indicators
and apply that structure to a wide variety of
financial indicators and a selected group of real
indicators as well.
This process is fundamentally more eclectic
than the usual econometric analysis which looks
for or constructs a “best” indicator, where “best”
typically refers to winning some narrowly de
fined contest of general purpose forecasting
ability measured over some preselected time
span.1 Unfortunately, experience tells us that
such a search is likely to end in failure. Eco
nomic history is full of examples of indicators,
such as stock prices and various monetary aggre

gates, which work for a short period of time
after their discovery and then fail dramatically
just as they become widely used. There are
many reasons for this, but one stands out. As
the following analysis will show, indicators do
well at different things and at different times.
Without an understanding of the limitations this
implies, these “best” indicators are often
stretched well beyond their capabilities. What
the business analyst really needs to know is the
type of information that an indicator possesses
and the types of purposes to which it can rea
sonably be put.
Indicators, like people, perform better or
worse depending on the context in which they
operate. Efficient usage requires matching
indicators both with appropriate questions and
with other complementary indicators. For
instance, some indicators, such as the Purchas
ing Managers’ Index of the National Associa
tion of Purchasing Management (NAPM), do
well at predicting short run changes in activity,
but do not do very well at pinning down the
level of activity over longer time spans. Other
indicators, such as the growth in real M2, fore
cast short run phenomena poorly, but do better
at predicting average activity over a longer time
Francesca Eugeni is an associate economist,
Charles Evans is a senior economist, and Steven
Strongin is vice president and econom ic advisor at
the Federal Reserve Bank of Chicago.
The authors w ould like to thank the participants of
the Special Meeting on Operating Procedures held
at the Federal Reserve Bank of St. Louis, June 18
and 19, 1992, and the participants of the Federal
Reserve Bank of Chicago's Macro W orkshop held
June 9, 1992, fo r their comments.

ECONOMIC PERSPECTIVES

span such as a year. Also, while some indicators
are very close substitutes, such as the twenty or
so interest rates sometimes used in econometric
studies, each providing little additional informa
tion beyond the first, other indicators possess
substantial independent information, thus pro
viding important confirming or contradicting
information. The analyst needs to know how to
match questions with indicators depending on
current needs. A swiss army knife is a fine gen
eral purpose tool, but it is hardly a substitute for
a well equipped workshop. It is not enough just
to produce a “best” model; rather, it is important
to understand what type of information is con
tained in a given indicator so that its message
can be properly evaluated and also to determine
how much weight to give that message given
what else is also known.
This article develops and implements a set
of procedures for evaluating indicators of eco
nomic activity that closely match the actual use
of such indicators by policymakers and business
men alike. We see that process as primarily
involving the reassessment of short to medium
term economic activity based on an indicator by
indicator analysis, with the primary decision
matrix being whether to revise the assessment of
activity up or down. We do not address related
issues of assessing long run growth, inflation,
interest rates, or the value of the dollar. Evaluat
ing indicators in this context has four primary
parts: ranking candidate indicators; characteriz
ing the nature of the information in those indica
tors; assessing their usefulness in practice; and
determining what relative weight should be
given to each indicator. The idea is to develop
the information that an analyst needs in order to
interpret information as it comes in and to
choose which indicators to watch depending on
the questions being asked.
All of our analyses will be carried out on a
bivariate (two variable) basis. Multivariate
regression models allow indicators to play off
against one another making it impossible to
determine exactly what information is in each
indicator. This in no way reduces the generality
of the methods developed in this study, in that
the forecast of a given multivariate model can be
treated as a single indicator, just like any other.
In fact, the National Bureau of Economic Re
search (NBER) Experimental Leading Index
examined in Section 4 is just such an indicator.
Once the indicators are assessed and charac
terized, the last section of the article formally

FEDERAL RESERVE

BANK OF CHICAGO

addresses the question of how to weight the
information in one indicator relative to another.
This is done through mixing models, which
effectively produce a forecast based on the
weighted average of the individual forecasts
generated by the indicators. There are a num
ber of advantages that are derived from using
this mixing approach over the classical multiva
riate forecasting techniques. First, when one of
the indicators begins to fail, which they do, you
can reweight or at least temporarily just ignore
that indicator. Second, by using only the pri
mary information in each indicator, these mod
els are less subject to the type of overfitting
arising from interactions between indicators
that plagues large econometric models. Third
and most important, the mixing approach al
lows a much more precise assessment of exact
ly the type and value of information that is
contained in each indicator and thus allows
analysts to reoptimize their choice of indicators
based on the type of question being asked.
Our investigation indicates that this type of
analysis is crucial to the effective use of indica
tors. First, we find that a number of commonly
used indicators, such as the monetary base and
M 1, actually contain negative information, in
the sense that forecasts based purely on the past
history of activity, ignoring these indicators, do
better in practice than forecasts which include
the information in these indicators. Second, we
find that long term interest rate levels provide
no additional information about future econom
ic activity beyond that contained in short term
interest rate levels, while the slope of the term
structure contains substantial additional infor
mation. This would seem to indicate that a rise
in long term interest rates is associated with an
improvement in the near term outlook of the
economy. It is interesting to note that this is
contrary to popular wisdom, according to which
a scenario with declining short term interest
rates and increasing long term rates is viewed
as negative. Third, we find that some indica
tors, such as the spread between the 3 month
eurodollar rate and the 3 month Treasury bill
rate, do a very good job of forecasting growth
during expansions, but rarely signal recessions,
while others, such as real M 1 and the mix be
tween bank and nonbank financing do better at
forecasting during recessions, even though they
are poor forecasters in general. Fourth, we find
that composite indicators, such as the Depart
ment of Commerce Composite Index of Lead

ing Indicators and the NBER Experimental
Leading Index, are very good predictors of
economic activity over a two quarter horizon,
while real M2 and the slope of the term struc
ture are more useful over a one year horizon.
This last finding illustrates a crucial point:
the forecast horizon is fundamental to the
choice of indicators. Short horizons favor inter
est rate risk spreads, such as the difference
between the 6 month commercial paper rate
and the 6 month Treasury bill rate (risk spreads
are yield differences between private and public
debt instruments with the same maturity), and
activity based indicators, such as the Purchas
ing Managers’ Index and the Sensitive Materi
als Price Index. Longer horizons, on the other
hand, favor monetary indicators, such as real
M2, and interest rate term spreads, such as the
difference between the 12 month Treasury bill
rate and the overnight federal funds rate (term
spreads are yield differences between two pub
lic debt instruments with different maturities).
This indicates that different types of informa
tion are important for forecasting growth at
different forecast horizons.
Methodology

As noted above, the primary focus of this
article is the examination of various data series
as indicators of changes in real economic activ
ity, which we measure as annualized quarterly
log changes in real GDP, except in the sections
of the article which focus on issues of timing,
in which case the annualized monthly log
changes in employment are used. Since the
employment data series is available at the
monthly frequency, it allows for more precise
estimation of the pattern of impact over time.
Throughout the article the indicators are
used to produce forecasts of economic activity.
The specific functional form of the forecasting
equation is always the same. One year of data
for the indicator and one year of lagged eco
nomic activity are included in the regression.
Thus, the exercise is strictly equivalent to a
bivariate vector autoregression (VAR) with one
year of lags: four quarters of lags for the real
GDP models and twelve months of lags for the
employment models. The models are estimated
in log differences and rates of change are annu
alized. Interest rates, interest rate spreads, and
some of the composite indicators are used in
their level form. In many of the tables an addi
tional forecast is provided with the label

“NONE.” In this case, the forecast is based
solely on the past history of economic activity,
that is, a pure autoregressive model with one
year of lagged data. This pure autoregressive
forecast is referred to as the no-indicator fore
cast. When the horizon of the forecast is var
ied, we simply change the dependent variable
in the regression rather than dynamically iterate
the one period ahead forecast. This optimizes
the parameterization for the forecast horizon in
question, rather than multiplicatively combin
ing estimation errors forward. Symbolically the
forecasting equation can be written:
0 ) Y,+k - Y, = A (W Y ' , + B (L )It_] + cd ;
where T is the log of economic activity at time
t, / is the indicator at time t, k is the number of
periods in the forecast horizon, and A(L) and
B(L) are polynomials in the lag operator L of
order one year.
The indicators are split into four groups,
which we call families. Each family is meant
to represent a natural division of indicators into
groups which are likely to share similar charac
teristics. The first family we examine is inter
est rate levels, the second is money based mea
sures, the third is interest rate spreads, and the
fourth is composite indicators, such as the De
partment of Commerce Composite Index of
Leading Indicators and the Standard and Poor’s
500 Stock Index. The fourth group also con
tains those series which do not fit neatly into
the overall classification scheme.
The idea is to first examine the indicators
within a family, characterize the information,
and find out which indicators within each fami
ly produce the best forecasts and contain the
most independent information. Then we take
these “best” indicators from all four families
and examine what is to be gained by mixing the
information from different families. This
serves a number of purposes. First, breaking
the large list of potential indicators into smaller
groups makes each examination more manage
able. Second, using natural groupings allows us
to look at questions such as what is the best
interest rate or the best money measure in a
natural way. Third, one key issue for indicators
is the degree to which they actually contain
independent information. Focusing on groups
which are already thought to have similar infor
mation provides a natural way to learn if these

ECONOMIC PERSPECTIVES

preconceptions are accurate or if some of these
groups contain more than one type of informa
tion. Lastly, by first selecting the best indica
tors at the family level and then mixing be
tween families, we can produce a mixed fore
cast which, as noted above, closely approxi
mates the way indicators are used in practice.
Each family of indicators is subjected to
the same analysis. First, each family of indica
tors is described. Then each of the indicators is
subjected to four evaluations: classical goodness-of-fit rankings; indicators’ performance in
practice; characterization of fit; and encom
passing tests. The results of our evaluations are
summarized in tables numbered as follows: the
first digit in the table’s number refers to the
family of indicators (for example, interest rate
levels constitute our first family), while the
second digit refers to the type of statistics dis
cussed (for example, multiperiod forecast re
sults are summarized in the second table of
each family). For example, Table 1.2 is the
second table in our first family of indicators.
The first part of our analysis focuses on
classical goodness-of-fit statistics, which are
based on simple full sample regressions esti
mated on data from January 1962 to December
1991. The results are presented in Table _ .l2 of
each family analysis section. In this table we
report the correlation coefficients produced by
the regression, and we rank the indicators in
each family according to their R2s. The idea is
that the best indicators are the ones that pro
duce the best fit as measured by the R2of the
regression. This closely approximates the stan
dard notions of evaluating indicators of eco
nomic activity. It is also closely linked to the
notion of Granger causality, which statistically
measures whether or not the indicator actually
helps forecast economic activity. The probabil
ity value for this test is also included in the
table. Low probability values, especially below
.05, are normally thought to indicate that a
variable is valuable in generating forecasts.
The second evaluation switches the focus
to how well the indicators are likely to work in
practice. To this end, goodness-of-fit is reinter
preted in a way closer to the way forecasts are
actually used. First, Table _.2 shows goodnessof-fit rankings recalculated for a series of fore
cast horizons using standard regression analysis
to provide a bench mark for evaluating out-ofsample forecasts. The one quarter horizon used
in Table _.l is first presented and then a two

FEDKRAI. RESERVE

RANK OF CHICAGO

quarter forecast horizon evaluation and a four
quarter forecast horizon evaluation.3 Table _.3 in
each section then repeats this analysis using
forecasting equations which do not contain any
prior information. Specifically, the forecasting
equations are estimated using Kalman filtering
techniques which recursively compute minimum
mean squared errors using only data available
prior to the forecasting period. This analysis
provides a more accurate assessment of how an
indicator is likely to perform in practice, since
this is the regression an analyst would have actu
ally estimated just prior to making the forecast,
rather than the regression the analyst would gen
erate today using all of the data since the forecast
period. These forecasts are then ranked by the
root mean squared error (RMSE) (the average
size of the error) of the forecasts from July 1973
onward. To see how the indicators perform
under different circumstances, we look at Kal
man forecasts in recessions and expansions, and
re-rank the indicators according to their RMSEs,
as shown in Table _.4.
Next, Figure _. 1 in each section graphs the
cumulative residuals for the Kalman forecasts.
These charts allow us to determine if these fore
casts tend to perform badly during recessions or
if there was some particular point in the past
where they did especially well or poorly. It also
tells us if the forecasts have tended to miss in
some systematic fashion over time. The residu
als are measured as the actual growth in econom
ic activity minus the forecasted growth. There
fore, although a flat cumulated residuals’ slope
indicates good overall performance, a path con
sistently close to the zero horizontal line would
be ideal. On the other hand, a downward trend in
the cumulative residuals would indicate a period
of overpredicting growth in activity, while an
upward trend would indicate a period of under
forecasting.
The third evaluation seeks to characterize
the type of information in the indicator. Typical
ly the question can be thought of as follows: if
the indicator goes up today how does that change
my expectations about economic activity in the
future? This is analyzed by calculating the dy
namic response path of employment for each of
the indicator forecasting equations, which shows
how a one standard deviation4 increase in the
indicator changes expectations about the future
growth rate of employment for each month for
the next 36 months.5 This allows us to character
ize the information in the indicator based on how

fast economic activity responds, how much it
responds and how long the change in activity
lasts. Figure _.2 in each family section graphs
the dynamic response path for selected indica
tors in the family, as well as the two standard
deviation bands on the estimates of the dynam
ic response paths to show the amount of uncer
tainty about the response path.
The fourth evaluation switches the focus to
independence of information. As noted earlier,
one of the most important factors to understand
about indicators is whether or not they contain
independent information relative to some other
indicator. This allows the analyst to assess
whether a new piece of information actually
contains any additional information or whether
it is simply the same information with a differ
ent label. This is evaluated through a set of
techniques called encompassing tests. In the
context of this paper, indicator A is said to
encompass indicator B if, given the forecast
implicitly based on A, there is no additional
information in indicator B. Indicator A is said
to dominate indicator B if A encompasses B
and B does not encompass A. The simplest
way to test this is to run a regression with eco
nomic activity as the dependent variable and
the forecast of activity based on indicator A and
the forecast of activity based on indicator B as
the independent variables. Symbolically this
can be written:
(2) AGDP= <J)for(A)' + ( l - Wor(B)t + e;
where for(A)i and for(B)i are the forecasts of
GDP based on indicators A and B respectively
and ()) is the relative weight an ordinary least
squares (OLS) regression assigns to for(A)t and
for(B)r If (]) is significantly different from 0
then we can reject that for(A) is encompassed
by for(B). Likewise if 1 —<)>is significantly
different from 0 then we can reject that for(B) is
encompassed by for(A). If neither is encom
passed then both indicators contain independent
information and a better forecast can be ob
tained by mixing both sets of information with
the relative weights given by (J). If only one is
encompassed, then it is said to be dominated
and only the other is necessary to produce an
efficient forecast. If both are encompassed then
either indicator alone can produce an efficient
forecast. This occurs when there is a very high
degree of collinearity and the standard error of
the parameter estimate is large. In this case the

indicator which has the best historical track
record would likely be the superior choice. The
generalization to longer horizons is straightfor
ward, though the calculations of the standard
errors are more complicated since the errors are
no longer independent.
Table _.5 in each family section contains the
encompassing tests. The table is read as follows.
The indicators are listed both along the top and
along the side of the matrix. The numbers in the
table refer to the test that the indicator listed
along the side is encompassed by the indicator
along the top. The statistics reported are the
significance levels for the test that the indicator
along the top does in fact contain all the infor
mation in the indicator along the side. Values
below .05 indicate substantial independent infor
mation possessed by the indicator listed along
the side. For the sake of readability, such values
are replaced by a dash in the table. In general,
the lower the number, the more likely it is that
the indicator listed along the side possesses inde
pendent information and the higher the number,
the more likely it is that the indicator listed along
the top encompasses the indicator along the side.
The way to interpret Table _.5 is that a side
indicator whose row is blank contains informa
tion that is independent of every other indicator
in the family. A top indicator whose column is
full of high numbers is said to encompass the
indicators on the side. An indicator that did both
would be said to dominate the family. In gener
al, we search for the set of indicators in each
family which contains all the information in the
family using as few indicators as possible. This
will mean that the best variable from the previ
ous tests will be included together with addition
al indicators which contain independent informa
tion, that is, the indicators that add the most.
Formally, this means that we include all indica
tors that are not encompassed by any other indi
cators in the family plus whatever additional
indicators are necessary to fully encompass or
cover all of the other indicators in the family.
This is analogous to finding a set of minimally
sufficient statistics.
The indicators that make it through this
process will then be tested in the mixing model
section of the article in between-family encom
passing tests, which examine whether or not
there is independent information between fami
lies. Then a set of “best” indicators will be se
lected in order to develop mixing models of
indicators which contain independent informa-

ECONOMIC PERSPECTIVES

tion for each of the forecasting horizons.
These models will contain estimates of the ap
propriate relative weights that should be applied
to the individual indicator-based forecasts.
Completing the circle of policy forecasts, the
mixing models will be time varying to see if
there is any gain from adjusting the weight ap
plied to these individual forecasts based on re
cent performance.
1. In te re s t ra te levels

TABLE 1.1

Classical goodness-of-fit statistics
R2

Correlation
with real GDP

P-value

Rank

0.338

-0.353

0.0000

TB03

0.293

-0.299

0.0001

Indicator

TB06

0.304

-0.295

0.0000

CM01

0.309

-0.282

0.0000

CM03

0.279

-0.257

0.0002

As shown in Table 1.1, we selected the
0.268
-0.251
0.0003
8
CM05
following levels of interest rates for investiga
-0.237
0.0009
10
0.253
CM10
tion: the federal funds rate (FF); the 3 and 6
0.354
-0.352
0.0000
1
EUR03
month Treasury bill rates (TB03 and TB06); the
2
0.348
-0.342
0.0000
CP6
1, 3, 5, and 10 year Treasury constant maturity
0.0007
BAA
-0.269
9
0.258
bond rates (CM01, CM03, CM05, and CM 10);
the 3 month eurodollar rate (EUR03); the 6
NOTE: Sample period is January 1962 - December 1991,
quarterly data.
month commercial paper rate (CP6); and the
BAA corporate bond rate (BAA). Goodness-offit tests show that all of these interest rates are
To determine how interest rates would actu
negatively correlated with real GDP, which
ally perform as indicators of economic activity,
indicates that an increase in interest rates this
we use Kalman filtering techniques to produce
period is associated with a decline in real output.
out-of-sample forecasts using only data available
The eurodollar rate, the commercial paper
prior to the forecasting period. When we rank the
rate, and the federal funds rate have the three
resulting RMSEs in Table 1.3 it becomes clear,
largest absolute correlation coefficients with
once again, that the overall performance of short
real GDP and produce the best fit to the model
term interest rates improves when we expand the
as measured by their individual R2s, ranking
forecast horizon. FF continues to perform best at
first, second, and third, respectively. The
the one year forecast horizon, while maintaining
strength of such relationships is not surprising
a standing similar to the in-sample results at
given the role that these instruments
play in money markets. For exam
TABLE 1.2
ple, because the federal funds rate
Multiperiod forecasts, in-sample
is a key instrument of monetary
policy and a bench mark for other
Real GDP
money market interest rates, fluctu
1 quarter
2 quarters
4 quarters
ations in the rate are strongly asso
Indicator
R2
Rank
R2
Rank
R2
Rank
ciated with future movements in
FF
0.338
3
0.463
3
0.530
1
real economic activity.
TB03
0.293
6
0.402
5
0.496
3
The predictive power of our
0.304
4
0.487
TB06
0.406
5
5
interest rate family is then tested at
different forecast horizons using
4
CM01
0.397
6
0.443
6
0.309
standard regression analysis over
7
0.377
7
0.279
7
0.350
CM03
the full sample period. The in0.332
8
0.346
8
CM05
0.268
8
sample results of Table 1.2 show
0.296
0.307
CM10
0.253
10
10
10
that while EUR03 loses some of its
0.354
1
0.471
2
0.490
4
EUR03
strength as the forecast horizon
CP6
0.348
2
1
0.516
2
0.475
increases, as shown by the recalcu
lated rankings, the fit of both CP6
BAA
0.258
9
0.329
9
0.315
9
and FF improves at longer forecast
NONE
11
11
11
0.118
0.123
0.076
horizons, with FF having the stron
gest predictive power at the four
NOTE: Sample period is January 1962 - December 1991, quarterly data.
quarter forecast horizon.

FEDERAL RESERVE

BANK OF CHICAGO

er maturity bonds, such as the 3, 5,
and 10 year Treasury bonds.
Kalman multiperiod forecasts, out-of-sample
Once the general strength of
Real GDP
an indicator is established, it be
1 quarter
2 quarters
4 quarters
comes important to determine how
Rank
RMSE
Rank
Indicator
RMSE
Rank
RMSE
the indicator would perform under
different economic circumstances,
1
FF
2
3
2.160
3.793
2.859
and Table 1.4 tells us how well or
TB03
3.969
9
3.075
6
2.260
5
how poorly our interest rate family
4
3.862
4
2.251
TB06
3.000
5
performs during recessions and
4
2.356
6
CM01
3.826
3
2.996
expansions. The strength of FF
7
3.094
7
2.483
CM03
3.876
5
deteriorates somewhat during both
3.144
2.552
recessions and expansions, when
3.936
7
8
8
CM05
compared to other interest rates.
3.949
3.249
10
2.683
9
CM10
8
On the other hand, EUR03 contin
1
2.754
1
2.222
3
EUR03
3.622
ues to perform strongly especially
2.827
2
2
2.216
CP6
3.880
6
during recessions, and CP6’s rank
3.197
9
2.725
10
BAA
4.006
10
ing improves during expansionary
periods.
It is also interesting to
11
11
2.819
11
NONE
4.015
3.358
note that our autoregressive indica
NOTE: Sample period is July 1973 - December 1991, quarterly data.
tor “NONE” ranks first in the
Kalman forecasts during expan
sions. This result demonstrates
that sometimes indicators can be misleading
shorter horizons. CP6, on the other hand, experi
during expansionary periods.
ences an out-of-sample deterioration at the one
The cumulated residuals from the Kalman
quarter horizon, but ranks second at both the two
forecasts in Figure 1.1 show that, overall, the
quarter and one year forecast horizons. In gener
indicators in our interest rate family consistently
al, our results indicate that shorter maturity instru
underforecasted real GDP between 1974 and
ments, namely FF and EUR03, outperform long
1982. The upward trend in the
cumulated residuals during this
TABLE 1.4
period can be explained in part by
an unprecedented increase in infla
Kalman 1 quarter ahead forecasts in
tion, which caused interest rates to
recessions and expansions
rise without the normally anticipat
Real GDP
ed
decline in output. On the other
Actual
Recession
Expansion
hand,
between 1983 and 1989, FF,
Rank
RMSE
Rank
RMSE
Rank
RMSE
Indicator
CP6, EUR03, and all of the Trea
4
4
3.801
FF
3.793
2
3.753
sury bill rates performed well, as
3.941
3.969
9
4.108
8
9
shown by the flattening of their
TB03
cumulated residuals’ slopes during
3.862
4
6
TB06
3.780
6
3.878
this period. Between 1990 and
2
3.857
CM01
3.826
3
3.663
5
1991, however, the indicators’
7
CM03
3.876
5
3.722
3
3.905
performance deteriorated again, as
7
3.814
7
3.959
10
CM05
3.936
all of the interest rates missed the
11
3.949
8
3.766
5
3.983
CM10
1990-91 recession and consistently
3.622
1
1
3.625
2
EUR03
3.605
overforecasted real GDP.
Figure 1.2 shows the dynamic
3.642
3.880
6
4.928
10
3
CP6
response
of the forecasted growth
BAA
10
4.377
9
3.930
8
4.006
rate of employment when FF in
creases. Because the response
11
5.817
11
1
NONE
4.015
3.563
paths of our interest rate family are
NOTE: Sample period is July 1973 - December 1991, quarterly data.
virtually identical across all indica-

TABLE 1.3

ECONOMIC PERSPECTIVES

TABLE 1.5

Multiperiod encompassing tests
(Probability value for null hypothesis: X is encompassed by Y)
Real GDP (1 quarter)
Y

TB03

TB06

CM01

CM03

CM05

CM10

0.796

0.830

0.061

—

—
—

0.403
0.723
0.803

0.601

EUR03

CP6

0.932

0.856

0.391

0.262

BAA

Maximum
P-value

X
FF

n.a.

TB03

0.482

n.a.

TB06

0.945

0.204

n.a.

0.947

—

CM01

0.677

0.103

0.342

n.a.

—

CM03

0.682

0.343

0.949

0.264

n.a.

0.065

CM05

0.637

0.375

0.910

0.412

0.251

n.a.

0.066

0.906

CM10

0.464

0.371

0.798

0.684

0.508

0.563

n.a.

0.818

EUR03

0.119

—
—

n.a.

0.272

—
—

—

CP6

—
—

BAA

0.326

0.221

0.638

0.485

0.407

0.253

—
—

Ci.431

—

0.932
—

0.830

0.241

—

0.947

0.524

—

0.723

0.053

0.949

0.702

0.154

0.910

0.976

0.380

0.976

0.240

—

0.240

0.659

n.a.

—

0.659

0.666

0.783

n.a.

0.783

Real GDP (2 quarters)
FF

—

n.a.

—

0.605

0.867

—

0.867

TB03

0.090

n.a.

0.925

0.310

—

0.340

—

0.925

TB06

0.337

0.448

n.a.

0.220

—

0.250

—

0.448

CM01

0.582

0.515

0.864

n.a.

—

—
—

—

0.293

—

0.864

CM03

0.617

0.959

0.443

0.109

n.a.

—

0.360

0.107

—

0.959

CM05

0.694

0.975

0.520

0.191

0.132

n.a.

—

0.450

0.197

0.137

0.975

CM10

0.665

0.763

0.418

0.210

0.096

—

n.a.

0.491

0.263

0.794

EUR03

0.231

—

—
—

n.a.

0.598

—

0.598

0.837

0.429

0.228

CP6

0.214

—

BAA

0.574

0.302

—
—

0.635

0.340

n.a.

—

0.340

0.989

0.742

n.a.

0.989

0.044

Real GDP (4 quarters)
FF

n.a.

—

TB03

0.963

n.a.

0.15'2

—

0.139

0.661

—

0.963

TB06

0.920

0.910

n.a.

—
n.a.

—

0.255

0.662

—

0.920

—

0.980

0.157

—

0.980

—

0.623

0.166

—

0.623

0.506

0.140

—

0.541

0.555

0.211

0.419

0.588

n.a.

0.785

—

0.785

0.052
0.767

n.a.
0.456

—

0.746
0.895

—

CM01

0.596

0.373

—

CM03

0.593

0.363

—

CM05

0.541

0.302

—

CM10

0.588

0.362

0.130

—
0.074

—
n.a.

—

0.072

—
n.a.

EUR03

0.539

0.263

'0.173

CP6
BAA

0.746
0.845

—
—
0.534

—
—
0.692

—
—
0.895

—
—
0.101

—

0.776

—

0.507

—
n.a.

NOTES: Values less than or equal to 0.05 are marked with a dash. Sample period is

tors, we chose the federal, funds rate as an ex
ample of how a one standard deviation increase
in the interest rate today changes the growth
rate of employment during the next 36 months.
The forecasted growth rate of employment
increases for approximtately two months and
then falls, plunging to very deep negative val
ues especially during the first year. Eventually,
the growth rate moves very close to zero as The
horizon expands, indicating that the change i n

FEDERAL RESERVE

BANK OF CHICAGO

n.a.

1962 - December 1991, qu arterly data.

FF does not impact employment forecasting
after approximately two years.
Finally, as shown in Table 1.5, our encom
passing tests indicate that both FF and EUR03
contain significant information but neither of
them dominates. This indicates that both inter
est rates are close substitutes, and using both
would not improve the forecasting results since
either interest rate contains all of the necessary
information. For example, at the one quarter

FIGURE 1.1

Interest rate levels
Fed funds(FF)

5 year Tre asury bond (CM05)

cumulated Kalman residuals
100

cumulated I Caiman residuals
75 r

3 month Treasury bill (TB03)

10 year "I Treasury bond (CM 10)

100 r-

75 r

— L_i

1 .1

6 month Treasury bill (TB06)

3 month eurodollar (EUR03)
100 r

1 year Treasury bond (CM01)

6 month cornmerciaT paper (CP6)

100 r

75 h

50 -

25 |-

0
-25

3 year Treasury bond (CM03)
100

BAA corporate bond (BAA,1

100
75

jl973

FIGURE 1.2

TABLE 2.1

Dynamic response of employment to FF

Classical goodness-of-fit statistics

annualized percent growth rates

Correlation
with real GDP

P-value

Rank

MBSTL

0.166

0.034

0.1744

0.145

0.013

0.4734

0.172

0.157

0.1284

0.219

0.236

0.0084

0.169

0.246

0.1483

Indicator

0.164

0.239

0.1993

DBTNF

0.124

0.180

0.9352

M1R

0.250

0.297

0.0012

M2R

0.346

0.353

0.0000

NBRX

0.249

0.154

0.0012

NOTE: Sample period is January 1962 - December 1991,
quarterly data.

forecast horizon EUR03 encompasses all of the
other indicators, but at the same time, EUR03
is encompassed by FF and CP6. However,
because EUR03 ranked first in the in-sample
forecasts at the one quarter horizon, and in the
out-of-sample forecasts at the one and two
quarter horizons, it is selected as our best indi
cator at both the one and two quarter forecast
horizons. Similarly, FF is chosen as the best
indicator at the one year forecast horizon for its
strong performance in-sample and out-of-sam
ple when the forecast horizon increases.

the indicators in our family of money based
measures are annualized log differences.
Goodness-of-fit statistics in Table 2.1 show
that all of the money based indicators are posi
tively correlated with real GDP. Not surpris
ingly, as the endogenous components of the
monetary aggregate increase, the contempora
neous correlation with economic activity rises.
Moreover, the broader monetary aggregates
seem to impact real GDP more than the narrow-

2 . M o n e y based m easures

Table 2.1 lists the monetary
indicators we selected for investiga
tion: a measure of the monetary
base developed by the Federal
Reserve Bank of St. Louis
(MBSTL); the Board of Governors’
monetary base6 (MB); Ml; M2;
M3; L;7 long term debt of domestic
nonfinancial institutions (DBTNF);
real Ml (MIR) and real M2 (M2R)
both deflated by the consumer price
index; and NBRX, which is the
ratio of nonborrowed reserves at
time t to total reserves at time t - 1.
Strongin (1991) found that this
normalized reserve aggregate
(NBRX) contains much of the in
formation about monetary policy
actions which Sims (1991) at
tributes to innovations in the federal
funds rate. Except for NBRX, all of

FEDERAL RESERVE

BANK OF CHICAGO

TABLE 2.2

Multiperiod forecasts, in-sample

Indicator

___________
1 quarter
R2
Rank

Real GDP
2 quarters
R2
Rank

4 quarters
R2
Rank

MBSTL

0.166

0.154

0.102

0.145

0.144

0.121

0.172

0.183

0.096

0.219

0.249

0.186

0.169

0.189

0.107

0.164

0.184

0.097

DBTNF

0.124

0.133

0.121

M1R

0.250

0.288

0.244

M2R

0.346

0.447

0.514

NBRX

0.249

0.327

0.292

NONE

0.118

0.123

0.076

NOTE: Sample period is January 1962 - December 1991, quarterly data.

er measures of money. This is
TABLE 2.3
probably due to the fact that broad
Kalman multiperiod forecasts, out-of-sample
er money measures consist of a
Real GDP
larger number of components, each
1
quarter
2
quarters
4 quarters
associated with movements in eco
RMSE
Rank
RMSE
Rank
Indicator
RMSE
Rank
nomic activity. M2R, M 1R, M3,
and L have the largest correlation
MBSTL
3.474
2.904
4.108
7
10
8
coefficients with GDP, and M2R
MB
4.114
7
7
8
3.426
2.840
and M 1R also show the strongest fit
4.149
M1
10
3.455
9
2.992
11
to the model, as their R2s rank first
3.944
4
M2
3
3.252
3
2.809
and second, respectively. NBRX
3.394
M3
4.073
5
6
2.948
10
and M2 are also statistically signifi
L
3.432
4.136
9
8
2.926
9
cant, ranking third and fourth, re
spectively.
DBTNF
4.242
11
11
3.495
2.820
6
The predictive power of our
M1R
4
4.097
6
3.285
2.775
3
money based indicators is then
3.674
M2R
1
2.844
1
2.219
1
tested at different forecast horizons,
NBRX
2
2
2
3.799
3.003
2.550
and in-sample results shown in
Table 2.2 indicate that M2R, MIR,
NONE
4
2.819
4.015
3.358
5
5
NBRX, and nominal M2 all contin
NOTE: Sample period is July 1973 - December 1991, quarterly data.
ue to perform well, providing addi
tional information to the forecasts
as the horizon increases. M2R,
however, clearly has the strongest predictive
Figure 2.1 provide another perspective of the
out-of-sample performance of our family of
power at all forecast horizons (ranking always
first), while M IR’s ranking slightly deteriorates
money based measures. In our case, the best
as the forecast horizon increases. On the other
indicator is again M2R as its cumulated residu
als’ path clearly stays near zero values, except
hand, NBRX’s performance improves at the
two quarter and four quarter horizons, ranking
for isolated periods of large forecast errors in
second in both.
1978 and 1981, when M2R underforecasted
Once again, to see how the
indicators would actually perform
TABLE 2 .4
using only data prior to the fore
Kalman 1 quarter ahead forecasts in
casting period, we use Kalman
recessions and expansions
filtering techniques. Out-of-sample
Kalman forecast results in Table
Real GDP
2.3 show M2R and NBRX to have
Actual
Recession
Expansion
Indicator
RMSE
Rank
RMSE
Rank
RMSE
Rank
the strongest fit at all horizons, as
shown by their individual RMSEs,
MBSTL
4.108
7
5.774
8
3.700
6
while MIR’s performance greatly
MB
4.114
8
5.534
7
3.777
7
improves in the long run. As
M1
4.149
10
4
5.245
3.901
9
shown in Table 2.4, M2R also con
M2
3.944
3
11
3.402
6.011
2
sistently performs well under differ
ent circumstances, and especially
M3
4.073
5
5.848
10
3.631
5
during expansionary periods. On
L
4.136
9
5.256
5
3.883
8
the other hand, while MIR is a
DBTNF
4.242
11
5.400
6
11
3.980
good predictor during recessions, its
M1R
4.097
1
3.949
6
4.793
10
performance considerably worsens
M2R
3.674
1
5.109
2
1
3.326
during expansions. NBRX’s per
NBRX
2
3.799
5.228
3
3.454
formance is noticeably consistent
3
during recessions and expansions,
NONE
4
4.015
5.817
9
3.563
4
as it ranks third during both.
The cumulated residuals from
NOTE: Sample period is July 1973 - December 1991, quarterly data.
the Kalman forecasts shown in

ECONOMIC PERSPECTIVES

FIGURE 2.1

Money based measures
St. Louis monetary base (MBSTL)

Nominal L (L)

cumulated Kalman residuals

FRB monetary base (MB)

Nominal nonfinancial debt (DBTNF)

Nominal M2 (M2)

Real M2 (M2R)

Nominal M3 (M3)

FEDERAL RESERVE

BANK OF CHICAGO

NBR/TR ratio (NBRX)

TABLE 2.5

Multiperiod encompassing tests
(Probability value for null hypothesis: X is encompassed by Y)
Real GDP (1 quarter)
Y

MBSTL

DBTNF

M1R

M2R

NBRX

Maximum
P-value

0.763

X
n.a.

0.064

0.150

0.462

0.178

0.094

0.763

0.759

0.411

0.726

n.a.

0.307

0.569

0.296

0.224

0.075

0.682

0.936

0.500

0.936

0.055

—

n.a.

0.506

0.105

0.054

—

0.658

0.855

0.671

0.855

MBSTL

—

n.a.

—

0.098

0.954

—

0.954

0.138

—

0.135

0.733

n.a.

0.174

—

0.327

0.653

0.149

0.733
0.449

0.119

—

0.136

0.407

0.324

n.a.

—

0.322

0.449

0.286

DBTNF

0.694

0.755

0.669

0.771

0.716

0.825

n.a.

0.829

0.970

0.755

0.970

MIR

—

n.a.

0.924

—

0.924

M2R

—

NBRX

n.a.

—

0.000

0.286

n.a.

0.286

Real GDP (2 quarters)
n.a.

0.266

0.760

0.817

0.484

0.359

—

0.959

1.000

0.595

n.a.

0.516

0.654

0.477

0.445

0.167

1.000
0.686

0.954

0.994

0.722

0.994

—

n.a.

0.667

0.112

—

0.803

0.970

0.845

0.970

—

n.a.

—

0.173

0.833

0.119

0.833

—

0.064

0.603

n.a.

0.197

—

0.323

0.560

0.193

0.603
0.333

MBSTL

—

0.258

0.294

n.a.

—

0.274

0.284

0.333

0.490

0.715

0.604

0.691

0.533

0.697

n.a.

0.774

0.973

0.745

0.973

M IR

—

n.a.

0.752

0.101

0.752

M2R

—

L
DBTNF

NBRX

n.a.

—

0.000

0.133

n.a.

0.133

Real GDP (4 quarters)
n.a.

0.930

0.341

0.604

0.525

0.344

0.659

0.840

0.782

0.896

0.930

0.336

n.a.

0.126

0.248

0.228

—

0.330

0.362

0.817

0.464

0.817
0.987

MBSTL
M1

0.658

0.693

n.a.

0.914

0.669

0.439

0.517

0.987

0.841

0.958

—

n.a.

—

0.263

0.430

0.400

0.430

0.452

0.392

0.424

0.612

n.a.

0.442

0.375

0.776

0.918

0.746

0.918

0.521

0.523

0.396

0.523

0.626

n.a.

0.652

0.802

0.824

0.975

DBTNF

0.196

0.331

0.072

0.230

0.209

0.089

n.a.

0.300

0.836

0.334

0.836

—

n.a.

0.257

0.305

M1R
M2R

—

n.a.

—

0.000

NBRX

—

0.473

n.a.

0.473

NOTES: Values less than or equal to 0.05 are marked with a dash. Sample period is January 1962 - December 1991, quarterly data.

economic activity. M2R’s performance was
again noticeably good between 1990 and 1991,
when most of the other money based indicators
clearly failed to predict the recession. NBRX
was relatively stable from 1973 to 1981, but has
shown a consistent pattern of overforecasting
output growth since 1982. This deterioration
may be due to increasing reluctance on the part
of banks to borrow from the discount window.
The performance of other monetary aggregates
is less reliable and clearly more volatile than

the behavior of M2R and NBRX. For example,
the two measures of the monetary base and M 1
consistently underforecasted real GDP between
1974 and 1977, as shown by their upward slop
ing paths. Overall, the path of nominal aggre
gates plunged during the credit control program
of 1980, overpredicting output growth during
the mild recession. From 1983 to 1988, these
nominal aggregates performed fairly well,
exhibiting uncharacteristic stability, except for
M 1 which did substantially worse between

ECONOMIC PERSPECTIVES

contains unique information and that adding
another money based indicator to the model
would add no additional information.
3. Interest rate spreads

1983 and 1984. Finally, between 1990 and 1991,
there was a considerable deterioration in the
performance of M l, L, and the two measures of
the monetary base, as they consistently overpre
dicted economic growth.
To see how changes in money based mea
sures affect the forecaster’s expectations over
time, we look at the dynamic response of em
ployment to our strongest indicator, M2R. Fig
ure 2.2 shows the response of the forecasted
growth rate of employment when M2R increases
by one standard deviation. In general, a positive
impulse in a money based indicator leads to an
increase in employment growth rates. In our
case, the response to a one standard deviation
increase in M2R is quick and persistent over a
period of appro ximately 15 months, with the
maximum impact occurring within the first year.
These results indicate that the impact of changes
ii M2R on real economic activity is very strong,
afhough somewhat short lived.
Finally, we test our family of money based
measures to determine the degree of independent
information they contribute to the model individ
ually. As shown in Table 2.5, our encompassing
tests slow that M2R is clearly the dominant
indicator within our family of monetary aggre
gates. Ift fact, M2R is not encompassed by any
of the other indicators at all forecast horizons.
The row labeled M2R in the table has dashes,
indicating that the hypothesis that M2R is en
compassed by any of the other indicators is con
sistently rejected. Similarly, the high signifi
cance levels in the column labeled M2R indicate
that M2R encompasses all of the other indicators
at all forecast horitons. This suggests that M2R

FEDERAL RESERVE

HANK OF CHICAGO

Recent research on financial market indica
tors of economic activity has brought renewed
attention to interest rate spreads. Laurent (1988),
Bemanke (1990), Estrella and Hardouvelis
(1991) , Friedman and Kuttner (1992), Kashyap,
Stein, and Wilcox (1991), and Stock and
Watson (1989b) all have suggested and tested
various interest rate spreads as predictors of
economic activity with significant success. The
idea behind most of these spreads is that the
difference in yields between two different debt
instruments has a greater informational content
than interest rate levels. The two primary types
of interest rate spreads that have been used are
risk spreads which measure the difference in
yield between a private debt instrument and a
government bond of equivalent maturity, and
term spreads which measure the difference in
yield between two government debt instruments
of different maturities.
Typically, risk spreads contain information
useful to the forecaster because the return on the
private debt instrument is a measure of the mar
ket’s assessment of the near term risk in the
relevant business environment, and higher re
turns are usually associated with higher per
ceived business risk. Friedman and Kuttner
(1992) have argued that this interpretation is
probably flawed since the spreads are typically
too large to be explained by any reasonable
estimate of the risk inherent in the private debt
instruments. Therefore, they suggest that liquidi
ty considerations play a significant role in the
pricing of private/public spreads. Following
their lead, we will also refer to these spreads as
private/public spreads.
Term spreads seek to measure the market’s
perception of the relative availability of credit
through time. The convention is that the yield
on the debt instrument with the shorter maturity
is subtracted from the yield on the instrument
with the longer maturity. Thus, a positive spread
would indicate that short term funding is cheaper
than long term funding, therefore boosting cur
rent economic activity. An alternative explana
tion is that the higher long term yields may sig
nal expectations of higher future credit demand
resulting from increased economic activity. An
additional interpretation is that by taking the
difference between long and short term interest
15

rates, the short term rate is corrected for changes
TABLE 3.1
in inflationary expectations and taxes, leaving a
Classical goodness-of-fit statistics
better measure of short run credit conditions. In
Correlation
any case, all of these term spread regressions
Indicator
R2
with real GDP P-value Rank
have the counterintuitive implication that a rise
in long term interest rates is good for the near
TB3FF
0.327
0.449
0.0000
3
term outlook of the economy. Estrella et al.
TB6FF
0.321
0.442
0.0000
4
(1991) and Strongin (1990) attempt to reconcile
TB12FF
0.330
0.425
0.0000
2
the term spread results with current theory, how
CM05FF
0.302
0.321
0.0000
6
ever with limited success.
CM10FF
0.309
0.309
0.0000
5
As shown in Table 3.1, we tested seven term
TB12TB3
0.238
0.225
0.0026
9
spreads and three private/public spreads.8 Five
of the seven term spreads are based on the feder
CM10CM1 0.284
0.170
0.0001
8
al funds rate (FF), and they are: the 3 month
EUROTB3 0.294
-0.378
0.0001
7
Treasury bill rate less FF (TB3FF); the 6 month
CP6TB6
0.339
-0.431
0.0000
1
Treasury bill rate less FF (TB6FF); the 12 month
BAACM10 0.234
-0.297
0.0033
10
Treasury bill rate less FF (TB12FF); the 5 year
Treasury constant maturity bond rate less FF
NOTE: Sample period is January 1962 - December 1991,
quarterly data.
(CM05FF); and the 10 year Treasury constant
maturity bond rate less FF (CM 1OFF). TB3FF is
a short term spread; TB6FF is a medium term
spread; and TB12FF, CM05FF, and CM 1OFF are
coefficient in absolute terms. An increase in
all long term spreads. Our term spreads also
the yield on private debt instruments may signal
a riskier economic environment, which is then
include two intermediate spreads: the difference
associated with a decline in investment and a
between the 12 month and the 3 month Treasury
drop in output. In this case, if the return on
bill rates (TB12TB3), and the difference between
the 10 year and the 1 year Treasury constant
public instruments is unchanged, the private/
public spread increases while economic activity
maturity bond rates (CM10CM1).
The three private/public spreads we investi
declines. CP6TB6 has also the strongest fit to
the model, as shown by its R2, followed by
gated are: the 3 month eurodollar rate less the 3
TB12FF and TB3FF.
month Treasury bill rate (EUROTB3); the 6
month commercial paper rate less
the 6 month Treasury bill rate
TABLE 3.2
(CP6TB6); and the BAA corporate
Multiperiod
forecasts, in-sample
bond rate less the 10 year Treasury
constant maturity bond rate
Real GDP
1 quarter
2 quarters
4 quarters
(BAACM10).9
Indicator
R2
Rank
R2
Rank
R2
Rank
Goodness-of-fit statistics in
Table 3.1 indicate that all of our
TB3FF
0.327
3
0.446
3
0.437
5
term spreads are positively associat
TB6FF
4
0.321
2
0.459
0.490
4
ed with real GDP, with the short
TB12FF
2
1
0.330
0.470
0.518
1
and medium spreads showing the
CM05FF
0.302
6
0.428
6
0.498
2
strongest correlation coefficients.
The positive association is not
CM10FF
4
0.309
5
0.435
0.491
3
surprising given that short term
TB12TB3
0.238
9
0.333
9
0.383
7
interest rates tend to be more vola
CM10CM1
0.284
8
0.374
7
0.396
6
tile than long term interest rates,
0.294
7
0.364
EUROTB3
8
0.230
9
and that a decline in short term
0.2FJ9
CP6TB6
0.339
1
0.429
5
8
interest rates is typically associated
0.234
BAACM10
10
0.175
10
0.138
10
with a steepening of the yield
curve. On the other hand, private/
NONE
11
11
0.118
0.123
0.076
11
public spreads are negatively corre
lated with GDP, with CP6TB6
NOTE: Sample period is January 1962 - December 1991, quarterly data.
having the strongest correlation

ECONOMIC PERSPECTIVES

The pred ictive power of our
famil y of int erest rate spreads is
Kalman multiperiod ffoneoastey out-of^sampib
next tested at different forecast
Real GDP
horizons, and in-sample results in
1 quarter
2 quarters
4 quarters
Table 3 Si show a strong deteriora
RMSE
Rank
Rank
RMSE
Rank
RMSE
Indicator
tion in \he performance of CP6TB6
at the two and four quarter forecast
5
2.253
2.674
1
1
TB3FF
3.609
horizons, while the strength of
2
2.081
2.691
2
TB6FF
3.691
3
TBUiFF improves considerably in
1
2.015
2.754
6
3
TB12FF
3.753
the kong run. In general, the predic
3
2.111
6
5
2.811
CM05FF
3.745
tive power of medium and long
4
2.161
7
2.785
5
3.763
CM10FF
team spreads seems to improve as
6
2.370
'the forecast horizon increases.
3.187
4.197
11
9
TB12T B3
Also, term spreads perform better
7
2.389
8
CM10'CM1
3.857
8
2.970
than private/public spreads across
2.721
8
7
4
2.886
3.698
EUROTB3
horizons, except for CP6TB6,
;2.744
9
4
2.760
3.656
2
CP6T B6
which is the strongest indicator at
11
2’.846
11
9
3.485
BAACM10
3.983
the one quarter forecast horizon.
This scenario is virtually unchanged
10
2.819
10
3.358
10
NONE
4.015
in the out-of-sample Kalman fore
NOTE: Sample period is July 1973 - December 1991, quarterly data.
casts shown in Table 3.3. As we
test the actual performance of our
indicators using only data available
formed fairly well from 1973 to 1980, tlv;y
prior to the forecasting period, we see tha t
clearly failed during the last three recessio ns. In
CP6TB6 remains very strong in the short run,
fact, they all underforecasted economic activity
although its ranking somewhat deteriorates
between 1980 and 1982, and then overpredicted
when compared to in-sample results. Although
real GDP between 1990 and 1991. Between
the out-of-sample performance of TB12FF at
1982 and 1989, their path was conspicuously
short term horizons considerably worsens, its
strength increases at the four quarter forecast
flat. This suggests that these spreads do well in
horizon, as its RMSE ranks first.
Under different circumstances, we
TABLE 3 .4
see that overall, private/public
spreads, such as CP6TB6 and
H&lftianiUquarter ahead 1fftnceastft in
EUROTB3, perform better during
reressions ami cocpamions
expansionary periods than our term
Real GDP
spreads, as shown in Table 3.4.
Actual
Recession
Expansion
On the other hand, term spreads
Rank
Indicator
RMSE
Rank
RMSE
Rank
RMSE
outperform private/public spreads
TB3FF
1
1
3.447
3
3.609
4.353
during recessions, as TB3FF and
TB6FF
4
3.691
3
4.634
3
3.479
TB12FF rank first and second,
respectively, according to their
TB12FF
2
3.753
6
4.599
3.566
9
individual RMSEs.
CM05FF
3.745
5
4.714
5
3.527
6
The cumulated residuals from
CM10FF
7
3.521
5
3.763
4.823
6
the Kalman forecasts in Figure 3.1
4.197
11
TB12TB3
11
5.172
8
3.980
show some striking similarities in
CM10CM1
3.857
4.707
4
3.670
10
8
the overall forecasting performance
7
2
EUROTB3
3.698
4
4.987
3.393
of our family of interest rate
spreads. Except for TB3FF,
CP6TB6
2
5.727
10
3.099
1
3.656
TB6FF, and TB12FF, all of our
3.557
7
BAACM10
3.983
5.698
9
9
spreads tend to overforecast real
GDP, as shown by their consistent
NONE
5.817
11
3.563
8
4.015
10
ly negative residuals. While
NOTE: Sample period is July 1973 - December 1991, quarterly data.
TB3FF, TB6FF, and TB12FF per

FEDERAL RESERVE

BANK OF CHICAGO

FIGURE 3.1

12 month T bill less 3 month T bill (TB12T&)
cumulated Kalman residuals

75 r

3 month eurodollar less 3 month T bill (EUROTB3)

5 y e a rT bond less fed funds (CM05FF)

■

i i

6 mo. commercial paper less 6 mo. T bill (CP6TB6)
25 r

fcMatttiffc p § iftp § e ff*f§

FIGURE 3.2

Dynamic response of employment to interest rate spreads
3 month T bill less fed funds (TB3FF)

12 month T bill less 3 month T bill (TB12TB3)

annualized percent growth rates

0.80 r

0.75 r-

0.50

0.25

0.40
0.20
0.00

0.00

0.25

6 month commercial paper less 6 month T bill (CP6TB6)

5 year T bond less fed funds (CM05FF)

0.25
0.00

0.25

0.50

0.75

1 11■ ■ ■ ■ 1■ * ‘ ‘

■■' ■■■ ■■‘ * ■ ■ ■ ■

-1.00

■*‘

BAA corporate bond less 10 ye a rT bond (BAACM10)

0.22

0.45

0.00
0.15

- 0.22

0.00

-0.44
- 0.66

-0.15

■ i . i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i

■ .......................... ■ I I 1 I 1 I I 1 I I I I I 1 1 1 t 1 1.1 L J

FEDERAL RESERVE

months

BANK OF CHICAGO

months

clearly overpredicted real GDP. All of the
private/public spreads followed the same gener
al pattern of mediocre performance from
1973 to 1981, and persistent overprediction of
economic activity thereafter. In general, we
conclude that, although a persistent bias in
forecasting exists in all of the interest rate
spreads we investigated, some of them did
fairly well during most of our sample period,
but failed during periods of large scale financial
restructuring.

forecasting “normal” periods of economic ac
tivity, but periodically fail in predicting reces
sions. Although CM05FF and CM 1OFF follow
a similar pattern between 1973 and 1981, after
1982 their cumulated residuals’ path never
stabilized but plunged to persistently negative
values. Our intermediate term spreads
(TB12TB3 and CM10CM1) failed during all of
the recessions in our sample period (including
the 1973-1975 recession), and developed a
consistently negative bias after 1982, as they

T A B L E 3 .5
M u l t i p e r i o d e n c o m p a s s in g te s ts
( P r o b a b ility v a lu e f o r n u ll h y p o th e s is : X is e n c o m p a s s e d b y Y )
Real GDP (1 quarter)
Y

TB3FF TB6FF TB12FF CM05FF CM10FF TB12TB3 CM10CM1 EUROTB3 CP6TB6 BAACM10

Maximum
P-value

X
TB3FF
TB6FF
TB12FF
CM05FF

n.a.
0.462

0.167

0.105

0.185
n.a.
0.227

—
—
0.093

0.109

0.389

0.062
0.333

0.231
0.797

—

0.106

EUR0TB3

—
0.125

0.215
0.430
0.454

—

CP6TB6

0.066

—

0.072

0.053

CM10FF
TB12TB3
CM10CM1

BAACM10

0.999
n.a.

—
—
n.a.

—
—
0.540
n.a.
0.413
0.699

0.156
0.109
—

—
—

0.098
0.077

n.a.

0.115

—
—
—

—
—

n.a.
—

—

0.055
—

n.a.

0.186

0.053
—

—
—
—
—
—

0.185
0.999
0.227
0.540
0.231
0.797

—

0.699

—

0.186

n.a.

—

0.104

n.a.

0.066
0.104

Real GDP (2 quarters)
TB3FF
TB6FF

n.a.
0.070

0.569

0.467

—

0.569

n.a.

—

—
—

0.155
0.092

0.798
n.a.
0.337

—

—
—

0.798
0.155
0.665

0.055

0.206

0.665
n.a.

—
—

—

—
n.a.
0.271

—

0.271

—
—
0.214

0.256

0.755

0.370

0.353

n.a.

0.071

—

0.126

0.876

—
—

n.a.
—
—

—
—

—
—
0.580

—
—
—

—
—

—
—
0.459

0.710
—
—

n.a.
—

0.222

—
—

0.908

0.991

0.436

0.935

0.807

n.a.
0.936

0.322
n.a.

0.548
0.197

—

n.a.
0.176
0.144

0.092
—
—

—

0.131
0.056
—

—
—

n.a.
0.720

0.170
n.a.

—

0.576
0.062

0.333
0.593

0.261
0.230

—
—

0.979

0.965
0.783
0.930

TB12FF
CM05FF
CM10FF
TB12TB3
CM10CM1
EUR0TB3
CP6TB6
BAACM10

0.093
0.545

n.a.

0.755
0.876
0.222
0.093
0.991

Real GDP (4 quarters)
TB3FF
TB6FF

n.a.
—
—

TB12FF
CM05FF
CM10FF

—

—
—

—
0.142

EUR0TB3

—
0.752

—
0.989

CP6TB6

0.883

0.870

0.840

0.899
0.774

BAACM10

0.500

0.392

0.442

0.863

TB12TB3
CM10CM1

—

n.a.

—

—
0.094

n.a.
0.428

—
0.111

0.548
0.197
0.027
0.176
0.720
0.576
0.593

—

0.560

—

0.115

n.a.
—

n.a.

—

0.989
0.883

0.973

0.569

0.575

n.a.

0.973

NOTES: Values less than or equal to 0.05 are marked with a dash. Sample period is January 1962 - December 1991,
quarterly data.

ECONOMIC PERSPECTIVES

To see how changes in interest rate spreads
may affect a forecaster’s analysis of real eco
nomic activity over time, we look at the dynamic
response of forecasted employment growth rates
to a one standard deviation increase in our family
of spreads. The paths depicted in Figure 3.2
show substantial differences between the re
sponse to changes in the term spreads and chang
es in the private/public spreads. The response of
forecasted employment growth rates when
BAACM 10 increases is a quick dip in the first
two months followed by a fast jump which peaks
after eight months and then dies quickly. The
response to the two shorter term private/public
spreads (EUROTB3 and CP6TB6) follows an
exact opposite path, first declining rapidly for
approximately ten months, and then rapidly flat
tening. With the exception of TB12TB3, the
response paths of the term spreads are all very
similar, with employment growth rates increasing
slowly, peaking at approximately ten months,
and then flattening thereafter. This means that
either a decline in short term interest rates or a
rise in long term interest rates would cause fore
casters to increase their predictions of future
economic activity. The scenario depicted thus
far indicates that the strength of the BAACM10
spread is in very short forecast horizons, as its
impact on real economic activity dies fairly
quickly compared to other spreads. On the other
hand, our analysis shows that the strength of
CP6TB6 is in the short and medium forecast
horizons, while term spreads’ overall impact on
real economic activity is extremely persistent.
The results of our encompassing tests shown
in Table 3.5 are exactly what we would have
expected, given our analysis thus far. That is, we
need to look at both a private/public spread and a
term spread to obtain all of the information nec
essary for forecasting economic activity using
interest rate spreads. This is due to the fact that
term spreads usually perform better at longer
horizons, while private/public spreads have a
stronger predictive power at shorter horizons.
CP6TB6 and TB12FF dominate their respective
groupings. At the four quarter horizon, CP6TB6
no longer contains additional information beyond
that contained in TB12FF. Now, however, a
longer horizon term spread such as CM 1OFF is
also necessary to fully cover the information set.
It is interesting to note that the analysis of all of
the encompassing results indicates that the sepa
ration between the private/public spreads and the
term spreads is not very clear. In fact, at some

FEDERAL RESERVE

BANK OF CHICAGO

forecast horizons the results reverse. This indi
cates that there are common multiple driving
forces in the determination of these spreads, and
that the driving factors associated with longer
horizons of economic activity predominate in the
term spreads, while the common factors that
drive short run performance dominate the pri
vate/public spreads.

4. Composite indicators
Table 4.1 lists the composite indicators we
investigated: the National Bureau of Economic
Research (NBER) Experimental Leading Index
(XLI); the NBER Nonfinancial Experimental
Recession Index10 (XRI2); the Department of
Commerce (DOC) Composite Index of Leading
Indicators (LEAD); the Purchasing Managers’
Index (PMI) of the National Association of Pur
chasing Management (NAPM); the Standard and
Poor’s 500 Stock Index (S&P); the percent
change in sensitive materials prices (SMPS);"
and the Kashyap-Stein-Wilcox “mix”
(KSWMIX), which is the ratio of bank lending to
the sum of bank lending and commercial paper
lending [see Kashyap et al. (1991)]. Note that
the NBER Experimental Leading Index includes
the 10 year Treasury bond/1 year Treasury bond
spread and the 6 month commercial paper/6
month Treasury bill spread, while the Depart
ment of Commerce Composite Index of Leading
Indicators includes real M2, all of which have
been discussed in previous sections. The two
composite leading indicators and the NBER
Nonfinancial Experimental Recession Index are
designed to predict economic activity at a six
month horizon, although the optimization for the
Department of Commerce Index is not as specifTABLE 4.1

Classical goodness-of-fit statistics
R2

Correlation
with real GDP

P-value

XLI

0.455

0.547

0.0000

XRI2

0.385

-0.649

0.0000

LEAD

0.405

0.600

0.0000

PMI

0.265

0.632

0.0005

S&P

0.205

0.185

0.0222

SMPS

0.232

0.278

0.0045

KSWMIX

0.243

0.316

0.0023

Indicator

Rank

NOTE: Sample period is January 1963 - December 1991,
quarterly data.

ic as either of the NBER indices.
TABLE 4.2
Except for S&P and LEAD, which
Multiperiod forecasts, in-sample
are annualized log differences, all
Real GDP
of the indicators in our family of
'I quarter
2 quarters
4 quarters
composite indicators are used in
Indicator
Rank
R2
Rank
R2
R2
Rank
levels. Also, because data on the
XRI2 start in January 1962, our
1
1
1
XLI
0.455
0.568
0.401
sample period for this family of
XRI2
0.382
3
0.316
3
0.168
6
indicators starts in January 1963.
0.341
LEAD
0.405
2
2
0.247
2
Goodness-of-fit tests in Table
PMI
4
7
0.265
0.203
5
0.173
4.1 show that, except for XRI2, our
7
7
S&P
0.205
0.216
5
0.152
composite indicators have a posi
SMPS
0.232
6
0.206
6
0.229
3
tive correlation with contemporane
ous economic activity. XRI2 has
0.249
4
KSWMIX
0.243
4
5
0.193
the strongest correlation with real
NONE
0.117
0.117
0.072
8
8
8
GDP in absolute terms, while XLI
has the strongest fit to the model as
NOTE: Sample period is January 1963 - December 1991, quarterly data.
it ranks first according to its R2.
LEAD and XRI2 also show consid
erable strength as their R2s rank second and third,
sionary periods. As expected, XRI2 is our best
performer during recessions.
respectively. The predictive power of our family
The cumulated Kalman residuals in Figure
of composite indicators is then tested in-sample
4.1 show some striking similarities and some
at different forecast horizons. The results report
ed in Table 4.2 show that XLI and LEAD contin
differences in actual performance across these
indicators. Except for KSWMIX, all of our
ue to perform very well at all forecast horizons,
while XRI2 loses strength at the four quarter
composite indicators have overforecasted real
horizon. PMI and S&P continue to show
GDP over time, as their cumulated residuals
are consistently negative. This bias is clearly
weakness, especially in the long run, while
evident during recessions and becomes more
SMPS’ performance slightly improves at the
four quarter horizon.
dramatic after 1980. After 1982, while the
negative bias is exacerbated in XLI and S&P,
The results of out-of-sample Kalman tests
the path becomes somewhat more stable for
in Table 4.3 show a picture very similar to the
in-sample results, as XLI continues to rank first
most of our indicators. XRI2 is our best per
former during this period, which is not surprisacross horizons. LEAD continues to rank sec
ond, except for a slight deteriora
tion in the four quarter forecast
TABLE 4 .3
horizon where it ranks third. XRI2
has again a strong predictive power
Kalman multiperiod forecasts, out-of-sample
in the short run, while its perfor
______
Real GDP
mance worsens at the four quarter
1 quarter
2 quarters
4 quarters
horizon. XRI2’s behavior is ex
Indicator
RMSE
Rank
RMSE
Rank
RMSE
Rank
pected, however, as the indicator
XLI
1
1
1
3.246
2.376
2.392
was created to forecast recessions
XRI2
3.427
3
3.026
with a six month horizon.
3
2.758
5
Under different circumstances
LEAD
3.307
3.024
2
2
2.669
3
we notice that XLI loses some of its
PMI
4
4
3.838
3.319
6
2.736
strength outside of “normal” eco
3.964
4
S&P
6
3.253
2.758
6
nomic activity, as shown in Table
SMPS
3.914
5
3.306
5
2.612
2
4.4. That is, XLI’s predictive pow
KSWMIX
3.377
4.078
8
8
2.846
8
er is slightly weaker during both
recessions and expansions. On the
NONE
4.052
7
7
7
3.369
2.799
other hand, LEAD performs well
NOTE: Sample period is July 1973 - December 1991, quarterly data.
during expansions, although its
performance worsens during reces

ECONOMIC PERSPECTIVES

The dynamic responses of fore
casted
employment growth rates to
Kalman 1 qu^termb^d'fp^eie^s in
changes in our composite indicators
in Figure 4.212 show somewhat simi
_________________ Raal GDP
._
lar patterns for XLI and LEAD,
Actual
Recession
Expansion
where the response peaks quickly
RMSE
Rank
Indicator
RUrf
RankRMSE_ —Bank.
within approximately five months.
1
4.65‘n
XLI
3.246
From the peak, both graphs exhibit
2
2
2.895
significantly different behaviors.
3.427
4.321
3
XRI2
3
1
3.226
The
path in the XLI graph stabilizes
3.307
2
5.148
LEAD
1
4
2.814
for four to five months and then
4
5.879
PMI
3.838
4
3
3.300
drops off before the end of the year,
8
3.964
5.919
6
S&P
6
3.460
while the path in the LEAD graph
3.914
5.711
5
5
SMPS
5
3.460
falls more quickly and more dramat
4.724
3
KSWMIX
4.078
8
ically, until the impact of the indica
3.941
8
tor on real economic activity disap
5.894
7
4.052
7
NONE
7
3.588
pears. The path of XRI2 is inverted
instead when compared to the path
daU
NOTE: Sample period is July 1973 December 1991, quarterly
of the two leading indicators. In
fact, as the graph shows, the reing since the index was originally developed in
ponse path plunges very rapidly during the first
response to the failure of XLI to forecast the
tve months, then increases for another six
1990-1991 recession.
months, and finally stabilizes thereafter. The

FEDERAL RESERVE

TAtJLE 4.4

BANK OF CHICAGO

FIGURE 4.1

NBER Experimental Leading Index (XLI)

S&P 500 Stock Index (fi&P)

cumulated Kalman residuals

cumulated Kalman

25 r

-25

-75

NBER Nonfinancial Recession Index (XRI2)

Change in sensitive materials prices (SMPS)

50 r

50 r -

■

-50

,75 * I ■ I ..............I l I I I I I I I 1_ i
DOC Composite Index of Leading Indicators (LEAD)

Bank lending/(bank lending + CP) ratio (KSWMIX)

50 r

-25

Purchasing Managers’ Index (PMI';
50 r

response path of employment to changes in
PMI and SMPS shows dramatic jumps in fore
casted growth rates within the first two months.
Employment growth then steadily falls in PMI
while it flattens in SMPS. The S&P graph
shows a path similar to that depicted in the PMI
graph, except for a rapid drop in the first
month. It is interesting to note that all of these
dynamic response paths are virtually insignifi

cant at the one year mark, although the initial
impact on real economic activity is fairly strong
and well defined. Finally, as a group, these
indicators seem to hold a lot of information
about short run changes in economic activity,
with most of that information centered at the
three to nine month horizon.
The encompassing results in Table 4.5
show that XLI strongly dominates this entire

ECONOMIC PERSPECTIVES

FIGURE 4.2

Dynamic response of employment to composite indicators
NBER Experimental Leading Index (XLI)

Purchasing Managers’ Index (PMI)

annualized percent growth rates

NBER Nonfinancial Recession index (XRI2)

DOC Composite Index of Leading Indicators (LEAD)

family of indicators, especially at the two and
four quarter forecast horizons. At the one quar
ter horizon, both LEAD and XRI2 are not en
compassed by any of the other indicators.
These results are not surprising in light of the
statistical results discussed earlier and the fact
that XLI was designed to provide the “best”
forecast of economic activity at a six month
horizon, using virtually all of the macroeco
nomic data available.
5. M ix in g m o d els fo r real G D P

This section analyzes those indicators
drawn from the previous sections that contain
independent information and did well in the
out-of-sample Kalman rankings. The indicators
are subjected to another round of encompassing
tests and rankings. Finally, the usefulness of

FEDERAL RESERVE

BANK OF CHICAGO

Change in sensitive materials prices (SMPS)

these final indicators is assessed in the context of
a time varying forecast mixing model.
Table 5.1 presents the Kalman forecast
RMSEs for the one, two, and four quarter horizon
forecasts of real GDP. For the one quarter hori
zon the best indicators are the NBER composite
indicators (XLI and XRI2), and the Department
of Commerce Composite Index of Leading Indi
cators (LEAD). The spreads and real M2 (M2R)
do the worst at this short horizon, but all of the
remaining indicators do contribute information
beyond the own past history of GDP (NONE).
At the two quarter horizon, the best indicator is
the NBER Experimental Leading Index (XLI)
with the 12 month Treasury bill/federal funds
spread (TB12FF) coming in a distant second:
XLI is 14 percent more accurate than TB12FF.
This is not surprising since XLI was constructed
by Stock and Watson to produce the “best” fore-

as the best monetary aggregate
considered here. Finally, notice
Kalman residuals for surviving indicators
that the 6 month commercial
paper/6 month Treasury bill
Real GDP
1 quarter
2 quarters
4 quarters
spread (CP6TB6) did not make
Indicator
RMSE
Rank
RMSE
Rank
RMSE
Rank
the final list at the two quarter
forecast horizon, but it is a com
4
2.754
EUR03
3.622
3
n.a.
n.a.
ponent of XLI.
FF
n.a.
n.a.
n.a.
2.160
2
n.a.
At the four quarter horizon,
3.674
4
M2R
6
2.844
5
2.219
three indicators are undominated:
4
CP6TB6
3.656
5
2.760
n.a.
n.a.
FF, M2R, and TB12FF. The
NBER Experimental Leading
TB12FF
7
2.002
1
3.753
2.751
2
Index (XLI) does not contain
CM10FF
n.a.
n.a.
2.161
3
n.a.
n.a.
independent in formation beyond
XLI
1
1
2.392
3.246
2.376
5
these indicators. CM 1OFF is
XRI2
3.427
3
n.a.
n.a.
n.a.
n.a.
included in the final list for three
LEAD
3.307
2
n.a.
n.a.
n.a.
n.a.
reasons: it is undominated at the
15 percent significance level, it
4.052
2.799
NONE
8
3.369
6
6
covers the NBER Experimental
NOTES: n.a.: The indicator is not an initial survivor at this forecast horizon.
Leading Index better than the
Sample period is July 1973 - December 1991, quarterly data.
shorter end of the term structure
(TB12FF), and it is interesting to
include a long term spread at this horizon since
cast of the growth in economic activity over the
Stock and Watson found a long term spread
six month horizon considered here. Turning to
useful at the two quarter horizon.
the four quarter horizon, it seems surprising that
The next step is to combine these forecasts
XLI comes in last after TB12FF, the federal
into a forecasting model (for each horizon)
funds rate (FF), the 10 year Treasury bond/
which allows the weights on the indicators to
federal funds spread (CM10FF), and M2R.
vary over time depending upon their recent
This demonstrates again that the choice of
performance. Essentially we would like the
economic indicators depends critically upon the
model to take the following form:
horizon being forecasted: at the four quarter
growth horizon, a different collection of interest
(3) F, = K f or(Ah + <t\ J°r(B )x + §Mfor (C)t ;
rate spreads than the ones selected by Stock and
Watson is useful.
where for(A) represents a forecast based upon
New encompassing results are displayed in
indicator A and Ft is the combined forecast.
Table 5.2. At this point, the purpose of these
The weights <t>.f should be nonnegative and sum
tests is to narrow the list of indicators in a struc
to one: in this case, the indicator’s weight is a
tured manner. However, a rigid adherence to a
direct measure of its importance for the fore
statistical significance level is not maintained if
cast. When the weights vary over time accord
an indicator is relatively useful and of indepen
ing to their forecast accuracy, the time path of
dent interest. At the one quarter horizon, XLI,
the weights provide a direct measure of the
XRI2, and LEAD are each undominated and
indicators’ reliability over time. We implement
together sufficient. The two quarter horizon is
this model in the following way. Let eit2be the
more interesting. Three indicators are clearly
sum of (recent) squared forecast errors based
necessary. XLI is undominated, and TB12FF is
upon indicator /’s model. In this paper, we take
undominated at the 10 percent level. The 3
“recent” to be one year of known forecast errors
month eurodollar rate (EUR03) is not covered
(4 quarters). Let avgr(e.-2) be the average of the
by these two indicators, and it is not dominated
e.(2s at time t and p. be the average of e.(2at the 11 percent significance level. M2R is
avgt( e 2) over time. Then (ft is defined to be:
also included in this final cut for two reasons:
it is only covered by XLI at the 14 percent
(4) <J>,= a. - (3, (e,2- avg/e.'2) - \i.), a , P,> 0 ;
significance level and it is of inherent interest

TABLE 5.1

ECONOMIC PERSPECTIVES

TABLE 5.2
M i x e d m u l t i p e r i o d e n c o m p a s s in g te s ts
(P r o b a b ilit y v a lu e f o r n u ll h y p o th e s is : X is e n c o m p a s s e d b y Y )
Real GDP (1 quarter)
Y

EUR03

M2R

CP6TB6

TB12FF

CM10FF

XLI

XRI2

LEAD

Maximum
P-Value

X
n.a.

0.100

—

0.107

—

0.107

0.958

n.a.

—

0.067

—

0.144

—

0.958

—
—

n.a.

0.055

0.168

n.a.

—
—

—

—
—

0.168

CP6TB6

—
—

0.288

—

0.288

TB12FF

0.186

0.193

—

n.a.

—

0.453

—

0.453

CM10FF

0.168

0.098

—

0.260

n.a.

0.809

—

0.809

—

n.a.

—

0.001

EUR03
FF
M2R

XLI
XRI2

—

n.a.

—

0.012

LEAD

—

n.a.

0.030

—
0.161
—
—
n.a.
0.228
—
—

—
—
—
—
—
n.a.
—
—

—
—
—
—
—
—
—
n.a.

—

—
—
—
—
—
—
—
—
n.a.

0.110

—

—
—
0.139
0.304
0.062
0.514
n.a.
0.370
0.761

Real GDP (2 quarters)
n.a.

0.110

—

0.868

n.a.

—

M2R

—
—
0.064
0.076
—
—

—
—
0.082
—
—
—

—

n.a.
—
—
—
—
0.066
0.230

—
n.a.
—
—
—
—
0.088

XRI2

n.a.
—
—
0.270
—
—
—
0.791

0.609
n.a.
—
0.327
—
—
—
0.817

LEAD

0.102

0.122

EUR03

CP6TB6
TB12FF
CM10FF
XLI
XRI2
LEAD

0.868
0.139
0.304
0.082
0.514
0.000
0.370
0.761

Real GDP (4 quarters)
EUR03

FF
M2R
CP6TB6
TB12FF
CM 10FF
XLI

—
—
n.a.
0.420
—
—
0.105
0.959
0.960

—
—
—
n.a.
—
—
—
0.364

—
—
—
0.850
n.a.
0.147
0.157
0.839

—
—
—
0.779
—
n.a.
0.298
0.711

—
—
—
0.401
—
—
n.a.
0.939

—
—
—
—
—
—
—
n.a.

—
—
—
—
—
—
—
0.690

0.609
0.023
0.007
0.850
0.011
0.147
0.298
0.959

—

0.240

0.300

0.420

—

n.a.

0.960

NOTES: Values less than or equal to 0.05 are marked with a dash. Sample period is January 1963 - December
1991, quarterly data.

where the parameters a and (3 can be estimated
by a linear regression model if the nonnegativi
ty constraints are ignored, or nonlinear meth
ods if the constraints are imposed. Since e.f2avg((e.(2) - (j.. is mean zero by construction, the
time variation due to the (3s nets out to zero
over time. Consequently, the a estimates repre
sent the average weight associated with each
indicator forecast. However, over short periods
of time when an indicator’s forecast misbe
haves, its errors e.2 will be larger than the aver
age errors; this will lead to the indicator’s
forecast receiving a temporarily smaller weight.
Table 5.3 displays the estimated a weights
for these models. The one quarter results indi

FEDERAL RESERVE

BANK OF CHICAGO

cate that XLI is the most reliable, having an
average weight of .533 in the combined fore
cast. The other indices (XRI2 and LEAD)
received about equal shares of the remaining
weight. The (3s in this case are estimated to be
zero; that is, there is no significant contribution
to the forecast accuracy by allowing the
weights to vary over time.
The two quarter results are more interest
ing. As was expected from the encompassing
results, XLI receives the bulk of the weight in
the final forecast (62 percent). This agrees with
the analysis of Stock and Watson who con
structed the NBER Experimental Leading In-

TABLE 5.3

Relative weights in mixing regressions
Indicator

_____________ Real GDP_____________
1 quarter
2 quarters
4 quarters
*

0.093
(0.260)

n.a.

0.105
(0.209)

M2R

0.414
(0.178)

CP6TB6

0.187
(0.227)
*

TB12FF

0.103
(0.238)

0.368
(0.259)

CM10FF

n.a.

XLI

0.533
(0.174)

0.617
(0.197)

0.114
(0.212)
*

XRI2

0.214
(0.155)

n.a.

LEAD

0.253
(0.206)

n.a.

EUR03
FF

n.a.

NOTES: Numbers in parenthesis are standard errors,
n.a.: The indicator is not an initial survivor at this
forecast horizon.
(*): The indicator is encompassed by other indicators at
this horizon.

dex explicitly for its ability to forecast at this
two quarter horizon. We do find that M2R
receives a substantial weight (19 percent), while
the TB12FF spread is at 10 percent and EUR03
is at 9 percent. Figure 5.1 graphs the time path
of the (|) weights for these four indicators, as well
as the two quarter GDP forecast and actual.
Notice first that the NBER Experimental Lead
ing Index forecasts have been quite reliable,
only once dropping below a 50 percent weight
in the combined forecast. M2R, however, has
varied dramatically in its usefulness, going
negative on two occasions: in 1976 and imme
diately following the 1981-82 recession. During
that recession, M2R did not forecast negative
growth at any time (although it did in the 1980
recession), whereas EUR03, TB12FF, and XLI
did forecast negative growth during some por
tion of this recession.13 This poor performance
is captured in the time varying model by de
creasing the weight on the M2R forecast tempo
rarily until it begins to improve. On the other
hand, during the most recent recession M2R has
gone above a 50 percent weight (keep in mind
that the average weight for M2R is .19). During
this time, M2R has grown only slowly and this

led to a forecast of slow growth during 1991
(see Figure 5.1). At this same time, EUR03,
TB12FF, and XLI signalled substantially higher
growth than was realized. Each of these indica
tors is currently receiving less than its average
weight. Consequently, the time varying mixing
model finds that M2R has been an unusually
useful indicator during the recent recession,
despite its generally erratic performance at this
horizon versus its relative failure at the twelve
month horizon.
By contrast the four quarter horizon results
in Figure 5.2 appear to be a picture of stability.
M2R and TB12FF receive the largest uncondi
tional weights, 41 percent and 37 percent re
spectively. FF and CM 1OFF receive consider
ably less (around 10 percent each). The graphs
of the time varying weights indicate that, at this
horizon, M2R and TB 12FF have been reason
ably reliable indicators, always staying near
their unconditional weight. On the other hand,
CM 1OFF has been extremely unreliable, going
to zero or negative in 1987-88 and during the
recent recession.
The contrast between the dominance of
XLI at the two quarter forecast horizon and its
submissiveness at the four quarter horizon dem
onstrates strongly the need for a different set of
indicators for each forecast horizon. The useful
ness of TB 12FF and M2R for forecasting real
GDP at the one year horizon indicates that a
different index would be constructed if this
forecast horizon was the relevant objective. A
note on standard errors is in order. Examination
of Table 5.3 indicates that the standard errors
associated with the parameters of these mixing
models are fairly large. This is not surprising in
light of the high degree of collinearity that
would be expected of a set of reasonably suc
cessful forecasts. In fact, it is typically the case
that only the strongest indicator at a given hori
zon is statistically significant. All this is saying
is that the relative weights among successful
indicators are subject to substantial uncertainty
and that the marginal information after the first
one or two indicators quickly drops toward 0.
Nevertheless, the point estimates and time paths
of these relative weights provide a useful bench
mark, even though the precision with which
they are estimated would not change strongly
held prior beliefs.

ECONOMIC PERSPECTIVES

FIGURE 5.1

Mixing results
2 quarter ahead forecast vs. actual
3 month eurodollar (EUR03)

Real M2 (M2R)

annualized growth rates

annualized growth rates
9.0 r
6.0
3.0

0.0
-3.0

- 6.0

I I I I l I

...........

NBER Experimental Leading Index (XLI)
9.0 r

3.0

0.0
-3.0
- 6.0

1973

Forecast reliability weight
3 month eurodollar (EUR03)

Real M2 (M2R)

weight

NBER Experimental Leading Index (XLI)

C onclusion

Four things became clear as the preceding
analysis developed. First, the forecast horizon
is an essential aspect of choosing and evaluat
ing indicators. Second, substantial information

FEDERAL RESERVE

BANK OF CHICAGO

resides in the term and private/public spreads
and both of these seemingly very different
types of spreads seem to include common as
well as independent information. Third, while
composite indicators may be extremely useful,

they are only as good as their design allows.
The NBER Experimental Leading Index does
very well at precisely what it was designed for,
that is, forecasting economic activity at a six
month horizon. Its usefulness beyond this hori

zon is far more limited than prior analysis
would have suggested. Fourth, the analysis also
suggests that the type of general purpose target
variable that the old monetary targeting litera
ture sought probably does not exist, at least in

ECONOMIC PERSPECTIVES

terms of real economic activity. Policymakers
will continue to need to mix information ac
cording to their current focus. Mixing models

of the sort used in this article are meant to be
preliminary work in this regard.

FOOTNOTES
'The NBER Experimental Leading Index (XLI) developed
by James Stock and Mark Watson is a clear exception,
since it was created as a single “best” indicator of economic
activity [see Stock and Watson, (1989b)].
2The following examples illustrate the notation we will use
in the Methodology section to indicate different classes of
tables: Table 1 refers to the first table in each family of
indicators, Table _.2 refers to the second table in each
family, and so forth.
3It should be noted that these are not iterated VAR fore
casts, rather, the forecast parameters are chosen to maxi
mize performance at the forecast horizon specified. This
can be thought of either as a state space estimation mini
mizing the t+ k forecast variance or as a simple OLS regres
sion with the t+ k growth rate as the dependent variable.
This avoids any problem that might result from an indicator
that performs poorly at high frequencies interfering with
longer frequency forecasting.
4The standard deviation measure used is the one from a
bivariate VAR for the indicator and the measure of eco
nomic activity. This is used to approximate the average
size of the movement in the indicator series.
5This is basically the same as an impulse response function
except that the identifying assumption is not derived from a
specific decomposition of the error matrix, but from the
assumed path of the actual series, that is, the indicator
changes given the level of current activity. This is arithmet
ically equivalent to an impulse response function using a
Choleski decomposition with the indicator ordered last.
6The monetary base is the sum of reserve balances at the
Federal Reserve Banks and currency in circulation.

7L is the broadest monetary aggregate, consisting of M3
plus the nonbank public holdings of U.S. savings bonds,
short term Treasury securities, commercial paper, and
bankers’ acceptances, net of money market mutual fund
holdings of these assets.
"These are the only commonly used spreads available for
the entire sample period.
9We used the 10 year Treasury constant maturity bond rate
because the 7 year bond rate, which might be preferred, is
not available for the entire sample period.
l0The NBER Nonfinancial Experimental Recession Index,
which estimates the probability that the economy will be in
a recession six months later, is based on a set of nonfinan
cial leading indicators. (See NBER Press Release, January
30, 1991.)
"SMPS is calculated as the quarterly average of the month
ly changes in sensitive materials prices, smoothed. The
sources for the monthly data are: U.S. Department of
Commerce, U.S. Department of Labor, and the Commodity
Research Bureau, Inc.
12The dynamic response graph for KSWMIX is not shown
because data on the mix are available only on a quarterly
basis, while employment data are monthly.
l3It is useful to remember that the primary components of
the NBER Experimental Leading Index are the 6 month
commercial paper/6 month Treasury bill spread and the 10
year Treasury bond/1 year Treasury bond spread. So it
should not be surprising that the NBER Experimental
Leading Index misbehaved during this period when the 3
month eurodollar rate and the 12 month Treasury bill/
federal funds spread also misbehaved.

REFERENCES

Bernanke, Ben S., “On the predictive power of
interest rates and interest rate spreads,” New
England Economic Review, November-December, 1990, pp. 51-68.
Chong, Y. and D. Hendry, “Econometric
evaluation of linear macro-economic models,”
Review of Economic Studies, 53, 1986, pp.
671-690.
Estrella, A. and G. Hardouvelis, “The term
structure as a predictor of real economic activi
ty,” Journal of Finance, 46, 1991, pp. 555-576.

FEDERAL RESERVE

BANK OF CHICAGO

Friedman, B. and K. Kuttner, “Why does the
paper-bill spread predict real economic activi
ty?” forthcoming in James H. Stock and Mark
W. Watson eds., New Research in Business
Cycles, Indicators and Forecasting, University
of Chicago Press and the NBER, 1992.
Kashyap, A,, J. Stein and D. Wilcox, “Mone
tary policy and credit conditions: evidence
from the composition of external finance,”
Federal Reserve Board, Working Paper No.
154, 1991.

Laurent, Robert D., “An interest rate-based
indicator of monetary policy,” Economic Per
spectives, Federal Reserve Bank of Chicago,
January/February, 1988, pp. 3-14.
National Bureau of Economic Research,
Press release, January 30, 1991.
Sims, Christopher A., “Interpreting the macroeconomic time series facts: the effects of mon
etary policy,” manuscript, 1991.
Stock, J. and M. Watson, “Interpreting the
evidence on money-income causality,” Journal
of Econometrics, Vol. 40, 1989a, pp. 161-182.

___________ , “New indexes of coincident
and leading economic indicators,” in NBER
Macroeconomics Annual, edited by O. Blan
chard and S. Fischer, The MIT Press, 1989b,
pp. 351-409
Strongin, Steven, “Macroeconomic models
and the term structure of interest rates,” Federal
Reserve Bank of Chicago, Working Paper No.
90-14, 1990.
____________, “The identification of monetary
policy disturbances: explaining the liquidity
puzzle,” Federal Reserve Bank of Chicago,
Working Paper No. 91-24, 1991.

Shaping the Great Lakes Economy
Conference on the Region’s Economy and Development Strategies
Indianapolis, Indiana
October 15, 1992
In conjunction with Indiana University’s Institute for Development Strategies and the
Great Lakes Commission, the Federal Reserve Bank of Chicago will hold a conference at
the University Place Conference Center and Hotel in Indianapolis.
The 1992 conference will focus on the state of the region’s economy and on its
strategies to promote economic growth and development.
Topics featured will include:

■ the state of the region’s economy
and its directions in the 1990s
■ state and regional development
policies and the Federal policy
environment
■ the profound changes now under
way in the manufacturing sector’s
organization, technology, and
labor force

If you are interested in receiving further
information and registration materials,
please contact:
Great Lakes Commission
The Argus II Building
400 Fourth St.
Ann Arbor, Michigan 48103-4816
Phone: (313) 665 9135
FAX: (313)665 4370

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Full text of Economic Perspectives (Federal Reserve Bank of Chicago) : September/October 1992, Volume XVI, Issue 5

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