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Economic Review
Federal Reserve Bank
of Cleveland
Quarter III 1985

The Impact of Bank Holding Company
Consolidation: Evidence from
Shareholder Returns ................................ 2
Several states have altered laws to give multi­
bank holding companies (MBHCs) the option
to convert to branch banking organizations by
merging their affiliates into a single large unit.
Economist Gary Whalen uses the event study
technique to estimate the efficiency impact
that such consolidation has had on a sample
of 21 BHCs that did this from 1976 to 1983.
The National Debt:
A Secular Perspective

.........................

11

Economists John B. Carlson and E.J. Stevens
examine the dynamics of federal debt over the
past 40 years. They believe that conditions
following World War II that led to a decline in
federal debt relative to GNP are not likely to
recur and that raising taxes and/or cutting
spending is the only sure way to avoid unprec­
edented peacetime levels of future federal debt.
The Ohio Economy:
A Time Series Analysis ....................... 25
In a study of the Ohio economy, economist
James Hoehn and research assistant James
Balazsy design a simple time series method of
analysis that can be applied to other regional
economies. They find, among other things,
that employment data from the establishment
survey are the most useful indicators of con­
ditions and that most regional variation is
due to national forces.
Economic Review is published quarterly by the
Research Department of the Federal Reserve Bank
of Cleveland, P.O. Box 6387, Cleveland, OH 44101.
Telephone: 216/579-2000.
Editor: William G. Murmann. Assistant editor:
Meredith Holmes. Design: Jamie Feldman. Type­
setting: Lucy Balazek.
Opinions stated in Economic Review are those of
the authors and not necessarily those of the Fed­
eral Reserve Bank of Cleveland or of the Board of
Governors of the Federal Reserve System.
Material may be reprinted provided that the source
is credited. Please send copies of reprinted materi­
als to the editor.

Gary Whalen is
an economist at the
Federal Reserve Bank
o f Cleveland. The
author would like
to acknowledge the
comments o f Jeffrey
Born and the re­
search assistance
o f James Balazsy.

1. See Mullineaux
(1976, p. 277).
2. See the succinct
summary o f William­
son 's views and sup­
porting empirical
evidence in A rm our
and Teece (1978).
3. It is also possible
that the expected net
benefits o f consoli­
dation are dependent
on size and other
characteristics o f a
particular MBHC.
4. In many o f these
states, MBHCs par­
tially consolidated
their subsidiaries.
Such companies were
not included in this
study because o f the
heterogeneous nature
o f their organiza­
tional changes.
5. The states are
New York, Florida,
Ohio, New Jersey,
Virginia, Alabama,
and Tennessee. The
number o f companies
drawn from each
state is seven, three,
three, one, four, two,
and one respectively.

The Impact of Bank
Bolding Company
Consolidation:
Evidence from
Shareholder Returns
by Gary Whalen

Many states have chosen to legally restrict
intrastate branching by banks to some degree.
In a large proportion of such states, banks are
able to circumvent the prohibition on state­
wide branching because they are permitted to
adopt a multibank holding company (MBHC)
form and to acquire affiliate banks through­
out the state. However, because subsidiary
banks in a MBHC continue to be separately
incorporated entities, and because a number
of legal-regulatory impediments to full organi­
zational integration exist, it has been argued
that MBHCs are imperfect substitutes for
branch banking systems.1 That is, MBHCs
may be less able to exploit size-related econo­
mies than pure branch banking organizations.
On the other hand, researchers such as
0. Williamson have argued that it might be
optimal for relatively large firms to operate as
multi-divisional holding companies, rather
than to merge all operating units into a single
subsidiary.2
Beginning with New York in the mid-1970s, a
number of states have amended their branch­
ing laws to permit MBHCs to transform their
affiliates into branches by merging them into
one large bank subsidiary (or several large
ones). Interestingly, in states where such
activity has been authorized, MBHCs have
chosen to consolidate their subsidiary banks
in varying degrees suggesting that the man­
agement of competing companies disagree about
the expected net benefits of consolidation or,
alternatively, about the costs of retaining the
MBHC form .3
No empirical evidence currently exists on
the net benefits of holding company consolida­
tion. Such evidence could be of value because
legislation authorizing such activity is cur­
rently being considered in several states.
Measurement of the impact of total consoli­
dation on the equity value of the consolidating
MBHC is the subject of this study.4
In brief, the expected net benefits of consoli­
dation are inferred by examining the behavior
of the daily stock returns of a sample of 21
bank holding companies in seven states when
the intention to merge their affiliates is first
announced.5 The behavior of their stock returns

6. See Fama et al.
(1969).
7. For various appli­
cations o f the event
study technique, see
any o f the various
studies cited in the
references.
8. See the discussion
in Eisenbeis et al.
(1984, p. 893) and
in Jain (1985,
pp. 2 2 1 -2 2 ).
9. There is somefrag­
mentary survey evi­
dence that suggests
that the impact o f con­
solidation might be
negative, particularly
in the short run.
There are several
reasons this might be
the case. Benefits o f
consolidation could
be long-term and/or
non-pecuniary. For
example, consolida­
tion might perm it the
parent to lim it sub­
sidiary risk-taking.
In addition, loss o f
subsidiary indepen­
dence might lower
morale and produc­
tivity. See the discus­
sion in the Associa­
tion o f Bank Holding
Companies (1978,
pp. 2 4 -2 9 ).
10. Some responding
M BHCs reported
that organizational
change was under­
taken in response to
financial difficulties.
See Association o f
Bank Holding Com­
panies (1978, p. 34).

over some period containing the announcement
date presumably reflects investor estimates
of the impact of the organizational change on
the future profitability and market value of
the banking organization. The event-study
framework first used by Fama et al. (1969)
is employed.6

I. The Event Study Framework
In the event-study framework, the focus is on
the observed behavior of a sample of firms’
stock market returns, actually the “ abnormal”
portion of these returns, around the time at
which some material development (the event)
potentially affecting each firm’s market value
is initially made known .7 “Abnormal returns”
presumably reflect the capital market’s esti­
mate of the expected net impact of the devel­
opment on the future profitability and market
value of the firm. Abnormal returns may be
observed prior to the event either because of
market anticipation or leakage of information
about the event. In an efficient market, only
normal returns should be evident after the new
relevant information is fully digested by mar­
ket participants. However, if the announcement
represents a strategic management decision,
it is possible that abnormal returns prior to the
event may precipitate rather than reflect the
impact of the decision. The time pattern of
the abnormal returns may suggest the direc­
tion of causality.8
In this study, the critical event is each
MBHC’s first public announcement of the
intention to consolidate all of its subsidiary
banks and effectively transform itself into a
branch banking organization. Positive abnor­
mal returns around the event date suggest
that the announced consolidation is expected
to boost future profitability and to generate
net benefits for holding company shareholders.
The interpretation of negative abnormal
returns is more difficult. Such returns may
indicate that investors expect the change to
depress the holding company’s market value.9

Alternatively, because the decision to con­
solidate is a strategic one, the announcement
might be the result rather than the cause of
the negative abnormal returns.10Again, the tim­
ing of the returns should suggest which one
of these interpretations is correct. In particular,
negative abnormal returns very close to the
announcement date suggest that the announce­
ment is responsible for the negative returns,
rather than the reverse.
It should be noted that the discovery of signif­
icant abnormal returns only provides insight
on the consolidation impacts expected by share­
holders. The presence of abnormal returns
does not permit the analyst to unambiguously
determine the effect of consolidation on social
welfare. For example, positive abnormal re­
turns could reflect either expected gains in effi­
ciency due to consolidation or expected prof­
itability increases due to consolidation-related
changes in competition at the local level. In
the latter case, the shareholders gain comes at
the expense of holding company customers.

II. Methodology
The basic procedure used to calculate the
abnormal returns for each company in this
study is the same as that used in a large
number of previous event studies published
to date.
First, the event date for each company had
to be determined. This date was defined to be
the date on which a company’s intention to
consolidate was first reported in the financial
press. These dates were discovered by search­
ing the indexes of three publications: The Wall
Street Journal, The American Banker, and
Funk and Scott’s Index of Corporations and
Industries. Thus, announcement dates (AD),
rather than effective dates, were used as event
dates. In efficient markets, investors presum­
ably react around the time at which a material
development is announced rather than when
the announced action is taken, and so cause
the firm’s stock price and market value to
adjust around announcement dates rather
than effective dates.

11. Different esti­
mation periods were
tried, but this did not
change the reported
results in any mate­
rial way.
12. A number o f
researchers have
found that there is
a strong industry
effect on the returns
o f bank stocks and
have argued that this
influence should
be controlled fo r in
event studies o f bank­
ing firm s. See Eisenbeis et al. (1984,
p. 883), Shick and
Sherman (1980),
and Keen (1983).
13. Alternative
versions o f equation
(2) were estimated
using techniques sug­
gested in Scholes
and Williams (1977)
and Dimson (1979)
to correct fo r statis­
tical problems caused
by infrequent secu­
rities trading. In
addition, standar­
dized abnormal re­
turns were generated
using the technique
reported in Linn and
M cConnell (1983).
Neither o f these two
methods produced
results different from
those reported and
so are not presented.
14. The average
proportion o f the
organization’s total
assets accounted fo r
by the lead bank fo r
these three large hold­
ing companies was
about 98 percent, vs.
about 5 6 percent fo r
the rest o f the sample.

Second, an interval around each company’s
event date, during which the impact of the
event is expected to be discernible had to be
determined. In this study, daily stock return
data were used, and abnormal returns over
the interval beginning 120 trading days before
and ending 90 trading days after each com­
pany’s event date were generated and exam­
ined.11 This period will be referred to here as
the examination period.
Third, one of a variety of methods had to
be used to generate “ normal returns” for each
company over the examination period. The first
step in this process was to estimate a form
of the “ market model” equation for each
company over the 140-day period beginning
260 trading days before its event date. This
140-day period is referred to as the estimation
period. In the market model, the stock returns
of a firm in any period are presumed to be a
linear function of returns on a broad market
index and occasionally of a second factor, the
returns on an industry index. In this paper,
the reported results were obtained using a twofactor version of the market model.12 Sym­
bolically, the estimated equations had the fol­
lowing general form:
(1)

Rjt = aj + bijRmt + b2jRbt + ejt,

where
Rjt = daily continuously com­
pounded rate of return of
company j,
Rmt = daily continuously com­
pounded rate of return of
Standard and Poor’s
500 Index,
Rbt = daily continuously com­
pounded rate of return of
OTC Index of bank stocks,
ejt = a stochastic disturbance
term with standard prop­
erties, and
a} , bij, b2j = regression coefficients to be
estimated.
“ Normal returns” for each company over the
examination period are simply its predicted
returns obtained using its estimated market

model equation and realized returns on each of
the two stock indices.13
“ Abnormal returns” for each company
over the examination period were generated
by subtracting normal returns from realized
returns. Symbolically, abnormal returns were
calculated using equation (2) below:
(2)

arjt = Rjt - RHATjt,

where
arjt
RHATjt

“ abnormal return” for the
;th company,
the predicted “ normal
return” for th e;th company
obtained using equation ( 1 ).

Because of the possibility that the returns of
various companies might be affected by a vari­
ety of company-specific developments (aside
from the specific event of interest) during the
examination period, the abnormal returns of
each company were not analyzed individually.
Rather, as is typically done in event studies,
various portfolios of subject firms were formed
in event time, and the abnormal returns of
the companies included in the portfolio were
averaged cross-sectionally at each point in
event time over the examination period to
produce a series of average abnormal returns
(AAR). Then this series was cumulated over
various segments of event time to produce
a cumulative average abnormal return meas­
ure (CAAR) for the particular sample of compa­
nies. These steps are represented in equa­
tion (3) and (4), respectively:
J

(3)

AAR, = ( 1 /J)% arj„
;=i

(4)

CAARl2, n = % A A R ,,
t=t\

where
AAR t = the average abnormal
return at event date t,
J = the number of companies
in the sample,
CAARt2, t\ = the cumulative average
abnormal return over the
t2 - 1 \ trading day inter­
val of event time.

The sign, size, and statistical significance of
the cumulative average return measures indi­
cate the capital market’s estimate of the market
value impact of MBHC consolidation and are
the focus of the analysis in this paper.
If the event is perceived to have no signifi-

Table 1 Average and Cumulative
Average Abnormal Returns
Entire sample
Event date

AD-90
AD-85
AD-80
AD-75
AD-70
AD-65
AD-60
AD-55
AD-50
AD-45
AD-40
AD-35
AD-30
AD-25
AD-20
AD-15
AD-14
AD-13
AD-12
AD-11
AD-10
AD-9
AD -8
AD-7
AD -6
AD-5
AD-4
AD-3
AD-2
A D -1
AD
AD +1
AD+10
AD+ 20
AD+ 30
AD+ 40
AD+ 50
AD+ 60

AAR

CAAR

NPa

-.0019
-.0019
.0067
.0055
.0015
-.0043

-.0019
-.0165

8
12

.0006
-.0066
-.0141
-.0188
-.0237
-.0177
-.0194
-.0319
-.0358
-.0402
-.0427
-.0500
-.0580
-.0631
-.0586
-.0551
-.0537
-.0576
-.0608
-.0644
-.0600
-.0582
-.0590
-.0608
-.0621
-.0602
-.0582
-.0585
-.0551
-.0659
-.0645
-.0656
-.0606
-.0577
-.0616

12
10
8

-.0002
-.0025

.0020

-.0016
-.0007
-.0045
.0013
-.0005
-.0032
-.0055
-.0050
.0045
.0034
.0015
-.0039
-.0032
-.0036
.0044
.0018
-.0008
-.0017
-.0013
.0018

.0020
-.0002

.0034
-.0034
-.0024
.0005
-.0008
.0041
-.0018

-.0102

a. Number of companies with positive residuals.

16

9
7

10
8
12
5

10
11
6
3

8
12
12
10
7

8
10
13
9

8
12
9

11

13
7
14
4

12
9

8
10
7

cant impact on firm value, both the average
return and cumulative average return measures
should fluctuate randomly around zero over
the examination period. If, on the other hand,
the event is expected to have a beneficial
impact on future firm profitability and mar­
ket value, a preponderance of the average
abnormal returns in the interval prior to the
announcement date should be positive, caus­
ing the cumulative average abnormal return
measure to be positive as well. A run of neg­
ative average abnormal returns in this period,
due either to perceptions that the costs of con­
solidation will outweigh the benefits, or pos­
sibly to some other exogenous factor, will
cause the cumulative average return meas­
ure to be negative.
If markets are efficient, and the consolidation
announcement is responsible for the average
abnormal returns observed, any marked runup
or decline in the cumulative average return
measure should cease once the information is
fully digested by the market. It seems rea­
sonable to expect that this process should be
complete by the end of the day following the
announcement date.

III. Results
Average and cumulative average abnormal
returns for selected trading days over the
period from 90 trading days before to 60 trad­
ing days after the announcement date for
the entire sample and several subsamples are
presented in tables 1 to 3. The subsamples
exclude one or more very large money center
institutions. The rationale for excluding such
institutions from the analysis is twofold. First,
virtually all of their banking assets were con­
centrated in their lead institution prior to
consolidation. Thus, consolidation might not
strongly influence their market value.14 Sec­
ond, two of these three institutions announced
their consolidation in 1975, when money cen­
ter bank stocks were depressed due to the deep
recession and related large loan losses.

15. Again, it is pos­
sible that MBHCs
consolidate to lower
profit variability,
rather than raise
profitability.

A plot of the CAAR measure for the entire
sample over the complete examination period
appears in figure 1. Plots for the two subsam­
ples are similar and are not included. CAAR
measures calculated over various sub-intervals
of the examination period and associated test

Table 2 Average and Cumulative
Average Abnormal Returns
Excluding Citicorp
Event date

AD-90
AD-85
AD-80
AD-75
AD-70
AD-65
AD-60
AD-55
AD-50
AD-45
AD-40
AD-35
AD-30
AD-25
AD-20
AD-15
AD-14
AD-13
AD-12
AD-11
AD-10
AD-9
AD -8
AD-7
AD -6
AD-5
AD-4
AD-3
AD-2
AD -1
AD
AD +1
AD+10
AD+ 20
AD+ 30
AD+ 40
AD+ 50
AD+ 60

AAR

CAAR

-.0025
-.0015
.0073
.0049
.0017
-.0052
.0005
-.0031
.0018
-.0024

-.0025
-.0142
-.0075
-.0006
-.0057
-.0137
-.0167
-.0203
-.0152
-.0171
-.0307
-.0327
-.0371
-.0397
-.0446
-.0515
-.0560
-.0518
-.0489
-.0467
-.0501
-.0539
-.0563
-.0513
-.0493
-.0508
-.0522
-.0526
-.0495
-.0461
-.0470
-.0451
-.0584
-.0511
-.0569
-.0493
-.0424
-.0514

-.0010
-.0041
.0009

.0012

-.0028
-.0054
-.0045
.0042
.0030

.0022

-.0035
-.0038
-.0024
.0050

.0021

-.0016
-.0014
-.0004
.0032
.0033
-.0008
.0019
-.0027

-.0012
-.0006
-.0008
.0072

-.0020

a. Number of companies with positive residuals.

NPa

7

12

16

11
10
7
9

6
9
7

11

5
9

11
6
3

8
11
11
10
7
7

10
13
9
7

12

9

11

13

6

13
4

12
8
8
10
6

statistics appear in tables 4 to 6. The meth­
ods used to develop the test statistics are de­
tailed in the appendix.15
Examination of the plot and the data in the
tables reveal that beginning roughly 50 to 60
trading days prior to the announcement date,
the CAAR measures turn negative and decline
more or less steadily until the event date. The
results are remarkably similar, regardless of
the sample used. Formal tests indicate that
the negative cumulative average abnormal
return measures calculated from AD - 90 to
AD + 1 are significantly different from zero for
all three samples (see tables 4 to 6).
In the post-announcement period, the CAAR
measures generally fluctuate around the level
attained on AD + 1, which implies that aver­
age abnormal returns are essentially random
during this period. Formal tests confirm that
the CAAR measures calculated in this time
period are not significantly different from zero.
Thus, if one looks only at the cumulative
average return measures calculated beginning
on AD - 90 and ending on AD + 1, the results
suggest that investors expect consolidation to
generate negative net benefits. This finding
raises questions about the motives of holding
company management.15
However, as noted above, the decision to
consolidate is a strategic one and could be
made in response to deteriorating corporate
performance. This suggests that the impact
of consolidation, particularly any positive
impact, might be evident only for a relatively
short time immediately around the announce­
ment date. Accordingly, cumulative average
abnormal return measures and appropriate
test statistics were calculated over a variety of
shorter sub-intervals within the examination
period.
The data in tables 4 to 6 reveal that negative
average abnormal returns in the pre-announcement period were heavily concentrated in
the period from AD - 45 to AD - 8. CAAR meas-

ures calculated during this interval and the
AD - 45 to AD - 3 period are negative and
significant.
In contrast, CAAR measures calculated
from the AD - 7 to AD + 1, AD - 2 to AD + 1
and AD - 2 to AD - 1 are uniformly positive,

IV. Summary and Conclusions

Table 3 Average and Cumulative
Average Abnormal Returns
Excluding three large money-center banks
Event date

AD-90
AD-85
AD-80
AD-75
AD-70
AD-65
AD-60
AD-55
AD-50
AD-45
AD-40
AD-35
AD-30
AD-25
AD-20
AD-15
AD-14
AD-13
AD-12
AD-11
AD-10
AD-9
AD -8
AD-7
AD -6
AD-5
AD-4
AD-3
AD-2
AD -1
AD
AD +1
AD+ 10
AD+ 20
AD+ 30
AD+ 40
AD+ 50
AD+ 60

AAR

-.0018
-.0015
.0084
.0039
.0013
-.0032
-.0003
-.0037
.0007
-.0013
-.0003
-.0025
.0009
.0007
-.0037
-.0052
-.0038
.0006
.0006
.0017
-.0027
-.0009
.0026
.0016

-.0011

-.0009

-.0001

-.0003
.0025
.0031
-.0004
.0019
-.0032

-.0020

-.0007
-.0024
.0074
-.0004

CAAR

NPa

-.0018
-.0147
-.0074
-.0043
-.0091
-.0161
-.0181

6
11

-.0210

-.0161
-.0163
-.0319
-.0303
-.0374
-.0381
-.0424
-.0471
-.0509
-.0503
-.0497
-.0480
-.0507
-.0516
-.0490
-.0474
-.0485
-.0494
-.0494
-.0497
-.0472
-.0441
-.0446
-.0427
-.0532
-.0504
-.0588
-.0516
-.0450
-.0501

a. Number of companies with positive residuals.

although their statistical significance is margi­
nal. For the subsamples excluding the large
money center institutions, the CAAR measures
approach significance at the 10 percent level
(two-tail test) and are significant for the AD - 2
to AD - 1 period.16

15
9

8
7

8
5
7
7

11

5

8

9
4
3

8

9
9
9
7
7

10
11
7

6
11
8
10
12
6
11
3

10
7

6
8
6

The results do not provide strong support
for the contention that subsidiary bank consol­
idation has a large positive impact on the
expected future profitability and market
value of MBHCs. In fact, negative significant
cumulative average abnormal returns are
observed for several time periods beginning
before and ending just after the announcement
date. The data indicate that the bulk of the
negative average abnormal returns are clus­
tered in the period beginning roughly 45 trad­
ing days before and ending just prior to the
announcement date. These results suggest that
investors expect that the costs of consolida­
tion typically outweigh any benefits.
If this interpretation of the results is cor­
rect, it is difficult to explain why holding com­
pany management pursues such a course of
action. It may be that partial rather than total
consolidation is optimal for the typical MBHC.
The observed preference of MBHCs for par­
tial consolidation lends credence to this view.
Alternatively, MBHC management might
consolidate to reduce profit variability rather
than raise profitability.17 At any rate, the evi­
dence indicates that the inability to consoli­
date does not impose significant efficiency
costs on MBHCs. The implication is that leg­
islation permitting total consolidation is likely
to generate marginal benefits.
However, cumulative average abnormal
returns are positive over very short inter­
vals immediately around the consolidation
announcement date and approach statistical
significance in some cases. In particular, the

noted that total con­
solidation is not the
only way to limit sub­
sidiary risk-taking.
Selective corporate
control over certain
key subsidiary deci­
sions and access to
timely subsidiary per­
formance data would
also allow the parent
company to monitor
and lim it the risktaking o f subsidiar­
ies, while retaining
the M BH C form .
17. M ost o f the
C A A R measures
calculated over short
intervals around the
announcement date
are significant at
the 10 percent level,
if a one-tail test is
used.

subsample results suggest that consolidation
is expected to yield greater benefits for smaller
MBHCs, which makes sense intuitively. Posi­
tive cumulative average returns following
negative cumulative returns also suggest that
consolidation might be the result rather than
the cause of poor performance and does gen­
erate positive expected net benefits, albeit of
rather modest proportions.
It should be noted that the failure to find a
large positive consolidation impact could be
due to a number of factors. The sample size is
rather small. Further, although great care
was taken in correctly identifying announce­
ment dates, it is possible that the intention to
consolidate may have been made public by
some companies prior to the date used in this
study. Other contaminating events, such as
earnings or merger announcements, may have
influenced the reported results. It is also pos­
sible that some part of the holding company
stock price reaction may have occurred when
it became apparent that state laws would be
changed to permit consolidation, rather than
when the company announced this action.

Company returns might also be influenced
by other provisions of the enacted legislation
that affected competitive conditions throughout
the state. More research on this issue is nec­
essary before the findings presented here can
be accepted as definitive.

Appendix
The procedure used to calculate the estimated
standard errors of the CAAR measures and
the resultant /-statistics is the same as that
used in Ruback (1982) and several other event
studies. The formula used to compute the
/-statistics is given in equation (Al) below:
(Al)

t = CAAR(2 , n /s c (CAAR(2t ti)

where
the cumulative aver­
age abnormal return
over the t2 - 1 1 trading
day interval of event
time, and
se(CAARt2 tti) - estimated standard
error.
The formula used to calculate this standard
error is given in equation (A2) below:

Fig. 1 Cumulative Average
Abnormal Returns
CAAR

(A2) se(CAAR t2, tl) = [Q •var{AAR )
+ 2( Q - 1)- cov (A A R )]1/2,

0.02

where
Q = t 2 - t l + 1,

0.00

-

var(AAR) = the variance of the AAR t
series calculated using
the following 60 trading
days: AD -120 to AD - 91
and AD + 61 to AD + 90,
cov(/L4i?) = the covariance of the AARt
series calculated over the
same 60 day interval.

0.02

-0.04

This formulation adjusts the estimated stan­
dard error for observed autocorrelation in the
-0.06
-120

-90

-60

-30

0

30

Day relative to announcement

60

90

AAR t series, possibly introduced by the clus­
tering of events in calendar time.

Table 4 Cumulative Average Abnormal
Returns: All Companies ( / = 21)
Time period

AD - 90 to AD + 1
AD - 45 to AD + 1
AD - 45 to AD - 8
AD - 45 to AD - 3
AD - 7 to AD + 1
AD - 2 to AD + 1
AD - 2 to AD - 1
AD + 2 to AD + 60

CAAR

t- statistic

-.0551
-.0373
-.0466
-.0443
.0093
.0070
.0039
-.0066

-2.27a
-2.143
-2.99a
-2.67a
1.25
1.43
1.18
-0.34

Table 5 Cumulative Average
Abnormal Returns: All Companies
Except Citicorp (J = 20)
Time period

AD- 90 to AD + 1
AD- 45 to AD + 1
AD- 45 to AD - 8
AD- 45 to AD - 3
AD- 7 to AD + 1
AD- 2 to AD + 1
AD- 2 to AD - 1
AD + 2 to AD + 60

CAAR

-.0452
-.0304
-.0416
-.0379
.0113
.0076
.0039
-.0063

t- statistic

-1.983
- 1 .883
-2.84a
-2.43a
1.57
1.59
1.95a
-0.34

Table 6 Cumulative Average Abnormal
Returns: All Companies Except Three
Large, Money-Center Banks (J = 18)
Time period

AD - 90 to AD + 1
AD - 45 to AD + 1
AD AD AD AD -

45 to AD - 8
45 to AD - 3
7 to AD + 1
2 to AD + 1

AD - 2 to AD - 1
AD + 2 to AD + 60

CAAR

-.0427
-.0302
-.0346
-.0347
.0063
.0070
.0056
-.0073

a. Significant at 10 percent level, two-tail test.

/-statistic

-1.943
-1.933
-2.48a
-2.33a
0.91
1.52
1.723
-0.42

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John B. Carlson is
an economist and
E. J. Stevens is
an assistant vice
president at the Fed­
eral Reserve Bank
o f Cleveland. The
authors would like to
acknowledge helpful
comments by Peter
Skaperdas and Owen
Humpage and the
diligent research
assistance o f Jim
Siekmeier.
1. For a more de­
tailed account o f the
short-term implica­
tions o f these projec­
tions, see John B.
Carlson (1985).
2. The fram ework
can in no way deter­
mine consistency
among assumptions;
this depends on the
model o f the econ­
omy used.
3. In practice, yearto-year changes in
the federal debt do
not precisely equal
the corresponding
annual federal bud­
get deficits. The
inequality results
because Congress
borrows to finance
net spending on cer­
tain off-budget pro­
grams, and because
the Treasury finances
a small portion o f
the deficit through
changes in various
assets such as its cash
balances. Here we
use the term deficit
to refer to both onbudget and off-budget
items; we ignore the
small changes in
Treasury assets.

The National Debt:
A Secular Perspective
by John B. Carlson
and E. J. Stevens

Recently, interest payments on the national
debt have been growing faster than the econ­
omy (figure 1). Since 1977, there has been an
11.5 percent average annual increase in inter­
est payments. If this difference between growth
rates were to continue unchanged until the
year 2013, the federal government would be
forced to borrow or tax the equivalent of the
entire gross national product simply to service
its existing debt.
This alarming possibility may not seem
likely, because Congress and the administra­
tion are seeking deficit reductions that would
slow future growth of the national debt and
debt service. Unfortunately, even a large defi­
cit reduction might not be sufficient to prevent
continued cancerous growth of interest pay­
ments if the interest rate cost of existing debt
were to continuously exceed the growth rate
of the economy. However, independent projec­
tions by both the Office of Management and
Budget and the Congressional Budget Office
have suggested that net interest payments are
not likely to grow faster than the economy
for very long .1
Even putting aside the alarming possibil­
ity of an economic disaster 30 years from now,
the fact still remains that the national debt
and debt service costs have been growing very
rapidly. In all but one of the past 10 years,
the federal government has had to borrow not
only the entire amount needed to pay the in­
terest on the national debt, but also additional
funds for non-interest expenditures. Moreover,
this situation would continue for as far as
the eye can see under all but the most sanguine
projections discussed in this article.
This is not the first time that federal defi­
cits have been large or that debt service needs
have loomed large in federal budgets. This
Economic Review offers two perspectives on the
current federal debt situation. One is a histo­
rical view of the past 40 years, during which
federal debt initially declined slightly from its
wartime peak, and then began to accelerate.
The other perspective is of the future, including
several scenarios of what the next 40 years

4. Although i, b,
and m are treated
as parameters here,
they all vary sub­
stantially with time.
Using average val­
ues only allows an
approximation o f a
time path.

could be like. The framework for looking at
both the past and the future is provided by
investigating the relative values of economic
growth, interest rates, tax rates, and seign­
iorage. The analysis shows that the factors
favorable to a net reduction in debt relative to
GNP during the past 40 years are not likely
to recur in the next 40 years. Substantial
expenditure and/or tax changes are the only
certain methods for preventing unprecedented
peacetime levels of the national debt in the
future.

A Primer on Government Debt
References to “the public debt” mask many details that,
upon closer inspection, are qualitatively important but
quantitatively small. The lion’s share of $1,577 trillion
dollars of the federal debt outstanding at the close of
fiscal year 1984 has been issued by the Treasury to fi­
nance budget deficits and, with the exception of savings
bonds, is in marketable form held by the general public.
The debt would be 21 percent greater if one were to
include $331 billion of outstanding interest-bearing
securities issued by non-government institutions (pri­
vately owned, not federally guaranteed, but with a spe­
cial relationship to the government, for example, federal
intermediate credit banks). Seventy-three percent of
public and agency debt outstanding in 1984 was held
by the public, U.S. government accounts held another
17 percent ($264 billion), and the Federal Reserve held
the remaining 10 percent. Of the $1,577 trillion of fed­
eral debt, only about 11 percent was held by foreign­
ers, and 80 percent of that was in the portfolios of for­
eign central banks and other official institutions. The
inference that can be drawn from these calculations is
that about 62 percent, or $1.0 trillion, of federal debt is
directly held by domestic private owners, over 90 per­
cent of which is in the form of marketable interestbearing instruments and 10 percent in nonmarketable
U.S. savings bonds.
Granted, a sizable federal debt exists, and most of it
is willingly bought in the market and held by domestic
private owners. What difference does it make whether
the debt becomes larger or smaller, either absolutely
or relative to the income and wealth of U.S. citizens?
Three different approaches to thinking about this ques­
tion can be identified, emphasizing the role of federal
debt in cyclical stabilization of the economy, in meet­
ing the portfolio needs of wealth owners, and as an
alternative to taxation.
Federal debt can be a cyclical necessity. Even if the
Treasury had no debt outstanding on average over a

I. Debt Dynamics
The behavior of debt over time is complex;
it involves the interaction of deficits, interest
rates, and economic activity. Nevertheless,
the government budget constraint provides
a straightforward accounting basis for exam­
ining dynamic consequences of alternative
assumptions as well as their consistency with
certain expected long-run characteristics of the
economy.2 The logic of accounting requires
that the change in total outstanding govern-

long sweep of years, debt might be issued in lean
years, then retired in fat years to serve a useful public
purpose. Cyclical variations in national income and
output, originating from sources outside the federal
budget, give rise to corresponding variation in tax
receipts and inversely corresponding variations in
expenditure, and thereby to federal deficits and debt
outstanding. The result is a federal budget that acts
as an automatic stabilizer as compared with one in
which receipts were required to balance expenditures
at all times. If the federal government is to act as an
automatic stabilizer, then some government debt may
be a cyclical necessity.3
Federal debt supplies a perfectly safe interest-bearing
asset for private wealth owners’ portfolios.15An increase
in outstanding federal debt will make a difference to
the functioning of the economy, because portfolio man­
agers must be induced to substitute less risky federal
debt for more risky private assets that directly or indi­
rectly finance real capital. In this way, rapid growth of
government debt would retard investment in new pro­
ductivity-enhancing capital, thus slowing the growth
rate of real income per capita.
Finally, there is the view that “ we owe it to our­
selves.” Government can finance its operations either
through taxes or through debts. The argument is that,
given a level of government expenditures, the econ­
omy is essentially unaffected by the choice between
these two methods of finance, because issuing debt
rather than taxing to finance government expenditures
implies that citizens would expect to pay future taxes
necessary to service the new debt. Recognizing those
increased future tax obligations, citizens would be ex­
pected to increase their saving as taxes are reduced.
a. The same function could be served by the Treasury accumulating
holdings of private assets in fat years and reducing them in lean years.
b. “ Perfectly safe,” of course, within a non-revolutionary environment.

5. Actually,
/(I - b)Dt_i is greater
than the recoupment
from the Federal
Reserve. The differ­
ence was about 11 per­
cent in 1984, repre­
senting the portion o f
Federal Reserve in ­
come used to finance
the operations o f
the Federal Reserve
System.

6. We ignore minor
secular elements
affecting the pri­
mary deficit that
arise as a result o f
economic growth.
These include the
tendency fo r taxes
to rise relative to
income as higher
individual (real)
incomes are taxed
at proportionally
higher rates and
governmental econ­
omies o f scale.

ment debt, D, equal the budget deficit, which is
the difference between federal government
expenditures, E, and total government reve­
nues, R.3 This is expressed as:

A - A-i

- E t - Rt-

Public discussion about growth of the
national debt typically focuses on the budget
deficit. To better appreciate the dynamic ele­
ments of deficits and debt, it is useful to break
the budget deficit into two components. One
is the primary deficit (or surplus), defined
as the difference between non-interest outlays
and total revenues. The other component is
interest outlays net of recoupments from fed­
eral taxes and the Federal Reserve. Combining
these two components, we have:
A - A - i = X t + i(l - m)(l - b)Dt-\,
where X is the primary deficit, i is the average
interest rate on Treasury debt, m is the aver­
age marginal tax rate, and b is the proportion
of debt held by the Federal Reserve.4
This dichotomy between the primary defi­
cit and interest payments is useful because it

Fig. 1

Interest Payments

Percent of GNP

1946

1956

1966

SOURCE: Congressional Budget Office.

1976

highlights the importance of interest payments
in determining debt momentum, that is, the
tendency of the debt to grow on its own. Debt
momentum is to a large extent predetermined
by the level of current debt and by the mar­
ket rates of interest at the various times that
existing debt issues were sold. Federal reve­
nues recouped from interest payments on the
debt reduce the effective interest cost and
thereby retard debt’s momentum. These rev­
enues include taxes on private holders’ interest
income from federal debt and the portion of
interest income on Federal Reserve holdings of
Treasury debt (seigniorage) that is returned
to the U. S. Treasury.5 While tax rates and Sys­
tem holdings of Treasury debt can be altered
to influence debt momentum, practical con­
straints limit the extent to which policymak­
ers can change them. For example, non-inflationary monetary policy clearly implies some
upper limit on Federal Reserve accumulation of
Treasury debt. Tax rates may be easier to
change, but any politically acceptable policy
probably could not greatly alter the average
marginal tax rate. Nevertheless, over long
periods, these factors can change.
The primary deficit (or surplus), of course,
also plays a role in debt dynamics by reinforc­
ing or offsetting debt momentum. The size
of the primary deficit is directly altered by
changes in the budget, such as the policy ini­
tiatives embodied in the recent Congressional
Budget Resolution for 1986. The primary defi­
cit also includes the cyclical elements of the
budget deficit that arise from the effects of the
business cycle on revenues and income main­
tenance programs. Thus, the primary deficit
tends to reinforce debt momentum during eco­
nomic slowdowns and to offset momentum
during economic recoveries.6
The magnitude of debt momentum by itself
is not very instructive. What is relevant is
its size relative to growth of the economy. Eco­
nomic growth eases the burden of servicing

7. See Carlson
(1985), Sargent and
Wallace (1981), Tobin
(1982), and Congress
o f the United States,
Congressional Bud­
get Office (February
1985).

debt. Additional national income and output
can add to revenues and can reduce spending on
social programs. The combination—sometimes
called a fiscal dividend—can be used to make
interest payments and, if sufficiently large,
to pay down outstanding debt. In this sense, the
burden of debt in the economy diminishes if
its growth lags the growth of nominal national
income. Thus, analyses concerned with eco­
nomic implications of debt dynamics typically
concentrate on the ratio of debt to income,
measured by GNP.
Much attention has been given to the poten­
tial for runaway debt, that is, the possibility
that the debt-to-GNP ratio will grow without
limit. Sufficient conditions for runaway debt
are that: 1 ) there be a primary deficit, and 2) the

Box 1 Federal Debt Dynamics
The steady-state properties of federal debt are derived
from the government budget constraint, which requires
that the change in total outstanding Treasury debt
(including Federal Reserve holdings) be equal to the
budget deficit. This is expressed as:
A - A-i - Et - Rt,
where D is outstanding interest-bearing Treasury debt,
E is government expenditures, and R is government
revenues.3 For simplicity, we abstract from government
transfers and assume that the average marginal tax
rate, m, is the same for all types of income and constant
over time.
Expenditures can be divided into non-interest out­
lays, E' and interest payments net of taxes and adjusted
for seigniorage:
ia = i(l - m)( 1 - b)Dt_u
where i is the nominal interest rate on Treasury secu­
rities, and b is the proportion of Treasury debt held by
the Federal Reserve. This allows separation of the bud­
get deficit into two components—the primary deficit:

xt = (e; - Rt),
and interest payments adjusted for taxes and seignior­
age.15Thus we have:
A ~ A-i = Xt + iBA-iAt time t, then, the level of federal debt equals:
A = xYt + (1 + i-) A -i,
where x = X/Y and is assumed fixed by fiscal policy.

interest rate on Treasury debt net of taxes
and adjusted for Federal Reserve holdings
be greater than the trend growth rate of nom­
inal GNP.7 Realistically, this situation could
not persist, because it would ultimately re­
quire that more than all of the income gener­
ated in the economy be used to purchase annual
additions to the federal debt. The structure
of runaway debt conditions therefore suggests
that the budget and/or economic assumptions
are untenable—that somehow something
must “ give.”
Even if the trend growth rate of nominal
GNP were greater than the net interest rate,
debt could still grow for a time relative to GNP.
This situation arises when the primary defi­
cit adds to the debt faster than the excess of the

Assuming nominal GNP grows at trend rate g, the
time path of debt-to-GNP (d) is given by:
4 = * + [(l + i - ) / ( l + *)4-i].
since

A-i = dt.x[y,/{\ +#)].
When the debt-to-GNP ratio is stable:
dt —dt.\ —d*.
Hence:
d*[l - (1 + ia)/(l + g)] =
also when i and g are small

(1 + ia)/(1 + g)

«

1 + ia - g,

and
d* = x/(g - ia).
The level of dt changes when d0 ^ d* At any subse­
quent time t:
dt = d* + (d0 -d * )(l + ia -g y.
It can be seen from this last equation, that if ia > g, the
debt-to-output ratio grows without bound. Also, it is
interesting to note debt grows relative to income when:
d* > d0 and ia< g.
a. For alternative derivations of these properties, see Congress of the
United States, Congressional Budget Office (February 1985), Tobin
(1982), and Wallich and Cohen (1985).
b. Because interest payments are net of tax recoupments and seign­
iorage, government revenues here are exclusively tax receipts on nom­
inal income.

8. The measure o f
primary debt was cal­
culated assuming
an average marginal
tax rate o f 12 percent.
9. Although Con­
gress did attempt to
maintain the real
value o f social secu­
rity benefits over
long periods, such
adjustments, made
through changes in
the benefit formula,
occurred infrequently
and with a lag. For
example, the benefit
formula was changed
only once between
1958 and 1971.

economic growth rate over the net interest
rate subtracts. Nonetheless, this situation
would not continue forever, because the alge­
braic value of the debt-to-GNP ratio would
eventually reach a steady-state level, even if
a primary deficit were allowed to persist at
something like its current size. That steadystate level can be shown to be approximated by
the ratio of the primary deficit (relative to
GNP) to the economic growth rate/net interest-rate differential (see box 1 ). There is no
a priori basis, however, for thinking that the
portfolio of the private sector could accom­
modate every possible algebraic value of the
steady-state debt-to-income ratio and still be
consistent with general equilibrium in the econ­
omy. Of course, if the primary deficit were
reduced sufficiently, then the debt-to-GNP ratio
would fall, until a low algebraic value of the

Box 2 Debt Buildup in World War II
Large deficits in the United States typically have been
limited to wartime. The deficits during World War II
offer the most extreme example: they averaged 25 per­
cent of GNP. The conditions for financing those defi­
cits were unique to wartime. Economic resources were
shifted from producing consumer goods to military uses.
To implement this reallocation, the federal government
instituted controls, including price controls and food and
gasoline rationing. Individuals accepted these controls
as requirements of patriotism, if not for their own long­
term interest. Although credit controls were imposed
to reduce demand for housing, automobiles, and appli­
ances, these items simply were not available, because
steel, wood, and labor were diverted to the war effort.
Individuals not in military service during the war typ­
ically worked a substantial amount of overtime. While
their incomes were high, there was little to spend it on.
Savings rates averaged 25 percent from 1942 to 1945,
compared with a peacetime average of 6percent. Thus,
while the federal debt increased five-fold during the war,
the government found many willing to purchase debt
at very low rates of interest. To help keep rates low, the
Federal Reserve was prepared to buy government secu­
rities not purchased by individuals. But the proportion
of debt monetized by the Federal Reserve did not increase
sharply, because private demand was sufficient. To pro­
mote private purchases of U.S. savings bonds, the gov­
ernment mounted an extensive advertising campaign
that appealed to the people’s patriotism.

steady-state ratio were reached—again, if that
were consistent with general equilibrium.

II. Debt Dynamics:
1946 to Present
During World War II, enormous primary defi­
cits caused a five-fold increase in the level
of federal debt (see box 2). Immediately after
the war, the large primary deficits ceased,
and the level of debt began an extended decline
relative to GNP. Not until 1974 did the com­
bined influence of primary deficits and inter­
est rates begin to generate another sustained
increase in the federal debt relative to GNP.
Figure 2 shows the absolute amount of
the federal debt held in the private sector (ex­
cluding the Federal Reserve) and that same
amount relative to GNP, both indexed to their
1946 levels. Although the dollar value of debt
trended upward slightly until 1974, the debtto-GNP ratio fell over the same period. This
decline—from a little more than one year’s
output to less than one quarter’s output—per­
sisted through the Kennedy tax cut and even
through the Vietnam military buildup. Reversal
of the decline in the mid-1970s was initially
a consequence of enlarged primary deficits
resulting from the severe 1973-1975 recession,
augmented by a one-time tax rebate in 1975.
By the peak of the business cycle in 1979, how­
ever, at least the primary deficit had been
eliminated (see figure 3).
An important characteristic of debt dynam­
ics during the 28-year period of declining debt
ratios, was the frequent occurrence of pri­
mary surpluses that actually produced a
small cumulative net primary surplus from
1946 through 1974.8 While many factors could
account for surpluses, an important factor
was the budget’s response to inflation. From
1946 to 1974, the GNP deflator rose at an
average annual rate of 5.5 percent, but until
1972, few federal spending programs were
indexed. Benefits from large entitlement pro­
grams, such as Social Security, did not increase
automatically with inflation .9 On the other

hand, tax rates were not indexed until 1985.
Revenues tended to grow proportionately more

Fig. 2 Federal Debt Held by Public
Percent of 1946 level

Fig. 3 Primary and Total Deficit3
Percent of GNP

a. Primary deficit assumes a marginal tax rate of 12 percent.

than income, as inflation placed more and
more taxpayers in higher tax brackets. Thus,
even a relatively low inflation rate was doubly
favorable for restraining the primary deficit,
because, without explicit federal action, it
tended to increase revenues faster than non­
interest expenditures.
Since 1974, the budget has produced a cu­
mulative primary deficit of about $430 billion.
This turnaround owes largely to the Eco­
nomic Recovery Tax Act (ERTA) of 1981, a
tax initiative that sharply reduced the rate of
growth of tax revenues. Large tax cuts were
instituted with the expectation that there
would be subsequent spending reductions in
nonmilitary programs as well as additional
revenues generated by more rapid economic
growth. Subsequent output growth was rela­
tively strong and generated proportionately
more revenues, but the impact of ERTA fell
short of supply-sider claims that it would
produce sufficient revenue growth to elimi­
nate the deficit. Moreover, Congress did not
accept all the spending cuts initially sought by
the administration. Because an important
feature of ERTA was to index tax rates for
inflation, the imbalance is likely to persist if
substantial deficit cuts are not achieved.
Another aspect of postwar debt dynamics
was the apparent failure of interest rates to rise
rapidly enough to anticipate the persistent,
accelerating inflation beginning in the late
1960s. Relative price stability of the 1950s and
early 1960s set a favorable tone for credit mar­
kets before the onset of more rapid inflation.
Most federal debt had been auctioned at rates
under 5 percent prior to 1966. When inflation
began to accelerate in the late 1960s, it was
apparently unanticipated. With a sizable por­
tion of debt “ locked in” at lower rates, the
interest-rate cost of servicing debt adjusted
only slowly to the higher rates of inflation
(see figure 4).
This inertial resistance essentially could
account for the continued decline of the debt-toGNP ratio after the mid-1960s. Figure 5 shows

a rough estimate of what might have happened
to the debt if inflation had been fully antici-

Fig. 4 Average Interest Rate
on Debt and Inflation3
Percent

- 2 ___________i__________ i---------------- 1—
1947

1957

1967

1977

Change in deflator Interest payments/debt
a. Debt is adjusted for Federal Reserve holdings.
SOURCE: Congressional Budget Office.

Fig. 5 Actual and Hypothetical Debt
Percent of GNP

Actual debt

Hypothetical debt

SOURCE: Congressional Budget Office.

pated after 1965. It presumes that the average
real interest rate would have equaled its aver­
age ex post rate during the low inflation period
of 1954-1963, and then adds actual inflation
rates for periods equal to the average maturity
of the debt. Multiplying interest payments on
the debt by the ratio of the adjusted interest
rate to the actual rate provides an approxima­
tion of debt payments and the debt-to-GNP
ratio, if inflation had been fully anticipated.
On this basis, debt would have stabilized rela­
tive to GNP near its mid-1960s level, rather
than declining further into the mid-1970s.
Taxes are another reason that, until recently,
interest-rate costs of government debt were
low relative to growth in nominal GNP (see fig­
ure 6). Estimates of the average marginal tax
rate typically fall in the range of 12 percent to
25 percent. Even assuming the average mar­
ginal tax rate was only 12 percent, the annual
interest-rate cost of the debt adjusted for taxes
heretofore has never exceeded the five-year
average growth rate of GNP.10 The momen­
tum of debt growth was never augmented by
interest-rate costs in excess of the longer-term
nominal growth rate of the economy.
When debt was declining relative to nominal
GNP, seigniorage also played an increasingly
important role in slowing the momentum of
debt. The monetary policy that accompanied
economic growth with low inflation in the 1950s
and early 1960s produced, as a byproduct, an
increase in Federal Reserve holdings of Treas­
ury securities almost proportional to the in­
crease in nominal GNP.11 With debt declining
relative to GNP, and Federal Reserve holdings
rising proportionately with GNP, private sec­
tor holdings of the debt necessarily declined
relative to GNP (see figure 7). In fact, Federal
Reserve holdings increased to almost 19 percent
of all outstanding federal debt in the postwar
period. This meant that by the early 1970s,
seigniorage was paying roughly one-fifth of the
interest cost of all debt held outside the fed­
eral government itself.

The turnaround and rapid growth of debt
since 1974 has not been matched by momentum-

Fig. 6 Interest Rates and GNP Growth
Percent

a. Five year average growth rate.
b. Interest payments/federal debt.
SOURCE: Congressional Budget Office.

Fig. 7 Federal Reserve Holdings
Percent of federal debt

III. The Next 4 0 Years

20

1940

1948

1956

1964

SOURCE: Congressional Budget Office.

1972

dampening seigniorage. Disinflationary mon­
etary policy since 1979 has constrained money
growth and the seigniorage it produces. As
debt has grown abruptly relative to GNP, the
share held by the Federal Reserve has dropped
sharply. Moreover, the Monetary Control Act
of 1980 reduced overall required reserves on
deposits. This, in turn, reduced the demand
for monetary base (and hence, Federal Reserve
holdings of debt) for a given level of nominal
GNP. Thus, the effects of seigniorage, so impor­
tant to debt dynamics before the 1980s, have
withered.
This historical perspective emphasizes
some unique conditions that influenced debt
dynamics in the postwar period. Of particular
importance were frequent primary surpluses,
low interest rates, and (relatively) high returns
from seigniorage. Recreating the social and
political forces leading to those same condi­
tions is not possible. History, therefore, offers
a poor basis for anticipating the future fed­
eral debt situation. But history does provide
a kind of benchmark. If future debt-to-GNP
levels are within the range of past experience,
at least we know that these levels once proved
manageable.

1980

Long-term projections of the national debt,
using the framework of primary deficits and
net interest payments, rest on assumptions
about the trend growth rate of nominal GNP,
on the size of the primary deficit relative to
GNP, on the level of interest rates, and on
marginal tax rates and seigniorage. To be
meaningful, a set of these assumptions must
be mutually consistent with attainable future
states of the economy. Lacking a generally
accepted quantitative, long-run, macroeco­
nomic model by which to generate a unique
plausible set of those assumptions, we consider
several different sets of assumptions to pro­
duce various debt scenarios. These scenarios
should not be viewed as forecasts, but simply as

10. For the methods
used in estimating
average marginal
tax rates, see Seater
(1985) and Barro
and Sahasakul
(1983).
11. It is true that
the monetary base
grew less rapidly than
GNP. However, Fed­
eral Reserve hold­
ings o f Treasury debt
tended to increase
more rapidly than
the monetary base
until the 1980s, after
which there seems to
be no clear trend.

potential levels of the debt-to-GNP ratio that
can be compared to levels experienced over
the past 40 years. Levels that fall outside the
range of past experience are, ipso facto, alarm­
ing. Moreover, the projections can be exam­
ined in the context of widely accepted beliefs,
or “ stylized facts,” about other long-run
economic relationships that are thought to
characterize the U. S. economy.
Table 1 contains an array of points along
various steady-state paths of the debt-to-GNP
ratio. Alternative values of the ratio for a com­
mon time horizon correspond to alternative
assumptions about ( 1 ) the size of future pri­
mary deficits and (2) the differential between
the rate of economic growth and the net rate of
interest on Treasury debt. The steady-state

values, based on the formula in box 1 , extend
in time to horizons of five, 10, and 40 years.
A final array, based on an infinite horizon,
approximates eventual steady-state values
toward which the debt-to-GNP ratio tends in
the very long run.
Two characteristics of these arrays are nota­
ble. First, the longer-run values of the debtto-GNP ratio are clearly sensitive to what
appear to be small differences in the values
chosen for the assumptions. Second, however,
the time paths of the alternative steady states
are somewhat slow to distinguish themselves
from one another. After five years, the debtto-GNP ratio appears relatively unaffected
by the indicated range of differences in the
growth/net interest assumption; after 40 years

Table 1 Debt-Output Ratio: Sensitivity to Changes in
the Primary Deficit and Growth-Interest Differential
A fter 10 Years

A fter 5 Years
X

0.5

1.0

1.5

2.0

2.5

1.5

.36

.38

.41

.43

.46

1.0

.37

.39

.42

.44

.46

0.5

.38

.40

.42

.45

.47

0.1

.38

.41

.43

.46

.48

A fter 4 0 Years

Legend:
x: Primary deficit relative to nominal GNP (percent).
g - ia: Growth-interest differential (percent).

L on g-R u n Steady State

12. It is assumed
here that the primary
deficit is zero after
1988, so that the
nominal level o f debt
grows at a rate equal
to the average inter­
est rate adjusted fo r
taxes and seignior­
age. Based on aver­
ages over the forecast
horizon, nominal
income growth and
nominal interest
rates are assumed to
be 7.8 percent and
7.5 percent.

the effect is quite significant (measured as a
percent of either the low or high value), al­
though nowhere near as substantial as in the
ultimate steady state. The same pattern is evi­
dent when the effect of differences in assumed
values of the primary deficit is traced. In this
case, however, even the difference between
the indicated high and low values at the end of
five years is quite noticeable—equivalent to
10 percent of GNP.
Three paths of the debt-to-GNP ratio appear
in figure 8, corresponding to three particular
sets of assumptions. The first, scenario A,
is not drawn from sets of values in table 1 , but
is based on our extrapolation of Congressional
Budget Office (CBO) estimates that assume
the July 1985 budget resolution is achieved.12
The CBO analysis only contained projections
through 1990 and was based on two impor­
tant additional assumptions: that the economy
would achieve an average real growth rate of
3.4 percent and that market interest rates
would decline, in part because of continuing
low inflation. The projections indicate that the
primary deficit would be eliminated by 1988,
and, in the absence of any rebound in the pri­

Fig. 8 Federal Debt
Percent of GNP

mary deficit and of any deviation from the eco­
nomic assumptions, our extrapolation shows
continuing decreases in debt and interest pay­
ments as a percent of GNP over the next 40
years—a refreshing outcome indeed.
Scenario B, also examined by the CBO,
assumes that none of the budget savings
included in the July 1985 budget resolution
is achieved. Again, the CBO projections only
extended through 1990. Without budget cuts,
the CBO projects that the primary deficit
would decline from the 1984 level of 3 per­
cent to about 1.5 percent in 1990, as the econ­
omy would approach its assumed full-employment growth trend. In extrapolating, we have
taken 2 percent as the value in the long run,
representing an average of lower and higher
values that might be achieved during future
business cycles .13 The other CBO assumption
was that while the level of market interest
rates would be slightly higher than the growth
rate of nominal GNP (as has been the case for
the past year), rates would nonetheless fall
short of the growth rate of nominal GNP by
1.5 percent, after adjusting for the marginal
tax rate on interest income and seigniorage. If
the primary deficit and the growth/net inter­
est-rate relationship were to stabilize at these
average levels, our extrapolations show that
the federal debt would continue to increase
relative to GNP until it eventually stabilized
at about one and one-third times nominal GNP
(shaded values in table 1). This result would
advance only gradually, however; at the end of
40 years, the federal debt would be “ only”
90 percent of a year’s nominal GNP.
Scenarios A and B suggest a range of possible
outcomes, extrapolating from medium-term
projections that were based on commonly used
methodology. Where in this range of outcomes
the future might lie depends on the extent to
which deficit reductions are achieved and
maintained.
Neither of these scenarios is entirely sat­
isfactory. The assumptions are drawn from
averages of medium-term projections as prox­
ies for long-run equilibrium values. Moreover,
the projections themselves are derived from

13. This assump­
tion is conceptually
equivalent to basing
an estimate o f the
primary deficit on a
mid-expansion esti­
mate o f the structural
deficit. For a discus­
sion o f the practical
advantages o f a midexpansion measure
o f the deficit, see
de Leeuw and Hollo­
way (1983).

macroeconomic models and economic “ rules
of thumb” heavily influenced by post-World
War II experience. But the unique combination
of secular influences of this period—demobili­
zation, rising inflation, and high seigniorage—
is not likely to be repeated. Thus, models esti­
mated over this period could be biased and,
as argued below, biased toward a high growthrate/interest-rate differential and a conse­
quent underestimate of future debt growth.
Scenario C is based on assumptions that
are consistent with a smaller growth-rate/interest-rate differental. Such a hypothetical
case might be described as follows: Accelerat­
ing inflation beginning in the mid-1960s appar­
ently was to some extent unanticipated. This
suggests that the interest rates of this period,
on average, were low relative to their “ true”
equilibrium values—that is, values consistent
with non-inflationary economic growth. This
experience is unlikely to be repeated. Inflation
awareness has grown with the experience of
rising inflation, as well as with the experience
of declining inflation. Furthermore, since 1979,
the Federal Reserve has maintained a policy
of disinflation. A major consequence has been
that interest rates have varied more immedi­
ately and substantially to impulses arising in
the real sector. This, in turn, makes it less
likely that future interest rates will be “ stuck”
below their equilibrium levels.
The case for a smaller growth-rate/interestrate differential seems even more plausible
when one considers the productivity experi­
ence of the current expansion. Even with rec­
ord levels of investment, productivity increases
have been below levels for comparable stages
of the cycle in the postwar period. If, in fact,
trend growth of productivity is increasing
around its 1970s rate of less than 1 percent,
and if labor force growth were to stabilize at
less than 1.5 percent, then trend output growth
could be less than 2.5 percent. Moreover, as
indicated in figure 6, nominal pretax interest
rates recently have exceeded the growth rate
of nominal income. In fact, in the third quar­

ter of 1985 nominal income grew at 6.7 per­
cent, while nominal interest rates on Treas­
ury securities averaged over 8.0 percent for a
wide variety of maturities. All of this suggests
that the equilibrium interest rate need not be
less than the nominal growth rate, let alone
the CBO assumption, which after tax is 1.5 per­
centage points lower.
A smaller growth-rate/interest-rate dif­
ferential would produce a smaller fiscal divi­
dend. Thus, it is likely to be associated with a
higher primary deficit relative to output. It
therefore seems reasonable that consistent
assumptions would involve both a lower
growth-rate/interest-rate differential and a
higher primary deficit. In the context of table 1,
the potential bias of secular elements would
result in assumptions toward the southeast for
each time horizon.
To illustrate, consider a growth-rate/w^
interest-rate differential of 0.5 percent. While
this scenario implies a pre-tax nominal interest
rate slightly above the growth rate of nomi­
nal GNP, it would still be associated with an
after-tax interest rate below the growth rate.
This is not as favorable as the CBO assumption
and is not as likely to be associated with the
vanishing primary deficit of scenario A. Sup­
pose that the primary deficit were reduced
to 1.0 percent of GNP, roughly one-third its
recent level, and half the 2.0 percent of sce­
nario B. The associated debt path appears as
scenario C in figure 8. The debt-to-GNP ratio
under this alternative would rewind over the
next 40 years back to a level comparable to
that during the Korean War. In the longer
run, the ratio would tend toward the unprec­
edented steady-state value of two times GNP,
five times its current value.
The relevance of economic assumptions may
be demonstrated in another way. How could
the eventual debt-to-GNP ratio be maintained
at its current 0.4 value if the growth-rate/net
interest-rate differential were the 0.5 value
assumed in scenario C? The primary deficit
would have to be 0.2, or the equivalent of a
$7.7 billion primary deficit today, roughly

14. This is not lit­
erally true. O ASD I
surpluses usually
are invested in nonmarketable Treas­
ury issues that are
included in debt sub­
ject to the debt ceil­
ing. The focus here,
however, is on debt
held outside the fed ­
eral govern men t and
Federal Reserve
System.

$110 billion less than its current value.
Useful projections—those with a semblance
of future reality—should not be found to de­
pend entirely on the precise values of their
underlying assumptions. The three scenarios
described here seem useful in that sense. The
first, assuming prompt, substantial, and per­
manent deficit reduction, yields a declining
debt-to-GNP ratio, with the speed of the decline
depending on the size of the excess of the eco­
nomic growth rate over the net interest rate.
The second, extrapolating current short-run
conditions into the long run, and the third,
using relatively general long-run economic rela­
tionships and a sizable cut in the primary
deficit, yield results quite different from the
first. In either case, the debt-to-GNP ratio will
slowly grow toward and might eventually
exceed even the extreme values of the past.
The higher the primary deficit and the higher
the net interest rate relative to the rate of
economic growth, the sooner those values will
be realized.

Fig. 9 Federal Share of Total Debt
Percent of GNP
200

Federal debt

Total debt3

a. Total domestic nonfinancial debt.
SOURCE: Board of Governors of the Federal Reserve System,
Flow o f Funds.

IV. Caveats
Judging the usefulness of these projections also
requires recognition that the assumptions
might be interdependent. As noted above, less
favorable economic assumptions might be asso­
ciated with a higher primary deficit, reflecting
a smaller fiscal dividend. The resulting debtto-GNP ratio would be even larger than implied
by the change in economic assumptions alone.
Or, an assumption of greater seigniorage in­
duced by expansionary monetary policy might
produce more rapid inflation. The increase
in the growth-rate/net interest-rate differen­
tial might be offset by a larger primary deficit
as nominal federal spending grows relative
to indexed tax receipts. The growth-rate/net
interest-rate differential also might narrow
as rising inflation expectations raise nominal
interest rates and, perhaps, lower real eco­
nomic growth. The resulting debt-to-GNP ratio
could be higher than implied by increased seign­
iorage alone.
Bearing these possibilities in mind, what
are the economic consequences of the various
scenarios of the future? Are they consistent
with widely held beliefs? Failure to follow
through with the recent budget resolution
both by actually achieving the entire deficit
reduction and by extending deficit reduction
beyond 1988, could mean that by early in the
next century, the federal debt relative to GNP
easily could exceed levels reached at the end
of World War II. The challenge is to imagine
how that result might be accommodated in an
economic and social atmosphere less struc­
tured than the war-based economy of World
War II.
An important budgetary caveat concerns
the ominous debt implications of this country’s
commitment to Social Security, especially
if demographic factors become less favorable.
Recent 75-year projections published by the
Social Security Administration indicate that
while the old age and survivor and disability
insurance (OASDI) trust funds will continue to
generate surpluses into the early part of the
next century, the rate of increase of these sur­

15. For a detailed
discussion o f this
phenomenon, see
David and Scadding
(1974). See also Fried­
man (1981) and
Wallich and Cohen
(1985), who argue
further that the con­
stant ratio o f debt
to output weighs
against the Ricar­
dian Hypothesis on
the irrelevance o f
debt.

pluses relative to GNP will begin to decline
in the 1990s. Because OASDI Trust Fund sur­
pluses reduce the borrowing needs of the Treas­
ury, the rapid buildup of these funds over the
next 10 years is an important force in keeping
the primary deficit from growing relative to
GNP.14 If deficit reduction measures are not
sufficient to reduce the primary deficit when
OASDI funds generate increasing surpluses,
what will happen to primary deficits and the
debt when OASDI surpluses begin to decline?
Another budgetary caveat is that tax re­
form legislation introduces additional uncer­
tainties. One has to do with achieving revenue
neutrality. For example, the administration
has presented a plan it describes as revenueneutral, but other analyses suggest that the
plan will actually reduce revenues and thereby
might widen the deficit. A second uncertainty
has to do with potential indirect effects of re­
form on net interest payments. To the extent
that average marginal tax rates were to be
reduced, the momentum of debt will accelerate
as the after-tax interest rate rises relative to
GNP growth.
Finally, a more fundamental economic
caveat is that a rising debt-to-output ratio
seems inconsistent with the observed con­
stancy of the private domestic savings rate
over the postwar period in the United States.
This phenomenon, sometimes called Denison’s
Law, is akin to another empirical regularity,
the relatively stable ratio of domestic nonfinancial debt (private and government) to nom­
inal GNP (see figure 9).15 An oft-cited implica­
tion of this proportionality is that a decrease
in the growth of federal debt augments the
growth of private (nonfederal) debt relative
to GNP and might enable more private domes­
tic investment. Thus, the current concern is
that federal credit demands could crowd out
private credit demands and thereby stifle
the private investment that is necessary to a
growing economy.
Secular trends in federal and private debt
from 1946 through the mid-1970s contrast
strikingly with their trends over the next 40

years according to scenarios B and C. The
decline in federal debt through 1973 was met
with a roughly equal rise in nonfederal debt,
particularly in debt of households and bus­
inesses. This decline might have helped ac­
count for robust postwar growth, particularly
in the 1960s.
Projections of a rising secular trend of fed­
eral debt imply that something must give.
Either the private domestic savings rate must
rise, breaking Denison’s Law in order to sup­
ply the extra funds required to finance higher
debt-to-GNP ratios, or the nation must expe­
rience rising rates of net foreign investment,
thus evading Denison’s Law in order to supply
the extra funds. A third possibility is that
investment in private capital must decline,
complying with Denison’s Law to offset the
government demand for extra funds.
So far in the current economic recovery, Den­
ison’s Law has been evaded. Enlarged private
and public demands for credit have been met by
a record inflow of net foreign capital. This
is not a cost-free consequence of a rising debtto-GNP ratio. Growing foreign indebtedness
requires growing payments out of GNP to ser­
vice foreign debt. Capital investment may main­
tain economic growth, but the fruits of that
growth will be enjoyed by the foreign investors
who made it possible. Moreover, substantial
adjustment costs must be paid as the capital
inflow drives up the foreign exchange value of
the dollar and reduces the competitive posi­
tion of trade-related industries. Thus the in­
ternational adjustments created by the rising
debt-to-GNP ratio carry significant costs, both
directly, and (potentially) indirectly through
inefficiencies associated with protectionist
measures.

V. Conclusion
Prospects for slowing growth of the national
debt improved somewhat in August 1985, when
Congress passed a budget resolution for fis­
cal year 1986. Although subsequent analysis
suggests that budget savings would be less
than purported, the impact on the national debt

still would be significant if the resolution’s
budget targets were achieved. But budget
resolutions are only resolutions and are fre­
quently foresaken, particularly during periods
of economic stress. The more recent congres­
sional effort to mandate a sequence of deficit
reductions leading to a balanced budget early
in the next decade may be viewed as building
annual legislative roadblocks in the path of
the growing national debt. Whether such road­
blocks could be effective can only be known
when future federal budgets are known.
Uncertainty about actual federal budgets for
1986 and beyond is not the only issue troub­
ling analysts. The reliability of deficit projec­
tions based on macroeconomic models and on
rules of thumb is always tenuous. Here we
have provided a secular perspective that dem­
onstrates that future economic conditions are
likely to be less favorable for constraining the
debt-to-GNP ratio than they were for most of
the postwar period. Whether this change is
embodied in the models on which deficit and
debt projections are based, is not clear.
Cutting the primary deficit remains the
most certain method of preventing continuing
increases in the debt-to-GNP ratio. The chal­
lenge is to look beyond annual increases to the
steady advance of unprecedented peacetime
levels of federal debt—and then to take the
budgetary initiatives required to reverse the
process.

References
Barro, Robert J., and Chaipat Sahasakul.
“ Measuring the Average Marginal Tax Rate
from the Individual Tax,” Journal of Busi­
ness, vol. 56, no. 4 (October 1983), pp. 419-52.
Carlson, John B. “ The Debt Burden: What You
Don’t See,” Economic Commentary, Federal
Reserve Bank of Cleveland, May 1,1985.
Congress of the United States, Congressional
Budget Office. The Economic and Budget
Outlook: An Update, a Report to the Senate
and House Committees on the Budget. Wash­
ington, DC: Congressional Budget Office,
August, 1985.

______ , The Economic and Budget Outlook:
Fiscal Years 1986-1990, a Report to the Sen­
ate and House Committees on the Budget—
Parti. Washington, DC: Congressional Bud­
get Office, February 1985.
David, Paul A., and John L. Scadding. “ Pri­
vate Savings: Ultrarationality, Aggregation,
and ‘Denison’s Law’ ” Journal of Political
Economy, vol. 82, no. 2 (March/April), 1974.
de Leeuw, Frank, and Thomas M. Holloway.
“ Cyclical Adjustment of the Federal Bud­
get and Federal Debt,” Survey of Current
Business, vol. 63, no. 12 (December 1983),
pp. 25-40.
Executive Office of the President, Office of
Management and Budget. Budget of the
United States Government, Fiscal Year 1986.
Washington, DC: U.S. Government Print­
ing Office.
Friedman, Benjamin M. “ The Roles of Money
and Credit in Macroeconomic Analysis,”
Working Paper No. 831, National Bureau
of Economic Research, December 1981.
Munnell, Alicia H. “ Social Security and the
Budget,” New England Economic Review,
Federal Reserve Bank of Boston, July/August
1985, pp. 5-18.
Sargent, Thomas J., and Neil Wallace. “ Some
Unpleasant Monetarist Arithmetic,” Quar­
terly Review, Federal Reserve Bank of Min­
neapolis, vol. 5, no. 3 (Fall 1981), pp. 1-17.
Seater, John J. “ On the Construction of Mar­
ginal Federal Personal and Social Security
Tax Rates in the U.S.,” Journal of Monetary
Economics, vol. 15, no. 1 January 1985),
pp. 121-35.
Tobin, James. “ Discussion,” Savings and Gov­
ernment Policy, Conference Series No. 25.
Sponsored by the Federal Reserve Bank of
Boston, October 1982, pp. 126-37.
Wallich, Henry C., and Darrel Cohen. “ Per­
spectives on U.S. Fiscal Policy,” Kredit und
Kapital, 65 (1985), pp. 109-24.

James G. Hoehn is
an economist and
James J. Balazsy is a
research assistant
with the Federal
Reserve Bank o f
Cleveland. Diane
Mogren and Gordon
Schlegel provided
helpful programming
assistance. The
authors have bene­
fited from discus­
sions with William C.
Gruben and Mark
Sniderman. Com­
ments on earlier
drafts were provided
by Michael T. Bagshaw, John Erceg,
Philip Israilevich,
William Lee, and
Richard M. Todd.

The Ohio Economy:
A Time Series
Analysis
by James G. Hoehn
and James J. Balazsy, Jr.

What do regional economic statistics, such as
those for Ohio, convey about the present and
future state of the regional economy? What
do they say about the sources of regional fluctu­
ations? To what extent do they reflect national
conditions versus regional factors? Which re­
gional and national series are most useful to
watch? What degree of accuracy can a regional
forecaster hope for?
These questions are addressed by regional
economic models of both the time series and
structural variety. The latter, in a setting
in which the nature of economic relationships
is already reasonably well known and data
sets are adequate, may best embody answers to
these and related questions. But given the
incomplete theory and data actually available,
time series methods can be very helpful in
interpreting and forecasting regional economic
statistics. Here we summarize both some sug­
gested time series methods and the answers
they provided to the above questions for the
Ohio economy. (The working paper by Hoehn
and Balazsy [1985] provides greater detail
on some of these methods and answers.)
The analysis here can augment or precede
efforts to make more elaborate structural inter­
pretations. The analysis also uncovers and
measures important phenomena—for example,
the decline in Ohio’s growth after 1977 that
cannot be attributed to overall national con­
ditions—that would probably not be as trans­
parent in a structural model and might be
distorted by its assumptions. Time series
methods provide measures of relationships
and events without elaborate interpretations
imposed on them; that is at once their advan­
tage and their drawback, vis-a-vis struc­
tural models.
An important impediment facing the regional
economist is the lack of reliable and timely
measures of aggregate activity. Direct compre­
hensive measures of output are unavailable.
In practice, regional economists have come to
place greatest emphasis on the establishmentsurvey, or payroll, employment series. They
are available on a timely basis, disaggregated
by major industrial categories. The survey

1. For example, pay­
roll employment was
more closely related
to personal income
than was householdsurvey employment.
The correlation co­
efficients o f quarterly
growth rates were
0 .8 7 and 0.55, re­
spectively. The cor­
relations with the
U. S. index o f approx­
imately coincident
indicators were 0.8 7
and 0.58.
2. The data shown
are those actually
used in the study,
and are given in
Hoehn and Balazsy
(1985).

directly covers a substantial minority of em­
ployment. The sample is relatively fixed from
one month’s survey to the next, so that move­
ments do not significantly reflect changes
in the sample. This is both a virtue and a vice:
the sample fixity prevents movements from
reflecting changes in the sample, as can occur
in the household-survey employment series,
but shifts of employment away from the mostly
large-firm employment that dominates the
survey can bias measured growth. The pay­
roll series is revised early each year to largely
eliminate accumulation of such bias, but it
can still build up within the year.
By contrast, the household-survey series,
because it is based on a small sample in terms
of individuals directly covered, reflects a sub­
stantial sampling error. Standard sampling
errors, even for quarterly growth rates, sug­
gested by the collecting agency are quite high
relative to the observed fluctuations in the
series. The accuracy of payroll figures is
most likely less affected than the household-

Fig. 1 Payroll Employment and Components
Log of employment
Random component
.05

.04

.03

.02

.01

.00
Employment

Regional random
component

NOTE: Shaded areas indicate recessions.

Employment
less component

survey series by changes in the labor force,
because the household survey series neces­
sarily require assumptions about population
growth that are confirmed only at the time of
population censuses. Of course, any employ­
ment series cannot exactly reflect output,
because of changes in technology or produc­
tivity and in nonlabor inputs.
Empirical findings to be presented here con­
form to expectations about the relative use­
fulness and accuracy of the employment series.
Payroll employment, as measured, displays
a closer coherence with the cyclical variation
in other series, both national and regional.1
Movements in the payroll series also tend to
persist from one quarter to the next, unlike
the household-survey series. Also, the former
tends to foreshadow the latter, although not
vice versa.
These properties of the payroll series suggest
that they are relatively more accurate indi­
cators of employment and are more useful in
understanding and predicting regional trends.
But lacking a comprehensive output series,
we have looked to personal income in particu­
lar and to the other regional series in general
for confirmation of conclusions drawn from
the payroll series. These series include house­
hold-survey employment and the labor force,
(nominal) personal income, retail sales, housing
starts, the factory workweek, and consumer
prices. The properties of these series are of
independent, if secondary, interest.
Figure 1 shows, as the solid dark blue line,
the quarterly averages of seasonally adjusted
Ohio payroll employment from 1965 to 1983.2
The most obvious characteristics of that series
are long-term growth and variability in growth.
The variability appears somewhat cyclical.
Factors determining fluctuations in regional
growth tend to persist in the same direction for
a short time (but typically less than a year,
as we shall see). Forecasts should therefore
reflect not merely the long-run growth of the

3. The most critical
assumption is that
the parameters are
stable over the sam ­
ple period. However,
this assumption is
less o f a problem in
the out-of-sample sim­
ulations we use as a
check on our within
sample period results.

series, but also give special consideration to
growth in the most recent quarters. These
characteristics pertain to the properties of the
series in isolation and require no theoretical
knowledge to acquire. For deeper understand­
ing, and possibly more accurate forecasts, the
series must be related to other series, regional
and national.
As a vivid illustration, consider the effects
of national recessions, as identified by the
National Bureau of Economic Research. They
are shown in figure 1 as the shaded areas. We
shall show how the national composite indexes
of leading and coincident indicators are par­
ticularly useful proxies for the national busi­
ness cycle. We formally express their relation­
ship with Ohio employment by a trickle-down
model.
A number of time series models for 10 sea­
sonally adjusted quarterly Ohio series will be
sequentially considered to establish the fore­
casting signals available from a variable’s
(a) own past, (b) other regional variables’ pasts,
(c) national variables’ pasts and, in some cases,
(d) contemporaneous relationships with other
variables. Analysis also helps us understand
the characteristics, quality, and usefulness
of various available regional indicators. Com­
parisons of the models’ performance in a 19651983 sample period and a 1979-1983 out-ofsample forecast simulation are designed to
assess these potential sources of information.
Finally, the particularly successful trickledown model is further studied to yield insight
into the sources of regional growth fluctua­
tions in Ohio from 1965 to 1983.

I. A Time Series Methodology
Before presenting results, some explanation
of methods is helpful. One major advantage of
the time series methods we use is that they
are quite transparent. They can be replicated
in this and other contexts. These methods are
appropriate in many contexts in which a priori
information about relationships is scarce or
inadequate. We regard the economic process
at the regional and national levels to be an

example of such contexts. Our methods are
informative, although less informative than
methods that use stronger correct prior infor­
mation. A reader in possession of such infor­
mation may rightfully regard a time-series
approach as neglecting it, resulting in ineffi­
ciency in extracting knowledge. We do not ask
the reader to accept an elaborate structural
hypothesis of our own at the outset of the
analysis, nor do we impose such a hypothesis
on the data. We shall make some structural
speculations and interpretations of our results
after the data have spoken through a set of
more neutral statistical hypotheses, in the
form of simple linear time series models. Of
course, even these models involve some ad hoc
assumptions, although they are minimal.3
Our objective is to model, consequently pre­
dict and, in some sense, explain, the movements
of Ohio series. Each quarter is treated as a
separate event. Each variable is analyzed in
terms of a quarterly growth rate, measured
as the change in the natural logarithm. (When
multiplied by 100, this rate is essentially a
percentage.) The various models to be consid­
ered condition expected growth rates on various
potential sources of information. By compar­
ing the performance of alternative models,
which differ by including or excluding some
variable or variables, we can assess the infor­
mation value associated with the addition of
a source or sources of information. We shall
always allow models to reflect information
about its parameters from historical data. The
comparisons will involve the effect on model
performance from the addition of some past
growth rates of the series itself (own-lags), or
that of some other series or group of series.
(Contemporaneous relationships are largely
irrelevant for forecasting, although important
for structural analysis.)
For example, the random walk (with drift)
model simply predicts that the historical aver­
age growth will occur in any quarter in the
future; it uses no past growth rates except,
of course, in the calculation of the average—
the key parameter in the random walk model.

The autoregressive model we consider uses
the past two quarterly own-lags to forecast a
quarter’s growth rate. The information gain
from using the series’ own past growth can be
measured by comparing the size of a typical
forecasting error of the autoregressive model
with that of the random walk model. If a vari­
able is characterized by cyclicity, or persis­
tence, then the autoregressive model will have
typically smaller errors.
Additional information from other variables,
both regional and national, was assessed by
measuring the reduction in typical forecast
error after including the first two lags of those
variables. We have tried a list of 27 possible
variables—the other nine regional and 18
national variables—each individually as pos­
sibly useful. Each of these trials created a
bivariate model, in which a series’ growth was
conditioned on its own recent growth rates
and those of one other variable. Finally, two
multivariate models, a trickle-down and a step­
wise model were tried. The trickle-down model
predicts a series’ growth rate using the two
most recent own-lags plus one lag each of pay­
roll employment, the U.S. composite index of
leading indicators, and the U.S. composite
index of approximately coincident indicators.
As it turned out, the (total) payroll variable
in each equation for the other nine regional
series generally had very little explanatory
power once the national variables (and ownlags) were included, justifying the characteriza­
tion “ trickle-down.” In order to use the trickledown model to forecast more than one quar­
ter ahead, we augmented it with equations for
the two national variables. They included, as
regressors, two own-lags and one lag of the
other national variable. The equation for Ohio
payroll employment and for the two national
variables are shown in the box in section III.
Their implications will be analyzed exten­
sively there.
The stepwise model used a variant of the
familiar stepwise regression procedure. It
searched opportunistically among regressors

suggested by their significance in the bivar­
iate tests, in order to find a well-fitting equa­
tion. A similar, but less mechanistic, method
of model construction proved successful for
Texas in an earlier study (Hoehn 1984). The
stepwise model helps us assess the total in­
formation available without regard to source,
and is less dependent on ad hoc, prior assump­
tions than the trickle-down model. In fore­
casting more than one quarter ahead, the step­
wise model used two-lag autoregressive equa­
tions to provide the prerequisite forecasts of the
national variables.
In implementing this methodology of assess­
ing information gain, we have necessarily
imposed certain ad hoc, although reasonable,
and commonly made, assumptions. First,
the lag structures described were assumed to
be sufficiently long to capture all the infor­
mation. The series were seasonally adjusted,
so longer lags would not be necessary to cap­
ture seasonal influences. We openly acknowl­
edge that the X -ll seasonal adjustment pro­
cedure may not be entirely adequate, however.
The models implemented were linear in the
growth rates and were estimated using ordi­
nary least squares.
The information value of a series for pre­
dicting another series was measured in two
different ways to provide confirmation. First,
the models (except the stepwise) were con­
structed from a long sample from 1965 to 1983.
The standard error of the equation for a given
model was used as the measure of a typical
forecasting error. Then the information gain
is measured by comparing the standard errors
of the equations. For example, the gain from
using two own-lags is measured by the reduc­
tion in the standard error of the autoregres­
sive model relative to that of the random walk
model (whose standard error is identical to
the standard deviation of the growth rate). The
reduction is stated as a percent of the stan­
dard error of the benchmark, or simpler, model.
The calculation of standard errors automat­
ically controls for the tendency of least squares
regression to “ overfit” a prespecified relation­
ship, so that addition of actually uninforma­

4. This reveals itself
as a lack o f fu rther
reduction in root
means o f square
error measured in
(log) levels o f series,
beyond the one-year
horizon.
5. We confess that
time aggregation—
the averaging o f data
from more than one
point in tim e—can
create spurious posi­
tive autocorrelation.
See Tiao and Wei
(1976). The use o f
monthly data would
eliminate this prob­
lem fo r the employ­
ment surveys, but
would make lag struc­
tures more complex,
the resulting models
less transparent, and
seasonal adjustment
issues more serious.

tive variables does not tend to reduce standard
errors or to produce spurious measured infor­
mation gains. However, the stepwise proce­
dure searched a long list of possible variables
for information, so that the overfitting ten­
dency cannot be adequately controlled by this
method. Its performance can only be assessed
by a second method.
The second method measures information
by the reduction in the root mean square error
(RMSE) of alternative models’ forecasts dur­
ing a simulation period from 1979 to 1983. To
simulate real-time forecasting, each model’s
forecast was based on parameter estimates
constructed using data for periods prior to the
period forecast. The stepwise model was speci­
fied (its information variables and their lags
chosen) using only data through 1978; it was
not respecified in the simulation, giving it a
handicap it would not suffer in real-time fore­
casting. (Of course, its parameter estimates
were updated during the simulation period.)
For all models, we give emphasis to and report
RMSEs for the one-quarter-ahead and fourquarter-ahead forecasts. Our results for longer
forecast horizons are less interesting, other
than to confirm the frequently bemoaned lack
of useful information about growth rates be­
yond a year.4 Models of longer-term growth
would involve demographic and other factors
not included in our cyclical analysis.

II. Time Series Properties
of Ohio Economic Statistics
This battery of time series tests and confirma­
tions yielded results that probably conform
to, yet may strengthen, refine, and extend, the
knowledge that economists studying regions
such as Ohio already possess. Some results,
such as the relative importance of the national
business cycle in accounting for regional fluc­
tuations, may vary across regions; other results
may be more general.

First, there is a degree of cyclicity, persis­
tence, or autocorrelation in the regional econ­
omy, according to comparisons of the auto­
regressive and random walk models. The first
column of numbers in table 1 shows signifi­
cant information gains for payroll employment,
personal income, and consumer prices, con­
firmed by the reductions in RMSEs shown in
the next two columns. We speculate that the
lack of autocorrelation in household-survey
employment and retail sales may, in large part,
reflect measurement error. As a simple illus­
tration, if the latter tended to reverse itself each
quarter in terms of the level of the series,
as would be the case for sampling errors, then
the observed first-order autocorrelation (cor­
relation between adjacent periods) in growth
rates would tend to be pulled away from its
true value toward minus one-half. Of course,
the nature of measurement errors is far more
complex (see Green [1969], Korns [1979] and
U.S. Department of Labor [1985]). Depending
on the exact nature of the measurement error,
the true cyclical properties of the underly­
ing series, and the relative influence on the
observed series of each, they might roughly
cancel out in the sense of producing no per­
sistence in the observed series. Measurement
and sampling errors are likely to be particu­
larly large for household-survey employment
and retail sales because the samples are small.
This interpretation of the household-survey
employment series is reinforced by the slight
negative autocorrelation in the labor force
series obtained by the same samples.5
The degree of persistence in payroll employ­
ment is not large; it accounts for less than
18 percent of the standard deviation of total
payroll growth rates, and about one-tenth of
its manufacturing and nonmanufacturing cat­
egories taken separately. Although this per­
sistence may be slightly understated due to
measurement problems, the conventional X-ll
seasonal adjustment procedure may tend to
overstate it somewhat. Examination of the
autocorrelation of adjacent growth rates sug­
gests that cyclical factors influencing total
payrolls tend to persist in the same direction

6. The potential o f
the interest rate and
inflation to provide
leading information
is consistent with new
interpretations o f the
business cycle that
stress changes in pro­
ductivity. A study
by Litterman and
Weiss (1983) suggests
that innovations in
real interest rates
precede innovations
in output.

for only a few quarters. Autocorrelations are
0.57, 0.32, and 0.22 for lags one through three,
respectively, 0.23 being equal to the approxi­
mate .05 two-tailed critical value.
The lack of substantial autocorrelation be­
yond a few quarters is consistent with the
notion that cyclical factors tend to persist in
the same direction for only a short period.
A short duration and relatively small ampli­
tude of the business cycle is suggested in
studies of national and international data
by Nelson and Plosser (1982) and Stulz and
Wasserfallen (1985).
Most persistence in Ohio payroll employ­
ment beyond a single quarter is attributed to
the nonmanufacturing category, whose auto­

Fig. 2 Information Sources
for Payroll Employment
Standard deviation = 100%

1

Standard error of autoregression

1 17.7% j
i
i
i
ii
i

Two-own lags, plus:
Ohio housing starts

8.2%
i

U.S. leading index

— 119.3%
U.S. coincident index

U.S. payroll employment

i
i
— 114.5%
i
i
<~\ 9.4%

U.S. industrial production
-«"!

8.0%

I
ii

Bond yield
-J

7.7%

correlations are significant at up to five lags. By
contrast, the manufacturing sector’s growth
rate is significantly autocorrelated only at the
first lag, although the second lag’s autocorre­
lation is nearly significant. Beyond the second
lag, manufacturing employment autocorrela­
tion declines rapidly. A higher magnitude of
persistence in total payroll employment in
comparison to its components seems paradox­
ical, but is due to independent fluctuations
in and intersectoral shifts between the two.
(Interestingly, once their relation with the U.S.
coincident index is controlled for, they dis­
play a slightly negative relationship.) Hence,
cyclical movements of the total are somewhat
obscured in the components.
The bivariate tests suggested that the two
national composite series contain particularly
valuable information about the future course
of Ohio payroll employment, confirming prior
notions upon which the trickle-down model
was built. Indeed, these two series proved more
informative than any others, as shown in fig­
ure 2, which depicts gains from the six most
informative series. Significant at the .01 level,
in descending order, were the two composite
indexes, U.S. payroll employment (one of four
components in the coincident index), Ohio
housing starts, U.S. industrial production (also
a coincident index component), a long-term
interest rate, the U.S. consumer price index,
U.S. manufacturing payroll employment, and
the gross national product deflator.
The composite indexes seem to summa­
rize reasonably well the information available
from national data. Perhaps the long-term
interest rate, classified as a “ lagging indicator”
but showing leading information here, is the
major element omitted from those two com­
posites.6 Among the regional series, only Ohio
housing starts gives significant leading infor­
mation about future payroll employment at the
.01 level in the bivariate tests. However, we
discovered later that the series did not add

7. We tried adding
m e lag o f starts to
fhe payroll equation
if the trickle-down
model. The standard
irror o f the equation
'ose as a result.

any incremental information after the lead­
ing and coincident series were included.7 The
payroll measure gives leading information
about the future household-survey employ­
ment and labor-force series, but not vice versa.
In fact, of all the intraregional bivariate lead­
ing relationships found, the strongest was
from payroll to household-survey employ­
ment, whose standard error was reduced by
over 13 percent. The manufacturing work­
week was included in our study in the hope
it would provide advance information about
manufacturing payrolls. Instead, the work­
week was foreshadowed by manufacturing pay­
rolls. This result is inconsistent with the pre­
vailing characterization of the workweek as
leading. (Its national counterpart is included in
the composite index of leading indicators.)
The result is nevertheless consistent with the

Table 1

results of Beveridge and Nelson (1981), who
find that its national counterpart is a lagging
indicator of the business cycle.
Based on the bivariate results, we regard
cyclicity in payroll employment as largely
linked to the national cycle, an interpretation
to be reinforced in the next section. Results
for personal income were quite similar in that
the same series that were informative about
payrolls were generally also informative about
income. The two composite indexes were again
most valuable, followed by U.S. payrolls, the
manufacturing component of U.S. payrolls,
and Ohio housing starts. However, the infla­
tion and interest-rate variables were insig­
nificant, while real gross national product
was significant, at the 1 percent level.
The leading or lagging character of the
series can be tentatively judged in view of

Information Gains and Forecast Simulation Results
General interdependence

Cyclicity
Autoregressive (univariate)
Reduction in
RMSE2

Stepwise

Trickle-down
Reduction in
RMSE5

Reduction in
RM SE5

Infor­
mation
gain4

1-step

4-step

gain1

1-step

4-step

Infor­
mation
gain3

17.7b

26.4

12.7

19.5b

20.2

6.8

34.2

14.6

6.3

10.1 b

14.7
28.2

1.1

25.3b
7.5a

24.7

15.6

0.0

14.8
-2.7

36.1
21.7

18.1
-9.8

3.9
-1.7

- 0.8

-1.9

- 2.0

16.1b

11.0

4.9

24.9

20.7

6.0

Labor force

2.4

-3.9

-4.2

7.6a

7.5

21.5

16.7

4.7

34.9

Personal income

7.6b

10.3

2.4

18.4b

23.7

5.1

26.3

-4.3

5.1

InforOhio Series

Payroll employment
(establishment
survey)
Manufacturing
Nonmanufacturing
Household-survey
employment

9.6b

1-step

4-step

1.4

-0.5

1.2

11.0

1.9

4.9

5.7

- 1.2

Housing starts

2.0
- 1.0

- 2.8

-2.5

9.0b

5.6

8.6

15.6

17.6

25.2

Factory workweek

-0.5

0.8

1.2

25.5b

17.6

17.6

37.5

5.6

7.8

Consumer prices

19. l b

7.7

9.1

0.7

0.0

3.3

7.7

-3.8

-5.9

Retail sales

a. Significant at the .05 level.
b. Significant at the .01 level.
NOTE: All series were seasonally adjusted. (Data sets and sources described in Hoehn and Balazsy [1985].)
1. The percent reduction in standard error of equation relative to the random walk model, for the 1965:IVQ to 1983:IVQ sample period.
2. The percent reduction in root mean square error relative to the random walk model, for the 1979:IQ to 1983:IVQ simulation period.
3. The percent reduction in standard error of equation relative to the univariate autoregressive model, for the 1965:IVQ to 1983:IVQ sample period.
4. The percent reduction in standard error of equation relative to the univariate autoregressive model, for the 1965:IVQ to 1978:IVQ sample
period. Warning: The calculated information gain does not control for the “ overfitting” arising from opportunistic selection of regressors.
5. The percent reduction in root mean square error relative to the univariate autoregressive model, for the 1979:IQ to 1983:IVQ simulation period.

the above results and interpretations of quar­
terly data. We regard housing starts as lead­
ing, hours as lagging, and most other series as
approximately coincident. The householdsurvey series for employment and labor force
would probably be coincident, aside from
the measurement errors they contain. The
labor force series may be a noncyclical series,
since it is contemporaneously uncorrelated
with any series other than household-survey
employment. Measurement errors in both
household-survey series may give them a lag­
ging appearance; the other series, particularly
the payroll series, are needed to help locate
their true, underlying level. The Ohio con­
sumer price series was virtually unrelated to
any other, except national price series, and so
could be called an irrelevant or non-indicator.
The trickle-down and stepwise models of
payroll employment and its components, and
of personal income, fit better, in the sense of
standard errors of equations, than either
the autoregressive or any of the bivariate
models. Employment according to the house­
hold survey was slightly more closely related
to two past values of the coincident index than

Fig. 3 RMSEs of the Payroll
Forecasts for Models
Random walk

Autoregression

Trickle-down

to the regressors of the trickle-down model
(of which the first lag of the coincident index
was the most powerful). The trickle-down
model’s standard errors for retail sales and
consumer prices were no smaller than for their
autoregressive equations, a result that con­
forms to the bivariate evidence that these vari­
ables cannot be forecast by using other infor­
mation. Although retail sales were related
to other series within a given quarter (the cor­
relation with payroll employment was 0.28),
no leading information about it from other
series was uncovered.
The out-of-sample forecasts of the trickledown and stepwise models provide evidence
that simple multivariate forecasting models can
perform successfully, having lower RMSEs
than simple autoregressive models. As shown
in table 1 , the improvements are reasonably
consistent across the 10 regional variables.
The trickle-down model had a RMSE at least
as small as the autoregressive model in onequarter-ahead forecasts for all variables and
provided statistically significant information
gains in eight cases, at the .05 level. For payroll
employment, the gain and the reduction in
RMSE was about one-fifth (figure 3). Much
of that improvement appears to come from in­
formation about manufacturing employment.
This evidence of the forecasting ability of
simple multivariate models roughly replicates
a previous result by Hoehn (1984) for Texas.
While the improvement over the univariate
autoregressions should not be exaggerated, it
is meaningful, consistent, and to our knowl­
edge has not been documented for structural
models or for unparsimonious time series
models (such as the “ Bayesian vector auto­
regressive” models) commonly employed.

Stepwise

i

i

i

.00

.01

.02

i
.03

■
l-step

4-step

l
.04

1
.05

III. National and
Regional Fluctuations
The trickle-down model can help address the
linkage between national and regional fluc­
tuations. It suggests that variations in payroll
employment over periods of several quarters

can be mostly attributed to national devel­
opments, as summarized, apparently rather
well, by the two composite indexes.
The trickle-down model describes the deter­
mination of payroll employment according
to the three equations shown in the accompa­
nying box. Movements in payroll employment
are attributed to the disturbances or shocks

The Trickle-Down Model
of Payroll Employment
Sample: 1965:IVQ to 1983:IVQ
(1)

MnPAYROLLt = -.0004
(.0008)
- .06AlnPAYROLL,^
(.20 )

+ .36A\nPAYROLLt„2
( . 12)

+ ASA\nLEADt.\
(.06)
+ A6 A\nCOINt-i + ext
(.13)
standard error of equation = .0065
(2)

AinLEAD, = .0057 + .84AlnL£,4A-i
(.0024) (.12)
+ .22A\nLEAD,_2

(.13)
- .89AlnCO/NM + e2t
(.19)
standard error of equation = .0192
(3)

AlnCOIN, = .0015 + .02A\r\COINt_x
(.0016) (.16)

to each of the three equations. These shocks
feed through the equations to generate the
observed changes in the three variables. (While
not observed directly, these disturbances can
be estimated as residuals in the fitted equa­
tions.) The shocks to the national indexes’
equations clearly reflect national events. But
so, to some extent, do those to the payroll
equation, creating some ambiguity. However,
this ambiguity is eliminated by attributing
any portion of payroll shocks that are statis­
tically related to the national equation shocks
to national events. The part of the payroll
shock (linearly) wwrelated to national events
can be found by regressing the residual from
the trickle-down equation for payrolls on those
for the national indexes. The residuals from
this regression represent both distinctly re­
gional events and idiosyncratic elements of the
region’s response to national events. In the
vector autoregression (“ VAR” ) literature, these
are called orthogonalized shocks because they
are “ washed” of correlation. These residuals
have a variance only 41 percent as great as
that of the payroll equation’s disturbance term,
because correlation with national equation
errors accounts for 59 percent (R 2). The in­
terpretation is that even short-run movements
in Ohio employment are largely accounted
for by national events. Over longer time hori­
zons, the importance of national events looms
larger, as national shocks create persistent

Random Regional Component

+ .22A\nCOINt_2
( .1 2 )

Let the national component of eu be:

+ .5lAlnLJL4Z),_i + e3t
(.09)

Then the orthogonalized error is:

standard error of equation = .0128
PAYROLL = Ohio payroll (establishmentsurvey) employment, season­
ally adjusted.
LEAD = Index of leading indicators.
COIN = Index of approximately coinci­
dent indicators.
NOTE: Figures in parentheses are the standard errors of estimates of
the parameters.

&\t ~ E[elt\e2t, e3t] = k\e2t+ k2 e3t.
eft = eu - 2 lt, and,
the random regional component of InPAYROLL, is:

(1 -

L)A( 1 + .061 - M L 2 )Ael,

where L is the lag operator.

fluctuations in the composite indexes that
trickle down and feed through the payroll equa­
tion. As shown in table 2, a 1 percent positive
shock to the leading index is followed by a
progressive increase in Ohio employment,
peaking at 0.81 percent in five quarters. The
typical movement of Ohio payrolls in the
wake of orthogonalized shocks to the coinci-

Table 2 Response of Ohio Payroll
Employment to Orthogonalized Shocks
National shocks

Quar­
ters
ahead

1
2
3
4
5

6
7

8
9

10

Index of
leading
indicators
Unit3

.13
.37
.57
.73
.81
.82
.79
.75
.71

.68

Standardb

.25
.71
1.09
1.40
1.55
1.57
1.52
1.44
1.36
1.30

Regional shocks

Index of
coincident
indicators
Unit3

Payroll
employment

Standardb

.46
.59
.59
.46
.29
.13

.44
.56
.56
.44
.27

.01

.12
.01

-.04
-.05
-.03

-.04
-.05
-.03

Unit3

1.00
.94
1.30
1.26
1.39
1.37
1.42
1.41
1.43
1.42

Stan­
dard5

.42
.39
.54
.53
.58
.57
.59
.59
.60
.59

a. Percent response of payroll employment to a 1 percent shock.
b. Percent response of payroll employment to a shock of typical size,
i.e., one standard deviation.

Table 3 Decomposition of Variance of Ohio
Payroll Employment Forecast Errors
Percentage of variance
attributable to
Quarters
ahead

Standard
deviation3

Leading
index

1
2

.65
1.18
1.79
2.37
2.91
3.35
3.73
4.04
4.31
4.54

14
40
55

3
4
5

6
7

8
9

10
a. Percent.

66
72
76
78
79
80
80

Coinci­
dent
index

Payroll
employ­
ment

45
36
26
18
13

41
23
19
16
15
14
14
14
14
14

10
8
7

6
5

dent index—washed of their correlation with
the shocks to the leading index—is more im­
mediate, but fades, meaning that increases in
the coincident index that are not validated
by the leading index tend to be followed by
unsustainable increases in Ohio payrolls.
Given the relative magnitudes of the orthog­
onalized errors, and the response patterns just
described, forecasting errors at long-term hori­
zons owe about 85 percent of their variance
to national events, as shown in table 3.
Although the national series, particularly the
leading index, have considerable leading in­
formation about regional employment growth,
this does not necessarily imply that Ohio
lags behind the economy over business cycles.
Other evidence suggests the relation between
national and Ohio payroll employment may
be essentially contemporaneous. The timing
relation can be summarized by the cross-correlation function—the correlation of growth
rates, after the latter are washed of autocor­
relation, at various leads and lags. (Spurious
results can arise without such a washing.) We
implemented the washing by using residuals
in regressions with two own-lags for the two
employment series. The contemporaneous cor­
relation of those residuals was 0.83. No other
correlations were significant, although the
correlation between the Ohio payroll residual
and the national payroll residual lagged once
was 0.21, not far from the 0.23 critical value for
the .05 significance level. The lagged correla­
tion, however, might easily be a result of larger
measurement error in the Ohio series, time
aggregation (Tiao 1972), or seasonal adjustment
problems. Hence, the evidence provides weak
support for anything other than a contempo­
raneous relation between Ohio payrolls and its
national counterpart.
The trickle-down model also permits a decom­
position of the historical values of the payroll
series into a long-run growth component and
random components attributable to national
and regional shocks .8 Figure 1 shows the over­
all payroll series, with the random regional com­
ponent (right-hand scale, blown up) and the
payroll series minus its random regional

I Our time series
nodel cannot break
Iown the long-run
growth o f the series
nto components atributable to national
\nd regional factors;
0 do so would require
\dditional structural
nformation.

1 Our colleague,
°hilip Israilevich,
peculates that
mailer increases
n (regulated) elecricity prices in Ohio,
ompared with the
ration, during the
nid-1970s oil price
ncreases may be
esponsible fo r the
incharacteristically
noderate decline o f
~)hio employment in
hat recession period.
1n alternative or comlementary explanaion would stress the
ncreased demand
ir new, less energyi tensive capital goods
s energy prices rose.
Ohio is a major cap'al goods producing
'ate.) We are unable
i provide convincig tests o f these
ypotheses without
n extensive, more
'ructural analysis,
hich is beyond the
•ope o f our study.

component superimposed. The random or cyc­
lical regional component reflects the impact
on the level of the payroll series arising from
the orthogonalized shocks to its equation. It
is essential to bear in mind that, because the
long-run growth has been removed, the ran­
dom regional component, which starts at zero,
necessarily also ends the sample at nearly
zero. It is the movements of the component
during particular periods, compared with other
periods in the sample, that is informative.
The random regional component rises dur­
ing the economic expansion of the late 1960s.
During the 1973-1975 recession, the compo­
nent again rose sharply, greatly cushioning the
impact of the national recession.9 Indeed, the
decline of 115,000 jobs during the six-quarter
recession would have been 90,000 larger with­
out the aid of the component. But from the
late 1970s to the end of 1983, the regional
component declined, accounting for a loss of
189,000 jobs from 1977:IIIQ to 1983:IVQ. In
contrast to the 1973-1975 recession, distinctly
regional factors appear to have aggravated
Ohio’s economic weakness in the early 1980s.
Furthermore, the rise and subsequent fall of
the component might reflect a kind of struc­
tural change in the region; perhaps the under­
lying long-run growth rate declined in a per­
manent way after the mid-1970s.

Conclusion
Time series methods can be used to exploit
limited prior information and data sets to
acquire insight into economic systems. In this
study, we designed and applied time series
methods to Ohio and (a) assessed the quality
and quantity of information in various indi­
cators of economic activity in Ohio, (b) devel­
oped relatively efficient forecasting schemes,
(c) provided insight into the sources of vari­
ation in sectors of the Ohio economy, and
(d) uncovered and measured phenomena for
further analysis. The methods employed were
simple and transparent and could be applied
in other contexts, such as in other regional
economies.

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The Federal Reserve
Bank o f Cleveland
publishes an infor­
mative research peri­
odical called E co­
nomic Com m en­
tary. Following, at
right, are the titles
published since April
1985. I f you are
interested in receiv­
ing this publication,
either futu re or back
issues, please contact
the Public Inform a­
tion Department,
Federal Reserve
Bank o f Cleveland,
P.O. B ox6387, Cleve­
land, OH 44101,
(216) 579-2048.

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Economic
Commentary
CRR and Monetary Control
Michael R. Pakko
5/15/85
The Financial Distress
in American Farming
Michael Bryan and Gary Whalen
6/1/85
Major Trends in Capital Formation
Robert H. Schnorbus
6/15/85
The Dynamics of Federal Debt
John B. Carlson and E.J. Stevens
7/1/85
Is Manufacturing Disappearing?
Michael F. Bryan
7/15/85
Solutions to the International
Debt Problem
Gerald H. Anderson
8/1/85

Tiao, G.C. “Asymptotic Behavior of Temporal
Aggregates of Time Series,” Biometrika,
vol. 59, no. 3 (1972) pp. 525-31.

Medicaid: Federalism and
the Reagan Budget Proposals
Paul Gary Wyckoff
8/15/85

U.S. Department of Labor, Bureau of Labor
Statistics. Employment and Earnings, vol. 32,
no. 9 (September 1985).

The Dollar in the Eighties
Owen F. Humpage and
Nicholas V. Karamouzis
9/1/85
Interstate Banking: Its Impact
on Ohio Banks
Thomas M. Buynak
9/15/85
The M l Target and Disinflation Policy
William T. Gavin
10/1/85