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The Federal Reserve Bank of San Francisco’s Economic Review is published quarterly by the
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Inflation, Uncertainty and
Capacity Utilization
I.
Introd uctio n and Sum m ary
4
II.
Inflation Expectations and Factor
Demands in M anufacturing
Joseph B isignano
6
...U n a n tic ip a te d in fla tio n can cause changes in factor-dem and
response by in d u cin g the s u b stitu tio n of labor fo r capital.
III. Estim ating a S table-Inflation
C apacity-U tilization Rate
Rose M cElhattan
20
... In fla tio n a ry pressures tend to increase when the operating rate
exceeds 82 percent of c a p a city— so there is little slack at this
stage of the cycle.
IV. Room for G row th: Speeds of A djustm ent of
Labor and Capital
Larry B u tle r
... The capital and labor m arkets need not reach fu ll-re so u rce use
at the same p o in t in the business expansion, because capital
and labor supplies e x h ib it d iffe re n t cyclica l patterns.
E ditorial co m m ittee fo r this issue:
H ang-Sheng Cheng, John Judd, Yvonne Levy
3
31
The economy has expanded substantially
of capital growth. Moreover, unanticipated-
since the dismal days of early 1975; indeed, this
inflation shocks, and their persistent effects over
expansion may be characterized as the longest
and the strongest peacetime recovery of the past
generation. At this stage of the business cycle,
therefore, we are interested in determining the
extent of the pressures (if any) developing in the
labor and capital markets. In other words, how
far can the expansion go without aggravating the
already severe inflationary pressures existing in
the economy? But in addition, we are interested
in determining the shifts (if any) in factor utilization created by the increased uncertainty characteristic of the inflationary 1970's. Other studies
have examined these questions in terms oflaborforce utilization. The three papers in this issue
extend the discussion, however, by analyzing
also the utilization of capacity in the industrial
sector of the economy.
Joseph Bisignano, in his paper, focuses on the
role that inflation plays in determining labor and
capital demand in manufacturing, especially
when price changes are unexpected. To help
analyze this question, he considers two measures
of inflation variability-~"unanticipated inflation," obtained from errors of forecasts of the
wholesale-price index six months into the future,
and "relative price variability," measured as the
variance of the rate of change in business capitalgoods prices. He incorporates these inflationvariability measures into a model of the demand
for two "stock" variables, capital and workers,
and two "flow" variables, capacity utilization
and average weekly hours.
Bisignano's study suggests that, over the 195975 period, unanticipated inflation has tended to
reduce the demand for investment goods in
manufacturing, and to increase labor demand
and the rate of capacity utilization. "Our tentative evidence suggests that unanticipated inflation can affect the demand for factors of production as well as the utilization of these factors.
This type of inflation thus may slow the process
a prolonged period, help explain why investment
demand has been sluggish since the early-1975
cyclical trough."
Bisignano raises an important question-whether unanticipated inflation affects labor
demand differently than capital demand. He
notes that unanticipated inflation creates' additional uncertainty regarding a firm's future output prices. The firm when expanding output thus
will attempt to minimize the future cost of its
forecasting errors by using more of its variable
factor, labor, and less of its fixed factor, capital.
The risk-averse firm, encountering greater uncertainty over the real value offuture streams of
income, wili attempt to minimize those investments that are least reversible, such as long-term
investment in plant and equipment. Unanticipated inflation thus causes changes in factordemand response by inducing the substitution of
labor for capital.
Rose McElhattan develops a combined price
equation, connecting inflation and capacity utilization, analogous to the inflation/unemployment relation so often discussed in the literature.
Her study suggests the existence of a fullcapacity utilization rate which is consistent with
the "natural rate of unemployment" concept.
(According to that view, there is only one fullemployment unemployment rate, towards which
the economy tends over time.) Attempts to
maintain a capacity-utilization rate above the
estimated full-capacity equilibrium rate appear
to be associated with a steadily increasing inflation rate.
At what specific point in the use ofthe nation's
industrial capacity are inflationary pressures
likely to increase? Many economists believe that
the yardstick is provided by the historical peak of
capacity utilization~-that is, the 87-to-88 percent
level of the 1973 period. McElhattan's analysis
suggests, however, that the full-capacity utiliza4
conflict may be apparent rather than real, because structural changes in the economy-such
as labor-force shifts-have made it difficult to
compare the measures over time. He claims,
however, that it is not necessary to resort to
structural arguments to explain the current divergence of the two rates. "Rather, the two
markets need not reach full-resource use at the
same point in the business expansion, because
capital and labor supplies exhibit different cyclical patterns. New additions to the capital stock
are concentrated in the mature-recovery portions of cyclical expansions, while new additions
to the labor force are concentrated in the brief
periods following cyclical troughs."
Butler deals with this problem by developing a
two-factor model-one which includes the capital market as well as the labor market used in the
standard (single factor) aggregate-demand model. The single-factor model adequately describes
such mature-recovery periods as 1956-57 and
1967-69, which were capital-constrained with
high levels of capacity utilization, and also laborconstrained with quite low levels of unemployment. However, the two-factor model provides a
much better explanation of three brief but important periods of transition to full employment-in 1955, 1965 and 1973. "More importantly, that model may be relevant to the period
immediately ahead, which is likely to be marked
by capital constraints but also by adequate
supplies of labor."
tion rate is reached at a somewhat lower level, so
that there is less non-inflationary slack in the
present economy than is commonly believed.
She argues that inflation tends to accelerate
when the operating rate surpasses 82 percent-or
more generally, the range of 80 to 83\-'2 percent.
"Once beyond that range, excess demand generates inflationary pressures as less efficient labor
and capital resources are called into use. Thus,
since utilization rates recently have approached
85 percent, we could expect mounting inflationary pressures from the domestic, nonfarm business sector of the economy."
Her estimates also indicate that for every
percentage-point increase in capacity utilization
above 82 percent, the rate of inflation should
increase .12 percentage points on average. For
example, if the yearly operating rate averages 88
percent-the historical peak value-the annual
inflation rate should increase .72 percentage
points on average. "Once capacity utilization
exceeds the range indicated, the increased inflation tends to become imbedded in future inflation, with the current period's higher prices being
reflected in the next period's expectations. When
the operating rate rises above the full-capacity
range, its return to that range will be accompanied by a higher rate of inflation."
Larry Butler analyzes the apparent conflict
between the unemployment rate and the
capacity-utilization rate-the two measures of
the available economic capacity at the nation's
disposal. He recognizes the argument that the
5
Joseph Bisignano*
gated components of the price deflator for business fixed investment. These inflation-variability
measures are incorporated into a model of the
demand for two "stock" variables, capital and
workers, and two "flow" variables, capacity
utilization and average weekly hours worked.
The demands for these factors of production are
considered "interrelated," with the adjustment in
one factor affected by the state of the other
factors. We statistically estimate the factor demands to determine the impact of inflation
variability, and then ask whether the results are
consistent with the observed growth in labor and
capital in the recovery period beginning in early
1975.
This study suggests that, over the 1959-75
period, unanticipated inflation has tended to
reduce the demand for investment goods in
manufacturing, and to increase labor demand
and the rate of capacity utilization. In addition,
anticipated (trend) inflation has had no statistically significant impact on either labor or capital
demand. The latter findings lend support to the
"natural-rate hypothesis" that there is no permanent beneficial trade-off between anticipated
inflation and unemployment.
Since the business-cycle trough in the first
quarter of 1975, economists have frequently
noted the rapid growth in aggregate employment
and the rather sluggish growth in real business
fixed investment. From March 1975 to July
1978, total employment grew at a 3.5-percent
annual rate, compared with a 2.4-percent average annual rate of growth for the previous four
business cycles. In contrast, real fixed investment
grew at a 5.5-percent annual rate over roughly
the same time-span, compared with a 7.3-percent
average growth rate in the previous four recoverIes.
Against that background, this paper focuses
on the role inflation plays in determining the
demand for labor and capital in manufacturing.
Will inflation tend to increase or reduce the
demand for these factors of production, and
under what conditions? To help answer the
question, we shall consider two measures of
inflation variability. The first is a measure of
"unanticipated inflation," obtained from errors
of forecasts of the wholesale-price index six
months into the future. The second measure;
referred to here as "relative price variability," is
the variance of the rate of change in business
capital-good prices, derived from the disaggre-
I.
Output Expansion With Known Relative Prices
labor force is usually considered variable in the
short-run; within certain limits, the labor force
can be expanded or contracted to meet the
requirement to produce a given amount of output.
The "long-run" is conceptually defined as a
period with variable supplies of both factors of
production, labor and capital; that is, both are
decision variables capable of being expanded to
meet desired levels of output. 1 A firm's long-run
production problem consists of determining the
desired physical plant size and the desired perm-
To understand how inflation may affect the
demand for, and utilization of, capital and labor,
we must first distinguish between short-run and
long-run firm behavior in an environment without any price uncertainty. The "short run" typically is defined as a period with fixed supplies of
at least one factor of production, usually capital
in the form of physical plant and equipment. The
'Director of Economic Analysis, Federal Reserve Bank of
San Francisco. Research assistance for this article was
provided by Jayant Kalawar. Jackie Kau and Steve Zeldes.
6
return to labor to the marginal return to capital is
exactly equal to the ratio of their respective
prices.
"Relative factor prices," that is, the ratio of the
price of capital to the price of labor, is equal to
the absolute value of the slope of the AA line.
Hence, since equal-cost line BB is parallel to AA,
line BB represents a greater expenditure on
capital and labor but at the same relative prices
as exist at constant-cost line AA.
The two equal-output curves Zl and Zz represent technical (or engineering) relationships between capital and labor. These equal-output
curves are shown as "smooth", under the assumption that very small incremental substitutions between capital services and labor services
can produce the same output level. The firm's
most economical expansion path, with unchanged relative prices, would be along the ray
OX, which technically is a straight line for a wide
variety of production functions. z The ray, OX,
depicts those points of minimum production
costs, at constant relative factor prices, as the
firm expands to higher output levels.
Relative factor prices play an important role,
first, in determining the most economical combination of factor inputs for producing a given
output level, and, secondly, in determining the
ratio of capital to labor as output expands. Chart
I shows that as output expands from level Zl to
Zz at constant factor prices, with constant utilization rates of capital and labor, capital and
labor stocks should expand in fixed proportion.
This constant proportionality cannot, of course,
be expected to hold over every point throughout
a business cycle. However, we should expect
long-run factor-expansion proportionality if
relative factor prices do not change considerably.
Given a significant-and permanent-increase
in the cost of capital relative to labor, the firm
and the industry will economize on the more
costly factor by employing relatively more labor.
For example, with the equal-cost line CC, the
firm faced with higher capital costs will produce
output level Zz by moving from Ez to E3•
When the firm plans to expand plant size and
work force, it does so presumably under the
assumption that it knows what relative prices
will be during the period when that expansion
takes place. Thus, to the extent that inflation
anent work force, while its short-run production
problem consists of determining the optimal
utilization of capital and labor, with some variation permissible in the size of the work force.
The firm's production process may have two
dimensions, a stock and a flow dimension, with
output being produced by the flow of services
from capital and labor. The stock of capital, K
(plant and equipment), times its utilization rate,
u, determines capital services; the stock oflabor,
W (production workers), times its utilization, h
(average hours worked) determines workerhours, or the service flow from labor.
Chart I depicts the interaction of capital
services Ku and worker services Who In the
short-run we consider K fixed, while W, u and h
are allowed to vary. In the long-run, with u and h
set at their long-run "full utilization" levels, both
the capital stock and the work force can vary to
achieve a higher level of output.
The "constant output" curves ZI and Zz depict
the combinations of capital and labor services
that can produce the same output level. (Zz
represents the higher output level of the two).
The line AA is a "constant-cost" line, meaning
that the same cost to the firm is incurred by
varying expenditures on capital and labor anywhere along line AA. Equilibrium for the firm is
achieved at point E, the most efficient combination of capital and labor given the prices oflabor
and capital. At point E, the ratio of the marginal
Chart 1
Capital and Labor Services
Ku
Capital
Services
x
B
C
A
A
B
Wh
Labor Services
7
(i.e., the rise in the aggregate price level) affects
long-run factor demands, the firm presumably
knows how inflation affects relative factor prices
over the planning horizon, when initial planning
begins. As Chart I illustrates, relative factor
prices will determine the most economical combination offactor inputs. Anticipated changes in
the aggregate price level affect factor demands
only to the extent that they alter relative factor
prices. The relevant question is how inflation
might affect relative factor prices, and what
response firms are likely to make to both
changing relative factor prices and variability in
such prices.
Given current corporate accounting procedures, relative factor prices are sensitive to the
aggregate rate of inflation even where the future
inflation rate is known with certainty. This effect
of anticipated inflation is analyzed in a recent
article by Feldstein, Green and Sheshinski. 3 In
their view, the real after-tax return to debt and
equity reflects changes in the rate of inflation,
because the U.S. tax system taxes the nominal
income from investment (i.e., nominal interest
and nominal capital gains) but permits borrowers to deduct nominal interest costs. The firm
typically minimizes its total cost of capital by
choosing an "optimal" debt-equity ratio, which
ratio depends on the schedule of corporate tax
rates and the rate of inflation. The shift in the
debt-equity ratio due to inflation alters the firm's
total cost of capital and, in turn, alters the firm's
"implicit rental price of capital," defined as the
incremental cost to the firm of a marginal increase in its real capital stock. 4
The authors further argue that historical cost
depreciation causes an implicit taxation of cash
flow which increases with the rate of inflation.
Quite simply, inflation reduces the real after-tax
cash value of a dollar's worth of depreciation
generated in the future. 5 This implicit taxation of
cash flow is borne by both debt and equity
holders. In addition, inflation aggravates a firm's
tendency to extend debt in lieu of equity because
of the deductability of nominal interest costs.
Anticipated inflation, they argue, tends on balance to decrease the net rate of return to capital
(which would increase the rental price of capital)
and, in turn, to reduce the ratio of capital to
labor.
These effects of fully anticipated inflation, by
increasing the relative price of capital vis-a-vis
the price of labor, should be captured in the
relative price variable. If inflation causes the
rental price of capital to rise more than the
inflation-induced rise in wage rates, the firm will
expand along a new expansion path, to the right
of OX in Chart 1.
Fully anticipated inflation should have no
effects independently of the relative price of
capital, since it is relative prices which determine
demands for factors of production. That is, fully
anticipated inflation, and its consequent effects
on the debt-equity ratio and the tax value of
depreciation, presumably are captured in our
measure of the firm's "rental price of capital."6
Unanticipated inflation, on the other hand, must
be incorporated in our model to capture the
independent effect of this variable on factor
demands in manufacturing.
II. Factor Demand and Unanticipated Inflation
Before considering how firms will respond to
measures of inflation variability, we must first
consider the aggregate relationship between inflation and employment, specifically, what has
come to be called the "natural rate of unemployment" hypothesis. This hypothesis states that
employment is a "real" phenomena and can
therefore be determined only by other "real"
phenomena~that is, it should be independent of
any "nominal" phenomena. (Nominal factors,
unlike real factors, depend on a monetary unit of
account.) The natural-rate hypothesis basically
states that there is no relationship (trade-off)
between the rate of inflation and the unemployment rate in the long-run. This hypothesis is
important because we are interested in the relationship of inflation to manufacturing employment, as well as to manufacturing capital demand and the utilization of capital and labor
in that industry. Thus we should consider whether our results are consistent with the natural-rate
hypothesis.
The natural-rate hypothesis does not necessarily preclude the existence of a relationship between employment and inflation in the shortrun. One recent explanation of this short-run
8
relationship concerns the way individuals form
their expectations of inflation-the "rational
expectations" argument. According to this argument, individuals have reasonably good knowledge in forming their inflation expectations.
While those expectations may be wrong, they are
not consistently wrong. Hence, there is no systematic error in the marketplace's expectations of
inflation. (In other words, individuals' expectational errors average out to zero.) Given the basic
premise that labor and capital demand is dependent on relative prices, and not on the level or
rate of change of prices, the rationalexpectations argument implies that any relationship between inflation and factor demand must
result from individuals' short-term errors in
forecasting inflation. These forecasting errors
cause firms to temporarily misjudge current and
future relative prices, thereby inducing a temporary relationship between inflation and employment. Yet because these errors are not systematic
but rather fluctuate around zero, there is no
systematic long-run relationship between employment and inflation.
Why do firms misperceive the rate of inflation,
and thereby create a temporary misperception of
relative prices? One possible explanation is simply incomplete information. Specifically, firms
may have better present and future knowledge of
their input prices, the prices of capital and labor,
than of the future aggregate price level which will
influence their output price. Thus if firms underestimate inflation, they may be led to believe that
their output prices will rise in the future, so that
they will then increase their demand for factors
of production. This "paradigm of incomplete
information,,7 implies that firms have better
"local" price information, affecting their input
prices, than "global" price information, affecting
the aggregate price level. Yet under the rationalexpectations model, only aggregate inflationexpectation errors trigger a factor-demand response. This argument thus suggests that factor
demand can be affected by only one "inflation
stock"-unanticipated inflation-and not by
either the variability of input prices or by anticipated inflation acting by itself (independent of
relative factor prices).
By including both the relative price variability
in investment goods (local information) and
unanticipated inflation (global information), we
are able to test directly the natural-rate, rationalexpectations argument. In the context of the
manufacturing industry, this argument states
that factor-demand adjustments are triggered by
the effects of unanticipated inflation in the aggregate price level, rather than by the variability of
inflation in input prices.
Other analysts have considered the aggregate
economy impact of unanticipated inflation, but
we are interested in an additional question which
deserves more empirical investigation 8 -namely,
whether unanticipated inflation affects labor
demand differently from capital demand. We
argue that since unanticipated inflation creates
additional uncertainty regarding a firm's future
output prices, the firm when expanding output
will attempt to minimize the future cost of its
forecasting errors by using more of its variable
factor, labor, and less of its fixed factor, capital.
A similar argument can be found in Albert
Gailord Hart's 1940 book Anticipations, Uncer-
tainty, and Dynamic Planning.
"The fact that uncertainty-specifically, a
high dispersion of anticipations around the
expectation-favors processes under which
durable equipment will be held to a minimum
lends color to the widely held view that an
increase in uncertainty will act upon the firm
like an increase in interest rates.,,9
Hart's argument would suggest that, because
of greater uncertainty in aggregate inflation,
firms will not expand output along the expansion path shown in Chart 1. This variability, as
measured by unanticipated inflation, causes
greater uncertainty over the real value of future
streams of income, so that the risk-averse firm
will choose to minimize those investments that
are least reversible, such as long-term investment
in plant and equipment. This argument complements the Feldstein-Green-Sheshenski argument, which states that a reduction of fixed
investment minimizes the implicit taxation of the
firm's cash flow due to the use of historical-cost
depreciation in an environment of uncertain
inflation. Our hypothesis thus states that unanticipated inflation causes changes in factordemand response by inducing the substitution of
labor for capital.
9
III. Price Variability Data
Two measures of price variability are used in
this study. The first measure consists of the
variance of the rates of change of prices for
individual components of business fixed investment from the average rate of change for the
group as a whole. 10 For example, if Pit is the price
of investment good i in period t, and P t is the
aggregate investment-goods price index, our
relative price variance, RPV, measures the nonproportionality of price changes across the entire
class of business-investment expenditures. It
should be noted that RPV is a measure of
relative price variability for investment goods.
The second measure of price variability consists of the forecast errors of projections of the
wholesale-price index six months in the future.
The forecasts have been compiled by Joseph
Livingston, the Philadelphia Inquirer's business
editor, and have been analyzed and cleansed for
computational errors by John A. Carlson. II We
used simple linear interpolation in order to
obtain quarterly data from the semi-annual
Livingston-Carlson series. These forecast errors
Chart 3
Unanticipated Price Change in Wholesale Price Index'
Percent
12
10
8
6
4
2
-2
•6-month Horizon Forecast Error: Actual Less Forecast/Actual
provide a measure of "unanticipated inflation,"
since they are obtained from actual survey forecasts of wholesale-price inflation. The
Livingston-Carlson forecasts can be said to be
"rational," in that they utilize past inflation data
to produce efficient and consistent inflation
forecasts. 12 Thus the unanticipated rates of
wholesale-price change utilized in our study
appear to provide adequate representations of
actual price-forecast errors that would take place
in factor markets.
Our data clearly show that relative prices of
investment goods displayed a good deal of stability for the 1958-69 period, but considerable
variability thereafter (Chart 2). The wholesaleprice forecast errors apparently fluctuated
around zero during the 1958-72 period, with no
prolonged cycle or trend, but they provided
substantial underforecasting thereafter (Chart
3). The forecast errors were calculated as the
actual price level less the forecast level, divided
by the actual level.
Chart 2
Relative Price Variance of Investment
1958.2 = 100
800
700
600
500
400
IV. Model of Factor Adjustment Behavior
The factor-adjustment model estimated in this
paper assumes that the demand for a factor is
dependent on the difference between the desired
and actual stock (or utilization) of the particular
factor and the difference between desired and
actual stocks of related factors of production.
For example, the demand for labor will depend
not only on the difference between the desired
and actual stock of labor, but also on a similar
differential for the stock of capital. Utilization
rates may also affect the demand for stocks. For
example, the demand for capital- and also the
demand for labor-may rise because a firm is
fully utilizing its current capital stock.
10
Yt
Factor demands are divided into four separate
categories. Two of them are stocks-physical
capital, K, and total manufacturing production
workers, W. The other two are flows-the utilization rate of capital, U, and the average workweek in manufacturing, H. 13 At the conceptual
level, output, Q, is described as a function of all
factor stocks and utilizations, or
Q = F(K,U,W,H)e yt
where Y it is the ith factor (e.g., workers),
is the
"desired" level of the jth factor. Equation (3) is
the interrelated adjustment model, previously
estimated for the manufacturing industry by
Nadiri and Rosen. 14 Appended to the adjustment
process are the random price-shock terms Wi,
which are the price-forecast error and the variance of the relative prices of investment goods.
The anticipated rate of wholesale-price inflation,
71", is included to test the hypothesis that there are
no independent effects of anticipated inflation
aside from the relative rental price of capital.
Hence the null hypothesis is that Tr should have
no statistically significant effect on factor demands.
There has been little empirical work measuring the effect of price uncertainty, first, on the
firm's optimal long-run capital stock, and secondly, on the adjustment path of capital-stock
accumulation. Some theoretical work suggests
that output price uncertainty should reduce the
optimal capital stock of the firm. But these
results, unfortunately, are very sensitive to the a
priori specification of the firm's underlying production function. IS
One important question relates to the differential impact of the two measures of inflation
variability on manufacturing factor demands.
Does the rise in unanticipated inflation have a
significantly different impact on the demand for
labor than on the demand for capital? If so, we
could obtain a better understanding of the behavior of capital and labor demand in the recent
economic recovery.
(I)
The y term measures the exponential rate of
technical progress in the production function for
the firm and, via aggregation over firms, for the
industry. If in the short-run the firm considers
output as given, and then minimizes costs associated with the production of this output level, it
will obtain a "desired factor-demand" equation
which is dependent on output, relative input
prices and a time trend.
Y~
= fi(Q,~,t)
i
= 1,2,3,4
(2)
where Q is output, C/ W the relative user price of
capital (i.e., the rental price of capital, C, divided
by the wage rate, W), and t a time trend. By
substituting (1) into (2) and assuming lagged
adjustment, we obtain
Yit - Y,t-'
=
.1 {3ij
[Yjf - Yjt - I
+
+ A2W2tJ~ YTrt + tt
J=I
A,Wl t
1= I,2,3,4
(3)
V. The Estimated Model
To repeat, the desired factor levels, denoted by
YJ in equation (3), are assumed to be determined
by output, the relative rental price of capital, and
a time trend. 16 The relative price variance of
investment goods and the unanticipated inflation variable are appended to this factoradjustment equation. In addition, anticipated
inflation (the Livingston series) is included as a
independent variable to test the hypothesis that
"surprise" or unanticipated inflation provides
the major inflation impact on factor demands
(aside from the relative user price of capital). All
variables except the time trend and the anticipat-
ed and unanticipated inflation variables are
entered as natural logarithms. The equations for
capital, production workers, the average workweek and the capacity-utilization rates were
estimated over the period 1959.111 to 1975.IV.
As shown in Table I, the "own rate of adjustment," that is, the portion of the discrepancy
between desired and actual stocks or utilization
of factors, is measured by one minus the estimated own-adjustment coefficient (e.g., the coefficient on K(t-I) in the K(t) equation). This
computation shows that capital adjusts the slowest, as expected, and the average workweek ad-
11
justs the most rapidly. These results need to be
qualified somewhat, because adjustment in any
one factor is constrained or augmented by the
gap between desired and actual stocks and utilization rates in other equations. For example, the
average workweek and the capacity-utilization
rate affect the capital-stock adjustment very
little, that is, the coefficients for H(t-l) and
U(t-l) are statistically insignificant. However,
an increase in the discrepancy between desired
and actual production workers will slow this
capital adjustment. (In equation (3), lagged
factor variables enter with a negative sign,
indicating a negative cross-adjustment coefficient on lagged workers in the capital equation.)
Similarly, the adjustment in workers, equation
(2) in Table I, is similarly constrained by the gap
between the desired and actual capital stock.
Interestingly, the estimated capital utilization
equation implies that the greater the gap between
desired and actual production workers, the greater the utilization of the existing capital stock.
Because of the dynamic specification of our
factor-adjustment model, the estimatedcoefficients on the exogenous variables can only be
considered short-run (first period) coefficients.
The short-run output elasticities are all statistically significant and reasonable in size except in
the capital equation. The relative rental price of
capital should, a priori, yield a negative coefficient in the capital equation and positive coefficients in the remaining equations. However, this
variable is statistically significant only in the
capital equations with the expected negative
sIgn.
As for our three inflation variables, we hypothesized that unanticipated inflation effects
ought to predominate over relative pricevariance effects if firms respond to "global" price
shocks-that is, price shocks over which the firm
Table 1
Estimated Factor Adjustment Equations in Manufacturing
(1959111-1975IV)
Dependent Variables*
Explanatory
Variables
Constant
K(tl)
W(H)
H(H)
U(tl)
(~)t Relative rental price of capital
Output (t)
Time trend
Anticipated inflation (t)
Unanticipated inflation (t)
Relative capital price variance (t)
_2
R
D.W.
RHO
SER
* t-statistics
(1)
Capital (K)
-.005
(0.0)
.871
(20.6)
.165
(2.3)
.034
(.2)
.032
(A)
.009
(2.9)
-.042
(1.3)
.0016
(4.1)
.0007
(.8)
-.0015
(3.1)
.0002
(.2)
.9992
1.78
-.30
.0064
(2)
Workers (W)
-.734
(1.0)
.204
(3.1)
.271
(2.5)
.005
(.02)
.048
(.5)
.001
(.3)
A48
(11.0)
-.0050
(7.6)
.0027
(1.9)
.0031
(3.8)
-.0008
(.6)
.990
1.88
AI
.0069
in parentheses
12
(3)
Hours (H)
2.635
(6.3)
.040
(1.1 )
-.264
(4.5)
.091
(.6)
.154
(2.8)
-.003
(I.I )
.158
(7.1)
-.0012
(3.3)
..0006
(.8)
.0010
(2.2)
-.0020
(2.8)
.928
1.99
.39
.0038
(4)
Utilization (U)
1.974
(1.6)
-.098
(.9)
-A64
(2.6)
-.071
(.2)
.377
(2.3)
-.008
(.9)
.767
(11.3)
.0052
(4.9)
.0038
(1.7)
.0043
(3.3)
-.0018
(.9)
.963
1.65
.36
.0115
Table 2
Long-Run Elasticities
has incomplete information. (This hypothesis
fits in with that of some rational-expectations
theorists.) This result, indeed, is implied by the
estimated coefficients. The unanticipatedinflation variable is statistically significant in all
of the four factor-demand equations, while the
relative price-variability variable is only significant in the average-workweek equation. An
increase in unanticipated inflation is found in the
short-run to decrease the demand for capital but
to increase the demand for workers, the capacityutilization rate and the average workweek. Also,
as hypothesized, anticipated inflation has no
independent effect on any of the four factor
demands, as this variable is statistically insignificant (at the 95-percent confidence level) in all the
equations.
The estimated coefficients represent only the
initial-period responses to a change in the exogenous variables. But we are also concerned with
"long-run elasticities" (Table 2), which represent
the total response of the factors to changes in
output, unanticipated inflation and the relative
rental price of capital. The long-run coefficients
should be used with the estimated coefficients to
determine the "reasonableness' of the estimated
model.
For the long-run effect of the relative rental
price of capital, all signs are as expected except in
the workers equation. As expected, a rise in this
variable is seen to decrease the demand for
capital. The long-run output effects are also of
correct (positive) sign in all the equations. And as
expected, the largest long-run output elasticities
are on capital and labor stocks.
The long-run effects of unanticipated inflation
are seen to be negative on capital demand, but
positive on worker demand and capacity utilization. There is no long-run effect on average hours
worked. These results imply that the overall
Exogenous Variable
Factor
Capital
Workers
Hours
Utilization
Relative
Rental Price
of Capital
~.0956
~0.235
.0024
.0198
Output
Unanticipated
Inflation
.942
.905
.021
.407
-.0062
.0028
.0000
.0057
effect of unanticipated inflation has been to
reduce the long-run demand for capital, but to
increase the long-run demand for labor and the
utilization rate of the capital stock. This would
thus imply a decline in the capital-labor ratio in
manufacturing. These empirical results are consistent with the theoretical argument of Feldstein, Green and Sheshinski-that inflation reduces the demand for capital-although their
argument stems primarily from a rise in steadystate or permanent inflation.
The results displayed in Tables! and 2 appear
to confirm the hypothesis that inflation affects
factor demand in manufacturing through unantic;ipated inflation, and not through the increased
variability in the relative price of investment
goods or independently through anticipated
inflation. Our results also imply that there may
indeed be a persistent long-run increase in labor demand because of unanticipated inflation,
but that this positive response in labor demand is
compensating for the reduced demand for capital from the same cause. These results would
suggest that, in order to reach a better understanding of inflation's long-run impact on the
economy, we should consider its effect on
capital-investment demand as well as its shortrun effect on the demand for labor.
VI. Dynamic Response to Inflation
To understand the dynamic behavior offactor
demands in manufacturing, we need to ask two
questions. First, is the interrelated laggedadjustment model stable? Technicalities aside,
the answer is yes. 17 That is, a unit change in any
exogenous variable will cause the factor demand
to respond over time, and as time goes on, the
level of the factor stock or utilization will return
to its long-run equilibrium value.
Secondly, how do factor demands respond
over time to a unit change in unanticipated
inflation? Because of the interrelated nature of
the adjustment process (where, say, the labor
adjustment is affected by the current level of
capacity utilization) we must use the entire adjustment matrix to see how anyone factor
13
Chart 4
demand changes over time. 18 As Chart 4 indicates, the capital stock in manufacturing adjusts
suprisingly quickly to unanticipated inflation.
Although the response is distributed over twenty
quarters, 75 percent of the impact occurs after
ten quarters. Again, the demand for workers
responds very rapidly to unanticipated inflation,
with almost all of the adjustment complete after
five quarters.
Most importantly, a rise in unanticipated
inflation leads to significant offsetting behavior,
with a reduced demand for capital being offset by
an increased demand for production workers.
Unanticipated inflation, in effect, acts like a rise
in the relative price of capital vis-a-vis the price
of labor.
"Surprise inflation" thus can have a statistically significant short-run impact on the process of
adjustment of factor demands, especially capital
and labor. But because of the substitutability of
the factors considered here, aggregate inflation
shocks can affect their interaction as well. As we
have seen, the capital stock tends to be reduced
while capital utilization tends to be increased
over the long run. Our results contradict the
"complete inflation neutrality" proposition that
inflation has no long-run impact on real variables. Our results, in contrast, indicate that if
significant unanticipated inflation continues
over a lengthy period, the capital stock in manufacturing will grow more slowly. Persistent unanticipated inflation thus could lead over time tp
a fall in the capital-labor ratio in manufacturing.
Response Pattern to a Unit Increase
in Unanticipated Inflation
0.0 , - - - - - . - - - - , - - - - , - - - - - ,
-.05
'"
I
0
'"
C
"
Capital
-.10
'0
;;::
Q;
0
()
"'"c
0
0.
-.15
"'"
0:
-.20
0
10
15
20
Quarters
.30
~
0
'"
C
.20
"
'0
;;::
Q;
Labor Force
0
()
"'"c
.10
a0.
"'"
0:
0.0
10
15
20
Quarters
-.10
VII. Forecasting the 1976-77 Recovery
cast the capital stock in manufacturing but
underforecast workers and the utilization rate.
The dynamic forecast was significantly worse
than the static forecast only for the capital
equation (Table 3). However, the root-meansquare percentage errors indicate that the worst
forecasts surprisingly did not occur in the capital
equation, but rather in the capacity-utilization
equation. The capital and workers equations had
almost equal root-mean-square percentage errors, but this statistic was almost double in size
for the utilization forecasts.
Since our dynamic forecasts were consistently
less than the actual rates of capacity utilization,
To evaluate the forecasting value of our interrelated factor-adjustment model, we performed two types of forecasts for the period
1976.I-1977.IV. The first (static) forecast utilized
actual values for all of the explanatory variables.
The second (dynamic) forecast utilized known
values for all exogenous variables except the
lagged values of the endogenous variable for
capital stock, workers, hours and utilization.
These latter values were set at their previous
forecasted values, where the lagged values for
1975.lV were the fitted values obtained in the
estimation.
The dynamic forecasts consistently overfore14
tion for the 1976-77 period. Indeed, the Vcoefficient is lowest for the capital-stock forecasts. These results support the use of the
estimated model in explaining the demand for
capital and labor, but they cast doubt on the
forecasting properties for the capacityutilization rate.
We also decomposed Theil's V-coefficient into
three components, to analyze further the source
of error in the utilization forecasts. The first two
terms capture systematic errors that should be
avoided in the forecasts, while the last (imperfect
covariation) involves nonsystematic random
error. 20 As Table 3 indicates, the largest source
of forecast error in capacity utilization occurs
because of nonsystematic random movements in
the capacity-utilization rate. The utilization forecasts have the largest ratio of imperfect covariation to bias. These forecast errors indicate that,
during the 1976-77 recovery, relatively greater
nonsystematic random behavior occurred in
capacity utilization than in capital demand,
labor demand or the average workweek. The
forecast performance also indicates that the
recovery surprisingly was characterized by a
greater-than-anticipated rate of capacity utilization.
we should not be asking why the aggregate
capacity-utilization rate was so low, but rather
why it was so high. Given the interrelated nature
of the demand for stocks and utilization of
capital and labor, our forecasts indicate that the
capacity utilization rate was higher during the
1976-1977 recovery period than expected. In
isolation, the rate may appear relatively low
when compared with previous recovery periods.
But this observation ignores the way the utilization of capital interacts with the utilization of
labor and the growth in the capital stock and
manufactuing labor force.
We used Theil's "V-Coefficient" to further
judge the overall forecasting accuracy of the
period 19761-1977 IV. A V-coefficient which
exceeds unity indicates that the ex ante forecast
of factor demands does not provide more useful
information than a simple "no change" forecast. 19 As Table 3 indicates, the V-coefficient is
less than unity for capital and workers, but
greater than unity for the average hours and
utilization equations. This suggests that the
estimated interrelated factor-adjustment model
was quite useful in forecasting the demand for
capital and workers, but not of much use in
forecasting average hours and capacity utiliza-
Table 3
Forecast Performance 1976 1-1977 IV·
Capital
Workers
RMSE-Dynamic
$1 ~60 bil.
210 thous.
RMSE~-Static
$0~80
196
RMS%E-~Dynamic
R MS%E--Static
bil.
thous~
Hours
~263
Utilization
hrs.
2.144 % points
~286 hrs~
I ~962 % points
13%
159(
0~65%
2~63%
0~66%
1.4%
0.71%
2.41%
Theil Inequality Coefficients
(Dynamic Forecasts)
U-coefficient
1~955
.422
~904
~06517
~OO 176
~OO
163
~00002
Unequal Variation
00048
~()O 137
,()0300
.33163
Imperfect Covariation
.16330
~87318
I 1379
1.4493
Unequal Central Tendency
*
I ~248
RMSE = root mean square error; RMS%E = root mean square percentage error.The RMSE statistics were obained by first
taking the antilogs of the forecasted variables~
15
VIII. Conclusion
process of capital growth. Moreover, unanticipated inflation shocks, and their persistent
effects over a prolonged period, help explain why
investment demand has been sluggish since the
early-1975 cyclical trough. While our evidence is
obviously tentative, it provides an avenue to a
more complete understanding of the inflationinduced factor-demand adjustments in U. S.
manufacturing.
Economists only recently have come to consider the effects of price uncertainty on the
behavior of the firm, either in output markets or
in factor markets. Yet this question must be
answered if economists are to be able to explain
how inflation affects the real economy. Our
tentative evidence suggests that unanticipated
inflation can affect the demand for factors of
production as well as the utilization of these
factors. This type of inflation thus may slow the
Appendix
Deviation of a RiSk-Adjusted Rental Price of Capital
Jayant Kalawar and Joseph Bisignano
where ¢
The procedure used to derive the rental price
of capital used in the text is similar in spirit to
most other definitions of this variable seen in the
investment literature. Basically, the rental price
of capital is defined as
c = (l-k) (l-wz)
Pk(r
+ 0)
long-term debt 4
long-term debt + stockholders' equity
rAaa
re
(AI)
(l-w)
where:
C
k
w
z
= rental price of capital
= investment tax credit!
= tax rate for manufacturing corporations,
computed as (provision for federal in-"
come taxes -;- income before taxes)2
present value of depreciation allowance,
computed as
where:
d
t
8
= (Aaa corporate-bond rate) (l-W)3
= tax lifetime of investment goods = 1/0
Pk
= implicit capital-stock price deflator (con-
r
= total cost of capital in manufacturing,
= depreciation rate = .054511 (constructed
by F. Brechling);
structed by F. Brechling)
defined as
r = (l-¢)re
=
+ ¢(l-w)rAaa
16
= Aaa corporate-bond
= cost
rate
of equity
It is quite common in investment studies to use
some readily available measure of r e , the cost of
equity, such as the dividend-price ratio. This
measure for r e was used here, but the implied
rental price of capital was not found to be
significant in the capital equation. In fact, utilizing alternative derivations of the rental price of
capital, we found the most significant measure of
c to be simply P k (rAaa + 8). However, this
variable was not used because it ignores important tax and equity cost considerations.
One of the authors (Kalawar) suggested constructin6 a risk-adjusted cost of equity for use in
our final derivation of the rental price of capital.
This was done by inferring the return demanded
on equity from the returns on bonds, the returns
on a "risk-free" asset, and measures of the "riskiness" of bonds and equity. To do so we utilized
the Sharp-Lintner capital-asset pricing model,
assuming that portfolios exist (consisting of all
Aaa corporate bonds outstanding and a portfolio of Standard and Poor's 500 common stocks)
which are efficient; that is, the risk-return characteristics can be simulated by holding the "market portfolio" in the appropriate proportions.
Under this assumption the following relationship holds, (Sd indicates standard deviation):
re
= rr + (rAaa -
rr)
Sd(rAaa)
* Sd(re)
The derived cost of equity and the ultimate
rental price of capital are shown in Charts Al
and A2, respectively.
(A2)
The above equation describes the "capital market line," with an intercept of rr (the risk-free
rate), and, since both the bond and equity portfolio lie on this straight line, the slope is given by
(rAaa - rr) / Sd(rAaa). Using thisrelationship, we
can construct a series of expected rates of return
on common stock which, in equilibrium, give us
the cost of equity. Specifically:
expected return on equity for S&P
re
500 stocks;
rr
yield to maturity, annualized, on 3month Treasury bills outstanding,
quarterly averages;
rAaa
= yield to maturity, annualized, of Aaa
corporate bonds outstanding, quarterly averages;
Sd(rAaa) = standard deviation of one-month
holding-period returns on all corporate bonds outstanding (industrial
and utility) with Moody's Aaa and
Aa rating;
Sd(re) = standard deviation of one-month
holding-period returns on S&P 500
common stocks.
Chart A1
Derived Cost of Equity Capital
Percent
T
15
10
5
Chart A2
Derived Rental Price of Capital
Percent
25
Twelve monthly observations were used to construct the standard deviations defined above,
and were computed from the data developed by
R. A. Ibbotson and R. A. Sinquefield. 5 The
construction of our measure of the cost of equity
requires one strong assumption, namely, that the
covariance between equity and bond returns is
zero. This assumption was made to ease the
empirical derivation of the cost of equity.
FOOTNOTES
1. For a concise summary of the important properties of
firms' long-run behavior, see Eugene Silberberg, "The
Theory of the Firm in 'Long-Run' Equilibrium," American Economic Review (September 1974).
2. The expansion path will be linear for any homogenous production function. The intertemporal maximization of the net wealth of the firm usually assumes
known fixed prices. See, for example, Dale W. Jorgenson, "Technology and Decision Rules in the Theory of
Investment Behavior," Quarterly Journal of Economics
(November 1973).
3. Martin Feldstein, Jerry Green and Eytan Sheshinski,
"Inflation and Taxes in a Growing Economy with Debt
and Equity Finance," Journal of Political Economy, Part
2 (April 1978l.
4. For a derivation of the "rental price of capital" see
Dale W. Jorgenson and James A. Stephenson, "Invest-
ment Behavior in U.S. Manufacturing, 1947-1960,"
Econometrica (April 1967).
5. See T. Nicolaus Tidemand and Donald P. Tucker,
"The Tax Treatment of Business Profits Under Inflationary Conditions," in Inflation and the Income Tax,
Henry J. Aaron, ed., Brookings Institution, Washington,
D.C. (1976l. An analysis of the erosion of capitalrecovery allowances by inflation is considered for
different inflation rates and for different taxdepreciation methods in Eric Schiff, "Inflation and the
Earning Power of Depreciable Assets," Domestic Affairs StUdy 25, American Enterprise Institute (November 1974).
6. See the appendix to this paper for the derivation of
our "rental price of capital."
7. For a review of the "paradigm of incomplete information" see Herschel I. Grossman, "Why Does Aggregate
17
Demand Fluctuate?" paper delivered at the August,
1978, meeting of the American Economic Association,
Chicago, Illinois.
8. For aggregate studies of the unemployment rate and
unanticipated inflation, see R. E. Lucas, Jr., "Some
International Evidence on Output-Inflation Trade-offs,"
American Economic Review (June 1973), and Thomas
J. Sargent, "Rational Expectations, the Real Rate of
Interest and the Natural Rate of Unemployment,"
Brookings Papers on Economic Activity (1973). Regarding the effect of inflation on the employment of fixed
and variable factors, Sheshinski and Weiss have shown,
in a model of costs of adjustment associated with
varying nominal output prices, that a firm will reduce
the employment of fixed factors If there Is an Increase In
inflation expectations. See Eytan Sheshinski and Yoram Weiss, "Demand for Fixed Factors, Inflation and
Adjustment Costs," Discussion Paper No.3, Stanford
Workshop on the Microeconomics of Inflation (March
1976).
9. Albert Gailord Hart, Anticipations, Uncertainty, and
Dynamic Planning, University of Chicago Press (1940).
10. The relative price variance, or RPV, is defined as the
measurement of the nonproportionality of price movements across a group of expenditure classes. Here the
group is business fixed investment. Specifically,
n
(a)
RPVt = 2: Wit(DPit- DPt)2
i=1
stores machinery, service industrial machinery, communications equipment, electrical transmission and
distribution, household appliances, miscellaneous
electrical, trucks, passenger cars, aircraft, ships and
boats, railroad equipment, instruments, photographic
equipment, and miscellaneous.
11 The data and comments on their construction and
interpretation may be found in John A. Carlson, "A
Study of Price Forecasts," Annals of Economic and
Social Measurement (1977).
12.. See Donald J.Mullineaux, "On Testing for Rationality: Another Look at the Livingston Price Expectations
Data," Journal of Political Economy, Vol. 86, No.2
(1978), and Carlson, cited above. Carlson could not
reject the hypothesis at the 5-percent significance level
that the consensus WPI forecasts are rational. Mullineaux conducted tests on the Carlson-livingston consumer price-index forecasts and found that these forecasts were also "rationaL"
13. One of the early papers incorporating the interrelationship between factor-demand adjustments was M. I.
Nadiri and S. Rosen, "Interrelated Factor D~mand
Functions," American Economic Review (September
1969). For an excellent review and extension of the costof-adjustment approach to dynamic firm behavior, see
Frank Brechling, Investment and Employment Decisions, Manchester (England) University Press (1975),
14. See M. Ishag Nadiri and Sherwin Rosen, "Interrelated Factor Demand Functions," American Economic
Review (September 1969), Their model, based on cost
minimization, is more fully described and disaggregated in A Disequilibrium Model of Demand for Factors of
Production, National Bureau of Economic Research
(1973), Two general points should be noted about the
estimated interrelated model. In matrix form the model
may be written as
where: DPit = log Pit - log Pi.t-1
Pit = price index of good i in period t
Wit = Wit - Wit-1
2
Wit = expenditure share of good i in period t
n
(b)
DPt = 2: WitDPit
i=1
The expression (DPit - DPt) is seen as the rate of change
in the ith relative price, i.e., the logarithmic difference in
the relative price Pit/Pt, where Pt is the aggregate price
level for the group of n goods. Thus the rate of change
of the index is defined as the weighted average of the
rates of change of the individual goods. Similarly, the
relative price variance is defined as the weighted sum of
squared deviations of the individual rates of price
change around the average rate of change. The rate-ofchange price index is recognized as a Divisia price
index. The use of such an index was suggested by
Richard W. Parks in "Inflation and Relative Price Variability," Journal of Political Economy (February 1978).
On the use and construction of Divisia indices, see
Henri Theil, Economics and Information Theory, Rand
McNally (1967).
The aggregate investment class used in construction
of the RPV series was business fixed investment, composed of structures and producers' durable equipment.
Producers' durables equipment was broken down into
27 durable-equipment investment classes. The producers' durable-equipment category is composed of
household furniture, other furniture, fabricated metals,
steam engines, internal-combustion engines, construction tractors, agricultural machinery, farm tractors, construction machinery, mining and oil-field machinery, metalworking machinery, special industrial
machinery, general industrial machinery, office and
Yt = {3Axt
+ (I-{3)Yt-1
where Yt is the vector of factor levels, {3 the matrix of
adjustment coefficients, A the matrix of behavioral
coefficients on exogenous variables (e.g., output, relative prices, etc,) where Y1 = AXt, and Xt the vector of
exogenous variables. I is the identity matrix. The matrices of estimated coefficients are {3A and (I-{3). Longrun desired demand coefficients are obtained from
A
A-
[I - (l-tlll- 1 {3A.
The dynamic stability of the system of factor demands
depends on the characteristic roots of (I-{3), Stability is
obtained if the modulus of the largest root, in absolute
value, does not exceed unity. The sequence of
distributed-lag coefficients in response to a unit increase in any of the exogenous variables is given by
(I-f3lk {3A for k = 1,2..... Note that Nadir! and Rosen
assume that firms are at each moment in time on their
production functions. This can only be insured by
imposing production-function coefficient constraints,
usually nonlinear, across the estimated factor equations, which is a non-trivial exercise. The importance of
such constraints can be seen in R, M. Coen and B. H.
Hickman, "Constrained Joint Estimation of Factor Demand and Production Functions," Review of Economics and Statistics (August 1970).
15. Kenneth R. Smith has shown that if the firm produces with a Cobb-Douglas production function, uncertainty with respect to the demand for the firm's
output (i.e., when the demand curve is random) will have
18
The F-tests indicate that we cannot reject the hypothesis that the coefficients remained the same overthe two
sub-sample periods.
18. The adjustment paths, or more correctly, the
impulse-response functions, are calculated as (1-[3) k
f1A, for k = 0,1,2, ... , where [3 is the adjustment matrix
and [3A the matrix of estimated coefficients on the
exogenous variables.
19. Let Fi and Ai be the forecast and actual percent
changes, respectively,for period i, where the forecasts
range from 1 to m. Theil's U (inequality) coefficient is
here defined as
the effect of reducing the firm's optimal capital stock.
See "The Effect of Uncertainty of Monopoly Price,
Capital Stock and Utilization of Capital," Journal of
Economic Theory (1969), One of the most interesting
empirical studies on the role of price expectations in
investment demand is Albert K. Ando, Franco Modigliani, Robert Rasche, and Stephen J. Turnovsky, "On the
Role of Expectations of Price and Technological
Change in an Investment Function," International
Economic Review (June 1974),
16. The output series used is the sum of manufacturers'
shipments and the changes in manufacturers' inventory, both for finished goods and work in progress. This
series is then deflated by the wholesale price index for
manufacturing to obtain the final real output series. The
source of this data is U.S. Department of Commerce,
Manufacturers' Shipments, Inventories and Orders.
See the appendix to this paper on the derivation of the
rental price of capital. Capital stock data were provided
by Professor Frank Brechling of Northwestern University. These capital-stock data utilize benchmarks of
1948 and 1966. The benchmarks are derived from the
net capital stocks based on double-declining-balance
depreciation (at 1958 dollars) regLllarly published in the
Survey of Current Business. Professor Brechling also
supplied the estimated price index of investment goods
in manufacturing. The utilization rate is the capacityutilization rate published by the Federal Reserve. Total
production workers in manufacturing and the corresponding average workweek may be found in Employmentand Earnings, 1909-75, U.S. Bureau of Labor
Statistics.
17. Stability of the dynamic system is determined by
examining the characteristic roots of(I-f1), where I is the
identify matrix and f1 the (4X4) adjustment matrix.
Stability requires that the absolute value of the modulus
of the largest root be less than unity. The characteristic
roots of the (1-[3) matrix shown in Table 1 are .901, .129,
.290 ± .0981. Since no root exceeds unity the interrelated adju$tment system is stable. The hypothesis that the
estimated coefficients remained the same over the
entire sample period was tested by estimating the
model over 1959.3-1968.4 and 1969.1-1975.4, and using
an F-test (Chow test) for equality of coefficients during
the two sub-sample periods. These F-tests appear
below, where
F
U
The numerator is seen to be the root-mean-square error
of the forecast (in percentage change), while the denominator is the root-mean-square error assuming
zero forecasted change. Perfect forecasts would yield a
0, while U = 1 implies a status quo (no change)
U
forecast. A U greater than 1 implies that the forecasts
are worse than the status-quo forecasts. See H. Theil,
Economic Forecasts and Policy, North-Holland Publishing Company (1965).
20. Theil's U-coefficient was decomposed into three
components as follows. The first component, called
"unequal central tendency," measures the squared
difference in the mean of the actual percentage change
to the mean of the forecasted percentage change; it is a
measure of forecast bias. The second component,
described as "unequal variation," measures the
squared difference in the standard deviations of the
actual percentage changes and forecasted percentage
change. The third component utilizes the correlation
between the actual and forecast percentage changes
and measures "imperfect covariation" between the two.
The first two terms capture systematic errors that
should be avoided in the forecasts, while the last involves nonsystematic random error. As we have computed them, the three components do not sum to the
aggregate U-coefficient.
SSR(H1)/(T1+T2-2k)
where SSR = sum of squared residuals
Ho
hypothesis that coefficients are the
same over the two sub-sample periods
H1
hypothesis that coefficients are not the
same over the two sub-sample periods
T1,T2 = number of observations for sub-sample
periods
= number of estimated parameters
k
APPENDIX FOOTNOTES
1. R. W. Kopcke, "The Behavior of Investment Spending
during the Recession and Recovery, 1973-76," New
England Economic Review, November/December
1977.
2. Securities and Exchange Commission, Quarterly
Financial Reports.
3. Federal Reserve Bulletin, Table 1.36.
4. Securities and Exchange Commission, "Balance
Sheet of Manufacturing Corporations," Quarterly Financial Reports.
5. R. A. Ibbotson and R. A. Sinquefield, "Stocks, Bonds,
Bills and Inflation: Year-by-Year Historical Returns,
1926-1974," Journal of Business, January 1976.
F-Tests for Equality of Coefficients
Calculated
F-statistic
1.698
0.673
0.887
1.270
Fi)2
i=1
(SSR(H o )-SSR(H1 ))/k
Factor
Capital
Labor force
Hours
Utilization
~m
V inI (Ai -
Critical FgCOS)
1.99
1.99
1.99
1.99
19
Rose McElhattan*
Since Phillips' seminal paper in 1958,1 the
economics profession has devoted considerable
effort to the study of the linkage between inflation and unemployment rates. That linkage,
popularly known as the Phillips Curve, is the
result of combining a price and a wage equation.
Because wages are related to the unemployment
rate, that approach establishes a direct link between unemployment and final-product prices,
which are considered to be a variable markup on unit labor costs. Other variables, of course,
also appear in the combined price equation: One
of these-the capacity-utilization rate-refl(':cts
aggregate-demand pressures on existing capacity, and thus is included in the equation because
these pressures determine the value of the
price/labor-cost markup. Consequently, the
combined price equation will contain two excessdemand variables-the unemployment rate, reflecting excess demand in labor markets, and the
capacity-utilization rate, reflecting excess demand in final-product markets. This result presents both a problem and an opportunity for
those interested in estimating the impact of these
variables upon inflation.
First, there is a problem because, with the
close historical association between unemployment and capacity utilization, we may not be
able with one equation to separate statistically
the effects of these two variables upon inflation.
The high historical correlation is in part related
to the fact that labor demand is a derived demand,so that excess demand in the final-product
market tends to produce excess demand in the
labgr Sector. In addition, as recent empirical
stu<ftessuggest, there may be limited substituta-
bility between capacity and labor utilization.
More intensive use of plant and equipment
requires more intensive utilization of labor. In
general, this results in higher employment
(hence, lower unemployment) when capacity
utilization rates are rising. In one recent'study,
Modigliani and Papademos stated that because
of the high correlation between the two excessdemand variables, they were unable to estimate
separate influences. 2 They therefore dropped
capacity utilization from consideration, because
they were primarily interested in measuring the
inflationary impact of alternative unemploy~
ment rates. In this paper, in contrast, we focus
upon the inflationary impact of alternative
capacity-utilization rates.
Thus, we have the opportunity with our combined price equation, which connects inflation
and capacity utilization, to make some interesting comparisons with the inflation/unemployment relation so often discussed in the literature.
Two schools of thought may be distinguished in
the literature. The "natural rate of unemployment" school believes that there is only one full
employment-unemployment
rate,
towards
which the economy tends over time. If governmentpolicy attempts to maintain a rate lower
than the natural rate, inflationary pressures will
accelerate as long as that lower rate is maintained. According to this school of thought,
there is no long-run tradeoff between inflation
and· unemployment. In contrast, the "nonaccelerating-inflation rate of unemployment"
school takes an eclectic approach to the question
of a trade-off. In this view, there may be several
equilibrium points, and there may also be unstable inflationary conditions at relatively low
unemployment rates, so that no permanent
trade-off exists.
Our study suggests the existence of a full-
*Economist, Federal Reserve Bank of San Francisco. Deborah Anderson provided research assistance for this paper.
Professor John Scadding of Stanford University provided
detailed comments on an earlier draft of this paper.
20
percent, Or within the range of 80~83 12 percent.
(In other words, 80 and 8312 percent represent
the 95-percent confidence limits of our 82percent point estimate.) Historically, the rate of
inflation increases when capacity utilization rises
above 8312 percent, while the rate of inflation
declines when capacity utilization falls below 80
percent.
One point should be clarified at the outset. The
relationship that we examine between inflation
and capacity utilization is one in which overall
inflationary pressures are Closely linked with
those in the U.S. manufacturing sector. Ifunusual pricing behavior occurs in the farm or import
sector, our model will not capture all ofthe initial
inflationary response, and we can observe increasing inflation although capacity utilization
rates are within the full capacity limits. In other
words, recent increases in inflation which have
been attributed to increases in food prices have
occurred regardless of aggregate demand pressures on available capacity. Nonetheless, should
capacity-utilization rates continue above the 83
12-percent upper limit of utilization, we could expect additional inflationary pressures to be generated by the nonfarm business sector of the U.S.
economy.
The next section of this paper provides a
simple testable model relating inflation and
capacity utilization. The following sections present the statistical results and the conclusions of
our analysis.
capacity utilization rate which is consistent with
the "natural rate of unemployment" concept. We
can detect no permanent, stable relation between
inflation and capacity utilization existing in this
country since the early 1950's. Attempts to maintain a capacity-utilization rate above the estimated full-capacity equilibrium rate appear to be
associated with a steadily increasing inflation
rate.
This raises the question of the actual level of the
stable-inflation capacity-utilization rate. In other words, at what point in the use of the nation's
industrial capacity are inflationary pressures
likely to increase? The recent rate of capacity
utilization-still below 85 percent in August,
according to the Federal Reserve series-would
seem to indicate some slack when compared with
the 87-88 percent post-World War II peacetime
peaks. Indeed, according to Senate Banking
Committee Chairman Proxmire, most witnesses
at a recent committee hearing felt that inflationary pressures would not build until those previous peak operating rates had been surpassed. 3
But our historical experience since the early
1950's does not substantiate such a conclusion.
Inflation has tended to accelerate well before
previous peak rates have been reached; a utilization rate compatible with price stability appears
to be a good deal lower than those peak rates.
Our statistical estimates suggest that the equilibrium rate of capacity utilization consistent
with a stable rate of inflation falls around 82
I.
Relationship Between Inflation and Capacity Utilization
changes to labor-market excess demand and
expected inflation. Aggregate-demand pressures-as represented by capacity-utilization
rates-affect the markup by which prices are
related to unit labor costs. As demand builds and
utilization rates increase, for example, the markup on costs may increase as final product prices
adjust to eliminate excess demand. An increase
in the markup during periods of increasing
demand may also reflect noncompetitive pricing
behavior by some firms who feel they can raise
prices without a serious loss in sales. 6
A general form of the price equation which
incorporates this behavior may be written:
We are accustomed to think about inflation in
terms of the inflation/ unemployment relation,
referred to as the Phillips Curve. 4 The association between capacity-utilization rates and inflation can be viewed within the context of that
relation. As an illustration, we derive here a
modified Phillips Curve, which is a general form
of those incorporated in most large structural
econometric models atKi recently in several monetarist models of the U.S. economy.5
The Phillips Curve is derived from the interaction of two basic structural equations: (1) a price
equation relating prices to a markup on unit
labor costs and (2) a wage equation relating wage
21
(1)
"f" are linear, and we define the variables as
follows:
where al2 and au are estimated coefficients and
"f' denotes a functional relationship. The inflation rate (IR) in the current period (t) is relatedto
the rate of change in nominal wages (\\1),. the
trend rate of productivity growth (T), and a
function (f) of the actual measured rate of capacity utilization (CU) relative to its expected normal
or equilibrium value (CUe). The value of f(CUCU')will be zero when measured capacity utilization is equal to its equilibrium rate; rates of
utilization above CUe will lead to higher inflation
and rates below equilibrium will lead to reduced
inflation.
A general form of the wage equation may be
written:
W= a 21 IRt + ant t
h(u - ue),
IR ~ = IR t -
Last period's inflation rate, measured by
the percentage change in the GNP implicit
deflator,
this period's expected rate.
T=
(2)
CU
- a l2 h (u - u e)
al3)t
- CUe)
+ f(CU
Federal Reserve capacity-utilization series for total manufacturing.
u = unemployment rate of prime-age males
(25-54)
This rate appears to be a better cyclical
indicator of demand pressure than the
overall
rate, which has
tended in the past decade to reflect the
changing structure in labor markets. s
All estimates use annual data. We further assume
that the
rates of
for
prime-age males (u e ), and capacity utilization
(CUC), have been constant over the 1953-77
sample period. Regarding the prime-age unemployment rate, available data suggest that the
rate averages roughly 3 percent at peacetime
cyclical peaks, with no discernible trend. Regarding the capacity-utilization rate, recent theoretical studies suggest that the equilibrium rate
of utilization is dependent upon economic costs
and the degree of labor-capital substitutability,
and therefore may vary over time. 9 However, we
maintain the hypothesis of a constant CUe on the
basis of our initial estimates of the impact upon
that rate of such economic variables as the
relative cost of capital to labor which were
statistically insignificant. (This point is reinforced by Joseph Bisignano's article in this
Review.) With these specifications, and with the
incorporation of both equilibrium values in a
constant term,
may be written:
t.
= al2a2IIR~ + (al2a23
TIME.
The trend rate of labor productivity
(output per worker hour) is represented
a
linear time trend; and
,,It.~rn,,tlVP]V by a two-year and a threeyear moving average of output per
worker-hour.
where a21 and a23 are estimated coefficients and
"h" denotes a functional relationship. IR * represents the expected inflation rate, u is the
measured unemployment rate and u e is its equilibrium value. The difference (u - u e ) represents
that part of unemployment most responsive to
changes in excess-demand pressures. Here, as in
the rest of the paper, excess demand may be
positive (reflecting greater quantity demanded
than supplied) or negative (reflecting greater
supply). The unemployment rate, or more exactly, (u - u e), enters the wage-adjustment equation
as a proxy variable representing excess labor
demand. According to the equation, when excess
demand for labor is zero, inflation-adjusted
wages (W t - a21 IRt) will rise in proportion to the
trend rate of growth in labor productivity, 7
We may derive a semi-reduced-form relationship for the inflation rate by substituting equation (2) into (l):
IR t
1
(3)
Equation (3), the general form of the Phillips
relation, provides the framework for the statistical tests in this paper. But before we can estimate
that equation, we must first specify the functional forms "h" and "f" and the variables in the
equation. We assume that the functions "h" and
22
+ bIIRt-l + b2TIME + b4CUt
IRt = bo
b3ut
cant, however, when equations were estimated
with only one or the other included. These results
are shown in Appendix 1.
Given the above conclusions, we may drop the
time trend from equation (3') and include capacity utilization as the sole proxy for excess demand
in the model. Other analysts, more interested in
the unemployment/ inflation relation, have
dropped capacity utilization from their models. 13
Our interest, however, lies with the capacityutilization variables, which leads us to replace
equation (3') with the following general form:
(3')
where
= a l2 a 21
b 2 = (a l2 a 23 -
bl
a l3 )
Economic theory and statistical results reported in the literature suggest the values of some of
the coefficients in equation (3'). We expect that
the coefficient of the trend term in labor productivity, b2, will not differ significantly from zero.
This can be seen from the elements of b2. The
values al2 and al3, derived from the price markup
equation (1), are the coefficients associated with
the change in nominal wages CW) and productivity ('T), respectively. In statistical tests of the price
equation, these coefficient values generally are
equal and are close to unity. 10 This indicates that
the relevant measure for pricing decisions is a
• •
measure of standard unit labor costs (W - T);
consequently, changes in money wages and trend
productivity would have the same quantitative
impact (but in the opposite direction) and would
be completely passed through to final prices. In
addition, we expect a23 = 1. This reflects the
assumption that, in equilibrium, the rate of
change in real wages is equal to the rate of change
in labor productivity.
We expect to find a close, although not perfect, association between changes in unemployment (u) and capacity utilization (CU), since
both reflect pressures originating from excess
demand in product markets. II In addition, recent
empirical evidence suggests that there is limited
substitutability between capacity and labor utilization.. The high correlation between the two
may prevent our obtaining independent estimates of the impact of either one on the inflation
rate in equation (3').12
Our estimate of equation (3') did, in fact,
substantiate our. expectations concerning the
significance • of. the independent variables.• In
particular, the trend coefficient, b2, was not
significantly different from zero, and neither
excess-demand variable added significantly to
the determination of inflation. Each was signifi-
IR t
= dl(CUt -
CUe)
+ d 2IRt-l
(4)
According to this specification, capacity utilization and inflation rates are linked in the current period through the value d l , but it is not a
unique contemporaneous relationship, since current inflation depends also on past inflation
through the lagged inflation-rate term. Our
ability to associate a certain inflation rate with a
certain level ofcapacity utilization depends upon
the value of dI/(l-d 2), and crucially upon the
value of d 2, the coefficient of past inflation. 14 If d2
is less than unity, past inflation rates will become
less and less important over time, and eventually
will tend to have no impact on current inflation.
Under such circumstances, we will observe in the
long-run a unique, stable relationship developing between capacity utilization and inflation. A
higher rate of capacity utilization will become
associated with a higher rate of inflation, and
conversely. It would be possible, then, for an
economy to lower its inflation rate by maintaining over time a lower average rate of capacity
utilization. 15
On the other hand, when d 2is equal to one, the
expression dI/ (l-d2) is infinite, so that no unique
association exists, even in the long-run, between
capacity utilization and inflation. A long-run
curve relating the two variables is vertical, as
illustrated by the line cc' in Chart 1. Under these
circumstances, a given operating rate will be
consistent with any rate of inflation, and the
equilibrium inflation rate will be determined by
other factors. 16
In statistical tests of equation (4)-under a
variety of specifications for the lagged structure,
the sample period and the inflation aggregate23
therefore, that the level of capacity utilization is
not uniquely related with any particular rate of
inflation. On the other hand, when dz is equal to
unity, there is a permanent and stable relationship between changes in the inflation rate and
capacity-utilization rates. Inflation thus tends to
accelerate when capacity utilization surpasses a
particular level. To illustrate this, we may write
equation (4) in terms of the change in the inflation rate, CIR, by moving past inflation to the
left-hand side since its coefficient value is one:
Chart 1
Inflation-Capacity Utilization Equilibrium Relationship
When Coefficient on Past Inflation is Unity
Inflation
rate
CIR,
= a(CU, -
CUe)
(5)
Thus, if actual utilization (CUt) is maintained
above the equilibrium rate, the rate of inflation
will steadily increase; the inflation rate will rise
each period by "a" percentage for each percentage point the current operating rate exceeds the
equilibrium rate. Conversely, at utilization rates
below CUe, inflation will generally decline over
time. Only at the equilibrium operating rate will
the change in inflation be zero, with stability in
the inflation rate.
C
Equilibrium rate
Capacity Utilization Rate
we found that the coefficient on past inflation, d z, was not significantly different from
unity. These results are reported in Appendix 2
for U.S. data since the early 1950's. It appears,
II. Estimating a Stable-Inflation Capacity-Utilization Rate
be zero, on average, when CUt = CUe. All
statistical tests, unless otherwise stated, utilize
annual data.
We first developed a regression for the 1954-73
sample period (Line 1 of Table 1). We omitted
the more recent years from this first estimation
because of the unusual price factors which surfaced during this period, such as the oil price
hike, agricultural shortages, and the overall
effects of imported inflation. 17 The estimate of
CUe is 81.95 for the 1954-73 period.
For the entire 1954-77 period, we would expect greater variance because of the unusual
price factors just cited-and this is exactly what
we see (Line 2). The standard error has about
doubled, yet the estimate of the CUe (81.92)
remains virtually unchanged. The constant term
is negative, as posited by our model, and the estimate of the "a" coefficient is statistically significant at the 5-percent level. We made alternative
specifications of the basic model in order to test
the robustness of the CUe estimate, yet in each
case the estimate remained close to 82 percent.
Equation (5), which is in terms of the change in
the inflation rate (CIR), is our basic model for
estimating the equilibrium rate of capacity utilization.
CIR t = a(CU, - cue)
(5)
By incorporating the CUe in the constant term,
the equation can be written:
CIR,
= -k + aCU t
(5')
where k = aCUO. Once we obtain an estimate of
"a" , an estimate of CUe may be derived by
dividing the constant term by that value, i.e.,
A
CUe = ~
A
a
The equilibrium rate is the full-capacity utilization rate associated with stability in the inflation
rate; that is, the change in the inflation rate will
24
Thisresulfalso held in the shorter (1954-73)
period, and therefore appears stable over different time spans. IS
We also tried various lag structures for the
variables CU and IR. However, the results for
the additional lagged values were not significant
at the 5-percent level. 19
We next estimated the 95-percent confidence
interval for the CUe, 20 realizing that policymakers obtain little benefit from knowing the average
utilization rate which leads to increased inflation
if there is a wide band of uncertainty associated
with that average estimate. The 95-percent confidence interval is 79.6-83.5 percent for the 195473 period (Line 1). Relatively wide confidence
intervals are associated with the extension of the
estimating period to cover the 1973-77 period,
but we can obtain a narrower confidence interval
by incorporating dummy variables to account
for the special price factors which dominated
those years. With those adjustments, the 95confidence interval for the CUe for the 1954-77
period is 79.8-83.4 percent (Line 6). This range
appears narrow enough, relative to historical
utilization rates, to provide a meaningful signal
of potential inflationary pressures.
Again, our estimates generally remaihed unaffected when we substituted a manufacturing
wholesale-price index in the. price series,and
when we substituted fourth-quarter to fourthquarter for annual-average price data.
We. introduced dummy variables into our
equations to adjust for the unusual price behaviorof the 1974-76 period and for the price
controls of the 1972 period (Lines 5 and 6). These
adjustments led to a substantial drop in the
standard error, to a point about equal to that
reported for the original (1954-73) regression,
and with coefficient estimates similar to the
earlier period also.
Our preferred regression (Line 6) indicates
that for every percentage-point increase above
81.9 percent of capacity utilization, the inflation
rate tends to increase by .12 percentage points.
For example, with an increase in utilization from
81.9 percent to 83.9 percent, we would expect the
inflation rate to increase by .24 percentage
points. If capacity utilization rose to 83.9 percent
in year 2, the inflation rate would rise from (say)
6.00 percent to 6.24 percent-and if capacity
utilization remained at 83.9 percent in year 3, the
inflation rate would rise further to 6.48 percent.
Table 1
Estimates of Change in Inflation Rate:j:
(Annual Data, 1954-77)
Change in
Inflation
Rate
CIR* (I)
Capacity
Utilization
Constant
CU (t)
0'
0'
E.-
R'
Estimation
Procedure
-.46
.55
CORC
81.95
79.62-83.53
.59
2.2
81.92
74-86-86.02
1.33
2.0
.21
OLSQ
82.53
75.70-88.57
2.98
1.8
.12.27
CORC
81.94
77.94-84.81
1.43
I~
.32
OLSQ
.12079
-9.84463
81.50
79.16-83.15
.755 4.334
3.796
(5.35)
(5.22)
1.36) (7.84) (6.60)
CIR (6)
.12119
9.9206
79.79-83.39
81.86
4.448
3698
(5.44)
(533)
(809) (6.45)
t-statistics in parentheses
Estimation period is 1954-73
**
Fourth quarter to fourth quarter
ClJ
Capacity utilization for total manufacturing
CIR
G. N. P. implicit deflator used for change in inllation rate
CIRW
Wholesale-price index (manufacturing) used for change in inllation rate
0'
I in 1972 and 0 elsewhere
0'
1 in 1974 and 0 elsewhere
0'
I in 1976 and 0 elsewhere
57
2.1
.42
.86
CORC
58
2.2
-.48
.85
CORC
CIR
(2)
CIRW(3)
CIR**(4)
CIR
9.88369
(-4.76)
13.7149
(2.67)
36.2811
(2.96)
18.8944
(3.40)
0'
95-percent
Stable-Inflation
Capacity-Utilization Confidence
Rate
Limits
Standard
CUe
for CUe ~ D.W.
120612
(4.85)
.167421
(2.70)
.439590
(2.99)
.230581
(3.44)
(5)
25
III. Instability Between Inflation Rate and Capacity Utilization
The relationship which we estimated between
the change in the inflation rate and capacity
utilization can be written in the following terms.
To simplify the discussion, we have not included
any dummy variables.
IR t
= .12(CU
t -
82.0)
+ IRt - 1
keeps shifting as long as the inflation rate keeps
changing. Consequently, we expect the relationship to trace a counterclockwise loop. This
behavior is analogous to what we find in the
inflation/unemployment relation, as rising inflation expectations shift the inflation/unemployment curve over time.
Consider an initial equilibrium at point a.
Suppose there is a disturbance which results in
capacity utilization increasing relative to CUe.
The rate of inflation will then follow the path a to
b. If capacity utilization begins to decline from
point b back towards its equilibrium value, the
inflation rate will follow the path b to c. Note
that the equilibrium inflation rate consistent
with a return to CUe is higher than its initial rate.
This is because the economy maintains a
capacity-utilization rate always greater than
CUe; hence, the current year's inflation is always
greater than last period's. To return to the initial
inflation rate, a, capacity utilization must fall
relative to CUe; for example, tracing the path c to
d, and then returning to a. Inflation need not,
however, ever return to its initial equilibrium
value if events prevent capacity utilization from
remaining less than CUe for a sufficient time or
amount to lower the inflation rate to point a.
(6)
This relationship may also be illustrated graphically (Chart 2). At the capacity-utilization rate
equal to equilibrium, CUe, the vertical line illustrates the lack of a long-run stable relationship
between the rate of inflation and the capacityutilization rate. Essentially this means that once
an economy departs from its equilibrium value,
it may return to it, but at a rate of inflation
different from its initial value.
If the capacity utilization rate is above CUe,
the inflation rate is expected to increase steadily.
If last year's rate of inflation remained constant,
the relationship between capacity utilization and
the current inflation rate would trace the path
denoted by SS' in the chart, where "a" represents
the point where this year's inflation is equal to
last year's rate.
But according to equation 6, a deviation of
capacity utilization from CUe will in fact change
this year's inflation rate, which will alter hext
period's rate, and so on-so that the line SS'
Chart 3
Inflation Rate and Capacity Utilization Rate
Inflation
Rate'
10
Chart 2
Capacity Utilization Rate and Change in Inflation Rate
Inflation
rate
Graphical Illustration
L'
1953-77
9
8
7
6
5
s'
4
3
2
o
Capacity Utilization Rate
CUe
Capacity
Utilization Rate
'Annuai Percent Change in GNP Implicit Deflator
26
crc,ssf:~d
the 82-percentcapacity-utilization line
double the initial rate of inflation. The contraction which foHowed was relatively short lived, and consequently the inflation
rate dropped very little.
The current recovery is apparently beginning
its counterclockwise loop. The price movements
of 1976 and 1977 appear closely associated with
the imbedded inflation from the pressures generated in the previous years of high capacity
utilization. If 1978 carries the economy to utilization rates beyond equilibrium, we may find the
next return to equilibrium at higher inflation
rates than we are now experiencing.
These counterclockwise loops
trated with recent U.S. historical
The colored line first traces the recovery which
began in· 1954, \Vith an inflation rate averaging
less than two percent. During the recovery, the
inflation rate. increased as capacity utilization
rose and remained above
so that the
return towards 82 percent was accompanied with
a higher inflation than at the start of the recovery. The business contraction in 1958 resulted
in inflation returning to about the 1954 value.
Again, the long recovery of the 1960's started
out with a relatively low inflation rate. Between
1969 and 1970, the economy turned down and
Summary and Conclusions
In this paper, we have combined a wage and a
price equation to derive a semi-reduced-form
model of inflation. Our equation for the CUe
relates changes in the inflation rate to deviations
ofcapacity utilization from its equilibrium value.
According to that equation, a stable inflation
rate is consistent with a full-capacity utilization
rate of 82 percent --or within the 80-to-83'/2
percentrange provided by our 95-percent confidence limits. These results were robust under
changes in the estimation period, the lag structure and the chosen inflation rate.
Many economists believe that the yardstick
for full use of the nation's productive resources is
provided by the historical peak of capacity
utilization--specifically, the 87-to-88 percent
level of the 1973 period. Our analysis suggests,
however, that the full-capacity utilization rate is
reached at a somewhat lower level, so that there
less non-inflationary slack in the present economy than is commonly believed. Indeed, inflation tends to accelerate when the
rate
more generally, the
surpasses 82
80 to 83
Once
that
range, excess demand generates inflationary
pressures as less efficient labor and capital re-
sources are called into use. Thus, since utilization
rates recently have approached 85 percent, we
could expect mounting inflationary pressures
from the domestic, nonfarm business sector of
our economy.
Once capacity utilization exceeds the range
indicated, the increased inflation tends to become imbedded in future inflation, with the
current period's higher prices being reflected in
the next period's expectations. Our analysis
suggests that when the operating rate rises above
the full-capacity range, its return to that range
will be accompanied by a higher rate of intlation.
For the inflation rate to decline, therefore, capacity utilization would have to fall below its
equilibrium value, such as generally happens in a
business recession.
We may conclude that, in the 1978 economy,
there is no more non-inflationary slack available.
The important policy task, therefore, is to steer a
steady course which does. not permit output
growth to exceed its long-run potential. Under
such circumstances, a stable rate of inflation can
be maintained with both capital and labor at
their full utilization rates.
27
Appendix Table I
Estimates of· Equation (3.') :j:
(Annual Data, 1953-77)
Dependent
Variable
[R
1
Constant
IR(t-1) TIME XM2
----
(I)
4.004
(.35)
.692
(3.29)
[R* (2)
!.l09
(.09)
.718
(3.31)
lR* (3)
1.566
(.13)
.752
(3.49)
C[R (4)
.018
(.002)
C[R (5)
11.698
( -2.40)
C[R (6)
2.305
(2.91)
CIR (7)
-1.345
( -1.73)
+
+
*
lR
CIR
TIME
XM2
XMJ
URM
CU
XM3
.075
(1.20)
.401
(.974)
.324
(.79)
URM(t) URM(t) CU(t)
R2
Standard
Error
OW
Estimation
Procedure
-.507
H·15)
-.024
-.20)
.71
1.28
1.82
OLSQ
-.472
(-1.025)
-.017
(-.137)
.70
1.3 [
1.82
OLSQ
-.506
(-1.09)
-.016
(-.12)
.69
1.32
1.86
OLSQ
.19
1.28
2.ll
OLSQ
.17
1.30
2.11
OLSQ
.22
1.26
2.09
OLSQ
.12
1.34
2.09
OLSQ
-.537
(-1.25)
.024
(.218)
.143
(2.44)
-.617
(-2.82)
4.655
(2.09)
t-statistics in parentheses
Estimation period is 1954-77
Annual rate of change in GNP implicit deflator
Change in [R
Linear time trend
Two-year moving average of output-manhours ratio. (Output includes nonfarm business sector and households;
manhours includes private domestic nonfarm business sector, including proprietors and unpaid family workers.)
Three-year moving average of output-manhours ratio
Unemployment rate of males aged 25-54
Federal Reserve capacity-utilization series
Appendix Table 2
Estimates of Inflation Ratet
(Annual data, 1954-77)
Capacity [nflation
[nflation
Utilization Rate,
Rate Constant
CU(t)
Lagged
lR
(I) -11.92[3
(-2.00)
[RW (2) -29.3233
(-1.95)
lR
(3)
[R
(4) -10.0484
(-4.75)
-10.6478
(-4.91)
0'
Stable-Inflation
Capacity-Utilization Standard
03
Rate (CUe)
Error
D.W.
.149276
(2.16)
.919
(7.15)
79.86
1.34
1.96
.364912
(2.10)
.781
(4.12)
80.36
2.97
1.81
Estimation
Procedure
P
.68
OLSQ
.22
.56
CORC
.12875
(5.14)
1.051
-.958 4.0154.250
(16.24) (-1.57) (5.92) (-5.22)
82.70
.578
2.15 -.40
.94
CORC
.122435
(4.99)
1.008
(16.64)
4.393 -3.77
(6.54) (-4.71)
82.07
.599
2.20 -.48
.94
CORC
:j:
t-statistics in parentheses
G.N.P.implicit deflator used for inflation rate
[R (t)
lR W (t) Wholesale-price index (manufacturing) used for inflation rate
28
0' = I in 1972 and 0 elsewhere
0 2 = I in 1974 and 0 elsewhere
0 3 = I in 1976 and 0 elsewhere
FOOTNOTES
reduced form similar to equation (3), dropped capacity
utilization because of the high correlation between the
unemployment-rate measure used in their equation
and capacity utilization. Modigliani and Papademos
then went on to measure the nonaccelerating inflation
rate of unemployment.
14. Equation (4) states:
1. See Phillips (1958),
2. See Modigliani andPapademos (1976),
3. "Required Reading," American Banker, May 3,1978,
page 4.
4. In the literature, the term Phillips curve refers to the
relation between the unemployment rate and the rate of
change in wages, but also to the relation between the
unemployment rate and the rate of change of finalproduct prices. We shall use the term only in the latter
sense.
5. See Eckstein (1972), Stein (1978) and Laidler (1973),
6. Numerous studies in the literature relate demand
pressures tothe inflation rate and use capacity utilization as a proxy for demand pressures with in the context
of a price-markup equation. See the articles in Eckstein
(1972) and HirSch (1977). One of the earliest studies is
Eckstein and Fromm (1968).
7. For wage equations of this general form, see those
incorporated in the models discussed in Eckstein
(1972),
8. The unemployment rate of males, (25-54) is relatively
insensitive to cyclical business conditions, so that
changes in their unemployment rate basically reflect
changes in job opportunities and in the demand for
labor in general. For a review of the use of unemployment rates in labor market stUdies, see Mincer (1966),
The aggregate unemployment rate, on the other hand,
reflects the changing composition ofthe labor force, so
that it may change even when demand pressures in
labor markets do not. For example, teenagers and
women historically have higher than average unemployment rates; thus, although their group unemployment rate may not change, an increase in their percentage . in the labor force will increase the overall
measured unemployment rate. Since the mid-1960's,
both these groups have increased their labor-force
participation substantially; consequently, the measured total unemployment rate has tended to overstate
the amount of slack in labor markets. The reader will
note that since equation (3) uses the variable (u - ue), the
aggregate unemployment rate could be used as a proxy
for excess demand provided we also included the
equilibrium unemployment rate. Recent research indicates· that the equilibrium rate has been increasing
since the early 1950's, although there is a good deal of
professional debate about its actual value. I have used
the unemployment rate of males (25-54) in the text,
since that group's equilibrium unemployment rate may
be represented as a constant.
9. See Winston (1974) for a review of this literature.
10. See Tobin (1972),
11. For an analysis of the unem ployment and capacityutilization relationship over the business cycle, see
Butler (1977).
12. Because the demand for labor is derived from the
demand for final output, we may expect a high correlation between excess demand in the two markets. In
addition, we may assume that once capital stock is in
place, there is limited substitutability between capacity
utilization and labor employment. Recent empirical
evidence appears to substantiate this assumption (see
Malcomson). This limited substitutability may be the
major reason why we observe a high correlation between labor and capacity utilization in U.S. data.
13. Modigliani and Papademos (1976), using a quasi-
(4)
Lagging equation (4), we obtain
(4')
Substitute (4') into (4), to derive
IRt = d1 (CUt - cue)
+ d~
+ d1d2 (CUt-1
IRt-2
- CUe)
(5)
Continuing this process, current inflation is seen to be a
distributed-lag of capacity utilization. Assuming a given level of CU through time, we obtain the infinite
geometric series0)
i
(6)
IRt = d1 r d2 (CU - CUe)
i=O
00
where d1
r
i=O
i
d2 = d1
-
1-d2
co
- d1d2
1-d2
If d2<1, expression (7) converges to a finite number
resulting, according to (6), in a stable, equilibrium
association between IR and CU. If d2>1, no stable
solution exists; any gap between actual and expected
inflation continually widens. If d2=1, there is no longrun solution of equation (6); the equilibrium inflation
rate is independent of the rate of capacity utilization.
15. The terms permanent, long-run and equilibrium are
used interchangeably in his paper, in the sense of a
situation that would exist indefinitely if not disturbed by
"exogenous" forces, such as mandated energy-price
increases or changes in fiscal and/or monetary policy.
16. For a similar derivation of the long and short-run
impact of unemployment upon inflation, see Tobin
(1972),
17. For an analysis of inflationary pressures over this
period, see Keran and Riordan (1976>'
18.· One other estimate of the stable-inflation capacityutilization rate was derived by Otto Eckstein and Gary
Fromm in their 1968 article, "The Price Equation".
Using quarterly data, 1954.1-1965.4, and the wholesaleprice index, they estimated a price equation ofthe form
(1) above. They found an equilibrium value for the
capacity-utilization rate of 82 percent. The capacityutilization index was the Klein-Summers estimate,
which at the time of their study averaged about 2 points
higher than the Federal Reserve Board Index used in
this paper. They also found that every additional point
of the operating rate raises prices by .03 percent a
quarter, or .12 percent a year as we have found.
Eckstein and Fromm's results, however, are not
strictly comparable to ours, since they used the
wholesale-price index instead of the GNP implicit de-
29
flator as a measure of inflation. In addition,the
capacity-utilization series have undergone sUbstantial
revisions since the time of their study, which could
affect their estimates.
Nevertheless, both studies, using different but con~
sistent models of pricing behavior-theirs a structural
price equation and mine a reduced form equation~
both similarly concluded that the stable~inflation full
capacity utilization rate is substantially less than the
estimated historical peak would indicate.
19. The reader will note that our estimation equation is
but one relation in a complete model of the U.S. economy. In our estimations, we treat capacity utilization as
an exogenous variable. In the context of a complete
model, the operating rate would be determined by other
economic variables including inflation. Consequently,
our estimates may be subject to simultaneous-equation
bias. We therefore estimated equations similar to those
reported on lines 1 and 2, Table 1, using a two-stage
least squares procedure where capacity utilization was
a function of past money supply growth. Our results did
not differ from those reported in Table 1; therefore, we
continued to use ordinary least squares or CochraneOrcutt procedures.
20. The formula for calculating the confidence limits
was supplied by John L. Scadding. The procedure for
obtaining the formula is described in "The Sarnpling
Distribution of the Liviatan Estimator of the Geometric
Distributed Lag Parameter," by Scadding in Econometrica, May 1973.
The formula for the lower and upper confidence
limits is
(2ab - 2t2Sab) ±
BIBLIOGRAPHY
1. Butler, Larry. "Unemployment, Unused Capacity and
the Business Cycle", Federal Reserve Bank of San
Francisco Economic Review (Spring 1977), pp. 46-52.
2. Eckstein, O. (ed.! The Econometrics of Price Determination, Washington, D.C.: Board of Governors of the
Federal Reserve System and the Social Science Research Council (1972).
3. __ and Fromm, G. "The Price Equation", American
Economic Review, vol. 58 (1968). pp. 1159-84.
4. Hirsch, Albert A. "Measurement and Price Effects of
Aggregate Supply Constraints", in Joel Popkin, ed.,
Studies in Income and Wealth, Vol. 42 (1977), National
Bureau of Economic Research, pp. 299-329.
5. Keran, Michael and Riordan, Michael. "Stabilization
Policy in a World Context", Federal Reserve Bank of
San Francisco Economic Review, (Fall 1976l, pp. 5-19.
6. Laidler, D.E.W. "The Influence of Money on Real
Income and Inflation: A Simple Model With Some
Empirical Tests for the U.S. 1953-1972", Manchester
School, vol. 41 (1973), pp. 367-95.
7.
"Money and Money Income: An Essay on the
'Transmission Mechanism' ", Journal of Monetary Economics (1978), pp. 151-91
8. Malcomson, James M. "Capacity Utilization, The
User Cost of Capital and the Cost of Adjustment",
International Economic Review, Vol. 16 (1975), pp. 35261.
9. Mincer, Jacob. "Labor Force Participation and Unemployment: A Review of Recent evidence," Prosperity
and Unemployment, Robert A. Gordon and Margaret S.
Gordon, eds. (1966).
10. Modigliani, Franco and Papademos, Lucas "Monetary Policy for the Coming Quarters: The Conflicting
Views", Federal Reserve Bank 01 Boston New England
Economic Review, (March/April 1976), pp. 2-35.
11. Phillips, AW. "The Relation Between Unemployment and the Rate of Change of Money Wages in the
United Kingdom, 1862-1957," Economica (25), pp. 28399.
12. Scadding, John L. "The Sampling Distribution of the
Liviatan Estimator of the Geometric Distributed Lag
Parameter," Econometrica, Vol. 41 (1973),
13. Stein, Jerome L. "Inflation, Employment and Stagflation", Journal 01 Monetary Economics, (1978), pp.
193-228.
14. Tobin, James. "The Wage-Price Mechanism: Overview of the Conference", in Eckstein, O. (1972).
15. Winston, Gordon C. "The Theory of Capital Utilization and Idleness", Journal of Economic Literature
(1974), pp. 1301-20.
j(2ab - 2t2Sab)2 - 4(b2 - t2S~) (a2 - t2S~)
2
2(b2 - t2Sb)
where
a = estimate of constant
b2 = estimate of coefficient of capacity utilization
2
Sa = square of standard error of estimated constant
2
Sa = square of standard error of b
oh
t
= student t variable, t n -2
Sab = estimate of covariance between a and b
30
Larry Butler*
Unemployed labor and unused capital stock
prices has tended to lower the nation's potential
capacity to produce. 2
provide two measures of the available economic
capacity at the nation's disposal. In the past, the
In this article, we argue that it is not necessary
two have generally followed the same path, and
to resort to these structural arguments to explain
most analysts have treated them as roughly
the current divergence of the unemployment and
interchangeable measures of the amount of
capacity-utilization rates. Rather, the two marpressure on resources. In recent years, however,
kets need not reach full-resource use at the same
that relationship has come to appear considerapoint in business expansions, because capital
bly weaker than before.
and labor supplies exhibit different cyclical patIn the summer of 1978, capacity utilization
terns. New additions to the capital stock are
approached 85 percent of the nation's capital
concentrated in the mature-recovery portions of
stock-relatively tight in terms of the postcyclical expansions, while new additions to the
World War II average of 81 percent-while the
labor force are concentrated in a brief period
unemployment rate stood at 5.9 percent of the
following cyclical troughs. Short-term movelabor force-relatively slack in terms of the
ments in the capital stock, unlike movements in
postwar average of 5.3 percent. Thus the two
the labor force, are largely dominated by shifts in
measures have been providing different signals
expected output. Firms make substantial adjustof the amount of resource pressure in the economents to their desired capital-output ratios in
my. The recent level of capacity utilization sugshort periods of time, through movements in
gests that we are already approaching full reinvestment which are substantially faster than
source use, so that new supply pressures could
the adjustments they make to changes in the
cause accelerating inflation. Indeed, on two
labor force-output ratio.
earlier occasions, capacity utilization went from
The standard Keynesian aggregate-demand
85 percent to the cyclical peak of 87-88 percent
model includes only one factor market-usually
very rapidly, within the space of two to three
the labor market-but in this article we add a
quarters. But the recent unemployment rate
second factor market-the capital market. Our
suggests that fiscal and monetary stimulus could
rationale is that capital normally adjusts more
be applied for a protracted period with little
rapidly than labor to changes in economic condidanger of accelerating inflation.
tions. The single-factor model has adequately
Which of these conflicting signals is correct?
described most early-recovery periods, when
Most recent studies have tried to show that the
both labor and capital were in ample supply.
signals may, in fact, not conflict as much as
Again, the single-factor model has· adequately
seems apparent, because structural changes in
described such mature recovery periods as 1956the economy have made it difficult to compare
57 and 1967-69, which were capital-constrained
the measures over time. According to some
with high levels of capacity utilization, and also
labor-market studies, the shifting age-and sexlabor-constrained with quite low levels of unemcomposition of the labor force have tended to
ployment. In other periods, however, that model
increase the economy's "normal" rate ef unemhas proved to be an inadequate description ofthe
ployment, so that the current level is actually
cyclical process.
close to "full employment."! According to some
The two-factor model provides a better excapacity studies, the OPEC-caused upsurge in oil
planation of three brief, but important, periods
*Senior Economist, San Francisco Federal Reserve Bank
of transition to full employment-in 1955, 1965
31
and 1973. More importantly, that model may be
relevant to the period immediately ahead, which
might be marked by capital constraints but also
by adequate supplies of labor. 3 Capital utilization is already quite high, so that strong real
growth over the next half-year could place the
economy under significant capital constraints.
But the unemployment rate at that point could
still be close to 6 percent, which means that the
economy could sustain a capital-constrained
expansion for at least a year before the labor
market showed severe signs of tightness.
In such a period, high levels of capacity utilization would tend to stimulate rapid investment,
prolonging the business expansion. This investment then would generate strong demands for
credit, applying substantial pressure on interest
rates. But it would be wrong to interpret rising
rates in this case as indicating an excessive
tightness of monetary policy-which might be
deemed inappropriate in view of the likelihood
of continued high unemployment. Indeed, if the
monetary authorities resisted the upward trend
in interest rates, they could ratify the demand
pressures from the capital-investment expansion
and thus set off a new spurt of inflation. Consequently, policymakers should monitor closely
the signals from both the capital and labor
markets over the coming year.
Section I of this article describes the factormarket regularities which tend to exist both in a
transition period where there is an excess supply
of only the labor input to production, and in a
mature-expansion period where there are no
excess factor supplies. The following section
discusses the implications of these factor-market
movements for the cyclical changes in fixed
investment, labor-force growth and interest
rates. Section 3 discusses the derivation and
operation of the two-factor model, and the
concluding section describes the implications of
this analysis for current policy.
There are two special problems in treating the
published unemployment and capacity-utili-
I.
zation rates as roughly equivalent measures of
the degree of pressure on the capital and labor
markets. These should be noted at the outset,
because their treatment in this article affects the
analysis at several points.
1. Measures of excess capacity are available
for manufacturing only. The non-manufacturing
"service" industries have no comparable measure, largely because of the ambiguity of the
concept as applied to these industries. We here
assume that the cyclical timing, though not the
amount of fluctuation, in the size of the capital
stock in service industries is much the same as in
manufacturing.
2. Because excess capacity is measured for
manufacturing only, the obvious labor-market
comparison is with the unemployment rate in
manufacturing. In fact, those rates do have very
similar cyclical patterns, with both tending to
reach cyclical lows before the overall unemployment rate reaches its cyclical low. However, they
do so for very different reasons. The early trough
in capacity utilization occurs because rising
demand causes producers to expand their capital
stock to meet this demand.
Other things equal, a larger capital stock
means lower capacity utilization. The early turning point in manufacturing unemployment occurs because the growing availability of goodpaying jobs in manufacturing brings about an
increase in the supply of manufacturing labor.
Thus manufacturing unemployment is a poor
guide to the general pressure on the labor market, so that we may assume that the overall
unemployment rate is the appropriate measure
of the state of the labor market.
Because manufacturing capacity utilization
appears to be an adequate measure of overall
capital usage, and because the overall unemployment rate appears to be the best measure oflabor
supply conditions, we can make the direct factormarket comparison provided in Section I without danger of involving an "apples and oranges"
type of inappropriate comparison.
Cyclical Behavior of Factor Utilization Rates
data are based on surveys, one of manufacturers
and the other of households. The questions
asked in the household survey are straightforward. The interviewer asks whether a person had
First, let us note some intrinsic weaknesses in
the factor-utilization data used in this section.
These numbers contain ambiguities. Both
capacity-utilization data and unemployment
32
worked, or had looked for work, during the
survey month. Even so, the survey fails to pick
up such phenomena as "discouraged
workers"-people counted by the survey as
having dropped out of the labor force entirely,
but who in fact have simply given up all hope of
finding a job.
The analogous survey problem for capacity
utilization concerns marginal plant and equipment. In the manufacturing survey, business
firms are asked to assess the degree of their
capacity usage, compared to full use under
"normal operating conditions." Each must decide whether pieces of hopelessly obsolete equipment-perhaps kept around to meet peak-load
problems-qualify as part of his "normal" capacity. The answer will vary from firm to firm, so
the concept of capacity utilization is intrinsically
somewhat fuzzier than that of the unemployment rate.
As noted above, we here assume that service
industries' economic behavior differs from manufacturers' by at most a scale factor. The assumption may not be entirely true, because many
services are substantially less cyclical than manufacturing. The analysis in Section III thus will be
supported by other evidence~for example, the
cyclical behavior of such series as investment and
interest rates. The first step in this approach,
however, must be an examination of the cyclical
character of movements in the factor-utilization
rates themselves.
Three postwar business expansions have
reached full maturity-in 1954-57, 1960-69 and
1970-73 (Table l)4- and the current period may
yet reach the same stage. Transition periods are
defined as those when capacity utilization first
approaches its peak level but when unemployment still remains above its cyclical lowpoint.
(Rather arbitrarily, the start of the transition
period is dated from the point whenJ.he capacityutilization rate first exceeds 841;2 percent.)
Mature-expansion periods are defined as those
when capacity utilization remains high, and
unemployment as well has reached its cyclical
low. This distinction between transition and
mature-recovery periods is most evident in the
long 1954-57 and 1961-69 expansions (Chart 1).
Still, it is evident even in the relatively short
1970-73 expansion, when the period of low
cyclical unemployment continued over five full
quarters. 5
In all of the post-Korea expansions, the rise in
capacity utilization was slightly faster than the
fall in unemployment (allowing for the difference
in scale of the two series). In all except the
abortive 1958-59 recovery, capacity utilization
reached its peak before unemployment reached
its trough. In each early-recovery period, unused
capacity and unemployment declined almost as
rapidly as they rose during the preceding recession period, that process continuing to about the
seventh quarter of recovery.6
The 1970-73 expansion represented a partial
exception to this pattern, however. Real GNp?
and capacity utilization rose during the early
part of that expansion at about the same rate as
in earlier cycles, but the unemployment rate did
not drop appreciably below the 6.0-percent
recession-trough figure until late 1972, six quarters after that trough. The jobless rate then
averaged 4.8 percent during the mature-recovery
period~-a full percentage point above the average for the two previous mature recoveries. This
difference in movement is attributable, first, to
the post-Vietnam reversal of the artificial lowering of the civilian labor force associated with that
conflict, and second, to the influx of unskilled
Table 1
Factor Usage and the Rate of Inflation in Three Expansions
Capacity Utilization
Unemployment Rate
Inflation Rate
1954-57 1961-69 1970-73 1954-57 1961-69 1970-73 1954-57 1961-69 1970-73
Year before transition
Transition period *
Mature expansion**
Year after end mature
expansion
*
**
--- --- --- --- ---
---
80.1
86.0
86.2
82.8
87.2
87.4
83.1
86.5
86.9
5.5
4.6
4.1
5.6
4.9
3.7
5.8
5.2
4.8
1.9
2.9
3.3
1.4
2.0
4.4
75.3
78.2
73.1
6.5
5.0
7.0
1.3
5.1
Dating of transition periods: 19551-195511: 19631V-1965IV: 1972IV-197311.
Dating of mature expansions: 19551Il-1957111: 19661-1969IV: 1973IIl-1974IlI.
33
--4.5
5.0
9.1
9.8
ture recovery and the 4.8-percent rate of the
1973-74 mature recovery. This variation underlines the importance of structural elements, such
as the demographic factors cited above, in determining the level of full employment. The labor
market thus contains an element of long-period
adjustment to changing demographics as well as
a normal cyclical adjustment-as we are certain
to see over the next decade as those earlier
factors begin to reverse themselves.
Another strong regularity during these cycles
has been the tendency for full-employment periods to determine the timing of acceleratedinflation periods. Both of the major inflationary
bursts-in 1966-69 and 1973-74-occurred during periods of mature expansion. In both cases,
the labor and capital markets showed considerable tightness, with little variation in either the
capacity-utilization rate or the unemployment
rate. Price acceleration also appeared to be
relatively large during the 1956-57 mature expansion, although it tended to be swamped by
the generally declining trend in the inflation rate
which marked the 1950's.10
younger workers and women workers into tht:
labor force.
A systematic difference between the two series
has typically emerged after the early-recovery
period. 8 On average, capacity utilization stopped
rising after the seventh quarter of recovery, while
unemployment continued to fall slowly throughout the expansion. All of the complete postKorea expansions-again with the exception of
the abortive 1958-59 recovery-went through
such a transition period and then entered a
mature-expansion period marked by both full
employment and full capacity utilization.
A striking regularity has been the narrow
range of movement of capacity utilization in
both the transition and mature-recovery period
of the average cycle. This is doubly striking in
view of the fact that the capacity utilization rate
exhibits five times as much overall cyclical variation as the unemployment rate. 9 Yet given its
smaller relative movement, the unemployment
rate clearly has varied more than the capacityutilization rate from cycle to cycle. A substantial
difference can be observed between the 3.7percent average jobless rate of the 1966-69 ma-
Chart 1
Unemployment and Capacity Utilization Rates·
Percent of
Labor Force
1953-78
9
Percent of
Capacity
70
8
75
80
6
85
90
3
Transition Periods
Mature Recoveries
34
II. Cyclical Patterns of Factor Growth
As we have seen, the capital and labor markets
exhibit some difference (although sometimes a
modest difference) in their cyclical rates of adjustment. This distinction may be traced to the
pronounced difference in the cyclical growth
patterns of the underlying stocks-business
fixed capital and the labor force. That difference
in turn probably reflects different treatments of
fixed and variable production inputs. Capital in
principle is a hybrid kind of factor; large quantities of available capital will be left unused in
recessions, but will then be brought back into use
during mature recoveries-depending on the
level of aggregate demand and hence on the
quantities available of variable production factors. However, this characteristic may not be
shared to the same extent by the labor input.
Fixed factors are those production inputs
whose available quantities are relatively independent of current rates of production. The
desired stock of a fixed asset responds primarily
to changes in the expected flow of services the
asset will yield over a long span of time. Asset
holdings should adjust slowly to changes in
relative prices as all expected future flows of
services become adjusted to the current market
rate of return. Because of the slowness of adjustment, fixed-factor markets will often appear to
be in a state of excess supply, yet with no
significant decline in rates of return. To explain
this, we may assume that the expected future rate
of return is high enough to make current owners
of unused assets willing to continue to hold them.
Firms will not scrap unemployed capital as long
as they expect those assets to be profitable in the
future; instead, they will simply report those
assets as idle capacity.
In principle-although not necessarily in practice-the same argument applies to the labor
market. II We may assume that expected wage
rates are high enough to persuade current owners
of unused skills-the unemployed-to be willing
to continue in the labor force. In the labor
market as in the capital market, these resources
are available factors for further expansion of the
economy. But from the overall view of society
rather than the limited view of individual firms,
labor is the major long-run fixed factor in the
economy. Rapid scrappage can reduce a stock of
obsolete capital fairly quickly, but the same
cannot be said for a group ofskilled workers who
are displaced by new technology.
According to the evidence of the two strongest
expansions (1954-57 and 1961-69), capacity utilization and labor utilization tend to move differently in the later stages of expansion, with
capacity utilization turning down long before the
unemployment rate reaches its low point (Chart
1). Because the two series tend to move together
in the preceding recession and early-expansion
phases, their divergent behavior in later stages of
the cycle suggests substantially different cyclical
behavior on the part of the underlying stocks of
labor and capital (Chart 2). The two series
exhibit similar cyclical amplitudes; the labor
force increases over the cycle by about I percent
of the underlying stock, while the amount of
investment increases by about I Yz percent of its
stock. However, their patterns of movement vary
considerably.
All of the cyclical increase of the labor force
typically occurs in the first year of expansion,
and is then followed by a prolonged period of
stagnation or decline. Thus the most substantial
growth occurs in the early-recovery period, when
the level of aggregate demand (though not its
growth rate) is still low. This pattern reflects the
underlying secular nature of labor-force
growth-plus a discouraged-worker effect, with
some potential workers leaving the labor force as
Chart 2
Cyclical Changes in Capital Stock and the Labor Force
(Average of five post war cycles)
Annual change (%)
4
Capital stock
3
2
Labor force
Average date of>
succeeding trough
35
Chart 3
market conditions worsen, but then returning to
the labor force as demand picks up in the earlyrecovery phase. Investment demand, in contrast,
is strongly pro-cyclical, so that its movements
cannot be explained in the same way as the
movements of the labor force. Again, its movements cannot be easily explained in terms of
interest-rate effects (Chart 3), because interest
rates, like investment, move in a strongly procyclical fashion. (Interest rates generally peak at
the GNP peak, and reach a low point just after
the GNP trough.) Interest rates can significantly
affect investment, of course, primarily by helping
to determine the best long-run ratio of capital to
output, but over the cycle, the level of output
tends to have more effect than interest rates on
new investment spending. Thus investment tends
to be concentrated in the transition and maturerecovery periods of the cycle, when by definition
the highest levels of output occur.
The transition and mature-recovery periods
are similar because both are periods of heavy
investment, but they differ in respect to patterns
of inflation-with accelerated inflation being
evident only in the mature-recovery phase. This
distinction may reflect the fact that capital is the
only effective factor constraint on continued
output growth during the transition period,
Cyclical Changes in Investment and Interest Rates
(Average of five post war cycles)
Annual Change (%)
6
lone-year Treasury bill yield
5
4
3
2
Net fixed investment/GNP
Average date of ~I
succeeding trough
whereas both capital and labor act as factor
constraints during the mature-recovery phase.
The different behavior of the economy in these
two periods implies that there is a systematic
difference in the economic response to the two
kinds of factor constraint.
III. Aggregate Demand and Supply
ally be reached before full employment, leading
to a supply function such as that shown in the
right panel of Chart 4. If output is below the fullcapacity level, neither capital nor labor will act as
a constraint. In that case, expansionary
aggregate-demand policy will tend to increase
income, lower unemployment, and increase capacity utilization. As in the single-factor model,
the factor markets would generate little inflationary pressure within this range of income.
When income reaches the full-employment
level, however, both available capital and available labor act as constraints on real output,
although capital does so only by requiring a
switch of resources away from consumption and
toward investment. When both labor and capital
are fully utilized, expansive monetary and fiscal
policy cannot be expected to produce further
large additions to output. At that point, the only
effective way of increasing real income will be a
In a single-factor model, with the unemployment rate used as a general measure of the
amount of demand pressure, the economy may
be faced with an aggregate supply function as
shown in the left panel of Chart 4. If output is
below its full-employment level, expansive
monetary and fiscal policy will tend to increase
aggregate demand and reduce unemployment
(shifting demand from DI toward D2), but with
relatively small inflationary consequences because of the availability of excess factor resources. If output is above its full-employment
level, however, expansive aggregate-demand
policy will have a greater impact on prices than
on output, because of the lack of available factor
resources.
This single-factor model may be incomplete in
certain circuII1stances, because of the different
rates of adjustment in the capital and labor
markets. Full capacity utilization will occasion36
Chart 4
Aggregate Supply and Demand
ghangein
inflation rate
Change in
inflation rate
Single-factor model
Two-factor model
Sl
S
\1
02
\\
\
02
\
~
1
t-------:7""-~~I;---Output
\
t--~---J'---~~---r----
Output
01"1
Full-employment
output
output
structural policy, designed to shift the supply
curve itself to the right.
Just as in the single-factor model, if both labor
and capital are less than fully employed (at
aggregate-demand line D I'), we may experience
little acceleration and perhaps even some deceleration of inflation. Inflation in actuality tends
to decelerate at low levels of aggregate demand-that is, in late recession and early recovery. But the slope of the aggregate supply schedule S' is quite low where it is crossed by the
low-aggregate-demand line Dr, which implies
that a large shortfall in aggregate demand is
required to produce a modest decrease in the
inflation rate. 12 In contrast, the slope of the
aggregate-supply schedule is steep where it is
crossed by the high-aggregate-demand schedule
D3', which implies that the policy impact on the
inflation rate mostly occurs during the maturerecovery period of very high aggregate demand.
Also, as we argued in Section I, a transition
period exists between the early-recovery and
mature-recovery periods, which is milrked by a
low transmission of inflation. We can now see
that this is the portion of the aggregate-supply
schedule .crossed by the middle aggregatedemand schedule D2'.
Between the stages of full capacity and full
employment, further growth depends on an
increased demand for investment goods at any
level of interest rates. As income approaches Ye,
the full-capacity level of income, the investment
function tends to shift upward as business increases its estimate of the future demand for
output (Chart 5). This in turn shifts upward the
IS schedule, the total demand for· goods and
services. We can then determine a complete
solution by adding the LM curve, which indicates the similar trade-off determined in the
financial markets. As IS shifts upward on reaching full capacity (Ye), income and investment
both increase, and so do interest rates.
Chart 5
Income and Interest Rates
Interest Rates
IS
Income
37
IV. Implications for Current Policy
pened in the closing stages of both the 1954-57
and 1970-73 expansions. 13
In both 1954-57 and 1970-73, the transition
was quite brief, with capacity utilization moving
from 8412 percent to cyclical peaks in the 87-88
percent range within two to three quarters.
Because of the brevity of those transition periods, the bulk of each cycle's net capital accumulation occurred in the mature-recovery period. In
contrast, the 1964-65 transition period was prolonged more than two years by shifting but
generally tight monetary policy measures which
permitted both higher interest rates and a higher
investment-output ratio.
The current recovery appears to be in its own
transition phase. The unemployment rate, at
slightly below 6 percent, is still quite high by the
standards of earlier cycles. Yet interest rates have
moved sharply upward, with Treasury bill rates
up almost 200 basis points to date this year, and
with the bill-futures market expecting even further increases. Meanwhile, the investm..:ntoutput ratio has begun to rise, from a static level
of 9.7 percent in 1977 to 10.2 percent in the
second quarter of 1978. That combination of
circumstances suggests that it would be wise to
avoid overstimulating the economy during this
transition phase. In particular, the rising level of
(present and prospective) interest rates appears
to be an integral component of real growth in a
capital-constrained economy. If such increases
are not resisted by policy, and if monetary
growth is kept to a steady path, the recovery
should be able to continue for some time without
a further acceleration of inflation.
In this paper, we have emphasized the fact that
the capital market adjusts more rapidly than the
labor market over the cycle, which implies that a
transition phase exists between the period offull
capacity use and the period of full employment.
This phase is relevant to us because the economy
now seems to be in the midst of just such a
transition, moving toward a mature-recovery
period. In the past, capital accumulation has
been significant only in the transition and
mature-recovery periods, and not in the earlier
stage of expansion. Thus, if we failed to enter
these cyclical phases, we might experience a
permanently reduced rate of growth of the capital stock and hence of productivity. On the other
hand, a mature recovery carries inflationary
seeds of destruction within itself, so that we must
recognize the warning signals and avoid overly
full use of the factor markets.
The upward shift in the investment schedule
which typifies the transition period is the clearest
guide to the policy signals which can be anticipated in the advanced stages of recovery. First,
we should look for a rapidly rising ratio of
investment to output. Secondly, we should recognize that any given setting of fiscal and monetary policy will produce more inflation than it
did earlier in the recovery. The danger at such a
point is that policymakers will resist the interestrate increases which characterize the transition,
and thereby overstimulate the economy and
bring it rapidly from a wasteful state of unused
resources to an inflationary state of overfull
employment. To some extent, this is what hap-
FOOTNOTES
longer than is indicated by the official National Bureau
data.
6. A more detailed examination of the recession and
early-recovery relation between the two factor-market
measures was presented in the Spring 1977 issue of the
Review. The present article focuses on this relation in
transition and mature recovery.
7. Real GNP has grown at an annual rate of almost
exactly 5 112 percent in the first eight quarters of each of
the five most recent business-cycle recoveries.
8. The narrow difference in the cycle averages accounts
for the general assumption that the two measures are
interchangeable. Statistical methods based on long
spans of time must account first and foremost for large
swings in behavior. In the factor markets, these are the
1. See George Perry (1974) and Michael Wachter. (1977)
2. See Robert Rasche and John Tatom. (1977)
2. The structural problems are important, as has been
seen in Rose McElhattan's article in this Review (1977J.
But the evidence should not be overemphasized, The
lowest post-Korea unemployment was not reached in
the expansions of the 1950s, but as recently as 1969.
4. The investment, labor force, and interest-rate implications of the factor-usage rates are discusSed in the
next section.
5. The dates where the labor market began to weaken
are chosen as the endpoints of mature recoveries.
Because of the short lag between GNP growth and
labor-market growth, the 1960-69 recovery is one quarter longer and the 1970-73 recovery three quarters
38
12. R.J. Gordon (1976), in a recent survey of the Phillips
Curve literature, argued that theory provides scant
guidance as to the slope of the aggregate-supply schedule. He also noted that empirical economists have
become steadily more gloomy concerning the strength
of this trade-off.
13. This is not to say that policy of itself ended either
expansion. Rather, policy led to a state of extremely
high aggregate demand, and thus made the economy
vulnerable to any sort of downward shock to either
aggregate supply or demand. The 1973 oil-supply
shock, for instance, marked the end of recovery, although full employment had not been reached by mid1973.
Bibliography
Michael L. Wachter, "Intermediate Swings in Labor
Force Participation,"Brookings Papers on Economic
Activity, 2:1977, pp. 545-574.
rn
large r1l()ve entsin factor use centered on the recession trough of the business cycle.
9. The average increase in unemployment in the last five
recessions was 3.1 percent of the labor force; the
average dec.line in capacity utilization was 14.9 percent
of total utilization. The ratio of the two-4.8-measures
the relative cyclicity of the two.
10. Monetary policy was generally restrictive throughout the Eisenhower years. Also, the end of Korean War
price controls in the Spring of 1953 pushed the inflation
above what might have been expected during the 195354 period of recession and early recovery.
11. Adjustment does occur in such markets. If low
employment persists for long enough, some of the
unemployed will lower their estimates of their future
earning power and either leave the labor force or lower
their wage offer. If low capacity utilization persists,
some firms will not replace depreciated plant and
equipment. Such changes in expected future returns to
capital and labor may also produce long-term stability
of factor-usage rates in these markets. A reduced
expected return to capital lowers the desired capital
stock and makes the hiring of labor more attractive, and
thus creates an incentive to sh ift to more laborintensive technology over the long term. Thus the
notion of a fixed factor is a short-term concept; in the
long term, all inputs to production are variable. But a
large difference remains in the way short-term fixed
and variable factors affect the nation's effective economic capacity.
George L. Perry, "Potential Output and Productivity,"
Brookings Papers on Economic Activity 1:1977, pp. 1148.
Robert Rasche and John Tatom, "The Effects of the
New Energy Regime on Economic Capacity, Production, and Prices, " Federal Reserve Bank of Saint Louis
Review, May 1977, pp. 2-12.
Robert J. Gordon, "Recent Developments on the Theory of Inflation on Unemployment, "Journal of Monetary Economics, 2:1976, pp. 185-219.
39
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