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Working Paper Series
C a p ita l U tiliz a tio n a n d R e t u r n s t o S c a l e
Craig Burnside, Martin Eichenbaum
and Sergio Rebelo
Working Papers Series
Macroeconomic Issues
Research Department
Federal Reserve Bank of Chicago
April 1995 (W P -95-5)
FEDERAL RESERVE BANK
OF CHICAGO
C A P IT A L U TILIZA TIO N and RETU RN S to S C A L E *
C ra ig B urnside*
M a rtin E ichenbaum *
Sergio Rebelo§
A pril, 1995
Abstract
This paper studies the implications of procyclical capital utilization rates for in
ference regarding cyclical movements in labor productivity and the degree of returns
to scale. We organize our investigation around five questions that we study using a
measure of capital services based on electricity consumption: (1) Is the phenomenon of
near or actual short run increasing returns to labor (SRIRL) an artifact of the failure
to accurately measure capital utilization rates? (2) Can we find a significant role for
capital services in aggregate and industry level production technologies? (3) Is there
evidence against the hypothesis of const amt returns to scale? (4) Cam we reject the
notion that the residuals in our estimated production functions represent technology
shocks? (5) How does correcting for cyclical variations in capital services affect the
statistical properties of estimated aggregate technology shocks? The arnswer to the first
two questions is: yes. The arnswer to the third and fourth questions is: no. The answer
to the fifth question is: a lot.
K e y Words: Returns to Scale, Capital Utilization, Technology Shocks.
JEL Classification: E32
‘The authors owe a deep debt of gratitude to Joe Beaulieu. This paper would not have been possible
without his help. In addition, we would like to thank Ben Bernanke, Mark Bils, Lawrence Christiano, John
Fernald, Joe Mattey, Julio Rotemberg, Mat Shapiro and Steve Strongin for useful conversations.
1University of Pittsburgh
*Northwestern University, NBER, and the Federal Reserve Bank of Chicago
5University of Rochester and NBER
1
1
In tro d u c tio n
This paper studies the implications of procyclical capital utilization rates for inference re
garding cyclical movements in labor productivity and the degree of returns to scale. To study
cyclical movements in capital utilization we use two measures of capital services: industrial
electrical use and data on the workweek of capital. The investigation addresses five questions
using different assumptions about the production technology:
1. Is the phenomenon of near or actual short run increasing returns to labor (SRIRL) an
artifact of the failure to accurately measure capital utilization rates?
2. Can we find a significant role for capital services in aggregate and industry level pro
duction technologies?
3. Is there evidence against the hypothesis of constant returns to scale?
4. Can we reject the notion that the residuals in our estimated production functions
represent technology shocks?
5. How does correcting for cyclical variations in capital services affect the statistical prop
erties of estimated aggregate technology shocks?
Briefly, the answers are: (1) yes, (2) yes, (3) no, (4) no, and (5) a lot.
Our investigation utilizes aggregate data and two new data sets: a panel on 2-digit SIC
industries and a panel on 3-digit SIC industries. We argue that the data are well described
by a constant returns to scale production function. The estimated coefficients on labor and
capital services are similar to the shares of labor and capital in national income, .64 and .36,
respectively. The estimated residuals from our estimated production technology have two
important properties. First, in most cases, they pass a variant of Hall’s (1988) invariance
test; they are consistent with a set of orthogonality conditions that candidate measures of
technology shocks ought to satisfy. In contrast, the traditionally calculated Solow residual
does not pass the Hall test. Second, they are much less volatile and less correlated with
aggregate output than the empirical measure of technology shocks used in the Real Business
Cycle (RBC) literature.
The observation that average labor productivity is procyclical, which goes back at least
as far as Fabricant (1942), is closely related to a well known puzzle: capital appears to play
no role in explaining cyclical movements in output. This puzzle has been stressed by Solow
2
(1964), Lucas (1970), Bernanke and Parkinson (1991), among others. Exploring different
data sets over different sample periods and using different estimation strategies, they arrive
at the same conclusion: capital enters estimated production functions with either the wrong
sign or not at all.
The typical reaction is to this finding is to ignore movements in capital when studying
cyclical productivity fluctuations. While disheartening, Perry (1973)’s rationale for doing
this seems compelling:
‘If capital is ignored, it is for a simple pragmatic reason: one cannot find an im
portant or statistically significant role for capital in a freely estimated aggregate
production function or any equivalent relation that one might use in estimating
potential output.’
An alternative response is to obtain better measures of capital services. This is the
strategy we pursue. And with better measures, we find that there is an important and
statistically significant role for capital services. Moreover, estimated returns to scale are
roughly constant.
A different reaction to the apparent unimportance of capital in estimates of production
functions is to stop estimating them. In the macro literature, authors like Hall (1988) have
studied returns to scale by relating the growth rate of output to a cost weighted sum of the
growth rates of inputs. We implement the Hall type strategy using our measures of capital
services to assess the robustness of our findings. The key result is that, with this approach
too, we cannot reject the hypothesis of constant returns to scale.
Using our measures of capital utilization, we argue that neglecting cyclical variations in
capital services affects inference about why average labor productivity is procyclical. This is
important because the procyclical nature of average labor productivity has played a central
role in recent debates about the causes of aggregate economic fluctuations. RBC theorists,
such as Kydland and Prescott (1982) and Long and Plosser (1983) emphasize the importance
of exogenous shocks to productivity as the main impulse to postwar US business cycles. W ith
shocks to the aggregate production technology, RBC models can account for the observed
procyclical nature of labor productivity. Other researchers, sometimes organized under the
3
‘New Keynesian’ banner, have sought to revive much of the common wisdom associated
with the IS-LM paradigm using models grounded on microeconomic foundations.1 These
researchers emphasize the importance of demand shocks as impulses to economic fluctuations.
In conjunction with increasing returns to scale, demand shocks too can generate procyclical
movements in productivity.2
Increasing returns to scale are also an essential ingredient in a recent strand of literature
that emphasizes the importance of multiple equilibria for understanding business cycles.3
In standard RBC models the competitive equilibrium can generally be characterized as the
solution to a planning problem, which, being a concave program, has a unique solution. With
increasing returns the resource constraints facing the economy no longer define a convex set,
so there can be more than one equilibrium path. Under these circumstances, recessions can
be the result of pessimistic, self fulfilling beliefs of agents in the economy. With increasing
returns to scale, low output and employment levels will be associated with low levels of labor
productivity.
An alternative explanation of procyclical productivity, and the one which is most rele
vant to this paper, focuses on cyclical movements of capital utilization and labor hoarding.
This explanation has recently been explored by, among others, Greenwood, Hercowitz and
Huffman (1988), Kydland and Prescott (1988), Burnside, Eichenbaum and Rebelo (1993),
Finn (1991), Basu and Kimball (1994), Bils and Cho (1994) and Burnside and Eichenbaum
(1994).
Given the importance of disentangling the sources of procyclical productivity, analyzing
the properties of the Solow residual and estimating the degree of returns to scale have become
priority items in the macroeconomics research agenda. Authors like Basu and Kimball (1994)
use industry level annual data to assess the contribution of unobserved input variation to
cyclical movements in total factor productivity. Shapiro (1993a) uses annual data to study
the importance of movements in the workweek of capital. A different body of research,
originally associated with Hall (1988, 1990), focuses on the returns to scale and externalities.
'See Mankiw and Romer (1991) as well as the references therein.
2Rotemberg and Summers (1990) combine labor hoarding behavior along with nominal price rigidities as
a way of rationalizing the cyclical behavior of average labor productivity. Perhaps this defines them as ‘Old’
Keynesians.
3See for example Farmer and Guo (1995), Rotemberg and Woodford (1995) and the references therein.
4
Hall (1988. 1990) claimed to find evidence of large markups and increasing returns to scale.
Using similar methods, Caballero and Lyons (1992) and Bartelsman, Caballero and Lyons
(1994) argue that there are large spillover externalities at the industry level.
Bartelsman (1993) suggests that Hall’s evidence of large increasing returns to scale can
be explained entirely by the presence of small sample bias in Hall’s econometric procedures.
A different criticism has been levied by Basu and Fernald (1994a,b) who argue that with
imperfect competition, the use of value added data leads to spurious findings of large in
creasing returns to scale and external effects. Indeed, they show that when gross output data
on 2 digit SIC industry level data is used, evidence of increasing returns and externalities
disappears.4 In addition, at this level of aggregation, findings of external spillover effects are
associated with an exceedingly improbable implication. Estimated total returns to scale is
roughly constant. So spillover effects emerge only at the cost of concluding that there are
very large internal
d ecrea sin g
returns to scale (see Basu and Fernald (1994a) and Burnside
(1994)). One exception to this characterization is the 4 digit SIC industry level study by
Bartlesman, Caballero and Lyons (1994).
All of the previous studies use variants of Hall’s (1988) methodology in conjunction with
annual data. Rather than rely solely on annual data, we consider different specifications of
technology that allow us to attack the problem with quarterly aggregate and industry level
panel data. As it turns out there are interesting tradeoffs involved in using different spec
ifications of technology. These involve the generality of the specification being considered,
the assumptions about market structure and data requirements that are needed to estimate
the parameters in question. But overall returns to scale is a dimension across which all of
the specifications can be compared. And as it turns out, inference is very robust on this
dimension.
In all cases we estimate the parameters of technology losing a three stage least squares
procedure that exploits the fundamental identifying assumption proposed by Hall (1988):
4The fact that value added and gross output data yield different estimates of the degree to scale can be
explained even in the presence of perfect competition. In order for value added output to correctly measure
the marginal productivity of primary inputs, one of the following three restrictions has to hold: ( 1 ) materials
and energy are used in fixed proportions with gross output (Leontief aggregation), (2) the relative price
of materials and energy in terms of gross output is constant (Hicks aggregation), and (3) the gross output
function has the form Y = F[(K, L), M, E ] (weak separability), where K. L, M, and E denote capital, labor,
materials and energy, respectively. See Bruno (1978).
5
shocks to technology ought to be orthogonal to variables that are ‘known neither to be
causes of productivity shifts nor to be caused by productivity shifts’. In our view, shocks to
monetary policy, say as measured by Christiano, Eichenbaum and Evans (1994), as well as
variables like the relative price of oil qualify to be included in this class.
The remainder of this paper is organized as follows. Our model is presented in Section
2. Econometric procedures and data sources are detailed in Section 3. Empirical results are
presented in section 4. Some important limitations of our analysis are discussed in Section
5. The key problem, as in the related literature, (see for example Hall (1988, 1990) and Basu
(1993) is the potential impact of unobserved overhead capital and labor on the interpretation
of our estimated parameters. Concluding comments are contained in Section 6.
2
M o d e l S p e c ific a tio n
We begin by providing an overview of the three specifications of technology used in our
empirical work. In addition we summarize the tradeoffs with each specification. These
pertain to the generality of the specification, assumptions about market structure and the
data needed to implement the model empirically.
Let
Yt
denote time
t
gross output. In our first specification we assume that
= min(Mt, Vt )
Yt
where
Mt
denotes time
t
(L t), the stock of capital
materials and
( K t)
Vt
(1)
denotes a function that involves hours worked
and electricity use
( E t ).
Capital services and
Et
are related
via a Leontief technology. Our second specification relaxes this assumption and allows for
substitution between capital services and
tion that
Mt
and
Vt
E t.
The third specification abandons the assump
are related via a fixed coefficients technology. Here we assume that
is a differentiable function of capital services (St), energy (Et),
Yt
=
F ( S t , L t , E tl M t ).
Lt
and
M
Yt
t:
(2)
The following Table summarizes the tradeoffs involved in using the different specifications.
6
Data Frequency
Industry Level
Goods Market
Specification 1
Quarterly, Annual
2 , 3 digit SIC
No Assumptions
Factor Markets
Specification 2
Quarterly, Annual
2 digit SIC
No Assumptions
Hours, Electricity:
Perfect Competition
No Assumptions
Specification 3
Annual
2 digit SIC
No Assumptions
All factors:
Perfect Competition
The advantages of the first specification are that it allows us to use quarterly 2 and 3 digit
SIC data and makes no assumptions about market structure. The cost is that it imposes a
Leontief relationship between
and
Et.
Mt
and
Vt
and a Leontief relationship between capital services
The advantages of the second specification are that it allows us to use quarterly 2
digit SIC data and assumes only that labor and electricity markets are perfectly competitive.
The cost is that it imposes a Leontief relationship between
Mt
and
Vt .
The advantage of the
third specification is that it imposes no restrictions on the production technology other than
differentiability. The cost is that we can only use annual data and we must assume that all
factor markets are perfectly competitive.
We turn to a more detailed discussion of the three technology specifications.
2 .1
S p e c i f i c a t i o n 1: T h e S i m p l e s t S t r u c t u r e o f P r o d u c t i o n
In our simplest production specification,
Yt
is produced combining value added, (K), and
materials, (Mt), according to the Leontief production function (1). Basu (1993) has argued
persuasively that this Leontief form provides a good approximation to the structure of pro
duction in manufacturing, since movements in materials track movements in gross output
very closely . An additional motivation for working with this specification, emphasized by
Bernanke and Parkinson (1991), is that it allows us to work with industry level gross output
data, despite the absence of observations on material inputs.
The value added produced in one hour by one worker is
benchmark case, we suppose that the function
and twice differentiable. The variable
state of time
t
Nt
F (-)
A t F ( 1, K t / N t ).
In setting up our
is homogeneous of degree one, concave
is the number of time
t
workers and
At
reflects the
technology and other exogenous factors that affect productivity. Since each
worker is employed for
Ht
horns, total value added produced by the firm in period
t
is:5
5This specification of technology is similar to the one used in Chari, Christiano and Eichenbaum (1994).
7
v t = N tH tA tF { 1 , K t/ N t)
=
A t F ( N t H t , K t H t ).
(3 )
So to measure capital services we need to multiply the capital stock by its workweek. In our
formulation this coincides with the number of hours that each worker is employed.6 This
correction for capital utilization is similar to the one originally employed by Solow (1957)
which involved multiplying the stock of capital by the employment rate.
The key problem involved in using this production structure is the absence of good
direct measures of capital services. Certainly none are available at the quarterly frequency.
However, following Griliches and Jorgenson (1967), we can measure these services indirectly
via electricity consumption. This strategy has also been employed by Costello (1993) in her
study of the properties of the Solow residual in an international context.
Suppose that electricity consumption per machine is proportional to its workweek,
Then total electricity consumption,
Et,
is given by:
Et
Defining total time
t
hours as
Lt
=
Ht.
N tH t,
=
4>Ht K t .
(4)
and using equation (1) we obtain
Y t = A t F ( L t , Et/4>).
(5)
From an empirical standpoint, this formula has an important advantage: observations on
all of its variables are available at the quarterly frequency for 2 and 3-digit SIC industries.7
The disadvantage is that it imposes the strong restriction that the elasticity of electricity
use with respect to capital use is equal to one. There are a variety of reasons why this may
not be true, such as the existence of overhead capital. The generalized technology discussed
6Notice that the production function exhibits increasing returns to scale in N t, Ht and K t - It is standard
to assume that there are increasing marginal costs associated with increases in Ht , say because the rate of
depreciation is an increasing function of H t. In this case we can optimize with respect to H t find obtain a
reduced form production function that is concave in N t and K t . See Greenwood, Huffman and Hercowitz
(1988).
7
A standard criticism of the use of electricity as a measure of capital utilization is the possible presence
of a trend in the electricity-capital ratio. This could reflect a change in the composition of capital away
from structures to equipment. We could capture this effect by allowing 4 to be a deterministic function of
>
time. If the function F( ) were Cobb-Douglas, this would simply change the unconditional growth rate of
technology.
8
in section 2.3 relaxes the unit elasticity assumption. In section 5 we discuss how neglecting
overhead capital (and labor) can bias our results.
L i n e S peed a n d L a b o r H oa rd in g
We now consider the effects of variations in labor effort and in the intensity with which
capital is used. Suppose that hourly capital services per worker in equation (3 ) are
so that the value added produced in one hour by a worker is
Xt K t / N t ,
A t F ( l , Xt K t / N t ).
Here
Xt
denotes the intensity with which capital is used or ‘line speed'. Also suppose that electricity
consumption per machine is proportional to the effective workweek of the machine,
Then
Et
is equal to
4>Xt H t K t
<pXt H t .
and equation (5) remains unchanged. So, according to this
simple formulation, using electricity consumption allows us to measure capital services in a
way that is robust to changes in line speed.
To allow for unobserved changes in labor effort, i.e. ‘labor hoarding’, define the number
of efficiency units of labor as
Here
electricity depends on effort so that
E t = <f)QHt K t .
Q
measures effort per hom. Suppose that total
Then equation (5) becomes:
Vt = A t F ( C t L u E t /4>).
Notice that
involves
Q,
Et
(6 )
still measures total capital services. However the production function now
unobserved labor effort. One way to incorporate labor hoarding into the analysis
is to specify the costs associated with supplying effort. We could then use the condition that
determines the optimal supply of effort to solve for
Q
as a function of unknown parameters
and observable variables. The resulting ‘reduced form’ production function could be used in
empirical work. This is the approach pursued by Burnside, Eichenbaum and Rebelo (1993),
Basu and Kimball (1994) and Burnside and Eichenbaum (1994). Here we wish to see how
far we can go in explaining the apparent short run increasing returns to labor by controlling
for capital utilization while remaining as eclectic as possible about market structure and the
determinants of labor supply. Because of this we abstract from variations in effort in our
empirical analysis. This will tend to bias our results
returns to scale.
9
a g a in s t
the null hypothesis of constant
2 .2
S p e c i f i c a t i o n 2: A S l i g h t G e n e r a l i z a t i o n
The second production specification that we consider is given by
Yt =
where
Vtm is
m i n ( M ty t' ) ,
defined as:
(7 )
Vt' = A t F { L u K't ).
Here /Q is given by a CES function of capital and electricity use:8
k
; = M H . K . r + (1 -
,
p
< 1.
(8)
This type of two level production function was first proposed by Sato (1967) and has often
been used in the applied general equilibrium literature (see for example Ballard, Fullerton,
Shoven and Whalley (1985)). Our assumption that the production function is weakly sepa
rable between labor and the two other inputs is consistent with Berndt and Wood’s (1979)
parameter estimates for a translog cost function fit to a panel of manufacturing industries.
To implement this formulation we need to make use of the optimality condition that
determines the firm’s demand for electricity. Suppose that the firm acts as a price taker in
the market for labor and electricity. Then cost minimization requires that the firm equate
the marginal rate of substitution between
W tH t/ P s t -
Here
Wt
Nt
and
Et
to the relative price of the factors,
denotes the real wage rate per hour worked at time
t:
A , F 1( L „ K ; ) ( l - i t ) ( K ; / E , ) ' - ' _ P e ,
F ,(L„K ;)
w, ■
>
Equation (9) holds regardless of whether the firm is a perfect competitor or not in the goods
market. Here
Fi
denotes the partial derivative with respect to the
i th
argument of
F.
In our empirical work we assume that F (•) has a Cobb-Douglas form so that
Yt = A t ( L t ) ai ( k ; p
.
(10)
Consistent with this notation we do not impose the a priori restriction that the production
function is constant returns to scale, i.e. we do not assume that
a.\ + a .2
= 1. Given (9)
8V ' does not correspond to measured value added because it depends upon Et- This is immaterial for
our empirical work since we use gross output data, rather than value added data.
10
and ( 10 ), gross output can be written as a geometric average of toted hours (L t), energy
consumption (E t) and the price of electricity relative to labor,
Yt
= ((1 -
p£t
:
(11)
p ) ^ y 2/PA t ( L t )Qi+a^ E ^ - a2/pp - ° 2/p.
Taking first differences and letting lower case letters denote logarithms, we obtain:
At/t = 70 + 7i Alt + 72Aet + 73 A p Et +
Here 70 +
et
denotes the growth rate of A t, 71 = a x +
a 2/ p ,
( 12 )
et .
72 = a 2 - a 2/ p and 73 = - a 2/ p .
Our basic production structure coincides with the special case in which the elasticity of
substitution between capital and energy is equal to zero
(p
= — ). Here (12) becomes9
00
Ayt = 70 4-a iA /t +o: 2Aet + et.
(13)
We now turn to a brief discussion of the differentiable technology (2).
2 .3
S p e c if ic a tio n 3: T h e D if f e r e n tia b le T e c h n o lo g y
Much of the recent literature that uses annual data to study productivity assumes that
output is produced according to (2). Taking a first order log linear approximation to this
technology yields
(14)
A y t = r ) A x t + et
where 7 denotes overall returns to scale, Axt is a cost weighted measure of the growth rate
7
of aggregate inputs,
Axt =
c S tA s t
+
c LtA l t
+ CMtArri! + cet A et.
Here lower case symbols denote logarithms of upper case symbols and
of factor
j
in total time
t
Cjt
denotes the share
cost.
In sum, our three specifications of technology give rise to three types of relations between
factor inputs and output, (12), (13) and (14). But absent further restrictions, these are
without empirical content. They hold as identities. To have content, identifying assumptions
must be imposed on the stochastic process e£. We turn to this issue in the next section.
9This relation can be derived directly from (3) under the assumption that Vt is Cobb-Douglas in L t and
K tH t, where the weights do not necessarily add up to one.
11
3
E c o n o m e tric M e th o d a n d D a ta
The fundamental identifying assumption underlying our analysis is that
et
is a stationary
technology shock (not necessarily i.i.d.). Suppose that we have observations on a subset
of those variables, which, in Hall’s (1988) terminology, are known neither to be causes of
productivity shifts nor to be caused by productivity shifts. Let
zt
denote the time t realization
of these variables. By assumption
E [ z t et] =
0.
(15)
We think of (15) as representing a set of necessary conditions that candidate measures of
technology shocks must satisfy. Suppose that the dimension of z t is greater than or equal to
the number of parameters in the production technology. Then (15) can be used to estimate
the parameters of ( 12 ), (13) and (14). We do so via three stage least squares.
In some cases we present ‘restricted’ estimates, using panels of industry level data. These
estimates are obtained by imposing the Unear restriction that the parameters of the produc
tion technology, with the exception of 70, are the same in all industries. The intercept term
for each industry is left unrestricted. When the dimension of
zt
exceeds the number of
parameters to be estimated, (15) generates overidentifying restrictions that can be tested.
We do so using Hansen’s (1982)
J
test. Parameters restrictions were tested using the Wald
statistic discussed in Eichenbaum, Hansen and Singleton (1988).
C h oice o f I n s t r u m e n t s
We now discuss our choice of instruments, i.e. the observable analogs to the vector
In principle the vector
zt
ought to satisfy two criteria. First, the elements of
zt
zt.
should
be ‘exogenous’ in the sense that they are uncorrelated with the growth rate of technology.
Second, they should be correlated with economic activity in the industry under consideration,
i.e.
they ought to be relevant.
Finding instruments that satisfy both of these criteria
is difficult. Different variables have been used in the Uterature. Burnside, Eichenbaum
and Rebelo (1993) use quarterly innovations to government consumption. Caballero and
Lyons (1992), Basu (1993), Bartelsman, Caballero and Lyons (1994) and Basu and Fernald
(1994a,b) and Burnside (1994) employ variants of the instruments used in Hall (1988) and
12
Ramey (1989). These consist of current and/or lagged values of the annual growth rates of
oil prices and real military expenditures as well as the political party of the President.
Shea (1993a,b) has criticized the last two of the Hall-Ramey instruments on the grounds
that they are not relevant. To make this point, Shea (1993a) regressed the growth rate of
industrial production in 20 manufacturing industries on a time trend, seasonal dummies, and
current and four lagged values of real military spending, using quarterly, seasonally unad
justed, data over the period 1958-1985. He found that military spending is not statistically
relevant for output in
any
of the industries he looked at. Similar results hold for the political
party of the President. According to Shea, results based on irrelevant instruments should
not be viewed as ‘better’ than ordinary least squares estimates. This line of reasoning may
provide an additional rationale for the maintained assumption in Shapiro (1993a) that, over
the sample period, 1978 - 1988, there were no aggregate technology shocks. Bernanke and
Parkinson (1991) make the same assumption using quarterly data over the interwar period
to justify the use of ordinary least squares.
In this paper we utilize a different set of instruments. While we do report results for
Hall-Ramey type instruments, we also use as instruments lags of the monetary policy shock
measures discussed in Christiano, Eichenbaum and Evans (1994). These shock measures are
particularly attractive in the present context because they are, by construction, orthogonal
to a large set of economic aggregates in the monetary authority’s reaction function. Specif
ically, Christiano, Eichenbaum and Evans (1994) identify monetary policy shocks with the
disturbance term in a regression equation of the form:
+
St =
Here
St
(16)
e»t-
is the policy instrument of the monetary authority, 0 is a Unear function,
information set available to the monetary authority and
e 3t
Qt
is the
is a serially uncorrelated shock
that is orthogonal to the elements of Vlt . To rationahze interpreting e st as an exogenous poUcy
shock, (16) must be viewed as the monetary authority’s rule for setting
orthogonahty conditions on
e st
correspond to the assumption that date
S t.
In addition, the
t
poUcy shocks do
not affect the elements of f2f. Christiano, Eichenbaum and Evans (1994) derive two measures
of policy shocks. These correspond to different specifications of S t . In both cases
13
Qt
is given
by
Qt =
Here
{ Q t . P t . P C O M t . Q t - T,
Q t . P t■P C O M t .
FFf.
Pt_r , P C O M t- T, F F (_r , iVPFt_r , 77?t_r : r = 1 , 4 . } .
NBRt
and
denote the time
TRt
value of the log of real GDP,
t
the log of the GDP deflator, the log of an index of sensitive commodity prices, the federal
funds rate, the log of nonborrowed reserves and the log of time
t
total reserves, respectively.
The two measures of S t are the log level of nonborrowed reserves and the federal funds rate.
The corresponding policy shock measures, denoted by
e^BRt
and
eppt ,
residual from the OLS regression of the corresponding measure of S t on
time
t
component of
St
that is orthogonal to the elements of
correspond to the
Qt,
i-e. they are the
Qt.
To see why policy shocks are useful instruments in our context, consider the vector
consisting of
time
of
t —t
Qt,
eNBRt
and
^FFt -
It follows that
technology shock for industry
i,
vt
vt
satisfies F[ut|Q(] = 0. We assume that the
e,t_r , lies in the space spanned by the elements
for all r > 0, so that
E [ v t elt- T]
Among other things, the statement that
eit
=0
> 0.
t
(17)
lies in f2t embodies the assumption that Chris-
tiano, Eichenbaum and Evans (1994) include enough contemporaneous information in the
Fed’s reaction function so that what they call a policy shock is not in part a reaction to
current technology shocks. Under our assumptions it is also true that
E [ e itv t. r } =
for all
t
>
0,
(18)
0. The simplest way to see this is to suppose that
ordered moving average representation e,t =
a ( L ) u tt
square summable polynomial in the lag operator
E [ e ltv t - T]
=
E [ { a 0u it + a iU tt- X H
----- +
L.
where
e lt
has an (invertible) infinite
= 0 and
a(L )
Then
aT_itttf_(T_i))vt_T] + F[(aTttit_r H
------ ) v t - T ]•
That the first term on the right hand side of this expression is zero follows from
0. That the second term equals zero follows from (17) and the invariability of
quently, (18) holds, so that instrument vectors
vt
satisfy identifying assumption (15).
is a
14
zt
=
a(L ).
Conse
that include current and lagged values of
An alternative way to rationalize the use of these instruments is to assume that eit is
an exogenous stochastic process that has an MA(q) time series representation. Then it is
appropriate to use c£ , r >
_r
q,
as instruments.
The solid lines in figure 1 , reproduced from Christiano, Eichenbaum and Evans (1994),
depict the estimated time series of eNBRt and eFFt. Since the policy shock measures are,
by construction, serially uncorrelated, they tend to be somewhat noisy. For ease of inter
pretation we display the centered, three quarter moving average of the shocks. Also, for
convenience we include shaded regions, which begin at National Bureau of Economic Re
search (NBER) business cycle peaks and end at troughs. The estimated standard deviation
of eFFt is 0.79 percent, at an annual rate, while the standard deviation of e ^ BBt is 1.61
percent. The two monetary policy shock measures have a correlation of 0.49.
When we work with quarterly data we consider two specifications of the instrument vector
zt .
The benchmark specification of
zt
is given by
Z\t = (1) & P o ,t-\-T ,tN B R t-2 -r, C
FFt_2_r, r = 0. —»3}.
Here A p ot denotes the growth rate in the price of oil. We lagged the policy shocks measures
by two quarters in an attem pt to mitigate any spurious correlation between Z\t and ett
that might arise because of misspecification in the monetary authority’s information set. In
practice our results were robust to this correction. Our second specification of z t , is given by
z 2t
Here A g t denotes the time
t
= {1, A Po.t-T, A g t- r ,
T
= 0, ...7}.
growth rate in military expenditures. We think of z2t as corre
sponding to the Hall-Ramey instruments. In practice, we measure p ot using the quarterly av
erage of the monthly producer price index of crude petroleum (CITIBASE acronym PW561).
We measure g t as real Federal government purchases for national defense (CITIBASE acronym
GGFENQ).
When we work with annual data we choose as our instruments (i) a constant, (ii) the
current and lagged annual growth rate of the price of oil, and (iii) ^ B R t~ i
eFFt~ i w^ ere
these are four by one vectors containing the quarterly NBR and FF based policy shock
measures from the year
t —1.
We use shock measures that are lagged by a full year to ensure
that the instruments do not contain information based on current input or output data.
15
To investigate the relevance of onr instruments we regress the growth rate of output, the
growth rate of hours worked and the growth rate of electricity consumption on three sets of
instruments: (i) r 1£. (ii) {Ap 0, t - i - r , T
0,
=
and (iii) {1, Ap0it_r , A ^ _ r , r = 0, ...3}. In
each case the regression was calculated using data from the aggregate manufacturing sector,
the aggregate durable goods sector and the aggregate nondurable goods sector. Table 1
reports the
R2
associated with these regressions. Notice that the
R2
associated with the
Hall-Ramey type instruments are quite low. They range from a low of .03 when the growth
rate of electricity consumption in the durables sector is used as the dependent variable to a
high of .10 when we used the growth rate of output in the manufacturing or durable goods
sectors as the dependent variable. Comparable
emerge with {Ap0|t_i_r , r = 0 , ...,3}. In
R2
contrast, our benchmark instrument list does much better. Here the
R2
range from a low
of .24 when the growth rate of electricity consumption in the nondurables sector is used
as the dependent variable to a high of .42 when we used the growth rate of output in the
manufacturing sector as the dependent variable. Evidently lagged values of
and
eppt
contain substantial amounts of information regarding the different measures of economic
activity that we consider, i.e. they are relevant.
In general, the asymptotic distribution of the technology parameters are affected by the
fact that eyvsRt and
cff(
are generated regressors. However, this is not the case in our
application as long as the growth rate in technology is an exogenous
includes only estimated values of
and
eppt
M A (q)
process and zlt
that are lagged by at least q periods .10 To
see this write regression equation (16) as
Zt
— 3' X t +
ts t-
Denote the estimated values of est as ?st- Consider a vector of instruments, V^-r, that includes
values of es t, lagged at least r >
q
periods. For simplicity sake, we consider the case in which
the number of instruments equals the number of parameters to be estimated. Suppose that
we estimate the parameters 7 in the relationship
W t = j'D t
10We thank Mark Watson for pointing this out to us.
16
+
et
via an instrumental variables procedure that imposes the orthogonality restrictions
= 0.
E [V t. r e t ]
Then
■JT( 7 - 7 )' =
77 E telfoK '-rl
f E il l A K '- r l
Since VJ-r = VJ_r + (/3 —0 y X t- T, it follows that
^
a
t ]
=
X M U ] + ^
- /»)'[£ £ ( * . - . « . ] •
As long r > <, T - 1 E£=i [^t-ret] converges in probability to zero. Next note that
7
= T- 1
so that T - 1 Er=i[A K '_r ] converges in prob
ability to the same matrix as
of
\/T
3 .1
T ~ l J2t= 1 [ D t Vt'_r \
T~x
E^= [D£V/_r], It follows that the asymptotic distribution
1
r
(7 —7 )' is unaffected by the fact that we must estimate Vt - r .
D a ta
Our empirical work utilizes data from a variety of sources. All data referred to in this
subsection are seasonally adjusted. We indicate the CITIBASE acronym for each variable
in brackets.
E c o n o m y W id e I n p u t a n d O u t p u t D a t a
In some of our empirical work we employ economy wide aggregates. Here our measure
of output is quarterly real GDP (GNPQ) over the sample period 1972:2 - 1992:4. Our
measure of hours worked is the quarterly average of monthly total employee - horns in
nonagricultural establishments (LPMHU). We considered two measures of the quarterly
growth rate in the retil capital stock. The first is taken from Hall (1994). The second is
an updated version (available only through 1988:4) of the measure discussed in Christiano
(1988).11 Our measure of aggregate electricity consumption is a quarterly average of a
monthly index of total electrical power usage in the industrial sector (manufacturing plus
mining plus utility industries ).12 When dealing with economy wide aggregates we measure
u We thank Jonas Fisher for making this data available to us.
12We thank Joe Beaulieu for making this data available to us in machine readable form. This raw data is
published on a monthly basis in Industrial Production, Federal Reserve Statistical Release G.12.3.
17
the relative price of electricity using the quarterly average of the producer price index for
electric power (PWO-54) and quarterly compensation per hour in :he non farm business sector
(LBCPU).
M a n u fa c tu r in g S e c t o r I n p u t a n d O u t p u t D a ta
We measure quarterly labor input at the 2 digit SIC level using quarterly averages of
monthly production worker hours. For each 2 digit industry this measure is constructed as
the product of two time series, average weekly hours of production workers (LPHRXX) and
production workers on nonagricultural payrolls (LPPXX). Here XX refers to the relevant 2
digit SIC code. For aggregate manufacturing it is also possible to obtain data on a broader
measure of labor input, total hours of all persons, worked by all employees (LMNM). This
broader measure of labor input is not available at the 2 digit SIC level. To justify abstracting
from non-production workers on the basis of the simple model of section 2 we need to assume
that their input is used in fixed proportions with value added. If this Leontief assumption
does not hold, the interpretation of our results continues to be valid only if the correlation
between non-production hours and production hours is one.
Annual labor input measures correspond to the annual averages of the monthly data. All
of the data are available over the period 1972:1-1992:4. Corresponding 3 digit level data for
the sample period 1977:1 - 1992:4 were obtained from the Board of Governors.
Electricity consumption was measured as kilowatts of electricity used at the 2 digit SIC
level. These data were obtained from the Board of Governors. The two digit SIC level data
are available over the period 1972:2 - 1992:4, while the 3 digit SIC level data are available
over the sample period 1977:1-1992:4. Quarterly and annual data correspond to averages of
the underlying monthly data.
Obtaining quarterly measures of industry level output is more difficult than obtaining
the corresponding input measures. The Federal Reserve Board uses three sources of data to
construct the industrial production index: measures of physical product, kilowatt hours of
electricity, and production worker hours. The weight on each of these underlying sources of
information depends on the industry in question. Averaging over all 2 digit SIC manufac
turing industries, roughly 43%, 31% and 26% of the output index is based on measures of
18
physical product, kilowatt hours and production worker hours data, respectively. Note that
the Board does not use a simple, mechanical rule for inferring output from inputs. Instead
it estimates output using time varying production factor coefficients. If we conceive of the
Board as producing an optimal prediction of output given the information at its disposal, it
4
is reasonable to use the Board data on output.13 Still, we would be nervous about basing
inference entirely on this data set.
Fortunately there are a number of ways to assess the robustness of our results to the use of
alternative data sources. First, we exploit the fact that there are many 3 digit SIC industries
where the output index produced by the Board is strictly based on physical product. We
constructed a database with the subset of these 3 digit industries for which we could obtain
matching labor input and electricity use over the period 1977:1 - 1992:4. The net result was
a panel of 26 three digit SIC industries. These are listed in Appendix A, along with the
three digit SIC codes and the corresponding 2 digit SIC industries. Second, we repeat our
analysis using annual data. At the annual frequency, the Board’s measure of output is not
based on input data. This is because data from various censuses provide actual production
data for most industries. Therefore the problem of inferring output from inputs is almost
entirely an issue for within year variation of industrial output.
4
E m p iric a l R e s u lts
S o m e B a s ic F a c ts
We begin our analysis with a brief review of some basic facts. Figure 2 displays the
quarterly growth rates of real GDP (A y t ), economy wide hours worked (AZt) and aggregate
industrial electricity consumption (Aet). It is clear that Aet is highly correlated with both
A y t and AZf, even though at the aggregate level it is difficult to obtain a measure of elec
tricity consumption that matches the output concept. The high correlation between these
aggregates is documented in the following table which presents the unconditional correlations
between A y t , AZt, Aet and the growth rate in our measure of capital, A k t . In contrast to
13See Miron and Zeldes (1989) for a discussion of different models of measurement error in this context.
19
Ae,, AA'( is basically uncorrelated with Ayt and A lt (as well as Aet).14 This is why analysts
have traditionally found that capital plays no role in explaining cyclical fluctuations in out
put - existing measures of capital are poor measures of capital services, at least at cyclical
frequencies.
Correlations: Economy
A y t A/t Aet
Ayt 1.0 .82 .72
A ht .82 1.0 .73
.72 .73 1.0
A et
A k t .09
.31 .07
Wide
Ak t
.09
.31
.07 *
1.0
Figures 3 and 4 are the analogs to figure 2 except they are based on quarterly and annual
manufacturing data. Figures 5 and 6 display, in a graphical manner, the quarterly and annual
correlations between (Ayt and A/t), (Ayt and Aet), and (A/t and Aet) for the individual
2 digit SIC industries underlying the aggregate manufacturing data. The following table
summarizes the correlations between A y t , A l t and
A et
for the manufacturing sector as a
whole.
Correlations: Manufacturing Sector
Annual
Quarterly
A yt A l t
& y t A It A et
Ayt 1.0 .94 .80 1.0 .95 .88
A lt
.94 1.0 .81 .95 1.0 .94
Aef .80 .81 1.0 .88 .94 1.0
A number of points are worth making here. First, as in the aggregate data, Aet is
highly correlated with A y t and
A lt.
Indeed, the correlation is even more pronounced in the
manufacturing data. This may reflect the fact that our measure of e t corresponds exactly to
the manufacturing sector. Second, the quarterly and annual correlations are very similar. If
anything Aet and A/f are slightly less correlated with output at the quarterly level. This is
very comforting given possible concerns about the use of input data in the procedure used by
the Board to construct some of the quarterly output data. Recall that while these concerns
are relevant for the quarterly data, they are not relevant for the annual data. So the basic
u This is also true if we redo the analysis over the sample period 1972:1-1988:4 using the measure of capital
discussed in Christiano (1988).
20
fact which drives our inferences - namely that Aet comoves positively with A y t and A/t cannot be dismissed as an artifact of the way the output data are constructed.
A different way to see this is to consider the correlations between (Ayt and A/t), (Ayt
and Aet). and (A/f and Aef) for the individual 3 digit SIC code industries where the Board’s
measure of output data is not constructed with the aid of any input data. These are displayed
in figure 7. Notice that while there are interesting differences between the industries, in the
vast majority of cases Aet displays a sharp positive correlation with Ayt and A lt.
Next we consider the cyclical properties of a different measure of capital services: the
workweek of capital, wkt. Shapiro (1993a), among others, has suggested that a measure of
wkt might be useful in correcting capital stock data for cyclical variations in capital services.
To pursue point, we obtained the measure of w k t used by Shapiro (1993a). This consists of
an updated version of the series published by Foss (1981). The data are annual, with each
observation corresponding to the fourth quarter workweek of capital. The sample period is
1976:4 - 1988:4. The following table summarizes the correlations between A yt, Alt, Aet, and
A w kt.15
Measured Work Week of Capital
A lt Aet A w kt
1.0 .95 .88 .88
A yt
.95 1.0 .90 .89
Alt
.88 .90 1.0 .74
A et
A w kt .88 .89 .74 1.0
Notice that A wkt displays a strong positive correlation with Ayt, A lt and A et. We take this
fact to be supportive of our basic hypothesis that capital utilization rates sire procyclical.16
We conclude this subsection by briefly documenting the apparent ‘short run increasing
returns to scale’ or SRIRL puzzle. All the results that we report were obtained using the
GMM procedure and the instrument list zlt discussed in section 3. The following table
presents the points estimates of t)i that result from estimating the relationship A yt = t]q +
ruAlt + et using aggregate and manufacturing sector data.
15A11 growth rates were calculated on a fourth quarter to fourth quarter basis.
16We also computed the correlations between the growth rate of toteil capital services, (k t -w k t) and ( A y t,
A l t , Aet). These are similar to the ones between w k t and ( A y t , A l t , A e t ).
21
1
| Economy Wide
Total Hrs. Prod. Worker Hrs.
.96
m 1.21
(.131
(.0 9 )
*
Returns to Labor
Manufacturing
Total Hrs. Prod. Worker Hrs.
1.25
.97
(-08)
Durables*
.92
(■06)
(.06)
Nondurables’
.98
(■10)
P ro d u ctio n W orker H ours
Notice that when total hours worked are used to construct
A l t , r)X is
estimated to be sig
nificantly greater than one. When production worker hours are used, rji is estimated to be
approximately one. This is true, regardless of whether we work with aggregate data, manu
facturing data, durables goods data or nondurables goods data. SRIRL appears to be alive
and well, even with our instruments.
The following table presents the point estimates of rjX that result from estimating the
relationship Ayt = 7o + 72Ae* + et.
m
Returns to Electricity
Economy Wide Manufacturing
Total Durables
.49
1.15
.83
(.0 7 )
(.1 4 )
(.0 9 )
Nondurables
.92
(.1 9 )
Notice that, for the manufacturing sector, measuring factor input by electricity alone or
hours alone yields very similar results. Indeed we even get ‘short run increasing returns to
electricity’. The estimated value of 72 is positive but smaller for the economy wide case.
7
Presumably this reflects the fact that we do not have as good a measure of electricity use
for the economy wide data.
CES Versus Leontief
The previous subsection documented the basic fact that the growth rate of electricity
consumption is highly correlated with the growth rates of hours worked and output. We now
consider how this fact affects technology parameter estimates. Table 2 reports the results of
estimating the parameters of the technology specification given by (6) - (7) which allows for
substitution between capital services and electricity. The first column presents economy wide
results, while the second column presents results pertaining to the total manufacturing sector.
The third column presents results obtained imposing the restriction that the technology
22
parameters are the same in all 2 digit SIC industries. The fourth and fifth columns are
the analogs to the third column except that they pertain to the durable and nondurable
goods industries. The row
reports the probability value associated with the statistic for
testing the overidentfying restrictions of the model. The row J2 reports the probability value
associated with the statistic for testing the hypothesis of constant returns to scale, a j + a 2 =
1. The last three rows report different statistics pertaining to the average ‘technology shocks’
et. For restricted panel runs, the reported statistic regarding et pertains to the average value
of the industry specific statistic. For example, < corresponds to the average value of the
r(
standard deviation of et across the different industries.
The key result is that across all of the cases considered, the estimated value of a, the
elasticity of substitution between the workweek of capital and electricity, is positive but very
small. Specifically, it ranges from a low of .03 for the aggregate manufacturing sector to a
high of .30 for the nondurables goods sector. In no case can we reject the null hypothesis
that a = 0. This case corresponds to the Leontief specification given by (3).17
A different way to assess the Leontief specification is to investigate the empirical rela
tionship between the growth rate of electricity and the growth rate of capital services, as
measured by the growth rate of the product of the workweek of capital (A w kt) and the stock
of capital (kt). The following Table reports the results of estimating the relationship
Aet = /3[Awkt + A fct]
using our three stage least squares procedure in conjunction with instrument list zlt.
0
Aggregate Manufacturing
1.23
(0 .5 5 )
Aggregate Durables
1.77
(0 .7 7 )
Aggregate Non Durables
.53
(0 .3 5 )
Notice that, in no case, can we reject the null hypothesis, 0 = 1. light of this result and our
previous findings regarding a, through much of what follows, we impose the restriction that
electricity use is proportional to the workweek of capital. Table 2 contains results generated
17It is interesting to contrast the restricted point estimates of Q i, a 2 and a in the manufacturing industries
(.71, .30. and .03) with the unrestricted point estimates for the underlying industries. One way to summarize
the unrestricted estimates is to focus on their median. The median point estimates of aq, a 2 and cr are .60
.38 and .16. The associated median standard errors are .37, .35 and .55. Evidently, the qualitative nature
of inference here is not affected by imposing the (false) restriction that the 2 digit industries have the same
technology coefficients.
23
without imposing that restriction. So the reader can verify that none of the conclusions
dis< ussed in the text are affected by the imposition of that restriction.
In the remainder of this section we address five key questions: (1) Does SRIRL vanish once
capital services are measured by electricity consumption? (2) Are capital services productive
when measured by electricity consumption? (3) Is there evidence against the hypothesis of
constant returns to scale? (4) Is there evidence against the overidentifying restrictions of our
model? and (5) W hat can we say about the properties of technology shocks? We address
these questions at three levels of aggregation: economy wide data, 2 digit SIC code level
data and 3 digit SIC code level data.
Economy Wide Data
Table 3 reports the results of estimating the model using economy wide data. The first
column reports results obtained using two different measures of the capital stock. The third
column reports results obtained measuring capital services by electricity consumption. A
number of results emerge here. First, when we use the capital stock data, SRIRL emerges,
i.e. cq is estimated to be greater one. In addition, the estimated value of c*2 is negative and
insignificantly different from zero. In sharp contrast, when we measure capital services by
electricity use, the SRIRL phenomenon disappears and capital services enters significantly
into the production technology.
Second, there is no evidence against the hypothesis of
constant returns to scale. Finally, according to the J\ statistic there is no evidence against
the model’s overidentifying restrictions.
Using electricity consumption as a measure of capital services has important implications
for the statistical properties of the technology shocks. As a benchmark, suppose we simply
set a! = .64 and c*2 = .36. Using the stock of capital and electricity consumption as measures
of capital services we obtain
Jl
<7e/&AY
PtCYY
ASt = A K t
.015
.67
.87
A St —Ae*
.42
.77
.06
respectively. Notice that with the stock of capital measure, there is substantial evidence
against the model’s overidentifying restrictions. There is virtually no evidence against these
24
restrictions when capital services are measured using electricity. Perhaps more importantly,
with the electricity measure and these parameter values, the technology shocks are virtually
uncorrelated with the growth rate of output. Moving to the estimated values of
and
q2
(.54)
(.30) lowers rr£/crAj, and raises p(Ay somewhat (see Table 3). But even there p€Ay is
only equal to .31. Tins small correlation seems very difficult to reconcile with existing RBC
models that are driven primarily by technology shocks. Finally, it is worth emphasizing that
our electricity based technology shocks are much less volatile and substantially less correlated
with output than those emerging from the measures of output, hours worked and stock of
capital that are typically used in the RBC literature.18
Manufacturing Sector Data
Table 4 reports results based on the 2 digit SIC data. Columns labeled ‘Aggregate’
pertain to aggregate manufacturing data while the columns labeled ‘Restricted’ refer to
results obtained using the panel on 2 digit SIC industries. Results are reported for both
quarterly and annual data.
Consider the quarterly results. First, for aggregate manufacturing, the point estimates of
Q! and a 2 are .69 and .31, respectively. The corresponding restricted panel point estimates
are .64 and .37.19 These estimates are remarkably close to national income based estimates of
labor and capital shares obtained using a constant returns to scale Cobb-Douglas production
function (see for example Christiano and Eichenbaum (1992)). Second, the J 2 statistics
reveal virtually no evidence against the hypothesis of constant returns to scale. Third, the
overidentifying restrictions associated with the aggregate model can be rejected at the 1%
significance level. However, there is very little evidence against these restrictions for the
restricted panel. Fourth, comparing our economy wide based estimates of a£/<7Ay and peAY
(.60 and .31) with those reported in Table 4 (.37 and .21), we see that these fall as we move
to the aggregate manufacturing sector. However, we are hesitant to make too much of this
18For example, suppose we use Christiano’s (1988) measure of capital, hours worked and output. In
addition set qj = .655 and a 2 = .345, the values estimated in Christiano and Eichenbaum (1992). The
resulting point estimates of <re and crt /trAy are .0114 and 1.05, respectively. The correlation coefficient
between et and A Y t , p t A Y ' is approximately equal to .80.
19The median unrestricted point estimates of c*i and q 2 across the 2 digit industries are .54 and .38. The
corresponding median standard errors are .20 and .22.
25
fact, because our estimates of <t/ c r a n d
x
rise to .63 and .54, respectively when we work
with the restricted panel data. But even these estimates are smaller than those used in the
RBC literature.
The key finding with the annual data is that the results are quite similar to those obtained
with the quarterly data. There is some difference in the point estimates associated with the
restricted panel.20 This sensitivity is also revealed in the portion of Table 4 reporting annual
results for the durable and nondurable good sector. This point aside, inference seems robust.
Specifically, (1) there is no evidence of SRIRL, (2) there is no evidence against the hypothesis
of constant returns to scale, (3) there is little evidence against the overidentifying restrictions
of the model, and (4) there is overwhelming evidence that capital services, as measured by
electricity, are an important factor of production. The fact that inference is robust to the
use of annual data is particularly comforting because annual output data is not constructed
using information on factor inputs. As a further check on the robustness of the 2 digit SIC
results, Appendix A reports results obtained by omitting 2 digit SIC industries in which a
particularly large proportion of the output index reported by the Board is based on input
data.
3 Digit SIC Sector Data
Table 5 reports results obtained using our 3 digit SIC data set. Recall that this data
set consists of 3 digit industries for which there are direct measures of physical output.
The columns labeled ‘Restricted’ refer to results generated under the restriction that the
coefficients Qj and <*2 are the same in all of the industries we looked at. The columns
labeled Unrestricted’ report results generated from the corresponding unrestricted runs.
Specifically, we report the median point estimate of ax and Q2 as well as the corresponding
median standard errors. In addition we report the median probability of the J2 statistic
as well as the median point estimates of cr€,cr£/<7Ay and peAy The probability value for
the
J \
statistic refers to the overidentifying restrictions associated with the entire system of
unrestricted runs.
20The median point estimates of qi and Q2 obtained using the unrestricted annual 2 digit using data are
.80 and .17. respectively, with corresponding standard errors of .13 and .15.
26
The key features to note here are as follows. First, as above, there is no evidence for either
SRIRL or increasing returns to scale. If anything there is some evidence of decreasing returns,
but only for the restricted specification where we do not distinguish between durable and
nondurable goods. This specification aside, we find very little evidence against the hypothesis
of constant returns to scale. Second, as was the case with our other data sets, we find a
substantial role for capital services, as measured by electricity, in producing output. T hird,
there is virtually no evidence against the overidentifying restrictions imposed by the model.
This is true regardless of whether we work with the entire panel or condition on durables
and nondurables goods industries. Finally, we find that the estimated values of < a ^ y and
r€/
pfJ y are somewhat larger than those emerging from the manufacturing and economy wide
\
data. Still, these estimates are substantially smaller than those used in the RBC literature.
We conclude that the main findings obtained with the aggregate and 2 digit SIC data are
confirmed by the 3 digit SIC data.
We now briefly comment on the results of working with the alternative instrument set, z2tTable 6 reports a subset of the results we obtained with the Hall-Ramey type instruments.
Specifically, we display results for the restricted 2 digit and 3 digit SIC panels as well as
the median estimates from the corresponding unconstrained specifications. The key point to
note is the robustness of our results to the change in instruments.
T h e D iffe re n tia b le T ech n ology
We conclude this section by reporting results obtained from estimating the returns to
scale parameter rj in the production technology given by (2). We estimated r) using three
measures of the growth rate of capital services, A St. These measures Eire the growth rate in
the stock of capital, the growth rate of electricity and the growth rate in the workweek of
capital times the stock of capital. The corresponding sample periods, which were dictated by
data availability, are 1961 - 1989, 1973-1989, and 1977 - 1988, respectively. In all cases the
data correspond to fourth quarter to fourth quarter growth rates. The instrument list is given
by Z\t- Results for aggregate manufacturing, durable and nondurable goods sure reported in
Table 7.
27
The key results can be summarized as follows. First, for aggregate manufacturing and
durable goods, the estimated value of 7 is highest when A 5£ is measured by A K t. Moving
7
to electricity or workweek of capital based measures of A 5t results in smaller rj. W ith these
measures we cannot reject the hypothesis of constant returns to scale. If anything, there is
some mild evidence of decreasing returns to scale in the nondurable goods industries. Third,
in all cases the estimated shocks to technology and their correlation with the growth rate of
output are much smaller than those used in the RBC literature.
Viewed as a whole we conclude that inference about returns to scale is quite robust across
the three specifications of technology that we considered. There just is not much evidence
in our data sets against the hypothesis of constant returns to scale.
5
Shortcom ings o f th e A nalysis
In this section we discuss how the presence of capital goods that do not use electricity,
overhead labor and capital, and multiple production shifts could affect the interpretation of
our results.
5.1
N on -P rod u ction W orkers and O verhead C osts
So far we have stressed mismeasurement of capital services as the main source for the ap
parent short run increasing returns to labor. An alternative and perhaps complementary
explanation for this phenomenon is the existence of large overhead costs. To see this, sup
pose that the production function is of the form:
Yt = At(Lt — <f)aiK ° 2.
Here
(19)
represents overhead hours. An infinitesimal increase in hours worked due to a demand
shock generates a change in labor productivity equal to:
d(Yt/ L t)
~ d iT
Yt u
lXr ,
,
= - [ ( a 1-l)L + V].
(20)
Suppose au < 1. Then, absent overhead costs (< = 0), this derivative is negative, sug
/?
gesting that labor productivity ought to be countercyclical in a model driven primarily by
demand shocks. However, for
ip >
(1 —au)/’. this derivative will be positive. This could,
.
28
in principle, rationalize procyclical productivity even in a model driven by demand shocks.
However a simple back-of-the-envelope calculation suggests that the required overhead costs
must be large. If
is roughly equal to .65, ^ ~t££,t) will be positive only if overhead costs
represent 35% of L t.
Even if overhead costs are not this large, the fact that we have neglected them could
bias our econometric results. Taking a first order log-linear approximation to the production
fimction (19) and first differencing yields the following expression for the growth rate of
output
At/t = A at + ai-;--- Alt + ct2A k t .
L — ip
(21)
As before lower case letters denote the logarithm of the corresponding variables. Also L
represents the point around which we linearize (19). The key point is that, as long as < > 0,
p
the sum of the coefficients on Alt and A kt , will not equal one even if Qi + a 2 = 1. This is
because the coefficient on A lt is biased upwards, away from a\. However this does not imply
that our estimate of local returns to scale, as defined by Rotemberg and Woodford (1995),
is biased. These authors define local returns to scale for a production function F (K , L) to
be
K F i(K , L) + LF2(K, L)
F (K , L)
For the function F(-) given by (19), v is given a i-[~ + a 2- So in this case, our estimate of
the sum of the coefficients on A kt and A lt is a consistent estimate of u.
On a priori grounds, it might be reasonable to assume that overhead costs are more
important for supervisory labor than for production workers. To the extent that this is true,
estimates of the coefficient on Alt should be higher when that variable is measured as total
hours worked rather than total production worker hours. Because of data constraints we can
only pursue this idea for the aggregate manufacturing sector. When we reestimate (13) with
this measure of A lt and electricity based measure of capital services, the point estimates of
the coefficients on Alt and Aet are .82 and .36. The corresponding standard errors are .26
and .20, respectively. Recall from table 2 that the analogue estimates obtained using total
production worker hours as the measure of A/t are .69 and .31. The corresponding standard
errors are .16 and .17, respectively. The fact that the point estimate of the coefficient on A lt
29
is higher in the ease of total worker hours is consistent with the presence of more overhead
costs for supervisory workers. However, we cannot reject the nypothesis that the coefficients
are actually the same in the two cases. So it is possible that there are important overhead
costs associated with labor, and that these might be contribute to the procyclicality of
labor productivity. But the empirical case that these types of costs are more important for
supervisory workers than for production workers is weak.
5.2
Issues R egarding th e Stock o f C apital
Supposing that there is overhead capital which enters the production in a manner similar to
overhead labor. Then, proceeding as above, it is straightforward to show that the coefficient
on the change in A k t, will be biased upwards, away from a 2. As above, this will not induce
a bias in our estimate of local returns to scale, v.
Next we consider the case in which only a subset of the capital stock employs electricity.
Specifically, consider our simplest specification of the production technology (3). Suppose
that K t = K u + K 2t, so that
Yt = A t(Lt)a'( K ltHt + K 2tHt)a\
(22)
where Ht denotes time t hours of work per worker. Also suppose that electricity use is given
by
Et = (pKuHt
and that K 2t does not require the use of electricity. Taking a log linear approximation to
(22) we obtain,
Ai" = Aa ‘ + a ' A l‘ + a * E T W J i A e‘ +
[Ah* + A h ,]'
(23)
In general, the bias depends critically on the correlation between the right hand side regres
sors. As a useful benchmark suppose that A k 2t = A ku = 0, so that Aet = Aht. This is
the case in which all variation in capital services corresponds to changes in the workweek of
capital. Then (23) can be written as
Ayt = Aat + cqA/t -I- a 2Aet ,
30
so that there is no bias whatsoever. A similar argument would hold had we written the
production function as Yt = A t(Lt)ai(K itH t)a2(K 2tHt)a3. Again the sum of the coefficients
on Alt and A (h tk u ) = Aet would be a biased estimate of total returns to scale. But to the
extent that K u and K 2t do not vary over the cycle the bias induced by working with the
simple Leontief production structure will be small.
5.3
M u ltip le Shifts
In our empirical work we ignored the fact that the capital stock can be utilized more in
tensely if plants use discrete multiple shifts. The available shift data is scarce but suggests
an interesting puzzle. In U.S. manufacturing the shift premium paid to workers is small.
Kostiuk (1990) estimates a premium for the second and third shift of only 5.3%. Despite the
small shift premium, most industries whose production process does not require continuous
operation make modest use of the second shift and little use of the third. Bils (1992) argues
that industries bunch their production in a small number of shifts because of increasing
returns to scale. Shapiro (1993) argues that the marginal premium is much higher than the
commonly reported average shift premium. He estimates the marginal premium to be 25%.
To discuss how the presence of multiple shifts could affect our estimates, we extend our
basic model to allow for two production shifts. Suppose that output is given by
Ff = A tH N°tl K f 2 + A tHN°t K ° 2■
(24)
Here Ntt denotes the number of workers employed in shift i, for i = 1,2. To simplify the
analysis, we assume that the shift length, H, is the same for both shifts. Taking a log linear
approximation to (24), we obtain the following expression for the growth rate of Yt:
A yt = Aat + a i
N ?1
A
N °l
A n u + -------------- Ario#
N ?1 + N p
N ° l + N22 2
4
(25)
The specification used in our empirical work can be written as:
A yt = A at + c*i
• .Vi A nn + Qi N 2
A n2t + a 2A k t .
N x + N2
.Ni + N2
(26)
Here N\ and N2 are the points about which we linearize the production function. To assess
the specification error associated with neglecting multiple shifts, we can compare the coeffi
cients used to aggregate A nlt and A n2t in (25) and (26). Shapiro (1993) reports that, for his
31
sample of non-continuous processor industries, the percentage of workers on the first, second
and third shifts is 68.2%. 20.7% and 11.1%, respectively. Suppose we aggregate the second
and third shifts and assume that
qj
is equal to .65. Then the implied coefficients on A nu
and A n 2t in (25) are .681 and .319. The corresponding coefficients in (26) are .621 and .379.
We conclude that while there is some bias, it is not of first order magnitude. The basic fact
driving this result is the puzzle pointed out by Shapiro (1993); Why isn’t there more shift
work?
6
C onclusion
This paper presented evidence that capital utilization rates are sharply procyclical. Our
evidence relies on an electricity based measure of capital services. Standard measures of
capital services seriously understate the procyclicality of actual capital services and lead to
misleading inference regarding cyclical movements in labor productivity and the degree of
returns to scale in the economy. Our results have three important implications for macroe
conomists. First, models that depend on large, increasing returns to scale as a source of large
propagation effects are inconsistent with the data. Granted, given the sampling uncertainty
asscociated with our parameter estimates, it is possible to maintain that there are small
increasing returns to scale. But viewed overall, there is virtually no evidence to suggest that
there are important deviations from constant returns to scale in the manufacturing industry.
Second, existing RBC models which depend on large, volatile aggregate technology shocks
and which predict that the growth rate of output is highly correlated with aggregate tech
nology shoks are empirically implausible. Third, our results strongly support models which
emphasizing cyclical movements in capital utilization rates as an important determinant of
movements in conventional measures of total factor and labor productivity. It seems very
difficult to rationalize the properties of electrical use by manufacturing industries in a way
that does not involve substantial cyclical movements in capital utilization.
32
7
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37
APPENDIX A
In this appendix, we summarize the 2 and 3 digit SIC codes of the manufacturing in
dustries considered in the paper. In addition we summarize the sensitivity of the results we
obtained with the 2 digit SIC industries to disregarding industries in which a particularly
large percent of the Board’s output measure is based on input data.
In our analysis we used the following 2 digit SIC industries.
SIC
20
21
23
24
25
26
27
28
31
32
33
34
35
36
37
38
39
2 Digit SIC Industries
Code Name
Food
Textiles
Apparel
Wood Products
Furniture
Paper
Printing - Publishing
Chemicals
Leather
Stone, Clay and Glass
Primary Metals
Fabricated Metals
Machinery
Electrical Machinery
Transportation Equipment
Instruments
Miscellaneous
The following 3 digit SIC industries were used in our analysis.
38
SIC Code
201
202
207
212
221,2
226
227
228
245
262
263
265
271
281
282
285
301
314
324
325
331
332
333
334
336
374
3 Digit SIC Industries
Name
Ouput Units
Meat Products
Pounds
Dairy Products
Pounds or Gallons
Fats and Oils
Pounds
Cigars
Units
Cotton and Synthetic Fabrics Bales or Linear Yards
Fabric Finishing
Linear Yards
Carpeting
Square Yards
Yarns and Thread
Pounds
Manufactured Homes
Units
Paper
Tons
Paper Board
Tons
Paperboard Containers
Feet
Newspapers
Tons
Basic Chemicals
Tons or Cubic Feet
Synthetic Materials
Poimds or Tons
Paint
Gallons
Tires
Units
Shoes
Pairs
Barrels
Cement
Structural Clay Products
Units
Basic Steel and Mill Products Tons
Tons
Iron and Steel Foundries
Tons
Primary Nonferrous Metals
Secondary Nonferrous Metals Tons
Pounds
Nonferrous Foundries
Railroad Equipment
Units
To assess the robustness of our results we redid the analysis underlying Table 4 excluding
two subsets of industries. Excluding SIC Industries 23, 25, 34, 35, 38 and 39 leaves us
with industries in which at least 30% of the Board’s measure of output is based on physical
output. If in addition we exclude SIC Industries 27, 28, 32, and 36, we are left with a panel
of industries in which at least 40% of the Board’s measure of output is based on physical
output. All of the results in the following table refer to restricted panel estimates based on
quarterly data..
39
Table A.l, 2 Digit SIC Data
j
= 7o + Qi A /f +
All 2 Digit SIC industries
| Manuf.
ai
q2
■h
■h
PeA Y
.64
Dur.
.61
Nondur.
.74
+ €t
Exclude SIC 23,25
34,, 35,38,39
Manuf. Dm-. Nondur.
.75
.84
.67
Also Exclude SIC 27, 28,
32, 36
Manuf. Dur. Nondur.
.82
.98
.61
(.05)
(.06)
(.09)
(.06)
(.10)
(.10)
(09)
(.14)
.37
.43
.39
.32
.24
.47
.27
.13
(.12)
.51
(.05)
(07 )
(.08)
(.06)
(,ii)
(08)
(•10)
(.16)
(•12)
.31
.75
.59
.66
.12
.38
.57
.59
.30
.10
.63
.60
.20
.18
.60
.56
.07
.15
.52
.42
.42
.09
.69
.55
.46
.09
.59
.53
.16
.10
.50
.45
.51
.22
.63
.55
40
.
Figure
1
Three Quarter, Centered Average of FF Policy Shocks
With and Without Commodity Prices
Quartarty Data
Three Quarter, Centered Average of NBRD Policy Shocks
W and Without Commodity Prices
ith
*i
1
I
a
< "
2
I •
]
1i
1
i
| |
j
L
u
1 1 »
I
1 1 /i a
1
i A
* 1
il
l
A IV 3 1|i 111
r t illi/iA W M
1|
A
I J i
|
UyVvvAl
IV
i|J \i
V
iL \i
]
}
iF
I
Ii
n
1
t
/
1u
1
/
.1Quattariy Oata
For the solid lines, the policy shocks are estimated as the orthogooalized innovations from the 6variable VARs which include Y. P. PCOM, FF. NBRD. and TR; for the dashed lines* the policy
shocks are estimated as the orthogonalized innovations from the 5-variable VARs which include
Y. P. FF. NBRD. and TR. In each case, the three-quarter, centered averages are computed with
equal weights applied to the time t-1, u and t+ 1 orthogonalized innovations.
F ig u r e 2
Q
u a rterly
G
row th
R a tes
of
E
conom y
W
id e
Data"
" Y represents real GNP, H represents total hours worked in nonagricultural establish
ments and E represents electrical power usage in the industrial sector. All series are plotted
as first-differenced logarithms. The data are described in more detail in the text.
F ig u r e 3
Q
u a rterly
G
row th
R
a tes o f
A g g r e g a t e M a n u f a c t u r in g D a t a "
’ Y represents industrial production in the manufacturing sector, H represents total
employee hours in the manufacturing sector, and E represents electrical power usage in the
manufacturing sector. All series are plotted as first-differenced logarithms. The data are
described in more detail in the text.
F ig u r e 4
A
nnual
G
row th
R a tes
of
A g g r e g a t e M a n u f a c t u r in g D a t a *
* Y represents gross output in the manufacturing sector, H represents total employee
hours in the manufacturing sector, and E represents electrical power usage in the manufac
turing sector. All series are plotted as first-differenced logarithms. The data are described
in more detail in the text.
F ig u r e 5
C
o r r e l a t io n s o f
Q
u a rterly
2 -D ig it S IC L e v e l D a t a *
Output and Hours
a
20
22
23
24
25
26
27
28
31
32
33
34
35
36
37
38
39
Hours and Electricity Use
o
" Y represents industrial production, H represents production worker hours and E rep
resents electrical power usage. All series are first-differenced logarithms. The x-axis labels
are the appropriate SIC codes.
F ig u r e 6
C
o r r e l a t io n s o f
A
nnual
2 -D ig it S I C
lev el
Data’
Output end Hours
20
22
23
24
25
26
27
28
31
32
33
34
35
36
37
33
39
34
35
36
' 37
38
39
Output and Electricity Use
20
22
23
24
25
26
27
28
31
32
33
Hours and Electricity Use
’ Y represents industrial production, H represents production worker hours and E rep
resents electrical power usage. All series are first-differenced logarithms. The x-axis labels
are the appropriate SIC codes. The correlation between Y and E for industry 20 is —
0.19.
F ig u r e 7
C
o r r e l a t io n s o f
Q u a r t e r l y 3 -D ig it S IC L e v e l D a t a ”
0.0 0 1 0.2 0 3 0 4 0.5 0.6 0.7 0.8 0 9 10
Output and Hours
0 0 0 1 0 2 0 3 0.4 0.5 0.6 0.7 0.8 0 9 1.0
Output and Electricity Use
201 202 207 212 22- 226 227 228 24-5 262 263 265 27 1 261 262 285 301 314 324 325 331 332 333 334 336 374
0 0 0.1 0 ? 0 3 0.4 0.5 0 6 0 7 0.8 0 9 1.0
Hours and Electricity Use
201 202 207 212 22* 226 227 228 245 262 263 265 271 281 282 285 301 314 324 325 331 332 333 334 336 374
’ Y represents industrial production, H represents production worker hours and E repre
sents electrical power usage. All series are first-differenced logarithms. The x-axis labels are
the appropriate SIC codes. Industry 22* is industries 221 and 222 combined. The correlation
between H and E for industry 201 is —
0.03.
Table 1: R 2 of Instrument Lists with Output and Inputs
|
Hall Instruments*
Sector
Output
Hours
Electricity
Manufacturing
0.10
0.09
0.05
Durables
0.10
0.09
0.03
Nondurables
0.09
0.09
0.08
Growth Rate of Oil Price: Lags 0-3
Output
Sector
Hours
Electricity
0.07
0.06
Manufacturing
0.02
Durables
0.07
0.05
0.00
Nondurables
0.07
0.08
0.03
Benchmark Instruments*
Sector
Output
Hours
Electricity
Manufacturing
0.42
0.38
0.34
Durables
0.40
0.39
0.34
0.36
0.29
Nondurables
0.24
* Growth Rate of Oil Price, Lags 0-3; Growth Rate of Military Spending, Lags 0-3
* Growth Rate of Oil Price, Lags 1-4; ( F F t Shock, Lags 3-6; ( N B R t Shock, Lags 3-6
Table 2: CES Specifications
Economy Wide
Manufacturing Sector
Aggregate
2 Digit SIC Code Level*
All Industries Durables Nondurables
<*i
0.74
(0.50)
0.71
(0.34)
0.76
(0.09)
0.63
(0.13)
0.90
(0.15)
a2
0.24
(0.17)
0.30
(0.30)
0.27
(0.08)
0.41
(0.12)
0.27
(0.12)
(7
0.15
(0.35)
0.03
(0.44)
0.26
(0.17)
0.04
(0.20)
0.30
(0.22)
0.98
(0.34)
1.00
(0.08)
1.03
(0.04)
1.04
(0.05)
1.17
(0.08)
+ 0.2
J
0.004
0.34
0.11
0.92
0.37
0.60
0.60
0.63
0.42
0.32
0.21
0.54
P(AY
* Coefficients restricted across industries, with industry fixed effects
0.33
0.67
0.56
|
Table 3: Economy Wide Data
AY* = c q + otiAHt +
k
+ 6^
j
A K* = A if "
A K* = A K c
A K* = A E
1.23
(0.14)
1.31
(0.24)
0.54
(0.27)
-0.32
(0.85)
-0.88
(1.81)
0.30
(0.11)
0.91
(0.80)
0.43
(1.61)
0.84
(0.19)
a2
C1 + #2
*
J
0.91
0.72
. 0.41
0.56
0.56
0.60
0.38
0.39
0.31
Pt,6Y
K h : Hal1 (1994) measure of capital
K c : Christiano (1988) measure of capital: 72:1-88:4
Table 4: Manufacturing Sector Data
A Yf = a o + ctxAi?{ + ctjA/Cj +
Annual
Quarterly
Durables Nondur.
Manufacturing
Durables Nondur.
Manufacturing
2-Digit SIC Code Level*
2-Digit SIC Code Level*
Aggregate
Aggregate
«i
0.69
(0.16)
0.64
(0.05)
0.61
(0.06)
0.74
(0.09)
0.69
(0.31)
0.43
a2
0.31
(0.17)
0.37
(0.05)
0.43
(0.07)
0.39
(0.08)
0.21
(0.35)
0.57
0-1 + Oi2
1.00
(0.07)
1.01
(0.04)
1.04
(0.05)
1.13
(0.08)
0.90
(0.09)
0.12
0.60
0.42
industries,
0.20
0.30
0.12
0.61
0.67
0.33
0.58
0.56
0.35
with industry fixed effects
0.31
0.01
0.63
0.37
0.54
0.21
Pt.&Y
* Coefficients restricted across
J
(0.02)
(0.02)
1.00
(0.01)
0.38
(0.06)
0.60
0.71
(0.06)
0.30
1.06
(0.03)
0.90
(0.07)
0.44
0.55
0.49
0.09
0.69
0.71
(0.12)
(0.12)
Tab le 5: 3-Digit S IC Code Level D a ta
A y* = Q + ctiAHt + o^A Kf +
:o
Restricted*
Unrestricted*
Manufct’rng Durables Nondur. Manufct’rng Durables
Nondur.
<1
*
0.52
(0.05)
0.73
(0.11)
0.45
(0.07)
0.52
(0.31)
0.64
(0.44)
0.56
(0.33)
a2
0.35
(0.04)
0.14
(0.08)
J.35
(0.06)
0.38
(0.25)
0.24
(0.36)
0.21
(0.26)
&l + &
2
0.86
(0.05)
0.87
(0.08)
0.81
(0.09)
0.87
(0.28)
0.89
(0.23)
0.92
(0.32)
0.26
0.50
0.20
0.19
0.75
0.88
0.95
0.84
0.78
0.82
0.86
0.84
Pt,AY
' Coefficients restricted across industries, with industry fixed
* Median coefficients across industries, with median standard
in parentheses
J
0.15
0.79
0.97
0.70
0.78
0.76
effects
errors reported
Table 6: Hall Instruments
L
+ €t
AYi:= Oq + Cti&Ht +
2-Digit SIC Code
3-Digit SIC Code
Restricted* Unrestricted* Restricted*
Unrestricted1
<1
*
0.54
(0.04)
0.61
(0.19)
0.79
(0.05)
0.50
(0.32)
a2
0.39
(0.04)
0.29
(0.18)
0.23
(0.04)
0.20
(0.25)
0.79
0.79
0.93
0.91
(0.20)
(0.05)
(0.28)
(0.04)
0.20
0.81
0.65
J
0.41
0.58
0.83
0.91
0.62
0.87
0.85
0.63
0.61
P(,AY
* Coefficients restricted across industries, with industry fixed effects
* Median coefficients across industries, with median standard errors
reported in parentheses
1+
CL
0-2
Table 7: Differentiable Technology Specification
Measure of A S t
A K t Aet A [wkt • K t
Aggregate Manufacturing
1.10 1.01 .98
n
(.06)
(.07) (05)
.05
.07
.27
Ji
.24
.24
.17
&e/ &Ay
.17
.26
.17
PeAy
AggregateDurables
1.16 1.06 1.08
T
)
(.05)
(.05)
(.05)
.35
.20
.30
Jl
.18
.16
.17
&e/&Ay
-.08 .11
.14
PeAy
Aggregate Non Durables
.83
.82
.86
V
(.13)
(.14)
(.12)
.22
.11
.13
Ji
.52
.50
.42
&e/&Ay
.67
.61
.43
PeAy
Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
REGIONAL ECONOMIC ISSUES
Estimating Monthly Regional Value Added by Combining Regional Input
With National Production Data
WP-92-8
P hilip R. Israilevich an d Kenneth N. K uttner
Local Impact of Foreign Trade Zone
WP-92-9
D a v id D. W eiss
Trends and Prospects for Rural Manufacturing
W illiam A. Testa
State and Local Government Spending~The Balance
Between Investment and Consumption
WP-92-12
WP-92-14
R ichard H. M attoon
Forecasting with Regional Input-Output Tables
P.R. Israilevich , R. M ahidhara , and G.J.D. H ewings
A Primer on Global Auto Markets
WP-92-20
WP-93-1
Paul D. B allew an d R obert H. Schnorbus
Industry Approaches to Environmental Policy
in the Great Lakes Region
D a vid R. A llardice , R ichard H. M attoon and W illiam A. Testa
WP-93-8
The Midwest Stock Price Index-Leading Indicator
of Regional Economic Activity
WP-93-9
W illiam A. Strauss
Lean Manufacturing and the Decision to Vertically Integrate
Some Empirical Evidence From the U.S. Automobile Industry
WP-94-1
Thomas H. K lier
Domestic Consumption Patterns and the Midwest Economy
WP-94-4
R obert Schnorbus an d Paul B allew
1
Working paper s r e continued
eis
To Trade or Not t Trade: Who P r i i a e i RECLAIM?
o
atcpts n
WP-94-11
Thom as H K lie r a n d R ic h a rd M attoon
Restructuring & Worker Displacement i the Midwest
n
WP-94-18
P a u l D . B a lle w a n d R o b e rt H . Sch n o rb u s
Financing Elementary and Secondary Education i the 1990s:
n
A Review of the Issues
WP-95-2
R ic h a rd H . M a ttoon
ISSUES IN FINANCIAL REGULATION
Incentive Conflict i Deposit-Institution Regulation: Evidence from Australia
n
WP-92-5
E d w a rd J . K a n e a n d G e o rg e G . Kaufm an
Capital Adequacy and the Growth of U.S. Banks
WP-92-11
H e rb e rt B a e r a n d Jo h n M c E lra v e y
Bank Contagion: Theory and Evidence
WP-92-13
G e o rg e G . K aufm an
Trading A t v t , Progarm Trading and the V l t l t of Stock Returns
ciiy
oaiiy
WP-92-16
Ja m e s T . M o se r
Preferred Sources of Market Discip i e Depositors v .
ln:
s
Subordinated Debt Holders
WP-92-21
D o u g la s D . E v a n o ff
An Investigation of Returns Conditional
on Trading Performance
WP-92-24
Ja m e s T . M o se r a n d Ja c k y C . So
The Effect of Capital on P r f l o Risk a Life Insurance Companies
otoi
t
WP-92-29
E lija h B re w e r I I I , Thom as H M on dsch ea n , a n d P h ilip E . Stra h a n
A Framework f r Estimating the Value and
o
I t r s Rate Risk of R t Bank Deposits
neet
e ail
WP-92-30
D a v id E . H u tch iso n , G e o rg e G . P e n n a cch i
Capital Shocks and Bank Growth-1973 t 1991
o
WP-92-31
H e rb e rt L B a e r a n d Jo h n N . M c E lra v e y
2
Working paper s r e continued
eis
The Impact of S&L Failures and Regulatory Changes
on the CD Market 1987-1991
WP-92-33
E lija h B re w e r a n d Thom as H . M on dsch ea n
Junk Bond Holdings, Premium Tax O f e s and Risk
fst,
Exposure a Life Insurance Companies
t
WP-93-3
E lija h B re w e r I I I a n d Thom as H M on dschea n
Stock Margins and the Conditional Probability ofPrice Reversals
WP-93-5
P a u l K ofm an an d Ja m e s T M o se r
I There L f f e After DTB?
s
i()
Competitive Aspects of Cross Listed Futures
Contracts on Synchronous Markets
WP-93-11
P a u l K ofm an , Ton y Bouw m an a n d Ja m e s T M o se r
Opportunity Cost and P u e t a i y A Representativerdnilt:
Agent Model ofFutures Clearinghouse Behavior
WP-93-18
H e rb e rt L Baer\ V irg in ia G . F ra n c e a n d Ja m es T M o se r
The Ownership Structure ofJapanese Financial I s i u i n
ntttos
WP-93-19
H esn a G enay
Origins of the Modem Exchange Clearinghouse: A History of Early
Clearing and Settlement Methods a Futures Exchanges
t
WP-94-3
Ja m e s T. M o se r
The Effect of Bank-Held Derivatives on Credit A
ccessibility
WP-94-5
E lija h B re w e r I I I , B ern a d ette A . M in to n a n d Ja m es T M o se r
Small Business Investment Companies:
Financial C a a t
h r c eristics and Investments
WP-94-10
E lija h B re w e r I I I an d H esn a G en ay
Spreads, Information Flows and Transparency Across
Trading System
WP-95-1
P a u l K ofm an an d Ja m e s T. M o se r
3
Working paper s r e continued
eis
MACROECONOMIC ISSUES
An Examination of Change i Energy Dependence and Efficiency
n
i the Six Largest Energy Using Countries-1970-1988
n
WP-92-2
Ja c k L . H e rv e y
Does the Federal Reserve Affect Asset Prices?
WP-92-3
V efa Ta rh a n
Investment and Market Imperfections i the U.S. Manufacturing Sector
n
WP-92-4
P a u la R . W orthington
Business Cycle Durations and Postwar S a i i a i n of the U.S. Economy
tblzto
WP-92-6
M a rk W. W atson
A Procedure f r Predicting Recessions with Leading I d c t r : Econometric Issues
o
niaos
and Recent Performance
WP-92-7
Ja m e s H . S to c k a n d M a rk W. W atson
Production and Inventory Control a the General Motors Corporation
t
During the 1920s and 1930s
WP-92-10
A n il K . K a sh ya p a n d D a v id W. W ilco x
Liquidity E f c s Monetary Policy and the Business Cycle
fet,
WP-92-15
L a w re n ce J . C h ristia n o a n d M a rtin Eich en b a u m
Monetary Policy and External Finance: I t r r t n the
nepeig
Behavior of Financial Flows and I t r s Rate Spreads
neet
WP-92-17
K en n eth N . K u ttn e r
Testing Long Run Neutrality
WP-92-18
R o b e rt G . K in g a n d M a rk W. W atson
A Policymaker’ Guide t Indicators ofEconomic Activity
s
o
WP-92-19
C h a rle s E v a n s , Steven S tro n g in , a n d F ra n c e sc a E u g e n i
Barriers t Trade and Union Wage Dynamics
o
WP-92-22
E lle n R . R issm a n
Wage Growth and Sectoral S i t : P i l p Curve Redux
hfs hli s
WP-92-23
E lle n R . R issm a n
4
Working paper s r e continued
eis
Excess V l t l t and The Smoothing of I t r s Rates:
oaiiy
neet
An Application Using Money Announcements
WP-92-25
Steven S tro n g in
Market S r c u e Technology and the Cyc i a i y ofOutput
tutr,
lclt
WP-92-26
B ru c e P e te rse n a n d Steven S tro n g in
The I e t f c t o ofMonetary Policy Disturbances:
dniiain
Explaining the Liquidity Puzzle
WP-92-27
Steven S tro n g in
Earnings Losses and Displaced Workers
WP-92-28
L o u is S . Ja co b so n , R o b e rt J . L a L o n d e , a n d D a n ie l G . S u lliv a n
Some Empirical Evidence of the Effects on Monetary Policy
Shocks on Exchange Rates
WP-92-32
M a rtin Eich en b a u m a n d C h a rle s E v a n s
An Unobserved-Components Model of
Constant-Inflation Pot n i l Output
eta
WP-93-2
K en n eth N ' K u ttn e r
Investment, Cash Flow, and Sunk Costs
WP-93-4
P a u la R . W orthington
Lessons from the Japanese Main Bank System
f r Financial System Reform i Poland
o
n
WP-93-6
Ta keo H o sh i, A n il K a sh ya p , a n d G a ry Lovem an
Credit Conditions and the Cyclical Behavior of Inventories
WP-93-7
A n il K . K a sh ya p , O w en A . La m o n t a n d Je re m y C . Stein
Labor Productivity During the Great Depression
WP-93-10
M ich a e l D . B o rd o a n d C h a rle s L . E v a n s
Monetary Policy Shocks and Productivity Measures
i the G-7 Countries
n
WP-93-12
C h a rle s L E v a n s a n d Fe rn a n d o Sa n to s
Consumer Confidence and Economic Fluctuations
WP-93-13
Jo h n G . M a tsu sa ka a n d A rg ia M . Sb o rd o n e
5
Working paper s r e continued
eis
Vector Autoregressions and Cointegration
WP-93-14
M a rk W. W atson
Testing fo Cointegration When Some of the
r
Cointegrating Vectors Are Known
WP-93-15
M ic h a e l T . K . H o rva th a n d M a rk W. W atson
Technical Change, Diffusion, and Productivity
WP-93-16
Je ffre y R . C am p b ell
Economic Activity and the Short-Term Credit Markets:
An Analysis of Prices and Quantities
WP-93-17
B en ja m in M . F rie d m a n a n d K enn eth N . K u ttn e r
Cyclical Productivity i a Model ofLabor Hoarding
n
WP-93-20
A rg ia M . Sb o rd o n e
The Effects ofMonetary Policy Shocks: Evidence from the Flow of Funds
WP-94-2
L a w re n ce J . C h ristia n o , M a rtin Eich en b a u m a n d C h a rle s E v a n s
Algorithms for Solving Dynamic Models with Occasionally Binding Constraints
WP-94-6
L a w re n ce J . C h ristia n o a n d Jo n a s D M . F is h e r
I e t f c t o and the Effects of Monetary Policy Shocks
dniiain
WP-94-7
L a w re n ce J . C h ristia n o , M a rtin E ich en b a u m an d C h a rle s L E v a n s
Small Sample Bias i G M M Estimation of Covariance Structures
n
WP-94-8
Jo se p h G . A lto n ji a n d L e w is M . S e g a l
Interpreting the Procyclical Productivity of Manufacturing S c o s
etr:
External Effects ofLabor Hoarding?
WP-94-9
A rg ia M . Sb o rd o n e
Evidence on Str c u a I s a i i y i Macroeconomic Time Series Relations
u t r l ntblt n
WP-94-13
Ja m e s H . S to c k a n d M a rk W. W atson
The Post-War U.S. P i l p Curve: A Revisionist Econometric History
hlis
WP-94-14
R o b e rt G . K in g a n d M a rk W. W atson
The Post-War U.S. P i l p Curve: A Comment
hlis
WP-94-15
C h a rle s L E v a n s
6
Working paper s r e continued
eis
I e t f c t o of Inflation-Unemployment
dniiain
WP-94-16
B en n ett T . M cC a llu m
The Post-War U.S. P i l p Curve: A Revisionist Econometric History
hlis
Response t Evans and McCallum
o
WP-94-17
R o b e rt G . K in g a n d M a rk W. W atson
Estimating Deterministic Trends i the
n
Presence of S r a l Correlated Errors
eily
WP-94-19
E u g en e C a n je ls a n d M a rk W. W atson
Solving Nonlinear Rational Expectations
Models by Parameterized Expectations:
Convergence t Stationary Solutions
o
WP-94-20
A lb e rt M a rc e t a n d D a v id A . M a rsh a ll
The Effect of Costly Consumption
Adjustment on Asset Price V l t l t
oaiiy
WP-94-21
D a v id A . M a rsh a ll a n d N ayan G . P a rekh
The Implications ofFirst-Order Risk
Aversion fo Asset Market Risk Premiums
r
WP-94-22
G e e rt B e k a e rt , R o b e rt J . H o d ric k a n d D a v id A . M a rsh a ll
Asset Return V l t l t with Extremely Small Costs
oaiiy
ofConsumption Adjustment
WP-94-23
D a v id A . M a rsh a ll
Indicator Properties of the Paper-Bill Spread:
Lessons From Recent Experience
WP-94-24
B en ja m in M . Frie d m a n a n d K enn eth N . K u ttn e r
Overtime, Effort and the Propagation
of Business Cycle Shocks
WP-94-25
G e o rg e J . H a ll
Monetary p l c e i the e
oiis n
arly 1990s~reflections
of the early 1930s
WP-94-26
R o b e rt D . L a u re n t
7
Working papers r e continued
eis
The Returns from Classroom Training forDisplaced Workers
WP-94-27
L o u is S . Ja co b so n , R o b e rt J . L a L o n d e a n d D a n ie l G . S u lliv a n
I the Banking and Payments System Fragile?
s
WP-94-28
G e o rg e J . B en sto n a n d G e o rg e G . K aufm an
Small Sample Properties of G M M fo Business Cycle Analysis
r
WP-95-3
L a w re n ce J . C h ristia n o a n d W outer den H aan
The Fed Funds Futures Rate as a Predictor of Federal Reserve Policy
WP-95-4
J o e l T . K ru e g e r a n d K en n eth N . K u ttn e r
Capital U i i a i n and Returns t Scale
tlzto
o
WP-95-5
C ra ig B u rn sid e , M a rtin E ich en b a u m a n d S e rg io R e b e lo
8
@FedFRASER