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Interpreting the Procyclical Productivity
of Manufacturing Sectors: External
Effects or Labor Hoarding?
Argia M. Sbordone

J

Working Papers Series
Macroeconomic Issues
Research Department
Federal Reserve Bank of Chicago
June 1994 (W P-94-9)

FEDERAL RESERVE BANK
OF CHICAGO

I n t e r p r e t i n g t h e P r o c y c l i c a l P r o d u c t i v i t y o f M a n u f a c t u r i n g S e c to r s :
E x t e r n a l E f f e c ts o r L a b o r H o a r d i n g ?
A r g ia M . S b o r d o n e *
Federal Reserve Bank of Chicago
230 S. La Salle Street
Chicago, II 60604-1413
internet: asbordone@frbchi.org
This draft: June 1994

A bstract
This paper investigates whether procyclical productivity results from cyclical vari­
ations in the rate of utilization of labor or from technological externalities. On the
ground that externalities should tie sectoral productivity to the level of aggregate ac­
tivity, empirical evidence is presented to distinguish the two hypotheses. The analysis
conducted on two-digit U.S. manufacturing industries shows that sectoral productivity
is more likely a function of the rate of change of aggregate activity. This result is con­
sistent with the interpretation that the cyclical behavior of productivity is driven by
cyclical variations in the rate of utilization of labor, which responds to expected future
industry conditions. The role of aggregate variables in production-function regressions
is therefore that of forecasting future industry conditions.*I

* T h is p ap er is a r e v ise d v e r sio n o f c h a p ters 2 a n d 4 o f m y P h .D . d is se r ta tio n a t th e U n iv e r sity o f C h ica g o .
I th a n k J o h n H. C o c h r a n e , L ars P . H a n sen , R o b e r t E . L u ca s, J u lio R o te m b e r g , a n d th e p a r tic ip a n ts at
w o rk sh o p s a t th e U n iv e r sity o f C h ic a g o , th e 1991 m e e tin g o f th e S E D C , a n d th e 1992 A E A m e e tin g for th eir
c o m m e n ts. M y sp e c ia l th a n k s g o to M ik e W o o d fo r d for h is c o n sta n t a d v ic e an d su p p o r t.




1. I n tr o d u c tio n
The procyclical movement of both average labor productivity and total factor productivity
is a well known feature of aggregate fluctuations. That is, hours and employment vary
proportionally less than output over the cycle.1 Fig.l illustrates these phenomena for U.S.
manufacturing. At the aggregate level the procyclical productivity of labor is better known
as “Okun’s Law”, according to which a 1% reduction in unemployment means a slightly
less than 3% increase in GNP (Okun (1962)). These empirical facts are puzzling because
they seem to contradict the neoclassical assumption of diminishing returns to factors of
production.
Indeed, some argue that procyclical productivity indicates the existence of increasing
returns to scale in production. These can be internal increasing returns, which require the
existence of firms with market power, as in the recent work of Robert Hall (1988, 1991),
or external increasing returns as, for example, in the business cycle model of Murphy et al.
(1989) or of Baxter and King (1991).
Another, older, explanation is “labor hoarding” (Solow 1964). If firms face adjustment
costs in hiring and firing workers, they tend to respond to short run fluctuations in production
by adjusting the rate of utilization of the labor force, as opposed to the labor force itself. As
a result, a relatively stable labor input may be observed despite large oscillations in output,
while the “effort” that workers supply varies over the cycle.
These explanations are not observationally equivalent. An explanation in terms of in­
ternal increasing returns implies that a simple production function relation between output
and hours in each sector is correctly specified - the problem with the standard measure of
growth in total factor productivity (the Solow residuals) is simply its use of the labor share
as a measure of the elasticity of output with respect to labor input. On the other hand,
in the case of either externalities or labor hoarding, there is an omitted variable problem
with any such production function. When there are external increasing returns the rela­
tion between output and inputs in a sector is affected by activity in other sectors; in the
labor hoarding case, the omitted variable is the variation in the rate of utilization of labor.
^^Most e v id e n c e o n th is p h e n o m e n o n co m es fr o m th e U .S . m a n u fa c tu r in g in d u str y . For an o v e r v ie w , see
B ern an k e an d P o w e ll (1 9 8 6 ). A m o n g th e ea rliest p a p e r s d e scrib in g th is p h e n o m e n o n are H u ltg r e e n (1 9 6 0 )
an d K u h (1 9 6 5 ). S ee a lso S im s (1 9 7 4 ).




1

Econometrically, this means that additional variables may be found to enter significantly
in production-function type regressions - direct or indirect measures of the activity that
produces the external effect, or any variable that may serve as a proxy for the unobserved
variation in labor utilization.
Recent papers by Caballero and Lyons (1990, 1992) and Bartelsman et al. (1991) have
shown that including aggregate output in sectoral production-function regressions results in
a significant coefficient on aggregate output in many sectors, and a substantial reduction in
the estimated elasticity of the sector’s output with respect to the sector’s own inputs. They
interpret the difference between the point estimates of the returns to scale parameter at the
two-digit and at the aggregate manufacturing level as a measure of an external effect.
However, it is also possible to interpret the findings of Caballero and Lyons as evidence
of “labor hoarding”. Bernanke and Parkinson (1991) suggest a number of reasons why, when
there is labor hoarding, cyclical indicators may be correlated with unobserved variations in
labor utilization. For example, an industry’s cost of adjustment may depend on the aggre­
gate labor market conditions; or fluctuations in industry demand due to cyclical conditions
may have different persistence properties than those due to idiosyncratic sectoral shocks, so
that firms will respond to shocks with different combinations of employment and utilization
adjustments.
In this paper I seek to discriminate between these two explanations for the procyclical
behavior of productivity generally, and for the Caballero-Lyons regressions in particular. It is
possible to do this by using the alternative theories’ different predictions about the dynamic
effects of aggregate variables in Caballero-Lyons-style production-function regressions.2
In a common interpretations of the externality hypothesis, each sector i’s production
function is assumed to be of the form

Qit —

where

Qu

(1.1)

LitQ itQ At)

indicates sector z’s output at date

t , Q ai

is the aggregate output,

K xt

is sector

i ’s capital stock, L,t is sector i ’s labor input, and 0 ,t represents an exogenous sectoral
2T o e x p lo re th e p o s s ib ilit y th a t th e ir r e su lts are d u e t o u n m e a su r e d v a r ia tio n s in fa c to r u tiliz a tio n ,
C a b a lle r o -L y o n s (1 9 9 2 ) in c lu d e d ir e c t p r o x ie s for effort in th e p r o d u c tio n -fu n c tio n r e g r e ssio n s. A lto u g h th e y
do n o t co n sid er a n y d y n a m ic im p lic a tio n o f th e tw o th e o r ie s, a s I d o h ere, th e y n o n e th e le ss fin d th a t th eir
m ea su re o f effort v a r ia tio n s, b o th r e la te d a n d u n r e la te d t o m e a su r e s o f o w n a c tiv ity , ca n e x p la in a b o u t h a lf
o f w h a t th e y ca ll th e m ea su r e d e x te r n a l effe c t.




2

productivity factor. If £,• > 0, aggregate output affects sectoral productivity in a manner
analogous to the exogenous productivity shock 0,<.3
Now suppose that fluctuations in aggregate output are persistent. It follows from the
specification in (1.1) that the induced effect on sector i’s productivity should be equally
persistent. In particular, suppose that an innovation in aggregate output at date
a

perm an en t

increase in aggregate output, of

Then (1.1) implies that there should be a
that it should be

k

k

t

implies

times the initial innovation (for some

perm an en t

increase in sector

Vs

k > 0).

productivity, and

times as large as the initial increase. The “thick market” effects, if present

and economy-wide, should operate equally in the long run as in the short run.
A labor hoarding explanation has quite a different implication in this regard. If pro­
cyclical productivity is due to labor hoarding, then following a shock that affects measured
productivity due to incomplete adjustment of the labor input, one should eventually observe
measured productivity return to normal. For even if the shock p e r m a n e n tly increases sectoral
output, the size of the workforce should eventually fully adjust to the new level of produc­
tion, so that the rate of labor utilization (or effort) can return to normal. Hence, even if an
innovation in aggregate output at date t implies a permanent increase in both aggregate and
sectoral output, the resulting effect on sector

Vs

productivity should be purely

tr a n s ito r y .

This suggests a simple empirical test. I measure the dynamic response of sectoral pro­
ductivity to innovations in aggregate output, for individual two-digit U.S. manufacturing
industries. I also measure the dynamic response of aggregate output to such an innovation,
and show that a large part of the initial increase in output is permanent. I then compare the
lo n g -ru n

response of sectoral productivity to the initial (contemporaneous) response. If the

labor hoarding explanation is correct, and true external effects are absent, there should be
zero long-run effects on sectoral productivity. If a direct, external effect on the production
function, as indicated in (1.1), is present, and there are no unmeasured variations in labor
utilization, there should be a

p o s itiv e

long-run effect, and it should be

response (multiplied by the fraction of the initial increase in
there is a positive long-run effect, but

le ss

Q ^t

a s large a s

the initial

that is permanent). If

than proportional to the extent that the increase

in aggregate output is permanent, some combination of the two types of effects would be
3B a x te r an d K in g (1 9 9 1 ) a n d C o o p e r an d H a ltiw a n g e r (1 9 9 3 ) are e x a m p le s o f a u th o r s w h o a ssu m e
p r o d u ctio n r e la tio n s o f th is form , an d c ite th e w ork o f C a b a llero a n d L y o n s a s e m p ir ic a l m o tiv a tio n for su ch
a sp e c ific a tio n . A co m m o n in te r p r e ta tio n o f su ch e x te r n a litie s is th a t th e y are d u e to “th ic k m a r k e t” effects;
red u ced m a rk e tin g c o sts w h en o th e r s sell a lo t m a y a llo w reso u rces to b e sh ifte d in to p r o d u c tio n .




3

needed to explain the contemporaneous response of sectoral productivity.
This approach to testing the labor hoarding hypothesis is, of course, somewhat indirect,
since it makes use only of that model’s prediction that variations in measured productiv­
ity (other than those due to true sectoral productivity shocks) should be purely transitory.
The model, however, makes additional strong predictions about the way in which aggregate
variables should be related to measured sectoral productivity. Specifically, it says that ag­
gregate variables should enter a sectoral production-function regression only insofar as they
represent proxies for the expected future path of sectoral activity. Hence I also develop here
the more detailed restrictions upon the form of Caballero-Lyons style production-function
regressions implied by an explicit model of labor hoarding presented in Sbordone (1993).
These restrictions are also tested.
Section 2 discusses generally the interpretation of production-function regressions, and
the econometric framework that I use. Section 3 present the test described above, based
on estimation of the long-run response of total factor productivity. Section 4 then develops
and tests the more specific restrictions implied by the model of Sbordone (1993). Section 5
concludes.

2. T h e R e la t io n b e t w e e n A g g r e g a te A c t iv it y a n d S e c to r a l P r o ­
d u c t iv it y
A standard neoclassical production function for a sector

i

of the economy can be written in

log differences as
A qi =

e’q K A k i

+

t q L{ A l i

where lowercase letters denote natural logs, and

+ A #j)

t q L, t q K

(2-1)

denote the elasticity of output with

respect to labor and capital respectively. In the following, I will denote true productivity
growth, A0,-, by £,• .
A traditional measure of cyclical variations in total factor productivity is the Solow
residual, computed as
SR{ = A qi

where

s lL

and

s'K

—s'LA l j —s'K A k i

(2-2)

are the share in total revenue of the factor rewards of labor and capital

respectively. Under the assumptions of price-taking behavior and constant returns the elas­
ticity of output with respect to each factor input should equal the corresponding factor share,




4

and the Solow residual is exactly the technology shock

£i

scaled by the labor share. This

measure, as fig. 1 shows for the manufacturing industry, has a marked procyclical pattern.
Alternatively, one can measure cyclical variations in productivity by estimating eq.(2.1);
a coefficient on labor bigger than the labor share implies that the measured Solow residual
covaries with the labor input. An estimated elasticity bigger than 1 implies the stronger
result of a procyclical average labor productivity. Some of the literature focuses on the
latter phenomenon, which again contrasts with the theoretical prediction of countercyclical
average labor productivity from models with constant returns and a cycle not driven by
technology shocks.
When there are technological externalities, the production function is eq.(l.l) where

6,

is the elasticity of sector i productivity with respect to aggregate output. The equivalent to
eq.(2.1) is then
=

^QK^i

+ eQlA^' +

External economies in sector i imply that the parameter

(2-3)
S{

in eq.(2.3) is positive. If aggregate

output is positively correlated with the inputs of the sector, OLS estimates of the specifica­
tion (2.1) result in overestimating the output elasticities, making the measured productivity
procyclical.
As discussed in the introduction, however, if the correlation between aggregate variables
and the inputs is due to external effects, than we should also observe that the effect of ag­
gregate activity on sectoral productivity should last at least as long as the perturbation to
the level of aggregate activity. If the effect of the externality is purely contemporaneous, as
suggested by the “thick market” story, and as is assumed in the stated specification (1.1),
then sectoral productivity should be high for exactly as long as

Qa

is high.4 Alternatively,

one might suppose that the effects of an externality occur with a time lag, or persist after the
cause has disappeared (as would be expected in the case of knowledge spill-overs). In this
case, sectoral productivity should remain high even after

Qa

ceases to be high. Therefore,

when a shock to aggregate activity is persistent, we would expect long-run effects on sectoral
productivity. This consideration leads to a simple identifying restriction: when aggregate
variables have some degree of persistence but do not display persistent effects on the produc­
4 From th e a b o v e e q u a tio n , o n e can e a sily se e th a t to t a l fa c to r p r o d u c tiv ity , c o m p u te d as th e c u m u la te
o f th e S o lo w re sid u a ls, d e p e n d s o n th e c u m u la te o f th e c h a n g es in a g g r e g a te a c tiv ity . W h e n a c h a n g e h a s
la stin g effects o n a g g r e g a te a c tiv ity itse lf, th e n it h a s to h a v e lo n g la s tin g effe c ts o n se c to r a l p r o d u c tiv ity as
w ell.




5

tivity of a sector, then their interpretation as sources of externalities is unwarranted. More
generally, the perturbation to sectoral productivity should not decay back to trend any faster
than aggregate output return to its trend path (if it does). Of course, if the effects of the
externality cumulate, productivity might return to trend more

slo w ly .

I test this long run restriction on total factor productivity implied by the externality
hypothesis in two ways. First, I look at the distributed lags of aggregate output in a
production-function regression. If there are external effects, aggregate output should en­
ter the production function with a non-negative coefficient at all lags (including zero). If
the external effect is purely contemporaneous, all lags greater than zero will have a zero
coefficient; if, on the other hand, some of the external effects occur with a delay, lagged
aggregate output may enter with a positive coefficient as well. But no lags should enter with
negative coefficients, and

th e s u m o f th e c o e ffic ie n ts on all la g s

(zero and greater) should be

an appropriate measure of the cumulative external effect. In the following specification of
the production function, consistent with the presence of possibly dynamic externalities
A q a = J iA k it

D {( 1)=

Sij

+

P iA h t

+

j
^ 2 S { jA q A ,t- j
i -o

+

Cit

is the measure of the long run effect of any perturbation to aggregate output

that I consider.
Under the null of no externalities, the labor hoarding hypothesis predicts that Z?,(l)= 0.
If instead the short run effect of aggregate output is entirely due to externalities (there is no
labor hoarding) one should actually expect £>j(l)>
the coefficients

D i(Q )=

6,o. I therefore test first whether

are individually significantly different from zero and in which direction;

if the contemporaneous coefficient is positive, but the lagged coefficients are statistically
significant and negative, the long run effect would not be bigger than the short run effect, and
the pure externality hypothesis would be rejected. Then I test whether

D ,{ 1)

is significantly

different from zero. If it is, the pure labor hoarding hypothesis would be rejected.
Second, to consider more properly the effect of “innovations” in aggregate output, I fit a
VAR model to the vector of sectoral output, sectoral inputs, and aggregate industry output.
I then compute and compare the impulse response function of sectoral productivity and
aggregate output to aggregate output innovations.




6

3. E m p ir ic a l R e s u lt s
Tables 1-4 report results of estimates using annual data on U.S. manufacturing for the period
1947-1988. For output I use value-added data and for hours I use production workers’ hours.
(Details relating to data and sources are in the Data Appendix).5 In all the specifications
I decided to exclude capital from the regressions because of empirical problems with the
series - estimated coefficients on capital are significant in only a few cases and often have
the wrong sign. The exclusion, however, does not in general affect the results.6
Tables 1 and 2 first illustrate the phenomenon of procyclical productivity with which I
am concerned. Column 1 of table 1 shows the computed value (with standard deviation
in parenthesis) of the labor share for the manufacturing industry and the twenty two-digit
sectors, while columns 2 and 3 report the estimated coefficient of labor hours -respectively
of production worker hours and of total manhours - in a production-function regression.7
With the use of either hour series, the estimated coefficient is, in many sectors, significantly
above the computed labor share. Table 2 demonstrates the relevance of aggregate output in
sectoral production-function regressions. In many sectors - notably those for which table 1
shows evidence of procyclical productivity - the inclusion of aggregate manufacturing output
drives down the estimated coefficient on hours. When the coefficient on aggregate output
is constrained to be the same across sectors, I get a very precise point estimate, which is
significantly different from zero.8 The question that I wish to address is how to interpret
this contemporaneous effect of aggregate output.
Tables 3 and 4 present the first test proposed in the previous section. Table 3 shows
that two lagged values of aggregate output are significantly negative: The long run effect of
aggregate pertubations therefore does not exceed the impact effect. In fact, the inclusion of
lagged aggregate output in the sectoral regressions drives the total effect of aggregate output
5T h e u se o f in d u str ia l p r o d u c tio n d a ta for o u tp u t a n d to t a l m a n h o u r s for la b o r in p u t d o e s n o t ch a n g e
th e ch aracter o f th e r e su lts (c o m p le te ta b le s o f r e su lts are a v a ila b le fr o m th e a u th o r ). A lth o u g h d a ta on
in d u str ia l p r o d u c tio n are th e o n ly o u tp u t d a ta a v a ila b le a t h ig h er fre q u e n c ie s, th e ir c o n str u c tio n is, for m a n y
sec to r s, b a sed o n la b o r d a ta , w h ic h m a k e s th e m n o t su ita b le for u se in th e p resen t c o n te x t.
6W h ere c a p ita l is sig n ific a n t, th e co efficien t o f la b o r is o n ly m a r g in a lly a ffected (u p w a r d ).
7A ll th e e s tim a te s in th e ta b le s are o b ta in e d u sin g th e Z e lln e r ’s s e e m in g ly u n r e la te d reg ressio n (S U R )
p ro ced u re, in order to p u rg e p o te n tia l c o n te m p o r a n e o u s co r r e la tio n o f errors a cro ss e q u a tio n s.
8T h e c o n str a in t th a t all th e p a r a m e te r s are th e sa m e a cro ss se c to r s is te s te d th r o u g h th e lik e lih o o d ra tio
s t a tis tic (L R ) r e p o r te d a t th e b o tt o m o f th e ta b le . D e ta ils o f th e c o m p u ta tio n o f th is s t a tis tic are in a p p e n d ix
B.




7

on sectoral productivity to nearly zero (a contemporaneous effect of .19 is washed out by
the negatives .064 and .056 of the next two periods. The chi-square statistic reported at the
bottom of the table shows no rejection of the restriction that the coefficients

Sj

sum to 0).

In table 4 the same result is shown in regressions where the parameters are constrained
to be the same for all sectors (this restriction allows more precise point estimates because
it increases the information of the sample, and it is not rejected in the data). Table 4
allows a comparison with the cases - discussed before for the individual sectors - in which
the production function is estimated with no aggregate variable (row 1) or including only
its contemporaneous value (row 2). The first column reports a pure SUR estimate. The
first row - no aggregate output is included - shows an estimated coefficient on hours (.911)
which is higher than the average labor share of the sectors, which is about .79. This value is
significantly diminished when contemporaneous aggregate output is included. The coefficient
So

is positive and highly significant. Next row shows the effect of introducing lagged output.

Two lags are indeed significant and negative, leading to a sum of the distributed lags not
significantly different from zero. The total effect is negligible (this restriction is tested by
the chi-square statistic on the bottom row).
Several words of caution should accompany the regression results.
First, (without making more assumptions on the information structure) it is not clear
which should be the variable on the left hand side of the equation, i.e. there is no reason to
believe that the error terms are uncorrelated with any of the variables [see Sims (1974)].
Second, if firms make input decisions after having some knowledge of the shock, labor,
capital and output may all be contemporaneously correlated with the technology shock com­
ponent of the error term. The econometric approach to this problem is to use instrumental
variables that are uncorrelated with technology movements. Demand-type instruments have
been advocated for this purpose.9 However, beyond the exogeneity property, one has to care
about the relevance of the instruments: the finite sample behavior of IV estimators is in
fact strongly affected by the correlation of the instruments with the variables instrumented.
When this correlation is very low, and the number of observations is small, the asymptotic
distribution is not a good approximation to the true distribution and in fact the central ten­
dency of the IV estimator is biased away from the true value [see Nelson and Startz (1990a)
and (1990b)].
9S ee H all (1 9 8 8 ), B e r n a n k e a n d P a r k in so n (1 9 9 1 ), C a b a lle r o a n d L y o n s (1 9 9 2 ).




8

The issue is complicated by the inclusion of aggregate output among the regressors. For
aggregate output to be orthogonal to the error term in production function regressions we
require the additional assumption that technology shocks are uncorrelated across sectors,
so that a given sector’s technology shock has little correlation with aggregate variables.
Although this is a reasonable property of true technology shocks, and is often assumed in
econometric estimation of sectoral production functions, it is not uncontroversial. For most of
the sectors in manufacturing, however, there is some empirical evidence of the predominance
of idiosyncratic shocks.10
Although there is some general consensus as to the poor performance of the demand
variable instruments that have been proposed in the literature to overcome the potential
endogeneity of regressors,11 in the second and third columns of table 4 I modify the estimates
of column 1 by including two sets of instrumental variables, as used by Hall (1988).12 As
argued above, since these variables should be uncorrelated with the technology shock, they
should correct potential upward bias in the estimate of the labor coefficient arising from
correlation between labor input and the technology component of the error term.

The

results are very similar to those of column 1, especially with the second set of instruments,
which has a better first stage i?2.13
The table clearly shows that the positive contemporaneous effect of aggregate output
‘reverts’ quite quickly to zero.14 Overall, the regressions’ results point to a purely transitory
effect of aggregate perturbations on sectoral productivity. However, to contradict the inter­
pretation of

S0

as an externality coefficient, one would like to assess the persistent nature of

aggregate perturbations, together with their transitory effect on sectoral productivity.
10S ee L on g an d P lo sse r (1 9 8 7 ). T o ta k e in to a c c o u n t a p o te n tia l s im u lta n e ity b ia s a risin g fr o m a co m m o n
a g g reg a te c o m p o n e n t in th e se c to r a l p r o d u c tiv ity sh o c k s, I a lso e stim a te d th e s y s te m u sin g la b o r in p u t o f
th e w h o le m a n u fa c tu r in g as th e a g g r e g a te v a ria b le (a s su g g e s te d in C a b a lle r o -L y o n s (1 9 9 2 )). N o q u a lita tiv e
ch a n g e in resu lts w a s o b ta in e d .
n S h e a (1 9 9 3 ) su g g e s ts to c o n str u c t v a lid d e m a n d -sh ift in s tr u m e n ts b y lo o k in g a t th e in p u t-o u tp u t lin k a g es
o f in d u str ie s, b u t h e fin d s few in s tr u m e n ts o n ly for 4 o f th e 2 -d ig it se c to r s.
12T h e y in c lu d e th e ra te o f g r o w th o f m ilita r y e x p e n d itu r e an d o f th e w o rld o il p rice, a n d a d u m m y
rep resen tin g th e p o litic a l p a r ty o f th e P r e sid e n t.
13I ta k e th is resu lt a lso as in d ir e c t e v id e n c e a g a in st a co m m o n te c h n o lo g y sh o c k e x p la n a tio n for th e
co rrela tio n o f se c to r a l p r o d u c tiv ity v a r ia tio n s w ith a g g r e g a te a c tiv ity .
14I o b ta in e d sim ila r r e su lts w ith n o n se a so n a lly a d ju ste d q u a rterly d a ta (in c lu d in g se a s o n a l d u m m ie s in th e
reg ressio n s, an d w ith a v a r ie ty o f d e m a n d -ty p e in s tr u m e n ts). I fo u n d v e r y w ea k e v id e n c e o f p e r siste n t effects
o f a g g reg a te p r o d u c tio n on th e tw o -d ig it se c to r s. C u rren t a g g r e g a te o u tp u t h a s a sig n ific a n t c o efficien t, b u t
th e c u m u la tiv e effect d isa p p e a r s w ith in s ix to e ig h t q u a rters.




9

My second test is therefore based on the moving average representation of the vector
time series composed of sectoral output, sectoral inputs, and aggregate output.
Let

=

wt

[qAt kit 9it ht]

he a first difference stationary vector with moving average

representation
(1 $(L) =
= fl for

4*0 — !■> and
t

=

s

L )w t

=

fi + $ ( L ) v t

is a vector of innovations, with E

(vt)

= 0 and E(

)

v t v's

and 0 otherwise. The multivariate Beveridge-Nelson decomposition is
(1 -

where <h* = —

4>k

L )w t = f i +

and 4>(1) =

[$(1) + (1 -

J2h=o 4k-

L ) $ * ( L ) \u t

The matrix 3>(1) controls the “persistence”

of the series: partitioning <1>(1) according to the size of the vector, the diagonal elements
measure the “size” of the random walk component in each series, while $ nj-(l) measure
the persistence of an innovation in

Wj

to

wn

. The hypothesis that an innovation to

is

“persistent” but does not permanently affect total factor productivity in sector i implies that
4>n (l) ^ 0 and $ 31(1) —s^ $ 4i(l) —s k $ 2i(l) = 0> where $ ni (n=2,3,4) are respectively the
long-run responses of capital, output, and labor of sector i to an innovation in aggregate
output. Note that total factor productivity (TFP) is defined, for a sector i, as
s*K kit,

qa

—s 'jla

—

so it is just the cumulate of productivity growth as measured by the Solow residual.

To test this long-run restriction, I recover the matrix

$ (L )

of the moving average repre­

sentation from the impulse response function to a unit innovation in aggregate production.
Figs. 2.1 to 2.6 report the results of this analysis performed on a number of two-digit sectors
of U.S. manufacturing, selected as the ones that display more clearly a significant short run
effect of aggregate output.
The impulse responses are generated by fitting a first order autoregressive model to the
vector

w t.

I impose the cointegrating restriction that the sectoral output/capital ratio is a

stationary variable15 and, assuming that the sector is ‘small’ with respect to the aggregate,
I rule out feedbacks from the sector to the aggregate by constraining to zero the coefficients
on lagged values of the sectoral variables in the equation for aggregate output. The errors
are orthogonalized by a lower triangularization of the residual covariance matrix. Part a)
of each figure reports the response of all the variables, while part b) isolates the response
15T h is r e str ic tio n is t e s te d b y a tw o -s te p p ro ced u re u sin g th e sta n d a r d A D F t e s t, a n d la r g e ly p a ss e s. T h e
im p u lse resp o n se fu n c tio n s g e n e r a te d b y a n u n r e str ic te d V A R are, h o w ev er, q u a lita tiv e ly v e r y sim ila r.




10

of aggregate output and sectoral total factor productivity, each with a two standard error
band generated by bootstrapping with 200 replications. In the typical pattern, hours in the
sector display a positive contemporaneous response to aggregate activity, but often a negative
response after the first period, which leads the level to decay. Capital responds instead with a
slowly increasing pattern to reach a higher long run level. Total factor productivity therefore
steadily declines to its original level, after a first period jump.
The key results of the graphs can be summarized as follows: First, aggregate output
does indeed have significant degree of persistence - an innovation affects its level far into the
future. Second, aggregate output innovations do affect sectoral variables, but the impact on
sectors’ productivity is short lived.
The fact that total factor productivity responds to aggregate innovations rules out purely
internal increasing returns. The fact that it declines to zero after a permanent shock to ag­
gregate output argues against external increasing returns. Moreover, it also offers some
evidence against a common technology shock interpretation of the effect of aggregate out­
put. The vector autoregression evidence rules out a spurious effect of aggregate output on
individual sectors’ productivity due to the correlation of aggregate and sectoral technology
shocks. Altogether, these facts seem more consistent with the explanation of the procyclical
productivity ‘puzzle’ based on labor hoarding. The next section will motivate the labor
hoarding hypothesis and test more direct predictions of a specific model of labor hoarding.

4. A M o r e S tr u c tu r e d P r o d u c tio n -F u n c tio n R e g r e s s io n
Labor hoarding implies that a proper specification of the production function involves a
variable rate of utilization of labor input, as well as the number of hours worked. The
production technology is therefore modified in
Q u — F ( K it, eitH itQ it)

where

Hu

(4-1)

is reported hours and elt is the rate of utilization of labor (labor effort). Variations

in utilization might be due to variations in work effort, of the kind reported by Schor (1987)
and Shea (1991); to variations in the number of workers assigned to non-production tasks
such as maintenance and training, as in the model of Bean (1989); or to variations in the
number of workers who are actually redundant, as reported by Fay and Medoff (1985). If
the unmeasured rate of utilization does not co-vary perfectly with the measured labor input




11

(worker-hours), other variables, such as aggregate output, may be correlated with it, serving
therefore as a proxy for it in the regression.
One argument for labor hoarding is the existence of hiring and firing costs, that make
labor somewhat immobile. Firms will then tend to ‘hoard’ workers (i.e., under-utilize them in
one of the senses listed above) when production is temporarily low. As a result, expectations
about how future sectoral output and employment will compare to present levels are an
important determinant of labor utilization. Aggregate variables that help to forecast future
conditions in the sector accordingly could enter a production-function equation like the one
above. In particular, aggregate output should enter with a positive coefficient if a
growth rate of aggregate output forecasts

lo w e r

h ig h er

future growth of sectoral employment, since

in this case firms subject to costs of adjusting employment would prefer a higher present
level of utilization of a smaller number of workers.
In contrast with the theory of technological externalities, labor hoarding need not imply
non-negative coefficients on all lags of aggregate output. In fact, “labor hoarding” models
typically imply that the sum of the coefficients on all lags should equal zero. The reason
is that labor utilization is a stationary variable - it returns to its ‘normal’ level once labor
inputs fully adjust to their desired level. Hence if fluctuations in aggregate output contain
a permanent component, the sum of all the coefficients on lagged output would have to be
zero, in order for a permanent increase in aggregate output to have no permanent effect on
labor utilization (the omitted variable in the production function). In other words, while
externalities tie total factor productivity of a sector to the level of aggregate output, labor
hoarding makes measured total factor productivity depend upon the changes in aggregate
output. Once output has stabilized at a new level, no effect persists on sectoral productivity.
In this section I briefly describe a model of labor hoarding that I developed elsewhere
(Sbordone (1993)). The model provides a structural framework for the two tests conducted
above. Although the validity of the interpretations proposed does not depend upon this
special model, it is interesting to see how the more detailed prediction of such model fit the
data.
The model describes a sector i of the economy, where a representative firm chooses inputs
to use in production, while facing each period a stochastic shock to its technology. Labor
is treated as a quasi-fixed factor, which is costly to adjust in response to every change
that occurs in the environment. The production function depends on reported hours and




12

unmeasured effort, as in eq. (4.1), and total labor costs are given by

(for ease of notation the subscript i is omitted).

Wt

denotes a base wage level, g ( ) indicates

the proportional increase in the cost of hours that are more fully utilized, and A( ) represents
the increase in costs associated with rapid adjustment of the labor force.
positive and strictly convex, and

H

g(

A( ) is a non-negative, convex function of

) is assumed

H.

A restricted cost function is obtained by solving effort out of the production function
and substituting this expression into the cost function. Then the problem of the firm is to
choose the sequence

{H t }

to minimize the expected sum of discounted costs

oo
E t J 2 R j { C ( H t+ j,H t+ j- U K t+J, Qt+j j

Wt+i)}

j=o

where

R

is a real discount factor and

Et

denotes expectations conditional on knowledge of

all the variables up to time t. The optimal decision rule can be characterized through a loglinear approximation of the first order condition of this minimization problem around the
sector steady state growth path. This procedure [the details are in Sbordone (1993)] leads to
a production-function equation which is suitable for empirical analysis. In first differences,
this equation is
A qt

= 7r0A h t

- 7t2A/^_ i -

7r3( E t A h t+ i - E t - i A h t )

+ 7t4A kt +

7rsA w t

where lowercase letters denote natural logarithms, and the coefficients

n

+

7r6e t

(4.2)

depend upon the

parameters of the cost function and of the production function. There are two things to
note in this equation: It includes a term in the difference between expected future growth of
hours and current hours, and its coefficient is negative. This term enters the equation because
the production function is specified in effective hours, and therefore it includes a term for
effort16. Equation (4.2) could be in fact interpreted as a log linearization of the production
function (4.1) into which has been substituted a solution for the unobservable effort in terms
of past observable hours and expected future growth of hours; this interpretation makes it
clear how the inclusion of effort as an additional unmeasured input results in the dynamics
of the production-function regression. It also explains the negative sign of the coefficient
16T h e fa c t th a t o n ly o n e le a d a n d o n e la g o f h o u rs are in c lu d e d d e p e n d s o n th e sp e c ific a tio n o f th e
a d ju s tm e n t co st as a fu n c tio n o n ly o f




13

7T3, because current effort is negatively related to the expected future growth of hours. The
intuition is that when output and hours are expected to grow, firms start to increase labor
today (the marginal cost of increasing labor is lower today, taking into account the reduction
of future adjustment costs), so decreasing effort today. The slow response of labor to cyclical
variations, due to costs of adjustment, generates a counterbalancing response of effort, which
is the variable factor.
In this framework, aggregate variables may be correlated with the productivity of indi­
vidual sectors for a reason that does not depend at all on external effects. This is because
aggregate variables help to forecast future labor growth. Under this hypothesis, a solution
for expected future labor growth involves lags of the rate of growth of aggregate output, as
well as lagged values of the other inputs. The number of lags will depend on the specification
of the process for the forcing variables. In the simplest case in which this process follows a
first order autoregression, the solution for hours will involve only one lag of aggregate output
qA

:
E t A h t+ i = c o n s t

+

p i ( k t - i - h t- X -

0t_i) +

fi2{k t - q t)+ U s A k t

+ ^4A qA t

+ f t 5e t

Substituting this term in eq.(4.2) gives a production function regression where output de­
pends on current and past values of the inputs and also on current and past values of the
aggregate variable:
A q t — i?iA h t

The coefficients

k t -(-

d

' d ^ A q A t ~ A q A t - \ ) + ^6(1 + p E )e%

(4.3)

are non linear combinations of the structural parameters of the model

and of the forecasting equation for hours. Equation (4.3) shows how the model constrains
the pattern of coefficients of a production-function regression. It also shows how the model
can rationalize the empirical results that find aggregate variables entering sectoral produc­
tion functions significantly. Aggregate variables are correlated with the expected future
labor growth of a sector because they are good forecasting variables. Therefore they en­
ter a production-function regression, and they do so with a specific pattern of coefficients:
coefficients on consecutive lags are the same but have opposite sign, so that the effect in
each period vanishes in the next. This is the implication we already test in the regression
analysis context, and lead us to reject the interpretation of aggregate variables as a measure
of external increasing returns.




14

However, in this more structured context, it should also be the case that aggregate vari­
ables do not simply proxy the information contained in the past values of sectoral inputs.
They should add explanatory power once the own-input dynamics is accounted for. Fur­
thermore, assuming constant returns to scale, the coefficients on current and lagged inputs
should sum to 1.
Table 5 presents estimates of eq.(4.3) and a test of the two implied restrictions, with
pooled data for the two-digit sectors of the manufacturing.

q_\t

is again value added for

the whole manufacturing. The first column is a pure SURE estimation, while columns two
and three contain instrumental variable estimates. Almost all the coefficients are significant
at the standard level, particularly if we restrict attention to the IV estimation. Two lags
of aggregate value added enter significantly the regression. [This implies that to fit best
the data either the model should include more lags in the adjustment cost function, or the
forecasting equation for hours should include more lags of the aggregate value added.]
The coefficients on lagged own inputs are significant and with the expected sign. The chisquare statistics reported in the bottom rows test the two restrictions indicated above. The
restriction that the inputs’ coefficients sum to one passes with the first set of instruments,
but is marginally rejected with the second set of instruments, and strongly rejected in the
uninstrumented estimate.

The restriction that the sum of the coefficients on aggregate

value added is not significantly different from zero is not rejected in any type of estimation.
Together, the two restrictions marginally pass in the instrumented estimation (chi-square
statistic on the bottom row).
To summarize, the key element of the model that drives the regression results is that
output growth depends on how future hours growth compares to present growth through the
parameter tt3; aggregate output is used to forecast such future variations. The parameter
7T3, in the model, depends specifically upon the curvature of the adjustment cost function.
In the absence of adjustment costs, this coefficient is equal to zero, eliminating the dynamics
in the production function and its dependence on aggregate variables. The intuition for this
result is that the dynamic implications of the model come exclusively from the movement of
effort, and without adjustment costs there is no cyclical variation of effort.
Finally, the labor hoarding model implies that variations of effort are purely transitory,
as argued earlier. Therefore any shock to aggregate variables, no m atter how persistent,
should affect sectors’ productivity only transitorily. The empirical analysis agrees with this




15

prediction of the model as well.

5. C o n c lu sio n
Aggregate variables have a persistent component yet do not show a persistent effect on the
productivity of individual sectors. I argue in this paper that cyclical variations in labor
utilization are able to generate exactly the type of response we saw in the data. I show
that a simple model of labor hoarding generated by adjustment costs, together with the
hypothesis that aggregate conditions are forecasting variables for the activity of individual
sectors, implies a specification of the production function regression that includes distributed
lags of aggregate output, whose coefficients sum to zero. This prediction is confirmed by the
empirical evidence. Estimation of a sectoral production technology gives a positive, impact
effect of aggregate output on sectoral productivity, but significant lagged negative effects, so
that the long run response of productivity is lower than the short run one and, moreover,
it is not statistically significant. These empirical results tend to confirm the conclusions
of Rotemberg and Summers (1990) and Burnside, Eichenbaum and Rebelo (1993), who although in different contexts and under different assumptions - also assign a role to labor
hoarding in generating procyclical factor productivity.
These results are not easily reconciled with a view that the relation between aggregate
activity and sectoral productivity is due to a direct external effect upon the sectoral produc­
tion technology, as many authors have recently proposed. Of course the range of possible
hypotheses involving “external effects” is very large, and it is impossible to address all of
them. But at least the simplest version of such a model can be clearly rejected, while a labor
hoarding model appears to offer a simple alternative that furthermore makes a number of
quite specific predictions which appear to be reasonably consistent with the evidence.

A . D a ta D e s c r ip tio n a n d S o u r c e s
Data on industrial value added are from the NIPA as published in the Survey of Current
Business (July issue); the capital stock (K) is net constant dollar fixed private capital, as
published in the Survey of Current Business (August issue).
Data are for the following two-digit manufacturing industries (the SIC code is in square
brackets): Food [20], Tobacco [21], Textile [22], Apparel [23], Paper [26], Printing and Pub­
lishing [27], Chemical [28], Petroleum [29], Rubber and Plastic [30], Leather [31], Lumber
[24], Furniture and Fixtures [25], Clay, Glass and Stone [32], Primary Metals [33], Fabri­
cated Metals [34], Nonelectrical Machinery [35], Electrical Machinery [36], Transportation




16

Equipment [37], Instruments [38], and Miscellaneous Manufactures [39].
Data on employment and average weekly hours of production workers are from “Em­
ployment, Hours and Earnings, United States 1909-1984”, vol. I, by U.S. Dept, of Labor,
Bureau of Labor Statistics, March 1985; update to 1988 is from Supplement to Employment
and Earnings, August 1989. The product of the two series makes total hours of produc­
tion workers. Total manhours by full-time and part-time workers, total labor compensation
and the value added deflator are from NIP A, as published in the Survey of Current Busi­
ness (July issue). To construct sectoral data for total manhours, I follow the procedure in
Shapiro (1987) and distribute one digit totals to two digit industries according to year by
year shares in total employment. The labor share is computed as the average ratio of total
labor compensation to nominal value added.

B . L R s t a t is t ic o f t a b le s 1-4
Defining L,N,p,T-q — det(J2r ) / d c t ( ^ u), where the subcripts r and u stands respectively for
restricted and unrestricted, the statistic L R = K log I/jv,P,r - 9 under the null is asymptot­
ically distributed as a XpN- The constant K is equal to T — q —0.5(AT —p + 1), where
T is the number of observations, q is the number of parameters estimated, N the number
of equations and p the number of parameters restricted ( p N is therefore the total num­
ber of restrictions). Letting /iviPj ’_g(a)be the a-significance point for Ljv,P)T -9, and defining
C N ,p,T -q+ \{o i) = K lN ,p ,T -q ((x )/x lN (a )> the test is conducted by computing the L R statistic
defined above and rejecting the null at the level a if L R > CisrtPtT - q+ i(o i) XP7v(°0- Since
CN,P,T -q+ i(o) > 1, the restrictions cannot be rejected if the statistic L R < xPjv(Q:)- The
proportional error in approximating the statistic by a XpN is equal to (CV)P)t - 9+i —1). This
error increases slowly with N and p (see Anderson (1984), p.298 ff.). In the cases considered
here this error is about the order of 2%, even for a chosen significance level of .001.

R e fe r e n c e s
[1] BARTELSMAN Eric J., Ricardo J. CABALLERO and Richard K. LYONS (1991)
“Short and Long Run Externalities”, NBER Working Paper No. 3810.
[2] BAXTER Marianne and Robert G. KING (1991) “Productive Externalities and Busi­
ness Cycles”, Institute for Empirical Macroeconomics, Discussion Paper 53.
[3] BEAN Charles R. (1989) “Endogenous Growth and the Procyclical Behavior of Pro­
ductivity”, European Economic Review 34, pp.355-363.4
[4] BERNANKE Ben S. and James L. POWELL (1986) “The Cyclical Behavior of In­
dustrial Labor Markets: A Comparison of the Prewar and Postwar Eras”, in Robert
J. GORDON, ed., The A merican Business Cycle: C ontinuity and Change, Univ. of
Chicago Press.




17

[5] BERNANKE Ben S. and Martin L. PARKINSON (1991) “Procyclical Labor Produc­
tivity and Competing Theories of the Business Cycle: Some Evidence from Interwar
U.S. Manufacturing Industries”, J o u rn a l o f P o litic a l E c o n o m y 99, pp. 439-469.
[6] BRAUN Anton R. and Charles L. EVANS (1991) “Seasonal Solow Residuals and Christ­
mas: A Case for Labor Hoarding and Increasing Returns”, Univ. of Virginia Discussion
Paper No. 227.
[7] BURNSIDE Craig, Martin EICHENBAUM and Sergio REBELO (1993) “Labor Hoard­
ing and the Business Cycle”, J o u rn a l o f P o litic a l E c o n o m y , pp. 245-273.
[8] CABALLERO Ricardo J. and Richard K. LYONS (1990) “Internal versus External
Economies in European Manufacturing”, E u ro p ea n E c o n o m ic R e v ie w 34, pp. 805-830.
[9] CABALLERO Ricardo J. and Richard K. LYONS (1992) “External Effects in U.S.
Procyclical Productivity”, J o u r n a l o f M o n e ta r y E c o n o m ic s 29, pp. 209-225.
[10] COOPER Russel and John HALTIWANGER (1992) “Macroeconomic Implications of
Production Bunching: Factor Demand Linkages” J o u rn a l o f M o n e ta r y E c o n o m ic s 30,
pp. 107-128.
[11] COOPER Russel and John HALTIWANGER (1993) “Evidence on Macroeconomic
Complementarities” NBER Working Paper n. 4577.
[12] FAY Jon A. and James MEDOFF (1985) “Labor and Output over the Business Cycle:
Some Direct Evidence”, A m e r ic a n E c o n o m ic R e v ie w 75, pp. 638-655.
[13] HALL Robert E. (1988) “The Relation between Price and Marginal Cost in U.S. Indus­
try”, J o u rn a l o f P o litic a l E c o n o m y 96, pp. 921-947.
[14] HALL Robert E. (1991) “Invariance Properties of Solow’s Productivity Residual”, in
P.A. DIAMOND, ed., G r o w t h / P r o d u c t i v i t y / U n e m p lo y m e n t, M.I.T. Press.
[15] HULTGREN Thor (1960) “Changes in Labor Cost during Cycles in Production and
Business”, NBER Occasional Paper 74.
[16] KUH Edwin (1965) “Cyclical and Secular Labor Productivity in United States Manu­
facturing”, R e v ie w o f E c o n o m ic s a n d S ta tis tic s 47, pp. 1-12.
[17] LONG John and Charles PLOSSER (1987) “Sectoral vs. Aggregate Shocks in the Busi­
ness Cycle”, A m e r ic a n E c o n o m ic R e v ie w 77, P a p e r s & P ro cee d in g s, pp. 333-336.
[18] MURPHY Kevin M., Andrei SHLEIFER and Robert W. VISHNY (1989) “Building
Blocks of Market Clearing Business Cycle Models”, N B E R M a c ro e c o n o m ic A n n u a l, pp.
247-287.19*
[19] NELSON Charles R. and Richard STARTZ (1990a) “The Distribution of the Instru­
mental Variable Estimator and Its t-Ratio when the Instrument is a Poor One”, J o u r n a l
o f B u sin e ss, pp. S25-S140.




18

[20] NELSON Charles R. and Richard STARTZ (1990b) “Some Further Results on the Exact
Small Sample Properties of the Instrumental Variable Estimator”, E c o n o m e tr ic a 58, pp.
967-976.
[21] OKUN Arthur M. (1962) “Potential GNP: Its Measurement and Significance”, reprinted
in Okun (1970) T h e P o litic a l E c o n o m y o f P r o s p e r ity , The Brooking Institution, Wash­
ington, D.C., pp. 132-145.
[22] ROTEMBERG Julio J. and Larry SUMMERS (1990) “Labor Hoarding, Inflexible Prices
and Procyclical Productivity”, Q u a r te rly J o u rn a l o f E c o n o m ic s 105, pp. 851-874.
[23] SBORDONE Argia M. (1993) “Cyclical Productivity in a Model of Labor Hoarding”,
Federal Reserve Bank of Chicago, Working Paper 93-20.
[24] SCHOR Juliet B. (1987) “Does Work Intensity Respond to Macroeconomic Variables?
Evidence from British Manufacturing, 1970-1986”, manuscript, Harvard University.
[25] SHAPIRO Matthew D. (1987) “Measuring Market Power in U.S. Industry”, NBER
Working Paper No. 2212.
[26] SHEA John (1991) “Accident Rates, Labor Effort, and the Business Cycle”, mimeo,
Univ. of Wisconsin.
[27] SHEA John (1993) “The Input-Output Approach to Instrument Selection”,
B u s in e s s a n d E c o n o m ic S ta tis tic s , pp.145-156.

J o u rn a l o f

[28] SIMS Christopher A. (1974) “Output and Labor Input in Manufacturing”,
P a p e r s on E c o n o m ic A c tiv ity , pp. 695-735.2
9

B ro o k in g s

[29] SOLOW Robert M. (1964) Draft of the Presidential Address to the Econometric Society
on the Short-Run Relation Between Employment and Output.




19

TABLE 1 1
OUTPUT / HOURS ELASTICITY
unconstrained system estimation - annual data 1948/87

A<iit = Ci + Pi A l* + uit 2
labor share

1 = hours of prod, wiles.

1 = total manhours

Manufacturing

0.692 (.003)

0.951** (.033)

1.124“ (.039)

Food

0.584 (.004)

Tobacco

(.204)

0.399 (.258)

0.169 (.005)

0.622“ (.182)

0.342 (.245)

Textile

0.77

(.005)

0.740

(.115)

0.867 (.138)

Apparel

0.845 (.004)

0.847

(.077)

1.009“ (.084)

Lumber

0.67 (.006)

0.832 “ (.098)

0.856* (.096)

Fumit. & Fix.

0.798 (.002)

0.922 * (.056)

1.083“ (.058)

0.65 (.006)

1.177“ (.165)

1.331“ (.176)

Print & Publ.

0.747 (.004)

0.606 (.113)

0.814 (.156)

Chemicals

0.558 (.006)

0.828 (.173)

0.809 (.167)

Petroleum

0.438 (.014)

0.282 (.112)

-0.016 (.185)

0.825 (.064)

1.026* (.090)

Paper

Rubber & PI.

.200

0.728 (.007)

Leather

0.833 (.005)

0.901 (.138)

1.16 “ (.149)

Q.,Glass,Stone

0.696 (.007)

0.952“ (.052)

1.094” (.060)

Primary Metals

0.714 (.011)

1.130“ (.064)

1.44“

Fabric. Metals

0.774 (.005)

0.891“ (.032)

1.015“ (.042)

Nonel. Mach.

0.747 (.007)

0.788 (.062)

0.992“ (.087)

Elect. Machia

0.776 (.006)

0.799 (.043)

0.944“ (.049)

Transp. Equipm.

0.73 (.018)

0.967“ (.065)

1.036” (.093)

Instruments

0.769 (.007)

0.763 (.063)

0.957* (.080)

Misc. Manuf.

0.734 (.007)

0.828

0.91

(.200)

In III = -134.48

(.088)

(.227)

In E| = -134.77

1 Standard errors in parentheses. The estimates for the twenty 2-digit sectors are obtained by SURE. lnlEI
indicates the log determinant o f the residual covariance matrix, which is minimized by the estimation procedure.
Asterisks indicate estimates o f the output/hours elasticity significantly bigger than the labor share (*=5% sign,
level, **=1 % sign, level).
2 Ax4indicates the log difference o f variable x in sector i. q is real value added, 1 is as specified in the appropriate
column.




20

TABLE 2 1
CONTEMPORANEOUS EFFECT OF AGGREGATE VALUE ADDED
annual data 1948/87

A<lit = c, + P, Aljt + 50i AqAt + uit 2
Pi

soi

Pi

80

Food

-0.413 (.230)

0.244 **(.083)

-0.432 (.204)

.211 "(.030)

Tobacco

0.614 (.187)

0.033 (.161)

0.552 (.193)

Textile

0.676 (.166)

0.112 (.203)

0.622 (.112)

Apparel

0.541 (.126)

0.278" (.106)

0.629 (.078)

Lumber

0.729 (.154)

0.142 (.224)

0.679 (.101)

Fumit. & Fixt.

0.839 (.091)

0.172 (.149)

0.823 (.057)

Paper

1.319 (.241)

0.023 (.195)

1.005 (.168)

Print & Publ.

0.311 (.147)

0.179“ (.076)

0.278 (.119)

Chemicals

-0.012 (.263)

0.674“ (.186)

0.745 (.182)

Petroleum

0.173 (.109)

0.195 (.110)

0.176 (.108)

Rub. & Plast.

0.714 (.127)

0.271 (.205)

0.784 (.065)

Leather

0.662 (.150)

0.464"(.166)

0.828 (.136)

Clay,Glass,St.

0.789 (.104)

0.218 (.122)

0.809 (.055)

Primary Met

1.042 (.104)

0.243 (.204)

1.024 (.066)

Fabric. Metals

0.687 (.075)

0.309“ (. 106)

0.768 (.034)

Nonel.Mach.

0.662 (.089)

0.247 (.169)

0.661 (.064)

Elect Mach.

0.684 (.067)

0.223 (.130)

0.727 (.044)

Transp. Eqp.

1.138 (.115)

-0.291 (.215)

0.909 (.069)

Instruments

0.589 (.083)

0.242 (.129)

0.647 (.062)

Misc. Manuf.

0.457 (.371)

0.479 (.356)

0.690 (.199)
lnlErl =-134.50

In 12,1 =-134.63

LR = 3.642 (sign. lev. = .999)3
Standard errors in parentheses. All estimates are SUR. In IZI indicates the log determinant o f the residual
covariance matrix, which is minimized by the estimation procedure. The subscripts u and r on the matrix Z refer
respectively to unrestricted and restricted estimation. The symbol * means significant at 5 % level; ** means
significant at 1%. Stars are included only for 80.
2
Ax£indicates the log difference o f variable x in sector i. ^ is, for each sector i, the logarithm o f value added
o f aggregate manufacturing excluding value added o f sector i. 1 indicates the logarithm o f hours o f production
workers.
3 The statistic LR test the constraint that the coefficient 80 is the same across the sectors. Its computation is
explained in Appendix B.




21

TABLE 3 1
DISTRIBUTED LAG EFFECT OF AGGREGATE VALUE ADDED
annual data 1948/87

Aqit = q + ft A 1* + 80AqAt+ 5, Aq^., + 52AqAt.2 + uit 2
Pi

80

5,

S2

Food

-0.368 (.218)

0.190" (.030)

-0.064" (.020)

-0.056"(.019)

Tobacco

0.747 (.178)

Textile

0.598 (.120)

Apparel

0.657 (.081)

Lumber

0.588 (.098)

Fumit. & Fix

0.892 (.056)

Paper

1.140 (.142)

Print & Pub.

0.410 (.120)

Chemicals

0.747 (.165)

Petroleum

0.231 (.106)

Rubber & PI

0.753 (.066)

Leather

0.836 (.115)

Clay;Glass, Stone

0.834 (.057)

Primary Metals

1.073 (.066)

Fabric. Metals

0.781 (.036)

Nonel.Machinery

0.650 (.067)

Elect Machinery

0.738 (.048)

Transp. Equipm.

0.962 (.068)

Instruments

0.692 (.066)

Misc. Manufact.

0.662 (.214)
In El = -136.56
Ej ^ = 0.071

Xx [£j Sj = 0] =2.434 (s.l.=.l 19)

LR = 59.34 (sign. lev. = .499)3
1 Standard errors in parentheses. A ll estimates are SUR. In IEl indicates the log determinant o f the residual
covariance matrix, which is minimized by the estimation procedure. The symbol * means significant at 5 % level; **
means significant at 1 % . Stars are included only for the parameters 5A.
2 Ax* indicates the log difference o f variable x in sector i. q* is, for each sector i, the logarithm o f value added o f
aggregate manufacturing excluding value added o f sector i. 1 indicates the logarithm o f hours o f production workers.
3

The statistic LR test the constraint that the coefficients 8£ are the same across the equations. Its computation is

explained in Appendix B.




22

TABLE 4 1
PRODUCTION-FUNCTION REGRESSION
constrained estimates - annual data 1950/1986

Aqit = c; +

A lit + 8 ^ + 51AqMrl +

SURE

+ uit 2

SURE-IV13

SURE-IV2 4

P

.911 (.018)

.930 (.047)

.908 (.032)

In El

-135.18

-135.19

-135.18

P

.792 (.020)

.901 (.031)

.875 (.030)

80

.183 (.023)

.117 (.032)

.138 (.031)

In El

-135.1

-135.18

-135.17

P

.807 (.022)

.897 (.029)

.865 (.029)

So

.166 (.025)

.117 (.030)

.143 (.030)

8,

-.068 (.019)

-.076 (.020)

-.074 (.019)

8a

-.060 (.019)

-.058 (.019)

-.057 (.019)

M i

.039 (.042)

-.016 (.047)

.011 (.046)

In El

-135.1

-135.23

-135.2

X,2[ M j = 0]
LR5

0.846 (s.lev.=.357)

0.112 (s.lev.=.737)

0.059 (s.lev.=.807)

96.96 (s. lev.=.095)

1.96 (s.lev.=1.0)

24.03 (s.lev.=1.0)

1 When not otherwise indicated, in parentheses are reported standard errors. In IEI indicates the log determinant
o f the residual covariance matrix, which is minimized by the estimation procedure.
2

Ax* indicates the log difference of variable x in sector i at time t.

is, for each sector i, value added o f

aggregate manufacturing excluding value added of sector i. 1 indicates hours o f production workers.
3 IV1 includes the rate o f growth o f military expenditure and the price o f oil, and a dummy representing the
political party o f the President
4

IV2 is IV1 plus one lag o f the price of oil.

5 The statistic LR test the constraint that the coefficients are the same across the sectors. Its computation is
explained in Appendix B.




23

TABLE 5 1
PRODUCTION-FUNCTION REGRESSION - TEST OF MODEL’S RESTRICTIONS
constrained system estimation - annual data 1950/1986

AQ j-

A hit + 02 A hitl+ 03Akit+ 04Akitl ^"05

i + e7 AqAt-2 + ^ 2

SURE

SURE-IV1 3

SURE-IV2 4

e,

.849 (.02)

.932 (.04)

.909 (.04)

e2

.052 (.02)

.090 (.03)

.079 (.03)

e3

-.144 (.05)

-.319 (.11)

-.311 (.11)

e4

.025 (.05)

.220 (.10)

.217 (.09)

e5

.135 (.03)

.123 (.03)

.138 (.03)

e6

-.101 (.03)

-.124 (.03)

-.114 (.03)

07

-.048 (.02)

-.059 (.02)

-.057 (.02)

In III

-133.78

-133.45

-133.46

27.72 (s.lev.=.00)

2.096 (s.lev.=.15)

4.179 (s.lev.=.04)

3.142 (s.lev.=.08)

2.166 (s.lev.=.14)

1.387 (s.lev.=.24)

30.86 (s.lev.=.00)

4.263 (s.lev.=.12)

5.566 (s.lev.=.06)

e=i]

x \

x \ [24j=10=1 and

^ 5 0,=0]
1 When not otherwise indicated, in parentheses are reported standard errors. In IZI indicates the log determinant
o f the residual covariance matrix, which is minimized by the estimation procedure.
2 Axu indicates the log difference o f variable x in sector i at time t.
is, for each sector i, value added o f
aggregate manufacturing excluding value added o f sector i. h indicates hours o f production workers, k is net capital
stock.
3 IV1 includes the rate o f growth o f military expenditure and the price o f oil, a dummy representing the political
party o f the President, and lagged values o f aggregate capital and hours.
4

IV2 is IV1 plus the lagged value o f the price o f oil.




24




Fig. 2.1 - PAPER
a) Response to a unit innovation in aggr. manufacturing G N P
.

0.07

|

.

|

i

|

.

|

»

|

i

|

.

|

i

0.06

Impulse R esponse

0.05

0.04

0.03

-

\
\

0.02

-

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

- \

~

\

^

\

------------------------------------------------------------------------- ---------------- -

-

~

“

... ...
— —
s e c t, c a p ital
• -------- - s e c t. C N P /K

'

0.01

—

s e c t. TFP

-

0.00
-0.01

\X

-0.02 0

"

\

2

4

"

6

8

10

12

14

16

years

b) Aggr. manuf. GNP and sectoral TFP with two std. err. bands
0.08

I ............... . i ”

'

I

....................................I----------------------- 1 -------------— 1--------------------- ' ----------------------1 --------------------r ~ " ...— T

™"

- i ------------ -T

Impulse R esponse

0.06

0.04

——
--■1

0.02

GNPstd.err.
Oflflf.GNP
aggr.GNPstd.err.
sect.TFPstd.err.
sect.TFP
sect.TFPstd.err.

0.00
-0.02

J __________ ___________ I___________u________- I ___________i___________l

-0.04
0




2

4

6

8

years

26

10

i___________I______________________ L

12

14

16

Fig. 2.2 - CHEMICALS

Impulse R esponse

a) Response to a unit innovation in aggr. manufacturing G N P

Impulse R esponse

b) Aggregate GNP and sectoral TFP with std. err. bands




27

Fig. 2.3 - CLAY, GLASS & STONE

Impulse R esp on se

a) Response to a unit innovation in aggr. m anufacturing GNP

Impulse R esponse

b) Aggr. manuf. GNP and sectoral TFP with two std. err. bands




28

Fig. 2.4 - PRIMARY METALS

Impulse R esponse

a) Response to a unit innovation in aggr. manufacturing G N P

Impulse Response

b) Aggr. manuf. GNP and sectoral TFP with two std. err. bands




29

Fig. 2.5 - FABRICATED METALS

Impulse R esponse

a) Response to a unit innovation in aggr. manufacturing G N P

Impulse R esponse

b) Aggr. m anuf. GNP and sectoral TFP with two std. err. bands




30

Fig. 2.6

MISC. MANUFACTURING

Impulse R esponse

a) Response to a unit innovation in aggr. manufacturing G N P

Impulse R esponse

b) Aggr. manuf. GNP and sectoral TFP with two std. err. bands




31

Working Paper Series
A series ofresearch studieson regional economic issuesrelating tothe Seventh Federal
Reserve District,and on financialand economic topics.

REGIONAL E C O N O M I C ISSUES
Estimating Monthly Regional Value Added by Combining Regional Input
With National Production Data
Philip R. lsrailevich and Kenneth N . Kuttner
Local Impact ofForeign Trade Zone
David D. Weiss
Trends and Prospects forRural Manufacturing
William A. Testa

WP-92-8
WP-92-9
WP-92-12

State and Local Government Spending-The Balance
Between Investment and Consumption
Richard H . Mattoon

WP-92-14

Forecasting with Regional Input-Output Tables

WP-92-20

Pi?. lsrailevich, R. Mahidhara, and G JD . Hewings
A Primer on Global Auto Markets
Paul D. Ballew and Robert H. Schnorbus

WP-93-1

Industry Approaches to Environmental Policy
in the Great Lakes Region
David R. Allardice, Richard H. Mattoon and William A. Testa

WP-93-8

The Midwest Stock Price Index-Leading Indicator
ofRegional Economic Activity
William A. Strauss

WP-93-9

Lean Manufacturing and the Decision to Vertically Integrate
Some Empirical Evidence From the U.S. Automobile Industry
Thomas H. Klier

WP-94-1

Domestic Consumption Patterns and the Midwest Economy
Robert Schnorbus and Paul Ballew

WP-94-4




1

Workingpaperseriescontinued

ISSUES IN FINANCIAL REGULATION
Incentive Conflict in Deposit-Institution Regulation: Evidence from Australia
Edward J. Kane and George G. Kaufman

WP-92-5

Capital Adequacy and the Growth ofU.S. Banks
Herbert Baer and John McElravey

WP-92-11

Bank Contagion: Theory and Evidence
George G. Kaufman

WP-92-13

Trading Activity, Progarm Trading and the Volatility of Stock Returns
James T. Moser

WP-92-16

Preferred Sources of Market Discipline: Depositors vs.
Subordinated Debt Holders
Douglas D. Evanojf

WP-92-21

An Investigation ofReturns Conditional
on Trading Performance
James T. Moser and Jacky C. So
The Effect of Capital on PortfolioRisk atLife Insurance Companies
Elijah Brewer III, Thomas H. Mondschean, and Philip E. Strahan
A Framework forEstimating the Value and
InterestRate Risk ofRetail Bank Deposits
David E. Hutchison, George G. Pennacchi

WP-92-24
W P-92-29

WP-92-30

Capital Shocks and Bank Growth-1973 to 1991
Herbert L. Baer and John N. McElravey

WP-92-31

The Impact of S&L Failures and Regulatory Changes
on the CD Market 1987-1991
Elijah Brewer and Thomas H. Mondschean

WP-92-33

Junk Bond Holdings, Premium Tax Offsets, and Risk
Exposure atLife Insurance Companies
Elijah Brewer III and Thomas H. Mondschean

WP-93-3




2

Workingpaperseriescontinued
Stock Margins and the Conditional Probability ofPrice Reversals
Paul Kofinan and James T. Moser
IsThere Lif(f)eAfter DTB?
Competitive Aspects ofCross Listed Futures
Contracts on Synchronous Markets
Paul Kofinan, Tony Bouwman and James T. Moser
Opportunity Cost and Prudentiality: A RepresentativeAgent Model of Futures Clearinghouse Behavior
Herbert L. Baer, Virginia G. France and James T. Moser
The Ownership Structure ofJapanese Financial Institutions
Hesna Genay
Origins of the Modem Exchange Clearinghouse: A History ofEarly
Clearing and Settlement Methods atFutures Exchanges
James T. Moser
The Effectof Bank-Held Derivatives on Credit Accessibility
Elijah Brewer III, Bernadette A. Minton and James T. Moser

WP-93-5

WP-93-11

WP-93-18
WP-93-19

W P-94-3
WP-94-5

M A C R O E C O N O M I C ISSUES
An Examination of Change inEnergy Dependence and Efficiency
in the Six Largest Energy Using Countries-1970-1988
Jack L. Hervey

WP-92-2

Does theFederal Reserve Affect Asset Prices?
Vefa Tarhan

WP-92-3

Investment and Market Imperfections in theU.S. Manufacturing Sector
Paula R. Worthington

WP-92-4

Business Cycle Durations and Postwar Stabilizationof the U.S. Economy
Mark W. Watson

WP-92-6

A Procedure forPredicting Recessions with Leading Indicators: Econometric Issues
WP-92-7
and Recent Performance
James H. Stock and Mark W. Watson




3

Workingpaperseriescontinued
Production and Inventory Control atthe General Motors Corporation
During the 1920s and 1930s
Anil K. Kashyap and David W. Wilcox
Liquidity Effects, Monetary Policy and the Business Cycle
Lawrence J. Christiano and Martin Eichenbaum
Monetary Policy and External Finance: Interpreting the
Behavior ofFinancial Flows and InterestRate Spreads
Kenneth N. Kuttner

WP-92-10

WP-92-15

WP-92-17

Testing Long Run Neutrality
Robert G. King and Mark W. Watson

WP-92-18

A Policymaker's Guide toIndicators ofEconomic Activity
Charles Evans, Steven Strongin, and Francesca Eugeni

WP-92-19

Barriers toTrade and Union Wage Dynamics
Ellen R. Rissman

WP-92-22

Wage Growth and Sectoral Shifts: Phillips Curve Redux
Ellen R. Rissman

WP-92-23

Excess Volatility and The Smoothing of InterestRates:
An Application Using Money Announcements
Steven Strongin
Market Structure, Technology and the Cyclicality of Output
Bruce Petersen and Steven Strongin
The Identification ofMonetary Policy Disturbances:
Explaining the Liquidity Puzzle
Steven Strongin
Earnings Losses and Displaced Workers
Louis S. Jacobson, Robert J. LaLonde, and Daniel G. Sullivan
Some Empirical Evidence of theEffects on Monetary Policy
Shocks on Exchange Rates
Martin Eichenbaum and Charles Evans




WP-92-25
WP-92-26

W P-92-27
WP-92-28

WP-92-32

4

Workingpaperseriescontinued
An Unobserved-Components Model of
Constant-Inflation Potential Output
Kenneth N. Kuttner

WP-93-2

Investment, Cash Flow, and Sunk Costs
Paula R. Worthington

WP-93-4

Lessons from theJapanese Main Bank System
forFinancial System Reform inPoland
Takeo Hoshi, Anil Kashyap, and Gary Loveman
Credit Conditions and the Cyclical Behavior ofInventories
Anil K. Kashyap, Owen A . Lament and Jeremy C. Stein
Labor Productivity During the Great Depression
Michael D. Bordo and Charles L. Evans
Monetary Policy Shocks and Productivity Measures
in the G-7 Countries
Charles L. Evans and Fernando Santos

WP-93-6
WP-93-7
WP-93-10

WP-93-12

Consumer Confidence and Economic Fluctuations
John G. Matsusaka and Argia M. Sbordone

WP-93-13

Vector Autoregressions and Cointegration
Mark W. Watson

WP-93-14

Testing forCointegration When Some of the
Cointegrating Vectors Are Known
Michael T. K. Horvath and Mark W. Watson
Technical Change, Diffusion, and Productivity
Jeffrey R. Campbell
Economic Activity and the Short-Term Credit Markets:
An Analysis ofPrices and Quantities
Benjamin M. Friedman and Kenneth N. Kuttner
Cyclical Productivity in a Model ofLabor Hoarding
Argia M. Sbordone




WP-93-15
WP-93-16

WP-93-17
WP-93-20

Woridngpaperseriescontinued
The Effects of Monetary Policy Shocks: Evidence from theFlow ofFunds
Lawrence J. Christiano, Martin Eichenbaum and Charles Evans

WP-94-2

Algorithms for Solving Dynamic Models with Occasionally Binding Constraints
Lawrence J. Christiano and Jonas D M , Fisher

WP-94-6

Identification and theEffects ofMonetary Policy Shocks
Lawrence /. Christiano, Martin Eichenbaum and Charles L. Evans

WP-94-7

Small Sample Bias inG M M Estimation ofCovariance Structures
Joseph G. Altonji and Lewis M. Segal

WP-94-8

Interpreting theProcyclical Productivity of Manufacturing Sectors:
External Effects ofLabor Hoarding?
Argia M. Sbordone




WP-94-9

6