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working paper
department
of economics
-Investment and Sales;, Some Empirical Evidence
by
Andrew B. Abel
and "^
Olivier J. Blanchard
Number 428
July 1986
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
-investment and Sal es;^ Some Empirical Evidence
by
Andrew B.^bel
and^'
Olivier J. Blanchard
Number 428
^
July 1986
Investment and Sales
:
some empirical evidence
Abstract
This paper attempts to give
a
structural interpretation to the
distributed lag of sales on investmentmanufacturing. It first presents
a
at
the two-digit level
m
US
simple model which captures the
various sources of lags and their respective implications. It then
estimates the model, using both data on investment and sales as well as
direct evidence on the sources of lags. The spirit of the paper is
exploratory
;
the model is used mainly as
a
vehicle to construct, present
and interpret the data.
We find that the following model can roughly generate the
distributed lag structure found in the data. Firms face delivery lags of
3
quarters. They also face adjustment costs, which lead them to take into
account expected future sales, with discount factor
.9
when constructing
the desired capital stock, and to close about 5% of the gap betwen actual
and desired capital per quarter. They pay for orders at a constant rate
between the time of order and that of delivery. The model is however not
very successful in explaining differences in dynamics across sectors.
J
(first
InvEEtfTient
and Sales
by Andrew E,
Ncbii
Abel
;
some empirical
and Olivier J.
u
1
19 36
hey I9B3)
;,'
dra-ft
es'idence
Blanchard^
* Harvard Univsrsity and NEEF;, and MIT and NBER respectively. We thank
idyotaki Tsr excellent reeearcii aeeietanze, and Jiir; Mines, Andy Lo. Jifn
r h
IX
Financial assistance - r n
c r help along the way.
-f
iTi
This paper atteffipts to give
sales on investment at the two digit
o-f
implications.
well
It
direct
as
e,-:ploretory
then estimates the model,
intoriT.
ation on the sources
the model
;
level
iTianu^acturing.
UB
in
which captures the various sources ot
model
EiiTiple
a
interpretation to the distributed lag
structural
a
lags and their respective
using both data on investment and sales as
The spirit
lags.
o-f
used mainly as
is
presents
-first
It
o-f
the paper
vehicle to construct,
a
15
present and
interpret the data.
Lags in the response
main sources.
-four
investment e>;penditure5 to sales
o-f
The -first
Investment depends on -future sales,
eiipectations.
is
The ne^t two come I'rom technology.
which themselves depend on current and past sales.
costs
One,
external
to the
u^
i
n yeEt
oec-cion
w
'.*
n
;
T
f
'.
L
stock
5nt
e v. p e n
-d
i
cowp
tur es
1
V
SnQW5
j
Section
et e
1
delivery lacs,
The other,
.
-firin
.-clrf-^*^
T
n
is
neither willing nor able
is
instantaneously to
and
y
-firir,
that the
irriply
w hie h
,
^h e
i
*'
f"
c =
P;
p
V—
- T
it:
cye
c.
The
sales.
in
en t s
n'""o'"c.
*
pn
'
i
r =
t-
^
r^
n^
presents the basic investiiient and sales characteristics
2
industries studied in the paper.
on
the
to
tne pacer
Oi
i.
•
fn
internal
is
Together, they
-firiT;.
its capital
to adjust
ab
adjustir^ent,
o-f
attributed to
be
cart
sales and the capital
stock,
estimates
It
showing
a
reduced
relation
-forni
each
o-f
the
o-f
investRent
o-f
patterns and di-f-ferences across
comiTion
industries.
Given the existence
can construct direct
the
b
*y
c
iT.
p
sector
£
i
t
o-f
i
n
o-f
est
o-f
i
1"
capital
destination.
data on orders and deliveries by sector
at es
by
o-f
i
These
d e
n d u 51
e st
i
1 :
?
it,
>
\'
lags by type
ery
^^«
^ ~
=
"
o-f
can constru;
ar =
'^
r == = n t ^d
dd
c
"
in
1
.
Given
origin,
i
n
r
-f
;
iT;
Ge ~t
o-f
i
r
,t,
Ve
one
at
r
y
n
i
i
on
ac s
Section
e
4
;.
o m
There appears to be
the effect
of
stochastic behavior
effect
of
of
e;;
o
univariate representations
in
relation between the degree
sales on investment,
i
>
y
it
.
sales and
of
5
^i
o«=
industries.
sales across
of
persistence
of
nd u £ t
trie
which supports the hypothesis that the
sales is an important
of
Bales in each
^
determinant
of
the distributed
lag
sales on investment.
more formal
A
a
stochastic behavior
the
n e £
differences
substantial
si:e of
i
the structural
test
the theory is carried
of
developed
model
section
in
1.
out
Section
in
The model
throuch estiniation
5,
somewhat successful
is
in
plaining the distributed lag structures and the differences across industries
through plausible structural parameters.
Section
Section
flexible accelerator model.
a
hypotheses that there
is
causal
a
at
the
as s
d at a=
'J.
.
(1)
U
(2)
K^^.n
(-)
\'^.,
correct,
is
That
see this
we
i
We
assume that investment behavior is
K*t* n
=
cd-rr)
E
•
'
-
t
cr'
r -n -
J
—n—
i
E
S
^ .,„
:
t
^
(
sh or c ut
?t
.
i
i
IJ
^
)
w
i
under the
r k
nv=51
;Ti
sn t
and
iri
a
i
n t a
i
n e
that no
While we do not believe that either of
mp t
n £
we
is,
relation from sales to
factors other than sales affect investment'.
these two
the paper.
of
lexible accelerator modi
i
specify
'tis
assesses the main results
res'iews and
i
c h
appropriate for
as
aracter
J
<
X
<
1
;
<
cr
<
1
:
:
;
ed
oc
by
>
:
a
first
1
c
i;
(4)
Xt
1
1=0
=0
where
15
the capital
is
the
t +
level
capital
oi
desired as
n,
place at the oe ginning
in
time
o-f
place at the beginning
in
orders at time
period
o-f
delivery at the beginning
investroent
oi
period t+n
Xt
is
investment e;;penditures in period
Bt
is
sales in period
M
St
is
a
S5t
is
the in-formation set at time t,
disturbance
t
t
is
It
period
dt
t,
-for
t
t
tr'^m
which includes at least
current and laqqed sales.
Consider
H-l1
H =
o-f
-!
1
<
i 1
lags,
V-
vc
t
!
= =
i
that
so
s r E
1
the case where
r st
.-
=nf
n
=
eQ uat
•:
i
r
:T;
i
cn
costs
-face
s
(
1
ad
o-f
j
as
iT;
ent
c ao
o-f
i
ta
but no
1
investment orders, e;;pendi tures an
this case,
In
0.
•?
net
)
i
n ve st
iTi
ent
is
ec ua
to
1
the cap between deaii-ed and actu
•.T.
Desired
investment is equal to net invrstaent plus
r
capital
expected -future sales, with discount
T
actor
in
J
;
Costs
discount
turn 'depends on the sequence
o.
is
adjusteiTiSnt
c-f
par a
the steady state ratio
r.
e t er
u.
rather -functions
o-f
the convexity
costs
o-f
give us two
o-f
o-f
ii?,
o-f
ad
j
portent parameters,
techno Iccical
ust
.t;
ent
investiTiSnt
reduces
spsa
I;
i
n g
and
For 5;;a!nple,
increases
slowly and look at expected sales -further in the -future.
directly as structural parameters.
gap para.Tieter
a
X
and
a
technological parameters, but
parar:eters^.
X
&Kt-i.
to sales.
capital
These are not strictly
underl'/ins
epl acerient
We
cr
:
shall
-f
i
r
it:
s
an
increase
adjust
howe\'er
i"
treat
in
or e
tneiii
Coniiuer now the zase whe^e
r
1
(Ti
a
i
1
z
ready tc use
time
the
in
rd
s
i
(T;
p
1
periods
n
e£
f
o e 5
e-fte--
it
t
(orders cannot be cancelled).
gap between
the e;;pected
time
at
t
orders at time
in
equation
as
D-T
time
+n-
assumption
th er e
e
;;
pend
t
To
more
a
r e
i
ur=5
summar
through
X
=
,
Fer
i
u1 }
i
Thus,
which is
,
i
This
equation
in
1.
n o
r-
n
as
o-f
HKt»n-j.
to
i
and c
.
.
,
,
n
.
st en ce
stocl-:
time
i
n g
that
capital
-
all
i
e ;<
d yn a
ri
i
c
^
:
v s
;-
e d
-fraction
a
er-d
At
time t+n
until
orders close
i
equations.
dut
stocl-:
1
o-f
the
at
time
t
Similarly replacement investment
,
o^
Equation
a
d e
£
sales
-from
(3)
is
capital
the actual
and
t + n
time
t
stock at time
t + n
and
t
+
t + n
on,
e;<pected
n-1
have no
accumulation
the modi-'ied
distributed lag on orders.
The
goods is made partly on order, partly
Delivery lags introduce
relation both between orders and sales and between
r der 5
e
,
or
,
mp
.
sales e;;pect5d between
that payment tor capital
is
Delivery lags are
I
(Tiodi-fies
(1),
ioz
v° r v
The e;;pected desired capital
gives expenditures as
(4)
c o
an d
characteristics
{
a = £ um
.
with the remainder said at delivery.
delivery,
T
D y
,
c-rcered*.
i£
given the delivery lags,
;
iiT:piicit
r e
"? y
d e
depends in turn on the sequence
Equation
-f
e
desired capital
are equal
t
(2)
t
1
EQuatiori.
b e
1
current investment decisions.
on
er-fect
b
-face
there is nothing the tirm can do about its capital
t,
stocl;
i
also
•fi'-;T)£
on
the dynamic relation between
investment and sales
the sales process throuch expectations,
delivery lags through
To
see how they interact,
o-f
sales,
costs
;onsider the case in whi
o-f
n
we
and on
cr d er -e
now consider
on
;;
a
costs
p en d
i
t u r
simple
d s p
dt
on
adjustment
;;
amp
1
e
adjustment and delivery lacs
•follow
a
stationary
-first
t h e
lags through
e
=
end s
order process.
t'
£c
It
1
V
1
=
C
n g
oA.y
The -first
^
cr
1
e
:;
p e
c:
redLcing the
a1
/
costs
dt
e-ft'ect
in
on s
1
(1-c7Pb1
(
Bt
]
i-f
also decreases the er-fect
It
the
e
T
-f
the er-fect
oi
ect
c-f
in
-for
on
S
dynamic, distributed lag relation is
will
i
invest
,'
Ot
^nP
T
nVe st; ent
iTi
snc
1
c u^ ^
utu
e:
e
r
;
;<
I
orders depend on
p =n c
p c
i
c ur es
n c r =
f"'
c
I
!
w
CI .
~
f-
1
gives
)
e-'-fert
ccsts
i
c
o-f
When
q
B
o-f
ori
The ne;,t
.
o,
Je,
two,
V
I,
leading
C",
e
•-,
look
e-f-fect
t'.e
less than one,
is
cr
X,
to
-firnis
and
cr
and
decrease
adJListiTi5-t
also decrease
this will
o-f
this
delivery lags and persistence on the sice
r e
!T:
i
at
uch
i
'/
e
1
y
s t r a
1
r r
p
1
Only
i-f
g h 1 1
or wa r d
sales -follow
o-f
1
on
the data
,
Indeed,
sales.
or
their
in
a
e
••
r'
;<
a
ii:
p
1
s
,
higher arosr process
^H
-ni
c
e
of
the
on
ec t
the above
that case,
In
with
uc ed
c-f
i
less obvious.
distributed lac
a
r
1
non-dyriair,
:onvo: ut
;
(
£;t
the
th= terci Os".
:
'
s
+
n
They also increase
5.
current orders.
a-f-fsct
:s
:
I.
sales on investment is
only current sales
o-f
c-nve;;
t'ore
costs,
adjustfrisnt
o-f
the size
less than one,
is
pG
Delivery legs are responsible
E.
(r-A i|::t.„.i
-^
a-f-fect
any change
;
replacing
and
/
adjustment,
o-f
c-f
2
sales ratio and
the capital
longer horicon
a
t
(1-ff)
Pe"
is-
are -funLtions
over
t -
Tive coe-f-ficients
Thus,
n.
'^
1 n
p
Ds
t ne
1
-K= n-,
1
::^.r^.
a q
o-f
r:B '/e
vie
quarterly
the
selected all
en
date"
2
or
digit
3
shipments and
crcers,
sectors end two 3-diqit sectors
mnemonics are Qiven
e:;penditure5 Br
s
in
the
directly
a
ir st
\'
ail able.
methods
Capital
problem must be mentioned in the
te:;t
:
major problem
in vest cent
-for
most
sectors except
and
nair.es
which are needed tor
in -formation
on
Append!
;-,
A
One data
the data.
shipments are collected on an establisnment
while investment expenditures are collected on
basis,
id
as
Their
investment expenditures.
o-f
r.
shipments and
Orders,
1.
series,
stocl..
i-;e
thirteen sectors, eleven 2-
o-f
Table
ot
construction and other
o-f
whicn
or
vehicles and aircra-ft).
(motor
two columns
i
i
erpenditures, as well
in\'est:Tient
estimation are constructed by accumulation
gives sources,
fnu-fartunng sector t
The result ^as the cnoice
associated p'"ice dc?-fl5tor5.
digit
fr,
F'etroleuiT:,
-for
expenditures by companies classi-fied
which
in
a
large proportion
petroleum takes place
in
(see appendix
activities largely unrelated to petroleum
This is rot
cocipany basis.
a
-for
A
details).
a
o-f
in
The
sa;T:pl =
period is 1953-1 to 1979-3.
examining the data, both
In
we assume
later,
.
oc n a=
5 11
'
.1
that in-.-estment
component.
We
:
n
-f
orma
: 1
or
using econometric
shipments have both
and
assume the deter
exponential time trend and seasonal
here,
y
d
i
mr
^
': i
e
~
n
.
i
et
i
^
am
x
a
z omd on ent
c
i
n
i
n "
deter:"! ni st
the
to be
the data
assumption that there is no deterministic time trend would be
u
use
" i
n
u
1
t
*""
t e c
nn
i
and
i
c
s
um
o-f
n e
a
but
i
q l e
a
an
*^
—rnaT
i
ve
have not
we
done it in this paper.
The -first six columns
o-f
numbers in table
means and the standard deviations
o-f
1
give the estimated growth rates,
the deviations -from trend and seasonal,
investment and shipments tor each sector.
While we shall not -focus on these
deterministic components
it
var
c
1
i
i
at
i
on
Pmen 1 5
what -follows,
must be noted that there is both wide
o-f
Ven
:
in
-for
'_
ratio,
c
^'
1
'-
i
i
the
;
1
e
1
I
.
r;
Ve 51
Mn
e n
fi!
gn t
n
1
c E
e
,.
p en d
C-
i
t j
''
e
;
and
rates
r ow1 n
ax
Qe
'"'
Food
FO
3,
Textiles
TX
1
Paper
PA
6
Che mi cal
CH
c-
F'etrol eum
PET
j ,7
3.
Rubber,
RU
-'
7,
6.
SCB
Clay
Stone
and 5 1 a = 5
Primary Metals PM
,
Fabri cated
FM
Metals
Non electrical NEM
Machinery
EM
Electrical
ri
acn
:
,
H.i
rcrat
n e
=
."
h-:
y
rT ==
,
c
1
1
,
1
,4
,
£. 9
n
E
-
J
c
e V
I
e 1
1
"7
20,,4
.8
.
D
r,
£
lions lli
2
1
1
.
B
tor cetinitii
appenC'ix
r,
i
X / X
)
,'
!J
50
,6
n
22,,B
1
.
2
2
.
1
2.B
.40
2.5
1. J
14,,B
O.B
.63
2.3
9
3.
43. 2
4.B
.5B
1.6
B
1.
-j
3c ,B
3
6
.24
1.7
6
4.0
.41
'7.
T
.
,
*"/
.,
s
.
41,,2
2, 9
D
variables at annual
C7
.31
1. 6
,
45,
t
ill
(
D.
t
y,y
:ee
)
1.2
5
.
5
s
5.
•
"'
1
:
7 2
0. g
,B
,
1,
£
E5,
2, 4
,
',
(I : /
0. 9
1
n 5
;
1
*
ri
2. 9
,
n
•-'
i
4.
Ct
.
A,
1
1
"
,
1
.
,
1
n
3
.
.
p me
X
3, c
,
i
Means
B
'.
.
s h
n
c
n sI r
!j
c 1
1
D
A
r
30
<
^
C7
B
'
2
One
the
-f
r ea = on e
across sectors is
=
gives
(?
ean
d
i
n e
;'
c
t
o
1
u
(T;
n
main outlier,
by
-factor
a
p et
r-
it,
p
e
1
iT;
shipments ratio, hill
coe-f-ficient
1 r
m
i
.
5
3
1
c
1
d
t a
ai-e
h a
i
-f
sh
1
i
p
j;
en
\'
e
sir.
ilar
c
ratios.
t s
ap
i
t a
1
/
the same ratio
o-f
c
o
where it is equal
-food
t t i
;
to
i
pm en t s
i
i
pme
•:
t
o
,
The
aD ove
,
the
=
•
shipments ratio, probably
to
varies between
en t
s h
ratios,
reasons explained
For
variation
o-f
.I''?,
and
.
LZ.
their mean cacital
in
denoted
This ratio,
shipments.
o-f
sh
respects ei'cept
all
in
R,
o-f
is
i
n v e s t
ri
en t
given in the
this ratio varies across sectors
5,
.
or each sector, estimates
V1 na
their
in
eren c e
less compared to
or
ore
the capital/shipiTients ratio
variation
c-f
-f
iti
gives -further evidence on the relation betvjeen investment and shipments,
:
D V
.
i
may move
n ve s t me n t
overestimates the true capital
,
Except tor
last column.
i
the
y
c a 5
Two sectors which
to the
h y
Otherwise,
2.
o-f
i
rj
1.
-^
w' t.
i
the relation
ot
-
u^
i
=
u-
;
it
•*
i-:t-i
5
i=0
lua-:
about the
i
nt o
iT:
at
i
set,
cn
described in equations
d e p 5n d
1
s n
a
i
p
en
nQ
ffi
en15
c ac
i
to
up
,
t a
these variables,
columns.
sum
d
i
N'
i
c
et
-f
i
c
o
i
)
to
(
a
}
=
i
s
uncer
,
the
c-f
o-f
sp;
the structural
model
The equation gives investment expenditures as
.
n r p v
i
qus
Quarter,
current and
on
order disturbance
g
a
constant,
t
i
In
i
aoc ed
values-
additior
deterministic exponential tise
a
dummies
en15
on
!.(-
1
by the mean
c ap
i
t
and S to
)
The next two columns
d ed
4
the end
at
1
i
on
the approximate reduced -form
regressions include
trend and seasonal
The
'
1
c
*
'!
i
(
-s
the sum
ve
= h
S
-i
n
-.
=n
t
r
are reported in the -first
)
c oe
c-f
?.
r
i
n
'
.
-f
"
-f
i
n
c
i
en t s
on
shipment;
seven
s p n
^
t-i
a
able
2
Sector
Reduced
.
V.i-1)
•
dr
it.
I
.
n
v
5(-l)
E*
FO
= 5 1
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en t
-1.1
0.3
1.7
2.2
0.1
FA
-
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(i
4.7
5. 1*
CH
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-2.2
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0.5
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-
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:"i
iTi
^,
.
i ci snts
on shipfiisnts are iT:i!lt;
coe-fficients on ships-ents
Slim 07 coe-ticier
on ship e
value G-f the liklihooc ratio teet etai
e n 1 5 do not a t e 1 in v eat e n t
5h 1 D
on
tr ansT ormeo var X a J ^ s s
SIC
level
all
5
-0.4
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0.
5-
1
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1
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2.9*
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9
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e n
3.6*
1.5
rV,
j
S;--;)
-0. IE
1
r.
5(-
TX
.
a
endina and deeeaeonal i aati
0:
.
e;-.
their aean C3p;tii
:ept tor
cclumn reports the
'he next
a i £
c
1
a t
with the
ed
:
5 1
-J
r b a n ;
the
and
e
c;
t h
e
=
F:
For tour
non durable
the sectors,
iTranu-f
tor
r £nd
e
u£
a
to
1
s
the
-f
s n
f
- 1 r an e
i
1
i
i
e
actur ng
i
the sire
j
the cumulative
>,
.
A
c
et
-f
i
c
i
=nt
e
-?
4
ot
t
ec t
;:
-i-
NEM,
EM,
c
i
n
and
fIV
AC
T
.^
r c
,
a 1
1
e1
1
p
1
a
i
n
nq
t a k
i
L
,
i
n
,
\'
e5
correlction
reriai
e r
i
c
1
men
*:
the
o-f
out the
n g
in
= h -
quantitatively small.
is
RU and
(PA,
T
r.
;
hC
durable manut actur i ng
)
1
P
ot
,
.31.
o-f
a
would then be
!]•'«,
adjustment
-full
i
n ves
sTi
to
ent
the
*~£C
~
f^
pattern,
ma n y
structure,
lag
n 3
in
SCB in
suppose that shipments -followed
actual
and
creases
signi-firant e-fte:t
no
ha.'e
particular no sign ot
in
s e c
;
,
c
e
T 1
1
c
on
1 )
to
bet ore we turn
to
i
e n 1 5
5
(
-
iarcer and more siqni-ficant than the others.
the rest
o-f
the paper,
we try to explain
di-f-fer
the characteristics
across sectors.
which
meas
i
rh
ally correlated and =j;plains
=
ect s
a
coed
1
But
o-f
these
these reduced t'orms.
even those where shipments are Quantitatively
the disturbance term,
highly
e
t
with an average cumulative et^ect
this task, we must mention another characteristic ot
.-
e
shipments as measured by
-f
ca'"'itsl
t h =
t
e1 1
i
.mpose constraints on the distributed
h
-f
bime acrosi eertors.,
in
e
o-f
a
the
durable manu-f ac tur ng
would then mean
''
t
(measured by Z/ o)
o-f
distributed lag structures and why they
c s
C' 1
shipments
F'M)
this coe-f-ficient,
o-f
k
CO
F'ET,
icr most
smooth decay as the lag length
In
r
variable;,
dr med
3
are
ratio
h ood
play no
pwen t s
e-f-fect
and FN,
,
-f
CH,
i~0,
and
•
S!-3)
1 ;
be
component.
seasonal
i
we
d
t n a :
^icipcted cap between desired
i
=
'j
very signi-ficant etT'ect,
a
To get, a -feel
r.
e
1
and the cumulative
shipments have
ill
:
the sectors
o-f
investment,
For eight ot
e
the
en
^
deter rainistic trend and the
on
v
wouic;
(Z/a)
The last two colufrins give the coeHicient
expenditures.
d
n / p
ratio,
Oijtjut
Var
a
nd
For ail
statistically siqni-fica:
lDSh Sci5=,
laoies DliiSr than
::
Th E
ad
J
P^
u 51 ed
in
is
(Ti
q5
which 5hip(T:Pnt5 are significant is
is
thus net due to shiptrients
in
(5)).
i
n Ve st
iTr
Even
ent
6ec1
In
1
,
there would be
cn
D
^. .
1
a
]a'"Qe
A
lot
:
5
1
e
in
-f
e;;
to
t
be
delivery
on
e
;;
1
a a 5
p
1
We proceed
each sector,
and then calculate the delivery lag
1
V5ry
in
and structure.
lag
by type
a
1
-four
Next,
steps.
we
We first
co.Tibine
t
-i
a
\'
ci-f
sec t a
•"
=
o-f
shipments on
.
ot
delivery lags tacing each
derive the capital
coaposit;
1
associated with each type
.
•
r; .-,'-;
r
>
—
.
r-.
(-,
r,
c-i
«
of
composition
delivery lags by sector.
study ivhether the delivery lag associated with each typ
Finally,
^ n
r\
"
'^ *' 1
fT.
<?
,-;
^ ^
^
^''
constant or, instead, varies cyclically with the output of tne sector producing the
racitci
;=ctDr5l
ccoos.
i
.Ti-rj f-|
We construct
S
a
capital flow tables,
sector, for both
;al
T
capital
stock decomposition for each sector
which give the amount of
1967 and
1972.
We
information about depreciation and
sector.
in
table
The details of
3
investment
of
each
\/ n p
ty;
*
o
f-
c
ach
then go from these flows to stocks by using
c r
the computation
kth
a^-e
in
investment
in
(Tio\'eiT:ent5
the information on capital
erage
the
-for
shipments are replaced by orders
ne d
construct direct estimates
we
part
plaining the ei-fects
the sectors.
eqiiipffisnt
its average value
;
(This 1= true also when
" e c t
this section,
.29''.
ol
were success-ful
we
i-f
very high
not
c ? ; e5
1
rates for each type
given in appendiK
of
B.
good and each
1
L ap
e
i
!-
ac h
ec t r
1
;
1
c a
t
a
eQ u
i
ra c h
]
and
ner y
it.
1
p
iTi
i
n
e
'"
o
t
or
ent
y
with
,
nearly
c o m e 5
s
r.
a 11 e
The
vehicles.
e
i"
De
1
rie
'/
l:
se
I'l
type
b v
1
c
ij
n t s
1
j
o
c;
'
e
i
c
o
+ r
o
c
-four
sectors,
iT;
n c
iron.
i
i
-f
o
capital
-f
to CDiTipletion
tiiTie
to
the construction
•for
types
dit'-ferent
1?,
stock.
all
c D
c
i
These
t
!•;
Ve
electrical
-f
have data on
We
th.'^ee
1 1
1
w
i
n q
sectors.
I-f
un
-f
i 1 1
e d
y
I
;
r o
i
s t " j c t u
a
s
r
electrical
,
-:
nor,
,
is
s
i
i
,Ti
i
1
a r
Isrgsr
tr.iic^-
structures
-for
a
q odd
as su
structures are directly
or
iii
pt
a s t
i
on s
i
sate
are
sachinery and
accroach
'-'
o-f
t h
hdw
eve
goods
4
3",;
i
-for
motor vehicles may be
;
un
T
,1
a
i
--i
si
•;
v=
P n
r
-t
1
1 i
ea
.=
c c
;-!
only
o-f
^f.
: r srl
r
nor
;Ti
ac
"1
1
ne ry
.
iv
V,/[l-bi)Si
l^e
sh
i
to
p - en t s
ccccs.
id
i-f
Kit"
-fabricated metals,
-for
assu,':: = d
o r c er s
y
5
on
as
these sectors produced only capital
e
2
-
r-
-
7.
-for
.-
4*
-
use
cap:
sales by the producing sector to wholesalers and retailers,
are Tro?; stock,
the -four sectors
G-f
and new orders as well
were produced to order
goods sold as capital
o-f
re
;
delivery lags
o-f
work is needed.
ntor e
mi
the regaining
would
ri
good
data exist on equip ent and
•for
c s
i
there-fore use them.
we
;
r
c a t e d
petroleum which has
-for
producing equip m ent, only three have delivery lags
sold
i
ia
ent
No such
be
ab r
equipment to
capital
t'
e/cept
v
capital.
in
diHerent approaches
Data on
available
lacs
er y
1
and equip
structures
o-f
1
r a 1
across sectors and close to unity,
pruportion
en
then estimate the r^ean delivery lag by
and only these sales,
Table
3
Comdo5
.
iector
Sector
Table
1
1
;
on
o
-f
oricin
the
c
ad
1
1 a
1
stoci
b v
FM
NEK
Er,
riV
FO
TX
PA
CH
04
00
Z-
0"
51
11
41
IB
27
PET
Ob
RU
01
3
rr
see
01
03
oe
05
o:
02
04
09
05
07
IE
04
06
03
D-f
t
PM
6
-,r
Fr,
00
4 J
tJEM
01
44
EM
nv
AC
00
00
00
3i
4
1
Delivery /construction laos by tyse
Averice lag,
Fabricated metals
Non electrical iTiachinery
Electrical Ciachinery
M
1
r
Veh
i
c
:
2
2
3
e5
Induistrialstructures
3-3
u
-i
iTi ill
erc
1
a
1
si r ct ur e e
able
•yeracs
r
Structures
destination
o-f
4.
sector
u
7X
FA
CH
PET
RU
SC5
PH
FM
NEM
EM
MV
-6
o-f
in
1
cood
quarters
cr '-
4 3
'_ _'
_'
03
02
02
06
02
07
04
03
03
05
46
B3
-0
.'
53
50
46
i4
44
41
44
11
are
where Vi,
Si
and bi
oportion
the prop
o-f
shipment
D
T
construction are given
are given
in
equip iTient
!
on
tal.es
in
wholesalers and ret
to
a p p e n d
i
B
;;
;
b
vanes between
j
All
those
4b
sector
arid
(Detaois
i.
The results
46",;).
Delivery lags appear similar across the di-ft'erent types
4.
to
a
more disaggregated level.
mean
d e
to
le-ft
do
of
to
is
delivery lags by type
for petroleum,
1 i
ver v
industrial structure while
an
ot
it
ta(:e5
It
approximately
receive equipment.
that is
ut
to build
year
a
destination are given
;;cept
lag
all
1
cf
Implied average delivery lags by
The main result,
2
.'
capital.
;
the
e
1
and 3.5 quarters^.
r e s c cn s e
of
of
constancy
orders and shipments for the capital
this assumption.
If
we
production is constant
ur
p o =
=s
,
s
that,
is
;
the
This is therefore not the
across sectors,
Ver y
models which assumed
investment, namely that
p
investment
Before leaving delivery lags, we return to
indeed of all
for our
sectors face very similar delivery leg structures
varies
a V
combine results about sectoral composition with
Table
in
the difference of
1
and
42
shipiiente an;
friean
or
this uni-forraity no doubt hides di-fterences at
average
iTiOnths
sii;
=
scld
5
orders,
un -filled
rtean
surprisingly, delivery lags are longer tor structures than Tcr equipment.
tvct
-f
table
respectively
of
a
a
maintained
as sumo t
i
dn
our model,
of
linear relation between demand and
delivery lags.
We
can use the
time series on
producing sectors to examine the validity
of
assume that the proportion of production to order in total
cver
the cycle,
then if delivery lags
relation between orders and shipments should be
run the followinq recressicn
:
c on s t an t
i.ra
c on st
through time.
a.
n t
We
,
the
t h
er rf o
e
Table
£
C v cl
.
i
z a
1
b e h 8 v
i
d^
c
delivery
-f
]
a q s
D
=
d(D)
Sectors
ot
n
electrical
(r.achmery
.29
(7.4)
(4.7)
.30
(9.2)
(2.9)
Elsctri cal
.
.3b;;10-
.12>;10-
33
.
16;<
lo-
iTioChinery
Period of esticiation 195B-3 tc 1979-3
statistics
t
a
:
mean
1
aa
-
Co
riL*
=
D
d(0)
ML
D
D
=
d(0)
D
'
ffo
ML
origin
Fabricated metals
N
D
in
parentheses
defined as
(
2d
(
)
/
1
(
- d
(
)
ll
60
29
.Bl
.30
.B5
1
.
00
1.77
.37
1.17
-
St
E Wit
-f
1
=
dt
d
Ot-i
constant £nd
L
a
eqijal
to
d
p a r am e t r
a
i
:
a1
1
on
i-j
h
Under the alternative hypothesis,
c
increasing
ci
= an
1
ag
-fLinctiDn
exponential
i
5
Q
i
Ven
b y
the level
c-f
2
d /
or
(
)
orders on shipments
: n
is
convenient under
i
f
is
R=5L;lt
=.
allowed to dif-fer
estimates
to
'.
aier
to
the null
be
and
one to
•rotr;
shipments are in response to
is
demand,
positive and the mean lag is an
iTieasured
by the
deviation
orders
or
-from
the
lable
in
'lean'
lag
i.
In
assume
we
addition to the estimates
when deviations
r> r-
c-f
p c
»-
e
* r
.-i
:
m
o-f
d
and
we
c,
cive
trend are respectively
ec u a1
plus and minus one standard deviation.
The results are quite clear and
show delivery lags to be
pr oc yc
1 i
c a
1
"
.
Having
duly registered this result,
we nevertheless proceed to estimate our
based on constant lags
these results make clear that tne linear relation
;
but
between investment and shipments is at best
research
m
i
a h t
a
.
good reasons to the contrary,
ot
ted
-
o-
is
d t
deter sinistic trend and season a Is.
the absence
.^<-
is
d o t h
The relation between shipCients and orders can be rewritten as
In
that
so
=
o-f
that some orders are cancelled and that not all
The
c
leg
The coe-f-ficient
-d
,
delivery legs,
c o n s t a n t
-f
i
r der s
an
'l-dt'^'i-T'dt', where
=
The disti-ibu. ted
d.
the alternative hypothesis.
re-flect
Wit
;
hypothesis
distribution,
1
5t
c(Dt-Ct)
-^
Under the null
Fes
+
=
uncover non-linearities.
a
rough
acpro
;;
i
mat
i
cn
and
model
which is
that -further
13
Section
behavior
Dynafrnc
4.
We have seen
sales
o-f
whether or not an increase in current sales is e;:pected to
that
persist is an iciportant determinant
shipments,
and
end
that di-f-ferences
the potential
to explain
ship Rents.
this section,
In
representation
Table
d
i
-f
t
we
e;:air.
presents the results
7
the relation
in
processes
erences
shipraents across
o-f
o-f
i
n
,
t n
e
d yn a
et er m
f
a5
:
n
n a
1
:
s e a
s
(
r. .- 1
scna
s ==.
^ n
1 i
t
^
r
^
y
table
presents
b
which provides
I
"iK
aD
1
1
e
persistence
a
t h
estimation
o-f
;
at
B
;.
:
yn a
iTi
i
p s c
ar oe
.
o-f
?
d
c s
c
In
c r
p
t
response
c
TX
;
AD
)
,
the hypothesis
ot
i
n ve 3 1
the
1
end,
ni
to
en t
the univariate
o-f
c-f
a
o-f
1
r eD
n r-
r,
;
processes
fiS(4)
e
;;
p cn
en t
n
.-.
i
a
1
(
4
An
in
r
I
p er s
:
s t en c
textiles, T'abricated
i
s-hipraents.
Ai
n Q p c
t
i c.
e
r e 5 e n t at
r e
)
trend and
:
Q
f
addition :o the coe-f-ficients and thai
ena t
n on-et at
-for
deterministic time trend and
J
S
J
I
1
p
III
qnar
:
t
y
C
!
I
U
s
(iietals,
iTiean
'.
003
electrical
In
cannot be rejected
,
»
sector;
electrical machinery, and air era it exhibit high persistence.
(
o-f
time between two successive do w n c r o s
variations in
the other
i
also include an
we
the table).
in
measure
snows
/
i
c
i'
sectors.
;
t n e
;iven
Thus,
,
shipments across sectors have
-for
ine the characteristics
discussed earlier, we maintain the assu.Tiption
:
between investiTient expenditures
two
o-f
e
-.'
;;
t-.
i
K
i'
i-
c
1
I
(-.
r.
and non
these secto;
(using the
^
Table
Univariate
7.
e
''
e
presentatip n 5
5
*'
!"i
1
1- t.
e
nt 5
Q
1
(27)
Cycle
5uii'=
1
r
07
e:
u
(->
-^
.
42
21.4
.50
6
6
.
.
9
21.0
.
95
16
5
.24
Bl
'
TV
,
Pfi
1.
17
-.36
07
.79
11.2
.
CH
1.41
-.65
01
.Et
IB.
.86
PET
.91
-.21
1
RU
.94
SC3
.38
PM
-. 14
E/o.'
en c t h =
'**
C2
.44*
.07
14
rn
64
7.6
15
.82
14.2
.86
. -/
-. 30
02
ti
33.
4
.83
9
.66
-.06
8
10.7
.77
7
B
.
FM
1. 15
-.26
20
.B9
9.6
.90
1
6
3
.20*
NEM
1.21
-.31
04
.66
24.6
.89
1
5
4
.33*
EM
1.35
-.46
01
02
.91
10.6
.92
17
1
.25*
11'
2
06
r.
^
.
.
04
11
4
.
-'j
*
9.
7
a
:
Q{27)
;=
the
It
is
distributed X=(27).
b:
Suiii
ot
coe-Ticients en lagged shipiT:ents
c
:
Cycle length,
:
Ncr
i
iTi
a
1 1
s e d
sum
d =
•?
d
-f
i
n ed
c
ce7
as
•?
i
X=;27)
/ c
cs~
en 1 5
en
36
c
79
.
9
.94
.
-7
1
level
03
nr-
n
1"'.9
i
-
^
TV
5
)
5h
i
(
,
.
i
at
where
p men 1 5
.
'.'
V
31*
13
24*
.43*
5
in
J
is
the
the correlation between
i
n
\'
estmen t
e
u at
i
n
S
-from
,
^
;
.
n
66
1
9
/
as5j;:=trd with the hypothesis that residuals are white,
statisti;:
Q
.
t!
and
14
rersistence is such tnat, even w:th delivery lags
et'-fects
S'jbitantial
n Ve H tKen t - E h
1
p
(Ti
5hipiT°r. ts
en 1 5
r e
1
a.
1
1
o
r,
t n
,
coe-fTicients on shiofr.entE in the
ceteris paribus,
1
:
1
en t 5
.
i
positive
a
1
a 1
on
b e
;
1
level.
persistence
o-f
The relation
more
a
equation implied by
Derivation
!
n p
••
is
shipments and
section provides
r f zf
=
step
(!)
a
strong
i
p
;-
en1 5
,
disturbance
i
hroriTiati on
and that
S
set
K
;
ar
^
L
.r.
;i
,,
=
i
e
'.
e
1
is
epual
r,
n cr
rr.
a
1
c e
t n
and
the
^:-,
<•
>:
tc
.'^2,
on
shipirients
o-f
>-
i
se d
s a
rr.
o-f
2.
One expects,
n or
ir,
-
a
an
1 i
s e d
1
c or
:
su
/r;
o-f
r
in
?
or
e
;<
amp
vestment.
1
e
has low
The next
to
given the sales process.
(4)
iinolied
bv
elisinatc unobservable expectations. We
un c or r e
1
at ed
at
r e c
a.
e 1 5
o-f
sh
i
'
t
ur es
that
and
leads and lacs with the
all
sh
ti:;
assuiTis
lagceo investment e;;penci
a.no
•
b
tc
;i)
m=
p me n t s
c
r
u s
i
n
t(
which is signi-ficant at
motor vehicles
;
pert
assessment by estimating the structural investment
shipments are
i
suiti
et'-fect
ihTormation set inciudes only current
sh
p e r s
,
-fortrial
to
is
heen
however not tight
the reduced -form
o-r
t
e
nel? e';piiin variations in
ria;,
investment equation, Tron taDle
1
we would
year,
c^de-'E.
investiTB'^t
indeed some relation between
is
h e r e
r e
f
column reports the
last
e
between cycle length and the ncrrialised
the
on
these di^ + ere'ices in processes
To see whether
i
cu'-rent
c-f
to
up
o-f
hd
i
nee;
i
t
cnal
on
the
ti
allows
the
more
a
i
RBw
:
n
i'
e 5 1
r
2
1
i
(6)
li i
:
i
ve
:
iT;
en t
n g
i
Zt
=
t
i
a n J
5h
n
np an
c D
Zt-i
A
=
I
n Ve
U
I
r-
=
1
(T.
tx(l-cr)£
ent
n V 5st
iTi
1
ri
t 5
n
-f
=
°
o
on
Let
.
r m
g
i
A^
r
.
z
4
/,
t
-
K
'•
*
^ r
....js^Cienz
•
in
distributed lac
c
sales
t
Zt
d=D =
the
p
'
'-
jc e e 5
E^-2 S^-3]
3t-,
equation
(2)
-f
r
-
iii
equation
(
(e-X)Kt.„-i
-f
r
om
1
-
e q uat
by
)
,
:;
^
i
cn
Equation
p a51
d
a t
ur
uJi
nd
Zt-l
'i't
,
s h
i
s
iTi
e n t =
e
i"
i
£ t
-f
1
1
o
>,
5
-f
r
it,
expenditures, not deliveries
on
three sets
D r
give-
[Eat
=
'
accumulation using
capital
e
:;
p en d
i
t u; es
e-
b
0]
(
4
)
by
,
:
+
E t^ilt:-!
o-f
troir;
to
(U-i
f..t:.n-i
,
oepen
tne
;
wni
.
the -fact that
o-f
:
Be -fore we do so,
capital.
1
'
t
is
Thus,
un
the
includes capital
goods were paid -fully on order,
our
c a
b s er vab
we make
two
e
.
We only observe
series constructed by
I--!
i
1
d
-for
ccrstructed
K^
but
wo;
not
delivered
vet
"^
C 3
r,
!
I
'
,
r
i
t^e ralaticr,
appro;: iiTictions:
The -first
i
:
(t-X)I UiKt-n-i-l
second depends on
a n : s3
dr
ct
: t
n
the equation to be estiiiiaied.
is
(7)
i
t
n
-^
e
and
c h a r £
then given by
is
determine past and current orders, and thus current
ur rent
e
:
i
n
t n
chari:! eristiCE
c a
;
between
"
Zt
I--A)-^ I
sKpenditures
=. ~.
j
0]
are given,
i
1
t!"i£
n
•'>
a 1
given by
15
expenditures are given,
en t
a-
-
Ve5
•-
n e
t ' e
[1
E.tcck
*:
-f
[St
=
S^
Zt,
=
'
Zt'
!
fI-rA)-i
Xcx(l-J)p A"
=
e
:
sectior
in
{!-crA)-i
A'^
dr ders
ffi
c-f
The desired capital
K^^.n
d
"\
where
2t
P
i
-
From the definition
E,:
n t r " p r e t a t
prcceEE c-erErted
shiptiier, t£
between
n t
•,
;
16
I
;
constructed
and we could use our
t » n
Gccds
than
to
attenpt to construct
te'"(ri
in
i7
may
h ow e
c
\'
-f
c
I
o
(
7
;
general,
In
order
I
.
is
c
:n
it
-f
to
p a ^ e d
bias the
er
The second
term in
in
-f
o
oe
-f
-f
X
,
:
c
Ui
n-
1
,
.
this is
i
i i
an
owed
AR
the disturbance term
(
i
i
n
)
i
1
'
e
(
7
)
i
,
convenience,
,
1 -
equation
in
1
(7);
i
capital
-f
constructed l\ would cerrectlv
i^t
,
.
.
.
,
l^t..,,-
average
by
our
1
to
>
t-
of
equation
in
1
Given tne slow
const-'ucted t't-i.
be
source
a
of
iTi
a
j
c
problems.
r
issue to which we shall
an
Rather
(7;.
capture the second
to
\'.
(Tieasuri
r e t u r n
It
.
the process -followed by the disturbance
o-t
disturbance term would
t n e
,
.
(tioving
capital,
on
en t
un
.
01'-
,
i-'t-^-i-i
the specitication
For computational
n.
',
two sided
a
simply proxy E
we
,
•
snould use our constructed
and we
the true It
t
"
instead paid -fully on deli
wEi"e
movement
>
s
1
;
i,
e
1
ignore this
we
o
1
1
an
ow
have an MA component
to
y
-'
-;
1
,
n
least
at
)
.
o
-f
component and assume that
'An
U= have -found that an AR(1)
the disturbance term -follows an hR process.
ARMA
appears
su-f-fioienttoyieldwhitenoiseresiduals.
w'
i
these two
th
app r o
;;
i
iTi
at
i
ons
equation
,
{
7
becomes
)
:
n
Xt =Xai l-r}£A" (I-c-A) -^
(S5
Zt-i
I Ui
(r->JKt-i
-^
+
iJti
rr
r.
where.
i=0
and
structural
"he
n Dn
-1r
have
i
i
V
n
-f
i
a
1
;;
c ep t
in
elements
r mat
i
n
From section
e
identi-ricati,
on
3
o -f
some
,
we
A
{
p
is
a
equation
vector
these
e
1
know that
n
,
o
-f
petroleum- approximate!
y
e
equal
.Ci
of
e nt s
the
t o
z
a
,
f z
1
and
wh
i
er aq e
3
.
;
G
'
=
we
c h
\'
i
)
.
we
i
a
i
J
a n d
1
t n e
From the previous section,
now
u=e
.
delivery lag is
Thus,
,
use
n=3
in
-for
wnat
_
c B .--.-;.- c
'_
I
L 1
-f
o
1
1
ows
—
we
In
l:
E e
c
(T:
i
s
these
b
1
n a 1
1
presence
Th
H
1
o
E
:
1
1
e e t
:
n
o
*'
-f
S
1
4
Qn
(r,
a t e j
the
t
c
3
(
c c
e
t
•?
d e s u
c:
p 1
- i
in
)
;
e 5 1
;
i"
en t e
c
i
1
cn
t
the
i
r:
c
;•
that
the parameters
eaVaE
a t ed
n e
d
'";
r = T
ves t
\
:
a
,
parameters to
negative,
a
in
e n :
,
c
is
n
:
v a r
uc t
;
:
a t r
i
t'
o
i
ows
i
=
1
''or
A
rr;
;<
an
-.
R
1
on £
o
e
ici
sect
!
A
','
;
iT:
p
and
h
,
[
u
,
;
.
.
.
.
,
1
"•
3
1
p
!-
'
ni
=
an t 5
We
.
The
.
:
3
left unconstrained,
la
-'orm
exactly.
Even
there
we
i-f
e.r
pseurio structural
a
e
ifTipose
practice overparametrired and we are
in
£
-f
equation.
E;:plaininc the reduced -form distributed lag by
up
r ep ^ e s en t a 1
a t e
the
that
" c
the reduced
-fit
the model
'j
e t r
the order -e;,penditure structure
structural
be non
have
we
,
expenditure lag structure. We there-fore constrain the lag structure
1:1-.
enough
that
el
the Ui
end
to
y
order
-Cuij-
to obey
:
uo tree
Ui
=
(1-uJo)
il-*-iJ-^u
= )-^(i)S
weights are e;:ponent
t)
'..;
_
^
i
a5y
cr*
=
-;
,
a
\'
e
1 c
TO u n
d
q r s a
L
al
Br
1
y
than
however that our
ally.
Thus,
it
is
i
=
D-f
the most
r,
1,2,3
declining
u
it
u
is
less than unity,
c.
and
e).:pc.-
ent
i
a
1
1
y
r
e=t
i
i"
a t e s
c
•
(X
}
c
were
h
i
g h
1
y
correlated
ispossible to estiaate precisely the discount pai-asete;
and we are -forced to assuffis rather
un-fortunate as
one
is
i
-for
than estimate the value
o-f
7.
This is
which measures the degree to which -firms discount the -future,
interesting parameters
(values between .55 and
.95 make little
the model,
c-f
d
i
-f
-f
er en
c e
k'e
choose
to the tit).
a
value
o-f
cr
o-f
is
.?
IB
and
;)•.
Using the values
-6).
o»'
Dveridenti-fying restriction on
estimate
to
values
o-f
and
the reaction
s 1
c
on
i.
!
fTi
n
1
i
n
1
ed
>.'
«
c-
and
X
;
can
we
Eections
in
eitner
usi'^iQ
unconstrained.
(X-9)
see that
we
cerived
•-
or
t>
eEtitr,
Given these estimates,
cne -from the eTt'ect
and
we
decide
We
>.
by using
can
ci
\
,
the
one -from
capital
the past
oi
(>»)
imposes sn
7
identities
just
9
and
2
ate £e;'arateiy
the previous sections construct two estimates
-frofri
investment to sales,
d+
e st men t
constrained
Esuation
equation
and
(Xo)
c:
(S,
returning to equation
Fin ally,
(S)
li
c e d
-forms
estimated by
is
(3)
r e d
:t,
reported in tables
B.re
and
e s 1
,T!U,ti
1
a;:
;
E
and
i
1
-
'r:el
a t
i
hood
Table
9.
structural
ed
*
*
oat
The -esults
.
reports the cce-^-ficients
B
constrained reduced torm and repeats Tor coixpa-'ison the coe-f-ficients
unconstrained reduced
already reported
-form
table
in
estimation
o-f
2.
Table
o-f
the
the
o-f
gives the values
^'
o-f
o-f
thestructuralpara meters.
we
tf;o
start
test statistics.
where ail
ine
table
i-jith
c oe
-f
-f
second one,
i
:
i
The -first one,
it
p
Dse
d
by the
the data.
-for
on
ent s
s h
i
-form,
structural
iTi
equation
ode
Other things equal,
the structural
pmen t s
LI,
tests the constrainsd model
are
es ua
tests tne -onstraineo
l.^,
unconstrained reduced
:
addition to tne coe-f-ficients, it gives the values ot
In
S.
iTi
ode
1
1
on
i
5
)
m,
;
1
to
zero
1,
equation
s h
Ks
;
it
t n er e
shows
vb>
-f
r e
against
t h er e
t
o
i-
e
a
iTiOdel
whether
agsinst tne
whether the constraints
the distributed lag on shipments are rejected by
high values
o-f
LI
and
low values
o-f
L2
are good news
7 a b
"i
£
e
Zorstr fjn e d an d
.
i;
sec: cr
FO
(
-
c
-0
03
03
ij
-0
IB
_
PET
L
-0
u
-
-
-0
26
11
'I
-0
-0
11
-0
u
-0. 00
3
c
SC5
PH
FK
-0. 03
r
-0 04
u
-0. Od
c
-0
V
-
B
•
.
1
Li
-0. w3
'-gdiiccd
5(-4)
-forn-is
5(-5)
Ci r.
ct
7
11
i
C
C
5*
4
1
3
-
9
4
B
n £ d
-
LI
S(-
1
,
1
-1
_ g
-
1
-
-
5
ij
7
n
_ n
1
/
1
^
1
i
ri
4
2
B
T
7
()
'^
1
c*
1
4
9
()
B
1
3.6
2.e
"l
--
^
A
- A
1
-0
_
—3
5
-3
2
^
1
1
1
.
('
**
_n
=^4
2
10.5*
95
~
-1
59
6
90
3
79
7
32
%^
-0
-0
-0
-0
91
34,6**
B.l
14. B**
1,
12.0**
1.5
13.0**
9
C7
1
9
n
1
5
-0
-0
'^
p
c
c
-0
_A
i
(';
^
-0
/
-0
T^
!.j**
3
lo.o*'*
•-1
f-.,
^
B*
^*
1.2*
1.6S *
!
'
tO.
,
2.5
2
.
9 9
-U
9
.
9£'
6
1959-2 to 197 9-3
t r de
table
r = p = at r d
i c i e n t =
on s h i p m s n t = are
li i
15 distributed X=(3)
L2 is distributed X=(4)
sigrii-ficsnt at the 5'; level
**
rT
4
1
-
1
4.9
1
1
r
7.5*
~
7*
i
9 4
1
1
6
6*
-0
^n
-1
3.4
\
constrained
c
LI"
5
4
3
1
-
4
7
'
1
1
B
-0
-0
•^
1
4
7
.
C)
7
1.'
;
i
-
estiiristion
i
1
6
.
un c Dn =trc
=
J
2
6
-
5
1
)
c
w'
.
"-1
.6
~
7
5
1
:' T'
•
4
J
1
1
1
n
n
t?
J
-C
1
1
2
1
1
-0
n
r
J
.
c
1
6*
.
I")
•->
^
0. 9
1
•
3
0*
-0
c-
c-
-B
•0.1
Pericd
/
-1
O
4
00
-
4
1
n
-
-0.
-0.
^
_ n
5.5*
5.2
u
-
1
n
-0
n
J
4
5
u
Mv
(--/
(.
C;
6
_.'.
r,
n
7
-0
-0
11
u
c
EM
5(-:)
1
-1
3
:i
(i
C'
u
NEM
'
"*
-1
6
1
-0 IB
-0 31
u
RU
-0
1
u
CH
r
'^
15
c
PA
5(-l
)
neC
:
LI
TX
1
ur.zcr' it'' ai
-f
it:
t
c.
1 i
ed
by
10"
LI
;
:
leant at
=
trie
1
/
1
1
3**
1
*
19
the values
-first
ExaiTiining
model
the structural
Overall
sectors.
Looking at LI,
level)
model
a
Looidng
the
at
level
1"/
shipments in
-for
in
6
out
9
imately two thirds
the
o-f
tne
(at
In
sectors
4
the
Z'/.
level,
and
in
3
model
are
them
o-f
(r'n,EM,
the structural
model
is
able in most sectors to generate
-flat,
a
or
success-ful
o-ften
at
NEM in particular).
(SCG,
slightly hump shaped distributed
Being able to replicate approximatrly the reduced -form is only good news
underlying estimated structural parameters
L
e
>:
The
structure.
lag
n5
1
p=n c
-from
1
r
!
Q
L
Apart -from
and u.
ao
5'/.
shipments does not help predict
replicating the unconstrained distributed lag structure
is
the
of
.
Turning to the coe-fticients,
model
sectors.
13
imposed by the structural
the sectors at
o-f
tonowing conclusions.
signi-ficantly outper-fcrms
lag on
the restrictions
L2,
at
appro;,
in
the constrained distributed
signii'icantly rejected
MV)
well
per-'orms
the constrained c.odel
with no rcle
(FO,F'A,CH,AC),
investment.
and L2 suggests the
LI
o-f
r
f-
o
=
i
I
a
t
ew
outliers,
the results imply
is
e s t
table
we construct
A,
i
;-
a
t e
s
c
-f
(
X
a)
and
(
e-
).
)
,
and
two estimates or
These are given in table
a
the
:S
relatively
to the available
well
•
From the
sense.
structure implied by
SKpenditLire lag
or
=
I'ake
e
=.
-flat
. 1 ^;
e V
trom table
the cap paracieter
>.
1.
9.
r3
or c er
cualit.
v ^1
i
:
c en c
and
1
e
9
o-f
The -first one,
.
th;
i-f
>-.
is
»
-A
obtained by dividing the estimated
response
o-f
subtracting
the lagged
i
:
X
,
umns
oi
investi-ent
-from
9
capital
f I K
1
p
O
to
(X a)
iaovements in
the estimated
and
by a,
shipiiients.
(9-X),
stock on investment.
and
Xi
is
implies that investment responds within
the gap between desired
and actual
c ac
i
t a
1
a
there-fore derived -from the
The second one,
thereiore obtained
and \z
they are iieasu red at annual
is
&!'s
rates.
Xs,
-from
is
obtained by
the
e-f-fect
o-f
reported in the last two
Thus,
quarter to close
an
a
estimated value
proportion
;
X / 4
o-f
)
of
X,
Table
9
S
.
t
•-
l'
c t ur a
p a > a
1
me
t
er;
A
(a a)
Sector
(
fr
- X
u
L'o
)
72
-0.007
0. 07
TX
023
-0.037
0.
PA
105
-0.077
-0.05
CH
2&
-o.ots
-0.04
125
-0.027
0.03
-0
103**
RU
SCG
0.
PM
F«-
0.
0.027
.
.=
l^"
-0.33
037
-O.OOI
0.20
0.
05o**
-0. 005
.
MV
0.
141**
-0.015
0.
OS
-0.003
0.
00
n -T
to
:ai
d = p r e c i_^ t
X
1
=
(
X
2
=
fi
X
t Dn-
a
-
)
sr:io;-enti
n
i
/
(
rite,
t
r o
it
1
T r
it;
t ab
1
D
=
B3*
56
0.
10
0.
106
0. 05
0.171
0.
0B4
-0. 059
0.111
4
0.
114
0.257
0.0B7
63
0.
110
0.273
0.
5B
0.
104
.
6B
n
0.
119
0.
154
0.
120
41
0.
115
0.34 3
0.
105
0.
45
0.
115
0.i2B
0,
120
27**
(j
45
0.
1 1
7
0.313
0.
105
74**
0.
30
0.
116
090
0.
119
3*
'J
1
22**
v
9
0.
0.
9**
;le
in
A
0.149
4
0.210
53
Ti
0. 07
0, 110
1
1
112
50
i.B*
1
0.117
93*
-1
0.22**
.010
0.300
0.
93**
-0.015
110
31
27**
04 0*
(V
'^.
0.
35*
96**
E«
0.
Q
0.
?*
1
-0.01
0.
-0 42
30**
172*
lAl*
NEM
1.
.
137
120
0.119
1
appendix
K
^-X
)
not convar qed
sipni-ficant at the 5)'. level
New
X
:
FD-
PET
0"
cx-
Raph5un
;
;
DF?
**
:
results
si cni
-f
i
(
n
can
t
standard
it
the
iV.
c e v
i
at
level.
i
ons
reported)
The estiiTiated
vanes between
value
.OB and
appro.'<irittely
5'/.
o-f
average value
o-f
Xs,
X
i
.17.
the
gap
.12
varies between
The avereqe
is
-.C'5
value
c^
and
>i
equal
is
closed within the quarter)
This result is interesting.
.
o-f
motor vehicles
that the
but
e-f-fect
estiamtes there-fore
But,
i-f
costs
o-f
we
:
ha\'e
large value
Xi,
o-f
adjustment were low,
also bs due to the use
\z can
series,
which leads to
the e-ftect
o-f
a
z
that
is
it
Consider {or example the
The structural
o-f
the lagged
o-f
capital
model
adjustment.
stock on
Such is not the case
5ut the result that
proxy lor the correct capital
bias towards zero in
a
)
higher than the
consistent with low costs
this sense investment acpears to overreact to sales.
e;-;cseds
of
that
(sc:
interpretation
investdent should be strongly negative and Xz should be large.
in
is
value
that the sales process is not very persistent
shipments on investment is large.
ot
a
seen
.19
to
and
Dne
captures the notion that investment overreacts to sales.
case
The estimated
.35.
its ccef-ficient,
and
in
Xj
stock
turn to
a
downwards bias in Xs
Section
We
s.
Conclusion
set out to give
s
structural interpretation to the distributed lag relation
between investment and shipments at the 2 digit level. We have learned the
(1)
E^a.T'.ination
Swandaro anc robust
o-f
s.ccs
the reduced
i
s!"
-foriTi
in
section
2
-f
o
i 1
ow
reveals that there
-4czor relation between investment and shiDments at
4-
)-
-
».
i
n
21
substantially acrosB sectors.
e;:
plained by shipments
indeed,
;
sectors,
all
In
in
a
good part
a
cases,
-few
investment is not
0+
there is no signi-ficant e-fiect
ct
shipments on investment.
When shipments a-ftect
investment,
they do so through
long
a
and rather
or
-flat,
humpshaped,distributedlag.
Because the composition
(2)
lag
o-f
capital
is
structures facing each sector are also very similar,
F'etroleum -face
a
mean delivery lag ot
delivery
very similar across sectors,
approximately
delivery lags are there-fore unlikely candidates to
3
e;;
fill
industries except
quarters.
Di-f-ferences
in
plain dif-ferences in the e-f-fects
o-fshipiTientsoninvestmentacrossscctors.
byproduct o^ our work on delivery lags is also to show that they appear
A
pro cyclical.
This suggests
a
n
on- linear spsciiication
investrcent that we do not pursue turther
signi-ficantly in their dsgrss ot
not
tight one,
a
5f T ect
between the
shipments
o-f
on
i
n
'/
= = t
d = g
ci
'-
5n t
5=
this paper.
in
This
.
persistence.
persistence
o-f
shipments on
0^
e-f-fect
The processes
Shipments -follow very di-f-ferent processes across sectors.
(3)
di-f-fer
the
o-f
suc c es
t s
o-f
There is
sh
i
p
iT:
relation, althcugh
a
the
and
en t s
s
i
:
e
t n
t
that the distributed lag in the
investment equation depends on the characteristics
o-f
the sales process
in
a
way
which is at least qualitatively consistent with the theory.
The results or
(4)
the -fella wing r.odel
data.
imply
Fifiiis
:
(
1
)
they take all
the gap between
o-f
the structural
can generate roughly the
face delivery lags of
consideration when
a
estimation
future
3
e
;;
quarters.
p e c t ed
model
constant rate between the time
of
capital
dt oer
-found
in
They also face adjustment costs,
sales,
with
d
i
sc cunt
;
the time of
factor
and
stock each quarter.
and
suggest that
5
distributed lag structure
constructing the desired capital stock
desired and actual
section
in
i
2
)
.
9
,
the
which
into
they close
5
"i
of
They pay for orders at
delivery.
while this
(j)
the data,
in
•found
can generate the
(Tiodel
the ability
long,
the structural
o-f
plausible explanations to di-f-fecences across secto'-s
poorly
some sectors.
in
It
adjustment and in order expenditure lags.
these costs
adjustment,
c-f
limited.
is
ind
The model
such as di-f-ferences in sales processes.
attributes these dit-ferences
it
each sectc"
to
lag
give
per -forms
does not attribute di-f-ferences in distributed lacs across
sectors to any single main cause,
particular,
tit
to
inodel
dist'-ibuted
huT:p-£hapeij,
or
I'lat
it
part to di-f-ferences in both costs oi
in
Although we do not have direct e\'idence on
clear why -especially given that capital
not
is
In
composition and delivery laps are so similar across sectors- costs
o-f
adjustment or
order-expenditure lacs should
It
would be
siitistantially across sectors.
di-fi'er
interesting to examine -formally how much
the di-f-ferences across sectors could be
o-f
explained by di-f-ferences in any one element,
tor example di-f-ferences in
processes with identical
a
sectors.
:
=
We set
rimat6s
z
o-f
he
up
estimation
q aD
t r o
m
response
e -f
investment to the
the response to
bias -from the presence
is
t
i
across
shipment ratio)
capital
n
o-f
o-f
the structural
c-f
parameter.
obtained
Ver r e ac
to
(up
nave not done it yet.
We
Kb)
technologies
shipment
A
sh
1
i
p
c
omo ar
i
";
e n t s
ot t =n
a c c ed
son
capital
errors in variables
investment to shipments.
-for
us
to
;
as
to
get two separate
these estimates shows the
e ;; c e e d s
st
so
oc
ic
i-f
.
the one obtained
The result may be
not,
it
and the
di-f
e
r
r om
; ;
p
su g g = st
i
ve
,
Terence between the
push it too strongly.
= st
1
a
i
i"
a
"he
i
n =d
by
may indicate an
While this result is
too crude and ignores too many -factors,
estimates o-ften too small
c-f
model
our model
tt-jo
Al
Apcend
I.
1
X
A
Data Sources
For the construction
o-f
quarterly,
manu-facturing
-for
industries, constant 197 2
Irom the Bureau oi Econoffiic Analysis
1,
Manufacturers'
[23
(T.anu-facturing
current
Statistics
195B-1
irom the Bureau
-for
shipments, monthly, 3- digit
19B0-12,
to
-from
the Bureau
o-f
delivery lag structures
and
ates
ot'
Labor
;
New structures and equipment by using industries,
[4]
iTi
C)
(tape)
For the construction
L i
198 -12,
to
-for
(tape)
1972=100,
canufacturing,
1947-1 to 19E2-
(tape)
1?5B-1
s,
Implicit price detlators
[3]
J,
inventories and orders, monthly,
shipments,
industries,
the Census M3-1-10
o-f
seasonally adjusted,
Plant and equip rrient e;<penditure5,
[1]
es
investment, orders and shipments time seri
ii
s t h
odo
I
og y
,
Bureau
Econ o
o-f
(Ti
i
c
19 72,
detailed
Analysis publication 035,
39pte(r;berl9B0
Capital
[53
Bus
i
n e£ 5
[63
Sept ember
,
Capital
Department
[73
-flow
o-f
1
tables
975
an d
1967 and
-for
J
u
3
y
stock estimates
Labor,
Survey
or
Current
9B
-for
Bulletin 2034,
Census of Manufacturers,
Statistics
1
1972,
I/O industries
:
methods and data,
1979
1977,
Volumes
II
and
III,
Industry
A2
Construction Reports, Department
[B]
70,
3-75,
12-70,
2.
12-7E,
B-79,
B-BO,
(1
B-El)
Data Construction
I/O codes
SIC and
o-f
the sectors
lie
code
I/D code
Food
(FO)
14
Textiles
(TX)
16,17,19
Raper
(PA)
2fc
24 ,25
Chemicals
(
CH
2B
27
Petroleum
(PET)
29
31
Rubber
(
Glass
to 30
30
RU
(5CB)
35 36
Priciary metals
(Pn)
37,33
Fabricated Metals
(Ffl)
39 to 42
(NEfi)
^J
to
Electrical Machinery
(EM)
53
to 53
Motor Vehicles
(MV)
AircraTt
(AC)
Stone,
Clay,
Non electrical
Machinery
yiscrepancirs oe-ween eetao.
,
and orders are collected on
an
60
r e n t
:
and
cOiTiputing
c-f
companies class i-fied in
the ratio
o-f
c osd an
a
c o
:"
estabiishEent basis.
sectors other than its main sector
activities
employees
o-f
J
59
371
Investment expenditures ar e collected on
in
various issues
CoiTirerce,
o-f
o-f
a
activity.
civ en
based data
v
p an y
A
basis
;
sh
i
p
;T;
en ts
company Kay operate
InTor;T;aticin
about
sector can be obtained by
these companies working
in
the
sector
A3
to
number
the total
Statistics
the Department
-from
Motor Vehicles
Commerce and aggregating to the
c-f
in
sectors except
all
Employees
the case for
not
is
(59'1}.
IZ'I.
using the Enterprise
these companies,
o-f
'^'
e t r o
1
eum
2
-digit
(67/'.)
and
Motor Vehicles companies not working
in
work however in sectors closely related to Motor Vehicles.
the sector
Such
errip^oyees
This ratio is over
level.
in
o-f
Construction
F'etroleura.
Investment
o-f
series &r
Ins'estment
e
Shipments and Orders
.
directly obtained
-from
[13.
Real
shipments and
orders series are obtained by deflation
of
detlators constructed by aggregation
3-digit de-flators in [33,
o-f
sei^ies
in
[23
by price
and by
time aggregation irom monthly to quarterly and trans-formation to annual
rates.
Construction
the capital
o-f
series tor sectoral
TiiTic
st oc
t;
series
stocks are constructed using the
capital
foilowingaccuiTiulationequaticn;
1-.
1
1
=
where
(
1
~o
)
c-f
K
9t
The series is
stock:
is
the rate
capital
equal
o-f
i
t -
1
'It
*"
the osprsciaticn rats
is
8s
construction
1
to
growth
is
!
described
n cn
iT,
ar
i.
ad
in
so
the mean level
of
iitai
-for
so per
r.
n
1
that the cisan level
o-f
stock value is used in table
as the
sector
h =
V
o-f
the capita]
investment expenditures divided by
investment plus the rate
capital /shipments ratio,
ot
1
to
of
depreciation. This mean
compute the me an
ratio of mean capital
to mean
shipments.
A4
This crude computation
the mean
o-f
level
capital
ot
to
ratios using alternative establishment based measures
as
those given in
[6]>
Columns
our estimated r;ean capital
and
A
5
o-f
the results are not strictly comparable).
B
!Ti
be re
=p =
ctis'
rate
o-f
i
=
type
a
ly the
nv= st
given year,
o-f
capital
iTi
en t
o-f
equ
i
p
j
C!
i
o-f
capital
di-f-fer
shipments
slightly and
The main discrepancy
is
i
-
and
ent
the level
=
Ki
Kij
=
(l^gij)Kij(-l)
or
a
(i-9i j}Ki
J
above.
the rate
Let
o-f
type
o-f
S
i j
growth
j
,
g
i
o-f
j
,
I i
j
,
K
capital,
sector
in
which
good,
i
.
i
Kij/Ki
)
(1-gi j)/ (Qi j-^Si j)
It
J
For
:
/EEHl^gi j)/(gi+9j)
)
li j3
j
This is the -forinula we use to cocipute capital
CDiripLite
t a
!;
e
the
the composition
aver aae
-for
two di-fT=rent years,
composition.
1967 and
j
th
(-1)
:
(
capital
o-f
structure.
capital
o-f
The above identities imply
=
or
on
the -following two identities hold
J
such
below give respectively
A
denote the type
depreciation rate,
J
Ii
co.T^posi t
denote the sector,
be either
ay
capital,
of
Delivery lacs
.
Lonstruction
i
CDCipa'^ed
due to the establishment/company discrepancy discussed
Appendix
Let
be
ratio and the mean capital
shipir.ents
ratio implied by [6](The two de-finitions
F'etrcleum,
table
can
We
1972 and then
a
Ijj
Rates
growth gij are assumed,
O'f
types
across all
Qij
are obtained by aggregation
Data for
are computed,
be
independent
the sector
o-f
equipment, 8ij
6j
=
all
-for
-for
given sector,
a
each sector
-for
lives
table
(table
Rates
depreciation
c-f
-for
in
i.
each type
o-f
o-f
table
A.
3
These are
equipment are assumed to
Depreciation rates
Aj
are then
-for
Thus,
-for
each type
Lj,
-from
o-f
IRS Bulletin
o-f
structures are allowed to di-fter across
o-f
lol
in
1
constructed as 2/Lj.
o-f
structures
are computed using structure composition -from
structure rrom table
only two \'alues ot
i,
which eouipment is used.
destination. Average lives
o-f
the same
be
These average lives are given in column
.
Depreciation rates
A.
sectors
ibl)
in
3
to
structures.
capital equipment are obtained -from average lives,
F
tables [5].
-'low
measures ^rom ttl.
depreciation Ojj
o-f
or
equipment and one
one tor
computed using net capital
Rates
Thus
ecuiDment.
o-f
i
capital
ot
.
[4]
-for
and
each sector,
lives by type
Li,
o-f
These average lives are given in column
2
Depreciation rates are computed as 2/Li
The implied sectoral
capital
compositions are reported
in
table
3
in
the text.
Finally,
time series
Si
=
L
the sector
-for
!
K
1
capital
j7 K
i
)
e
speci-fic
in
depreciation rates used to compute the
each sector,
ftj,
are computed as
;
i J
J
The constructed deoreciation rates are aiven in column
Constr u c t
i
on
o-f
d =
1 i
verv
lacs by
t
!-f
oood
3
o-r
table
A.
Deliver',
I&gs are computed using
are respectively unfilled
the fDrmuia V',/(l-bi)Si,
orders,
shipments and the proportion
bi
and Ei
o-f
shipments sold to wholesalers and retailers.
t'roiTi
the
values
[7]
for
1977 and bi
ti
ar e
A 6
of
7.
for FM,
is
A
2'/.
V,
N'EM
and
Ak'/.
are obtained
and Si
obtained from table 13a
for
for
Ett.
in
[7].
The
delivery lags can be compared to estimates by the Department
(Survey of
Current Business,
are very similar.
July 1975)
where Vj,
using
a
The
implied
of
Cociraerce
different approach
;
they
Footnotes
Even
1.
i-f
we
tal-e
given that
as
possible candidates, production,
depends on demand,
investirient
orders and sales
leaves orders or shipments.
the technology is
a
technology is
starts upon receipt
hers
technology
"re-feree report"
orders,
o-f
Because
in
that the cost
leaving
IT
capital
o-f
out
it
mo
is
a
Not
knowing what
believe that the relation
we
c e
i
,
t n ey
th:
n V e >;
-f
-f
ec t s
(see Blanc hard
investment, but our reading
c ar a
r.
depend on
;
t
V
o
t n
t n e
t
obtained
e t er s
cost
t
ur
h
:
n
1
believe
we
;
empirical
c h
t n
e
T
an
rm
1
i
is
work:
the standard quadratic cost
-from
r!
o-f
(19 So))
-from
sales substantially.
unlik:ely to bias the coe-f-ficients on
are the
an
c"
u51ment
^^,11
the
I-f
only report results using shipments
we
shipments to investment is indeed largely causal
.1
which orders are shelved until
have done estimation both using shipments and
we
To state more explicitly our position,
that
I-f
which production takes time and production
space constraints,
o-f
This
results using orders are not qualitatively di-f-ferent.
;
2.
in
orders are more appropriate.
technology is more appropriate,
using orders.
high Quality.
o-f
Which one is appropriate depends on the technology,
"pipeline" technology,
a
reduction data must
requirements are more closely related to shipments.
capital
processed,
4.
F'
constructed using Hnished goods inventory data and are not
be
a
(shipments).
there are three
d
= * =
•
c
-f
s ccu n t s
^T
i
d j u£t men t
.
They are
iws
Jorge n 5 on and Stephenson
ordering
o-f
capital
(1967)
the rirst arrival
and
Tor di-f-ferent delivery lags.
However,
heterogenous.
)
empirical
E'
spec:
e e
-f
:
Lucas
cat i on
also assume that
(
.
1
9c5
-for
a
o-f
capital.
n
An
periods elapse between the
sk
tension would be to allow
doing so is interesting only
discussion.
This leads to too
capital
It
c o
r,
p
1
e
;;
an
is
5
Th=
mcdei
to
use
(S-,
counterpart
the
in
is
This
(X
a p p r
annual
at
/4)
o-f
,;
i
it^
a
ma
t
e
1
1
an
by
n
That
hR
tor
It
:
nVss t
o-f
r;
we
Bnt
(
1
a
)
appears in the
o-f
:
r,
1
to
.'
(
,
e s su
:t,
2=c ause
we
t
in
,
e
c
not
or
e
u
1'
i
a
va
f
t't-i
c-f
om
the
as
an
5
"
r u; t u" c
e(r,pirical
b s er v ab
wed
by
the disturbance
o
1
1
i
e
1
"^
.
h e
ether
t
er
iti
.
capital
annual
to
X
shipiiients,
investment will
,
desired and actual
also eK pressed
is
>,
close during
a
quarter
This is why the number
capital.
4
te;;t.
level
-for
-f
u n
(see
tor
e;;
is
tact consistent with previous
in
ample re-ferences in the surveys by Jorgenson
These studies usually report the
ed
q ci n g
which is
-f
In
;;
a
ir,
p
1
e
e
I
en 1
1
y
that
s
c.
:Ti
r e
r =
i
the
c-f
always exceeds .9.
e
Lecn1
s'
correction tor
e
it
orc er s
an t
variables,
the original
on
capital
o-f
the technology to be
any explicit
1;
R=^
case tcr e;;ac:ple,
our
recognized explicitly the heterogeneity
partly to stock,
-from
'
which initially surprised us,
L)ri(19B2)).
and
" f
5.
capital, the longest delivery lag would be
T" .
^
process
the
-f
t
One 13 the use
roe.
(
{act
=
given value
a
which is obviously such higher.
B.
^.
Section
in
is,
studies at the sectoral
and
ire
i
the di-f-ference between
1
due to
is
"
denotes the ratio
o
This result,
(1971)
i
discussed
rates.
rather than
7.
?-
variable implied by
the
t c
Because
6.
a^ p " o
two appro,: iciati en
-iurther
IS
"
-f
1
e
than the
t n e
-
are
s at
ot
the various types
in
-f
sodel
our
in
iT:
e sn
lag.
i:
i
st
i
e d
without lag
the snei-f, the estiiiiated mean lag is i^ucn shorter than the estimated delivery
lag constructed
10.
earlier.
This joint assurrption ispiies that investr^ent should not help predicz sales
given past sales and is thus testable.
level,
and in two
(Pet rol euci
,
the results below are biased,
Aircratt)
r
cr
It
at
is
rejected
the
1'/.
in
level.
the other ten sectors,
three sectors at the
Thus,
-for
5"/.
these two sectors,
the assuniptiDn
in
the
te;-;t
We
11.
have else ccne estimation assuring
di-f-ferences
13.
and n=5
'r
Fetrcieuii,
(6)
and
(B)
siiriultaneously,
we
its estimated counterpart.
estimation
is
linear but is less asymptotically e-f-ficient.
in
The
The diT-ficulty
o-f
estimate
estimating precisely the discount rate
in
that ts-De
c-f
estimation has c-ften been documented.
I
^
.
The likelihood
convergence.
matrix
o-f
-function
Newton-Raphson
the estimated
is
is
maxi::.
i:ed
using
tnen used to obtain
parameters.
('6)
This procedure is mucn cheaper as
by
A
.
-first
(B)
replace
the -first
=4
substantial.
rather than estitriating
Thus,
12.
and
are not
n
D=
vidon-Fletcher-?^owe;l
in
estimate
o-f
the
until
cox'ariance
Re-fere nces
Olivier
Blanc hard,
Economic Activity
J
JoLirnal
"Econometric Studies
1971,
9-4,
,
December,
Jorgenson, Dale and James Stephenson,
Behavior in United States flanu-facturing,
Statistics,
Lucas,
49-1,
1965,
i
Ver£
i
t
Uri,
y
cf
!^;
Noel,
i
nn E5
19c2,
1
a
FrE
.
'^'apers
on
Investment Behavior
6
:
A
Survey",
1111-1147
"The Time Structure ot
1967,
1947-1960",
Review
o-f
Investment
Economics and
Investment Policy",
EKcectaticns and Economic Folicv
,
in
Robe'-t
Veil,
s s
"Testing
Economics and Statistics
o-f
"Distributed Lags and uptimal
Luc£5 and Thomas Sargent ecs. Rational
Un
kings
16-27
February,
Robert,
P'-qo
-forthcoming
Economic Lit t era ture
o-f
Comment on Matthew Shapiro,
19 86,
i9B6-l,
,
Dale,
or gen son,
,
-4
-
1
-for
,
Stability
February,
o-f
the
117-125
Investment Function", Review
4953 08
I
If
Date Due
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AUG.
2
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i
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1
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