(kaldor) crecimiento económico y la ley de verdoon
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7/23/2019 (Kaldor) Crecimiento Económico y La Ley de Verdoon
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Economic Growth and the Verdoorn Law--A Comment on Mr Rowthorn's Article
Author(s): Nicholas KaldorSource: The Economic Journal, Vol. 85, No. 340 (Dec., 1975), pp. 891-896Published by: Wiley on behalf of the Royal Economic SocietyStable URL: http://www.jstor.org/stable/2230633 .
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The Economic ournal, 85 (December
975),
89I896
Printed n GreatBritain
ECONOMIC
GROWTH
AND THE VERDOORN
LAW-
A COMMENT ON MR ROWTHORN'S ARTICLE
In an article in the March
I
975 issue
of this JOURNAL'
Mr Rowthorn chargesme
with using an unusual method
to test the relationship
between produc-
tivity growth
and employment growth and asserts that
if I had used
a more
direct method,
the results could not have been obtained,
except perhaps
for
a
particular period,
and for a particular sample of
twelve countries which
included Japan.
This criticism
is based partly on
misunderstanding and partly on misrepresen-
tation.
The misunderstanding is perhaps
an excusable one
for someone who had
apparently
read my Inaugural Lecture2 but not the
subsequent papers,3
for
the
manner
of
exposition adopted in
the lecture left something to
be
desired.
Moreover what
Rowthorn (and
others)
have taken to
be the
main
message
of
that
lecture
-
that the
slow
rate
of
economic growth
of
the
United
Kingdom
was
mainly due
to
the shortage of
labour resulting from economic
maturity
-
is one which
I
have since abandoned as a result of fresh
statistical evidence,
as
well
as
further
historical
experience. This
answer to
Rowthorn's criticism
provides an opportunity
to state my present views on these issues.
It
is
best to
start
by dealing
with the misrepresentation
first.
This lies
in
his
assertion that
I
derived
an
implicit estimator
of
the relationship
of
productivity to employment
from a
regression of productivity
on output, using
for the
purpose
the
formula
which
he
gives
at
the
foot of
page
I
6,
after
having
transformed algebraically
the
regression
coefficient
of
productivity
on
output
into a coefficient
of employment on output. This is totally
untrue.
From
the point
of view of
my analysis,
however,
it is
also irrelevant.
I was not
concerned with estimating the regression of p on e as such. I was concerned to
find empirical
support
for
the Verdoorn
Law,
which is
usually written
in
the
form
p
=
xa+,fq,
with
/>0, (I)
but which
I
preferred
to write in the form
e_
y+aq,
with
o <
a
< I,
(2)
because
I
regarded,
and still regard, the existence of
a significant relationship
between
the growth
of employment and output as the
main test for deciding
whether the Verdoorn Law asserts something significant about reality, or
whether it
is a simple statistical mirage. Clearly, since
by definition
P-q-e
1
What remains of Kaldor's Law?
ECONOMICJOURNAL,
March
I975,
PP.
IO-I9
2
Causesof the Slow EconomicGrowth f the UnitedKingdom Cambridge University Press, I966).
3
Cf.
in
particular my Reply to the criticism of my inaugural lecture
by J. N. Wolfe, in Economica,
November I968,
PP.
385-9
I
[ 89I ]
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892 THE
ECONOMIC JOURNAL [DECEMBER
in any
situation in which e
is either zero or a constant
there mustbe a perfect cor-
relation
between p and q
-
but one
which does not assert anything,
since it is the
automatic consequence of
measuring
the same thing twice over.'
In this
way I found that in at least
two sectors,
Agriculture and Commerce,
the Verdoorn equation did not produce meaningful results. In each case the
regression
coefficient of p
on q was around
I,
with
R2s between o-8 and
og9,
and t values of
7-IO;
but the
corresponding relationship of e on q
produced
R2s
of
ooI-o o4,
with t
values of
1-1
On
the
other hand
in
manufacturing, where the
regression coefficients
for
both p on q
and e on q were around
o
5,
the
R2s
were very similar
(o-826
in
the
one case
and
o
844
in
the
other) and the t values of
the
coefficients were
as
high
as
7
in
both cases.
These findings were not
dependent
on the
inclusion
ofJapan
in
the
sample. IfJapan is
excluded from the sample, the
results for the
remaining
I I
countries (based on the data shown in table
2,
p.
I2,
of my Lecture) are as
follows:
p
=
IP359 +o 4I7q,
R2 =
o0536,
(O*
I
29)
e
=
-I'33I
+o574q,
R2
=
o-685.
(0 I
30)
The
exclusion ofJapan reduces the
closeness of the fit (and also the
numerical
value
of
the
Verdoorn coefficient, from
o
5
to 0.4) but the results,
in
terms
of
t
values
and R2s, are
still
sufficiently good to
convey something significant.
The
coefficient of e on q
has a t value of over 4, and is
significantly
smaller than
I, by the
test of the t value related to
the
difference
f
the coefficient from unity.
On
the other hand
I
nowhere suggested
in
my
lecture that
a
statistically
significant
positive correlation between p
and e is
a
necessary est of the Verdoorn
Law. The reason for this
was a simple one. Since I
regarded
output
as
being
in
general
the exogenous variable
(determined by
demand) any error or dis-
turbance
would be
associated with the
employment term; and
all such
dis-
turbances
would
automatically
be
reflected
-
with
the
opposite
sign
-
in
the
productivity series, thereby generating a spurious negative correlation between
p and
e.
It follows that the
existence of
statistically significant relationships
between
p and q and
e
and q
does
not
carry
with it that the
relationship
between
p
and
e is
also
statistically significant. The latter
may happen,
if
the
relationship between
e
and q gives
a
sufficiently close fit, but it
would not hold
if
the latter
relationship
is
not close
enough. There is nothing
very surprising therefore in the
fact that
it
is
only by
including Japan
that the regression
equation between
p
and
e
(as
calculated
by Rowthorn)
is
statistically significant; even
so,
the
R2
in
the latter
equation is only
o0447
as against o-844 on the basic equation of e on q, while
the
t value of
the
regression
coefficient is
less
than
3
(as against
over
7
in
the
basic
equation).
1
Rowthorn
is
correct
in
saying
that the coefficients
of
(2)
can
be
algebraically derived from (i),
or
vice
versa;
but
whereas
a
significant
relationship
between e
and
q (with
o
<
a < i)
automatically
ensures that
equation (i)
(the
Verdoorn
equation )
is
also
significant,
this is
not
true the
other
way
round
-
not
unless one also
specifies
that
the
coefficient
,B
in
that
equation
is
significantly
less than i,
which has not
hitherto been
regarded
as an
integral
property
of the
Verdoorn
Law.
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1975] ECONOMIC
GROWTH AND THE VERDOORN
LAW
893
I conclude therefore that a sufficientcondition for the presence of static or
dynamic economies of scale
is
the existence of a statistically significant
relation-
ship between e and q, with a regression coefficient which is significantly
less than I.1
If this condition is not satisfied, there are several possibilities. First, that there
is a significant relationship, but the coefficient of e on q is either not significantly
different from unity or is significantly greater than unity. This
latter case
is
sufficient to reject the increasing-returns-to-scale hypothesis.
Second,
that
there
is
no
significant relationship between e
and q at
all
-
and
this
is
consistent
with all
kinds of interpretations.
It
is
in
this second
sense
that
the Verdoorn Law can be
said
to
have
broken down
in
the period
I965-70.
Rowthorn's equations and scatter diagrams (taken from Gomulka)
relate
entirely
to the
relationship
between
p
and
e, and we
are
not
told whether
the
underlying relationships between e and q are of a neo-classical kind (with
employment varying in a
I
for
I
relationship with output), or the anarchical or
nihilistic kind (with employment being unrelated to output),
or of the type
described
on
page 892
above.
One interpretation
of
the Gomulka-Rowthorn theory is that
the rate
of
growth
of
employment
in
manufacturing is exogenously determined,
indepen-
dently
of
demand.2
In
that
case (but only
in
that case) his strictures
concerning
Kaldor's law would be pertinent.3 But my whole thesis, originating from
the remarkable
correlation between the growth of
GDP and
the growth
of
manufacturing output,4 amounted to a denial of this position; I asserted that
the
hhouir ahbsorhed
in
mrniifhctiirincr
in
the
coiirse
of
indnstri1ialtion
does
It was certainly unfortunate that Cripps and
Tarling, in dealing with my hypothesis that there is
a positive association between productivity and
employment
in
manufacturing, produced
a
correlation
in
support of
it
between p and e, the validity of which depended (apparently without their realising it)
on a
single extreme observation, Japan, and the significance of which (given the low value of R2) was in
any case dubious. If my above argument is correct this
was not necessaryor supporting the hypothesis
that increasing returns prevail in manufacturing. For that they had very much stronger evidence for the
1950-65
period
in
terms of the nature of the correlation between e and q from which the
relationship
between p and q automatically follows. For the I965-70
period, on the other hand, they found no
significant relationship between e and q and hence no
statistical support for the Verdoorn Law. (Cf.
T.
F. Cripps and R. J. Tarling, Growth n AdvancedCapitalist Economies,
950-1970,
D.A.E. Occasional
Paper, no. 40, Cambridge University Press,
1973).
2
This
would be the case, for example,
if
one
assumed (a) that the total labour force effectively
employed grows at an exogenous rate; (b) the proportion
of the labour force available to the manufac-
turing sector is given. Both these assumptions are
patently untenable, especially if we take into account
inter-regional and inter-national migration of labour (which can be shown to have been largely demand-
induced) as well as the very large changes (over time)
in the inter-sectoral distribution of the labour
force
of
any particular region.
3
It
could be argued that since in the lecture I regarded U.K. manufacturing output as being con-
strained by labour shortage, this is tantamount to
saying
that in the case of the United
Kingdom
I
regarded e as exogenous. However this is irrelevant,
since
the
regression equations
of
e
on
q and p on
q were derived from a sample of countries for which e (i.e. the rate of growth of employment in manu-
facturing industry) was
not
exogenously given.
4
Since readers could hardly be expected to remember this equation, published more than
I0
years
ago,
it is
worth reproducing
it here
(using
the notation
adopted in the Cripps-Tarling
paper):
qGDP
=
II53+0 6I4qMF,
R2
=
0-959.
(o o8o)
This
relationship has since been confirmed by other
investigators such
as
the
ECE
(EconomicSurvey
of Europe...
(I969), p.
78), UNCTAD, Cripps and Tarling, etc.,
and
I am
sure
that it
holds
equally
for
Gomulka's
sample
of
39
countries as
for my sample
of
I2
countries;
and
that
it
holds for the
I965-70
period, as well as earlier periods. An important property of
the equation
is
that
the
regression coefficient
is
significantly
less than
unity (implying that for growth
rates exceeding 3 %
a
year, industrial production
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894
THE ECONOMIC
JOURNAL
[DECEMBER
not diminish production
in
the
rest
of
the
economy, owing
to the
existence
of
surplus
labour
in agriculture (and also, though
I
did
not
say
so
explicitly,
in
services)
which is
only eliminated
at
a
late stage
of
industrial
development,
at the
stage
of
economic
maturity .
This view has been strikingly confirmed by Cripps and Tarling's findings in
two
remarkable
correlations
(not
mentioned
by
Rowthorn)
which
explain
the
overall
productivity
growth
of the
economy
(the rate of growth
of
GDP per
head)
in terms
of the
rate
of growth
of
industrial
output
and
the (relative)
diminution
of
non-industrial
employment.
This
relationship
has
in
no
way
been
impaired
by
the failure
of
the
Verdoorn
Law
in
manufacturing
in the
post- I965
period;
indeed
the
correlation
coefficient
is
even
higher
for the
I965-70
period
than for
the I950-65
period.
The two
equations
are:
I950-65:
PGDP
=
PI
72
+o0534qlND-
o8I2eNJ,
R2
=
o805,
(oo58)
(0o202)
I965-70:
PGDI
=
I
I53+0
642qlND-o872eNI,
R2
=
0958,
(oo058)
(O-
I
25)
where
PGDI1,,
qIND,
eNI stand
for the
rate
of growth
of
GDP per
employed
person,
the
rate
of
growth
of
industrial
production
and
the rate
of growth
of
non-
industrial
employment
respectively.'
The important thing to note is - and herein lies Rowthorn's misunderstanding
-
that the existence
of
increasing
returns
to scale
in
industry
(the
Verdoorn
Law)
is not a
necessary
or indispensable
element
in
the interpretation
of these
equations.
Even
if industrial
output
obeyed
the
law
of constant
returns,
it could
still
be
true
that the
growth
of
industrial
output
was the
governing
factor
in the
overall
rate of
economic
growth
(both
in
terms
of
total output
and
output
per
head)
so
long
as
the growth
of industrial
output
represented
a net
addition
to
the effective
use of resources
and
not just
a
transfer
of resources
from
one use
to another.
This
would
be the
case
if
(a)
the capital
required
for industrial
production
was
(largely
or
wholly)
self-generated
- the accumulation of capital was an aspect,
invariably
rises
faster
than
the GDP
as a whole);
the standard
error
is
very
small-t
= I
5
in
the
above
equation;
Cripps
and Tarling
(p.
22)
fouind
that t
=
20
in
a
corresponding
equation
for a
bundle
of
43
observations-and
as
I have
shown
in the
Appendix
to
my lecture,
the
equation
owes
nothing
to
auto-correlation
since
the
structure
and
the
coefficient
of
the
equation
remain
much
the same
if
manufacturing
is
excluded
from
the
GDP on
the LHS
of
the
equation.
I
Cf.
Cripps
and
Tarling, Op.
it.
p. 30. To see how
far
(if
at
all)
these
equations
would
be affected
by
the
exclusion
of Japan,
I asked
Roger Tarling
to re-compute
the
two
regressions
by excluding
Japan
from
the
sample.
The
results
are
as
follows.:
Eleven
countries, xcluding
apan
I 950-65:
PGDP
=
I.768+o0369qIND-o
647eNI,
R2 =
o0678,
(o-o63)
(0o
I
7
)
I 965-70:
PGDP
=
o
8I9+O07IoqIND-o0848eNI,
R2 =
0-930.
(O
I
24)
(0
I
35)
It is interesting
to
note
that
whereas
the
exclusion
ofJapan
somewhat reduces
the fit, and the
explana-
tory
power
of
the
equation
(as
measured
by
R2and
the size of
the
constant)
for the
I95o-65
period,
it
makes
virtually
no
difference
for the
I965-70
period.
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I975]
ECONOMIC
GROWTH
AND THE VERDOORN
LAW
895
or a
by-product,
of the
growth
of output;
and (b)
the labour
engaged in
industry
had
no true
opportunity-cost
outside
industry,
on account
of the
prevalence
of disguised
unemployment
both
in agriculture and services.
There
is plenty
of
direct
evidence
to
substantiate
both
of these
assumptions.
The important implication of these assumptions is that economic growth is
demand-induced,
and not resource-constrained
-
i.e. that
it
is to
be
explained
by
the growth
of
demand
which is
exogenous
to the industrial
sector'
and
not
by
the (exogenously
given)
growth
rates of the
factors
of
production,
labour and
capital,
combined
with
some
(exogenously
given)
technical progress
over
time.
While
in
the
Lecture
I gave
the main
emphasis
to the
Verdoorn
Law
as
an
explanation
for
the
difference
in growth
rates, and
still
believe
in its impor-
tance,
I
would now regard
the existence
of surplus
labour,
and
the
critical
role
of profits
and
profit
expectations
in
capital accumulation
as the
more basic
cause
of the
difference
of view between the neo-classical and Keynesian (or
post-Keynesian)
schools
of thought:
the
question,
that is, whether
one
regards
economic
growth
as
the resultant
of demand
(i.e. the growth
of
markets)
or of
(exogenously
given)
changes
in resource-endowment.
On
the
other
hand, I
now
believe
that
I
was wrong
in
thinking
in
I966
that
the United
Kingdom
had
attained
the stage
of
economic
maturity
(in
the
sense
I
defined
that
term)
and
that
her
comparatively
poor
performance
was
to
be
explained
by inability
to
recruit
sufficient
labour
to
manufacturing
industry rather
than
by
poor
market
performance
due to
lack of
international
competitiveness.
Statistical
studies
that
have
since
come
to light2
make
it
doubtful
whether
I was
correct
in thinking
that
earnings
in the
service
trades
of
the United
Kingdom
had come
to be
fully
competitive
with
earnings
in
manu-
facturing
or that
the growth
of manufacturing
industry
in
the
United
Kingdom
was
constrained by
labour shortages
other
than in
a
purely
short-term
sense
-
e.g.
of not having
sufficient
skilled
labour
in
engineering
to sustain
a rapid
expansion
of
engineering
production
(which
from a long-run
point
of view
is
itself
a consequence
of
a
low
trend
rate
of growth
of
demand).3
But
while
1
In
saying
that
growth
is explained
by
the increase
in demand which
is
exogenous
to
the
growing
sectors
I am conscious
of the fact
that
this statement
in itself is a
simplification
but
one
which
does not
invalidate
the statistical
inferences
derived
from
it. The
growth
of industrial
output for any region
is
governed
in part by
the growth
in
productivity
which
itself influences
demand
through
the
change
in
competitiveness
which
is induced
by it.
It is this
reverse
link which
accounts
for
the
cumulative
and
circular
nature
of growth
processes.
There
is
a
two-way relationship
from
demand
growth
to
productivity
growth
and
from productivity
growth
to
demand
growth;
but
the second relationship
is,
in
my view,
far
less regular
and systematic
than
the first.
2
Sleeper,
R.,
Manpower
Redeployment
and
the Selective
Employment
Tax,
Bulletin of
the
Oxford
University
nstitute
of
Economics
nd
Statistics,
November,
I970.
3
The belief
that the
expansion
of
manufacturing
production
and thus
of
exports
was
hindered
by
the
inelastic supply of labour
to manufacturing
industry undoubtedly
played
a role
in the
introduction
of
Selective
Employment
Tax (as
was explained
in the Government
White
Paper
issued
on
its
introduction).
But
Rowthorn
is
wrong
in thinking
that the
existence
of increasing
returns
in
manufacturing
industry
was
a necessary
part of
its justification.
Given
the fact
that
over
850%
of U.K. exports
were
manufac-
tured
goods,
and that
the U.K.
economy
was threatened
by
a balance-of-payments
crisis due
to
an
insufficiency
of
exports,
the existence
of a
labour shortage
would
have
been
a perfectly adequate
reason
for securing
the release
of labour
from services,
irrespective
of
whether
increasing
returns
or
constant
returns
prevailed
in
industry.
(In the
actual
case,
as events
have shown, the improvement
of
export
performance
needed
a
devaluation,
however,
to
improve
the competitiveness
of British
goods
in
foreign
markets.)
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896 THE
ECONOMIC JOURNAL
[DECEMBER
I975]
I
would now
modify the story concerning the
United Kingdom, such modifica-
tion would
definitely not be in the direction of
Rowthorn, Gomulka
or
the neo-
classicals.
In
particular, I would
now place more, rather than
less, emphasis
on
the
exogenous
components of demand, and in
particular on the role of exports,
in determining the trend rate of productivity growth in the United Kingdom
in relation to
other industrially advanced
countries.1
NICHOLAS KALDOR
King's College
Cambridge
Date of receipt
qf
typescript:April
1975
1
Gomulka's
thesis,
favoured
by
Rowthorn
-
that the more
rapid growth
of
productivity
of late-
corners like Japan was to be explained by the diffusion of technical knowledge - could hardly explain
how the higher
productivity growth rates
could have continued after the
productivity levels of the
diffusees came to
surpass those of the diffusants.
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