(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 ]







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.







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







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.







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.)







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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(Kaldor) Crecimiento Económico y La Ley de Verdoon

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