Economic Growth and the Verdoorn Law--A Comment on Mr Rowthorn's Article Author(s): Nicholas Kaldor Source: The Economic Journal, Vol. 85, No. 340 (Dec., 1975), pp. 891-896 Published by: Blackwell Publishing for the Royal Economic Society Stable URL: http://www.jstor.org/stable/2230633 . Accessed: 24/08/2011 07:33 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Blackwell Publishing andRoyal Economic Society are collaborating with JSTOR to digitize, preserve and extend access to The Economic Journal. http://www.jstor.org
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: Blackwell Publishing for the Royal Economic SocietyStable URL: http://www.jstor.org/stable/2230633 .
Accessed: 24/08/2011 07:33
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact [email protected].
Blackwell Publishing and Royal Economic Society are collaborating with JSTOR to digitize, preserve and
In an article in the March I975 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 I6, 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 tofind empirical support for the Verdoorn Law, which is usually written in the
formp =
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, orwhether 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-I92 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,
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 theregression 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 R2swere 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 asfollows: 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 differencef 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 oppositesign - in the
productivity series, thereby generating a spurious negative correlation betweenp and e.
It follows that the existence of statistically significant relationships between
p and q and e and q does notcarry 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, whilethe 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), orvice versa; but whereas a significant relationship between e and q (with o < a < i) automaticallyensures that equation (i) (the "Verdoorn equation") is also significant, this is not true the other wayround - not unless one also specifies that the coefficient ,Bin that equation is significantly less than i,
which has not hitherto been regarded as an integral property of the Verdoorn Law.
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 significantlydifferent 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 ornihilistic 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 isa positive association between productivity and employment in manufacturing, produced a correlationin 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 inany case dubious. If my above argument is correct this was not necessaryor supporting the hypothesisthat increasing returns prevail in manufacturing. For that they had very much stronger evidence for the1950-65 period in terms of the nature of the correlation between e and q from which the relationshipbetween p and q automatically follows. For the I965-70 period, on the other hand, they found nosignificant 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 accountinter-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 KingdomI regarded e as exogenous. However this is irrelevant, since the regression equations of e on q and p onq 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 yearsago, 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 (EconomicSurveyof Europe... (I969), p. 78), UNCTAD, Cripps and Tarling, etc., and I am sure that it holds equally forGomulka'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 coefficientis significantly less than unity (implying that for growth rates exceeding 3 % a year, industrial production
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 intwo 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) fouindthat 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.:
Elevencountries, xcluding apan
I950-65:
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 I24) (0 I35)
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.
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 isdemand-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 hadattained 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 ratherthan 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
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 Kingdomin relation to other industrially advanced countries.1
NICHOLAS KALDOR
King's College
Cambridge
Date of receiptqf 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 explainhow the higher productivity growth rates could have continued after the productivity levels of thediffusees came to surpass those of the diffusants.
