kaldor - economic growth and the verdoorn law

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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: Blackwell Publishingfor the Royal Economic SocietyStable URL: http://www.jstor.org/stable/2230633.

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The Economic ournal, 85 (December975), 89I896Printed n GreatBritain

ECONOMIC GROWTH AND THE VERDOORN LAW-A COMMENT ON MR ROWTHORN'S ARTICLE

In an article in the March I975 issue of this JOURNAL' Mr Rowthorn chargesmewith using an unusual method to test the relationship between produc-tivity growth and employment growth and asserts that if I had used a moredirect method, the results could not have been obtained, except perhaps fora particular period, and for a particular sample of twelve countries whichincluded Japan.

This criticism is based partly on misunderstanding and partly on misrepresen-tation.The misunderstanding is perhaps an excusable one for someone who hadapparently read my Inaugural Lecture2 but not the subsequent papers,3 for themanner of exposition adopted in the lecture left something to be desired.Moreover what Rowthorn (and others) have taken to be the main message ofthat lecture - that the slow rate of economic growth of the United Kingdomwas 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, aswell as further historical experience. This answer to Rowthorn's criticismprovides an opportunity to state my present views on these issues.

It is best to start by dealing with the misrepresentation first. This lies inhis assertion that I derived an implicit estimator of the relationship ofproductivity to employment from a regression of productivity on output, usingfor the purpose the formula which he gives at the foot of page I6, after havingtransformed algebraically the regression coefficient of productivity on outputinto 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 notconcerned 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 theform 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 relationshipbetween the growth of employment and output as the main test for decidingwhether the Verdoorn Law asserts something significant about reality, orwhether it is a simple statistical mirage. Clearly, since by definition

P-q-e1 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,November I968, PP. 385-9 I

[ 89I ]


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892 THE ECONOMIC JOURNAL [DECEMBERin 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 theautomatic 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 producedR2s of ooI-o o4, with t values of 1-1

On the other hand in manufacturing, where the regression coefficients forboth p on q and e on q were around o 5, the R2swere very similar (o-826 in theone case and o 844 in the other) and the t values of the coefficients were as highas 7 in both cases. These findings were not dependent on the inclusion ofJapanin the sample. IfJapan is excluded from the sample, the results for the remainingI 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 tvalues 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 thanI, 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 statisticallysignificant positive correlation between p and e is a necessary est of the VerdoornLaw. The reason for this was a simple one. Since I regarded output as beingin 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 theproductivity series, thereby generating a spurious negative correlation betweenp and e.

It follows that the existence of statistically significant relationships betweenp and q and e and q does notcarry with it that the relationship between p and e isalso statistically significant. The latter may happen, if the relationship betweene and q gives a sufficiently close fit, but it would not hold if the latter relationshipis not close enough. There is nothing very surprising therefore in the fact that itis only by including Japan that the regression equation between p and e (ascalculated by Rowthorn) is statistically significant; even so, the R2 in the latterequation 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 thebasic 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.


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1975] ECONOMIC GROWTH AND THE VERDOORN LAW 893I 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 thereis 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 issufficient to reject the increasing-returns-to-scale hypothesis.

Second, that there is no significant relationship between e and q at all - andthis is consistent with all kinds of interpretations. It is in this second sense thatthe Verdoorn Law can be said to have broken down in the period I965-70.

Rowthorn's equations and scatter diagrams (taken from Gomulka) relateentirely to the relationship between p and e, and we are not told whether theunderlying relationships between e and q are of a neo-classical kind (withemployment varying in a I for I relationship with output), or the anarchical ornihilistic kind (with employment being unrelated to output), or of the typedescribed on page 892 above.

One interpretation of the Gomulka-Rowthorn theory is that the rate ofgrowth 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 fromthe remarkable correlation between the growth of GDP and the growth ofmanufacturing output,4 amounted to a denial of this position; I asserted thatthe 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. OccasionalPaper, no. 40, Cambridge University Press, 1973).

2 This would be the case, for example, if one assumed (a) that the total labour force effectivelyemployed 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 labourforce 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 I965-70period, 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


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894 THE ECONOMIC JOURNAL [DECEMBERnot diminish production in the rest of the economy, owing to the existence ofsurplus labour in agriculture (and also, though I did not say so explicitly, inservices) 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 theoverall productivity growth of the economy (the rate of growth of GDP perhead) in terms of the rate of growth of industrial output and the (relative)diminution of non-industrial employment. This relationship has in no way beenimpaired by the failure of the Verdoorn Law in manufacturing in the post- I965period; indeed the correlation coefficient is even higher for the I965-70period 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 betrue that the growth of industrial output was the governing factor in the overallrate of economic growth (both in terms of total output and output per head) solong as the growth of industrial output represented a net addition to the effectiveuse of resources and not just a transfer of resources from one use to another. Thiswould 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 aboveequation; Cripps and Tarling (p. 22) fouindthat t = 20 in a corresponding equation for a bundle of43 observations-and as I have shown in the Appendix to my lecture, the equation owes nothing toauto-correlation since the structure and the coefficient of the equation remain much the same ifmanufacturing 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 bythe exclusion of Japan, I asked Roger Tarling to re-compute the two regressions by excluding Japanfrom the sample. The results are as follows.:

Elevencountries, xcluding apanI 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 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, itmakes virtually no difference for the I965-70 period.


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I975] ECONOMIC GROWTH AND THE VERDOORN LAW 895or a by-product, of the growth of output; and (b) the labour engaged in industryhad no true opportunity-cost outside industry, on account of the prevalenceof disguised unemployment both in agriculture and services. There is plentyof 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 bythe growth of demand which is exogenous to the industrial sector' and not bythe (exogenously given) growth rates of the factors of production, labour andcapital, combined with some (exogenously given) technical progress over time.

While in the Lecture I gave the main emphasis to the Verdoorn Law as anexplanation 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 roleof profits and profit expectations in capital accumulation as the more basiccause of the difference of view between the neo-classical and Keynesian (orpost-Keynesian) schools of thought: the question, that is, whether one regardseconomic 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 thatthe United Kingdom hadattained the stage of economic maturity (in thesense I defined that term) and that her comparatively poor performance wasto be explained by inability to recruit sufficient labour to manufacturingindustry rather than by poor market performance due to lack of internationalcompetitiveness. Statistical studies that have since come to light2 make itdoubtful whether I was correct in thinking that earnings in the service trades ofthe United Kingdom had come to be fully competitive with earnings in manu-facturing or that the growth of manufacturing industry in the United Kingdomwas 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 rapidexpansion of engineering production (which from a long-run point of view isitself 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 growingsectors I am conscious of the fact that this statement in itself is a simplification but one which does notinvalidate the statistical inferences derived from it. The growth of industrial output for any region isgoverned in part by the growth in productivity which itself influences demand through the change incompetitiveness which is induced by it. It is this reverse link which accounts for the cumulative andcircular nature of growth processes.There is a two-way relationship from demand growth to productivitygrowth and from productivity growth to demand growth; but the second relationship is, in my view, farless regular and systematic than the first.2 Sleeper, R., Manpower Redeployment and the Selective Employment Tax, Bulletin of theOxfordUniversity nstituteof 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 ofSelective 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 industrywas 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 aninsufficiency of exports, the existence of a labour shortage would have been a perfectly adequate reasonfor securing the release of labour from services, irrespective of whether increasing returns or constantreturns prevailed in industry. (In the actual case, as events have shown, the improvement of exportperformance needed a devaluation, however, to improve the competitiveness of British goods in foreignmarkets.)


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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 onthe 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 KALDORKing's CollegeCambridgeDate 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.

kaldor - economic growth and the verdoorn law

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