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Cambridge Journal of Economics2016,1 of 23doi:10.1093/cje/bev067

The Author 2016. Published by Oxford University Press on behalf of the Cambridge Political Economy Society.

All rights reserved.

International competitiveness in post-Keynesian growth theory: controversiesand empirical evidence

Luciano Boggio and Laura Barbieri*

A fundamental starting point for post-Keynesian theory concerning growth inopen economies is succinctly expressed in the following statement by Kaldor:[T]he main autonomous factor governing both the level and the rate of growthof effective demand of an industrial countryis the external demand for its exports:and the main factor governing the latter is international competitiveness, which in

turn depends on the level of its industrial cost relatively to other industrial exporters(Kaldor, 1971, p. 7; italics added). Moreover, thanks to increasing returns inmanufacturing, export expansion and international competitiveness would inter-act so as to create vicious or virtuous circles of cumulative causation. A few yearslater Kaldor, having found a positive correlation between the time changes ofthe main industrial countries relative manufacturing export shares and that oftheir relative unit costsa correlation that became known as the Kaldor para-doxdismissed his original cumulative causation theory and adopted a versionclose to Harrods foreign trade multiplier. The purpose of this paper is to reaf-firm the Kaldorian cumulative causation theory in its original version, by provid-ing a firmer analytical basis and showing that, contrary to the Kaldor paradox,time changes in export performance must be explained by levels rather than bychangesin unit costs.

Keywords: International competitiveness, Post-Keynesian growth theory, Kaldorparadox, replicator equation

JEL classifications:F43, O10

Manuscript received 8 August 2013; final version received 13 January 2015.Address for correspondence:Laura Barbieri, Universit Cattolica del Sacro Cuore, Dipartimento di Scienze

Economiche e Sociali, Via Emilia Parmense, 84 29122 Piacenza, Italy.

*Universit Cattolica del Sacro Cuore. Financial help by 2007 PRIN Heterogeneous Sectors, Growthand Technical Change is gratefully acknowledged. The authors would like to thank the Final Conference

participants of that project, held in Naples (2729 April 2011), as well as Antonella Palumbo and otherparticipants of the S.I.E., Annual Scientific Meeting, held in Rome (1415 October 2011) for the stimulat-ing discussions and, last but not least, they would like to thank Bruno Soro for his insightful comments onKaldors and Harrods views. This paper is based on the research that was being carried out by ProfessorBoggio, who died unexpectedly as the work was coming to its conclusion. Laura Barbieri is deeply consciousof the debt she owes him finishing the work in his absence and feels honoured to have collaborated with himon the project. She would like to extend her gratitude to all those who assisted her in finishing it, in particularEnrico Bellino, Antonella Palumbo and Mariacristina Piva.

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Page2 of23 L. Boggio and L. Barbieri

1. Introduction

According to the mainstream theory of growth, based on the assumption of full

employment of factors of production, economic growth is simply the combined effect

of increases in the supply of factors and in their productivity. No room is left for an

autonomous role of effective demand, its pressure on productive capacity and factor

employment, nor its role in determining the rate of investment.According to another view, proposed in particular by the post-Keynesian theory

of growth and shared by the present writers, the assumption of full employmentof

labour in particularwhen the time period considered is not a secular one is not the

most useful starting point for explaining differences in growth performances.

An extreme version of this view was given by Nicholas Kaldor in the following

terms: economic growth isalways demand-inducedand not resource-constrained.

Resources, such as capital and labour do not determine growth, partly because they

are mobile between regions, and partly because they are never optimally allocated

(there are always economic sectors where labour is in surplus in the sense that its mar-

ginal productivity is zero or even negative, as e.g. in agriculture); and partly because

capital (in the sense of industrial capacity) is automatically generated as part of, and

in consequence of, the growth of demand (Kaldor, 1981, p. 603; italics in original).

As long as post-Keynesian theory deals with open economies, the following state-

ment by Kaldor (1971, p. 7; italics added) offersin the writers opiniona funda-

mental starting point: [T]he main autonomous factor governing both the level and

the rate of growth of effective demand of an industrial country with a large share of

exports in its total production and of imports in its consumption is the external demandfor its exports: and the main factor governing the latter is international competitiveness,

which in turn depends on the level of its industrial cost relatively to other industrial

exporters. Moreover, thanks to increasing returns in manufacturingVerdoorns

lawexport expansion and international competitiveness would interact so as to cre-

ate vicious or virtuous circles of cumulative causation (Myrdal, 1957; Kaldor, 1970).1

This position was partly modified a few years later in a paper where Kaldor (1978)

compared the time changesover periods longer than ten yearsof the main indus-

trial countries relative manufacturing export shares with that of their relative unit

costs2and found apositivecorrelation between the two variables.This paradox has various explanations. The simplest is that [h]igher prices could

equally well reflect higher quality, which, in turn, might justify higher wages. From this

perspective higher growth in relative unit labour cost (RULC) could just as well be seen

as an indicator of growing quality relative to other countries or increasingrather than

deterioratingcompetitiveness (Fagerberg, 2002, p. 1). A second (ambitious) inter-

pretation, which has a clear Kaleckian flavour, is that lower unit labour costs (ULCS)

should not necessarily be interpreted as implying that an economy is more competi-

tive, i.e., that it will grow faster, and vice versa. In wage-led growth economies, an

increase in the wage share leads to an increase in the equilibrium capacity utilizationrate, which leads to an increase in the growth rate of the capital stock. Hence it is pos-

sible to find that the countries with fast-growing ULCSare the ones registering faster

1 Boyer and Petit (1981), while discussing Un modle dinspiration kaldorienne, summarized the essenceof their arguments in the diagram they presented on p. 1128, which offers an immediate comprehension.

2 A useful way of visualising this relationship can be obtained from the first two columns ofTable 1fromFagerberg (1996), p. 41.

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International competitiveness: controversies and empirical evidence Page3of23

growth in exports or in GDP, [so that] Kaldors paradox ceases to be an anomalous

result (Felipe, 2005).3

A further explanation is that a third factor, like GDP growth, is positively linked to

growth in both exports and wages, hence in unit labour costs (GDP growth in turn

being strongly influencedaccording to the prevailing viewby technology4), thus

creating a positive link between the two time series.Or, as Kaldor himself put it, several years after the previous sentence quoted: There

is only one important matter on which the events of the 1970s caused me to change my

mind. This concerns the relative importance of price (or cost?) competition, as against

other non price factors, such as superiority of design or quality, length and reliability

of delivery dates, after-sales service, etc. Exchange rate adjustments operate mainly on

cost and prices, and despite vast changes in relative exchange ratesin real, and not

just in nominal termsthere was little effect on the pattern of trade in manufacturing

(Kaldor, 1986, p. 25).

The perverse (positive) relationship between export growth and price/unit labourcosts growth became known as the Kaldor paradox. This paradox was a damaging

blow for Kaldors thinking and led him to dismiss his own theory and endorse Harrods

foreign trade multiplier5 and Thirlwalls model of balance-of-payments-constrained

growth (Kaldor, 1981).

In that paper, cumulative causation was reduced to the fact that, because of increas-

ing returns (in the production of goods and technical progress), success breeds further

success (ibid., p. 596), whilst when increasing competitiveness and the widening of

international market shares were an essential feature of the cumulative causation pro-

cessas in the earlier Kaldorian formulationit appeared a much more importantand powerful phenomenon.

We believe that the theory, put forward in the 1960s and 1970s by Kaldor (and

Beckerman before him) to explain the contrast between the fast growth of Japan and

some countries of continental EuropeWestern Germany and Italy in particular

and the slow growth of the United Kingdom and the United States, is still very useful

nowadays for understanding contemporary experiences, like those of the Asian NICs,

of fast growth with strong international competitiveness.6

The purpose of this paper is to reaffirm the Kaldorian cumulative causation theory

in its original version, by providing a firmer analytical base and showing, on the basis

of empirical evidence, that the Kaldor paradox is a weaker empirical regularity than

others fully favourable to that theory.

3This Kaleckian explanation of Kaldors paradox essentially implies that growth is not really export led,but rather domestically led. Actually, many post-Keynesians have expressed scepticism about the whole ideathat growth is always or typically export led, and favour an investment-driven approach instead (especiallyfor larger countries, and maybe for all countries). We thank one of the anonymous referees for drawing ourattention to that point.

4This explanation of the paradox appears consistent with the sectoral investigations of the determinants

of export performance which began to appear in those years, and which gave an essential role to technologi-cal variables, in contrast to the poor or perverse (that is, positive) sign, in such investigations, of (the growthof) unit labour cost or wages. See Table 3of Fagerberg (1996), summarizing five research projects of thiskind, Dosi and Soete (1983), and Dosi et al.(1990), ch. 6.

5 In his 1981 paper, Kaldor asserts that the Harrod multiplier (Thirlwalls model) is dynamically stable(we thank Bruno Soro for attracting our attention to this point). This assertion seems rather unwarranted,but some kind of crude proof had been in Kaldor (1970), p. 342. On this point, see also Palumbo (2009),pp. 35152. Both Palumbo (2009)and Soro (2011)show that Harrod himself did not share this assertion.

6 Data and analysis supporting this proposition can be found in Boggio (1995) for Italy and Boggio(2003)for the Asian NICS.

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Later studies seem to confirm the paradox. For instance, Fagerberg (1996)shows

that, considering the period 197894, unit labour costs growth, a typical variable

expressing technological factors affecting competitiveness, has poorer explicative

power for exportgrowththan changes in GDP and in R&D as a share of GDP.

In effect, the consequence of the Kaldor paradox can be expressed by letting the

traditional multiplicative form of export demand be

x p p yx x x x

= + + > ( ) , , 0 (1)

where x,p,p*andy*are the growth rates of, respectively, exports, home and foreign

price indexes measured in common monetary unit, and rest of the world income; and

x

and x

are the price and income elasticities of export demand. Hence, (p+p*) is

the relative price of foreign goods.

Because of the paradox, there is a change of sign in the relative price effect and the

addition of other variables of technological factors expressed by T:

x p p y T x x

= + + ( ) . (2)

In the light of these premises, the aim of this paper is twofold. First, we theoretically

and empirically reassert the importance of cost competitiveness as a channel through

which cumulative growth dynamics can be sustained in open-economy growth mod-

els. Second, we show that in macrodynamics, the growth rates of some variables may

depend on the levels (rather than the growth rates) of other variables when replicatordynamics governs out-of-equilibrium behaviour.

In Sections 2 and 3, we briefly examine the two main theoretical strands of Kaldorian

derivation, namely the Kaldorian models of balance-of-payments-constrained growth

(BPCG) and the Kaldorian models of export-led growth (ELG), in order to assess

their relationship with the Kaldorian cumulative causation theory. In Section 3, we

propose an alternative approach to that theory, based on the replicator equation and

Beckerman model. After a brief examination of the literature on the replicator equa-

tion, an empirical comparison between the ability of the Kaldor paradox and the repli-

cator-like approach in explaining the growth of export is presented in Section 4.

2. Kaldorian models of balance-of-payments-constrained growth (BPCG)

A problem with the original Kaldorian approach is that the possibility of balance-of-

payments problems is not considered.Thirlwall (1979)suggests a simple model for

avoiding the possibility based on traditional demand equations for both exports and

imports and their equality. It can be summarized using the standard multiplicative

form of export demand, equation (1), expounded above, and similarly also for import

demand:

m p p ym m m m

= + > ( ) , , 0 (3)

where m,p,p*andyare the growth rates of imports, home and foreign price indexes,

and domestic income, respectively, while m

and m

are the price and income elastici-

ties of import demand.

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But if, as Thirlwall maintains, either relative prices did not vary in the long run,

p p = 0, (4)

or, alternatively, x m

+ 1 0 , then we get

x m x m

y y y y = =/ / , (5)

which explains growth rate differentials in terms of income elasticity differentials.

Thirlwall showed that the growth rate of income of the main industrial countries dur-

ing the period 196073 was approximated very well by the formula

y yx m

= / . (6)

According to him (Thirlwall, 1979, pp. 5253), and supported by Kaldors opinion

(Kaldor, 1981, p. 603), the income elasticities of this model reflect the innovative abil-

ity and adaptive capacity of the producers in different countries.

Many empirical estimates have been produced in subsequent years about the two

crucial assumptions of the BPCG model, each eliminating the role of relative prices:

a) no long-run changes in relative prices; and b) the sum of price elasticities of export

and import demand approaching one. They tend to support the view that in the very

long period (50 years or more)but notfor shorter periods, ranging from one to a few

decadessuch assumptions are likely to be confirmed.7What matters more from ourviewpoint is that here the Kaldorian cumulative causation processes are not considered and no

theoretical foundation is offered to them.

3. Kaldorian models of export-led growth (ELG)

The Kaldorian theory of cumulative causation circles in open economies during the

past decades has not ceased to attract the attention of economists.

The algebraic translation of a Kaldorian ELG model goes back to Dixon and

Thirlwall (1975), who established a tradition, with which we disagree on a fundamen-

tal point, namely the export equation. In this exposition, we shall use the more recent

versionsvery similar to the first oneby Setterfield and Cornwall (2002)(p. 72) and

Blecker (2013). The ELG model can be written using the symbols already introduced:

x p p yx x x x

= + + > ( ) , . 0 (7)

It is interesting to see that the Kaldor paradox is completely neglected/forgotten.

By the small country assumption, foreign price p* is taken as exogenously given.Setting wand qas changes in wages and labour productivity, changes in domestic price

are determined by changes in unit labour costs (w q) and the gross profit markup, :

p w q= + . (8)

7For an accurate discussion of the literature on this point, see Blecker (2013)and Garcimartn et al.(2010).

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By Verdoorns law:

q q y= + < 0

sufficient conditions foryE> 0 are

> 0 (is satisfied if the sum of the direct and indirect effects ofy*on xis positive),

1 / >x x

(is satisfied if the Verdoorn effectis small relative to the price effect

viaexports ony, or f fPR DR x x

= > =1 / ).

There is a further problem with the above equation system: the behaviour of the econ-

omy outside the constant rate of growth cannot be established.

But if we introduce a lag in the system, as Dixon and Thirlwall (1975)did, we can

deal with the problem. We may, for instance, assume a slow Verdoorn effect, so that

q f y y qt PR t t+

= +1

1

0( ) (19)

y f qt DR t = ( ) (20)

y f q f f yt DR t DR PR t + +

= =

1 1

1( ) [ ( )]. (21)

The stability will prevail if and only if

f fPR DR x x

/ ,=

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4. Beckerman model and the replicator equation

4.1. Replicator equation

To capture Darwins notion of the survival of the fittest, Fisher (1930)introduced what

are now calledafter Richard Dawkins (Dawkins, 1976, pp. 1321)replicator equa-

tions9

, of which we give below a very simplified version.Let us consider a population composed of ndistinct competingvarieties of a

given natural species and denote by x i n xi i i

, , ,..., , ,= =1 2 1 the relative frequen-

cies of the ith variety in the population. To each variety, let us associate its fitness

level expressed by function f xi i( ) . In continuous time, their evolution might be

described by the following equations (as usual, dot over the variable denotes a time

derivative):

x x f x f x f f x x f xi i i i i i i i i

= > [ ( ) ( )], , ( ) ( ). 0 (23)

This equation embodies the principle of natural selection: varieties with above-average

fitness will expand, those with below-average fitness will contract and the average fit-

ness f x( ) will increase. If the fitness functions f xi i( ) are simple constants, the average

fitness will increase monotonically towards a state where only the varieties (or group of

varieties) with maximum fitness survive(s).

Notice that the last equation can be put in the form

x x f x f xi i i i / ( ) ( ),= (24)

which can be read as the proportional change in the share of the ith variety is an

increasing function of its fitness advantage.

But for the purpose of empirical analysis, a discrete version is necessary. It can be

obtained by adaptingVerspagen (1993), p. 191.

Let xitbe the level of export in country iat time t, t = 1 2 3, , , ..., i n=1 2, ,... andyit

the country is share of world export at time t:

yx

xy y y y

it

it

n

i it

it it it it

, ( ) / .+1

(25)

Then the rate of change ofyit, namely yit , is given by

( / ), , ,..., ,,

y E E E y E j mit j

m

j jit jt jt i

n

it jit = = 1 1 2 (26)

where Ejit

is the competitiveness variable jof country iat time t, and j

the corre-

sponding (fixed) parameter to be estimated.

Equation (26) represents a typical R-like equation.

9 For a more detailed analysis, see Hofbauer and Sigmund (1997); for economic applications, seeSilverberg (1997)and Silverberg and Verspagen (1995).

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4.1.1. The replicator-like equations in the literature.Empirical tests of R-like equations

found in the existing literature are very few, since the bulk of the literature on the effect

of international competitiveness on export growth is based on growth rather than

levelsof competitiveness variables. On the whole, they show that unit cost/wage levels

are significant (with the expected sign) in the explanation of export shares, sometimes

more significant than technology variables.In Verspagen (1993), regressions are performed for the whole sample of pooled

observations (196487) for each of the 18 industrial sectors. The equation employed

is a modified version of (26), and the whole exercise is explicitly under the heading of

the replicator equation.

In the various specifications tried, wage and labour productivity variables give good

results, much better than those for the specifications of the patent variables (p. 215).

The paper of Amendola et al.(1993)deals with manufacturing export market shares of

16 OECD countries from 1967 to 1987. It is the only one that refers to the total manufac-

turing export of each country. Starting from an equation almost identical to equation (26),a general autoregressive-distributed lag (ADL) is derived, giving rise also to long-run mul-

tiplier estimates. The independent variables are unit labour cost, investment in machinery

and total patents. However, in the reformulated ADL equations with long-run multipliers,

the independent variables are again time changes. The Kaldor paradoxthey assert

[a]s a long-term phenomenonseems the outcome of a spurious correlation (p. 465).

Amable and Verspagen (1995)present an estimation of an empirical model of mar-

ket share dynamics for five industrialized countries and 18 industries. In their paper, a

long-run export market shareX*is built as follows:

X k a PC b IN c PTij ij ij ij ij ij ij ij

= + + + . (27)

PCis a measure of unit labour cost, IN is (derived from) the ratio of investment to

production and PT is based on total patents for each sector. For each independent

variable, the following bell-shaped lag structure is adopted:

Z Z Z Z Z PC IN PT= =( ( )) ( ( )) ( ( )) , , , .1 2 303 04 03 (28)

The error-correction mechanism is built on the long-run value of the market share

(27), giving

X X Xij i ij ij

= + ( )[ ( )], 1 (29)

where iis a country dummy.

The unit labour cost variable on average performs very well, better than the other

two. Verspagen and Wakelin (1997)do not specify their model in the form of an exactreplicator, but base their functional specification upon earlier empirical models, such

as Amendola et al.(1993)and Amable and Verspagen (1995). Market shares of each

market are estimated for 10 countries and 15 manufacturing sectors. The average rate

of growth of a market share is regressed on the average of competitiveness variables for

the period 198085. These are patents and R&D, share of investment in output and

wages in dollars (significant in 16 or 22 cases out 45), share of investment in output

(significant in 29 cases) and wages (significant in 20 cases).

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4.2. Beckerman model

In this subsection, we shall consider the model published by W. Beckerman in 1962,

a few years beforeKaldors papers mentioned above that anticipated some of the main

ideas, in particular the cumulative growth model in open economies.10But, differently

from all later Kaldorian models, Beckerman implicitly adopts an R-equation (shorthand for

replicator equation) form for his export equation, therefore also anticipating the application ofthat idea to economic problems.11

In this model, export changes are a decreasing function of the price of given country

relative to competitor countries (Beckerman, 1962, p. 914). More precisely, the rate

of growth of the share of world exports held by a given country, hence the differences

in the growth of exports, depends not on time changesof relative priceas in the tra-

ditional approach to export determination, exemplified by the exports equation of the

BPCG and ELG modelsbut on cross-country price differences.

The first reason we adopt the latter approach is that, accordingly with the Kaldors

non-equilibrium thinking, we believe market shares are often far from their long-run

equilibrium value and that their rates of change over time can be approximated by a

replicator-type equation. This statement becomes clearer if we express the main reason

we stress cross-country differences in levelsof unit costs or prices: normally, they also

imply cross-country differences in profit margins, hence in the ability of the single firm

to invest, expand its productive capacity, pursue technical progress and spend in non-

price competition. In this waycontrary to an export growthbased approach on the

demand side only, as in the model described in the previous sectionswe implicitly

introduce also the supply sideof the firms.12

We shall now describe the Beckerman model (Beckerman, 1962, pp. 91819), intro-

ducing slight modifications that will make further formal developments easier.

The symbols used are the same as those to be used in later years by the models

expounded above, but for the productivity growth rate, for which we shall maintain q

as above.

The most interesting equations are the first ones, embodying the replicator equation

principle:

x a b= + ( ),1 (30)

where is the price level of a given country relative to competitor countries and acan

represent the rate of increase in world trade (ibid., p. 919). The meaning of is made

more clear by explicitly introducing the levelof prices in the two countries: letpibe

the level of prices (in common units) in country i, i = 1 2, , where 1 is the home country

and 2 a competitor country. Then p p1 2

/ and x a b1

1= + ( ) .

Then we have

10 Dixon and Thirlwall (1975)noticed that Beckermans model bears many similarities to Kaldors andpredates it (p. 202, fn. l), but (mis)interpreted Beckermans export equation as a wrong specification of anexport demand (p. 211). Cf. alsoThirlwall and Dixon (1979)and Cornwall (1977).

11 In the writers opinion, Beckermans model could be seen as embodying the replicator equation prin-ciple even if the author does not consciously refer to it.

12 Models spelling out a plausible description of the causal link between across firms differences in unitcost levels on one side and differences in profits, investments and productive capacity growth on the othercan be found in Boggio (1974, 1996, 2003).

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productivity (output per head) equation13

q c dx1 1

= + , (31)

wage equation

w z vq n1 1

1= +

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x a b = ( ),1 (38)

the left-hand side is the rate of growth of the share of the countrys exports on the

world total, which is made dependent on the competitiveness factor .

Let us further develop this model (see also Boggio and Seravalli, 2003).

If we maintain the assumption that the parameters in the basic equations are thesame in all countries (Beckerman, 1962), then

( / ), ( ) = = = >d

dtp p v bd

log

1 2 1 1 0 (39)

= d

dt

( ),2 1 (40)

so that the model gives rise to a differential equation and assumes the following graphic

representation seen in Figure 1.

Within the open interval ( , )0 , only one equilibrium, = 1, exists. Outside this equilib-

rium, moves away from it, entering either a virtuous circle of cumulative causation or a

vicious one. In the former case, competitiveness, the growth of exports, output, productiv-

ity and wages all increase and, for a while, at an increasing speed. In the latter, competitive-

ness, the growth of exports, output, productivity and wages decrease at an increasing speed.

Fig. 1. Beckerman models representation in (, ).

14 Beckerman, on the basis of his observation of European countries, rejected the suggestionthat dif-ferential rates of growth of the labour force may be an important explanation for differential growth ratessimply does not stand up to empirical verification (ibid., 921, fn. 2). See also his Reply (Beckerman, 1963)to Balassa (1963).

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Obviously, only proximity to the equilibrium should be considered as economically

meaningful, because, as long as a less extreme version than Kaldors of the premises

of the post-Keynesian theory of growth is adopted, it should be stressed that many

supply-side factors concur in dampening the divergence brought out by the model.14

Similarly, one should remember that in the real world, technical progress not amenable

to Verdoorns law may turn out to be most important.As with all models, ours is an abstraction, a glimpse of reality, that, if accepted,

catches a true aspect of reality.

Ours is one of the divergent circles of cumulative causation based on national com-

petitiveness as in the original Kaldorian theory.

5. Empirical evidence

As mentioned before, empirical tests of R-like equations found in the existing literature

show that unit cost/wage levels are significant (with the expected sign) in the explanation ofexport shares, sometimes more significant than technology variables.

Therefore, we decided to try some preliminary tests, in order to begin to assess the

relevance of Kaldors paradox relative to that of R-like equations.15

5.1. Our first tests

Very simple regression equations were performed, starting from OECD data for 33

countriesincluding India, China and Brazilon aggregate good exports in US dol-

lars (EXP) and manufacturing unit labour costs (ULC) for the 15-year period 19932007. The regressions are based on equation (26) (replicator equation): the dependent

variable yit

is the average growth rate of export share (EXPGR)16of country iover the

15 years, while Ejitis the value of thejth competitiveness indicator for country i; the

independent variables are the average unit labour costs (ULCAV) and their average

growth rate (ULCGR) over the 15 years (see Appendix Afor more details).

According to the Kaldor paradox, EXPGRshould mainly be determined by ULCGR

(with positive coefficient) and according to replicator-like equations by ULCAV(with

negative coefficient). The results of the cross-section analysis are inTable 1.

The ULCAVvariable is always significant, also when coupled with ULCGR. The latternever reaches a standard level of statistical significance. Hence, the replicator-like speci-

fication turns out very relevant, whilst the Kaldor paradox specification is not significant.

In order to take advantage of the time-series dimension of the disposable data, which

can be relevant for the phenomenon under consideration, we also implemented a panel

data analysis, which fully confirms the previous results about the relationship between

EXPGR, ULCAVand ULCGR.

First, the three regressions presented in Table 1have been re-estimated in pooled

data (see Appendix Bfor details on the variables construction and some descriptive

15 Alonso and Garcimartn (1998)and Len-Ledesma (2002), starting from a BPCG and an ELG model,respectively, developed additional refinements based of the theory here illustrated and empirically tested itwith econometric estimates. Nevertheless, their models differ from our design, which focuses on the use ofreplicator equations and avoids lag complexity referring to a different and less monetary instable historicalperiod (19932007 in our case).

16 Following the original specification proposed by Kaldor (cf. Kaldor, 1978, fn. 2, p. 102), our design isbased on export shareinstead of on the quantity of exportas in Len-Ledesma (2002).

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statistics). The results are reported in the first three columns ofTable 2; it is easy to

note that they confirm the conclusion of the cross-section analysis.Specifically, as regards the first regression, the ULCvariable seems to have a significantly

negative impact on the dependent variable, while the second regression shows that the

ULCGRvariable is not significant. Finally, when we insert both independent variables in

the regression, the significance of the ULCvariable is confirmed with a negative coefficient.

Moreover, in order to control for potential endogeneity of the unit labour cost

growth rate regressor (i.e. not only slower growth of relative unit costs promotes more

rapid export growth, but also successful export growth leads to more rapid increases

in relative unit costs), the significance of the lagged regressors has been verified. The

results, reported in column (4) ofTable 2, prove the absence of reverse causality.We reach the same results considering the random-effects model,17 for which we

obtain the results inTable 3.

5.2. Introducing technology variables

As amply discussed in the first part of this paper, several authors, while highlighting

the Kaldor paradox, stressed the role of technical progress as an alternative explana-

tion of trade flows. Therefore, we would like to introduce in our equations a variable

expressing such a role.To this end, after having considered the measures of technological capabilities pro-

posed byArchibugi and Coco (2005)(see Appendix Cfor more details), we choose the

average gross domestic expenditure in R&D of the 19952000 period (GERDAV) and,

17We chose a random-effects model after considering alternatives from fixed-effects and random-effectsmodels and implementing the Hausman test, which did not reject the null hypothesis, suggesting we userandom-effects model.

Table 1. OLS estimation of the replicator equation. Cross-section analysis

Dependent variable: export share growth - EXPGR

Independent Variables (1) (2) (3)

ULCAV -0.137*** -0.137**(0.042) (0.057)

ULCGR -0.001 1.60E-05(0.001) (0.001)

const 0.094*** 0.010 0.095**(0.028) (0.007) (0.036)

Number of obs. 33 33 33R-squared 0.202 0.047 0.202

JB(2) 2.114 3.449 2.119

Reset(2) 1.196 0.043 1.191

White(2) 6.037** 2.216 7.551

1.Data refer to 33 OECD countries.2.Standard errors are in parenthesis. In the first equation, they are corrected for the presence of heteroske-

dasticity, given the results of the White test.3.*Statistically significant at the 10% level; **significant at the 5% level; ***significant at the 1% level.4.JB stays for the Jarque-Bera statistic for normality; Reset is the Ramsey test for specification errors;

White is the homoskedasticitys test.

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alternatively, the average gross domestic product of the same period (GDPAV) as the

main variables that should capture the innovation capability of a country.

By inserting the GERDAVvariable into our third equation, we obtain the results

reported in Table 4.

The GERDAVvariable is not significant, and its effect on the equation results is neg-

ligible. The ULCAVvariable is significant at the 5% level, while ULCGRis not. This

seems to confirm the validity of the replicator approach against the Kaldor paradox

and technological capabilities.

However, things are not so simple: if we take the GDPAV variable as expressing

the technological capabilities and introduce it into our equations, in spite of the high

Spearman correlation between GDPAVand GERDAV, the results turn out very differ-

ently. If we replace the latter by the former variable in the last three equations, the only

significant variable turns out to be GDPAVitself (see model (2),Table 4).

Various specificationsintroducing dummies for the UE or the Eurozone, as well as

weights based on GDP, distinguishing countries according to an income threshold

did not significantly change the results.18

However, GDPAVnot only expresses the technological level of the country, but it

approximates the manufacturing productivity, which in turn is the denominator of

the ULCAV. This suggests, followingVerspagen (1993)and Verspagen and Wakelin

(1997), that the latter could be conveniently replaced by the wage rate. To this aim,

we introduced the WAGESAV independent variable, computed for each country as

Table 2. OLS estimation of the replicator equation. Pooled regressions


Independent Variables (1) (2) (3) (4)

ULC -0.111*** -0.111***(0.025) (0.028)

ULCGR 0.0003 0.0002(0.0003) (0.0003)

ULC(t1) -0.112***(0.029)

ULCGR(t1) 0.0002(0.0003)

const 0.079*** 0.014*** 0.079*** 0.079***(0.016) (0.004) (0.017) (0.017)

Number of obs. 448 440 440 411R-squared 0.036 0.002 0.038 0.038

JB(2) 0.456 0.476 0.439 0.210

Reset(2) 0.034 0.346 0.028 1.196

White(2) 5.121* 0.151 5.228 5.022

1.Data refer to the 33 OECD countries over the period 19932007.2.Standard errors are in parenthesis. In the first equation, they are corrected for the presence of

heteroskedasticity.3.*Statistically significant at the 10% level; **significant at the 5% level; ***significant at the 1% level.

4.JB stays for the Jarque-Bera statistic for normality; Reset is the Ramsey test for specification errors;White is the homoskedasticitys test.

18 Results are available upon request.

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Table 3. Random effects GLS regression for panel data



ULCAV -0.088** -0.084**(0.038) (0.039)

ULCGR 0.0003 0.0002(0.0003) (0.0003)

const 0.065*** 0.014** 0.064***(0.023) (0.006) (0.024)

Number of obs. 440 440 440R-squared within 0.001 0.002 0.001 between 0.175 0.013 0.191

overall 0.036 0.002 0.038Wald(2) 5.320** 0.750 5.510*

1.Data refer to the 33 OECD countries over the period 19932007.2.Standard errors are in parenthesis. In the first equation, they are corrected for the presence of

heteroskedasticity.3.*Statistically significant at the 10% level; **significant at the 5% level; ***significant at the 1% level.

Table 4. OLS estimation of the replicator equation with technological variables. Cross-sectionanalysis



ULCAV -0.136** -0.090

(0.058) (0.064)WAGESAV -3.08E-06***

(1.07E-06)

ULCGR 3.46E-05 0.001 -4.84E-04(0.001) (0.005) (0.001)

GERDAV -6.37E-06(1.94E-05)

GDPAV -1.49E-06** 1.21E-06(5.92E-07) (1.02E-06)

const 0.097*** 0.104** 0.071***(0.037) (0.038) (0.019)

Number of obs. 31 31 27R-squared 0.205 0.274 0.484

JB(2

) 2.270 0.941 2.450Reset(2) 1.581 10.078 1.259

White(2) 10.128 7.519 7.203

1.Data refer to 33 OECD countries.2.Standard errors are in parenthesis. In the first equation, they are corrected for the presence of heteroske-

dasticity, given the results of the White test.3.*Statistically significant at the 10% level; **significant at the 5% level; ***significant at the 1% level.4.JB stays for the Jarque-Bera statistic for normality; Reset is the Ramsey test for specification errors;

White is the homoskedasticitys test.

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the average wage of the 15 disposable annual data (see Appendix Afor more details),

obtaining the results shown in the last column ofTable 4.

The main result is that the level of the wage rate, expressed by WAGESAV, when

per capita GDP (GDPAV) is included in the regression, is very significant, whilst the

growth of unit costs (ULCGR) has a coefficient smaller than the standard error. Similar

results are obtained when using GERDAVinstead of GDPAV, or when the logarithm ofGDP or the above described DUMMIES are introduced.

6. Concluding remarks

Since we consider the original Kaldorian cumulative causation theory as the most

important tool of analysis to understand the historical experiences of fast-growing

open economies, the main purpose of this paperas stated at the beginningis to

reaffirm such a theory, by providing a firmer analytical basis and showing that Kaldors

paradox cannot impair that basis.We believe that our discussion of the replicator equation and the developments we

presented of Beckermans model may provide these firmer theoretical bases. Also, the

results of the quantitative work done along the lines of the replicator equation by vari-

ous authors and by ourselves may support the view that export growth depends on lev-

els of competitiveness factorslabour cost in particularrather than on their growth.

Hence, the Kaldor paradox, though statistically significant in some papers discussed in

the introduction, in recent years is a weaker hypothesis than the replicator-type equa-

tions, and thus cannot diminish the importance of the original Kaldorian cumulative

causation theory as interpreted in light of Beckermans model.The results we obtained when per capita GERD and GDP are introduced could

suggest that, even with variable expressing technological capabilities, the fundamental

results of this paper are confirmed: namely, the validity of the replicator approach vis-

-vis the Kaldor paradox.

This shows that replicator dynamics are a potential boon to Kaldorian growth the-

ory (with its emphasis on growth as an out-of-equilibrium or non-equilibrium pro-

cess), and may assist in both the further development and advancement of this theory

and reconciliation of Kaldorian growth theory with empirical evidence.

Conflict of interest statement. None declared.

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A. Data used and main variables

The source of the data used is OECD. Data used:

export data of the International Trade (MEI) data set measured in billions of US

dollars (EXPORT);

unit labour costs, which measure the average cost of labour per unit of output (ULC);

gross domestic product (expenditure approach) per head, US dollars, constantprices, constant PPPs, OECD base year (GDP);

gross domestic expenditure on R&D per capita population (current PPP $) from the

OECD, Main Science and Technology Indicators (GERD);

average annual wages in 2009 USD PPPs and the 2009 constant pricesaverage

annual wages per full-time, full-year equivalent, dependent employee(WAGES).

As regards the cross-section analysis, the dependent variable EXPGR is the average

growth rate of the export shares (EXPshare) over the 19932007 period for 33 OECD

countries.19The export shares are computed as the ratio of the exports of country i

in year tand the sum of the exports of all the countries under consideration in year t;

that is,

19The sample includes Australia, Austria, Belgium, Brazil, Canada, China, Czech Republic, Denmark,Estonia, Luxembourg, Mexico, Finland, France, Germany, Greece, Hungary, India, Ireland, Israel, Italy,Japan, Korea, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Slovak Republic, Slovenia,Spain, Sweden, United Kingdom, and the United States.

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EXPshareEXPORT

EXPORTit

it

i it

=

(41)

with i = 1 33,..., and t = 1993 2007,..., , and so

EXPGR

EXPshare EXPshare

i

i i=

log log ( ) ( ), ,2007 1993

14 (42)

with 14 being the number of annual periods divided into the 19932007 interval.

The independent variables are the average unit labour costs (ULCAV) and their

average growth rate (ULCGR) over the 15 years computed as replicator equations

ULCAVULC

i

t it=

15

(43)

ULCGRULC

ULC EXPsharei

i

i i avi

=

1, (44)

where ULCiis the average growth of the ULCof country iover the period consid-

ered, i.e.

ULC

ULC ULC i

i i=

log log ( ) ( ),

, ,2007 1993

14 (45)

and

EXPshare

EXPORT

EXPORTav

t

it

i

t

iti

=

15

15

33

.

(46)

An additional independent variable computed on the wages and introduced in Section

5.2 is

WAGESAVWAGES

i

t it=

15, (47)

i.e. the average country wage computed on the disposable time period.

B. Panel data analysis

In the panel data analysis, the variables are computed also considering their time-series

dimension: thus, the dependent variable EXPGR is the annual growth rate defined

modifying equation (42) as follows:

EXPGR EXPshare EXPshareit i t i t

=

log( ) log( ),, , 1

(48)

with i= 1,,33 and t= 1993,,2007.

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The independent variables are the unit labour costs (ULCit) and their annual growth

rate (ULCGR) computed as replicator equations:

ULCGRULC

ULC EXPshareit

it

i it t it

=

[ ( )],1 (49)

where ULCitis the annual growth of the ULCof country ifrom time t 1 to t, i.e.

ULC ULC ULC it it i t

=

log( ) log( ), 1

(50)

We considered the descriptive statistics of the variables concerned; seeTable 5.

As far as the export variable is concerned, we can note that the within variabil-

ity overcomes the between variability, meaning that the variability over time in each

country in the period under consideration prevails over the variability of exportsbetween countries.

On the contrary, as far as the ULCvariable is concerned, the between variability

overcomes the within variability, pointing at wider differences among countries than

the individual dynamics.

As regards the ULCGR, the results seem to highlight a predominance of the indi-

vidual dynamic variability over the variability across countries.

C. Technology variable selectionIn order to introduce into our equations a variable expressing the technical progress, we

shall consider the variables studied in the work of Archibugi and Coco (2005)to cap-

ture the technological capabilities of a country. In their paper, alternative measures are

considered of national technological capabilities that generate country rankingsthese

are precisely the measures proposed by the World Economic Forum (WEF Technology

index), the UN Development Program (UNDP Technology Achievement index),

the UN Industrial Development Organization (Industrial Development Scoreboard

UNIDO), the RAND Corporation (Science and Technology Capacity Index STCI)

and a measure proposed by the authors (Technological Capabilities Index ArCo).20

The variables considered in Archibugi and Cocos paper, from our viewpoint, suffer

an important shortcoming: they cover only a small part of our equations time interval.

To obviate it, we shall consider the use of two variables that do not suffer that short-

coming, namely per capita GDP and per capita GERD (gross expenditure on R&D),21

and test their ability to fulfill the role of indicators of national technological capabilities

by comparing them with Archibugi and Coco variables.

20 Similarities and differences between the various methodological results at the aggregate level are ana-lyzed without considering the nature of technological capabilities available in each country. Specifically, theauthors show that the results frequently diverge because of the different social indicators taken into account.Nevertheless, a strong similarity in the rank correlations is interpreted as evidence of the reliability of eachindicator. This supports the idea that it is impossible to generate a unique measure of technological capa-bilities, but methodological variety helps create a better understanding of social phenomena. Moreover, allingredients of technological capability are as relevant as the final measure, and in order to assess the impactof technological capabilities on economic and social indicators, individual indicators and sub-indexes shouldbe taken into account.

21 SeeAppendix Afor more details.

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For the sake of homogeneity with the latter indexes (almost all of which are com-

puted over the 19972000 or 19952000 period), averages of per capita GDP and per

capita GERD of the 19952000 period are calculated (namely GDPAVand GERDAV,

respectively). The sample of countries selected is common to the Archibugi and Coco

set, i.e. 28 countries.

The rankings of our indicators, reported inTable 6, are very similar to those of theindicators considered by Archibugi and Coco (2005, p. 186,Table 2), as confirmed by

Table 7, which shows for the 28 countries the co-graduation matrix among rankings

by means of Spearman correlations.

There is a high correlation between our indicators and the other indexes confirming

our hypothesis that the two variables could be valid indicators of national technologi-

cal capabilities.

The highest correlation coefficients, however, are found for GERDAV. GDPAVshows

significant correlation, in one case equal to GERDAV, but lower in the other cases.

In view of these results, we choose GERDAVas the main variable that should cap-ture the innovation capability of a country.

Table 5. Descriptive statistics of the panel data variables

Variable Mean Std.Dev. Observations

EXPGR overall 0.014 0.077 N=440between 0.037 n=33within 0.69

ULC overall 0.590 0.132 N=440between 0.119 n=33within 0.057

ULCGR overall -0.490 11.267 N=440between 3.338 n=33within 10.758

1.Data refer to 33 OECD countries over the period 19932007.

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Table 6.Technology indicators

GERDAV GDPAV

Australia 14 4Austria 9 6Belgium 10 8Canada 12 5China 28 28Czech Republic 21 23Finland 5 15France 7 12Germany 6 7Greece 24 20Hungary 25 24Ireland 16 10

Israel 4 17Italy 17 14Japan 3 9Korea 15 22Mexico 27 26Netherlands 8 3New Zealand 19 18Norway 11 1Poland 26 27Portugal 22 19Slovak Republic 23 25

Slovenia 18 21Spain 20 16Sweden 1 13United Kingdom 13 11United States 2 2

Table 7. Spearman correlations

GERDAV GDPAV WEF UNDP ARCO RAND

GERDAV 1()

GDPAV 0.75 1(5.74) ()

WEF 0.67 0.67 1(4.59) (4.61) ()

UNDP 0.83 0.72 0.85 1(7.73) (5.28) (8.06) ()

ARCO 0.90 0.74 0.78 0.88 1(10.55) (5.69) (6.73) (9.43) ()

RAND 0.93 0.78 0.79 0.89 0.96 1(12.62) (6.39) (6.60) (9.75) (16.89) ()

1.t-statistics are in parenthesis, showing that all correlations are significant at the 1% level.

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