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11.12 The Convergence Debate

Since 1945 the economies of what used to known as the Third World have

been viewed as participating in an attempt to achieve economic development

and thereby begin to ‘catch up’ the rich countries of the world in terms of per

capita income. The growing awareness of the wide variety of experiences

observed among developing countries in this attempt has been a major factor

in motivating renewed research into the important issue of economic growth.

It is generally accepted that the Third World’s efforts to join the ranks of the socalled

‘mature industrial countries’ represent one of the major social, economic

and political phenomena of the second half of the twentieth century. This attempted

transition to modern economic growth will rank with the taming of the

atom as the most important event of this period. (Fei and Ranis, 1997)

Modern discussion of the convergence issue began with the contribution of

Gerschenkron (1962), who argued that poor countries could benefit from the

advantages of ‘relative backwardness’ since the possibilities of technological

transfer from the developed countries could vastly speed up the pace of

industrialization. However, this debate has much earlier origins, dating back

to 1750, when Hume put forward the view that the growth process would

eventually generate convergence because economic growth in the rich countries

would exhibit a natural tendency to slow through a process of ‘endogenous

decay’ (Elmslie and Criss, 1999). Oswald and Tucker (see Elmslie and Criss,

1999) rejected Hume’s arguments, putting forward an endogenous growth

view that ‘increasing, or at least non-decreasing, returns in both scientific and

economic activity will keep poor countries from naturally converging towards

their rich neighbours’. Elsewhere, Elmslie has also argued that in the

Wealth of Nations, Smith (1776) took up an endogenous growth position

since societal extensions to the division of labour will allow the rich countries

to continuously maintain or extend their technological lead over poorer countries

(see Elmslie and Criss, 1999). This argument also lies at the heart of

Babbage’s 1835 thesis that the perpetual advances in science provide the

foundation for further advancement and economic progress. Elmslie and

Criss argue that Babbage’s case against the restrictive laws on the export of

machines is ‘the best statement of endogenous growth in the classical period’.

For, as Babbage argued, the growth of other countries does not pose an

economic threat because ‘the sun of science has yet penetrated but through

the outer fold of Nature’s majestic robe’.

In more recent times the issue of convergence began to receive a great deal

of attention from the mid-1980s and this growth of research interest stems

mainly from the growing recognition that many poor economies were failing

to exhibit a tendency to close the per capita incomes gap with rich countries

(see Islam, 2003). The conundrum of non-convergence of per capita incomes

across the world’s economies was first clearly articulated by Paul Romer

(1986). The convergence property in the Solow model stems from the key

assumption of diminishing returns to reproducible capital. With constant

returns to scale, a proportional increase in the inputs of labour and capital

leads to a proportional increase in output. By increasing the capital–labour

ratio an economy will experience diminishing marginal productivity of capital.

Hence poor countries with low capital-to-labour ratios have high marginal

products of capital and consequently high growth rates for a given rate of

investment. In contrast, rich countries have high capital-to-labour ratios, low

marginal products of capital and hence low growth rates (see the aggregate

production function A(t0)kα in Figure 11.5). The severity of diminishing returns

depends on the relative importance of capital in the production process

and hence the size of the capital share (α) determines the curvature of the

production function and the speed at which diminishing returns set in (see

DeLong, 2001). With a small capital share (typically α = 1/3), the average

and marginal product of labour declines rapidly as capital deepening takes

place. It is obvious from an inspection of the production function in Figures

11.3–11.5 that in the Solow model capital accumulation has a much bigger

impact on output per worker when capita per worker ratios are low compared

to when they are high. In a risk-free world with international capital mobility

this tendency for convergence will be reinforced (Lucas, 1990b). In the long

run the neoclassical model also predicts convergence of growth rates for

economies which have reached their steady state. However, as pointed out by

Romer, the neoclassical hypothesis that low income per capita economies

will tend to grow faster than high income per capita economies appears to be

inconsistent with the cross-country evidence.

In his seminal 1986 paper Romer raised important doubts about the preference

economists display for a growth model which exhibits diminishing

returns to capital accumulation, falling rates of growth over time, and convergence

of per capita income levels and growth rates across countries. Evidence

relating to falling rates of growth can be found by examining the historical

growth record of ‘leader’ economies compared to other economies (where

leader is defined in terms of the highest level of productivity). Maddison

(1982) has identified three leader economies since 1700, namely: the Netherlands,

1700–85; the UK, 1785–1890; and the USA, 1890–1979. As the

twenty-first century begins, the USA remains the leader economy. But, as

Romer notes, the rate of growth has been increasing for the leader economies

from essentially zero in eighteenth-century Netherlands to 2.3 per cent per

annum for the USA in the period 1890–1979. Historical data for industrial

countries also indicate a positive rather than negative trend for growth rates.

Hence, rather than modify the neoclassical growth model, Romer introduced

an alternative endogenous theory of growth where there is no steady state

level of income, where growth rates can increase over time, and where

income per capita differentials between countries can persist indefinitely.

The general property of convergence is often presented as a tendency of

poor countries to have higher rates of growth than the average and for rich

countries to grow more slowly than average. In the world as a whole ‘no such

tendency is found’ (Sachs and Warner, 1995). However, there is strong evidence

of convergence among the OECD economies as well as between US

states, Japanese prefectures and European regions within the European ComThe

renaissance of economic growth research 617

munity (Baumol, 1986; DeLong, 1988; Dowrick, 1992; Barro and Sala-i-

Martin, 2003). The conflicting evidence led Baumol to suggest that there may

be a ‘convergence club’ whereby only those countries with an adequate

human capital base and favourable institutions can hope to participate in

convergent growth. More recently, DeLong and Dowrick (2002) have shown

that ‘what convergence there has been has been limited in geography and

time’ and, as a result, to use Pritchett’s (1997) words, there has been ‘Divergence,

Big Time’ (see Jones, 1997a, 1997b; Melchior, 2001).

The research inspired by Barro (1991) has shown how the prediction of

convergence in the neoclassical model needs considerable qualification. If all

economies had identical savings rates, population growth rates and unlimited

access to the same technology, then relative capital intensities would determine

output per capita differentials between countries. Poor countries with

low capital intensities are predicted to grow faster than rich countries in the

period of transitional dynamics en route to the common steady state equilibrium.

In this situation there will be unconditional or absolute convergence.

Clearly, given the restrictive requirements, this outcome is only likely to be

observed among a group of relatively homogeneous countries or regions that

share similar characteristics, such as the OECD economies and US states. In

reality, many economies differ considerably with respect to key variables

(such as saving propensities, government policies and population growth)

and are moving towards different steady states. Therefore the general convergence

property of the Solow model is conditional. ‘Each economy converges

to its own steady state, which in turn is determined by its saving and population

growth rates’ (Mankiw, 1995). This property of conditional convergence

implies that growth rates will be rapid during transitional dynamics if a

country’s initial output per capita is low relative to its long-run steady state

value. When countries reach their respective steady states, growth rates will

then equalize in line with the rate of technological progress. Clearly, if rich

countries have higher steady state values of k* than poor countries, there will

be no possibility of convergence in an absolute sense. As Barro (1997) notes,

‘a poor country that also has a low long-term position, possibly because its

public policies are harmful or its saving rate is low, would not tend to grow

rapidly’. Conditional convergence therefore allows for the possibility that

rich countries may grow faster than poor countries, leading to income per

capita divergence! Since countries do not have the same steady state per

capita income, each country will have a tendency to grow more rapidly the

bigger the gap between its initial level of income per capita and its own longrun

steady state per capita income.

This can be illustrated as follows. Abstracting from technological progress,

we have the intensive form of the production function written as (11.34):

y = kα (11.34)

Expressing (11.34) in terms of growth rates gives (11.35):

y˙/y = αk˙/k (11.35)

Dividing both sides of Solow’s fundamental equation (11.26) by k gives

equation (11.36):

k˙/k = sf (k)/k − (n + δ) (11.36)

Therefore, substituting (11.35) into (11.36), we derive an expression for the

growth rate of output per worker given by equation (11.37):

y˙/y = α[sf (k)/k − (n + δ)] (11.37)

In Figure 11.6 the growth rate of the capital–labour ratio (k˙/k) is shown by

the vertical distance between the sf(k)/k function and the effective depreciation

line, n + δ (see Jones, 2001a; Barro and Sala-i-Martin, 2003). The

intersection of the savings curve and effective depreciation line determines

the steady state capital per worker, k*. In Figure 11.7 we compare a rich

Figure 11.6 Transition dynamics

sf (k)/k

k ·

/k

sf (k)/k

n + δ

k* k

Figure 11.7 Conditional convergence

sf (k)/k

s sR f (k)/k Pf (k)/k

kP k*P kR k*R k

SP

SR

b e

c

d

(n + δ)P

(n + δ)R

a

developed country with a poor developing country. Here we assume (realistically)

that the developing country has a higher rate of population growth than

the developed country, that is, (n + δ)P > (n + δ)R, and also that the developed

country has a higher savings rate than the developing country. The steady

state for the developing country is indicated by point SP, with a steady state

capital–labour ratio of kP * . Similarly, the steady state for the developed country

is indicated by points SR and kR * . Suppose the current location of these

economies is given by kP and kR. It is clear that the developed economy will

be growing faster than the developing country because the rate of growth of

the capital–labour ratio is greater in the developed economy (distance c–d)

than the developing country (a–b). Figure 11.7 also shows that even if the

developed country had the same population growth rate as the developing

country it would still have a faster rate of growth since the gap between the

savings curve and the effective depreciation line is still greater than that for

the developing country, that is, a–b < c–e.

Robert Lucas (2000b) has recently presented a numerical simulation of

world income dynamics in a model which captures certain features of the

diffusion of the Industrial Revolution across the world’s economies (see

Snowdon, 2002a). In discussing prospects for the twenty-first century Lucas

concludes from his simulation exercise that ‘the restoration of inter-society

income equality will be one of the major economic events of the century to

come’. In the twenty-first century we will witness ‘Convergence, Big Time’!

In short, we will witness an ever-growing ‘convergence club’ as sooner or

later ‘everyone will join the Industrial Revolution’.

In Lucas’s model the followers grow faster than the leader and will eventually

converge on the income per capita level of the leader, ‘but will never

surpass the leader’s level’. As followers catch up the leader Lucas assumes

that their growth rates converge towards that of the leader, that is, 2 per cent.

The probability that a pre-industrial country will begin to grow is positively

related to the level of production in the rest of the world which in turn reflects

past growth experienced. There are several possible sources of the diffusion

of the Industrial Revolution from leaders to followers, for example:

1. diffusion via spillovers due to human capital externalities (Tamura, 1996),

the idea that ‘knowledge produced anywhere benefits people everywhere’;

2. diffusion via adopting the policies and institutions of the successful

countries thus removing the barriers to growth (Olson, 1996; Parente and

Prescott, 1999, 2000);

3. diffusion due to diminishing returns leading to capital flows to the lowincome

economies (Lucas, 1990b).

Lucas’s simulations predict that the diffusion of the Industrial Revolution

was relatively slow for the nineteenth century but accelerated ‘dramatically’ in

the twentieth century, finally slowing down towards the year 2000 ‘because

there are so few people left in stagnant, pre-industrial economies’. In Lucas’s

simulation, by the year 2000, 90 per cent of the world is growing. Given the

rate of diffusion, world income inequality at first increases, peaking some time

in the 1970s, and then declines, ‘ultimately to zero’. According to Lucas, the

long phase of increasing world income inequality, discussed by Pritchett (1997),

has passed. The growth rate of world production is predicted by the model to

peak ‘around 1970’ and thereafter decline towards a rate of 2 per cent sometime

just beyond the year 2100. The predictions of Lucas’s model appear ‘consistent

with what we know about the behaviour of per capita incomes in the last two

centuries’ (Lucas, 2000). However, Crafts and Venables (2002) do not share the

optimism of Lucas. Taking into account geographical and agglomeration factors,

they conclude that the playing field is not level and therefore the convergence

possibilities among the poor countries are much more limited than is suggested

by Lucas. Rather, we are likely to observe the rapid convergence of a selected

group of countries (for detailed and contrasting views on the evolution of

global income distribution see Sala-i-Martin, 2002a, 2002b; Bourguignon and

Morrisson, 2002; Milanovic, 2002).

While Solow’s model predicts conditional convergence and explains growth

differences in terms of ‘transitional dynamics’, an alternative ‘catch-up’ hypothesis

emphasizes technological gaps between those economies behind the

innovation frontier and the technologically advanced leader economies

(Gerschenkron, 1962; Abramovitz, 1986, 1989, 1990, 1993). The ‘catch-up’

literature also places more emphasis on historical analysis, social capability

and institutional factors (see Fagerberg, 1995).

Whereas in the Solow model the main mechanism leading to differential

growth rates relates to rates of capital accumulation, in the catch-up model it

is the potential for low income per capita countries to adopt the technology of

the more advanced countries that establishes the potential for poor countries

to grow more rapidly than rich countries. In other words, there appear to be

three potential (proximate) sources of growth of labour productivity, namely:

1. growth through physical and human capital accumulation;

2. growth through technological change reflecting shifts in the world production

frontier;

3. growth through technological catch-up involving movement toward the

world production frontier.

In other words, poor countries have the additional opportunity to grow faster

by moving toward the technological frontier representing ‘best practice’ technology,

or as P. Romer (1993) puts it, poor countries need to reduce their

‘idea gaps’ rather than ‘object gaps’. Kumar and Russell (2002) find that

there is ‘substantial evidence of technological catch-up’ while Parente and

Prescott (2000) have emphasized that in many countries the failure to adopt

‘best practice’ technology is due to barriers that have been erected to protect

specific groups who will be adversely affected (at least in the short run) by

the changes that would result from technological change. Both the neoclassical

and catch-up arguments imply that economic growth rates are likely to be

closely related to per capita GDP, with poor economies benefiting in terms of

economic growth from their relative backwardness. There is also accumulating

evidence that more open economies converge faster than closed economies

(Sachs and Warner, 1995; Krueger, 1997, 1998; Edwards, 1993, 1998; Parente

and Prescott, 2000). While this appears to be true in the modern era, Baldwin

et al. (2001) argue that during the Industrial Revolution international trade

initially contributed to the divergence between rich and poor countries. However,

they also suggest that in the modern era, the huge reduction in the

transaction costs of trading ideas ‘can be the key to southern industrialisation’

(see also Galor and Mountford, 2003).

Finally, we should note that while there has been ‘Divergence, Big Time’

with respect to per capita GDP, this is in ‘stark contrast’ to what has been

happening across the globe with respect to life expectancy, where there has

been considerable convergence. Becker et al. (2003) compute a ‘full income’

measure for 49 developed and developing countries for the period 1965–95

that includes estimates of the monetized gains from increased longevity. By

estimating economic welfare in terms of the quantity of life, as well as the

quality of life, Becker et al. show that the absence of income convergence is

reversed. ‘Countries starting with lower income grew more in terms of this

“full income” measure. Growth rates of “full income” for the period average

140% for developed countries, and 192% for developing countries’ (see also

Crafts, 2003).