Accounting for the Sources of Economic Growth
Economists not only need a theoretical framework for understanding the
causes of growth; they also require a simple method of calculating the relative
importance of capital, labour and technology in the growth experience of
actual economies. The established framework, following Solow’s (1957) seminal
contribution, is called ‘growth accounting’ (see Abel and Bernanke, 2001.
Some economists remain highly sceptical about the whole methodology and
theoretical basis of growth accounting, for example Nelson, 1973). As far as
the proximate causes of growth are concerned we can see by referring back to
equation (11.28) that increases in total GDP (Y) come from the combined
weighted impact of capital accumulation, labour supply growth and technological
progress. Economists can measure changes in the amount of capital
and labour that occur in an economy over time, but changes in technology
(total factor productivity = TFP) are not directly observable. However, it is
possible to measure changes in TFP as a ‘residual’ after taking into account
the contributions to growth made by changes in the capital and labour inputs.
Solow’s (1957) technique was to define technological change as changes in
aggregate output minus the sum of the weighted contributions of the labour
and capital inputs. In short, the Solow residual measures that part of a change
in aggregate output which cannot be explained by changes in the measurable
quantities of capital and labour inputs. The derivation of the Solow residual
can be shown as follows. The aggregate production function in equation
(11.28) shows that output (Y) is dependent on the inputs of capital (K), labour
(L) and the currently available technology (A), which acts as an index of total
The renaissance of economic growth research 613
factor productivity. Output will change if A, K or L change. In equation
(11.28) the exponent on the capital shock α measures the elasticity of output
with respect to capital and the exponent on the labour input (1 – α) measures
the elasticity of output with respect to labour. The weights α and 1 – α are
estimated from national income statistics and reflect the income shares of
capital and labour respectively. Since these weights sum to unity, this indicates
that (11.28) is a constant returns to scale production function. Hence an
equal percentage increase in both factor inputs (K and L) will increase Y by
the same percentage. Since the growth rate of the product of the inputs will
be the growth rate of A plus the growth rate of Kα plus the growth rate of L1–α,
equation (11.28) can be rewritten as (11.31), which is the basic growth
accounting equation used in numerous empirical studies of the sources of
economic growth (see Maddison, 1972, 1987; Denison, 1985; Young, 1995,
Crafts, 2000; Jorgenson, 2001).
ΔY/Y = ΔA/A + αΔK/K + (1− α)ΔL/L (11.31)
Equation (11.31) is simply the Cobb–Douglas production function written in
a form representing rates of change. It shows that the growth of aggregate
output (ΔY/Y) depends on the contribution of changes in total factor productivity
(ΔA/A), changes in the weighted contribution of capital, αΔK/K, and
changes in the weighted contribution of labour (1 – α)ΔL/L. By rearranging
equation (11.28) we can represent the productivity index (TFP) which we
need to measure as equation (11.32):
TFP = A = Y / KαL1−α (11.32)
As already noted, because there is no direct way of measuring TFP it has to
be estimated as a residual. By writing down equation (11.32) in terms of rates
of change we can obtain an equation from which the growth of TFP (technological
change) can be estimated as a residual. This is shown in equation
(11.33):
ΔA/A = ΔY/Y −[αΔK/K + (1− α)ΔL/L] (11.33)
Data relating to output and the capital and labour inputs are available. Estimates
of α and hence 1 – α can be acquired from historical national income
data. For example, in Solow’s original paper covering the US economy for
the period 1909–49 he estimated that the rate of growth of total output (ΔY/Y)
had averaged 2.9 per cent per year, of which 0.32 percentage points could be
attributed to capital (αΔK/K), 1.09 percentage points could be attributed to
labour (1 – αΔL/L), leaving a ‘Solow residual’ (ΔA/A) of 1.49 percentage
points. In other words, almost half of the growth experienced in the USA
during this period was due to unexplained technological progress! In Denison’s
(1985) later work he found that for the period 1929–82, ΔY/Y = 2.92 per cent,
of which 1.02 percentage points were be attributed to ΔA/A. More recent
controversial research by Alwyn Young (1992, 1994, 1995) on the sources of
growth in the East Asian Tiger economies has suggested estimates of rates of
growth of TFP for Taiwan of 2.6 per cent, for South Korea of 1.7 per cent, for
Hong Kong of 1.7 per cent and for Singapore a meagre 0.2 per cent! So
although these economies have experienced unprecedented growth rates of
GDP since the early 1960s, Young’s research suggests that these economies
are examples of miracles of accumulation. Once we account for the growth of
labour and physical and human capital there is little left to explain, especially
in the case of Singapore (see Krugman, 1994b; Hsieh, 1999; Bhagwati,
2000). Going further back in history, Nick Crafts (1994, 1995) has provided
estimates of the sources of growth for the British economy during the period
1760–1913. Crafts’s estimates suggest that ‘by twentieth century standards
both the output growth rates and the TFP rates are quite modest’ (Crafts,
1995).
The most obvious feature of the post-1973 growth accounting data is the
well-known puzzle of the ‘productivity slowdown’. This slowdown has been
attributed to many possible causes, including the adverse impact on investment
and existing capital stocks of the 1970s oil price shocks, a slowdown in
the rate of innovation, adverse demographic trends, an increasingly regulatory
environment and problems associated with measurement such as
accounting for quality changes (Fischer et al., 1988).
In a recent survey of the growth accounting literature Bosworth and Collins
(2003) reaffirm their belief that growth accounting techniques can yield
useful and consistent results. In the debate over the relative importance of
capital accumulation v. TFP in accounting for growth Bosworth and Collins
conclude that ‘both are important’ and that ‘some of the earlier research
understates the role of capital accumulation because of inadequate measurement
of the capital input’.
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
616 Modern macroeconomics
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 Com
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
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’
The renaissance of economic growth research 621
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).
Economists not only need a theoretical framework for understanding the
causes of growth; they also require a simple method of calculating the relative
importance of capital, labour and technology in the growth experience of
actual economies. The established framework, following Solow’s (1957) seminal
contribution, is called ‘growth accounting’ (see Abel and Bernanke, 2001.
Some economists remain highly sceptical about the whole methodology and
theoretical basis of growth accounting, for example Nelson, 1973). As far as
the proximate causes of growth are concerned we can see by referring back to
equation (11.28) that increases in total GDP (Y) come from the combined
weighted impact of capital accumulation, labour supply growth and technological
progress. Economists can measure changes in the amount of capital
and labour that occur in an economy over time, but changes in technology
(total factor productivity = TFP) are not directly observable. However, it is
possible to measure changes in TFP as a ‘residual’ after taking into account
the contributions to growth made by changes in the capital and labour inputs.
Solow’s (1957) technique was to define technological change as changes in
aggregate output minus the sum of the weighted contributions of the labour
and capital inputs. In short, the Solow residual measures that part of a change
in aggregate output which cannot be explained by changes in the measurable
quantities of capital and labour inputs. The derivation of the Solow residual
can be shown as follows. The aggregate production function in equation
(11.28) shows that output (Y) is dependent on the inputs of capital (K), labour
(L) and the currently available technology (A), which acts as an index of total
The renaissance of economic growth research 613
factor productivity. Output will change if A, K or L change. In equation
(11.28) the exponent on the capital shock α measures the elasticity of output
with respect to capital and the exponent on the labour input (1 – α) measures
the elasticity of output with respect to labour. The weights α and 1 – α are
estimated from national income statistics and reflect the income shares of
capital and labour respectively. Since these weights sum to unity, this indicates
that (11.28) is a constant returns to scale production function. Hence an
equal percentage increase in both factor inputs (K and L) will increase Y by
the same percentage. Since the growth rate of the product of the inputs will
be the growth rate of A plus the growth rate of Kα plus the growth rate of L1–α,
equation (11.28) can be rewritten as (11.31), which is the basic growth
accounting equation used in numerous empirical studies of the sources of
economic growth (see Maddison, 1972, 1987; Denison, 1985; Young, 1995,
Crafts, 2000; Jorgenson, 2001).
ΔY/Y = ΔA/A + αΔK/K + (1− α)ΔL/L (11.31)
Equation (11.31) is simply the Cobb–Douglas production function written in
a form representing rates of change. It shows that the growth of aggregate
output (ΔY/Y) depends on the contribution of changes in total factor productivity
(ΔA/A), changes in the weighted contribution of capital, αΔK/K, and
changes in the weighted contribution of labour (1 – α)ΔL/L. By rearranging
equation (11.28) we can represent the productivity index (TFP) which we
need to measure as equation (11.32):
TFP = A = Y / KαL1−α (11.32)
As already noted, because there is no direct way of measuring TFP it has to
be estimated as a residual. By writing down equation (11.32) in terms of rates
of change we can obtain an equation from which the growth of TFP (technological
change) can be estimated as a residual. This is shown in equation
(11.33):
ΔA/A = ΔY/Y −[αΔK/K + (1− α)ΔL/L] (11.33)
Data relating to output and the capital and labour inputs are available. Estimates
of α and hence 1 – α can be acquired from historical national income
data. For example, in Solow’s original paper covering the US economy for
the period 1909–49 he estimated that the rate of growth of total output (ΔY/Y)
had averaged 2.9 per cent per year, of which 0.32 percentage points could be
attributed to capital (αΔK/K), 1.09 percentage points could be attributed to
labour (1 – αΔL/L), leaving a ‘Solow residual’ (ΔA/A) of 1.49 percentage
points. In other words, almost half of the growth experienced in the USA
during this period was due to unexplained technological progress! In Denison’s
(1985) later work he found that for the period 1929–82, ΔY/Y = 2.92 per cent,
of which 1.02 percentage points were be attributed to ΔA/A. More recent
controversial research by Alwyn Young (1992, 1994, 1995) on the sources of
growth in the East Asian Tiger economies has suggested estimates of rates of
growth of TFP for Taiwan of 2.6 per cent, for South Korea of 1.7 per cent, for
Hong Kong of 1.7 per cent and for Singapore a meagre 0.2 per cent! So
although these economies have experienced unprecedented growth rates of
GDP since the early 1960s, Young’s research suggests that these economies
are examples of miracles of accumulation. Once we account for the growth of
labour and physical and human capital there is little left to explain, especially
in the case of Singapore (see Krugman, 1994b; Hsieh, 1999; Bhagwati,
2000). Going further back in history, Nick Crafts (1994, 1995) has provided
estimates of the sources of growth for the British economy during the period
1760–1913. Crafts’s estimates suggest that ‘by twentieth century standards
both the output growth rates and the TFP rates are quite modest’ (Crafts,
1995).
The most obvious feature of the post-1973 growth accounting data is the
well-known puzzle of the ‘productivity slowdown’. This slowdown has been
attributed to many possible causes, including the adverse impact on investment
and existing capital stocks of the 1970s oil price shocks, a slowdown in
the rate of innovation, adverse demographic trends, an increasingly regulatory
environment and problems associated with measurement such as
accounting for quality changes (Fischer et al., 1988).
In a recent survey of the growth accounting literature Bosworth and Collins
(2003) reaffirm their belief that growth accounting techniques can yield
useful and consistent results. In the debate over the relative importance of
capital accumulation v. TFP in accounting for growth Bosworth and Collins
conclude that ‘both are important’ and that ‘some of the earlier research
understates the role of capital accumulation because of inadequate measurement
of the capital input’.
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
616 Modern macroeconomics
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 Com
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
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’
The renaissance of economic growth research 621
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).
No comments:
Post a Comment