An Augmented Solow Model: A Neoclassical Revival?
As it stands, the neoclassical growth model, relying as it does on differences
in capital–labour ratios across countries to explain the wide disparities in
levels of per capita output, cannot satisfactorily explain world income differentials.
In response to this deficiency Mankiw et al. (1992) ‘augment’ the
Solow model by including the accumulation of human capital as well as
physical capital. The key to their approach is the argument that the conventional
estimate of α, capital’s income share, may not be a good indicator of
the overall contribution of capital. By adding human capital to the model the
production function becomes (11.43):
Y = KαHβ (AL)1−α−β and α + β < 1 (11.43)
Here we now have four factors of production combining to produce output
where H is the stock of human capital and AL is the labour input measured in
efficiency units, which captures both the quantity of labour and the productivity
of labour determined by available technology (see Mankiw, 2003). The production
function exhibits constant returns to scale and with α + β < 1 there
are diminishing returns to ‘broad capital’. But with a larger capital share (α +
β = 2/3) the average product of labour declines more slowly as accumulation
takes place since the size of the capital share determines the curvature of the
production function and hence the speed at which diminishing returns set in.
Diminishing returns to the broader concept of capital will be much less
severe than in the traditional Solow model where α = 1/3. When α is small,
the curvature of the production function in Figure 11.3 is large. But by
augmenting the model with human capital, the transition to the steady state is
much slower and 80 per cent of international differences in living standards
can be explained by differences in the rate of population growth and the
accumulation of both human and physical capital (Mankiw et al., 1992;
Mankiw, 1995). The transitory impact of any increase in the rate of investment
in the MRW model will have prolonged effects. However, because the
exponents on K and H sum to less than one, this ‘neoclassical revival’ in
growth theory does not provide a model of endogenous growth. Per capita
income will eventually settle down in a steady state and grow at the
exogenously determined rate of technological progress.
For some critics the MRW model, by taking the public-good view of
technology, has failed to address the crucial issue of variations in total factor
productivity growth and technical efficiency across nations (Klenow amd
Rodriguez-Clare, 1997a; 1997b). While the augmented Solow model better
explains international differences in living standards, it cannot account for
the persistence of economic growth. Endogenous growth theory attempts to
show how persistent growth may take place without having to resort to
exogenous technological progress (Bernanke and Gurkaynak, 2001).
As it stands, the neoclassical growth model, relying as it does on differences
in capital–labour ratios across countries to explain the wide disparities in
levels of per capita output, cannot satisfactorily explain world income differentials.
In response to this deficiency Mankiw et al. (1992) ‘augment’ the
Solow model by including the accumulation of human capital as well as
physical capital. The key to their approach is the argument that the conventional
estimate of α, capital’s income share, may not be a good indicator of
the overall contribution of capital. By adding human capital to the model the
production function becomes (11.43):
Y = KαHβ (AL)1−α−β and α + β < 1 (11.43)
Here we now have four factors of production combining to produce output
where H is the stock of human capital and AL is the labour input measured in
efficiency units, which captures both the quantity of labour and the productivity
of labour determined by available technology (see Mankiw, 2003). The production
function exhibits constant returns to scale and with α + β < 1 there
are diminishing returns to ‘broad capital’. But with a larger capital share (α +
β = 2/3) the average product of labour declines more slowly as accumulation
takes place since the size of the capital share determines the curvature of the
production function and hence the speed at which diminishing returns set in.
Diminishing returns to the broader concept of capital will be much less
severe than in the traditional Solow model where α = 1/3. When α is small,
the curvature of the production function in Figure 11.3 is large. But by
augmenting the model with human capital, the transition to the steady state is
much slower and 80 per cent of international differences in living standards
can be explained by differences in the rate of population growth and the
accumulation of both human and physical capital (Mankiw et al., 1992;
Mankiw, 1995). The transitory impact of any increase in the rate of investment
in the MRW model will have prolonged effects. However, because the
exponents on K and H sum to less than one, this ‘neoclassical revival’ in
growth theory does not provide a model of endogenous growth. Per capita
income will eventually settle down in a steady state and grow at the
exogenously determined rate of technological progress.
For some critics the MRW model, by taking the public-good view of
technology, has failed to address the crucial issue of variations in total factor
productivity growth and technical efficiency across nations (Klenow amd
Rodriguez-Clare, 1997a; 1997b). While the augmented Solow model better
explains international differences in living standards, it cannot account for
the persistence of economic growth. Endogenous growth theory attempts to
show how persistent growth may take place without having to resort to
exogenous technological progress (Bernanke and Gurkaynak, 2001).
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