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11.16 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−αβ 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).