# 11.13 Beyond the Solow Model

Although the lack of a theory of technological change is a clear weakness of

the basic neoclassical growth model, Mankiw (1995) argues that many general

predictions from the theory are ‘broadly consistent with experience’. For

example, cross-country data indicate a strong negative correlation between

population growth and income per capita and a strong positive correlation

between income per capita and savings/investment rates (Jones, 2001a). As

predicted by the model, rates of growth in the rich OECD economies are

relatively low while rapid growth rates have been observed in countries

moving from an initial position of relatively low income per capita and low

capital intensity. There is also strong evidence of convergence among relatively

homogeneous economies such as the OECD and between regions and

states within the USA, Europe and Japan (Baumol, 1986; Barro and Sala-i-

Martin, 1995). In larger, more diverse data sets there is little evidence of the

expected negative relationship between growth rates and some initial (for

example 1960) level of income per capita, that is, absolute convergence (P.

Romer, 1986, 1989; DeLong, 1988). However, ‘the central idea of conditional

convergence receives strong support from the data’ (Barro, 1991, 1997)

and has considerable explanatory power for both countries and regions. The

growth accounting research of Alwyn Young (1992, 1994, 1995) has shown

that the rapid growth of the Asian Tiger economies is easily explicable and

can be attributed mainly to rapid accumulation of factor inputs rather than

unusually high total factor productivity growth. As Paul Krugman (1994b)

argues, an implication of this research is that this rapid growth can therefore

be expected to slow down considerably in the future, as it has already done in

Japan. The Solow model has also been used to provide a plausible ‘reconstruction’

account of the ‘miracles’ of Japanese and German post-1945 growth,

and also the relatively good growth performance of France and Italy, in terms

of the transitional dynamics towards a high income per capita steady state. It

seems plausible that these economies grew rapidly in the post-war period

because they were ‘reconstructing’ their capital stock following the destruction

resulting from the Second World War.

However, there are a number of important deficiencies and puzzles which

the Solow model finds difficult to overcome and explain. First, in the Solow

model, while economic policy can permanently influence the level of per

capita output (for example by raising the savings ratio via tax inducements),

it cannot alter the path of long-run growth. Growth rates can only be increased

temporarily during the transitional dynamics en route to the new

steady state. Cross-country growth differentials are also explained in terms of

the transitional dynamics which allow countries to grow faster than their

long-run sustainable growth rates. Sustained growth in the Solow model is

only possible if there is technological progress, since without it per capita

income growth will eventually cease due to the impact of diminishing returns

to capital accumulation. Given that per capita incomes have been rising for

over 100 years in a large number of countries, and growth rates have displayed

no overall tendency to decline, the role of technological progress in

the Solow model in explaining sustainable growth becomes crucial. But

herein lies the obvious shortcoming of the neoclassical model since ‘the

long-run per capita growth rate is determined entirely by an element – the

rate of technological progress – that is outside the model … Thus we end up

with a model of growth that explains everything but long-run growth, an

obviously unsatisfactory situation’ (Barro and Sala-i-Martin, 1995). Furthermore,

as P. Romer (1989) highlights, in terms of policy advice for long-term

growth the neoclassical model has little to offer!

A second problem relates to the evidence, which clearly shows that income

per capita differentials across the world are much greater than predicted by

the model. Differences across countries in capital intensities are too small to

account for the observed disparities in real incomes. Using a Cobb–Douglas

production function framework it is possible to allocate differences in the

level of per capita incomes between countries to variations in levels of total

factor productivity growth and the accumulation of factor inputs. In particular

it is possible to estimate how much of the income disparities witnessed

between rich and poor countries can be attributed to different capital intensities

since total factor productivity is common across all countries. Substituting

from equation (11.34) to equation (11.26) gives equation (11.38):

k˙ = skα − (n + δ)k (11.38)

Setting this equation equal to zero (the steady state condition) and substituting

into the production function yields (11.39):

y* = [s/(n + δ)]α/(1−α) (11.39)

Equation (11.39) is now in a form that enables a solution to be found for the

steady state output per worker (y*). As Jones (2001a) highlights, we can see

from equation (11.39) why some countries are so rich and some are so poor.

Assuming exogenous technology and a similar value for the capital exponent

(α), countries that sustain high rates of saving, and low rates of population

growth and depreciation, will be rich. According to the neoclassical growth

model the high-income economies have achieved their high living standards

because they have accumulated large per worker stocks of capital. However,

although the model correctly predicts the directions of the effects of saving

and population growth on output per worker, it does not correctly predict the

magnitudes. As Mankiw et al. (1992) and Mankiw (1995) argue, the gaps in

output per worker (living standards) between rich and poor countries are

much larger than plausible estimates of savings rates and population growth

predict using equation (11.39). The crux of the problem is that with α = 1/3

there are sharply diminishing returns to capital. This implies that a tenfold

gap in output per worker between the USA and India would require a thousandfold

difference in the capital–labour ratios between these countries! (It

should be noted that this result is highly sensitive to the choice of α = 1/3 for

the share of capital in GDP.)

A third problem with the Solow model is that given a common production

function (that is, exogenous technology) the marginal product of capital

should be much higher in poor countries than in rich countries. Given the

parameters of the Solow model, the observed tenfold differential in output

per worker between rich and poor countries implies a hundredfold difference

in the marginal product of capital if output gaps are entirely due to variations

in capital intensities. Such differentials in the rate of return to capital are

simply not observed between rich and poor countries. As David Romer

(1996) observes, such differences in rates of return ‘would swamp such

considerations as capital market imperfections, government tax policies, fear

of expropriation and so on and we would observe immense flows of capital

from rich to poor countries. We do not see such flows.’ But the rate of return

to capital in poor countries is less than expected and the anticipated massive

flows of capital from rich to poor countries have not been observed across

poor countries as a whole (Lucas, 1990b).

A fourth difficulty relates to the rate of convergence, which is only about

half that predicted by the model. The economy’s initial conditions influence

the outcome for much longer than the model says it should (Mankiw, 1995).

In conclusion, it appears that within the Solow growth framework, physical

capital accumulation alone cannot account for either continuous growth of

per capita income over long periods of time or the enormous geographical

disparities in living standards that we observe. In terms of Figure 11.3, the

data on output per worker (or income per capita) that we actually observe

across the world reveal much greater disparities than those predicted by the

Solow model based on differences in capital per worker.

The new growth models emerging after 1986 depart from the Solow model

in three main ways. One group of models generates continuous growth by

abandoning the assumption of diminishing returns to capital accumulation.

To achieve this, Paul Romer (1986) introduced positive externalities from

capital accumulation so that the creation of economy-wide knowledge emerges

as a by-product of the investment activity of individual firms, a case of

‘learning by investing’ (Barro and Sala-i-Martin, 2003). A second approach

models the accumulation of knowledge as the outcome of purposeful acts by

entrepreneurs seeking to maximize private profits; that is, technological

progress is endogenized (P. Romer, 1990). A third class of model claims that

the role of capital is much more important than is suggested by the α term in

the conventional Cobb–Douglas production function shown in equations

(11.28)–(11.30). In their ‘augmented’ Solow model, Mankiw et al. (1992)

broaden the concept of capital to include ‘human capital’. The first two

classes of model constitute the core of endogenous growth theory whereas

the Mankiw, Romer and Weil (MRW) model constitutes what Klenow and

Rodriguez-Clare (1997a, 1997b) call a ‘neoclassical revival’. The central

proposition of endogenous growth theory is that broad capital accumulation

(physical and human capital) does not experience diminishing returns. The

growth process is driven by the accumulation of broad capital together with

the production of new knowledge created through research and development.

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