Original the rate of depreciation. From this we can

Original Solow growth model

In 1956 Robert Solow
proposed an economic model that attempts
to explain long-run economic growth by looking at physical capital accumulation, exogenous population
growth and exogenous technological progress. It predicts that countries
reach different steady states. The higher the saving rate and the lower the
population growth rate, the richer a country is. 

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!

order now

The underlying assumptions
of this model are: decreasing returns to K, positive diminishing marginal
products, constant returns to scale and the Inada condition. The model is based on a ?obb-Douglas production function (Y) with
two inputs, physical capital (K) and labour (L), while also considering the
level of technology (A):



Where a is capital’s
share of income, 0 0.33; for
intermediate countries a = 0.59 ± 0.02 > 0.33; for OECD countries a = 0.36 ± 0.15 » 0.33. Therefore, original Solow
growth model is mostly incorrect. a


Human capital augmented Solow growth model

The Solow model was
augmented by introducing the effect of human capital accumulation, H. The
augmented model lowers the estimated effects of s and n rates to Y/L. Moreover,
it accounts for approximately 80% of the cross-country variation in income. The
augmented model provides an almost complete explanation on why some countries
are rich and others are poor.

The augmented Solow growth
model follows the same assumptions as the original model. The new production
function is:


To explain why this model
works, we must firstly consider three further assumptions. People devote a
fraction of their income to human capital (sH) the same as they do
to physical capital (sK), so a » b » 1/3. sH depreciates at the
same rate as sK, d, so
accumulation of H mirrors that of K. Y produced in the economy
can be used for either consumption or both types of investment.

Following this we are going to prove that the level of growth
should be positively correlated with the initial level of H the same as it is
for K.

Now we rewrite our
production function in the effective labour units (AL) and obtain:  


 where y=Y/AL, k=K/AL, h=H/AL

From this we can determine
the behavior of k and h:

kt· = sKyt
– (n+g+d)kt =

ht· = sHyt
– (n+g+d)ht =


Then by setting the values
of kt·=ht·=o, we get the steady state
values for k and h:

According to the
behavioral equations above, the level of steady-state Y/L is positively related
to sK and sH.. Therefore, an increase in sH
shifts the steady-state level of income upwards, leading to a higher long-run
growth path.

The transitional dynamics of this model are
similar to those of the original Solow model. An upward shift of the steady
state due to an increase in either rate of investment leads to a temporarily
higher economic growth rate while the economy converges to its new steady
state. The graphs below describes the evolution of the growth rate when either
sH or sK are changed.

In the augmented model, the elasticity of
income with respect to the rate of investment is higher than in the original
Solow model. This is because a higher s raises the steady-state level of
income. Therefore, H increases as well even if sH remains unchanged.
Consequently, the level effect due to a change in the investment rate is more
pronounced in the augmented Solow model than in the original version without H.

According to the
behavioral equations, sH has no effect on the long run economic
growth rate, but the rate of technological progress does (g). The augmented model treats H in exactly same way as K.
It is accumulated by investing a fraction of income in its production, it depreciates
at the same rate as K and it is produced with the same technology as both K and
consumption. Therefore, like in the original Solow model, long-run growth is
exogenous and its rate is the same as g.

hypotheses is done similarly as before. We must show that estimated a »
estimated b »
1/3. All the same parameters are chosen as previously and sH (or
SCHOOL) is chosen as the percentage of the working-age population that is in
secondary school.

We can see that R2 has increased significantly
to » 80% for non-oil and intermediate countries,
and to 28% for OECD countries. This represents a better fit of the model. Furthermore,
the estimated values of a are lower for all the samples
compared to the original model and a » b » 1/3 in general. For
non-oil countries a = 0.31 ± 0.04 » 0.33 and b = 0.28 ± 0.03
is not statistically different from 0.33; for intermediate countries a = 0.29 ± 0.05 » 0.33 and b = 0.30 ± 0.04 » 0.33; for OECD
countries a = 0.14 ±
0.15 is proven to be not
statistically different from 0.33 and b = 0.37 ± 0.12 » 0.33.

The conclusion is that the augmented Solow growth
model is an extension of the original model. We assume that our extra input in
the production function – H – is accumulated in the same way as K. When we
increase the stock of H, it does not have any effect on the long-run growth
rate (g). Instead, it has a level effect, which means that the transitional
growth occurs. Y/L grows faster than g in the short run, but in the long run it
converges back to g. The model also predicts that, other things being equal, a
country should have a higher level of Y/L if it has a high amount of H. These
results are the same as in the original Solow growth model. The only difference
is that the results estimated by the augmented model are closer to reality: the
magnitude effects of the s and n coefficients on the Y/L are lower than in
the original model.



·       Lecture Notes

Mankiw N.G., Romer D. and Weil D.N., May
1992, “A contribution to the Empirics of Economic Growth”

Schütt F., August 2003, IWIM – Institute for
World Economics and International Management; “The importance of human capital
to economic growth ”

C.J. “Growth and Human Capital Accumulation – The Augmented Solow model”

·       Ding S. and Knight J., Janyary 2008,
“Can the Augmented Solow model explain China’s economic growth? A Cross-Country
Panel Data Analysis”