macro chapter 6 summary
chapter 6 education and growth
1. The quality and skills of the labour force are of obvious importance in human production. In
th is chapter we amended the Solow model to include human capital, defined as the stock of
skills accumulated by workers through education and training. The stock of human capital
was included among the essential inputs besides physical capital and 'raw' labour.
2. In some respects human capital was treated just like physical capital: we assumed that in
each period there is a certain stock, H,. of human capital, that human capital enters into an
aggregate production function with constant returns to scale, Y, = K;'Hy(A,L,) 1 - " - "', parallel
to the way physical capital enters, and that human capital accumulates by a certain fraction,
sH, of GOP being added to it each year. While empirical estimates of investment rates in
physical capital are directly available from national accounts, nothing similar is true for Sw We
argued that since the most important part of investment in human capital is the GOP and
income forgone while people educate themselves, the fraction of people of working age in
education should give a good approximation of Sw Using th is idea, empirical estimates of sH
can be obtained across countries.
3. In one important respect human capital must be treated differently from physical capital: since
human capital is embodied in persons, a firm cannot change its input of human capital and of
(raw) labour independently. We made the simplifying assumption that each worker is
equipped with the same amount of human capital, so each worker embodies a human capital
of h,= H,/L,, and hiring one worker means increasing raw labour input by one unit and
increasing the input of human capital by h,. Hence there is no separate market for the services
of human capital: these are traded together with raw labour, and the return to human capital
appears as a part of the real wage which is thus really a mix of a reward to raw labour and a
return to human capital. Furthermore, in the computation of the marginal product of labour that
determines the real wage, one should take human capital per worker, not total human capital,
as given.
4. Our considerations on how to deal with human capital led to a model characterized by the following
features:
e The aggregate production function was as stated above. From empirical evidence on
labour's share and on average wages compared to the wages of unskilled workers, we
inferred that plausible parameter values could be a. = cp = ~·
e The prices of capital and labour were given by the marginal products.
e The stocks of physical and human capital accumulated as implied by given investment
rates, sK and sH, respectively, and a common depreciation rate.
e The labour force as well as the technological variable A to grew at exogenously given rates.
5. The model implied convergence to a well-defined steady state in which GOP per worker
follows a specific growth path with constant growth rate (equal to the exogenous growth rate
of A,). The 'steady state equation' told how the growth path depends on model parameters.
According to the steady state equation:
• An increase in sK has a larger positive impact on GOP per worker than in the general
Solow model because the rise in GOP occurring as more physical capital is accumulated
will cause more human capital to be accumulated, reinforcing the increase in GOP.
e An increase in the population growth rate has a stronger negative impact on GOP per
worker than was the case in the general Solow model, because population growth now
means thinning out of both physical and human capital.
• An increase in sH has a positive impact on GOP per worker similar to that of an increase
in SK .
These features were promising for an empirical test since they appeared to remedy the
empirical shortcomings of the general Solow model's steady state prediction that we had
identified.
6. Confronting our model's steady state prediction with cross-country empirical evidence under
the heroic assumptions that the countries considered were in steady state in year 2000 and
all had the same technological level in that year, we found that the model did remarkably well
and actually went a long way towards solving the empirical problems with the general Solow
model's steady state prediction. This was evidence that countries are perhaps not as technologically
different as usually thought.
7. The steady state analysis supported policy recommendations of ensuring adequate savings
and investment rates and keeping population growth rates down, the latter now being even
more strongly supported than earlier. The really new issue was government polic ies to provide
for or subsidize education. Such policies are recommendable according to our model in so far
as one cannot fully trust private decision making and markets to devote a suffic ient amount of
resources to educational purposes. We gave several reasons why a market-determined
allocation would not be optimal, implying that educational policies should be at the forefront
of structural policies to promote prosperity and growth (as indeed they are in many countries).
8. The general prediction of economic performance derived from the Solow model with human
capital is the convergence process implied by the model. From the model one can derive a
'convergence equation' telling how a country's average annual growth rate of GOP per worker
over some period should depend on parameters and on the country's initial GOP per worker.
The structure of the equation is such that the growth rate equals the underlying technological
growth rate adjusted upwards for how far below steady state the country was initially, and for
the speed by which the country converges to steady state. The rate of convergence depends
in a simple way on model parameters and (ceteris paribus) it is smaller for the Solow model
with human capital than for the general Solow model. The reason is that capital accumulation
takes time and delays convergence, and there is more capital to accumulate when there is
also human capital. This was again promising from an empirical point of view since we have
found the general Solow model to overestimate the rate of convergence.
9. Estimating the model's convergence equation on cross-country data gave a remarkably good
result and in particular a much improved accordance between the estimated rate of convergence
and the one predicted by the model. The good result was strongly in support of the
idea of conditional convergence among the countries of the world and gave an indication that
countries are perhaps also more similar with respect to their technological growth rates than
usually thought.
10. We closed this chapter with a discussion of where to go from here. We concluded that a main
further job is to explain the technological growth rate that is the source of long-run economic
growth. This points further to theories of endogenous growth.
1. The quality and skills of the labour force are of obvious importance in human production. In
th is chapter we amended the Solow model to include human capital, defined as the stock of
skills accumulated by workers through education and training. The stock of human capital
was included among the essential inputs besides physical capital and 'raw' labour.
2. In some respects human capital was treated just like physical capital: we assumed that in
each period there is a certain stock, H,. of human capital, that human capital enters into an
aggregate production function with constant returns to scale, Y, = K;'Hy(A,L,) 1 - " - "', parallel
to the way physical capital enters, and that human capital accumulates by a certain fraction,
sH, of GOP being added to it each year. While empirical estimates of investment rates in
physical capital are directly available from national accounts, nothing similar is true for Sw We
argued that since the most important part of investment in human capital is the GOP and
income forgone while people educate themselves, the fraction of people of working age in
education should give a good approximation of Sw Using th is idea, empirical estimates of sH
can be obtained across countries.
3. In one important respect human capital must be treated differently from physical capital: since
human capital is embodied in persons, a firm cannot change its input of human capital and of
(raw) labour independently. We made the simplifying assumption that each worker is
equipped with the same amount of human capital, so each worker embodies a human capital
of h,= H,/L,, and hiring one worker means increasing raw labour input by one unit and
increasing the input of human capital by h,. Hence there is no separate market for the services
of human capital: these are traded together with raw labour, and the return to human capital
appears as a part of the real wage which is thus really a mix of a reward to raw labour and a
return to human capital. Furthermore, in the computation of the marginal product of labour that
determines the real wage, one should take human capital per worker, not total human capital,
as given.
4. Our considerations on how to deal with human capital led to a model characterized by the following
features:
e The aggregate production function was as stated above. From empirical evidence on
labour's share and on average wages compared to the wages of unskilled workers, we
inferred that plausible parameter values could be a. = cp = ~·
e The prices of capital and labour were given by the marginal products.
e The stocks of physical and human capital accumulated as implied by given investment
rates, sK and sH, respectively, and a common depreciation rate.
e The labour force as well as the technological variable A to grew at exogenously given rates.
5. The model implied convergence to a well-defined steady state in which GOP per worker
follows a specific growth path with constant growth rate (equal to the exogenous growth rate
of A,). The 'steady state equation' told how the growth path depends on model parameters.
According to the steady state equation:
• An increase in sK has a larger positive impact on GOP per worker than in the general
Solow model because the rise in GOP occurring as more physical capital is accumulated
will cause more human capital to be accumulated, reinforcing the increase in GOP.
e An increase in the population growth rate has a stronger negative impact on GOP per
worker than was the case in the general Solow model, because population growth now
means thinning out of both physical and human capital.
• An increase in sH has a positive impact on GOP per worker similar to that of an increase
in SK .
These features were promising for an empirical test since they appeared to remedy the
empirical shortcomings of the general Solow model's steady state prediction that we had
identified.
6. Confronting our model's steady state prediction with cross-country empirical evidence under
the heroic assumptions that the countries considered were in steady state in year 2000 and
all had the same technological level in that year, we found that the model did remarkably well
and actually went a long way towards solving the empirical problems with the general Solow
model's steady state prediction. This was evidence that countries are perhaps not as technologically
different as usually thought.
7. The steady state analysis supported policy recommendations of ensuring adequate savings
and investment rates and keeping population growth rates down, the latter now being even
more strongly supported than earlier. The really new issue was government polic ies to provide
for or subsidize education. Such policies are recommendable according to our model in so far
as one cannot fully trust private decision making and markets to devote a suffic ient amount of
resources to educational purposes. We gave several reasons why a market-determined
allocation would not be optimal, implying that educational policies should be at the forefront
of structural policies to promote prosperity and growth (as indeed they are in many countries).
8. The general prediction of economic performance derived from the Solow model with human
capital is the convergence process implied by the model. From the model one can derive a
'convergence equation' telling how a country's average annual growth rate of GOP per worker
over some period should depend on parameters and on the country's initial GOP per worker.
The structure of the equation is such that the growth rate equals the underlying technological
growth rate adjusted upwards for how far below steady state the country was initially, and for
the speed by which the country converges to steady state. The rate of convergence depends
in a simple way on model parameters and (ceteris paribus) it is smaller for the Solow model
with human capital than for the general Solow model. The reason is that capital accumulation
takes time and delays convergence, and there is more capital to accumulate when there is
also human capital. This was again promising from an empirical point of view since we have
found the general Solow model to overestimate the rate of convergence.
9. Estimating the model's convergence equation on cross-country data gave a remarkably good
result and in particular a much improved accordance between the estimated rate of convergence
and the one predicted by the model. The good result was strongly in support of the
idea of conditional convergence among the countries of the world and gave an indication that
countries are perhaps also more similar with respect to their technological growth rates than
usually thought.
10. We closed this chapter with a discussion of where to go from here. We concluded that a main
further job is to explain the technological growth rate that is the source of long-run economic
growth. This points further to theories of endogenous growth.
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