University of South Florida
Economic Growth
Department of Economics
Diogo Baerlocher
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1. The Quality of Labor
Given the results from the quantitative exercises from last week, our goal is to search for
reasons why countries with the same quantity of factors of production would achieve different
outputs. Differences in the quality of labor were posed as a strong candidate. For example,
France and Bhutan may have similar labor force sizes, but one would expect that the French
are more productive. Importantly, this productivity must not be due to the larger stock of
capital French workers have available. It must be something related to the individual ability
to produce. We call this individual ability human capital.
Introducing human capital to the Solow model is simple. Just take the production function
and replace raw labor L with the stock of human capital H. But note that the stock of human
capital is the raw labor times the average human capital of workers h. That is H = hL. Then,
Yt = AKtα (Ht )1−α = AKtα (hLt )1−α = (Ah1−α )Ktα Lt1−α .
Therefore, the average stock of human capital acts similarly to the total factor productivity
A such that we can simply replace A with (Ah1−α ) in the steady-state equations we found
previously:
α
α
1−α
1−α
1
1
γ
γ
ss
1−α 1−α
1−α
y = (Ah
)
=A
h
.
n+δ
n+δ
Therefore, this extended version of the model adds the prediction that countries with a larger
stock of human capital per worker must be richer. It also adds the possibility that the average
stock of human capital is pushing the steady-state level of capital outwards, hence being the
engine of growth. Nonetheless, up to this point, we only gave the problem a new name. We
don’t know what total factor productivity is, so we introduce human capital, which we don’t
know as well. Fortunately, we have a better theory for the latter.
2. What is Human Capital?
Again, human capital is anything that boosts the intrinsic worker’s ability to produce.
Traditionally, economists have focused on education as the main component of human capital. The idea is that a college graduate can perform tasks more efficiently than high-school
graduates. You may find this statement too strong. That is why economists tried to incorporate many other components such as experience, in-job training, and health. However, let’s
maintain the assumption that human capital is mainly explained by education attainment.
This lecture is based in the Chapter 6 from David Weil’s textbook.
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HUMAN CAPITAL
The key to computing the stock of human capital per worker is assuming that workers are
paid their marginal product. Then, the wages reflect the worker’s productivity. Additionally,
labor economists tell us that wages increase as years of schooling increase according to a rate
of return to education. For example, suppose that the rate of return to education is 0.1, then
an individual with two years of schooling will earn 10% more than an individual with only
one year of schooling. Labor economists also suggest that this rate decreases as the years of
schooling decreases. They provide the following values for the rate of return to education:
0.134 for the first four years of schooling, 0.101 for the next four years, and 0.068 for years
beyond the 8th year.
Let’s try one example. What is a worker’s wage with ten years of schooling relative to a
worker with no schooling? The first year of schooling gives the worker a wage which is 13.4%
higher, thus 1.134. The second year gives a wage 13.4% higher than a worker with only one
year of schooling. With that, the wage of an individual with two years of schooling is 1.134
× 1.134, or 1.1342 , higher than the wage of an individual with no schooling. Note that the
same happens for years three and four, such that the wage of an individual with four years of
schooling relative to no schooling is 1.1344 . The fifth year provides a smaller return over the
gains from the previous years such that the wage of an individual with five years of schooling
is 1.1344 × 1.101 relative to no schooling. The same return applies to years six, seven, and
eight such that the relative wage of an individual with eight years of schooling is 1.1344 ×
1.1014 . Finally, years nine and ten increase wages by a rate equal to 6.8%. Then, the wage of
an individual with ten years of schooling relative to an individual with no schooling is 1.1344
× 1.1014 × 1.0682 , or 2.77. It means that an individual with ten years of schooling earns
wages – and thus has productivity – almost three times higher than an individual with no
schooling.
Using the same idea, we can compute the average productivity of workers relative to a
worker with no education for countries with information about the years of schooling of the
labor force. With that, we can assess the role of human capital on income differences across
countries.
3. Assessing the Extended Model
Using the data on human capital computed as above, we verify that richer countries are
associated with a larger stock of human capital per worker. This finding is in accord with the
predictions of the model. The remaining question is whether it is quantitatively relevant. Let’s
continue with the countries we analyzed last time: Japan, Uganda, and the US. Recall that the
actual income gaps to the US in 2009 were 0.03 and 0.73 for Uganda and Japan, respectively.
Also, recall that differences in the investment rate and population growth predicted income
gaps of 0.69 and 1.31, respectively. Now we want to add human capital to the accounting.
Using the steady-state equation of income per worker derived above we arrive at the following
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3
equation for the income gap to the US
yi
hi
=
yU S
hU S
γi
nU S + δ
×
γU S
ni + δ
α
1−α
.
In 2010, the average working-age population in the US had 12.4 years of schooling. This
number is 11.5 in Japan and only 4.7 in Uganda. Using a similar approach as in the previous
section, we arrive at an average human capital of 3.28, 3.21, and 2.01 in the USA, Japan,
and Uganda, respectively. Note that if Uganda and the US differ only in the stock of human
capital per worker, the predicted income gap to the US of Uganda would be 61%. If we
add the differences in investment rate and population growth, the predicted gap for Uganda
is 42%. The same exercise would lead to a gap of 1.29 for Japan. Repeating the exercise
for all countries with data available, we find that the correlation between the predicted gap
and the actual gap increases from 0.27 to 0.55 when we account for differences in human
capital. Adding human capital to the model helps get closer to the actual gap, but it is far
from enough. There is still much variation in income per worker across countries that are not
explained by human capital, investment rates, and population growth.
4. Improved Measurement
Many researchers see human capital as the most important factor to explain differences
in income across countries. They argue that years of schooling measure only a small part
of total human capital such that the measure we used above underestimates differences in
human capital across countries. They stress the following points:
(1) Developed countries have a labor force with more experience – measured by age –
than developing countries;
(2) Developed countries provide more in-job training than developing countries;
(3) Developed countries provide education of better quality than developing countries;
when measured by average scores in international tests; and
(4) Developed countries have a healthier labor force.
We will briefly discuss the effects of adding these differences next week. There is also another
important argument in favor of human capital. In measuring human capital, we consider only
the private return from education, that is, the wage rate. However, many researchers argue
in favor of positive externalities of human capital that are not accounted for by their wages.
Once again, the existence of positive externalities means that we are underestimating our
measure of human capital.