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Human Capital
• The exogenous growth model of Solow presents a
number of unresolved questions:
– The growth rate of the economy in the steady state is
not explained by the model
– The preferences of the population (the propensity to
save) do not affect the growth rate of growth, and
therefore, this rate is insensitive to the economic policy
– The hypothesis of convergence between countries
predicted by the model finds little empirical support
Human Capital
• The introduction of human capital in the
neoclassical growth model, initially
proposed by Uzawa (1965) and later taken
over by Lucas (1988), is a possible way out
of these difficulties.
• We will see later the endogenous growth
Human Capital
change in Cobb-Douglas
• qL: improving human capital, where q changes in
production efficiency and quality
• production function of the final good, in CobbDouglas form, is amended as::
Y= T* Kα (qL)β
Where T *: remaining technical progress,
qL: human capital
By investing in 'education' workers increase their
Human Capital
change in Cobb-Douglas
• But not enough to express the production function
as a function of human capital improvements, but
we need to take account of changes in the age
composition of the labor :
Δ(qL)/(qL) = ΔL/L + δL - δL ΔE
• namely, the improvement of the work is given by:
Growth of physical units
Average rate of growth of quality
The effect of changes on the average
Human Capital
change in Cobb-Douglas
• The growth of production is explained in
more detail:
rY= rT*+ αrK + αδk - αδk ΔA + βrL + βδL + βΔE
• Two influencing factors:
-Work Experience
-Specialty Schools that influence the
average quality L and its distribution by age
Human Capital
• Agents can accumulate human capital by
transferring part of their working time from
production to investment in 'education'. Lucas
assumes that the increase in human capital is
proportional to both the initial stock of human
capital, both at the time of labor employed:
Where u is the fraction of time spent working in
the production of the final good Y, and δ is a
Human Capital
• With these assumptions the steady state growth rate of per
capita income is:
gy = δ (1-u)
exactly equal to the growth rate of the stock of human
In this way, you get growth 'endogenous' in a double sense:
-the growth rate is explained by investments in human
-The growth rate depends on the choice of allocating labor
time to produce work or invest in human capital and is
therefore dependent on the preferences of the agents
Human Capital
• Policy implications:
encouraging or less human capital
investment, the decision maker of economic
policy can affect the growth rate of per
capita of the economy.
Human Capital
• The issue of convergence:
'checking' for human capital, that is, by inserting the rate of
investment in human capital between the dependent variables of
the equation for estimating the growth rate of per capita, the
convergence hypothesis is partially confirmed (Mankiew, Romer
and Weil, 1992).
This result is known as 'conditional convergence': once you
take into account the different level of human capital in the
various countries it is true that having a low stock of physical
capital has a positive effect on growth.
Human Capital
• However:
There remains the question of causality
between human capital and growth. And 'the
growth rate of the economy to be influenced by
human capital or vice versa?
The estimates cross-section used in the
literature on convergence are able to identify
correlations rather than causal relations