Long-Run Growth Effect of the Physical Capital-Human Capital Complementarity: An Approach by Time Series Techniques

 

 

6 

properties of production functions.  Post 1980 studies by R.J. Barro (1991) and W.J. Baumol 

(1986)  included initial human capital stocks and institutionalist factors to the growth models. 

One other important feature of neoclassical growth models is that discontinuities in 

technological advances will lower existing growth rates.  The possible explanation for such an 

outcome goes back to diminishing marginal returns initiated by D. Ricardo  and T. Malthus. 

 Starting 

from 

1960’s neoclassical theory has been transformed to endogenous growth 

models where  technology had been  endogenized with learning by doing and vintage approaches. 

In this respect, especially Arrow’s contribution in 1962 is a mile stone. In this study,  individual 

innovations spread around the economy very fast due the fact that technology being a non 

competitive product. In cases where spread adjustment slows down, innovations will be 

transformed to be the product of the R&D sector where the market is imperfectly competitive. 

Inevitably, this brings in the need for some changes to the neoclassical growth models. The  

contribution to the neoclassical theory delayed till P.M. Romer’s contribution to the theory in 

1980’s. But we should not omit the fact that D. Cass and T. Koopmans work in 1965 sets up the 

roots of household optimization decisions. While this new approach  had examined  the 

dynamics towards development phase, it did not go beyond  conditional convergence. In this 

respect, endogenous nature of savings did not alter dependence of exogenous technological 

improvements on long term Per capita GDP growth.  

 

1970’s, were the years where little had been contributed to growth theory and most 

contributions in economics focused on Monetarist, Neo-Keynesian and Rational Expectation 

theories. From mid 1980 ‘s on, economists like P.M. Romer, R.E. Lucas, S.Rebelo, P.Aghion, 

P.Howitt, E.Helpman, G.M.Grossman focused on physical capital, human capital, R&D sector, 

externalities and imperfect competition factors in explaining the economic growth process which 

could be summarized under the heading of endogenous growth models. This development which 

could be named as “new endogenous economic growth theory” endogenizes technology 

(knowledge stock) through human capital. On the other hand, human capital variable had been 

omitted in the neoclassical models or simply been taken as manna from heaven. Romer’s 

supporting efforts via increasing returns to the endogenous growth models enabled several 

endogenous growth models to be developed in the post 1980 period.  These studies accept the 

following four elements as the major source of economic growth. First group involves profit 

seeking R&D sector (Romer, 1990; Grossman ve Helpman, 1991; Aghion and Howitt, 1992). 

Second group has physical capital and learning by doing models (Romer, 1986; Rebelo, 1991; 

d’Autume ve Michel, 1993). Third group involves human capital accumulation (Lucas, 1988; 

Jones, 1996), and the fourth group involves public investment under the endogenous economic 

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7 

growth theory (Barro, 1990). Common features of the above  mentioned models stem from 

broadening the definition of capital and including increasing and decreasing returns to growth 

theory.  

 

In the Solow growth models, every production factor works under decreasing  returns, and 

growth in per capita GDP is simply a function of technological improvements.  In contrast, basic 

features of endogenous growth models come from the non existence of decreasing returns. Ak 

type endogenous growth model (Rebelo, 1991) has these features and the following simple 

structure; 

 (1)  

Y

AK

=

 

Here A, shows the technology level,; K, shows the technology, human capital, learning by doing 

level. Putting the function into factor income form, we get 

y

Ak

=

. The model could also be 

expressed in terms of capital accumulation ratio; 

(2)  

γ

δ

k

k

k

sf k

k

n

=

=

− +

!

( )

(

)

 

Here, 

γ

k

, shows capital accumulation ratio; n shows increases in labor supply;

δ

, shows the 

depreciation. This equates the average productivity of capital to technological level 

f k

k

A

( ) /

=

. 

Re-defining the capital accumulation process; 

(3)  

γ

δ

k

sA

n

=

−

+

(

)

 

As long as we have a positive technology term (A), average  and marginal productivity of capital 

will be a constant.. This makes the sA term a constant and if we like to have positive capital 

accumulation,  sA>(n+

δ

) condition should hold. Thus without exogenous technological 

improvements it is possible to create capital accumulation.  Under Ak type  endogenous growth 

steady state equilibrium Per capita GDP, capital and consumption growth ratios are equal; 

(4)  

γ γ

δ

= ∗=

−

+

sA

n

(

)

 

Although changes in population increase solely leads to level effect in Solow growth model, in 

endogenous growth models it is also possible to lead to growth effects. While it is technically 

possible to have convergence towards steady state condition, in Ak type models Per capita 

income growth being independent from Per capita income levels, does not permit such a 

convergence.. But Jones and Manuelli (1990), had merged , Ak type endogenous models with 

neoclassical

  growth models yielding 

Y

F K L

AK

BK L

=

=

+

−

( , )

α

α

1

. In this production function, 

marginal productivity of capital reaching to zero, while the capital amount goes to infinity, Inada 

conditions can not be fulfilled. In  Ak type models return on capital is a constant. To overcome 

this problem, the narrow definition of capital should be improved. Enabling K to show human 

capital elements as well as physical capital could be a remedy to solve such a problem. . 

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