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



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An alternative, could be taking K as the source of learning by doing process as in the case 

of  Arrow (1962) or Romer (1986). In these models, learning process which is created by 

physical capital investments, dissemination among the producers leading to an overall gain of the 

economy (positive externalities),  thus, altering the decreasing returns process of physical capital 

to a constant returns stage.  In this respect, physical capital becomes the engine of growth. In the 

Solow growth model, investments do not have economic growth effect.  The structuralized 

nature of learning in endogenous growth  models have been developed by Romer (1986). 

Production function then will look like; 

(5) 


   

Y

AK

L

=

+



α β


α

1

     



Different from neoclassical growth models the function has a 

β

 coefficient as an exponential 



value for capital. This constant term reflects the spreading pace of knowledge accumulation to 

the rest of the economy.  The rare case 

α

+

β



=1 shows the case where capital output ratios leads to 

steady growth. This Ak type, is similar to savings driven economic growth process as in the case 

of endogenous economic growth models.  The contribution of physical capital on economic 

growth has been tested empirically by, Romer (1987), De Long and Summers (1991, 1992). In 

this empirical study, explanatory power of share of investment in GDP has been tested against 

the economic growth rate.  Barro and Lee (1994), in their empirical study found that % 1 increase 

in investment leads to a %0.12 increase in economic growth rate.  On the contrary to Barro and 

Lee, Levine and Renelt (1992), asserts the weaknesses of the explanatory power of the above 

cited regression results.  

 

If the regressed economies can be examined under the assumption of steady state 



equilibrium, the functional relationship will be inconsistent with the neoclassical economic 

growth assumptions. Reason being, economic growth effect of saving and investment can be only 

realized if the economy is not under steady state equilibrium.. These growth rates, after the non-

existence of convergence, which is the phase where steady equilibrium has been reached 

(Mankiw, Romer and Weil, 1992). Grossman and Helpman (1991), ties the investment growth 

interaction to technology creation in the R&D sector. Thus, their endogenous economic growth 

model will have the following form. 

 (6)   


!K

Y

r

Y

Y

=

+



αγ

γ

 



Here 

γ

Y

, shows the national income growth as a result of resources devoted to R&D; 

α

 shows 



capital-national income elasticity and; r shows the discount factor. The model shows the 

contribution of physical capital to long term economic growth. 




 

 



 

Human capital factor is another key factor frequently discussed effecting the economic 

growth process. Lucas (1988,  1990), argues the importance of human capital with respect  to 

physical capital. He asserts that, investment to the education sector creates positive externalities 

which enables increasing returns.  Under steady state equilibrium, Per capita income increase 

should lead to equal to Per capita human capital increases. Romer (1990), makes the distinction 

between rival and nonrival environments for inputs of production.  Production function with 

these two inputs if written in the following form (



F D X

( , )


),  copying argument, states that 

doubling of nonrival inputs will be increasing output in larger amounts.. This argument relies on 

the assumption that,  X is a rival and reproducible input while D is  nonrival  and having no 

replacement input cost. D being a productive input, F function can not be written in a concave 

form. In other words

F

D X

F D X

(

,



)

( , )


λ λ

λ

>



. This argument is not very new in economic growth 

literature. Solow (1956) accepts the case of externalities; Arrow accepts the case as learning by 

doing (1962); Lucas accepts the case as (1988) nonrival and non-excludable goods..  

 

To sum up within the recent economic literature, Romer (1990) argues that increasing 



returns  stems from the externalities in R&D sector.  For him, endogenous economic growth 

models can be examined under two alternatives. The first one, asserts that existing knowledge is 

the source of human capital which disappears by death. The second one is, basic technology 

knowledge that is passed over generations which shows continuity in itself. At an empirical level 

we see that years of schooling is taken as a measure for human capital (Barro, 1991; Barro and 

Lee, 1993; Tallman and Wang, 1994). 



 

3. The Formal Model 

As hypothesized above in the introduction section,  the slow GDP growth rates in the 

developed countries could be verified by the spread between technology and human capital 

existence. To test our hypothesis, we will use vector auto regression (VAR) technique in 

assessing whether innovations in K/H (external shocks to K/H) towards long-run GDP growth 

short phase divergences from the average which verifies that K/H is a dominant criteria 

explaining GDP growth in developed countries. In this respect, we also would like to test 

whether neoclassical (Solow, 1956; Swan, 1956; Cass, 1965; Koopmans, 1965; Arrow et al., 

1961) and endogenous (Romer, 1986 and 1990; Lucas, 1988; Rebelo, 1991; Mankiw, Romer 

Weil,  1992) growth theories factor substitutability holds contradicting with the above depicted 

hypothesis. Impulse response functions estimated via VAR technique will show us that whether 

K/H shows complementarity or substitutability towards GDP growth rate for developed 

countries. Impulse response functions explosive or declining nature will support factor 





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