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



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substitutability toward economic growth while stabilizing around the average in the short-run 

will lead to K/H complementarity in explaining the economic growth process. 

The above model can be best expressed by logistic curve which has been put forward in 

our previous study (Erk, Altan and Ateş,  1998) showing why GDP growth rates alter between 

developed and developing countries. 

 

Graph 2. GDP Level-K/H Logistic Curve 

 

 

 



 

 

 



 

 

 



In brief, increasing at and increasing rate segment of the logistic curve coincides with the 

developing countries and the increasing at and the decreasing rate segment represent the 

developed countries slope of the logistic curve alternative growth rates between developed and 

developing countries. 

 

In testing the formal model, we have the following assumptions; 



• 

Labor human capital is far more important than the labor itself in the production process. 

• 

Technological change is a function of  physical capital growth. 



• 

Human capital measured with Barro-Lee data permits human capital in its broadest 

definition. 

• 

Human capital and physical capital factors show complementarity 



 

In a dynamic relationship between GDP growth rate and physical capital-human capital 

concentration ratio, our formal model is given by the following equation: 

(7)  


t

t

t

t

H

K

L

B

g

L

A

g

ε

+



+

=



)

/

)(



(

)

(



1

 

g



t                              

:   GDP growth rate 



A(L)

 and B(L):   lag operator 



K                   

:   physical capital 



H                   

:   human capital 



GDP 

H

K

e

GDP

/

1



+

=

α



 

K/H 


 

 

11 



 

 

4. Findings of the Study 

 

Looking at the data used to test the model, we have taken human capital data for Austria, 

Australia, Canada, France, Germany, Italy, Japan, Norway, Sweden, Switzerland, United 

Kingdom and the United States  human capital data from Barro-Lee data set (1993), physical 

capital stock data from Nehru-Dharashwar (1993) and GDP data from World Bank International 

Statistics (1994). Human capital and physical capital stock data has been annual data adjusted for 

quarterly data looking at the flow nature of accumulation in both. GDP data has been corrected 

for its base year to be 1990. All calculations had been conducted under TSP software (version 

1.0A) to test impulse response functions and variance decompositions. Our hypothesis to be 

tested assumes that innovations towards K/H concentration ratio will to move to averages, in the 

short run, showing that key factor explaining GDP growth stand from K/H concentration and 

other variables have zero growth effect in the long-run. Besides this, we also expect short 

disturbances in the impulse response functions due to the complementarity property of physical 

capital stock and human capital stock. 



 

In the test of dynamic time series analysis, to determine the stationarity of the data, 

initially ADF test has been used. In this respect all GDP data showed stationary behavior. Some 

K/H series also showed stationary behavior, while very limited country data showed non-

stationary behavior, corrected by taking the differences.  In implementing optimal lags for the 

model  Schwartz Information Criteria  has been used.  Some non-stationary data has shown  

second degree cointegration.  



 

 

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Table 1. Dynamic Impulse-Response of Growth Rates to One Standart 

Physical Capital-Human Capital Ratio Innovation 

 

Period Austria  Australia  Canada  France  Germany 



Italy 

1 0.000  0.000  0.000  0.000  0.000  0.000 

2 0.007  0.460  -0.027 -0.031 0.197 0.323 

3 0.121 0.719 0.067 -0.058 0.309 0.310 

4 0.046  0.583  0.075 -0.076  0.426  0.197 

5 0.029  0.243  0.065 -0.086  0.297  0.041 

6 0.057  0.122 0.049 -0.091 0.321 -0.069 

7 -0.002  -0.200  0.035  -0.092  0.284  -0.132 

8 -0.008  -0.254  0.9025 -0.090  0.154 -0.148 

9 -0.012 -0.242 0.017 -0.086  0.068  -0.127 

10 -0.035  -0.240  0.012 -0.082  0.026  -0.081 

11 -0.025  -0.121 0.008 -0.076 -0.043 -0.026 

12 -0.026  -0.042  0.005  -0.071 -0.073  0.023 

13 -0.025  -0.001 0.004 -0.065 -0.077 0.055 

14 -0.014 0.066 0.002 

-0.060 


-0.070 0.067 

15 -0.012 0.063 0.002 

-0.055 

-0.051 0.059 



16 -0.006  0.055  0.001 -0.050 -0.026  0.040 

17 -0.002  0.050  0.001 -0.046 -0.003  0.015 

18 -0.002  0.017 0.001 -0.042  0.017 -0.008 

19 -0.001 0.004 0.000 

-0.038 0.029 -0.023 

20 -0.002  -0.006  0.000  -0.035  0.034  -0.030 

30 -0.008  0.003  0.000  -0.016 -0.008  0.000 

40 -0.008  0.000  0.000  -0.010 0.000  0.002 

50 -0.008  0.000  0.000  -0.008  0.000  0.000 

60 -0.008  0.000  0.000  -0.007  0.000  0.000 

 

Period 

Japan 

Norway 

Sweden 

Switzerland 

United Kingdom 

United States 

1 0.000  0.000  0.000  0.000 

0.000 

0.000 


2 -0.014 0.211 0.135 0.219 0.235 

-0.079 


3 0.073  0.069  0.072  -0.037 

0.313 0.064 

4 -0.021 0.045  0.043  0.180 0.194 -0.170 

5 -0.160 0.017 0.025  0.134 0.144 -0.201 

6 -0.125 0.006  0.013 0.087  0.119 -0.206 

7 -0.133 -0.001 0.006  0.073 

0.092  -0.175 

8 -0.140 -0.004  0.002  0.044 

0.071 -0.114 

9 -0.103 -0.006 -0.001 0.025  0.055  -0.059 

10 -0.069  -0.007  -0.003 

0.014 0.043 

-0.012 

11 -0.038  -0.008  -0.004 



0.005 

0.033 


0.019 

12 -0.003  -0.008  -0.004 

0.001 0.026 0.034 

13 0.020  -0.008  -0.005  -0.001 0.020 0.036 

14 0.036  -0.008  -0.005  -0.002 

0.016 0.031 

15 0.045  -0.009  -0.005  -0.002 

0.012 0.022 

16 0.044  -0.009  -0.005  -0.002 

0.009 


0.012 

17 0.038  -0.009  -0.005  -0.001 0.007 0.004 

18 0.028  -0.009  -0.005  -0.001 0.006 -0.002 

19 0.017 -0.009 -0.005  -0.001 0.004 -0.005 

20 0.006  -0.009  -0.006 

0.000 


0.003 

-0.006 


30 0.002  -0.009  -0.006 

0.000 


0.000 

0.000 


40 -0.001 -0.009 -0.006  0.000 

0.000 


0.000 

50 0.000  -0.009  -0.006 

0.000 

0.000 


0.000 

60 0.000  -0.009  -0.006 

0.000 

0.000 


0.000 

 




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