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

 

 

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Looking at Table 1 and Graph 3, we have derived Table 2 showing that 

innovations in K/H stabilizes in the very short-run around averages. In this respect, Jones (1995) 

defines long-run beyond the period of 25 years. Thus, these findings verify our hypothesis that 

physical capital-human capital concentration ratio is a strong proxy in explaining GDP growth of 

selected developed countries. Discrepancy between neoclassical-endogenous and our hypothesis 

is potentially accounted for by the positive trend in labor, human capital and physical capital 

trend among countries. This finding also confirms our second hypothesis that in an era where 

technological changes are frequent, labor, human capital and physical capital complementarity 

becomes more important than factor substitutability in its classical sense. In brief, the findings 

related to selected developed countries could be taken as sharp criticism towards neoclassical and 

endogenous growth models. The transitory effect on growth rates of innovations and long-run 

stabilization in very short time periods makes neoclassical and Ak models with endogenous 

growth patterns misleading. Equally similar findings have been derived by variance 

decomposition of growth rates for one standard physical capital-human capital ratio innovation. 

All selected developed countries confirm above given hypothesis, and the variance 

decomposition values (Table 4). 

 

Table 2. Impulse Response Values Showing Stabilization Around 

Average and Maximum variation Impact on GDP Growth Rate 

 

Countries Stabilizing 

Around 

Average (Years) 

Max. Variation in GDP Growth 

(%) 

Austria 

4 0.12 

Australia 

5 0.70 

Canada 

4 0.08 

France 

13 0.09 

Germany 

6 0.04 

Italy 

6 0.03 

Japan 

7 -0.15 

Norway 

2 0.20 

Sweden 

2 0.13 

Switzerland 

3 0.22 

United Kingdom 

6 0.30 

United States 

5 -0.20 

 

 

 

 

 

 

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Table3. Cumulative Impulse Response of Growth Rates to One Standard 

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 0.129 

1.178 0.040 -0.088 0.505 0.633 

4 0.174 

1.761 0.115 -0.164 0.931 0.830 

5 0.204 2.004  0.181 -0.251 

1.228 0.871 

6 0.261 2.126 0.230 -0.342 1.549 0.801 

7 0.259 1.925 0.265 -0.434 1.833 0.669 

8 0.251 

1.672 0.290 -0.524 1.987 0.521 

9 0.240 1.430 0.307 -0.610 2.056  0.394 

10 0.205  1.190 0.319 -0.692 2.081 0.313 

11 0.180 

1.068 0.327 -0.768 2.038 0.286 

12 0.153 

1.026 0.332 -0.839 1.965 0.309 

13 0.128 

1.025 0.336 -0.904 1.888 0.364 

14 0.114 

1.091 0.338 -0.964 1.818 0.431 

15 0.103 

1.155 0.340 -1.019 

1.767 0.490 

16 0.097  1.210 0.341 

-1.069 

1.741 0.530 

17 0.095  1.259 0.342 -1.115 

1.738 0.545 

18 0.093  1.276 0.342 -1.157 

1.755 0.537 

19 0.092  1.280 0.343 -1.195 

1.785 0.514 

20 0.090  1.274 0.343 -1.230 

1.819 0.485 

30 0.011 

1.232 0.344 -1.458 

1.862 0.480 

40 -0.064  1.230 0.344 -1.579 

1.876 0.467 

50 -0.143 

1.230 0.344 -1.665 

1.869 0.464 

60 -0.223  1.230 0.344 -1.736 

1.870 0.465 

 

 

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 0.059 0.280  0.207 

0.182 0.548 

-0.015 

4 0.038 0.325  0.250 

0.362 

0.742 

-0.186 

5 -0.122 0.342  0.275 

0.496 

0.887 

-0.387 

6 -0.247 0.348  0.289 

0.582 

1.006 -0.592 

7 -0.380 0.347  0.295 

0.655 

1.098 -0.767 

8 -0.519 0.343  0.297 

0.700 

1.169 -0.881 

9 -0.622 0.337  0.296 

0.725 

1.224 -0.940 

10 -0.691 0.329  0.294 

0.739 

1.267 -0.952 

11 -0.730  0.321 0.290 

0.744 

1.300 -0.934 

12 -0.732  0.313 0.285 

0.745 

1.325 -0.900 

13 -0.712 0.305  0.281 0.743 

1.345 -0.864 

14 -0.676  0.296  0.276 

0.741 

1.361 -0.833 

15 -0.631 0.288  0.270 

0.739 

1.373 -0.811 

16 -0.587  0.279  0.265 

0.737 

1.382 -0.799 

17 -0.549  0.271 0.260 

0.735 

1.390 -0.795 

18 -0.521 0.262  0.254 

0.734 

1.395 -0.798 

19 -0.504  0.254  0.249 

0.734 

1.400 -0.803 

20 -0.498  0.245  0.243 

0.734 

1.403 -0.809 

30 -0.571 0.159 0.188 0.734 

1.414 -0.818 

40 -0.552  0.072  0.132 0.734 

1.415 -0.818 

50 -0.555  -0.016 0.075 

0.734 

1.415 -0.818 

60 -0.555  -0.105 0.018 0.734 

1.415 -0.818 

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