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



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Graph 3. Dynamic Impulse Response of Growth Rates to One Standart 

Physical Capital-Human Capital Ratio Innovation for Selected Developed Countries 

 

Austria

-0.050

0.000


0.050

0.100


0.150

1

4



7 10 13 16 19 22 25 28 35 50

Period__Impulse_Responses__France'>Period

Impulse Responses

Australia

-0.400


-0.200

0.000


0.200

0.400


0.600

0.800


1

4

7 10 13 16 19 22 25 28 35 50



Period

Impulse Responses

Canada

-0.040


-0.020

0.000


0.020

0.040


0.060

0.080


0.100

1

4



7 10 13 16 19 22 25 28 35 50

Period

Impulse Responses

France

-0.100


-0.080

-0.060


-0.040

-0.020


0.000

1

4



7

10 13 16 19 22 25 28 35 50



Period__Impulse_Responses__United_States'>Period

Impulse Responses

Germany

-0.200


-0.100

0.000


0.100

0.200


0.300

0.400


0.500

1

4



7

10 13 16 19 22 25 28 35 50



Period

Impulse Responses

Italy

-0.200


-0.100

0.000


0.100

0.200


0.300

0.400


1

4

7



10 13 16 19 22 25 28 35 50

Period

Impulse Responses


 

 

16 



Japan

-0.200


-0.150

-0.100


-0.050

0.000


0.050

0.100


1

4

7



10 13 16 19 22 25 28 35 50

Period

Impulse Responses

Norway

-0.050


0.000

0.050


0.100

0.150


0.200

0.250


1

4

7



10 13 16 19 22 25 28 35 50

Period

Impulse Responses

Sweden

-0.020


0.000

0.020


0.040

0.060


0.080

0.100


0.120

0.140


0.160

1

4



7

10 13 16 19 22 25 28 35 50



Period

Impulse Responses

Switzerland

-0.050


0.000

0.050


0.100

0.150


0.200

0.250


1

4

7



10 13 16 19 22 25 28 35 50

Period

Impulse Responses

United Kingdom

0.000


0.050

0.100


0.150

0.200


0.250

0.300


0.350

1

4



7

10 13 16 19 22 25 28 35 50



Period

Impulse Responses

United States

-0.250


-0.200

-0.150


-0.100

-0.050


0.000

0.050


0.100

1

4



7

10 13 16 19 22 25 28 35 50



Period

Impulse Responses


 

 

17 



 

Cumulative impulse response of growth rates for one standard physical capital-human capital 

ratio innovation shows the overall effect on GDP growth of innovations of the system. As in the 

case of variance decomposition slight deviations (not many) could be stemming from the nature 

of physical capital and human capital data that is being used in our models. Unavailable physical 

capital stock data reflecting the marketable production capacity of the capital stock is the first 

shortcoming of our model. Secondly, human capital data which is commonly used as an index for 

formal education in no way incorporates factors like learning-by-doing, economies of scope, 

research and development, managerial talent and other components of health and migration. 

Another explanation of small disturbances could come from the manipulation of annual data for 

quarterly adjustments. Apart from this, human capital data taken as years of schooling index 

assumes that there are significant similarities among educational institutions within and among 

nations. On the other hand, economies of scope effecting human capital generation and 

economies of scope in terms of physical capital generation should not be expected to show 

similarities among nations. 

 

 



Cumulative impulse response values show the smallest absolute values for Sweden and 

Norway where the countries have very similar human capital and physical capital formation. 

Germany, France and UK having relatively high cumulative impulse response reactions could be 

interpreted as beyond dissimilarities in K/H behavior, countries could have different institutional 

structures effecting physical capital and human capital generation which can be further clarified 

by political setting, taxes, legislatures, bureaucratic procedures, established institutional 

procedures. Hall and Jones (1999) also uses similar variables in explaining differing economic 

growth rates but in no way we can accept that physical capital-human capital and productivity 

could be used in explaining differing growth rates. Because are econometric tests confirm that K 

and H complementarity explains growth rates for selected countries where the process should in 

fact be K and H complementarity first effecting the productivity levels and then GDP growth 

rates. This in no way, decreases the importance of infrastructure of a country in the physical 

sense which directly influences physical capital stock and human capital generation. But 

nonetheless, even for countries with higher cumulative impulse response growth rates on one 

standard physical capital-human capital ratio innovation contributes to a very small segment of 

unexplained GDP growth by K/H. 




 

 

18 



Table 4. Variance Decomposition of Growth Rates for One Standard 

Physical Capital-Human Capital Ratio Innovation 

 

Period Austria  Australia  Canada 



France  Germany  Italy 

1 0.00  0.00  0.00  0.00  0.00  0.00 

2 0.00  6.11 0.02 0.06 1.71 3.94 

3 0.47  15.53 0.08  0.19 4.34 4.62 

4 0.43  18.46 0.15 0.39 7.38 4.56 

5 0.44  19.26 0.20  0.63  8.71 4.42 

6 0.52  19.46 0.22  0.88 10.53 4.50 

7 0.52  19.88 0.23  1.14 

11.98 4.68 

8 0.51 


19.94 0.24  1.39 

12.32 4.78 

9 0.51 20.58  0.24  1.62 

12.19 4.77 

10 0.52  21.14 0.25  1.83 

11.99 4.72 

11 0.53  21.24 0.25  2.01 

11.78 4.70 

12 0.54  21.25 0.25  2.16 

11.73 4.70 

13 0.56  21.25 0.25  2.29 11.78 4.73 

14 0.56  21.29 0.25  2.40 11.86 4.75 

15 0.56  21.29 0.25  2.50 11.90 4.75 

16 0.56  21.33 0.25  2.58 11.89 4.74 

17 0.56  21.35 0.25  2.64 11.86 4.74 

18 0.56  21.35 0.25  2.69 11.84 4.74 

19 0.56  21.35 0.25  2.74 11.82 4.74 

20 0.56  21.35 0.25  2.78 11.83 4.75 

30 0.58  21.36 0.25  2.95 11.86 4.74 

40 0.59  21.36 0.25  2.99 11.86 4.74 

50 0.60  21.36 0.25  3.02 11.86 4.74 

60 0.62  21.36 0.25  3.03 11.86 4.74 

 

Period 

Japan 

Norway 

Sweden 

Switzerland 

United Kingdom 

United States 

1 0.00 0.00  0.00  0.00 

0.00 

0.00 


2 0.01 0.53  0.36  1.13 

1.26 0.20 

3 0.21 0.56  0.44  0.86 

2.76 


0.23 

4 0.17 0.58  0.46  1.26 3.07  0.70 

5 0.78 0.59  0.46  1.47 3.20  1.31 

1.12 0.59  0.47  1.55 3.30  1.97 



1.52 0.58  0.47  1.62 3.35  2.45 

1.97 0.59  0.47  1.64 3.38  2.64 



9 2.19 0.59  0.47  1.65 3.39  2.68 

10 2.26  0.59  0.47  1.66 3.41 2.66 

11 2.25  0.59  0.47  1.66 3.41 2.65 

12 2.20  0.59  0.47  1.66 3.42  2.66 

13 2.18 0.59  0.47  1.66 3.42  2.68 

14 2.19 0.59  0.47  1.66 3.42  2.70 

15 2.23  0.59  0.47  1.66 3.42  2.70 

16 2.27  0.59  0.47  1.66 3.42  2.71 

17 2.30  0.59  0.47  1.66 3.42  2.70 

18 2.31 0.59  0.47  1.66 3.42  2.70 

19 2.32  0.59  0.47  1.66 3.42  2.70 

20 2.31 0.59  0.47  1.66 3.42  2.71 

30 2.32  0.60  0.48  1.66 3.42  2.71 

40 2.32  0.61 0.48  1.66 3.42  2.71 

50 2.32  0.62  0.49  1.66 3.42  2.71 

60 2.32  0.63  0.49  1.66 3.42  2.71 

 



 

 

19 



 

Table 4 shows variance decomposition of GDP growth rates for one standard physical 

capital-human capital ratio innovation.  This estimate also shows that  physical capital,  human 

capital concentration ratio is a determinant of  GDP growth rates.  Estimated values showing low 

numerical values confirm that, physical capital  and human capital components show 

complementarity  for all selected developed countries. Largest values for variance decomposition 

of GDP growth rates for one standard physical capital-human capital ratio innovation is in 

Germany confirming impulse-response results. 

 

  5.  Conclusion 

 

We began this paper with the modest goal, namely to test the hypothesis whether capital 



concentration with respect to human capital has an explanatory power with growth rates. All 

model estimates using dynamic time series confirm our hypothesis. In brief, innovations towards 

H/K, leads to small and short instability in GDP growth and stabilizing in very short time 

intervals.  The second  contribution, which we believe that is at least as important as the first 

finding that, unlike endogenous growth models,  K represented by physical capital stock and H 

represented by human capital shows complementarity mainly in times of frequent innovations. 

As a policy measure we can conclude that,  for the tested group of developed countries, 

optimal combinations in physical capital stock and human capital will yield better results than 

investing in each separately. Given the  statistically significant estimates we have to take into 

consideration above cited shortcomings related to our econometric estimations. We strongly 

believe that studies towards, in depth data for human capital data and other components of 

human capital formation and firm level testing will create stronger evidence towards our 

hypothesis. 

 

 



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Özet 



Fiziksel Sermaye-Beşeri Sermaye Tamamlayıcılığının Uzun Dönemli 

Ekonomik Büyüme Üzerine Etkisi: Zaman Serisi Yaklaşımı 

 

 

Bu çalışma uzun dönem ekonomik büyüme üzerinde fiziksel ve beşeri sermayenin 



tamamlayıcılığını araştırmaktadır. Hipotezimiz, sık teknolojik ve yönetsel yeniliklerin yaratıldığı 

bir dönemde, ulusal gelir düzeyindeki değişimlerin açıklanmasında, faktör tamamlayıcılığının, 

faktör ikamesine oranla daha anlamlı olacağıdır. Vektör oto regresif model testlerinden elde 

edilen sonuçlar, fiziksel ve beşeri sermaye tamamlayıcılığı açıklayıcılarının, GSYİH 

değişimlerinde iyi bir ölçüt olacağını ortaya koymaktadır. Ekonometrik sonuçlar, modele dahil 

edilen gelişmiş ülkelerde fiziksel sermaye-beşeri sermaye yoğunlaşma oranına gelebilecek 



ekonomik şokların, GSYİH'de kısa süreli ve zayıf genli salınımlara yol açtığını doğrulamaktadır. 

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