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

Nejat ERK Çukurova Üniversitesi, İktisat Bölümü, P.K. 393, 01330, Adana-TÜRKİYE

erk@mail.cu.edu.tr

Sanlı ATEŞ Çukurova Üniversitesi, İktisat Bölümü, P.K. 393, 01330, Adana-TÜRKİYE

asanli@mail.cu.edu.tr

Uluslararası ODTÜ Ekonomi Kongresi III 8-11 Eylül 1999

Ankara

METU International Conference in Economics III September 8-11, 1999

Ankara

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

Nejat ERK

Çukurova University, Department of Economics, 01330 , Adana, Türkiye. E-mail: erk@mail.cu.edu.tr

Sanlı ATEŞ

Çukurova University,Department of Economics, 01330, Adana, Türkiye.E-mail: asanli@mail.cu.edu.tr

Abstract

This paper aims to explore physical capital (K) and human capital (H) complementarity

impact on long-run economic growth. It is hypothesized that in times of frequent innovations factor complementarity plays a more significant role in explaining GDP growth than factor substitutability adopted among neoclassical and endogenous growth models. VAR results confirm that physical capital and human capital accord showing complementarity is a good proxy in explaining GDP growth for selected developed countries. The estimates yield results showing very short term and stabilizing impacts on innovation for all tested countries.

1. Introduction

Economic growth theory had faced significant changes during the last fifty years. This in

no way decreases the importance of different long term economic growth rates both for

developed and developing countries. In fact, major economic literature concentrates on whether

future growth rates will lead to a convergence or divergence of Per capita income which is an

extension of “catch-up thesis” (Baumol, 1986; Barro, 1994; Jones, 1997). Besides these debates,

consistency of low long-run growth rates of developed countries relative to developing countries

needs to be explored to create rationale for the divergence or convergence of Per capita income

among countries. Introduction of human capital factor to economic growth theory is not new. But

as in the case of Ak type models, human capital has been added to the production, economic

growth and to the Hamiltonian functions with the assumption that this independent factor does

not need any concentration with other factors of production. To clarify the concentration of K/H

(physical capital stock/human capital stock) concept, we should look into factors like

technological absorption, diffusion, managerial applications, learning by doing and other

endogenous factors, not reflected in traditional Ak type models. Existing technological level and

improvements in it, needs similar improvements in human capital component in its broadest

sense to stir up long term economic growth in all countries. Developed countries with

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devastating technological improvements had not been able to capture high growth rates because

of the relative inadequacy of human capital endowments. Thus, not the absolute sizes of K and H

but their relative concentration values should be the key determinant of long term economic

growth. We start with the historical developments in economic growth theory for the last

decades. In the empirical section, to test our hypothesis, that for a given time interval higher K/H

values will be represented by low growth rates which coincides with high per capita income

countries will be tested using tests of VAR technique (Sims, 1980; Enders, 1995).

The debate over complementarity and substitutability of inputs of output is not new. But

in recent years economics of complementarity has been major area of research interest

(Matsuyama, 1996; Young, 1993; Teulings, 1999). Thus, the economic history of economic

growth, looks at the nature of inputs to be used, as well as the mathematical functional form in

explaining GDP growth. In this respect, it is possible to categorize debates around

complementarity of labor ( human capital ) and physical capital under three alternative

approaches. One group of thought looks at widening Wageskilled and Wage unskilled differences and

argues that aggregate technology is capital-skill complementary (Krusell et all, 1997; Goldin and

Katz, 1996). Second approach looks at physical and human capital complimentarity within the

scope of "creative destruction" (Matsuyama, 1999; Young, 1993 ). And the last approach looks at

technological innovations and its impact on the complementarity of input requirements

(Bresnahan et al., 1999) Economist interest in skilled and unskilled wage dispersion and its outcomes could be

explained by capital-skilled complimentarity. Growth's in stock of equipment, reflecting as

higher technological levels increases the MPPL of skilled labor while lowering the MPPL

unskilled labor. As an outcome, almost in all economies we see that increased wage inequality

can be a consequence of capital-skill complimentarity. ( Krussel et al., 1997). Similar findings

have been put forward by Twellings (1999). Investment in human capital in terms of training

increases the skill level by an equal amount increase in relative wage gain, equal to loss of less

skilled, expressed as complexity parameter. Along the same lines, physical capital and more

advanced technology should be regarded as relative compliment of human capital (Goldwin and

Katz, 1997). When cost reduction in an industry reflect productivity increases, we see that key

determinant is employee involvement programs which could also be interpreted as another way

of investment in human capital (Helper, 1997). The author argues that, unit cost of a product is

not a function of quantity produced but mainly by the amount of commitment and skill

improvements.

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Along the same line with our argument above literature shows that in an environment

where there are frequent innovations (post 1970 period), once the technology turns to an

innovation (marketable form) capital and human capital factors are no longer substitutes of

production, on the contrary becomes complimentary which on the overall effects productivity

rates reflecting to faster economic growth rates. In this respect, physical capital and human

capital complimentarity simply reflects that skilled and more skilled educated labor is more

complimentary with new technology or physical capital than low human capital endowed labor.

This also explains the wider inequality among skilled and unskilled labor wages.

Second approach looks at physical and human capital complementarity in terms of market

structure. The argument states that complementarity arise through the nature of equilibrium

interaction (Matsuyama, 1999). Although an economy may never find itself in an unstable

equilibrium suggest multiplicity of stable equilibrium position. This could well reflect presence

of complimentarity which alters the structure of equilibrium observed.

Along the market structure arguments, in time new technologies are substitutes to older

ones. But, at the same time new technologies complements to older technologies. The importance

of complementarity can be best shown by balance between inventive and productive activity

(Young, 1993).

As an outcome of the second argument of complementarity, unlike Romer (1987, 1990)

argument gains from specialization for all inputs could only be true with complimentary skill and

human capital levels. In this respect, Young's argument towards complimentarity is dominated by

steady state compliments our K/H criteria in explaining existing economic growth rates.

Third approach to complementarity could be viewed as the micro foundations at a firm

level. As the skilled labor use information technology, the pace of complimentary innovation

improves (Bresnahan et al., 1999). Thus, the author conclude that skilled-biased technological

change is a function of information technology. Along the same line, Grilliches (1969) and

Berndt et al. (1994) argue that skilled-biased technological change is a function of the way goods

and services are produced. From this argument the human capital development phase at the firm

level increases in the firms information technology stock that is associated with productivity

increases where high levels of human capital is available. However, firms which implement only

one component without the others are often less productive than firms which implement none at

all.

To sum up, classical, neoclassical and endogenous economic growth theories,

independent of inputs taken into consideration, have neglected physical capital-human capital

complementarity. To be modest, this complementarity component could have become more

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dominant factor of economic growth and productivity changes in an era continues innovation. As

stated earlier, given the innovation lengthy time component can create a component for higher

substitutability among factors of production. But, in times of heavy industrial technologies (e.g.

smoke-truck), which changes every other five years ( unlike 20 years in pre 1970 period) and

high technological innovations change every other two years. As a result, substitutability of

inputs becomes less important than complementarity of inputs. This is why we have literatures

around like TQM, JIT, Benchmarking etc. All this explanations reflects economic theory as, in

the classical isoquant approach continuity and slope of the isoquant showing the level of

substitutability makes isoquants more convex to the origin, longer the use of that technology.

Graph 1. Changing Structure of Isoquants in Time of Adaptation

Thus, in a dynamic sense isoquant properties change in time reflecting stronger elements

of complementarity in the first phase and decreasing in time. So, in times of frequent

technological changes, innovations force physical and human capital complementarity converge

to achieve faster economic growth rates.

As in the case of Uzawa (1965) and Lucas (1988), there are economists incorporating k

relationship, with z (gross average product of physical capital) trying to show the scarcity of

human capital.

On the contrary, our attempt hypothesis that, increasing improvements in technology and

a number of innovations is aggravating the difficulty of human capital substitutability with the

existing technology. This dynamics is expected to be a more dominant retardant of economic

growth at the growing stages of globalization. The key element that led to globalization of

market seems to be low cost of information, know-how and technology transfer among regions

K

H

t

Increased Substitutabilty

Eckaus Phase

Innovation

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and countries. But this in no means guarantee the absorption, diffusion and learning by doing of

this product to every production element involved in the creation of GDP. Thus, given the

increasing share of schooling, R&D and other innovative efforts in GDP in developing

countries, the gap between technological improvements and human capital creation is widening

in terms of absorption and diffusion of technological advances which are commercialized with

short time lags due to increased competition. The hypothesis put forward, if proven to be true,

seems to have the potential to explain low growth rates of developed countries. As long as

technological improvements and competition rules stays the same, any country converging in

terms of income with the developed world will face similar problems, thus will be forced to

lower their growth rates.

Traditional human capital theory incorporates, educational (formal and informal),

managerial, health and migration components. In our hypothesis widening of technology and

human capital incorporates R&D and innovation, absorption, diffusion and learning by doing

within the human capital component.

2. Recent Developments in Economic Growth Theory

Frank Ramsey’s 1928 dated publication “A Mathematical Theory of Saving” could be

named as the first contribution to the modern theory of economic growth. The developed theory

aims to optimize the decision making process between different time spans. In 1950’s R.F.

Harrod and E.D. Domar had an attempt to turnaround the static Keynesian growth model to a

dynamic model.

But unfortunately 1929 Great Depression reduced the popularity of above cited economic

models and economists. 1950’s also witnessed another important contributions to growth theory

by R. M. Solow. The contribution of Solow to economic growth theory can be summarized as

diminishing marginal returns on inputs and constant returns to scale which is very typical for

neoclassical production functions. Advancements in the Solow’s theory integrated with constant

saving ratios had been utilized in developing the simplified general equilibrium model.

Neoclassical features of the model depicts that relatively lower GDP holding countries will be

facing faster growth rates. Solow reaches to this striking result, by looking at the capital factor

which faces diminishing marginal returns. In other words, countries with low physical capital per

worker will have higher capital return ratios, thus will have higher growth rates where this

occurrence will reflect to the incomes of developed countries. This type of convergence is known

as absolute convergence in economic literature. The narrow degree of convergence stems from;

stable nature of physical capital per labor, savings rate, population growth rate and from the

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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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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 δkkk

sf kk

n= = − +! ( ) ( )

Here, γk , 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 δk 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 α1 . 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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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 α1

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) !KY r

Y

Y=

+αγ

γ

Here γY , 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.

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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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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) tttt HKLBgLAg ε++= − )/)(()( 1

gt : GDP growth rate

A(L) and B(L): lag operator

K : physical capital

H : human capital

GDP

HKeGDP /1+

= α

K/H

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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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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

14

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

15

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

Impu

lse R

espo

nses

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

Impu

lse R

espo

nses

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

Impu

lse R

espo

nses

France

-0.100

-0.080

-0.060

-0.040

-0.020

0.0001 4 7 10 13 16 19 22 25 28 35 50

Period

Impu

lse R

espo

nses

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

Impu

lse R

espo

nses

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

Impu

lse R

espo

nses

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

Impu

lse R

espo

nses

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

Impu

lse R

espo

nses

Sweden

-0.0200.0000.0200.0400.0600.0800.1000.1200.1400.160

1 4 7 10 13 16 19 22 25 28 35 50Period

Impu

lse R

espo

nses

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

Impu

lse R

espo

nses

United Kingdom

0.0000.0500.1000.1500.2000.2500.3000.350

1 4 7 10 13 16 19 22 25 28 35 50

Period

Impu

lse R

espo

nses

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

Impu

lse R

espo

nses

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 6 1.12 0.59 0.47 1.55 3.30 1.97 7 1.52 0.58 0.47 1.62 3.35 2.45 8 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.