Y. Turganbayev (D. Serikbayev East Kazakhstan state technical university, Kazakhstan )
Y. Batalov (D. Serikbayev East Kazakhstan state technical university, Kazakhstan )
S. Rakhmetullina (D. Serikbayev East Kazakhstan state technical university, Kazakhstan )
N. Denisova (D. Serikbayev East Kazakhstan state technical university, Kazakhstan )
THE MODEL OF ESTIMATION OF THE ROLE OF HUMAN CAPITAL IN
ECONOMIC GROWTH OF KAZAKHSTAN REGIONS
This paper tests empirically the importance of human capital for economic growth
of a sample of Kazakhstan regions over the period 2001-2007. Human capital is treated as
one of production factors. Two types of production functions are considered, in which
human capital enters as input. The panel regression results show the positive and
significant role of human capital in economic growth of Kazakhstan regions over the
considered period.
Keywords: human capital; role of human capital; the modelling; the production function;,
economic growth.
1. Introduction
Factors which influence economic growth of regions of a country are numerous,
ranging from the geographical conditions to infrastructure development, from the availability
of physical capital and labour force to their quality and structure. Besides, it appears that
growth factors influence more developed and less well developed countries in different ways.
However, many growth theories emphasize the role of human capital as an engine of
economic growth.
In spite of diminishing returns from physical capital, which is considered a main growth
factor in the neoclassical growth theory, many countries, including the United States and
some European countries, have experienced continued growth for more than one hundred
years. The commonly accepted explanation for this fact is “... the expansion of scientific and
technical knowledge that raises the productivity of labour and other inputs in production”
(Becker 1993, p.24). Denison (1985) calculated that a quarter of the US per capita income
growth during 1929-1982 was caused by an increase in the stock of human capital. The
impressive economic development of Japan, South Korea, Taiwan, Singapore, and other
countries in recent years also illustrates the significance of human capital to economic
growth. These countries grew rapidly relying only on their labour force without having
natural resources, and investing huge money in human capital.
In this paper, the human capital dimension is investigated across the regions of
Kazakhstan to establish the possible role and linkage of human capital with their economic
growth. The purpose of this paper is to test empirically the importance of human capital for
economic growth of a sample of Kazakhstan regions over the period 2001-2007. In this, we
try to contribute to the solution of the fundamental problem of growth theory, which consists
in finding the conditioning factors, which explain better the growth patterns across countries
and regions.
2. Literature Review
2.1. Conceptual Definitions of Human Capital.
The notion of human capital appears in the second half of the twentieth century due to the
publications of Theodore Shultz and Gary Becker (Schultz 1961, Becker 1964). According
to them, human capital is determined by the aggregation of investments in activities that
increase an individual productivity in the labour market, such as health, education, migration,
and on-the-job training.
This definition of human capital has been widened to include non-market activities. For
instance, Laroche, Mérette and Ruggeri (1999, p.89) give a broader definition of human
capital: “Human capital is the aggregation of the innate abilities and the knowledge and skills
that individuals acquire and develop throughout their lifetime.”
There are also many other definitions of human capital. For example, Korchagin (2005, p.21)
gives a wider definition of human capital including an environment, in which human capital
operates: “Human capital is an intensive complicated productive factor of the development of
an economy and society, which includes labour resources, knowledge, instruments of
intellectual and managerial labour, an environment of living and intellectual work, providing
effective and rational operation of human capital as a productive factor of the development.”
In its ability to be a productive factor, human capital is similar to physical capital. However,
there are significant differences between these notions. The main distinction from physical
capital is the fact that “...you cannot separate a person from his or her knowledge, skills,
health, or values the way it is possible to move financial and physical assets while the owner
stay put...” (Becker 1993, p.16).
Laroche, Mérette and Ruggeri (1999) highlight another set of the differences between these
two types of capital with respect to property rights and marketability, accumulation,
depreciation, returns, financing and taxation. Another difference between human and physical
capital is the way of their measurement. While the stock of physical capital is measured by its
cost, the measurement of human capital is a rather ambiguous task.
2.2. Measurement of Human Capital
Since economists recognise human capital as one of the crucial economic growth factors, it is
highly important to measure accurately its stock and influence on economic processes. The
definition of human capital as a stock of knowledge, health, skills, experience, and culture
embodied in individuals that are used for the maintenance of social, personal, and economic
welfare assumes impossibility of developing of the uniform exact approach to measurement
of the human capital. All possible estimates of human capital must be indirect because of the
intangible nature of human capital. There are three main approaches to the measurement of
the amount of human capital: “cost-based”, “income-based”, and “educational stock-based”
(Le, Gibson and Oxley 2003). All the approaches to measure human capital have their
advantages and drawbacks. However, in this paper, taking into account data availability and
possible biases caused by these disadvantages, we use educational stock-based approach to
measure human capital of Kazakhstan regions.
As education is at the core of the human capital notion, the educational stock-based approach
of its measuring is the most popular method among the researchers. There are several proxies
within this framework, which are usually used to assess the human capital stock such as adult
literacy rates, school enrolment ratios, educational attainment levels, and average years of
schooling (Wößmann 2003).
In the framework of educational stock-based approach, the most commonly used and popular
proxy of the human capital stock is average schooling years and levels of educational
attainment (Benhabib and Spiegel 1994, Gundlach 1995, Islam 1995, O’Neill 1995, Temple
1999, Barro 1997, 2001, Krueger and Lindahl 2001, Barro and Sala-i-Martin 2003).
The schooling average years quantify the accumulated educational investment embodied in
the current labour force. It is really a stock variable, and it considers the formal educational
attainment obtained by the labour force, which takes part in the current production process.
2.3. Human Capital and Economic Growth
The role of human capital in economic growth process has been extensively studied in the
literature (Nelson and Phelps 1966, Lucas 1988, Romer 1990, Azariadis and Drazen 1990,
Freire-Serén 2001, Temple 2001a, 2001b, and others). These studies specify two channels
through which human capital can influence growth.
Firstly, human capital can be treated as one of the factors of production (Mankiw, Romer and
Weil 1992, Coulombe and Tremblay 2001, Abu-Qarn and Abu-Bader 2007, Vinod and
Kaushik 2007). In this sense, the accumulation of human capital is assumed to generate
directly the growth of the output.
Secondly, human capital can influence the growth through the total factor productivity,
namely raising technical progress, since education eases the diffusion and adoption of new
technologies (Benhabib and Spiegel 1994, Islam 1995, Nelson and Phelps 1966).
On the other hand, there is no common opinion among researchers on the important question:
“What is more significant for economic growth: the accumulation of human capital or its
stock? In this regard, Aghion and Howitt (1998, p.327) distinguish two approaches to
modelling and analysing the link between human capital and growth. “The first one was
initiated by Lucas (1988) and inspired by Becker’s theory of human capital. It describes the
economic growth as being driven by the accumulation of human capital. So that the
differences in growth rates across countries are mainly determined by the differences in
accumulation of human capital over time of those countries. The second approach, which
stems from the work of Nelson and Phelps (1966) and finds its continuation in Schumpeterian
growth literature is based on the idea that economic growth is driven by the stock of human
capital , which is a decisive factor in a country’s ability to innovate or catch up with more
advanced economies.”
3. Human Capital as a Factor of Economic Growth of Kazakhstan Regions
3.1. The Model and Methodology
In this paper we study the human capital's impact on economic growth of Kazakhstan
regions considering it as a factor of production. The used methodology is the inclusion of
human capital into the production function. The micro-level findings that the educational
attainment of workers determine their marginal products serve as an argument for this
methodology (Fleisher and Wang 2001, 2004, Fleisher et al. 2010). Thus, the aim is to study
direct effect, according to which employees with higher level of human capital have a higher
marginal product in comparison with those who have achieved lower level of human capital.
In order to study the direct effect of human capital on output, we consider two aggregate
production functions, which take the Cobb-Douglas form with physical capital and labour
taken as inputs.
The distinctive feature of the first function is that labour input includes two categories:
(1) workers with higher education; (2) workers with below higher education (Fleisher, Li and
Zhao 2010).
𝛽 𝛽ℎ 𝛽𝑛 𝑢𝑖𝑡
𝑌𝑖𝑡 = 𝐴𝑖𝑡 𝐾𝑖𝑡𝑘 𝐿ℎ𝑖𝑡
𝐿𝑛𝑖𝑡 𝑒
(1)
where 𝑌𝑖𝑡 is output, 𝐾𝑖𝑡 is capital, 𝐿ℎ𝑖𝑡 is the quantity of employees with higher
education or above, 𝐿𝑛𝑖𝑡 is the quantity of employees who have below higher education, 𝑢𝑖𝑡
is a disturbance term, for region 𝑖 = 1,2, … , 𝑛 from years 𝑡 = 1,2, … , 𝑇. Parameters 𝛽𝑘 , 𝛽ℎ , 𝛽𝑛
are the elasticities of corresponding factors with respect to output, which are estimated by the
regression procedure.
Next, following Mankiw, Romer and Weil (1992), we consider another production
function, which includes physical capital 𝐾, labour 𝐿, and human capital ℎ as inputs:
𝛽 𝛽 𝛽
𝑌𝑖𝑡 = 𝐴𝑖𝑡 𝐾𝑖𝑡𝑘 𝐿𝑖𝑡𝑙 ℎ𝑖𝑡ℎ 𝑒 𝑢𝑖𝑡
(2)
Again, the corresponding elasticities of inputs 𝛽𝑘 , 𝛽𝑙 , 𝛽ℎ are estimated using regression
method.
3.2. Data
We take the data on GRP and investment from various years of the Regions of
Kazakhstan statistical issue (1993-2009). These data are deflated over time by an official
GDP deflator with 1993 taken as a base year.
In assessing the level of physical capital input to the production function, we use the
conventional assumption that it is proportional to the capital stock level. To assess the last the
perpetual inventory method (PIM) is usually employed (Abu-Qarn and Abu-Bader 2007).
This method can be expressed by the following equation:
𝐾𝑖𝑡 = (1 − 𝛿)𝐾𝑖,𝑡−1 + 𝐼𝑖𝑡
(3)
where 𝐾𝑖𝑡 is the capital stock of 𝑖-th region at time 𝑡, 𝐼𝑖𝑡 is the real investment in fixed assets,
𝛿 is the depreciation rate, assumed to be 5% (Miyamoto and Liu 2005).
We deflate gross investment in fixed assets available in Regions of Kazakhstan (1993-2009)
and calculate real investment flows 𝐼𝑖𝑡 . There are some controversies regarding the deflator
used for deflating investment series (Islam, Dai and Sakamoto 2006). For example, Ezaki and
Sun (1999, p.44) use the “price index of investment in fixed assets,” which is the weighted
average of the “producer price index of machine building industry” and the “total output price
index of construction” at the country level. The weights 1/3 and 2/3 are taken quite arbitrary.
Another approach is to use the official deflator for the formation of gross fixed capital, but
the data on this deflator has only been available since 1996. Therefore, we take the GDP
deflator, available in the Statistical Yearbook of Kazakhstan (1993-2009), to deflate
investment series. The year 1993 is taken as the benchmark for the deflator.
As an initial stock of capital the balance (book) cost of fixed assets as of 1993, available in
Regions of Kazakhstan (1993-2009), is taken. In order to diminish the influence of the initial
capital stock on the calculated series, the capital stock is computed from 1993, even though in
the model, these data are used from 2001.
The data on employed population with higher education serving as a measure of the
level of human capital are given by the Economical Activity of the Population of the
Republic of Kazakhstan statistical issue (1993-2009). Unfortunately, these data are available
only for the period 2001-2007 that essentially confine the period of the study of the influence
of human capital on economic growth of Kazakhstan regions.
3.3. Empirical Results
In order to study the influence of human capital on economic growth of Kazakhstan
regions, we start with the production function (1), which considers physical capital and two
types of labour as inputs.
Having the panel data of GRP, physical capital, and two kinds of labour force across
Kazakhstan regions over the period of 2001-2007, first, we choose whether fixed or random
effect model is more appropriate to analyze them. In doing this, we use a Hausman test, in
which the null hypothesis is that the preferred model is random effects; while the alternative
is that the preferred model is fixed effects (Hausman 1978). This test checks the correlation
between unique errors and regressors. Under the null hypothesis, they are not correlated. We
run the Hausman test using the Stata command hausman fixed random. As
regressors logarithms of physical capital and two types of labour are taken. The results of its
implementation are presented in Table A.1.
As the value of the 𝑃𝑟𝑜𝑏 > 𝑐ℎ𝑖2 is equal to 0.1759, we can not reject the null
hypothesis of no correlation between unique errors and regressors. This means that the
random effects model is more preferable in this case.
Afterwards, we run Breusch-Pagan Lagrangian multiplier test (Breusch and Pagan
1979), which helps to choose between the random effects regression and a simple OLS
regression. We use the Stata 10 command xttest0 after running the random effects model.
The results of this test shown in Table A.2 allow to conclude that the null hypothesis of
the test can be rejected in favour of the alternative, meaning that there is a panel effect and
the random effects model is more preferable than the simple OLS regression.
Next we use the Wooldridge test for the presence of serial correlation in our data
(Wooldridge 2010) applying the xtserial Stata command. The results of this test show the
rejection of the null hypothesis of the absence of autocorrelation in favour of the alternative
of the first order autocorrelation.
Thus, to study the influence of human capital on the output of Kazakhstan regions, we
apply the random effects model with first-order autocorrelation property of standard errors.
We use the Stata 10 command xtregar with random effects option to run this regression.
Table 1: Random effects model regression with the property of first-order autocorrelation of
standard errors (production function with two types of labour)
[95% Conf.
LnGRP
Coef.
Std. Err.
z
P>|z|
Interval]
LnCapital
.685
.043
15.79
0.000
[.600, .770]
LnHigher
.291
.058
5.06
0.000
[.178, .404]
LnNonHigher
.116
.064
1.81
0.070
[-.009, .242]
_cons
.117
.512
0.23
0.819
[-.886,1.121]
rho_ar
.658
(estimated autocorrelation coefficient)
sigma_u
.119
sigma_e
.092
rho_fov
.627
(fraction of variance due to u_i)
theta
.435
Error! Reference source not found. reports results of the random effects model
estimation of the region-level production function (1) with two kinds of labour grouped
according to the educational accomplishment. The capital input elasticity estimate is positive
and significant at 1% confidence level and equals to 0.685. The estimate of the elasticity of
more educated labour is equal to 0.291 and is significant at 1% confidence level, while the
estimate of the elasticity of less educated labour is equal to 0.116 and is significant only at
7% confidence level. The former estimate is larger than the latter in 2.5 times. In this
specification, estimates of elasticities of three inputs: physical capital and two types of labour
sum up to 1.09 that confirms the hypothesis of constant returns to scale. Thus, the human
capital expressed as the number of employees with higher and below higher education enters
positively and significantly in the production function of the type (1). The regression results
show that the elasticity of the labour force with higher education is 2.5 times higher than of
the elasticity of the labour force with below-higher education that confirms the importance of
human capital as a production factor.
Next, we study the role of human capital in the economic growth of Kazakhstan regions
using production function of the type (2). Again, we apply several econometric tests to
determine what type of regression is more appropriate for the panel data. The results of these
tests are presented in Tables A.3-A.5. According to these tests we use the random effects
model with first-order autocorrelation property of standard errors. This model is realized by
the xtregar Stata command with random effects option.
Table 2: Random effects model regression with the property of first-order autocorrelation of
standard errors (production function with labour and human capital)
[95% Conf.
LnGRP
Coef.
Std. Err.
z
P>|z|
Interval]
LnCapital
.688
.043
15.89
0.000
[.603, .773 ]
LnLabour
.413
.070
5.92
0.000
[.276, .550]
Ln_h_it
.217
.075
2.88
0.004
[.069, .365]
_cons
-1.087
.514
-2.11
0.035
[-2.095, -.078]
rho_ar
sigma_u
sigma_e
rho_fov
.662
.120
.092
.634
(estimated autocorrelation coefficient)
(fraction of variance due to u_i)
theta
.438
Table 2 reports regression results of the random effects model with the property of firstorder autocorrelation of standard errors of the production function of the type (2). The
estimates of the elasticities of all three inputs: physical capital, labour, and human capital, are
positive and significant at 1% confidence level. The estimate of the human capital variable,
approximated by the percentage of employed population with higher education, is equal to
0.217.
4. Conclusion
Thus, to study the direct effect of human capital on economic growth of Kazakhstan
regions we considered two types of production function. In the first specification, the labour
input was divided into two types: workers with higher education and workers with education
below higher. The regression results of this specification, within the framework of the
random effects panel model, showed an evidence of positive and significant direct effect of
human capital on the production function resulted from the workers with higher education
rather than from those with less than higher education.
In the second specification, the Cobb-Douglas type production function along with
physical capital contained labour and human capital variables. Again the estimates of the
elasticities of all three inputs were positive and highly significant.
Thus, human capital, measured using educational stock-based approach and considered
as one of production factors, played a significant positive role in economic growth of regions
of Kazakhstan over the period of 2001-2007.
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APPENDICES:
Table A.1: Hausman test to check whether fixed or random effects model is more appropriate
(production function with two types of labour)
Coefficients
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
fixed
random
Difference
S.E.
LnCapital
.844
.663
.181
.075
LnHigher
-.037
.309
-.3465
.137
LnNonHigher
-.245
.057
-.302
.181
Notes: b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(3) = (b-B)'[(V_b-V_B)^(-1)](b-B) =4.94
Prob>chi2 = 0.1759 (V_b-V_B is not positive definite)
Table A.2: Breusch and Pagan Lagrangian multiplier test for random effects (production function
with two types of labour)
Var
sd = sqrt(Var)
LnGRP
.362
.602
e
.011
.106
u
.023
.153
Notes: Test: Var(u) = 0
chi2(1) = 109.83
Prob > chi2 = 0.0000
Table A.3: Hausman test to check whether fixed or random effects model is more appropriate
(production function with labour and human capital)
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B)) S.E.
fixed
random
Difference
LnCapital
.797
.667
.129
.073
LnLabour
-.005
.379
-.384
.270
Ln_h_it
.066
.259
-.193
.096
Notes: b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(3) = (b-B)'[(V_b-V_B)^(-1)](b-B)= 6.72
Prob>chi2 = 0.0813
Table A.4: Breusch and Pagan Lagrangian multiplier test for random effects (production function
with labour and human capital)
Var
sd = sqrt(Var)
LnGRP
.362
.602
e
011
.107
u
.023
.153
Notes: Test: Var(u) = 0
chi2(1) = 110.14
Prob > chi2 = 0.0000
Table A.5: Wooldridge test for autocorrelation in panel data (production function with labour and
human capital)
F(1,15)
27.598
Prob > F
0.0001
Notes: H0: no first-order autocorrelation