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JOURNAL OF INTERDISCIPLINARY RESEARCH
and 5 are discussed within their parts. Finally, the section 6
summarizes the main points of the topic and presents the original
results of the analyses.
2 Methodology applied
The methodological approach utilizes two concepts of
convergence that lean on neoclassical model of growth,
β-
convergence and
σ-convergence (Barro & Sala-i-Martin, 1992;
Sala-i-Martin, 1996). The convergence criterion is the real gross
domestic product expressed per capita (Y).
β-convergence
concept is defined as a situation in which poorer regions (i.e.,
regions with lower income per capita) grow faster than richer
regions. In a simplified way the actual course of
β-convergence
for the period T can be quantified by means of (1) using the
regression function:
(1)
,
−
,0
=α
1
−
1
∙
,0
+
,
where i refers to the region, 0 and T refers to two time instants.
β-convergence assumes a positive value of regression parameter
β
1
; the regression function enables to analyze how the
convergence has been achieved over the monitored years t =
0,1,2, ... T. If all regions are at the same steady state,
α
1
and the
period is long enough to enable the regions to converge to this
steady state, the parameter
β
1
will be equal to 1, which is an
ideal case. The parameter
β
1
reflects what difference was
eliminated on average to the steady state. This formula also
assumes a steady state with zero growth per capita. In the
context of empirical
β-convergence examination, the modified
regression (2) can be utilized:
(2)
(
T) =
1
∙log�
,
,0
�=α+∙
,0
+
,
in which the left side represents the average growth of log-
product per capita over the period t = 0…T dependent on the
initial economic level Y
i,0
. T is the total number of years of the
monitored period,
α is a constant, β is the regression coefficient,
ε
i
is a random component. This formula implicitly assumes
identical steady states in the surveyed regions (Slavík, 2007).
If the regression coefficient is significant and negative, and the
coefficient of determination R
2
is high (i.e., straight lines well
capture the variability of the variable), it can be assumed that the
poorer regions grow on average faster than richer regions.
However, it does not mean, that the dispersion of Y among
regions reduces.
The decreasing variability of Y can be captured by the
σ-
convergence. It consists in reducing the variance, or respectively
the standard deviation of Y among regions, which occurs if
inequality (3) is true:
(3)
2
≥
2
where t < T,
2
,
2
are variances of Y at times (years) t, T,
respectively.
σ-convergence is identical with an intuitive understanding of
convergence in the sense of reduction disparities among regions;
β-convergence is in the case of large differences in the initial
levels among regions necessary but not sufficient condition for
the existence of
σ-convergence (
Rapacki & Próchniak, 2009)
.
The question of the contribution of FDI in terms of their impact
on the unemployment development in the Czech regions, further
on referred as UR or unemployment rate, will be evaluated based
on regression and correlation analysis. This procedure is
commonly used in the analyses of FDI impacts on economy as
shown e.g., in
Novák et al. (2016) or Schmerer (2014
).
3 Data description
The analysis is based on regional data available from public
databases of the Czech National Bank (CNB, 2019) and the
Czech Statistical Office (CSU, 2019). The convergence analysis
uses the data from the period 2000-2017. The analysis covering
the FDI data is based on cumulated regional FDI flows in the
period 1999-2015, with the UR and GDP per capita delayed by
one year, i.e., in period 2000-2016. The monitored regions
correspond to territorial division described by NUTS 2.
Figure 1 shows the development of the three studied indicators,
GDP per capita, cumulated FDI per capita and UR, in the Czech
Republic.
The development of unemployment in the monitored period was
significantly affected by its cyclical component due to the
outbreak of the global financial crisis in 2008, which negatively
affected all Czech regions (the greatest impact of the crisis on
regional unemployment growth can be observed between 2009-
2013). Simultaneously, the crisis led to decrease in GDP. This
period is accompanied by slowdown in the FDI flows. The
considered period contains several short-time economic cycles;
therefore, it provides an opportunity to compare relations of
analysed indicators under non-homogeneous conditions.
Figure 1: Development of the GDP (the upper graph), the
development of cumulated FDI (the middle graph), both
expressed in 1000 CZK per capita, and the development of UR
(the lower graph) in the Czech Republic. Source: own
processing, based on the data of CSU (2019) and CNB (2019)
In terms of the FDI distribution among the Czech regions, the
capital Prague markedly differs from the other regions, hence it
is not included in further analysis. In the subsequent parts, 13
regions are considered for analyses, namely: Central Bohemia
(SC), South Bohemia (JC), Plzen region (PL), Karlovy Vary
(KV), Usti (US, Liberec (LI), Hradec Kralove (HK), Pardubice
(PA), Vysocina (VY), Olomouc (OL), South Moravia (JM), Zlin
(ZL), Moravian-Silesian region (MS).
4 Results of analysis of
β-convergence and σ-convergence of
regions in the Czech Republic
Results of
β-convergence of the Czech regions based on relation
(2) are shown in Figure 2. The horizontal axis represents the
natural logarithm Y (= GDP per capita) in the initial year t
0
=
2000, the vertical axis represents the average annual growth of
product in accordance with the left side of relation (2) for a
given period T = 17, namely
(4)
(17)=
1
17�
(2017)
(2000)�
The data in Figure 2 are interleaved with a regression line by
means of the least squares. Both the estimated regression (
β) and
correlation coefficient (
ρ) are negative, but non-significant with
β = - 0,0194, ρ = -0,2711, with p-value 0,3704 of the
corresponding t-test. The regression model captured in Figure 2
is based on data summarized in Tab. 1.
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