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JOURNAL OF INTERDISCIPLINARY RESEARCH
employed part-time and whether individual V4 countries have a
tendency to shift away from other EU countries in terms of
seniors' part-time employment or a tendency to approach them.
During the analysis, we will use the methods of regression
analysis, beta convergence and we will construct a correlation
diagram. Data were obtained from the Eurostat (2017, (1), (2))
database. The period analysed was 2009-2016.
2.2 Research Methodology
Regarding the set objective, we will use regression analysis to
outline linear trends in the seniors' part-time employment in the
V4 countries. We will use the method of least squares to
estimate parameters. The method minimizes the sum of the
squared errors in the data series Y.
A simple linear trend of the data series Y is
n
t
t
y
t
t
...
3
,
2
,
1
,
=
+
+
=
ε
β
α
α
is the constant term in model,
ß is the regression coefficient,
Ɛ
t
is the t
th
noise term, random error
n is the number of periods.
From the estimated parameters of the linear trends we will derive
an average annual increase, better said a decline in the share of
seniors employed part-time out of the total number of seniors in
the V4 countries.
Beta convergence is one of the methods for convergence
analysis, better said region divergence analysis. It is based on the
assumption that regions converge over the period analysed if
regions that had low levels at the beginning of the period show a
faster growth than regions with higher values at the beginning of
the period. On the contrary, regions diverge if regions that had
low levels at the beginning of the period show a slower growth
than regions with higher values at the beginning of the period. In
order to find out which regions out of the analysed ones tend to
shift away from the others or to delay we used a chart called
correlation diagram. Beta-convergence procedure and the
correlation diagram are performed as follows:
In the period analysed, the initial values of the indicator and the
values of the indicator at the end of the period for all regions are
determined. The average growth factor is calculated from the
data using the geometric mean.
From the time series of growth coefficient k
t
for t=2, 3,...,T ,
which were determined from the values of the time series
t
y
for
t= 1, 2,...,T, the average growth coefficient will be calculated as
(1)
(1)
Using the least squares method, linear regression parameters are
determined, where the dependent variable is the logarithm of the
average growth coefficients and the independent variable is the
logarithm of the initial values. If the estimated linear regression
function is declining, we are talking about predominant tendency
towards convergence. If the linear regression function is
increasing, we are talking about predominant tendency to
divergence.
The coefficient of determination is determined in the linear
models. It explains how many percent of total variability are
explained by the model. If the values of the coefficient of
determination are high, we are talking about highly demonstrated
convergence or divergence.
The correlation diagram is a point chart where the dependent
variable is the logarithm of the average growth coefficients and
the independent variable is the logarithm of the initial values.
The points in the figure are separated by lines. One goes through
the arithmetic average of the logarithm of the initial values. The
second goes through the arithmetic average of the logarithm of
the average-growth factor. Thus, all the points are divided into
four groups with a below-average or above-average value of the
logarithm of the initial values and with a below-average or
above-average value of the logarithm of the average-growth
coefficient.
In the first group, there are regions with above-average initial
values and an above-average growth factor. They reduce
convergence. They tend to shift away from the others. In the
second group, there are regions with below-average initial values
and an above-average growth factor. They tend to move into the
first group, i.e., into a group in which there are regions that tend
to shift away from the others. In the third group there are regions
with below-average initial values as well as a below-average
growth factor. They tend to delay the others. In the fourth group,
there are regions with above-average initial values and a below-
average growth factor. They tend to move into the third group,
i.e., into the group in which there are regions that tend to delay
the others
(Minařík, Borůvková, Vystrčil, 2013).
3 Research Results and Discussion
Before the analysis of seniors employed part-time we analysed
the share of seniors out of the total population and the ageing
index in all V4 countries. The share of seniors out of the total
number of people tended to increase in all developed EU
countries. At the beginning of the period analysed, the highest
share of seniors was in Hungary. The lowest share was in the
Slovak Republic. At the end of the period analysed, the highest
share of seniors was in the Czech Republic and Hungary. The
lowest share was in the Slovak Republic. The average annual
growth factor of the share of seniors was the highest in the
Czech Republic (102.98%). The lowest average annual growth
factor of seniors was in Hungary (101.58%). The share of
seniors out of the total number of people in % is in Table 1.
Table 1 Proportion of population aged 65 and over out of the
total population (%)
Eurostat, database
The aging index, expressed as the share of seniors per 100
people aged 0-14 was the highest in Hungary in the period
analysed. The lowest values were achieved by the Slovak
Republic. The highest average annual growth factor of the
ageing index in the period analysed had Poland, the lowest
annual average growth factor had the Czech Republic. The
ageing index in % is in Table 2. In the next step, we expressed
the share of seniors employed part-time out the total number of
seniors (Table 3).
Table 2 Ageing index (%)
2009
2010
2011
2012
2013
2014
2015
2016
Czech
Republic
104.93 106.99 107.59 110.20 113.51 116.00 117.11 118.83
Hungary 110.07 112.93 114.38 116.55 119.44 121.53 123.45 126.21
Poland
88.24
88.89
88.89
92.72
95.36
99.33
102.67 106.67
Slovakia
78.21
80.00
81.82
83.12
85.06
88.24
91.50
94.12
Processed according to Eurostat database
Table 3 The share of seniors employed part-time out of the total
number of seniors
2009
2010
2011
2012
2013
2014
2015
2016
Czech
Republic
2.63
2.59
2.47
2.60
2.63
2.55
2.99
3.19
Hungary
0.90
0.90
1.07
1.04
0.93
0.96
1.00
1.18
Poland
2.67
2.59
2.55
2.47
2.29
2.36
2.09
2.10
Slovakia
0.59
0.69
0.77
0.64
0.76
0.65
0.96
0.92
EU 28
2.53
2.57
2.71
2.90
2.96
3.09
3.12
3.18
Processed according to the Eurostat database
In the first three years of the period analysed, the highest share
of seniors employed part-time out the total number of seniors
had Poland (in 2010 together with the Czech Republic).
However, in the following five years, the Czech Republic had
2009
2010
2011
2012
2013
2014
2015
2016
Czech
Republic
14.9
15.3
15.6
16.2
16.8
17.4
17.8
18.3
Hungary
16.4
16.6
16.7
16.9
17.2
17.5
17.9
18.3
Poland
13.5
13.6
13.6
14.0
14.4
14.9
15.4
16.0
Slovakia
12.2
12.4
12.6
12.8
13.1
13.5
14.0
14.4
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