Modeling of GNI growth dependency on macroeconomic factors
Вибірка з 10 країн, що представляють всі чотири рівні людського розвитку, сформована на основі прогресу цих країн у рейтингу ІЛР у 2005-2012 роках. Комбінаторний метод МГУА обрано для оцінки впливу частки зайнятих у загальній кількості населення, прямих іноземних інвестицій, сумарного коефіцієнта де...
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irk-123456789-835972015-06-21T03:02:31Z Modeling of GNI growth dependency on macroeconomic factors Tutova, О. Вибірка з 10 країн, що представляють всі чотири рівні людського розвитку, сформована на основі прогресу цих країн у рейтингу ІЛР у 2005-2012 роках. Комбінаторний метод МГУА обрано для оцінки впливу частки зайнятих у загальній кількості населення, прямих іноземних інвестицій, сумарного коефіцієнта демографічного навантаження і загального обсягу резервів на ВНД у Бєларусі, Ірані і Танзанії. Выборка из 10 стран, представляющих все четыре уровня человеческого развития, сформирована на основе прогресса в рейтинге ИЧР в 2005-2012 годах. Комбинаторный метод МГУА выбран для оценки влияния доли занятых в общей численности населения, прямых иностранных инвестиций, суммарного коэффициента демографической нагрузки и общего объема резервов на ВНД в Беларуси, Иране и Танзании. A sample of 10 countries representing all four levels of human development was chosen based on their progress in HDI rating during 2005-2012. Combinatorial GMDA was chosen as a method to assess influence of employment to population ratio, foreign direct investment, total dependency ratio, and total reserves on GNI in Belarus, Iran, and Tanzania. 2014 Article Modeling of GNI growth dependency on macroeconomic factors / О. Tutova // Економіко-математичне моделювання соціально-економічних систем: Зб. наук. пр. — К.: МННЦІТС НАН та МОН України, 2014. — Вип. 19. — С. 361-377. — Бібліогр.: 6 назв. — англ. XXXX-0009 http://dspace.nbuv.gov.ua/handle/123456789/83597 364.2:331 en Економіко-математичне моделювання соціально-економічних систем Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
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Вибірка з 10 країн, що представляють всі чотири рівні людського розвитку, сформована на основі прогресу цих країн у рейтингу ІЛР у 2005-2012 роках. Комбінаторний метод МГУА обрано для оцінки впливу частки зайнятих у загальній кількості населення, прямих іноземних інвестицій, сумарного коефіцієнта демографічного навантаження і загального обсягу резервів на ВНД у Бєларусі, Ірані і Танзанії. |
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Tutova, О. Modeling of GNI growth dependency on macroeconomic factors Економіко-математичне моделювання соціально-економічних систем |
| author_facet |
Tutova, О. |
| author_sort |
Tutova, О. |
| title |
Modeling of GNI growth dependency on macroeconomic factors |
| title_short |
Modeling of GNI growth dependency on macroeconomic factors |
| title_full |
Modeling of GNI growth dependency on macroeconomic factors |
| title_fullStr |
Modeling of GNI growth dependency on macroeconomic factors |
| title_full_unstemmed |
Modeling of GNI growth dependency on macroeconomic factors |
| title_sort |
modeling of gni growth dependency on macroeconomic factors |
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Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
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http://dspace.nbuv.gov.ua/handle/123456789/83597 |
| citation_txt |
Modeling of GNI growth dependency on macroeconomic factors / О. Tutova // Економіко-математичне моделювання соціально-економічних систем: Зб. наук. пр. — К.: МННЦІТС НАН та МОН України, 2014. — Вип. 19. — С. 361-377. — Бібліогр.: 6 назв. — англ. |
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Економіко-математичне моделювання соціально-економічних систем |
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2025-07-06T10:24:52Z |
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| fulltext |
Економіко-математичне моделювання соціально-економічних
систем
Збірник наукових праць
Київ – 2014, випуск 19
361
3. Mowshowitz A. Virtual organization // Association for Computing
Machinery. Communications of the ACM; New York; Sep 1997. –
New York, 1997. – P. 631-634.
4. Тимашова Л.А., Семесенко Т.М. Проблеми розвитку
фінансової системи підприємств середнього та малого бізнесу //
ЗНП – К.: МНУЦ ІТ та С НАНУ і МОНУ. – 2012. – С.23-31.
УДК 364.2:331 О. Tutova
MODELING OF GNI GROWTH DEPENDENCY ON
MACROECONOMIC FACTORS
Вибірка з 10 країн, що представляють всі чотири
рівні людського розвитку, сформована на основі прогресу
цих країн у рейтингу ІЛР у 2005-2012 роках.
Комбінаторний метод МГУА обрано для оцінки впливу
частки зайнятих у загальній кількості населення, прямих
іноземних інвестицій, сумарного коефіцієнта
демографічного навантаження і загального обсягу
резервів на ВНД у Бєларусі, Ірані і Танзанії.
Ключові слова: індекс людського розвитку, дохід на
душу населення, комбінаторний алгоритм МГУА.
Выборка из 10 стран, представляющих все четыре
уровня человеческого развития, сформирована на основе
прогресса в рейтинге ИЧР в 2005-2012 годах.
Комбинаторный метод МГУА выбран для оценки влияния
доли занятых в общей численности населения, прямых
иностранных инвестиций, суммарного коэффициента
демографической нагрузки и общего объема резервов на
ВНД в Беларуси, Иране и Танзании.
Ключевые слова: индекс человеческого развития,
доход на душу населения, комбинаторный алгоритм
МГУА.
Економіко-математичне моделювання соціально-економічних
систем
Збірник наукових праць
Київ – 2014, випуск 19
362
A sample of 10 countries representing all four levels of
human development was chosen based on their progress in
HDI rating during 2005-2012. Combinatorial GMDA was
chosen as a method to assess influence of employment to
population ratio, foreign direct investment, total dependency
ratio, and total reserves on GNI in Belarus, Iran, and
Tanzania.
Key words: human development index, per capita
income, combinatorial GMDH algorithm.
Introduction. Over time there has been a better
understanding of the social consequences of economic
development, and above all an acknowledgement by
governments and the public at large that not only is human
development achievable, but that it has practical meaning for
social and economic progress and the overall prosperity of
nations and states [1].
Twenty years ago, the Human Development Index (HDI)
was proposed as an alternative to conventional assessments of
development based on measures of per capita income. It
complements income with health and education indicators.
HDI classifications are relative – based on quartiles of HDI
distribution across countries and denoted very high, high,
medium and low HDI. Because there are 187 countries, the
four groups do not have the same number of countries: the very
high, high and medium HDI groups have 47 countries each,
and the low HDI group has 46 countries [2].
Previous research analysis. The first Human
Development Report introduced a new way of measuring
development by combining indicators of life expectancy,
educational attainment and income into the composite HDI.
The breakthrough for the HDI was the creation of a single
statistic which was to serve as a frame of reference for both
social and economic development. The HDI sets a minimum
Економіко-математичне моделювання соціально-економічних
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and a maximum for each dimension, called goalposts, and then
shows where each country stands in relation to these goalposts,
expressed as a value between 0 and 1.
The education component of the HDI is now measured
by mean of years of schooling for adults aged 25 years and
expected years of schooling for children of school entering age.
Mean years of schooling is estimated based on educational
attainment data from censuses and surveys available in the
UNESCO Institute for Statistics database. Expected years of
schooling estimates are based on enrolment by age at all levels
of education and population of official school age for each
level of education. Expected years of schooling are capped at
18 years. The indicators are normalized using a minimum value
of zero and maximum values are set to the actual observed
maximum value of mean years of schooling from the countries
in the time series, 1980–2012, that is 13.3 years estimated for
the United States in 2010. Expected years of schooling are
maximized by its cap at 18 years. The education index is the
geometric mean of two indices.
The life expectancy at birth component of the HDI is
calculated using a minimum value of 20 years and maximum
value of 83.57 years. This is the observed maximum value of
the indicators from the countries in the time series, 1980–2012.
Thus, the longevity component for a country where life
expectancy birth is 55 years would be 0.551.
For the wealth component, the goalpost for minimum
income is $100 (PPP) and the maximum is $87,478 (PPP),
estimated for Qatar in 2012.
Purchasing power parity (PPP) is an economic theory and
a technique used to determine the relative value of currencies,
estimating the amount of adjustment needed on the exchange
rate between countries in order for the exchange to be
equivalent to (or on par with) each currency's purchasing
Економіко-математичне моделювання соціально-економічних
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Київ – 2014, випуск 19
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power. It asks how much money would be needed to purchase
the same goods and services in two countries, and uses that to
calculate an implicit foreign exchange rate. Using that PPP
rate, an amount of money thus has the same purchasing power
in different countries.
The decent standard of living component is measured by
Gross National Income (GNI) per capita (PPP$) instead of
Gross Domestic Product (GDP) per capita (PPP$) The HDI
uses the logarithm of income, to reflect the diminishing
importance of income with increasing GNI. The scores for the
three HDI dimension indices are then aggregated into a
composite index using geometric mean.
The HDI facilitates instructive comparisons of the
experiences within and between different countries. [3].
Combinatorial group method of data handling (GMDH)
algorithm was used to build models describing dependence of
human development index on macroeconomic factors [4].
Inductive GMDH algorithms give possibility to find
interrelations in data automatically, and to select optimal
structure of model.
Unsolved problems. Theoretical essentials of human
capital reproduction, analysis of indices of social and economic
progress are subject for research for many studies. Though, due
to its complexity issues of human development are still not
examined completely. Taking into consideration the
importance of this field for the whole mankind, comprehensive
studies of human development should be continued.
Goal. The goal of this article is to find out what countries
made the most remarkable progress in their human
development during 2005-2012. The choice will be based on
HDI ranking during the above stated period.
The goal of this paper is modeling of influence of
macroeconomic factors on the growth of national income as a
Економіко-математичне моделювання соціально-економічних
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component of human development index. Indicators
influencing national income growth should be analyzed.
Models that give possibility to analyze what macroeconomic
indicators are the most influential on the national income
growth will be developed. Also these models enable to assess
how national income will change with changing given
indicator.
The bulk material. 10 countries with different levels of
human development from different regions demonstrated
remarkable progress in rating of HDI. Hong Kong, Special
Administrative Region of China and Singapore have very high
level of human development. Belarus, Saudi Arabia, Bolivarian
Republic of Venezuela, Islamic Republic of Iran, and Ecuador
have high level of human development. Ghana and United
Republic of Tanzania have respectively medium and low level
of human development. HDI for these countries in 2005-2012
is presented in the Table 1.
Singapore data from 2006 till 2008 are omitted in the
Table 1. Combinatorial algorithm GMDH was used for
modelling to restore those values. They are shown in italics in
the Table 1.
Models of dependency of restored variable on all others
were developed for this purpose. Therefore, we should build
dependency of the following type:
20122011201020092008200720052006 ,,,,,, HDIHDIHDIHDIHDIHDIHDIHDI =
This model is obtained for 2007:
201220052007 575,04818,00538,0 HDIHDIHDI ++−= ,
parameters of model: 000109,0=AR ; 00307,0=BS .
Економіко-математичне моделювання соціально-економічних
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Table 1.
Human development index
Country Human Development Index (HDI) value
2005 2006 2007 2008 2009 2010 2011 2012
Hong Kong, 0.857 0.865 0.877 0.892 0.894 0.9 0.904 0.906
Singapore 0.852 0,863 0,872 0,887 0.877 0.892 0.894 0.895
Chile 0.789 0.791 0.8 0.807 0.808 0.813 0.817 0.819
Belarus 0.73 0.743 0.756 0.768 0.78 0.785 0.789 0.793
Venezuela 0.694 0.703 0.712 0.738 0.741 0.744 0.746 0.748
Iran 0.685 0.704 0.706 0.717 0.723 0.74 0.742 0.742
Ecuador 0.682 0.686 0.688 0.715 0.716 0.719 0.722 0.724
Ghana 0.491 0.493 0.506 0.52 0.534 0.54 0.553 0.558
Tanzania 0.395 0.401 0.408 0.414 0.458 0.466 0.47 0.476
Source: Human Development Index (HDI) value: HDRO
calculations based on data from UNDESA (2011), Barro and Lee (2011),
UNESCO Institute for Statistics (2012), World Bank (2012) and IMF
(2012).
Similarly three omitted values for Singapore are restored.
Stated above 10 countries have experienced significant
growth of GNI for 2005-2012.
It is an aggregate income of an economy generated by its
production and its ownership of factors of production, less the
incomes paid for the use of factors of production owned by the
rest of the world, converted to international dollars using
purchasing power parity (PPP) rates, divided by midyear
population and presented in the Table 2.
Since GNI is important component of HDI, it is
important to determine what factors influence income and to
measure their impact. Four influential factors were chosen.
The Organization for Economic Co-operation and
Development defines the employment rate as the employment-
to-population ratio (shown in the Table 3). This is a statistical
ratio that measures percentage of the population ages 25 years
or older that is employed.
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Table 2.
Gross National Income (GNI) per capita
Country 2005 2006 2007 2008 2009 2010 2011 2012
Hong Kong, 35,720 38,643 41,057 42,591 40,393 42,591 45,160 45,598
Singapore 42,330 46,112 48,344 49,075 47,502 51,259 52,439 52,613
Chile 11,600 11,678 12,294 13,097 12,942 13,551 14,407 14,987
Belarus 8,540 9,407 10,187 11,311 11,329 12,245 12,770 13,385
Saudi Arabia 20,780 20,896 20,580 20,964 20,552 20,858 21,812 22,616
Venezuela 9,770 10,656 11,599 11,891 11,210 10,848 11,068 11,475
Iran 9,060 9,503 10,177 10,316 10,390 10,834 10,936 10,695
Ecuador 6,190 6,423 6,458 6,936 6,863 7,073 7,288 7,471
Ghana 1,190 1,075 1,130 1,225 1,394 1,451 1,596 1,684
Tanzania 1,050 1,095 1,149 1,197 1,230 1,288 1,324 1,383
Source: GNI per capita in PPP terms (constant 2005 international
$): HDRO calculations based on data from World Bank (2012), IMF (2012)
and UNSD (2012).
This includes people that have stopped looking for work.
The International Labor Organization states that a person is
considered employed if they have worked at least 1 hour in
"gainful" employment in the most recent week.
Employed persons are all those who, (1) do any work at
all as paid employees, work in their own business or profession
or on their own farm, or work 15 hours or more as unpaid
workers in a family-operated enterprise; and (2) all those who
do not work but had jobs or businesses from which they were
temporarily absent due to illness, bad weather, vacation,
childcare problems, labor dispute, maternity or paternity leave,
or other family or personal obligations — whether or not they
were paid by their employers for the time off and whether or
not they were seeking other jobs.
Unemployed persons are all those who, (1) have no
employment during the reference week; (2) are available for
work, except for temporary illness; and (3) have made specific
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efforts, such as contacting employers, to find employment
sometime during the past 4-week period.
Table 3.
Employment to population ratio
Country 2005 2006 2007 2008 2009 2010 2011
Hong Kong, 60.8 61.4 61.9 62 61.1 60.9 61.2
Singapore 66.3 67.7 68.7 69.3 68.5 69 69.2
Chile 58.3 59 59.8 60.6 59.6 62.3 62.9
Belarus 55.6 55.2 54.8 54.4 53.8 54.2 54.4
Saudi Arabia 61.2 60.4 60.8 60.6 60 59.9 59.7
Venezuela 66.8 67.7 68.4 68.9 68.4 68 68.1
Iran 49 48.3 47.9 45.7 46 46.2 46.1
Ecuador 72.2 73.1 72.4 70.8 70.7 71.2 71.5
Ghana 82.1 81.2 81.3 81.4 81.4 81.5 81.3
Tanzania 84.3 84.5 84.4 84.4 84.4 84.4 84.2
Source: Employment to population ratio, population 25+: ILO
(2012). ["Key Indicators on the Labour Market: 7th edition". Geneva:
ILO.].http://www.ilo.org/empelm/what/lang--en/WCMS_114240. Accessed
March 2012.
Included in the group ‘Not in the labor force’ are all
persons in the civilian non-institutional population who are
neither employed nor unemployed. Information is collected on
their desire for and availability to take a job at the time of the
interview, job search activity in the prior year, and reason for
not looking for work in past 4-week period.
Multiple jobholders are employed persons who, have two
or more jobs as a wage and salary worker, are self-employed
and also held a wage and salary job, or work as an unpaid
family worker and also hold a wage and salary job.
Foreign direct investment presented in the Table 4 is a
sum of equity capital, reinvestment of earnings, other long-
term capital and short-term capital, expressed as a percentage
of GDP.
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Table 4.
Foreign direct investment, net inflows (% of GDP), (%)
Country 2005 2006 2007 2008 2009 2010 2011
Hong Kong, 18.9 23.7 26.3 27.7 25 31.7 34.1
Singapore 12.5 21.1 22 5.1 8.7 18.1 -
Chile 5.7 4.7 7.2 8.4 7.5 7 -
Belarus 1 1 4 3.6 3.8 2.5 7.2
Saudi Arabia 3.8 5.1 6.3 8.3 9.7 4.8 2.8
Venezuela 1.9 -0.3 0.7 0.4 -0.8 0.3 1.7
Iran 1.6 0.7 0.6 0.5 0.9 - -
Ecuador 1.3 0.7 0.4 1.9 0.6 0.3 -
Ghana 1.4 3.1 5.6 9.5 5.5 7.9 -
Tanzania 6.6 2.8 3.5 1.9 1.9 1.9 -
Source: Foreign direct investment, net inflows (% of GDP): World
Bank (2012a). "World Development Indicators 2012." Washington, D.C.:
World Bank. http://data.worldbank.org. Accessed April, 2012.
It is a direct investment into production or business in a
country by a company in another country, either by buying a
company in the target country or by expanding operations of an
existing business in that country. Foreign direct investment is
in contrast to portfolio investment which is a passive
investment in the securities of another country such as stocks
and bonds.
Foreign direct investment has many forms. Broadly,
foreign direct investment includes mergers and acquisitions,
building new facilities, reinvesting profits earned from
overseas operations and company loans. In a narrow sense,
foreign direct investment refers just to building new facilities.
Total dependency ratio shown in the Table 5 is ratio of
the sum of the population ages 0–14 and ages 65 and older to
the population ages 15–64.
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Table 5.
Total dependency ratio
Country 2005 2006 2007 2008 2009 2010 2011 2012
Hong Kong, 35.9 35.1 34.2 33.4 32.6 32 32.1 32.3
Singapore 39 38.2 37.5 36.8 36.3 35.9 35.6 35.4
Chile 49.2 48.4 47.6 46.8 46.2 45.7 45.4 45.2
Belarus 43 42.3 41.5 40.8 40.3 40 40.2 40.5
Saudi Arabia 57.6 55.1 53.3 52 50.9 49.9 49.5 49
Venezuela 56.9 56.2 55.5 54.9 54.4 54 53.6 53.3
Iran 45.2 43.3 41.8 40.7 39.8 39.2 38.9 38.7
Ecuador 60.9 60.2 59.5 58.9 58.3 57.7 57 56.3
Ghana 76.1 75.7 75.2 74.6 74.1 73.6 73.3 73
Tanzania 90.6 90.9 91.1 91.3 91.5 91.8 92.2 92.6
Source: Total dependency ratio: UNDESA (2011). 2010 Revision of
World Population Prospects.
Countries that with high dependency ratio have more
people who are not of working age, and fewer who are working
and paying taxes. The higher the number, the more people that
need to be looked after.
Total reserves minus gold shown in the Table 6 is a sum
of special drawing rights, reserves of International Monetary
Fund (IMF) members held by the IMF and holdings of foreign
exchange under the control of monetary authorities, excluding
gold holdings, expressed as a percentage of GDP.
In order to explore the level of impact of these factors on
HDI GMDH should be used. It was shown how GMDH can be
used for revealing of dependencies in social and economic data
and their analysis. Models were developed by Combinatorial
GMDH algorithm [5,6].
GMDH is a family of inductive algorithms for computer-
based mathematical modeling of multi-parametric datasets that
features fully automatic structural and parametric optimization
of models.
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Table 6.
Total reserves minus gold
Country 2005 2006 2007 2008 2009 2010 2011
Hong Kong, 69.9 70.1 73.7 84.7 122.2 119.7 117.1
Singapore 93.9 97.8 96.6 104.3 106.6 105.8 99.1
Chile 13.8 12.5 9.7 12.8 14.6 12.9 16.9
Belarus 3.8 2.9 8.7 4.4 9.8 6.2 10.9
Saudi Arabia 49.1 63.4 79.4 92.9 108.8 98.7 93.7
Venezuela 16.4 16 10.5 10.5 6.6 3.3 3.1
Iran 3.2 5.2 7.6 8.4 12.2 20.1 16.3
Ecuador 4.6 3.6 6.2 6.9 5.5 2.5 2.5
Ghana 16.4 10.3 8.1 6.2 13 14.8 14
Tanzania 14.5 15.8 17.2 13.8 16.2 17 15.7
Source: Total reserves minus gold: World Bank (2012a). "World
Development Indicators 2012." Washington, D.C.: World Bank.
http://data.worldbank.org. Accessed April, 2012.
GMDH algorithms are characterized by inductive
procedure that performs sorting-out of gradually complicated
polynomial models and selecting the best solution by means of
the so-called external criterion.
A GMDH model with multiple inputs and one output is a
subset of components of the base function (1):
∑
=
+=
m
i
iin faaxxY
1
01 ),...,( (1)
where f are elementary functions dependent on different sets of
inputs, a are coefficients and m is the number of the base
function components.
In order to find the best solution GMDH algorithm
consider various component subsets of the base function (1)
called partial models. Coefficients of these models are
estimated by the least squares method. GMDH algorithm
gradually increase the number of partial model components and
find a model structure with optimal complexity indicated by
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the minimum value of an external criterion. This process is
called self-organization of models.
The most popular base function used in GMDH is the
gradually complicated Kolmogorov-Gabor polynomial (2):
∑ ∑∑ ∑∑∑
= = = = = =
++++
=
n
i
n
i
n
j
n
i
n
ij
n
jk
kjiijkjiijii
n
xxxaxxaxaa
xxY
1 1 1 1
0
1
...
),...,(
(2)
The most influential factors for HDI were chosen for
research of their impact on GNI growth for all 10 countries.
Values of pair correlation between HDI and all other
parameters were calculated for that purpose. Those parameters
for which the value of pair correlation was more than 0.9 were
selected. Since GNI shows the level of prosperity, it was
chosen as an output variable:
y - gross national income per capita.
Four most influential factors were selected:
1x - employment to population ratio;
2x - foreign direct investment, net inflows (% of GDP),
(%);
3x - total dependency ratio;
4x - total reserves minus gold.
Two options of models – regression model by least
square method and model by combinatorial algorithm GMDH
– were developed. Models for Belarus, Iran, and Tanzania are
presented below.
This model is obtained with least square method:
4321 066,0777,1174,0181,1292,19 xxxxy −−++= .
Економіко-математичне моделювання соціально-економічних
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This model is obtained with combinatorial algorithm
GMDH by regularity criterion with after-determination by bias
error criterion [5]:
31 109,2643,1926,7 xxy −+= .
Parameters of model: ;014,0=AR .310,0=BS
Results of modeling by least square method (LSM) and
combinatorial algorithm GMDH (Combi) for Belarus are
presented in the Table 7.
Table 7.
Influence of those four factors on GNI for Belarus
Belarus
1x 2x 3x 4x y )(mod LSMy )(mod Combiy
2005 55,6 1 43 3,8 8,54 8,4891 8,5348
2006 55,2 1 42,3 2,9 9,407 9,3202 9,3545
2007 54,8 4 41,5 8,7 10,187 10,4077 10,3852
2008 54,4 3,6 40,8 4,4 11,311 11,3948 11,2050
2009 53,8 3,8 40,3 9,8 11,329 11,25083 11,27435
2010 54,2 2,5 40 6,2 12,245 12,2687 12,5643
2011 54,4 7,2 40,2 10,9 12,77 12,6576 12,4708
1x and 3x turned out to be the most influential factors
for Belarusian GNI. Furthermore, increase of employment to
population ratio to the level of 2005 will increase GNI by
approximately 11 %. And increase of total dependency ratio to
the level of 2005 will have the same effect.
Similarly models for Iran are obtained. This model is
obtained with least square method:
4321 039,0212,0205,0048,0428,16 xxxxy +−−+= .
This model is obtained with combinatorial algorithm
GMDH by regularity criterion:
431 0026,035,0111,0434,19 xxxy −−+= .
Економіко-математичне моделювання соціально-економічних
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Parameters of model: ;0166,0=AR .428,0=BS
Results of modeling by least square method (LSM) and
combinatorial algorithm GMDH (Combi) for Iran are presented
in the Table 8.
Table 8.
Influence of those four factors on GNI for Iran
Iran
1x 2x 3x 4x y )(mod LSMy )(mod Combiy
2005 49 1,6 45,2 3,2 9,06 9,0159 9,02899
2006 48,3 0,7 43,3 5,2 9,503 9,6480 9,61183
2007 47,9 0,6 41,8 7,6 10,177 10,0618 10,0868
2008 45,7 0,5 40,7 8,4 10,316 10,2412 10,2259
2009 46 0,9 39,8 12,2 10,39 10,5147 10,5648
2010 46,2 1,6 39,2 20,1 10,834 10,821 10,777
2011 46,1 0,7 38,9 16,3 10,936 10,9134 10,8807
For Iran increase of employment to population ratio to
the level of 2005 will lead to increase of the GNI by 1% and
increase of total reserves to the level of 2010 will have the
same influence.
This model is obtained with least square method for
Tanzania:
4321 0004,0212,0008,02,0736,35 xxxxy −+++−= .
This model is obtained with combinatorial algorithm
GMDH by regularity criterion:
43 0008,018,03,15 xxy ++−= .
Parameters of model: 005,0=AR ; 464,0=BS .
As fertility levels decline, the dependency ratio falls
initially because the proportion of children decreases while the
proportion of the population of working age increases. The
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period when the dependency ratio declines is known as the
“window of opportunity” when a “demographic dividend” may
be reaped because society has a growing number of potential
producers relative to the number of consumers. However, as
fertility levels continue to decline, dependency ratios
eventually increase because of the proportion of working age
starts declining and the proportion of older persons continues
to increase. As populations grow older, increases in old-age
dependency ratios are indicators of the added pressures that
social security and public health systems have to withstand.
Tanzania and Ghana may face this challenge in future.
Results of modeling by least square method (LSM) and
combinatorial algorithm GMDH (Combi) for Tanzania are
presented in the Table 9.
Table 9.
Influence of those four factors on GNI for Tanzania
Tanzania
1x 2x 3x 4x y
)(mod LSMy )(mod Combiy
2005 84,3 6,6 90,6 14,5 1,05 1,0484 1,0554
2006 84,5 2,8 90,9 15,8 1,095 1,1176 1,1106
2007 84,4 3,5 91,1 17,2 1,149 1,1411 1,1478
2008 84,4 1,9 91,3 13,8 1,197 1,1868 1,1811
2009 84,4 1,9 91,5 16,2 1,23 1,2203 1,2192
2010 84,4 1,9 91,8 17 1,288 1,2827 1,274
2011 84,2 1,9 92,2 15,7 1,324 1,3361 1,345
Summary. Ten countries with different levels of human
development from different regions were chosen in order to
explore the reasons for their remarkable progress in the rating
of HDI during 2005-2012. HDI growth means growth of the
per capita income along with improvement in the field of
education and health care. Since the gross national per capita
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income characterizes decent standard of living, it was chosen
as the main component of HDI for research.
For that purpose macroeconomic data influencing the
gross national per capita income were analyzed. Values of pair
correlation between HDI and all other parameters were
calculated for that. Impact of such indicators as employment to
population ratio, total dependency ratio, amount of foreign
direct investment, and amount of total reserves minus gold on
the gross national per capita income was explored by the
example of Belarus, Iran, and Tanzania. Two types of
economical and mathematical models were developed for that.
Regression model was built by least square method, and the
other model was built by combinatorial algorithm GMDH by
regularity criterion with after-determination by bias error
criterion.
Both models display that employment to population ratio
and total dependency ratio are turned to be the most influential
indicators for growth of the gross national income in Belarus.
Thus, increase of employment to population ratio to the level
of 2005 will increase the GNI by approximately 11 %. And
increase of total dependency ratio to the level of 2005 will have
the same effect. For Iran increase of employment to population
ratio to the level of 2005 will lead to increase of the GNI by
1% and increase of total reserves to the level of 2010 will
increase the GNI by 1% as well. Total dependency ratio has the
most significant impact on the GNI of Tanzania.
References
1. Тутова О.В. Концептуальні основи формування людського
капіталу. - Економіко-математичне моделювання соціально-
економічних систем. Збірник наукових праць. Вип. 17 // Відп. ред.
– докт. тех. наук, професор Л.А. Пономаренко. – Київ:
Міжнародний науково-навчальний центр інформаційних
технологій та систем НАН України і МОН України, 2012. – 379 с.
– С. 119-129.
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систем
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Київ – 2014, випуск 19
377
2. Human Development Report 2013 / [Електронний ресурс] - Режим
доступу: http://hdr.undp.org/en/reports/global/hdr2013
3. Human Development Report 2010 / [Електронний ресурс] - Режим
доступу:http://hdr.undp.org/en/reports/global/hdr2010/
4. Ивахненко А.Г. Индуктивные методы самоорганизации сложных
систем. – Київ: Наук. думка, 1982. – 296 с.
5. Savchenko Ie., Tutova O. Analysis of Human Development Level by
Inductive Algorithms. - Proceedings of International Workshop of
Inductive Modeling. Kyiv, 8-14 May. – 2012. – P. 28 – 33.
6. Savchenko E., Tutova O. Use of GMDH for investigation of impact of
non-income components on HDI. – Індуктивне моделювання
складних систем, випуск 4, 2012. – с.28-37.
УДК 336.5 О.М. Чистик
АДАПТИВНА МОДЕЛЬ ВИЗНАЧЕННЯ
ЕФЕКТИВНОСТІ ПРОГНОЗУВАННЯ
ФІНАНСОВИХ РЕСУРСІВ НА РОЗВИТОК
ЗБРОЙНИХ СИЛ УКРАЇНИ
Анотація У статті розглядаються актуальні
питання оцінки ефективності використання бюджетних
коштів на закупівлю новітнього озброєння та військової
техніки. Також запропоновані шляхи визначення та
перерозподілу кошторисних призначень Збройних Сил
України з використанням адаптивних моделей та
програми Excel.
Ключові слова фінансові ресурси Збройних Сил
України, адаптивна модель, ефективність використання
фінансових ресурсів.
Аннотация В статье рассматриваются
актуальные вопросы оценки эффективности
использования бюджетных средств на закупку новейшего
вооружения и военной техники. Также предложены пути
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