Economics and Innovative Technologies. Vol. 2019, No. 5, september-october
83
5/2019
(№
00043)
Forecasting economic growth by multi-factored model
Kholmurod Muminov Isroilovich
1
Alisher Djurayev
2
1
Ph.D., Associate-professor at the BSU
2
Student of Master program at the BSU
E-mail:
Abstract
:
The article is devoted to modeling and forecasting economic growth. Effects of
labor force, capital and innovation costs, the coefficient of elasticity, the results of regression and
correlation analysis is shown.
Keywords:
Tourism, correlation, time series, regression analyze, model, forecasting.
Introduction
Economic growth and sustainable economic growth are the main factors in solving
the socio-economic problems and welfare of the country. President of the Republic of
Uzbekistan Shavkat Mirziyoev in his Address to the Oliy Majlis on December 28, 2018,
highlighted the key priorities for the development of our country in 2019 and emphasized
the importance of macroeconomic stability and economic growth as following: "First, we
must ensure macroeconomic stability and high economic growth rates. In the transitional
period, it is important to keep statistics on the economy and to accurately assess the
economic potential of the state. It will help to achieve an objective assessment of GDP” [1].
Gradual implementation of economic reforms and well-thought-out monetary and
credit policy provide broad opportunities and favourable conditions for entrepreneurship
in all sectors and areas, ensure macroeconomic stability and high rates of economic
growth.
An in-depth analysis of the progress of the past, the growing competition on the
world stage requires the development and implementation of fundamentally new
approaches and principles for more sustainable and dynamic development of our
economy.
The key factor of achieving high results is an analysis of the progress made over the
years of independence, the well-defined goal of further deepening economic reforms and
accelerating the country's development.
The third priority of the Strategy of Action for the five priority areas of development
of the Republic of Uzbekistan in 2017-2021, called the further development and
liberalization of the economy, and according this the first main aim is to maintain
macroeconomic stability and maintain high economic growth rates [2].
The importance of developing an econometric model and forecasting GDP growth in
the near future, achieving objective estimates of GDP, macroeconomic stability and high
economic growth rates, changing its timings, and regression and correlation analysis on the
factors influencing high GDP substantiates the actuality of the research topic.
Analysis of literature
Modeling and forecasting of economic processes has been carried out by many
economists, and this process is still relevant today.
Hodiev B., Shodiev T., Berkinov B. showed the tendency changing indicators of
complex social phenomena is only by one or another equation or line of trend, and in
Economics and Innovative Technologies. Vol. 2019, No. 5, september-october
84
5/2019
(№
00043)
practice the use of linear, parabolic, hyperbolic, exponential, logarithmic and logistic types
of time series trends. They also gave a description of the models and gave an idea of how
to calculate the trend [3].
Z.M.Mamaeva showed in details the use of the Foster-Stewart method for
determining the trend in time series, the way to determine the quality of the model based
on the time series, the statistical content of the regression equations and parameters, the
quality of the trend models,expressed rules of the Student's T-criterion, Fisher's F-rate, and
Darbon-Watson's d-criterion outline the use of theoretical indicators in the table, working
out model and forecast [4].
Allen L. Webster shows the need to use linear regression by creating slippery lines
in softening time lines, exponential softening and the use of linear trend equations and
exponential alignment and linear trend equations [5].
Indian Dr. Amit Kundu examines the link between economic growth and
government spending in 1961-2014 on a time-series basis, and proves the long-term link.
Research with the VAR model shows that costs do not supply economic growth.
Government spending does not affect short-term economic growth at all [6].
Studying economical growth in time line base, Indian scientists Aruna Kumar Dash,
Aviral Kumar Tiwari, Pradeep Kumar Singh analysed factors affecting the economic growth
of the country in 1973-2013, economic processes in the sectors. Using ARDL model
scientists showed that the development of tourism in the country influences economical
growth for short and long period. Creating opportunities for tourism development in the
country is a prerequisite for economic growth [7].
Methodology of research
Gross domestic product is a commodity that is estimated at market prices of goods
and services produced during the year for final use by economic resident units in the
economic territory of the country and is a key indicator of the system of national accounts.
Quantity increase in production, and the growth of the GDP ratio to the average
population means macroeconomic growth.
If the rate of economic growth is completely different from last year's GDP, the rate
of economic growth is calculated as a percentage of the GDP for the current year.
Quantitative changes in economic growth mean quantitative changes in products and
services produced at the national level, and changes in the quality of economic growth
mean consumption of goods at the level of consumer demand.
Whereas the gross domestic product depends on natural and labor resources,
capital, relative economic growth rates, growth rates and rates depend on the use of
resources, the net investment, the use of scientific and technological development in
production, ie the introduction of innovative technologies and technologies in production.
The study investigated multivariate linear modelling and forecasting, which is
considered to be the simplest model of multi-factor modelling and forecasting, and
developed a forecast for GDP variability and possible quantities.
Multi-factored straight lined model has the following formula:
𝑦 = 𝑎
0
+ ∑
𝑎
𝑛
𝑥
𝑛
𝑛
𝑖=1
ёки
𝑦 = 𝑎
0
+ 𝑎
1
𝑥
1
+ 𝑎
2
𝑥
2
+ ⋯ + 𝑎
𝑛
𝑥
𝑛
(4);
Here: y - result, an arbitrary variable;
а
0
, а
1
, а
2
, … а
n
–parameters of regression equation;
x
1
, x
2
, … x
n
– factors, free variables.
Economics and Innovative Technologies. Vol. 2019, No. 5, september-october
85
5/2019
(№
00043)
We create a result and a matrix of factors to identify the key factors influencing GDP
(Table 3). Investments in fixed assets in GDP, employment rates, and innovation costs have
a higher impact than other factors, suggesting that the interconnection of factors is lower
than the result. It is known that the coefficient of determination is in the range of 0–1.0,
and the value is close to 0, which means that the link is weak and about 1.0 is the high
degree of bond.
At the same time, we can identify 5-10 factors affecting GDP with a high correlation
to GDP, ie, with a coefficient of determination greater than 0.5, and we take into account
that the ratio below 0.5 is poor.
The elastic coefficients are used to study the effect of the factor on the results using
the regression equation. This coefficient represents the average percentage change in the
sign
:
(6);
Here: Э-coefficient of elasticity;
a
i
– parameter of regression equation;
х̅
– average sum of factor;
у̅
– average sum of result.
Analysis and results
The gross domestic product of the Republic of Uzbekistan has been growing steadily
over the years, and the contribution of various sectors in the GDP has been changing at
different levels across the country. (Table 1).
Table 1.
Changes in the Gross Domestic Product of the Republic of Uzbekistan and the
Share of Sectors by Years
Year
GDP current
price, mln sums
Share of sectors, %
Net tax , %
Industry
Agriculture
Building
Service
2000
3 255,6
14,9
26,8
7,5
36,4
14,4
2001
4 925,3
14,3
29,0
6,7
36,6
13,4
2002
7 450,2
14,2
30,1
6,0
37,2
12,5
2003
9 844,0
14,2
30,2
5,8
37,3
12,5
2004
12 261,0
14,5
30,1
4,9
37,9
12,6
2005
15 923,4
15,8
28,6
4,5
37,4
13,7
2006
21 124,9
17,1
26,8
4,5
37,6
14,0
2007
28 190,0
20,7
25,0
4,9
38,4
11,0
2008
38 969,8
22,1
24,1
5,1
39,5
9,2
2009
49 375,6
24,0
21,7
5,5
39,3
9,5
2010
62 388,3
22,3
19,4
5,6
43,3
9,4
2011
78 764,2
24,0
18,0
7,0
44,0
7,0
2012
97 929,3
24,0
17,5
6,8
49,0
2,7
2013
120 861,5
24,2
16,8
4,0
53,0
2,0
2014
145 846,4
26,0
16,4
3,8
44,3
9,5
2015
171 808,3
26,2
17,4
4,2
42,9
9,3
2016
199240,0
23,3
28,8
5,7
39,0
11,2
2017
249136,4
14,9
26,8
7,5
36,4
14,4
2018
407514,5
14,3
29,0
6,7
36,6
13,4
)
(
Э
y
x
a
Э
i
*
Economics and Innovative Technologies. Vol. 2019, No. 5, september-october
86
5/2019
(№
00043)
Source: information of State statistics committee of the Republic of Uzbekistan.
The share of agriculture and services in GDP is high, while the share of industry and
construction products has been increasing over the years.
We have not elaborated on the above methods, as the trend equations based on
the time series are approximated by extrapolation smoothing, average sliding, and
extending the studied period. In time-based forecasting of economic indicators, a more in-
depth analysis of changes in economic processes over time, and the impact of time only on
the development of forecasts for future years. The key factors influencing the size of the
indicator in modelling and forecasting on the basis of factor analysis of the reasons for
quantitative changes in economic indicators and future forecast of the indicator under the
influence of these factors will be studied.
According to many scientists, capital and labour are the main factors influencing
GDP. In addition to these factors, the study also takes into account the cost of innovation,
which has had a significant impact on economic growth in recent years (Table 2.).
Table 2.
The degree of linkage of factors affecting GDP
GDP
Investment to main
amount
Number of
sectors
Expense of
innovation
GDP
1,000
Investment to main amount
0,999
1,000
Number of sectors
0,899
0,877
1,000
Expence of innovation
0,946
0,933
0,940
1,000
Source: Prepared by author's researches.
Table 2 presents the multivariate linear regression equation based on the above
factors, given the high impact of changes in GDP on capital investment, number of jobs,
and innovation costs on other factors.
When the regression equation was developed based on the change in outcome and
factor values for the period 2008-2018, a linear regression equation was generated as
follows.
𝑦
𝑌𝑎𝐼𝑀
= −106027,82 + 3,46𝑥
1
+ 10,03𝑥
2
+ 0,62𝑥
3
(5);
If you note, the influence of a sectors is inversely related (а
0
=-106027,82), This
means that the change in GDP will have a significant impact on the correct investment in
fixed assets, the number of employees and the costs of innovation. These factors, which
have a high impact on GDP growth, and the dramatic increase in investment in fixed assets
in recent years, are contributing to high GDP growth. (Table 3).
According to investment elastic coefficient to main amount is 0,844
(3,4*36509/147447), by sectors is 0,849 (10,03*12469/147447), for innovative expence is
0,027 (0,62*6332/147447) when investment to main amount is increased to one billion
sums, when GDP is increased to additional 844 mln sums, sectors to one thousand people,
GDP reaches up to 849 mln sums, when innovation expence increased to 1,0 billion sums,
GDP increases to 27,0 mln sums.
Because the model's quality and accuracy are positive, we used regression
equations with zero error values, first of all, to determine the forecasted possible
quantities of the factors over the next five years, with the coefficient of determination
based on Table 4 data:
Economics and Innovative Technologies. Vol. 2019, No. 5, september-october
87
5/2019
(№
00043)
Table 3.
Characteristics of multi-factored straight lined model of GDP
Years
t
GDP,
billion sums
Multi-
factored
forecast of
GDP, billion
sums
Investment to
main amount, х
1
,
billion sums
Sectors, х
2
,
thousand
people
Expence of
innovation, х
3
,
billion sums
2008
1
38969,8
37184,4
9555,9
11035,4
521,5
2009
2
49375,6
50935,2
12531,9
11328,1
333,7
2010
3
62388,3
64194,0
15338,7
11628,4
264,4
2011
4
78764,2
76680,3
17953,4
11919,1
372,6
2012
5
97929,3
97040,3
22797,3
12223,8
311,9
2013
6
120861,5
121121,0
28694,6
12523,3
4634,2
2014
7
145846,4
147206,6
35233,3
12818,4
3757,4
2015
8
171808,3
172371,4
41670,5
13058,3
5528,3
2016
9
199325,1
203144,8
49770,6
13298,4
2571,4
2017
10
249136,4
243702,0
60719,2
13520,3
4162,3
2018
11
407514,5
408339,2
107333,0
13800,0
5283,7
2019
12
424365,8
110376,7
14130,8
20049,9
2020
13
505883,7
132726,4
14407,8
24200,3
2021
14
597034,5
157810,4
14684,8
28858,4
2022
15
698182,1
185731,7
14961,9
34043,5
2023
16
809676,4
216590,2
15238,9
39774,0
Regression equation
𝑦
𝑌𝑎𝐼𝑀=
− 126304
+ 3,46𝑥
1
+ 11,82𝑥
2
+ 0,03𝑥
3
𝑦
𝑖𝑛𝑣=
9490,17
+ 202,2𝑡
2,5
𝑦
𝑏𝑎𝑛𝑑=
10806,2
+ 277,0𝑡
𝑦
𝑖𝑛𝑛
= 1315,0 + 37,6𝑡
2,5
Coefficient of
approximation, %
1,81
11,37
0,29
12,33
Coefficient of determination
0,99
0,93
0,99
0,98
Source: Worked out on the base of information of State statistics committee of
the Republic of Uzbekistan.
The model of investment sum according timeline to main amount:
𝑦
𝑖𝑛𝑣𝑒𝑠𝑡𝑖𝑡𝑠𝑖𝑦𝑎
= 9490,17 + 202,2𝑡
2,5
(7);
Sectors sum change model on timeline:
𝑦
𝑏𝑎𝑛𝑑
= 10806,2 + 277,0𝑡
(8);
Model of innovative expence sums o timeline:
𝑦
𝑖𝑛𝑛
= 1315,0 + 37, 6
2,5
(9);
Instead of the time factor (t) in the above-linear double regression equation we
placed the sum from table 4, after accounting GDP factors forecast sum for 2019-2023, we
have worked out GDP multi-factored straight lined regression equation on the base of GDP
forecast ушбу даврга мўлжалланган ЯИМнинг кўп омилли тўғри чизиқли регрессия
тенгламаси асос (Picture 1).
Economics and Innovative Technologies. Vol. 2019, No. 5, september-october
88
5/2019
(№
00043)
Picture 1. Forecast data on GDP based on time series and multivariate linear regression
equation.
Source:Worked out by the author on the base of Uzbekistan state statistics
committee materials.
Even nineteen years of nominal GDP with no autocorrelation used as a database in
the study of time series modeling, as the model based on the multivariate linear
regression equation is more accurate than the one based on the time series model, it can
be seen from the data in Figure 1 that the forecast data for this model for 2019-2023 is
growing comparatively with previous periods of GDP.
According to the multivariate linear regression projections, GDP is expected to be
809,676.4 billion sums in 2023 and 768273.5 billion soums in the forecasted model based
on time series.
The projected data is based on the market value of GDP for 2008-2018, and the
impact of price changes has not been taken into consideration. The rising inflation rate in
recent years may lead to an artificial increase in GDP, and the model and forecast data
based on that data may be different from the real situation. In our next research, we will
also take into consideration the problem of developing a model and forecasting of fixed
price GDP.
Conclusion and offers
Given that quantitative and qualitative changes in gross domestic product are a key
factor in the welfare of the population, in recent years a model and forecast of GDP
changes have been developed based on time series and multivariate linear regression
equation.
Although studies show that the nominal GDP doubles in the next five years on both
models,the multivariate linear model and the predicted data based on it show the accuracy
of the time series model and the prediction data, and it is efficient to develop multivariate
model and forecast data in situations where time series data are available.
In the process of developing models and forecasts based on time series, it is
necessary to make sure that the autocorrelation, that is, the year data, is not
interconnected.
38969,8
49375,6
62388,3
78764,2
97929,3
120861,5
145846,4
171808,3
199325,1
249136,4
407514,5
424365,8
505883,7
597034,5
698182,1
809676,4
2 0 0 8 2 0 0 9 2 0 1 0 2 0 1 1 2 0 1 2 2 0 1 3 2 0 1 4 2 0 1 5 2 0 1 6 2 0 1 7 2 0 1 8 2 0 1 9 2 0 2 0 2 0 2 1 2 0 2 2 2 0 2 3
GDP, billion sums
Multi-factored forecast of GDP, billion sums
Economics and Innovative Technologies. Vol. 2019, No. 5, september-october
89
5/2019
(№
00043)
In the development of a multidimensional model, it is necessary to develop a
correlation matrix in selecting the factors and, consequently, to consider the factors with
the highest coefficient of determination. In the development of the multivariate model,
the development of multiple models and the coefficient of approximation are the lowest, if
the same value is the same or similar across different models, You will need to select a
model that meets Fisher's F-criterion and Student's T-criteria.
References
1.
Decree of the President of the Republic of Uzbekistan dated February 7, 2017
No UP-4947 “On the Strategy of Action for the Five Priority Areas for the Development of
the Republic of Uzbekistan in 2017 - 2021 years” Source:
2.
Address of The President of the Republic of Uzbekistan Shavkat Mirziyoyev to
the
Oliy Majlis
of Uzbekistan on December 28, 2018. Source:
3.
Ҳодиев Б. Шодиев Т, Беркинов Б. Эконометрика. Ўқув қўлланма, Т.:
Иқтисодиёт, 2018. -175 б.
4.
Мамаева З.М. Введение в эконометрику.Учебное пособие, Нижний
Новгород.: Нижегородский госуниверситет, 2010.– 72 стр.
5.
Allen L.Webster. Applied Statistics for Business and Economics.USA, Bredley
University. 1995. -1047 p.
6.
Dr. Amit Kundu “Economic Growth & Government Expenditure in
Pakistan - A Time Series Analysis”, Indian Journal of Economics, 389, Vol. XCVIII October
2017.
7.
Aruna Kumar Dash, Aviral Kumar Tiwari
,
Pradeep Kumar Singh “Tourism and
Economic Growth in India: An Empirical Analysis” Indian Journal of Economics, 392, Vol.
XCIX July 2018.
