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17
ANALYZING INVESTMENT IN FIXED ASSETS UTILYSING DYNAMIC MODELS
IN FERGANA REGION
PhD, assoc. prof.
Akhunova Shokhistakhon Numanjanovna
Fergana Polytechnic Institute
Askarov Farhod Rakhmatovich
Fergana Polytechnic Institute
Abstract.
This article provides an analysis of the Almon lag model based on statistical data
from the Fergana Region. The model facilitates the study of relationships between variables over
time by accounting for distributed lag effects. Using the available data, the research examines the
dynamics of key factors in the Fergana Region and identifies the optimal lag structure. The results
enhance the understanding of the region's economic dynamics and offer valuable insights for
policymakers and researchers alike.
Keywords:
dynamic model, Almon lag model, ordinary least squares, auto regression model.
FAR
G‘
ONA VILOYATIDA ASOSIY VOSITALARGA INVESTITSIYALARNI DINAMIK
MODELLARDAN FOYDALANIB TAHLIL QILISH
PhD, dots.
Oxunova Shoxistaxon Numanjonovna
Farg‘ona politexnika instituti
Asqarov Farhod Raxmatovich
Farg‘ona politexnika instituti
Annotatsiya.
Ushbu maqola Farg‘ona viloyatining statistik ma’lumotlari asosida Almon lag
modeli tahlilini taqdim etadi. Model vaqtli qatorlar bilan o‘zgaruvchilar o‘rtasidagi
bog‘lanishlarni o‘rganishga imkon beradi, bu esa taqsimlangan lag ta’sirlarini his
obga oladi.
Mavjud ma’lumotlardan foydalangan holda, tadqiqot Farg‘ona viloyatidagi asosiy omillarning
dinamikasini tahlil qiladi va optimal lag strukturasini aniqlaydi. Tadqiqot natijalari viloyatning
iqtisodiy dinamikasini yaxshiroq tushunishga yordam beradi va investorlar hamda tadqiqotchilar
uchun qimmatli fikr-
mulohazalar bilan o‘rtoqlashadi.
Kalit so‘zlar:
dinamik model, Almon lag modeli, oddiy eng kichik kvadratlar, avtomatik
regressiya modeli.
U
O‘K:
338.12.017, 338.001.36, 338.27
XII SON - DEKABR, 2024
17-23
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18
АНАЛИЗ ИНВЕСТИЦИЙ В ОСНОВНЫЕ СРЕДСТВА С ИСПОЛЬЗОВАНИЕМ
ДИНАМИЧЕСКИХ МОДЕЛЕЙ В ФЕРГАНСКОМ ВИЛОЯТЕ
к.э.н., доц.
Ахунова Шохистахон Нуманджановна
Ферганский политехнический институт
Аскаров Фарход Рахматович
Ферганский политехнический институт
Аннотации.
Эта статья представляет анализ модели Алмона на основе
статистических данных Ферганской области. Модель позволяет изучать взаимосвязи
между переменными во времени, учитывая эффекты распределенных лагов. Используя
доступные данные, исследование анализирует динамику ключевых факторов в
Ферганской области и определяет оптимальную структуру лагов. Результаты
способствуют лучшему пониманию экономической динамики региона и предоставляют
ценные рекомендации для инвесторов и исследователей.
Ключевые слова:
динамическая модель,
модель лага Алмона, метод наименьших
квадратов, модель авторегрессии.
Introduction.
Presidential Decree 158, issued on September 11, 2023, outlines Uzbekistan's ambitious
vision for sustainable development, prioritizing key sectors as drivers of progress. The decree
underscores the nation's dedication to boosting investment in the digital economy, research,
education, infrastructure, and green initiatives (Decree, 2023). This article examines the
strategies and initiatives proposed in the decree, highlighting how Uzbekistan plans to leverage
these sectors to stimulate economic growth, promote innovation, empower its workforce,
improve connectivity, and protect the environment. By addressing both social and economic
dimensions, the country aims to achieve growth, prosperity, and enhanced well-being for its
citizens. Additionally, as nations worldwide seek sustainable development, understanding the
link between fixed asset investment and GDP becomes essential. This article explores the
complex relationship between these factors, analyzing how investment in fixed assets impacts
GDP and identifying the mechanisms that drive economic growth.
Literature review.
Let’s begin by defining what investment is. Below are several definitions of investment
provided by renowned economists:
•
"Investment is an activity that involves sacrificing current consumption to achieve
greater future consumption." - Samuelson and Nordhaus(2009).
•
"Investment is the sacrifice of current consumption in order to secure future benefits."
- Keynes(1936).
•
"Investment is the commitment of resources to a project or venture in the expectation
of gaining an additional income or profit."
–
Mankiw (2021).
•
"Investment is the process of committing resources in a strategic manner to achieve
long-term goals with an expectation of generating positive returns."
–
Graham (2005).
Several notable Russian economists, including Kondratiev, Abalkin, and Domar, have
made important contributions to the study of investment. Their works frequently explore
investment theory and its impact on economic development. These definitions offer various
viewpoints on investment, highlighting ideas such as forgoing current consumption, strategic
allocation of resources, generating returns, creating wealth, and pursuing financial gain.
Let’s define the meaning of fixed assets:
•
fixed assets
under
IAS 16
are physical assets with long-term use in business operations.
They are initially recognized at cost, and over time, they are depreciated (except for land) and
Iqtisodiy taraqqiyot va tahlil, 2024-yil, dekabr
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19
periodically reviewed for impairment. Their measurement can either follow the
cost model
or
the
revaluation model
, offering businesses flexibility in how they report these long-term
assets on their financial statements (MyBib Contributors, 2019).
Research methodology.
1) The method of analysis and synthesis
is applied to evaluate investment outcomes and
their correlation with GDP in the context of developing Uzbekistan's digital economy.
2)
Scientific abstraction,
along with the methods
of induction and deduction
, is employed
in research to compare similarities and evaluate findings from various scientists.
3) The abstract-logical
method is applied to theoretically synthesize the research findings
and derive conclusions.
4) The mathematical, econometric and statistical, analysis
of research results entails
examining the collected data using various methods, including ranking, scaling, classification,
systematization, differentiation, grouping, and graphical representation.
Analysis and discussion of results.
The recent presidential decree of the Republic of Uzbekistan, released on September 11,
2023, sets an ambitious target of doubling the GDP by 2030. The decree outlines various
objectives, including poverty reduction, boosting investments in research, technology,
education, and healthcare, as well as attracting more investors to the economy [1]. However,
the question remains: What is the current situation? By applying dynamic econometric models,
it becomes possible to analyze both current and future outcomes using data gathered over the
past decades.
Dynamic models in econometrics consider the values of variables not just at the current
point in time but also at earlier points. These models capture the time-based changes in
variables and enable the analysis of how past values influence both present and future
outcomes.
Not every model built with time series data is classified as dynamic in econometrics. The
term "dynamic" here refers to how each individual time point, denoted as t, is considered,
rather than focusing on the entire period for which the model is constructed. An econometric
model is considered dynamic if, at any given time t, it incorporates the values of the variables
in the model that are relevant to both the current and past time points. In essence, a dynamic
model captures the evolving nature of the variables at each specific moment in time (
Елисеева
и
др
., 2003).
Using the Ordinary Least Squares (OLS) method is not always efficient and, in some cases,
can be ineffective or even meaningless. Building distributed lag models and autoregressive
models involves certain specific challenges. First, estimating the parameters of autoregressive
models and, in most cases, distributed lag models cannot be done with OLS due to violations of
its assumptions, necessitating the use of specialized statistical methods. Second, researchers
must address challenges like selecting the optimal lag length and determining its structure.
Finally, there is a relationship between distributed lag models and autoregressive models, and
in some instances, it may be necessary to switch from one model type to another(Almon, 1965).
𝒚
𝒕
= 𝒂 + 𝒃
𝟎
⋅ 𝒙
𝒕
+ 𝒃
𝟏
⋅ 𝒙
𝒕−𝟏
+. . . +𝒃
𝒑
⋅ 𝒙
𝒕−𝒑
+ 𝜺
𝒕
.
(1)
Lags that can be represented using polynomials are known as Almon lags, a term derived
from Shirley Almon, who was the first to highlight this form of lag representation.
Formally, the model that represents the relationship between the coefficients
b
j
and the
lag magnitude
j
in polynomial form can be expressed as follows:
For a 1
st
-degree polynomial:
𝑏
𝑗
= 𝑐
0
+ 𝑐
1
𝑗;
For a 2
nd
-degree polynomial:
𝑏
𝑗
= 𝑐
0
+ 𝑐
1
𝑗 + 𝑐
2
𝑗
2
;
For a 3
rd
-degree polynomial:
𝑏
𝑗
= 𝑐
0
+ 𝑐
1
𝑗 + 𝑐
2
𝑗
2
+ 𝑐
3
𝑗
3
and etc.
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In its most general form, for a polynomial of degree
k
, we have:
𝑏
𝑗
= 𝑐
0
+ 𝑐
1
𝑗 + 𝑐
2
𝑗
2
+. . . +𝑐
𝑘
𝑗
𝑘
(2)
where
b
j
denotes the coefficient at lag
j,
and
c
0
and
c
1
are the parameters to be estimated.
Each of the coefficients
b
j
in model (1) can be expressed as follows:
𝑏
0
= 𝑐
0
;
𝑏
1
= 𝑐
0
+ 𝑐
1
+ ⋯ + 𝑐
𝑘
;
𝑏
2
= 𝑐
0
+ 2𝑐
1
+ 4𝑐
2
+ ⋯ + 2
𝑘
𝑐
𝑘
;
𝑏
3
= 𝑐
0
+ 3𝑐
1
+ 9𝑐
2
+ ⋯ + 3
𝑘
𝑐
𝑘
;
…
𝑏
𝑙
= 𝑐
0
+ 𝑙𝑐
1
+ 𝑙
2
𝑐
2
+. . . +𝑙
𝑘
𝑐
𝑘
;
(3)
By substituting the derived relationships for
𝑏
𝑗
into equation (1), we obtain:
𝑦
𝑡
= 𝑎 + 𝑐
0
⋅ 𝑥
𝑡
+ (𝑐
0
+ 𝑐
1
+. . . +𝑐
𝑘
) ⋅ 𝑥
𝑡−1
+ (𝑐
0
+ 2 ⋅ 𝑐
1
+. . . +2
𝑘
⋅ 𝑐
𝑘
) ⋅ 𝑥
𝑡−2
+
+(𝑐
0
+ 3 ⋅ 𝑐
1
+. . . +3
𝑘
⋅ 𝑐
𝑘
) ⋅ 𝑥
𝑡−3
+. . . +(𝑐
0
+ 𝑙 ⋅ 𝑐
1
+. . . +𝑙
𝑘
⋅ 𝑐
𝑘
) ⋅ 𝑥
𝑡−𝑙
+ 𝜀
𝑡
.
Let’s reo
rganize the terms in equation (4):
𝑦
𝑡
= 𝑎 + 𝑐
0
⋅ (𝑥
𝑡
+ 𝑥
𝑡−1
+ 𝑥
𝑡−2
+. . . +𝑥
𝑡−𝑙
) + 𝑐
1
⋅ (𝑥
𝑡−1
+ 2 ⋅ 𝑥
𝑡−2
+ 3 ⋅ 𝑥
𝑡−3
. . . +𝑙 ⋅ 𝑥
𝑡−𝑙
) +
+𝑐
2
⋅ (𝑥
𝑡−1
+ 4 ⋅ 𝑥
𝑡−2
+ 9 ⋅ 𝑥
𝑡−3
. . . +𝑙
2
⋅ 𝑥
𝑡−𝑙
) + 𝑐
3
⋅ (𝑥
𝑡−1
+ 8 ⋅ 𝑥
𝑡−2
+ 27 ⋅ 𝑥
𝑡−3
. . . +𝑙
3
⋅ 𝑥
𝑡−𝑙
) +
. . . +𝑐
𝑘
⋅ (𝑥
𝑡−1
+ 2𝑘 ⋅ 𝑥
𝑡−2
+ 3
𝑘
⋅ 𝑥
𝑡−3
. . . +𝑙
𝑘
⋅ 𝑥
𝑡−𝑙
) + 𝜀
𝑡
.
(5)
In this model, it is assumed that the polynomial degree,
k
, is smaller than the maximum
lag value,
l
.
Let’s repre
sent the terms within the parentheses as new variables, denoted by
c
j
:
𝑧
0
= 𝑥
𝑡
+ 𝑥
𝑡−1
+ 𝑥
𝑡−2
+ ⋯ + 𝑥
𝑡−𝑙
= ∑ 𝑥
𝑡−𝑗
𝑙
𝑗=0
;
𝑧
1
= 𝑥
𝑡−1
+ 2 ⋅ 𝑥
𝑡−2
+ 3 ⋅ 𝑥
𝑡−3
+ ⋯ + 𝑙 ⋅ 𝑥
𝑡−𝑙
= ∑ 𝑗 ⋅ 𝑥
𝑡−𝑗
𝑙
𝑗=0
;
𝑧
2
= 𝑥
𝑡−1
+ 4 ⋅ 𝑥
𝑡−2
+ 9 ⋅ 𝑥
𝑡−3
+ ⋯ + 𝑙
2
⋅ 𝑥
𝑡−𝑙
= ∑ 𝑗
2
⋅ 𝑥
𝑡−𝑗
𝑙
𝑗=0
;
…
𝑧
𝑘
= 𝑥
𝑡−1
+ 2
𝑘
⋅ 𝑥
𝑡−2
+ 3
𝑘
⋅ 𝑥
𝑡−3
+. . . +𝑙
𝑘
⋅ 𝑥
𝑡−𝑙
= ∑
𝑗
𝑘
⋅ 𝑥
𝑡−𝑗
𝑙
𝑗=0
;
(6)
Let’s express the model (5)
again, incorporating the relationships from (6):
𝑦
𝑡
= 𝑎 + 𝑐
0
⋅ 𝑧
0
+ 𝑐
1
⋅ 𝑧
1
+ 𝑐
2
⋅ 𝑧
2
+. . . +𝑐
𝑘
⋅ 𝑧
𝑘
+ 𝜀
𝑡
.
(7)
Let's analyze the efficiency of invested funds in fixed assets in the Fergana region,
Uzbekistan, using the Almon lag model. To accomplish this, we will utilize the data provided in
Table 1:
From Table 1, which includes GDP of Fergana Region and Investment in fixed assets in
billion soums from 2000 to 2023, we can observe that there are 23 observations in total. These
observations represent the values of the variables over time, allowing for analysis of their
trends and potential relationships (Gujarati and Porter, 2009).
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Table 1
GDP of Fergana Region (Gross Regional Product) and Investment in
Fixed Assets (billion soums), 2000-2023.
year
GDP of
Fergana
region
Investment
in fixed
capital
Z0
Z1
Z2
2000 374.2
52.4
2001 495.2
110.1
2002 727.2
156,8
2003 898,9
105,3
2004 1089,4
120,1
544.7
1220.0
3606.6
2005 1419,0
162,3
654.6
1376.9
4255.7
2006 1880,8
178,2
722.7
1545.2
4897.6
2007 2638.5
272.9
838.8
2070.9
6739.5
2008 3224.6
484.5
1218.0
3275.4
11083.2
2009 3752.9
663.4
1761.3
4831.1
16244.7
2010 5417.5
930.9
2529.9
6955.7
23075.9
2011 7228.5
1261.4
3613.1
9649.6
31698.6
2012 9113.0
1505.8
4846.0
12332.6
39832.4
2013 10966.4
2130.0
6491.5
16491.1
53608.7
2014 13549.5
2295.3
8123.4
19844.2
63179.4
2015 16342.4
2542.3
9734.8
22820.9
71360.3
2016 18106.3
2643.6
11117.0
24921.9
76489.5
2017 24218.2
2954.5
12565.7
27128.7
83528.9
2018 31814
5539.1
15974.8
38849.4
128332.8
2019 38116.4
8685.4
22364.9
59911.5
203279.8
2020 43413.1
11040
30862.6
84248.9
279919.4
2021 55831.9
12625.2
40844.2
106530.7 341643.9
2022 65516.9
15419.3
53309.0
130318.2 413181.0
2023 77670.6
19955
67724.9
162368.3 519594.5
Source:
compiled by authors. (stat.uz, n.d.)
Correlation matrix shows the following:
Z
0
Z
1
Z
2
GDP
Z
0
1
Z
1
0.99803272 1
Z
2
0.99653181 0.99968397 1
GDP
0.98587212 0.98778852 0.988293985 1
Parameters of regression equation (7) after applying method of ordinary least squares
(OLS):
𝑦
𝑡
~
= 3622.528 + 1.106𝑧
0
+ (−1.143)𝑧
1
+ 0.458𝑧
2
.
𝑅
2
= 0,9782
(1072.98) (1.08) (1.445) (0.339) - standard errors
Using the found regression coefficients for the variables
𝑧
𝑖
, 𝑖 = 0,1,2
and ratios (3), it is
possible to calculate the regression coefficients of the original model:
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𝑏
0
= 1.106
𝑏
1
= 1.106 − 1.143 + 0.458 = 0.421
𝑏
2
= 1.106 + 2 ∗ (−1.143) + 4 ∗ 0.458 = 0.652
𝑏
3
= 1.106 + 3 ∗ (−1.143) + 9 ∗ 0.458 = 1.799
𝑏
4
= 1.106 + 4 ∗ (−1.143) + 16 ∗ 0.458 = 3.862
The distributed lag model has the following form:
𝑦
𝑡
= 3622.528 + 1.106 + 0.421𝑥
𝑡−1
+ 0.652𝑥
𝑡−2
+ 1.799𝑥
𝑡−3
+ 3.862𝑥
𝑡−4
;
𝑅
2
= 0.9782
The analysis of this model indicates that a 1 billion sum increase in investment in fixed
capital during the current period will result in an average GDP growth of 7.84 billion sum after
4 years(1.106+0.421+0.652+1.799+3.862), based on the coefficients.
Let's determine the relative coefficients:
𝛽
0
= 1.106/7.84 = 0.140
𝛽
1
= 0.421/7.84 = 0.053
𝛽
2
= 0.652/7.84 = 0.084
𝛽
3
= 1.799/7.84 = 0.229
𝛽
4
= 3.862/7.84 = 0.494
Over half of the factor's effect on the outcome materializes with a 4-year lag, with 14% of
the impact occurring immediately in the current period. For a more precise analysis, it is crucial
to have a larger dataset. Furthermore, all analyses should be conducted under the assumption
of ceteris paribus (Ahmadjonovich and Rakhmatovich, 2023) meaning that other relevant
factors are held constant. This approach allows for isolating the effect of the specific variable
being examined, leading to a clearer understanding of its impact.
Investment in fixed assets can be directed towards various sectors, such as education
and tourism, each providing unique opportunities for growth and development. In the
education sector, investments could focus on acquiring new educational equipment (Akhunova
et al., 2024), upgrading classrooms, or introducing advanced technologies to enhance the
learning experience. Meanwhile, in the tourism industry(Akhunova and Askarov, 2023)
investments could be channeled into high-tech innovations, such as AI-driven programs
(Muminova et.al., 2024), smart systems for managing tourism services, or cutting-edge
infrastructure to improve visitor experiences and efficiency. These investments not only
contribute to the growth of their respective sectors but also foster broader economic
development. Additionally, attention to environmental sustainability is crucial, ensuring that
these investments promote eco-friendly practices (Muminova et.al., 2024) alongside economic
growth.
Conclusion and suggestions.
Investment in fixed assets in regions undeniably affects GDP. The high correlation
coefficient of 0.98 between fixed asset investment and GDP indicates a strong positive
relationship between these two variables. This suggests that investment in fixed assets plays a
crucial role in driving the growth of the Gross Regional Product (GRP). Our analysis and
research provide evidence supporting this finding.
In conclusion, this article presented an analysis of the Almon lag model using statistical
data from the Fergana Region. If an investor puts 1 billion soums into the Fergana region, they
could expect a return of 7.84 billion soums. Furthermore, the data suggests that 14% of this
return (7.84 billion soums) could be realized by the end of the first year. The study aimed to
explore the relationship between variables over time, factoring in distributed lag effects. While
the Almon lag model provides valuable insights into the region’s economic dynamics, it also has
some limitations. These include challenges in estimation and interpretation, potential
violations of assumptions, limited ability to capture nonlinear relationships, difficulties in
determining optimal lag length, and data requirements. Despite these limitations, the findings
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offer a clearer understanding of the economic conditions in the Fergana Region and present
useful insights for policymakers and researchers. Future research could investigate alternative
modeling approaches to further validate and complement the results derived from the Almon
lag model.
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Ahmadjonovich, U.A. and Rakhmatovich, A.F., (2023). UTILIZING DYNAMIC MODELS IN
ANALYZING INVESTMENT ACTIVITIES IN REGIONS. The American Journal of Management and
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QUALITATIVE AND QUANTITATIVE DEVELOPMENT OF EDUCATION IS A CRUCIAL FACTOR IN
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And Economics Fundamental, 4(04), pp.07-19.
Almon, S., (1965). The distributed lag between capital appropriations and
expenditures. Econometrica: Journal of the Econometric Society, pp.178-196.
Decree (2023) Presidential Decree of Uzbekistan #158, issued on 11th of September, 2023.
Graham, B. and McGowan, B., (2005). The intelligent investor. New York: Harper Collins.
Gujarati, N.D. and Porter, D.C., (2009). Basic econometrics. International edition McGraw-
Hill/Irwin, a business unit of the McGraw-Hill companies. Inc., New York.
Keynes, J.M., (1936). The General Theory of Employment Terest and Money. Macmillan and
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