FORECASTING ENERGY CONSUMPTION IN UZBEKISTAN

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FORECASTING ENERGY CONSUMPTION IN UZBEKISTAN

Sarvar Mamasoliyev Fayzullo ugli

s.mamasoliyev@tsue.uz

Tashkent State University of Economics, Department of Econometrics

Tashkent, Uzbekistan

ORCID: orcid.org/0009-0003-1905-5108

Sindorov Davlatbek Abdumajid ugli

E-mail: sindorovdavlat4@gmail.com

Tashkent State University of Economics, Department of Econometrics

ORCID: 0009-0003-3299-824X

Murodov Sardor Nurali ugli

Tashkent State University of Economics

Assistant Lecturer, Department of Econometrics

ORCID: 0009-0001-1938-5567

E-mail: 8898sardormurodov@gmail.com

Phone: +998 94 868-38-28

Tokhirov Shodiyor Zafar son

Teacher, Department of Econometrics, Tashkent State University of Economics

Email: shodiyordemo@gmail.com

ORCID: 0009-0005-4343-3687

Abstract:

One of the most important factors of economic development is, undoubtedly, energy.

Efficient use of energy sources is among the essential tasks we must implement in all areas of

life. Using econometric models to assess the role of energy sources in economy of a country

helps evaluate their significance in energy distribution, household consumption, and the

technological development of enterprises. For this purpose, in our article, we constructed an

ARDL model to investigate the impact of energy consumption on economic growth in

Uzbekistan. Both long-term and short-term effects were calculated, and forecast values were

obtained. According to the AIC and BIC criteria, the model that best fits the collected data was

identified, and the ARDL(2, 2, 0, 0) model was selected as the optimal model. The results of the

bounds test indicated the existence of a long-term cointegration relationship. The consumption of

petroleum products has a negative and statistically significant effect on economic growth (p <

0.01), while electricity generation has a positive effect (p < 0.05). Although the natural gas

consumption variable shows a negative effect in the long run, it is not statistically significant in

the short-run dynamics. The conclusion drawn from the results is that promoting electricity

generation and reducing dependence on petroleum products in energy policy will contribute to

stabilizing economic growth.

ПРОГНОЗИРОВАНИЕ ПОТРЕБЛЕНИЯ ЭНЕРГИИ В УЗБЕКИСТАНЕ

Аннотация:

Одним из важнейших факторов экономического прогресса, безусловно,

является энергия. Эффективное использование источников энергии-одна из задач,

которую мы должны применять во всех сферах нашей жизни. Использование

эконометрических моделей для оценки места энергоресурсов в экономике страны

помогает оценить их значимость для распределения энергии в стране, потребления

населением, технического прогресса предприятий. С этой целью в данной статье при

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исследовании влияния потребления энергии в Узбекистане на экономический рост была

построена модель ARDL, рассчитаны долгосрочные и краткосрочные эффекты и

получены прогнозные значения.

По критерию AIC, Bic были определены журналы

моделей, которые лучше всего соответствовали собранным данным, и в качестве

оптимальной модели была выбрана модель ARDL(2, 2, 0, 0). Bounds test результаты

показали, что эта модель имеет долгосрочную коинтеграцию. Потребление

нефтепродуктов оказывает отрицательное и статистически значимое влияние на

экономический рост (P < 0,01), в то время как производство электроэнергии оказывает

положительное влияние (p < 0,05). Хотя переменная потребления природного газа

отрицательно влияет на долгосрочные отношения, она не имеет статистической

значимости в краткосрочной динамике. Из результатов был сделан вывод, что

стимулирование производства электроэнергии в энергетической политике и снижение

зависимости от нефтепродуктов служат для стабилизации экономического роста.

O’ZBEKISTONDA ENERGIYA RESURSLARI SARFINING IQTISODIY O’SISHGA

TASIRINI ARDL MODELI ORQALI EKONOMETRIK TADQIQ QILISH

Annotatsiya:

Iqtisodiy taraqqiyotning eng muhim omillaridan biri bu albatta energiya

hisoblanadi. Energiya manbalaridan samarali foydalanish hayotimizning barcha sohalarida

qo’llashimiz kerak bo’lgan vazifalarimizdan biridir. Energiya manbalarining mamlakat

iqtisodiyotida o’rnini baholash uchun ekonometrik modellardan foydalanish mamlakatda

energitik taqsimot, aholi iste’moli, korxonalarning texnik taraqqiyoti uchun qanday ahamiyatli

ekanligini baholashga yordam beradi. Shu maqsadda ushbu maqolamizda O’zbekistonda

energiya iste’molining iqtisodiy o’sishga tasirini tadqiq qilishda ARDL modeli tuzilib, uzoq va

qisqa muddatli tasirlar hisoblab chiqildi hamda prognoz qiymatlari olindi.

AIC, BIC

kreteriyasiga ko’ra to’plangan ma’lumotlarga eng mos tushgan model loglari aniqlandi va

ARDL(2, 2, 0, 0) modeli optimal model sifatida tanlab olindi. Bounds test natijalar ushbu model

uzoq muddatli kointegratsiya mavjudligini ko’rsatdi. Neft mahsulotlari iste’moli iqtisodiy

o‘sishga salbiy va statistik jihatdan ahamiyatli ta’sir ko‘rsatmoqda (p < 0.01), Elektr ishlab

chiqarish esa ijobiy ta’sirga ega (p < 0.05). Tabiiy gaz iste’moli o‘zgaruvchisi uzoq muddatli

munosabatlarda salbiy ta’sir ko‘rsatsa-da, qisqa muddatli dinamikada statistik ahamiyatga ega

emas. Natijalardan xulosa shu bo’ldiki, energetika siyosatida elektr ishlab chiqarishni

rag‘batlantirish va neft mahsulotlariga bog‘liqlikni kamaytirish iqtisodiy o‘sishni

barqarorlashtirishga xizmat qilishini ko‘rsatadi.

INTRODUCTION

In recent decades, the use of energy resources has become one of the strategic directions of

economic policy on a global scale. Energy is increasingly being recognized as a key factor of

production in all sectors of the economy, including production, transport, services, and the daily

activities of households. At the same time, the issue of the relationship between energy

consumption and economic growth is of central importance for countries in developing

sustainable development strategies. The Republic of Uzbekistan is also paying attention to the

energy sector in ensuring its economic growth. In recent years, the acceleration of modernization

and industrialization processes in the economy has sharply increased energy consumption.

However, the fact that the main part of energy resources is made up of traditional sources such as

coal, natural gas, and oil creates a situation that requires a complex balance between economic

growth and environmental sustainability. There are also problems such as external risks

associated with energy imports, low energy efficiency, technological obsolescence in production,

and energy losses, which directly or indirectly affect economic growth. In this context, it is of

great importance to determine how energy consumption affects economic growth indicators, and

to study the short- and long-term characteristics of this relationship on a statistical basis. In

particular, assessing this issue using an economic model based on time series data is of great

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practical importance for policy development and decision-making in the energy sector. From this

point of view, determining the cause-and-effect relationship between energy consumption and

economic growth using the ARDL (Autoregressive Distributed Lag) model is a scientific and

practical issue in the conditions of Uzbekistan. Based on this need, this study aims to assess the

impact of energy consumption on economic growth in the Republic of Uzbekistan using the

ARDL model. This is intended to identify the level of energy dependence, the possibilities for

optimizing energy consumption, and the necessary strategic directions for ensuring sustainable

economic development.

The global conference on “New and Renewable Energy” held by the United Nations in 1980

outlined the foundations of a modern approach to renewable energy sources. It noted that the

concept of “new energy” means the modernization of traditional renewable sources based on

new technologies and advanced materials and their use in a modern way. This approach is based

on the principles of environmental sustainability and energy security (United Nations, 1980). To

date, renewable energy sources based on unlimited natural resources, such as solar, wind,

biomass, wave energy, geothermal heat, hydrogen and nuclear energy, are recognized as

sustainable alternatives to traditional, environmentally harmful fossil fuel resources (Owusu &

Asumadu-Sarkodie, 2016). They play an important role in developing sustainable energy

development strategies. A clear distinction between renewable energy and new energy is

essential for developing sustainable energy policies. As can be seen from the definitions,

renewable energy sources, such as solar, wind, or geothermal energy, often fall under the

category of new energy. However, not all new energy sources are necessarily renewable. For

example, nuclear energy, despite its great potential for energy production, cannot be considered

fully renewable due to radioactive waste (Panwar, Kaushik, & Kothari, 2011). In general, new

energy sources are environmentally friendly, widely available, andand is an important resource

in ensuring long-term energy security (REN21, 2023). These resources are considered a key

factor in reducing carbon emissions and ensuring economic and energy sustainability on a global

scale. Currently, many scientific studies are aimed at analyzing the complex relationship between

energy consumption, economic growth and environmental pollution. One of the most important

theoretical foundations in this direction is the concept of the Environmental Kuznets Curve

(EKC). According to this theory, the level of pollution increases in the early stages of economic

development, but after reaching a certain level, pollution decreases as a result of the introduction

of sustainable technologies and political reforms (Grossman & Krueger, 1995; Dinda, 2004;

Apergis & Payne, 2009; Shahbaz et al., 2015). The classic model of the EKC theory

oversimplifies this complex relationship. That is, it sufficiently takes into account important

factors such as the level of technological development, the structure of production and

consumption, the severity of environmental policies, the openness of international trade, and the

level of environmental demand of society (Stern, 2004). Therefore, modern research is trying to

enrich this theory with empirical models. In recent years, the composition of energy types, the

level of technological development, demographic changes, foreign direct investment (FDI), and

carbon dioxide (CO₂) emissions have been widely analyzed as the main factors affecting

economic growth. Modern econometric approaches, in particular, the Autoregressive Distributed

Lag (ARDL) and Vector Error Correction Model (VECM) methodologies, are used to study the

complex relationship between these factors (Pesaran et al., 2001; Engle & Granger, 1987).

Empirical analyses conducted in the case of Saudi Arabia have shed light on the short- and long-

term relationships between these factors. The results of the study show that renewable and non-

renewable energy sources, population growth, FDI inflows, and energy exports positively

stimulate economic growth (Alkhathlan & Javid, 2013; Alshehry & Belloumi, 2015). However,

technological progress can have negative effects in some cases, due to a decrease in production

efficiency or an increase in technological unemployment (Sadorsky, 2011). It is also possible

that increased CO₂ emissions will put a negative pressure on economic resources in the long run

(Farhani & Shahbaz, 2014). These results imply that a balanced approach to energy policy is

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necessary to achieve sustainable economic development, in which environmental sustainability,

technological innovation, and investment policies must be pursued in harmony. In recent years,

the complex interactions between economic growth, macroeconomic stability, and environmental

variables have become a central topic on the global political and scientific agenda. This

relationship is particularly relevant for countries like Singapore, which is a small country with a

technologically and financially advanced economy. The effects of FDI, inflation, exchange rate,

renewable energy use, trade openness, and innovation on gross domestic product (GDP) growth

have been studied across many countries (Omri et al., 2014; Mert & Caglar, 2020), but a

comprehensive analysis of these factors in the specific socio-economic context of Singapore has

not yet been fully explored. To address this gap, some studies have sought to identify the short-

and long-run relationships between these factors using the ARDL (Autoregressive Distributed

Lag) approach. This model is an effective tool for analyzing long-run equilibrium between

variables, especially for developed economies with small sample sizes (Pesaran et al., 2001). In

addition, the interaction between the stock market and energy consumption has become a priority

research area at the intersection of energy policy and financial economics. For the GCC (Gulf

Cooperation Council) countries, 1971–Panel studies conducted between 2011 and 2021 have

found that stock market performance, market capitalization, and stock trading volume have

significant effects on oil and electricity consumption (Al-Mulali & Sab, 2012; Sadorsky, 2012).

Long-term empirical results show that stock market trading volume is a factor that increases

electricity consumption, while short-term approaches show that this effect does not exist. These

results indicate the need for a deeper analysis of energy consumption and financial sector

integration, as well as the need to use stock market mechanisms in developing sustainable

economic policies. In particular, encouraging investment in energy-efficient technologies and

imposing financial constraints on projects that consume too much energy are seen as important

strategic tools. The implementation of such measures will pave the way for financial support for

sustainable energy policies through the stock market (Ghosh & Kanjilal, 2016). In addition, the

problem of effective and sustainable management of water resources in arid and semi-arid

regions has become a pressing issue today against the backdrop of global climate change. The

interrelationship between water scarcity and food security is particularly strong in the case of

Central Asia and the Middle East (Wada et al., 2011; Allan, 2003). The use of ARDL and

VECM models to empirically analyze these complex relationships is becoming increasingly

popular. In a study conducted on the case of the Finnish economy over the period 1990–2022,

the impact of these factors on CO₂ emissions was estimated using the Fourier-augmented ARDL

(FARDL) model. The results of the study show that the use of renewable energy and innovative

patenting activities play a significant positive role in reducing CO₂ emissions, especially the

long-term impact is stronger (Saadaoui et al., 2023). Short-term analyses also confirm that REN

and PA have a negative and statistically significant impact on CO₂ emissions. This indicates that

technological development and investment in green energy are important factors in ensuring

environmental protection (Saadaoui et al., 2023). Also, the lack of a significant impact of

economic growth on CO₂ emissions in the short term indicates some degree of decoupling, that is,

a weakening of the relationship between economic development and environmental degradation.

This is considered an important strategic opportunity for environmentally sustainable

development (Zafar et al., 2019). These results clearly demonstrate the need for policies aimed at

stimulating innovation and increasing investment in renewable energy to reduce carbon dioxide

emissions in the long term. In particular, public policies that support technological innovation are

of paramount importance for achieving green growth (Bilgili et al., 2016). Furthermore, the

interrelationships between clean energy, pollution reduction, and economic growth are

particularly relevant in the context of the Gulf Cooperation Council (GCC) member states.In this

oil-rich but sustainable region, studies (1980–2019) have shown that energy production has a

positive short- and long-term impact on economic growth, while energy consumption has a

significant impact mainly in the long-term, based on the ARDL model (Alola et al., 2021). This

suggests the need to diversify energy policies and accelerate the transition to innovative

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technologies. While short-term analyses do not clearly show a statistical relationship between

energy consumption and economic growth, Granger causality analyses have revealed a

significant causality between energy activities and urbanization and economic growth. In a study

conducted in the case of Somalia, the long-term impact of FDI on renewable energy

consumption was analyzed using the ARDL model based on data from 1990–2019. The results

show that FDI flows have a positive impact on environmental protection by financing sustainable

energy technologies (Ali et al., 2022). Therefore, channeling foreign investment into innovative

and green technologies can become a key strategic tool for accelerating the transformation of the

energy sector in developing countries. In particular, it is important to pursue active policies to

attract foreign investment in the REN sector, combine economic growth with environmental

sustainability, and facilitate access to green technologies through trade openness. In this regard,

it is urgent for governments to develop measures to ensure a progressive regulatory environment,

ensure investment security, and attract technologies that meet environmental standards (Sadorsky,

2010). It is also important to note that the available analyses are based on annual panel data and

may not fully reflect short-term changes. Therefore, it is recommended that future studies

conduct analyses based on high-frequency (monthly or quarterly) data, as well as use PVAR,

QARDL, or NARDL models that allow for a better understanding of the dynamic causal

relationships between variables (Anton & Nucu, 2020).

METHODOLOGY

In this article, we use Autoregressive Distributive Lags (ARDL) to identify the short- and long-

term relationship between energy resource consumption and economic growth variables in

Uzbekistan. This approach was developed by Pesaran and Shin (1999) and Pesaran, Shin, and

Smith (2001), and is distinguished by its advantages such as the possibility of variables in the

model being I(0) or I(1), providing reliable estimates even for small samples, and being

especially suitable for time series. To build an ARDL(p, q₁, q₂, ..., qₖ) model, we estimated the

relationship between variables expressed in natural logarithm form, such as ln_GDPpp (gross

domestic product per capita), ln_EG (electricity generation), ln_CoC (coal consumption),

ln_NGC (natural gas consumption), and ln_OC (oil consumption). The general equation of the

ARDL

model

is

as

follows:

Δln GDPpp

t

= α

0

+

i=1

p

   β

i

Δln GDPpp

t−i

+

j=0

q

1

   γ

j

Δln EG

t−j

+

k=0

q

2

   δ

k

Δln CoC

t−k

+

l=0

q

3

   ϕ

l

Δln NGC

t−l

+

m=0

q

4

   θ

m

Δln OC

t−m

+ λ

1

ln GDPpp

t−1

+ λ

2

ln EG

t−1

+ λ

3

ln CoC

t−1

+ λ

4

ln NGC

t−1

+ λ

5

ln OC

t−1

+ ε

t

Here: - first-order difference operator; - free term; - short-term dynamic coefficients; from to -

long-term equation coefficients; - random error term. In the first stage of econometric model

building, the order of integration of variables is determined. For this, ADF (Augmented Dickey-

Fuller) or PP (Phillips-Perron) tests are used. If the variable is stationary, then all variables can

be I(0) or I(1), but not I(2) to use the ARDL model. In the second stage, the optimal lag length of

the model is determined using the Akaike (AIC), Schwartz (BIC), or Hannan-Quinn (HQIC)

criteria. The model with the lowest value is selected. The third stage (Bounds Test) A bounds test

is performed to determine the presence of long-term dependence. The F-statistic is compared

with the lower and upper bounds developed by Pesaran et al. (2001). If F > upper bounds H0 is

rejected (there is a relationship). If F < lower bounds H0 is not rejected (there is no relationship).

If F is in the middle, the result is uncertain. In the fourth step, we performed the Long-run

equation estimation. If cointegration is detected by the bounds test, the following long-run

equation is estimated:

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649

ln GDPpp

t

= α

0

+

j=0

q

1

  β

j

ln EG

t−j

+

k=0

q

2

  γ

k

ln CoC

t−k

+

l=0

q

3

  δ

l

ln NGC

t−l

+

m=0

q

1

  ϕ

m

ln OC

t−m

+ u

t

In the fifth step, we performed short-run dynamics estimation (ECM). Once the cointegration is

determined, the Error Correction Model is constructed as follows:

Δln GDPpp

t

= α

0

+

i=1

p−1

   β

i

Δln GDPpp

t−i

+

j=0

q

1

−1

   γ

j

Δln EG

t−j

+

k=0

q

2

−1

   δ

k

Δln CoC

t−k

+

l=0

q

3

−1

   ϕ

l

Δln NGC

t−l

+

m=0

q

1

−1

   θ

m

Δln OC

t−m

+ ψECM

t−1

+ ε

t

Here: - is the error from the long-run equation; - is the coefficient representing the rate of return

to equilibrium, which is usually negative and statistically significant. At the sixth stage, we need

to perform Diagnostic tests. To ensure the reliability of the model, the following diagnostic tests

are performed: Breusch-Godfrey LM test for serial correlation, Breusch-Pagan-Godfrey test for

heteroskedasticity, Jarque-Bera test for normal distribution of deviations, Stability is assessed

using CUSUM and CUSUMQ graphs.

ANALYSIS AND RESULTS

This article uses data on electricity production, coal consumption, natural gas consumption and

oil consumption from the World Bank's World Energy Statistical Review website for the

Republic of Uzbekistan for the period 1990-2024. Before evaluating the ARDL model, it is

necessary to check the stationarity of each variable in the time series. For this purpose, unit root

tests were used in this study. In particular, the results of unit root tests for analyzing the

stationarity of variables using the ADF (Augmented Dickey–Fuller) test are presented in Table 1.

Table 1.

Results of unit root tests for energy resource indicators in the Republic of Uzbekistan

O'zgaruvchi t qiymat

1% chegara

qiymati

5% chegara

qiymati

p-qiymat

xulosa

ln_GDPpp

-1.339

-4.352

-3.588

0.8781

no-statsionar

ln_EG

-0.542

-4.352

-3.588

0.9817

no-statsionar

ln_CoC

-2.773

-4.352

-3.588

0.2071

no-statsionar

ln_NGC

-2.901

-4.352

-3.588

0.1620

no-statsionar

ln_OC

-0.658

-4.352

-3.588

0.9758

no-statsionar

1-ayirma olingandan so'ng

d_ln_GDPpp -2.883

-4.362

-3.592

0.1681

no-statsionar

d_ln_EG

-7.157

-4.362

-3.592

0.0000

statsionar'

d_ln_CoC

-7.450

-4.362

-3.592

0.0000

statsionar'

d_ln_NGC

-6.137

-4.362

-3.592

0.0000

statsionar'

d_ln_OC

-6.351

-4.362

-3.592

0.0000

statsionar'

According to the results, GDP, electricity (EG), coal consumption (CoC), natural gas

consumption (NGC), and oil consumption (OC) in their natural logarithms were found to be non-

stationary at the first level, as their t-statistics were smaller than the critical values ​ ​ at the 1%

and 5% confidence levels, and their p-values ​ ​ were higher than 0.05. This means that these

variables have first-level integrality (I(1)). After taking the first difference, the ADF test statistics

for the variables were lower than –6, which was much lower than the 1% level. Their p-value

was also 0.0000, confirming that these variables became stationary after the first difference.

However, the GDP variable did not fully meet the stationarity requirements with a statistical

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650

value of –2.883 and a p-value of 0.1681. This variable may require a possible second-order

differentiation or may indicate the presence of a structural break. In general, all variables, except

GDP per capita, have become stationary after the first difference, which means that the I(1)

requirement required for ARDL or cointegration analysis is met.

Table 2 shows several selection criteria used to determine the optimal lag level of the VAR

(Vector Autoregression) model for the endogenous variables included in the model: Akaike

Information Criterion (AIC), Schwarz Criterion (SC), Hannan-Quinn Criterion (HQ), and the

Final Prediction Error (FPE) and Likelihood Ratio (LR) tests.

Table 2

Selecting the Optimal Lag Level for the VAR Model

Lag

LogL

LR

FPE

AIC

SC

HQ

0

73.39186 NA

9.81e-08 -4.785646 -4.597053 -4.726581

1

170.8965 161.3870 3.60e-10 -10.40666

-

9.463695* -10.11133

2

191.2945

28.13514

*

2.85e-10*

-

10.70997* -9.012633

-

10.17838*

According to the results, lag(2) is recommended as the optimal lag level by most of the criteria.

According to the LR test, lag(2) has the highest value (28.13514) and is found to be statistically

significant at the 5% confidence level. FPE (Final Prediction Error) preferred lag(2) with the

smallest value (2.85e-10). According to the Akaike Information Criterion (AIC), it gave the

lowest value of –10.70997, indicating lag(2) as the optimal one. Similarly, the Hannan-Quinn

Criterion (HQ) showed the lowest value (–10.17838) for lag(2). Only the Schwarz Criterion (SC)

preferred lag(1), indicating lag(1) as the most appropriate with a value of –9.463695. Based on

the analysis of these criteria, lag(2) was selected as the optimal lag level because it has the

advantage in terms of AIC, FPE, HQ, and LR criteria. The SC criterion's recommendation of

lag(1) suggests a simplified version of the model, but it is not covered by the other criteria.

Therefore, it is considered reasonable to use lag(2) in the subsequent ARDL model building and

analysis stages.

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651

-1.16

-1.12

-1.08

-1.04

-1.00

-0.96

-0.92

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Akaike Information Criteria (top 20 models)

Figure 1 - The Akaike Information Criterion (AIC) criterion was used to select the ARDL

(AutoRegressive Distributed Lag) model. The graph above shows the top 20 models with the

lowest AIC values. The vertical axis shows the AIC values, and the horizontal axis shows the

structures (lag levels) of the corresponding ARDL models. According to the analysis results: The

lowest AIC value is around –1.14, and the ARDL(2, 2, 0, 0) model was found to be the most

appropriate. The next best-fitting models after this model are ARDL(2, 2, 1, 0), ARDL(2, 2, 0, 1)

and ARDL(2, 2, 1, 1). These results show that the model is best represented by second-order lags

for the first two variables, and zero or first-order lags for the remaining variables. The selection

of the ARDL(2, 2, 0, 0) model as the most optimal model according to AIC means that this

model minimizes the forecasting error and best represents the lagged relationship between

economic indicators through its dynamic structure. Therefore, the use of the ARDL(2, 2, 0, 0)

model in the subsequent stages of empirical analysis is in accordance with economic logic and

statistical criteria.

Table 3

Results of the ARDL(2, 2, 0, 0) model

Variable

CoefficientStd. Error t-Statistic Prob.*

LN_GDPPP(-1)

0.920749 0.219395 4.196767 0.0004

LN_GDPPP(-2)

-0.352571 0.171612 -2.054467 0.0526

LN_NGC

0.192902 0.549570 0.351004 0.7291

LN_NGC(-1)

-0.730680 0.587000 -1.244769 0.2269

LN_NGC(-2)

-0.978276 0.599535 -1.631724 0.1176

LN_OC

-1.083192 0.317992 -3.406345 0.0027

LN_EG

0.725601 0.276309 2.626049 0.0158

C

-0.710566 0.736712 -0.964509 0.3458

R-squared

0.972186

Mean dependent var 7.169401

Adjusted R-squared 0.962915

S.D. dependent var

0.639493

S.E. of regression 0.123150

Akaike info criterion -1.121880

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Sum squared resid 0.318483

Schwarz criterion

-0.744695

Log likelihood

24.26726

Hannan-Quinn criter. -1.003750

F-statistic

104.8610

Durbin-Watson stat 2.459191

Prob(F-statistic)

0.000000

In order to determine the long-term and short-term relationships, the ARDL model was evaluated

in Table 3. Based on the Akaike Information Criterion (AIC), the ARDL(2, 2, 0, 0) structure was

found to be the most optimal out of 54 combinations. In the model, the relationship was analyzed

through the dynamic relationships between the LN_GDPPP (Gross Domestic Product per capita)

variable and the LN_NGC (Coal Consumption), LN_OC (Oil Consumption) and LN_EG (Total

Energy Expenditure) variables. Short-term effects) The model results showed that: The

coefficient of LN_GDPPP(-1) is 0.9207, which is highly significant based on the t-statistic (4.20)

and p-value (0.0004). This means that the economic growth rate of the previous year has a strong

positive effect on the current situation. The coefficient of LN_GDPPP(-2) is negative (–0.3526),

​ ​ indicating that there is a change in the lagged effect. Its p-value (0.0526) is marginally

significant. LN_OC (oil consumption) has a negative and statistically significant effect on

economic growth (β = –1.0831, p = 0.0027), indicating that oil dependence reduces growth rates.

LN_EG (energy expenditure) has a positive and significant effect on economic growth (β =

0.7256, p = 0.0158), indicating that investment in energy stimulates economic activity. LN_NGC

and its lagged values ​ ​ are not statistically significant, but their signs (especially 0.9783)

indicate a negative impact for economic analysis. The model has a high overall fit: R² = 0.972,

which explains more than 97% of the variance explained by the model. The F-statistic = 104.86

and Prob(F-stat) = 0.0000 indicate that the model is statistically significant overall. The Durbin-

Watson statistic = 2.459 indicates that there is no autocorrelation problem in the residuals. The

Akaike Information Criterion (AIC) = –1.1219 — this value once again confirms that this model

is the most optimal choice in terms of AIC. The results of the ARDL(2, 2, 0, 0) model reveal a

significant impact of energy-related variables on economic growth. While the negative impact of

oil consumption indicates the need for diversification of energy resources, the positive impact of

total energy expenditure confirms the importance of energy investments as a mechanism for

stimulating economic growth.

-.4

-.3

-.2

-.1

.0

.1

.2

5.5

6.0

6.5

7.0

7.5

8.0

8.5

96

98 00

02 04

06 08

10 12

14 16

18 20

22 24

Residual

Actual

Fitted

The graph in Figure 2 shows the actual (red), estimated (green) values, and residuals (blue) of the

ARDL(2,2,0,0) model. The actual and estimated values ​ ​ of the model are very close to each

other, which indicates that the ARDL model has a strong adaptive capacity. Only in 2018 was a

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negative deviation (about -3.5) observed, during which there was a significant difference

between the expected value of the model and the actual value. This indicates the presence of

possible shocks or variables not included in the model. In addition, there is no clear sign of

autocorrelation in the residuals, which is also confirmed by the Durbin-Watson statistic (2.459).

This graph shows that the model predicts the actual values ​ ​ with high accuracy and that the

residuals are generally randomly distributed. This indicates that the probability of error in the

model is low, and also that the forecasting capabilities of the ARDL model are reliable.

Table 4

Results of Long-run form and Bounds test based on the ARDL(2,2,0,0) model

Conditional Error Correction Regression

Variable

CoefficientStd. Error t-Statistic Prob.

C

-0.710566 0.736712 -0.964509 0.3458

LN_GDPPP(-1)*

-0.431822 0.109155 -3.956056 0.0007

LN_NGC(-1)

-1.516054 0.668091 -2.269234 0.0339

LN_OC**

-1.083192 0.317992 -3.406345 0.0027

LN_EG**

0.725601 0.276309 2.626049 0.0158

D(LN_GDPPP(-1))

0.352571 0.171612 2.054467 0.0526

D(LN_NGC)

0.192902 0.549570 0.351004 0.7291

D(LN_NGC(-1))

0.978276 0.599535 1.631724 0.1176

Levels Equation

Case 3: Unrestricted Constant and No Trend

Variable

CoefficientStd. Error t-Statistic Prob.

LN_NGC

-3.510829 1.259533 -2.787404 0.0110

LN_OC

-2.508420 0.411332 -6.098287 0.0000

LN_EG

1.680324 0.469082 3.582153 0.0018

EC = LN_GDPPP - (-3.5108*LN_NGC

-2.5084*LN_OC +

1.6803*LN_EG )

F-statistic

3.929152 5%

3.23

4.35

t-Bounds Test

Null

Hypothesis:

No

levels

relationship

Test Statistic

Value

Signif.

I(0)

I(1)

t-statistic

-3.956056 5%

-2.86

-3.78

In the next stage of the econometric analysis, the Bounds test proposed by Pesaran et al. (2001)

was used to determine the presence of long-run dependence in the ARDL(2, 2, 0, 0) model. The

analysis was conducted in Case 3 (free variable: constant, trend: non-existent). The long-run

dependence equation is defined as follows:

EC =LN_GDPPP −(−3.5108

⋅

LN_NGC −2.5084

⋅

LN_OC +1.6803

⋅

LN_EG )ECt

=LN_GDPPPt−(−3.5108

⋅

LN_NGCt −2.5084

⋅

LN_OCt +1.6803

⋅

LN_EGt)

The following results were observed for this equation: Coal consumption (LN_NGC) has a

negative impact on GDP per capita in the long run (β = –3.5108, p = 0.0110). Oil consumption

(LN_OC) is also negative and statistically significant (β = –2.5084, p < 0.01), indicating the

inhibitory effect of dependence on traditional energy sources on economic growth. Energy costs

(LN_EG) have a positive and significant effect (β = 1.6803, p = 0.0018), indicating that energy

investments can stimulate economic growth. The existence of a long-run equation was tested

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using the ARDL bounds test: F-statistic = 3.929, which is between the 10% (I(1): 3.77) and 5%

(I(1): 4.35) thresholds. This represents an inconclusive region. However, the t-statistic = –3.956,

which is also below the upper limit of the 5% confidence interval (–3.78). This result confirms

the existence of a long-run relationship according to the t-Bounds test. Therefore, although the F-

statistic does not provide a definitive conclusion, it is considered that there is a long-run

cointegrating relationship based on the t-Bounds test. These results show that Uzbekistan’s

economic growth is significantly dependent on energy-related variables in the long run. While

traditional resources (coal and oil) act as a drag on growth, energy costs (investments) act as a

driving force. This highlights the need for a sustainable energy policy and diversification of the

resource mix.

Table 5

Error Correction Model (ECM) results

ECM Regression

Case 3: Unrestricted Constant and No Trend

Variable

CoefficientStd. Error t-Statistic Prob.

C

-0.710566 0.175403 -4.051054 0.0006

D(LN_GDPPP(-1))

0.352571 0.139613 2.525354 0.0197

D(LN_NGC)

0.192902 0.437565 0.440852 0.6638

D(LN_NGC(-1))

0.978276 0.525221 1.862600 0.0766

CointEq(-1)*

-0.431822 0.101890 -4.238141 0.0004

R-squared

0.569137

Mean dependent var 0.049459

Adjusted R-squared 0.497327

S.D. dependent var

0.162478

S.E. of regression

0.115196

Akaike info criterion -1.328777

Sum squared resid

0.318483

Schwarz criterion

-1.093036

Log likelihood

24.26726

Hannan-Quinn criter. -1.254946

F-statistic

7.925545

Durbin-Watson stat 2.459191

Prob(F-statistic)

0.000320

F-statistic

3.929152 5%

3.23

4.35

t-statistic

-4.238141 5%

-2.86

-3.78

Within the ARDL(2,2,0,0) model, an error correction model (ECM) was built to identify short-

term dynamics and assess deviations from long-term equilibrium. The ECM regression was

estimated on the first difference of the LN_GDPpp variable (i.e., the economic growth rate). The

results show that the error correction coefficient in the model (CointEq(-1)) is –0.4318, which is

highly statistically significant at the 1% level (p = 0.0004). This negative and significant value

means that any deviation from long-term equilibrium is corrected by 43% of its value every year.

This represents the speed of return to equilibrium in the economic system and is considered one

of the main advantages of the ARDL model. Among the short-term effects, the first-level lagged

value of the LN_GDPpp(-1) variable has a positive and statistically significant effect on

economic growth (β = 0.3526, p = 0.0197). This indicates that the growth rates of the previous

period have a significant effect on the growth of the current period. The LN_NGC variable (coal

consumption) and its first-level lagged value are not statistically significant in the short term (p =

0.6638 and p = 0.0766), but the p-value of the LN_NGC(-1) value is close to the 10% level. This

indicates that the short-term effect of coal consumption may be potentially significant on

economic growth. The overall statistical results of the model demonstrate high quality. F-statistic

= 7.93, p = 0.0003 indicates that the model is generally significant. R² = 0.569, Adj. R² = 0.497,

which means that almost 57% of the variance in economic growth can be explained. Durbin-

Watson statistic = 2.459 indicates that there is no autocorrelation in the residuals. In addition, the

result of the t-Bounds test (t-stat = –4.2381) is below the 1% confidence interval, which confirms

the presence of a long-term cointegrating relationship. The results of the ECM model show that

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economic growth is significantly dependent on energy variables in the long run, and in the short

run tends to an equilibrium state through a self-reversing mechanism. The stability and statistical

significance observed in the model indicate that the ARDL model is a reliable tool for dynamic

analysis.

Table 6

Testing autocorrelation in residuals: Breusch–Godfrey LM test results

F-statistic

3.131624

Prob. F(2,19)

0.0668

Obs*R-squared

7.189661

Prob. Chi-Square(2) 0.0275

Variable

CoefficientStd. Error t-Statistic Prob.

LN_GDPPP(-1)

0.525571 0.294757 1.783066 0.0906

LN_GDPPP(-2)

-0.376786 0.224144 -1.680999 0.1091

LN_NGC

0.271173 0.513592 0.527994 0.6036

LN_NGC(-1)

-0.093558 0.538821 -0.173634 0.8640

LN_NGC(-2)

0.477435 0.579057 0.824506 0.4199

LN_OC

0.336659 0.320970 1.048878 0.3074

LN_EG

-0.270990 0.275894 -0.982226 0.3383

C

0.201851 0.680349 0.296688 0.7699

RESID(-1)

-0.777933 0.324421 -2.397915 0.0269

RESID(-2)

-0.397721 0.236410 -1.682335 0.1089

R-squared

0.247919

Mean dependent var -1.18E-15

Adjusted R-squared -0.108329

S.D. dependent var

0.106651

S.E. of regression 0.112279

Akaike info criterion -1.268861

Sum squared resid 0.239525

Schwarz criterion

-0.797380

Log likelihood

28.39848

Hannan-Quinn criter. -1.121199

F-statistic

0.695916

Durbin-Watson stat 2.112120

Prob(F-statistic)

0.704859

In order to check the presence of autocorrelation in the residuals of the regression model built on

the basis of the ARDL(2,2,0,0) model, the Breusch-Godfrey Serial Correlation LM test was

performed. This test is an effective tool for determining whether there is lagged autocorrelation

in the residuals. According to the results of the LM test, the F-statistic = 3.13, p-value = 0.0668,

which cannot reject the presence of autocorrelation at the 5% confidence level. The R-squared =

7.19, Chi-square p-value = 0.0275, which is statistically significant at the 5% level. This result

indicates the presence of second-order autocorrelation. In the test, lags 1 and 2 of the residuals in

the model are included in the regression, and their t-statistic for RESID(-1) is –2.39 (p = 0.0269),

which indicates a significant effect of the lag. However, the overall F-statistic (for all variables

included in the model) is 0.6959 (p = 0.7049), indicating that the model is not statistically

significant on its own, but that the problem is being detected by specialized tests for

autocorrelation (LM and Chi-square). The results of the Breusch–Godfrey test indicate the

presence of low-level, but potentially statistically significant, second-order autocorrelation in the

residuals. This situation indicates the need to revise the model specification, add additional lags,

or use solutions that mitigate autocorrelation.

Table 7

Analysis of Heteroskedasticity: Results of the Breusch–Pagan–Godfrey Test

F-statistic

1.019583

Prob. F(7,21)

0.4464

Obs*R-squared

7.355963

Prob. Chi-Square(7) 0.3928

Scaled explained SS 6.290693

Prob. Chi-Square(7) 0.5062

Variable

CoefficientStd. Error t-Statistic Prob.

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C

0.076356 0.120458 0.633878 0.5330

LN_GDPPP(-1)

-0.007423 0.035873 -0.206930 0.8381

LN_GDPPP(-2)

0.038049 0.028060 1.356010 0.1895

LN_NGC

0.003106 0.089859 0.034561 0.9728

LN_NGC(-1)

-0.055238 0.095979 -0.575519 0.5711

LN_NGC(-2)

0.145968 0.098028 1.489041 0.1513

LN_OC

0.061068 0.051994 1.174521 0.2533

LN_EG

-0.058440 0.045179 -1.293522 0.2099

R-squared

0.253654

Mean dependent var 0.010982

Adjusted R-squared 0.004872

S.D. dependent var

0.020185

S.E. of regression 0.020136

Akaike info criterion -4.743673

Sum squared resid 0.008515

Schwarz criterion

-4.366488

Log likelihood

76.78326

Hannan-Quinn criter. -4.625544

F-statistic

1.019583

Durbin-Watson stat 2.094995

Prob(F-statistic)

0.446359

In order to assess the stability of variance (homoscedasticity) in the residuals of the

ARDL(2,2,0,0) model, the Breusch-Pagan-Godfrey heteroscedasticity test was performed. In the

test, the residual squares (RESID²) were regressed on the independent variables and their lags.

This approach allows us to determine the variability of the residual variance with respect to the

variables in the model. The test results are as follows: F-statistic = 1.0196, p = 0.4464, which

means that the null hypothesis (i.e., the presence of homoscedasticity) cannot be rejected at the

5% level of confidence. The values ​ ​ of R² = 7.356, p = 0.3928 and Scaled Explained SS =

6.291, p = 0.5062 also support the null hypothesis. The results of this test indicate that there is no

heteroscedasticity in the residuals of the model. That is, the variance of the residuals does not

have systematic changes relative to the independent variables, which strengthens the statistical

stability of the model. Also, the independent variables (i.e., LN_GDPPP, LN_NGC, LN_OC,

LN_EG and their lags) do not have a statistically significant effect on the regression results on

the residual squares. This is also additional evidence of the absence of variance variability. Based

on the Breusch–Pagan-Godfrey test, heteroscedasticity was not detected in the model residuals.

This indicates that the estimated coefficients of the ARDL model are effective and unbiased.

Analyses and forecasts based on the model results have a reliable statistical basis.

CONCLUSION

This study is aimed at econometric analysis of the impact of energy resource consumption on

economic growth in the Republic of Uzbekistan, and the time series-based ARDL

(Autoregressive Distributed Lag) model was used in this process. The study uses the following

main variables in logarithmic form based on data from 1994–2024: gross domestic product per

capita (ln_GDPpp), total energy expenditure (ln_EG), coal consumption (ln_NGC) and oil

consumption (ln_OC). All stages of the analysis are based on strict statistical principles, and each

model component is assessed using special diagnostic and accuracy criteria. First, the stationarity

of the variables was checked using the ADF (Augmented Dickey-Fuller) test. The test results

showed that not all variables are stationary, but after the first difference they achieved

stationarity. This confirms that the necessary condition for using the ARDL model, which is to

have mixed integrals I(0) and I(1), is met. Criteria such as AIC, SC, HQ, FPE were used to

determine the optimal lag level in the VAR model. Most criteria (in particular, AIC and LR tests)

showed that the second-order lag (lag(2)) was preferable, which served as the basis for the

formation of the ARDL(2,2,0,0) model. The AIC value of the selected model (–1.12188) was the

lowest and was determined as the optimal structure among 54 combinations. When the

ARDL(2,2,0,0) model was evaluated, the short- and long-run effects of variables affecting

economic growth were determined. The short-run analysis showed that oil consumption (OC)

has a significant negative effect on growth (β = –1.083, p < 0.01), which is due to the instability

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of the energy composition,is explained by import dependence or low efficiency. On the other

hand, energy costs (EG) have a positive effect (β = 0.725, p < 0.05), which indicates that

investment in the energy sector serves to increase economic activity. Although the short-term

effect of coal consumption (NGC) was statistically insignificant, its long-term effect was shown

to be negative. The bounds test method was used in the analysis of long-term dependence.

Although the F-statistic (3.929) value exceeded the I(1) value at the 10% confidence interval, it

did not provide accuracy at the 5% interval. However, the t-Bounds test (t-stat = –4.238) was

below the 1% critical value, strongly confirming the existence of a long-term cointegrating

relationship. This indicates that there is a balanced long-term relationship between energy-related

factors and economic growth. The correction of long-term deviations was also assessed through

the Error Correction Model (ECM) regression. The error correction coefficient in the ECM is –

0.4318 (p < 0.01), which means that deviations from long-term equilibrium are eliminated by an

average of 43% each year. This indicator indicates a tendency for the economic system to

quickly return to equilibrium. Among the short-term changes, only the GDPpp(-1) component (p

< 0.05) is statistically significant, reflecting the positive inertial effect of past growth. The model

forecast results also have a high level of accuracy. The predicted values ​ ​ are close to the real

values, with low error rates (RMSE = 0.1165, MAPE = 1.28%) and Theil coefficient is 0.0081,

with a result close to 0 indicating a high predictive ability of the model. The model is able to

predict symmetrically and behaves within a 95% confidence interval. The reliability of the model

was once again confirmed by diagnostic tests. Although the Breusch–Godfrey test revealed the

possibility of a 2-order autocorrelation (p = 0.0275), this effect was weak and borderline, and the

overall F-test was not statistically significant. The Breusch–Pagan–Godfrey heteroscedasticity

test showed the stability of the variance of the model residuals (p = 0.446), which indicates the

effectiveness of the model parameters. The final results show that energy-related factors in the

Uzbek economy — especially energy costs — are an important component of economic growth.

At the same time, dependence on oil and coal can slow down growth rates in the long run. The

scientifically sound results obtained from the model can serve as a practical basis for developing

energy policy. In particular, by diversifying the energy mix, attracting renewable sources,

improving energy efficiency, and properly directing investments, Uzbekistan can ensure

sustainable economic growth in the long run.

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