CC BY
23
УДК 330; 330.4
DOI: http://dx.doi.org/10.21686/2500-3925-2023-2-21-40
Цель исследования. В статье анализируется влияние мировых цен на нефть (внешние и внутренние факторы) на ВВП страны, рассматриваются колебания мировых цен на нефть, их влияние на национальную экономику Азербайджана и интегрируемость этих макроэкономических показателей.
Материалы и методы. Изучение динамики функционирования временных рядов на основе исходных данных выявило их нестационарность, что не позволяет построить «качественную» прогностическую модель. Для достижения целей исследования и «повышения качества» формируемой модели, которая используется для расчета прогнозных оценок, были проведены соответствующие эконометрические процедуры и исследована интегрируемость временных рядов. В частности, используется метод векторной модели коррекции ошибок — VECM. Тест основан на использовании уравнений коинтеграции между переменными, где длина лагов и определения причинности по Грейнджеру решаются в рамках этой модели. При формировании модели VECM выдвинутые в работе гипотезы проверялись на основе использования эконометрических тестов. Отклики импульсной функции на независимые переменные модели изучались методом графического представления на основе значений модели и ее невязок.
Н.С. Айюбова
Бакинский Государственный Университет, Баку, Азербайджан
Республики)
Результаты. Определено, что долгосрочную равновесную связь между переменными можно считать устойчивой, так как после нарушения в краткосрочные периоды от шоковых реакций устойчивость восстанавливается. Примененный метод декомпозиции дисперсий ошибок прогноза для определения влияния экзогенных переменных на эндогенную переменную показал, что наибольшую неопределенность в прогноз для ВВП, марок Azeri_light, Brent и West дают собственные изменения в течение первого триместра рассматриваемого периода.
Заключение. Полученные результаты могут быть полезными для выявления реальных тенденций ВВП Азербайджана и определения его взаимозависимостей с другими макроэкономическими переменными, для определения его взаимозависимостей с вариацией цен на энергоносители на основе анализа динамики рассматриваемых показателей, для разработки рекомендаций и образования направлений перспективного развития ВВП.
Ключевые слова: ВВП Азербайджана, мировые цены на нефть, векторная модель коррекции ошибок, реакции импульсных функций отклика, декомпозиции переменных.
Анализ влияния мировых цен
на нефть на ВВП
(на примере Азербайджанской
Natavan S. Ayyubova
Baku State University, Baku, Azerbaijan
Analysis of the Impact of Global Oil Prices On GDP
(on the Example of the Azerbaijan Republic)
Purpose of the study. The article analyzes the impact of world oil prices (external and internal factors) on the country's GDP, considers fluctuations in world oil prices, their impact on the national economy of Azerbaijan and the integrability of these macroeconomic indexes. Materials and methods. The study of the dynamics of the functioning of time series based on the initial data revealed their non-stationarity, which does not allow creating a "qualitative " predictive model. In order to achieve the goals of the study and "improve the quality" of the model being formed, which is used to calculate predictive estimates, appropriate econometric procedures were carried out and the integrability of time series was investigated. In particular, the method of vector error correction model - VECM is used. The test is based on the use of cointegration equations between variables, where lag lengths and Granger causality definitions are solved within this model. When forming the VECM model, the hypotheses put forward in the work were tested using econometric tests. The responses of the impulse function to the independent variables of the model were studied by the method of graphical representation based on the values of the model and its residuals.
Results. It has been determined that the long-term equilibrium relationship between variables can be considered stable, since after short-term disturbances from shock reactions, stability is restored. The applied method of decomposition of forecast error variances to determine the influence of exogenous variables on the endogenous variable showed that the greatest uncertainty in the forecast for GDP, Azeri_light, Brent and West is given by their own changes during the first trimester of the period under consideration. Conclusion. The results obtained can be useful for identifying real trends in Azerbaijan's GDP and determining its interdependencies with other macroeconomic variables, for determining its interdependencies with variations in energy prices based on an analysis of the dynamics of the indexes under consideration, for developing recommendations and forming directions for the long-term development of GDP.
Keywords: Azerbaijan GDP, world oil prices, error correction vector model, reactions of impulse response functions, decompositions of variables.
Introduction
When improving the system of state macroeconomic regulation, the effectiveness of the application of elements of economic policy is important. It is of great importance to identify and study the relationships between indicators of sectors of the economy, between internal and external indicators, quantify these relationships, identify patterns, develop trends that characterize the dynamics of development of different areas of the economy and their application in management.
Econometric models based on mathematical and statistical methods make it possible to identify relationships between the quantitative characteristics of economic objects in order to prepare mathematical conditions for the forecast, to determine the values of all parameters in the model and ensure its adequacy with the real behavior of the parameter under study, to obtain effective values of the model parameters, to check the theoretical and economic provisions and conclusions based on empirical information [1, 2, 3, 4].
The issue of forecasting important economic indicators is very relevant in the management and state regulation of the economy. Forecast estimates of the main indicators of the state of the economy, such as GDP dynamics, price index, current account balance of payments, crisis prediction, etc. may vary. The structure, structure of various economic indicators in solving an identical problem may dictate specific requirements, an individual approach to each of them, which requires a preliminary detailed study and analysis of phenomena.
Relevance
In econometric studies, the modeling of economic indicators with the study of the reactions of indicators to various
shocks has become widespread. That is, forecasting is not only quantitative, but also qualitative. In other words, the researcher can simply indicate the quantitative change in the indicator under study, and can also indicate on what other indicators this change may depend and how. Preparation of models for forecasting is a statistical analysis of data, analysis of dependencies and relationships between factors.
To predict changes in the future of the studied economic objects, such as rising or falling prices, changes in the exchange rate, GDP growth, economic crises, etc. specialists in economic phenomena prefer to rely on experience, knowledge in the relevant field and on intuition. In such situations, the relationship of economic indicators may be incorrectly assessed, or some of them may be missed, which can have a strong enough impact on the analyzed situation. But, they do not take into account the advantages of mathematical modeling, where all the relationships of variables can be evaluated both quantitatively and qualitatively. Such econometric models, with a clear economic interpretation of specialists, make it possible to predict a better and more reliable forecast. Moreover, the simplicity and clarity of the explanations of the mechanisms and the obtained results of the models increases the corresponding audience.
Dynamic models include relationships of variables over time. In statistical models, in particular, series values are used, which are variables in dynamic models. Such models apply mechanisms, variational calculations, difference and differential equations, describe the nature and strength of mutual influences in the economy, which determine the algorithm of economic processes.
Vector autoregressive models and vector error correction models, the use of which has become very popular in
econometric studies due to their wide possibilities, allow representation in a structural form, allow solving analytical problems, the solution of which was impossible or created difficulties in the implementation of regression modeling.
Work analysis
A complex algorithm of macroeconomic indicators
associated with economic crises, cycles, with a change in economic trends and with an unstable economy associated not only with internal but also with external phenomena make the analysis, study of non-stationary time series and the construction of econometric models based on them especially relevant and important.
The mathematical model of an economic indicator in the form of a system of equations, logical and interrelated relationships, graphs is its homomorphic display, in a conditional way. Analysis, study of these models substantiate and develop more effective solutions to the issues under study.
The work of Polbin A.V. [5] is devoted to the econometric assessment of the impact of changes in the conditions of trading operations, world oil prices, fixed capital accumulation, household consumption in Russia, using the method of constructing a vector model of error correction with exogenous variables. The results of the author's research demonstrate that permanent the change in oil prices generated a «domed» response in the dynamics of the level of production. The author concludes that the impact of the increase in oil prices on GDP growth rates is positive in the short term and negative in the medium term. Analysis of the sensitivity of national economies to changes in world oil prices has always been an interesting and researched issue[6] considers in his work the problem of modeling the dynamics of oil prices. The
author, substantiating the need to distinguish two periods, offers aggregated models. These models reflect the conditions in the oil market and in the national economy for the selected periods. The paper assesses the impact of possible monetary policy priorities on the dynamics of macroeconomic indicators and oil prices. Also, the importance of supplementing the analysis with a study of the impact of high oil prices on the most sensitive to rising fuel prices, intensive industries and industries is substantiated. Zulfigarov F. and Neuenkirch M. in [7] analyze oil price shocks in a six-variable model, where most variables are presented in the form of the first logarithmic difference, determines the significance of shocks in oil prices for the variances of the considered variables. Using variance decomposition, the author predicts the variation of variables when a shock is applied to the oil price variable and to each of the other macro variables included in the system. Rautava in work [8] analyzes the impact of world oil prices and the real exchange rate on the Russian economy and fiscal policy using the VAR methodology and cointegration methods. The results show that in the long run, a 10% increase or decrease in world oil prices is associated with an increase or decrease in Russian GDP by 2.2%. The influence of external economic conditions on the dynamics of the Russian economy is considered in most econometric models developed by Russian scientists. In the article[9], the author, analyzing the relationship of economic indicators in the Russian economy with the volatility of world oil prices, evaluates and proposes a system of simultaneous econometric equations, with the help of which he puts forward and tests a number of hypotheses about the sensitivity of macroeconomic stability to fluctuations in external factors. By studying the relationship
between macroeconomic
parameters and world oil prices, researchers in [10] identify factors that have a long-term positive relationship with oil prices, using mathematical approaches such as vectorial autoregression, Granger, Dickey-Fuller. It was revealed that a 1% increase in GDP leads to a strengthening of the ruble by 1.47%, that the price of oil and GDP has the greatest impact on the ruble exchange rate in the short term according to Granger, and actions are formulated to improve the effectiveness of macro indicators. Ybrayev Z. analyzes [11] the exposure of Kazakhstan's long-term economic growth to macroeconomic constraints. Balance-of-payments-constrained growth models predict that a country's growth rate can be approximated by the ratio of export growth rate to the income elasticity of demand for imports. The Johansen cointegration method was used to evaluate trading parameters. A vector error correction model is used to analyze short-term adjustments in income elasticity. The results show that average growth rates project long-term economic growth in Kazakhstan at about 2%, and current economic growth is limited by aggregate demand. A study [12] examines the direction of the causal relationship between the balance of trade and oil price shocks in the context of Pakistan over the period 1975—2010. The result shows that there is a significant negative relationship between oil prices, exchange rate and trade balance in Pakistan i.e. oil prices and exchange rate cause trade imbalance in Pakistan. Also, there is a positive relationship between the output gap and the trade balance, which indicates inefficient allocation and use of resources in production. The Granger causality result indicates that there is a bidirectional causal relationship between oil prices and the exchange rate in Pakistan. In work Pilnik N.P. and Shaikhutdinova M.F. [13] formulates a model that allows
you to explore and predict foreign economic activity using and applying balance of payments indicators. The developed model makes it possible to accurately characterize the dynamics of the balance of payments indicators in the format of econometric and balance ratios and presented in three scenarios of the state of the balance of payments and can be used for short-term forecasting, which takes into account different combinations of external economic conditions, prices on world markets, etc. The work [14] studies the modeling of the dynamics of the balance of payments of Azerbaijan based on changes in the exchange rate, export-import operations, general and foreign investments in Azerbaijan. On the basis of statistical methods and an analytical approach to the analysis of the problem, an econometric model has been developed in the form of a multiple regression equation, which takes into account the influence of the main factors on the country's balance of payments. Also, to check the adequacy of the model and the significance of explanatory factors, the corresponding econometric tests with accompanying comparisons were carried out. Using the model, the authors interpret the dynamics of the development of the main macro-indicator of the country's foreign trade. The article [15] conducts an econometric analysis of the dynamic processes of Azerbaijan's balance of payments, discusses the formation of an econometric trend suitable for forecasting. Stationarity verification is important for econometric models, which is given sufficient space in this paper. Hypotheses about the absence of autocorrelation, heteroscedasticity in residuals, etc. are also tested. In [16], to create a cointegration ratio that can be used to measure the impact of Azerbaijan's GDP on the current account balance of payments in the long run
Fig. 1. Production of crude oil in Azerbaijan from 2000 to 2020 [18] Рис. 1. Добыча сырой нефти в Азербайджане с 2000 по 2020 гг. [18]
Fig. 2. Azeri Light oil price dynamics from 2000 to 2022 [19] Рис. 2. Динамика цен на нефть Azeri Light с 2000 по 2022 гг. [19]
and then to create a model for correcting errors and predicting economic development. Pre-econometric analysis of the time series of macroeconomic indicators taken into account for the presence of stationary was performed. According to the results of the Johansen test, linear and quadratic trends with similar results indicate the presence of cointegration relation and carried out Trace and Maximum Eigenvalue tests. In this work, both test statistics show the presence of one cointegration relation. As a result, an alternative hypothesis about the existence of one vector of cointegration and from two trends with similar results, a linear one was chosen trend. The results of this study provide an opportunity to identify actual trends development of the current account of the balance of payments and determine its interdependence with GDP. In [17], the impact of oil shocks and the change in the dynamics of oil price uncertainty associated with economic and political events are determined. In contrast to previous studies, the results of this study show that the sharp increase in oil price uncertainty over recent decades has a detrimental effect on output growth and that output growth responds symmetrically or asymmetrically to positive and negative shocks over the period.
Analysis of the state of time series by model parameters
The most important exogenous factor of the Azerbaijani economy is oil prices, which is justified by the structure of the national economy and the country's export potential. Changes in world oil prices inevitably affect the volume of GDP, investment in the country, the real exchange rate, the level of average income and life of the population, and so on. Despite the steadily strengthening exchange rate of the national currency due to regulated measures at the state level, the increase in world
oil prices, which increase the financial flow to the country and are closely related to the prices of other energy carriers, the growth or decrease in world oil prices strongly affects the dynamics of economic processes in the country of traders. oil products. This fact makes the close dependence of the Azerbaijani economy on the export of oil products an acute problem affecting the country's macroeconomic stability.
Having reached a record high of 1072 barrels per day per thousand in June 2009 and a record low of 168 barrels per day per thousand in February 1997, Azerbaijan's crude oil production as of April 2022 was 690 barrels per day per thousand. Fig. 1 presents data on crude oil production in Azerbaijan (20002020).
Azerbaijan's exports for the first quarter of 2022 increased by 2.1 times, which amounted to 8.1 billion dollars, and imports
by 16.8%, which amounted to 2.7 billion dollars. Oil and gas exports increased 2.2 times and amounted to 7.4 billion dollars. The average market price for Azeri light oil reached $86.5 in the first quarter of 2022, and by the third quarter it rose by $3.5 to $128.80. In March 2022, this mark reached its all-time high this year at $136 per barrel. The dynamics of prices for Azeri light oil can be seen in Fig. 2.
Fig. 3 shows the dynamics of Brent and West Texas Intermediate oil prices from 1996 to 2020.
Analysis of Fig. 2 and Fig. 3 allows us to trace similar price dynamics for the three brands Azeri Light, Brent and West Texas Intermediate. According to the State Statistics Committee, Azerbaijan's GDP in 2021 increased by 5.6% compared to the previous period, and by 6.2% in the first half of 2022. The growth of the oil and gas sector
Fig. 3. Brent and West Texas intermediate oil prices dynamics (1996-2020) [20,21] Рис. 3. Динамика промежуточных цен на нефть марок Brent и West Texas (1996-2020 гг.) [20,21]
amounted to 1.8% and 0.2%, respectively. In 2021, the nominal volume of Azerbaijan's GDP amounted to 92 billion 857.7 million manats. For 6 months, the same indicator amounted to 63 billion 364.4 million manats.
In the first half of 2022, 75.7% of the production volume fell on the mining industry, 20.4% on the processing industry, 3.4% on the production and distribution of electricity, 0.5% on the water supply and waste processing. Investments in fixed assets for the 1st half of 2022 amounted to 6.3 billion manats, which is an increase of 0.7% over 6 months of 2021, in the structure of which the volume of foreign investments amounted to 1.606
billion manats, and the volume of domestic investments 4.693 billion manats[22].
To visually analyze the relationship between GDP and oil prices, we use a graphical method. Fig. 4 shows a combined graph of Azerbaijan's GDP and Azeri Light, Brent, West Texas Intermediate oil prices. The figure clearly shows similar dynamics of all four parameters, which confirms the close and strong impact of oil prices on the economic growth of Azerbaijan.
The main results of the study
First of all, it should be noted the main advantage of vector error correction models, which
Fig. 4. Combined graph of Azerbaijan's GDP and Azeri Light, Brent, West Texas
Intermediate oil prices (2000-2020) [23] Рис. 4. Комбинированный график ВВП Азербайджана и промежуточных цен на нефть марок Azeri Light, Brent, West Texas (2000-2020 гг.) [23]
allow expanding the applicability of regression models, also to non-stationary time series. The assumption that model variables are interdependent can form several equations when tested. These equations can be reduced to one after testing the degree of exogeneity of the variables.
To find the rank of cointegration of the vector model for Azerbaijan's GDP and world oil prices, a preliminary analysis of time series by parameters should be carried out. Statistical data for conducting econometric tests were taken from the official website of the State Statistics Committee of Azerbaijan [24], from the website of the Central Bank of Azerbaijan [25], from open international information Internet sources [26].
To conduct tests that determine cointegration relations, it is necessary to make sure that the series under study are firstorder integrated series. According to the results of the regression analysis, where GDP was taken as dependent variables, and Azeri Light, Brent, West as independent variables, the formal model looks like this:
GDP = 354.02267Azeri_ light + 540.268Brent-
105.9412West-6701.798 (1)
R2 was found to be 82%, F-statistic 27.1(Probability
0.000001), Akaike info criterion 21.55, Schwarz criterion 21.75, Durbin-Watson statistic 0.78,
2002 2004 2006 2008 2010 2012 2014 2016
I a Total stocnastic -GDP |
Brent crude oil from GDP
•ч / \л \\\ In
9 ■ V
2002 2004 2006 2008 2010 2012 2014 2016 2018 I Total stocnastic -GDP~|
West Texas Intermediate from GDP
1 п-ja ft ^ \ л- a
f \j
1 Hi Total stochastic -GDP | Azeri light from GDP
, ll __ □ O-Qm
|| 11 cr
2004 2006 2008 2010 2012 2014 2016 2018 2020 I I J Total stochastic -GDP I
2004 2006 2008 2010 2012 2014 2016 2018 2020 I i-1 Total stocnastic -Brent cruae c* |
Brent crude oil from Brent crude oil
/I L. 1
r If* 1
2010 2012 2014 2016
I 1=» Tota"
West Texas Intermediate from Brent crude oil
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Azeri light from Brent crude oil
1 uA J
□
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f=K. П п cn
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Brent crude oil from West Texas Intermediate
ß n,,
«Ц1- 1 ■ - l
2002 2004 2006
2010 2012 2014 2016 2018
West Texas Intermediate from West Texas Intermediate
/4 .Ml" \
II'" ■J-^I \l
2002 2004 2006 2008 2010 2012 2014 2016 2018 2020
Azeri light from West Texas Intermediate
"1 Шя У
2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 I L:—J Tota stocnastic
2004 2006 2008 2010 2012 2014 2016 2Q18 2020 I Total stocnastic -Azen IgfiTl
Brent crude oil from Azeri light
2004 2006 2008 2010 2012 2014 2016 2018 2020 I I—I Total stocnastic -Azen «длТ]
Azeri light from Azeri light
- weet Texas Intermectate |
2006 2008 2010 2012 2014 2016 2018 2020 I 1 I Total stocnastic -Azen fcjhTl
Fig. 5. Historical decomposition using Cholesky weights for variables in split form Рис. 5. Историческая декомпозиция с использованием весов Холецкого для переменных в разделенной форме
Fig. 6. Historical decomposition using Cholesky weights for variables in combined
form
Рис. 6. Историческая декомпозиция с использованием весов Холецкого для переменных в комбинированной форме
Fig. 7. Structural VAR Residuals Using Cholesky Factors Рис. 7. Структура остатков по факторам с использованием разложения по
Холецкому
t-criterion for Azeri Light 2.442708(Probability 0.0258), for Brent 3.318517 (Probability 0.0041) and for West -0.927554 (Probability 0.3666). Among the results there are positive indicators for modeling. The coefficient of determination explains the choice of factors for the model by 82%, leaving 18% for random components, which is assessed as satisfactory. The Fisher criterion is 27.75 with a high probability, the Student criteria for Azeri Light and Brent are also obtained with high probabilities. But, the statistics of Durbin Watson are very unsatisfactory and indicate the presence of a positive autocorrelation. By the number of observations n1 = 21 and by the number of degrees of freedom n2 = 3, respectively, the lower and upper limits of the critical points, with 95% probability, are d, = 1.026 and du=1.669. Since the criterion is DW = 0.78 and is located to the left of these points, this explains the positive autocorrelation in the regression model and the non-stationarity of the model.
Using the Historical Decomposition using Cholesky weights procedure in the Eviews package, decomposition was carried out for time series and, based on the results, in all cases a trend was found that characterizes the series as non-stationary. Graphs were built for each variable separately and in combined form and are presented in Fig. 5 and 6.
To study the stationarity, dynamics, nature of time series, it is also important to analyze the residuals of these series. In Fig. 7, for each time series, with the help of VAR Structural Residuals using Cholesky Factors, graphs were constructed showing the structure of the residuals for the variables under study.
As can be seen from the graphical analysis of decompositions and the structure of the residuals of the original time series covering the period from 2000 to 2020, the GDP,
Azeri Light, Brent, West series are non-stationary, which requires consideration of data from a different aspect, since in this situation according to the initial data, the construction of an adequate model suitable
for forecasting is impossible. Based on the first or second data difference for variables, time series can be revised and reexamined for stationarity [27], which is an advantage of the Augmented Dickey-Fuller test. In
some cases, this procedure allows you to get the desired results and continue the study.
The Dickey-Fuller test and similar procedures KPSS, PhillipsPerron, Breusch-Godfrey serial correlation LM-test, Ljung-Box and Augmented Dickey-Fuller are used in autoregressive modeling to determine stationarity in series. The Augmented Dickey-Fuller test is an extended form of the Dickey-Fuller test. With this test, applying the method of differences on series data, you can remove the existing autocorrelation from time series and test them for stationarity. The extended Dickey-Fuller unit root test computes a value for the t-test with a p level of significance, and also offers critical values for the t-test with 1%, 5%, and 10% probabilities. These results help to conclude that the series is stationary. The null hypothesis determines the unit root, and stationarity is determined by the alternative hypothesis. The estimate of the coefficient 4 = 1 means the presence of a unit root in the time series, which characterizes the non-stationarity of the series
[28]. Mathematically, the Dickey-Fuller test can be represented as follows:
yt = + v, (2)
where yt — is the time series under study at moment t; 4 — is the coefficient determining the unit root; vt is white noise, which is a random process, a special case of stationary series. This is a random sequence for the values y1, ..., yp, if they are independent of each other and the conditions E(y) = 0, D(yt) = const are satisfied. The unit root test determines whether the stochastic component of the equation consists of a unit root
[29].
For an extended analysis of the residuals of the model, a parameter was added as an independent factor representing the residuals and a regression analysis was performed. At the next step, using the Dickey-
Fuller test for a unit root, the stationarity of the first difference for the variables was tested.
The regression analysis for the multiple model for GDP with four independent parameters gave very positive results as follows. R2 was 98%, F-statistic 6.38E + 14 (Probability 0.000024), Akaike info criterion -9.3, Schwarz criterion -9.04, DW statistic 1.88, t criterion for Azeri Light 12435701(Probability 0.00566), for Brent 16894399(Probability 0.0038), for West -4722128. (Probability 0.000002) and for Mresid 20990517(Probability 0.00003). The Fcriterion is 6.38E + + 14 with the probability 0.000024, which is more than the critical values at all significance levels: Fcalc. > 2.25(0.1); Fcalc. > > 2.87(0.05); > 4.43(0.01). Durbin Watson's statistics are
very satisfactory and indicate no autocorrelation. According to the input parameters n1 = 21 and n2 = 4, with 95% probability, the lower and upper limits of the critical values for DW are d = 0.927 and du= 1.812. Since the criterion is DW= 1.883 and is located to the right and approaches the mark 2, which confirms the absence of autocorrelation in the regression model.
Akaike and Schwarz information criteria allow you to select the best results. The lowest values of these criteria help researchers in choosing the best model:
AIC = 2k - 2ln(l);
BIC = -2ln(l) + kln(n), (3)
where k is the number of independent factors; l is the log-likelihood estimate; n - sample size.
Table 1 (Таблица 1) Results of the augmented Dickey-Fuller test Результаты расширенного теста Дики-Фуллера
Variables crit.value 1% crit.value.5% crit.value10% t statistic Probability
According to original rows
GDP -3.831511 -3.029970 -2.655194 -1.798420 0.3698
Azeri_Light -3.831511 -3.029970 -2.655194 -2.296535 0.1828
Brent -3.808546 -3.020686 -2.650413 -1.679454 0.4258
West -3.808546 -3.020686 -2.650413 -1.679454 0.4258
Mresid -3.831511 -3.029970 -2.655194 -2.571647 0.1158
By rows with second differences
GDP -3.886751 -3.052169 -2.666593 -4.436996 0.0034
Azeri_Light -4.004425 -3.098896 -2.690439 -4.032918 0.0095
Brent -4.004425 -3.098896 -2.690439 -4.151370 0.0077
West -3.857386 -3.040391 -2.660551 -8.843333 0.0000
Mresid -4.004425 -3.098896 -2.690439 -5.460860 0.0008
Table 2 (Таблица 2) Results of descriptive statistics of variables Результаты описательной статистики переменных
GDP Azeri_Light Brent West Mresid
Mean 38154.56 52.46227 63.46000 75.53143 -0.000529
Median 42693.00 52.18517 61.51000 64.78000 756.0769
Maximum 75234.70 103.9699 111.6300 124.2300 16908.11
Minimum 5272.800 7.319492 24.45000 31.86000 -20587.48
Std. Dev. 23615.69 25.98500 28.84630 29.76424 9814.413
Skewness -0.068729 0.163608 0.347257 0.451374 -0.146638
Kurtosis 1.812306 2.611764 1.966200 1.782927 2.298478
Jarque-Bera 1.250823 0.225572 1.357204 2.009194 0.505876
Probability 0.535041 0.893342 0.507326 0.366192 0.776516
Sum 801245.8 1101.708 1332.660 1586.160 -0.011100
Sum Sq. Dev. 1.12E+10 13504.41 16642.18 17718.20 1.93E+09
Observations 21 21 21 21 21
Table 3 (Таблица 3)
Variation coefficients for variables (%) Коэффициенты вариации переменных (%)
xi GDP Azeri Light Brent West Mresid
vx- 61.9 49.5 45.4 39.4 18.5
7 - -
II
Series: GDP
Sample 2000 2020
Observations 21
Mean 38154.56
Median 42693.00
Maximum 75234.70
Minimum 5272.800
Std. Dev. 23615.69
Skewness -0.068729
Kurtosis 1.812306
Jarque-Bera 1.250823
Probability 0.535041
10000 20000 30000 40000 50000 60000 70000 80000
Fig. 8. Histogram of the standard distribution of residuals for the GDP time series Рис. 8. Гистограмма стандартного распределения остатков для временного
ряда ВВП
Correlation matrix Корреляционная матрица
Table 4 (Таблица 4)
GDP AZERI LIGHT BRENT WEST MRESID
GDP 1 0.83402437667324 0.86490338310344 0.51209909750483 0.41558867083991
AZERI LIGHT 0.8340243766732 1 0.767529430116969 0.46458612090521 -5.85995208256e-09
BRENT 0.86490338310344 0.767529430116969 1 0.70408479187499 3.5498988979e-08
WEST 0.51209909750483 0.46458612090521 0.704084791879944 1 2.49011693338e-08
MRESID 0.41558867083991 -5.85995208584e-09 3.549898892879e-08 2.4901169338e-08 1
The Akaike and Schwartz criteria do not always select the same model. Criteria values can be the same or different. This is due to certain specific criteria. For the model under study, the Akaike and Schwartz criteria almost coincide and have the smallest values, respectively, -9.049 and -9.041.
The regression model takes the following form:
GDP =354.0227Azeri_light + + 540.268Brent - 105.9412West + + Mresid-6701.798 (4)
Table 1 shows the results of the extended Dickey-Fuller test for rows with original data and for rows with second data differences.
By changing the parameters, a Dickey-Fuller test was carried out with 2nd order differences, without a trend, with a constant, using the Schwartz criterion, with a maximum number of lags of 4, and results were obtained that accept the alternative hypothesis of stationarity for time series for all factors in the model, on all levels of significance.
To build a quality model, it is important that the independent variables in the model, i.e., the regressors, have a fairly wide range of change. The range of variation can be measured on the basis of the coefficient of variation, which is defined as the proportion of the ratio of standard deviations of parameters to their mathematical expectations.
The results of the descriptive statistics in Table 2 were used to analyze the variability of the model variables. All results obtained must be at least 10% to ensure variability, otherwise, if this condition is not met for any variable, then it is more appropriate to remove the variable from the model or replace it with another variable.
There is no need to replace or delete variables, since the required condition is met and the coefficients of variation for all variables have received values of more than 10% (see Table 3).
The Jarque-Bera test tests observational errors for normality by checking third and fourth order central moments against the central moment of a normal distribution. This test examines the null hypothesis about the normality of the distribution, against the alternative hypothesis that does not accept the normality of the distribution of observational errors.
For GDP, the Jarque-Bera test obtained the following value: JBGDP = 1.250823, with prob. = 0.535041 > 0.05, which confirms the normality of the distribution. The test results are presented in Table 3 and Figure 8. The null hypothesis of normal distribution is accepted. The histogram in Fig. 8 of the standard residual distributions for the GDP time series confirms the test results. At one level, there is a deviation from the general
trend with a normal distribution, which is confirmed by the values for the skewness and kurtosis coefficients: Kskew = -0.068; Kcurt = 1.812306. There is a very slight deviation of the coefficients from the values for the normal distribution: X^. = 0; Kcurt. = 3, which does not interfere with the decision on the normality of the distribution for the observational errors of the GDP time series.
Estimates of the tightness and direction of relationships between the parameters are presented in Table 4, in the form of a correlation matrix. Correlation coefficients between factors falling within the interval (0.7; 0.9) are estimated as strong and not random. If these values fall within the interval (0.5; 0.7), then the relationship is of medium tightness, that is, noticeable. In other cases, the relationship is assessed as weak and random. The
correlation between the resultant factor GDP and the independent factors Azerijight and Brent is considered to be close and direct. The connection between GDP and West is also not weak and quite noticeable.
Structural residuals play an important role in a broad analysis of VAR, where their calculations are required, including impulse estimation, decomposition of the forecast variance.
To check the stability of the parameters included in the model over the entire sample, you can use the Cusum test, which, by calculating the accumulated sums of recursive residuals and the accumulated sums of squares over the residuals, builds graphs for variables. If the recursive estimates of the residuals for the model parameters go beyond the critical boundaries of the 95% confidence intervals, this indicates their instability. If the blue line does not intersect with the red ones on the graphs, then the model parameters are stable and the null hypothesis is accepted. Otherwise, the H1 hypothesis about parameter instability is accepted.
The graphs shown in Fig. 9 show recursive and standardized estimates of residuals as a result of the CUSUM test. The analysis of the diagram in Fig. 9 confirms the null hypothesis about the stability of the model parameters, since the corresponding conditions are met. In other words, the recursive estimates of the residuals do not fall outside the confidence interval with 95% probability. So, recursive and standardized estimates of residuals for the residuals of the model indicate the stability, stability of the developed model.
To analyze the autoregressive model of the endogenous variable, the inverse roots of the characteristic equation of the polynomial from the shift operator are calculated, which serves to check the stationarity of the AR model. Using the Roots of Characteristic Polynomial test,
Fig. 9. Recursive and standardized residual estimates Рис. 9. Рекурсивные и стандартизированные оценки остатков
Table 5 (Таблица 5) The result of the test for the roots of the characteristic polynomial Результат проверки корней характеристического полинома
Root Modulus
0.645249 - 0.141177i 0.660513
0.645249 + 0.141177i 0.660513
Fig. 10. Plotting unit roots for GDP Рис. 10. Построение единичных корней для ВВП
inverse AR roots for GDP were calculated to check the state of stability.
The values of the roots in table 5 do not exceed one. Figure 10 shows a unit circle, which can also be used to determine the state of stability and stationarity of the series. It can be seen that no root lies outside the unit circle. This means that the VAR for GDP satisfies the stability condition and the considered process is assumed to be stationary.
For linear regression, it is important to check the Ramsey test, which determines the significance of non-linear combinations of independent variables in the model, which serves to explain the dependent variable. Using this test, you can determine the presence of variables that are not included
in the model, the correlation between explanatory variables and the random component, the incorrect functional form of the dependencies between the resultant and explanatory factors, etc. These phenomena lead to a shift in the mathematical expectation of the residuals of the model.
According to the test, the null hypothesis is accepted if the F-statistic value is less than the critical value and the model specifications are accepted as correct. If this condition is not met, then the functional form of the model is incorrect according to the alternative hypothesis. The results of the Ramsey test are shown in Table 6. With input parameters k1 = 4, = 21 (in the table of critical values for F-statistic for k2 = 22 was used)
Table 6 (Таблица 6)
Results of the Ramsey test Результаты теста Рамси
Value df Probability
t-statistic 0.047672 15 0.9626
F-statistic 0.002273 (1, 15) 0.9626
Likelihood ratio 0.003181 1 0.9550
White's test results Table 7 (Таблица 7)
Результаты теста Уайта
F-statistic 1.195072 Prob. F(14,6) 0.4384
Obs*R-squared 15.45691 Prob. Chi-Square(14) 0.3477
with probabilities 0.1; 0.05; 0.01 were defined critical values for F-statistic, respectively, 2.22; 2.82; 4.31 and compared with the calculated value for F-statistic. Since the condition Fcalc. = 0.002273 < Fcrit on all probabilities, then the hypothesis about the acceptability of the functional form of the model is accepted as correct.
The White test is a procedure for testing the random error heteroscedasticity of a linear regression model that does not impose large restrictions on the structure of heteroscedasticity. The null hypothesis assumes that the errors of the model are homoscedastic, under which the Gauss-Markov conditions are satisfied. The overall significance of the auxiliary equation is checked using the x2 test. If nR2 > x2^, where y — is the significance level; k — degree of freedom, then the homoscedasticity hypothesis is rejected. The number of degrees of freedom k is equal to the number of explanatory variables of the auxiliary equation.
The results of the White test are shown in Table 7, where prob. F(14,6) = 0.4384 > 0.05. At n = 21 Obs*R2 — coefficient of determination is equal to 15.45691 and it is less than the value X034(14) = 17.12. The required condition for H0 is satisfied. The corresponding p-value is greater than the significance level of 0.05 (0.34 > 0.05), i.e. the null hypothesis that the random term is homoscedastic may not be rejected. This means that the hypothesis of heteroscedasticity is rejected, and according to the White test, we conclude that there is no heteroscedasticity in the residuals.
Autocorrelations of residuals is the relationship between them, as a result of which their values are either overestimated or underestimated, which negatively affects the quality of the model. The Breusch-Godfrey serial correlation LM-test is used to test serial correlation in random errors of linear models and is
based on the LM-statistic, which is equal to nR2. Here n is the volume of observations, R2 is the coefficient of determination of the model. If the value of the LM statistics exceeds the critical value of the distribution X2rK, then the autocorrelation is considered significant and the null hypothesis is rejected. If the opposite condition is met, then the autocorrelation is considered insignificant.
The results of the Breusch-Godfrey LM test for autocorrelation are shown in Table 8. At n = 21, the nR2 -determination coefficient is 0.005004 and it is less than the critical value Xo99(2) = 0.02. p-value exceeds the significance level of 0.05 (0.9975 > 0.05), i.e. the hypothesis of the significance of autocorrelation is rejected. The serial correlation for the residuals is not significant.
As a result of the Engle Granger test and the Johansen test, it was determined that the variables are cointegrated and that there are 1 cointegrating equations at the level of 0.05, for all types of trends. Thus, it is possible to present the relations under study in the form of VECM (vector error correction model), which expresses a long-term equilibrium relationship between variables
[30]. At this stage of the study, in order to avoid the formation of a singular data matrix with a zero determinant, the MRESID variable was removed from the independent variables. Error correction equations for second-order differences for the series GDP, Azeri_light, Brent, West based on quarterly initial data were compiled to enable the implementation of the VEC Estimates test.
The results of the Engle Granger and Johansen test for the cointegration of time series with a lag interval from 1 to 3 showed that the best values according to the Akaike and Schwartz information criteria were -9.451096* and -9.56012*. Trace and Maximum Eigenvalue tests were carried out with the first differences of the time series variables, where the null and alternative hypotheses were tested (see Table 9). For both tests, when testing hypotheses, in cases where the calculated values of the statistics exceeded the critical values, alternative hypotheses were accepted about the presence of one cointegration equation at a significance level of 0.05. So, one cointegration relation with a 95% probability has been obtained. The results obtained indicate a long-term relationship and the
Table 8 (Таблица 8)
Results of the Broesch-Godfrey LM test Результаты LM-теста Бройша-Годфри
F-statistic 0.001668 Prob. F(2,14) 0.9983
Obs*R-squared 0.005004 Prob. Chi-Square(2) 0.9975
Table 9 (Таблица 9)
Trace and Maximum Eigenvalue test results for linear deterministic trend Результаты теста трассировки и максимального собственного значения для линейного детерминированного тренда
Hypothesis Alternative hypothesis Trace Statistic Critical Value 5% Probability
Н0 : r = 0* HA : r > 0 567.1163 3.841466 0.0000
Hypothesis Alternative hypothesis Max-Eigen Statistic Critical Value 5% Probability
Н0 : r = 0* HA : r > 0 567.1163 3.841466 0.0000
* means rejection of the hypothesis at the 0.05 level.
* означает отклонение гипотезы на уровне 0,05.
authenticity of the correlation between the time series of variables.
When conducting the Granger test of causation, the results showed that there are both direct and inverse relationships between variables. This makes it possible to construct error correction models both for the dependent variable and for all other variables [19].
a(aGDP)=0.026(aGDP(-1) -30279.16aAzeri_light(-1) +33113.55aBrent(-1)-277.54aWest(-1)+30603.56)-
0.605a(aGDP(-1))-0.299375a(aGDP(2))+368.32a (aAzeri_light(-1))+22.8 a (aAzeri_light(-2))-350.48a(a(Brent(-1)) +33.07a(aBrent(-2)) +56.18a(aWest(-1))-33.17a (aWest(-2)+267.83 (5)
a(aAzeri_ light) = 0.00018(aGDP(-1) -30279.16aAzeri_light(-1) +33113.55aBrent(-1)-2771.54aWest(-1)+30603.56)-0.00102a(aGDP(-1))-0.00068a(aGDP(2))+3.26a
(aAzeri_light(-1))-3.3622a( aAzeri_light(-2)) -3.3483a(aBrent(-1)) +3.3211 a(aBrent(-2))+ 0.034a(aWest(-1))-0.147913a(aWest (-2))+0.77 (6)
a(aBrent)=0.00017(aGDP(-1)
-30279.16aAzeri_light(-1) +33113.55aBrent(-1)-2771.54 aWest(-1)+30603.56)-0.001019a(aGDP(-1)) -0.00072a(aGDP(-2)) +3.55a(aAzeri_light(-1)) -3.25a(aAzeri_light(-2))-
3.37a(aBrent(-1)) +3.24a(aBrent(-2))+0.054a(aWest(-1))+ 0.76a(aWest(-2))+0.76 (7)
a(aWest)=0.00022(aGDP(-1) -30279.16aAzeri_ light(-1)+33113.55 aBrent(-1)-2771.54 aWest(-1)+30603.56)-0.0014a(aGDP(-1))-0.00083a(aGDP(-2)) +3.9a(aAzeri_light(-1)) -2.75a(aAzeri_light(-2)) -3.8a(aBrent(-1)) +2.78a(aBrent(-2)) +0.15a(aWest(-1))-0.23 a(aWest(-2))+0.8
(8)
The presented vector model of error correction makes it possible to analyze and predict
the dynamics of the Azerbaijani economy within the framework of world oil prices.
VAR Residual Normality Tests (test about the normal distribution of residuals) checks whether the distribution is normal. The null hypothesis for the test indicates a normal distribution of the residuals. The test results are presented in Table 10.
From the results in Table 10 it can be seen that in the distribution of residuals, the asymmetry for all components is close to zero, which means that the observed asymmetry of the residuals is insignificant, minimal. The kurtosis slightly exceeds the value of 3, that is, the peaked distribution is also insignificant. For both characteristics, the distribution can be considered normal. According to the Jarque-Bera test, the distribution is also normal. JB=36.09779, with prob.= 0.5327>0.05, which indicates the normal distribution of the residuals. The hypothesis of a normal distribution of model residuals was accepted.
The impulse response functions characterize the time of return of the endogenous variable to the equilibrium trajectory under a single shock of the
Table 10 (Таблица 10) Table 10. Results of the test about the normal distribution of residuals Таблица 10. Результаты теста на нормальное распределение остатков
Component Skewness Chi-sq degree of freedom probability
1 0.006312 0.000571 1 0.9809
2 -0.131035 0.246105 1 0.6198
3 0.102521 0.150651 1 0.6979
4 -0.607311 5.286520 1 0.0815
Joint 5.683846 4 0.2240
Component Kurtosis Chi-sq degree of freedom probability
1 3.898909 2.895466 1 0.0888
2 5.405499 20.73470 1 0.0855
3 3.671168 1.614169 1 0.2039
4 4.201117 5.169611 1 0.0730
Joint 30.41394 4 0.3401
Component Jarque-Bera degree of freedom probability
1 2.896037 2 0.2350
2 20.98080 2 0.3355
3 1.764821 2 0.4138
4 10.45613 2 0.0547
Joint 36.09779 8 0.5327
exogenous variable. The response responses of the impulse function characterize the median estimate with a 90% confidence interval of the endogenous variable to the standard deviation of the exogenous variable. As a result of the evaluation of the VECM model, we obtained the functions of impulse responses to structural shocks. So, the graphs of the responses of the considered series built on EViews 10 for a 10-year time period are shown in Figure 11. As can be seen from the graphs of the response of impulse functions of variables to structural shocks, they cover the first 3 years of a 10-year period, with a further gradual transition to a stable period. Also, Figure 12 shows graphs for the reactions of variables to innovations, and Figure 13 shows the reactions of impulse response functions of variables individually. These charts show similar responses of impulse functions except for the responses of Brent impulse functions to shocks from GDP, Azeri_light, West, which cover a longer period of 4-5 years in a 10-year period. An analysis of the tabulated values of the response of impulse functions of variables to structural shocks presented in Table 11 confirms the above conclusions.
To determine the influence of exogenous variables on the endogenous variable, the econometric method of decomposition of forecast error variances was also applied. This method determines the contribution of the change in the considered variable to its variance of forecast errors and the variance of other variables. The test was carried out for the next 10 years. The results of the verification of the relevant tests are shown in Table 12.
The results in Table 12 show that in the annual GDP forecast, the largest errors are in the GDP, Azeri_light, Brent and West shocks, respectively, at 86% in the second year, 20.3% in the tenth year, 9.8% in the ninth
20,000 T 16.00012,000-8.0D0 -4,000-
-4,000-8,000 -I-,-,-,-,-,-,-
1 2 3 4 5 6 7
Отклик GDP
Отклик Brent
year and 11.08% for the tenth year; for Azeri_light these values are in the respective order 22.3% for the first year, 79.9% for the second year, 15.13% for the ninth year, 8.99% for the tenth year; for Brent, respectively, 22.1% for the first year, 79.7% for the second year, 15.4% for the ninth year and 8.86% for the tenth year; for West, respectively, 25.7% for the first year, 74.6% for the second year, 19.27% for the eighth year and 7.15% for the first year. The results of the analysis show that the greatest uncertainty in the forecast for GDP, Azeri_light, Brent and West is given by their
Отклик Azeri light
Отклик West Texas Intermediate
AZERI_LIGHT WEST
AZERILIGHT WEST
own changes during the first trimester of the period under review.
Conclusions
According to the results of the study devoted to the construction of a vector model for error correction, the following conclusions can be drawn:
- The constructed model is quite adequate, demonstrates stationarity for time series for both endogenous and exogenous variables, and can be used to determine forecast values of GDP both in the short term and in the long term;
Fig. 11. Reactions of impulse response functions Рис. 11. Реакции функций импульсного отклика
Fig. 12. Responses of variables to innovation Рису. 12. Реакция переменных на инновации
Response of GDP to GDP
Response of GDP to AZERMJGHT
Response of GDP to BRENT
Response of GDP to WEST
-1,000-
-1.000-
-1,000.
-1,000-
-1-1-1-1-1-1——I 1 —
123456789 10
Response of AZERI_LIGHT to GDP
Response of AZERMJGHT to AZERMJGHT
Response of AZERI_LIGHT to BRENT
Response of AZERMJGHT to WEST
Response of BRENT to GDP
Response of BRENT to AZERMJGHT
Response of BRENT to BRENT
Response of BRENT to WEST
l l l l i i г I I
123456789 10
Response of WEST to GDP
Response of WEST to AZERI LIGHT
Response of WEST to BRENT
Response of WEST to WEST
Figure 13. Responses of impulse response functions of variables individually Рисунок 13. Реакции функций импульсного отклика переменных по отдельности
Table 11 (Таблица 11)
Response values of impulse response functions of variables in individual order. Response of GDP Значения реакций функций импульсного отклика переменных в индивидуальном порядке. Реакция ВВП
Period GDP Azeri_light Brent West
1 1601.757 0.000000 0.000000 0.000000
2 1082.972 748.7850 215.8003 21.14351
3 1245.389 663.5198 374.7529 -263.0360
4 1135.223 751.0387 562.5039 -384.7947
5 1086.088 704.9781 585.3035 -477.8916
6 992.4868 682.4451 562.1951 -540.7227
7 919.0981 643.0173 506.0328 -583.8947
8 849.9804 612.4495 447.2353 -603.4631
9 793.6230 584.0202 393.2147 -605.5368
10 745.6509 560.4645 350.0791 -594.6483
Response of Azeri_light
Period GDP Azeri_light Brent West
1 4.688542 8.759332 0.000000 0.000000
2 4.555509 10.23990 1.141442 -1.261373
3 5.118996 9.282723 3.813678 -2.540903
4 4.852163 8.041928 5.179456 -2.830709
5 4.278502 6.636689 5.188674 -2.994585
6 3.599932 5.399687 4.560590 -3.142687
7 3.007089 4.367038 3.694193 -3.199349
8 2.530941 3.565660 2.838273 -3.130662
9 2.182655 2.962164 2.114631 -2.959465
10 1.940680 2.519814 1.568056 -2.723135
Response of Brent
Period GDP Azeri_light Brent West
1 4.692027 8.797974 0.507269 0.000000
2 4.508444 10.14590 1.409810 -1.157245
3 4.982358 9.165276 3.913333 -2.461722
4 4.701179 7.899264 5.174092 -2.782250
5 4.120872 6.497934 5.127036 -2.948699
6 3.450418 5.268465 4.470623 -3.089352
7 2.868926 4.248602 3.598068 -3.135857
8 2.406218 3.459594 2.748051 -3.058609
9 2.070230 2.867423 2.035928 -2.881784
10 1.838811 2.434322 1.501853 -2.643104
Response of West
Period GDP Azeri_light Brent West
1 4.861297 7.856381 0.257976 2.565969
2 4.162328 9.441776 1.590181 1.155655
3 4.661874 8.328819 4.240741 -0.715871
4 4.221017 7.100060 5.466879 -1.424341
5 3.558137 5.678466 5.244684 -1.896281
6 2.816507 4.471999 4.419610 -2.251627
7 2.209924 3.483271 3.408855 -2.441646
8 1.746843 2.742530 2.469097 -2.453650
9 1.431444 2.204033 1.710193 -2.332216
10 1.231158 1.826606 1.163504 -2.129252
Table 12 (Таблица 12)
Values of decompositions of variables in individual order. Variance Decomposition of GDP Значения декомпозиции переменных в индивидуальном порядке. Дисперсионная декомпозиция ВВП
Period St.error GDP Azeri_light Brent West
1 1601.757 100.0000 0.000000 0.000000 0.000000
2 2084.742 86.01760 12.90059 1.071518 0.010286
3 2558.716 80.79156 15.28842 2.856402 1.063612
4 2977.297 74.20981 17.65506 5.679189 2.455942
5 3333.442 69.81532 18.55670 7.613505 4.014478
6 3629.193 66.37891 19.19151 8.822866 5.606719
7 3876.372 63.80521 19.57369 9.437697 7.183401
8 4085.096 61.78091 19.87228 9.696498 8.650308
9 4263.827 60.17442 20.11729 9.751095 9.957191
10 4418.879 58.87301 20.33897 9.706430 11.08159
Variance Decomposition of Azeri_light
Period St.error GDP Azeri_light Brent West
1 9.935206 22.27009 77.72991 0.000000 0.000000
2 15.07350 18.80858 79.91773 0.573428 0.700259
3 18.98905 19.11877 74.25468 4.394823 2.231727
4 21.99181 19.12223 68.73362 8.823467 3.320687
5 24.12221 19.03969 64.69859 11.96055 4.301173
6 25.58657 18.90225 61.95852 13.80769 5.331549
7 26.58324 18.79103 60.09835 14.72290 6.387718
8 27.26986 18.71807 58.81974 15.07412 7.388073
9 27.75633 18.68606 57.91494 15.13078 8.268218
10 28.11412 18.68997 57.25354 15.05919 8.997294
Variance Decomposition of Brent
Period St.error GDP Azeri_light Brent West
1 9.983826 22.08650 77.65534 0.258157 0.000000
2 15.04224 18.71278 79.70322 0.992132 0.591870
3 18.88039 18.84176 74.15670 4.925827 2.075717
4 21.80552 18.77387 68.71869 9.323254 3.184188
5 23.86770 18.65085 64.76897 12.39615 4.184029
6 25.27567 18.49438 62.09879 14.18203 5.224799
7 26.22824 18.37187 60.29398 15.05251 6.281644
8 26.88096 18.29176 59.05780 15.37548 7.274954
9 27.34125 18.25439 58.18597 15.41664 8.143000
10 27.67838 18.25378 57.55069 15.33779 8.857741
Variance Decomposition of West
Period St.error GDP Azeri_light Brent West
1 9.591959 25.68559 67.08578 0.072334 7.156295
2 14.22470 20.24156 74.56181 1.282594 3.914035
3 17.66184 20.09685 70.60288 6.597124 2.703145
4 20.29985 19.53661 65.67834 12.24650 2.538549
5 22.09280 19.08812 62.05694 15.97498 2.879957
6 23.25137 18.70059 59.72587 18.03567 3.537872
7 23.98385 18.42480 58.24275 18.97098 4.361475
8 24.45230 18.23596 57.29049 19.27068 5.202864
9 24.76258 18.11597 56.65595 19.26774 5.960337
10 24.97850 18.04708 56.21548 19.15306 6.584385
- The vector model of error corrections (5-8) developed during the study can be considered statistically significant. This justifies the positive results of a large number of hypotheses and graphical analysis tests;
- The constructed vector model of error correction makes it possible to quantify the characteristics of the studied indicators, the links between them in the short and long term, to evaluate the prospective dynamics of the indicators;
- The long-term equilibrium relationship between variables can be considered stable, since after a violation in short-term periods
from shock reactions, stability is restored. The constructed models make it possible to measure both deviations from the equilibrium state and the rate of equilibrium restoration. Analysis of graphs and tabular values showed that the reactions of impulse functions of variables to structural shocks cover the first 1-3 years of a 10-year period, with a further gradual transition to a stable period;
- The method of decomposition of forecast error variances was applied to determine the influence of exogenous variables on the endogenous variable. The analysis of the results showed that the greatest uncertainty
in the forecast for GDP, Azeri light, Brent and West is given by their own changes during the first trimester of the period under review;
- The results obtained can be useful for identifying real trends in Azerbaijan's GDP and determining its interdependencies with other macroeconomic variables, for determining its interdependen-cies with variations in energy prices based on an analysis of the dynamics of the indicators under consideration, for developing recommendations and forming directions for the long-term development of GDP.
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Литература
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Сведения об авторе
Айюбова Натаван Солтан
К.э.н, доцент Бакинский Государственный Университет, Факультет Математической Экономики, Баку, Азербайджан Эл. почта: nayyubova50@gmail.com
Information about the author
Ayyubova Natavan Soltan
Cand. Sci. (Economics), Associate Professor Baku State University, Department of Mathematical Economics, Baku, Azerbaijan E-mail: nayyubova50@gmail.com
