Energy intensity determinants based on structure-oriented cointegration by embedding a knowledge box in a time series model: evidence from Iran

Energy intensity reduction is an exigent issue for Iran, where energy consumption is so high. Therefore, finding effective policies to reduce energy intensity is essential. With this in mind, the impact of financial development, government investment, oil revenues, and trade openness on energy intensity is assessed in this study. We combined structural vector error correction model (SVECM) and directed acyclic graphs (DAG) technique to examine the relationships between study variables. The results of DAG prove that financial development, government investment, oil revenues, and trade openness influence the intensity of energy. Besides, the significant and long-run relationships among variables allowed us to apply SVECM. Impulse response functions and variance decomposition analysis indicate that government investment, oil revenues, and trade openness are negatively associated with the intensity of energy. Also, financial development positively influences energy intensity. Meanwhile, the impact of government investment is more significant than oil revenues, trade openness, and financial development impacts. So, government investment is the most effective policy regarding optimizing the consumption of energy and reducing energy intensity. We also advise policymakers to use oil revenues to increase government investment, enhance trade openness, and tax the private sector to improve the level of energy intensity.


Introduction
Energy plays an essential role in human societies' economic and social life and is one of the crucial indicators of development (Mirzaei and Bekri 2017). However, the dramatic and unprecedented increase in energy consumption since the Industrial Revolution has raised concerns for human beings. The depletion and scarcity of fossil energy resources as the world's most important source of energy and environmental degradation due to the rapid growth of fossil energy consumption are the root of these human concerns regarding energy (IEA 2020). The most commodious and effective solution to address these challenges is optimizing energy consumption and enhancing its efficiency (Pham et al. 2020;Zhu and Lin 2020). Energy intensity is the most practical and strategic indicator of the energy consumption situation that developed and developing countries are trying to reduce. Energy intensity shows how much energy is used to produce a certain amount of Gross Domestic Product (GDP); thus, countries are trying to reduce energy intensity to lower energy conversion costs per unit of GDP, and this is one of the tangible goals of sustainable development (Samargandi 2019;Zaidi et al. 2019).
The energy intensity level is affected by various variables and factors. Over the past years, the effects of free trade, financial development, and government investment on energy intensity have become prominent. Trade openness and eliminating trade barriers by creating global competition can encourage countries to raise the host country's innovations and propel energy intensity reduction Samargandi 2019). Furthermore, governments can achieve desirable results in reducing energy intensity by enhancing Responsible Editor: Roula Inglesi-Lotz construction investment and promoting low-carbon and low-consumption technologies (Aller et al. 2018;Fu et al. 2013;Yanli Wang et al. 2020). Finally, financial development from three main channels can affect energy consumption and intensity: Wealth effect, Business effect, and Direct effect. Financial development through direct effect can increase consumers' access to money and encourage them to buy energy-intensive goods. The business effect of financial development is to boost businesses, which in turn amplifies their energy demand. Through the wealth effect, financial development reduces investment uncertainties and boosts the stock market, leading to economic growth and increased energy consumption (Acheampong 2019;Chen et al. 2019;Pan et al. 2019a, b, c). Meanwhile, proponents of negative links between financial development and energy intensity argue that financial development encourages R&D investments and leads to service and goods innovations (Tamazian et al. 2009). Consequently, energy efficiency and renewable energy consumption are enhanced .
Iran is one of the developing and oil-exporting countries that have vast energy resources. Iran's energy consumption has been steadily rising over the past decades due to factors such as low energy prices and government subsidies (Hosseini Nasab et al. 2012). The residential, industrial, and transportation sectors are the primary consumers of energy in Iran, and the contribution of different energy-consuming sectors can be seen in Fig. 1. Figure 2 shows that Iran does not have a favorable situation about the consumption of energy for goods and services. Hence, it has an inefficient energy consumption pattern and is a country with very high energy intensity. According to Iran's energy Balance (2017), Iran's energy intensity is higher than in developing countries and the world. However, it is also even higher than in oil-rich countries such as Venezuela and Saudi Arabia. Thus, to reduce the intensity of energy, corrective policies should be adopted because, with this energy consumption trend, Iran may be forced to import energy in the future.
Due to the need to increase energy efficiency and its environmental consequences, extensive studies have been conducted in this regard. For this purpose, different approaches and methods of econometrics have been used. The method of S. Johansen and Juselius (1990) is one of the most powerful methods for examining long-run relationships between variables. After determining the existence of long-run relationships between variables, the Vector Error Correction Model (VECM) can be used. Economic considerations and theories are not considered in the VECM, but this problem can be solved using the structural VECM (SVECM). Therefore, it is an attractive and efficient model to study and analyze the factors affecting energy intensity. Furthermore, we focused on Iran in this study, which has a high energy waste, and it is critical to improving its energy intensity. Meanwhile, the effect of variables of financial development, trade openness, government investment, and oil revenues, which are very vital in the Iranian economy, on energy intensity has been examined.
This study has been compiled in the following sections. After the introduction, the relevant literature on energy intensity debate in Sect. 2; Sect. 3 explicates the Methodology and Data; Sect. 4 states the empirical results and discussions. The conclusions and policy implementation are interpreted in Sect. 5.

Literature review
Various international organizations, such as the International Energy Agency and Economic and Social Council of the United Nations, have identified energy intensity as one of the indicators of energy for sustainable development. Today, reducing the intensity of energy has become a vital issue for all countries in the world because energy wastage and inefficiency not only have consequences for environmental degradation but also are an obstacle to sustainable development (Abban and Hongxing 2021;Abban et al. 2020;Neagu and Teodoru 2019). Therefore, many researchers have studied the factors that affect energy intensity. In these studies, different variables are used, such as trade openness, energy prices, foreign direct investment, technological innovations. Karanfil (2009) stated that financial variables could be added to the energy consumption models to augment them. We will now examine the results of some studies in this regard. Adom (2015) found that energy prices and foreign direct investment affected energy intensity significantly and negatively, and also, rising energy prices reduced the intensity of energy. Besides, structural changes increase energy intensity. Du and Lei (2017) proved that technological progress, energy prices, the mix of energy, the structure of the economy, and the intensity of energy have a relationship in the long run. Technological progress is the most critical factor in Fig. 1 Contribution of different energy-consuming sectors in Iran. Source: Iran's energy balance (2017) reducing the intensity of energy. Conversely, the prices of energy, energy mix, and technological progress do not significantly reduce the intensity of energy in the short run. Aboagye (2017) concluded the existence of a long-run relationship between the growth of the economy and the intensity of energy. In the short run, trade openness reduces the intensity of energy. Besides, both urbanization and the intensity of energy affect each other. Nevertheless, the relationship between industrialization and the intensity of energy is one way. Finally, the absence of a relationship between the intensity of energy and foreign direct investment is proved. Barkhordari and Fattahi (2017) found that energy prices, in the long run, affect the intensity of energy, and technological changes have a beneficial effect on the intensity of energy. Adom (2018) concluded that trade openness leads to a decrease in the intensity of energy, while democracy leads to an increase in the intensity of energy. Bi et al. (2019) realized that the impact of transportation infrastructure on the intensity of energy is significant and negative, and this effect gradually becomes more robust. Deichmann et al. (2019) concluded a negative correlation between economic growth and energy intensity. Pan, Uddin, Han, et al. (2019) realized that the impact of economic growth is more substantial on the intensity of energy in the short run. The impact of trade openness is growing over time. Technological innovations also improve the intensity of energy. On the contrary, Samargandi (2019) concluded that technological innovation does not significantly affect the intensity of energy. Besides, trade openness and energy price reduce and increase the intensity of energy, respectively.
Rising energy prices, such as crude oil, will increase OPEC oil rents and increase their energy consumption. Therefore, it leads to an increase in energy intensity. Chen et al. (2019) found that financial development in non-OECD countries reduced energy intensity, while in OECD countries, it was statistically insignificant. Financial development in non-OECD countries first reduces the intensity of energy and then increases it. Thus, the relationship between them is U-shaped. He and Huang (2020) concluded that investment, population, enterprise size, and urbanization decrease the intensity of energy, while policy instruments and industrial structure increase it. Cao et al. (2020) found that foreign direct investment has an insignificant effect on the intensity of energy. Table 1 describes the details of these studies.
Many studies have been conducted on Iran's energy intensity, and many of these studies have examined the factors that reduce the energy intensity of Iran. In some of these studies, trade openness and financial development variables have been identified as influential variables in reducing energy intensity. Because Iran is an oil exporter country and oil revenues significantly impact Iran's economy, it has consistently been recognized as a vital variable in the Iranian economy. The government sector in Iran's economy is vast, so government investment plays a significant role in various sectors of Iran. Therefore, in this study, we intend to examine the impact of financial development, government investment, oil revenues, and trade openness on Iran's energy intensity in a multivariate framework. Besides, many studies have used methods such as Granger causality to understand the causal flow between variables. However, the DAG technique is a more accurate and   Adom (2015) 1971-2011 Nigeria FMOLS Energy price, foreign direct, industry structure The effect of energy price on energy intensity is negative and significant. The effect of foreign direct inflows on energy intensity is negative and significant. The relationship between industry structure and energy intensity is significantly positive. Du and Lei (2017) 1985-2014 China ARDL bounds approach, VECM Energy price, technological progress, economic structure, energy mix The long-run relationship between energy price, technological progress, economic structure, energy mix, and energy intensity.
Aboagye (2017) 1981-2014 Ghana ARDL Economic growth, trade openness There is a long-run relationship between economic growth and energy intensity. Trade openness reduces energy intensity. Barkhordari and Fattahi (2017) 1986-2015 Iran ARDL Energy prices, technological improvement There is a long-run relationship between energy prices and energy intensity. Technology changes have a constructive impact on energy intensity in Iran's industry.

2006-2015 China
Dynamic optimal theoretical framework Population, investment, urbanization, industrial structure, policy instrument, enterprise size Population, investment, urbanization, and enterprise size decrease the energy intensity.
Nevertheless, industrial structure and policy instruments drive it up.
Source: Current Research efficient method that uses data, the results of previous studies, and economic theories to identify the simultaneous causal flow among variables, which has been considered in few studies.

Model specification
Vector autoregressive (VAR) models are widely used after Sims (1980) critique of simultaneous equations. These models have become valuable tools in macroeconomic studies and have been widely used to investigate the relationship between variable innovations. SVECM can be used when the data is not stationary at the level, and the cointegration test indicates the presence of a cointegration vector. The SVECM identifies structural shocks based on economic theory (Nizamani et al. 2017). The SVECM has been developed by King et al. (1987), which considered only long-run restrictions beyond its model. In contrast, Breitung et al. (2004) expanded the SVECM to include long-run and short-run restrictions (Ivrendi and Guloglu 2010).
The ρ order of SVECM is as follows: where A is a (K × K) matrix and represents the simultaneous relationships between y t variables, (K × 1) vector of y t = (y 1t , …, y Kt ) ' shows endogenous variables, Π * is the coefficient matrix, Γ * i j ¼ 1; …; ρ−1 ð Þdisplays the parameters of structural form, and is a (K × K) matrix. ε t is a (K × 1) white noise error terms of structural form vector with zero mean, and they are not correlated serially, and matrix of variance-covariance is Ω (Nizamani et al. 2017).
Multiplying Eq. (1) by A −1 , the reduced form can be obtained.
Assuming all variables are stationary at the first difference, the reduced form of VECM in Eq. (2) can be rewritten as follows: where y t is observable variables' vector, α represents the (K × r) loading coefficients matrix, and β is the (K × r) matrix of cointegration. Here, r is the number of cointegration relationships between the variables. The αβ ' y t − 1 is related to the error correction term. The u t is a white noise error with zero mean and the matrix of variance-covariance ∑ u A −1 Ω(A −1 ).
As Johansen (1995) stated, by using the Granger representation theorem (GRT), the structural model can be written as the moving average (MA) representation of Beveridge-Nelson decomposition of y t as follows: It decomposes y t into two parts I(0) and I(1). Matrix Ξ represents the effects of shocks in the long run and includes the K = n − r components of I(1) in y t (Boufateh et al. 2013). Matrix Ξ is shown as follows: Ξ * (L)u t is the matrix of transitory effects and includes r components of I(0) in y t and is polynomial of infinite order in the lag operator with Ξ * j the matrix that lim Matrix Ξ * (L) is shown as follows: It is worth noting that if the system's cointegrating rank is r, the Ξ has to rankK − r. Whereas Ξ * j 's has transitory effects, it shows forecast error impulse response long-run effects. y * 0 includes all initial values.
The restriction must impose on matrices A and B to identify the structural form from the reduced form. Since the main focus of this research is on residuals, B-model is commonly used to identify structural innovations. So, matrix A is considered as an identity matrix, and the restrictions will be imposed on matrix B.
By placing Eq. (7) in Eq. (4), the following equation will be obtained: B and ΞB represent the short-run and long-run effects of structural innovations, respectively. At most, r columns of the matrix ΞB must be zero. In other words, structural innovations can have r and K − r transitory and permanent effects, respectively. The ΞB matrix's rank is K − r, and every zero column is only K − r independent restrictions. Therefore, the r zero columns demonstrate only r(K − r) independent restrictions.
In model B, K K−1 ð Þ 2 restrictions are required for local just-identify structural innovations. Based on the structure of the model cointegration, there are r (Kr) independent restrictions. Therefore, to accurately just-identify structural Þ additional restrictions are required, which must be imposed on B and ΞB matrices based on the structure of economics and theory. r r−1 ð Þ 2 are for transitory effects and must be imposed on matrix B, and K−r ð Þ 2 are for permanent effects and must be imposed on the matrix ΞB (Lütkepohl 2005).
To determine these zero restrictions, we intend to use the causal relationship between variables and economic theories. In most previous studies, the Granger (1969) causality method has been used to discover the causal relationship among variables, which does not show the real causal relationship (Bessler and Yang 2003). Pearl (2000), Spirtes et al. (2000), and Demiralp and Hoover (2003) introduced the DAG technique in their studies to identify the causal relationship among economic variables contemporaneously.
In this paper, the DAG technique is chosen to explore the simultaneous causal relationship between the study variables. In DAG, arrows indicate the causal relationship between two variables. Thus, the absence of an edge between X and Y (X Y) exhibits the lack of a causal relationship between them. If there is a covariance between the two variables, but there is no causal relationship between them, it is displayed with an edge without direction (Y − X). Also, the one-sided edge (X → Y) demonstrates that the causal relationship is from Y to X, and Y causes X. Finally, the two-sided edge (Y ↔ X) indicates the simultaneous effect of X and Y on each other (Pan, Ai, et al., 2019).
In the Tetrad program, the PC algorithm introduced by Peter and Clark can be used to directed graphs (Spirtes et al. 2000). This algorithm seeks to eliminate edges and apply causal flows between variables. Therefore, this algorithm initially only connects variables with a line called edges that are directionless (Miljkovic et al. 2016). Then, by implementing the correlation test, it removes the edges between the two variables in the absence of correlation base on vanishing a correlation of zero-order or partial correlation of high order (Yang and Bessler 2008). Subsequently, between a pair of variables' correlation conditional on the third variable for the remaining edges is checked. Based on the PC algorithm, the edges between variables with a conditional correlation of zero from the first order are removed. If N variables exist, the PC algorithm examines the conditional correlation up to N-2 order between the variables (Pan, Uddin, Han, et al., 2019).
Conditional variables on the edges eliminated between every two variables are called separate sets whose edges have been eliminated. If an edge is removed by considering the unconditional correlation, it will have a separate empty set. Finally, the edges that remain can be oriented according to the steps of the PC algorithm by using a separate set. Videlicet, suppose X − Y − Z pattern, X and Y are next together and like Z and Y. They are called adjacent, but the variables of Z and X do not consider as adjacent. Thus, if Y is not in the X and Z separate set, the mentioned pattern can show as X → Y ← Z (Ji et al. 2018).
The statistic of Fisher's z in the PC algorithm is for testing the correlations and conditional correlation of the estimated sample against zero (Z. Wang et al. 2007). The mentioned test statistic is displayed as follows: where n shows the observation's number in the correlation estimation, ρ(i, j|k) represents the i and j correlation of population conditional on k, |k| declares variable number in k. z[ρ(i, j|k)n] − z[r(i, j|k)n] is distributed normally if the distribution of i, j, and k is normal, and r(i, j|k) represents the i and j sample correlation conditional on k (Pan, Uddin, Han, et al., 2019). The test of likelihood ratio introduced by Sims (1980) is for testing the DAG identifying restrictions for over-identification. The T[log(det(Ω)) − log(det(∑))] test statistic is obtained from the equation Aet = νt, and its purpose is to investigate the relationship between the restrictions of the observed shocks (et) parameter and orthogonal shocks (νt).
The distribution of this statistic is chi-squared, and T represents the observations' number. log declares transformation in logarithmic, det represents the determinant operator, Ω is the matrix of variance-covariance obtained from the A-matrix restrictions. Finally, ∑ is the matrix of variance-covariance obtained from the observed non-orthogonal shocks (Pan, Uddin, Han, et al., 2019;Yang et al. 2006).

Data
This study examines the impact of four economic variables, including financial development, trade openness, government investment, and oil revenues, on energy intensity during the years 1967 to 2017. Various proxies for financial development have been used in studies such as domestic credit to the private sector to GDP ratio, stock market capitalization to GDP ratio, and so on (Pan et al. 2019a, b, c). Here, following Kahouli (2017), Pan, Ai, et al. (2019), and Gómez and Rodríguez (2019), we used the domestic credit to the private sector to GDP ratio as a proxy for the financial development. We extracted this data from GFDD (2020). Following You Wang and Gong (2020), the sum of exports and imports to GDP is used to calculate the trade openness and the data received from WDI (2020). Besides, the government investment and oil revenues data are attained from WDI (2020) and OPEC (2020), respectively. The ratio of energy consumption to GDP is obtained to calculate the energy intensity and energy consumption, and GDP data are collected from Iran's Energy Balance (2017) and WDI (2020), respectively.
We got the idea to select these variables from Pan, Ai, et al. (2019) study, which dealt with the relationship between trade openness and financial development with energy intensity. The oil revenues are chosen because the results of the Yıldırım et al. (2020) study showed that oil revenues have a significant impact on financial development; it also plays a crucial role in the economies of OPEC member countries. Finally, the relationship between oil revenues and government investment became apparent in Rodríguez (2020) study. So, the government investment is elected, and the present study wants to examine whether these variables can affect the energy intensity or not. Hence, by carefully reviewing previous studies and the importance of these variables in the Iranian economy, we selected our variables to propose effective policies to improve Iran's economic and environmental situation. All variables are converted to natural logarithms. Our data vector y t = (LnFD, LnEI, LnIG, LnOR, LnTO)' includes the variables of financial development (LnFD), energy intensity (LnEI), government investment (LnIG), oil revenues (LnOR), and trade openness (LnTO).

Empirical results
In the first step, we examined the descriptive statistics of the data, the result of which are shown in Table 2. The results show that energy intensity in 1972 and 2013 had its lowest and highest values, respectively. Table 3 shows the strength of the correlation between variables. The results show that the correlation between energy intensity and other variables is high. Also, it has a positive correlation with financial development and a negative correlation with trade openness, government investment, and oil revenues.
The empirical study applied the variance inflation factor (VIF) test to detect potential multicollinearity between independent variables. Table 4 demonstrates that all VIF values are less than ten; it implies that selecting variables is accurate and appropriate (Belsley et al. 2005;Tsioumas et al. 2021). Therefore, the model satisfies the absence of multicollinearity condition.
Stationary has particular importance in studying time-series data, as non-stationary behaviors such as random walk, trend, or cycles cause unusual regressions (Benjamin and Lin 2020; Pan et al. 2019a, b, c). Therefore, we used two unit root tests of Augmented Dickey and Fuller (1979) and Phillips and Perron (1988) to check the stationary of the data. MacKinnon (1996) p values of one-sided are used in the test of Augmented Dickey-Fuller for critical values. Newey-West using Barlett kernel specifies the Phillips-Perron test bandwidth (Pan et al. 2019a, b, c). Table 5 demonstrates the results of the Augmented Dickey-Fuller and Phillips-Perron tests. In these two tests, the existence of a unit root is its null hypothesis. According to Augmented Dickey-Fuller and Phillips-Perron tests, the variables of financial development, government investment, oil revenues, trade openness, and energy intensity are I(1).
Since all variables at the first difference are stationary and integrated of order one, we can use the cointegration test. The cointegration test shows the presence of a long-run relationship between variables, for which we must first determine the optimal lag. The optimal lag selected by the Schwarz  Information Criterion (SIC) and Akaike Information Criterion (AIC) is lag one. So, the VAR model of order one is estimated. Then, the S. Johansen and Juselius (1990) cointegration test is applied to check the existence and order of cointegration. Trace and maximum eigenvalue statistics are used to examine this test, the results of which are represented in Table 6. The null hypothesis of the zero cointegration equation is rejected at 5%. Therefore, the results recommend the existence of one cointegration equilibrium relationship between financial development, trade openness, government investment, oil revenues, and energy intensity. Consequently, VECM is the appropriate method for this study (Hasanov 2020).
Since VECM cannot consider the structures of the economy, we intend to use the SVECM (the results of the VECM estimation can be seen in Appendix A). As discussed in the methodology, we have to impose restrictions on matrices A, B, and ΞB. In the B-model, we consider A as I 5 and impose restrictions on matrix B and ΞB to identify the structural innovations. Given that K = 5, we need ten independent restrictions for local just-identify structural innovations. Since the results show that r = 1, we must set a matrix column ΞB to zero and consider this column as four independent restrictions; six remaining restrictions must be imposed on matrices B and ΞB. Since the identification of transitory shocks requires zero restrictions, matrix B is already identified in this model, and no restrictions are imposed on matrix B. Therefore, all of these 6 zero restrictions must be imposed on the matrix ΞB.
It is common for researchers to turn to economic theories and previous studies to determine which elements of these matrices should be imposed. It is noteworthy that previous studies have different results depending on the period and countries that were selected. Nevertheless, we are looking for a gateway to apply relevant data in addition to previous studies and economic theories. Therefore, we intend to use the DAG technique, in which, in addition to data of studies, the results of previous studies can be added to the knowledge box, and more accurate results can be achieved.
As mentioned, DAG analysis is an effective way to find simultaneous causal flows between variables. Hence, we used this method to explore the contemporaneous causal relationship between the variables of financial development, trade openness, government investment, oil revenues, and energy intensity. To obtain the DAG graph, we loaded the data into the Tetrad program and applied the PC algorithm to it. The PC algorithm first binds all the variables together and then removes edges according to the correlation or partial correlation at the predefined significance level. Spirtes et al. (2000) stated that this significance level should be determined based on the number of observations. Thus, for samples with less than 100 observations, a significance level of 20% was suggested. For samples with 100 to 300 observations, a 10% significance level was suggested, and for extensive samples with more observations, a significance level of 5% or 1% was recommended.
We also defined a knowledge box in which we used the results of studies dealing with the relationship between the  Notes: *, **, *** denote statistically significant at the 10%, 5%, and 1% levels, respectively ). Then, we used the likelihood ratio test to identify the over-identification of the restrictions; the p value of 29% showed that the restrictions were applied correctly and matched the data. The result of the DAG graphic pattern is shown in Fig. 3. Then, according to the DAG results, we applied the zero restrictions to matrices B and ΞB. As discussed above, these restrictions are very robust and reliable and are as follows: In matrices, B and ΞB, the columns represent the variables of oil revenues, financial development, energy intensity, government investment, and trade openness, respectively. After applying these zero restrictions, the following estimate was obtained by the maximum likelihood ratio method that the value in parentheses represents the t-statistic: The estimation results show that the t-statistic of some matrix elements is small, which may tempt us to identify more permanent and transitory effects. According to the unit root and cointegration test results, we were not allowed to impose further restrictions on the B and ΞB matrices. So, we conducted our analyses based on the just-identify model. Now, according to structural innovation, we can analyze impulse response functions (IRF). Fig. 4 illustrates IRF for ten periods using the Cholesky Degree of Freedom. Due to the main focus of this study on energy intensity, here we interpret the response of energy intensity to innovations of other variables in the confidence intervals of 90% and 95% determined by the Hall percentile method (see Appendix B). The results show that energy intensity responds positively and insignificantly to financial development innovations during the ten periods, which is more intense in the initial periods and gradually decreases. Financial development in Iran has affected the growth of energy intensity by facilitating capital for enterprises to increase investment and production and the necessary funds to purchase machinery and replace labor. Furthermore, financial development enhances the consumption of goods and services by reducing household budget constraints and providing financial resources at low cost and risk. Hence, consumers encourage to buy energy-intensive goods and directly affect the level of energy consumption and its intensity.
Besides, energy intensity responds negatively to one standard deviation shock of government investment, oil revenues, and trade openness. It worth mentioning that the effect of these variables is significant only in the early periods. Expanding global trade leads to economic growth and production enhancement. Nevertheless, the critical point is that global trade requires countries to comply with environmental standards. Therefore, trade liberalization improves technology and energy consumption by facilitating low-carbon and low-consumption equipment and machinery. Furthermore, oil revenues and government investments can improve Iran's technologies by improving and strengthening the infrastructure. Therefore, government investment and oil revenues, which provide the bulk of the government budget, are critical to financing infrastructure and construction projects.
We analyze the variance decomposition as the last step of the empirical analysis. Variance decomposition in the context of VEC and VAR models is interpreted as a part of the total variance of the variables derived from structural innovations (Taghizadeh-Hesary et al. 2020). Variance decomposition shows the explanatory power of variables for energy intensity variations (see Appendix C). Fig 5 shows the variance decomposition results, restricted to ten periods. The results show that the most robust variation in energy intensity is explained by its innovations and increases in the long run. Also, government investment, oil revenues, and trade openness in the early periods significantly impact energy intensity variations, and their effects are gradually diminishing. It is worth noting that the impact of government investment on energy intensity variations is stronger than the impact of oil revenues and trade openness, and financial development has no explanatory power on energy intensity variations neither in the short run nor in the long-run.
Overall, the government sector in Iran is vast. The results clearly show the reality that the government sector is the main nut of Iran's economy. Since the 1970s, with oil shocks and On the other hand, government investments are financed through oil revenues and borrowing from the central bank. Therefore, the implementation of construction projects and energy optimization goals is achieved through government investments and oil revenues. The Iranian government, especially since the 2000s, has developed practical and targeted programs to amplify government investment and improve energy consumption patterns. Nevertheless, since the Iranian economy has always been under widespread pressure and tensions, these plans have not been realized in the long run; it has not improved energy consumption patterns. The most important obstacles that have affected the implementation of construction projects and the improvement of Iran's infrastructure over the last decade are the financial crisis that occurred from 2007 to 2010 and the sanctions imposed on Iran from 2010. Iran was not directly affected by the global financial crisis due to its negligible role in global monetary and financial markets and its insignificant contribution to foreign direct investment. The crisis slowed economic growth in China, India, and other major world economies. Consequently, global oil demand declined rapidly and led to the world's oil price reduction. Also, the sanctions imposed on Iran since 2010 caused significant damage to the Iranian economy by limiting Iran's revenues through the sale of oil. Hence, if reforming the pattern of energy consumption and its optimization is still a fundamental and unresolved problem in Iran, it is due to the strong dependence of the government and its budget on oil revenues, the fluctuations of which directly affect Iran.

Conclusion and policy implications
One of the strategic policies pursued by most countries is to improve energy efficiency by reducing energy intensity. The fundamental question is which policies must be adopted to be effective. Given the focus of this study on Iran's energy intensity, we examined the impact of financial development, government investment, oil revenues, and trade openness on energy intensity. To this end, we used SVECM and DAG technique and considered the data from 1967 to 2017. Empirical results shed light on that government investment, oil revenues, and trade openness negatively influence energy intensity, and the impact of financial development on the intensity of energy is positive. Likewise, government investment and financial development have main and minor effects on energy intensity variations, respectively.
Our upshots have particular importance to policymakers because if it does not pay attention to energy intensity, Iran will become one of the energy importers in the coming years. Accordingly, we propose that the government increase infrastructure expenditures. The government can also use oil revenues to replace worn-out equipment. The Iranian government must also make great efforts to raise public awareness, as much energy resources are wasted on misuse. Meanwhile, besides educating the private sector and individuals, the government must guide them to optimize consumption. In this regard, the government can use incentive and punishment policies. Thus, subsidies and low-interest loans for complying with energy consumption standards should be allocated to the private sector.
In contrast, high-energy wasted institutions and enterprises should be fined with heavy taxes. Hence, institutions will take the necessary measures to improve their technologies. In Fig. 5 Variance Decomposition of energy intensity addition to maintaining their production and profitability, they will achieve desirable results to save energy resources. It is also vital that the government does not only rely on oil revenues for its investments so that construction and infrastructure projects will fail in events like sanctions and crises. Among how the government can finance its investments is the elimination of unnecessary subsidies and strengthening of the tax system. Finally, the government must take action to facilitate trade liberalization and increase its ties with other countries. Increasing foreign relations due to competition in global markets will both strengthen the quality of domestic products and comply with environmental regulations and energy consumption. Consequently, by implementing these policies, Iran can amplify economic growth, the quality of manufactured goods, and reduce environmental degradation and use its energy resources optimally.
In line with studies on energy intensity, our results confirm the studies such as Aboagye (2017), Adom (2018), He and Huang (2020), Samargandi (2019) and also are not similar to Chen et al. (2019) and Pan et al. (2019aPan et al. ( , 2019bPan et al. ( , 2019c. Furthermore, according to countries' economies, more and newer variables such as exchange rate and economic policies can be added to the model to get more accurate results. On the other hand, instead of considering the energy intensity in general, the energy intensity of energy carriers can be examined separately, similar to Guo et al. (2021) and McKenzie et al. (2019) studies. Also, instead of using SVECM, models such as general equilibrium can be used to examine the relationship between variables like He and Huang (2020).

Appendix B
Here the IRF of financial development, government investment, and trade openness are displayed. Fig. 6, Fig. 7, Fig. 8 illustrates the Structural IRF of financial development, government investment, and trade openness to other variables, respectively. The oil revenues are not dependent on Iran's macroeconomic variables, so we did not examine them.