The current study is Malaysia specific; therefore, we discuss here the available literature on the subject both in the bivariate and in the multivariate framework concerning Malaysia. A multivariate study was conducted by Tang and Tan (2013) on energy–growth nexus by including energy prices and technological innovation in the model to investigate the causal relationship between the variables from 1970 to 2009. The estimated results of the study showed a long-run positive impact of income on electricity consumption, while energy prices and technology innovation negatively influenced electricity consumption in the long run. The causality was running from innovative technology to electricity consumption and economic growth in Malaysia in the long run, while energy consumption and income showed bidirectional causal association in both the long run and the short run. A study was conducted by Chandran et al. (2010) in both bivariate and multivariate environments using the ARDL bound test over the period 1971–2003, and electricity consumption caused GDP in the short run. Economic Growth Granger caused electricity generation in uni-direction, but a causal relationship was evidenced between prices and GDP (Lean and Smyth, 2010), over the period 1971–2008. In a multivariate research framework, Azlina and Mustapha (2012) investigated a relationship between energy utilization, economic growth, and CO₂ by applying the VECM on annual data over the period 1970–2010 and concluded that causality was running from energy consumption to GDP and from CO₂ to energy consumption as well as economic growth in Malaysia. The ARDL bound test, DOLS test, and SLM U (Sasabuchi–Lind–Mehlum U) test confirmed that energy consumption/capita and GDP (Chen et al., 2021) per capita have positive impact on CO₂, but the impact of population growth was non-significant in Malaysia (Begum et al., 2015). A multivariate study conducted by Razali et al. (2015) over the period 1971–2013 using VAR and VECM procedures, in the case of Malaysia, concluded that a long-run relationship was present between energy consumption, income per capita, population growth, and trade openness.

Augmented Dickey–Fuller (ADF) (Shahbaz et al., 2021), Kwiatkowski–Phillips–Schmidt–Shin (KPSS) (Lean and Smyth, 2010), and Ng–Perron tests were applied.

Keeping in mind the objectives of this paper and the nature of the data, we tested unit root issues, if any of the variable(s) has. The time of the data is longer, so is a likelihood that the series exhibit upward or downward trends. The trending behavior of the data indicates that location and scale parameters are time-dependent. In such cases, the estimated results of ordinary regression proved to be spurious. Inferences based on these results mislead and are detrimental to both short-term and long-term policies. Thus, to empirically check the stationarity issue, various unit root tests, such as ADF (Shahbaz et al., 2021), KPSS (Lean and Smyth, 2010), and Ng–Perron tests, were applied. The ARDL bound test developed by Azlina and Mustapha (2012) was applied to test the long-run co-integration between the variables. For investigation of the long- and short-run relationships between series energy consumption and real per capita GDP, the following equations specified: Δ O t = λ 1 + λ T T + λ O O t − 1 + λ E E t − 1 + λ C C t − 1 + λ L L t − 1 + λ U U t − 1 + ∑ i = 1 p λ i Δ O t − i + ∑ j = 0 q λ E Δ E t − j + ∑ k = o r λ L Δ L t − k + ∑ l = 0 s λ C Δ C t − l + + ∑ m = 0 s λ U Δ U t − m + ε 1 t , (3) Δ E t = α 1 + α T T + α O O t − 1 + α E E t − 1 + α C C t − 1 + α L L t − 1 + α U U t − 1 + ∑ i = 1 p α i Δ O t − i + ∑ j = 0 q α j Δ E t − j + ∑ k = o r α k Δ L t − k + ∑ l = 0 s α l Δ C t − l + ∑ m = 0 s α m Δ U t − m + ε 2 t ............ , (4) Δ C t = γ 1 + ∑ i = 1 p γ i Δ O t − i + ∑ j = 0 q γ j Δ E t − j + ∑ k = o r γ k Δ L t − k + ∑ l = 0 s γ l Δ C t − l + ∑ m = 0 s γ m U t − m + ε 3 t , (5) Δ L t = μ 1 + μ T T + μ O O t − 1 + μ E E t − 1 + μ C C t − 1 + μ L L t − 1 + μ U U t − 1 + ∑ i = 1 p μ i Δ O t − i + ∑ j = 0 q μ j Δ E t − j + ∑ k = o r μ k Δ L t − k + ∑ l = 0 s μ l Δ C t − l + ∑ m = 0 s μ m Δ U t − m + ε 4 t , (6) Δ U t = π 1 + π T T + π O O t − 1 + π E E t − 1 + π C C t − 1 + π L L t − 1 + ϕ U U t − 1 + ∑ i = 1 p π i Δ O t − i + ∑ j = 0 q π j Δ E t − j + ∑ k = o r π k Δ L t − k + ∑ l = 0 s π l Δ C t − l + ∑ m = 0 s π m Δ U t − m + ε 4 t . (7) Here, Δ = operator for difference and ε t i = residual of the t-th-period time.

For optimal lag of the first difference regression, we used the Akaike information criterion (AIC) and SBC. The F-distribution can be calculated appropriately. Once the appropriate lag orders of the included series are determined, then F-statistics are used. The joint significance of the coefficients of lagged variables is tested by F-test (Pesaran et al., 2001), with the null (no long-run relationship) and alternative hypotheses as H 0 : λ O = λ E = λ C = λ L = λ U = 0     v s   H 1 : λ O ≠ λ E ≠ λ C ≠ λ L ≠ λ U ≠ 0

For investigating the co-integration relationship between variables, two separate, asymptotic critical values were calculated: one for a lower critical bound (LCB) and the other for an upper critical bound (UCB) (Pesaran et al., 2001). The series is assumed to be I(0), in the case of LCB; however, in the case of UCB, all the variables of the series are assumed to be I(1). The value may likely be anywhere in these two bounds. Thus,

1. If F c a l is less than the LCB, then the variables are stationary at level ⇒ No co-integration is possible.

Yoo and Ku (2009) provided biased estimates (Borozan, 2013). Chen et al. (2021). Since our study has only one I(0) variable, we set that variable as exogenous and the rest of all variables as endogenous. For a small sample, the critical values of Pesaran et al. (2001) are biased estimates. However, for the large sample values within a range of t = 500–4,000, they are more appropriate ³ . We tested variables, real per capita GDP, income per capita, energy consumption, capital, labor, and urbanization for causality once co-integration was confirmed. The computed value and estimated results of co-integration guide us toward the application of an appropriate econometric technique. If ARDL results showed co-integration, then the error correction model (ECM) is appropriate. But if some of the variable(s) are found to be of order zero, i.e., I(0), and the VECM ⁴ is applied, then those variables be set exogenous (Granger, 1969). Since our study has only one I(0) variable, we have set that variable as exogenous and the rest of all variables as endogenous. The VECM for the variables can be written as Δ O t = λ 1 + ∑ i = 1 p λ 11 Δ O t − i + ∑ j = 0 q λ 22 Δ E t − j + ∑ k = o r λ 33 Δ L t − k + ∑ l = 0 s λ 44 Δ C t − l + + ∑ m = 0 s λ 55 Δ U t − m + π 1 E r r o r T − 1 + ε 1 t , (8) Δ E t = α 1 + ∑ i = 1 p α 11 Δ O t − i + ∑ j = 0 q α 22 Δ E t − j + ∑ k = o r α 33 Δ L t − k + ∑ l = 0 s α 44 Δ C t − l + ∑ m = 0 s α 55 Δ U t − m + π 2 E r r o r T − 1 + ε 2 t , (9) Δ C t = γ 1 + ∑ i = 1 p γ i Δ O t − i + ∑ j = 0 q γ j Δ E t − j + ∑ k = o r γ k Δ L t − k + ∑ l = 0 s γ l Δ C t − l + ∑ m = 0 s γ m U t − m + π 3 E r r o r T − 1 + ε 3 t , (10) Δ L t = μ 1 + ∑ i = 1 p μ 11 Δ O t − i + ∑ j = 0 q μ 22 Δ E t − j + ∑ k = o r μ 33 Δ L t − k + ∑ l = 0 s μ 44 Δ C t − l + ∑ m = 0 s μ 55 Δ U t − m + π 3 E r r o r T − 1 + ε 4 t , (11) where Δ = differenced operator and Error_t-1= error term assumed to be i.i.d.(0, σ 2 ).

The significance of the error term (Error_t-1) suggests that a long-run relation is present in the given variables. It also suggests that the specified models can get adjusted from the short-term shocks in the long run, if any. A significant negative error term shows that the variables are correlated in the long run and the system converges to equilibrium. The differenced form of models investigates the short-run causality. In this study, the coefficients λ 22 , j ≠ 0 , ∀ j , indicate energy consumption causes economic growth. However, α 11 , i ≠ 0 , ∀ i , means that output causes energy use. In the end, the presence or absence of the short-run and long-run causality among given variables was investigated. For this purpose, we applied the Wald test on the lagged term of the given series on the error term as was also used by Davidson and MacKinnon, 2004; Heckman, 2008; Shahbaz et al., 2012.

For the current research, we used yearly data over the period 1971–2014. Data were collected on real per capita GDP, per capita energy consumption, capital, labor, and urbanization. The real per capita GDP data were measured in constant 2005 prices, in local currency. The measurement of energy consumption was tons of oil equivalents. We extracted data on GDP per capita, capital, and labor from the World Development Indicators (WDI, 2015) database. However, we gathered data on urbanization and energy consumption from SESRIC (the Statistical, Economic and Social Research and Training Centre for Islamic Countries). We used the natural logarithm to transform the variables to get results in direct elasticity form. Independent variables were selected on the basis of theoretical and practical relations to the dependent variable. Theoretically, it has been observed that the higher the level of GDP, the greater the use of energy. Higher GDP leads to more energy consumption at household and aggregate levels. Rapid urbanization also causes increase in energy consumption as more people wish to live comfortable lives and gain maximum facilities for their livelihood. Urbanization also leads to increase in GDP because more educated and technically skilled persons enter into services and other sectors of the economy, leading to increased production levels. Skilled labors boost up GDP by actively participating in the labor market.

The ARDL bound test was used to find the long-run co-integration association between the variables. As one of the presumptions of the ARDL test is that a series be a mixture of I(1) and I(0), and no variable(s) is to be I(2). For this purpose, we used ADF, KPSS, and Ng–Perron unit root techniques to find the unit root behavior of variables and the integrated orders of the variables. All these tests confirmed first-order stationary behavior (at first difference stationary) of the variables except labor which was level stationary, and no variable was found to be I(2). The ADF and Ng–Perron tests are based on the null hypothesis (H₀) of non-stationarity versus H_a of no unit root. However, the KPSS test is based on the null hypothesis of stationarity against the alternative hypothesis of non-stationarity ⁵ .

Unrestricted error correction models (UECMs) were formulated from Eq. 3 to Eq. 7—particular types of ARDL models for the study. Next, the AIC and Schwarz criterion (SC) lag order selection was used to choose optimal lags of the regressand and the regressors to capture the dynamic links and select a better ARDL model for estimation. The ADF and Ng–Perron tests are based on the null hypothesis (H₀) of a unit root versus the alternative hypothesis (H_a) of no unit root. However, the KPSS test is assumed H₀ stationary against H_a non-stationary.

Equations 3, 7 were specified to allow the presence of long-run equilibrium by taking output, energy use, capital and urbanization as endogenous variables by estimating the short-run and long coefficients through ARDL Bound test and Error Correction Model (ECM) technique for the extended period of 1971-2014. We used the AIC and SB maximum lag length selection criteria of optimal lag length of the variables. For the final model specification, the selected optimal lags for each variable are separately reported in Table 1 ⁶ . The estimated long-run and short-run coefficients (elasticities) along with the t-ratios are presented in Tables 3, 4, respectively. Tables 3, 4 are divided into sub-sections such as Tables 3A–D, respectively, to better explain the estimated results of the models. For model stability and correct functional form specification of the model, we used the CUSUM test, CUSUMSQR test, and Ramsey RESET test.

In the next step, we applied the ARDL bound F-test to investigate the long-run association between real-term GDP per capita, energy use, capital, labor, and urbanization. Table 2 reports the ARDL bound test statistic–estimated co-integration results along with the upper and lower asymptotic critical bound values on the left-hand side (LHS) and various diagnostic test results on the right-hand side (RHS). Table 2 reports bound test results showing the long-run co-integration relationship between GDP per capita and other variables (energy consumption, capital, labor, and urbanization) as the computed F-value 4.032 was > the 5% upper critical bound value of 3.05. The model passed the relevant diagnostic tests as shown on the RHS of the table. The model was free of serial correlation and heteroskedasticity problems. We used the Ramsey RESET test to get the correct functional form and CUSUM and CUSUMSQR for analyzing the stability of the model. Figures 1, 2 suggest that the model was stable for the short and the long run as the blue line is within the 5% red band of the test. This means that the specified model can observe shocks if any, and the results would not change due to such changes. Similarly, the other models were checked for and analyzed for structural stability. All the specified models were found stable. All these models may observe any shock(s) if appeared and results would not be changed for such structural changes. The models stability to shocks can be seen from the Figures 3‐8, as all the blue lines are within the red bends of the CUSUM and CUSUMS. Taking energy consumption as a dependent variable and other variables as exogenous in the model F_EC(EC/O,C,L,U), it was confirmed that the variables have a long-run co-integration relationship, as the F-value 5.75 exceeded the 5% asymptotic ARDL bound critical value of 3.49. In the same table, the model F_C(C/O,EC,L,U), with computed F-value 8.09>3.97 tabulated value, shows significant long-run co-integration association between the variables at 5% significant ARDL bound test value. Furthermore, the model F_U(U/O,EC,C,U) results also confirmed a long-run co-integration. For this model, the reported calculated F-statistic value 7.26 > 3.97 tabulated value of ARDL bound test at 5% clearly represents long-run co-integration between the variables. Similarly, the other variable F_O(O/EC,C,L,U) when treated as endogenous also confirmed a long-run co-integration relationship as the F-calculated values are larger than the reported ARDL bound test critical values at the given 5% upper bound.

Based on Table 3A, estimated results of the long-term real GDP per capita elasticity value turned out positive and statistically significant at a 5% significance level for the Malaysian economy as was generally expected. The estimated long-run elasticity of 0.28635 showed that keeping all else constant, a 1% increase in energy consumption increased GDP per capita by 0.29% in real terms. It means that energy use is an important driver and a source of economic growth in Malaysia. It also implies that Malaysia’s economy is energy-dependent, and hence, the economic growth of the country would be adversely affected if the economy gets any energy supply shock or if conservation policies are adopted. The government in her Ninth Malaysia Plan initiated various energy-saving programs to economically utilize the energy resources to minimize the adverse environmental effects. These programs were centric on industrial, transportation, and commercial sectors. However, the industrial sector was restricted to adopt energy-saving programs and improve installed plants and equipment in the production processes. If these programs are implemented as mandatory, it would probably adversely affect the industrial growth of the country. Being an industrial revolutionary country, policymakers should devise economic growth-friendly policies regarding energy conservation and implementing bodies should implement such policies with caution so that economic growth is not affected. Our study’s estimated results were in line with the earlier studies’ estimated results, for example, Tang and Tan, 2013; Zachariadis, 2007; Wang et al., 2011; Ocal and Aslan, 2013; Yoo and Ku, 2009; Borozan, 2013. However, a little trade-off effect was found between energy consumption reduction and adopting new and efficient technologies (Chen et al., 2021). The long-run effect of capital on real-term output was also positive and significant at a 5% significance level over the period for the sampled economy. The estimated elasticity coefficient of capital 0.303 indicated that a 1% change in gross fixed capital formation enhanced economic growth by 0.303% in the long run. This result indicated that capital was recognized as an important contributor that determines Malaysian economic growth. The possible reason could be that Malaysia is a highly attractive investment economy because of its consistent and better economic performance based on sound economic buildings and having more openness to trade policies. Next, the economy has a good macro policy in terms of growth in the pro-private sector form. Furthermore, the country has a well-developed, efficient capital market and bank as well as having the best physical and telecom systems with good infrastructure and matured industrial foundations. However, the other variables such as labor and urbanization showed non-significant influence on the real-term output of the country over the study period. In contrast to Table 3A, the estimated long-run results of Table 3B are non-significant for all the variables.

The observed long-run results of Table 3C between output in real-term per capita and labor were positively and significantly influencing the dependent variable capital. The elasticities for output and labor were 1.62 and 4.94, respectively. A 1% increase in fixed gross capital formation rose real per capita GDP out of the country to 1.62% points. Similar results were obtained in previous literature, for example, Shahbaz et al., 2021; Lean and Smyth, 2010. However, the other variables showed non-significant implications.

In the last part of Table 3D, the long-run association between real per capita GDP and urbanization was reported as significant but negative, which was in contradiction to the economic expectation. The possible reason could be that rapid urbanization growth might slow down the economic growth of a country for the sample data over the specified period. The other reason might be improper urban planning of the country, or it could be that urbanization has marginally influenced economic growth negatively. This result of the study was inconsistent with the results of the previous study (Shahbaz et al., 2021). However, the influence of energy consumption was estimated as positive and significant with the elasticity value of 0.0461, which indicated that growing urbanization increased energy use as people demanded more energy for houses, offices, restaurants, business points, shopping malls, etc. Previous studies’ results supported our study’s estimated results, see Azlina and Mustapha, 2012; Shahbaz et al., 2021; Lean and Smyth, 2010.

Table 4 reports estimated results of short-term equilibrium dynamic association established in Eq. 8–Eq. 11. The estimated coefficients, t-ratios, and corresponding probabilities along with lagged error terms and error correction model results are presented in the table as well.

Considering the estimated results of Table 4A, while taking differenced real per capita output as a dependent variable and other differenced variables as exogenous, it was revealed all the exogenous variables in the short run influenced real per capita GDP. The one-period lagged error term was found to be significant and negative as was the presumption of the model. The negative and significant error term is technically called the speed of adjustment, which measures the rate of convergence of the endogenous variable to adjust to its equilibrium position when the model gets exogenous shocks. The highly significant negative value -0.68 of the error term showed that the real per capita GDP has a relatively quick adjustment of 0.68% to converge to equilibrium when the model got extraneous shocks in the form of exogenous variables. Table 4B reports no short-run relationship between energy consumption and other regressors of the model. However, the error term was found to be negative and significant with an estimated value of 0.49, as was expected. Looking at the estimated results of Table 4C, it is shown that the first period lagged value does not affect the current value of capital; however, the second and third period own lagged values of capital positively and significantly affect the current value of the capital in the short run. Moreover, short-term gross fixed capital formation and real per capita GDP at the current level as well as the past one period have a positive and significant relationship. It means that, in the short run, capital was positively and significantly influenced by current and past one-period real outputs. In the model, impact of current energy consumption was non-significant; however, the last period of energy use has a positive and significant effect on the gross fixed capital formation. The short-term error term was negative and significant, which showed that the model gets adjusted to its equilibrium relatively at a quicker rate of 0.90% speed in the short run. Keeping in view the reported results of Table 4D, by taking differenced urbanization as a dependent variable and other differenced predictor variables as exogenous, it was revealed all the exogenous variables in the short run influenced urbanization except difference of output and difference of labor. The highly significant negative value -0.041 of the error term showed that urbanization has relatively a bit slow adjustment of 0.041% to converge to equilibrium when the model got extraneous shocks in the form of exogenous variables.

In Table 4, it can be seen that capital and labor were found statistically significant for the dependent variable output at 1 and 5% significance levels. This significance of the variables showed a short-run causal link between the variables. Similarly, taking capital as a dependent variable and other variables as independent variables, output revealed statistical significance at a 1% significance level, so short-run causality existed between the variables.

Once the estimated results of the ARDL bound test confirmed the co-integration, in the next step, we tested the variables for causality for both the short and the long run. The ARDL bound test results showed co-integration behavior, so we applied the VECM framework for Granger causality. The VECM provided us with information about the short-run and long-run causality among energy consumption, income, capital, labor, and urbanization. The negative and significant one-period lagged value of the error term indicated a long-run causal relationship, while the joint significance values of the exogenous variables showed the short causation between the variables. We report causality analysis results in Table 5. Real per capita GDP and capital showed a bidirectional short run and long run, while labor Granger causes income in one direction in both the short run and the long run. Moreover, all other variables were Granger caused long run, and causality was running in both directions.