Energy-growth hypothesis: testing non-linearity by considering production function approach for Spanish economy

Targeting output growth is among one of the prime concerns of any economy in both the developing and developed world. Energy utilization and exports are important drivers that would help in boosting production activities in any economy. Therefore, beyond labor force and capital formation, exports and energy utilization can be among the important inputs for accelerating economic growth in any economy. This research is conducted to investigate the linear impact of exports and the non-linear effect of energy consumption on economic growth considering the production function approach in the Spanish economy. After considering the bounds test for a period from 1980 to 2019, the study provides evidence of the inverted-U-shaped effect of energy consumption on economic growth. The findings also expose that exports, labor force and capital formation significantly accelerate economic growth in Spain. These findings are consistent with the diagnostics applied in the study. This research proposes that energy consumption should not be increased beyond a certain threshold for reaping the positive fruits of economic growth. Beyond that cutoff, it will become harmful to economic growth. Policy advisors may consider exports to target economic growth in Spain as it helps in expanding production activities in the Spanish economy.


Introduction
Unlike industrial economies, emerging economies and under-developed economies of the world are also consuming a great proportion of energy for meeting their needs. This reveals that the importance of energy is increasing as the economies are growing. Consumption of energy is among one of the most common measures which help in assessing the economic progress of any country. Various scholars reported positive effects of aggregated and disaggregated forms of Energy Consumption (EC) on Economic Growth (EG) (Satti et al. 2014;Wasti and Zaidi 2020;Rahman and Velayutham 2020;Hassan et al. 2018;Smolovic et al. 2020;Shahbaz et al. 2020;Chen et al. 2020;Umurzakov et al. 2020;Adebayo et al. 2021;Mahmood et al. 2021a, b;Abbasi et al. 2021;Pearson 2021;Parveen et al. 2021;Yasmeen et al. 2021;Rahman and Alam 2021;Bulut and Apergis 2021;Elfaki et al. 2021;Ozturk et al. 2022;Ahmad et al. 2022), which motivate us for testing the energy-led growth hypothesis.
After reviewing various studies on determinants of economic growth, we come across the fact that exports are among the most important predictors of economic growth, which would help in accelerating the economic progress of any economy. However, we see that Duru and Ezenwe (2020) and Awan and Bibi (2021) have reported the absence of a significantly accelerating role of exports towards economic prosperity while Shahbaz et al. (2011), Ee (2016), Fatemah and Qayyum (2018), Khan and Emirullah (2019), Nguyen (2020), Islam (2021), and Subhan et al. (2021) disclosed significantly escalating effects of exports on economic growth. These studies drive us to test the export-led hypothesis for the Spanish economy.
Besides this discussion, if we look at the trends of 5 years average growth of per capita Gross Domestic Product (GDP), exports, and energy use, then we would be able to know how the Spanish economy is performing in these indicators from 1980 to 2020. The performance of growth rate of 5 years' average per capita GDP remains 4.29%, which is the highest during 1986-1990, while it remained at −0.47% during 2015-2020, which is the lowest or worst performance. Like per capita GDP, we may see that in 5 years, the average growth rate of exports is 8. 29% during 1991-1995, and it is the highest performance of exports during 1980-2020, but exports perform the worst like −1.18% during 2015-2020. Similarly, 5 years average growth of EC per person is witnessed as 4.60% during 1996-2000, which is the highest performance. But if we see the 5 years from 2011 to 2015, then the average growth rate of per capita EC is witnessed as −1.67%, and this is the poorest performance (World Bank 2022).
After this, the yearly growth performance of per capita GDP, exports as a share of GDP, and per capita EC is presented in Fig. 1. The economic growth rates and energy consumption growth rates are moving in the same direction mostly, which depicts a chance to have a significant relationship between both. However, the economic growth rates and export growth rates are moving in opposite directions till 2000. But, these are moving in the same direction afterward. Thus, the relationship between exports and economic growth is not clear from the graphical presentation, which needs further investigation.
Based on the above discussion, energy consumption is a basic determinant of the economic growth in any economy, which is termed as energy-led growth hypothesis. The testing of the energy-led growth hypothesis is missing in the Spanish literature. Moreover, Wang et al. (2022) suggested testing the quadratic effect of EC on EG and this non-linear testing is scant in global literature. Thus, the present study is designed for inquiring about the non-linear impact of EC on the EG of the Spanish economy by taking into account the annual data for the period from 1980 to 2019. Besides this, the study is also going to inspect the presence of the export-led growth hypothesis so that it can be tested whether it is relevant in recent times or not. This study is unique because the literature does not provide rich evidence on the non-linear impact of EC on EG in the Spanish economy accompanied by testing exports as an engine of growth hypothesis in one study. The present study is going to fill this gap. Therefore, this study will seek great attention from its readers.
The second portion of this research discusses the literature review. In the third section, the model and estimation approaches are discussed. The fourth section contains empirical findings and debates. The last section concludes the study with policy implications.

Literature review
Energy consumption and economic growth nexus Hassan et al. (2018) considered the Johansen Multivariate cointegration technique for a period from 1977 to 2013 and observed a positive impact of the labor force, natural gas consumption, and capital on EG in Pakistan. Besides this, Gozgor et al. (2018), by using panel Autoregressive Distributive Lag (ARDL) and panel Quantile Regression from 1990 to 2013, demonstrated a positive relationship of EG with EC of renewable and nonrenewable in 29 OECD economies. The positive impact of EC on EG was also found by Wasti Fig. 1 Trends of growth rates of production, energy consumption, and exports and Zaidi (2020) for Kuwait. Nathaniel and Bekun (2020) shared the same results in the relationship between electricity consumption and EG from 1971 to 2014 in the Nigerian economy. Rahman and Velayutham (2020) demonstrated the positive impact of labor, capital, and renewable and nonrenewable EC on EG of five selected South Asian countries from 1990 to 2014 by applying FMOLS and DOLS approaches. In another study,  considered FMOLS and CCR methods for a period from 1981 to 2016 and discovered the positive effects of consumption and production of coal, gas, and oil on EG in China.
According to Smolovic et al. (2020), EG is significantly increased due to the increase in renewable energy and capital in European economies, using pooled mean group estimator from 2004 to 2018 for their analysis. Moreover, Shahbaz et al. (2020) confirmed the positive impacts of labor, capital, renewable EC, and nonrenewable EC on EG in 38 economies. By using a sample period from 2000 to 2015, Fan and Hao (2020) examined an insignificant effect of renewable EC on the EG in 31 Chinese provinces. For the sample of 103 countries and the data series from 1995 to 2015, the contribution of Chen et al. (2020) showed a positive impact of renewable EC on EG in the case of OECD, Non-OECD, and developing economies while nonrenewable EC left a significantly positive effect on EG in the same sample countries. However, when renewable EC goes beyond a threshold level in the selected sample economies, then it revealed a positive effect on EG. The study of Umurzakov et al. (2020) employed Pedroni's DOLS, FMOLS, and OLS methods for a period from 1990 to 2018 and provided evidence of escalating effects of EC on EG in 26 post-communist economies. Moreover, using a period 1965-2019, Adebayo et al. (2021) reported a positive impact of EC on economic performance in the South Korean economy. They also reported an insignificant effect of capital on economic performance. In another study, Abbasi et al. (2021) reported a significantly escalating impact of EC on EG for both the short and long run for the period from 1972 to 2018 in the Pakistani economy. Further, Pearson (2021), employing the ARDL from 1996 to 2018, found a significantly elevating impact of renewable EC on per head GDP in the long run for the Croatian economy. Parveen et al. (2021) used the CCR approach from 1975 to 2018 and exposed the positive effect of EC on EG for the Pakistani economy. In another study, Yasmeen et al. (2021) considered the SEM technique on the quarterly data from 1990:Q1 to 2018:Q4 and confirmed that the significant and positive impact of conventional energy is stronger than the significant and positive impact of clean energy on economic growth in Pakistan. Elfaki et al. (2021) applied FMOLS, DOLS, CCR, and ARDL approaches from 1984 to 2018 and provided evidence of a significantly escalating effect of EC on EG for the Indonesian economy. After using PMG, FMOLS, and DOLS estimators on the 20 economies for the period from 1980 to 2018, Rahman and Alam (2021) disclosed the positive effect of EC on EG. The study also revealed a positive effect of capital on EG while labor reported similar results through PMG and FMOLS estimators. Bulut and Apergis (2021) tested the significantly positive responses of GDP to solar and renewable EC in the case of the USA for quarterly data from 1984 to 2018. Hassan et al. (2022b) employed Gregory Hansen's cointegration approach on the sample period from 1972 to 2020 and reported a positive impact of electricity consumption on economic growth in France, Finland, and Portugal.
Literature has corroborated the positive effect of EC on EG. But, environmental effects of energy consumption cannot be ignored (Mahmood 2022). In this context, literature explored and found that environmental awareness would influence the demand for green products (Zameer et al. 2021b;Zameer and Yasmeen 2022;Li et al. 2022), which would affect ecological efficiency (Zameer et al. 2020b). Moreover, technological innovation and environmental regulation would play their role to improve energy and ecological efficiency (Yasmeen et al. 2020). In addition, the green competitive advantage also played a role in influencing green products and environmental performance (Zameer et al., 2020a(Zameer et al., , 2021a.

Exports and economic growth nexus
In a study, we find that Shahbaz et al. (2011) confirmed the presence of the export-led growth hypothesis in Pakistan for the quarterly sample period from 1990 to 2008 with an unstable graph of the cumulative sum. Afterward, Ee (2016) analyzed four selected Sub-Saharan African economies from 1985 to 2014 and confirmed the export-led growth hypothesis for the selected economies. Besides this, Fatemah and Qayyum (2018) inquired export-led growth hypothesis for Pakistan's economy. They employed Johansen's multivariate cointegration method for the period from 1971 to 2016 and confirmed that the export-led growth hypothesis remained valid for both the long and short run for the Pakistani economy. The study by Khan and Emirullah (2019) tested the effects of exports on EG in Pakistan and India. After employing the FMOLS from 1990 to 2016, the study exposed the positive effect of exports on EG in both economies. In a study, we see Nguyen (2020) who used data series from 1997 to 2018 and validated the export-led-growth hypothesis in Vietnam. Duru and Ezenwe (2020) tested the negative impact of exports on EG in Nigeria from 1980 to 2016, hence concluding that exports did not help in expanding EG in Nigeria. In the estimates of ARDL from 1980 to 2015, Awan and Bibi (2021) disclosed the positive but insignificant impact of exports on EG in the case of Pakistan's economic growth. Besides them, we find that Islam (2021) applied the ARDL from 1986 to 2018 and presented a positive effect of ready-made garments exports on EG in Bangladesh. After using the VAR methodology for the period from 1961 to 2015, Subhan et al. (2021) reported a positive impact of exports on EG in India. In the trade and environmental debate, Wang et al. (2021) investigated trading networks in trading partners and concluded that carbon emissions were transferring from developed to developing countries due to exporting trade networks.
Labor force, capital formation, and economic growth nexus Solarin (2020) Pasara and Garidzirai (2020) investigated the impact of gross capital formation on EG in South Africa. They utilized the VAR technique on the sample period from 1980 to 2018 and reported that gross capital formation elevated EG. In a study, Topcu et al. (2020) utilized the panel VAR from 1980 to 2018 for 124 economies and reported a significant and positive influence of capital formation on EG in highincome economies while the influence turned negative and significant in the case of low-income countries.

Summary of literature review
The literature confirmed the positive effects of labor and capital on economic growth mostly. Moreover, most literature corroborated the positive effect of exports on economic growth, which is termed as exports-led growth hypothesis. However, Duru and Ezenwe (2020) reported a negative effect of exports on economic growth and Awan and Bibi (2021) reported an insignificant effect of exports on economic growth. Thus, the exact relationship between exports and economic growth is an empirical question. The reviewed literature has also signified the importance of EC on EG as most of the cited literature corroborated the positive effect of EC on EG in the aggregated and disaggregated analyses, which is called the energy-led growth hypothesis. However, the testing of the energy-led growth hypothesis is missing in the case of Spain. Moreover, the testing of the non-linear effect of energy consumption on economic growth is scant in global literature (Wang et al. 2022). Thus, the present study contributes to this literature gap by inquiring about the non-linear effect of energy consumption on economic growth in Spain along with testing the exportsled growth hypothesis.

Theoretical justification
Energy consumption is a basic input for any economic growth of a country (Bulut and Apergis 2021;Shahbaz et al. 2020). Thus, the testing of the energy-led growth hypothesis in Spain is our basic motivation. However, there is a chance to have a non-linear effect of EC on EG (Wang et al. 2022). Thus, we hypothesize the quadratic effect of EC on EG. This expected quadratic effect is mostly ignored in past literature. For instance, the linear impact of coal consumption as a source of EC on EG was tested by Satti et al. (2014) for the Pakistan economy. They did not use the production function approach for their analysis. However, energy consumption is a prominent factor in any production process and past literature has considered energy variables as an input to the production function. For example, we see Hassan et al. (2018) who used the production function approach to find out the linear effect of natural gas consumption on EG for Pakistan's economy. Moreover, Hassan et al. (2022b) considered the production function approach and reported elevating the role of electricity consumption in EG in Finland, Portugal, and France. In another study, Wang et al. (2022) also used the production function approach to find out the non-linear impact of renewable and non-renewable EC on EG in Pakistan. These studies guide us to use the production function approach for capturing the non-linear effects of EC on EG. This will keep us closer to the theory of production function and will give a sound understanding to the readers that after incorporating energy as an input in the production function what kind of changes emerge in the production function of the Spanish economy? In another study, Hassan and Siddiqi (2010) inquired about the impact of trade openness on EG in Pakistan's economy. Besides them, Bilas et al. (2015) found a positive impact of exports on EG for the Croatian economy. After them, Nguyen (2020) found a significantly appreciating impact of exports on EG in Vietnam. Similarly, we see Bajo-Rubio (2020) found a significantly elevating impact of exports on EG for the Spanish economy. These studies motivated us to incorporate exports as a control variable in the production function to test the export-led growth hypothesis for the Spanish economy. Moreover, this discussion derives motivation for us to use the production function approach for testing the non-linear impact of EC on EG by controlling exports, labor, and capital in the model of the Spanish economy.

Model
This study captures the non-linear impact of EC on EG for the Spanish economy by considering the double log transformation approach. A similar approach was used by various scholars such as Hassan et al. (2022aHassan et al. ( , 2021Hassan et al. ( , 2018Hassan et al. ( , 2016Hassan et al. ( , 2015Hassan et al. ( , 2014, Mamoon et al. (2017), Iftekhar et al. (2016Iftekhar et al. ( , 2017, Wang et al. (2022), Hassan (2013, 2014), and Satti et al. (2014Satti et al. ( , 2016. The results turn out to be more efficient and robust by using this transformation approach as advocated by the earlier stated research. The variables of the study are discussed in Table 1. Our model based on the last section's discussions is as follows:

Sample and sources
In the present study, the non-linear impact of EC on EG is captured for the Spanish economy. The study uses annual data from 1980 to 2019 for empirically testing and reporting results. The data for per capita GDP, labor force, capital, and exports have been collected from the World Bank (2022). The data for primary EC is collected from the British Petroleum Company (2022). (1)

Estimation strategy
Macroeconomic data usually have trends and could have a unit root problem. Thus, the testing of data normality and stationarity should be the first step of estimation. Therefore, the status of stationarity will be tested by applying Ng and Perron's (2001) test. This test is efficient in case of a small sample size as in our case. Moreover, this test will help in investigating the presence or absence of unit root in the selected data series of the study. The null hypothesis is that data series are non-stationary. It can be accepted if the calculated value of the MZa test will remain greater than the 10% critical value (−5.70). After testing all the variables for stationarity, we will conclude with the order of integration and then we would apply the cointegration test in the next step. The equation of MZa is reported as below: The order of integration from the unit root test will allow us to apply a suitable cointegration method. There are many cointegrating tests. But the ARDL procedure proposed by Pesaran et al. (2001) is most suitable if the order of integration is mixed [I (0) & I (1)] and it is also convenient to use it even if the order of integration is one [I (1)]. Moreover, this technique is parsimonious in nature and choose the different optimum lag length for each variable, which would save the degree of freedom in the model and provide more robust results. Hence, Pesaran et al. (2001) cointegration technique is superior to the other techniques. Therefore, the present study considers this ARDL bounds testing approach for examining the cointegration between economic growth and its factors for the Spanish economy. The calculated value of the F-test will help in determining the status of cointegration between the variables. If the calculated F-test will remain larger than the upper critical bound, then the alternate hypothesis of "Cointegration exists between the variables" will be accepted and the long run parameters may be computed as: After estimating long run coefficients, the study will also calculate the long threshold or cutoff point that will determine at which value of the natural log of energy consumption, the natural log of per capita GDP turns to be maximum. After finding long run results, the short run parameters may be estimated and reported using the error correction model, which can be estimated by modifying Eq. (3) in such a way that the terms with the first lag of level forms will be replaced with one period lagged error term from Eq. (3). Then, Eq. (5) will be developed, which will signify the speed of adjusting disequilibrium in the presence of the negative coefficient of ECT t-1 . It will reveal that disequilibrium is reducing and soon the long run equilibrium will be restored. The required time for achieving a long run path can be found by using the below-provided formula: The equation for computing short run coefficients is provided below: Afterward, the study will compute and report the graphs for the stability of mean and variance in the form of Cumulative Sum (CUSUM) and CUSUM Square graphs. If the computed mean and variance will be found within corresponding critical values, then the stability of results will be ensured, and the absence of structural instability will be confirmed. After confirming the absence of structural instability, the study will also report a graphical representation of the non-linear impact of EC on EG in the Spanish economy. (3)

Required Time to Achieve Long run Equilibrium
The study will use "WolframAlpha website templates" for developing non-linear graphs. Besides this, the estimated results and their discussion will be presented in the "Estimated results and discussion" section of this study. Table 2 shows the basic summary of statistics in the form of the mean, standard deviation, and normality status of the variables of the study. The probability value for the natural log of per capita GDP, labor, capital, linear and squared terms of energy consumption, and exports as a share of GDP are found to be insignificant which allows us to accept the H 0 of normal distribution in the Jarque-Bera test.

Estimated results and discussion
After carrying out a discussion on descriptive statistics, we demonstrate the estimates of variance inflation factors. The calculated value of the Variance Inflation Factor (VIF) should be less than 10 for concluding that there is an absence  of multicollinearity in the study. Table 3 discloses the results of the variance inflation factor matrix. From Table 3, we may see that the value of VIF for all the explanatory variables is less than 10. Therefore, we conclude that there is no evidence of the presence of multicollinearity between the explanatory variables of this study. After explaining the results of the variance inflation factor, the study now reveals findings of the Ng Perron unit root test. The results are provided in Table 4.
From Table 4, we may view that at level specification, the calculated values of MZa statistics for per capita GDP, labor, linear and squared terms of energy consumption, and exports are witnessed as larger than the 10% asymptotic critical value "−5.7". Therefore, we accept the null hypothesis of non-stationary series in the case of the above-stated variables. While the calculated value of the MZa test for the capital falls in the critical region at the level specification. Hence, we may accept the alternate hypothesis for capital at the level specification and conclude that capital is a stationary variable at the level specification. Moreover, we have tested all variables at the first difference, which are stationary at the first difference specification. This concludes a mixed order of integration. Afterward, the next step is to apply a suitable cointegration approach for inspecting long run equilibrium among variables. As in our case, the unit root test reports a mixed order of integration. Therefore, we are applying the ARDL bounds testing approach, presented in Table 5.
In Table 5, we may see that the estimated F-test is 4.2769, which is greater than 10% corresponding Upper Critical Bound of 3.7118, hence allowing us to accept the alternate hypothesis of "Model is cointegrated". This concludes a cointegration between EC and EG, controlling exports, labor, and capital in the model. The W-test also exposes a similar conclusion. Besides this, all the diagnostics like serial correlation test, functional form test, normality test and heteroskedasticity test report that the error term has no serial correlation issue, the functional form of the study is well specified, error term follows a normal distribution, and variance of the error term is homoscedastic. After confirming the long run cointegrating connection between EG and EC, the study is going to demonstrate the long run coefficients, and the results are exposed in Table 6. The long run coefficients of both labor force and capital disclose that they have a positive effect on EG in Spain. This means when we increase units of labor and units of capital by 1%, then the EG will significantly expand by 0.5519 and 0.5308%, respectively, in the long run in the Spanish economy. The coefficient of the labor force is relatively stronger as compared to the coefficient of capital. It is a surprising result, which corroborates higher labor productivity compared to capital productivity. It may be due to the uptrend of educational attainment in Spain, which makes the labor more productive. Moreover, capital also augments the labor productivity and high-tech investment may also raise the per labor output. For instance, the automotive industry and shipbuilding sectors are mostly automotive and are major industries of this  economy, which have a high potential to generate high per labor output. On whole, both labor and capital are two basic inputs of the production function, and both are positively contributing to the production and economic growth of the Spanish economy. The findings are consistent with the findings of Hassan et al. (2018) and Wang et al. (2022). Besides this, the coefficient of exports is also found to be positive and significant, which elucidates that economic growth significantly expands due to expansion in exports in the long run in Spain. Moreover, exports are a direct component of the GDP of any economy. Hence, increasing exports have a significant contribution to the income of the economy. For instance, the exports percentage of GDP was about 14% in 1980, which had almost a positive trend and reached about 35% in 2019 (World Bank 2022). This fact shows that the role of exports in economic growth is increasing over time.
Thus, this also confirms the export-led growth hypothesis for the Spanish economy, which has also been corroborated by Nguyen (2020) in Vietnam and by Bajo-Rubio (2020) in Spain. After this, the study also tested the non-linear impact of EC on EG and the results disclose that in the early stage of EC, EG improves but if we keep on increasing EC, then it will start harming EG in the Spanish economy in the long run. It may observe from the fact that Spain is using oil, which is more than 40% of the total energy mix. Oil prices are highly volatile (Siddiqui et al. 2020), which keeps economic growth uncertain. Moreover, increasing oil prices would generate cost-push inflation, which may discourage economic growth with excessive use of energy in the economy. It develops an inverted U-shaped impact of EC on EG. The long run cutoff point is found to be 1.3709. This means that when the natural log of energy consumption reaches 1.3709 (3.9387 exajoules), then the natural log of per capita GDP becomes maximum in the economy. After shedding light on estimates of the long run, now the study carries out a discussion of short run coefficients.
Results disclose in Table 7 that labor force and capital significantly elevate EG in the short run. If the labor force and capital increase by 1%, then EG will enhance by 0.1738 and 0.1671%, respectively. This means that both inputs are growth-promoting in the Spanish economy. This finding is supported by Wang et al. (2022). Besides this, the study also confirms the short run export-led growth hypothesis in Spain. Economic growth significantly improves by 0.2067% if exports are expanded by 1%. The positive coefficient of exports is also supported by the finding of Bajo-Rubio (2020).
Afterward, the non-linear impact of EC on EG is tested in the short run. The linear term of EC significantly increases EG, but the squared term of energy consumption significantly condenses EG in the short run in Spain. This shows that in the early phase of EC, economic growth responds positively but beyond a certain threshold, if energy consumption continues to expand then economic growth will start decreasing. This makes an inverted U-shaped impact of EC on EG in the short run in Spain. Moreover, the study also finds the short run cutoff point, which is 1.3710. This shows that if the natural log of energy consumption reaches 1.3710, then at this point the natural log of per head GDP becomes maximum in the short run. Beyond 1.3710 of energy consumption, per capita GDP will start decreasing in the short run.
One period lagged term (ECT t-1 ) is negative (−0.3148), which confirms that the present study has achieved long run and stable equilibrium. The short run disequilibrium might be corrected 31.48% by each year and the long run equilibrium will be restored after 3.18 years. These findings are consistent with Arshed et al. (2022), Yasmin et al. (2021), Hassan et al. (2017), Huan et al. (2022), andYu-Ke et al. (2022). These findings are robust to all the diagnostics applied in the study. Besides carrying out discussion upon short run coefficients and cutoff points, the stability of estimates for the Spanish economy is tested by considering the CUSUM and CUSUM square graphs. If both graphs remain within their corresponding critical bounds, then we may conclude that estimates remain stable. Hence, the coefficients for the long and short run are witnessed as stable in Fig. 2 and these do not report any structural instability. The non-linear impact of EC on EG is captured and presented in Fig. 3 for the Spanish economy. Fig. 3 is constructed based on estimated coefficients of PEC t and PEC t 2 , which are in natural lag form. Thus, the cut-off point in the figure needs to be taken as an exponent to see its value in exajoules of PEC t . The graph exposes the relationship between EC and EG in the long run. Once, energy is utilized in the Spanish economy up to a certain threshold, [exponent of 1.3709 = 3.9387 exajoules], then it will be beneficial for production activities but beyond that threshold point (3.9387 exajoules) if further energy is utilized, then it will start hampering production activities and EG. Hence, this inculcates an inverted U-shaped impact of EC on EG in the long run.

Conclusions
The non-linear effect of EC and linear effect of exports are inquired on economic growth by taking the production function approach into account for the Spanish economy. The study applies the ARDL bounds test for a period from 1980 to 2019 for inspecting the long run cointegrating connection between economic growth and its factors in Spain. The long and short run coefficients are obtained after the confirmation of the cointegrating relation. The results demonstrate that the linear term of EC significantly enhances EG in both the long and short run but the squared term of EC significantly hampers EG. This means that energy consumption in the early stages is beneficial but in the later stages, it hampers EG in Spain. This confirms the presence of the non-linear or inverted-U-shaped effect of EC on EG in Spain. Besides this, the study also finds the positive impact of exports on economic growth in both the long and short run, and hence this confirms the presence of the export-led growth hypothesis in the Spanish economy. The study further reveals significantly elevating effects of the labor force and capital formation on EG. All these findings are robust to all the diagnostics employed in the study. The graphical demonstration regarding CUSUM and CUSUM square discloses the absence of structural instability in the model.

Policy implications
Based on the results, exports can boost the economic growth process in the Spanish economy. Thus, the policy advisors should put emphasis on expanding exports to  accelerate the economic progress of this economy. For this purpose, financial and non-financial incentives should be provided to exporters to boost exports, which may promote the export-led growth phenomenon consequently. Moreover, labor and capital also support the economic growth of the economy. Thus, the government should give incentives for investments in the economy, which will demand labor and capital in response to support the economic growth in the economy. Lastly, the linear term of energy consumption has boosted the economic growth in Spain. However, beyond a certain threshold of energy consumption, which is 3.9387 exajoules, if energy consumption is further expanded, then it will start condensing production activities and EG in Spain. Therefore, energy consumption should be controlled to the estimated threshold point (3.9387 exajoules). So that, the fruits of energy consumption can be reaped before this threshold point. After the threshold point, energy consumption should be discouraged, which may reduce the progress of economic growth.

Future direction
The present study has investigated the energy-growth relationship at the aggregate level. However, future research may be conducted to use the sectoral growth and sectoral energy consumption to see which economic sectors are following the energy-growth hypothesis.
Author contribution Muhammad Shahid Hassan: Conceptualization and Formal Analysis, Haider Mahmood: Writing Original Draft, Saba Yousaf: Methodology, Review and Editing. All authors read and approved the final manuscript.

Data availability
The data sets used during the current study are available from the corresponding author on reasonable request.

Declarations
Ethics approval All the authors declare that the present research is organized by considering all the ethical standard.

Competing interests
The authors declare no competing interests.