A General Cross-Country Panel Analysis for the E ﬀ ects of Capitals and Energy on Economic Growth and Carbon Dioxide Emissions

: To clarify the e ﬀ ects of generalized capitals and energy footprint on aggregate incomes and total carbon dioxide emissions, a cross-country panel analysis is applied in the present study. The generalized capitals included in this study are human capital, manufacture capital, natural capitals (as rents of fossil fuels, forest, and minerals). The energy footprint is represented by the primary energy consumption to index the overall domestic energy use. A Cobb–Douglas production function is used to empirically study on a panel of 21 European Union countries. Annual data of rents of natural capitals are used to represent the economic value of natural capitals that ﬂows to the economy. The following are the main ﬁndings of this study: (1) Employing human and manufactural capital makes contributions to income growth and carbon reduction. This study’s evidence guides to clarify the misunderstanding of capital and capitalism. Innovations through well-developed and well-managed human and manufactured capital can help sustain income and reduce carbon dioxide emissions. (2) Energy footprint is the vital determinant to total carbon dioxide emissions and hence the most important part of climate policy. (3) The value currently commeasured by monetary terms and compiled by the World Bank is evidenced, not persistently contributed to the income, rather contributed to total carbon dioxide emissions, for the sake of the energy-intensive attributes in the resource-extracting industry. The natural capitals represented by the rent of extracting endowed natural resources can only represent part of the value of natural capitals to human beings. The virtue values of natural capitals in terms of amenity and life supporting are inevitable, but intangible and hence incommensurable. This value is still ignored and unable to enter the contemporary gate of monetary national accounting system. evidence from the present study that well-managed and innovative development of human and manufactured capital can approach the balance of the two major policies of mitigating climate changes and sustain income. The two policies are not always against each other, though. The estimated huge magnitudes indicated that the e ﬀ ects are extremely large. Author Contributions: Conceptualization, W.-J.C.; Methodology, W.-J.C and C.-H.W.; Software, W.-J.C.; Validation, W.-J.C and C.-H.W.; Formal Analysis, W.-J.C.; Investigation, W.-J.C.; Resources, W.-J.C.; Data Curation, W.-J.C.; Writing-Original Draft Preparation, W.-J.C.; Writing-Review & Editing, W.-J.C.;


Introduction
Conventionally, capital is one of the production factors. The role of capital has long been the focus of economic theory and practices. In the economic school of classical and neoclassical economics, in addition to labor, capital is one of the two simplified production inputs. The straightforward definition of capital is the factor able to accumulate and contribute to production. The capacity to be contributive had made capital become assets and wealth in an economy. The non-consumptive services flowing from the capital assets makes it becoming input factor in the production process. The implicit but deep influences of many significant input factors were neglected in the traditional analysis. On the accumulative and non-consumptive basis in the definitions of "capital", the term "capital" was extended and generalized to thoroughly cover these ignored but significant production emitted from energy combustions, one of the main causes of climate change. The overall energy consumption in the aggregate production processes in an economy can be represented by the primary energy consumption in that economy. The primary energy consumption is an input factor that drives the economic activities. It is the energy footprint in that economic system. Hence, the specific set of generalized capitals and energy footprint in the present study contains (1) manufactural capital, (2) human capital, (3) natural capitals, and (4) primary energy consumption as an index of energy footprint.
Regarding the effects come from the abovementioned generalized capitals, scant literature had together empirically estimated the effects of the generalized capitals, together with energy footprint, on economic growth and on climate change mitigation. The reality about its effects is still inconclusive. Macroeconomics of climate changes focused on the combination of both climate change analysis and macroeconomics. In addition, the ecological economic analysis has to paid sufficient attention to the macroeconomic level both in terms of theory and modeling [15]. This study aims to probe more relevant knowledge on the effects of the generalized capitals and energy footprint on the economy and on mitigation behaviors, respectively. This empirical investigation looks to answer the following questions: (1) What are the effects of the generalized capital and energy footprint on aggregate income in the European Union? Do natural capitals and energy footprint, as well as other generalized capitals, contribute to or hinder aggregate income? What are the magnitudes of these effects? (2) What are the effects of the generalized capital and energy footprint on total carbon dioxide emissions in the European Union? Do natural capitals and energy footprint, as well as other generalized capitals, decrease or increase total carbon dioxide emissions? What are the magnitudes of these effects?
This study aims to unveil the role played by the generalized capitals and energy footprint in the macroeconomic model by utilizing a Cobb-Douglas production function. Referring to the capital variables included in the model specifications of the aggregate production function introduced in the literature [16][17][18], the interpolative and extrapolative econometric techniques are applied in this investigation. A panel of 21 European Union countries is empirically tested for these effects on the patterns of economy and carbon dioxide emissions over the period from 1970 to 2010. The countries located close together and considered or classed together. The European Union is the most actively involved party in carbon dioxide emission reduction under the international movement for climate mitigation, such as the treaty of Kyoto Protocol. Among the 27 members of European Union, 21 countries are included in this study. The 21 countries have been chosen due to higher data availability. They are Austria, Belgium, Bulgaria, Cyprus, Denmark, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Luxembourg, Malta, the Netherlands, Poland, Portugal, Romania, Spain, Sweden, and the United Kingdom. The United Kingdom was a member state of the European Union and of its predecessor the European Communities from 1 January 1973 until 31 January 2020. United Kingdom left the European Union on the 31st of January 2020. However, in the most of our research period , it was a member state. Six European Union countries (the Czech Republic, Estonia, Latvia, Lithuania, Slovakia, and Slovenia) are excluded from this study because their carbon dioxide emission data, obtained through the Carbon Dioxide Information Analysis Center, does not cover the entire study period . The data have only been available since 1992. This paper utilizes panel data covering the 21 European Union countries in the period from 1970 to 2010. The rents of natural resources of these countries reported by the World Bank [19] is used to represent heterogeneously endowed natural capitals in these countries. The data compilation of the World Bank is the mostly consistently organized time series data of natural capitals.

Generalized Capitals
The literature on the manufactured and human capital on the productions of a country is abundant [20]. In classical economics, capital is one of the factors for production. Capitalism contributes to the economy. The stocks of capital and/or the flow of extracting capital can be used in economic production and contribute to economic growth, improve social welfare and boost living standards. Stocks of capital are assets and wealth of an economy. However, the academic literature regarding capital includes a great variation of positive and negative comments. Capitalism was criticized as the cause of climate change and the preventor of an effective mitigation of climate change [6]. To reveal the role played by the capital is the major objective of the present study.
The issues related the capitals have attracted extensive attentions from academia, and research had proposed extended definitions of the capitals by their contributions to the aggregate productions. Four categories of the capitals are extended in the study of Ekins, Dresner and Dahlström [2] and five capitals were defined in the research of Maack and Davidsdottir [3]. The four capitals are manufactured capital, human capital, natural capitals, and social capital. The five capitals are manufactured capital, human capital, natural capitals, social capital and financial capital. Their definitions are shown in Table 1.

Human capital
Human capital generally refers to the health, well-being and productive potential of individual people. Types of human capital include mental and physical health, education, motivation and work skills. These elements not only contribute to a happy, healthy society, but also improve the opportunities for economic development through a productive workforce.

Manufactured capital
Manufactured (or human-made) capital is what is traditionally considered as capital: produced assets that are used to produce other goods and services. Some examples are machines, tools, buildings, and infrastructure.

Natural capitals
In addition to traditional natural resources, such as timber, water, and energy and mineral reserves, natural capitals include natural assets that are not easily valued monetarily, such as biodiversity, endangered species and the ecosystems that perform ecological services (e.g., air and water filtration). Natural capitals can be considered as the components of nature that can be linked directly or indirectly with human welfare.

Social capital
Social capital, like human capital, is related to human well-being, but on a societal rather than individual level. It consists of the social networks that support an efficient, cohesive society, and facilitate social and intellectual interactions among its members. Social capital refers to those stocks of social trust, norms and networks that people can draw upon to solve common problems and create social cohesion. Examples of social capital include neighborhood associations, civic organizations, and co-operatives. The political and legal structures that promote political stability, democracy, government efficiency and social justice (all of which are good for productivity as well as being desirable in themselves) are also part of social capital.

Financial capital
Financial capital is seen as a liquid asset to facilitate interchange between the other categories, the capital stock of manufactured (human-made, or durable), natural, human, and social capitals.
Note: The four capitals (manufactured, natural, human, and social capitals) are defined by Ekins, Dresner and Dahlström [2], and the definition of financial capital was in the studies of Pearce and Atkinson [1] and Maack and Davidsdottir [3].
Human capital accumulation affects income per capita in a similar fashion as manufacture capital accumulation does as a production factor. Many advanced studies have researched the role of human capital. Recent research had studied the model for climate change effects driven by human capital [21] by revisiting the demography population variables. In early econometric research on exogenous macroeconomic analysis, educational attainment was found having accumulated effects on income increases, like manufactured capital. The composite elements of education attainment and labor employment were treated as a standard input of production and named as "Human capital" in exogenous models of economic growth [22]. The stock of human capital is the activator promoting technological innovation and foreign technology adoption [23][24][25], rather than the increasing rate in the stock of human capital. Therefore, considering the contributions of human capitals in these early studies on the macro-econometrics, this study introduces the stock of human capital by multiplying the composite of education attainment and labor employment as human capital inputs.
Manufactured capital and human capital are transformed from two inputs straightforwardly from the traditional production factors, i.e., capital and labor. Manufactured capital was the capital considered in classical economics. Manufactured capital is made on purpose to be used in production process to generate other goods and services. Some examples of manufactured capital are machines, tools, buildings and infrastructure [2,3]. Labor extended its role in aggregate production to be human capital, and had played a critical role in the fields of economic growth [26,27] and aggregate productivity production function [16][17][18], as well as education policy formulation [28,29].
In addition to human and manufactured capital, the accumulation of natural capitals, social capital and financial capital were also proposed in the literature [2,3], due to their significant contributions. Natural capitals are referred to the natural asset which enable the production of goods and services. It is a marginal physical and service flow of raw materials provided by the natural environment. It is referred to include all ecological service in recent studies, as well as the service produce from the stock of all natural resources [30][31][32][33]. Hence, natural capitals are flows from the stocks of natural assets in an economy. They are extraction flows from the natural assets for the economic production (the flows of raw input materials in production). Mal-exploitation and/or over-exploitation has caused the problems of exhaustion and degradation. Optimal extraction, the rent of natural capitals, and the extensions of Hoteling model proposed by Hoteling in 1931 [34] were often addressed in the literature. The rents of natural resources are referred as natural capitals which indicate the flow of natural assets [16][17][18]. The World Bank [19] has reported statistics for the rent of natural capitals. The World Bank and OECD (Organisation for Economic Co-operation and Development) had carried out a promised compilation of the natural capitals accounting for the changing wealth of nations [35,36]. Agarwala et al. [12] suggested that more governments collaborate their natural capitals accounting to promote sustainability and combat climate change.
Social capital is the attributes of social organization that can improve the efficiency of society by facilitating collective actions. It can be trust, norms and networks in a society [37][38][39]. It is intangible assets in a society, and frequently narrated qualitatively in studies of climate adaptations in terms of how best to adapt to the potential impacts that future climate change poses significant challenges for society. The dynamic social process and the ability of societies to adapt is determined in part by the ability to act collectively [37][38][39][40][41]. Social capital is mostly relevant in the policy for adaptation rather than mitigation. Hence, the present study of quantitative mitigation do not address the effects of social capital on adaptation. Moreover, financial capital is a liquid asset to facilitate interchange between the other four capital categories, manufactured, natural, human, and social capitals [3]. The present study does not discuss the dynamic changes of the capitals and financial capital is not included in the present study.
Energy is usually not referred to as a capital; however, it is one of the important factors driven economic production. Primary energy consumption in a country represents the energy footprint of an economy. It is the input activating machinery for the economic activities. It is a complement input to manufactured capital. The thermodynamics were introduced into economic analysis firstly by Georgescu-Roegen [42,43], attracting later economists [10,[44][45][46] to take up the issues of incorporate energy into the analysis of economic production in depth. More recent research attentions on the mitigation of climate change had re-engaged the roles of energy inputs in macroeconomics of climate changes [47][48][49] in econometric analysis, as well as general equilibrium analysis [50].

Natural Capitals
Natural capitals are in the list of generalized capitals in the present study. The studies of natural resources, natural capitals and their relationships to the economics are usually on the interdisciplinary academics which rising recently by integrating multiple academic fields. Accordingly, in this section, natural capitals are introduced in detail. Natural resources are what people can use which come from the natural environment. They are endowed without the input of human beings. Therefore, natural capitals are the natural resources that can make contribution to production as they are extracted or used as inputs in that economy or society. Over-extractions are to destroy the stocks, and equivalent to assets and wealth decrease. Feasible management is required to wisely sustain the stocks, the assets, and the wealth.
The endowments of natural resources among countries are heterogeneous, and their spatial distribution varies greatly. Their existence in a country is the assets indexing the implicit well-being of that county.
They are the stocks, the flows, the assets/wealth in an economy. Firstly, it is the stocks. According to OECD (2009) [35], natural capitals are defined as the endowed stocks of natural resources, including the stocks of fossil fuels, the forest, the biodiversity, the water, the fishery, and the forest resources. Secondly, it is the flows. Extracting the stocks of natural capitals can generate or provide the input materials for economic production, and this flow of natural capitals is cited as the flow of the endowment stocks [19,51]. A flow of ecological and environmental services, coming from extracting and utilizing the stocks, automatically provides inputs that contribute to economic production for human beings. Thirdly, it is the assets/wealth of a nation. Natural capitals are deemed as assets of a country. Employing natural capitals, the economic production is activated. Profound stocks of natural capitals in a country are ready to contribute towards fiscal revenue, income, and poverty reduction. These are assets of a countries. Since the stocks reflect the real wealth of a nations, and the stocks are the assets indexing the implicit well-being of a county, over-extraction of natural capitals and environmental degradations would reduce the stocks and hinder the functional capability of the flows to contribute to the economic production [51]. Therefore, natural capital endowments need to be taken into account in national income accounting [19].
It is worthwhile to note that the national accounting in most of countries included output of their production and manufactured capitals was accounted as fixed capital that ready to be used as inputs in economic production activities. Most countries do not fully account the endowed natural assets existing in their environment. Owing to this, there are academic many studies on the roles of a series of natural capitals in the economy [17][18][19].
Nevertheless, OECD had offered a manual to measure these capitals. The literature in OECD [35] showed how far research undertaken with the objective of improving methodology for natural assets may be directly relevant to, or have implications for, the stock of fixed assets. OECD [35] indicated several similarities between fixed and natural assets. Their values are derived from the inputs they contribute to production, and they both are valued by the present value of the inputs that they are expected to provide over their service lives. The decline in the value of the stock of a natural asset as it used up in production, namely depletion, parallels the decline in the value of a fixed asset, namely depreciation [35].

The Analysis
The model specifications for the present empirical analysis is based on a Cobb-Douglas production function. This functional form is often used in the production function with assumption of constant return to scale. Based on the specification of Cobb-Douglas production function, the present study empirically investigated the relationships of the capitals on the economy and the CO 2 emissions from fossil fuel combustions, by investigating a panel of European countries with the econometric techniques. The model of macroeconomics is empirically applied in this investigation.
The production inputs make an economic contribution to the economy and to the carbon dioxide emissions. In the present study, the manufactural input remains its role; the traditional input of the labor is extended to human capital.
In the conventional production analysis, energy and natural capitals are often neglected variables which make its virtue and vital influences along the economic development. Past policies made on the conventional economic studies had misleading toward an unsustainable future. Jorgenson, and Schreyer [52] studied on the role of capital on the economy and the role of natural capital services was recommended have to be explicitly acknowledged. Moreover, even though numerous recent studies had focused on the role of energy precisely played in economic development and economic growth [53][54][55][56], the contentiousness of the energy role in its relations with other inputs remains unresolved, so as to its role to the economy.
This study is aimed to demonstrate the contributed effects of the virtual determinants to the economic growth and to the carbon dioxide emissions for policy references. In addition to the traditional production inputs, energy footprint and natural capitals are included in the analysis.

The Model
Brandt, Schreyer, and Zipperer [16,17] and Schreyer, Brandt and Zipperer [18] studied the changes in the standard measures of MFP (marginal factor productivities) to the national aggregate output (Y) with model specifications with and without fossil fuel energy as natural capital (S). Their empirical results on the OECD productivity evidenced traditional MFP are biased when natural capital inputs are not considered. Brandt, Schreyer and Zipperer [18] found that fossil fuel energy as natural capital has both positive and negative influence on productivity. Since the directions of the bias come from the effects of natural capital on the productivities, the capitals are suggested to be one of the determinant factors [18]. The purpose of the present study is slightly different from the study of Brandt, Schreyer and Zipperer [18]. The present study is neither to investigate the productivity of traditional inputs, nor to analyze their contributions to the total productivity. How the capital played as determinants and their effects on aggregate income and carbon dioxide emissions is the focus of the present study. A Cobb-Douglas production function is employed by the present study to investigate the effects on the aggregate output (Y), and on total carbon dioxide emissions (TCO2), as considering the generalized capitals as determinants.
The present study proposed a Cobb-Douglas production model with variables K (manufactured capital), hL (h, human capital indexing by schooling years; and L, employment) as Equation (1). Brandt, Schreyer and Zipperer [18] had added natural capital (S) in their analysis for comparison. The role of capital services was recommended have to be explicitly acknowledged in the literature [18,52]. Following Brandt, Schreyer and Zipperer [18] and the literature [18,52], Equation (2) additionally includes the variable of natural capital.
where Y is national aggregate output, K is manufactured capital, A is productivity, h is human capital represented by yearly schooling of labor, L is labor employed, S is natural capital, and α and β are parameters. The overall energy consumed in an economy is an input factor that drive the economic activities and the dominant factor for its carbon dioxide emissions. It is the energy footprint for an economy and can be represented by the primary energy consumption. Due to the inevitable role of energy footprint played, variable E is introduced into Equation (1). We can get Equation (3).
Thanks to the reliability and availability of the natural capital data reported by the World Bank [19], Equation (3) can be further expanded by introducing variables of natural capitals to become Equation (4).
It is worthwhile to note that the services and materials flows are explicitly included into the production faction [18,52].
where S is the vector containing the variables of the flows of natural capitals into the process of aggregate production, and γ is the coefficient vector corresponding to S. In addition to aggregate output, total emissions of carbon dioxide are also investigated for the effects from determinants in the present study. However, the structural models on carbon dioxide emissions are still on the way to be established. There is no consensus on model specifications in the literature. Since carbon dioxide is usually regarded as a by-product from the economic activities, this study strongly assumes that the variables included in the abovementioned equations are also the determinants of the carbon dioxide emissions. Accordingly, the effects on carbon dioxide emissions are estimated.
Since the fixed power of the Cobb-Douglas production function is the elasticities in the production theory, the parameters in Equations (3) and (4) and in Equations (5)-(7) represent the generalized capital elasticities of the aggregate income and the carbon dioxide emissions, respectively.

Econometric Empirical Functional Forms
Empirical econometric equations are derived by taking logarithm for the both sides of the equations of the models (1), (3), (4) described in the previous section as Equations (8)-(10), respectively. To investigate the effects between variables, these econometric specifications are estimated. The endowments of natural capitals vary across countries under this investigation. Due to this heterogeneity in the nature capital endowments and extraction differences among countries, it is not feasible to include the cross-term of the various natural capitals in the panel country analysis of the present study. ln where e is the error term. The variables are double indexed by i representing the cross section (number of countries) and t referring to particular year. The models of carbon dioxide emissions as the by-products from the economic activities, Equations (5)- (7), are estimated as the econometric Equations (11) to (13).
Fix effect Panel analysis allows exploring the relationship between the variables of the independents and the dependent variables within the entities (the countries). Since the present study is on the analysis of the effects from the generalized capitals that vary over time, Fixed Panel (cross-section fixed by dummy variables) are feasible to be used in estimation. The error term e it in the Fixed Panel models in this section contains unknown intercepts (modeled by dummies) and white noise. Then, the interpretation of the estimated coefficients in the transformation regression specifications would be: for the studied countries, when the generalized capitals varies across time by one %, the dependent variable would increases or decreases by the magnitudes (%) of the estimated coefficients.

Data
The data representing the variables used in this empirical study are retrieved from several sources. They are listed in Table 2. The data of total carbon dioxide emissions of the economies (TCO2) are derived from "Carbon Dioxide Information Analysis Center (CDIAC)" [57]. It is the total emissions from fossil-fuel burning, cement production, and gas flaring; expressed in thousand metric tons of carbon (not carbon dioxide). The CDIAC data measure emissions as thousands of metric tons of carbon emitted from fossil fuel burning.
The conventional economic variables are derived from various versions of Penn World Table [58], including PWT 7.1, 8.1, and 9.0. Feenstra et al. [59] offered detailed description about PWT. Since the present study is focused on the aggregate output, the variable Y is the multiplying product of the real GDP and Population. The per capita real output per capita is represented by the series RGDP1 in PWT 7.1 (2005 international dollar per person, 2005 PPP, USD). Since the present study is on the effects of aggregate income, per capita real GDP retrieved from PWT 7.1 (RGDP1) is multiplied by population size. Population is retrieved from PWT 8.1 (in millions). Human capital (h) is represented by the human capital index, based on years of schooling and returns to education. Employment (L) is number of persons engaged (in millions). The cross term, hL, is used to show the effects of human capital delivers to the economy through people employed in the economy. Both data of human capital and employment are reported in PWT 9.0 and the data series of HC and EMP. Moreover, K is the variable of manufactured capital (capital stock at current PPPs, in mil. 2011 USD), retrieved from PWT 9.0 as the data series of CK.
Variable, E, is represented by the primary energy consumption reported by British Petroleum Global [60]. It is used as the energy footprint in an economy.
There are numerous types of natural resources and their spatial distribution is very different. A universally accepted and common defined natural capitals and its services flow from the endowed stock is demanded in the present study. This study used the pertaining natural capital data reported by the World Bank [16], which is reliable to represent the rents of natural capitals as the services and material flow from the countries that extracts their endowed natural resources. The data were estimates based on sources and methods described in the World Bank document, "The Changing Wealth of Nations: Measuring Sustainable Development in the New Millennium" [36]. This article [36] integrates several points to calculate the value of natural resources.
Most intangible services delivered by the stock of natural capital are still under study. The economic rent of a natural resources is the value of capital services flows rendered by the natural resources given by the value after its extraction. For the economic perspective, the economic values of natural resource extraction have been academically studied and developed for two decades. Common recognized measure of the monetary value for the flow as utilizing natural resources. It is a reasonable and effective approach to apply this measure of the rent of natural resources to represent the flow value of the natural assets. A substantial literature pertaining the methodology and the measurement had suggested the reliable common monetary measures. However, Stiglitz, Sen, and Fitoussi [4] recommended that the measures of economic values for the natural capitals that have market prices are much reliable, and noticed that credible measurement practices remain problematic. The market prices of energy, minerals and timber can enable a reliable monetary measurement. Following the suggestions made by the notable paper by Stiglitz, Sen, and Fitoussi [4], the World Bank [19] compiles the economic value of the extracted flow of energy, mineral and timber in their comprehensive statistical reports.
The economic values of the natural capitals are measured by the rent of the natural resources in a country [16][17][18]36]. The World Bank [19] had reported rents of natural capitals measured by percentage of GDP in its wealth accounting, including coal rents, forest rents, mineral rents, natural gas rents, oil rents and, total natural resources rents (summations of rents of the natural resource mentioned above). Total natural resources rents are the sum of rents of forest, mineral, coal, oil, and natural gas reported by the World Bank [19].
The last column of Table 2 shows panel unit root test on logarithmic value of the data of 21 European Union countries in the period from 1970 to 2010 by Levin, Lin and Chu (LLC) test with null of nonstationary. At 0.001 significant level, all variables under tested are nonstationary, except natural capital of forest.

Two Alternative Empiric Specifications for Natural Capitals
There are two alternatives to employ natural capitals for Equations (10) and (13) in this empirical study. One is to introduce total natural resources rents (ST) as the single variable of natural capital. The Equations (10) and (13) becomes (14) and (15) as investigating the effects for aggregate income and total carbon dioxide emissions.
ln (15) The other empiric alternative to introduce natural capital is to introduce all of the individual natural capitals in one equations, including rent of fossil fuels (SFF, summation of coal rents, oil rents, and natural gas rents), rent of forests (SF), and rents of minerals (SM). In this way, the Equations (10) and (13) are marked as (16) and (17).
Total natural resources rents are the summation of the rent of fossil fuels (SFF, summation of coal rents, oil rents, and natural gas rents), rent of forests (SF), and rents of minerals (SM). For the sake of data availability, and avoidance of multi-collinearity, the empirics are set out in these two alternatives.
This study shared similar data with the study of Chen [61] on the modeling for carbon dioxide emissions in the European Union. Chen [61] analyzed the patterns of carbon dioxide emissions for each average person. The data are tested with panel analysis as nonstationary and cointegrated [61]. The present study is on the generalized capitals as determinants for aggregate income and total dioxide emissions. The aggregate data are tested with panel analysis as nonstationary and cointegrated, as well.
The logarithmic transformation data for most variables are nonstationary, since the null of nonstationary (H 0 : unit root) y are all rejected at 0.001 significant level by panel unit root test, based on the logarithmic value for 1970-2010 data with LLC (Levin, Lin and Chu t*), except natural capital of forest, ln(SRF). The statistics are shown in Table 2. Furthermore, the variables in Equations (14)- (17) (14)- (17), respectively. The following section will study the long-term relationship between variables based on the above numerical characteristics of the data. The panel analysis process is extremely complex, and a perfect analysis process is under development.

Empirical Results
The empirical research studies 21 European Union countries. These countries have highly developed economy with profound natural resources. They have pioneered data of their resource extraction, and it is reliable. A panel of 1970-2010 aggregate data of 21 European Union countries are used to estimate the empirical equations for the determinants of aggregate income and total carbon dioxide emissions, as applying econometric technique of panel data estimation methods.
Panel data are applied to estimate the empiric econometric equations. The natural capital data in the 21 countries do not all fully cover 1970-2010. As estimating the econometric equations mentioned in above section, countries without data fully cover the study period 1970-2010 were redundant and subsequently removed, and then the number of countries was different.
Since the present study is interested in analyzing the impact of variables that vary over time, Fixed Panel (cross-section fixed by dummy variables) are used to estimate. Fix effect Panel analysis allows exploring the relationship between the variables of the generalized capitals and the dependent variables within the entities (the countries). The interpretation of the estimated coefficients would be the elasticity. For the studied countries, when the general capital variables change over time by one %, the dependent variable would increase or decrease by the magnitudes (%) of the estimated coefficients.
The estimated results are reported in Tables 3 and 4 for the effects on aggregate income and total carbon dioxide emissions, respectively.
Regarding the effects on aggregate output, several findings can be drawn, based on the results shown in Table 3. Firstly, both human and manufactured capital are the conventional input factors. They have extreme impacts on aggregate income, as indicated by the huge magnitudes in the estimates of all equations shown in Table 3. Secondly, primary energy consumption represents the overall energy employed and the energy footprint used. As demonstrated, the estimation results of Equation (9) in Table 3, in addition to human and manufactural capital inputs, primary energy consumption is also a significant factor to aggregate income, when introducing variables of primary energy consumption (E) as an additional input. Thirdly, the estimated signs of human and manufactured capital persist significant and positive influences on income as the variable of primary energy consumption (E) and natural capitals are introduced. Accordingly, both human and manufactured capital are of persistent significant relationship with aggregate output, and these effects are kept huge as in indicated by the estimated magnitudes of their coefficients. Fourthly, regarding the effects of natural capitals to aggregate output, there are several important findings. As demonstrated estimates of Equation (14) in Table 3, total rents of natural resources are insignificant to aggregate income. However, the individual natural capital reveals its significant influence on the total effect on human capital, as that of Equation (16) in Table 3. The results that show insignificant effects from the lump-sum composite of individual natural capital might be due to endowment difference of the natural resources. For the present study, it is not relevant to show the income effects by the total rents of natural resources when the countries under study are of heterogeneous natural resources endowment and extraction. When it comes to the effects of the individual natural capital, as the results shown in Table 3, natural capital of fossil fuels is significant with positive signs, and both forest capital and mineral capital is negatively contributed to aggregate output. They are interesting. Rent of forest is the economic values from harvesting forest products and rent of mineral is the economic values from mineral extractions, according to the data retrieved from the World Bank. The results seem reflect that, in the European Union countries under this study, these two flows out of the endowed natural resources are barely contributing to income, they have, in fact, made negative effects on their own income.
Regarding the effect of natural capital to total carbon dioxide emissions, there are several findings to be evidenced by the estimation results in Table 4. Firstly, the estimate of human capital is positive and manufactural capital is negative on total carbon dioxide emissions, as shown in the Equation (11) in Table 4. However, the positive sign of the estimates of human capital turn to be negative as primary energy consumption is taken into account, and the significance of the negative signs become stronger in its effects on carbon dioxide emissions, as the additional variables of natural capitals are taken into account. Energy is one of the main input factors that drives economic activities. As primary energy consumption is introduced as variable of energy use in the present study, the strong positive effects on carbon dioxide emissions from primary energy consumption are revealed.    Regarding the effects of natural capitals to total carbon dioxide emissions, there are significant findings. Total rent of natural capital is positively related to the total carbon dioxide emissions, as shown in the estimation results of Equation (15) in Table 4. The effects from the individual natural capitals on total carbon dioxide emissions is estimated and the results are shown in Equation (17) in Table 4. The variables of rent of fossil fuels and mineral rents has positive coefficients. Forest rents have positive but insignificant coefficients. Therefore, the extraction of natural resources is of positive relation to the carbon dioxide emissions in the resource extracting countries.

Coefficient (t-Statistics)
Conclusively-taking the extraction of natural capitals and the use of overall energy consumption, say the primary energy consumption, into account-both variables of human and manufactural capital have negative coefficients which indicate their effects on carbon dioxide emissions. That is, it is possible that the reduction of carbon dioxide will be approached through the increasing of the advances in human capital and the progress in the manufactural capital, and through the conservation of energy and reduction of natural resource extraction.

Major Findings and Discussion
Conventional aggregate economic analysis had picked up certain theoretical prejudices as its omission on the roles of the energy and natural capitals. In addition to conventional labor and capital inputs, the conceptual arguments of four and/or five extended categories of capitals are addressed in the literature by expanding the narrow definition of capital in the traditional economics. Labor is extended as human capital as accounting the inevitable contributions of knowledge and skills accumulated through education. Manufactural capital keeps its conventional role as the capital is made ready for commodity production. The energy is consumed to drive the manufacture capital with controversial complementarity and/or substitutability to manufactural capital. The environment is the base of the economic system and provides supporting services and materials to the economic system. The services and materials provided from the environment are taken as granted. They were not attracted enough attentions in the analysis of economic productions and in the role played in the climate changes. This study focuses on investigating the role of capital, including human capital, manufactural capital, and the missing natural capital, for their effects on aggregate income and carbon dioxide emissions.
The empirics in the present research is on 21 European Union countries as an example due to data availability and the wide range of natural capitals endowed and extracted. In this empirical research, the inputs include human capital, manufactured capital, primary energy consumption and several categories of natural capitals.
Capital is referred as any forms of assets/wealth being employed or capable of being employed in the production of more wealth. Some referred capital in terms of the wealth in the physical form of the assets or its money value. Three phases of capitals are usually referred to as (1) the stocks in their backdrop system, such as an economy, a society, or an ecology system, (2) the flows of the service and materials from the stocks (3) the assets in the system. Even though the generalized capitals could be measured by its individual applicable physical term, a monetary commeasured term is usually acquired in an econometric analysis on macroeconomics. What phase of the capitals takes its effects in the macro-economics of climate change? It is the service and material flows from the stock of natural capitals. This analysis does not address the background supporting system of the ecology and the nature environment, though.
Both the endowments of fossil fuels and the stocks of global aquatic and land plants are critical natural resources closely related to the mitigation of climate change.
It is worthwhile to mention that this research does not address all respects of the natural capitals and technology progress, even though the stocks of natural capitals can sequestrate carbon dioxide through mother natural mechanisms of photosynthesis in aquatic and land plants with chlorophyll, and current mitigation policy for climate change is promoted by lowering the concentrations of carbon dioxide in the atmosphere by reducing carbon dioxide emissions and storing extracted atmospheric carbon dioxide through carbon sequestration and new technology development. It is not merely due to availability of the long-term data regarding the stock of the natural capitals, but also due to its feasibility in the macroeconomic climate model.
According to the study findings, human and manufactured capital persistently have positive contributed to aggregate income. However, as the ignored natural capitals are taken into consideration, human and manufactured capital have strong negative relationships with carbon dioxide emissions. Without considering variables of energy and natural capitals, the estimates in a conventional production function might be biased. Variable omissions cause biased policy. This bias is the basis we human beings have done for centuries on our economic policy. Now it is the time for us to go further on and to extend to interdisciplinary integration, at least considering more in terms of the nature, the environment, and the ecology.
In this study, we are on the effects on total carbon emissions and aggregate output. In the literature (the thorny problem), the per capita carbon dioxide emissions is evidenced decreases along the income growth by following an inverted environmental Kuznets curve and this trajectory is equivalent to the decreasing in the rate of carbon intensity, caused by the economic incentives of energy cost saving and economic growth. In addition to the analysis on the potential phenomenon for the per capital dioxide emissions, the present research investigates the total carbon dioxide emissions. In addition, the valuable evidence reveal that sustained income and decreased carbon dioxide emissions can be approached by promote innovations on both human and manufactural capital. The innovation here does not been estimated by a specific variable representing technology progress over time. The innovation implied the implicit enforces that drive the rapid changes of the specific capitals over time, and hence determinate the change of aggregate income and emissions of carbon dioxide.
The idea to discuss the innovation is not directly from an explicit variable of technology progress. The innovation implied the implicit enforces that drive the rapid changes of the capitals over time.
For the sake of this implicit innovation, the progress of human and manufactured capital allows the commitment of a Fix Panel model, as described by Torres-Reyna [62]-the fixed effects will not work well with panel data for which within variation is minimal or for slow changing variables over time.
There is another major finding to guide government policy and the evidence are shown in the results as including rents of natural capitals in the present empirical investigation. As shown as the results of the Equation (14) in Table 3 and that of (15) in Table 4, the total natural capital (ST), accounted by the total sum of the rents of individual capitals reported by the World Bank [19], is a capital that make no significant contribution to the total income of the countries as a whole, but make the badly significant increase in total carbon dioxide emissions in the European Union countries as a whole. It is interesting that extracting natural capital is futile to economic growth and is important for the growth of carbon dioxide.
Let us dive deeper into the details. When the individual natural capital is empirically regressed, the individual natural capital takes their own individual effects on income and carbon dioxide emissions. As the results in Equation (16) in Table 3 show, the economic rents from extracting forest and mineral have negative effects and the rent from energy extraction has a positive effect on income. The positive and negative effects from different individual natural resources would offset each other as evidenced by the insignificance coefficient of total natural capital (ST), as in the abovementioned results of Equation (14) in Table 3. Economic rent of forest capital from extraction has no significant effect on carbon dioxide emissions. However, the rent of energy and mineral has negative effects on carbon dioxide emissions. The effects of the summing rents of these three natural capitals remain positive on carbon dioxide emissions.
Furthermore, overall energy usage in an economy indexed by primary energy consumption is evidenced a critical factor that supports aggregate income and is a main source of carbon dioxide emissions.
Based on these insightful findings, discussions are made to clarify our specious, misunderstandings, or confusing concepts and the related argument.
It is affirmed by the evidence from the present study that well-managed and innovative development of human and manufactured capital can approach the balance of the two major policies of mitigating climate changes and sustain income. The two policies are not always against each other, though. The estimated huge magnitudes indicated that the effects are extremely large.
Capitals and capitalism had been criticized as the cause of climate change and the hinder to effective mitigation of climate change [6]. The empirical evidence of the present research suggest that well innovating along the path of capitalism regarding human and manufactural capital does contribute to income growth and to reductions of carbon dioxide emissions. The carbon dioxide emissions are mainly due to the energy consumption and energy-intensive resource extractions in an economy. How and what kind of the energy employed in a country is the problem. Best policy and effective regulations would be on making their energy use emit less carbon dioxide, especially from fossil fuel energy combustion, in fact. Policy on the purpose to reduce carbon dioxide emissions could be making a real and good effort on adjusting the structure of energy inputs. It is highly possible to reduce the carbon dioxide emissions to create incentives for spontaneous energy cost reduction by economic individuals. Fossil fuels remains its status as dominant energy. The combustion emits carbon dioxide. Energy cost is high in production process. Energy cost paid by the economic individuals create continuous incentives for reducing its use. Technology progress to improve energy efficiency, energy conservation, alternative energy development, and substitution technology are on their way. It will also be helpful to reduce the energy-intensive extracting activities, such as mining fossil fuel energy and minerals.
On the purpose of keeping reported data precise and credible, the World Bank compiled the data of rents of the natural capitals from existing country parallel publications that reach a consensus on methodology and international comparability [4,5,36]. They are the accurate monetary flows from the stocks of resources that have market prices. By using these reliable data (rents of natural capitals), the empirics of the present study would make suggestions on guiding the policy on extracting natural capitals in an economy. The extracting purpose is exactly on the market advantages and its side effects has triggered climate change. It is true that these data reported by the World Bank only partially account for the services form natural assets possessed by a nation. In fact, they exclude huge non-market services that humans rely heavily on [63,64]. It is true that nature and people are inextricably linked in social-ecological systems. The non-market services it provides are under threat from impacts of economic activities [65]. The World Bank reported data of the rents of natural capitals do not cover the intermittent reports in many of the reports in the literature on the non-market values for services of ecological systems to the functioning of the Earth's life-support system that people immerse in. The critical role of the non-marketed services from natural capitals is not in the scope of this study.

Conclusions
The policy pursuit of carbon reduction and economic growth seems to be in contradiction for some countries. The role of capital seems ambiguous. From these perspectives of climate change mitigation policies, this study investigates the effects of generalized capital and energy footprint on income growth and carbon dioxide emissions to clarify the roles of generalized capitals and other driven forces. To reveal the empirics by credible data and sound mathematical technique in this analysis allows substantive understanding of how real-world economies operate. Three main findings and corresponding policy implementations are made according to this empirical analysis.
The first finding is about the effects of energy footprint on carbon dioxide emissions and income. Primary energy consumption measures the overall energy use in an economy and is used to represent energy footprint in this study. Based on the facts that fossil fuels are the predominant energy consumed in most countries, the primary energy consumption persists its positive influence on carbon dioxide emissions in all model specifications. This affirms that energy consumption should be at the core in the carbon reduction policy.
On the contrary, the influence of energy footprint to income does not persist among different model specifications. It seems that there is somewhat likelihood to a disconnection between changes of energy footprint and income growth.
We are generally believed that energy footprint energized the economic activities and emitting carbon dioxide which is the main causes of global climate change. We usually believe that policy to mitigate carbon emissions is harmful to income. Is this always correct? Based on empirical findings from this study, seeking economic growth that does not rely on energy footprint is far more powerful than not generating carbon emissions from the energy footprint. This contains profound policy implications and deserves research for reference to carbon reduction policies. Energy footprint has significant effect on carbon dioxide emissions, and the use of energy resources is critical as policy is aimed to mitigate the climate change.
Secondly, human and manufactural capital has kept their positive contributions to humanity along the long-term economic development in the European Union. These assertions are affirmed by the evidence provided in this study, as the evidence demonstrated in Tables 3 and 4. As the effects of energy use is taken into account by including primary energy consumption in the regression models, human and manufactural capital demonstrates constructive impacts on humanity with (1) increase effects on income and (2) the decrease effects on carbon dioxide emissions. These evidence help to clarify the specious and misunderstanding regarding the traits of capitals and capitalism on the perspective of income growth and economic growth. Human and manufactural capital can make contribution to both aspects of sustaining economic growth and mitigating climate change in terms of reducing carbon dioxide emissions.
By integrating the first and second findings, we can conclude that to balance the climate change mitigation and economic growth, the governments are suggested to make efforts on all perspectives of energy use, rather than putting blame on capitalism.
Thirdly, the rent of natural capital is evidenced not a consistent and obvious contributor to national income. Even though the rent of a natural capital was compiled to represent part of the economic value of that natural capital, it is not feasible to be regarded as a creation of national income. To exploit natural resources would be likely to hurt income. The evidence are demonstrated in Tables 3 and 4. The significance of the variables of natural capitals does not persistent, though. There are negative effects from the rent of forest capital, positive effects from the rent of fossil fuels and the rent of minerals. Negative effects from the rent of forest offset by the positive effects from the rent of fossil fuels and the rent of minerals, as indicated by the insignificant estimates of the variable of the summing rents of natural capitals.
Fourthly, the energy footprint does not persist its significant influence to income as this empirical analysis interpolatively includes the natural capitals in terms of individual variables (shown in Equation (14), Table 3) and lump-sum variable (shown in Equation (16), Table 3), respectively. The effects of energy footprint shift to be insignificant as the energy-intensity activity of mining and extracting natural resources is taken into consideration. The energy footprint does not always make a positive contribution to aggregate income. There is policy implementation. As taking the rent of natural resource exploitation into account, the energy footprint (overall energy consumption) of countries will not always keep its role as a contributor to national income. Contrarily, the significant and positive effects of energy footprint on carbon dioxide emissions are persistent as this study interpolatively introduces variables of the rent of natural resources (shown in Equation (17), Table 4). According to this fourth findings, the influence of energy footprint persists on carbon dioxide emissions and less persists on income, as taking natural capital exploitation into account.
Conclusively, there are important policy implementations. Based on the findings of this study, it is still possible to balance the growth of the economy and reduction of the carbon dioxide emissions. The interaction and the intervention of energy, in fact, is in the centric of the problems of climate change we need to encounter. The government is best to deal with all aspects about energy use. The ideal mitigation policy to reduce carbon dioxide emissions and sustain income is to reduce energy footprint, to turn down fossil fuels energy use and to downward energy-intensive resource extractions. Furthermore, it is inevitable that the ongoing accumulation of the human and the manufactural capital make contribution to income growth and carbon reduction. Their income contribution is already well-regarded in the literature. When it comes to carbon dioxide reduction, it is reasonable to have cost-saving incentive in employing energy. Huge production cost associated with the accelerated use of fossil fuel energy has driven the cost-saving incentives that make continuous progress of human and manufactural capital in reducing carbon dioxide emissions. Through innovative progress on human and manufactural capital, the capitals need to be well-regarded, rather than hostile rejection without good management, especially under the situation that we are concerning long-term benefits of all mankind. In fact, the knowledge and experiences of human beings has been kept its accumulating since the beginning of human history. The invention of manufactured capital had started before the ancient picked a stone to create a handmade tool as a mean to secure the necessities of their life. The innovation and accumulation are keeping going on and cannot be stopped. All we have to do is to reveal the knowledge down to earth.
Furthermore, this article demonstrates the evidence by including the economic rents of the natural capitals compiled by the World Bank in empirical macroeconomic models. The present study makes effort on helping substantive understanding of how real-world economies operate, by making full use of existing data under the best consensus. The analysis does not consider the ecological services regarding amenity and life-support. National accounting only takes part of our human life into account. The data that fully represent the ecological services in the life of human beings are continuous to be left out of the official records in most of the countries in the world. Many countries are making their efforts on expanding current accounting, as so-called green national accounting, to thoroughly cover the genuine output, to well index the life of humanity, and to guide policy makers toward a true wellbeing for humanity. Future availability of long-term continuous data can enhance better understanding about the full supports from our background environments. It is also true that there is difficulty on the way on getting common consensus for the measurement of capital goods. For instance, measurement of manufacture capital has aroused Cambridge capital controversy in the 1950s to the 1970s.