**3. Methodology**

This section explores some theoretical considerations based on the EKC model to identify the baseline empirical model. The next sub-section identifies the estimation method followed by a discussion on the data sources, control variables, and variables for robustness tests.

### **3.1 Theoretical considerations**

The Environmental Kuznets Curve (EKC) describes the possibility of an inverted *U*-shaped relationship between environmental pollution and economic growth. As the economy progress via an increase in income, pollution is hypothesized to increase until it reaches a certain inflection point where pollution began to decrease [29]. In the early stages of economic development, it is assumed that industrialization would take place and contribute a large percentage towards GDP growth. Industrialization is expected to use large amounts of energy which results in environmental pollution in the form of CO2 emissions. CO2 emission stems from (i) burning of fossil fuels such as burning solid, liquid, gas fuel, or gas flaring, or from the production of cement, (ii) production of electricity and heat production, (iii) liquid fuel consumption for example the use of petroleum-derived fuels, (iv) combustion of fuels from the manufacturing (for example from coke inputs to blast furnaces) and construction sectors, (v) solid fuel consumption from the use of coal, (vi) transport activities such as aviation, domestic navigation, road, rail and pipeline transport, and (vi) use of natural gas. In the agriculture sector, greenhouse gas emissions from livestock, such as cows, rice, wheat, and corn production contribute to pollution. Other forms of pollution include methane which is emitted during the production and transport of coal or natural gas, from livestock such as cows, and the decay of waste in the soil.

As the economy progressed and began wealth accumulation, countries would be able to invest in research and development (R&D) towards the production of machines and mechanisms that could minimize the impact on the environment. Examples include the use of green technology in production. As a result, even as the economy continues to progress, the impact on the environment is minimized. Another reason for the possible decline in pollution is due to both public and private awareness of the negative impact of pollution left unchecked. International organizations such as the United Nations, World Bank, and the International Monetary Funds have made concerted efforts on environmental sustainability such as the use of renewable energy and the promotion of a circular economy. Governments have come together towards embracing green policies and the adoption of greener technologies to reduce CO2 emissions. At a micro level, non-governmental organizations (NGOs) are also propagating reduction in environmental pollution via recycling, upcycling, and more recently, replacing the end-of-life concept with the restoration which leads to changes in business models, operations, systems, use of materials, and reduction in the use of harmful chemicals. In other words, producers are responsible for the whole lifecycle of the products.

In countries where inequality and poverty are prevalent, the poorer segment of the economy are more concerned with their survival, therefore, have less interest in environmental policies or programs [30] unless they can monetize from the policies. For example, via the collection of paper, glass, or tin that could be sold to recycling industries. According to the Median Voter Theory, poorer societies are more concerned with material wellbeing and would be less interested to support environmental related policies [31]. Ridzuan [32] (2019) suggests that society's interest in environmental protection could be downplayed if income inequalities are predominant within the society. On a similar note, Franzen and Meyer [33] and Facchini et al. [34] argued that when income inequality is high, the public is more concerned focused on economic growth and redistribution compared to environmental issues. Consequently, income inequality reduces government expenditures on environmental protection [35]. On the other hand, the richer segment of the society could easily fulfill their daily needs and have excess wealth which could be directed towards the consumption of environmentally friendly products and comply with other environmentally friendly policies.

### **3.2 Estimation method**

The System GMM (S-GMM) is used in this study to examine the impact of inequality and other control variables on environmental pollution. S-GMM overcomes the shortcomings of the standard GMM where biases increase the number of instruments proliferate and weak instrument problems, and the problem of poor finite sample properties in terms of bias and precision in Difference GMM and the problem of lagged levels [36]. S-GMM corrects endogeneity such as in *CO*2 and *GDP* by introducing more instruments to considerably improve efficiency and transforms the instruments to make them uncorrelated (exogeneous) with the fixed effects, permits a certain degree of endogeneity in the other regressors and optimally combines information on cross country variation in levels with that on within-country variation in changes [37].

The baseline empirical model can be described as follows:

$$\text{CO2}\_{it} = \alpha\_1 \text{CO2}\_{it-1} + \beta\_2 \log \text{GDP}\_{it-1} + \beta\_3 \text{GDP}\_{it-1}^2 + \beta\_4 \text{GDP}\_{\mathcal{F}\_{it-1}} \tag{1}$$

$$+ \beta\_5 \text{Dom}\_{\text{Credit}\_{it-1}} + \beta\_6 \text{Trade}\_{it-1} + \beta\_7 \text{Gini}\_{i \text{dip}\_{it-1}} + \rho\_{it} + \varepsilon\_{it} + v\_{it}$$

where *CO*2*it* denotes environmental pollution proxied by CO2 and methane emission for individual *i* in period *t*, *CO*2*<sup>i</sup>*,*t*�1is the lagged of environmental pollution in the previous period and *ρit* þ *εit* þ *vit* represents the error components decomposition of the error term which allows for unobserved heterogeneity (*εit* hereafter). Other

assumption includes *vi*,*<sup>t</sup>* is serially uncorrelated. The control variables include growth of GDP (*gdp\_gr*), trade openness (*trade*), domestic credit (*dom\_credit*), and a measure of inequality (*Gini\_disp*). To empirically examine whether the effect of income inequality on CO2 emission is conditional on GDP, trade, and government environment expenditure, the baseline model is modified to incorporate a multiplicative interaction term of income inequality and the three variables which are the (i) size of the economy and income inequality (*GDP* � *Gini\_disp*), (ii) the impact of trade on income inequality (*Trade* � *Gini\_disp*) and (iii) the interaction of government expenditure on environment protection and income inequality (*GE* � *Gini\_disp*) and (iv) the combined effect of economic growth and financial development on income inequality (*GDP* � *Dom\_credit* � *Gini\_disp*). The interaction models are as follows:

*CO*2*it* <sup>¼</sup> *<sup>α</sup>*1*CO*2*it*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> *log GDPit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*3*GDP*<sup>2</sup> *it*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*4*GDPgrit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*5*DomCreditit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*6*Opennessit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*7*Ginidispit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*<sup>8</sup> *GDP* � *Ginidisp it*�<sup>1</sup> <sup>þ</sup> *<sup>ρ</sup>it* <sup>þ</sup> *<sup>ε</sup>it* <sup>þ</sup> *vit* (2) *CO*2*it* <sup>¼</sup> *<sup>α</sup>*1*CO*2*it*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> *log GDPit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*3*GDP*<sup>2</sup> *it*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*4*GDPgrit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*5*DomCreditit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*6*Opennessit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*7*Ginidispit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*<sup>8</sup> *Trade* � *Ginidisp it*�<sup>1</sup> <sup>þ</sup> *<sup>ρ</sup>it* <sup>þ</sup> *<sup>ε</sup>it* <sup>þ</sup> *vit* (3) *CO*2*it* <sup>¼</sup> *<sup>α</sup>*1*CO*2*it*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> *log GDPit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*3*GDP*<sup>2</sup> *it*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*4*GDPgrit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*5*DomCreditit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*6*Opennessit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*7*Ginidispit*�<sup>1</sup> <sup>þ</sup> *<sup>β</sup>*8ð*GE* �*Ginidisp*Þ *it*�<sup>1</sup> <sup>þ</sup> *<sup>ρ</sup>it* <sup>þ</sup> *<sup>ε</sup>it* <sup>þ</sup> *vit* (4)

#### **3.3 Data**

A panel of unbalanced data from 120 countries was chosen based on the availability of the focal variables which are CO2 and income inequality data. The sample ranges from 1985 to 2019, drawn from various datasets. The sample was further disaggregated according to the level of income to control for the effect of income and to ensure that inferences were made based on samples that belong to some similar criteria which is in this case, the level of income. The segregated sample consists of 42 high-income, 35 upper-middle-income, and 43 lower-middle- and low-income countries. Segregation of the sample allows analysis and comparison of the impact of the different variables on CO2. In addition, more specific results can be obtained based on the characteristics, conditions, and resources of countries with similar income levels. This would allow understanding the nature and degree of association amongst the variables. The sample was segregated into three categories of income which are highincome countries, upper-middle-income countries, and lower-middle- and lowincome countries. The categorization is based on The World Economic Situation and Prospects (WESP), United Nations [38]. The list of countries is listed in Appendix I. Data on CO2 and methane were derived from the WDI, World Bank and Emissions Database for Global Atmospheric Research (EDGAR), European Commission.

Income inequality (*gini\_disp*) is represented by the Gini coefficients derived from the Standardized World Income Inequality Database (SWIID) V9.1 originally by Solt [39, 40]. SWIID is the best available proxy for income inequality since it covers the longest period and the largest number of countries compared to other databases.

SWIID 9.1 provides Gini coefficients for market incomes and net incomes (disposable Gini) which allows for international comparison. For the purpose of this study, only disposable Gini is used since it is an after-tax Gini which is calculated after taking out the effect of taxes and after considering the effect of transfer payments. It should be noted that Gini coefficients are not available for all countries for the stipulated time, hence, regression is based on unbalanced panel data. Alternative measures of income inequality such as wage inequality or ratio inequality, market income (income before taxes and transfers), disposable income (household income after pensions, unemployment insurance, social assistance transfers, and other government cash benefits), post-tax income (gross income minus all direct and indirect taxes) and gross income (market income plus government cash benefits) are available albeit calculated differently. Nevertheless, the range of countries offered by these alternative proxies is limited to a few countries only, making extensive international comparison difficult. Therefore, SWIID is the best available proxy.

The proxy for income is real GDP from the World Development Indicator (WDI) database, World Bank which serves the role to control for the size of the economy and the EKC effects. GDP growth controls for the effect of the level of development where wealthier economies are presumed to have a larger public sector which is bound to affect the design of fiscal policy and redistribution. Wagner's Law stipulates that higher economic development would result in greater redistribution, which subsequently suppresses the problem of income inequality. According to Wagner, as economies developed, more resources are available for redistribution which later, promotes economic growth through higher income and increase aggregate demand [41]. Other control variables include domestic credit to capture financial development and trade openness to represent globalization and the effects of international market integration. Trade openness is defined as total imports plus export as a percentage of GDP. Both data were drawn from the WDI database. The role of government expenditure on the environment is captured by the amount of government expenditure on environment protection as a percentage of total government expenditure. Data is extracted from the Expenditure by Functions of Government (COFOG), Government Finance Statistics, and the International Monetary Fund (IMF).
