One of the major and urgent challenges in the global dimension is energy supply for sustainable development, air pollution, and climate change due to the emission of pollutant gases from fossil fuels (e.g, coal, oil, and gas) for use in production. Various goods and services are produced and eventually lead to global warming (Adams, 2006). Studies of greenhouse gas production indicate that in the course of economic development, the emission of gases such as methane and nitrous oxide have played far less of a greenhouse effect over the past 60 years. It also has a longer life span than the other greenhouse gases in the atmosphere. This makes climate change and pollution caused by increased carbon emissions more important than other greenhouse gases (IEA, 2009).

Theoretical framework:

In the Kuznets curve, there is an inverse relationship between environmental degradation and economic growth, meaning that per capita income increases at early growth, then decreases as per capita income reaches a threshold (Jafari Samimi & Mohamadi Khayare., 2012). Many studies have used the Cobb-Douglas production function to analyze the relationship between pollution spread and economic growth (Amri, 2016; Zhixin & Xin, 2011; Saidi & Hammami, 2015). Economic activity generates income and wealth, but neglecting environmental considerations and the excessive use of natural resources and the release of pollutions during economic growth have a negative impact on the environment. Accordingly, it can be argued that the causal link between income level and environmental quality is not necessarily one-way from income to environmental quality and can have a two-way effect (Pigou, 1920).

In this study, we introduce the 3GR model and its components, which illustrate the trilateral relationships between carbon emissions, GDP, and pollution intensity, and explain their dual correlation in terms of growth rate.where  and is equivalent to the value of carbon emissions from GDP and the pollution intensity, respectively.  is annually GDP.  is pollution intensity annually. In addition,  is an unknown function that points to the interactive effect on carbon emissions. In order to directly compare the effect of carbon dioxide emissions, their absolute contribution to the pollution emission is calculated by equations 2, 3 and 4.

Based on Equations 2 to 4, the absolute contribution of GDP, pollution intensity and their interactive effect on carbon emissions is shown in Table 1.

 Since the effect of ED for all developing and less developed countries is over 50%, so is the major factor in the changes in carbon emissions (PE). But in developed countries, the main cause of changes in carbon emissions is the pollution intensity (PI) because it is the most prevalent factor. The interactive effects of GDP and the pollution intensity for these countries range from 1 to 7 percent. Whereas Turkey's interactive share is the lowest among the least developed countries and is closer to the developed countries, but the interactive effect for Iran is close to 7%, which is similar to the least developed countries.

Conclusion and Suggestions:

The results show that based on the 3GR model there is a direct relationship between carbon emission rate and economic growth rate or carbon emission rate and pollution intensity growth rate, while the relationship between pollution intensity growth rate and economic growth rate in selected countries when their equivalent value is constant, is inverse. The value equivalent to the rate of economic growth in developed countries is lower than in other countries. However, for the pollution intensity growth rate this relationship is inverse. The results also show that economic growth factors and pollution intensity in developed countries are approximately equal, but the share of economic growth rate in greenhouse gas emissions in developing and less developed countries is higher than pollution intensity. Also, the interactive effect between economic growth and pollution intensity introduced in the model as an unknown factor (which may be political, cultural, or social) is more common in less developed and developing countries.