An Application of Differential Equations on Anthropogenic Climate Change

The relationship between Carbon Dioxide (CO₂) emissions, temperature change, and growth in Germany is examined with the use of a system of differential equations and data for the period 1991–2016. Two models are examined: the first considers that growth, measured as the proportionate change in the per capita Gross Domestic Product (GDP) is affected by per capita CO₂ emissions and the level of per capita GDP. Also, the proportionate change in per capita CO₂ emissions is affected by the level of the per capita GDP and the level of per capita CO₂ emissions. The second model considers that growth is affected by the per capita CO₂ emissions, temperature, and the level of per capita GDP. Also, the proportionate change in per capita CO₂ emissions is affected by the level of the per capita GDP and the level of per capita CO₂ emissions. Finally, in this model, the proportionate change in temperature is affected by the level of the per capita GDP and the level of per capita CO₂ emissions. It was found that the signs of the estimated coefficients in the two models are the expected ones.