Modelling global fossil CO2 emissions with a lognormal distribution

Carbon dioxide emissions have emerged as a critical issue with a profound impact on the environment and the global economy. The steady increase in atmospheric CO${}_2$ levels has become a major contributor to climate change and its associated catastrophic effects. A global effort is needed to tackle this pressing challenge, requiring a deep understanding of emissions patterns and trends. This paper focuses on identifying the underlying distribution of CO${}_2$ emissions analysing the hypothesis that the fossil CO${}_2$ emissions data, at the country level, can be described by a 2-parameter statistical model for the whole range of the distribution (all world countries). We consider that modelling with a simple distribution can be particularly useful in understanding CO${}_2$ emissions and we are looking to make our findings more accessible to policymakers. We utilize data from four databases and analyse six candidate distributions (exponential, Fisk, gamma, lognormal, Lomax, Weibull). Our findings highlight the adequacy of the lognormal distribution in characterizing emissions across all countries and years studied. A comprehensive analysis of Gibrat’s Law from 1970 to 2021 is also presented, employing a rolling window approach for the short, medium, and long term. Our findings reveal that Gibrat’s Law appears to be a short-term phenomenon for original CO${}_2$ emissions, but not for per capita emissions, aligning with conclusions from previous research. Finally, we employ the lognormal model to predict emission parameters for the coming years and propose two policies for reducing total fossil CO${}_2$ emissions.