Prediction of annual CO 2 emissions at the country and sector levels, based on a matrix completion optimization problem

In the recent past, annual CO _2 emissions at the international level were examined from various perspectives, motivated by rising concerns about pollution and climate change. Nevertheless, to the best of the authors’ knowledge, the problem of dealing with the potential inaccuracy/missingness of such data at the country and economic sector levels has been overlooked. Thereby, in this article we apply a supervised machine learning technique called Matrix Completion (MC) to predict, for each country in the available database, annual CO _2 emissions data at the sector level, based on past data related to all the sectors, and more recent data related to a subset of sectors. The core idea of MC consists in the formulation of a suitable optimization problem, namely the minimization of a proper trade-off between the approximation error over a set of observed elements of a matrix (training set) and a proxy of the rank of the reconstructed matrix, e.g., its nuclear norm. In the article, we apply MC to the imputation of (artificially) missing elements of country-specific matrices whose elements come from annual CO _2 emission levels related to different sectors, after proper pre-processing at the sector level. Results highlight typically a better performance of the combination of MC with suitably-constructed baseline estimates with respect to the baselines alone. Potential applications of our analysis arise in the prediction of currently missing elements of matrices of annual CO _2 emission levels and in the construction of counterfactuals, useful to estimate the effects of policy changes able to influence the annual CO _2 emission levels of specific sectors in selected countries.