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.

最近，出于对污染和气候变化日益关注的推动，人们从不同的角度审视了国际层面的年度二氧化碳排放量。然而，据作者所知，处理国家和经济部门层面此类数据潜在不准确/缺失的问题却被忽视了。因此，在本文中，我们应用一种称为矩阵补全 (MC) 的监督机器学习技术来预测可用数据库中每个国家的年度 CO \(_2\)部门层面的排放数据，基于与所有部门相关的过去数据以及与部分部门相关的最新数据。MC 的核心思想在于制定一个合适的优化问题，即最小化矩阵（训练集）的一组观察元素的近似误差与重构的秩的代理之间的适当权衡。矩阵，例如其核范数。在本文中，我们将 MC 应用于对特定国家矩阵的（人为）缺失元素进行插补，该矩阵的元素来自年度 CO \(_2\)在部门层面进行适当的预处理后，与不同部门相关的排放水平。结果表明，相对于单独的基线，MC 与适当构建的基线估计的组合通常具有更好的性能。我们的分析的潜在应用在于预测年度 CO \(_2\)排放水平矩阵中当前缺失的元素以及构建反事实，有助于估计能够影响年度 CO \(_2\)的政策变化的影响)选定国家特定部门的排放水平。