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This paper introduces a novel methodology for estimating carbon total factor productivity based on the Cobb–Douglas production function. The research method introduced in this article expands upon the framework for assessing total factor productivity through the Solow residual method. It unifies the conceptual and methodological aspects of carbon total factor productivity with those of single factor productivity. Utilizing panel data from various provinces between 2010 and 2021, we computed carbon total factor productivity to understand its implications for China in combating global climate change. We demonstrate that (i) we have introduced a method to handle negative coefficients in the Cobb–Douglas production function by incorporating productivity in lieu of input factors during calculations. (ii) Carbon total factor productivity, encapsulating the geometric weighted mean of labor, capital, and carbon productivity, holds notable economic relevance. Further, it serves as an integrative metric comprising carbon productivity intertwined with the mean labor and capital carbon factors. And (iii) the influence of carbon total factor productivity growth on economic progression remains relatively subdued, with escalating labor force growth posing detrimental effects on several provincial economies. Enhancing carbon total factor productivity emerges as an imperative to harmonize robust economic growth with strategic carbon curtailment. Our analytical framework provides nuanced perspectives on productivity determinants, accentuating the thrust towards sustainable evolution amidst climatic challenges. This investigation bears profound significance for policymakers endeavoring to sculpt a carbon-conscious economic paradigm in consonance with global climatic ambitions. [ABSTRACT FROM AUTHOR]

Amid global climate imperatives and intensified economic competition, pivoting from China's conventional growth paradigms to innovative economic catalysts emerges as pivotal for its transformative agenda. Drawing on panel data from 141 principal urban conglomerates spanning 2011–2021, this investigation delves into the intricate nexus between the digital economy and carbon total factor productivity. Our empirical analysis unveils a U-shaped trajectory characterizing the digital economy - carbon total factor productivity interplay, accompanied by a congruent spatial spillover dynamic. While digital economy fortifies environmental governance mechanisms through amplified data and media channels, such regulatory frameworks, albeit efficacious in emission abatement, may inadvertently impede economic vitality, thus attenuating carbon total factor productivity. Progressing from digital economy's foundational phase to its comprehensive deployment, its reverberations on capital productivity manifest in a U-shaped curve, invigorating local carbon total factor productivity while potentially undermining adjacent regions. This digital economy - carbon total factor productivity interrelation is accentuated in advanced, non-resource-reliant metropolises with subdued innovation propensities. This discourse proffers nuanced policy implications for sculpting digital economy trajectories and bolstering carbon total factor productivity in a sustainable context. [Display omitted] • The digital economy demonstrates a U-shaped spatial spillover impact on carbon total factor productivity. • The digital economy influences carbon total factor productivity through governmental environmental regulations. • The digital economy influences carbon total factor productivity through capital productivity. [ABSTRACT FROM AUTHOR]