The rapid growth of the digital economy (DE) globally and its potential environmental impact have garnered significant attention. In China, the DE is considered crucial for high-quality economic development, and the government aims to leverage it for a low-carbon transition. Improving carbon total factor productivity (CTFP) is a key aspect of this transition. This paper addresses two major challenges in measuring the impact of DE on CTFP: the lack of a uniform DE definition and the endogeneity issue (reverse causality and measurement error). To overcome these, the paper proposes a novel analytical framework using an endogenous stochastic frontier analysis (SFA) method, providing a more comprehensive and accurate assessment of DE's impact on CTFP.

Existing research on the DE's green development effects is still emerging. While studies have explored DE's impact on economic growth, enterprise efficiency, energy efficiency, and total factor productivity, the focus on its effect on carbon emissions and CTFP is relatively recent. Previous studies have employed different DE indicators (digital finance, internet technology, big data), but they often lack comprehensiveness and fail to fully address the endogeneity issues inherent in assessing the impact on CTFP. The two-step approach (measuring efficiency first, then regressing it on impact factors) often suffers from bias due to the correlation between the non-efficiency term and the regression residual. This paper aims to overcome these limitations by developing a comprehensive DE indicator and utilizing an endogenous SFA method.

This paper employs panel data from 223 Chinese cities between 2004 and 2017. CTFP is measured using a carbon Shephard distance function incorporating capital stock, labor, energy, gross industrial output, and CO2 emissions. The DE development index is constructed using principal component analysis, incorporating four dimensions: digital information base, internet platform, digital technology, and new economic models and industries. The endogenous SFA approach is employed to address the endogeneity between DE and CTFP, accounting for bidirectional causality and the correlation between the non-efficiency term and regression residual. The model uses a second-order Taylor expansion of the carbon Shephard distance function. Robustness checks involve changing instrumental variables, altering the DE indicator construction method, and using a Cobb-Douglas production function. Mechanism analysis utilizes proxy variables for efficiency improvement, green innovation, and environmental regulation. Heterogeneity analyses explore differences based on public environmental awareness, resource abundance, and human capital levels.

The endogenous SFA results show a significant positive impact of DE on CTFP in China. A 10% increase in DE leads to a 0.25% rise in CTFP, controlling for endogeneity. Robustness checks confirm the findings. Mechanism analysis reveals that DE positively influences CTFP through efficiency improvements, green innovation, and enhanced environmental regulation. Heterogeneity analysis reveals that the positive impact of DE on CTFP is stronger in regions with higher public environmental awareness, lower resource abundance, and higher human capital levels. Three scenarios for balanced DE development (province, region, national) show significant CO2 emission reduction potential, with the highest potential under the national scenario (3502.86 million tons).

The findings highlight the significant role of DE in China's low-carbon transition by improving CTFP. The endogenous SFA method is crucial for obtaining unbiased estimates of DE's impact. The mechanism analysis clarifies how DE contributes to CTFP improvement, emphasizing the importance of policy interventions targeting efficiency enhancement, green innovation, and environmental regulation. The heterogeneity analyses underscore the contextual factors influencing DE's effectiveness, with public awareness and resource abundance playing crucial roles. The substantial CO2 emission reduction potential demonstrates the economic and environmental benefits of promoting balanced regional DE development.

This study offers valuable insights into the relationship between DE and low-carbon development in China. The key contribution is the development and application of an endogenous SFA framework to accurately estimate DE's impact on CTFP, accounting for endogeneity. Future research could focus on firm-level analyses to gain deeper insights into the microeconomic mechanisms, exploring the interactions between DE and specific technological innovations within various sectors. The findings advocate for policies promoting DE development, green technology integration, and balanced regional development to accelerate China's low-carbon transition.

The study relies on city-level data, limiting the granularity of the analysis and potentially obscuring firm-level variations. The DE index, though comprehensive, may not capture all aspects of DE development. The reliance on specific proxy variables for mediating mechanisms (efficiency improvement, green innovation, environmental regulation) could influence the results. Further research incorporating more disaggregated data and alternative measures of mediating mechanisms would enhance the study's robustness.