The global energy system faces unprecedented challenges, with carbon emissions reaching a peak in the last decade. Sustainable low-carbon economic development is crucial, and the digital economy holds significant promise for emissions reduction. However, there's no consensus on its precise impact. The digital revolution, fueled by declining sensor costs, improved data storage, advancements in analytics, and faster data transmission, has increased electricity demand in data centers and networks, globally consuming approximately 2% of total power and projected to increase. Blockchain technology, particularly Bitcoin, also consumes substantial electricity. Previous research often focuses solely on the digital industry's direct emissions, neglecting the broader digital economy, which encompasses both digital industrialization (digital industries) and industrial digitalization (digital technologies in traditional industries). This study addresses this gap by analyzing the carbon impact of the digital economy at a regional level in developing nations, where a "Digital Economy Paradox"—higher digital development correlating with higher emissions—exists. The study aims to create a more comprehensive logical framework and explain this paradox, utilizing granular data from Chinese regions and counties and employing big data analysis to mitigate sample selection bias.

Existing research on the digital economy's carbon impact is inconclusive. Micro-level studies highlight carbon emissions from mobile networks and data centers. Meso-level research identifies a considerable carbon footprint from the digital industry, with predictions of its emissions reaching 1.97% of global emissions by 2030. Macro-level studies present mixed results, some suggesting a limited inhibitory effect or an inverted U-shaped relationship between digital technology and carbon emissions, while others find a promoting effect. The misconception that the digital economy promotes emissions stems from neglecting the distinction between the digital industry and the broader digital economy. While the digital industry contributes significantly to emissions, the digital economy's overall impact, encompassing both digital industrialization and industrial digitalization, remains debated. This study thus hypothesizes that the digital economy can reduce carbon emissions, through low-carbon technological innovation and industrial diversification, while acknowledging that digital industrialization might hinder these efforts.

This study uses data from 2735 counties in China from 2004-2017, comprising 19,766 observations after excluding missing values. Carbon emissions (CO2) are derived from satellite imagery (DMSP/OLS and NPP/VIIRS), employing nighttime light data and an artificial neural network to address data discrepancies. The digital economy (Digital) is measured by the number of digital patents in core digital industries within each region, overcoming limitations of previous text analysis methods based on government work reports which may not accurately reflect actual implementation. Low-carbon technological innovation (Li) is quantified using the IncoPat database, focusing on patents related to alternative energy production, energy conservation, and waste management. Industrial diversification (Div) is measured using a modified Herfindahl-Hirschman index based on employment proportions across industries. Control variables include administrative area (Area), total power of agricultural machinery (Machine), household population (Popu), value added of the primary industry (Str), general public budget expenditure (Budget), and the number of industrial enterprises above a designated size (Industry). A causal mediation model, employing quasi-Bayesian Monte Carlo approximation, is used to analyze the direct and indirect effects of the digital economy on carbon emissions, accounting for the mediating roles of low-carbon technological innovation and industrial diversification. Robustness checks include propensity score matching and using carbon sequestration data as an alternative outcome variable. An endogeneity test, using the number of fixed telephone lines and post offices in 1984 as instrumental variables, addresses potential endogeneity issues. Finally, an interaction term between digital industrialization (Din) and the digital economy is used to investigate the "Digital Economy Paradox."

The results show a significant negative relationship between the digital economy and carbon emissions (-0.123, p<0.01), confirming the direct effect. All control variables are significant. Larger administrative areas, household population, and the number of industrial enterprises above a designated size promote carbon emissions, while the total power of agricultural machinery and government budget expenditure reduce emissions. The causal mediation analysis reveals that the digital economy significantly increases low-carbon technological innovation (0.025, p<0.01) and industrial diversification (0.022, p<0.01), which in turn reduce carbon emissions. The average causal mediation effect (ACME) through low-carbon technological innovation is -0.007, and through industrial diversification is -0.010. Both are statistically significant. Robustness checks, using propensity score matching and an alternative outcome variable (carbon sequestration), confirm the negative effect of the digital economy on carbon emissions. The endogeneity test, using instrumental variables, also supports the findings. Analysis of the "Digital Economy Paradox" reveals that digital industrialization significantly weakens the negative relationship between the digital economy and carbon emissions (0.033, p<0.01), suggesting that the dominance of digital industrialization might offset the overall carbon reduction benefits.

The findings challenge the notion that the digital economy inherently increases carbon emissions. The study demonstrates that considering both digital industrialization and industrial digitalization is crucial. Digital technology can improve resource allocation efficiency and facilitate cross-industry emissions reduction through technology spillovers. The negative relationship between the digital economy and carbon emissions persists even after controlling for various factors and addressing endogeneity concerns. The mediating effects of low-carbon technological innovation and industrial diversification highlight the mechanisms through which the digital economy achieves carbon reduction. The "Digital Economy Paradox" is explained by the counteracting effect of digital industrialization, emphasizing the need for balanced development of both digital industrialization and industrial digitalization.

This study provides robust evidence that the digital economy can reduce carbon emissions through low-carbon technological innovation and industrial diversification. The "Digital Economy Paradox" is explained by the potentially counteracting effect of digital industrialization. Future research should focus on a more granular analysis of specific industries within the digital economy and further explore the long-term impact of digitalization on carbon emissions and sustainable development. Policy implications include promoting balanced digital development, focusing on both digital industrialization and industrial digitalization, and prioritizing energy efficiency measures in digital infrastructure development.

The study focuses on Chinese county-level data, limiting its generalizability to other contexts. The measurement of the digital economy relies on patent data, which might not fully capture all aspects of digital economic activity. While the endogeneity test addresses some potential biases, other unobserved factors might influence the relationship between the digital economy and carbon emissions. Future studies should address these limitations by exploring data from diverse geographical regions and employing more comprehensive indicators of the digital economy.