Assessing the Effect of Digital Financial Inclusion on Provincial Sustainable Development in China from the Perspective of Synergistic Efficiency of Pollution Reduction and Carbon Abatement Based on DDF Measurement and a Bartik Instrumental Variable (2012–2022)

Under the background of the “dual-carbon” goals and the ecological ecological-civilization-construction strategy, improving the synergistic efficiency of pollution reduction and carbon abatement is a key to promoting green high-quality development. Based on a panel of 30 provincial-level regions in China for 2012–2022, this paper evaluates the impact of digital financial inclusion on the synergistic efficiency of pollution reduction and carbon abatement. First, using a global-frontier directional-distance function (DDF), we characterize the improvement space of “desirable-output expansion—simultaneous contraction of pollution and carbon emissions” under given input constraints, and construct a synergistic efficiency indicator (eff_main). Second, we present a correlation benchmark within a two-way fixed-effects (TWFE) framework and use lead/lag (placebo) tests to probe potential endogeneity; we further construct a Bartik (shift–share) instrumental variable and employ Two-Stage Least Squares (2SLS) to strengthen causal identification. The results show that in TWFE regressions, digital financial inclusion (dif100) is positively and significantly correlated with synergistic efficiency, with a coefficient of 0.113 (i.e., an increase of 100 index points in the digital financial inclusion index is associated with an average increase of 0.113 in eff_main), but a significant lead effect is present, so this result should be interpreted as correlational only; 2SLS estimates indicate a robust positive causal effect of digital financial inclusion on synergistic efficiency, with a baseline coefficient of 0.405, rising to 0.501 under lagged specifications—exhibiting a dynamic feature of “gradual release in subsequent years.” The study suggests that developing digital financial inclusion helps raise regions’ comprehensive green-transition performance and sustainable development capacity; policy implications include accelerating the closing of digital infrastructure gaps, improving green-finance institutions and performance constraints, and guiding funds more effectively toward energy-saving, emission reduction and low-carbon technology areas.