The efficiency of sustainable development goals 4 and 8 in China: impact of low fertility

China’s declining birth rate is gradually eroding the demographic dividend, potentially affecting education, employment, and the economy. This study constructs a meta two-stage dynamic Directional Distance Function (DDF) Data Envelopment Analysis (DEA) model under exogenous variable. It considers the birth rate as an exogenous variable to assess the efficiency of 30 Chinese provinces in achieving SDGs 4 and 8. Key findings include: (1) Integrating the birth rate into the analytical framework has enhanced overall efficiency in most provinces, particularly in the central region. The average efficiency across 30 provinces was 0.8, with minimal regional disparities. (2) The birth rate positively influences both SDG 4 and SDG 8, notably boosting SDG 4 efficiency. (3) Efficiency varies by province: 17 exhibit high efficiency in both SDG 4 and SDG 8, one shows low SDG 4 but high SDG 8 efficiency, two have high SDG 4 but low SDG 8 efficiency, and ten are inefficient in both goals. (4) Hebei, Shandong, and Guangdong have significant redundancy in education and social security investments. Hebei, Henan, and Shanxi show considerable deficiency in economic growth and employment, while Xinjiang and Inner Mongolia require further enhancements in energy efficiency.