Study on the interaction between residents’ expenditures of living system and carbon emission efficiency of production system in Beijing-Tianjin-Hebei urban agglomeration

• Interactions in Beijing, Tianjin and Hebei are investigated respectively. • The interaction of Beijing-Tianjin-Hebei urban agglomeration is investigated. • Fuzzy cognitive map is applied to access the impact degree. • Key sectors are founded in Beijing-Tianjin-Hebei urban agglomeration. To achieve regional synergies that benefit both the economy and the environment, it is crucial to understand not only the interactions between living and production systems within cities, but also those across different cities. In Beijing-Tianjin-Hebei urban agglomeration, the impacts between nine urban residents’ expenditures and seven production sectors’ carbon emission efficiency were calculated using fuzzy cognitive map. Time series data from 2012 to 2021 is used. The results of fuzzy cognitive map showed that in Beijing, the highest positive impact of food expenditure is on housing expenditure with a weight of 0.75. Beijing’s food expenditure has the highest positive influence on Tianjin’s residence expenditure (0.97). Increased food consumption in Beijing can drive demand for agricultural products from Tianjin. Unified environmental standards should be developed across Beijing, Tianjin, and Hebei to achieve the sustainable development goal.