Based on the carbon emission data in the Beijing–Tianjin–Hebei urban agglomeration from 2007 to 2016, this paper used the method of social network analysis (SNA) to investigate the spatial correlation network structure of the carbon emission. Then, by constructing the synergetic abatement effect model, we calculated the synergetic abatement effect in the cities and we empirically examined the influence of the spatial network characteristics on the synergetic abatement effect. The results show that the network density first increased from 0.205 in 2007 to 0.263 in 2014 and then decreased to 0.205 in 2016; the network hierarchy fluctuated around 0.710, and the minimum value of the network efficiency was 0.561, which indicates that the network hierarchy structure is stern and the network has good stability. Beijing and Tianjin are in the center of the carbon emission spatial network and play important “intermediary” and “bridge” roles that can have better control over other carbon emission spatial spillover relations between the cities, thus the spatial network of carbon emissions presents a typical “center–periphery” structure. The synergetic abatement effect increased from −2.449 in 2007 to 0.800 in 2011 and then decreased to −1.653 in 2016; the average synergetic effect was −0.550. This means that the overall synergetic level has a lot of room to grow. The carbon emission spatial network has a significant influence on the synergetic abatement effect, while increasing the network density and the network hierarchy. Decreasing the network efficiency will significantly enhance the synergetic abatement effect.

Environmental efficiency evaluation is an effective way to assess the synergetic development degree between the economy and environment. In order to realize the mechanism of the effects of urban sprawl and industrial agglomeration on environmental efficiency by using the super efficiency Slacks-based Measure (SBM) model with undesirable outputs, this paper firstly calculates the environmental efficiency of the 13 cities in the Beijing–Tianjin–Hebei urban agglomeration from 2006 to 2017. Then, based on the panel data of the 13 cities, we empirically examine the influence of urban sprawl and industrial agglomeration on environmental efficiency by adopting the panel Tobit regression model. The results show that large gaps exist in the degree of the cities’ environmental efficiency in the research period, and only Beijing’s environmental efficiency exhibits full efficiency in the 13 cities, with the overall environmental efficiency of the Beijing–Tianjin–Hebei urban agglomeration presenting a decreasing trend. Additionally, the Tobit regression results indicate that urban sprawl has a significantly negative impact on environmental efficiency, but with the continual improvement of industrial agglomeration, the negative effects of urban sprawl will be partially offset. From the regression results of control variables, economic growth and urbanization developments have an inhibiting effect on the promotion of environmental efficiency. Furthermore, industrial structure optimization and technological innovation are helpful to improve environmental efficiency. The opening-up policy has had a significantly positive impact on environmental efficiency, and the “pollution paradise” hypothesis was untenable in the Beijing–Tianjin–Hebei urban agglomeration.

Energy demand forecasting is the basis for responding to high-quality economic development requirements and targeted adjustments to the Beijing-Tianjin- Hebei energy structure. This paper selects five main factors that affect energy demand, constructs a combined forecasting model of a combination of multi-factor gray neural network and ARIMA-BP neural network, and introduces the idea of chaos optimization on this basis to simulate and analyse data from 2012 to 2016, and predict the energy demand in the Beijing-Tianjin-Hebei region in 2020 and 2025.The results show that: 1. Compared with the CGA-ARIMA-BP model and the CGA-GNN model, the CGA-GNN-ARIMA-BP model has higher prediction accuracy; 2. It is estimated that in 2020 and 2025, the energy demand in the Beijing-Tianjin-Hebei region will reach 493 and 552 million tons of standard coal.

The economic development of the Beijing-Tianjin-Hebei region is extremely uneven. The coordinated development of the economy and resources is a major challenge for achieving sustainable development. This article uses MFA method to describe the metabolic situation of Beijing-Tianjin-Hebei economic-environmental system from 2007 to 2016, and establish Tapir decoupling model to analyze the decoupling state and driving factors of its economic development and resource environment. The results show that in the decoupling state of Beijing-Tianjin-Hebei GDP and environmental pressure I, Beijing and Tianjin are dominated by strong decoupling and weak decoupling (accounting for 93.3% and 83.3%), while Hebei Province has relatively frequent changes.