Care facilities are the mainstay of social services for the elderly. As the trend of empty nesting among elderly families intensifies due to the aging population, it is becoming difficult for families to take on the responsibility of caring for the elderly on their own, and the elderly need more formal care to be provided by society. The contradiction between the lag in the construction of care facilities and the growth in the social demand for elderly care has been highlighted, and the spatial equality of care facilities is an important means of achieving an optimal allocation of resources for elderly care. In this paper, we use the two-step floating catchment method to measure the spatial accessibility of care facilities from a fine-grained perspective, using big data, including mobile phone signaling data and points of interest. Then, we use the Gini coefficient to analyze the equality of the spatial allocations of different types of urban care facilities. The results of the study show that, first, the spatial equality of care facilities is good in terms of the Gini coefficient, but the overall spatial accessibility of care facilities is at a relatively low level compared to that in developed cities. This means that the layout of Changchun’s care facilities is good, but there is insufficient service capacity. Second, the spatial accessibility of residential care facilities is characterized by a gradual decline, with high levels in the core and low levels in the periphery. Fewer facilities are located in the peripheral areas of the city, and spatial accessibility is at a lower level, a characteristic different from that seen in cities with a higher level of economic development, such as Beijing. Third, the spatial accessibility of community care facilities showed a polycentric, contiguous distribution. The effect of the study scale on the spatial accessibility of community care facilities was more pronounced, with large scales obscuring the high values of the spatial accessibility of community care facilities in peripheral areas. Fourth, Changchun has better overall equality of care facilities, with differences in the different types and areas of care provided. The spatial balance of care facilities in the core area is better than that observed in other regions. In conclusion, this paper underscores the value of big data, such as mobile phone signaling data, in supporting refined urban research. Furthermore, our comprehensive analysis of social care facility equality can inform policy making and spatial planning.

Based on the neoclassical framework, we propose the convergence hypothesis of carbon productivity under sustainable growth and prove the different effects of knowledge spillover and technology diffusion on convergence. The convergence hypothesis is tested using China’s provincial spatial dynamic panel data from 1995 to 2019. The results show that China’s provincial carbon productivity has conditional convergence and club convergence characteristics. The convergence speed of dynamic panel regression estimation is greater than that of cross-sectional regression. The convergence rate of dynamic spatial panel regression estimation is faster depending on the spatial spillover difference between the two technologies. In the early stage, the provincial spatial dependence of China’s carbon productivity is mainly knowledge spillover, and the convergence rate is lower than that of the closed economy. Over the past decade, the spatial spillover, dominated by low-carbon technology diffusion, has become the dominant force. The convergence rate is significantly faster than that of a non-spatial-dependent economy. In addition, the mechanism test found that the development of energy efficiency dominates the spatial transfer of technology, so the overall convergence of carbon productivity in China mainly comes from the apparent convergence of energy efficiency in provinces and cities. Our conclusion provides a new reference for the emission reduction actions of countries worldwide because the spatial knowledge spillover carried by capital flows is not conducive to the pursuit of carbon productivity in less developed regions. On the contrary, the dissemination and diffusion of low-carbon technologies can significantly reduce carbon equivalent input in the production process, accelerating the pursuit of developing countries or regions.