## 3 Models and Data Sources
### Variables in the Spatial Econometric Model  
In our study, when investigating the impact of aging on GTFP, GTFP is the dependent variable in the model, whereas aging is a core independent variable. As per the data availability in the _China Statistical Yearbooks_, we have adopted an aging index widely used in most empirical studies, defined as the ratio of people aged 65 or older to the total population [48]. This index increases as the population ages. According to the World Health Organization (WHO), when the index reaches 7% or higher, a country is called an aging society; 14% or higher, an aged society; and 20% or higher, a super-aged society [49]. Along with the aging index, other exogenous independent variables also need to be controlled for in order to prevent omitted-variable bias. Specifically, we consider five control variables, namely, fiscal decentralization (_FD_), environmental regulation (_ER_), energy structure (_ES_), the proportion of medical expenditure to the total (_Med_), and income (_PerGPP_). **Fiscal decentralization (FD)**. The impacts of FD on GTFP are twofold. First, it may have a negative impact on GTFP because the GDP-oriented tournament urges local governments to pay closer attention to rapid economic growth than to pollutant emissions control and environmental protection, which in turn may inhibit GTPP. In other words, as the extent of FD increases, the higher the fiscal autonomy of local governments, and the lower GTFP. On the other hand, FD can promote GTFP since fiscal decentralization can give greater autonomy to local governments, which in turn can allocate resources as per their specific conditions and thus improve resource use rates to increase GTFP. Since the conclusions are ambiguous, we do not hypothesize the impact of the FD on GTFP. FD is defined as the ratio of fiscal expenditure of local governments to that of the central government. **Environmental regulation (ER)**. The impact of environmental regulation is also twofold, namely negative and positive. Negatively, environmental regulation by the government will increase the production costs of regulated enterprises because they need to adjust the optimal production scale and allocate resources to R & D activities, which may impair GTFP. Positively, appropriate environmental regulation may motivate regulated enterprises to increase innovation capabilities and enhance competitive advantage ([PERSON], 1991), which may ultimately contribute to technological progress and GTFP growth. As with FD, we do not hypothesize the impact of ER on GTFP. Besides, _ER_ is defined as the proportion of pollution discharge expenses to the total. **Energy structure (Energy)**. Coal as the conventional energy is the primary energy source in China. According to the latest statistics, in 2020 it still accounted for 67.6% of the total energy consumption [3]. Since coal combustion is the main source of various pollutants, e.g., SO\({}_{2}\), it is primarily responsible for environmental degradation in China. Notably, as the largest coal consumer in the world [50], China is one of the most polluted countries. China's historically coal-dominated energy consumption structure is blamed for environmental pollution which consequently impairs GTPP growth. That is, the higher the share of coal, the lower the GTPP. Therefore, we hypothesize that energy structure (_Energy_) has a negative impact on GTPP. The variable _Energy_ is defined as the proportion of coal consumption to total consumption. **Medical expenditure (Medical)**. Medical expenditure may exhibit either a positive or a negative impact on GTPP. Specifically, on the one hand, increasing this expenditure not only contributes to the accumulation of health capital, but may also promote GTPP growth, giving it a positive impact. On the other hand, as governments face the ever-growing aging population, they will have to expand fiscal expenditure on healthcare and aging care, which could otherwise have been used for production activities or other fields, e.g., environmental protection.