## 4 Empirical Results  
### Spatial Distribution of the Aging Index  
Before quantifying the impact of aging on GTPP, it is of great practical significance to exhibit the aging index of each province in maps. We apply a geo-visualization technique to map the spatial distribution of population aging in 2002, 2006, 2012, and 2018, as shown in Figure 1.  
From a spatiotemporal perspective, the aging index of all provinces shows gradually increasing trends from 2002 to 2018. At the very beginning of the sample period, provinces with a high aging index are mainly located in the eastern coastal region, specifically, Beijing, Tianjin, Jiangsu, Shanghai, and Zhejiang. Notably, the Yangtze River Delta region has a high aging index. Provinces with a medium aging index are mostly concentrated in southwestern (e.g., Sichuan and Guangxi) and central China (e.g., Hubei and Hunan). The northeastern provinces (e.g., Inner Mongolia, Gansu, Ningxia, Xinjiang, and Qinghai) and two northeastern provinces (Heilongjiang and Jilin) have low aging indexes characterized by low economic levels. In contrast, we found that two economically developed eastern provinces, namely Guangdong and Fujian, have relatively low aging indexes in 2002. One possible interpretation is that, in those two provinces, people followed the tradition of high birth preferences, making the aging index lower than those of other eastern regions [51; 52]. Gradually, the high aging index indicates a dispersed trend from east to west. Although we observed some differences in the growth rates of the aging index, most provinces are indeed facing a serious population aging issue. From 2002 to 2006, the eastern region witnessed rapid growth. However, the index slows from 2006 to 2012. By 2018, population aging in most eastern provinces is prominent. In the meantime, the aging index for the middle provinces continues rising from 2002 to 2018. Importantly, two western provinces (Sichuan and Chongqing) and three northeastern provinces (Heilongjiang, Jilin, and Liaoning) experienced rapid aging rates over the sample period and are now considered to be aged provinces because of the out-migration of the labor force. Young people have migrated from the five provinces to the economically advantageous eastern region for work opportunities and higher salaries; this in turn has aggravated population aging. However, the aging process in other provinces, such as Xinjiang and Qinghai, is relatively slow. Attention should also be paid to Guangdong, an economically developed eastern province. The aging index in 2018 is 8.26%, much lower than the age of Guangdong, and the higher salaries. Figure 1: Spatial distribution of population aging in 2002, 2006, 2012, and 2018.  
than that of other eastern provinces, indicating an optimal young population structure. In addition to strong birth preferences, Guangzhou has attracted a significant number of the young labor force who wish to settle down; this further optimizes the population structure and lowers population aging. We surmise that this particularity accounts for the continued rapid economic growth in Guangzhou. The final study period of 2018 shows that all 30 provinces have become aged: the aging index surpasses 7%. However, to better display the changes in the growth rates of the aging index, we calculated the differences in the aging index between 2002 to 2018; the spatial distribution is shown in Figure 2.  
In Figure 2 we observe that, with the exception of Beijing and Tianjin, provinces with the slowest aging rates are situated in the southeastern region. The reason is twofold. First, in 2002 Beijing and Tianjin provinces already have a relatively high aging index. Second, a large influx of younger migrants tends to optimize demographic structures and slow aging rates. Similarly, three western provinces, Xinjiang, Yunnan, and Guangxi, have the lowest aging rates in 2002 due to high birth rates.