The population aging is an inevitable result of the transformation of demographic structure. In the first half of the 21st century, China will become the developing country with the highest degree of aging. During the 30 years of strict implementation of Family Planning, new problems have emerged in Chinese population environment, such as the long-term decline in fertility, the aging acceleration and labor shortage in the future. Looking forward to the development of China in the 21st century, population aging will further affect Chinese demographic structure and social development. Therefore, many scholars have discussed the relationship between population aging and social security expenditure. Zhang Tianfang  (2006) established a non-parametric regression model to analyze the dynamic relationship between population aging and the expenditure of social security and employment. The research shows that the population aging is increasing in China, and government finance will face more pressure on the expenditure of social security and employment. Tong Yufen and Liu Guangjun  (2008) took Beijing as an example to establish a binary linear regression equation, which found that the proportion of the expenditure of social security and employment will increase by about 2.029 percentage points if the proportion of aging of population over 65 increases by 1 percentage point. Li Hongxin and Li Wei  (2012) used time series data and took the dependency ratio of the elderly population as control variable to establish regression model, which noted that aging of population increases fiscal expenditure by contributing to an increasing in fiscal expenditure on social security and employment. Liu Luji  (2014) analyzed the relationship between population structure and the financial expenditure of social security with using the elderly population dependency ratio and children dependency ratio as the core explanatory variables. Zhang Pengfei and Su Chang  (2017) used SYS-GMM to study the effect of aging of population and social security expenditure on financial burden. However, this paper uses panel data from 1998 to 2016 to analyze the direct influence of population aging on social security expenditure by establishing entity fixed effect regression model.
2. Theoretical Basis
The general form of the entity fixed effect regression model  for panel data is that:
Null hypothesis for the test of the model is that: : . Under the null hypothesis , we obtain the following:
Among them, RRSS is the sum of the residuals of the mixed regression model, and URSS is the sum of the square of the entity fixed effect regression model. N is the number of sections and T is the number of time points, and K is the number of explanatory variables. Therefore, it is reasonable to set the model as an entity fixed effect model if null hypothesis is rejected at a given significance level.
3. Empirical Analysis
3.1. Data Selection and Description
This paper chooses elderly dependency ratio and social security expenditure as independent variable and dependent variable. The social security expenditure is divided into absolute index and relative index. Absolute index refers to the expenditure of per capita financial social security which excludes the influence of the total population. Relative index refers to the proportion of fiscal social security expenditure in Gross Domestic Product. Absolute index is used in this paper. Because Chinese fiscal expenditure statistical caliber was adjusted in 2007, and
3.2. Unit Root Test
If two mutual independent variables have unit roots, they will appear pseudo-regression. Therefore, in order to avoid the pseudo-regression between Social Security Expenditure and Elderly Dependency Ratio, we must test the stationarity of the two variables, firstly.
From the time sequence diagrams of the two variables, we can see that all the two variables have an obvious upward trend, so the unit root test including individual intercept and trend is used.
Table 1 shows that the two horizontal sequences of (which refers to social security expenditure and is an explained variable) and (which refers to elderly dependency ratio and is an explanatory variable) have at least 4 P-values less than 5% at 5% significant level, indicating that the null hypothesis that there are unit roots in the two horizontal sequences is rejected, so the two horizontal sequences are stable.
3.3. Co-Integration Test
According to the co-integration theory, if there was a long-term co-integration relationship between and , they would have the same order. Because the horizontal sequences of and are stationary, which meet the premise of co-integration.
It is not difficult to see from Table 2 that the Panel rho-Statistic and Group rho-Statistic of Pedroni-test cannot reject the null hypothesis without co-integration relationship, but the other statistics of Pedroni-test reject the null hypothesis, and the ADF statistics of Kao-test rejects the null hypothesis that there is without co-integration, so we can think that and have co-integration relationship (Figure 1 and Figure 2).
Table 1. Unit root test.
Table 2. Co-integration test (test results and test results).
Figure 1. Time series diagrams of .
Figure 2. Time series diagrams of .
3.4. Model Estimation
3.4.1. Likelihood Ratio Test (LR Test)
The null hypothesis of LR-test is that the fixed effect is superfluous, so it is clear from the results of Table 3 that the original hypothesis is rejected at 5% confidence interval, that is, introducing the fixed effect is appropriate.
3.4.2. Model Form
By calculation, we obtain that:
Among, , ; , , . At a given significance level of 5%, the corresponding critical value from the F-distribution table are that: . Because of , being refused, the introduction of entity fixed effect regression model is appropriate. Therefore, we obtain the regression coefficients for the model.
(i = 1_Beijing, 2_Tianjin, ¼ , 31_Xinjiang).
From the above model, we can see that population aging has a positive correlation with social security expenditure. And it is clear that every 1% increase in population aging, social security expenditure will increase by 4.302043%. The cross-sectional effects in Table 4 (the cross-sectional effect data of 31 regions in China show the degree of deviation from the overall mean) reflect the difference between population aging and social security expenditure in different regions of China.
This paper uses static panel model to study the relationship of population aging and social security expenditure in China from 1998 to 2016. The empirical results show that: 1) the population aging has a significant positive impact on social security expenditure, and there is a long-term co-integration relationship between them. 2) Per capita expenditure on social security expenditure will increase by 4.302043 percent for an increase of 1 percent in population aging. 3) a) From the regression results of Table 4, we can see that the cross-section effects of Qinghai, Tibet, Ningxia and Xinjiang are obvious, which lead to the increase of intercept terms of linear equation, reflecting that population aging in the west regions of China has great impact on social security and employment spending because of the low level of economic development and living standards in the
Table 3. Fixed effect test (LR test).
Table 4. Regression results of the model.
western regions; b) The cross-section effects of Jiangsu, Sichuan, Zhejiang and Chongqing are negative, and its absolute values are larger, and as a result, the intercept terms of the linear equation are reduced, reflecting that population aging in the central regions of China has less impact on social security and employment spending because of the better economic development and the higher living standards of the people than the western in these regions.
This work is supported by the National Natural Science Foundation of China (No. 11561056) and Natural Science Foundation of Qinghai (No. 2016-ZJ-914).