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Based on the panel data of 31 provinces and municipalities inChinafrom 1998 to 2016, this paper studies the effect of demographic structure on social security expenditure inChinaby using entity fixed effect regression model. The results show that there is a long-term co-integration relationship between population aging and social security expenditure in the demographic structure, and there is a positive correlation between population aging and social security expenditure. And the different cross-sectional effects in 31 regions of China reflect the difference between population aging and social security expenditure in different regions of China.

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 [

The general form of the entity fixed effect regression model [

y i t = δ + λ i + ∑ k = 2 K β k x k i t + μ i t (1)

Null hypothesis for the test of the model is that: H 0 : λ 1 = λ 2 = λ 3 = ⋯ = λ N − 1 = 0 . Under the null hypothesis H 0 , we obtain the following:

F = ( R R S S − U R S S ) / ( N − 1 ) U R S S / ( N T − N − K + 1 ) ~ F ( N − 1 , N ( T − 1 ) − K + 1 ) (2)

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.

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 China liberalized its Two-child policy after 2016, which would certainly have an impact on the expenditure of social security. Therefore, this paper selects the data from 1998 to 2016 for study. The data are derived from China Statistical Yearbook and China Demographic Yearbook. In order to avoid the heteroscedasticity in the process of analysis, the data are on a logarithm analysis and denoted as ln S and ln O , respectively.

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.

According to the co-integration theory, if there was a long-term co-integration relationship between ln S and ln O , they would have the same order. Because the horizontal sequences of ln S and ln O are stationary, which meet the premise of co-integration.

It is not difficult to see from

variables | LLC | Breitung | IPS | Fisher-ADF | Fisher-PP |
---|---|---|---|---|---|

LnS | −9.83496 (0.0000) | 2.73659 (0.9969) | −5.68917 (0.0000) | 149.753 (0.0000) | 169.315 (0.0000) |

LnO | −5.77779 (0.0000) | −5.85274 (0.0000) | −3.70324 (0.0001) | 101.302 (0.0012) | 91.4300 (0.0089) |

Alternative hypothesis: common AR coefs. (within-dimension) | ||||
---|---|---|---|---|

Statistic | Prob. | Weighted Statistic | Prob. | |

Panel v-Statistic | 41.49205 | 0.0000 | 42.04641 | 0.0000 |

Panel rho-Statistic | 0.078105 | 0.5311 | −0.153613 | 0.4390 |

Panel PP-Statistic | −12.57958 | 0.0000 | −12.37828 | 0.0000 |

Panel ADF-Statistic | −3.212892 | 0.0007 | −3.281447 | 0.0005 |

Alternative hypothesis: individual AR coefs. (between-dimension) | ||||

Statistic | Prob. | |||

Group rho-Statistic | 2.336004 | 0.9903 | ||

Group PP-Statistic | −3.545959 | 0.0002 | ||

Group ADF-Statistic | −3.006709 | 0.0013 | ||

ADF (Kao test) | −4.596027 | 0.0000 |

The null hypothesis of LR-test is that the fixed effect is superfluous, so it is clear from the results of

By calculation, we obtain that:

F = ( 720.1091 − 436.8212 ) / 558 436.8212 / 30 = 30.66246 (3)

Among, U R S S = 720.1091 , U R S S = 436.8212 ; N = 31 , T = 19 , K = 1 . At a given significance level of 5%, the corresponding critical value from the F-distribution table are that: F α ( 30 , 558 ) ≈ 1.46 . Because of F > 1.46 , H 0 being refused, the introduction of entity fixed effect regression model is appropriate. Therefore, we obtain the regression coefficients for the model.

ln S = − 4.598746 + 4.302043 ln O + λ i ,

(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

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

Effects Test | Statistic | d.f. | Prob. |
---|---|---|---|

Cross-section F | 12.040844 | (30,557) | 0.0000 |

Period F | 294.427880 | 30 | 0.0000 |

Regions | Effects of cross-section | Regions | Effects of cross-section | Regions | Effects of cross-section |
---|---|---|---|---|---|

1_Beijing | 0.542103 | 12_Anhui | −0.997632 | 23_Sichuan | −1.315523 |

2_Tianjin | −0.164709 | 13_Fujian | −0.494906 | 24_Guizhou | −0.780011 |

3_Hebei | −0.276577 | 14_Jiangxi | −0.282374 | 25_Yunnan | 0.353008 |

4_Shanxi | 0.621482 | 15_Shandong | −1.077571 | 26_Tibet | 1.980996 |

5_Mongolia | 1.074443 | 16_Henan | −0.472158 | 27_Shaanxi | −0.007736 |

6_Liaoning | 0.183299 | 17_Hubei | −0.419379 | 28_Gansu | 0.505121 |

7_Jilin | 0.847504 | 18_Hunan | −0.882014 | 29_Qinghai | 2.223997 |

8_Heilongjiang | 0.933642 | 19_Guangdong | 0.222020 | 30_Ningxia | 1.672924 |

9_Shanghai | −0.753308 | 20_Guangxi | −1.088594 | 31_Xinjiang | 1.497526 |

10_Jiangsu | −1.520621 | 21_Hainan | 0.260937 | ||

11_Zhejiang | −1.273520 | 22_Chongqing | −1.112372 |

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).

Shen, S.C. and Wu, Y. (2018) The Influence of China Demographic Structure on Social Security Expenditure―Based on Panel Data Model. Open Journal of Statistics, 8, 556-561. https://doi.org/10.4236/ojs.2018.83036