*3.1. Descriptive Statistics*

The minimum, maximum, mean, and standard deviation statistics of each variable were computed (Table 2). The mean value of life satisfaction, self-rated health, and depression level among the survey respondents was 3.946, 3.495, and 22.718, respectively. This indicates that the overall life satisfaction, physical health level, and mental health level of the elderly were all high. Further analysis of the CHECS provided for the elderly revealed that the coverage of elderly services was narrow, and some of the services were low in content and accessibility, which could not effectively meet their needs. The statistics from the questionnaire indicate that nearly half of the communities where the elderly resided provide MCS. Other CHECS were rarely provided, with only 14.1% of senior communities providing LCS, 26.2% providing SCS, and 34.6% providing RLS. In terms of lifestyle habits, Chinese older adults have fewer smoking and drinking habits, and sleep well, while nearly 70% of Chinese older adults have annual medical examinations but rarely participate in positive aging behaviors that require high physical mobility, such as exercising. Finally, it is worth noting that most children still live with the elderly and offer them health, financial, and emotional support under the traditional family concept of "filial piety" culture. Family aging is still an important way of aging for the elderly in China.


**Table 2.** Descriptive statistics of variables.

#### *3.2. Overlap Test*

The common support hypothesis requires that the propensity scores of the treatment and control groups have a common range of values. To ensure the matching quality of the sample data, the kernel density function plots were further plotted after deriving the propensity scores to assess the common support domain after matching, as shown in Figures 1–4. The propensity scores of the sample receiving the CHECS and the sample not receiving these services have an extensive range of overlap. Most of the observed values were within the common range of values. Therefore, it can be assumed that the matching effect is ideal, and the common support hypothesis was satisfied.

**Figure 1.** Kernel density function plot (LCS).

**Figure 2.** Kernel density function plot (MCS).

**Figure 3.** Kernel density function plot (SCS).

**Figure 4.** Kernel density function plot (RLS).

#### *3.3. Balance Test*

To ensure the reliability of the propensity score matching results, this work draws on Lian et al.'s work [37] and adopts the mean examination balance hypothesis. Table 3 lists the mean *t*-tests of the matched variables for the four CHECS types. Based on the *t*-values, after matching, no significant systematic difference in the covariates was reported between the control and treatment group, except for the difference in life satisfaction.


**Table 3.** Results of balance test.

Note: \*\*\*, \*\*, and \* indicate that the estimation results are significant at the 1%, 5%, and 10% levels.

#### *3.4. Average Effect Analysis*

This study measured the average treatment effect of four types of CHECS provision on the life satisfaction of the elderly. The estimation results after matching with three different methods (Table 4) were consistent, indicating that the sample data have good robustness. Therefore, the arithmetic mean of the effects was chosen to characterize the effects for the subsequent empirical analysis.

After the counterfactual estimation of PSM, the impact of LCS on Chinese older adults' life satisfaction was insignificant for all three matching methods. MCS significantly affected Chinese older adults' life satisfaction only in the kernel match, with a net effect of 0.046. This indicates that access to MCS contributes to a significant increase in Chinese older adults' life satisfaction of 0.046, after accounting for Chinese older adults' selectivity bias. SCS and RLS significantly affect the life satisfaction of Chinese older adults in all three matches. The ATT for the treatment group of SCS was 0.060, indicating that access to SCS significantly increased life satisfaction by 0.060 when other factors were excluded. The ATT for the treatment group of RLS was 0.080, indicating that access to RLS significantly increased life satisfaction by 0.080 when other factors were excluded. The model results indicated that the three types of CHECS, namely, MCS, SCS, and RLS, could significantly improve the life satisfaction of the elderly, in the order of: RLS (ATT = 0.080) > SCS (ATT = 0.060) > MCS (0.046). LCS had no significant effect on the life satisfaction of Chinese older adults.


**Table 4.** Results of average effect analysis.

Note: \*\*\*, \*\*, and \* indicate that the estimation results are significant at the 1%, 5%, and 10% levels.

#### *3.5. Heterogeneous Effect Analysis*

Due to the different levels of physical health, mental health, and living conditions, the needs of various types of CHECS vary considerably [38]. In the prior study, the ATT of the treatment group was chosen to measure the net effect of CHECS on the life satisfaction of the elderly. However, the ATT can only reflect the mean value of the change in life satisfaction of the elderly who received CHECS but cannot reflect the structural differences in the effect of the elderly sample. Thus, exploring the heterogeneous effect of various types of older adults can enrich the existing literature on the welfare effects of CHECS on Chinese older adults. In this work, the sample was grouped and processed by using the ADL, the depression level, and whether the elderly lived with their families as markers to assess the group differences of the effect of four types of CHECS on their life satisfaction. The comparison results are shown in Table 5.

Heterogeneity tests demonstrate that, for Chinese older adults with restricted ADL, higher levels of depression, and those living on their own, the effects of all four types of CHECS on their life satisfaction were not significant under all three matching methods. For the elderly with unrestricted ADL, all three types of services, except for LCS, significantly increased their life satisfaction under the three matching methods, in the order of RLS (ATT = 0.116) > SCS (ATT = 0.088) > MCS (ATT = 0.064). SCS and RLS significantly improved the life satisfaction of Chinese older adults with low depression levels, with the degree of impact being SCS (ATT = 0.082) > RLS (ATT = 0.062). For Chinese older adults living with their families, all three types of services, except for MCS, significantly increased their life satisfaction, with the degree of impact being RLS (ATT = 0.084) > SCS (ATT = 0.075) > MCS (ATT = 0.071).


**Table 5.** Results of heterogeneous effect analysis.

Note: \*\*\*, \*\*, and \* indicate that the estimates are significant at the 1%, 5%, and 10% levels, with significant *t*-values in parentheses.
