*2.3. Methodology*

Compared with traditional linear regression methods, the PSM method can effectively overcome the "selection bias" caused by biased estimation and sample "self-selection" [35]. Since PSM does not require prior assumptions about the functional form, parameter constraints, and error term distribution, nor does it require the explanatory variables to be strictly exogenous, it has advantages in addressing the endogeneity of the treatment variables. Therefore, this work adopts this method for model estimation and empirical analysis, which is performed in the following four steps.

In the first step, covariates were selected. Drawing on the relevant literature, the factors affecting the life satisfaction of Chinese older adults and the supply of CHECS were included in the model, namely, personal characteristics, lifestyle habits, physical and mental health levels, and family support status, to ensure that the negligibility assumption was met.

In the second step, the propensity scores were calculated. In this study, we applied the Logit model to compute the propensity score value for the individual to receive CHECS.

In the third step, PSM was performed. (1) The matching method was selected. It is well known that there is no superiority or inferiority in matching methods, but various matching methods have particular measurement biases. Therefore, even when processing the same sample data, different measurement results may be generated. No consensus was reported by the academic community on which matching method should be employed to optimize the results. However, if the results after applying multiple matching methods were similar or consistent, the matching results were robust and the sample validity was good [36]. Therefore, to enhance the reliability of the research findings, k-nearest neighbor matching, radius matching, and kernel matching were used for matching. (2) The balance was tested. If the propensity scores were estimated more accurately, a standardized deviation could be employed to assess whether the matched distribution between the treatment and control groups achieved statistical data balance.

In the fourth step, the average treatment effect was computed. The average treatment impact comprises three categories. The first is the average treatment effect (ATT) of the treatment group, which is the average change in the life satisfaction of the elderly who received the community elderly home care service. The second is the average treatment effect (ATU) of the control group, which is the average change in the life satisfaction of the elderly who did not receive the community elderly home care service. The third is the average treatment effect (ATE) of the total sample, which is the mean of the change in the life satisfaction of the random sample of the elderly. Since this study explores the contribution of community home care services to the life satisfaction of the elderly, focusing on those who received community home care services, ATT is more appropriate for the analysis.
