Our data is drawn from the waves of 2016, 2018 and 2020 of the China Family Panel Studies (CFPS). The CFPS is a nationally representative, large-scale longitudinal survey which was implemented by the Institute of Social Science Survey (ISSS) of Peking University. The CFPS covers 25 provinces (municipalities and autonomous regions) in China, and surveys all family members in the sampled households. It is designed to collect detailed information on sociodemographic characteristics, health status, chronic diseases, family and social relationships and health behaviors. For this study, we focus on adults aged 16 and above. After deleting observations with missing values, the final sample consists of 19,264 observations. Figure 1 provides a flow chart illustrating how the final analytical sample was derived.

Flow chart on how the final analytical sample was derived from the China family panel studies 2016, 2018,2020

Life satisfaction was used to assess caregivers’ subjective wellbeing. Life satisfaction is the commonly used subjective well-being measure and often used and recommended as a suitable overall summary indicator of subjective well-being [33]. In CFPS, respondents were asked: “How satisfied are you with your life?”. There were five responses: “very dissatisfied”, “dissatisfied”, “fair”, “satisfied”, “very satisfied”, and “very satisfied”, which were assigned on an ordinal scale from 1 (very dissatisfied) to 5 (very satisfied).

We used two variables to measure informal caregiving: whether respondents provided informal caregiving and frequency of care. For the first variable, the CFPS asked respondents: “Over the past 6 months, did you take care of your father’s/mother’s household chores or his/her meals?” A binary indicator was given a value of 1 if respondent answered “yes” and 0 if the respondent answered “no.” The second variable was created from the question: “Over the past 6 months, how often did you perform household chores for your father/mother or take care of his/her food and living?” The frequency of care was defined as high frequency of care if the response is “almost every day” and as low frequency of care if the response is “3–4 times a week”, “1–2 times a week”, “2–3 times a month” and “one time a month”.

Based on previous studies [23, 34], we control for a set of socioeconomic, demographic and household characteristics which include age, gender(1 = female, 0 = male), marital status(1 = married, 0 = others), area of residence(1 = urban, 0 = rural), having medical insurance(1 = yes, 0 = no), the education variable included three categories: primary school or less, secondary school, and college or more; working status(1 = working, 0 = not working), log of income per capita, having chronic diseases (1 = yes, 0 = no), smoking(1 = yes, 0 = no), drinking(1 = yes, 0 = no), whether they lived with parents(1 = yes, 0 = no), whether they have children(1 = yes, 0 = no), whether one of the parents is still alive (yes = 1,0 = no) and family size.

We select four variables to examine the channels through which informal caregiving affects caregivers’ subjective wellbeing. First, we employed the depression index developed by Centre for Epidemiological Studies Depression Scale (CES-D) to assess caregivers’ psychological stress. It is constructed from eight questions about respondents’ feelings and perceptions over the past week, such as what extent they felt depressed, everything was an effort, poor quality of sleep, hopeful, lonely, happy, had trouble keeping mind, and could not get “going”. All responses are rated on a three-point scale ranging from 0 (almost none) to 3 (most of all the time). The scores for the eight questions are then totaled and the sum score ranged from 0 to 24, with a higher score indicating more depressive symptoms. Second, we used the logarithm of wage income to measure the effect of informal care on caregivers’ loss of job opportunities. Third, we further used leisure time and sleep time to measure the time cost of caregiving.

Given that subjective wellbeing is measured on categorical scale, ordinary least squares (OLS) may not be appropriate in this case. To account for the nonlinear nature of our dependent variable, we employed the ordered logit model to estimate the impact of informal caregiving on caregivers’ subjective wellbeing, which can be specified as follows:

$$_^=\beta Car_+_\delta +_+_+_, t=1,\cdots ,3;i=1,\cdots ,N.$$

(1)

$$_=k if _<_^\le _ k=1,\cdots ,5$$

(2)

Where,\(_^\) denotes the latent variable of caregivers’ subjective wellbeing, \(_\) refers to the observed subjective wellbeing of the caregivers. \(_\)refers to informal caregiving provided by individual \(i\)at time \(t\). \(_\)represents a set of socioeconomic, demographic, and household variables, \(_\)is unobservable individual fixed effects and \(_\) is year fixed effects. \(_\) is an intercept term, and \(_\) is the random disturbance term. \(_\)are the response thresholds which are assumed to be strictly increasing (\(_<_\) ∀k) and\(_\)=\(-\), \(_\)=\(\), and \(k\)is the response categories for wellbeing, taking values from 1 to 5. \(\beta\)is the coefficient of interest.

If the error term in Eq. (1) is uncorrelated to informal caregiving decision ordered logit model will yield unbiased and consistent estimator. However, informal caregiving decisions may be endogenous. There are some unobservable factors, such as family circumstances and work preferences, which may cause informal caregiving to be related to the error term systematically. Moreover, caregiver’s well-being status may also affect his/her informal caregiving decision. Individuals with subjective well-being are more likely to provide informal caregiving. To address the endogeneity of informal caregiving, we employ fixed-effects model to control for the potential bias.

A common approach is to use fixed effects in linear regression. However, we cannot easily use linear regression procedures for fixed effects in nonlinear panels because the reliance on linear models for the analysis of categorical data can lead to inconsistent and biased effect estimates [35]. To address this issue, we apply the ‘‘blow-up-and-cluster’’ (BUC) estimator developed by Baetschmann et al.Footnote 1 [36, 37], which collapsed the observed outcomes \(_\) into a set of K binary variables \(_^\) with \(_^=1\) if \(_>k\) and then using conditional maximum likelihood estimations for binary outcomes and clustering standard errors on the individual level.

We further employ mixed effects ordered logit model to estimate the impact of informal caregiving on caregivers’ subjective well-being. This model combines fixed effects, which capture relationships at the population level, with random effects, which account for variations within different clusters or groups. Therefore, it provides more accurate estimates by considering both within-subject and between-subject variability. All models are estimated in Stata 18.