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We measure parents’ depressive symptoms using the 10-question version of the Center for Epidemiologic Studies Depression Scale, CES-D 10. The validity of this measure has been established for the elderly Chinese by Boey (1999). Respondents were asked to indicate how frequently they experienced the following ten items during the week before the interview: (1) I was bothered by things that don’t usually bother me; (2) I had trouble keeping my mind on what I was doing; (3) I felt depressed; (4) I felt everything I did was an effort; (5) I felt hopeful about the future; (6) I felt fearful; (7) My sleep was restless; (8) I was happy; (9) I felt lonely; (10) I could not get "going." The answers have four frequency categories, from rarely or none of the time, to some or a little of the time (1-2 days), to occasionally or a moderate amount of the time (3-4 days) and to most or all of the time (5-7 days).

We score the CES-D 10 answers using the metric suggested by Radloff (1977). It assigns values from 0 to 3 to frequencies from rarely to most of the time for negative emotions such as “I felt depressed”. For positive emotions such as “I was happy”, the scoring is reversed assigning 0 to most of the time and 3 to rarely. Summing over the 10 components gives the total score ranging from 0 to 30, where a higher number reflects a higher level of depression. A threshold of 12 has been suggested to indicate the likely presence of clinically significant depression among 60+ Chinese (Cheng & Chan 2005). Results are similar using this alternative outcome, and are thus omitted to save space. A question on life satisfaction was answered on a five-point scale with 1 for “completely satisfied”, 2 for “very satisfied”, 3 for “somewhat satisfied”, 4 for “not very satisfied” and 5 for “not at all satisfied”. The constructed indicator for being satisfied with life is equal to one for ratings below 4.

Given the subjective nature of the CES-D 10 and life satisfaction questions, we first conduct an indirect check on whether one-child parents use different standards when evaluating mental wellbeing. To make it possible to test for reporting heterogeneity, existing surveys often use vignettes, i.e. descriptions of the condition of hypothetical persons (King et al. 2004). The rationale behind it is that, as vignettes represent fixed states, any systematic correlation between respondents’ characteristics and their ratings of the vignettes indicates heterogeneous reporting. While vignettes are not available directly for CES-D 10 or life satisfaction, they are available for self-reported health in the related affect domain in CHARLS baseline. Technical details of the test and results are provided in

Appendix 3.A. In general, we do not find evidence for reporting heterogeneity even though the vignette descriptions covered life satisfaction and many of the CES-D 10 components, and the severity rating – a five-point scale ranging from no problem to extreme problem – is arguably more subjective than the frequency rating used in CES-D 10 questions. This lends support to the use of CES-D 10 and life satisfaction for comparing parents with only one child and those with more children.

Cognitive skills are measured using episodic memory and mental intactness, constructed from questions that are similar to those used in HRS. Specifically, episodic memory is measured by the number of words (0-10) recalled in any order four minutes after they were read to the respondent; mental intactness by the number of correct answers to 12 questions taken from the Telephone Interview of Cognitive Status (TICS) battery. In CHARLS, these 12 questions include naming the date of the survey (month, day, year, and season), the day of the week, serial 7 subtraction from 100 (up to five times), whether the respondent used paper and pencil or other aid for calculation, and the ability to redraw a picture of two overlapping pentagons shown to the respondent.

Figure 3.2 and Figure 3.3 plot for mothers and fathers respectively the CES-D 10 score, episodic memory score, mental intactness score, and the proportion satisfied with life against age and by the number of children (one versus two or more). The two figures show that in general the CES-D 10 score, episodic memory, and mental intactness deteriorate over time, except that fathers’ cognitive skills experience an improvement during early 60s. The pattern in life satisfaction is less clear, except that mothers with two or more children appear to be increasingly satisfied with life over time. For both mothers and fathers and in most age groups, those with only one child have distinctly better outcomes than parents with two or more children.

To explore the mechanisms through which fertility affects parents’ mental wellbeing, we obtain information on three types of parent-child interactions. The first type relates to children’s residence. Traditionally, children have provided old-age support to parents through co-residence or living close by. Such living arrangement remains to be a popular way to care for elderly parents, especially in rural China (Cai et al. 2012). Thus, we construct an indicator for co-residence, which is equal to one if at least one child lives in the same household. Another indicator for having a child living close by is equal to one if at least one child lives in the same village/neighborhood or in another village/neighborhood but within 10 kilometers.15

The second type of parent-child interactions relates to how frequent parents are contacted by non-co-resident child(ren), which cannot directly be inferred from geographical proximity. Parents were asked about how often they saw each non-resident child, and if less frequent than once a week, they were further asked about the frequency they receive phone calls, text messages, mails or emails from that child. Communication with children is an important way through which elderly parents remain connected to the society and emotional intimacy with children can bring much joy and satisfaction. To capture this aspect of parent- child interactions, we combine the information from all children and construct indicators for

parents receiving any form of contact, in-person contact, and non-in-person contact, respectively from any child at least once a month.

The last type of interaction concerns money and in-kind transfers from children. In addition to care-giving and emotional support, financial help is also an important way to improve the quality of life for elderly parents. Moreover, the gesture of making a transfer in itself is considered a sign of filial piety. It may bring happiness and satisfaction even when the amount is offset by that from parents back to children. Therefore, two transfer variables are constructed. The indicator for any transfer is equal to one if any child provided any transfer. The other indicator for net transfer is equal to one if the monetary amount of transfers from children was larger than that from parents back to children.