Las acciones y los resultados relevantes obtenidos durante el período comprendido del 01 de enero al 30 de junio de 2012:

We aim to estimate the causal effect of having only one child on parents’ mental wellbeing in later life. Using OLS would yield biased results because both variables are likely correlated with community-level and household-level characteristics that are unobserved or difficult to measure. Previous papers using Chinese data have tried to address this endogeneity problem using the natural occurrence of twins (Rosenzweig & Zhang 2009; Li et al. 2008). However, this strategy requires either a dedicated twins dataset or a very large sample of the general population. Moreover, the benefits (e.g., joy) and costs (e.g., mothers’ forgone labor income, stress) of having twins are likely to be different from having two sequential births.

Other frequently used strategies exploit variations in the implementation of the one-child policy, e.g., exemption of ethnic minorities (Li & Zhang 2007; Li & Zhang 2009), or the one- and-a-half-child policy in rural areas (Qian 2009; Islam & Smyth 2015). However, ethnic minorities comprised only 8% of the total population by 199020 _{and differ in various ways} from Han people. Instruments exploiting the one-and-a-half-child policy were not ideal either because of the use of the rough NBS urban-rural definition, which ignores the substantial heterogeneity within urban and rural regions and raises concerns about the monotonicity assumption. Furthermore, sex of the first child was subject to selection given the widespread availability of ultrasound since the 1980s (Yi et al. 1993), which casts doubt on the validity of instruments derived from it.

We try to improve on existing measures by incorporating more accurate enforcement information and allowing the instrument to reflect different policy impacts on women at different stages of childbearing.21 _{Formally, we first define a binary measure of policy exposure} for the mother from household i in community j at age t as

𝑧!,!,!= 𝕀 𝑂𝐶𝑃!,!= 1 , 𝑡 = 15, 16, … , 40 (3.1)

where 𝑧!,!,!= 1 indicates that the mother from household i was subject to the one-child

restriction at age t, and 𝑧!,!,!= 0 otherwise. For each household, we then obtain the

accumulated years of exposure by mother’s age T, calculated as

𝑍!,!,!= 𝑧!,!,! ! !!!"

, 𝑇 = 15, 16, … , 40 (3.2)

We first test the relevance of these policy exposure measures to having only one child, a condition for their use as instruments. An indicator for having only one children is regressed on each of the 36 binary instruments, 𝑧!,!,!, and the 36 continuous measures, 𝑍!,!,!,

respectively, controlling for the characteristics of the mothers, fathers and the communities (explained after Equation (3.3). Figure 3.1 plots the first-stage F-statistics of our binary and continuous measures separately against mothers’ age. Beyond the age of 21, the F-statistics remain above the rule of thumb of 10 in the test for weak instruments. The binary measure displays, as expected, an increasing impact of policy exposure on fertility during early childbearing years and a decreasing impact during later years. Maximum F-statistic is achieved at age 28 for the binary measure, and a few years later at age 31 for the continuous measure. We choose 𝑍!,!,!" as our preferred instrument for its strength (F-statistics 28.0) and also its

ability to better capture differential policy impacts on women of different ages (compared to a binary instrument).

20 _{Source: http://www.stats.gov.cn/tjsj/tjgb/rkpcgb/qgrkpcgb/200204/t20020404_30320.html} 21 _{Though Wang (2012) also used the accumulated years of policy exposure to account for the}

differential policy impacts on women of different ages, the author did not have the more refined urban-rural classification.

The second condition – the exclusion restriction – requires that the instrument can only affect parents’ mental wellbeing through the induced changes in fertility. This assumption is not directly testable. However, a careful examination in Section 3.3.3 of factors associated with the enforcement of the one-child restriction provided evidence against two most potential alternative pathways – local income level and parents’ childhood health. Furthermore, in addition to controlling for the important predictors of the one-child restriction, we allow for differential time trends by location and Hukou type. This reduces the possibility that our instrument affects parents’ mental wellbeing through its correlation with other social and welfare policies, of which the impact also varies by location and Hukou type, and is linearly correlated with women’s age.

Last, the monotonicity assumption requires that people who are affected by the instrument be affected in the same way. This assumption is likely to hold because there is little reason to suspect that (1) people who had only one child in communities without one-child restriction would have more children in communities with one-child restriction, and (2) mothers would have given birth to more children had they been exposed to the one-child restriction for more years.

Our second-stage model is specified as follows: 𝑌_!= 𝛼 + 𝛽𝑂𝑛𝑒𝐶ℎ𝑖𝑙𝑑!+ 𝛾!𝑋!,! ! + 𝜁!,! !!!"#$,!"# !"#$,!"# !"#" !"# !"#", !"#$%$&$"' + 𝜂!,! !!!"#$ !"#$",!"# !"#$ + 𝜀! (3.3)

where outcome 𝑌!,! includes mothers’ and fathers’ CES-D 10 score (range 0-30) and its 10

components (range 0-3) for their individual interest, episodic memory score (range 0-10), mental intactness score (range 0-12) and satisfaction with life (binary); 𝑂𝑛𝑒𝐶ℎ𝑖𝑙𝑑! is a dummy

for having only one child; 𝑋!,! includes a set of mother characteristics (5-year age categories,

ethnicity, Hukou type, five education levels and dummies for being married and widowed), a set of father characteristics (5-year age categories, ethnicity, Hukou type, and five education levels), household per capita expenditure quintiles, household size; 𝜁!,! is a set of community-

level fixed effects (province, administrative type, village status before 1980, urban status in 2011, and the autonomous region status) and 𝜂!,! allows the time trend to differ between

agricultural and non-agricultural Hukou and between different administrative types of the communities.