## Abstract

In this study, we consider household decision-making on living arrangements and maternal labor supply in extended families with young children. In such a context, decision-making is driven by the concerns that the companionship of children is a household public good and that family members share childcare and related domestic duties. The incentive to share children’s companionship is affected by son preference, whereas the economic motive of labor division hinges on the potential wage rate of the mother. Both channels play important roles in households with mothers whose wage rates are high, while sharing the companionship of (grand) sons is the main driving force in households with mothers whose wage rates are low. Using China Health and Nutrition Survey (CHNS) data, we find that among less-educated mothers, the incidence of a family coresiding with the paternal grandmother is at least 8.6 percentage points higher if the firstborn is a boy. At the same time, maternal labor supply increases by 2.9 days per month. By contrast, for educated mothers, the propensity for coresidence is higher, the working hours are longer, and the impact of the child’s sex is not significant. Our study not only provides a better understanding of the demographic and economic factors determining coresidence and intrahousehold time allocations but also lends empirical support to policies aiming to increase female labor supply and improve the well-being of girls.

## Introduction

Women contribute a large fraction of aggregate labor hours, earnings, and labor force participation in most countries. However, the aggregated female labor supply is elastic and fluctuating compared with men’s. For example, China’s population census data show that between 1990 and 2010, the labor force participation rate for women at prime working ages decreased by 8 percentage points, which is in sharp contrast to the 2 percentage point decline for men (Shen et al. 2016). A better understanding of household arrangements regarding women’s labor supply is useful for policy-makers aiming to increase labor force participation and improve economic growth, especially under the pressure of an aging population.

Much of the empirical work on households’ decision-making process concerning female labor supply has found that this arrangement hinges on the presence of a grandmother who assumes responsibility of childcare and domestic duties (Chun et al. 2009; Compton and Pollak 2014; Ogawa and Ermisch 1996; Pagani and Marenzi 2008). In China, grandparents are the dominant alternative to maternal labor market withdrawal (Chen et al. 2011; Cook and Dong 2011; Shen et al. 2016).1 Different from these studies, which stopped at documenting the correlation or estimating the unidirectional causal effect of coresidence on maternal labor supply, we go a step further to build a more general analysis framework and investigate how economic and demographic factors jointly determine living arrangements and maternal labor supply.

In fact, in an extended family with young children, the joint decisions on coresidence and time allocations are driven by the concerns that the companionship of children is a household public good and that childcare and related chores are domestic duties divided among family members. In the public good dimension, if son preference exists, grandparents derive higher utility from grandsons than granddaughters. Therefore, a boy—along with his parents—is more likely to coreside with the grandparents and presumably receives their help with domestic duties. On the dimension of labor division, under the assumption of large wage gaps between generations, mothers’ potential earnings motivate the grandparents’ auxiliaries in the domestic realm and coresidence. We formalize these two possible incentives in a simple model.

An important feature of this framework is that the economic incentive for labor division is rather weak among women who are low-wage earners: that is, women with low opportunity costs of missing work. In other words, the coresidence decision is mainly driven by sharing children’s companionship and therefore is closely tied to the child’s sex in instances of son preference. By contrast, for women who are high-wage earners, the economic incentive of labor division assumes a strong motivation of coresidence and time transfers from the grandmother. As a result, the impact of son preference will seem weakened. This interesting implication—namely, that economic incentives can undo gender norms in instances of son preference—speaks to the idea that gender patterns can result from or at least be affected by economic motives (Bursztyn et al. 2017; England 2010; Kazianga and Wahhaj 2013).

In light of this simple model, our empirical analysis compares the likelihood of coresidence across different child genders and different levels of maternal schooling, which we use as a proxy for potential labor market wages. The analysis uses China Health and Nutrition Survey (CHNS) data. In the household module of the CHNS, married women under age 52 were asked about their birth history and intergenerational linkages to their parents and in-laws, including living arrangements. To estimate the effect of child gender, our analysis focuses on families with preschool-aged firstborn children because prior research has found that the sex of the firstborn child is arguably exogenous (Ebenstein 2010; Li 2007; Li et al. 2005; Sun and Zhao 2016).2

We find that among mothers with potentially low wage rates—that is, mothers with only a primary school education or no education—those with a firstborn boy are 8.6 percentage points more likely than those with a firstborn girl to live with their mother-in-law during the child’s preschool years. At the same time, among these less-educated mothers, those with a male (vs. female) firstborn spend 2.9 more days per month on paid work and significantly less time on family chores, such as cooking food and washing and ironing clothes. We find no evidence of a reduction in maternal childcare if the preschool child is a boy, possibly because the labor of the mother and grandmother in terms of feeding, washing, and supervising children is not fully substitutable.3 Consistent with the implications of economic incentives weakening gender norms, we find that among educated women, who generally earn higher wages, the impact of child sex on coresidence almost disappears.

The remainder of the article is organized as follows. We first provide background information on household divisions and childcare arrangements and the rising intergenerational income gap in China. We then provide a theoretical framework and derive testable predictions. We start empirical analysis by presenting summary statistics and graphical evidence. We then describe reduced-form specifications, report empirical results, and provide interpretations. In the last section, we offer concluding remarks.

## Family Division, Childcare Arrangements, and the “Leaning in” of Grandparents

Extended families dominate Chinese society. Family and kinship ties are guided by a strong patriarchal and patrilocal tradition. Sons are regarded as permanent members of the family line, while daughters leave their natal family behind and move to live with their husbands’ families at the time of marriage.4 Using CHNS data, Table A1 in the online appendix summarizes the factors behind increases in household size. Most of these increases occur when brides move in with their in-laws. According to Lang (1946), the extended family is generally composed of parents, their unmarried children, and one or more married sons with their wives and children.

The extended family later splits, in a process referred to as family division, which is generally defined as one married son and his wife and children moving out from the parents’ house when the extended family has multiple married sons (Cohen 1992).5 Several studies have found that economic factors in large part determine when adult children move out of their parents’ house (Kahn et al. 2013; Manacorda and Moretti 2006), and also that demographic factors and social norms play important roles (Aquilino 1990; Zhang 2019).6

Figure 1 depicts the proportion of coresidence against the age of the firstborn child in China. The ratio of coresidence has been declining, a finding consistent with the patrilocal tradition that women move to their in-laws’ house after getting married and later live in their own home. The greatest drop-off in the coresidence ratio is during the period when the firstborn child is aged 0–6, when the proportion of coresidence declines from .75 to .42. China’s Law of Compulsory Education stipulates school entrance at age 6. Childcare by household members is most important before the child attains school age, and the intensiveness of childcare demand declines with the child’s age.

Table 1 presents the percentage of each living arrangement across the age of the firstborn child. If we compare households in which the firstborn child is below school age with households where the firstborn child is aged 6–12, the ratio of coresiding with the paternal grandmother drops from 50.4 to 30.03 percentage points, and the ratio of living in an adjacent dwelling or the same courtyard, in another house in the same village or community, or in another village or community in the same county or city increases by 11.94, 6.51, and 3.86 percentage points, respectively. By contrast, only a small portion of children live with their maternal grandmothers, and the ratio of coresidence does not change with the child’s age. This is not surprising considering the patrilocal tradition.

The lack of formal institutions providing domestic services, including childcare, in China is well documented (Jacka 1997; Kilburn and Datar 2002). Moreover, the scarce facilities are targeted more toward toddlers and children than infants. In our sample, more than 60 % of the women had never used any kind of childcare service provided by a nonhousehold member. Paternal grandmothers play important roles in helping with childcare and other family chores. Figure 2 provides direct evidence of the time paternal grandmothers contribute to domestic activities. According to Fig. 2, a coresiding paternal grandmother spends an average of 10.5 hours per week on childcare, 19.4 minutes per day cleaning the house, 30.4 minutes cooking, and 53.3 minutes washing and ironing clothes.

Paternal grandmothers’ role in assisting domestic activities gains much more importance in the context of China’s rapid economic growth between 1978 and 2012. Li and Ding (2003) and Zhang et al. (2005) indicated that the rate of private returns to education increased from less than 2 % in the early 1990s to around 10 % at the beginning of the new century. This has led to a wider income gap between workers with different education levels.

The stock of human capital shows a sharp gradient across generations (Cai 2015). Among the working-age population in China, the education level gets lower with age. For instance, people aged 20 have nine years of education, on average, while those aged 60 have only six. Their higher level of education enables younger generations to benefit more from China’s rapid economic growth.

Considering the big wage gap between generations, grandparents’ decision to help raise their grandchildren makes clear economic sense, and the “leaning in” observed among grandparents is documented by researchers (Hermalin et al. 1998; Maurer-Fazio et al. 2011; Silverstein and Cong 2013) and reported by many journalists.7

## Model

Assume that the extended family is composed of a preschool child, a mother, and a grandmother. Suppose the wages for the mother and the grandmother in family i are $wiP$ and $wiG$, respectively. In the context of China’s fast economic growth, without loss of generality, we assume that $wiG=0$ to simplify our analysis. To ensure a positive consumption for the grandmother, we assume that she has unearned income y > 0. Both parents and grandparents have a time endowment of T hours.

Suppose the utility function of the parent (P) is
$UPxiPzi=xiP+zi,$

where xi is private consumption, and zi is the child’s quality.

The utility of the grandparent (G) is
$UGxiGsi=xiG+siifCxiGifNC.$

Assume that the grandparent derives utility si from a child’s companionship only when coresiding (C) with the child and drives no utility if not coresiding (NC). To sharpen the idea of the model, we incorporate the grandparent’s son preference by assuming that the grandparent cares only about the sex of the child: that is, si is 1 if the child is a boy and 0 if the child is a girl.

A child’s quality zi is produced by the time input of mother (tP) and grandmother (tG), and maternal time is partially substitutable by the grandmother’s time: that is, the effective childcare input is $ti=tiP+βtiG$, 0 < β < 1. Specifically, the production function of zi is given by
$zi=ftiPtiG=−∞iftiP+βtiGt¯,$

where ρ(ρ ≠ wi) is the marginal product of time input, which is a constant for simplicity. This production function assumes lower and upper bounds of time input, respectively. That is, (1) raising a child requires a minimal effective input of t, and (2) any more input beyond$t¯$ cannot further increase the child’s quality.

Regarding maternal time spent on domestic activities, the mother involves herself in child-rearing and family chores. We assume that βT < t, implying that a minimum amount of maternal time (t – βT) is required in child-rearing—for example, breastfeeding. By contrast, we suppose that running a household requires d hours on chores, which can all be conducted by the grandmother. Let $t¯+d, implying that if not at a job outside the home, the mother is able to provide all family chores.

If the mother and grandmother live separately (tG = 0), the grandmother gets utility y, and the mother solves the following problem:

$maxtiP,xiPxiP+ftiP0NCs.t.xiP=T−d−tiPwi.$

NC represents noncoresidence. The optimal maternal time on childcare is
$ti,NCP=t¯ifwi<ρt_ifwi>ρ.$

Then consider the scenario of coresidence (C). Assume that there exists a disutility εi for family i due to the loss of privacy, and so forth. εi is a standard normal distribution with cumulative distribution function Φ(ε). The joint family solves

$maxxiP,tiP,diP,xiG,tiGxiP+ftiPtiG+xiG+si−εiCs.t.xiP+xiG=T−diP−tiPwi+ytiG+d−diP=T,$
where $diP$ is the mother’s time on chores. We then derive
$di,CP=0ti,CP={t¯−βT−difwi<ρt_−βT−difwi>ρ.$

See all the proofs to derive ($di,CP$, $ti,CP$) in the online appendix.

### Lemma

All else equal, upon coresidence, the maternal labor supply increases by d + β(Td) compared with noncoresidence.

The intuition of the lemma is as follows. Because the grandmother’s and mother’s time are fully substitutable with regard to family chores and because the grandmother is less productive in childcare, upon coresidence, the grandmother will then assume all the family chores (d) and spend the rest of her time (Td) on childcare. Correspondingly, compared with separate living, the maternal labor supply will increase by d + β(Td), where β(Td) is the effective time input on childcare by the grandmother.

Denote the sum of the mother and grandmother’s utility upon noncoresidence as Vi,NC(wi) and that upon coresidence as Vi,C(wi, si) − εi. The household members compare the two utilities, and coreside if
$εi<Δi≝Vi,Cwisi−Vi,NCwi,$
where Δi is the surplus from coresidence. In the online appendix, we show that
$Δi=d+βT–dwi+si.$

The first term, d + β(Td) wi, represents the surplus from labor specialization between the mother and grandmother, which is the increase in mother’s wage income. The second term, si, represents the surplus from sharing the companionship of the child.

Analyzing the effect of wi and si on the likelihood of coresidence, denoted as ψ(wi, si) = Φ[(d + β(Td))wi + si], leads to the following propositions. (Find all the proofs of propositions and the lemma in the online appendix.)

### Proposition 1

All else equal, coresidence is more likely when the child is a boy.

### Proposition 2

All else equal, coresidence is more likely when the mother’s wage is greater.

### Proposition 3

When the child is a boy, as the mother’s wages increase, the probability of coresidence does not increase as much as when the child is a girl.

Proposition 3 implies a greater effect of the child sex on coresidence for low-wage mothers. In our setup, the benefit from labor specialization ([d + β(Td)]wi) is smaller for those with lower maternal wage; hence, the child being a boy plays a more important role in enabling the total surplus to jump over the hurdle of coresidence. Together with the lemma, Proposition 3 also implies greater effects of the sex of the child on maternal labor supply for low-wage mothers.

## Data and Graphical Evidence

### Data Descriptions

The analyses use CHNS data. Using a random cluster process, the CHNS draws a sample of approximately 4,400 households with a total of 26,000 individuals in nine provinces. Using a fixed frame, the survey has been conducted every three to four years since 1989.8 We use data from all waves except for 1989, in which key variables are unavailable.

In the CHNS’s household frame, married women under age 52 were asked about their birth history and intergenerational linkages. These linkages include living arrangements, defined by the location of the parents’ and parents-in-law’s dwellings relative to that of the married women, and the basic demographics of the parents and in-laws. This detailed information on intergenerational linkages is important, considering that household members in most panel data do not necessarily live jointly.

Survey data on married women can then be linked to information on how they allocate their time, including for jobs on the market, childcare, and household chores (such as preparing and cooking food, washing and ironing clothes, and housecleaning). The employment module includes both labor supply and the wage rate. However, in the CHNS adult survey, 58 % of the women in rural areas are self-employed, and wage rate is thus unavailable. Therefore, we use education as a predictor of wage.

### Mean Comparison and Graphical Evidence

In line with prior literature (Ebenstein 2010; Li 2007; Li et al. 2005; Sun and Zhao 2016), this study considers the sex of the firstborn child as exogenous. The sample is confined to women whose firstborn child is below school age.

Figure 3 presents the structure of living arrangements against that of women’s education levels by the sex of their firstborn. For the less-educated women (the bars to the left), a firstborn son predicts a higher propensity of coresidence. By contrast, for educated women (the bars to the right), no such gender difference is exhibited.9

Figure 4 shows maternal labor supply by gender and by schooling: less-educated women work more if they have firstborn sons, but the work levels of educated women do not vary much by their firstborn’s gender. Figs. 3 and 4 are consistent with the model propositions.

To see the significance levels of the mean comparisons, we conduct a t test on the likelihood of coresidence, maternal labor supply (days per month), and time spent on different family chores. Columns 1 and 4 of Table 2 show the combined mean of coresidency status or maternal time use by maternal education levels. Columns 2, 3, 5, and 6 show the mean comparison between the sex of the child within the same maternal education set.

As shown in Table 2, columns 2 and 3, among those with only primary education or no education, mothers with firstborn sons are 10.6 percentage points more likely to coreside with the paternal grandmother than mothers with firstborn daughters. The difference is significant at the 1 % level. At the same time, among less-educated mothers, those with firstborn sons work 3.2 more days per month on the job and spend significantly less time on family chores than those with firstborn daughters. The difference in time use is significant at least at the 10 % level. Columns 5 and 6 show that the differences according to the sex of the child are mitigated as maternal education increases.

## Regression Evidence and Interpretations

### Living Arrangements

The main regression analysis uses the sample of households in which the firstborn child is below school age. We focus on the firstborn because its sex is arguably exogenous. Dahl and Morretti (2008) used the firstborn sex in a reduced-form specification to detect the demand for sons, using data from the United States. Li (2007), Li et al. (2005), Ebenstein (2010), and Sun and Zhao (2016) examined China’s population census data and found that the sex of the firstborn is quite random.

The specification is
$coresidei=α+FBSi·β1+SCHi·β2+FBSi×SCHi·β3+Xiδ+λp+τt+εi.$
1

In Eq. (1), coresidei is a dummy variable indicating whether mother i and the paternal grandmother live jointly. FBSi is a dummy indicator of whether mother i’s firstborn child is a boy. SCHi is a dummy indicator of whether mother i finishes middle school education, λp is the provincial fixed effect, and τt is the calendar-year fixed effect. Xi includes the woman’s age and age squared to control the life cycle pattern of coresidence. We also include covariates reflecting matching quality, which we discuss in sensitivity checks. The standard errors are clustered at the province level and adjusted using the Moulton factor.10

The coefficient of interest, β1, captures the gender difference in coresidence for households with less-educated mothers. β2 reflects the difference in coresidence between mothers with different education levels if the firstborn is a girl. The effect of the mother’s opportunity cost of missing work is likely to be absorbed in β2. β3 reflects the mitigation of child gender disparity by maternal education. Thus, β3 is expected to be negative.

Using the sample in which the firstborn is below school age, columns 1 and 2 of Table 3 report the gender difference in coresidence among households. Column 1 presents the estimands, controlling for calendar-year fixed effects and provincial fixed effects. Column 2 further controls for parental age and the father’s education level.11 Compared with the probit model in panel B, the linear probability model in columns 1 and 2 of panel A shows a more conservative estimand: among less-educated mothers, a firstborn son leads to an 8.6 percentage point increase in the likelihood of coresidence, and the difference is significant at the 5 % level.

Using multinomial logit as an alternative model, we analyze multiple living arrangements. Because very few women live in a different village than their in-laws, we use women living in the same village but a different neighborhood as the reference group and examine the relative occurrence of coresidence and of living in an adjacent dwelling or the same courtyard. In Table A2 of the online appendix, column 1 reports the ratio of the probability of choosing coresidence over the probability of choosing the baseline category, and column 2 reports the z score. The pattern of results is very similar to that presented in Table 3. Columns 3 and 4 of Table A2 show that the risk of living in an adjacent dwelling relative to the base group is not affected by the sex of the child or maternal education. This is consistent with the conjecture that economic connections are most intensive among coresiding members and weaken after the married son moves out from the parents’ house.12

How differences in coresidence align with differences in the sex of firstborn grandchildren should not be easily attributed to a preference for sons (and grandsons) without considering other channels. For example, the sex of the firstborn could affect family size. Jensen (2003) analyzed the son-preferring fertility-stopping rules in India and found that girls, on average, have more siblings than boys. In China, during the period of our sample, the family planning policy for rural residents allowed only one child if the firstborn was a boy but allowed for a second birth when the firstborn was a girl. Having more children requires more childcare time and presumably an extra caregiver. However, the effect of family size on coresidence is unclear. On the one hand, coresidence could be more likely as family size increases because of the higher productivity of the grandmother; on the other hand, the mother’s domestic productivity also rises, which decreases her labor supply and therefore decreases the coresiding surpluses from labor specialization.

As a robustness check on the estimands in columns 1 and 2 of Table 3, we confine the sample to households with only one child. Columns 3 and 4 present the results using this subsample. The magnitudes of the coefficients are very similar to those presented in columns 1 and 2, and the significant level drops a little because of a smaller sample size. The consistency of the results indicates that the firstborn gender is unlikely to affect coresidence through affecting the number of preschool children.

We conduct another robustness check to test the premise that decisions on family living arrangements hinge on the demand for childcare and related domestic work. We fit Eq. (1) using the placebo composed of households in which the oldest child is aged 16 or older, the age at which most children finish compulsory education and start to be regarded as adults in most legal and social circumstances. Table A3 in the online appendix shows that among these households, neither the sex of the child nor the maternal education level is significantly related to coresidence. In addition, the magnitudes of the coefficients are much smaller than those in Table 3.13

Finally, we address the possibility that the gender difference could reflect a different demand for care; that is, boys could be genetically different from girls and need more care, or their caregivers could believe this to be so. However, similar to what Barcellos et al. (2014) found in India, researchers in China have found that infant mortality is consistently higher among girls than boys. According to China’s 2000 population census, female infant mortality is 33.75 per thousand, but male infant mortality is only 23.92 per thousand. This difference does not support the thesis that boys need more care than girls.

### Maternal Participation in the Labor Force and Domestic Realm

In this subsection, we investigate the model’s implication for maternal time use. As predicted by the lemma, upon coresidence, the mother will adjust her time use. In particular, because the time of the mother and grandmother are largely substitutable regarding family chores (such as cooking and washing clothes), the mother will likely reduce her time on these activities and spend more time on the job. The empirical work focuses on households with less-educated mothers because as shown in Table 3, within this subset, the sex of the firstborn exhibits a stronger impact on coresiding with the paternal grandmother.14

This implication is clearly illustrated by the mean comparison in Table 2. Compared with mothers who have firstborn girls, those who have firstborn sons are 10.6 percentage points more likely to coreside with a mother-in-law, work 3.2 days more per month, and spend significantly less time on family chores.15

To get a more precise estimation, we fit the following regression:
$yi=α+FBSi·γ+Xiθ+λp+τt+εi,$
2

where yi is the outcome variable. In particular, we examine time spent on work (days per week) and each domestic activity, respectively. FBSi is the dummy indicator of having a firstborn son, Xi is maternal age and age squared, λp is the provincial fixed effect, and τt is the calendar-year fixed effect. Standard errors are clustered at the provincial level and corrected using the Moulton factor.

Table 4 reports the results of estimation. Panels A and B, column 1, show the results of the ordinary least squares (OLS) and probit estimation, respectively. The more conservative estimand is that among less-educated mothers, a firstborn son increases the likelihood of coresidence by 8.9 percentage points. This difference is significant at the 5 % level. In columns 2–6, panels A and B show OLS and Tobit estimands, respectively. Column 2 shows that having a firstborn son increases labor supply by at least 2.9 days per month. The estimand is significant at the 10 % level. Columns 3–5 show that if the firstborn is male, the mother spends less time on domestic chores (such as cleaning the house, cooking, and washing clothes). This is consistent with the interpretation that because the time of the mother and grandmother is highly substitutable on these chores, coresidence shortens the mother’s time spent on these activities. The estimands of the child’s gender effect are not as significant compared with the mean comparison shown in Table 2, presumably because controlling provincial and survey-year fixed effects reduces the variations. The OLS and Tobit estimands on the effects on maternal time spent on washing clothes are significant at the 10 % level. The effect on the length of time spent cooking is significant only in the Tobit estimation, whereas that on the length of time spent on cleaning the house is not statistically significant in either estimation when we control for provincial and survey-year fixed effects.

Column 6 of Table 4 presents the effect of the sex of the firstborn on maternal time spent on childcare. Neither the mean comparisons using raw data in Table 2 nor the regression results in Table 3 are significant. The t value in Table 2 is –0.53. Therefore, we find no evidence that help from the grandmother crowds out the mother’s time on childcare.16 The insignificant difference could be due to the large measurement error of childcare time data. Besides the possibility of large measurement error of the childcare time data, this lack of evidence is presumably because in the CHNS the physical care of children is defined as washing, dressing, feeding, and supervising children; it does not include cooking food, and washing the children’s clothes or cleaning the children’s room. The former cannot be fully substituted by the grandmother (breastfeeding offers an extreme example), and the latter is likely to be the margins at which grandmothers are more likely to contribute.

In Table 4, the sample sizes vary across outcomes. In column 3, the survey question about time spent on cleaning house covers only the 1997 wave and after. In column 2, the labor supply for agricultural workers covers only the 2000 wave and after. Although the questions on time use in columns 4–6 were asked in all waves of the survey, the sample sizes vary across columns because of the response of “do not remember” the exact time or time range spent on a specific activity. We use a smaller yet more consistent sample composed of observations from the 2000 wave and thereafter to replicate the results of all the regressions in Table 4. As shown in online appendix Table A4, the results are very similar, suggesting that the pattern discovered in Table 4 is not driven by the missing-value issue.

Similar to the robustness check conducted when estimating the effect of the sex of the child on coresidence, we confine the sample to households with only one child and fit Eq. (2); the results are presented in online appendix Table A5. The magnitudes and significance levels of the coefficients are similar those that in Table 4. The robustness alleviates the concern that maternal time allocation could be mostly affected by fertility.

Regarding time use, together with the lemma, Proposition 3 predicts a mitigation of the impact of child sex among educated women. The mean comparison in columns 1 and 4 in Table 2 are in favor of the prediction. To probe this heterogeneity in the use of time more precisely, we fit Eq. (2) using the subsample of women with a middle school or higher education; the regression evidence is shown in Table 5. None of the estimands on the impact of the sex of the firstborn child are significant in Table 5, and the magnitudes are much smaller compared with those in Table 4.

Finally, we conduct a placebo test to show that the sex of the child affects maternal time allocation through grandmother’s time transfers. In online appendix Table A6, we show that for extended families in which the paternal grandmothers have passed away, the sex of the child has no impact on time use among the less-educated mothers.

### Validity of Maternal Education as the Proxy for Job Opportunities

We use education as a proxy for maternal job opportunities. We address the validity from the following few perspectives. First, the heterogeneity could be caused by differences in more- and less-educated women’s choices of spouse:17 when estimating Eq. (1) using the whole sample, we include spouses’ characteristics to control matching quality, including the schooling years and age of the husband. As shown in columns 2 and 4 of Table 3, the estimands remain very similar to that in the benchmark analysis. The consistency indicates that the heterogeneity is less likely driven by marriage matching to the extent that the pattern detected remains when important matching dimensions, such as spouses’ education and age, are controlled.

Second, maternal education could reflect the mother’s attitude toward childcare and toward coresidence and time use. Evidence suggests that educated mothers do not regard the caretaking activities of other caregivers as substitutes for maternal care. For example, Bertini et al. (2003) found that breastfeeding is associated with high maternal education. In addition, compared with less-educated mothers, educated mothers likely appreciate privacy, making the cost of coresidence higher. In both cases, we would expect to see that more-educated mothers are less likely to coreside with their in-laws, which is contrary to the results in Table 3.

Third, the variation in education level could be in line with that in urban/rural residency status because urban residents generally acquire more education. To rule out the possibility that the heterogeneity across maternal education is due to education-level differences between rural and urban areas, we control urban/rural status in all the regressions. We also replicate all the regressions using the subsample of rural subjects. As shown in online appendix Table A7, the results are very similar to those of the benchmark analysis.

Fourth, maternal earnings have an income effect. On the one hand, if more-affluent mothers are better able to afford durable goods (such as housing and television), the income effect predicts that they will be more likely to move out of their in-laws’ house. On the other hand, more-affluent mothers are more capable of providing instrumental help to elderly in-laws and could therefore be more likely to stay with them. This channel also predicts that educated mothers are more likely to live with a mother-in-law. However, if coresidence is driven by the incentive of providing instrumental help to elderly parents, the correlation between maternal schooling and coresidence should be stronger among older women, which is disproved by the results shown in Table A3. When we focus on households in which grandchildren are aged 16 or older, maternal schooling has no impact on living arrangements.

## Concluding Remarks

In this work, we consider two driving forces behind intergenerational coresidence and household time allocations. Specifically, coresidence and grandparents’ time transfers can be motivated by having the companionship of children and the gain of household income from labor division. The latter exists only among mothers who are high-wage earners. For women who are low-wage earners, the decision regarding coresidence is likely to be driven primarily by children’s companionship and thus more strongly affected by son preference.

Our findings carry two important policy implications. First, in China, childcare is mostly provided by grandparents, and this decision is largely affected by (grand)son preference. For women with a daughter, if their potential labor income is rather low even when freed to work in the labor market, the grandparents will have little incentive to help with childcare. In such circumstances, women are likely to retreat from the labor market and be limited to the domestic realm. Even if women can manage to maintain a job while running their households, the stress could cause both short- and long-term negative consequences for their health and well-being (Short et al. 2002). Therefore, an affordable gender-neutral public childcare service is essential to improve maternal labor supply and women’s well-being.

Second, the finding that child gender inequality in coresidence and maternal labor supply is more prevalent among households with less-educated mothers is rather disconcerting. These households have fewer resources and are thus more dependent on a grandmother’s help. Therefore, (grand)son-biased coresidence potentially can do more harm to girls who are already in a disadvantageous economic situation. China has launched a series of programs aiming to improve the well-being of girls. For example, the Care for Girls program involves lectures to grandparents on gender equality, aiming to change grandparents’ bias against girls. Moreover, this program provides small loans and employment opportunities to the mothers in families with only daughters to raise their economic value in their households. Our work lends empirical support to such policies.

## Acknowledgments

Ang Sun acknowledges financial support from the National Natural Science Foundation of China (71703187). Chuanchuan Zhang acknowledges financial support from the National Natural Science Foundation of China (71503282) and the Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China. Ang Sun and Chuanchuan Zhang are the co-corresponding authors of this paper.

## Notes

1

The linkage between grandparents’ help and maternal labor supply is weaker in developed countries with easy access to the childcare market (Del Boca 2015).

2

We want to focus on families with preschool-aged child(ren) (i.e., those aged 0–6) because for most families, help with domestic work is most needed in this critical period.

3

In the CHNS, childcare includes only physical labor devoted to feeding, washing, and supervising children. Activities such as washing children’s clothes and cooking children’s meals are regarded as family chores instead of childcare.

4

This patrilocality norm is not unique to China but is also prevalent in other Asian countries, such as India and Vietnam (Ebenstein 2014).

5

Parents rarely live alone because the only son is obliged to take care of his elderly parents and provide for their funerals (Silverstein et al. 2006).

6

Intergenerational coresidence is of two main types. Grown-up sons and their wives and children may live in their parents’ place, or they may move their parents into their own houses to take care of them. The first type is the most prevalent. According to CHNS data, when focusing on coresiding households, 82.04 % of the households report the household head to be one of the grown-up sons’ parents, and only 15.47 % report the household head to be a grown-up son.

7

As reported in The Atlantic (Yang 2013), a 68-year-old interviewee, Ida Lang, said, “My role staying home with the kids allows for my family’s success.” To her, the decision to provide childcare for her grandchildren is not difficult. “Just look at how much money she can make!” she exclaims, referring to her daughter-in-law.

9

We also conduct a survival analysis of coresidence for male and female children and yield results similar to those shown in Fig. 3. See also Fig S1 in the online appendix.

10

Because the variable of interest—the sex of the firstborn—is time-invariant, we use the longitudinal data as repeated cross-sections.

11

About 13 % of the control variables are missing in the CHNS. To keep the sample consistent across specifications, we apply the missing indicator method: that is, we replace the missing value with the imputed mean of the included control variable and add a dummy variable indicating “missing value” in the regression function. The results obtained when leaving out the observations of missing-value controls are very similar to those shown in Table 3 and are available upon request.

12

For example, Zeng and Xie (2014) examined the impact of grandparents’ characteristics on grandchildren’s schooling, finding that this impact exists only among households that include grandparents.

13

The insignificant coefficients reported in Table A3 (online appendix) are not because of the higher mortality of the grandmother: compared with the mortality rate of 14.8 percentage points for the paternal grandmother in households with preschool children, mortality in the placebo group increased to only 20.5 percentage points.

14

Educated mothers are likely to coreside with their mothers-in-law regardless of the sex of the child, presumably because of the potentially big surpluses from labor division between generations. Perhaps educated mothers have more resources, which render the grandmother’s role less critical. We discuss this heterogeneity in more detail in the next subsection.

15

As a simplifying assumption, in the model, we suppose no son preference for the parent. If the mother also has son preference to the extent that she would want to spend more time with a son than a daughter, maternal son preference predicts less maternal labor supply given maternal wage rate, which yields a prediction opposite to the lemma. Thus, the results of mean comparison of maternal labor supply can be regarded as a “lower bound” of that suggested by the lemma.

16

However, if grandmothers are also involved in childcare (as shown in Fig. 2, panel d), boys are likely to receive more hours of physical care in the presence of a grandmother.

17

For example, more-educated women could want to marry a husband from a family with a weaker son preference.

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