The Long-term Consequences of Fertility on the Elderly’s Labor Supply

doi:10.21203/rs.3.rs-4612417/v1

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The Long-term Consequences of Fertility on the Elderly’s Labor Supply

https://doi.org/10.21203/rs.3.rs-4612417/v1

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Two trends are shaping the demographic structure in China in recent decades: population ageing and declining fertility. This paper explores the long-term effect of fertility on the elderly’s labor supply in China. By applying the instrumental variable methods on the China Health and Retirement Longitudinal Study (CHARLS) dataset, I find that having more children decreases the elderly’s labor supply, especially for the disadvantaged elderly, including females, those living in rural regions and those with low levels of educational attainment. The negative effect is concentrated on the effect on the extensive margin of labor supply, rather than the intensive margin. I rule out co-residence with adult children and providing care to grandchildren as potential channels for the negative effect on the elderly’s labor supply. The increase in the net transfer from children as the number of children increases can be a viable explanation for the negative effect. The linkage between fertility and labor supply of the elderly has important policy implications.

fertility

labor supply

elderly

retirement

number of children

intergenerational transfer

Around the world, populations are ageing in both developed countries and developing countries in recent decades. Figure 1 shows the change in the population age structure in China. Population ageing has profound effects on the social security system, labor force and economic growth. An ageing population combined with fixed statutory retirement age manifests a shrinking and ageing labor force, which would negatively affect the economic growth. Many developed countries have been experiencing social security program reform to cope with population ageing. Similar reform in terms of raising the statutory retirement age has been proposed in China since 2012, but the uncertainty in the consequences of the reform has brought the reform in a halt. There is an extensive literature on the determinants of retirement intentions and realization in the context of developed countries, but studies of causal effects in the context of China is scarce (See Blundell et al., 2016 for a review).

Data source: China Statistical Yearbook 1991–2021.

In the meanwhile, fertility rate is declining fast in China, even though the family planning policy has been relaxed since 2014. In the recent three years, the fertility rate in China is stable at 1.7 births per women, below the replacement level and well below the fertility rate in the 1980s when the one-child policy was introduced.

Family and work are two important aspects in an adult’s life. And the linkage between fertility and labor supply has important policy implications. Previous literature on the effect of fertility on labor market outcomes, in general, find a negative effect for female – motherhood penalty, and a positive effect for male – breadwinner bonus (Angrist and Evans, 1996; Bedi, et al., 2022; Bergemann and Riphahn, 2023; Budig and England, 2001; Cao, 2019; Cooke and Fuller, 2018; Dankmeyer, 1996; Glauber, 2018; Guo, et al., 2018; He and Zhu, 2016; Jacobsen, 1999; Lundberg and Rose, 2000; Mari, 2019; Meng, et al., 2023; Takaku, 2019; Wang, 2023; Wu, 2022). But these studies focus on the effects for adults of childbearing age. Whether there is a long-lasting effect of fertility on elderly’s labor supply is the focus of this study.

The novel contributions of this paper are as follows. First, it quantifies the effect of fertility on the elderly’s labor supply in a developing country, and examines the effects on both the extensive margin and the intensive margin of labor supply. Previous studies mostly focus on the determinants of retirement, i.e., the extensive margin of elderly’s labor supply; however, the intensive margin of labor supply is underexplored (Haider and Loughram, 2011; Rao and Zhang, 2024; Sewdas, et al., 2017). Moreover, using rich data from the 2018 wave of the China Health and Retirement Longitudinal Study (CHARLS), I find some results that are different from the findings in studies based on data from developed countries.

Second, to address the potential endogeneity issue related to fertility, I use the gender of the first-born child as an instrument for fertility, given the son preference social norm in China. The results show that having more children decreases the elderly’s labor supply, especially for the disadvantaged elderly, including females, those living in rural regions and those with low levels of educational attainment. The findings are quite different from the findings in Hank and Korbmacher (2013) who find that having more children is associated with later retirement among men and later retirement among women of pre-1940 birth cohort in Europe. And the heterogenous effects have important policy implications.

Third, potential mechanisms of the negative effect of fertility on the elderly’s labor supply are explored. I rule out co-residence with adult children and providing care to grandchildren as potential channels. The increase in the net transfer from children as the number of children increases can be a plausible explanation for the negative effect. This result is partially in line with the findings in Oliveira (2016), Chen and Fang (2021) and Rao and Zhang (2024): Oliveira (2016) and Rao and Zhang (2024) find that having more children is associated with more transfer and more informal care from children and higher likelihood of co-residing with an adult child in China, while Chen and Fang (2021) find that fewer children due to China’s “Later, Longer, Fewer” (LLF) campaign is not associated with fewer coresiding children or less intergenerational transfer from children. A possible reason for the discrepancy in the findings could be that we estimate different local average treatment effects as we employ different instrumental variables for fertility. Oliveira (2016) uses first-born twins as an instrument for fertility. Chen and Fang (2021) and Rao and Zhang (2024)’s findings reflect the consequences of China’s LLF campaign in the early 1970s which prevented high-order births.

The remainder of the paper is organized as follows. Section 2 reviews the relevant literature. Section 3 discusses the conceptual framework and the empirical methodology. Section 4 describes the data and variables. Section 5 presents the results, and Section 6 concludes.

This study contributes to two strands of literature. First, this paper contributes to a better understanding of the determinants of retirement decision. Previous studies often find gender, health, level of education, marriage status, financial commitment and constraints, level of pension income, occupation and work characteristics are important determinants of whether retire on time (Haider and Loughram, 2011; Sewdas, et al., 2017. Also see Blundell et al. (2016) for a review). Especially, being male, having good health status, have very high or very low level of education, not having a partner, poor financial situation, low pension income, working in healthcare, voluntary work are associated with working beyond retirement age. Studies on the causal relationship between fertility and the elderly’s retirement and working decision are scarce. Three studies using data from developed countries are closely related to my study (Han and Korbmacher, 2013; Jeong and Kim, 2020; Miller, et al., 2018). Jeong and Kim (2020) use first-born twins and child deaths as instrumental variables for fertility, and find that parents retire earlier when they have more children in South Korea. The first instrument they use is the same as the one in Oliveira (2016). The second instrument is the death of a child which actually captures more effect than a pure decrease in the number of children for a parent, as the early death of a child is a catastrophic shock to parents. Han and Korbmacher (2013) use discrete-time logit model on the Survey of Health, Ageing and Retirement in Europe (SHARE) dataset, and they find that having more children is associated with later retirement among men and later retirement among women of pre-1940 birth cohort, but not for women of post-1940 birth cohort. They point out that different economic and institutional opportunities for women can potentially explain their results. The cultural, economic and institutional settings in China are quite different from those in the European countries, and extrapolating their results and explanations for the elderly in China may not be appropriate. Miller, et al. (2018) use the Health and Retirement Study (HRS) dataset to examine whether unanticipated events in the lives of adult children affect parents’ retirement realizations in the US. They find that children moving out of the parental home decreases elderly parents’ expectations and realizations of working after 65, while children’s marriage and divorce, and loss or gain of employment have no significant effect. They confirm the role of financial transfer from parent to adult children as a mechanism. Though Miller, et al. (2018) touch the topic of the effect of children on parental retirement timing, it does not provide direct evidence of fertility on the elderly’s labor supply.

Secondly, this paper provides further evidence of the long-term consequences of fertility on elderly’s well-being. Previous literature has explored the long-term consequences of fertility on elderly’s physical and mental health, happiness, household income, consumption and savings and female empowerment in China (Bonsang and Skirbekk, 2022; Chen and Fang, 2021; Choukhmane, et al., 2023; Ge, et al, 2018; Huang, et al., 2021; Islam and Smyth, 2015). Lower fertility rate as a consequence of China’s LLF campaign is associated with more severe depression symptoms, which may be caused by fewer children living close by and fewer contacts and visits from children. But lower fertility is not found to be associated with worse physical health status or lower consumption of elderly parents or lower amount of transfer from children to the elderly parents (Chen and Fang, 2021). Lower fertility rate as a consequence of the one-child policy is associated with better self-rated health, higher household income, higher consumption, higher savings, more female happiness and female empowerment (Choukhmane, et al., 2023; Ge, et al, 2018; Huang, et al., 2021; Islam and Smyth, 2015). None of these studies investigate the long-term effect of fertility on elderly’s labor supply in China, except Oliveira (2016) and Rao and Zhang (2024) which are most closely related to this study. Oliveira (2016) studies the effect of fertility on old-age support, whereas the focus of this paper is the long-term effect of fertility on the elderly’s labor supply. In addition, Oliveira (2016) uses first-born twins as an instrument for fertility, which examines different local average treatment effects from this study. Lastly, among 8818 observations in Oliveira (2016), first-born twins only account for less than 2 percent of the sample, and the small number of treatment observations may lead the study to be underpowered. There are two major distinctions between this study and Rao and Zhang (2024). First, Rao and Zhang (2024) study the impact of fertility and child gender on old-age labor supply, focusing on the elderly’s labor participation decisions. In this study, in addition to the total effect of fertility on labor supply, I also investigate both the extensive margin and the under-explored intensive margin of labor supply of the elderly. Second, Rao and Zhang (2024) use the age-specific exposure to the LLF policy and the gender of the first-born child as the instrumental variables, the former of which imposes more sample restrictions to the data, resulting in different local average treatment effects and thus different policy implications from my study.

3.1. Conceptual framework

Conceptually, having more children can have two opposite effects on the elderly’s labor supply. On the one hand, the filial piety social norm in China implies that parents may rely on their adult children for support in old age (Chu, et al., 2011; Guo and Zhang, 2020; Shi, 2009; Xie and Zhu, 2009). And therefore, more children may provide more support which results in reduced labor supply of the elderly. On the other hand, not only is raising children costly, but parents also often need to provide financial support for adult children in need. Financial transfer from parents to adult children can be sizable, which levies substantial financial burden on the elderly parents (Miller, et al., 2018). Therefore, having more children may delay parents’ retirement and increase their labor supply (Reitzes, et al., 1998). The overall effect of fertility on the elderly’s labor supply is uncertain in theory, and deserves to be examined empirically.

3.2. Empirical methodology

3.2.1. Labor supply

The main dependent variable in this study is labor supply. First, I measure labor supply using weekly working hours. Because it is bounded by zero, I adopt a tobit model, in which the latent variable, ${Y}_{iac}^{\text{*}}$, is the desired weekly working hours for individual $i$ of birth cohort a in city $c$, and ${Y}_{iac}^{}$ is the observable actual weekly hours worked which takes the value of ${Y}_{iac}^{\text{*}}$ if ${Y}_{iac}^{*}>0$, and zero otherwise.

$${Y}_{iac}^{*}={\beta }_{0}+{\beta }_{1}Chil{d}_{iac}+ {\beta }_{2}{X}_{iac}+{\gamma }_{c}+{\theta }_{a}+{ϵ}_{iac} \left(1\right)$$

$${Y}_{iac}=\left\{\begin{array}{c}{Y}_{iac}^{*} \text{if} {Y}_{iac}^{*}>0 \\ 0 \text{otherwise}\end{array}\right. \left(2\right)$$

In Eq. (1), $Chil{d}_{iac}$ is the number of children, which is the key variable of interest; ${X}_{iac}$ is a vector of explanatory variables; ${\gamma }_{c}$ is the city fixed effect which captures the local labor market situation; ${\theta }_{a}$ is the birth cohort fixed effect; and ${ϵ}_{iac}$ is the error term clustered at the city level. A positive sign of ${\beta }_{1}$ implies that having more children is associated with more labor supply. Equations (1) and (2) can be combined into

$${Y}_{iac}=\text{max}\left\{0,{Y}_{iac}^{*} \right\}=\text{max}\left\{0,{\beta }_{0}+{\beta }_{1}Chil{d}_{iac}+ {\beta }_{2}{X}_{iac}+{\gamma }_{c}+{\theta }_{a}+{ϵ}_{iac} \right\}. \left(3\right)$$

The fertility variable may be endogenous, as many factors determining fertility may also affect the elderly’s labor supply decades later, including those that are unobservable. To address the endogeneity issue, I employ an instrumental variable approach and use the gender of the first-born child as an instrument for the number of children, based on the prevailing son preference social norm in China. The intuition is that parents with a female first-born child have higher incentive to have more children because of their preference for having a son; thus, having a female first-born child is associated with higher fertility.

The gender of the first-born child in my sample is exogenous and satisfies the exclusion restriction. First, fetal sex diagnosis using ultrasound technology is not prevalent in China until the late 1980s, by which time the individuals in my sample had given birth to their first child (Chen, et al., 2013).1 Second, the sex ratios at birth data in China provide further evidence for the exogeneity of the gender of the first-born child. It appears that the sex ratios at birth have not been severely distorted until the middle 1980s. According to the census data, the sex ratios at birth were between 105.8 and 108.8 between the 1960s and the 1970s, and the ratios were 107.4 and 107.2 in 1980 and 1982 when the one-child policy was introduced. These numbers match the natural sex ratio at birth for human. Lastly, the sex ratios for the first-born were least distorted by fetal sex diagnosis. Ebenstein (2010) and Li and Wu (2011) both provide evidence that parents did not manipulate the gender of the first-born child in general. For example, the sex ratio for the first-born were 106.6, 101.5 and 107.1 in 1985, 1988 and 1997, but, in contrast, the sex ratio for the second-born were 115.9, 114.5 and 116.6 in 1985, 1988 and 1997. The former set of ratios match the natural sex ratio at birth for human, whereas the latter was much higher. Therefore, I can safely assume that the gender of the first-born child is exogenous in my sample and satisfies the exclusion restriction.

The first-stage equation is given by the equation below,

$$Chil{d}_{iac}={{\alpha }}_{0}+{\alpha }_{1}{femalefirstborn}_{iac}+{\alpha }_{2}{X}_{iac}+{{\lambda }}_{c}+{\tau }_{a}+{\xi }_{iac} \left(4\right)$$

where the coefficient of the female first-born child, ${\alpha }_{1}$, is expected to be significantly positive. I estimate equations (3) and (4) by ivtobit in Stata. Sample weight is applied in all regressions.

3.2.2. Extensive margin vs. intensive margin

To draw a clearer picture of the effect on labor supply, I also look into the extensive margin and the intensive margin. The extensive margin of labor supply is measured by a dummy variable, ${Z}_{iac}$, which equals to one if an elderly individual works, and zero otherwise. Therefore, I use a probit model in which the latent variable, ${Z}_{iac}^{\text{*}}$, is the payoff the individual $i$ of birth cohort a gets from working in city $c$.

$${Z}_{iac}^{*}={\beta }_{10}+{\beta }_{11}Chil{d}_{iac}+ {\beta }_{12}{X}_{iac}+{\delta }_{c}+{\vartheta }_{a}+{\epsilon }_{iac} \left(5\right)$$

$${Z}_{iac}=\left\{\begin{array}{c}1 \text{if} {Z}_{iac}^{*}>0 \\ 0 \text{otherwise}\end{array}\right. \left(6\right)$$

where $Chil{d}_{iac}$ is the number of children, which is the key variable of interest. The observed binary variable, ${Z}_{iac}$, is equal to 1 when an individual has positive payoff from working and 0 otherwise. A positive sign of ${\beta }_{11}$ implies that having more children is associated with higher likelihood of working. To tackle the potential endogeneity problem, I estimate equations (4), (5) and (6) jointly by ivprobit in Stata.

The intensive margin of labor supply is measured by conditional weekly working hours, ${W}_{iac}$, conditional on working. The linear regression is given by

$${W}_{iac}={\beta }_{20}+{\beta }_{21}Chil{d}_{iac}+ {\beta }_{22}{X}_{iac}+{\mu }_{c}+{\pi }_{a}+{\upsilon }_{iac} . \left(7\right)$$

Equations (4) and (7) are estimated using two-stage least squares regression, and a positive sign of the coefficient on $Chil{d}_{iac}$, ${\beta }_{21}$, implies that having more children is associated with more working hours conditional on the working status.

[1] 98% of observations in my sample had their first child by 1987.

4.1. Data

The data used in this study is the CHARLS 2018, which is the Chinese version of Health and Retirement Study (HRS).2 It is a nationally representative sample of Chinese residents aged 45 and older (Zhao et al., 2014). The 2018 wave covers 122 cities in 28 provinces in mainland China. I start with a raw sample of 19816 observations and place the following sample restrictions. First, to study the elderly’s working decision, I restrict the sample to individuals aged 60–79.3 This restriction excludes 51% of the raw sample. Second, because the instrumental variable in this study requires at least one child, I further exclude 99 childless observations. Third, I exclude those with missing information on key variables. The final sample includes 6455 observations.

4.2. Variables and descriptive statistics

The main dependent variables are measures of labor supply, including weekly working hours, working status (the extensive margin), and conditional weekly working hours (the intensive margin). The key independent variable is the number of living children. I use living children instead of birth children, because the former is a more important determinant for the elderly parents’ labor supply; nevertheless, the two variables are highly correlated, with a correlation coefficient of 0.943. A dummy variable indicating whether the first-born child is female serves as the instrumental variable for the number of living children.

The control variables include gender, ethnicity (ethnic Han is the default), marital status, educational attainment (primary education or below is the default), self-reported health, hukou (household registration) status, region of living (urban is the default), an interaction term of rural hukou and rural region dummies to capture the migration status, pension status, log of pension income, financial wealth in thousand yuan, birth cohort fixed effect, and city fixed effect.

Panel A in Table 1 presents the summary statistics of the variables used in the analysis. The elderly in the sample work for 18.8 hours per week, on average. Those who are working make up 51.9% of the sample, and among those who work, they work for 36.2 hours per week on average, which is equivalent to the hours of a full-time job. On average, they have 2.71 living children. Having a female first-born child accounts for 48.1% of the sample, and the corresponding sex ratios for the first-born is similar to the natural sex ratio at birth for human. For the relatively younger cohort (aged 60–69) in our sample, who were more likely to be affected by the one-child policy when they had their first child, the first-born sex ratio for them is 1.05. These statistics provide compelling evidence that the sex ratios for the first-born in the sample were not distorted, and can be taken as random.

Table 1. Summary Statistics

Panel A. Full sample
			Mean		S.D.		Obs.
key variables
weekly working hours			18.801		26.262		6455
working			0.519		0.500		6455
conditional weekly working hours			36.197		26.422		3729
#children			2.708		1.288		6455
instrumental variable
female first-born child			0.481		0.500		6455
control variables
age			67.427		5.174		6455
male			0.502		0.500		6455
ethnic Han			0.992		0.091		6455
married			0.837		0.369		6455
middle school or above			0.315		0.464		6455
poor self-reported health			0.288		0.453		6455
rural hukou			0.709		0.454		6455
rural region			0.528		0.499		6455
rural hukou living in rural areas			0.498		0.500		6455
have pension			0.865		0.341		6455
pension income (yuan)			11407.494		18290.627		6455
financial wealth (thousand yuan)			34.668		117.534		6455
Panel B. by gender of the first-born child
	female first-born			male first-born				difference
	mean	st.d.		mean		st.d.		mean
#children	2.829	1.319		2.597		1.248		0.232***
male	0.506	0.500		0.498		0.500		0.008
age	67.337	5.146		67.511		5.199		-0.174
ethnic Han	0.994	0.077		0.990		0.102		0.004*
Years of schooling	5.358	4.236		5.257		4.170		0.101
poor self-reported health	0.284	0.451		0.292		0.455		-0.008
married	0.841	0.366		0.834		0.372		0.007
rural hukou	0.705	0.456		0.713		0.452		-0.008
rural region	0.516	0.500		0.539		0.499		-0.023
have pension	0.862	0.345		0.869		0.338		-0.007
pension income (yuan)	11234	17904		11568		18644		-334
financial wealth (thousand yuan)	31.391	116.610		37.710		118.321		-6.319
* p < 0.10, p < 0.05, * p < 0.01
Data source: CHARLS 2018.

Panel B in Table 1 shows the summary statistics of the individual characteristics by the gender of the first-born child. As expected, individuals who have a female first-born child have 0.23 more children than individuals with a male first-born child, on average, and the difference is significant at 1 percentage level. The other individual characteristics include gender, age, education, self-reported health, marital status, hukou status, region of living, pension status, pension income and financial wealth show no significant difference between the two groups at 10 percentage level. Yet, individuals who have a female first-born child are 0.4% more likely to be ethnic Han, compared to individuals with a male first-born child, and the difference is marginally significant at 10 percentage level. Given the small proportion (0.8%) of ethnic minority in the sample, I perform robustness check by deleting the ethnic minority sample in Section 5.3, and find that the main results are robust. Overall, the summary statistics provide further evidence that the gender of the first-born child in the sample appears random and satisfies the exclusion restriction. Given that the gender of the first-born child also satisfies the relevance condition, it could serve as a valid instrumental variable for the key variable of interest.

[2] I only use the 2018 wave instead of the panel data of CHARLS, because using panel data with individual fixed effect, the changes in the key variable of interest – the number of living children will capture those changes due to re-marriages and child deaths, which are not directly related to fertility. This will bias the estimated effect of fertility.

[3] Given that the healthy life expectancy at age 60 in 2019 is 15.9 and the active life expectancy at age 60 is 19.4 during the period of 2011-2013, I use 79 as the upper bound for the sample age (WHO, 2020; Huang, et al., 2021). In the sample, the proportion of working elderly is 23.16% at the age of 79, yet the proportions drop sharply at the age of 80 and onwards.

5.1. Main results

5.1.1. Labor supply

Table 2 reports the main results for the effect of number of children on the weekly working hours. Columns 1, 2, 3 and 4 present the estimates from the OLS model, the two-stage least squares regression, the tobit model and the ivtobit model, respectively. Standard errors clustered at the city level are reported in the paratheses, and the marginal effects from the tobit model and ivtobit model are reported in the brackets. In Columns 1 and 3, the results from the OLS and tobit estimations show that there is no association between fertility and weekly working hours of the elderly. However, those estimates are probably biased due to the endogeneity problem. This is confirmed by the test statistics in Columns 2 and 4. The endogeneity test of endogenous regressor from the 2SLS estimates in Column 2 (p-value = 0.039) rejects the null hypothesis that fertility can be treated as exogenous, and the Wald test of the exogeneity of the endogenous variables from the ivtobit estimation in Column 4 reject the null hypothesis that the correlation between the residuals from the main equation and the residuals from the auxiliary equation is zero (rho = 0).

Table 2

Effect of number of children on weekly working hours
	OLS	2SLS	Tobit	IVTobit
#children	0.270	-6.100*	0.463	-13.146**
	(0.400)	(3.387)	(0.640)	(6.080)
			[0.237]	[-6.727**]
male	7.347***	6.414***	13.919***	11.925***
	(0.823)	(1.138)	(1.783)	(2.317)
ethnic Han	-6.041	-5.224	-11.304	-9.586
	(5.922)	(6.018)	(9.520)	(9.901)
middle school or above	-1.682*	-1.721*	-4.621**	-4.689**
	(0.957)	(0.957)	(1.937)	(2.034)
poor self-reported health	-7.695***	-7.229***	-16.342***	-15.394***
	(0.841)	(0.912)	(1.704)	(1.782)
married	2.748***	3.181***	6.435***	7.348***
	(0.943)	(0.980)	(1.977)	(2.079)
rural hukou	4.462**	6.321**	18.109***	22.112***
	(2.044)	(2.456)	(4.503)	(5.284)
rural region	3.950	5.450*	21.663***	24.932***
	(2.712)	(2.918)	(5.289)	(5.871)
rural hukou living in rural areas	1.258	-0.247	-12.792**	-16.042**
	(2.830)	(3.132)	(5.518)	(6.237)
have pension	12.868***	18.493***	32.435***	44.254***
	(3.661)	(4.315)	(6.809)	(8.436)
ln(pension income)	-1.840***	-2.626***	-4.546***	-6.206***
	(0.450)	(0.517)	(0.876)	(1.083)
financial wealth (thousand yuan)	0.004	0.003	0.004	0.002
	(0.005)	(0.006)	(0.009)	(0.012)
first-stage
female first-born child		0.277***		0.277***
		(0.043)		(0.042)
Observations	6455	6455	6455	6455
R² / Pseudo R²	0.231		0.063
Under identification test P-value		0.000
F-stat for weak identification		41.950
Endogeneity test P-value		0.039
rho				0.358**
				(0.153)
* p < 0.10, p < 0.05, * p < 0.01
Note: Data source is CHARLS 2018. All specifications also control cohort fixed effects and city fixed effects. Regression coefficients are reported in the table, standard errors clustered at the city level are reported in the parentheses, and the marginal effects are reported in the brackets.

The first-stage results show that having a female first-born child is significantly positively associated with fertility, as expected. And the F-test statistics for the weak identification test is 41.95, way above the rule of thumb of 10. These IV estimation results show that having more living children significantly decreases the elderly’s weekly working hours. The average marginal effect from the ivtobit estimation suggests that having one more living child decreases the elderly’s weekly working hours by 6.727, all else held equal.

With regard to other regressors in the models, I find that higher educational attainment (secondary education or above) and higher pension incomes are negatively associated with less labor supply; in another word, the elderly with lower educational attainment and low pension incomes work more on average, which is more consistent with financial reasons (working for money) than psychological reasons (working for enjoyment and interest in making a contribution). Moreover, males, those who are married, and migrants (both rural hukou holders living in urban regions and urban hukou holders living in rural regions compared to urban hukou holders living in urban regions) also work more, whose coefficients are significant at the 1 percentage level. Lastly, those who report poor health and the rural hukou holders living in rural regions (compared to urban hukou holders living in urban regions) work less.

5.1.2. Extensive margin

Table 3 reports the main results for the effect of number of children on working status. Columns 1, 2, 3 and 4 show the estimates from the linear probability model (LPM), the two-stage least squares regression, the probit model and the ivprobit model, respectively. Standard errors clustered at the city level are reported in the paratheses, and the marginal effects from the probit model and ivprobit model are reported in the brackets.

Table 3

Effect of number of children on working status
	LPM	2SLS	Probit	IVProbit
#children	-0.006	-0.136***	-0.020	-0.446***
	(0.006)	(0.049)	(0.021)	(0.128)
			[-0.006]	[-0.139***]
male	0.122***	0.103***	0.432***	0.329***
	(0.016)	(0.020)	(0.058)	(0.079)
ethnic Han	-0.077	-0.060	-0.322	-0.234
	(0.079)	(0.081)	(0.265)	(0.247)
middle school or above	-0.046**	-0.047**	-0.183***	-0.170**
	(0.018)	(0.018)	(0.069)	(0.067)
poor self-reported health	-0.171***	-0.161***	-0.582***	-0.500***
	(0.013)	(0.014)	(0.045)	(0.065)
married	0.075***	0.083***	0.236***	0.246***
	(0.018)	(0.018)	(0.061)	(0.056)
rural hukou	0.190***	0.228***	0.654***	0.722***
	(0.041)	(0.045)	(0.132)	(0.130)
rural region	0.257***	0.287***	0.829***	0.855***
	(0.050)	(0.053)	(0.161)	(0.161)
rural hukou living in rural areas	-0.151***	-0.181***	-0.525***	-0.580***
	(0.055)	(0.058)	(0.176)	(0.171)
have pension	0.357***	0.472***	1.150***	1.422***
	(0.074)	(0.089)	(0.251)	(0.257)
ln(pension income)	-0.049***	-0.065***	-0.161***	-0.199***
	(0.009)	(0.011)	(0.030)	(0.031)
financial wealth (thousand yuan)	-0.000	-0.000	-0.000	-0.000
	(0.000)	(0.000)	(0.000)	(0.000)
first-stage
female first-born child		0.277***		0.274***
		(0.043)		(0.043)
Observations	6455	6455	6401	6401
R² / Pseudo R²	0.339		0.273
Under identification P-value		0.000
F-stat for weak identification		41.950
Endogeneity test P-value		0.006
rho				0.449***
				(0.154)
* p < 0.10, p < 0.05, * p < 0.01
Note: Data source is CHARLS 2018. All specifications also control cohort fixed effects and city fixed effects. Regression coefficients are reported in the table, standard errors clustered at the city level are reported in the parentheses, and the marginal effects are reported in the brackets.

Due to the bias caused by the endogeneity problem, the results from the LPM and probit estimations in Columns 1 and 3 in Table 3 show that there is no association between fertility and working status of the elderly. Actually, both the endogeneity test from the 2SLS regression in Column 2 (p-value = 0.006) and the Wald test of the exogeneity from the ivprobit estimation in Column 4 reject the null hypothesis that we can treatment the number of children as exogenous. With the instrumental variable technique, the estimates from Columns 2 and 4 show that having more living children significantly decreases the elderly’s probability of working. The average marginal effect from the ivprobit estimation suggests that having one more living child decreases the elderly’s probability of working by 13.9%, all else held equal.

5.1.3. Intensive margin

Table 4 reports the main results for the effect of number of children on the conditional weekly working hours, conditional on the working status. Columns 1 and 2 present the estimates from the OLS model and the two-stage least squares regression, both of which suggest that there is no significant effect of having more living children on the elderly’s conditional weekly working hours.

Table 4

Effect of number of children on conditional weekly working hours
	OLS	2SLS
#children	0.726	-1.849
	(0.633)	(5.278)
male	4.800***	4.265***
	(1.073)	(1.538)
ethnic Han	-6.078	-5.571
	(5.490)	(5.438)
middle school or above	0.165	0.368
	(1.350)	(1.420)
poor self-reported health	-3.269***	-3.064**
	(1.180)	(1.272)
married	1.810	2.345
	(1.337)	(1.676)
rural hukou	-5.775	-5.892
	(3.556)	(3.626)
rural region	-10.414**	-10.523**
	(4.257)	(4.281)
rural hukou living in rural areas	12.735***	12.964***
	(4.357)	(4.507)
have pension	1.142	3.399
	(5.277)	(6.679)
ln(pension income)	-0.271	-0.575
	(0.682)	(0.839)
financial wealth (thousand yuan)	0.005	0.006
	(0.009)	(0.010)
first-stage
female first-born child		0.249***
		(0.047)
Observations	3729	3729
R²	0.162
Under identification P-value		0.000
F-stat for weak identification		28.270
Endogeneity test P-value		0.616
* p < 0.10, p < 0.05, * p < 0.01
Note: Data source is CHARLS 2018. All specifications also control cohort fixed effects and city fixed effects. Standard errors clustered at the city level are reported in the parentheses.

In sum, it appears that having more children significantly decreases the elderly’s labor supply, and the changes in labor supply is driven by the changes in the extensive margin measured by the working status; there is no significant effect of fertility on the intensive margin measured by the conditional weekly working hours.

5.2. Mechanisms

Having more children may affect the elderly’s labor supply decision through three potential channels. First, having more children involves more intergenerational financial transfers, but the direction of the net transfer is unclear, based on the literature. In view of the filial piety social norm in China, the net transfer from children to the elderly parents is likely to be positive, which helps to reduce the elderly’s labor supply. Second, having more children may result in higher likelihood of co-residence with an adult child, given the prevalence of co-residence in China. With the support of an adult child, the elderly are less likely to work. Third, more children imply more grandchildren, and providing care for grandchildren may crowd out the elderly’s labor supply in the market. All three channels can potentially explain the negative relationship between fertility and the elderly’s labor supply in China. In this subsection, I will empirically examine the validity of each channel.

Table 5

Effect of number of children on the channel variables
Panel A. Net transfer from children
	(1)	(2)
	OLS	2SLS
#children	0.470**	3.855**
	(0.221)	(1.722)
Observations	6450	6450
R²	0.185
F-stat for weak identification		40.978
Endogeneity test p-value		0.034
Panel B. Coresidence with adult children
	(1)	(2)	(3)	(4)
	LPM	2SLS	Probit	IVProbit
#children	0.005	0.079	0.005	0.079
	(0.009)	(0.055)	(0.008)	(0.049)
Observations	6450	6450	6426	6426
R² / Pseudo R²	0.127		0.096
F-stat for weak identification		40.978
Endogeneity test p-value		0.173
Exogeneity test Wald p-value				0.121
Panel C. Caregiving for grandchildren
	(1)	(2)	(3)	(4)
	LPM	2SLS	Probit	IVProbit
#children	-0.018*	0.054	-0.019*	0.062
	(0.010)	(0.071)	(0.010)	(0.070)
Observations	7176	7176	7174	7174
R² / Pseudo R²	0.180		0.145
F-stat for weak identification		36.608
Endogeneity test p-value		0.347
Exogeneity test Wald p-value				0.246
* p < 0.10, p < 0.05, * p < 0.01
Note: Data source is CHARLS 2018. Control variables are the same as those in Table 2, including gender, ethnicity, marriage status, education, health, hukou status, region of living, hukou and region interaction term, pension status, log of pension income, and financial wealth, as well as cohort fixed effects and city fixed effects. Average marginal effects are reported in the table, standard errors clustered at the city level are reported in the parentheses.

Table 5 reports the results for the mechanism analyses. Panels A, B and C report the results for the net transfer from children to the elderly, the results for co-residence, and the results for caregiving to grandchildren, respectively. Similar to Table 3, Columns 1 and 2 of Table 5 present the results from the OLS and 2SLS estimations; Columns 3 and 4 present the marginal effects from the probit and ivprobit estimations.

If the channel is valid, there should be a positive relationship between the corresponding dependent variable and fertility. Panel A suggests that fertility has a significantly positive effect on the amount of net transfer from children to the elderly parents, which is consistent with the hypothesis of the net transfer from children being a channel. Based on the 2SLS estimation, having one more child increases the net transfer by 3.855 thousand yuan, all else held equal. Panel B shows that there is no significant effect of fertility on the probability of co-residence. Therefore, I reject the hypothesis of co-residence being a valid channel. Panel C indicates that the effect of fertility on the probability of caregiving for grandchildren is negative, though the IV estimates are statistically insignificant. Thus, I reject the hypothesis of caregiving for grandchildren being a valid channel.

All in all, I find evidence which supports the net transfer from children to the elderly parents being a valid channel for the negative effect of fertility on the elderly’s labor supply in China. And I rule out co-residence with adult children and caregiving for grandchildren as the potential mechanisms.

5.3. Heterogeneity analysis

Table 6 presents the heterogeneity analyses by gender (female vs. male), by region of residence (rural vs. urban), and by educational attainment (primary education or less vs. secondary education or above). Columns 1–3 in Panel A show the estimates for female and Columns 4–6 show the estimates for males. The results reveal that there are statistically significant negative effects of fertility on the labor supply and its extensive margin for elderly women, but the effects for elderly men are not statistically significant; the effects on the intensive margin are not significant for either men or women. Thus, the negative effect of fertility on women’s labor supply is mainly due to its effect on its extensive margin. The average marginal effects from the ivtobit model and ivprobit model suggests that having one more living child decreases elderly women’s weekly working hours by 7.686 and decreases elderly women’s probability of working by 16.3%, all else held equal.

Table 6

Heterogeneity Analysis
Panel A. by gender
		Female			Male
	labor supply	extensive margin	intensive margin	labor supply	extensive margin	intensive margin
#children	-7.686**	-0.163***	2.769	-4.427	-0.078	-2.775
	(3.195)	(0.061)	(5.744)	(3.821)	(0.055)	(5.619)
Observations	3257	3208	1669	3198	3152	2060
Panel B. by rural/urban region
		Rural region			Urban region
	labor supply	extensive margin	intensive margin	labor supply	extensive margin	intensive margin
#children	-4.089*	-0.108***	1.107	-6.279	-0.098	-11.977
	(2.478)	(0.040)	(4.146)	(4.661)	(0.098)	(12.528)
Observations	4076	4072	2786	2379	2307	943
Panel C. by educational attainment
	Primary education or less			Secondary education or above
	labor supply	extensive margin	intensive margin	labor supply	extensive margin	intensive margin
#children	-7.873***	-0.195***	1.495	1.974	0.052	-7.290
	(2.915)	(0.048)	(4.589)	(3.784)	(0.080)	(10.859)
Observations	4724	4700	2868	1731	1644	861
* p < 0.10, p < 0.05, * p < 0.01
Note: Data source is CHARLS 2018. The sample includes individuals aged 60–79 with at least one child. Columns 1 and 4 are the average marginal effects from ivtobit model, Columns 2 and 5 are the average marginal effects from ivprobit model, and Columns 3 and 6 are the estimates from two-stage least squares. Control variables are the same as those in Table 2, including gender, ethnicity, marriage status, education, health, hukou status, region of living, hukou and region interaction term, pension status, log of pension income, and financial wealth, as well as cohort fixed effects and city fixed effects. Standard errors clustered at the city level are reported in the parentheses.

Columns 1–3 in Panel B of Table 6 present the estimates for the rural elderly and Columns 4–6 present the estimates for the urban elderly. The results suggest that there are statistically significant negative effects of fertility on the labor supply and the probability of working for the rural elderly, and the effects for the urban elderly are negative but not statistically significant; the effects on the intensive margin are not significant for the elderly in either region. The average marginal effects from the ivtobit model and ivprobit model suggest that having one more living child decreases the rural elderly’s weekly working hours by 4.089 and decreases the rural elderly’s probability of working by 10.8%, all else held equal.

Columns 1–3 in Panel C of Table 6 present the estimates for the elderly with primary education or less (low education) and Columns 4–6 present the estimates for those with secondary education or above (high education). The results reveal that there are statistically significant negative effects of fertility on the labor supply and the probability of working for the elderly with low educational attainments, whereas the effects for the elderly with high educational attainments are not statistically significant; the effects on the intensive margin are not significant for the elderly with either educational category. The average marginal effects from the ivtobit model and ivprobit model suggest that for the elderly with low education, having one more living child decreases their weekly working hours by 7.873 and decreases their probability of working by 19.5%, all else held equal.

Altogether, I find a negative effect of fertility on the labor supply and its extensive margin for elderly women, the rural elderly and the elderly with low educational attainment. Thus, the negative effect is more prominent for the disadvantaged elderly.

5.4. Robustness checks

In this subsection, I provide six kinds of robustness checks. First, I substitute the number of birth children for the number of living children as the key variable. Second, I substitute the work on the main job for all the working jobs as the dependent variable. Third, I delete the ethnic minority observations (0.8% of the full sample) and only keep the ethnic Han sample. Fourth, I restrict the sample to age of 60–75 instead of 60–79. Fifth, I control for birth cohort linear trend, instead of birth cohort fixed effect. And lastly, I delete self-reported health, marital status and financial wealth as controls, as those variables may be potentially affected by fertility and therefore affect the elderly’s labor supply; in another word, they may work as mediators.4 The estimation results for the robustness checks are shown in Table 7.

Table 7

Robustness checks
Panel A. Number of birth children
	labor supply	extensive margin	intensive margin
#children	-7.199**	-0.147***	-1.909
	(3.258)	(0.052)	(5.430)
Observations	6455	6401	3729
Panel B. Main job
	labor supply	extensive margin	intensive margin
#children	-6.173**	-0.139***	-0.199
	(2.893)	(0.049)	(4.872)
Observations	6455	6401	3729
Panel C. Ethnic Han sample
	labor supply	extensive margin	intensive margin
#children	-5.974*	-0.128***	-1.404
	(3.056)	(0.049)	(5.429)
Observations	6885	6832	3979
Panel D. Sample of age 60–75
	labor supply	extensive margin	intensive margin
#children	-6.752**	-0.136***	-1.702
	(3.213)	(0.049)	(5.049)
Observations	5873	5829	3538
Panel E. Linear cohort trend
	labor supply	extensive margin	intensive margin
#children	-6.912**	-0.142***	-1.517
	(3.312)	(0.051)	(5.370)
Observations	6455	6401	3729
Panel F. Fewer control variables
	labor supply	extensive margin	intensive margin
#children	-5.297**	-0.105***	-1.459
	(2.331)	(0.038)	(4.271)
Observations	8074	8017	4490
* p < 0.10, p < 0.05, * p < 0.01
Note: Data source is CHARLS 2018. Column 1 reports the average marginal effect from ivtobit model, Column 2 reports the average marginal effect from ivprobit model, and Column 3 reports estimates from two-stage least squares. Control variables are the same as those in Table 2, including gender, ethnicity, marriage status, education, health, hukou status, region of living, hukou and region interaction term, pension status, log of pension income, and financial wealth, as well as cohort fixed effects and city fixed effects, except Panel E which control for cohort linear trend instead of cohort fixed effects and Panel F which does not include controls for self-reported health, marital status and financial wealth. Standard errors are clustered at the city level.

The estimates from the robustness checks in Table 7 show the same consistent pattern as the main results: there are statistically significant negative effects of fertility on the labor supply and its extensive margin for the elderly, but the effects on the intensive margin are not significant. The magnitudes of the marginal effects in the robustness checks are also very similar to the main results: depending on the specification, the average marginal effects from the ivtobit model and ivprobit model suggests that having one more child decreases the elderly’s weekly working hours by 5.3–7.2 and decreases the elderly’s probability of working by 10.5–14.7%, all else held equal. Therefore, the results are robust to different variations in the specifications.

[4] I also run regressions of number of children on these variables, and the results show that there are no significant effects.

This study examines the long-term effects of fertility on the elderly’s labor supply in China. Using rich data from the CHARLS 2018, I find some results that are different from the findings in studies based on the data from developed countries. To address the potential endogeneity issue, I use the gender of the first-born child as an instrument variable for the number of children, given the son preference social norm in China. The results show that having more children decreases the elderly’s labor supply and its extensive margin, especially for the disadvantaged elderly, including females, those living in rural regions and those with low levels of educational attainment. I rule out co-residence with adult children and providing care to grandchildren as potential channels. The increase in the net transfer from children as the number of children increases can be a viable explanation for the negative effect on the labor supply in old age. The results are robust to different model specifications.

Labor supply by the elderly is an important factor in helping countries to deal with the ongoing demographic transition toward an older population. Therefore, the topic deserves attention from policymakers and researchers. The findings of this study have important policy implications. First, it sheds light on the feasibility of the impending retirement reform in China. The results imply that fertility is negatively associated with labor supply in old age. As the fertility rates stay at the historically low level in China, the elderly’s incentive to work is likely to be relatively high. And therefore, they may make less-than-expected resistance against the social security reform in terms of raising the statutory retirement age in China. Secondly, the results imply that fertility is negatively associated with labor supply in old age, especially for women. Thus, females’ human capital including the level of education, training and health will put more weight in shaping the level of labor force human capital in China. Thirdly, the elderly’s labor supply is mainly driven by financial reasons in China, and having more children helps to alleviate the financial burden of the elderly through intergenerational transfer. The Chinese government could take the fact that childbirth is rewarding in old age as a selling point in the pronatalist campaigns, when battling against population ageing problem. Lastly, financial transfer from adult children to the elderly parents helps to explain the channel from fertility to labor supply of the elderly, and filial piety social norm plays an important role in the nexus. Thus, as a caveat, the negative relationship between fertility and the elderly’s labor supply is likely to be more prominent in countries/regions with filial piety social norm. How much role filial piety social norm plays may be tested using cross country data, which could be an avenue for future research.

Funding

Partial financial support was received from the National Natural Science Foundation of China (Grant #72273163) and the Program for Innovation Research at Central University of Finance and Economics.

Competing Interests

The author has no known competing financial or non-financial interests to disclose.

Data availability statement

The data that support the findings of this study are openly available at the China Health and Retirement Longitudinal Study (CHARLS) official website,

https://charls.charlsdata.com/pages/data/111/en.html.

A description of the CHARLS can be found at

https://charls.pku.edu.cn/en/About/About_CHARLS.htm.

Author Contribution

This is a single-authored paper. Wang did all the work.

Acknowledgement

Wang acknowledge the partial financial support from the National Natural Science Foundation of China (Grant #72273163) and the Program for Innovation Research at Central University of Finance and Economics.

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No competing interests reported.

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The Long-term Consequences of Fertility on the Elderly’s Labor Supply

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Abstract

Figures

1. Introduction

2. Literature review

3. Conceptual framework and empirical methodology

3.1. Conceptual framework

3.2. Empirical methodology

3.2.1. Labor supply

3.2.2. Extensive margin vs. intensive margin

4. Data and variables

4.1. Data

4.2. Variables and descriptive statistics

5. Results

5.1. Main results

5.1.1. Labor supply

5.1.2. Extensive margin

5.1.3. Intensive margin

5.2. Mechanisms

5.3. Heterogeneity analysis

5.4. Robustness checks

6. Conclusion

Declarations

Author Contribution

Acknowledgement

References

Additional Declarations

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