Discussion Paper No.352
Number of Children and Living Arrangements of theElderly in China

Fengming CHEN, Hiroshi YOSHIDA

August 2016

TOHOKU ECONOMICS RESEARCH GROUPGRADUATE SCHOOL OF ECONOMICS AND
MANAGEMENT TOHOKU UNIVERSITY

27-1 KAWAUCHI, AOBA-KU, SENDAI,
980-8576 JAPANNumber of Children and Living Arrangements of the Elderly in China

Fengming CHENa, Hiroshi YOSHIDAba

Graduate School of Economics and Management, Tohoku University, 27-1, Kawauchi Aoba-ku, Sendai, Miyagi
980-8576, Japan; E-mail: cfmdbdx@gmail.com.

bGraduate School of Economics and Management, Tohoku University, 27-1, Kawauchi Aoba-ku, Sendai, Miyagi
980-8576, Japan; E-mail: hiroshi.yoshida.e2@tohoku.ac.jp.

ABSTRACTThis study examines the effects of the number of children on the living arrangements ofmarried and widowed individuals using data from the 2008 wave of the ChineseLongitudinal Healthy Longevity Survey. While the literature offers mixed results owing to
the endogeneity bias from the number of children, we use sex dummy variables of the firstand second parity as instrumental variables to correct the bias and find that the number ofchildren has a statistically significant and positive effect on the probability of cohabitation
for both subsamples. The magnitude of this effect in the widowed subsample is about 1.64
times that in the married subsample, indicating that children play a more important role inthe case of widowed individuals.
Keywords: living arrangements, one-child policy, China, marital status, elderly population.
JEL classification: D13, J1

1

1.

Introduction
With medical technology innovations and the resultant extension in lifespan, China is
experiencing a dramatic increase in its aging population. An increasing rate of its elderly
population is reorganizing their living arrangements because of changing individual
characteristics, such as the deterioration of their functional ability. Faced with anunderdeveloped social security system, China’s elderly population is generally dependent
on their adult children to provide physical, emotional, and financial support (Korinek,
Zimmer, & Gu, 2011). This situation is more adverse in China compared to otherdeveloping and developed countries due to the lack of a mature social security system andits large aging population. Moreover, majority of China’s elderly population, especially inthe rural areas, live below the poverty line. A factor that further impeded traditional routesof elderly support is the government’s one-child policy, although it was later relaxed in2015 to a maximum of two children per couple. While such policy measures may influence
the decision of childbirth and relieve the burden of elderly support in the long-run,predicting the short-run effects is difficult. Moreover, given the dramatic speed at which theelderly population is increasing, we lack sufficient time to confirm related policy effects in
China.
The effects of the number of children on one’s living arrangements in old age havegained much attention from policymakers and economists alike. However, since theone-child policy was implemented in 1979, the elderly who were completely affected by it
are too young to make living arrangements. Thus, we use data for individuals aged 65 year
and older to predict the effects of the number of children on living arrangements of theelderly keeping other factors constant.
Several studies examine the determinants of living arrangements of the elderly(Hoerger, Picone, & Sloan, 1996; Guo, 2002; Meng & Luo, 2008; Ren & Treiman, 2014;
Zhang, 2015), although most of them focus on economic factors such as pension benefits
and bequest motives (Edmonds, Mammen, & Miller, 2004; Engelhardt et al., 2005; Meng &Luo, 2008; Yin, 2010) and include number of children as a control variable. While
researchers find that the number of children positively affects the probability of
cohabitation (Börsch-Supan, Haijvassiliou, Kotlikoff, & Morris, 1992; Hoerger et al., 1996;
Ren & Treiman, 2014), some others report negative effects (Guo, 2002; Ren & Treiman,
2014; Zhang, 2015). The literature, thus, lacks reasonable explanations owing to the adverse
causality between number of children and living arrangements of the elderly. Hence, in thisstudy, we focus on the causal effects of the number of children on living arrangements ofthe elderly using instrumental variable design to correct the endogeneity bias. To the best of
our knowledge, this study is the first to examine this causal relationship by correcting theendogenous bias.
2This study estimates the effects of the number of children on the living arrangementsof married and widowed individuals using an instrumental variable design to eliminate any
endogenous bias arising from the number of children. Angrist and Evans (1998) accounted
for parental preference for a mixed sibling-sex composition to construct instrumental
variables to estimate the effects of childbearing on labor supply. Following their study, we
correct the endogeneity bias of the number of children using the preference for a male child.
We use data from the 2008 wave of the Chinese Longitudinal Healthy Longevity
Survey and find that the number of children has a statistically significant and positive effecton the probability of cohabitation for both subsamples. The magnitude of the effect in thewidowed subsample is about 1.64 times that in the married subsample, indicating thatchildren play a greater role in the case of widowed individuals. This result is contrary tothat in the extant literature that does not control for the endogeneity bias.
The remainder of this paper is organized as follows. Section 2 describes the data andsummary statistics. Section 3 presents our hypothesis. Sections 4 and 5 discuss theempirical strategy to estimate causal effects and the results. Section 6 provides concluding
remarks and policy implications.
2.

Data
2.1 Data
Data used in this paper are from the 2008 wave of the Chinese Longitudinal Healthy
Longevity Survey (CLHLS). CLHLS data were collected by Peking University Center for
Healthy Aging and Family Studies and China Mainland Information Group. The baseline
survey was administered in 1998 to a randomly selected number of counties and cities from
China’s 22 provinces: Liaoning, Jilin, and Heilongjiang (northeast); Beijing, Tianjin, Hebei,
and Shanxi (north); Shanghai, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, and Shandong(east); Henan, Hubei, Hunan, Guangdong, and Guangxi (central/south); and Chongqing,
Sichuan, and Shaanxi (west). An enumerator and a nurse or medical school student
conducted the interview and a basic health examination at each interviewee’s home.
The total number of interviewees in the 2008 wave was 16,540, including 341 adultchildren younger than 65 years of age. Since we focus on the living arrangements of theelderly, we exclude adult children from our analysis. In addition, given our objective to
identify the causal effects of the number of children on living arrangements of the elderly,
we use an over-identified model and exclude the elderly with one or no children.
2.2 Dependent Variable
The dependent variables measure three types of living arrangements for the elderly:
living with family members, independently, or in institutions for the elderly. Family
members include spouse, children, relatives, and parents, and a majority of the total sample
3

(83.25%) reportedly lived with their family. Given the focus of our study, we exclude
respondents who lived with relatives and parents because of systematic difference fromcohabitating with children. About 14.89% of the sample stated they lived independently,
which means to live alone without a spouse or any other family member. Finally, only
1.86% of the sample lived in an institution. We excluded such respondents because most ofthem receive financial support from China’s local governments.
Some researchers classify living with a spouse as “living independently” (Hoerger etal., 1996; Meng & Luo, 2008; Zhang, 2015). Studies have shown a significant rise incohabitation following widowhood (Korinek et al., 2011), indicating that marital status is an
important determinant of living arrangements. In addition, sex preferences for children
differ by generation and we cannot use cross-sectional data to control for such preferences.
Table 1 presents the summary statistics of the variables. As shown in the table, the averageage of the married and widowed subsamples ranges from 78.197 to 91.533. It is possible tocontrol for cohort effects from age using different subsamples; thus, we create two
subsamples on the basis of marital status.
The married subsample includes respondents with a living spouse at the time of thesurvey. We define the dependent variable, cohabitation, in the married subsample as follows.
Respondents living with a spouse and children are assigned the value of one and zerootherwise. We apply a similar definition of cohabitation for the widowed subsample, which
includes respondents who were widowed during the survey. Respondents living with theirchildren were assigned a value of one and zero otherwise. We selected 4,102 and 9,491
valid respondents for the married and widowed subsamples. Unmarried respondents were
excluded from our analysis. Although we use cohabitation as a dependent variable formarried and widowed individuals, its contents differ between both subsamples.
Table 1 shows a wide variation between the two subsamples in terms of cohabitation(married: 30.6% and widowed: 78.2%), suggesting that marital status is an important
determinant in the living arrangements of the elderly (Hoerger et al., 1996; Zhang, 2015).
The elderly tend to live with their children following the death of their spouse. This isreasonable since the elderly need physical support owing to deterioration in functional
abilities or emotional support in the case of a deceased spouse (Korinek et al., 2011).
2.3 Independent Variables
In China, public pension and social welfare systems remain underdeveloped and theelderly primarily depend on their children for physical, emotional, and financial support(Korinek et al., 2011). Before the 1970s, China mainly depended on agriculture. The only
way to improve output and increase their wealth was to extend their labor force by fostering
several children. Consequently, the average number of children (Children) in our
subsamples is more than four (married: 4.510 and widowed: 4.925). The high average
number of children should be explained with some caution. To employ an over-identified
4

model, we exclude individuals with one child or no children, which seems to increase thesample average. However, those who were subject to the one-child policy had one child,unless they were exempted (Zhu, 2003). Thus, we see an obvious decline in the average
number of children before and after the one-child policy.
We control for age (Age) and the quadratic form of age (Age_2) to capture thenonlinear trend of cohabitation. According to previous studies, the sign of age can be
modified before and after a certain threshold. We expect the sign of age to be negative andthat of its quadratic form to be positive. This is because the elderly tend to need lessphysical or emotional support before the threshold and live independently; however, as theygrow older, these needs are likely to increase, especially after the threshold. As mentioned,
the age widely varies between the two subsamples (married: 78.197 and widowed: 91.533).
The rate of elderly mortality rapidly grows with an increase in age and thus, the average age
in the widowed subsample is higher than that in the married subsample.
We believe activities of daily living (ADL) are the most appropriate instrument tomeasure elderly health status given the tasks accounted for (bathing, dressing, toileting,indoor transferring, feeding, and continence). We use a dichotomous variable to measureeach of the six items (respondents are assigned a value of one when they need assistanceand zero otherwise) and calculate the total score, ranging from zero to six, where zeromeans no limitation on ADL. The two subsamples considerably vary in ADL (married:
0.229 and widowed: 0.839), indicating that the respondents in the married subsample arehealthier than those in the widowed subsample. This may also imply that the probability of
cohabitation in the married subsample is lower than that in the widowed subsample owing
to the greater need for physical support in the latter. However, the causal explanation of
ADL may be subject to the endogeneity bias in health conditions; thus, one should becautious when explaining the causal effects of ADL when not accounting for endogeneity.
In this study, however, we include ADL because our primary aim is to minimize omitted
variable bias rather than interpret the causal effects of ADL estimates (Van Houtven &Norton, 2004).
We use annual household income in the previous year (Income), ownership of realestate property (Ownership), and main financial support (Financialrt, Finacialch,Financiallg, and Financialwb) to control for the effects of economic factors. We find no
significant difference in the average annual household income of the previous year 1
between the two subsamples (married: 22.030 and widowed: 22.573; unit: 1,000 yuan). In
the case of a higher annual household income, the elderly may be economicallyindependent and live away from their children and possibly with their spouse. Since we
1

According to CLHLS’ coding book, if the annual household income in the previous year was higher than
100,000 yuan, the final data recorded it as 100,000 yuan. We made the following rectification to correct suchdata bias: if the respondent reported an annual income of 100,000 yuan, we recorded it as 125,000 yuan.

5cannot clearly determine contribution by an elderly member to annual household income,we explain income with some caution. The rate of real estate owners in the marriedsubsample is about three times that in the widowed subsample but only 14.4% on average.
We expect that this economic factor is a good proxy for bequest motivation. If the elderly
own real estate, it is likely that their adult children will cohabitate with them to inherit theproperty by providing informal care (Yin, 2010). The main source of financial support
includes retirement pension, adult children, local government aid, self-employment, andother support measures. We use binary variables to define main sources of financial support.
If the main financial source is retirement pension, Financialrt takes the value of one andzero otherwise. We treat Financialch (adult children), Financiallg (local government),
Financialwb (self-employment), and other sources as reference groups. The most importantsource of financial support in our subsamples is adult children (married: 42.3% andwidowed: 78.6%) (Korinek et al., 2011). In addition to annual household income, we use
retirement pensions (Financialrt) to measure the degree of economic independence(married: 29.4% and widowed: 11.3%).
Sex is measured dichotomously: the variable takes the value of one in the case of amale respondent and zero for a female respondent. The rate of male respondents in themarried subsample (66.9%) is more than twice that in the widowed subsample. This result
can be attributed to the shorter life span of males. The rural variable is also dichotomously
coded on the basis of the respondents’ residence in 2008: the respondent takes the value of
one if he/she is from a rural area or town and zero otherwise. However, there is no
significant difference between the two subsamples in terms of residence (married: 57.9% vs.
widowed: 62.7%). We also control for ethnicity (ethnic = 1, non-ethnic = 0). Education ismeasured by a continuous variable. Most of the elderly in our sample did not have theopportunity to enroll in school and therefore, educational attainment levels are rather low.
Table 1 shows that educational attainment for the married subsample is three times that for
the widowed subsample (3.434 years). Finally, we control for variation in provinces(reference group: Shaanxi), which are not shown in Table 1.
Table 1 Summary Statistics
MarriedWidowedVariables

MeanStandard deviation

Mean

Standard deviation

Cohabitation

0.306

0.461

0.782

0.413

Children

4.510

1.764

4.925

2.037

Age

78.1979.134

91.533

9.656

Age_2

6198.255

1472.594

8471.548

1717.555

Sex

0.669

0.471

0.300

0.458

Rural

0.579

0.494

0.627

0.484

Ownership

0.140

0.347

0.041

0.199

6

Ethnicity

0.039

0.194

0.055

0.228

Income22.03026.64922.57326.507

ADL

0.229

0.931

0.839

1.651

Education

3.473

4.060

1.261

2.706

Financialrt

0.294

0.456

0.113

0.316

Financialch

0.423

0.494

0.786

0.410

Financiallg

0.035

0.183

0.052

0.222

Financialwb

0.176

0.381

0.033

0.177

Observations

4,102

9,491

Note: Income is presented in units of 1,000 yuan.

3.

Hypothesis

3.1 Hypothesis
Economic theory of fertility indirectly determines fertility as a result of parental choice
between current and future consumption; thus, children can be thought of as an investment
good (Cochrane, 1975). This is particularly the case in developing countries, where public
pension and social welfare systems are largely rudimentary. The elderly have to depend on the
support of their adult children in their later life. However, previous studies offer mixed resultson the effects of number of children on cohabitation with the elderly. Thus, this study attempts
to provide empirical evidence on the topic by correcting the endogeneity bias. We consider
cohabitation as the most efficient way of gaining physical and emotional support as it
minimizes transaction costs such as travel time (Hoerger et al., 1996). Accordingly, wehypothesize that, ceteris paribus, an additional child increases the probability of cohabitation.
4.

Empirical strategy
4.1 Identification strategy

This study aims to examine the causal effects of the number of children on living
arrangements of the elderly. However, using an OLS or probit model may give us biased
estimation results owing to the endogeneity from the number of children. For example, theelderly may try to obtain sufficient support and accordingly, decide the optimal number ofchildren, indicating the possibility of a reverse causal relationship. We draw on Angrist andEvans (1998), who use parents’ sex preferences and mixed sex preferences regarding children
as instrumental variables to correct the endogeneity bias and estimate the impact of number ofchildren on parents’ labor supply. As China mainly depended on agriculture prior to the 1970s,
there were strong preferences for a son who could improve output and join the labor force. We
assume a direct influence of preference for a male child on the number of children.
7

To correct the endogeneity bias, we apply an instrumental variable approach using maledummies for the first and second parities. We use a dichotomous variable to measure each
instrumental variable. Respondents with a son are assigned the value of one and zerootherwise. We assume that the bearing of a male child decreases the total number of children
because parents’ demand for a male child is satisfied. Thus, the signs of both instrumental
variables are assumed to be negative.
The following regression models are used to link the number of children and our
instrumental variables:Childreni = α1 + β1firstparityi + β2secondparityi + X λ + ηi,(1)where Childreni denotes number of children, subscript i is respondent number, firstparityi andsecondparityi are dummy variables indicating male of first and second parities, λ is acoefficient vector, and ηi is an error term. X is a vector for control variables including age,square of age, sex dummy, ethnicity dummy, rural area dummy, ADL, educational attainment,
ownership of real estate property dummy, annual household income in the previous year, main
financial support dummies, and prefectures dummies. We expect the signs of β1 and β2 to be
negative, indicating that preferences for a son decrease the optimal number of children.
In the first stage, we use equation (1) to predict the number of children. In the second
stage, we use equation (2) to estimate the effects of the number of children on living
arrangements for the elderly:
Y i = α2 + β3PChildreni + Zδ + εi,(2)where Yi denotes living arrangements of the elderly defined using dichotomous variables(cohabitation: Yes = 1, No = 0), subscript i refers to respondent number, PChildreni is thepredicted number of children using equation (1), and β3 is the causal effect of our interest. We
expect β3 to be positive, indicating that an additional child increases the probability of
cohabitation. δ is a coefficient vector and Z is a vector for control variables including age,square of age, sex dummy, ethnicity dummy, rural area dummy, ADL, educational attainment,
ownership of real estate property dummy, annual household income in the previous year, main
financial support dummies, and prefectures dummies. εi is an error term.
5. Estimation results
5.1 Estimates of children equation
Table 2 presents the first stage results of the children equations for the two subsamples.
Column 1 shows negative first (male) and second (male) parities for the married subsample,
indicating a decrease in the total number of children without controlling for covariates, which8

is consistent with our expectation (first parity: −0.226 and second parity: −0.178). We see thatthe magnitude of coefficients in column 2 reduces compared to that of coefficients in column
1. However, the results show that the coefficients of the two variables are negative andstatistically significant at the 1% level (first parity: −0.194 and second parity: −0.167). The
results for the widowed subsample are presented in columns 3 and 4. The signs of thecoefficients for the first and second parity dummies in column 3 are both statisticallysignificant and negative without controlling for covariates. However, the coefficient of thesecond parity (male) is statistically non-significant at the 10% level when controlling forcovariates2. The magnitude of all coefficients in the widowed subsample is less than that ofcoefficients in the married subsample, indicating that the effects of preference for a son on
childbearing differ between the two subsamples, possibly because of a cohort effect. Overall,our results are consistent with the hypothesis that a male child (first and second parities)
decreases the total number of children.
Table 2 Estimates of Children Equations
MarriedWidowedIndependent variable

(1)

(2)

(3)

(4)

First parity−0.226***−0.194***−0.099**−0.101**(0.055)(0.049)(0.042)(0.042)−0.178***−0.167***−0.079*−0.067#(0.050)(0.049)(0.042)(0.041)Other covariates

No

Yes

No

Yes

Adj R20.00610.21490.00070.0427

Obs.

4,062

4,062

9,360

9,360

Second parity

Notes:
Dependent variable: number of children*, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. # represents
statistical significance at the 10.3% level.
The figures in parentheses are standard errors.

5.2 Married subsample
Columns 1–3 in Table 3 present the estimation results for the married subsample.
Column 1 shows the probit model estimates for the probability of cohabitation without
correcting the endogeneity bias of the number of children. The covariates include age, squareof age, sex dummy, ethnicity dummy, rural area dummy, ADL, educational attainment,
2

We find that the coefficient of the second parity (male) is statistically significant at the 10.3% level.

9ownership of real estate property dummy, annual household income of the previous year,
main financial support dummies, and prefectures dummies. It also shows that the coefficientfor number of children is statistically significant and negative at the 1% level. As for themagnitude, an additional child decreases the probability of cohabitation by 1.4 percentage
points, which is in contrast to our expectation. This is possibly because a higher number ofchildren mean greater potential for daily care or financial support, thus diminishing the
likelihood of cohabitation (Zhang, 2015). However, this estimation result may becontaminated by the endogeneity bias. To correct this, we use an instrumental variables
approach and find that the coefficients for number of children becomes positive andstatistically significant at the 5% level (columns 2 and 3 of Table 3), which is in line with our
expectations. We also find that, after controlling for effects from other factors, an additionalchild increases the probability of cohabitation by 66.6 percentage points and the marginal
probability is about 10 percentage points higher than that without covariate estimates.
In terms of age (column 3 of Table 3), we find that an additional year significantly
decreases the probability of cohabitation by 62.3 percentage points. When using the quadratic
form of age to capture increasing effects, the quadratic must eventually turn around and thesign of the quadratic is expected to be positive. Thus, when age passes the turning point, theprobability of cohabitation will increase with age. We can obtain a turning point using thecoefficient for age that is more than twice the absolute coefficient value for the quadratic formof age (Wooldridge, 2012). The turning point in this study is 78. In addition, we find thatmales and those belonging to an ethnic minority cohabitate with a higher probability thantheir counterparts. The likelihood of cohabitation for the elderly living in rural areas
significantly decreases by 28.1 percentage points compared to those residing in the city.
Although additional ADL significantly increases the probability of cohabitation by 9.7
percentage points, the potential endogeneity of limitations in ADL may bias the causal
explanation for the estimated results. Thus, one must exercise some caution with explaining
ADL. The purpose of including ADL is to reduce variation in the error term and improve thepreciseness of estimated coefficients. The coefficient for educational attainment shows apositively correlation with the likelihood of cohabitation but is statistically non-significant.
The coefficient for retirement pension as a main financial resource is statistically positive,
indicating that adult children consider retirement pension to be an attractive factor when
deciding to cohabitate with their elderly parents. This result is contrary to our expectation that
financial independence decreases the likelihood of cohabitation for the elderly. However,since cohabitation results from negotiation between elderly parents and their adult children,the latter may not live economically independent from their parents and have to cohabitate
with them, which is consistent with the result for annual household income in the previous
year. In the case of affluent parents or households, adult children prefer to live with theirelderly parents. We do not find ownership of real estate property to significantly increase theprobability of cohabitation, indicating that bequest motivation is too small to detect or real10

estate ownership may not be a good proxy for bequest motivation.
In general, two indexes are applied when validating instrumental variables. A good
instrumental variable must be satisfied by two conditions. First, the instrumental variables
must be highly correlated with the endogenous variable. We use first stage F-statistics toevaluate the correlation between the instrumental and endogenous variables. We derive
F-statistics (columns 2 and 3) of 13.42 and 31.89, which is greater than 10, indicating that our
instrumental variables are highly correlated with the endogenous variable (Stock & Watson,2011). The second condition is that the instrumental variables are not correlated with the error
term. Since we construct an over-identified model using two instrumental variables, we use
Amemiya–Lee–Newey’s minimum chi-square statistic to test the second condition. The null
hypothesis is that instrumental variables are not correlated with the error term. The result does
not reject the null hypothesis at the 5% significance level and thus, our instrumental variables
are valid.
5.3 Widowed subsample
We adopt the same estimation method as that for the married subsample. We use a probit
model to estimate the effects of number of children on the probability of cohabitation. The
results are reported in column 4 of Table 3 and include the same covariates as those in themarried subsample. The coefficient that is of interest to this study, number of children, isstatistically significant at the 1% level. An additional child decreases the probability of
cohabitation by 0.8 percentage point. However, it is doubtful whether this result can beinterpreted as the real causal effect of number of children on the probability of cohabitation
owing to the endogeneity bias.
To eliminate the bias, here as well, we use preference for a son as an instrumental
variable to estimate the coefficient for number of children. The results are presented incolumns 5 and 6 of Table 3. After controlling for the covariates, we find that the magnitude of
the coefficients in column 6 increases to more than the magnitude of those in column 5 andthe coefficients for number of children are positive and statistically significant at the 5% level.
The results in column 6 show that an additional child increases the probability of cohabitation
by 109.3 percentage points. Although the first stage F-statistics in column 5 are less than 10,
indicating the instrumental variables may be weak instruments, after controlling for thecovariates, we find that our instrumental variables are highly correlated with the endogenous
variable given that the F-statistics are greater than 10.
As for age effects, we find that an additional year of age decreases the probability of
cohabitation by 29.7 percentage points. We find no significant result for sex or ethnic minority.
The effect of the rural dummy decreases the probability of cohabitation by 23.4 percentage
points, which is a finding similar to that for the married subsample. Since ADL is highly
correlated with age, the effect of ADL significantly increases the probability of cohabitation
by 17.7 percentage points. Here as well, it is important to explain ADL with some caution.
11

Next, we find that retirement pension and annual household income statistically increase theprobability of cohabitation, indicating that retirement pension and annual household income
are attractive factors for adult children to cohabitate with their elderly parents. Widowed
elderly may need more physical and emotional support from their children and thus, children
as the main financial resource increases the probability of cohabitation, which is in contrast
with our findings for the married subsample. An interesting result is that ownership of realestate property significantly decreases the probability of cohabitation by 37.9 percentage
points. A possible explanation is that the probability of inheriting property increases as parents
grow older and all children may want to cohabitate owing to strong bequest motives. In thiscase, elderly parents may find it difficult to choose which child to live with and this may
influence the cohabitation behavior of the elderly.
Although the magnitudes of the estimation results for the two subsamples differ, the signof the coefficients is consistent with our hypothesis that the likelihood of cohabitation
increases with the number of children.
Table 3 Probit and IV probit estimates for living arrangement models
MarriedWidowed

(1)

(2)

(3)

(4)

(5)

(6)

Estimation method

ProbitIV probit

IV probit

ProbitIV probit

IV probit

Children−0.014***0.559***

0.666***−0.008***1.031**

1.093**(0.005)(0.186)(0.220)(0.002)(0.418)(0.471)−0.081***−0.623***−0.023***−0.297***(0.013)(0.130)(0.007)(0.098)0.000***

0.004***

0.000***

0.002***(0.000)(0.001)(0.000)(0.001)0.018

0.261***−0.056***−0.066(0.017)(0.092)(0.0101)(0.090)0.112***

0.337**

0.054***

0.050(0.044)(0.152)(0.016)(0.159)−0.034*−0.281***−0.019**−0.234**(0.018)(0.090)(0.009)(0.092)0.035***

0.097***

0.048***

0.177***(0.008)(0.030)(0.004)(0.022)−0.001

0.015−0.0010.008(0.002)(0.010)(0.002)(0.013)0.058

0.364**

0.072***

0.678**(0.035)(0.143)(0.024)(0.281)0.118*

0.192

0.115***

0.508**

Age

Age_2

Sex

Ethnicity

Rural

ADL

Education

FinancialretFinancialch

12

Financiallg

Financialwb

Ownership

Income(0.032)(0.127)(0.035)(0.221)

0.024

0.054

−0.0260.390(0.053)(0.191)(0.036)(0.317)

0.030

0.074

−0.0390.225(0.036)(0.133)(0.039)(0.305)−0.062***−0.032−0.125***−0.379**(0.023)(0.106)(0.027)(0.150)0.003***

0.012***

0.002***

0.007***(0.000)(0.001)(0.000)(0.001)

Prefecture

Yes

No

Yes

Yes

No

Yes

Obs.

4,102

4,062

4,062

9,491

9,360

9,360

First stage F-statistics

-

13.42

31.89

-

4.43

12.6

Chi-sq. statistic

-

0.408

0.006

-

0.008

0.000

P-value-

0.52290.9358-0.93010.9951

Note:
Dependent variable: cohabitation with children (Yes = 1, No = 0).
*, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.
“Chi-sq. statistic” represents the Amemiya–Lee–Newey minimum Chi-square statistics.
The figures in parentheses are standard errors.

6. Discussion and Conclusions
Studies have examined the effects of economic resources and demographic changes onliving arrangements of the elderly using number of children as a control variable, but havelargely provided mixed results owing to the endogeneity bias. This study, however, focuses on
the causal effects of the number of children on the living arrangements of the elderly in China
using an instrumental variable design to correct the endogeneity bias. In addition, we use
preference for a male child as an instrumental variable, which is reasonable given that such apreference prevails in China. Our study reveals that the number of children positively affects
the probability of cohabitation in China.
Cohabitation seems to be the most efficient way to support the elderly in China.
However, to control the population scale, in 1979, the Chinese government imposed theone-child policy. The policy aimed to reduce the pressure of increasing population on natural
resources by limiting the number of children to one per set of parents, with some exceptions.
As the exogenous shock of number of children significantly affects the probability of
cohabitation, parents who were influenced by the one-child policy may not obtain sufficient
support from their children in their old age. In addition, weak public pension and social
welfare systems may widen the gap between the demand and supply for physical, emotional,
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and financial support and the elderly were likely to foster many children to ensure sufficient
support.
Although the Chinese government abolished the one-child policy, allowing all couples tohave two children, it has not arrested its efforts to control the population scale. According toour estimation results, an additional child increases the probability of cohabitation; however,
the Chinese people still cannot choose to bear their desired number of children. Since therespondents in our data are mainly 65 years or older, their childbearing behavior was not or
partially affected by the one-child policy and their average number of children is greater thanfour. However, parents completely affected by the one-child policy may have only about
one-fourth of the average number of children compared to that in our sample. In the future,
we do not expect the influencing factors considered in this study (Table 1) to drop as rapidly
as the number of children.
The number of children can significantly affect the living arrangements of the elderly.
With the public pension and social welfare systems developing, the function of children insupporting the elderly may gradually weaken. However, the development of such systems ishighly dependent on the younger generation. For example, the present “pay as you go”
pension system is entirely supported by the younger generation, in the absence of which thesystem could collapse. Therefore, abolishing family planning policies and improving thefertility rate play a crucial role in China’s response to the increasing elderly population.
Despite its contribution, this study is subject to certain limitations. The data used in thisstudy are from the 2008 wave of the Chinese Longitudinal Healthy Longevity Survey.
Although we try to control for the cohort effect of age and use two subsamples to estimate theeffects of the number of children, we cannot completely detect the cohort effect on living
arrangements, which may bias the estimation results. Thus, future studies should consider
applying panel data to control for the cohort effect of age and other dynamic factors.
Acknowledgments
We thank the seminar participants at Tohoku University and conference for theircomments. We especially appreciate the valuable comments by Yoko Ibuka, Midori
Wakabayashi, and Kentaro Nakajima. We acknowledge the data provided by the ChineseLongitudinal Healthy Longevity Survey, Center for Healthy Aging and Family Studies,
Peking University. All remaining errors are our own.
This study was also financially supported by the JSPS KAKENHI [grant number
JP26380356].

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