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Psychological Well-Being of Only Children: Evidence from the One-Child Policy

  • Albert Park and Lingwei Wu EMAIL logo
Published/Copyright: April 28, 2025

Abstract

This paper examines the effect of growing up as an only child on individual psychological well-being. Using national survey data – the China Family Panel Studies (CFPS), we employ the Kessler-6 scale to measure psychological well-being. Considering family fertility decisions are made endogenously, we use the instrumental variable (IV) strategy using both regional and cohort variations generated by the One-Child Policy in China. Our results show that being an only child as a result of the One-Child Policy is associated with a higher level of psychological distress.

JEL Classification: J13; I31

Corresponding author: Lingwei Wu, School of Economics, Fudan University, Shanghai Institute of International Finance and Economics, Shanghai, China, E-mail: 

We are grateful to the editor and two anonymous referees for their helpful comments and suggestions. We are also grateful to Isabelle Attané for sharing the IFPPR data, and colleagues and participants of the Asian Conference on Applied Microeconomics/Econometrics, seminar at the Shanghai University of Finance and Economics, the QMP Methodology Seminar, and the Family/Gender Workshop at Mannheim for their helpful comments. Wu acknowledges financial support from the 2024 Applied Economics Peak Program of Shanghai Institute of International Finance and Economics, and this study is also sponsored by the Shanghai Pujiang Programme. All remaining errors are our own.


Funding source: Applied Economics Peak Program of Shanghai Institute of International Finance and Economics

Funding source: Shanghai Pujiang Programme

  1. Research funding: This work was supported by the Applied Economics Peak Program of Shanghai Institute of International Finance and Economics and Shanghai Pujiang Programme.

Appendix A: Robustness Checks and Heterogeneous Analysis

This section provides the robustness checks, further discussions regarding the policy intensity measure, as well as heterogeneity analyses in addition to the main analysis.

A.1 Robustness Checks

In the first robustness check, we validate our IV by examining whether the timing of the firstborn is influenced by the introduction of the One-Child Policy. In particular, one may be concerned that mothers would alter the timing of their first births in response to the policy. To empirically test this concern, we conduct a mother-level analysis, where the dependent variable is the mother’s age of having the first birth, and the key explanatory variables include the interaction terms between the mother’s year of birth dummies and the IFPPR, province fixed effects, and mother’s year of birth fixed effects. As shown by Figure A4, the province policy intensity does not systematically explain the timing of the first births .

Next, Table A3 compiles multiple robustness checks of the baseline specification. First, we use both measures of psychological distress generated from the sum of scores and factor analysis. The results are shown in Column 1–3 and 4–6, respectively, for the two measures. In the second layer of robustness checks, we construct alternative policy exposure measures, with different birth spacing distributions. As discussed earlier, our baseline IV uses the birth spacing distribution within a 5-year window. In the robustness checks, we use two different distributions, with the distribution of birth spacing with range [1,10] and [1,15] (see Panel B and C, in Figure A3 respectively).[11] In Table A3, Column 1 and 4 use E x p o s u r e c 10 , while Column 2 and 5 employ E x p o s u r e c 15 .

In the third layer of the robustness checks, we employ an alternative measure of the policy intensity – the EFR used by Li and Zhang (2017) and Zhang (2017). Specifically, Li and Zhang (2017) calculates the excess fertility rate (EFR) of Han women over and above the one-child rule in 1981. Thus this measure essentially captures the degree of deviation of the fertility outcomes from the policy target, and we used the reversed scale of the EFR so that a higher value of it would capture more strict policy implementation. By conditioning on pre-existing fertility preferences and other regional socioeconomic characteristics, the excess fertility rate can capture the intensity of policy implementation. Thus, when using the EFR, the instrument is Exposure c  × EFR p , where the exposure variable sticks to the baseline construction of IV. The results using this alternative IV are shown in Columns 3 and 6 of Table A3.

In all robustness checks shown in Table A3, we account for individual controls, parental controls, province-cohort controls, and we also control for province fertility preference, which is proxied by the standardized average number of ancestry halls in the community in the CFPS. As shown by the estimates of the only child effect, the coefficient estimates are largely similar to the estimate from Table 1.

In addition to the regression specifications, we also provide robustness checks for standard errors. The baseline regressions imposed standard errors clustered at the province by year of birth level, and in Table A3 we also add the Wild bootstrap p-value when clustering by province (number of clusters = 25 provinces). With clustering by province, the effect of being an only child is marginally statistically significant at the 15 % significance level for EFR-Instrument, while the counterpart for IFPPR-Instrument stays more robust.

A.2 Discussion of Policy Intensity Measures

This section provides discussions regarding the comparison between Attane (2002)’s measure of One-Child Policy intensity (IFPPR) and the widely used measure of fines in Ebenstein (2010). In particular, the fines used in Ebenstein (2010) reflect variations in the punishments for excess fertility across provinces and years. In this vein, comparing the IFPPR measure and the fertility fines would be important and informative.

Table A4 shows the Pearson correlation coefficient between different policy intensity measures, including (i) the province average fine rate between 1979 and 2000, (ii) the IFPPR intensity variable, and (iii) an indicator variable of whether a province had a high fine rate, which is defined by being above the median value of the average fine rate between 1979 and 2000. This table shows a significant positive correlation between the IFPPR and the average fine rate between 1979 and 2000. Moreover, when using a binary indicator variable of whether a province had a high fine rate, we find that the IFPPR intensity variable is also positively correlated with the likelihood of being a province with relatively high fertility fine rates.

A.3 Heterogeneity Analysis

In addition to the main analysis, this section examines heterogeneity of the only child effects by gender and Hukou status, respectively.

The first heterogeneity analysis examines whether the only-child effects may differ by gender of the first birth, where we add the interaction term between the gender dummy and the only-child indicator. The instrumental variable for the interaction term is the interaction term between the IV and the gender dummy. In a similar vein, the second heterogeneity analysis examines the rural-urban Hukou differences of the only-child effects. We add the interaction term between an urban indicator variable and the only-child indicator, and the instrumental variable for this interaction term is the interaction term between the IV and the urban Hukou dummy.

Table A5 presents the results for the heterogeneity analysis, where Column 1 and Column 2 show the heterogeneity results by gender and by Hukou status, respectively. As shown in Column 1, we observe a negative coefficient of the interaction term between the male dummy and the only child status. However, the gender difference is not statistically significant from zero, and the results do not reveal significant evidence regarding the heterogeneity effects by gender. In Column 2, we examine the results regarding the urban-rural heterogeneity analysis. As shown by the results, the only child effect for the rural sample is marginally significant at the 15 % significance level, while the magnitude is comparable to the baseline results (=0.699, as in Column 6 of Table 1). Regarding the interaction term between the urban Hukou status and the only child indicator, we find that the coefficient is small in magnitude and not statistically significant. Thus, the results do not reveal evident urban-rural disparity in Column 2.

Appendix B: Appendix Tables and Figures

B.1 Appendix Figures

Figure A1: 
Fraction of children by birth order. Note: Authors’ calculation based on the CFPS survey 2010.
Figure A1:

Fraction of children by birth order. Note: Authors’ calculation based on the CFPS survey 2010.

Figure A2: 
Distribution of psychological distress from K-6 scale. Note: This graph shows the distribution of psychological distress as measured by the K-6 self-report measure Kessler et al. (2003). Panel A shows the standardized values of the sum of the K-6 scores, and Panel B illustrates the psychological distress factor generated by a factor analysis to the 6 items.
Figure A2:

Distribution of psychological distress from K-6 scale. Note: This graph shows the distribution of psychological distress as measured by the K-6 self-report measure Kessler et al. (2003). Panel A shows the standardized values of the sum of the K-6 scores, and Panel B illustrates the psychological distress factor generated by a factor analysis to the 6 items.

Figure A3: 
Distribution of birth spacing between the first and second birth. Note: This graph shows the distribution of birth spacing between the first and second birth of mothers. The birth spacing distribution between the first- and second-born is calculated based on mothers with full fertility history in the CFPS 2010 survey, where the sample is restricted only to those who have completed the second birth before 1975. Panel A, Panel B, and Panel C show the distribution of birth spacing with different restrictions of windows, in [1,5], [1,10], and [1,15]. Thus, Panel A, B, and C impose 




∑


k
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1


5


d

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k

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=
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${\sum }_{k=1}^{5}d(k)=1$



, 




∑


k
=
1


10


d

(

k

)

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1


${\sum }_{k=1}^{10}d(k)=1$



, and 




∑


k
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15


d

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k

)

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${\sum }_{k=1}^{15}d(k)=1$



, respectively. In the baseline analysis, we use the distributional information in Panel A, and the robustness checks employ the information from Panel B and C.
Figure A3:

Distribution of birth spacing between the first and second birth. Note: This graph shows the distribution of birth spacing between the first and second birth of mothers. The birth spacing distribution between the first- and second-born is calculated based on mothers with full fertility history in the CFPS 2010 survey, where the sample is restricted only to those who have completed the second birth before 1975. Panel A, Panel B, and Panel C show the distribution of birth spacing with different restrictions of windows, in [1,5], [1,10], and [1,15]. Thus, Panel A, B, and C impose k = 1 5 d ( k ) = 1 , k = 1 10 d ( k ) = 1 , and k = 1 15 d ( k ) = 1 , respectively. In the baseline analysis, we use the distributional information in Panel A, and the robustness checks employ the information from Panel B and C.

Figure A4: 
Mother’s exposure to the policy and their age at first birth. Note: For this figure, the regression is specified at the mother-level, where the dependent variable is mother’s age at first birth, and the key explanatory variables include the interaction terms between the mother’s year of birth dummies and the policy intensity (IFPPR), province fixed effects, and mother’s year of birth fixed effects. The base group includes mothers who were born in 1935. This figure shows the coefficient estimates of the interaction terms between the mother’s year of birth and the IFPPR.
Figure A4:

Mother’s exposure to the policy and their age at first birth. Note: For this figure, the regression is specified at the mother-level, where the dependent variable is mother’s age at first birth, and the key explanatory variables include the interaction terms between the mother’s year of birth dummies and the policy intensity (IFPPR), province fixed effects, and mother’s year of birth fixed effects. The base group includes mothers who were born in 1935. This figure shows the coefficient estimates of the interaction terms between the mother’s year of birth and the IFPPR.

B.2 Appendix Tables

Table A1:

Summary statistics.

Variables Obs Mean Std. dev. Min Max
Panel A: individual level summary statistics (first-born sample)
Only child 3,016 0.25 0.43 0 1
Year of birth 3,016 1,975.55 5.81 1,965 1,984
Male 3,016 0.49 0.50 0 1
Father’s years of schooling 3,016 6.70 4.38 0 21
Mother’s years of schooling 3,016 4.53 4.42 0 16
Psychological distress (std.) 3,016 −0.11 0.84 −0.79 5.40
Psychological distress (factor) 3,016 −0.11 0.77 −0.71 5.04
Mother’s year of birth 3,016 1,951.84 6.03 1,935 1,965
Mother’s age at first birth 3,016 23.72 3.50 16 42
Panel B: province level summary statistics
IFPPR (std.) 25 0.00 1.01 −1.87 1.75
EFR (std.) 25 0.02 1.05 −2.34 1.68
Log GDP pc at birth year 25 5.84 0.70 4.69 7.94
Log GDP pc at age 5 25 6.25 0.77 4.86 8.28
Log GDP pc at age 10 25 6.77 0.92 4.97 8.80
Tertiary industry share at birth year 25 0.20 0.03 0.14 0.26
Tertiary industry share at age 5 25 0.22 0.05 0.14 0.33
Tertiary industry share at age 10 25 0.26 0.06 0.15 0.37
  1. Notes: This table shows the descriptive statistics of the sample, where we explicitly focus on the first-born individuals for analysis. Panel A shows individual-level summary statistics, and Panel B shows province-level summary statistics of key variables.

Table A2:

The Kessler 6 scale.

During the past 30 days, All of Most of Some of A little of None of
about how often did you feel … the time the time the time the time the time
…nervous? 1 2 3 4 5
…hopeless? 1 2 3 4 5
…restless or fidgety? 1 2 3 4 5
…so depressed that nothing could cheer you up? 1 2 3 4 5
…that everything was an effort? 1 2 3 4 5
…worthless? 1 2 3 4 5
  1. Notes: The above questions ask about the frequency of respondents’ feelings according to each item during the past 30 days in the CFPS survey. For each question, respondents are invited to indicate the case that best describes the frequency of their feelings.

Table A3:

Robustness checks.

Sample = the first-born
Dep. var: psychological distress (std.) Dep. var: psychological distress (factor)
Alternative exposure Alternative intensity Alternative exposure Alternative intensity
Birth spacing in [1,10] Birth spacing in [1,15] EFR Birth spacing in [1,10] Birth spacing in [1,15] EFR
(1) (2) (3) (4) (5) (6)
Only child 0.561* 0.561* 0.538** 0.508* 0.508* 0.492**
(0.295) (0.295) (0.263) (0.268) (0.268) (0.239)
Wild bootstrap p-value 0.0861 0.0851 0.151 0.0871 0.0881 0.150
Observations 3,016 3,016 3,016 3,016 3,016 3,016
Prov. FE Yes Yes Yes Yes Yes Yes
Year of birth FE Yes Yes Yes Yes Yes Yes
Individual controls Yes Yes Yes Yes Yes Yes
Fertility pref. Yes Yes Yes Yes Yes Yes
Province-cohort controls Yes Yes Yes Yes Yes Yes
Parental controls Yes Yes Yes Yes Yes Yes
First-stage F-stat. 78.57 78.71 71.11 78.57 78.71 71.11
  1. Notes: Onlychild is a dummy variable indicating whether one is an only child. Columns 1–3 employ the standardized measure of psychological distress, and Columns 4–6 employ the factor measure of psychological distress. In terms of birth spacing distributions used, Columns 1 and 4 use the window of [1,10], and Columns 2 and 5 use the window of [1,15]. In terms of policy intensity measures, Columns 1, 2, 4, and 5 use the IFPPR measure, whereas Columns 3 and 6 employ the EFR measure (Li and Zhang 2017). Here, a higher value of the reversed EFR scale represents stricter policy enforcement. The provincial fertility preference is proxied by the standardized average number of ancestry halls in the community. The Wild bootstrap p-value is added when the standard error is clustered by province (number of clusters = 25 provinces). *** p < 0.01, ** p < 0.05, * p < 0.1.

Table A4:

The one-child policy intensity measures: a comparison.

Pearson correlation coefficient Average fine rate (1979–2000) IFPPR (std.) High average fine indicator
Average fine rate (1979–2000) 1
IFPPR (std.) 0.3728*** 1
High average fine indicator 0.8106*** 0.2419*** 1
  1. Notes: This table shows the Pearson correlation coefficient between different policy intensity measures, including (i) the average fine rate between 1979 and 2000, (ii) the IFPPR intensity variable, and (iii) an indicator variable of whether a province had a high fine rate, which is defined by being above the median value of the average fine rate between 1979 and 2000.

Table A5:

Only children and psychological distress: heterogeneous analysis.

Dependent variable Psychological distress (std.)
IV estimates (1) (2)
Only child 0.885** 0.647
(0.379) (0.419)
Only child × Male −0.296
(0.241)
Only child × Urban Hukou 0.068
(0.309)
Observations 3,016 3,016
First-stage F-stat 39.21 34.84
Prov. FE Yes Yes
Year of birth FE Yes Yes
Individual controls Yes Yes
Parental controls Yes Yes
Province-cohort controls Yes Yes
  1. Notes: Individual control variables include dummies for gender, and Hukou status. The First-stage F-statistic denotes the Cragg-Donald Wald F-statistic for testing weak instruments. Parental controls include the father’s and mother’s years of schooling. The province-cohort controls include the provincial log GDP per capita and proportion of tertiary industry at one’s year of birth, age 5, and age 10, respectively. Standard errors are clustered at province-year of birth level. *** p < 0.01, ** p < 0.05, * p < 0.1, p < 0.15.

Table A6:

Only children and psychological distress: the role of personality traits.

Estimator: TSLS Panel A. The impact of being an only child on mechanism variables: personality traits
Big five traits Conscientiousness Extraversion Agreeableness Openness Neuroticism
Dep. var. Rigorous Lazy Efficient Talkative Outgoing Conservative Rude Tolerant Considerate Creative Artistic Imaginative Worried Nervous Relaxed
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)
Only child −0.336 0.739** 0.071 −0.015 −0.300 −0.376 0.213 −0.114 −0.431* −0.027 −0.593 0.500 0.069 −0.355 0.039
(0.237) (0.376) (0.237) (0.301) (0.344) (0.348) (0.336) (0.247) (0.235) (0.350) (0.374) (0.306) (0.371) (0.386) (0.278)
Observations 1,973 1,973 1,972 1,973 1,972 1,969 1,973 1,973 1,972 1,972 1,968 1,970 1,973 1,972 1,972
R-squared 0.020 0.016 0.035 0.035 0.015 0.037 0.034 0.032 0.005 0.073 0.023 0.010 0.070 0.044 0.030
Prov. FE Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
Year of birth FE Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
Individual controls Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
Parental controls Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
Province-cohort controls Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
F stat 64.42 64.42 64.39 64.42 64.39 65.13 64.42 64.42 64.39 64.42 65.09 64.32 64.42 64.39 64.39
Estimator: OLS Panel B. Relationship between psychological distress and personality traits, dependent variable: psychological distress (std.)
Personality traits Rigorous Lazy Efficient Talkative Outgoing Conservative Rude Tolerant Considerate Creative Artistic Imaginative Worried Nervous Relaxed
Coef. of traits −0.043 0.045*** −0.072*** −0.009 −0.042** 0.031* 0.014 −0.040 −0.019 −0.025 −0.007 0.016 0.098*** 0.068*** −0.060***
(0.028) (0.017) (0.024) (0.019) (0.020) (0.017) (0.018) (0.030) (0.024) (0.018) (0.017) (0.018) (0.017) (0.017) (0.022)
Observations 1,973 1,973 1,972 1,973 1,972 1,969 1,973 1,973 1,972 1,972 1,968 1,970 1,973 1,972 1,972
R-squared 0.044 0.046 0.047 0.043 0.045 0.043 0.043 0.044 0.043 0.044 0.042 0.042 0.058 0.051 0.047
  1. Notes: *** p < 0.01, ** p < 0.05, * p < 0.1. This table examines the role of personality traits as mechanisms regarding the impact of being an only child on psychological distress. Panel A shows the results of the impact of being an only child on mechanism variables, including 15 personality traits items. The estimated effects are based on the baseline IV strategy with the full set of controls, including province fixed effects, year of birth fixed effects, individual controls, parental controls, and province-cohort controls. Specifically, the individual control variables include dummies for gender and Hukou status. Parental controls include the father’s and mother’s years of schooling. The province-cohort controls include the provincial log GDP per capita and proportion of tertiary industry at one’s year of birth, age 5, and age 10, respectively. Panel B shows the correlation between the mechanism variables (i.e., the personality items) and psychological distress, where OLS estimates are shown. Standard errors are clustered at province-year of birth level.

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Received: 2024-08-05
Accepted: 2025-03-27
Published Online: 2025-04-28

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