OSIPP Discussion Paper : DP-2018-E-004

Can Two Consecutive Generations’ Data Predict Longterm Intergenerational Transition?
Evidence from China with three generations
April 10, 2018
He Zhu†Graduate student of Osaka School of International Public Policy (OSIPP)

Tsunehiro Otsuki
Professor, Osaka School of International Public Policy (OSIPP)JEL Classification: J25, O14, J62
Keywords: Intergenerational Human capital transition, China, Human capital
Abstract:
Most of the studies on long-term intergenerational human capital transition are restricted totwo consecutive generations based on the Becker-Tomes model, and assume that thetransition will be wiped out during the third generation. However, in developing countries
such as China, ancestors play a key role in the family decision-making process. Thus, thisresearch uses a data set of China rural households, which includes three generations of data,
to analyze the long-term intergenerational transition. The results provide empirical evidence
that separate generations have had an independent and significant influence on the offspring’s
human capital outcome. Precisely, the grandparent generation influences the child generation
independently rather than influencing the child generation through the parent generation.
Therefore, the influence of generations on educational achievements has been overestimatedby the data that only encompass two consecutive generations.

†"Corresponding author. Osaka School of International Public Policy, Osaka University,
Address: 1-31 Machikaneyama, Toyonaka, Osaka 560-0043, JAPAN.
Email: zhuhesi@gmail.com"

1 Introduction
Disparity of intergenerational human capital transition exists widely in education, income, andsocial status. In China, there is a social norm that the level of education changes people’s
fortune, which drives all society to pursue high educational achievements. Thus, this research
focuses on the education transition between generations. The scope of the past research on
long-term intergenerational human capital transition has been restricted to two consecutive
generations: the parents and their children. The most cited method on measuring long-term
intergenerational human capital transition is the Becker-Tomes model. This model assumes
that the achievement of the child generation is influenced by the parent generation, and the
grandparents influence the child generation through influencing the parent generation. If theprediction of the Becker-Tomes model were to be considerate perfect, the separate generation
would have no influence on the human capital, in which the grandparent generation shall haveno direct influence on the child generation.
There is a branch of overseas studies that discussed the long-term intergenerational humancapital transition and relied on using data from just two consecutive generations (Golley, 2013;
Labar, 2011; Congbin, 2008; Borjas, 1992; Cork, 2013; Chetty, 2014). However, a research
conducted by Clark (2012) pointed out that the validity of two consecutive generations’analysis relies heavily on the validity of that assumed model. In addition, Stuhler (2013) showsthat the extrapolation error — the difference between the extrapolated long-run persistence andtrue long-run persistence — cannot be ignored when only being based on data from twoconsecutive generations. Mikael (2016) argued that the Becker-Tomes model cannot easily berecovered from data only covering two generations, because it requires that the transition be
an AR(1), either with a serially correlated endowment term that is uncorrelated with parents’outcome, or with a serially uncorrelated endowment term that might be correlated with parents’outcome. Therefore, the predictions based on two generations can be misleading.
China is known as a country that values family, and the family structure has thus played a
key role in Chinese society. Considering the role of grandparents in the family, multiple
channels may exist for them to influence the child generation and transform human capital
independent of the parent generation. First, especially when their spouse dies, a grandparent
may influence children directly by living with them. Second, a grandparent may give financial
support through presents to the grandchildren directly if their grandchildren are admitted to auniversity, and for festival celebrations. Last, grandparents may influence their grandchildren
directly by making decisions for them. Within the Chinese traditional family structure, there
are several studies in the humanity field that discuss the grandparents’ impact on children. Onestudy done by Shi (1993) concluded that the grandparents play a significant role in raising thechildren when the parents are away for work. Chen (2000) examined how the physicalconditions and well-being of the elderly in families are influenced by children, and the results
showed that retired elderly parents gain personal satisfaction and self-esteem from taking careof their grandchildren. Therefore, the grandparents play a significant role in Chinese typicaltraditional families, and may have a strong independent influence on the young generation
through several channels and for several reasons. Nevertheless, research on long-term
intergenerational human capital transition is still mainly based on the data of two consecutive
generations.
Since the Becker-Tomes model may be biased, it is necessary to analyze whether the longterm intergenerational human capital transition can be estimated with more than two
consecutive generations’ data. This research uses a data set of China rural households, which
includes three generations for each household, to analyze the long-term intergenerationaltransition. We use the term “grandparents” for the first generation, “parents” for the second
generation, and “children” for the third generation throughout this paper. The main purpose ofthis research is to measure to what extent can the data of two consecutive generations analyze
the long-term intergenerational human capital transition. We began with a measurement of
whether the grandparent generation directly influences the child generation’s educational
outcome, and compared the difference between the predicted transition and the real transition
measured by two and three generations’ data, respectably. The results confirmed that humancapital transition has been overestimated by the data of only two consecutive generations.
In addition, we estimated another two models to prove. First, we used the educational
outcome from the grandparent generation as the instrument for the outcome of the parent
generation in the model suggested by Clark (2012). The results concluded that the AR(1) model
failed to predict the long-term intergenerational transition due to the generation-specificdeviations from the long-term social position of families. Second, we ran an AR(2) model that
included both the parent and grandparent generation’s educational achievement. The results
suggested that the grandparent generation has a significant independent influence on the childgeneration’s educational achievement.
Last, we explored whether the gender differences influence the intergenerational
educational transition. The findings indicated that gender differences influence the outcome of
the transition from the elders to their offspring.
This paper is organized as follows. Section 2 gives a short introduction of the internationaland China literature review for this research. A brief description of the data set is provided inSection 3, and the empirical methodology and results are shown in Section 4. Section 5
discusses the gender differences between education mobility. The last section summaries theconclusion of this research and discusses the implications of the findings.
2 Literature review
The estimation of transition from parents to children is widely used in predicting the long-term
intergenerational human capital transition. A research conducted by Chetty (2014) used
population data of The United States to predict the intergenerational income transition throughthe parent to child generation. Their research concluded that intergenerational transition varies
across the national income distribution and different regions. They suggested that the reason
for spatial variation may be caused by factors of residential segregation, income inequality,
school quality, social capital, and family structure. Solon (2002) discussed how the genderdifferences influence the income transition from the parent to child generation, and concluded
that intergenerational income transition is consistently weaker for daughters than for sons.
Clark’s (2013) research discussed what is the true rate of social mobility in Sweden with asure name analysis. In this research, he introduced a latent variable of “luck of family social
status” for each generation !, which can be interpreted as,"#$% = '"# + )# , (1)*# = + "# + ,# , (2)*#$% = -*# + .# , (3)where " is the latent variable, * is the outcome of social status, ), ,, and . are the error terms.
In this situation, it could be possible that ' is not equal to -, for,0 -+ = '

%
24

%$( 3
4)

, (4)

25

Thus, it is clear that the result from two AR(1) model’s prediction will be different than theprediction from the data of two separate generations apart. This comparison is provided in
Section 4, and the results showed that the prediction is almost 10 times different between these
two methods.
The studies in China that followed up with international research only used two consecutive
generations of data to predict the intergenerational human capital transition. Qin (2016) usedthe 1989–2009 China Health and Nutrition Survey (CHNS) data to analyze the impact of theintergenerational transmission of human capital on the income mobility in China from theparent to child generations. Fan (2015) conducted a research using the 2010 Chinese Family
Panel Studies (CFPS) to investigate the temporal patterns of cross-sectional inequality andintergenerational mobility during the economic reform era in China. Magnani (2015) analyzed
China social mobility from the data of the 1990 and 2000 Chinese Population Censuses, andconclude that the intergenerational transition from the parent to child generations becomesincreasingly stronger in China urban areas. Considering that the obtained predicted transition
with two consecutive generations’ data can be biased, this paper explores whether the longterm intergenerational human capital transition can be consistently predicted by the data of
only two consecutive generations in China.
3 Data description
This research uses the household survey data called the Longitudinal Survey on Rural Urban
Migration in China (RUMiC) from the Institute for the Study of Labor (IZA). The previous
studies that used this data set focus on three different aspects of migration. The first one isregarding the relationship between remittance and migration. The second one is on the wage
gap (Klaus et al. 2016; Rachel et al. 2015; Björn et al. 2014; Hartmut and Yuhao 2013; Klaus
et al. 2014; Zhong et al. 2014). The last one concentrated on the well-being of migrants (WeiHuang 2015; Xin Meng and Chikako Yamauchi 2015) or education attendance of migrants’children (Massimiliano Tani 2016).
The RUMiC data set consists of three parts: The Urban Household Survey, Rural Household
Survey (RHS) and Migrant Household Survey. The survey was initiated by a group of
researchers at the Australian National University, the University of Queensland and the Beijing
Normal University under a support of the IZA, which provides the Scientific Use Files. The
financial support for RUMiC was obtained from the Australian Research Council, theAustralian Agency for International Development (AusAID), the Ford Foundation, the IZA
and the Chinese Foundation of Social Sciences. The RUMiC dataset is based on a face-to-faceinterview, and the interviews were conducted in 2008. This paper used the RHS dataset of 2008.
The sampled households were selected randomly from nine provinces in China, namely
Sichuan, Chongqing, Anhui, Hubei, Henan, Guangdong, Zhejiang, Jiangsu and Shanghai. ThisRHS dataset contains the information of the highest education accomplished for eachhousehold, which allows us to analyze the education transition within the household. The
reason for using RHS only rather than combining it with the Urban Household Survey is thatduring the Chinese Culture Revolution, the parents of urban families had been sent to rural
areas and may have had an influence on the analysis of education transition. Thus, we restricted
our data to rural household data to analyze the education outcome correlation between thegenerations in the long term.

For all generations, we restricted the samples of households that have information for all
three generations. The educational level was measured as years of schooling, which we
calculated by the average years required for the highest educational degree accomplished. For
the third generation, we discarded samples with ages younger than 20 in order to assure that
our samples have the possibility to accomplish the compulsory education (in China thecompulsory education consist of 6 years of primary education and 3 years of secondary
education, which is generally completed at age 15 or 16). With these conditions, we were left
with 772 useful samples of households usable for our estimation.
The intergenerational human capital transition is shown in Figure 1, and the educational
achievement is presented in Figure 2. Table 1 gives the descriptive statistics for all the variablesin the empirical analysis. Since the numbers of observations is almost the same acrossgenerations as shown in Figure 1, we are allowed to conduct the intergenerational transition
analysis. From Figure 2, we find that the educational achievement is very low for eachgeneration in China’s rural areas. However, the years of education still shows slow growththrough each generation from the grandparent to child generation.

Figure 1. The generation transition through three generations
G1"770"(1909+1947)"

Grandparents

Male 239"Female"531

770

G2"772"(1936+1971)

Head"of"househould"

Male"399"Female"373

and"spouse
772

G3"771"(1964+1989)

Sons/daughters" and"their"spouseMale"447"Female"324771

Source: RHS 2008

0.2

Density.4.6.8

Figure 2. Educational achievement for each generation

5
10
Years of education of parent

0.2

Density
.4

.6

.8

0

0

5

10
Years of education of child15

20

Source: RHS 2008

Table 1. Descriptive statistics""
Grandparent"
Parent"Child"""
Male"
Female"Male"
Female"Male"
Female"Years&of&schooling&&Mean"
3.196653"
1.401501"
8.822055"
6.935657"
8.910515"
8.707692"
Std."Dev."
3.354263"
2.657122"
2.644975"
3.331366"
4.188501"
3.82133"
Min"Max"[0,"12]"[0,"12]"[0,"16]"[0,"16]"[0,"19]"[0,"16]"
Observations"
239"
533"
399"
373"
447"
325"
"
Age&&
&
Mean"
80.2887"
80.69868"
52.26065"
50.32976"
26.03132"
24.82716"
Std."Dev."
7.138215"
7.053139"
6.548024"
6.434626"
5.193468"
4.772963"
Min"Max"[62,"97]"[62,"100]"[38,"73]"[37,"68]"[20,"45]"[20,"42]"
Observations"
239"
531"
399"
373"
447"
324"
Source: RHS 200815

4 Methodology
As addressed before, the most cited model of intergenerational human capital transition is the
Becker-Tomes model. The Becker-Tomes model measures mobility between the twogenerations using the framework of the first-order autoregressive process (AR(1)) of the timeseries regression. The Becker-Tomes’ two generation model is specified as:*# = ∅*#8% + 9)# + :# , (5))# = ;)#8% + <# , (6)where, * is the outcome such as educational achievement, ) represents endowment, : and <are the error terms, ! indicates the child generation, ! − 1 indicates the parent generation, ∅ isthe estimated level of influence from the parent generation, and τ is the estimated level ofendowment for the child generation. This model is under the strong assumption that τ = 0
or+; = 0. Although the Becker-Tomes model has an analogy with the AR(1) process byregarding the generation as time dimension, two-generation data only allows them to include
the variables of a pair of parents and their children, which existed at the time of the survey.
Under this condition, the AR(1) model omitted the endowment variable or assumed that theendowment is uncorrelated with the parents’ outcome, and simplified their model into a crosssection model that can be estimated by the ordinary least squares (OLS). In addition, thisframework can be easily extended to the three generation case by replacing *#8% with *#8@ ,allowing us to measure the grandparents transition so long as three-generation data is available.
Thus, the estimation models for the two-generation and three-generation models can be writtenas:*#,A = ' + -*#8B,A + C′EA + :A , (7)where F+ ≥ +1, *# is the education of the child and *#8B is the education of the parents when j =1, and grandparents when j = 2, and H indicates the household i. "A is a vector of controls
including a cubic in age for generation ! and generation ! − +F , and gender dummies forgeneration ! and ! − F, and :A is the error term. When j = 2, this model allows us to measure
the influence of the grandparent generation on the child generation. Thus, through this model,
the influence of the grandparent generation can be compared with that of the parent generation.

The estimation of this model allows us to discuss our results both from the regression
coefficient and the predicted correlation coefficients. If the measuring of Becker-Tomes modelholds well, the actual intergenerational transition therefore should be the same with thepredicted transition from the two consecutive generations’ data.
Figure 3 presents the difference between the concepts of our model (the dynamic model) and
Becker-Tomes’. Our model allows us to examine the direct impact of the grandparent
generation on the outcome of the child generation, instead of examining the indirect impact on
the child generation through a direct impact on the parent generation.

Figure 3. Intergenerational transition in China rural area

The"Becker+Tomes"model
Grand"
parents

Parents

Children

Parents

Children

The"Dynamic"model
Grand"
parents

Children

Parents

Table 2. Intergenerational human capital transition results from rural households
Years"of"schooling""

Variables"

Parent"generation"""
0.110***"(0.0395)"""
Years"of"schooling"of"grandparents"
Years"of"schooling"of"parents""
Controls"
Constant""
Observations"
R+squared"
Prediction""
yes"+208.0**"(83.48)"770"0.186"""

Child"generation"""""
0.137**""(0.0584)""
0.118**"(0.0565)"
yes"
yes"
53.05"
61.22"(116.2)"(55.30)"769"
771"
0.062"
0.064"
0.01298"(0.11*0.118)"""

Note: each column represents different regression results.
Figures in parentheses are t statistics.
*** Significant at the 1% level** Significant at the 5% level* Significant at the 10% level

The prediction from the Becker-Tomes model is shown in the Prediction line at the level of
0.01298. Table 2 presents the intergenerational human capital transition in two generations: (1)the education transition from the grandparent generation to the parent generation is 0.11, thethe education transition from the grandparent generation to the child generation is 0.137, andthe the education transition from the parent generation to the child generation is 0.118; (2) the
education from the grandparent to child generation is statistically significant and not equal to0; (3) the prediction from the Becker-Tomes model of the education transition from the
grandparent to child generations is approximately 0.013(0.11*0.118), and almost 10 times
smaller than the result from the regression, which is 0.137.
Therefore, we can conclude that the data of two consecutive generations has overestimatedin the long-term intergenerational human capital transition. At the same time, we can reject the
hypothesis that the data of two consecutive generations is adequate to analyze the long-term
intergenerational human capital transition.
Next, in order to interpret why our results are different from the data of two consecutive
generations, we conducted two other analyses after the main regression. One is the instrumental
variable model suggested by Clark (2012), and the other is the AR(2) model where we extended
the AR(1) model by including both the parents and grandparents generation in the regression.
The Clark model is an instrumental variable model using the grandparent generations’ dataas the instrumental variable to indicate the child generations’ outcome, and is written as:

*#,A = ' + -*#8%,A + C′EA + :A , (8)*#8%,A = I′*#8@,A + J′EA + KA , (9)where *# is the outcome of the child and *#8% is the outcome of the parents, *#8@ is the outcomeof the grandparents, t represents the generation and H indicates the child. "A is a vector ofcontrols,+:A and KA are the error terms.
Table 3. Comparing the results between the basic model and the iv-model(1)"
Years"schooling"of"child"(2)"Years"schooling"of"child"

0.110***"

0.118**""(0.0395)"(0.0565)""

Observations=770"

Observations=771"

R+squared=0.186"

R+squared=0.064"

1.295**"

1.295**"(0.561)"(0.564)"

VARIABLES"
OLS&&

Years"schooling"of"parent"

"
IV&

&

Years"schooling"of"parent""
Controls"

yes"

yes"

Constant"

161.4**"

159.1**"(78.48)"Robust"score"chi2(1)"(79.09)"7.47148**"7.45565**"

Robust"regression"F(1,758)"

7.37214**"7.35635**""

0.929403"(p"="0.3350)"

Observations=771"

Observations=769"

Years"schooling"of"grandparents"

Yes"

Yes"

Age"of"grandparents"

No"

Yes"

"

Test"of"over+identifying"restrictions"
Score"chi2(1)""Instruments""

Note: each column represents different regression results.
Figures in parentheses are t statistics.
*** Significant at the 1% level** Significant at the 5% level* Significant at the 10% level

Table 3 presents the results both from the Becker-Tomes model (OLS/AR(1) model) andthe instrumental variable model. The upper portion of column (1) shows the results from the
grandparents’ education attendance to the parents’ education attendance, and the upper portionof column (2) shows the results of the parents’ education attendance to the children’s education

attendance. The lower portion from Table 3 presents the results from the instrumental variable
model on education attendance for the parent generation to the child generation. The lower
portion for column (1) shows the results of using the variable of “years of schooling of
grandparents” as the instrumental variable to “years of schooling of parents”, and the lower
portion for column (2) presents the results of using the variables of both “years of schooling of
grandparents” and “age of grandparents” as the instruments. From Table 3, we can conclude
that for the analysis regarding the relationship of education attendance between the parent
generation and the child generation, the iv model is more superior than the AR(1) model, giventhat all of the falsification tests (endogenous test, weak iv test and over identifying test) support
the iv strategy.
The AR(2) model is based on the AR(1) model, but includes a prior generation, and can bebeen written as:*A# = ' + -% *A#8% + -@ *A#8@ + C L "A + ,A , (10)where * is the outcome, H is the individual household, ! denotes the generation and :A# is theerror term.
Table 4. Comparison between grandparents and parents
VARIABLES"""
Years"schooling"of"parent""
Years"schooling"of"grandparent""
Controls"
Constant"""
Observations"
R+squared"

Years"schooling"of"child"""
0.102**"(0.0499)"
0.127***"(0.0458)"yes"
108.4"+101.6"769"
0.073"

Note: Figures in parentheses are t statistics.
*** Significant at the 1% level** Significant at the 5% level* Significant at the 10% level

Table 4 gives the results of the AR(2) model. The results are clear in that the impact fromthe grandparent generation is significantly different from 0; in rural areas of China, “years
schooling of grandparent” increased 0.127 years, and the education years to child generationrose by 1 year.

Therefore, we can conclude that only using two consecutive generations’ data will overestimate the long-term intergenerational human capital transition.
5 Extended research of gender differences
We discuss the influences of gender power on intergenerational human capital transition in thisextended research section. Table 5 shows the transition from the parent generation to childgeneration. Table 6 presents the transition from the grandfathers, and Table 7 yields thetransition from the grandmothers.

Table 5. Transition from parent generation to child generation""
Father""to"Son"
Father"to"Daughter"
Mother"to"Son"
Mother"to"Daughter"
VARIABLES"
Years"of"education"" Years"of"education"" Years"of"education" Years"of"education"
Education"of"parent"
0.197*"+0.240*"0.238**"
0.0709"+0.109"+0.13"+0.092"+0.0933""
Controls"
yes"
yes"
yes"
yes"
Constant"
186.7**"
28.53"+70.9"
212.4**"+79.89"+92.21"+113.5"+88.21"""
Observations"
R+squared"

241"
0.094"

158"
0.08"

206"
0.111"

166"
0.069"

Note: each column represents different regression results.
Figures in parentheses are t statistics.
*** Significant at the 1% level** Significant at the 5% level* Significant at the 10% level

Table 6. Transition from grandfather
VARIABLES"
Education"of"
grandfather""
Controls"
Constant"""
Observations"
R+squared"

Education"of"Father"

Education"of"
Mother"

Education"of"
Son"

Education"of"
Daughter"+0.108*"(0.0577)"
yes"+159.4"(178.8)"0.211**"(0.103)"yes"+278.4"(364.1)"+0.194*"(0.0994)"yes"
85.72"(263.4)"0.0287"(0.131)"yes"+405.8"(361.3)"146"
0.112"

93"
0.225"

133"
0.108"

106"
0.055"

Note: each column represents different regression results.
Figures in parentheses are t statistics.
*** Significant at the 1% level** Significant at the 5% level* Significant at the 10% levelTable7. Transition from grandmother
VARIABLES"
Education"of"
grandmother""
Controls"
Constant"""
Observations"
R+squared"

Education"of"Father"

Education"of"
Mother"

Education"of"
Son"

Education"of"
Daughter"

0.148**"+0.0657"
yes"+302.7**"(120.6)"0.218***"+0.0685"yes"+136.0"(142.4)"0.357***"+0.115"yes"288.3"(177.6)"0.15"+0.0951"
yes"+241.6"(169.2)"252"
0.098"

279"
0.130"

312"
0.150"

218"
0.086"

Note: each column represents different regression results.
Figures in parentheses are t statistics.
*** Significant at the 1% level** Significant at the 5% level* Significant at the 10% level

From Tables 5, 6 and 7, we find that there are some differences in transition through elders
by gender. First, females in general have a larger and positive influence on their offspring. It
can be possible that most of the female elders are spending more time on taking care of theiroffspring. Second, male elders have a possible opposite influence on their offspring. This may
be considered as male elders having a tendency to prefer one child among their offspring. Third,
the females of the child generation tend to gain a small and non significant influence from theirancients compared with males.
6 Conclusion
This research provided evidence that the persistence of long-term intergenerational humancapital transition in China’s rural area is much stronger across three generations than two
generations. In addition, this result has been confirmed by the Instrumental Variable model andthe AR(2) model that include the information of three generations rather two generations.
One possible explanation for the result of the long-term intergenerational human capitaltransition in China is that the Chinese traditional family is a structure where the elderly are thedecision makers who influence the whole family and other offspring.
Through the main empirical analysis and the further analysis models (the IV model and theAR(2) model), we can reject that the two consecutive generations data is adequate to analyze
the long-term intergenerational human capital transition in China. Furthermore, our results line

up with other overseas studies on long-term intergenerational transition (Lindahl 2015; Stuhler2013). By dividing the sample by gender through the analysis of intergenerational humancapital transition, we find that that there are some differences in transition through elders bygender.
The implication of this research is that only using two consecutive generations’ data on
long-term intergenerational human capital transition should be interpreted with caution,
especially for those who are interested in developing countries and have similar traditionalfamily cultures as China.

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Appendix
The representative of RUMiC data.
Compared with 2000’s China’s census data, the parent generation’s data shows that the
distribution of educational achievement is remarkably similar with each other. The following
table provided the distribution of educational achievement for the parent generations from the
RUMiC data as compared to the census data, obtained from the National Bureau of Statisticsof the People’s Republic of China, weighted to 10 million people.
Table of educational outcome from census and RUMiC
Education"achievement"
Census(10"million)"
Parent"generation"
Elementary"school"
318"
251"
Junior"middle"school"
244"
324"
Senior"middle"school"
30"
116"
Specialized"secondary"school"
8"
14"
Polytechnic"college"
3"
4"
Undergraduate"
1"
3"
Postgraduate"""
Wave"of"year"
2000"
2008"

Educational"outcome
350
300
250
200
150
100
50
0
Elementary"school

Junior"middle"
schoolSenior"middle"
Specialized"
schoolsecondary"school

Census(10"million)

Polytechnic"
college

Parent"generation

Undergraduate