Intergenerational earnings mobility in Japan among sonsand daughters : levels and trends ∗Arnaud LEFRANC†

Fumiaki OJIMA‡

Takashi YOSHIDA§

October 26, 2012

Abstract
This paper estimates the extent of intergenerational income mobility in Japan amongsons and daughters born between 1935 and 1975. Our estimates rely on a two-sample
instrumental variables approach using representative data from the Japanese Social Stratification and Mobility (SSM) surveys, collected between 1965 and 2005. Father’s income
is predicted on the basis of a rich set of variables including education, occupation and job
characteristics and we discuss changes in the Japanese earnings structure for cohorts born
between the early 1900s and the 1960s. Our main results indicate that the intergenerational
income elasticity (IGE) for both sons and daughters, in Japan lies around .35, which is anintermediate value, by international standards. We discuss the sensitivity of the IGE tousing either personal or family income as the income variable for both fathers and children
and perform some robustness analysis with respect to the first-step specification and to theage selection rule for children. We also examine changes across cohorts in the IGE. Results indicate that intergenerational mobility has been roughly stable over the last decades.
Lastly, we estimate the intergenerational correlation of earnings.

JEL Codes: D1, D3, J3
Keywords: Intergenerational mobility, elasticity, correlation, earnings differentials, income,inequality, trends, Japan, assortative mating, education.

∗ We thank Jaap Dronkers, Nobuo Kanomata, Tadashi Yagi and seminar participants at Keio university andDoshisha university for useful comments. Access to the SSM data was granted through the SSM 2005 ResearchCommittee, whose support is gratefully acknowledged. This research received financial support from the French
National Research Agency, under the grant TRANSINEQ (ANR-08-JCJC-0098-01).
† Corresponding author. Université de Cergy-Pontoise, THEMA, and IZA. Corresponding address : Université
de Cergy-Pontoise, 33 boulevard du Port, THEMA, F-95011 Cergy-Pontoise. Email: arnaud.lefranc@u-cergy.fr.
‡ Department of Sociology, Doshisha University.
§ Faculty of Humanities and Social Sciences, Shizuoka University

1

Introduction

Over the last fifteen years, an abundant literature has analyzed the extent of intergenerational economic mobility and has revealed that, in many developed countries, a large fraction of economic inequality is transmitted from one generation to the next, within families(Solon 1999, Black & Devereux 2010). While available evidence has contributed to a rich description of the extent of intergenerational transmission, the mechanisms responsible for thistransmission remain largely unstudied. In particular, although evidence seems to suggests thatcountries where income inequality is lower also exhibit more intergenerational mobility, as discussed for instance in Björklund & Jäntti (2009) and Lefranc, Pistolesi & Trannoy (2008), thecontribution of key ingredients of the mobility process, such as such labor market institutions,wage inequality and educational institutions is still, from an empirical perspective, unclear. To
this end, the gathering of international evidence on the extent of intergenerational mobility incountries with different social and economic structure appears as an important step. Anotherimportant limitation of existing evidence, however, in this perspective, is that it has, until recently, mostly focused on western developed countries and much less is known about the extent
of intergenerational mobility in other parts of the world, including Asian countries. The objective of this paper is to fill in this gap and to measure the extent of intergenerational income
mobility in Japan.
Several characteristics of Japan make it an interesting case for the study of intergenerational earnings mobility, in particular from a cross-country comparative perspective. First,
Japan is often seen as a fairly equal society characterized by compressed income differentials
and limited poverty. Indeed, this image seems largely sustained empirically, at least comparedto other countries and until the increase in inequality that occurred in the 1990s (Gottschalk& Smeeding 2000, Tachibanaki 2009).1 The extent to which this high degree of income and,more generally, social equality translates into a high level of economic mobility is of course
an important question, both for the comprehension of contemporary Japan and for the understanding of the intergenerational income mobility process. In this respect, opposing views canbe found. On the one hand, occupational and educational success are often thought, at least inJapanese popular views, to depend little on family origin but rather on individual effort. Thisis summarized by the popular meritocratic belief : ”Doryoku wa mukuwareru” (effort pays).2
1 Whether Japan still is, in the most recent period, an “equal” society seems highly debatable, as discussed in

Tachibanaki (2009).
2 The relevance of this view was challenged with great force in general-audience debates by the book of Toshiki
Sato (Sato 2000) who made the (controversial) claim that the Japanese society had been closing down after the
bubble-growth era of the 1990s.

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On the other hand, Japan is characterized by a strongly differentiated and very competitive
educational system, where success at entering the most prestigious universities, largely conditions future labor market prospects and henceforth motivates considerable financial investmentby the parents. As a consequence, one would expect family background to strongly influence
individual outcomes. Which view is the most relevant is the key question addressed in thispaper.
Evidence on the extent of intergenerational economic mobility in Japan is currently rather
limited, in comparison to the vast literature that has focused on social and educational mobility(e.g. Ishida 1993, Ojima 1998, Imada 2000, Kondo 2000). To our knowledge, only two papers
have examined the extent of intergenerational income mobility in Japan.3 Lefranc, Ojima &Yoshida (2008) provided a first assessment. As the present paper, it relies on the SSM dataset,i.e. a large representative data set covering the second half of the twentieth century. But theanalysis is limited to father-son pairs and the prediction of fathers income rests on a narrow setof individual characteristics. Ueda (2009) offers estimates of intergenerational income elasticities
for male and female based on the Japanese Panel Survey of Consumers. However, this data set
has several limitations that may influence the estimation of the intergenerational elasticity, as
discussed below.
The main contribution of our paper is to offer a robust and in-depth analysis of intergenerational income mobility in Japan among sons and daughters. We measure mobility by the now
standard intergenerational earnings elasticity (IGE), which can be obtained by regressing thelog of individual annual earnings on the log of their father’s earnings. Our analysis relies on
the Social Stratification and Mobility (SSM) survey, a rich survey conducted between 1955 and2005 that gathers information on individual income as well as family and social background.
In the lack of direct observation of father’s income, we use a two-sample instrumental variables
approach as in e.g. Björklund & Jäntti (1997). Father’s income is predicted on the basis ofa rich set of variables including education, occupation and job characteristics. The SSM data
allow to measure intergenerational mobility for a representative sample of children born between
1935 and 1975 and we also examine changes across cohorts in the IGE.
We also perform several robustness analysis. First, our data includes two distinct measuresof income : the first one refers to the individual’s own income; the second to his or her family
income. Having both measures allows in particular to isolate the contribution of marital outcomes to the intergenerational mobility process and we examine the sensitivity of the IGE to
3 A third paper is that of Yoshida (2008) but it is only available in Japanese.

2the income measure used in the analysis. We also evaluate the robustness of our estimates of
the IGE to various changes in the econometric specification, including changes in the first-stepequation used to predict father’s income and changes in the sample of children used to estimate
the IGE.
Incidentally, the prediction of father’s income requires us to examine changes in the Japaneseearnings structure for a large set of cohorts born between the early 1900s and the 1960s, using
income data for the years 1965 to 1995. As a result, an important by-product of this study is to
document long-term trends in the Japanese earnings structure. Compared to existing studies,
our analysis of trends in inequality in Japan offers several advantages. First, it covers a longer
time span than what is usually studied in other papers. Second, it relies on microeconomic
data unlike most studies that have, up until recently, largely used aggregated data. Third, ouranalysis covers all employment sectors, firm size and employment status unlike many studies
that have focused on salaried workers in large firms from the manufacturing sector.
Lastly, we also provide two extensions of our basic estimates of the IGE. The first one
examine possible changes across cohorts in the IGE. The second extension estimates the intergenerational correlation of earnings (IGC). One of the limitations of the intergenerationalelasticity is indeed its sensitivity to changes in the extent of cross-sectional inequality over time,
between the generation of the parents and that of the children. The intergenerational correlation (IGC) is, on contrary, not influenced by such changes and offers a useful complementarymeasure of the degree of intergenerational mobility.
The main result of our analysis is that intergenerational income elasticity in Japan is around.35, which is an intermediate figure in comparative perspective. This elasticity is rather similar
for sons and daughters. It seems constant over time. Lastly, in the case of sons, their overall family income seems less related to parental income than their own individual incoming,suggesting that marital sorting dampens slightly the intergenerational persistence of inequality.
The opposite holds true for daughters. The rest of the paper is organized as follows. Section 2
discusses the estimation procedure and section 3 presents the data used in the analysis. Section
4 presents the results of the first-step estimation and analyzes the main characteristics of theincome structure in Japan and its evolution over time. Section 5 presents the main results forthe estimation of the IGE for sons and daughters and section 6 discusses the sensitivity of theseresults to changes in the specification and sample selection rules. Section 7 examine time-trends
and estimates the intergenerational correlation.

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2

Estimation method

Most of the economic analysis of intergenerational mobility focuses on estimating the IGE inpermanent (or long-term) earnings.4 This elasticity is given by the coefficient β in the followingintergenerational regression model :Yi = β0 + βXi + "i(1)where Yi denotes the log of individual i’s long-term earnings Xi denotes his father’s long-term
earnings. As abundantly discussed in the literature, β should not be seen as a structuralparameter measuring the causal effect of parental resources on child’s earnings, but rather as
a descriptive measure of the intergenerational association in earnings, capturing all possible
channels of transmission.5
Direct estimation of equation 1 requires a considerable wealth of information. Not only
does it call for a linked data set in which both father and child’s earnings are observed but
it furthermore requires one to observe a time-series of individual earnings in order to measure
long-term earnings. Very few data sets satisfy this requisite.
Without such data, β can be estimated using a two-sample instrumental variables (TSIV)
estimation, an approach originally derived in Angrist & Krueger (1995) and Arellano & Meghir(1992). This method was first applied to the estimation of the IGE by Björklund & Jäntti (1997).
The basic principle behind TSIV estimation is to replace Xi in equation 1 by a prediction X̂iformed on the basis of some observable father’s characteristics, Zi .
The data requirements for TSIV estimation are significantly less stringent. The prediction
is derived from a first-step equation which is estimated on a sample that is representative of thefathers’ population, and in which we observe both earnings and the characteristics Zi . Given
the estimation of the first step, the data requirement for the estimation of β is to observe bothchild’s income and father’s characteristics.
TSIV has been extensively used for the estimation of the IGE and its properties are discussed
in several papers including Solon (1999) and Nicoletti & Ermisch (2007). These properties
depend on the choice of the instrument. If the instrument only affects child’s earnings through its
effect on father’s earnings, the estimation of β is consistent. Indeed, in this case TSIV estimation
4 An alternative approach is to estimate siblings correlation (e.g. Björklund, Eriksson, Jäntti, Raaum &Österbacka 2002).
5 For general discussions and surveys of the causal mechanisms underlying the intergenerational transmissionof inequality, see in particular Bowles & Gintis (2002) and Black & Devereux (2010). For recent analysis, seefor instance Anger & Heineck (2010) and Liu & Zeng (2009).

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offers the significant advantage of over-riding the attenuation bias that typically arises, becauseof classical measurement errors, when estimating equation 1 with long-term earnings replaced bycurrent earnings (Solon 1992, Zimmerman 1992, Mazumder 2001). However, if the instrument
has a direct effect on the child’s outcome, than the TSIV estimates are biased and the directionof the bias depends on the sign of the direct effect. For most of the instruments used in thepresent paper, the expectation is that the direct effect will be positive, hence resulting in an
overestimation of the IGE. However, in practice, the papers that have estimated the extent
of this bias generally conclude that the order of magnitude is rather small (see for instanceBjörklund & Jäntti 1997). In section 6, we address this issue and examine the sensitivity of ourIGE estimates to the characteristics used to predict fathers’ income.
The recent literature has also pointed to another potential source of bias in the estimationof the IGE. This second bias, referred to as the life-cycle bias (Jenkins 1987, Grawe 2006,
Haider & Solon 2006), arises when using current earnings instead of permanent earnings in theestimation of the IGE. In the presence of individual heterogeneity in earnings growth over thelife-cycle, current earnings measure permanent earnings with error. Furthermore, the error is
not of the classical type and is correlated with both true permanent earnings and age.6 If ageearnings profiles are steeper for high income individuals, current income differentials, measured
at an early (respectively late) stage of the life-cycle, will underestimate (resp. overestimate)permanent income differentials. This introduces an asymmetric bias in the estimation of β.
Using current earnings early (resp. late) in the life-cycle, as a proxy for child’s permanentearnings will lead to underestimate (resp. overestimate) β. Conversely, using current earnings
early (resp. late) in the life-cycle, as a proxy for father’s permanent earnings will lead tooverestimate (resp. underestimate) the IGE. To address this source of bias, we rely on the
results of Haider & Solon (2006) who indicate that life-cycle bias is small if not nil around age
40.7 As a consequence, our measure of father’s income is predicted at age 40 (see below) andour sample of children is centered around age 40. We also perform several robustness in section
6.
In the end, the specification for the second-step equation comes as follows:

Yit = αt + β X̂i + g(ageit ) + eit(2)

6 The classical measurement error case refer to the situation where measurement error is independent of thetrue value.
7 Since their study is based on US data, one should of course question the relevance of their results in theJapanese context. In the absence of direct replication of their study using Japanese data, this question cannot
be addressed directly.

5where i and t are indices for individual and time. The αt s denote time dummies and g isa fourth order polynomial function in age.8 X̂i is predicted father’s earnings at age 40; thevariable age is normalized to zero at age 40.
Let us now turn to the econometric model used in the first-step to predict fathers’ income.
Our objective is to predict father’s income at the age of 40 on the basis of his education, occupation and job characteristics. In practice, two main issues have to be taken into considerationin the specification of this equation. First, some cohorts, in particular the oldest ones, are observed far away from their mid-career. Hence, to accurately predict earnings differentials at age
40 we need to account for heterogeneity in age-earnings profiles. This is done by introducing
group-specific age-earnings profiles where groups are defined on the basis of their education andemployment status.9 Second, since the first-step equation is estimated on a a large range ofcohorts, covering more than 60 years and there is no reason to expect the effect of individual
characteristics on earnings to be constant over such a long period. Hence we allow the effect ofindividual characteristics to vary across cohorts.10
Given that extreme cohorts, old and young, are not observed over their full working career, it
is not possible to be fully flexible when modeling the interaction of age, individual characteristics
and birth cohorts in the wage equation. In particular, it is not possible to allow age profiles tovary with both individual characteristics and birth cohort. So we only allow age profiles to varywith individual characteristics. Furthermore, given the size of our sample, letting the effect ofindividual characteristics vary freely with birth cohorts would lead to imprecise estimates. As aresult, we impose some parametric restrictions on the shape of cohort trends. We let the effectof individual characteristics vary by interacting these characteristics with a function of birthcohort. We consider three possible functional form for cohort trends : (i) a quadratic functionof birth cohort; (ii) a piece-wise linear trend in birth cohorts that allows trends to differ between
cohorts born before and after 1945; (iii) a step-wise function that allows the effect of individual
characteristics to differ across three broad groups of cohorts : before 1930, 1931-1950, after
1950. We defer to the next section the discussion of the relevance of these functional forms.
8 In principle, the use of polynomial function for age would allow to simultaneously include time and cohort
dummies. Cohort dummies however turn out to be insignificant when added to this specification and their
inclusion does not affect the results.
9 A larger set of interaction terms could be introduced, such as occupation-age interactions. This is done insection 6. In practice, they turned out to be non-significant.
10 In most specifications, the characteristics whose effects are allowed to vary across cohorts are age, educationand self-employment status. We consider other variables in section 6.

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In the end, the first-step model we estimate can be summarized by the following equation :Xict = αt + φ(Zic , c) + ψ( ageict , Zic ) + eict

(3)

where i, c, t are indices for individual, cohort and time; Zic are the father’s individual characteristics, φ captures the effect of these characteristics, which is allowed to vary with c; ψdenotes the heterogenous age profile which is allowed to vary with individual characteristics
and is normalized to be equal to zero when ageict = 40.
Lastly, predicted father’s earnings is given by :X̂ict = φ̂(Zic , c)(4)where φ̂ is a estimate of the function φ.

3

Data

Our data come from the Social Stratification and Social Mobility (SSM) surveys. The SSM
survey has been the primary data source for studies of social and educational mobility in Japan(Ishida 1993, Ojima 1998, Imada 2000, Ishida & Miwa 2008). The first wave of the survey
was conducted in 1955 by the Japanese Sociological Society. Since then, similar surveys wereconducted at intervals of ten years. The earliest waves (1955, 1965 and 1975) focused only on
males. A female sample was collected since the 1985 survey. The questionnaire of the last waveof the survey (2005) has also been used for similar surveys in Korea and Taiwan.
The SSM samples are designed to provide a national representative sample of the population
between 20 and 70 years old. Across the different waves, the size of the male sample varies
between two and three thousands individuals. The questionnaire focuses on the description ofsocial status, educational attainment, social origin, class identification and the perception of
inequality. The most important variables in our analysis are income, which is the main variableof interest, and educational and occupational attainment, which serve to predict father’s incomein the first-step equation. Respondents to the SSM survey are asked to report their income,education, occupation and job characteristics as well as the education, occupation and job
characteristics of their father. As often the case, father’s information is reported ex post by thesurvey respondent and refer to father’s main occupation.
All SSM waves record two distinct measures of income. The first one is individual own

7income. The second one is family total pre-fisc income. In both cases, the variable measuresannual primary income, in the year preceding the survey, before any tax or transfer and includes
both labor and asset income. Furthermore, income information is available for both salaried
and self-employed workers. For most individuals of working age and who actually work, theprimary component of pre-fisc income is labor earnings. Family income is the total of eachfamily member’s individual income in the respondent’s household. Income is available in all
waves of the survey in bracketed form, except for 1965 where income is coded continuously.
The bounds and number of brackets vary across waves, between 17 and 30 main brackets.
Higher income are not top-coded though and a response beyond the top category was coded
continuously. In the regressions, we assign the mid-value of the bracket and use standard linear
regression techniques.11
One of the appealing features of the SSM data is to provide individual data on income forthe entire Japanese labor force, including all industries and employment status, over a long time
period. This represents a significant advantage of SSM, compared to alternative data sources.
In studies of the Japanese wage structure and trends in inequality, the most commonly used data
set has been the Basic Survey of Wage Structure (BSWS) collected by the Japanese Ministryof Health, Labor and Welfare.12 However this data suffers several limitations. In particular,
it is restricted to salaried workers employed in firms with more than 10 employees. Hence, it
excludes in particular self-employed workers, as well as workers in irregular employment forms.
Second, unlike the SSM surveys, the sampling design of the BSWS data has changed over time
which makes its use problematic for studying long term trends.
The education classification used in the different waves of the survey varies across waves
and cohort, reflecting the changes in the Japanese educational system that occurred over thelast century. For older cohorts, the classification distinguishes between five educational levels:
elementary school (6 years of formal schooling), upper elementary (8 years), middle school (11years), college (14 years) and university (17 years). For more recent cohorts, the five educational levels are: junior high school (9 years), high School (12 years), junior college (14 years),
university (16 years) and graduate school (18 years). Given sample size and to assure cross-year
consistency of the education classification, we used a reduced classification that distinguishes
between three educational levels: lower secondary education (or lower), upper secondary education and tertiary education. This corresponds, for instance, to the classification used in Kondo
11 Lefranc, Ojima & Yoshida (2008) uses interval regression to deal with the bracketed form of income andshow that the impact on the estimated IGE is negligible.
12 Among others, Katz & Revenga (1989) and Kambayashi, Kawaguchi & Yokoyama (2008) analyze theJapanese earnings structure and its evolution using BSWS data.

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(2000).
Social status is coded using the Erikson-Goldthorpe-Portocarero (EGP) classification. We
use a variant of the classification in 9 groups, since a change of the questionnaire about the
number of employees between 1985 and 1995 makes it impossible to distinguish between IVa(Small employer) and IVb (Independent) (Kanomata, Tanabe & Takenoshita 2008). In theend, we use the following eight-categories13 : I- Higher-grade professionals, administrators,
and officials, managers in large industrial establishments, large proprietors; II - Lower-grade
professionals, administrators, and officials; higher-grade technicians, supervisors of non-manual
employees; III- Routine non-manual employees, higher grade (administration and commerce)
and lower grade (sales and services); IV- small proprietors and self-employed workers ; V- Lowergrade technicians supervisors of manual workers; VI- Skilled manual workers; VII- Semi- andunskilled manual workers; VIII - Farmers and farm workers. In addition to social status, SSM
also includes additional characteristics of occupation and job position. We use firm size and an
indicator of self-employment status.
In the main samples used in this paper to estimate both the first- and the second-stepequations, we exclude those without positive earnings in the year preceding the survey. The
sample used in the estimation of the first-step equation draws on five available survey waves,
1965, 1975, 1985 and 2005. The reason for excluding 1955 is that income information is missingin that wave for farmers who accounts for a large share of the employment in older cohorts.
The sample is restricted to individuals aged 30 to 59 years old. The main reason for excluding
individuals older than age 60, is that many people in this sample start retiring and living on
pension from this age in Japan, a problem also encountered in the study of Ueda (2009).
Second-step estimations are based on the three most recent waves (1985, 1995 and 2005).14
For reasons already discussed, the children sample is restricted to individuals aged between 30
and 50 years old, i.e. close to the middle of their working career. For each individual in thesecond-step sample, we form a prediction of his father’s income using estimates of the first-stepequation. The prediction is based on reported father’s education, EGP classifications, residential
area and other occupational information. In most cases, individual in the second-step sample
report their father’s birth year. In this case, we use the relevant age-specific returns to education
to predict father’s income. When information on father’s birth year is not available, we predict
fathers income on the basis of the observed distribution of father’s birth cohort, conditional on
13 Our analysis relies on the coding developed by Shirakawa in the SSM research group.
14 The reason for not using earlier waves of the SSM for the second-step is that women are only interviewed
starting in 1985. Furthermore, some information on family background is missing or not recoded homogenously
before 1985.

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child’s birth cohort. Mean values in the samples are presented in table 1.
Lastly, when predicting father’s income for early cohorts, we are limited by the scope of
our first-step sample. The first-step equation is only estimated on individuals born after 1905.
However, about half of the sample born in 1935 have a father born before 1905. To predict
the income of fathers born before 1905, we make the assumption that the earnings structure
among cohorts born before that date is similar to the earnings structure of the 1905 cohort. As
discussed in the appendix, our results are insensitive to this assumption.

4

First-step estimates and long-term trends in income inequality in Japan

Main effects

First-step estimates are presented in tables 2 and 3 for personal and family

income respectively. These estimates are based on the sample representative of the fathers
cohorts and include only male. The first salient result that emerge from this table is therelatively limited extent of earnings differentials across the various groups. For instance, thegap between the two extremes of the social ladder, higher-grade professionals and farmers, isless than .7 log points. Similarly, the difference between the low- and high-education groups
is less than .2 log points. Of course, the ceteris paribus analysis of the coefficients is largely
artificial given the collinearity of the different dimensions but even if we cumulate the above
mentioned earnings gaps, they lead to modest earnings differentials, in comparison to what canbe found in other countries. An interesting comparison can be established with the results of
Lefranc & Trannoy (2005) who use similar approach and classifications. In the case of France,
which is often thought to occupy an intermediate position among developed countries in termsof earnings inequality, they find a gap between the top and bottom social groups of .9 to 1 log
points and of .3 to .4 between top and bottom education groups.
The finding of a relatively small earnings differentials by occupation and education confirms
the previous results obtained in studies based on a narrower period and using the BSWS data
which only covers salaried workers outside small firms (Koike 1988, Katz & Revenga 1989). In
particular Koike (1988) also documents that wage differentials by occupation and educationalgroups are narrower in Japan than in EC countries and the US. Ishida (1990, 1993) using datafor 1975, also finds that the college premium in Japan was much smaller than in the US, even
before the large rise in US inequality.
In contrast to occupation and education, results in tables 2 and 3 indicate that employment

10

characteristics lead to non-negligible earnings differentials in Japan. First, firm-size has a strong
impact on individual earnings : the benefit of being employed in a large firm is larger than theincome gap between the high- and low-education groups. This confirms previous findings oflarge firm-size effects in Japan (Oi 1990, Tachibanaki 2009).15 On the contrary, the effect ofself-employment status on earnings has been seldom analyzed, largely because self-employedworkers fall outside the scope of commonly used data sets such as the BSWS. Our results
indicate that self-employment also positively affects income and has a significant effect.
Tables 2 and 3 also report earnings differentials by residential area. The reference category
are the 6 largest Japanese cities16 . Earnings differentials by residential are sizable, especiallygiven the fact that we already control for education, occupation and employment characteristics.
The main effect of the socio-demographic and employment characteristics tends to be higher
in the case of personal income than in the case of family income. This result is indeed rather
intuitive since we should expect other family members’ income to be less correlated to theindividual’s characteristics than his own income. The only exception is self-employment thathas a stronger impact on family than on personal income. One possible explanation is that thewives of self-employed are often also employed as family workers in family-owned businesses, anactivity from which they would derive an income higher than the average female income.
The second part of tables 2 and 3 report the estimated age-earnings profiles by level of
education and self-employment status. In the specification of the first-step equation, we only
included a quadratic function of age since higher-order terms were not significant. We alsopresent the age-earnings profile in figure 2, panel A. As expected, the slope of age-earnings
profiles increases markedly with education. At the beginning of individual careers, the income
effect of 10 years of individual experience amounts to about .3 log points for individuals withhigher education against about .2 for individuals with secondary education or less. This isconsistent with the findings of Shimada (1981) and Koike (1988). On the contrary, the incomeage profile of self-employed individuals appears, other things equal, flatter than that of othergroups. This confirms the findings of Genda & Kambayashi (2002) using narrower data, fromthe 1989 and 1994 National Survey on Family Income and Expenditure.
15 Since our estimation does not control for job seniority, one may argue that firm-size effects partly reflect
differences in seniority by firm-size. However, the controversy on the extent of returns to job seniority has
also suggested that seniority effects might themselves partly arise from firm fixed-effects (see in particular
Topel 1991, Altonji & Williams 2005). (Hashimoto & Raisian 1985) discuss seniority distribution and its effecton earnings in Japan.
16 Tokyo, Yokohama, Osaka, Nagoya, Kyoto, Kobe.

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Cohort trends Tables 2 and 3 report the estimated changes across cohort in the effect ofeducation, self-employment status and type of area of residence. Figure 2 reports these trends
in the case of respondent’s own income. As already discussed, we consider three possible specifications for cohort trends. In column 1 of the tables and panel B of the figure, trends arecaptured by a quadratic function of birth cohort. In column 2 and panel C, we assume piecewise linear cohort trends, where we allow trends to change among cohorts born after 1945.
Lastly, in column 3 and panel D, the trend is captured by a step-wise function that allows theeffect of individual characteristics to differ across three broad groups of cohorts : before 1930,
1931-1950, after 1950.
For all specifications, trends across cohorts indicate a compression of earnings differentials
in the long-run. Let us first focus on income differentials by level of education. The income
gap between rural and urban area falls markedly as does the advantage of the larger cities
over other rural areas. The earnings gap associated with being self-employed, which is positive
among older cohorts, stays approximately constant among cohorts born before 1940. It falls
with birth cohort afterwards, to reach a value close to zero. The changes in the youngest cohorts
is consistent with the finding in Genda & Kambayashi (2002) who report a fall in the returns
to self-employment in the 1990s, controlling for worker’s age.
According to the quadratic trend specification, the income gap between the bottom educationgroup and the top two decreases from a high value of .5 log points for cohorts born at the
beginning of the twentieth century to a low value of about .2 for cohorts born after World War
II. According to the step-wise specification, the gap falls from around .27 log points to about.22 log points between the extreme cohorts. All specifications indicate that this reductionof the education-income gap is not monotonic over the period. It occurs for the most part
between cohorts born in the early century and cohorts born around WWII. In contrast, earning
gaps are rather constant across cohorts born in the 1945-1965 interval. This time patternroughly coincides with the pace of educational expansion that occurred in Japan throughout
the twentieth century. As shown in figure 1, educational attainment rose markedly over thisperiod, with the bulk of the educational expansion occurring between the early century cohorts
and the cohorts born in the late 1940s. At the end of our period, the downward trend in earnings
differentials seems inverted and we observe a slight increase in earnings inequality. This small
rise in inequality is however much smaller than the one documented in Tachibanaki (2009).
It may be due in particular to the fact that our first-step equation is estimated on a sample
of males aged between 30 and 59 and born before 1975, who were less affected by the rise in12earnings inequality.
Evidence on long term changes in the Japanese earnings structure is relatively sparse andnot always available in English but is largely consistent with the evidence reported here. In its
1996 White Paper, the Economic Planning Agency estimated the returns to college for threebirth cohorts : 1935, 1950 and 1965. The returns to college fall by 25% between the 1935 and1950 cohorts and later rise by 10% between the 1950 baby-boomers and the 1965 cohort. Other
studies have examined changes over time in the returns to education. Most studies conclude toa fall in the returns to education, at least up until the 1980s. For instance Yano (1982), using
BSWS, finds evidence of a fall in the return to college between 1967 and 1980. There is lessconsensus regarding trends at work after 1980. Kambayashi et al. (2008) provide evidence ofa fall in the returns to education between 1989 and 2003. However, this fall mostly concerns
the gap between junior high-school graduates and more educated workers. On the other hand
the gap between high-school graduates and college graduates seems to be relatively flat. Genda(1994) examines trends in the returns to education between 1965 and 1990 using BSWS data
for salaried workers outside small firms. For all cohorts grouped together, his results indicate
an uninterrupted fall in the returns to education, over the period. However, different patterns
emerge by age group. For older workers aged 40 to 50, the returns to education are also
continuously falling. On the contrary, in the age group 20-30, there seems to be a slow rise in
the returns to education after 1980. In other terms, the returns to education seem to be on therise, at least in the early stage of the career, for workers born in the 1950s and after. This isprecisely the trend inversion indicated by our estimates. It is also interesting to note that all
three specifications are consistent on that point.17
While all three specifications indicate the same overall pattern, they differ in terms of theextent of the changes occurring. In particular, the quadratic and piece-wise linear trends specification suggest a larger fall in the returns to education than what is showed by the step-wisefunction. In order to accurately predict father’s income over a broad range of cohorts, it isimportant to know which specification is the most accurate. One first indication is provided by
the various goodness of fit statistics (R-squared, adjusted R-squared, AIC, BIC). Although thedifferences are small, all fit measures indicate that the step-wise linear function better adjusts
the data. Beyond these internal fit criteria, external evidence tend to support the quadraticor piece-wise linear trends assumptions. One of the assumptions of the step-wise function isthat the returns to education and other characteristics are constant within each broad group
17 In the case of the piece-wise linear and step-wise functions, the inflexion is of course constrained a priori by
the parametric hypothesis but this is not the case for the quadratic function.

13

of cohorts. However, existing studies suggest that this does not hold, especially in the case ofolder cohorts. The previously cited evidence from Genda (1994) imply that the college wage
premium, measured at age 40 to 50, has fallen by about 25% between the cohorts born around1920 and those born around 1930. Similarly, Yano (1982) indicates a continuous fall in the return to education between the 1910 cohort and the 1930 cohort. Our quadratic and piece-wiselinear trends are consistent with these pieces of evidence. On the contrary, the step-wise trends
specification is missing part of the long-term changes in the earnings structure.

5

Main results

Table 4 provides estimates of the IGE, based on equation 1 for sons and daughters. Coefficientsin columns 1 to 3 of table 4 give the estimated value of the IGEs for different measures of the childand father’s income. In column 1 the child’s own income is regressed on the (predicted) father’s
income; in column 2, it is regressed on the father’s family income; in column 3 the child’s family
income is regressed on the father’s family income. For each combination of income measures, we
present three different IGEs corresponding to the three specifications of the first-step equation
discussed in the previous section.

5.1

Results for sons

Our main estimates of the IGE for sons are given in panel A of table 4. Estimates range between.28 and .42, with a mean value of .34. The estimated IGE varies with both the measure of income
and the specification of the first-step equation.
Let us first discuss the sensitivity of IGE estimates to the variable used to measure income inboth the fathers’ and children’s generations. Most values reported in international assessmentsof the intergenerational elasticity are estimated using personal labor income. Hence international estimations are most closely comparable to the coefficients reported in column 1, that are
based on reports of both father’s and son’s personal income. This coefficient lie between .32 and.36. The major discrepancy in the measurement of income, between the data used in column
1 and most international estimates is the inclusion of asset income in our measure of personal
income. Strictly speaking, estimates in column 1 represent an average of the intergenerationalelasticity for labor earnings and for asset income, weighted by the contribution of both sources
to personal income. Previous estimates indicate that the intergenerational elasticity for wealthis significantly larger than for labor earnings (e.g. Mulligan 1997). So for the purpose of in-14

ternational comparisons of the extent of the mobility in the personal labor earnings, the figureof .33, in column 1, should be seen as an upper bound estimate of the elasticity in Japan. Of
course, the order of over-estimation is probably rather small, given the share of asset income inoverall income.
Compared to column 1, column 2 regresses sons’ personal income on the overall family
income of their parents. Measuring parental economic status by means of the total family
income, instead of the sole father’s income leads to a slightly higher IGE in the range .36-.42,
i.e .04 to .05 higher than the coefficients in column 1. This suggests that total family income
may better capture the broad nexus of factors that shape individual success. This confirms
results already obtained in several other papers (e.g. Lucas & Kerr forthcoming). In fact, inJapan, the gap between the two estimates appears smaller than what has been found in othercountries, for instance the United States. For this country, Solon (1992) indicates a differencein the estimated IGE using both measures of .09, with the IGEs being respectively .39 and .48
when using father’s earnings or family income.18
Lastly column 3 provides estimates of the IGE based on the regression of sons’ family
income on their parents’ family income. Compared with estimated in column 2, since family
income aggregates the income of both spouses, estimates based on this variable will reflect boththe influence of assortative mating on mobility, and the direct intergenerational transmission
between parents and children. More precisely, as discussed in Chadwick & Solon (2002), theestimated IGE in column 3 is the weighted average of (i) the intergenerational elasticity of
son’s own income to his parents’ family income and (ii) the elasticity of his spouse’s personal
income to the son’s parents’ income, where the weights are given by the share of each of thetwo spouses’ income in the total family income. Using family income (column 3) rather thanpersonal income (column 2) as a dependant variable leads to a fall in the IGE by about .09,
with estimates in the range .29-.32. This suggests a relatively low elasticity between the wife’s
own income and her parents-in-law family resources. Ermisch, Francesconi & Siedler (2006)
report similar results for the UK.
Finally, it is worth discussing the sensitivity of the estimated IGEs with respect to thespecification of cohort trends in the first-step equation. Estimates tend to be lower under
the assumption of a continuous trends (quadratic trends (QT) and piece-wise linear (PW)
specifications) than under the assumption of a stepwise (SW) change in the earnings structure.
18 Other evidence on the incidence of the measure of family economic status in the US can be found in Altonji& Dunn (1991) and Mulligan (1997). Our findings of a smaller gap between the IGEs find using both variables
may be partly attributable to the fact that our measure of father’s income, contrary to earnings measures usedin the US, already incorporates the asset earnings of the father.

15

The gap between the SW and the other two specifications ranges between .035 and .055, ie. 10
to 15% of the estimated IGE. This mostly arises from differences in the prediction of father’s
income in older cohorts. Observed inequality among children is, of course, unaffected by the
choice of the first-step specification. However, predicted inequality among older fathers is lower
under the piece-wise specification than under the QT and PW specifications. Since the IGE
roughly measures what share of father’s inequality is transmitted to their children, a lower
predicted inequality among fathers mechanically translates, for a given degree of inequality
among children, into a higher estimated IGE. As already discussed we believe that the step-wise
specification does not accurately capture trends among fathers, and we believe that specifications
QT and SW better capture trends in the Japanese earnings structure and henceforth provide a
better estimate of the IGE.

5.2

Results for daughters

Estimates of the IGE for daughters are given in panels B and C of table 4. OLS estimates arepresented in panel B for the subsample of individuals reporting positive personal income. This
the case of only 60% of our daughters sample, because of non-participation to the labor force.
Since non-participation is likely to be endogenous, we report selectivity-corrected estimates inpanel C.
The OLS estimates of the IGE for daughter’s personal income, reported in colums 1 and 2 ofpanel B, appear particularly low. With one exception (SW specification, father’s family income)all estimates lie in in the interval .21-.26, which is low by any standard. On the contrary, the
OLS estimates obtained when regressing daughters’ family income on their parents’ predictedfamily income is significantly higher, in the interval .37-.39.
Of course, the large gap between the two sets of estimates might partially arise from theexistence of sample selection in the equation for personal income, since non-response is much
more frequent for this variable. This is confirmed by the estimates in panel C, obtained using
Heckman’s sample selection model. In the selection equation, an indicator for the report ofincome is regressed on marital status, indicators of the number of children, spouse’s income
and education when married, as well as age profile and year indicators. Overall, IGE estimatesobtained in the case of personal income are markedly higher than those obtained using OLS.
These results indicate negative sample selection : women with the greatest income potential
are less likely to participate to the labor market and thus report their own income, which leads
OLS to underestimate the extent of the IGE. Once sample selection is taken into consideration,

16

the IGE rises by about .15.
In the end, this suggests a value of about .35 when regressing daughter’s own income on
fathers’ own income, predicted under the assumption of quadratic or piece-wise linear trends.
As in the case of sons, the IGE appears slightly higher when regressing child’s income on total
parental income rather than father’s personal income : about .4, again, under the QT or PW
specification of the first-step equation. However, it should be noted that once sample selectionis accounted for, the IGE for daughters appears slightly higher (although not significantly so)than the IGE for sons : this indicates a relatively high degree of correlation between daughter’s
potential income and the income of their parents.
Lastly, it is worth noting that the IGE for daughters is less sensitive than for sons to theuse of family income as a measure on child’s outcomes. In the light of the model developedby Chadwick & Solon (2002), this first suggests a rather high correlation between daughter’s
parents’ income and her husband’s own income. Compared to what we found for sons, thispoints to a gender asymmetry in the elasticity of own income to parents-in-law’s income. Thisasymmetry could largely be explained by a more compressed earnings distribution for daughter’sin Japan, together with gender neutral correlation between the characteristics of spouses andthat of their in-laws.

5.3

Comparison with previous estimates

Overall, our results point to a value for the IGE in Japan slightly higher than .3 for sonsand slightly lower than .4 for daughters. More precisely, for sons, the average IGE acrossall estimated specifications is .34 (.33 when ignoring coefficients based the step-wise trends
specification of the first-step equation) and the average IGE for daughters is .39 (.37 without
the step-wise trends specification). This represents an intermediate degree of intergenerational
mobility for sons, compared to other developed countries. Based on available estimates, Japanturns out to be more mobile than countries such as the United-States, France and Italy. It isalso less mobile than most Scandinavian countries.
The results found here also differ slightly from previous results obtained for Japan, in
Lefranc, Ojima & Yoshida (2008) and Ueda (2009). First, the IGE reported in table 4 are slightly
higher than those reported for sons in our previous study (Lefranc, Ojima & Yoshida 2008).
This study suggested a value of the IGE in the inteval 0.22-0.31. However, this estimate wasbased on a less detailed first-step equation. Furthermore, self-employed workers were excluded
from the main sample used in the analysis.

17Our results are also differ from those of Ueda (2009). Based on her estimates, she concludes
that : “The estimated intergenerational elasticity using predicted parental income is 0.41–0.46
for married sons, 0.30–0.38 for married daughters, and marginally less than 0.30 for single
daughters”. Her estimates are based on the Japanese Panel Survey of Consumers for years 1994
to 2004. One major advantage of this data set over the SSM surveys used is that it directly
asks children to report their father’s earnings and income. However, for most individuals in thesample, this information is collected in bracketed form using only 7 intervals.19 Furthermore,
only one observation of parental income is available, which leads Ueda to use predicted father’s
earnings in her analysis, in order to avoid attenuation bias, which is rather similar to ourapproach. Yet, several differences in the sample selection and prediction procedures are likely
to explain the gap between her favorite estimates and those of the present paper. First, ourestimates are based on a much broader range of cohorts. Second, income is observed at thesame time for children and parents. Hence children are observed fairly early in their life-cycle
and parents are observed fairly late. Ueda accounts for possible life-cycle biases by controllingfor age effects but this strategy is only valid if the earnings structure has remained constantover time. On the contrary, section 4 indicates that earnings differentials have diminished overtime. Third, in the case of sons, the results of Ueda only concern married individuals, since
single men, who represent about 30% of the relevant population, are excluded from her data.20
If there is selection into the marriage market this will bias her estimates, presumably downwardthough. At the end of the day, we believe that our estimates are based on a broader and more
representative sample and that our estimation procedure better takes into account the changes
in the earnings structure in the fathers’ generations. Lastly, although Ueda’s conclusions differ
from those of the present paper, it is worth noting that our estimates are still consistent withher broader set of estimates.

6

Robustness analysis

Not being able to observe the long-term earnings of both fathers and their children, leads us toimpose several restrictions on our empirical model. The first ones pertain to the empirical model
used to predict fathers earnings. The second pertain to the way we deal with life-cycle effects
in order to derive estimates of the long-term earnings elasticity from point in time measures ofincome. In this section, we evaluate the sensitivity of our estimates to the first-step specification
19 Earnings are only measured in continuous form for single daughters still living with their parents.
20 According to the 2005 census, 30% of men between 30 year old and 59 year old and 25% of women are single.

18and to the life-cycle effects.

6.1

Sensitivity to first-step specification

In the previous section, we have already discussed the sensitivity of our IGE estimates withrespect to the specification of cohort trends in the earnings structure. We now examine the sensitivity of our estimates to the set of variables used to predict father’s income. When presenting
our econometric model, we have already mentioned that TSIV estimates by be inconsistent if
the variables used as instruments for predicting father’s income also have a direct effect onchildren’s earnings. Most studies tend to conclude that this bias is relatively small. Yet, sincesome instruments might have a more pronounced direct effect on child’s outcomes than others, it is worth investigating how IGE estimates vary when using a broader or narrower set of
instruments.
Results are presented in table 5 and 6. Each table provides results for five possible setsof explanatory variables in the first-step equation and consider the three possible parametricspecifications of cohort trends (QT, PW, SW). Specification A corresponds to the reference
specification of the first-step equation whose results were presented in section 4 and used in the
IGE estimates of the previous section. It includes the following father’s variables : education,social class, self-employment status, firm size, heterogenous age-effects, and interactions between
birth cohort and education, self-employment status and residential area.
Specification B allows for more flexibility in cohort trends and age profiles by allowing forcohort trends in the earnings differentials by EGP social class, as well as EGP-class-specificage profiles. For both sons and daughters, this specification leads to slightly lower IGEs. The
difference with the base specification is rather small though and is around .01 to .02. One
should also note that these differences, as well as all the differences discussed in this section
are not statistically significant. This is an important caveat that should be kept in mind wheninterpreting the changes in coefficients.
Specification C builds on specification B but removes education main effects as well asinteractions between education and cohort or age. Comparing specifications B and C indicatesthat the inclusion of education and interaction terms as instruments tends to dampen the IGE
slightly. Again, the effect stays relatively small. This result differs from the result usuallyobtained in other studies according to which estimates obtained with using education as an
instrument tend to be larger than without, because of a stronger direct effect of education.
This does not seem to be the case in our data. Conversely, specification D removes the EGP-

19

social class from the prediction of father’s earnings. Comparing specifications B and D indicatesthat the inclusion of social class as an instrument tends to increase the estimates of the IGE.
The effect is relatively large, around .05, for the elasticity of sons’ family to the predicted family
income of their parents. On the contrary, in the case of daughters, the effect of excluding father’ssocial class from the set of instruments is very small.
Excluding self-employment status and region of residence from the base specification in
specification E, leads to slightly lower estimates (.01 to .03) for both daughters and sons and in
most cases, although the effect is virtually zero for daughters in column 3 and for daughters incolumn 1.
All in all, this sensibility analysis suggests that the IGE estimates previously discussed are
fairly robusts to variation in the set of first-step instruments. If anything, alternative sets of
instruments lead to slightly lower estimates.
On the opposite, IGE estimates are strongly sensitive to the adequate modeling of cohort
trends in the earnings structure. This is demonstrated by specification F, which builds upon
specification A but removes all cohort trends in the effect of education, employment status andgeographical area. This results in higher estimates for both sons and daughters. Of course, inthe presence of significant trends, these estimates are incorrect.

6.2

Sensitivity to age selection

The recent literature has emphasized the sensitivity of IGE estimates to the age at which bothchildren and their fathers are observed (Jenkins 1987, Grawe 2006, Haider & Solon 2006). Thishas been referred to as the life-cycle bias in IGE estimates. This bias arises from the presenceof individual heterogeneity in age-earnings growth rates, when using current earnings, insteadof permanent earnings, in the estimation of the IGE.21 As shown in several papers, individualspecific earnings growth rates tend to be positively correlated with initial earnings level. As aconsequence, inequality of current earnings underestimates permanent earnings inequality whenmeasured early in the life-cycle and overestimates it when measured at the end of the career.
This introduces an asymmetric bias in the estimation of the IGE. Using current earnings early(resp. late) in the life-cycle, as a proxy for child ’s permanent earnings will lead to underestimate(resp. overestimate) β. Conversely, using current earnings early (resp. late) in the life-cycle,
as a proxy for father ’s permanent earnings will lead to overestimate (resp. underestimate) theIGE.
21 As already discussed, classical measurement error also introduce an attenuation bias. TSIV estimation
corrects for this attenuation bias but is still subject to the life-cycle bias.

20

Several solutions have been offered to account for this bias. Based on the analysis of individual age-earnings profiles in the United States, Haider & Solon (2006) conclude that earnings
observed at ages ranging from the early thirties to the mid forties are fairly representativeof lifetime earnings inequality. Furthermore, if idiosyncratic departures from the mean age–permanent-earnings profile are uncorrelated across generations of the same family, then regressing child’s current earnings measured in the early thirties to mid forties will provide a consistentestimate. In line with this result, we chose an age interval for sons centered around age 40 and
excluding early and late ages (below 30 and above 50). For similar reasons, we predicted father’s earnings at the age of 40. Provided that the results of Haider and Solon generalize to theJapanese case, this should purge our estimates from possible life-cycle bias. However, several
issues should be discussed and taken into account in our estimation.
One first difficulty is that there might be some residual bias arising from the fact that current
earnings are not necessarily representative of lifetime inequality over the entire age interval 30
to 50 years. If this is the case, our results might fail to provide consistent estimates of the IGE
in long-term economic status. To address this concern, Lee & Solon (2009) propose to explicitly
model the dependency of the IGE with respect to the age of children by including an interaction
term between age and father’s income. This leads to an equation of the form :Yit = αt + β X̂i + f (ageit ) × X̂i + g(ageit ) + eit(5)

The age profile f will parametrically capture the life-cycle bias, which varies with age. Lee andSolon suggest to normalize the age profile f to be equal to zero at age 40, i.e. at an age where
current earnings differentials are representative of lifetime earnings inequality. In this case, themain effect of father’s income, β is consistent for the IGE under the assumptions of Haider &Solon (2006).22
A second difficulty is raised by the recent paper of Nybom & Stuhler (2011). These authors challenge the assumption of Haider and Solon that individual departures from the mean
age–permanent-earnings profile are uncorrelated across generations of the same family. If this
22 Lee & Solon (2009) suggest including the interaction between child’s age and father’s income, in an OLS
context. A further issue arises in our case from the fact that we are implementing a TSIV estimator, i.e. using
predicted father’s permanent income instead of the true value (or a good proxy of it, as provided by multiyear averages). As discussed in Nybom & Stuhler (2011), the results of Haider & Solon (2006) (henceforthHS) carry over to the TSIV context. Under the assumptions of HS, predicted father’s income at age 40 willconsistently estimate lifetime permanent income differentials among fathers. Substituting father’s predicted
income for father’s lifetime income will still be distorted by the presence of non-classical measurement error in
the right-hand side variable compared to the TSIV estimate one would obtain in the absence of measurement
error in the RHS. However, correcting for life-cycle bias can also be undertaken in this context using the ruleof thumb of HS, or using the parametric interaction term of Lee and Solon, provided that the age-profile of thelife-cycle bias can be proxied by a parametric functional taking value zero at age 40.

21

assumption is invalid, the proper age for consistently estimating the IGE might differ from theage at which current earnings are representative of lifetime earnings inequality within a given
generation. Using long-term earnings profiles for Sweden, they show that this is indeed the case.
The pessimistic conclusion they draw is that the IGE could never be satisfactorily estimatedwithout full earnings chronicles, which is obviously impossible to implement in most countries,
including Japan, given data limitations. One important practical, and less radical, conclusionthat can be derived from their analysis, however, is that one should carefully examine how theestimated IGE varies with the age selection rule for children.
In the light of these difficulties, it seems important to gauge the robustness of our results toalternative modelings of age effects. We consider two approaches. The first is to implement theparametric control for life-cycle bias introduced in Lee and Solon. The second is to vary theage criterion for selection in our sample of children. Results are given in table 7 for sons andtable 8 for daughters. All estimates are presented for the piece-wise linear trends specification of
the first-step equation. Column 2 reproduces the coefficients discussed in the previous section.
Including an interaction between father’s predicted income and a quadratic function of child’sage, in column 1, turns out to be statistically insignificant and has no impact on the estimatedmain effect. This holds true for both sons and daughters and regardless of the combination ofincome variables used.
In columns 3 to 6, we change the age interval for children and consider three partitions of
the reference age group (30-50) : 30-40, 40-50, 35-45. We also consider a broader age interval: 25-55. All in all, results are very stable across these different age intervals. For sons results
vary by less than .02 in absolute value and the difference in point estimates is never statisticallysignificant. For daughters, the results seem more sensitive in the case of the IGE of personal
income to father’s personal income. For the younger age group, the IGE is .5 and .27 forthe older age group, with a reference value of .35. Yet, estimates are fairly imprecise and thedifference in point estimates is not statistically significant. When regressing family income on
family income of the parents, the results for daughters are again insensitive to the age selection.
These results partially contradict previous evidence that have emphasized the sensitivity of IGE
estimates to the age of children. Two effects are likely to account for this result. The first-one
is that the age groups we consider are all centered around age 40 and are never restricted to thesole groups of young or old children. Second, when changing the age interval, the set of cohorts
used in the estimation will mechanically change and we might mix up cohort heterogeneity in
the IGE with age effects. For this reason, we replicate our analysis on the sample of children

22born between 1945 and 1965 : since data for children are collected in 1985, 1995 and 2005, allcohorts between 1945 and 1965 will be used in the estimation, regardless of the age selection
rule that we consider. Results are given in columns 7 to 12. They confirm that our estimatesof the IGE are very robust to changes in the age selection rule for children.

7Complementary results

We now supplement our analysis of intergenerational mobility in Japan with two complementary
discussions. The first one focuses on changes across cohorts in the IGE. The second one pertains
to the estimation of the intergenerational correlation coefficient.

7.1

Changes across cohorts in the IGE

To examine the possibility of changes over time in the value of the IGE, we interact our measureof predicted father’s income with a dummy variable equal to one for cohorts born after 1952.
The choice of the cut-off date roughly splits our sample in two equal-sized groups and allows to
isolate the most recent cohorts who entered the labor market after the period of high economic
expansion that followed World War II.
As discussed in Hertz (2007) and Lee & Solon (2009), one of the difficulties of estimating
trends in the IGE is to separate cohort trends from the potential confounding influence of lifecycle effects. As discussed in the previous section, cohorts in our sample are observed at different
points of their life-cycle. In particular, the youngest cohort are only observed in the early stageof their career while the oldest ones are observed at the end of it. This is not true of the middle
cohorts : given the age restrictions we impose and the survey waves used, individuals born
between 1945 and 1965 are typically observed twice in their mid-career, i.e. in their thirties
and in their forties. Hence we test for trends on two distinct sample : first, the entire sample
of children; second, the subsample of individuals born between 1945 and 1965.
Results are given in table 9, for sons (columns 1 to 3) and daughters (columns 4 to 6). They
indicate that the IGE was remarkably stable across cohorts over the period studied here. This
converges with the results of Ishida & Miwa (2008) who find that social mobility has remained
stable in Japan in the second half of the twentieth century. For sons, the estimated change is
not statistically significant. This is mostly due to the small estimated value of the change in
the IGE (less than 3% of the mean sample’s value), rather than to an imprecise estimate ofchanges at work. For instance, we computed the 95% confidence interval for the IGE changes,

23

which shows that we can rule out changes larger than .026 in absolute value. As a comparison,(Aaronson & Mazumder 2008) report that the IGE in the United States fell by over .3 between
the cohorts born in the 1900s and those born in the 1930s and Lefranc (2011) reports a fall ofalmost .15 in two decades in France.
The same picture holds true for daughters when looking at the elasticity of daughter’s family
income to their parents’ family income (column 6) : the change is very small and not statisticallysignificant. Results for the changes in the elasticity of daughters’ own income to their father’s
income are slightly different. The change in the IGE in columns 4 and 5 is larger and suggests
a rise in the IGE for daughters in recent cohorts. This change is even significant at the 10%
level for column 4, on the subsample of daughters born between 1945 and 1965. The rise in the
IGE for female could be explained by changes over time in the Japanese female labor market.
For women born before 1952, employment concentrates in low-status and low-wage occupations,so called ’pink-collar’ jobs, where the status attainment process is very limited compared withmen (Imada 1998) with little promotion perspectives (Suzuki 2005). A large share of part-timework is also observed, together with a high share of family employment. This leads to a fairly
compressed wage structure that will be reflected directly into a low IGE. One should of course
be cautious when interpreting these trends since they are only marginally significant.

7.2

Intergenerational correlation

As a measure of economic mobility, the IGE has sometimes been criticized for being sensitive
to changes in cross-sectional inequality between the parents and the children’s generations. For
instance, a reduction in earnings inequality among children will “mechanically” lead to a fall in
the IGE. One might of course reasonably argue that such a fall in the IGE would indeed capturea ‘true’ rise in economic mobility. At the same time, this sensitivity might be problematic, forinstance when comparing countries that have experienced different trends in cross-sectional
inequality.
This suggests to supplement the IGE with an alternative measure of mobility that would
be independent of cross-sectional changes in earnings inequality. This is the case of the intergenerational correlation coefficient (IGC). The IGC, which we will denote by ρ, measurespositional mobility and is by construction unaffected by changes in the variance of earnings in
the children’s or father’s generation. The link between the IGC and the IGE is given by:

β=ρ

24

σY
σX

(6)

In the steady state, the variance of earnings is constant across generations and the IGE and
IGC are identical. This is no longer the case whenever σY and σX differ. Furthermore, thisformula makes clear that changes in the IGE will reflect both changes in positional mobility
and the evolution across generations of earnings inequality.
To infer the IGC, we rescale our estimates of the IGE using an estimate of the ratio σσX.
YThe main challenge here is that we do not observe permanent (log) earnings for children (Y )and fathers (X), but only current earnings, denoted respectively by y and x. To estimate
permanent earnings inequality, we make the assumption that current earnings inequality at age
40 are representative of lifetime inequality. More precisely we posit the following model, forcurrent log earnings y:
y = E(y|Z, age) + u
where Z denote some variables used to predict earnings, u is assumed to be distributed independently of age, and the conditional expectation is modeled as the first-step equation discussed in
section 2. Given Z and u, and assuming that the error term u is an individual fixed-effect, log
earnings at age 40, ỹ, can be predicted as :ỹ=E(y|Z, age = 40) + u=

E(ỹ|Z) + u

Under the assumption that current earnings inequality at age 40 are representative of lifetime
inequality, permanent-earnings inequality can be proxied by σ(ỹ) = σ(ỹ|Z) + σ(u). The assumption that the error term u is an individual fixed-effect is innocuous. The only substantial
assumption made on the residual is that it homoscedastic with age and that current-earnings
residual inequality is a good proxy for permanent-earnings residual inequality. Alternatively,
one might assume that the residual heterogeneity is purely transitory and vanishes in the longterm. This would lead to proxy permanent earnings inequality by σ(ỹ|Z). Both approaches canYin order to derive an estimate of the IGC.
be used to predict the ratio σσX

Results are given in table 10. IGC1 is computed under the first approach discussed above
to infer permanent earnings inequality. IGC2 corresponds to the second approach. In the caseof sons, earnings inequality at age 40 is very similar in the children and fathers’ generations
and, in most cases, only slightly lower for children. As a result, the adjustment factor σσXisY
close to one and usually slightly higher than one. This produces estimates of the IGC that are
only slightly higher than the values of the IGE previously discussed. In fact, in the case of the25elasticity of sons’ family income to their fathers’ family income, the IGC is almost identical to
the IGE, at .3, and independent of the method used to estimate permanent earnings inequality.
For the elasticity of childs’ own income to their father’s own income, the IGC is slightly higher
and lies in the interval .34-.36.
For daughters, the analysis is complicated by the large prevalence of part-time employmenton the Japanese female labor market. This prevalence results in a much larger degree of inequality of own income among women then among men : in fact, the standard deviation of
own income for women is almost twice as high as the one found for men. As a result, theadjustment factor σσXestimated for daughters lies close to one half. And the estimated IGC forY
women in the case of own income lies between .17 and .19. One can correct this estimates forthe incidence of part-time work. This is undertaken in column 4, where we predict potential
full-time earnings on the basis of a sample selection model whose wage equation is estimatedon the sole subsample of women working full-time. This model predicts a much lower degree of
earnings inequality among women and leads to estimates of the IGC that are much higher, andaround .27. In the end, the estimates in columns 1, 2 and 4 indicate that parental income has asizable influence on female potential full-time earnings but is less strongly associated with theoccurrence of part-time work. Since part-time work is an important driver of earnings inequality in Japan, the overall association between women’s actual earnings and their father’s incometurns out to be modest. However, this is no longer the case when looking at family income.
While own income is somewhat less correlated to parental income for daughters than for sons,the correlation in family income turns out to be very close in the case of family income, andslightly higher for female (.33) than for male (.30).

8Conclusion

In this paper, we have examined the extent of intergenerational transmission of income inequality
for sons and daughters in Japan. Our estimates suggests that a value of the IGE around.35 adequately summarizes the persistence of inequality between fathers and children for bothsons and daughters. Overall, this value puts Japan in an intermediate position, compared toother developed countries, on the scale of intergenerational mobility. For instance, among thecountries surveyed in Björklund & Jäntti (2009), Japan appears more mobile than the UnitedStates, the United Kingdom, Italy and France, all of which exhibit an IGE greater than .4,
comparable to Germany but less mobile than Scandinavian countries, Australia and Canada.
At first sight, this rather high degree of mobility may seem hard to reconcile with the alleged26

importance of parental investment in child’s education at work in Japan. As already abundantly
described in several studies, access to higher education in Japan is often expensive and selective,
forcing families to elaborate complex educational strategies and to undertake significant financial
investments to support them. For instance families cover between 71 and 86 % of the annual
expenditures of university students (Kondo 2000). Furthermore, besides tuition fees, parents
often invest significant amounts in “shadow education” such as cram schools and private tutoring.
Two factors, however are likely to limit the incidence of these investments for the transmission of income across generations. Both factors, emphasize the role of compressed earnings
differentials, but at different stages of the intergenerational mobility process. The first argument emphasizes the small degree of inequality among Japanese parents. In such a context,
even if parents invest a large share of their income in their children’s education, in the end, theresulting distribution of human capital in the next generation will also be relatively equal. Thisis confirmed by the analysis of “shadow education” undertaken in Stevenson & Baker (1992),
who emphasize the following three aspects of private investment in education in Japan. First,
family financial investment is high on average. Second, such investment is efficient at improving
educational attainment. But third, financial investment and the use of shadow education seemto vary little with characteristics of the family background such as parental education or family
income. The second argument applies to the end of the intergenerational transmission process.
As discussed for instance in Solon (2004), lower returns to human capital, as seems to be thecase in Japan compared to most developed countries, will translate into a lower IGE and limit
the income consequences of inequalities of parental investment.
Part of the high degree of intergenerational mobility observed in our sample may also be
explained by the specificities of the high economic expansion period that develop after WorldWar II. Of course, the high aggregate growth that Japan experienced in this period came alongwith a wave of rapid industrial development and occupational change that may have fosteredintergenerational mobility. However, it is important to stress that our results do not suggest any
slowdown in the mobility process for the cohorts of children born after 1952 and who entered
the labor market after the high-growth era. Whether this relatively high degree of mobility will
be maintained in the face of the recent rise in earnings inequality described in for instance inTachibanaki (2009) is of course an open question.

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31

32

0.178
0.230
0.210
0.197
0.184

1965
1975
1985
1995
2005
I- Higher service
II- Lower service
III- Routine clerical/sales
IV- Small employer and Independent
V- Manual foreman
VI- Skilled manualVII- Semi-Unskilled manualVII- Farmers/Farm workers
primary or lower secondary education
upper secondary education
higher education>1000
government
othersurvey yearsocial status (EGP class)education

firmsizeln(individual income)ln(family income)income

7170

0.687
0.650

14.957

2656

6.190
6.449

0.125
0.643
0.232

0.236

0.187
0.119
0.694

0.129
0.501
0.370

0.145
0.229
0.130
0.134
0.095
0.085
0.149
0.033

0.000
0.000
0.371
0.336
0.293

1953.814

0.531
0.518

9.901

2598

5.003
6.495

0.134
0.641
0.225

0.196

0.099
0.091
0.810

0.099
0.601
0.300

0.028
0.181
0.428
0.050
0.005
0.073
0.220
0.015

0.000
0.000
0.224
0.411
0.365

1956.203

mean

0.913
0.560

9.702

sd

Daughters sample

Notes: sd refers to the standard deviation; N refers to the maximum number of observation. Actual numbers may vary because of missing observations.
Fathers and sons samples exclude individuals with missing or zero earnings. Individuals with zero or missing earnings are kept in the descriptive statistics
for female except for computation of mean income.

N

0.137
0.584
0.279

6 major cities
urban
rural

residential area

5.940
6.203

0.321

self-employed

0.164
0.106
0.730

0.344
0.419
0.237

0.118
0.183
0.105
0.167
0.081
0.100
0.153
0.094

1941.127birth year

sd

mean

mean

sd

Sons sample

Fathers sample

Table 1: Descriptive statistics

33

REF
0.134***
0.185***
REF-0.205***-0.430***-0.422***-0.292***-0.522***-0.545***-0.680***0.174***
0.263***
0.131***
REF-0.0769**-0.117***0.0135***-0.000414
0.002150.00906**-0.0000996-0.000151-0.000332-0.000445*

primary or lower sec. education
upper secondary education
higher education

EGP class I
EGP class II
EGP class III
EGP class IV
EGP class V
EGP class VI
EGP class VII
EGP class VIII

self-employedfirm size : >1000
firm size : government

residential area : 6 major cities
residential area : urban
residential area : rural

age
age2

age × upper secondary educ.
age × higher educ.
age2 × upper secondary educ.
age2 × higher educ.

age × self-employedage2 × self-employedcoef.

(0.00255)(0.000207)(0.00281)(0.00324)(0.000233)(0.000273)(0.00297)(0.000231)(0.0235)(0.0264)(0.0177)(0.0216)(0.0293)(0.0239)(0.0275)(0.0285)(0.0301)(0.0290)(0.0268)(0.0326)(0.0238)(0.0293)

std.err.

(1)
quadratic trends

0.00000242-0.000501*

0.002140.00878**-0.0000888-0.0000857

0.0136***-0.000430

REF-0.0270-0.0466

0.262***
0.130***

0.194***

REF-0.203***-0.428***-0.421***-0.289***-0.518***-0.543***-0.674***REF
0.125***
0.171***

coef.

(0.00255)(0.000206)(0.00281)(0.00323)(0.000232)(0.000271)(0.00321)(0.000237)(0.0288)(0.0336)(0.0176)(0.0215)(0.0339)(0.0239)(0.0274)(0.0284)(0.0301)(0.0289)(0.0268)(0.0326)(0.0278)(0.0341)std.err.

(2)
piece-wise linear trends

Table 2: First-step estimates - dependent variable : own income

std.err.

(0.0177)(0.0216)(0.0316)(0.00256)(0.000206)(0.00279)(0.00321)(0.000231)(0.000270)(0.00275)(0.000218)

continued on next page

-0.000317-0.000505*

0.001820.00846**0.0000308
0.0000611

0.0107***-0.000487*

REF-0.109***(0.0257)-0.168***(0.0295)

0.261***
0.133***

0.170***

REF-0.209***(0.0239)-0.431***(0.0275)-0.418***(0.0285)-0.293***(0.0302)-0.524***(0.0290)-0.546***(0.0269)-0.684***(0.0325)

REF
0.137***(0.0252)
0.191***(0.0318)

coef.

(3)
step-wise trends

34
0.00291*-0.0000717

0.00607***-0.000160*

cohort × residential area : urbancohort2 × residential area : urbancohort × residential area : urban × pre1945
residential area : urban × pre1931
residential area : urban × post1950

cohort × residential area : ruralcohort2 × residential area : ruralcohort × residential area : rural × pre1945
residential area : rural × pre1931
residential area : rural × post1950-0.00401***-0.0000867-0.00190
0.000179*

cohort × higher educ.
cohort2 × higher educ.
cohort × higher educ. × pre1945higher education × pre1931
higher education × post1950

cohort × self-employedcohort2 × self-employedcohort × self-employedself-employed × pre1931
self-employed × post1950-0.00227
0.000149*

coef.

cohort × upper secondary educ.
cohort2 × upper secondary educ.
cohort × upper secondary educ. × pre1945
upper secondary education × pre1931
upper secondary education × post1950

Table 2 - continued from previous page(1)

(0.00154)(0.0000748)(0.00134)(0.0000672)(0.00119)(0.0000547)(0.00173)(0.0000784)(0.00159)(0.0000679)

std.err.

(0.00310)(0.00441)

0.0172***(0.00370)

0.0111**-0.00302(0.00256)(0.00346)

0.00573-0.00321(0.00250)(0.00422)-0.00830*-0.00681**(0.00315)

0.00192(0.00378)-0.00628

std.err.
(0.00298)(2)0.000543

coef.

(3)

(0.0476)(0.0512)(0.0439)(0.0450)(0.0324)(0.0353)(0.0456)(0.0512)(0.0361)(0.0476)std.err.

continued on next page

-0.160***0.109*-0.0526
0.05950.0609-0.0492

0.0929*0.03830.125***
0.0222

coef.

35

7170
0.459
0.456
10597.010879.0(0.0000110)(0.000000363)

0.00000894-0.000000460

std.err.
(0.000189)(0.00000553)(1)0.0000983
0.00000834

coef.

(0.0000284)

0.0000917**

7170
0.460
0.457
10581.810863.8(0.000350)(0.0000234)

0.000126-0.0000663**

std.err.
(0.000240)(2)-0.000367

coef.

(3)

7170
0.458
0.455
10613.010908.80.00489-0.000734*
0.00318-0.000520

coef.

(0.00476)(0.000308)(0.00286)(0.000306)

std.err.

Notes : The dependent variable is the log of respondent’s own income; standard errors in parentheses; * p<0.10, ** p<0.05, *** p<0.01; the age variable
is centered at age 40; the cohort variable is centered around birth cohort 1945; preYY is a dummy variable equal to one for cohorts born before year YY;
postYY is a dummy variable equal to one for cohorts born after year YY; All equations include intercept and year dummies.

Observations
R-squared
Adjusted R-squared
AIC
BIC

cohort × age
cohort2 × age
cohort × age × pre1945
cohort × age2
cohort2 × age2
cohort × age2 × pre1945
age × pre1931
age2 × pre1931
age × post1950
age2 × post1950

Table 2 - continued from previous page36

0.262***
0.198***
0.128***

self-employedfirm size : >1000
firm size : government

0.0111***-0.000139
0.00157
0.00350-0.000151-0.000138
0.0000385-0.000361

age
age2

age × upper secondary educ.
age × higher educ.
age2 × upper secondary educ.
age2 × higher educ.

age × self-employedage2 × self-employed

REF-0.02210.00367

REF-0.149***-0.302***-0.394***-0.221***-0.408***-0.422***-0.571***

EGP class I
EGP class II
EGP class III
EGP class IV
EGP class V
EGP class VI
EGP class VII
EGP class VIII

residential area : 6 major cities
residential area : urban
residential area : rural

REF
0.135***
0.174***

primary or lower sec. education
upper secondary education
higher education

coef.

(0.00249)(0.000202)(0.00275)(0.00317)(0.000228)(0.000268)(0.00303)(0.000228)(0.0228)(0.0257)(0.0172)(0.0211)(0.0286)(0.0234)(0.0270)(0.0277)(0.0295)(0.0285)(0.0264)(0.0318)(0.0233)(0.0287)

std.err.

(1)
quadratic trends

0.000218-0.000387

0.001480.00304-0.000150-0.0000712

0.0105***-0.0000807

REF
0.01940.0712*

0.198***
0.127***

0.271***

REF-0.148***-0.301***-0.394***-0.220***-0.407***-0.422***-0.567***

REF
0.120***
0.140***

coef.

(0.00249)(0.000202)(0.00275)(0.00317)(0.000227)(0.000266)(0.00317)(0.000232)(0.0282)(0.0329)(0.0172)(0.0210)(0.0331)(0.0234)(0.0270)(0.0277)(0.0295)(0.0285)(0.0264)(0.0318)(0.0272)(0.0333)

std.err.

(2)
piece-wise linear trends

Table 3: First-step estimates - dependent variable : family income

std.err.

(0.0172)(0.0211)(0.0308)(0.0235)(0.0271)(0.0278)(0.0296)(0.0286)(0.0265)(0.0316)(0.00250)(0.000202)(0.00274)(0.00316)(0.000227)(0.000266)(0.00266)(0.000213)

continued on next page

0.00000844-0.000367

0.00105
0.00181-0.0000568
0.0000862

0.0103***-0.000125

REF-0.0583*(0.0248)-0.0545(0.0285)

0.196***
0.130***

0.258***

REF-0.151***-0.304***-0.393***-0.224***-0.413***-0.426***-0.580***REF
0.143***(0.0244)0.173***(0.0309)

coef.

(3)
step-wise trends

37
0.00736***-0.000192*

cohort × residential area : ruralcohort2 × residential area : ruralcohort × residential area : rural × pre1945
residential area : rural × pre1931
residential area : rural × post1950-0.00266*-0.0000434

cohort × self-employedcohort2 × self-employedcohort × self-employedself-employed × pre1931
self-employed × post1950
0.00251-0.000102-0.00190
0.000175*

cohort × higher educ.
cohort2 × higher educ.
cohort × higher educ. × pre1945higher education × pre1931
higher education × post1950

cohort × residential area : urbancohort2 × residential area : urbancohort × residential area : urban × pre1945
residential area : urban × pre1931
residential area : urban × post1950-0.00399*
0.0000527

coef.

cohort × upper secondary educ.
cohort2 × upper secondary educ.
cohort × upper secondary educ. × pre1945
upper secondary education × pre1931
upper secondary education × post1950

Table 3 - continued from previous page(1)

(0.00158)(0.0000757)(0.00134)(0.0000671)(0.00120)(0.0000548)(0.00186)(0.0000825)(0.00173)(0.0000726)

std.err.

(0.00318)(0.00445)

0.0181***(0.00371)

0.0107**-0.00220(0.00259)(0.00347)

0.00286-0.00324(0.00254)(0.00435)-0.0129**-0.00410(0.00335)

0.00532(0.00395)-0.00578

std.err.
(0.00321)(2)-0.000211

coef.

(3)

(0.0460)(0.0509)(0.0423)(0.0446)(0.0314)(0.0352)(0.0443)(0.0527)(0.0349)(0.0493)

std.err.

continued on next page

-0.208***0.139**-0.06410.07060.0473-0.0299

0.108*
0.08300.108**
0.00374

coef.

38

5.764***
6814
0.452
0.449
9448.99728.8(0.0384)(0.0000110)(0.000000368)-0.00000493-0.000000249

std.err.
(0.000198)(0.00000565)(1)-0.0000382
0.00000853

coef.

(0.0382)(0.0000290)

0.0000557

5.778***
6814
0.454
0.450
9435.79715.6(0.000351)(0.0000241)-0.000376-0.0000477*

std.err.
(0.000251)(2)0.00000141

coef.

(3)

5.777***
6814
0.451
0.447
9467.39760.90.00392-0.000109
0.00469-0.000540

coef.

(0.0431)(0.00458)(0.000298)(0.00286)(0.000310)

std.err.

Notes : The dependent variable is the log of respondent’s family income; standard errors in parentheses; * p<0.10, ** p<0.05, *** p<0.01; the age variable
is centered at age 40; the cohort variable is centered around birth cohort 1945; preYY is a dummy variable equal to one for cohorts born before year YY;
postYY is a dummy variable equal to one for cohorts born after year YY; All equations include intercept and year dummies.

Constant
Observations
R-squared
Adjusted R-squared
AIC
BIC

cohort × age
cohort2 × age
cohort × age × pre1945
cohort × age2
cohort2 × age2
cohort × age2 × pre1945
age × pre1931
age2 × pre1931
age × post1950
age2 × post1950

Table 3 - continued from previous page

Table 4: IGE estimates for sons and daughters : main results

Child’s income variable
Father’s income variablebase specification - quadratic trends (QT)base specification - piecewise linear trends (PW)base specification - stepwise trends (SW)
Observations

base specification - quadratic trends (QT)base specification - piecewise linear trends (PW)base specification - stepwise trends (SW)
Observations

base specification - quadratic trends (QT)base specification - piecewise linear trends (PW)base specification - stepwise trends (SW)
Observations

(1)

(2)

(3)

own
own

own
familyfamilyfamilyA- sons, linear regression
.3239
.3657
.2897
(.02918)(.03397)(.03440)
.3368
.3738
.2969
(.02999)(.03444)(.03488)
.3669
.4200
.3254
(.0317)(.03706)(.03772)
2265
2265
2106
B- daughters, linear regression
.2155
.2551
.3748
(.068555)(.07925)(.03897)
.2273
.2660
.3759
(.07025)(.08035)(.03953)
.2676
.3252
.3991
(.07462)(.08679)(.04272)
1555
1555
1921
C- daughters, heckman selection model
.3444
.4043
.3724
(.07603)(.08799)(.03925)
.3544
.4136
.3738
(.07783)(.08915)(.03981)
.4079
.4915
.3968
(.08275)(.09643)(.04302)
2456
2456
2456

Notes: standard errors in parentheses. Columns 1 to 3 report IGE estimates for sons and daughters based onequation 2 for different combinations of father’s and child’s income variables. For each pair of income measures, thedifferent lines report the IGE estimates obtained for the three specifications of the first-step equation presented incolumns 1, 2 and 3 of tables 2 and 3. Panels A and B are estimated using 2SLS. Panel C is estimated using the
Heckman’s sample selection model. The selection equation uses the following regressors : marital status, indicatorsof the number of children, spouse’s income and education when married, age profile and year dummies.

39

Table 5: IGE estimates for sons : sensitivity to first-step specification

Child’s income variable
Father’s income variable

Specification

Father’s characteristics
in first-step equation

(A)

base

QT

SW

(A)+ trends for EGP-class+ EGP-class specific age profiles

QT
PW
SW

(C)

(B) - father’s education variables

QT
PW
SW

(D)

(A) - father’s EGP class

QT
PW
SW

(E)

(A) - job characteristics- regional information

QT
PW
SW

(F)

(2)

(3)

own
own

own
familyfamilyfamily.3239(.02918).3368(.02999).3669(.03176).3657(.03397).3738(.03444).4200(.03706).2897(.03440).2969(.03488).3254(.03772).3082(.02822).3078(.02803).3593(.03107).3433(.03213).3449(.03186).4071(.03556).2772(.03248).2767(.03219).3171(.03617).3066(.02926).3268(.03014).3914(.03443).3366(.03324).3732(.03490).4443(.03948).2944(.03357).3040(.03530).3475(.04020).2871(.03469).3014(.03582).3561(.04005).3060(.03911).3159(.03980).3821(.04521).2378(.03942).2455(.04012).2791(.04587).3006(.02869).2966(.02840).3467(.03167).3494(.03348).3441(.03303).4046(.03705).2892(.03376).2878(.03329).3301(.03754).4018(.03420).4661(.03991).3534(.04077)

2265

2265

2106

Trendsspecification

PW

(B)

(1)

notrends

Observations

Notes: standard errors in parentheses. Columns 1 to 3 report IGE estimates for sons and daughters based onequation 2 for different combinations of father’s and child’s income variables. For each pair of income measures, thedifferent lines report the IGE estimates obtained for various specifications of the first-step equation used to predict
father’s income. Specifications differ in both the variables used in the first-step equation and the parametric form
used for modeling changes cohort in the coefficient of various predictors in the wage equation. As far as trends
specification is concerned, QT denotes quadratic cohort trends, PW denotes piece-wise linear trends, SW denotes
step-wise changes across cohorts. See p.6 for a full discussion. The variables included in the first-step equation are: (A) : see variable list in table 2; (B)=(A) plus trends for EGP-class and EGP-class specific age profiles; (C)=(B)minus father’s education variables and their interactions; (D)=(A) minus father’s EGP class; (E)=(A) minus job
characteristics and regional information; (F)=(A) without cohort trends.

40

Table 6: IGE estimates for daughters : sensitivity to first-step specification

Child’s income variable
Father’s income variable

Specification

Father’s characteristics
in first-step equation

(A)

base

QT

SW

(A)+ trends for EGP-class+ EGP-class specific age profiles

QT
PW
SW

(C)

(B) - father’s education variables

QT
PW
SW

(D)

(A) - father’s EGP class

QT
PW
SW

(E)

(A) - job characteristics- regional information

QT
PW
SW

(F)

(2)

(3)

own
own

own
familyfamilyfamily.3444(.07603).3544(.07783).4079(.08275).4043(.08799).4136(.08915).4915(.09643).3724(.03925).3738(.03981).3968(.04302).3368(.07456).3313(.07386).3957(.08158).3719(.08420).3795(.08366).4574(.09287).3485(.03752).3418(.03733).3744(.04145).3193(.07621).3401(.07852).4229(.08915).3470(.08586).3961(.09021).4806(.10126).3289(.03869).3403(.04074).3696(.04589).2594(.08791).2649(.09045).3438(.10159).2914(.09861).2989(.10034).3973(.11440).3698(.04451).3703(.04533).4158(.05154).3513(.07749).3400(.07628).4022(.08442).3814(.08987).3787(.08852).4518(.09828).3546(.03990).3478(.03939).3856(.04392).4404(.08936).5523(.10421).4391(.04661)

2456

2456

2456

Trendsspecification

PW

(B)

(1)

notrends

Observations

Notes: standard errors in parentheses. Columns 1 to 3 report IGE estimates for sons and daughters based onequation 2 for different combinations of father’s and child’s income variables. For each pair of income measures, thedifferent lines report the IGE estimates obtained for various specifications of the first-step equation used to predict
father’s income. Specifications differ in both the variables used in the first-step equation and the parametric form
used for modeling changes cohort in the coefficient of various predictors in the wage equation. As far as trends
specification is concerned, QT denotes quadratic cohort trends, PW denotes piece-wise linear trends, SW denotes
step-wise changes across cohorts. See p.6 for a full discussion. The variables included in the first-step equation
are : (A) : see variable list in table 2; (B)=(A) plus trends for EGP-class and EGP-class specific age profiles;(C)=(B) minus father’s education variables and their interactions; (D)=(A) minus father’s EGP class; (E)=(A)minus job characteristics and regional information; (F)=(A) without cohort trends. All IGE’s are estimated using
the Heckman’s sample selection correction.

41

42
2106

.2969
(.03488)

2265

.3368
(.02999)

30-50

(2)

1037

.3126
(.04992)

35-45

(5)
25-55

(6)
30-50

(7)
30-50

(8)
30-40

(9)
40-50

(10)

1242

3138

.3504
(.02665)

.617

1604

.0002515(.0010464)-.005497(.005871).3339(.05087)

1604

.3426
(.03498)

843

.3503
(.04392)

863

.3234
(.05161)

1164

.2778
(.04699)

1171

.3041
(.04362)

2890

.3141
(.03160)

.637

1502

.0000364(.001236)-.006455(.006835).3052(.05919)

1502

.3065
(.04051)

800

.3178
(.05311)

796

.2881
(.05817)

B- child’s family income regressed on father’s family income
1945-1965 cohorts

1236

.3249
(.03955)

A-child’s own income regressed on father’s own income
1945-1965 cohorts.3211(.04248)

all cohorts

1132

.3450
(.03998)

(4)
40-50

all cohorts

30-40

(3)

848

.3086
(.05158)

900

.3357
(.04613)

35-45

(11)

1788

.3360
(.03897)

1922

.3501
(.03273)

25-55

(12)

Notes: Standard errors in parentheses. Columns 1 to 12 report estimation results using various children age groups for sons. Estimates are based on equation 2 where in the first-step, father’s
earnings are predicted using the base specification of tables 2 and 3, using a piece-wise linear cohort trends specification. Columns 1 and 7 include interactions terms between child’s age andfather’s earnings. The reported p-values are for the test of joint significance of these interactions terms. In panel A, the IGE is estimated for the regression of child’s own income on father’s
own income. In panel B, the IGE is estimated for the regression of child’s family income on father’s family income. Estimates for daughter are based on the Heckman sample selection model.

.716

p-values-.0004776(.001053)

ln(father’s income) × age22106-.003875(.005789)

ln(father’s income) × age

Observations.3158(.05057)

IGE

.769

p-values.0005315(.0008942)

ln(father’s income) × age22265-.002079(.004928)

ln(father’s income) × age

Observations.3190(.04355)

30-50

IGE

age interval for children(1)

Table 7: IGE estimates for sons : sensitivity to age effects

43
2456

.3738
(.03981)2456.35441(.0778)

30-50

(2)

1237

.3507
(.05782)

25-55

(6)
30-50

(7)
30-50

(8)
30-40

(9)
40-50

(10)

1270

.3866
(.1185)

3526

.3548
(.06267)

.4133

1775

.001712(.002673)-.01817(.01423).3104(.1301)

1775

.3416
(.09006)

808

.4707
(.15278)

1069

.2847
(.1068)

1321

.3906
(.05194)

1270

.3269
(.05344)

3526

.3464
(.03523)

.541

1775

.001301(.001418).004040(.007725).3307(.06732)

1775

.3798
(.04629)

808

.3616
(.06365)

1069

.3951
(.06162)

B- child’s family income regressed on father’s family income
1945-1965 cohorts

1321

.2724
(.0921)

all cohorts

1237

.5019
(.1308)

35-45

(5)

A-child’s own income regressed on father’s own income
1945-1965 cohorts

40-50

(4)

all cohorts

30-40

(3)

960

.3202
(.06151)

960

.4854
(.1414)

35-45

(11)

2147

.3587
(.04391)

2147

.3538
(.08197)

25-55

(12)

Notes: Standard errors in parentheses. Columns 1 to 12 report estimation results using various children age groups for sons. Estimates are based on equation 2 where in the first-step, father’s
earnings are predicted using the base specification of tables 2 and 3, using a piece-wise linear cohort trends specification. Columns 1 and 7 include interactions terms between child’s age andfather’s earnings. The reported p-values are for the test of joint significance of these interactions terms. In panel A, the IGE is estimated for the regression of child’s own income on father’s
own income. In panel B, the IGE is estimated for the regression of child’s family income on father’s family income. All IGE’s are estimated using the Heckman sample selection correction.

.401

p-values.001449(.001219)ln(father’s income) × age2

2456

.002874(.006533)

ln(father’s income) × age

Observations.3183(.05873)

IGE

.311

.002141(.002165)ln(father’s income) × age2

p-values-.01525(.01132)ln(father’s income) × age

2456

.2971
(.1100)IGE

Observations

30-50

age interval for children(1)

Table 8: IGE estimates for daughters : sensitivity to age effects

44[-.026 , .010][-.024 , .010]

1604-0.006951(0.008885)

sons
0.3889(0.04037)[-.020 , .007]

2265-0.006151(0.006827)

sons
0.3765(0.03457)

ownfamily(2)[-.013 , .056]

2456

0.02123(0.01753)

0.3446(0.07841)[-.019 , .016]

1502-0.001471(0.009026)

0.3070(0.04064)[-.007 , .087]

1775

0.03970(0.02390)

0.3200(0.09083)

B - 1945-1965 cohorts[-.015 , .013]

2106-0.0007549(0.007016)

0.2973(0.03502)

(4)
own
own

A - all cohorts

familyfamily(3)[-.009 , .082]

1775

0.03653(0.02311)

daughters
0.3981(0.1036)[-.014 , .053]

2456

0.01946(0.01697)

daughters
0.4048(0.08965)

own
family(5)[-.014 , .026]

1775

0.006030(0.01024)

0.3765(0.04666)[-.022 , .008]

2456-0.007192(0.007533)

0.3781(0.04005)

familyfamily(6)Notes: Standard errors in parentheses. Columns 1 to 6 report IGE estimates for sons and daughters based on equation 2 for different combinations offather’s and child’s income variables. Estimations include interactions between father’s predicted income and a dummy variable equal to one for cohorts
born after 1954 (post1954). The table only reports the main effect of father’s predicted income and the interacted term. The estimation is performed forthe whole sample of children (panel A) and for the subsample born between 1945 and 1965 (panel B). Coefficients for daughters are estimated using the
Heckman sample selection correction.

95% confidence interval for IGE change

1604-0.007592(0.009166)ln(father’s income) × post1954

Observations

0.3458(0.03519)[-.020 , .007]ln(father’s income)

95% confidence interval for IGE change

2265-0.006529(0.007041)

ln(father’s income) × post1954

Observations

0.3398(0.03016)

own
own

ln(father’s income)Child’s income variable
Father’s income variable(1)

Table 9: Trends in the IGE : sons and daughters

Table 10: IGE and IGC: sons and daughters
(1)

(2)

(3)

(4)

Child’s income variable
Father’s income variable

own
own

own
familyfamilyfamilyown, full-timeown

σ(Ỹf )σ(Ỹf |Zf )σ(uf )

.5243
.264
.4574

.5009
.2181
.4555

.5009
.2181
.4555

.5243
.264
.4574

σ(Ỹc )σ(Ỹc |Zc )σ(uc )

.4893
.2592
.4238

.4893
.2592
.4238

A- sons
.4801
.2126
.4357

IGE
IGC1
IGC2

.3368
.3608
.3430

.3738
.3826
.3145

.2969
.3097
.3045

σ(Ỹc |Xc )σ(Ỹc )σ(uc )
IGE
IGC1
IGC2

1.0971.48878.98227
.3544
.1693
.1914

1.0971.48878.98227
.4136
.1888
.1845

B- daughters
.5728
.2406
.5198
.3738
.3268
.3388

.6976
.3486
.6043
.3544
.2663
.2683

Notes: The table presents values of the IGE, the intergenerational correlation (IGC) and the standard-deviationof the log of income for fathers, sons and daughters and for different combinations of father’s and child’s income
variables. u denotes the residual of the income regression presented in tables 2 and 3; ỹ|Z denotes the predicted log
income at age 40 (see discussion p.25); ỹ = ỹ|Z + u. Subscript c indicates that standard-deviations are estimatedon the sample of children; subscript c indicates that standard-deviations are estimated on a sample of individuals
with birth year representative of the fathers of the children sample. For daughters, we re-estimated the model oftables 2 and 3, column 2, using Heckman sample selection procedure, where the selection equation included thefollowing regressors : marital status, indicators of the number of children, spouse’s income and education whenmarried, age profile and year dummies. In column 4, own income is considered as censored when the daughter is
not working full-time so Y refers to full-time potential income. IGEs are the same as in table 4. IGC1 is computed
as IGE×σ(ỹf )/σ(ỹc ). IGC2 is computed as IGE×σ(ỹf |Z)/σ(ỹc |Z).

45

0share (in percent)
20
40

60

Figure 1: Distribution of education by birth cohort

1900

1920

1940
cohorthigher educ.
prim/lower sec. educ. or less
Notes: Source : authors’ computation from SSM data.

46

1960
upper sec. educ.

1980

.2

1900

30
age

prim/lower sec. educ.
higher educ.

40

45

1940
higher educ.
rural area

cohort55

self-employedNotes: see table 2 for coefficient estimates.

upper sec. educ.
urban area

1920

1960

upper sec. educ.
self-employed50

C- Cohort effects - piecewise linear trends

35

A- Age-earnings profiles

1900

1900

1940
higher educ.
rural area

cohortupper sec. educ.
urban area

1920

1940
higher educ.
rural area

cohortD- Cohort effects - stepwise trends

upper sec. educ.
urban area

1920

B- Cohort effects - quadratic trends

Figure 2: Age and cohort effects, first-step income equation - own income

income differential (in log points)-.50.5income differential (in log points)
0
-.2
.4
-.4
.2

income differential (in log points)
0
-.1
-.2
.1

-.3

income differential (in log points)
-.2
0
-.4
.2
.4

-.6

47

self-employed

1960

self-employed

1960

Appendix : early fathers cohorts
Given the age restrictions we impose and the survey years available, our oldest cohort of children
was born in 1935 and our oldest cohort of fathers was born in 1905. The tabulation of father’sbirth cohort by child’s birth cohort, in table 11 below indicates that for the oldest child cohorts,
a significant fraction of the fathers were born before 1905. This raises the question of how theirincome should be predicted given the limited information exploited in the first-step equation.
Table 11: Father’s birth cohort by child’s birth cohort
Child’s birth
Cohort

mean

1935
1936
1937
1938
1939
1940

1902.57
1902.59
1904.33
1904.61
1904.29
1907.63

Father’s birth cohort
p10
p25
p75
1892
1893
1897
1896
1895
1902

1899
1899
1900
1898
1899
1904

1906
1908
1909
1912
1910
1912

p90
1910
1912
1910
1913
1911
1913

Notes: Source : authors’ computations from SSM data. pxx designates thevalue of the xxth percentile.

We considered four options. The first, which we use in the rest of the paper, was to assume
that the earnings equation estimated for the 1905 cohort was also valid for the cohorts born
before 1905. The second one amounts to retropolate the cohort-trends in the earnings structure
estimated after 1905. The third one was to drop all individuals whose father was born before
1905. The fourth one is to exclude all child’s cohorts in which a significant share of the fathers
was born before 1905.
All four procedures produce very similar results, as shown in the table below, in the case of
the piece-wise linear trends specification.

Table 12: IGE estimates for various treatments of fathers born before 1905

Child’s income variable
Father’s income variable
w/ trends extrapolationNno trends extrapolationNexcl. fathers born before 1905
N
only children born after 1940
N

(1)

(2)

(3)

own
own

own
familyfamilyfamily.3321682(.0297205)
2265.366469(.0340147)
2265.2925363(.0344422)
2106.3368869(.0299921)
2265.3738406(.0344416)
2265.2969808(.0348861)
2106.343647(.0317294)
2056.3854528(.036683)
2056.3001721(.0373722)
1901.3290154(.030755)
2092.365947(.0353181)
2092.2922087(.0359411)
1937

Notes: Source : authors’ computations from SSM data.

48