The Intergenerational Transmission of Income and Education: A Comparison of Japan and France

Abstract

This chapter compares the extent of intergenerational earnings and educational correlation in Japan and France. it uses very similar repeated surveys that provide information on educational attainment and family background, conducted in Japan and France. To insure comparability, similar sample restrictions and specifications are imposed. For Japan, we use waves 1965, 1975, 1985, 1995 and(?) 2005. For France, we use waves 1965, 1970, 1977, 1985, 1993 and 2003. Intergenerational elasticity in years of education can be readily estimated using available information. On the other hand, intergenerational earnings elasticity cannot be directly measured given the lack of information on parental income in both surveys. This leads us to apply Björklund and Jäntti’s (1999) two-sample instrumental variables estimation strategy. Lastly, we discuss to what extent differences in earnings mobility is related to differences in educational mobility and to differences in returns to education between the two countries.

Appendix: First-Step Equation

To predict father’s income, we rely on a first-step equation in which yearly income is regressed on a set of education dummies interacted with birth cohort. Hence, we allow for the possibility of change over time in the returns to education. It is then possible to use father’s education and birth cohort, as reported by the child, to form a prediction of his father’s earnings.

In the first-step equation, we do not use father’s occupation, although this information is available in our data sets. Using reported father’s occupation to predict father’s income raises some difficulties, given our objective, discussed in the Section “Econometric Model” to predict father’s income at age 40. Occupation typically varies over the course of a career and children report the occupation of their father at a specific point in time. For instance, occupation when the child was aged 17, may or may not correspond to occupation when the father was 40. If not, then it is difficult to use reported occupation at age 17 to assess father’s earnings at age 40. There are further difficulties that differ between the French and Japanese surveys. In France, individuals are asked to report their father’s occupation at the time they finished going to school: this is problematic because those who finish school later will report the occupation of their father at a later stage of the father’s career. This would lead to spurious correlation between father’s occupation and child’s education. In Japan, the situation is different. In some cases, individuals are asked to report their father’s occupation without any indication regarding the period, in the father’s career. So it is unclear what occupation is precisely reported. Yet, it is likely that younger cohorts (whose parents are still active) will report current occupation of their father while older cohort will report end of career occupation. Again, there is a distortion that may affect our results. Lastly, as documented in Lefranc and Trannoy (2005), using education as the only instrument or using both education and occupation has a very limited impact on the estimated IGE.

The specification used in the first-step equation is the following:

$$X_{ict}=\alpha _{t}+\Sigma _{j=1}^{n_{e}}\beta _{0j}^{c}Ed_{ij}+\Sigma _{j=1}^{n_{e}}Ed_{ij}(\Sigma _{k=1}^{4}\beta _{kj}({\rm{age}}_{i}-40)^{k})+\nu_{t}$$

where X _ict denotes the earnings of the individual i, taken from the sample of fathers, who belongs to the cohort $c,$ at date t; α _t is a time effect, common to all cohorts (it may for instance capture inflation, overall income growth, ...); Ed _ij is a dummy variable that takes the value 1 if individual i has the level of education j; age _i is the age of individual i at time t.

This equation assumes that the returns to education at the age of 40 differ across cohorts: for instance, in some cohorts, the premium attached to higher education can be bigger than in other cohorts. In fact, there are no reasons to expect that the coefficients $\beta_{0j}^{c}$ will remain unchanged across cohorts. It also assumes that the effect of age on earnings varies according to the level of education. We expect that the effect is bigger for more educated people.

How to predict from the above equation the earnings at the age of 40? Note the relationship between age, time and cohort: age = t − c. So age 40 corresponds to t = c + 40. By construction, the terms (age _i − 40)^k will be zero at age 40. So for an individual of cohort c, the predicted earnings at age 40 is simply given by:

$$X_{icc+40}=\alpha _{c+40}+\Sigma _{j=1}^{n_{e}}\beta _{0j}^{c}Ed_{ij}$$

The problem is that for many cohorts, we may not have a snapshot of their father’s earnings exactly at age 40. And consequently, we will not be able to estimate α _c+40, although we do estimate the values of $\beta _{0j}^{c}.$ But this is of little consequence, since this term is common to all individuals of that cohort, independent of their level of education.

To be more specific, let $\{Ed_{ij}^{{\rm{father}}}\}_{i=1...n_{e}}$ denote a set of dummy variables characterizing the education of the father of individual i. Let c denote the cohort of father of individual i. The predicted father’s income for individual i takes the form:

$$X_{i}=\alpha _{c+40}+\Sigma _{j=1}^{n_{e}}\beta _{0j}^{c}Ed_{ij}^{{\rm father}}$$

The standard IGE equation is:

$$\begin{array}{l} \quad Y_{i} =\beta +\gamma _{0}X_{i}+\varepsilon _{i} \\ \Leftrightarrow Y_{i}=\beta +\gamma _{0}(\alpha _{c+40}+\Sigma _{j=1}^{n_{e}}\beta _{0j}^{c}Ed_{ij}^{{\rm{father}}})+\varepsilon _{i} \\ \Leftrightarrow Y_{i}=(\beta +\gamma _{0}\alpha _{c+40})+\gamma _{0}(\Sigma _{j=1}^{n_{e}}\beta _{0j}^{c}Ed_{ij}^{{\rm{father}}})+\varepsilon _{i} \end{array}$$

So controlling for the cohort of birth of the father (for instance, using a set of dummy variables for each cohort or a polynomial function) in the second-step equation is enough to capture the term $\beta +\gamma _{0}\alpha _{c+40}$. So we can just regress child’s earnings on father’s cohort and the terms $\Sigma _{j=1}^{n_{e}}\beta _{0j}^{c}Ed_{ij}^{{\rm{father}}}$ that we are able to estimate. Given child’s age, we only exploit variation in earnings among fathers of the same birth cohort but with different educational level. We do not rely on differences in father’s age, as a source of wage variation.

In our case, we want to estimate the IGE controlling for life-cycle effects. For simplicity, let us drop higher-order terms in age. The equation we wish to estimate is:

$$\begin{array}{l} \quad Y_{i} = \beta +\gamma _{0}X_{i}+\gamma _{1}X_{i}\times ({\rm{age}}_{i}-40)+\varepsilon _{i} \\ \Leftrightarrow Y_{i} = \beta +(\alpha _{c+40}+\Sigma _{j=1}^{n_{e}}\beta _{0j}^{c}Ed_{ij}^{{\rm{father}}})(\gamma _{0}+\gamma _{1}({\rm{age}}_{i}-40))+\varepsilon _{i} \\ \Leftrightarrow Y_{i} = (\beta +\gamma _{0}\alpha _{c+40}+\gamma _{1}\alpha _{c+40}({\rm{age}}_{i}-40))\\\quad\qquad\, +(\Sigma _{j=1}^{n_{e}}\beta _{0j}^{c}Ed_{ij}^{{\rm{father}}})(\gamma _{0}+\gamma _{1}({\rm{age}}_{i}-40))+\varepsilon _{i} \end{array}$$

Now to take care of the first parenthesis on the right-hand side, we need to account for the cohort of birth of the father (because of $\gamma _{0}\alpha _{c+40}$) and the age of the individual (because of $\gamma _{1}\alpha _{c+40}({\rm{age}}_{i}-40)$). This can be done using dummies for father’s birth cohort and a polynomial for individual age. To simplify things, if we assume that α _t is a smooth function of time, we can simply put a polynomial in the cohort of the father. Of course, we should put an interaction between father’s cohort and child’s age.

Lastly, it is important to realize that if we don’t know, for each individual, the birth cohort of his/her father, we will treat all children of a given age as having fathers of the same birth cohort (in fact, a mix of different likely cohorts). In this case, it is enough to control for child’s age.