1.4 Empirical Analysis
1.4.2 Intergenerational Educational Mobility
Education attainment is measured by the maximum educational attainment. In particular, we consider five classes: None Education (NE), Primary School (PS) (five years), Lower Secondary School (LSS) (eight years), Upper Secondary School (USS) (thirteen years) and University Degree (UD) (eighteen and more than eigh- teen years of education)8.
To our scopes the presence of a compulsory regime of education introduces a crucial bias in the estimate of intergenerational educational mobility. In the considered period there was a progressive increase in the years of compulsory school: at the
7Other studies that use these two variables arePiraino(2007) and Checci et al.(1999). We
select only fathers to follow the standard procedure adopted in most of similar studies of social mobility (e.g. Checchi(1997) andPiraino(2007))
8The classification into five classes, both for children and their fathers, is based on the data
retrieved in the questionnaire of Bank of Italy (respectively card A16 and card A24). As regard sons, the first class corresponds to the answer 1 (None Education) of the card A16, the second one corresponds to the answer 2 (Primary School), the third corresponds to the answer 3 (Lower Secondary School), the fourth category corresponds to the answers 4 and 5 (Vocational and Upper Secondary School) and the last one corresponds to the answers 6, 7 and 8 (Three and Five year University Degree and Postgraduate Qualification). For fathers, the first three classes are similar to those of children, while the fourth class corresponds to the answer 4 (Upper Secondary School) of the card A24, and the last class corresponds to the answers 5 and 6 (University Degree and Postgraduate Qualification).
beginning of period (1947) the compulsory age of education was 10 years; in 1962 a reform raised years to 14 (lower secondary school in our classification).
In order to take into account the presence and the changes in the compulsory regimes of education we use only three classes of educational attainment, where the first includes NE, PS and LSS (denote it CS), the second USS and the third UD.
Tables 1.2, 1.3 and 1.4 report the estimate of transition probabilities between the three educational classes for three cohorts.
Table 1.2: The estimated transition matrix of educational attainment for Cohort I (1947-1956).
Fathers\ Children CS USS UD N.Obs.
CS 0.579 0.339 0.080 4457
USS 0.093 0.480 0.425 346
UD 0.087 0.373 0.539 169
N.Obs. 2579 1785 608 4972
Table 1.3: The estimated transition matrix of educational attainment for Cohort II (1957-1966).
Fathers\Children CS USS UD N.Obs.
CS 0.479 0.446 0.073 4262
USS 0.052 0.570 0.377 489
UD 0.047 0.342 0.610 212
N.Obs. 2095 2238 630 4963
Table 1.4: The estimated transition matrix of educational attainment for Cohort III (1967-1976).
Fathers\Children CS. USS UD N.Obs.
CS 0.470 0.439 0.090 2330
USS 0.070 0.607 0.322 430
UD 0.028 0.258 0.712 141
N.Obs. 1137 1336 428 2901
As expected during the considered period there was a general increase in the level of educational attainment of children with respect to fathers for all three cohorts. Elements above the main diagonal in transition matrices are indeed generally
higher than elements below the main diagonal and the changes in the distributions of fathers and children across the three classes tends to favour classes USS and UD in all three cohorts (see Tables 1.8, 1.9 and 1.10). The overall impression is, however, that the advance in educational attainment was very strong for Cohort I, much less strong for Cohort II and, very weak for Cohort III. These findings are consistent with the results in Checchi (2010), who uses the same dataset but apply a different methodology of analysis (the estimate of elasticities).
Tables1.2,1.3and1.4show that the persistence increases from Cohort I to Cohort III for classes USS and UD (0.48 vs 0.57 and 061 for USS and 0.54 vs 0.61 and 0.71 for UD) and decreased for CS (0.58 vs 0.48 and 0.47).9 The estimates of index
IS reported in Table 1.5 suggests that the overall educational mobility decreased
from Cohort I to Cohort III. Tests of equality between IS of Cohort I and Cohort
III and between IS of Cohort II and Cohort III is rejected at 1% significance level
(see Table 1.6).
The off-diagonal elements stress that the probability that a child with a father in class CS of obtaining a higher educational attainment than the one of his/her father is increasing from Cohort I to Cohort III, but not from Cohort II to Cohort III (0.34 vs 0.45 and 0.44)10. On the contrary, the probability that a child with a father in class USS takes an UD decreases from Cohort I to Cohort III (0.43 vs 0.37 and 0.32)11. Checchi (2010) discusses a similar evidence. This finding is particularly puzzling since both the dynamics of the demand side of labour market, thanks to changes in technology in favour of more skilled workers, and the dynamics of supply side of labour market, thanks to the reduction in the imperfections of capital market and the higher wealth of household, would suggest that UD should be more likely over time independent of the class of educational attainment of parents (father).
9The null hypothesis of equality for all these transition probabilities can be rejected at the
usual confidence level of 5%.
10We can reject the null hypothesis of equality between the transition probabilities of Cohort
I and II at the usual confidence level of 5%.
11We can reject the null hypothesis of equality for all these transition probabilities at the usual
Table 1.5: Mobility indices of educational attainment for the three different cohorts. Index\Cohort I (1947 − 1956) II (1957 − 1966) III (1967 − 1976) (1947 − 1976) IS 0.68 (0.022) (0.019)0.67 0.605(0.022) 0.643(0.013) IB 0.131 (0.006) 0.112(0.005) 0.093(0.007) 0.111(0.003) IBM 0.072 (0.003) 0.059(0.003) 0.052(0.004) 0.065(0.002) IF L 0.239 (0.004) 0.274 (0.004) 0.273 (0.005) 0.263 (0.00)
Standard errors are reported in parenthesis; they are computed via a bootstrap procedure with 300 bootstraps (seeEfron and Tibshirani(1993))
Indexes IB and IBM confirm that the overall educational mobility decreased from
Cohort I to Cohort III (see Table 1.5). Test of equality between indexes IB and
IBM of Cohort I and III and between Cohort II and III are all rejected at 5%
confidence level. Index IF L shows a different dynamic: from Cohort I to Cohort II
the index increases and the two values are statistically different at 5% confidence level. From Cohort II to Cohort III IF L decreases but from the test of equality we
conclude that the values of the indexes are not statistically different (see Table1.6).
Table 1.6: P-values of the test of equality between mobility indexes of different Cohorts.
Index\Cohort I vs III II vs III
IS 0.007 0.013
IB 0 0.017
IBM 0 0.042
IF L 0.047 0.454
As mentioned in the introduction of this chapter, a Perfect Mobile Society is rep- resented by a transition matrix where the probability of entering a particular class is independent of the class of one’s father and where its elements are equal to those of the ergodic distribution. We construct this transition matrix for all cohorts and we apply the mobility indexes to it.
Table 1.7 shows the ratio between the mobility indexes computed on the actual transition matrices and the mobility indexes computed on the perfect mobility
transition matrices. This ratio gives an idea of how a society is far from being a perfectly mobile society and it allows us to avoid the problem concerning the structural occupational changes that occur in the society over the considered pe- riod.
IF Ldisplays a ratio greater than 1, but it is due to the fact that it weights the tran-
sition probabilities with the actual distribution, whereas when it is computed on the perfect mobility’s transition matrix, the transition probabilities are weighted by the ergodic distribution being the latter equal to the actual distribution. The Table 1.7 suggests that from Cohort I to Cohort III, the educational mobil- ity tends to decrease. In particular for IS and IB, the ratio decreases of 0.8 and
0.10 percentage points12. This result shows an increase of the “distance” from the
perfect mobility.
Table 1.7: “Distance” from a Perfect Mobile Society
Index\Cohort I (1947 − 1956) II (1957 − 1966) III (1967 − 1976) (1947 − 1976) IS 0.68 (0.043) 0.67(0.04) (0.039)0.60 (0.038)0.64 IB 0.67 (0.013) (0.012)0.68 (0.011)0.57 (0.013)0.63 IBM 0.53 (0.012) 0.57(0.01) (0.009)0.51 (0.011)0.58 IF L 1.22 (0.016) (0.013)1.66 (0.015)1.68 (0.013)1.52
Standard errors are reported in parenthesis; they are computed via a bootstrap procedure with 300 bootstraps (seeEfron and Tibshirani(1993))
The ergodic distributions reported in Tables 1.8, 1.9 and 1.10 highlight how the distribution dynamics is far to be exhausted: the mass of class UD of the youngest children should increase from 0.15 (the mass of actual children in Cohort III) to 0.50 in the long run; at the same time class CS should decrease from 0.40 to 0.08. The ergodic distributions of Cohorts II and III appear very similar, confirming the previous intuition that not appreciable changes in the distributional dynamics of educational attainment happened in the two periods.
Table 1.8: The ergodic distribution of educational attainment for Cohort I (1947-1956). CS USS UD Distribution of Fathers 0.89 0.07 0.03 Distribution of Children 0.52 0.36 0.12 Ergodic Distribution 0.18 0.40 0.42
Table 1.9: The ergodic distribution of educational attainment for Cohort II (1957-1966).
CS USS UD
Distribution of Fathers 0.85 0.09 0.04 Distribution of Children 0.42 0.45 0.12
Ergodic Distribution 0.09 0.45 0.46
Table 1.10: The ergodic distribution of educational attainment for Cohort III (1967-1976).
CS USS UD
Distribution of Fathers 0.80 0.14 0.05 Distribution of Children 0.40 0.46 0.15
Ergodic Distribution 0.08 0.42 0.50