Gianfranco De Simone Φ Fondazione Giovanni Agnelli

1.Methodology 1.Methodology: If you want to do research on the dynamics of cognitive achievement but longitudinal data are unavailable, don’t loose your hope! 2.Policy 2.Policy: The origin of intergenerational persistence of educational attainment and eventually social immobility lies in the compulsory education level. The largest part of learning divide across students with diverse socio-cultural background originates in lower secondary school. Φ Fondazione Giovanni Agnelli

1.Methodology 1.Methodology: If you want to do research on the dynamics of cognitive achievement but longitudinal data are unavailable, don’t loose your hope! 2.Policy 2.Policy: The origin of intergenerational persistence of educational attainment and eventually social immobility lies in the compulsory education level. The largest part of learning divide across students with diverse socio-cultural background originates in lower secondary school. Φ Fondazione Giovanni Agnelli

 Learning is a cumulative process: longitudinal value added models are usually employed to single out the contribution of a specific stage of the educational process.  The individual net cognitive gain is computed as the difference between the observed final level of knowledge and competence and the entry level.  In order to disentangle the net contribution of lower secondary education as measured at the end of the first cycle of education (t), we need to control for the student level of achievement at the end of the primary school (t-s, where s is the length in years of lower-secondary education).  So we can define an autoregressive model of the following type: (1) where y denotes the achievement of student i in the two grades, X and Z are sets of time-variant and time-invariant individual characteristics, respectively, δ is a class fixed effect (capturing teaching quality, peer effects, etc.), φ is a school fixed effect (capturing management quality, organization, contextual factors, etc.) and ε is a residual component. Φ Fondazione Giovanni Agnelli

 To estimate eq (1) one should rely on performance data collected for the same individuals over time which are not available for Italian students.  Moffitt (1993) suggest an alternative strategy: a consistent estimation of (1) can be obtained with data collected in repeated cross-sections (RCS) where sets of individuals are independently drawn from population at two or more points in time.  In fact, even if RCS lack lagged values for y i, we can replace y i,t-s with a value estimated through the projection: (2) where coefficients (γ) are consistently estimated from data on the cross- section at time t-s on different individuals than those drawn at time t, by means of the reduced form defined by the orthogonal projection: (3) Φ Fondazione Giovanni Agnelli

 Basically, the information needed to estimate past achievements can be derived by time-invariant variables in Z and from the time-varying observables in X that can be backcasted with reasonable accuracy.  Eq (1) now becomes: (4) where the measurement error (asymptotically uncorrelated with the predicted value) adds up to the residual component (5)  When we are able to observe the same cohort of individuals - although not the same individuals – over time, equation (4) can be consistently estimated by OLS as there are no cohort effects in the unobservables.  A second condition for consistency is that the X should be uncorrelated with residuals. Φ Fondazione Giovanni Agnelli

Two main messages from the paper: 1.Methodology 1.Methodology: If you want to do research on the dynamics of cognitive achievement but longitudinal data are unavailable, don’t loose your hope! 2.Policy 2.Policy: The origin of intergenerational persistence of educational attainment and eventually social immobility lies in the compulsory education level. The largest part of learning divides across students with diverse socio- cultural background originates in lower secondary school. Φ Fondazione Giovanni Agnelli

 The INVALSI, a government agency, has administered standardized test in reading and math in the 2 nd, 5 th, 6 th and 8 th grade of Italian school since Individual scores are not linked over time.  Unfortunately, we cannot apply pseudo-panel techniques to the Invalsi data for two reasons: ◦ different sampling frames have been used across different grades and over time; ◦ information on individual characteristics are not collected in all grades, thus we cannot identify students with the same profile in different grades.  However, Italy has taken part to Trends in International Mathematics and Science Study (TIMSS) in 1995, 1999, 2003 and TIMSS measures trends in math and science achievement at the 4 th and 8 th grade.  Given the timing of waves, TIMSS provides information about relative progress across grades: the cohort of students assessed at the 4 th grade in one cycle moves to the 8 th grade four years later.  In Italy, the 8 th grade corresponds to the final year of lower secondary education, while the 4 th grade is one year away from the completion of the primary school. Φ Fondazione Giovanni Agnelli

 Book possession and the parents’ education attainment for 8 th graders in 2007 reveals a clear association among the two covariates. Φ Fondazione Giovanni Agnelli

 To estimate the entry point at the lower secondary schools for a student that was assessed in 2007 at the 8 th grade, we need to estimate how a comparable student did in 2004 at while he/she was in the 4 th grade.  Thus, we first estimate the value of relevant coefficient on 4 th graders in  We cannot include neither class- nor school-level variable as, proceeding from primary to lower-secondary school, Italian students often face a change of school. Φ Fondazione Giovanni Agnelli

Φ Impact of time-invariant observables on test scores - Grade 4 - Weighted OLS estimation MATHSCIENCE abab Female-10.29***-10.93***-5.109*-5.353** [2.851][2.219][2.870][2.297] Parents' nationality (ref. Both Italian) One parent born abroad-15.13***-12.58***-11.63** [5.025][4.239][5.646][5.036] Two parents born abroad-35.94***-25.27***-38.82***-28.27*** [6.465][5.674][7.132][5.754] Age of arrival (ref. Native) Under ***-30.54***-18.40**-20.98** [8.932][8.451][8.911][8.120] Between 5 and ** [13.38][8.925][12.82][11.60] Books at home (ref. Up to a shelf) One bookcase17.11***15.92***16.21***14.69*** [3.325][2.678][3.644][2.829] Two bookcases17.79***17.54***21.22***19.40*** [4.473][3.382][5.130][4.097] Three or more bookcases9.604*11.30***16.12***16.44*** [5.173][4.050][5.110][4.423] Constant520.3***508.1***529.9***517.4*** [4.741][1.757][4.883][1.764] Area dummiesYesNo YesNo School fixed effectsNoYesNoYes Observations3,832 R-squared Robust standard errors in brackets. Errors clustered at the class-level. *** p<0.01, ** p<0.05, * p<0.1.

 We are now able to predict the test scores as 4 th graders for the 8 th graders in We simply substitute the appropriate Z values for 8 th graders and we employ the vector of estimated coefficient, as parameters for the following projection:  The limited variability is not surprising given the small impact of socio- demographic factors (Z) on performances at grade 4. Φ Fondazione Giovanni Agnelli Descriptive statistics Estimated entry levels for 8th graders ObsMeanStd. Dev.MinMax Math Science

 Now we can take into account the dynamics of cognitive achievement by estimating: where X is a set of individual-level time-variant variables impacting learning at the 8 th grade,is the classmates average test score capturing class- level factors that affect individual performance, φ is a school fixed effect and  As discussed above, since we observe the same cohort of individuals over two points in time, there are no cohort effects in the unobservables.  Furthermore, to estimate equation (9) consistently with OLS we need to make sure that observables in X are uncorrelated with the residual term.  So we include in the X two variables that are likely not to show an auto- regressive process: a) the time spent doing homework; b) the student perception of being safe in school. Φ Fondazione Giovanni Agnelli

Φ Determinants of achievements – Grade 8 - Weighted OLS estimation MATHSCIENCE StaticDynamic StaticDynamic Estimated test score at grade ***1.090*** 1.593***1.524*** [0.128] [0.122][0.123] Female-7.303*** *** ** [2.266][2.608][2.717] [2.121][2.219][2.253] Parents' nationality (ref. Both Italian) One parent born abroad ***14.49*** ***19.11*** [4.272][4.497][4.435] [4.532][4.682][4.572] Two parents born abroad-27.24***25.16***25.11*** ***49.21***47.73*** [7.147][8.693][8.785] [7.010][8.204][8.113] Parents education (ref. Up to lower sec) High-school degree32.43***29.04***27.31*** 28.64***22.35***20.97*** [2.750][2.659][2.691] [2.748][2.717][2.700] Post-secondary education37.32***32.62***30.84*** 38.12***27.96***26.38*** [3.262][3.277][3.296] [3.265][3.317][3.309] Classmates average scores0.252***0.248***0.220*** 0.273***0.258***0.231*** [0.0699][0.0696][0.0684] [0.0690][0.0685][0.0676] Constant343.5***-246.7***-251.0*** 347.2***-481.5***-477.4*** [33.50][73.63][72.74] [34.40][73.21][72.91] Time spent doing homework Perception of being safe at school School fixed effects No Yes No Yes No Yes No Yes Observations3,924 R-squared Robust standard errors in brackets. Errors clustered at the class-level. *** p<0.01, ** p<0.05, * p<0.1

Φ Fondazione Giovanni Agnelli  We focus on learning divides across social-groups in the first cycle of the Italian education system (primary and lower secondary school).  We show that intergenerational educational persistence and social immobility originates in the early stages of the schooling process through the influence of family background on achievements.  We provide evidence that such an inequality of opportunities arises at the lower secondary school.  On the other hand, Italian middle schools do not deteriorate further the gender gap in math and promote a noteworthy recovery of immigrant students.  In order to disentangle the specific responsibilities of the primary and the lower secondary schools we define a linear dynamic model of cognitive gain that is taken to the data by means of a pseudo-panel technique.  We show that, when longitudinal data are not available, information collected in repeated cross-sections can be a suitable substitute in system-level analysis of the dynamics of cognitive achievement.