The Effect of High Achieving Peers Leaving The Class - Evidence From Hungary Mi van akkor, ha a legokosabb gyerekek elmennek az osztályból? A kisgimnáziumi szelekció következményei Fritz Schiltz, Deni Mazrekaj, Daniel Horn, and Kristof De Witte Szirák 09.11.2018 Budapest

Overview What happens to „children left behind” when the highest-achieving are cherry-picked by elite schools? We exploit a unique institutional setting, coupled with good data. We contribute to the tracking literature by focusing on potential mechanisms that change staying-students’ outcomes. Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Main results Instrumenting the percentage of leaving peers suggests 1) moderately negative total effects especially in math and aspirations 2) but heterogeneous effects. More negative for girls, and for the top quartile left behind in Math, reading, behavior & aspirations Positive for the bottom quartile in Reading, behavior & aspirations Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Setup Grade Age 8 14 NABC 8 12 6 10 Data collected in Grade 6 and Grade 8 2008 (2010) – 2015 (2017) Total of 635,713 students Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Setup Spatial variance in 6-year-long elite tracks Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Setup Spatial variance in 6-year-long elite tracks Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Setup Spatial variance in 6-year-long elite tracks Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Elite schools for ‚elite’ students Stayers Leavers 49% 52% 19% 48% 26% 52% 1,485 1,657 1,474 1,649 17,105m 7,314m 461,666 26,823 Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Identification strategy I (baseline) Goal: Look at the performance of those who stayed! Problem: % of leavers can be endogenous better primary schools „produce” better students more can leave but less would like to leave -> sign of bias is unclear Exogenous variation: distance from nearest elite track! median class distance in 6th grade measured in meters covered by bus (Volan) from home to nearest elite track Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Identification strategy I   Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Identification strategy I Spatial immobility in Hungary is low! 90% does not move between grade 6 and grade 8 Only 0.5% of students moves to a region with elite schools movers & non-movers equally likely to leave Two out of three movers does not leave school % leavers to elite schools class median distance to nearest elite school (km) Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Identification strategy I Validity of distance as instrument Elite schools 10km further away 1.5% less leavers (mean=6%) Robust to alternative specifications 1. Exclusion Distance is independent of test scores in grade 6 2. Exogeneity Current spatial dispersion of elite tracks is independent of individual place of living (w/ free school choice) Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Identification strategy II Panel fixed effect models. Utilize the fact that there is variation in the number /percentage of leavers by school through the years. Problem: unbalanced panel (several schools have no leavers in several years). This is just a robustness check! Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Identification strategy II % of observations Number of leavers to elite schools per class Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Identification strategy II % of observations in classes where at least 1 student is leaving to elite schools % of leavers to elite schools per class Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Results (IV) (when 10% leaves) Mean Q1 Q2 Q3 Q4 Mathematics OLS -0.018*** -0.009*** -0.008*** -0.011*** (N=498,606) (0.003) First stage -0.013*** -0.010*** -0.012*** -0.014*** -0.015*** (0.001) (0.004) 2SLS -0.057*** -0.107*** -0.076*** -0.045*** -0.010 (0.015) (0.021) (0.018) (0.016) Reading -0.008** -0.006** (0.002) -0.012 -0.014 -0.062*** -0.035** -0.001 0.026** (0.011) (0.017) (0.014) (0.013) Controls: Gender, books at home, mother education, score in grade 6, leave-out-means at class level. Regional and cohort FE. SEs clustered at class level. Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Results (IV) – alternative outcomes (when 10% leaves) 65 – 75 % observed Mean Q1 Q2 Q3 Q4 GPA 2SLS 0.004 -0.020** 0.019* 0.018 0.020* (N=320,073) (0.008) (0.011) (0.012) Behavior 0.008 -0.017 0.003 0.030** 0.039*** (N=370,048) (0.013) Aspirations -0.015*** -0.054*** -0.013 0.013** (N=385,044) (0.005) (0.010) (0.009) (0.007) (0.006) Controls: Gender, books at home, mother education, score in grade 6, leave-out-means at class level. Regional and cohort FE. SEs clustered at class level. Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Heterogeneous effects Gender Same effect by leavers’ gender More negative effects for staying girls Socio-economic background (~quartiles) More negative effects for high SES Positive effects for low SES: Reading Behavior Aspirations Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Identification strategy II (cohort variation) Effect by ability and gender Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Mechanism Competition Q1 competed with left-students -> lack of incentives 2. Increased/depleted confidence Q1 tried but failed Q4 increased in relative ability 3. Teaching to the mean? More time for Q4? Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Conclusion Positive effects: Lowest ability students Reading, behavior & aspirations Negative effects: Girls, high ability/high SES Math, reading, behavior & aspirations Policy relevance This is effect of small changes in composition Positive effect for leavers Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Thank you for the attention Daniel Horn Horn.Daniel@krtk.mta.hu 09.11.2018 Szirák

Instrument robust to alternative specifications First stage % students in a class leaving to elite schools   (1) (2) (3) (4) (5) (6) Median class distance (10km) -1.61*** (0.06) -1.56*** -1.49*** -1.14*** (0.05) -1.53*** Individual level X Class level Cohort FE Region FE F-statistic 752.75 755.70 209.45 157.57 80.76 582.27 Students 432,134 Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Results robust to alternative instruments   Median class time bus (minutes) Median class distance car (km) Median class time car (minutes) Mathematics Reading % leaving -0.0054*** -0.0007 -0.0056*** -0.0006 -0.0008 (0.0019) (0.0013) (0.0018) F-statistic 77.53 77.54 81.27 81.32 78.53 78.57 Students 432,103 432,125 Schiltz-Mazrekaj-Horn-DeWitte Peer effects

Results robust to alternative specifications   Reshuffling classes Student growth Mathematics Reading % leaving to -0.0064*** -0.0012 -0.0058*** -0.0013 elite schools (0.0021) (0.0015) (0.0019) (0.0013) F-statistic first stage 84.78 85.70 69.01 67.67 Students 408,553 432,134 Schiltz-Mazrekaj-Horn-DeWitte Peer effects