How are inequality of opportunity and mean student performance related? A quantile regression approach using PISA data Zoltán Hermann – Dániel Horn Institute of Economics of the Hungarian Academy of Sciences Economics of Crisis, Education and Labour Chinese - Hungarian International Conference 30th June -1st July 2011, Budapest

Research question 1.Is there a trade-off between equity and quality in education? 2.Is this relationship varies with respect to (unobserved) student ability? two approaches: inequality of opportunity inequality of outcomes attributable to factors outside the individual’s control measurement in education: the strength of the family background effect (FBE) on student achievement inequality of outcomes the dispersion of outcomes this paper focuses on inequality of opportunity (policy relevance) our contribution: measuring inequality of opportunity for students with different ability and exploring the relationship with mean performance

Existing evidence direct evidence inequality of outcome - „virtuous trade-off”: Freeman–Machin–Viarengo, 2010 (sensitive to measurement) inequality of opportunity - no association: Woessmann, 2004; OECD, „virtuous trade-off”: Chiu–Khoo, 2005 indirect evidence related to early tracking inequality of outcome - no association: Hanushek–Woessmann, 2006 inequality of opportunity - trade-off: Ariga–Brunello, no association or „virtuous trade-off”: Horn, trade-off conditional on educational institutions: Schuetz–Ursprung–Woessmann, 2008 the FBE varies along the test score distribution Fertig–Schmidt, 2002; Fertig, 2003; Freeman–Machin–Viarengo, 2010

Data PISA 2000, 2003, 2006, 2009 Programme for International Student Assessment (OECD) student achievement reading, math and science test scores family background number of books at home the best available proxy for socio-economic status, internationally comparable (Schuetz–Ursprung–Woessmann, 2008; Fuchs-Woessmann, 2006) 6 categories, considered as a continuous variable (Schuetz–Ursprung–Woessmann, 2008: good approximation: linear effect) restricted sample of countries for this paper OECD and EU member countries (137 country-year observations) number of books is assumed to be a better indicator within this group

Econometric specification: 1. step Two-step estimation procedure: 1. estimating the FBE for each country in each year SCORE i = α + β BOOK i + γ Z i + ε i baseline estimation: OLS allowing for individual heterogeneity: quantile regression FBE for country j in year t : β control variables: gender, immigrant status of the student and of parents

Econometric specification: quantile regression quantile regression aims at analysing the effect of the explanatory variables at different points in the conditional distribution of the dependent variable family background test score

Patterns of the estimated FBE Finland Czech Republic the Netherlands ♦: math, 2009; ●: reading, 2009; ▲: science, 2009

Patterns of the estimated FBE: China, Hungary Hong Kong Macao Shanghai Hungary ♦: math, 2009; ●: reading, 2009; ▲: science, 2009

Econometric specification: 2. step 2. The asssociation of FBEs and mean performance at the country level MEANSCORE ct = κ + λ FBE ct + φ R ct + ν ct MEANSCORE ct = κ + λ 20 FBE 20 ct + λ 50 FBE 50 ct + λ 80 FBE 80 ct + φ R ct + ν ct Specifications: pooled (1)(2)(3) fe (4)(5)(6) year dummiesyes share of students with few and many booksnoyes noyes GDP per capitanononoyesno yes country fixed-effectsnonono yes Bootstrap standard errors bootstrap replicate sample of schools repeating both steps of the estimation for each replication

Mean performance and FBE, math FBE FBE at the 80 th quantile FBE at the 50 th quantile FBE at the 20 th quantile

Mean performance and FBE: China, Hungary math reading ● Shanghai ● Macao ● Hong Kong ● Hungary

Results Pooled cross-sectionFixed effects (1)(2)(3)(4)(5)(6) math fbe_q ***-5.849***-4.723***-1.400**-1.453**-1.781*** fbe_q fbe_q **2.189**1.199* reading fbe_q ***-3.596***-2.940*** * fbe_q fbe_q **1.549** *0.955*0.926* science fbe_q ***-4.710***-4.033***-1.300***-1.207***-1.193*** fbe_q * fbe_q ***2.276***1.700*** math fbe-1.403***-1.476***-0.695***-1.403***-1.506***-1.490*** reading fbe-1.075***-1.047***-0.813***-0.813*-0.764*-0.750* science fbe0.333* ***-0.799**-0.805**

Interpreting the results association, no evident cause and consequence a possible interpretation: poor and high ability students benefit most from improving educational quality Family background Test score A hypothetical change in inequality of opportunity and mean performance ●: before policy change ○: after policy change

Results for subgroups of students books: few medium many pooledfepooledfepooledfe math fbe_q ***-1.631***-6.041***-1.865***-4.846***0.068 fbe_q fbe_q ** ***0.630 reading fbe_q ***-1.520**-3.567*** **0.228 fbe_q fbe_q **1.143*2.191***1.365*** science fbe_q ***-1.640***-5.185***-1.692***-3.844***0.457 fbe_q * *0.313 fbe_q ** *** ***0.492

Conclusions the overall association between inequality of opportunity and mean performance is ambiguous: no association or „virtuous trade-off” inequality of opportunity seems to be heterogeneous with respect to student ability: poor students with high and low ability encounter different constraints → this heterogeneity should be taken into account when the equity effetc of policies is evaluated educational systems with more equality of opportunity among high achiever students tend to perform better in general equality of opportunity among medium and low achievers is not clearly related to mean performance → casual mechanisms should be explored in further research