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  • 1

    Migrants at School: Educational Inequality and Social Interac- tion in the UK and Germany

    Verein für Socialpolitik, Magdeburg, 9 September 2009

    Horst Entorf and Eirini Tatsi

    Goethe University Frankfurt

    1. Motivation (Inequality, Schooling Systems) 2. Modelling Social Interaction and Identification of Social Multipliers 3. Econometric Results 4. Conclusions

    entorf Textfeld First presented at meeting of the Anglo-German-Foundation, London, 22 May 2009

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    1. Motivation PISA results in 2000, 2003, 2006 in the UK and Germany

    Reading Maths Sciences

    Note: s.e. in 2006: a) UK: Reading 2.3, Maths 2.1, Sciences 2.3, b) Germany: Reading 4.4, Maths 3.9, Sciences 3.8.

    Reactions to PISA scores in Germany (“PISA Schock”) and in the UK:

    “Being above Germany in the education league table might not be as much fun as beating them at foot- ball, but it could prove more important for the UK in the long run”(The Times, 7 December 2001)

    “A league table to worry us all.”, “The suggested decline of the UK scores [...] raises questions about the direction of educational policy in England over the past 10 years” (The Guardian , 8 January 2008)

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    Inequality in Educational Achievements, PISA Maths Score, 2006

    Inequality between Natives and Migrants/ Schooling Systems: Selected Variables (Data: OECD, PISA 2006)

    Germany UK

    Share of migrants 0.143 0.088

    Differences in ISEI (socioeconomic status) -11.010 -1.935

    Share of all migrants (=100%) in top 10% Schools 0.055 0.144

    Share of all migrants in bottom 10% schools 0.213 0.158

    Schooling systems => Share of between school variance 0.668 0.313 *Observations are weighted by student weights. Authors’ own calculations.

    UK Germany

    Pooled Sample 495.990 503.111 Natives 499.903 518.339 Migrants 474.391 445.179 Difference 25.512 73.160

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    2. Social Interaction and Social Multiplers Motivation of Social Multiplier Related to building expectations in autoregressive time series models Assumptions:  Consider student i at school s  Neighbours (”peers“) of student i are sorted according to their influence on student i,

    i.e. (i-1) has highest impact on i, (i-2) has highest impact on (i-1), (i-3) on (i-2) etc.  Educational achievement depends on individual factors and on educational achievement

    of the (most important) neighbour:

    1.is is i s isP X P     , where 0 1  Multiplier of any exogenous impact:  Performance of student i benefits from exogenous resources of his neighbour:

     1. 2. 1.is is i s i s i s isP X X P           

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     Eventually educational achievement of student i is subject to the exogenous characteris-

    tics of all peers, with the weight of influence autoregessively decreasing with increasing distance to student i:

    1 1

    . . 0 0 0

    n n k k n

    is i k s i k s s k k

    P X P      

       

        .

     Assuming ( )js sE X  for all peers( )i k attending class s as well as zero expected error terms, for large n the limit value is

    ( ) 1is s

    E P   

     

    Conclusion: The expected impact of some exogenous change depends on the size of the so-

    cial multiplier, i.e. on 1

    1  .

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    Motivation based on aggregates:

    Individual educational achievements are determined by peer group; each active student has an impact on her own peer group:

     Feedback between peer group and members of peer group: Social Inter- action

    Does an exogenous individual impact translate into reinforced aggregate effects?

    Yes, in case of ‘social interaction’ (n large):

               1 1i iPISA X PISA PISA X

    Identification of endogenous social effects - The reflection problem (Manski, 1993) Mean Regression of y on ( , )x z : ( | , ) ( | ) ( | ) ' ' 'E y x z E y x E z x z x         . Each of the parameters ,  and  represents an endogenous, an exogenous and a corre- lated effect respectively.

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    Application of Manski’s approach to estimate peer group effects at school

    ( ) ( )is is i s s i s isP X X Z P          

    where  isX = exogenous individual characteristics (parental SES, etc).

     ( )i sX  = 1

    1 1

    s

    j j i

    n

    js s

    X n 

      

    = correlated exogenous effects, i.e. mean of exogenous peer group characteristics, e.g. common language of peers, average educational and SES background of peers’ parents, their resources at home, etc  sZ = correlated exogenous environmental factors, e.g. due to common

    teachers, neighbourhood etc.

     ( )i sP  = 1

    1 1

    s

    j j i

    n

    is js s

    P P n 

       = endogenous effect

    Aggregation, n large: 1 1 1s s s

    P X Z     

       

      

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    Estimation:

     Impossible to identify both endogenous and correlated group effects (perfect multicollinearity between ( ) ,i s sX Z and ( )i sP  )

     Omitting exogenous peer group background ( )i sX  , i.e. setting 0  , leads to

    ( )is s i s iis sP Z PX        

    and (for large groups) to

    111s ss

    P ZX   

     

        

    The social multiplier (SM) results from the ratio of the aggregate marginal effect to the indi- vidual marginal effect:

    1

    1 sngroup

    micro

    SM   

    

      

    (Glaeser, Scheinkman 2000)

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    Extending Glaeser et al. (2000, 2003): Interaction within and between two groups

     Modelling channels of influence between groups: native native native migrant

    migrant native migrant migrant

     Interaction might be subject to schooling systems:  Early tracking by skill level (Germany, Austria)  Comprehensive schools (Scandinavia, UK)

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    Consider two-equation system of migrants and natives:

    ( ) ( )

    ( ) ( )

    m m m m n m is m is m s m i s n i s is

    n n m n n n is n is n s m i s n i s is

    P X R P P

    P X R P P

        

          

     

        

        

    where s  1, …, S, schools in national samples i  1,… , sn sn = Number of students at school s ( )

    m i sP   PISA score of migration peer group of (without contribution of student i,

    if applicable) ( )

    n i sP   PISA score of native peer group of (without contribution of student i,

    if applicable) isX  Vector of student-specific characteristics

    sR  Vector of school-specific characteristics (correlated environmental effects)

     Parameter  jk , j, k = m, n, measure degree of social interaction

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    Calculation of Social Multipliers

    Aggregation of individual equations ( sn is large) and producing reduced forms provide di- rect (within groups) and indirect (between groups) effects

            m nm nnm m nm nm M XM XP R R         n mn mmn n mn mn M XM XP R R

    Total aggregate multipliers:  

     

      

          

    1

    1 1

    m n

    n n

    m n mm mM (migrants)

      

     

            

    1

    1 1

    n m

    m m

    n m nn nM (natives)

    Compare Glaeser et al. (2000, 2003), e.g.    11m mmM

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    ‘Within Effect’ for migrants, mM ‘Between Effect’ of natives on migrants,  m nn M :

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    3. Econometric Analysis

    PISA data

     Programme for International Student Assessment (PISA), conducted by OECD 2000, 2003, 2006

     Assessment of the performance of 15-year olds in cognitive abilities, mathematics, science

     Here: focus on the 2006 Report and scores in mathematics Determinants of educational success?  Schooling inputs in educational production functions seem to be less relevant (Ha-

    nushek 1986, Hoxby 2000, Woessmann 2003 etc.)

     Dominating factors: Family, socioeconomic status of parents, presence of migration background

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     Neglected factor:

     ‘Peer Groups’, in particular in presence of early segregation

     Does social interaction amplify initial pre-school differences?  Existence of Social Multipliers?