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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

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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

. . 00 0

n nk k n

is i k s i k s sk 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 sE 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

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s

jj i

n

jss

Xn

= 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

11

s

jj i

n

is jss

P Pn

= endogenous effect

Aggregation, n large: 1 1 1s s sP 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 ssP ZX

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

1

1sn

group

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

n n m n n nis 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 ( )

mi sP PISA score of migration peer group of (without contribution of student i,

if applicable) ( )

ni 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 nn

mm n

m

nm M XM XP R R

n mn mm

nn m

n

mn M XM XP R R

Total aggregate multipliers:

1

11

m n

nn

m n mmmM (migrants)

1

11

n m

mm

n m nnnM (natives)

Compare Glaeser et al. (2000, 2003), e.g.

1

1m 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? -> Interaction within groups What is the influence of between-group interaction? (migrants/ natives)

Estimated equations:

( ) ( )

( ) ( )

,

.

m m m m m kis is k s k m i s n i s is

n n m n n kis is k s k m i s n i s is

P X R P P

P X R P P

Estimation problems...

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Results: Estimation of Baseline Model for Pisa Maths Scores 2006, Germany and the UK

Dependent Variable:

Mathematics Score Germany United Kingdom (UK) Natives Migrants Natives Migrants

Female -32.278 (2.321)

[0.000]

-29.529 (5.288)

[0.000]

-14.776 (2.302)

[0.000]

-13.063 (8.606)

[0.133] .

.

.

National Language at Home 24.839 (7.008)

[0.001]

18.251 (5.927)

[0.003]

-16.205 (11.276)

[0.153]

4.144 (8.818)

[0.640]

More than 100 Books at Home 24.839 (2.677)

[0.000]

6.636 (5.818)

[0.257]

29.364 (2.998)

[0.000]

30.807 (8.473)

[0.000]

Home Educational Resources 3.063

(1.415) [0.032]

-1.108 (2.937)

[0.707]

11.472 (1.714)

[0.000]

15.006 (6.565)

[0.025]

Economic, Social and Cultural Status 1.773 (1.634)

[0.280]

9.406 (3.285)

[0.005]

13.557 (1.945)

[0.000]

16.551 (4.499)

[0.000]

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Table 2: (continued)

Dependent Variable:

Mathematics Score Germany United Kingdom (UK) Natives Migrants Natives Migrants

Student Teaching Staff Ratio 0.301 (0.213)

[0.160]

0.630 (0.704)

[0.373]

-0.005 (0.401)

[0.989]

2.716 (2.013)

[0.181]

Quality of School’s Educational Resources -0.389 (0.898)

[0.666]

4.694 (2.992)

[0.120]

0.439 (0.835)

[0.599]

3.172 (3.657)

[0.388]

Village / Small Town -0.647 (2.246)

[0.774]

0.533 (6.130)

[0.931]

-0.852 (1.941)

[0.661]

-3.919 (10.439)

[0.708]

Selection by Residence -3.627

(2.515) [0.151]

-3.233 (6.493)

[0.620]

-0.244 (1.855)

[0.895]

0.512 (10.278)

[0.960]

Selection by Performance -1.195 (2.240)

[0.594]

-4.244 (5.994)

[0.480]

18.318 (4.143)

[0.000]

12.619 (16.324)

[0.442]

Responsibility for Curriculum and Assessment -1.568 (1.352)

[0.248]

6.981 (4.296)

[0.107]

1.454 (1.252)

[0.247]

-4.925 (7.616)

[0.519]

Responsibility for Resource Allocation 1.772 (2.560)

[0.490]

7.059 (6.676)

[0.293]

-1.072 (0.952)

[0.262]

5.198 (5.932)

[0.383]

Public School 0.645 (6.364)

[0.919]

20.268 (18.400)

[0.273]

5.974 (4.125)

[0.149]

-30.982 (20.220)

[0.129]

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Dependent Variable:

Mathematics Score Germany

United Kingdom (UK)

Natives Migrants Natives Migrants

Mean of Maths Scores, Natives 0.670 (0.051)

[0.000]

0.715 (0.074)

[0.000]

0.577 (0.039)

[0.000]

0.328 (0.139)

[0.021]

Mean of Maths Scores, Migrants 0.103 (0.031)

[0.001]

0.030 (0.079)

[0.700]

0.057 (0.013)

[0.000]

0.197 (0.103)

[0.059] R - Squared 0.633 0.653 0.376 0.449

Observations 2332 410 3850 379

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Table of Social Multipliers:

Recall:

1

11

m n

nn

m n mmmM ,

1

11

n m

mm

n m nnnM

m nm nn

mm n

m

nm M XM XP R R

n mn mm

nn m

n

mn M XM XP R R

Compare to Scandinavia (Denmark, Sweden, Norway): 1.1/1.7 (migrants/natives)

mM (Migrants)

nM (Natives)

Germany 1.339 (0.132)

3.936 (0.790)

United Kingdom 1.318 (0.174)

2.501 (0.245)

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Conclusions

Novelty: Analysis of social multipliers under consideration of segregation

’Migrants/ natives’: Schooling system of early separation into different-ability schools might causes adverse peer effect

Amplification of origin-caused differences between children from families with a disadvantaged (migrant) background and more privileged families, par-ticularly in Germany

Policy conclusions?

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2. Modelling Social Interaction and Identification of Social Multipliers

(Identification of endogenous social effects - The reflection problem)

(Manski 1993, 1995, 2000).

Empirical analysis of social interaction and behaviour is hindered by the fact that it re-sembles the situation at which a person sits in front of a mirror and can see his reflec-tion but, nevertheless, it cannot be distinguished whether at the same time the moves the person makes are caused by his own reflection or are merely reflected.

Simultaneously, a second impediment is selection, for individuals tend to choose their peers, neighbourhoods or networks. Thus, unlike identification of parameters in market outcomes, behaviour in non-market settings and environments is still under the scope of broad analysis and develops constantly.

Key questions to be answered refer to the influence that the group behaviour might ex-ert on individuals’ behaviour of the same group and the tendency of the group’s indi-viduals to behave in a similar manner.

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Following Manski (1993, we usually assume - at first - that a random sample ( , , )y x z is available from the population. y would represent the scalar outcome or behaviour, x all variables which capture same institutional environments and/ or group characteristics and, finally, ( , )z u summarize direct socio - economic composition and ability.

The scalar outcome y is specified in the following way:

(1) ( | ) ( | ) ' ' y E y x E z x z u

meaning that, econometrically, the outcome is modelled so that it varies with the mean of the outcome conditional on all variables that represent similar institutional environments. Note, though, that the conditional on both x and z the mean of the error term is different from zero: ( | , ) 'E u x z x (absence of zero conditional mean assumption).

Taking the conditional expectation with respect to both x and z by using the law of ite-rated expectations, we obtain the mean regression of y on ( , )x z :

(2) ( | , ) ( | ) ( | ) ' ' 'E y x z E y x E z x z x .

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Each of the parameters , and represents an endogenous, an exogenous and a correlated effect respectively.

Source of the reflection problem: Outcome varies with the mean of the outcomes of the peers, i.e. 0 .

Parameter 0 depicts the exogenous effect, for variable z includes the exogenous va-riables. Likewise, parameter 0 expresses the correlated effect, capturing similarity in behaviour among peers (presence of group effects).

Furthermore, by assuming that the mean regressions of y on ( , )x z , of y on x and of z on x can be consistently estimated, one can use equation (2) and integrate it with re-spect to z , assume 1 and solve for ( | )E y x in order to obtain the ‘social equili-brium’:

(3) 1( | ) ( | ) ' ' 1 1 1

E y x E z x x

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As seen above, it is possible to identify functions of the parameters of interest if 1 , but not the parameters themselves and, of course, cannot distinguish among endogen-ous, exogenous and correlated effects. Substituting ( | )E y x from (3) into (2), yields the reduced form equation:

(4) 1( | , ) ( | ) ' ' '1 1 1

E y x z E z x z x

.

Although we are not able to discern between endogenous and exogenous social effects, we are allowed to detect the presence - if any - of a social effect provided [1, ( | ), , ]E z x x z are linearly independent in the population and 0 for the nume-rator, i.e. either 0 or 0 must be true.

Identification can only be achieved using some exclusion criteria:

o First, by assuming exclusive presence of endogenous effects, which amounts to imposing 0 on the parameter vector. This pure endogenous model can be estimated in a two–stage procedure; by using sample data one can retrieve a non-

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parametric estimate of the mean outcome given x , and use this estimate later on to identify the social interactions parameter with least squares.

o The second case is described by Graham and Hahn (2005), where one assumes ab-sence of exogenous social effects, i.e. 0 . Using a quasi-panel approach, esti-mating the between groups model identifies , and upon the availability of an in-strumental variable, 2SLS provide an estimate for the composite parameter

/(1 ) ; thus, the magnitude of the (endogenous) social effect can be inferred in a completely parametric procedure.