The Market for Education in England

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The Market for Education in England

• Simon Burgess
• Public Organisation Conference, June 2008

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Education Market in England

• Market problem is an assignment problem
• Everyone is assigned to a school, but which
  pupils go to which schools?
• Focussing on the equity implications of the
  market here.
• This talk
• mostly drawing on School Assignment, School
  Choice and Social Mobility with Adam Briggs
• partly drawing on School Quality, School Access
  and the Formation of Neighbourhoods with Tomas
  Key

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Introduction

• Not all schools are good schools
• Which pupils go to the good schools?
• To the extent that children from poor families
  are allocated to worse schools, this perpetuates
  disadvantage, reducing social mobility
• Questions
• What is the extent (if any) of a differential
  chance of going to a good school?
• How does it happen?
• What would be the impact of increasing choice?

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School choice

• School choice
• Promise of a well-functioning school choice
  system is that it reduces role of location
• Countervailing view is that a choice system
  without fully flexible school size will increase
  the role of choice by schools, and the scope for
  the middle class to beat the system.
• Relative role for location as opposed to working
  the system is important.

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What we do

• We estimate the chances of poor and of non-poor
  children getting places in good schools
• One of the key factors is location distance
  between school and home.
• Our dataset allows us to measure distance very
  precisely and characterise the pupils very local
  area
• We compare pupils living in the same place.
  Exploit within-street variation and also control
  for other personal characteristics including
  prior test scores.
• The difference is relatively small compared to
  the overall difference.

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Results

• Poor children half as likely to go to good
  schools.
• Much of that, but not all, comes through
  location. That is, accounting fully for location,
  the gap is much smaller, but not zero.
• Controlling for location, this gap doesnt vary
  much by degree of choice.
• Children from poor families tend not to go to a
  good school, even if it is their nearest.
• Our econometric strategy is not to identify
  causal relationships in this paper (future work).

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Modelling Framework

• We model the assignment of children to schools,
  as a function of the characteristics of the
  school and of the children. Its a matching
  problem.
• The observed data on the outcome of this
  assignment are realisations of an underlying
  process, composed of two decisions
• applications by parents and children for places
  in particular schools (demand),
• and the administrative procedures that allocate
  children to schools given their choices
  (assignment rule)

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• Given the basic structures of the problem,
  parents then formulate their response strategy
• the role of location
• make any implicit advantages of their children
  visible to the admissions authorities, working
  the system
• Our strategy is to isolate how much of the
  difference in outcomes works through location,
  and how much through other channels, controlling
  for location.

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Allocation

• Write a general model of the outcome of the
  allocation as
• where

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Reverse causation?

• We interpret the estimated relationship between
  the schools quality score qa(i, t), t-6 and a
  students personal characteristic, fit, as
  representing the outcome of the assignment
  process.
• Alternative from student characteristics to the
  outcome score.

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• Timing the quality score derives from the
  performance of a group of children 6 years older
  than the current intake.
• But persistence in school attendance. Two
  interpretations
• Islands story Schools located on islands,
  with no mobility between them. All students from
  succeeding generations therefore go to the school
  on their island.
• Correlation from one generations poverty to the
  next.
• But this is not what Englands schools look like
• Half of children do not go to local school
• See map of Birmingham

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Figure 1 School Distance Contours in Birmingham
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• Dynasties pupils living in particular
  locations always go to the same school. And with
  persistence in area poverty, particular locations
  always house poor families.
• poverty of succeeding generations is correlated,
  score of one generation of pupils drawn from that
  area is correlated with the poverty of the next.
• Econometrically, estimating
• Will be biased because omitted variable of the
  nature of is location is correlated with fi, and
  with the nature of the previous cohort of pupils
  who generated the school quality score.
• Response control for location to remove omitted
  variable bias within postcode variation.

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Data

• Data on pupils
• Data on schools
• Data on location
• Our sample

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Pupils

• PLASC/NPD Census of all children in state
  schools in England, taken each year in January.
• Key variable for our purposes is an indicator of
  family poverty, the eligibility for Free School
  Meals (FSM).
• Gender, within-year age, ethnicity, SEN,..
• Key-stage 2 test taken at age 11 as the pupils
  finish primary school. This is a nationally set
  group of tests (in English, Maths and Science),
  marked outside the school

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Schools

• Quality of the secondary school that each child
  attends use the publicly available and widely
  quoted measure of the proportion of a schools
  pupils which passes at least 5 GCSE exams at age
  16 (repeated using value-added).
• Define a good school as a school in the top
  third nationally of the distribution of 5A-C
  scores (repeated using top third locally)
• Dating we use the score for each school from
  the time that the cohorts made their decisions on
  school applications, so deriving from the results
  of a cohort of pupils 6 years older.

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Location

• We have access to each pupils full postcode.
  This locates them quite precisely.
• Also the coordinates of the school, which locates
  it exactly.
• We rely on the postal geography of the UK for
  this analysis. Overall, there are about 1.78m
  unit postcodes covering 27.5m addresses. On
  average, there are 15 addresses in a unit
  postcode, but this varies.
• Using pupils postcodes, we match in data on
  neighbourhoods, on two scales postcode, and area
  (ward approx 12k people).

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Sample

• We take the cohort of new entrants into secondary
  school from each PLASC, so pupils in their first
  year of secondary school. Roughly 0.5m pupils in
  each cohort we use 3 cohorts so our full sample
  is 1.57m pupils.
• State schools in England non-selective LEAs
  (this cuts out 13.4 of the pupil total) omit
  pupils from some special schools, a few pupils
  are omitted if they have missing data.
• Sample for the overall regressions is 1.24m, 91
  of the available total in non-selective LEAs.

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Results

• How much of the difference in probability of
  attending a good school is due to location?
• Need to control completely for location.
• Interpretation location not exogenous
  estimating how important choice of location is
  for parents strategy.

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Table 5 Statistics on numbers of pupils per
postcode
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Figure 5 Differences in school quality by
differences in FSM status
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Table 6 Postcode-cohort FE regressions of school
quality
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Table 7 LEA FE on full sample of whether pupil
attends a good school
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Econometric Issues

• Reverse causation? Unlikely. The measure of
  quality used is essentially unrelated to the
  performance of the children in the postcode
• the measure relates to a cohort of children
  passing through the school 6 years previously.
• the focus children clearly constitute a
  negligible fraction of the actual attendees of
  the schools
• the use of within-postcode variation controls for
  any location effects.
• Selection bias? Likely. Direction seems clear.
  Will do some analysis of possible extent.

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Table 9 Postcode-cohort FE on School Quality by
deciles of minimum distance to three schools
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Results

• Specialise school allocation question to whether
  a child goes to her/his nearest school.
• Focus on the interaction of child characteristic
  (FSM) and school quality.
• Again control for location

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Figure 6 Probability of pupils attending their
nearest school
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Summary

• Children from poor families half as likely to go
  to good schools.
• Much of that, but not all, comes through
  location. That is, accounting fully for location,
  the gap is a lot smaller.
• Children from poor families tend not to go to a
  good school, even if it is their nearest.

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School Quality and Neighbourhood Formation

• Some results from (as yet incomplete) follow-up
  project on school quality and moving.
• Same data source, using more cohorts, tracking
  families moving house over five years.
• Comparing poor and non-poor families.
• Lot of care modelling default secondary school
  for any location three ways.

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Who moves, impact on default school quality
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Probability of Moving
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Results so far

• Moving probability for the non-poor is influenced
  by quality of default school.
• For the poor this effect completely disappears.
• Moving within local area ten times more sensitive
  to school quality than cross-labour market moves.
  
• Main econometric challenge is initial conditions
  problem in dynamic non-linear panel model with
  unobserved heterogeneity. Follow Wooldridge
  (control for initial and lagged move status,
  stock of moves, initial quality) and results
  remain.

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Conclusions

• On-going project to understand the education
  market in England.
• Role of different assignment rules
• Equity aspects
• Analysing the chance of children from poor
  families going to good schools
• How this comes about
• Efficiency aspects too todays talk is dynamics
  from perspective of children, but static view of
  school.
• There may be trade-offs between assignment rules
  good for equity and those good for efficiency.

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• Why do FSM-eligible children have lower
  probabilities of attending good schools?
• Where they live
• Over-subscribed schools find ways of choosing
  pupils according to their incentives
• middle class parents are better at working the
  system of school admissions
• Costs of exercising choice prohibitive.

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Results and choice

• Promise of a well-functioning school choice
  system is that it reduces role of location
• Countervailing view is that a choice system
  without fully flexible school size will increase
  the role of choice by schools, and the scope for
  the middle class to beat the system.
• Findings cast some light on this debate
• location is associated with most but not all of
  the differential school quality.
• policy which reduced the factor contributing to
  the greater part of the gap at the potential
  expense of widening the smaller part might have
  some attractions

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Annex
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Notation

• There are S schools denoted s, and P children
  denoted i.
• A childs poverty status is measured by her Free
  School Meals (FSM) eligibility, denoted fi.
• The school average FSM eligibility is
• A childs GCSE score is qi, and prior ability is
  ki. The average GCSE score of school s for
  time/cohort t is qs,t.
• This generated from a production function

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Location and distance

• A pupils location is Li.
• Denote pupil is nearest school as n(i).
• The distance between pupil i and school s is dis.
  
• Denote pupil is actual school attended as a(i)

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Quality of school assigned to pupil i

• Quality score for a school s at time t is the
  school mean GCSE score for the cohort finishing
  in t, qs,t
• School to which i is assigned is a(i, t).
• So quality of the school to which pupil i from
  cohort t is assigned as qa(i, t), t-6

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Figure 2 Good to total school places per LEA for
Non-FSM and FSM pupils
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Figure 3 Good to total places ratio for FSM
pupils against good to total places ratio for
Non-FSM pupils
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Table 2 Probit of whether pupil goes to a good
school
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Selection bias

• The bias can be signed
• Assume equal dwelling-specific house prices
  within a unit postcode.
• Expect FSM-eligible households living in the same
  street as ineligible households to be among the
  better off of such households.
• Similarly, FSM-ineligible households living next
  door to FSM-eligible families are likely to be
  relatively poor compared to other FSM-ineligible
  households.
• So income differences between households of
  different FSM status and living in the same
  street are likely to be lower than unconditional
  income differences between households of
  different FSM status.
• If link between FSM status and school assignment
  is a relationship between household income and
  school assignment, our estimated differences are
  likely to be an underestimate of the true
  relationship.
• Similarly, we would expect the FSM-eligible
  households in mixed neighbourhoods to be
  relatively interested in education, and the
  FSM-ineligible households relatively less.

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Figure 4 FSM vs Non-FSM gaps in school quality
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Table 8 Role of feasibility of choice
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Table 10 Probits estimating the probability that
a pupil attends their nearest school
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Figure 6c Fitted values
Based on col 3 of table 10 for a white, female
pupil born in September with average KS2 mean,
English as first language, no SEN, attending a
school in an urban area and with the mean
distance to nearest good school