School quality, school access and the formation of neighbourhoods Simon Burgess and Tomas Key...

School quality, school access and the formation of neighbourhoods

Simon Burgess and Tomas KeyNovember 2008

PLUG, Nov 2008 www.bris.ac.uk/CMPO 2

Motivations

• Understanding the role of income in gaining access to good schools.

• School access – if proximity matters, how does that come about? Look at differential “strategic” moving rates.

• Formation of communities – how segregated communities are formed, in relation to school quality.


Results

• Estimating the process of moving house in its possible relationship to school quality.

• We show that school quality matters.• Strong differences between poor and non-poor

families:– For non-poor families there is a relationship between

school quality and moving; not so for poor families.

• Different process for within- and across-labour market moves.


Plan

• Literature

• Framework

• Data

• Results

• Conclusions


Literature

• Results relating house price premia to school quality (Black; Machin & Gibbons).

• General equilibrium models of residential location and school selection. – In the US, Epple and Romano; Nechyba; and

Bayer and McMillan.– In the UK, a different setting.


Framework• Simplified story is:

– Families start out w/out children, and choose where to live on that basis

– Acquire children and consider relocating before the key date for school assignment

– If they choose to move, they attempt to move with increasing effort.

– Of course, there are other (random) reasons for moving too.


Framework 2

• Assumptions:– In overall equilibrium in the sense that all the

distributions of income, tastes, labour market states, amenities and school qualities are fixed.

– Within that, individuals move and change within a cohort as it ages.

– So house prices are fixed; people move between locations, but in equilibrium, prices remain constant.

– School quality and neighbourhood quality are exogenous, unaffected by the people learning or living there (future work …).


Model

• i = family (ie kid/parent); L = location

• The family chooses L to maximise U(), L*. • With given supply of housing:

• Bayer and McMillan, …

LLmLqkLpyUU iiii .,,,)(

,,,),(),(),()(* kyLLmLqfnLp


• Choice of L* with kids or not:• Pick L*(0) to start with at k=0 so q is irrelevant.

So necessarily live somewhere nicer in terms of and/or cheaper.

• L* (k=1) cannot be at a lower q than L*(k=0), unless is correlated in strange way.

• The decision whether to move at all or not is balancing the extra cost of higher price p, with the value of higher quality, q.


• Invest in attempting to move, c.

• So ia = f(c*), and c* = f(a, Uia), where between k = 0 and k = 1.

• Approximate:

iiiiia mqpypyU *

0*1

**0

*1 .. pyyIpypy iii


• So, within TTWA m = 0:

• p* substituted out by q, and location.

• Allow for heterogeneity in response to q

• Include q or q?

iiiia qpfU *


Data

• PLASC/NPD• 5 censuses merged together• Non-selective, non-middle schools LEAs• Looked at TTWAs as unit, LEAs.• Spatial controls:

– TTWA dummies, LEA dummies– LLSOA dummies– Smoothed LLSOA effects from contiguous

areas


Timeline

Year 1Year 1 Year 5Year 5 Year 6Year 6 Year 7Year 7

Primary SchoolPrimary School Secondary SchoolSecondary School

S O N D J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A

CensusCensus KS2KS2CensusCensus CensusCensus

Apply for SS: need ‘good’ p’code hereApply for SS: need ‘good’ p’code here

S O N D J F M A M J J A

CensusCensus

Moving house here could be strategic

Moving house here could be strategic

P’code changes here could be realisations of coding errors

P’code changes here could be realisations of coding errors


• We have tried several different controls for spatial context:- Dummies for Travel To Work Area - Dummies for Lower Layer Super Output Area (LLSOA)- Smoothed LLSOA effects from contiguous areas, using the IMD Score for neighbouring LLSOAs, as well as the pupil’s own IMD score.

• Varying these controls has no qualitative impact on the results.


• Two different ways of defining ‘default’ secondary school:– Nearest secondary school– Modal secondary school given primary school

attended• Lots of cleaning work on changing postcodes, to

eliminate redistricting, input errors and mis-coding

• We attempt to identify siblings in our data, and pick out eldest mover only. We do this by grouping pupils who move from/to the same postcode, and count these pupils as a family if there are less than 8 of them.


Cleaning of p/code changes• We use Royal Mail information about postcode redistricting.• We do not count as moves postcode changes that leave the first

and last two characters of the postcode unchanged. • If all in former postcode moved, and all includes more than 8 pupils

(our cut-off for a family), then we do not count this as a move: it is likely to have been a redistricting.

• We do not count moves of less than 100m.• We do not count as a move cases where either of the first or last

two characters of the postcode only change.• We do not count as a move cases where the first or last two

characters only are coded in reverse compared with the postcode for the other academic year.

• We do not count as a move cases where there are changes in the postcode length by one character, e.g. AB1 becoming AB12 or B12 becoming CB12, with all remaining characters unchanged.


Results

• Descriptive analysis of moves• Basic analysis of probability of moves• Analysis by within- and across-TTWA moves• Analysis by pupil age• Dynamic, non-linear panel data models with

unobserved heterogeneity and initial conditions problems.– Panel analysis 1– Panel analysis 2


Summary Statistics


Moves 1


Moves 2

Pre-move GOR (Note eg Post-move GOR, London – 9286m)


Changes in School Quality


Changes in Neighbourhood Poverty

Note – negative means a fall in the IMD, so an improvement


Basic Results

(i) (ii) (iii) (iv) (v) FSM Status 0.045

(83.81)** 0.029

(60.51)** 0.028

(59.02)** 0.019

(18.37)** 0.014

(12.89)** Nearest Secondary School’s Quality -0.012

(10.82)** -0.017

(15.13)**

Modal Secondary School’s Quality -0.017 (14.76)**

-0.024 (19.72)**

Nearest Secondary School’s Quality Interacted with FSM 0.021 (10.02)**

Modal Secondary School’s Quality Interacted with FSM 0.034 (14.34)**

IMD Score of LLSOA 0.004 (19.15)**

0.003 (18.06)**

0.004 (19.22)**

0.004 (18.52)**

Mosaic Postcode Classification Dummies? N Y Y Y Y R2 0.01 0.02 0.02 0.02 0.02 Obs. 7355284 7355284 7355284 7355284 7355284


Within- and across-TTWA moves


By age

Nearest School’s Quality Modal School’s Quality Age FSM Coefficient Quality Coefficient FSM Coefficient Quality Coefficient (i) (ii) (iii) (iv) 5-6 0.034** -0.010** 0.034** -0.017** 6-7 0.032** -0.011** 0.031** -0.018** 7-8 0.029** -0.011** 0.029** -0.017** 8-9 0.028** -0.011** 0.028** -0.017** 9-10 0.024** -0.014** 0.023** -0.015** 10-11 0.023** -0.016** 0.023** -0.019** 11-12 0.025** -0.001 12-13 0.024** -0.003* 13-14 0.023** -0.004** 14-15 0.021** -0.003*


Econometric Issues

• Potential problems:– Omitted variables? Neighbourhood – well

covered; schools – GCSE results, other things likely correlated; Families – repeated obs.

– Reverse causation? Timing, local controls, movers are small fraction of any school.

– Initial conditions problem: current school quality might result from previous choices – a (non-random) group of families may already have moved.


Main threat to identification:

Birds of paradise behaviour

(Some) birds of paradise build a nest first and then seek a mate – not least through having a nice nest to live in.

The equivalent here is families moving to get a good default school before having a child to send to the school.

If pre-kid location chosen independent of school quality, then in principle this is ok as an initial condition.

Separate practical problem that we don’t see everyone from the start.


Econometric Issues

• Assume q (age = 0) is exogenous, we first see people at age = A. Some movers may already have moved by then.

• Who would move early? People with high preference for schooling, low preference for other amenities

• So expect a bigger coefficient if capture more and earlier part of families’ lives. Confirmed: get bigger coefficient on short early window, and on long window.


Panel Analysis

• Use Wooldridge’s approach for dynamic nonlinear models with unobserved effects and initial conditions problems.

• Approach models the distribution of the unobserved heterogeneity conditional on the initial value.

• Essentially a random effects probit model with controls for initial state.


Panel data model 1


Panel data model 2

(i) (ii) (iii) (iv) (v) (vi)

FSM Status 0.020 (38.49)**

-0.010 (10.52)**

-0.010 (10.52)**

-0.011 (10.51)**

-0.011 (9.90)**

-0.011 (9.88)**

Nearest Secondary School’s Quality -0.009 (8.78)**

-0.019 (7.59)**

-0.019 (7.53)**

-0.022 (8.23)**

-0.022 (8.09)**

-0.022 (8.17)**

Move in First Period (y0) 0.050 (53.98)**

0.050 (53.92)**

0.005 (4.01)**

Lag of Move Variable (yt-1) 0.018 (18.10)**

0.018 (18.09)**

0.058 (46.48)**

Initial Quality of Nearest School -0.007 (3.71)**

-0.010 (4.87)**

Stock of Moves = 1 0.053 (36.43)**

0.057 (78.72)**

Stock of Moves = 2 0.114 (31.48)**

0.124 (52.66)**

Stock of Moves = 3 0.178 (18.64)**

0.193 (22.35)**

IMD Score of LLSOA 0.001 (60.05)**

0.002 (57.70)**

0.002 (57.70)**

0.003 (61.41)**

0.003 (61.94)**

0.003 (64.00)**

Values of RHS Variables in Each Time Period Included?

N Y Y Y Y Y

Observations 2595244 1946433 1946433 1946433 1946433 1946433 Number of groups 648811 648811 648811 648811 648811 648811


Conclusions

• Implications for school access.

• Implications for the formation of neighbourhoods. – Invert estimated moving model to analyse the

composition of neighbourhoods.

• Future work: … joint model of school performance and neighbourhood formation

School quality, school access and the formation of neighbourhoods Simon Burgess and Tomas Key...

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