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Applying Circular Statistics to Applying Circular Statistics to the Study of Graduate Job the Study of Graduate Job Search: The Case of Great Search: The Case of Great Britain.Britain.

Alessandra FaggianAlessandra Faggian11, Jonathan Corcoran, Jonathan Corcoran22 and Philip McCann and Philip McCann33

11School of Geography, University of Southampton, UKSchool of Geography, University of Southampton, UK22UQ Social Research Centre University of Queensland, AustraliaUQ Social Research Centre University of Queensland, Australia

33Management School, The University of Waikato, NZManagement School, The University of Waikato, NZ

48th ERSA Congress48th ERSA Congress, 27, 27thth – 31 – 31stst August 2008, Liverpool, UK August 2008, Liverpool, UK

Introduction

Role of space on the graduate labour market How does human capital investment affect

graduate migration patterns? What are the geographical characteristics of

the UK graduate job search areas? How do University, personal and regional

characteristics affect these movements?

Theoretical framework Job search (e.g. Lippman and McCall 1976a,b and 1979) and

human capital (Sjaastad, 1962) theories both predict that the radius of the job search area increases with an increase in human capital. So, assuming jobs are randomly distributed over space:

Lower HK

Higher HK

Radius Expansion (all directions)

Theoretical framework

BUT, are jobs are randomly distributed over space? Aren’t higher quality/higher wage jobs more likely to be concentrated in urban areas rather than randomly scattered in space?

If this is the case, shouldn’t we observe a different pattern for people with different human capital levels?

In the case of University graduates, shouldn’t we observe different patterns between ‘high achievers’ (1 or 2.1) and ‘low achievers’ (2.2 or below)

Theoretical framework

Lower HK

Higher HK

• We cannot talk about ‘radius’ of search.

• The assumption of jobs being randomly distributed over space is a better approximation for less qualified job seekers

Theoretical framework Traditionally, the summary measure used to describe

graduate movements is the ‘average distance’ (linear measure) moved after graduation (which is a proxy for the search radiussearch radius). So, according to expectations:University Average distance

moved by graduates (meters)

Percentage of "migrants"

Ranking(2001)

The University of Cambridge

149,841 96.9 1

The University of Oxford

136,978 96.5 2

The University of Southampton

121,832 92.8 11

Strathclyde University 64,522 59.9 51

Liverpool Hope University

74,216 56.7 88

Thames Valley University

52,027 53.7 123

BUT, how do we capture the ‘shape’ of the job search area?

We need some non-linear (circular) (circular) measures, which allow use to identify: The ‘direction’‘direction’ of graduate movements on top

of the average distance moved using data at University level (circular average) (circular average)

The ‘spread’‘spread’ of graduate movements (circular (circular variance)variance)

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Theoretical framework

A “curious byway of statistics…somewhere between the analysis of linear and the analysis of spherical data” (Fisher 1993, p.1)

Deal with directional data (either a compass direction or some unit of time)

Early roots date back to the mid-eighteenth century (Bernoulli, 1734)

Why circular measures???

Methodology: Circular measures

Consider a hypothetical origin zone with 5 moves each with a single student centred around a northerly direction; 3400, 3500, 80, 100, 230

´Origin zone

34003500 80 100

230

Individual journey to a job destination

(i) Circular measures

Computing the standard linear mean (340 + 350 + 8 + 10 + 23 / 5) equates to 146.20, or around a south-easterly direction – the fallacy of the linear measure!

´Origin zone

34003500 80 100

230

Individual journey to a job destination

Linear mean

(i) Circular measures

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Circular mean and circular varianceCircular mean and circular variance

n

iiA

1

)sin(

n

iiB

1

)cos(

180/

and

where

2

1221

1 BAn

R

1

1

arctan( / ) 0

arctan( / ) ) 0

A B if B

A B if B

And the circular variance R-bar (spread) is:

Applying the circular mean to the hypothetical example given above, equates to 2.230 or just around north. Circular variance = 0.035 (i.e. low spread)

´Origin zone

34003500 80 100

230

Individual journey to a job destination

Linear mean

Circular mean

(i) Circular measures

Compute for each origin zone and classify into sectors for thematic mapping Number of sectors

determined by data 4 sectors 8 sectors etc

337.50 to 22.50

8 sectors (450 slices)

(i) Circular measures

Data

~12 million observations on students in the academic years between 1995/96 and 2005/06 (Source: Students Data by HESA) HESA)

~1.5 million observations on graduates jobs (Sources: First Survey Destination, 95-00 and Destination of Leavers in Higher Education by HESA, 2002-05)

Focus in this paper: 1999/2000 cohort (~300,000 observations)

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1. Average direction of graduates by HEI

250 250

250

250

200 200

200

200

150 150

150

150

100 100

100

100

50 50

50

50

0

90

180

270

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2. ‘Spreads’: examples…UNIDIRECTIONALITY

250 250

250

250

200 200

200

200

150 150

150

150

100 100

100

100

50 50

50

50

0

90

180

270 250 250

250

250

200 200

200

200

150 150

150

150

100 100

100

100

50 50

50

50

0

90

180

270

Mean Vector (µ) 214.975°Variance (R) 0.357

Average direction

Mean Vector (µ) 214.975°Variance (R) 0.357

Mean Vector (µ) 215.307°Variance (R) 0.347

15km TTWA 50km

HEI n.114:low variance

Different definitions Different definitions of non-migrantof non-migrant

50 50

50

50

40 40

40

40

30 30

30

30

20 20

20

20

10 10

10

10

0

90

180

270

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MULTIDIRECTIONALITY

95% confidence

intervalAverage direction

15km TTWA 50km

50 50

50

50

40 40

40

40

30 30

30

30

20 20

20

20

10 10

10

10

0

90

180

270 40 40

40

40

30 30

30

30

20 20

20

20

10 10

10

10

0

90

180

270

Mean Vector (µ) 54.218°Variance (R) 0.743

Mean Vector (µ) 67.111°Variance (R) 0.744

Mean Vector (µ) 35.652°Variance (R) 0.543

HEI n.90: high variance

Different definitions of ‘non-migrant’Results for the 15km radius area and TTWAs are incredibly similar, with the only exception of HEIs located along the border between two TTWAs (in which case the 15Km might even be preferable)

3. Determinants of spread of movements

Based on previous work on graduate migration in GB (Faggian and McCann 2006, Faggian et. al 2006, 2007a and b)

and on human capital migration theory and gravity type models, we expect the circular variancevariance to be related:

POSITIVELY POSITIVELY (more randomly (more randomly distributed movements)distributed movements)

NEGATIVELY NEGATIVELY (more focused movements)(more focused movements)

• Selectivity of HEI attended• Degree classification obtained• Age of graduates• Degree of specialisation of HEI attended• Spatial constraints of HEI location (coast)• London attraction• Previous migratory behaviour (distance moved from home to HEI)

• Ethnic minority status• Female students

??????

• Subjects• Socio-economic background

Regression resultsDependent Variable: Circular Variance

Model 1: 15 km radius Model 2: TTWA Model 3: 50 km radiusOLS Robust OLS Robust OLS Robust

Dist (Uni to Job) -1.25e-06*** -1.39e-06*** -105e-06** -1.22e-06*** -1.37e-06*** -1.45e-06***

Russell group -.149*** -.141*** -.121** -.118** -.130** -.133**% Asian -.005 -.003 -.000 .000 -.005 -.007% Black .012* .008 .003 .001 .014* .014Ratio Female/Male

.068* .073** .013 .014 .041 .043

% Professional Background

-.452 -.406 -.469 -.490 .060 .063

% Mature -.635** -.646** -.014 -.033 -.600** -.640**% Good degree -.270* -.307* -.073 -.067 -.322** -.319*% London -.144* -.105 -.205** -.193** -.165** -.132Herfindhal Index (concentration of subjects)

-.385*** -.414*** -.263** -.261** -.086 -.090

Coastal Dummy -.133*** -.130*** -.143*** -.131*** -.169*** -.163***% Education .362*** .358*** .326*** .328** .107 .101% Engineering .327* .373** .184 .214 .101 .147% Maths 1.47* 1.37 .996 1.07 .728 .823Constant .839*** .856*** .729*** .733*** .794*** .797***

Number of obs. 105 105 105 105 102 102R-squared 0.588 0.499 0.530 0.490 0.490 0.553

Conclusions More selective Universities (Russell or 94 group) tend to

produce more ‘focused’ out-migration movement (low variance) Also the case for more specialised HEIs (as measure by the

Herfindhal index) Mature graduates and those with a higher HK (2:1 or first) tend

to move further, BUT are more ‘focused’ Female and black students tend to search in different directions

(more locally) Attraction of London (higher of % jobs there makes movements

more focused) Subject dummies significant (Education, Maths and

Engineering) tend to be associated with greater spread of movements

Correction for Coastal proximity

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End