1 Applying Circular Statistics to the Study of Graduate Job Search: The Case of Great Britain. Alessandra Faggian 1, Jonathan Corcoran 2 and Philip McCann 3 1 School of Geography, University of Southampton, UK 2 UQ Social Research Centre University of Queensland, Australia 3 Management School, The University of Waikato, NZ 48th ERSA Congress, 27 th – 31 st 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 search radius 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 radius). So, according to expectations: UniversityAverage distance moved by graduates (meters) Percentage of "migrants" Ranking (2001) The University of Cambridge 149, The University of Oxford 136, The University of Southampton 121, Strathclyde University64, Liverpool Hope University 74, Thames Valley University 52,

BUT, how do we capture the ‘shape’ of the job search area? (circular) We need some non-linear (circular) measures, which allow use to identify: ‘direction’ (circular average) The ‘direction’ of graduate movements on top of the average distance moved using data at University level (circular average) ‘spread’(circular variance) The ‘spread’ of graduate movements (circular variance) 7 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; 340 0, 350 0, 8 0, 10 0, 23 0 Origin zone Individual journey to a job destination (i) Circular measures

Computing the standard linear mean ( / 5) equates to , or around a south-easterly direction – the fallacy of the linear measure! Origin zone Individual journey to a job destination Linear mean (i) Circular measures

11 Circular mean and circular variance and where And the circular variance R-bar (spread) is:

Applying the circular mean to the hypothetical example given above, equates to or just around north. Circular variance = (i.e. low spread) Origin zone 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 to sectors (45 0 slices) (i) Circular measures

Data ~12 million observations on students in the academic years between 1995/96 and 2005/06 HESA) (Source: Students Data by HESA) ~1.5 million observations on graduates jobs (Sources: First Survey Destination, and Destination of Leavers in Higher Education by HESA, ) Focus in this paper: 1999/2000 cohort (~300,000 observations)

15 1. Average direction of graduates by HEI

16 2. ‘Spreads’: examples… UNIDIRECTIONALITY Mean Vector (µ) ° Variance (R) Average direction Mean Vector (µ) ° Variance (R) Mean Vector (µ) ° Variance (R) kmTTWA50km HEI n.114: low variance Different definitions of non-migrant

17 MULTIDIRECTIONALITY 95% confidence interval Average direction 15kmTTWA50km Mean Vector (µ) ° Variance (R) Mean Vector (µ) ° Variance (R) Mean Vector (µ) ° Variance (R) 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 variance 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 variance to be related: POSITIVELY (more randomly distributed movements) NEGATIVELY (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 results Dependent Variable: Circular Variance Model 1: 15 km radiusModel 2: TTWAModel 3: 50 km radius OLSRobustOLSRobustOLSRobust 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 % Black.012* *.014 Ratio Female/Male.068*.073** % Professional Background % Mature-.635**-.646** **-.640** % Good degree-.270*-.307* **-.319* % London-.144* **-.193**-.165**-.132 Herfindhal Index (concentration of subjects) -.385***-.414***-.263**-.261** Coastal Dummy-.133***-.130***-.143***-.131***-.169***-.163*** % Education.362***.358***.326***.328** % Engineering.327*.373** % Maths1.47* Constant.839***.856***.729***.733***.794***.797*** Number of obs R-squared

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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