(Segregation) Index Wars: Progress or Regression? Martin Watts Centre of Full Employment and Equity University of Newcastle NSW Australia Paper prepared for the New Directions in Welfare Congress, OECD, Paris, 6 -8 July

Centre of Full Employment and Equity Introduction  Segregation: groups of individuals differ in access to occupations, social networks, schools etc (Reardon & Firebaugh, 2002).  Reliance directly or indirectly on paid work for economic welfare so school & occupational segregation particularly important.  Academic disciplines (demography, economics & sociology) active. 50 year index war since seminal article (D&D, 1955).  War punctuated by comprehensive reviews (James & Taeuber, 1985; White, 1985; Watts, 1998; Reardon & Firebaugh, 2002a) but, despite warnings, skirmishes have continued post  Research should rigorously document pattern of segregation & changes over time/across space, via index. Then develop & test hypotheses about trends or x-country differences in segregation.

Centre of Full Employment and Equity Introduction  Different methodologies: axiomatic – but math tractability problem (Hutchens, 2001, 2004; Chakravarty & Silber, 2006; Alonso-Villar & Del Río, 2010; Frankel & Volij, 2011) ad hoc: indexes satisfying desirable properties used for particular research study (Flückiger & Silber, 1999; Reardon & Firebaugh, 2002a,b; Watts 2003; Mora & Ruiz-Castillo, 2003, 2005, 2008, 2009a,b,c, Charles & Grusky, 2004; Deutsch & Silber, 2005).  Also disagreements persist over desirability of particular properties

Centre of Full Employment and Equity Outline of Paper 1)Reflect on recent debates about segregation properties: index decomposability; construction of local indexes; & Margin Independence. 2) Calculate Karmel/MacLachlan & Mutual Information Indexes of gender segregation (43 occupations) in Australia

Centre of Full Employment and Equity Segregation Index Criteria Notes: IS denotes multi-group KM index; IDG is multi-group analog of Index of Dissimilarity; SQR is Hutchens’ two group square root index; H is Theil Entropy Index; G is Gini Index; A is Charles & Grusky (two group) Index; & M is Mutual Information Index. ‘2’ indicates that property only hold in 2 group case. Bolded properties are forms of Internal Decomposability. Source: Reardon & Firebaugh (2002a:56), Frankel & Volij (2011:15) & author’s own analysis.

Centre of Full Employment and Equity Segregation Indexes: Linear  Multi-group KM Index (IS) is related to multi-group ID (IDG): (1) p gn = T gn /T = share of all individuals (T) in group g & organisation n; p g. = T g. /T = share of T in group g; p.n = T.n /T is share of T in occupation n & (Frankel & Volij, 2011:11).  IS = weighted local indexes based on both organisations & groups (Alonso-Villar & Del Río, 2010) due to Transpose Invariance; but normalising factor I removed, so no Scale Interpretability.

Centre of Full Employment and Equity Segregation Indexes: Non-Linear  Mutual Information Index (M): (3) is conditional probability. Conversely  M = reduction in uncertainty about individual’s group after discovering organisation to which individual belongs (0 if no segregation), & via transpose invariance, reduction in uncertainty about individual’s organisation …..

Centre of Full Employment and Equity Segregation Indexes: Non-Linear  Frankel & Volij (2011): M satisfies: Scale Invariance, Symmetry, Independence, School & Group Division Property; Strong, Weak Transfers; Local, Strong Organisation & Group Decomposability.  M is Transpose Invariant (Mora & Ruiz-Castillo, 2009a,b). Normalisation, via E or E*, for Scale Interpretability, rejected – similar to IS.  Properties shown in red also characterise IS.  Neither M nor IS are CI or OI – so not margin free.

Centre of Full Employment and Equity Contemporary Debates - Decomposability  ‘Horses for courses’ approach. So internal decomposability may be less useful than construction of local indexes & use of Deming & Stephen (1940) algorithm to neutralise Margin Dependence.  If meaningful clustering of groups or organisations, then index should satisfy Strong Decomposability (SD), such as M Index.  School segregation: relevant benchmark of socio-economic composition is local catchment area (LCA), so between & within decomposition based on LCAs appropriate but not Margin Free.  Using M, Frankel & Volij (2011:18) geographically decompose total US school US segregation by race into 4 components.

Centre of Full Employment and Equity Contemporary Debates - Decomposability  BUT Inter-city comparisons of segregation meaningless due to margin dependence & unequal number of schools.  Time series comparisons more robust but still vulnerable to MD. From policy perspective, time series comparisons more useful.  Index exhibiting Internal Decomposability is misleading if investigating rates of integration of ‘homogeneous’ occupational clusters, e.g. Managerial, Professional, Sales & Service, Skilled Blue Collar & Unskilled (cf. Reardon & Firebaugh, 2002b:90).  Skilled Blue Collar (SBC) occupations low female employment shares (Watts, 2003). Within cluster segregation very low. 

Centre of Full Employment and Equity Contemporary Debates - Decomposability  OTOH, between cluster component picks up sum of disparities between overall & cluster based female employment shares.  Incorrect benchmark, so internal decomposition yields no insight about segregation trends across clusters to inform policy.  IS & M: correct local decomposition, but Margin Dependent.  Two approaches to achieving Margin Free measurement. i) Employ MF index, such as A. ii) External decomposition of index with desirable properties.

Centre of Full Employment and Equity Contemporary Debates – Margin Dependence  A is Margin Free (Charles & Grusky, 2004) but no Organisational Equivalance – all organisations same weight.  Jerby et al (2005a): index class exhibits singularity; undefined for zero (fe)male population in organisation j, non –linearity.  Simple ad hoc solutions fail because of both sensitivity & absence of Organisational Equivalence (Jerby et al, 2005a).  Debate whether zeros are sample or structural in traditional societies, where cultural norms restrict organisation (occupation) access to some group(s).

Centre of Full Employment and Equity Contemporary Debates – Margin Dependence Jerby et al (2006) segregation defined by margins, so margin attributes endogenous to segregation; cf. purging MD. Jerby et al (2006) MF index is valid for ‘students of segregation interested in capturing segregation through prism of occupational categories’. Occupations as ontological entity. Segregation measurement should capture individuals’ distribution across occupations, but TI indexes allow both interpretations.  Jerby et al: segregation as outcome of ‘selection process with a double barrier’. 1st barrier: entry into LM & 2 nd barrier to occupations.

Centre of Full Employment and Equity Contemporary Debates – Margin Dependence  Define ISR (index for segregation regime):  2nd term = LM entrance barrier, 0 if F=M, equal representation.  Barriers to individual occupations, revealed (& measured) as variation of occupational measure around aggregate measure.  Jerby et al (2005b): depict 2 dimensions, ISR & on x axis.  Inclusion/exclusion mechanisms (cultural forces, G policy, eg tax policy), impact on women’s LFP & occupational attainment.  BUT not clear conceptual & empirical separation of women’s representation in employment & occupational attainment.

Centre of Full Employment and Equity Contemporary Debates – Margin Dependence  2nd approach to obtain MF measure: external decomposition of index to reveal changes (differences) in segregation, after impacts resulting from changes in group shares & organisational distribution (margin dependence) have been excised.  Iterative procedure, (Deming & Stephan, 1940), transforms initial (period 1) G*N segregation array into adjusted segregation array, with same total populations by organisation & same overall group shares of total population as later (period 2) array.  Procedure eliminates MF problem because measure of change based on comparison of ‘like with like’, namely adjusted array & period 2 array. Margin Dependence finessed.  If index exhibits Organisational Equivalence then organisational weights used, overcoming potential sampled zeros problem.

Centre of Full Employment and Equity Contemporary Debates – Margin Dependence  If time series data, then procedure can re-specify all time series observations according to a common (period 2) base.  Segregation arrays corresponding to W time series observations enables construction of W*W matrix, where k,m = 1,2,…W & diagonal elements are simple gross index values;  Each column represents consistent (MF) time series with common base period, but which to choose? Suggest column with max. average correlation with other columns so representative.

Centre of Full Employment and Equity Australian Gender Segregation:  Both KM & M exhibit many other desirable properties, as noted so now illustrate use of DS algorithm for Aus quarterly employment data by occupation & 43 occupations for  Figure 1: Australian Gender Segregation, – M & KM indexes  High correlation between 2 indexes (0.975).

Centre of Full Employment and Equity Australian Gender Segregation: Figure 2: Segregation by Occupational Group, : M index – Margin Free Notes: M (shown in White) overall M index; MA denotes Managerial; PR denotes Professional/Paraprofessional; SS is Clerical, Sales &Service; SK denotes Blue Collar Skilled and US denotes Unskilled.  Chosen base period Feb high average correlation 99.73% (overall KM index) & 97.5% (M) with corresponding time series associated with other base periods.

Centre of Full Employment and Equity Australian Gender Segregation: Figure 3: Segregation by Occupational Group, : KM index – Margin Free Notes: M (shown in White) overall M index; MA denotes Managerial; PR denotes Professional/Paraprofessional; SS is Clerical, Sales &Service; SK denotes Blue Collar Skilled and US denotes Unskilled.  Only Managerial & Professional occupations experienced a rising share of employment over sample period, although all occupations experienced employment growth.

Centre of Full Employment and Equity Australian Gender Segregation:  Evidently disparities between index outcomes (unsurprising) but broad trends similar.

Centre of Full Employment and Equity Concluding Comments  Properties of multi-group segregation measures reviewed.  More use of axiomatic approaches, but limited by mathematical tractability & constraints of internal decomposability (IntD).  IntD enables construction of between & within cluster measures, but IntD not always suitable & sensitive to Margin Dependence. Local Decomposability (LD) addresses first issue.  IS & M: good properties, including LD but Margin Dependent.  Margin Free A, Index: no Organisational Equivalence & affected by sampled zeros, sensitivity & limited to 2 groups.  DS decomposition enables MF measures of change in segregation (typically time series). Illustrated with Australian data.

End of Talk