Closing he Gap beween Absolue and Relaive Measures of ocalizaion, Concenraion or Specializaion by Frank Bickenbach, Eckhard Bode, Chrisiane Krieger-Boden No. 660 November 200
Kiel Insiue for he World Economy, Düsernbrooker Weg 20, 2405 Kiel, Germany Kiel Working Paper No.660 November 200 Closing he Gap beween Absolue and Relaive Measures of ocalizaion, Concenraion or Specializaion Frank Bickenbach, Eckhard Bode, Chrisiane Krieger-Boden Absrac: This paper solves one of he puzzles in he analysis of regional and indusrial disribuions of economic aciviy, he discrepancy beween absolue and relaive measures. I shows ha he difference beween an absolue and a relaive Theil index of localizaion can be expressed in erms of absolue and relaive concenraion and specializaion measures. This helps undersand and explore why absolue and relaive measures frequenly evolve in opposie direcions. The paper shows for he EU-5 and for UK manufacuring ha his divergence originaes mainly from he indusrial dimension and is largely a saisical arifac inheried from he characerisics of indusry classificaions. Keywords: ocalizaion, Concenraion, Specializaion, Theil index JE classificaion: C43, R2 Frank Bickenbach Kiel Insiue for he World Economy Hindenburgufer 66 D-2405 Kiel, Germany Email: frank.bickenbach@ifw-kiel.de Chrisiane Krieger-Boden Kiel Insiue for he World Economy Hindenburgufer 66 D-2405 Kiel, Germany E-mail: chrisiane.krieger-boden@ifw-kiel.de Eckhard Bode (Corresponding auhor) Kiel Insiue for he World Economy Hindenburgufer 66 D-2405 Kiel, Germany Email: eckhard.bode@ifw-kiel.de The responsibiliy for he conens of he working papers ress wih he auhor, no he Insiue. Since working papers are of a preliminary naure, i may be useful o conac he auhor of a paricular working paper abou resuls or caveas before referring o, or quoing, a paper. Any commens on working papers should be sen direcly o he auhor. Coverphoo: uni_com on phoocase.com
. Inroducion Saisical measures of he regional concenraion of an indusry or of he indusrial specializaion of a region or counry have been used frequenly in he lieraure o explore he evoluion of he spaial or indusrial disribuions of economic aciviy in he European Union (EU) or oher pars of he world. They have been used, among ohers, o explore wheher or no here is a endency of innovaive, dynamic indusries o concenrae in some regions, leaving oher regions wih aging, orpid indusries. More recenly, Bickenbach and Bode (2008) have shown ha measures of concenraion and specializaion explore wo sides of he same coin, and can be nesed in measures of he localizaion of an economy, which capure boh concenraion and specializaion simulaneously. Mos of he saisical measures of localizaion, concenraion and specializaion are borrowed direcly or indirecly from he income inequaliy lieraure. 2 These measures quanify, in one way or anoher, he differences beween he disribuion of economic aciviy (employmen, value added) across regions and/or indusries observed from he daa and a possibly hypoheical reference disribuion, which is he disribuion of economic aciviy considered o represen no localizaion, concenraion or specializaion. They map hese differences ino a scalar measure, he localizaion, concenraion or specializaion measure. There has been confusion in his lieraure arising from he fac ha he wo ypes of references used mos frequenly, absolue and relaive references, have frequenly led o opposie resuls wih respec o he evoluions of localizaion, concenraion or specializaion. For example, Krieger-Boden and Traisaru-Siedschlag (2008) have found ha localizaion in he EU decreased for a relaive reference bu increased for an absolue reference. Even hough measures wih absolue and hose wih relaive references differ fundamenally from each oher in erms of wha is considered o represen no localizaion, concenraion or specializaion, 3 he evaluaion and explanaion of why hey change over ime in opposie direcions is no rivial. Mos sudies ha have found absolue and relaive measures o evolve in opposie direcions have failed o explain heir resul inuiively. This lieraure is reviewed in Combes and Overman (2004), Brakman e al. (2005), and Curini (200). 2 Examples of such inequaliy measures are he Theil index, he Gini coefficien, he coefficien of variaion, and he relaive mean deviaion (Krugman index). In addiion, darboard measures (Ellison and Glaeser 997, Ellison e al. 200), and saisics relaed o on Ripley s K (Duranon and Overman 2005, Marcon and Puech 200) have been used o measure concenraion. 3 For relaive measures, he reference has usually been drawn from conemporaneous higher-level aggregaes. The acual indusry composiions of all regions in a specific year are compared o he composiion of he economy a large (counry or EU) in his same year, or, equivalenly, he regional disribuions of all indusries are compared o he regional disribuion of oal economic aciviy. For absolue measures, he reference has generally been chosen o be he uniform disribuion. In his case, he acual disribuion is compared o a siuaion where all region-indusries are of he same size.
The presen paper solves his dichoomy beween absolue and relaive measures by showing, for he example of he Theil index, ha he difference beween an absolue and a relaive localizaion measure can iself be expressed in erms of absolue and relaive concenraion and specializaion measures. Calculaing he difference beween an absolue and relaive localizaion measure requires employing a specific, unconvenional decomposiion of he wo measures ino hree componens each. The firs componen, which we label a measure of inernal localizaion, is he same for he wo localizaion measures. This similariy consiues he bridge beween he wo localizaion measures. The second componen is an absolue or relaive, respecively, concenraion measure, which is he same as he beween-regions componen obained by convenional decomposiion of he localizaion measures by regions. And he hird componen is an absolue or relaive specializaion measure, which is he same as he beween-indusries componen obained by convenional decomposiion of he localizaion measures by indusries. In conras o he second and hird componens, he firs componen, he measure of inernal localizaion, can usually no be obained by convenional decomposiion. I is equal o he wihin componen of a convenional decomposiion in special cases, hough. The nex secion inroduces he mehodology of he specific decomposiion ha faciliaes calculaing he difference beween absolue and relaive measures, aking he Theil index, one of he measures used frequenly in he lieraure, as an example. Exending his mehodology o oher decomposable measures, including he whole class of generalized enropy (GE) measures is lef o fuure research. 4 Secion 3 provides an illusraion for he evoluion of localizaion across 5 indusries and 95 NUTS2 regions in he EU 5 from 980 2003, and Secion 4 concludes. 2. The link beween absolue and relaive measures Consider an economy such as he EU ha comprises a se I of indusries, indexed by i =,, I, and a se R of regions, indexed by r =,, R. e he variable of ineres be employmen in each region-indusry, ir. The indusries can be aggregaed o a se S of muually exclusive secors, indexed by s =,, S (wih I s being he number of indusries in s), or o he aggregae economy, indexed by a do ( ). ikewise, he regions can be aggregaed o a se C of muually exclusive counries, indexed by c =,, C (wih R c being he number of regions in c), or o he EU economy, indexed by a do. For any poin in ime, indexed by, we can quanify he degree of localizaion of employmen across all indusries and regions by 4 This mehodology may also be used o compare pairs of measures wih oher references and weighs o each oher. For example, Bickenbach e al. (200) use i o evaluae he differences beween measures based on iniial-year and measures based on conemporaneous references and weighs. 2
he Theil index (T) of localizaion, which is generally defined as (see Bickenbach and Bode 2008) () T θ ir ir Πir θ Πir θ = wirθ ln. i I r R ir ir wir θ wirθ i I r R Πirθ i I r R Πirθ Π irθ denoes he reference ha can be hough of as reflecing he value of ir considered o represen no localizaion, and w irθ he weigh of region-indusry ir in he localizaion measure. 5 The index θ characerizes he reference, which we ake o be eiher uniform for he absolue Theil index of localizaion (θ = ), in which case we se Π irθ = Π ir =, or he produc of conemporaneous indusry and region oals for he relaive Theil index of localizaion (θ = ), in which case we se Π irθ = Π ir = i r /. 6 i := Σ r ir denoes oal employmen in indusry i, r := Σ i ir oal employmen in region r. and := Σ i Σ r ir is oal employmen across all indusries and regions. The mehodology we propose requires he weighs, w irθ, o be proporional o he reference. We consequenly se w irθ = w ir = /IR for he absolue measure, or w irθ = w ir = i r /( )² for he relaive measure. Noe ha he w irθ always sum up o one, and herefore (ir) =0 if ir/π irθ is he same for all ir. T denoes he θ T Theil index. Is suffixes (ir) define he unis of analysis in he indusrial and he spaial dimension, is subscrips he ses of hese unis (all indusries and all regions) and is superscrips he reference and weighs ( for absolue measures, for relaive measures). As references and weighs are proporional o each oher, () can be simplified o he absolue Theil index (θ = ) of localizaion (2) ir ir T = ln IR, i I r R or o he relaive Theil index (θ = ) of localizaion ir (3) ir T = ln. i I r R i r Observe ha (2) and (3) differ from each oher only in a single erm, he firs erm in he logs. This erm is equal o he inverse of he weighs w irθ, or, equivalenly, proporional o he 5 All weighs are sandardized such ha hey sum up o uniy across he I indusries and R regions under sudy. 6 Since he raios ir /Π ir are sandardized by he denominaors in (), he scale of Π irθ may differ arbirarily from ha of ir. 3
inverse of he references Π irθ. In he following, we will essenially show ha localizaion measures like (2) and (3) can be decomposed in a specific way ino a erm ha is he same for boh indices, and wo addiional erms ha pick up hese firs erms in he respecive logs. The erm ha is he same for boh indices is a Theil index of inernal localizaion, and he remaining wo erms are equal o he beween-indusries and beween-regions componens obained from convenional decomposiions of (2) and (3) by indusries or regions (see Bickenbach and Bode 2008). We do no derive his specific decomposiion for he localizaion indices for he economy as a whole because he beween-indusries and beween-regions componens of he relaive measure are zero in his special case. Insead, we derive his decomposiion for he more general case of Theil indices of localizaion of a single secor s (wih I s indusries) in a single counry c (wih R c regions), where none of he beween componens is zero. We obain hese counry-secor-specific absolue and relaive localizaion measures from (2) and (3) (see Bickenbach and Bode 2008) as (4) T = i s r c ir ln I sr c ir, and ir (5) ir T = ln. i s r c i r s c ir / is he share of region-indusry ir in counry-secor sc. Observe ha he weighs (and references) in he relaive measure are sill drawn from he economy as a whole. i / s is he share of indusry i in secor s a he aggregae (raher han he counry) level (e.g., EU), r / c he share of region r in oal (raher han secoral) employmen of he counry. We now expand he logs in (4) and (5) by ( ic / ) ( sr / ) and is inverse, which yields, afer some reorganizaions, (6) T = i s r c ir ln ic sr ir I s ic R c sr, and ir (7) ir ic sr T = ln. i s r c ic sr i r s c 4
We hen spli up (6) and (7) ino hree erms, which are (8) T ir ic ir ic = ln + ln I s + i s r c ic sr i s r c = T * + T ( i) + T ( r), sr ln R c sr and (9) T ir ir ic ic = ln ln + + i s r c ic sr i s i r c s = T * + T ( i) + T ( r). sr ln r c sr The firs erm on he righ-hand sides of (8) and (9), which is he same for boh indices, is he * Theil index of inernal localizaion of counry-secor sc, which we denoe by (ir). I compares he variable of ineres, ir, o he secor and counry oals, represened by he produc ( ic / ) ( sr / ), where ic / is he share of indusry i in secor s in he counry under sudy, c, and sr / is he share of region r in counry c in he secor under sudy, s. This Theil index of inernal localizaion differs from he relaive Theil index of localizaion in (5), T (ir), only in is references and weighs. While he relaive localizaion index in (5) compares region-indusries o he aggregaes over all indusries and regions, wih Πir = i r /, and w ir = i r /( )² in he noaion of equaion (), he inernal localizaion index in (8) and (9) compares hem only o he aggregaes over all indusries and * * 2 regions in he counry-secor sc under sudy, wih Π ir = icsr / and w ir = icsr /. The second erms on he righ-hand side of (8) and (9), T ( i) and T (i), are he absolue and he relaive Theil index of specializaion (across indusries) of secor s in counry c, respecively. They are equal o he beween-indusries componens of he decomposiion of he convenional localizaion indices in (4) and (5) by indusries. And he hird erms on he righ-hand side of (8) and (9), T (r) and T (r), are he absolue and he relaive Theil index of concenraion (across regions) of secor s in counry c, respecively. They are equal o he beween-regions componens of he decomposiion of he convenional localizaion indices in (4) and (5) by regions. Subsiuing (9) ino (8) via he common inernal localizaion measure, (0) T = T + [ T ( i) T ( i) ] + [ T ( r) T ( r) ], * T T, finally gives 5
which is he main resul of his paper. (0) allows us o express he difference beween he absolue and he relaive localizaion measures, T T, in erms of concenraion and specializaion measures. More specifically, i allows us o race he difference beween localizaion measures, which cover boh he indusrial and he regional dimension, back o a difference beween specializaion measures, which cover only he indusrial dimension, and a difference beween concenraion measures, which cover only he regional dimension. The insigh ha he difference beween absolue and relaive measures mus have o do wih he difference beween heir references is cerainly no new. Wha is new, however, is he insigh ha, for localizaion measures, his difference can be expressed in erms of concenraion and specializaion measures. New is also ha differenly referenced (absolue and relaive) localizaion measures have a common elemen, he inernal localizaion measure. This helps undersand, and explore in more deail why absolue and relaive measures ofen evolve in opposie direcions (see he following Secion 3). The localizaion measures for he economy as a whole (equaions 2 and 3) can be decomposed in a similar way. The relaive beween-indusries and beween-regions componens, T ( i) and T () r, are zero in his special case, however, so ha he relaive Theil index of * localizaion in (3) is equal o he Theil index of inernal localizaion, i.e., T T. As a counerpar o (0), we hus obain for he economy as a whole () T = T + T ( i) T ( r). + = where T ( i) = Σ ( / ) ln( I / ) and T ( r) = Σ ( / ) ln( R / ). i i i r r Equaion () shows ha, for he special case of measures for he economy as a whole, he difference beween he absolue and he relaive measure is given by he sum of he absolue specializaion across indusries and he absolue concenraion across regions. 3. Empirical illusraion r We illusrae he (main) relaionships beween relaive and absolue measures discussed in he previous secion by an empirical example based on a panel daa se of indusrial and regional employmen figures compiled by Cambridge Economerics. The daa se repors employmen for 5 indusries across 95 European NUTS-2 regions for he period 980-2003. The 5 indusries cover he full range of economic aciviy and are grouped ino hree secors; agriculure, manufacuring and services. 7 The 95 regions cover he 5 member saes 7 The hree secors comprise he following indusries: Secor, agriculure, comprises jus one indusry, agriculure, foresry and fishing. Secor 2, manufacuring, comprises mining and energy supply, food beverages and obacco, exiles and clohing, fuels, chemicals, rubber, and plasic producs, elecronics, ranspor equipmen, oher manufacuring, and consrucion. Secor 3, services, 6
of he European Union as of 2003, excluding Eas-Germany. 8 For our illusraion, we firs consider he localizaion of overall EU-5 employmen (all 5 indusries and 95 regions) and hen focus on a paricular secor and counry pair, namely he manufacuring secor (8 indusries) in he Unied Kingdom (37 regions). Overall EU-5 localizaion The bars in Figure depic, for hree seleced years, he absolue and he relaive localizaion of EU-5 employmen, as measured by he absolue and relaive Theil indices (ir) and T (ir), respecively (see equaions 2 and 3 in Secion 2). The figure shows ha he absolue localizaion increased while he relaive localizaion deceased beween 980 and 2003. This divergence beween absolue and relaive measures has been observed frequenly bu lef largely unexplained in sudies like Krieger-Boden and Traisaru-Siedschlag (2008). To explore he reasons for his divergence, we decompose he wo ypes of localizaion in he way described above ino hree componens, inernal localizaion of he EU-5 (lower pars of he bars), concenraion of aggregae employmen across regions (middle pars), and specializaion of he EU-5 as a whole across indusries (upper pars). Figure : Absolue and relaive localizaion in he EU-5 T Noe: Theil indices of localizaion, decomposed in he way described in Secion 2. comprises wholesale and reail, hoels and resaurans, ranspor and communicaion, financial services, oher marke services, and non-marke services. 8 The counries are Ausria (9 NUTS2 regions), Belgium (), Wesern Germany (30), Denmark (3), Spain (8), Finland (5), France (22), Greece (3), Ireland (2), Ialy (20), uxembourg (), he Neherlands (), Porugal (5), Sweden (8), and he Unied Kingdom (37). 7
The inernal localizaion of he EU-5 (, lower pars) is he same for boh ypes of localizaion, and i is equal o relaive localizaion because all oher componens of his relaive localizaion are zero. This inernal localizaion has decreased from abou 0.06 in 980 o abou 0.073 in 2003 in he EU-5, which indicaes ha he indusrial specializaion paerns of he regions converged (on average) owards he EU-average paern, and hus owards each oher. Equivalenly, i indicaes ha he regional concenraion paerns of he indusries converged owards he regional concenraion of aggregae employmen. * T The remaining wo componens, which are sricly posiive only for he absolue localizaion measure, accoun for he difference beween he absolue and he relaive localizaion. I is obvious from Figure ha he divergence beween he absolue and he relaive localizaion of he EU-5 is exclusively due o he hird componen (upper pars), which represens he absolue specializaion of EU-5 across indusries ( (i) ). This specializaion increased considerably from 0.268 in 980 o 0.455 in 2003, which indicaes ha he disribuion of employmen across indusries diverged from he uniform disribuion. Smaller indusries ha accouned for less han /5 of oal employmen ended o become even smaller while larger indusries ha accouned for more han /5 of oal employmen became even larger. The remaining, second componen, he absolue concenraion of aggregae employmen across regions ( (r), middle pars), is of considerable magniude, which is due o he fac ha he T regions differ in heir employmen sizes, bu did no change much over ime, which indicaes ha he size disribuion of he 95 regions in he EU-5 was remarkably sable. Even hough he empirical observaion ha absolue specializaion and, as a consequence, absolue localizaion increased over ime may be ineresing per se, i is of lile use for idenifying he economic forces ha drive he evoluion of he spaio-indusrial disribuion of economic aciviy. The reason for his is ha he uniform disribuion does no represen an economically reasonable reference (Combes and Overman 2004). Acually, he fac ha srucural change leads o an increase of absolue specializaion is largely a measuremen arifac. I is an immediae consequence of he characerisics of indusry classificaions, which are, ulimaely for hisorical reasons, finer for he shrinking manufacuring indusries han for he growing service indusries. As a consequence, he employmen shares of manufacuring indusries are ypically below he shares given by he uniform disribuion and are furher decreasing over ime while hose of service indusries are ypically above hose given by he uniform disribuion and are furher increasing over ime. The Cambridge Economerics daabase used for his paper disinguishes eigh manufacuring indusries bu only six service indusries, even hough manufacuring accouned for only abou one hird of oal employmen in he EU-5 in 980 (one fourh in 2003) while services accouned for 55% (7%). All of he eigh manufacuring indusries winessed decreasing shares in oal employmen beween 980 and 2003 while five 8 T
of he six service indusries winessed increasing shares beween 980 and 2003. This is no a problem specific o he Cambridge Economerics daabase, bu a problem inheren in mos sandard indusry classificaions. For example, in he European NACE (Rev. 2) indusry classificaion, manufacuring and services accoun for abou 46% of he 65 4-digi indusries each even hough services accouned for more han 70% and manufacuring for less han 25% of oal employmen (EU-5) in 2008. One could of course aggregae over some of he smaller manufacuring indusries o make indusries more equally sized. Bu his would no remove he arbirariness inheren in inferences drawn from absolue localizaion, specializaion, or concenraion measures. One should raher explicily conrol for he size differences beween he indusries or regions by using relaive measures. Even hough hese relaive measures are no enirely immune o he delineaion of indusries or regions, 9 inferences drawn from relaive localizaion, specializaion, or concenraion measures are significanly less affeced by he arbirariness of hese delineaions. However, by adoping conemporaneous references and weighs, relaive measures are unable o reflec aggregae employmen shifs beween indusries or regions, including, for insance, he general EU-wide rend away from agriculure and manufacuring indusries owards services indusries. As an alernaive one may herefore use measures wih references and weighs ha are ime-invarian and sill conrol for indusry and region sizes. Bickenbach e al. (200), for example, use he observed indusrial and regional disribuions of employmen in he iniial year as ime-invarian references and weighs for all years under sudy. This allows hem o explore he exen of aggregae indusrial and regional srucural changes in he EU while accouning for he arbirariness of he indusry and region classificaions. ocalizaion of UK manufacuring As shown in Secion 2, our specific decomposiion of localizaion becomes slighly more complicaed if we focus on a single secor in a single counry. The difference beween absolue and relaive localizaion measures depends on four raher han wo erms in his case (see equaion 0). In addiion o his, he measure of inernal localizaion common o boh measures is a paricular localizaion measure ha feaures counry-secor-specific raher han EU-wide references and weighs. Figure 2, which has a similar shape as Figure, depics he absolue and he relaive localizaion of UK manufacuring for hree seleced years, 980, 99 and 2003. I shows ha absolue and relaive localizaion generally changed in opposie direcions in UK 9 These relaive measures are, among ohers, subjec o he modifiable areal uni problem (Arbia 989, Combes and Overman 2004) in general and aggregaion biases more specifically. Indusry or region aggregaes may be delineaed improperly, and may bury he exising variey wihin hese aggregaes. 9
manufacuring. Absolue localizaion increased from 0.4 in 980 o 0.5 in 2003, whereas relaive localizaion decreased from 0.28 o 0.6. 0 ike in Figure, absolue and relaive localizaion are decomposed ino he hree componens inroduced in Secion 2 (see equaions 8 and 9): he inernal localizaion of UK manufacuring (lower pars of he bars), which is common o he absolue and he relaive measure, he concenraion of UK manufacuring across regions (middle pars), and he specializaion of UK manufacuring across indusries (upper pars). The inernal localizaion in he lower pars of he bars is equivalen o he relaive localizaion wihin UK manufacuring. I evaluaes he disribuion of employmen across regions and manufacuring indusries relaive o oal manufacuring employmen in he UK (raher han o oal employmen in all secors and counries in he EU-5). This inernal localizaion decreased from abou 0.09 in 980 o jus above 0.05 in 2003, which indicaes ha, on average, he UK regions became more similar o each oher wih respec o he indusrial composiions of heir manufacuring secors, or, equivalenly, ha he manufacuring indusries became more similar o each oher wih respec o heir regional disribuions in he UK. Figure 2: Absolue and relaive localizaion of UK manufacuring Noe: Theil indices of localizaion, decomposed in he way described in Secion 2. 0 The relaive localizaion decreased only during he 980s while i increased slighly during he 990s, hough. 0
The concenraion of UK manufacuring as a whole across regions (middle pars) conribues o a noable exen o he difference in levels beween he absolue and he relaive localizaion. I does, however, no conribue o he divergence beween hese wo measures over ime. While he absolue concenraion decreased (from 0.4 in 980 o 0.0 in 2003), he relaive concenraion increased (from 0.026 o 0.037), implying a declining difference beween he wo. In conras, he absolue localizaion increased and he relaive localizaion decreased, implying an increasing difference beween he wo. I is hus he hird componen of he localizaion measures, he specializaion of UK manufacuring across indusries (upper pars), ha was responsible for he divergence beween absolue and relaive localizaion. This componen was no only much larger for he absolue han for he relaive measure already in 980. I also expanded much faser for he absolue measure. Absolue specializaion increased from 0.8 in 980 o 0.36 in 2003 while relaive specializaion increased from 0.0 o 0.024. Absolue specializaion was so much higher han relaive specializaion because i does no ake ino accoun he specifics of he underlying indusry classificaion. The size disribuion across he UK manufacuring indusries differs much sronger from he uniform disribuion han from he size disribuion across manufacuring indusries in he EU-5. And i grew so much faser over ime because several of he smaller indusries, such as mining and exiles, conraced sronger han larger indusries, such as consrucion. The relaive measure accouns for hese general long-erm changes in he size disribuion across indusries. 4. Conclusion By uncovering he reasons for he discrepancy beween absolue and relaive localizaions measures his paper solves one of he puzzles in he exploraory analysis of he localizaion of economic aciviy. Using he Theil index of localizaion as an example, i shows ha he difference beween an absolue and a relaive localizaion measure can be expressed in erms of absolue and relaive concenraion and specializaion measures. This helps undersand, and explore in more deail why absolue and relaive measures frequenly evolve in opposie direcions. For wo examples where absolue localizaion increased while relaive localizaion decreased, he paper shows ha he divergence beween absolue and relaive localizaion originaes mainly from he indusrial dimension, i.e., from a sronger increase of he absolue as compared o he relaive specializaion. This sronger increase of he absolue specializaion is largely due o a saisical arifac inheried from he specifics of radiional indusry classificaions. Mos indusry classificaions are, ulimaely for hisorical reasons, much The concenraion of UK manufacuring as a whole across regions evaluaes he deviaions of he regional disribuion of manufacuring from he uniform disribuion (absolue measure) or from he regional disribuion of oal employmen (relaive measure).
coarser wihin he service secor or for modern indusries, such as rade or finance, han wihin he manufacuring secor or for maure indusries, such as mining or exile indusries. As a consequence of his, smaller indusries diverge from he uniform reference because hey end o become even smaller, and larger indusries also diverge from he uniform reference because hey end o become even larger, a leas in developed counries. Thus, a leas if boh manufacuring and services indusries are included ino he analysis and sandard indusry classificaions are used, we can be almos cerain a priori o find absolue specializaion of employmen o increase for essenially all developed counries. This paper inroduces he mehodology for comparing localizaion measures wih differen references for only one pair of references, absolue and relaive references, and for only one projecion funcion, ha of he Theil index. Exending his mehodology o Theil indices wih oher references, such as he opographic reference (Brülhar and Träger 2005) or he iniialyear reference (Bickenbach e al. 200), is sraighforward. Exending i o oher decomposable projecion funcions, such as hose of he generalized enropy class of measures, may be less rivial, by conras, and is lef o fuure research. 2
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