Incom moblty and conomc nqualty from a rgonal prspctv JUAN PRIETO RODRÍGUEZ Unvrsdad d Ovdo * JUAN GABRIEL RODRÍGUEZ Insttuto d Estudos Fscals and Unvrsdad Ry Juan Carlos And RAFAEL SALAS Unvrsdad Complutns d Madrd Submttd: Fbruary 2009; Accptd A ncssary condton for moblty to rduc th popular dsr for rdstrbuton s a sgnfcant postv corrlaton btwn nqualty and moblty. In Prto t al. (2008), a sgnfcant postv rlatonshp was found at th natonal lvl. Th objctv of ths study s to stablsh mprcally whthr such a rlatonshp s mantand at th rgonal lvl. Th ndcs ar calculatd for th st of EU rgons usng th Europan Communty Houshold Panl survy. Total moblty s dcomposd nto thr trms: growth, dsprson and xchang. By stmatng a hrarchcal lnar modl, t s shown that ths postv rlatonshp s robust. JEL cods: D3, D63, H24, J60 Kywords: socal moblty; nqualty; ncom dstrbuton. I. Introducton Rcnt ltratur stablshs that socal dmand for rdstrbuton has two man dtrmnants: socal moblty and blfs rgardng whthr ncom dffrncs ar du to ffort or luck. Pktty (996) fnds that strongr blfs that ncom dffrncs ar th rsult of luck togthr wth lowr socal moblty ncras th lvl of support for ncom rdstrbuton. Ravallon and Lokshn (2000), Corno and Grunr (2002) and Fong (200) confrm ths rsults: gratr moblty rducs th popular dsr for rdstrbuton; and a frm blf that ndvdual ffort s th prncpal caus of ncom dsprson smlarly producs a gratr avrson to rdstrbutv polcs. In ths contxt, Prto t al. (2008) stmat th rlatonshp btwn socal moblty and ncom nqualty for countrs n th Europan * Juan Prto-Rodrguz, Dpartamnto d Economía, Facultad d Cncas Económcas, avnda dl Crsto s/n, 33006 Ovdo, Span. E-mal: juanprto@unov.s. Juan Gabrl Rodríguz, Insttuto d Estudos Fscals and Dpartamnto d Economía Aplcada, Facultad d CC. Jurídcas y Socals, Pso. d los Artllros s/n, 28032 Madrd, Span E-mal: juangabrl.rodrguz@urjc.s. Rafal Salas, Unvrsdad Complutns d Madrd, Dpto. d Fundamntos dl Análss Económco I,Facultad d Cncas Económcas y Emprsarals, Campus d Somosaguas, 28223 Madrd, Span. E-mal: r.salas@cc.ucm.s. W acknowldg th usful commnts and suggstons provdd by an anonymous rfr and Marana Cont-Grand, dtor of JAE. Ths rsarch has rcvd fnancal support from th Spansh Mnstry of Scnc and Tchnology Projct SEJ2007-64700/ECON and Insttuto d Estudos Fscals, Mnstro d Economía y Hacnda. Th usual dsclamrs apply.
Unon. Thy fnd a sgnfcant postv rlatonshp btwn both varabls. Thrfor, a ncssary condton for socal moblty to dmnsh th socal prdlcton for rdstrbuton s fulflld. In ths papr, w contrast th rlatonshp btwn nqualty and moblty at th rgonal lvl. Th advantags of ths approach ar th followng. Frst, t allows us to contrast th snstvty and robustnss of Prto t al. s rsults. For ths task, w us a mor accurat dfnton of ncom and a hrarchcal lnar modl whch allows us to consdr ndvdual ffcts not only by country but also by rgon. Furthrmor, w tak th ffct of ach moblty componnt as th avrag ffct ovr all possbl dcomposton squncs nstad of just on dcomposton squnc as n Prto t al. (2008). Scond, thr s a larg gan n sampl sz whn th study s basd on rgonal obsrvatons. If w study th rlatonshp for -yar, 3-yar and 5-yar moblty, w mak us of 509, 359 and 209 obsrvatons (or rgons) nstad of 94, 66 and 33 obsrvatons (or countrs), rspctvly. Th ncras n sampl sz guarants a gan n th statstcal sgnfcanc of th rsults. Thrd, rdstrbutv polcs n th Europan Unon (EU) ar dtrmnd not only at th natonal lvl but also at th rgonal lvl. In fact, a mx of natonal and rgonal polcs dtrmns th dgr of rdstrbuton. Thrfor, rsults at th rgonal lvl ar also rqurd to undrstand rdstrbutv polcs n Europ. Th sourc of th data usd n ths papr s th Europan Communty Houshold Panl (hraftr ECHP), whch has th sgnfcant advantag of bng a homognous panl databas; t thus prmts a mor rgorous analyss of ncom dstrbuton n th varous rgons of th Europan Unon. W us th Thl nqualty ndx (Thl, 967) and th ndcs of socal moblty proposd by Flds and Ok (999) for th Europan rgons. Morovr, total moblty s dcomposd nto thr dstnct trms: moblty du to conomc growth, moblty producd by dsprson and xchang moblty rsultng from rrankng. 2 It s thus possbl to dtrmn whch typ of moblty s th most mportant factor whn attmptng to xplan th rlatonshp btwn nqualty and socal moblty. Furthrmor, th moblty ndcs ar calculatd for prods of on, thr and fv yars to contrast thr robustnss. Ths dffrnt tm prods allow for an analyss of th snstvty of th rsults, barng n mnd th varous hypothss that xst rgardng moblty n th short, mdum and long trm. Aftr computng all ndcs, a hrarchcal lnar modl shows that a postv and sgnfcant rlatonshp xsts btwn moblty and ncom nqualty at th Many paprs adopt a rgonal prspctv to analys ncom dstrbuton, howvr thy typcally focus on just on of ths varabls. S Ezcurra t al. (2005) for nqualty n th Europan Unon, Dcky (200) for ncom nqualty n th UK and Salas (999) for moblty n Span. 2 Th frst trm solats th ncras n th man ncom of th dstrbuton producd by conomc growth; th scond trm valuats th varaton n th nqualty of dstrbuton wthout ncom bng rrankd. Fnally, th thrd trm shows th magntud of th rrankngs among ncoms. 2
rgonal lvl. Ths rlatonshp corroborats th robustnss of th lnk btwn gratr socal moblty and rducd dmand for rdstrbuton. In th followng scton, varous nqualty and moblty ndcs mployd n th currnt study ar dscrbd, as s th dcomposton of total moblty that s prformd. In Scton III, w commnt on th databas and notons of ncom nqualty usd n ths artcl. Scton IV prsnts th rsults, and fnally, Scton V provds th man conclusons of th study. II. Moblty and ncom nqualty ndcs Th ltratur has provdd a substantal numbr of ndcs for th masurmnt of socal moblty, ncludng Shorrocks (978a and 978b), Kng (983), Chakravarty t al. (985), Cowll (985), Dardanon (993) and Flds and Ok (996 and 999). Furthrmor, svral dcompostons of moblty hav bn proposd (s, among othrs, Markandaya, 982; Ruz-Castllo, 2004, and Van Krm, 2004). Concrtly, socal moblty may b dcomposd nto thr dffrnt componnts: growth, dsprson and xchang. Th frst of ths solats th ncras n th man ncom of th dstrbuton producd by conomc growth. Th dsprson componnt valuats th dgr to whch ncom convrgnc occurs by studyng th varaton n th nqualty of dstrbuton wthout ncom bng rrankd. Fnally, th xchang componnt shows th magntud of th rrankngs among ncoms. In ths study, socal moblty s dcomposd nto growth, dsprson and xchang trms. 3 Lt X = (x,..., x N ) b th ntal ncom dstrbuton dfnd for N housholds. W shall dfn X as th vctor of quvalnt ncoms, that s, montary ncoms dvdd by th quvalnc scal. Thrfor, for xampl, for houshold th quvalnt ncom s dfnd as x x = () N ) ( whr N s th numbr of houshold mmbrs, and s th quvalnc scal, whr N. Lt us adopt th paramtrc scal proposd n Buhmann t al. (988) and Coultr t al. (992): ( N ) = α N, 0 α. (2) 3 Prto t al. (2002) study th rlatonshp btwn xchang moblty and nqualty for th EU countrs usng a rrankng ndx and a famly of gnralsd Gn ndcs (s Donaldson and Wymark, 980 and 983 and Ytzhak, 983, rspctvly). 3
As s usual n ths ltratur (s for xampl OECD, 2005 and Rodríguz t al., 2005), w lt α = 0. 5. Morovr, w wght ach houshold by th numbr of mmbrs n th houshold, followng Ebrt (997 and 998) and Ebrt and Moys (2000). W shall assum that th vctor of quvalnt ncoms X s rankd n ascndng ordr: 0 x x... x (3) 2 N Consquntly, w can valuat th nqualty ndx proposd n Thl (967) n th ntal prod as: T N N ( X ) = ln (4) = x µ X x µ X whr µ X s th man of quvalnt ncoms n th ntal prod. Th fnal dstrbuton of quvalnt ncom s Y = y, y,..., y ), whr Y s ordrd from lowst to ( 2 hghst. Thrfor, th Thl nqualty ndx n th fnal prod s: N T ( Y ) = N N = y µ Y ln y µ Y (5) whr µ Y s th man of quvalnt ncoms n th fnal prod. Moblty s masurd usng th approach proposd n Flds and Ok (999), namly, th transformaton X Y : N M ( X, Y ) = = ln( y ) ln( x ) (6) N Total moblty s dcomposd nto thr lmnts: moblty du to growth (M G ), moblty rsultng from dsprson (M D ) and xchang moblty (M E ). To ths nd, w follow Van Krm (2004) and dfn G ( X ; X ), D ( X ; X ) and E ( X ; X ) as thr functons that, whn appld to th ncom vctor X wth ncom vctor X usd for calbraton, gnrat growth, dsprson and xchang componnts, rspctvly. In partcular, w consdr th followng transformaton functons (s Van Krm, 2004): µ G ( X ; X ) = X (7) µ µ D ( X ; X ) = R X (8) µ E ( X ; X ) = P X (9) 4
whr µ and µ ar th mans of X and X, rspctvly, R s an N x N dagonal matrx wth lmnts X / x r ( x ) (r(x ) s th rank ordr of x n vctor X), and P s a N x N prmutaton matrx that ranks th ncom vctor X n ncrasng ordr. Th functon G solats th chang n th man ncom of X producd by conomc growth, th functon D valuats th varaton n th nqualty of X wthout ncom bng rrankd, and th functon E sorts th ncom vctor X n th ordr of X. For xampl, f w apply th squnc growth-dsprson-xchang, w obtan th followng componnts: G M ( X, Y ) = M ( X, G ( X ; Y )) (0) M M D E ( X ( X, Y ; Y ) = M ( X, D o G ( X ; Y )) M ( X, G ( X ; Y )) () ) = M ( X, Y ) M ( X, D o G ( X ; Y )) (2) whr M + G D E ( X, Y ) = M + M M. Unfortunatly, ths dcomposton s squntal; that s, t dpnds on th squnc adoptd to ntroduc th componnts. Thrfor, th squnc growth-dsprson-xchang adoptd n Prto t al. (2008) s just on possblty among a total of 3! dcompostons. To dal wth a stuaton n whch all squncs ar qually rlvant, w apply th Shaply valu. 4 Th procdur mrgs from coopratv gam thory, whch consdrs th mpact of lmnatng ach componnt n succsson, and thn avragng ths ffcts ovr all squncs (Rongv 995, Chantrul and Trannoy, 999, Sastr and Trannoy, 2002, Rodríguz 2004). Ths dcomposton has th advantag of bng xact and symmtrc. III. Databas Th databas usd n ths papr s th Europan Communty Houshold Panl (ECHP). It s a homognous panl databas that prmts a rgorous analyss of ncom dstrbuton n th varous rgons of th Europan Unon. Indcs for socal moblty and nqualty ar computd for th 75 rgons of th Europan Unon n th prod 994-200. Not that th data for Swdn n th ECHP ar rpatd cross-sctons. Accordngly, w dsrgard th sampl rgons n Swdn. Rgonal dvsons ar basd on a mx of NUT-0 (Dnmark, th Nthrlands and Luxmburg) 4 If th dcomposton s hrarchcal two varants of th Shaply valu can b appld: th nstd Shaply and th Own valu (Sastr and Trannoy, 2002, Rodrguz, 2004). 5
and NUT- classfcatons. 5 Th only xcpton s Portugal whr rgons ar dfnd usng th NUT-2 classfcaton, as th NUT- dvson consdrs th contnntal trrtory as a whol. Furthrmor, th cty dstrcts of Brln, Brmn and Hamburg n Grmany ar aggrgatd togthr wth th surroundng rgons of Brandnburg, Ndrsachsn and Schlswg-Holstn, rspctvly. As an llustraton of our datast, w dsplay th sampl sz of housholds wthn ach rgon for th fourth wav n th databas (yar 997) n Tabl. [Tabl about hr] Snc th countrs ncludd n ths databas dd not ntr th panl at th sam yar, w hav lss than ght yars of data for ach rgon. Howvr, a balancd panl wthn countrs s usd to guarant th rqurd obsrvaton prsstnc. Morovr, th ncom concpt usd n ths study s th currnt houshold ncom. Othr studs hav consdrd th annual total ncom n th prcdng calndar yar ; howvr, changs n houshold structur durng th prvous calndar yar and btwn th prvous calndar yar and th ntrvw dat oftn lad to masurmnt rrors that spcfcally affct masurs of ncom moblty (Dbls and Vandcastl, 2008). For ths rason, w do not us th sam ncom varabl usd n Prto t al. (2008) at th country lvl. Fnally, a basd stmaton of nqualty and moblty ndcs du to xtrm data s avodd by droppng ngatv and zro ncoms. 6 IV. Estmaton rsults Fgur shows th ndcs for fv-yar moblty and nqualty for all panl yars and all moblty concpts for th EU rgons as a whol. A clar and postv corrlaton can b obsrvd btwn th ndcs of socal moblty and th nqualty of ncom dstrbuton. In fact, th poold ordnary last squars stmaton for total moblty prsnts an R 2 qual to 0.50. [Fgur about hr] 5 Th trm NUT rfrs to th nomnclatur of trrtoral unts for statstcs. It provds a sngl and cohrnt trrtoral brakdown for th complaton of EU rgonal statstcs. A complt lstng of th classfcaton s avalabl at http://c.uropa.u/urostat/ramon/nuts/codlst_n.cfm?lst=nuts. 6 Snc partcularly hgh ncom valus could lad to both nqualty and moblty masurs arbtrarly larg, w hav also stmatd th nqualty and moblty ndcs trmmng th top % of th data. Th rsults wr smlar (thy ar shown n th Appndx); thrfor th stmats n Scton IV can b consdrd robust. 6
A prlmnary analyss shows that th obsrvatons ar apparntly groupd by countrs and/or rgons, whch ndcats that thr xst ndvdual ffcts n th rlatonshp btwn socal moblty and ncom nqualty. Th nflunc of nsttutonal factors sms suffcntly mportant n th short trm to avod strong varatons n th moblty and nqualty ndcs of a partcular rgon. Accordngly, w control for ndvdual ffcts not only at th rgonal lvl but also at th country lvl. To ths nd, w stmat a hrarchcal lnar modl (Camron and Trvd, 2009), as th data hav two nstd groups: countrs and rgons. Th hrarchcal lnar modl can b wrttn as follows: T jt = c + M β + u + v + ε, (3) jt j j t jt whr M s a moblty ndx, T s an nqualty ndx, c s an ntrcpt, and th subscrpts, j and t rprsnt th country, rgon and tm prod undr consdraton, rspctvly. Not that u j dnots th unobsrvabl rgonal spcfc ffct, whl v t dnots th unobsrvabl structural ffct (.., country- and tm-spcfc ffcts). By applyng ths hrarchcal lnar modl w frst spcfy a random ntrcpt for ach country, controllng for th busnss cycl by ncludng tm ffcts,.., w assum that th cycl ffct may vary across countrs. Thn, a random ntrcpt and slop for ach rgon ar ncludd. In ths mannr, not only spcfc rgonal ffcts (that shft th rlaton up and downwards) may xst but also th slop that lads th rlatonshp btwn nqualty and moblty may b dffrnt for ach rgon. Th hrarchcal lnar modl can b stmatd by Fasbl Gnralzd Last Squars, so ts stmats ar mor ffcnt. Howvr, bfor mplmntng ths stmaton, w apply th lklhood tst for th null hypothss that th paramtrs ar constant. Gvn th stmatd modls, th statstc s dstrbutd accordng to a χ 2 wth 4 dgrs of frdom. Th crtcal valus for p = 0.0 and p = 0.05 ar 3.28 and 9.49, rspctvly. Thrfor, w clarly rjct th null hypothss n all cass (s Tabl 2), and w stmat a hrarchcal lnar modl. Morovr, th global sgnfcanc of th rgrssors s contrastd by Wald s tst whch s dstrbutd accordng to a χ 2 wth k dgrs of frdom, whr k s th numbr of paramtrs mnus. Inqualty as masurd by th Thl ndx has a sgnfcant postv rlatonshp wth total moblty for on yar. In partcular, th postv coffcnt for ncom moblty (0.06473) s sgnfcant. Gratr moblty wthn th st of Europan rgons has producd an ncras n nqualty among thm. Furthrmor, ths rlatonshp s not dpndnt upon th tm prod undr consdraton. That s, th corrlaton rmans postv and sgnfcant whn 7
th xplanatory varabl of moblty s analyzd at thr or fv yars; th coffcnts ar 0.0374 and 0.036, rspctvly. In fact, th gratst postv coffcnt for moblty s achvd n th long-run. [Tabl 2 about hr] To xamn th factors xplanng ths postv corrlaton, w also prsnt n Tabl 2 th rsults producd by rgrssng nqualty on th varous componnts of total moblty. Not that aftr controllng for cycl, country and rgon ffcts, th rsults for growth moblty show that thr xsts a ngatv and sgnfcant rlatonshp btwn nqualty and th growth moblty ndx. Th coffcnts for growth moblty at, 3 and 5 yars ar -0.0943, -0.4805 and -0.04484, rspctvly. Thrfor, growth s not th factor that accounts for th postv rlatonshp. Bsds, ths ngatv rlatonshp dclns n th long-run. Inqualty s postvly rlatd wth th dsprson moblty componnt. In fact, th postv and sgnfcant coffcnt of th xplanatory varabl (0.4469, 0.50897 and 0.573 at, 3 and 5 yars, rspctvly) ncrass ovr tm. Fnally, thr s a sgnfcantly postv rlatonshp whn th xplanatory varabl s xchang moblty for all prods. Th stmatd coffcnts ar 0.30672, 0.39467 and 0.4508 at, 3 and 5 yars, rspctvly. W s that th stmatd coffcnts ar lowr than thos for th dsprson trm of moblty. It s thus shown, on th on hand, that th xplanatory powr of th growth factor s not statstcally sgnfcant and, on th othr hand, that th dsprson and xchang componnts xplan th postv assocaton of total moblty wth nqualty. Nvrthlss, th coffcnts of th dsprson moblty componnt show th gratst magntud. As xpctd, ths stmatons ar mor sgnfcant than th rsults n Prto t al. (2008). In partcular, som varabls ar now statstcally sgnfcant, for xampl, th growth moblty varabl n th -yar and 3-yar rgrssons and th xchang moblty varabl n th 5-yar rgrsson. Our analyss has consdrd only on partcular nqualty ndx, th so-calld Thl ndx. Othr nqualty masurs, such as th Gn ndx, th Atknson ndx or Gnral Entropy masurs could b usd to chck th robustnss of our rsults. For ths task, w stmat th corrlaton matrx of th Gn coffcnt, th Atknson 0.5 and ndcs, and th Thl 0 and ndcs. Tabl 3 rports that th corrlaton btwn ths nqualty ndcs s hgh. In fact, th lowst corrlaton s 0.92, and corrsponds to th corrlaton btwn th Gn and Thl ndcs. 8
Consquntly, w can b assurd wth lttl margn of rror that our rsults also hold for altrnatv nqualty masurs. Fnally, w provd on possbl xplanaton of our rsults: bcaus ncrasd socal moblty producs a gratr chang n th rlatv poston of ndvduals, nqualty s sn as bng lss unaccptabl. An ndvdual may arn lss than th avrag ncom prvalng n hs/hr conomy today, but tomorrow ths prson may arn mor. If socal moblty s suffcntly hgh, th concrns producd by nqualty may dcras, thrby rducng th dmand for rdstrbuton. Ths dcrasd socal prssur for rdstrbuton would, n th nd, rsult n a gratr nqualty of fnal ncom. Thrfor, socal moblty and rdstrbuton would b postvly corrlatd; no xchang occurs btwn ths two varabls. Morovr, th prsnc of obsrvatons groupd by countrs suggsts that gvn a st of conomc rstrctons, socal prfrncs dtrmn th combnaton of ncom dsprson and socal moblty n ach country. V. Conclusons To analyz th rlatonshp btwn ncom and socal moblty from a rgonal prspctv, ths study provds mprcal vdnc of th postv rlatonshp btwn ths two varabls. Gratr socal moblty maks gratr nqualty ndx valus mor tolrabl. Th rsult found n Prto t al. (2008) s thus confrmd at th rgonal lvl. Howvr, th sgnfcanc of Prto t al. s rsults s mprovd by our stmatons, whch us a much largr numbr of obsrvatons. Morovr, our analyss ponts out that th common practc of basng th study of moblty xclusvly upon ndcs of rrankng mght bas th rsults undr crtan crcumstancs. Bblography Buhmann, Brgtt, L Ranwatr, Gunthr Schmauss and Tmothy Smdng (988), Equvalnc scals, wll-bng, nqualty and povrty: snstvty stmats across tn countrs usng th Luxmbourg Incom Study Databas, Th Rvw of Incom and Walth 34: 5-42. Camron, A. Coln and Pravn K. Trvd (2009), Mcroconomtrcs usng Stata. Collg Staton, TX: Stata Prss. Chakravarty, Satya R., Bhaskar Dutta and John A. Wymark (985), Ethcal Indcs of Incom Moblty, Socal Choc and Wlfar 2: -2. Chantrul, Francos and Alan Trannoy (999), Inqualty dcomposton valus : th trad-off btwn margnalty and consstncy, THEMA Workng Paprs 99-24, Unvrsté d Crgy-Pontos, Franc. Corno, Gacomo and Hans P. Grunr (2002), Indvdual prfrncs for poltcal rdstrbuton, Journal of Publc Economcs 83: 83-07. Coultr, Fona A., Frank A. Cowll and Stphn P. Jnkns (992), Dffrnc n Nds and Assssmnt of Incom Dstrbutons, Bulltn of Economc Rsarch 44: 77-24. 9
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Fgur. Inqualty (Thl ndx) vs moblty (Flds and Ok ndx) Inqualty (Thl Indx) 0..2.3.4.4.6.8.2.4 Fv-yar Total Moblty Inqualty (Thl Indx) 0..2.3.4 0.2.4.6 Fv-yar Growth Moblty Inqualty (Thl Indx) 0..2.3.4..5.2.25.3.35 Fv-yar Dsprson Moblty Inqualty (Thl Indx) 0..2.3.4.2.3.4.5 Fv-yar Exchang Moblty
Tabl. Sampl sz of housholds by rgons for yar 997 COUNTRY REGION 2 3 4 5 6 7 8 9 0 2 Th Nthrlands 2,86 Blgum 200 823 776 Franc 6 767 260 385 624 479 458 459 Irland,04 327 Italy 367 429 454 22 444 205 273 436 576 389 279 Grc,29 893 635 407 Span 535 54 323 649 744 650 2 Portugal 624 730 340 329 468 446 474 Austra 8 485 655 Fnland 548 790 33 32 76 Grmany 508 537 368 273 34 352 799 366 223 36 237 224 Luxmburg,668 Untd Kngdom 236 362 296 69,052 323 327 384 9 337 2
Tabl 2. Hrarchcal lnar modls by rgon: 994-200 Dpndnt varabl: Thl nqualty ndx -yar moblty 3-yar moblty 5-yar moblty Constant 0.364*** 0.205*** 0.05895*** (0.00942) (0.062) (0.049) M 0.06473*** 0.0374** 0.036*** (0.0756) (0.0579) (0.0794) Random-ffcts Paramtrs Country random ntrcpt Standard dvaton 0.0056 0.0099 0.02252 (0.0056) (0.00233) (0.0049) Rgon Standard dvaton (M) 0.06474 0.05028 0.04445 (0.0845) (0.0840) (0.02394) Standard dvaton (ntrcpt) 0.05479 0.05954 0.03205 (0.00884) (0.0098) (0.02096) Wald's Tst Lklhood tst of paramtr constancy 3.58 443.353 5.532 205.733 33.340 89.672 Constant 0.4507*** 0.5873*** 0.4642*** (0.00579) (0.00625) (0.038) M G -0.0943*** -0.4805*** -0.04484 (0.03402) (0.0246) (0.03675) Random-ffcts Paramtrs Country random ntrcpt Standard dvaton 0.0060 0.0099 0.0474 (0.0046) (0.008) (0.00828) Rgon Standard dvaton (M G ) 0.4208 0.08393 0.320 (0.02792) (0.02775) (0.03789) Standard dvaton (ntrcpt) 0.04628 0.04478 0.03460 (0.00445) (0.0052) (0.00999) Wald's Tst Tst of paramtr constancy 7.685 587.337 36.89 363.438.488 44.28 Constant 0.07777*** 0.0592*** 0.02348 (0.00929) (0.065) (0.0483) M D 0.4469*** 0.50897*** 0.573*** (0.05382) (0.05696) (0.07284) Random-ffcts Paramtrs Country random ntrcpt Standard dvaton 0.00998 0.034 0.0223 (0.005) (0.00256) (0.00384) Rgon Standard dvaton (M D ) 0.9303 0.8765 0.238 (0.05503) (0.05496) (0.08958) Standard dvaton (ntrcpt) 0.0599 0.05450 0.03763 (0.00876) (0.002) (0.0923) Wald's Tst Tst of paramtr constancy 68.722 473.69 79.842 203.987 6.59 08.204 Constant 0.0703*** 0.02503** -0.002 (0.0038) (0.0264) (0.0533) M E 0.30672*** 0.39467*** 0.4508*** (0.03620) (0.03869) (0.04549) Random-ffcts Paramtrs Country random ntrcpt Standard dvaton 0.02 0.0303 0.02049 (0.0060) (0.00320) (0.00355) Rgon Standard dvaton (M E ) 0.0803 0.05679 0.03792 (0.03635) (0.04208) (0.03373) Standard dvaton (ntrcpt) 0.0589 0.042) 0.00359 (0.0093) (0.0388) (0.034) Wald's Tst Tst of paramtr constancy 7.783 483.570 04.078 226.565 98.37 5.955 N 509 359 209 Numbr of groups (m) 75 75 75 ***: Sgnfcant at th % lvl. **: Sgnfcant at th 5% lvl. Standard dvatons n parnthss. M: Total moblty; M G : Growth moblty; M D : Dsprson moblty; M E : Exchang moblty. 3
Tabl 3. Corrlaton matrx of nqualty ndcs Gn Thl 0 Thl Atknson 0.5 Atknson Gn Thl 0 0.9885 Thl 0.9232 0.9463 Atknson 0.5 0.978 0.9907 0.9802 Atknson 0.994 0.9995 0.944 0.9889 4
Appndx Tabl A.. Hrarchcal lnar modls by rgon (top % cnsord) Dpndnt varabl: Thl nqualty ndx -yar moblty 3-yar moblty 5-yar moblty Constant 0.0904*** 0.087*** 0.04454*** (0.00660) (0.0084) (0.00985) M 0.06640*** 0.0585*** 0.0955*** (0.094) (0.0259) (0.0359) Random-ffcts Paramtrs Country random ntrcpt (by wav) Standard dvaton 0.00458 0.00465 0.0789 (0.0007) (0.00098) (0.00307) Rgon Standard dvaton (M) 0.04785 0.05264 0.0344 (0.0378) (0.0328) (0.00983) Standard dvaton (ntrcpt) 0.04355 0.04360 0.0092 (0.00589) (0.00844) (0.00673) Wald's Tst Lklhood tst of paramtr constancy 30.896 703.02 2.578 342.48 49.389 50.72 Constant 0.745*** 0.83*** 0.0908*** (0.00450) (0.00480) (0.00840) M G -0.03497-0.02587 0.0354 (0.0238) (0.0203) (0.02906) Random-ffcts Paramtrs Country random ntrcpt (by wav) Standard dvaton 0.00494 0.00545 0.02586 (0.00073) (0.00098) (0.0057) Rgon Standard dvaton (M G ) 0.08720 0.09263 0.3053 (0.02429) (0.0949) (0.02755) Standard dvaton (ntrcpt) 0.03746 0.0354 0.03594 (0.00332) (0.00384) (0.00702) Wald's Tst Tst of paramtr constancy 2.276 868.037.53 480.73.463 94.782 Constant 0.06809*** 0.04874*** 0.0948* (0.00655) (0.00735) (0.0075) M D 0.36720*** 0.3958*** 0.5052*** (0.0386) (0.04476) (0.05702) Random-ffcts Paramtrs Country random ntrcpt (by wav) Standard dvaton 0.00408 0.0030 0.0822 (0.00067) (0.00096) (0.00296) Rgon Standard dvaton (M D ) 0.4275 0.3569 0.9738 V (0.04639) (0.07208) (0.06459) Standard dvaton (ntrcpt) 0.04044 0.02205 0.02899 (0.00579) (0.0442) (0.0396) Wald's Tst Tst of paramtr constancy 90.44 763.237 76.526 368.372 77.368 63.468 Constant 0.06883*** 0.03749*** 0.003 (0.00693) (0.0080) (0.0095) M E 0.243*** 0.2733*** 0.35789*** (0.0240) (0.02727) (0.03474) Random-ffcts Paramtrs Country random ntrcpt (by wav) Standard dvaton 0.00446 0.00378 0.0735 (0.00069) (0.00092) (0.0027) Rgon Standard dvaton (M E ) 0.08650 0.02354 0.09673 (0.02950) (0.02692) (0.0240) Standard dvaton (ntrcpt) 0.04225 0.087 0.0205 (0.00597) (0.0076) (0.00740) Wald's Tst Tst of paramtr constancy 79.07 760.374 00.328 36.402 06.46 72.30 N 509 359 209 Numbr of groups (m) 75 75 75 ***: Sgnfcant at th % lvl. *: Sgnfcant at th 0% lvl. Standard dvatons n parnthss. M: Total moblty; M G : Growth moblty; M D : Dsprson moblty; M E : Exchang moblty. 5