VOLUME 13, ARTICLE 3, PAGES PUBLISHED 19 AUGUST DOI: /DemRes

Transcription

1 Dmogrhi Rsrh fr xdid onlin journl of r-rviwd rsrh nd ommnry in h oulion sins ublishd by h Mx Plnk Insiu for Dmogrhi Rsrh Konrd-Zus Sr. 1 D Rosok GERMANY DEMOGRAPHIC RESEARCH VOLUME 13 ARTICLE 3 PAGES 63-8 PUBLISHED 19 AUGUST 005 h:// DOI: /DmRs Rsrh Aril Ag-sifi onribuions o hngs in h riod nd ohor lif xny Vldimir Cnuds-Romo Robr Shon 005 Mx-Plnk-Gsllshf.

2 Tbl of Conns 1 Inroduion 64 Priod nd ohor lif xny 64 3 Priod nd ohor lif xny g-domosiion 66 4 Chngs in riod nd ohor lif xny Priod nd ohor modls of morliy Trnds gs nd lgs involving riod nd ohor lif xnis Ag-sifi onribuions o hngs in riod nd ohor lif xny 7 5 Exmining riod nd ohor morliy in Swdn 76 6 Conlusions 79 7 Aknowldgmns 79 Rfrns 80

3 Dmogrhi Rsrh: Volum 13 Aril 3 rsrh ril Ag-sifi onribuions o hngs in h riod nd ohor lif xny Vldimir Cnuds-Romo Robr Shon Absr Priod lif xny hs inrsd mor slowly hn is ohor ounrr. This r xlors h diffrns bwn lif xnis givn im h g nd h im rquird for riod lif xny o rh h urrn lvl of ohor lif xny h lg. Addiionlly o undrsnd h disriy bwn h wo lif xnis w idnify nd omr g-sifi onribuions o hng in lif xny. Using morliy modls nd hisoril d for Swdn w xmin h ff of morliy hngs ovr im. Our rsuls indi h h widning of h g bwn h wo lif xnis is rimrily onsqun of h drmi morliy dlin oldr gs h ourrd during h wnih nury. Ths rsuls imly h h divrgn bwn h wo msurs is likly o bom vn grr in h fuur s rduions in dhs r onnrd oldr gs. h:// 63

4 Cnuds-Romo & Shon: Ag-sifi onribuions o hngs in h riod nd ohor lif xny 1. Inroduion Cohor lif bls follow h morliy of givn birh ohor ovr is lif ours. Som indusrilizd ounris hv uninrrud d snning svrl nuris h llow suh nlyss. Priod lif bls whih rquir d from only on yr n di h imliions of rn rs. Priod lif xnis hv bn usd for omrisons ovr im nd ross oulions s mr of d ri. Howvr Bongrs nd Fny 00 suggsd h h onvnionl riod lif xny is n inur msur for ounris wih low morliy. Rgrding h indusrilizd world subsnil gs nd lgs bwn riod nd ohor lif xnis hv bn shown by Goldsin nd Whr 005 whih simuld inrs in h subj. As dfind by hs uhors g lls how muh riod lif xny givn im is lss hn h lif xny of h ohor born in h yr. Th lg or forwrd lg is h im rquird for riod lif xny o rh h urrn lvl of ohor lif xny. In ninnh nury Swdn h wo lif xnis hd similr vlus bu ovr im h disriy bwn hm grw s inrss in ohor lif xnis ousrid inrss in riod lif xnis. Rognizing h mhnisms h rl riod nd ohor rsivs on h vrg lngh of lif onribus o h nlysis of s urrn nd fuur rnds in morliy. In his r w rsn som siml rlions bwn h gs nd lgs rising from h disin lvls of riod nd ohor lif xnis. W hn us domosiion hniqus o sudy h g-sifi onribuions o hngs in lif xny h driv ggrg rnds. In h nx sion w bring dfiniions rlvn o our sudy of morliy followd wih n xminion of hngs ovr im in lif xnis. Thn g-sifi onribuions o riod nd ohor lif xnis r luld nd omrd using n g-domosiion of lif xny. Morliy modls r usd o simlify h rlions bwn gs nd lgs in lif xnis nd o dmonsr how riod nd ohor lif xnis hng undr diffrn morliy rns. Finlly liions o h morliy xrin of ninnh nd wnih nury Swdn r rovidd.. Priod nd ohor lif xny Th mos ommonly known msurs of morliy r h riod nd ohor lif xny. In h lif bl onx riod lif xny g nd im is luld s h rson-yrs livd bov g dividd by h numbr surviving o g. For xml h riod lif xny birh im n b xrssd s 64 h://

5 Dmogrhi Rsrh: Volum 13 Aril 3 ω l d 0 0 = 1 l 0 whr l is h riod lif bl survivorshi funion o g undr h rs im nd ϖ is h highs g ind. If h rdix of h bl is on i.. l 0 = 1 hn l is h riod lif bl robbiliy of surviving from birh o g. A im his robbiliy is funion of h for of morliy from g 0 o g x. Dnoing h for of morliy g nd im by µ w n wri h lif bl robbiliy of surviving from birh o g s l = x µ x dx. 0 Th subindx in quions 1 nd dnos h hs r riod msurs. In h rs of h x subsri will b usd o idnify ohor msurs. For xml l is h lif bl robbiliy of surviving from birh o g for h ohor born im - i.. l = x µ x + x dx. b 0 nd 0 is h ohor s lif xny. Hr i should b nod h x g nd im h riod nd ohor for of morliy r qul hrfor µ dos no hv subsri. Howvr his is no h s wih h rs of h riod nd ohor msurs. In onmorry low morliy ounris hr is lrg diffrn bwn riod nd ohor lif xnis. For xml Goldsin nd Whr 005 show h in h indusrilizd world h riod lif xny yr is roximly qul o h ohor lif xny for rsons born hlf nury go or Sifi mhods o nlyz hng in lif xny ovr im hv bn dvlod by vrious dmogrhrs. Unid Nions 198 Pollrd Arrig 1984 Prss 1985 nd Andrv 198; Andrv l. 00 fousd on disr diffrns in lif xny bwn wo riods of im. Kyfiz onsidrd oninuous hng nd drivd formul for h im-driviv of lif xny. Mir 1978 Dmrius 1979 Goldmn nd Lord 1986 Vul 1986 Hokkr 1987 Hill 1993 nd Vul nd Cnuds-Romo 003 furhr dvlod his roh. h:// 65

6 Cnuds-Romo & Shon: Ag-sifi onribuions o hngs in h riod nd ohor lif xny Svrl of hs domosiion mhods lso offr h ossibiliy of luling g-sifi onribuions o h hng in lif xny. Thus n inrsing qusion o xmin is how hng in morliy givn g nd im onribus o hng in boh riod nd ohor lif xnis. This lds o sudying hngs in lif xnis whn h disribuion nd lvl of morliy r hnging ovr im. To ursu hs nlyss w follow som of h rodurs dvlod in Vul nd Cnuds-Romo Priod nd ohor lif xny g-domosiion W nd o inrodu wo msurs usd in h dvlomns h follow. L h riod robbiliy dnsiy funion dsribing h disribuion of dhs i.. lifsns in h lif bl oulion g nd im + b dnod s f + = µ + l + nd is ohor ounrr born yrs rlir s f = µ + l. Anohr msur ndd in h drivions o follow is h r of rogrss in rduing dh rs dfind s h driviv of h ln µ + logrihm of h for of morliy ρ + =. In h rs of h x do ovr vribl is usd o dno h ril driviv wih rs o im of & µ + h vribl.g. ρ + =. µ + Vul nd Cnuds-Romo 003 show h n g-sifi onribuion o h hng in lif xny is qul o h rodu of hr omonns. Ths omonns r h r of morliy imrovmn h g h rmining lif xny h g nd h morliy dnsiy funion h g. For h riod lif xny birh im + h g-sifi onribuion of g dnod s & 0 is hn + & 0 + = ρ + + f. 3 + Adding hos onribuions ovr g givs h ol hng in riod lif xny birh & 0 +. Prllling quion 3 i is ossibl o dfin n g-sifi onribuion o h hng in ohor lif xny. Th rio of riod o 66 h://

7 Dmogrhi Rsrh: Volum 13 Aril 3 h:// 67 ohor g-sifi onribuions 0 0 & & + hn llows us o s whih gs morliy hngs ff ohor mor hn riod lif xny. Bus h r of morliy imrovmn + ρ is h sm in h riod nd ohor rsiv h rio simlifis o 0 0 f f f f + + = = + ρ ρ & &. Using h robbiliy dnsiy funions dsribing h disribuion of dhs bing f + = µ l for h ohor nd f + + = + µ l for h riod w obin 0 0 l l & & + + = +. 4 As shown in quion 4 his rio n lso b xrssd in rms of h rio of h riod ovr h ohor rmining lif xny ims h rio of riod o ohor survivl funion o h g. Th xrssion on h righ of quion 4 is surrising rsul bus h omrison dos no onin our xlii msur of hng + ρ. To gin n riion of how h riod nd ohor g-onribuions diffr h following sion rsns oninuous modl whr morliy hngs ovr g nd im onsn rs. 4. Chngs in riod nd ohor lif xny 4.1 Priod nd ohor modls of morliy Modl oulions rovid usful wy o xmin g-sifi onribuions o hngs in riod nd ohor lif xny. Th formulion usd hr is n xnsion of h Gomrz modl of morliy whr hr is n infn morliy omonn nd oninuous r of dlin ovr im. This modl is ombinion of h modl

8 Cnuds-Romo & Shon: Ag-sifi onribuions o hngs in h riod nd ohor lif xny roosd by Silr 1979 nd h oninuous r of dlin modl disussd by Vul 1986 nd Shon l Th for of morliy g nd im is dfind s µ = A x[ B1 C1] + A x[ B C] + A3 x[ C 1 ] 5 whr hr r hr onsn rms whih rfl h vlu of µ 00 = A 1 + A + A3 ; rmrs B 1 nd B h r fixd rs of morliy dlin nd inrs ovr g rsivly whih oun for infn nd snsn morliy; nd rmrs C 1 nd C h r onsn rs of morliy drs ovr im. Prmrs As nd Bs om from h Silr modl whil h Cs r usd in Gomrz modls wih oninuous r of dlin Vul 1986 nd Shon l In h rmining x w rfr o quion 5 s h Silr morliy hng modl. In h modl w bgin wih firly high infn morliy 03 r housnd rsuling from h vlus of A 1 = 0. A = nd A = Th rly dlin ovr g rods of B = 1 1 wih n ovrll inrs wih g r of B = Ths vlus for rmrs A nd B hv bn dd from omrison of h Silr modl wih h diffrn modl lif bls lbord by Col nd Dmny Gg nd Dyk A im 0 riod lif xny is Ths vlus roh hos obsrvd in oulions wih hisoril d. For xml in Swdn in h yr 1800 infn morliy ws 7 r housnd nd lif xny 3.19 yrs. For h of morliy imrovmn w hv hosn C = nd C = Ths vlus orrsond o 1.5% dlin youngr gs nd morliy imrovmn of on rn oldr gs. Th dlin youngr gs in svrl Euron ounris ourrd n vn fsr r Woods l nd 1989 nd h r of on rn is blow h urrn vrg morliy dlin in h Ws. 68 h://

9 Dmogrhi Rsrh: Volum 13 Aril 3 4. Trnds gs nd lgs involving riod nd ohor lif xnis Figur 1 shows h riod nd ohor lif xnis for h Silr morliy hng modl in quion 5 ovr 600 yrs. Figur 1: Priod nd ohor lif xny in Silr morliy hng modl wih rs of dlin ovr im of C1=0.015 nd C= LE Cohor Priod Tim / birh ohor A im zro h riod nd ohor lif xnis r 38.5 nd 4.4 rsivly. Ovr im boh msurs inrs n iniilly rid bu sdy dlining r of inrs. Th iniil fs of inrs is rld o infn morliy imrovmns. Th n b sn from Silr morliy hng modl wih no snsn morliy imrovmn C = 0 no shown hr whih rodus similr rnd in boh lif xnis. As infn morliy flls o low lvls is im dlins owrd zro. In Figur 1 fr 00 yrs h Silr morliy hng modl boms Gomrz modl s hngs in infn morliy r lmos ngligibl. Th inrs in lif xny boms vry los o h slos drmind by rmrs B nd C. For riod lif xny h slo is los o C / B. For h ohor LE i is bou h:// 69

10 Cnuds-Romo & Shon: Ag-sifi onribuions o hngs in h riod nd ohor lif xny C /[ ] B C so ovr im h hng in h ohor msur is grr hn is riod ounrr Shon nd Cnuds-Romo 004. Goldsin nd Whr 005 sudid gs nd lgs bwn h riod nd ohor lif xnis in modl h llowd hngs ovr im o vry ll gs. Hr w fous on simlr modl h imlis nrly linr im rjoris for h riod nd ohor lif xnis. Th g indis h numbr of yrs givn im bwn riod nd ohor lif xny. For xml in our Figur 1 im 100 h g is bou 6 yrs whil im 450 i is bou 10.1 yrs. In onrs h im lg indis h numbr of yrs bwn h im h ohor LE rhs givn lvl nd h riod LE ins h lvl. As shown in Digrm 1 from h simd slos for h riod nd ohor LE nd h g vlus i is ossibl o obin good sims for h lgs. Digrm 1: Rlionshi of h gs nd lgs bwn riod nd ohor lif xny Cohor LE 0 + h g+h Priod LE g lg θ θ 0 = 0 h h Digrm 1 shows h h g bwn ohor LE nd riod LE im is lso qul o h diffrn bwn h riod LE im nd im +h. Th slo of h riod lif xny is qul o h ngn of h ngl rd bwn h LE urv 70 h://

11 Dmogrhi Rsrh: Volum 13 Aril 3 C nd horizonl lin h lvl of h riod LE n θ =. This is lso h B dfiniion of h driviv wih rs o im of his linr riod lif xny C & 0 = n θ =. Two idnil ringls r formd bwn h vril B lins im nd +h h horizonl lins h lvls of h riod nd ohor lif xnis im nd h urv of h riod LE. Th ngn of h ngl n lso b xrssd in rms of h sids of h ringls s h g ovr h lg g n θ =. Thrfor h lg bwn ohor LE im nd riod LE lg im +h is qul o B [ ] = = 1 lg g C & 0 In Figur 1 im 450 h g is 10.1 nd h lg is 101 yrs whih is xly h rsul from lying quion 6 wih our vlus of C = nd B = A similr rodur n b rrid ou o find h g im +h using h slo of h ohor LE nd h rvious lg C g + h = lg. 7 B C For xml h vlu of h ohor lif xny im 450 orrsonds o h riod lif xny im 551 lg of 101 yrs. A im 551 h obsrvd g bwn h ohor nd riod lif xny is 11. = whih lso is h rsul rovidd by quion 7. From quions 6 nd 7 nd for our vlus of C = nd B = 0. 1 h lg im will b 10 ims h g obsrvd h im whil h g im +h will b on-ninh of h lg. Furhrmor i is ossibl o rl gs diffrn oins in im by going bkwrds subsiuing h im h rlions in quions 7 nd 6. For xml h g im n b xrssd in rms of h rvious lg lg h1 s shown in 7 nd his lg n b subsiud by h rvious g s shown in quion 6 h:// 71

12 Cnuds-Romo & Shon: Ag-sifi onribuions o hngs in h riod nd ohor lif xny B C g = g h 1 = g h1 C B C B B C For our rvious xml h g im 551 is 11. whih is 1.11 ims h rvious g im 450 of Ths ss n b rd o rl ny wo gs. For xml if wo gs r srd by n known lgs w hv h following rlion n B g g Ln B C = 8 whr L n is h ddiion of h n lgs h sr h wo gs. This ol lg is found s h ddiion of h individul h lgs L n = h1 + h hn. Similr lulions n b don o rl wo lgs bsd on known gs. To furhr nlyz h disriy bwn h riod nd ohor lif xny h nx sion rsns h xminion of g-sifi onribuion o hngs in hs msurs Ag-sifi onribuions o hngs in riod nd ohor lif xny Figurs b show h Lxis surfs of h g-sifi onribuions o h hng in riod nd ohor lif xny in Silr morliy hng modl. Th riod nd ohor rns in Figur b r vry similr. Iniilly hngs rly gs hv gr im on ovrll lif xny bu h diminishs ovr im. As shown in Figur 1 his is lso h im whn boh lif xnis inrs h fss. On h infn onribuion hs vnishd h g-sifi onribuions inrs ovr g o mximum round h gs whr mos of h dhs r onnrd. For xml yr 400 whn h riod lif xny is 96.5 his mximum ours bwn gs 90 nd 130. Finlly h vry high gs hr is ronound dlin in im. Th k of h disribuion of g-onribuions in lif xny inrss ovr im s h dh disribuion movs o oldr gs. During his sond hs of h modl whr minly snsn morliy is king l inrmns in lif xny r slowr. 7 h://

13 Dmogrhi Rsrh: Volum 13 Aril 3 Figur : Ag-onribuions o h hng in h riod lif xny nd in h ohor lif xny b r housnds Silr morliy hng modl wih wo rs C1=0.015 nd C=0.01 b h:// 73

14 Cnuds-Romo & Shon: Ag-sifi onribuions o hngs in h riod nd ohor lif xny Figur 3 dis h Lxis surf for h rio of i h g-sifi onribuions o h hng in riod lif xny ovr ii h orrsonding g-sifi onribuions o h hng in ohor lif xny. Figur 3: Rio of g-sifi onribuions o h hng in h riod ovr hng in h ohor lif xny Silr morliy hng modl wih rs of dlin ovr im C1=0.015 nd C=0.01 Figur 3 shows h sdy inrs ovr im in h g whih h rio is 1. In h rly yrs h rio is bov 1 mos gs. Th indis h mos gs mk grr g-onribuions o h riod LE s infn morliy lys lrgr rol. A im 600 mos of h rios r blow 1 showing h ohors bnfi mor ovr wid rng of gs. Howvr yr 600 riod LE is nd i is dvnd gs whr mos of h imrovmns in morliy r ourring. This inrs in h g whih h rio is on rllls h inrs of lif xnis in Figur 1 wih n lrd h bginning nd slowr lr. To furhr nlyz h g rn of his rio w r-xmin quion 4. Th rio of g-onribuions n b srd ino wo rms rfling s nd fuur riod nd ohor xrin i.. 74 h://

15 Dmogrhi Rsrh: Volum 13 Aril 3 & & = l + +. l Highr morliy in h s uss fwr ohor survivors o g l hn in h orrsonding riod l + imlying numbrs lwys bov 1 for his msur of h s. Conrry o his is h rio of rmining lif xny whr ohor vlus r highr hn riod indiing rio lwys blow 1 for his msur of h fuur. Figur 3 shows h ny givn im h rio inrss wih g. For youngr gs i is blow on indiing h hngs hos gs hv mor im on ohor hn riod lif xny. Wih morliy dlining ovr im young ohors im will xrin dh rs oldr gs lowr hn hos xrind by oldr rsons im whil diffrns in survivorshi rmin mods. Thrfor in quion 4 h rio of riod o ohor LE domins h rio of riod o ohor survivorshi. Th invrs ross ours oldr gs whr h vlus of h rio r bov on. Th ohors h rh dvnd gs im hv xrind dh rs rlir gs grr hn hos sn in h riod whil h riod o ohor LE rio is mods. Unil now w hv disussd rsuls of hngs in morliy ourring ovr riods. Howvr h rlions found hr lso hold in h s of hngs ourring ovr ohors s vrifid by nlyss of modl oulions no shown. Furhrmor similr rsuls r obind if insd of h snsn morliy rm in quion 5 w inlud logisi modl s hos sudid by Bongrs 005. h:// 75

16 Cnuds-Romo & Shon: Ag-sifi onribuions o hngs in h riod nd ohor lif xny 5. Exmining riod nd ohor morliy in Swdn To ssss g-sifi onribuions o riod nd ohor lif xny in Swdn w us d drivd from h Humn Morliy Dbs 004. To lul h gsifi onribuions o ohor lif xny for ohors h r no xin w hv xrold fuur morliy. Th ws don using oninully dlining morliy modl similr o h in quion 5 wih onsn of dlin of C=0.01. For xml if h ls yr wih vilbl d is 00 hn h g-sifi dh rs for h yr µ 00 r h bs vlus for h modl. For g nd yr > 00 h for of morliy is C 00 µ = µ Figur 4 rsns h riod nd ohor lif xnis in Swdn wih xrold ohor vlus for h yrs 191 o 00 using h dh rs givn by quion 9. Figur 4: Cohor nd riod lif xny wih ohors omld wih oninuous dlining in morliy of C=0.01 Swdn Lif xny Cohor LE Priod LE Esimd CLE Yr 76 h://

17 Dmogrhi Rsrh: Volum 13 Aril 3 During h ls yrs of h wnih nury h fluuions obsrvd in h riod msur hv lrgly disrd. Th simd vlus of h ohor lif xny wih h sld dlin ovr im orrsond o g of round 7 yrs bwn h wo lif xnis for Bfor 1900 howvr h g ws muh smllr nd mor rri. Th g obsrvd bwn riod nd ohor lif xnis bgins h middl of h ninnh nury in Swdn. This is lso h riod of gr imrovmn in infn morliy whih onribus o h inrs in boh lif xnis bu mor mrkd for h ohor msur. From bou 1880 on h rn in Figur 4 rsmbls h in Figur 1. Equions 6-8 show h rlions bwn gs nd lgs in siml morliy modl. Ths quions n b usd for Swdn ssuming h lif xny movs linrly wih onsn slo. This linr ssumion hs bn shown o b rlisi in dvlod ounris ovr h ls hlf of h 0h nury Whi 00. For Swdn in 1911 h ls yr wih full informion on ohors h riod nd ohor lif xnis wr 58.0 nd 65. rsivly. Th g bwn riod nd ohor lif xnis ws hus 7. yrs. Cluling h driviv s h vrg of ll nnulizd hngs in riod lif xny from 1911 o h yr from 191 hrough 1950 w obin n vrg slo of Alying quion 6 lg of 4 yrs is found. Comring h ohor lif xny of 65.3 in 1911 wih 64.9 h riod LE in yr 1935 givs disrny of only 0.4 yrs. Priod lif xny in h indusrilizd world hs followd linr rnd during h sond hlf of h wnih nury so quion 6 should giv good roximion of h lgs imlid by h obsrvd gs Goldsin nd Whr 005. For xml in 1950 ohor lif xny ws 79.5 yrs wih riod lif xny 8.4 yrs lowr. For h yr 1999 riod lif xny is 79.5 rhing h ohor vlu of 49 yrs rlir. Wih h slo of riod lif xny luld s 0.18 quion 6 givs lg of 46.7 yrs whih is.3 yrs blow h ul lg of 49 yrs. Howvr h riod lif xny for 1997 h simd yr ws 79.3 giving n rror in h lg of only 0. yrs. For Swdn bwn 1900 nd 00 Figur 5 shows h Lxis surf for h rio of h g-sifi onribuions o riod rliv o ohor lif xnis s luld from quion 4. h:// 77

18 Cnuds-Romo & Shon: Ag-sifi onribuions o hngs in h riod nd ohor lif xny Figur 5: Rio of h riod ovr h ohor g-onribuion Swdn Cohors omld wih of dlin ovr im C=0.01 Rsuls similr o h Silr morliy hng modl of Figur 3 n b sn in Figur 5 silly fr Th young gs mk grr onribuions o ohor LE whil oldr gs h riod LE gins mor. Thr is lso lr uwrd im rnd in h rossovr vlu of 1. A h bginning of h wnih nury h vlu of on is found g 0 bu h riss o g 60 h nd of h nury. Thr is n inrruion of h rn during h Snish flu ndmi in Th shr ris in morliy during h yr imd h riod muh mor hn ny ohor nd ld o grr ohor gins in LE u ino high gs. 78 h://

19 Dmogrhi Rsrh: Volum 13 Aril 3 6. Conlusions Th disriy bwn riod nd ohor lif xny n b msurd givn im or ovr h numbr of yrs i ks for riod LE o in h ohor lvl. For our oninuously dlining morliy modl hs wo msurs r linkd by siml rlionshi. For h indusrilizd world whr ounris hv xrind linr rnds in lif xny in h ls hlf nury similr hough roxim rlionshi xiss. Whil h ohor-riod g is firly smll nd grows slowly ovr im h lg is sizbl nd grows muh mor ridly. To furhr nlyz h dynmis of h wo lif xnis w xmin h gsifi onribuion of hngs in dh rs o riod nd ohor lif xny. Cohor lif xny gins mor from hngs youngr gs whil h riod msur gins mor oldr gs. Th rio of h onribuions o riod ovr ohor lif xny n b sn s h rodu of wo rms ouning for s nd fuur hngs in morliy. A h g whn s morliy xrin is blnd by fuur hngs h rio is on. As infn morliy flls o low lvls imrovmns r onnrd oldr gs nd h blning g riss. Th rsn rn of morliy hng suggss widning ohor-riod gs nd silly lgs s xrin mor nd mor gs onribus mor o ohor LE hn o riod LE. 7. Aknowldgmns Th firs uhor grfully knowldgs suor from h DWi Wll osdoorl fllowshi wrdd by h Poulion Counil. Th uhors hnk h wo nonymous rfrs for hir hlful ommns. h:// 79

20 Cnuds-Romo & Shon: Ag-sifi onribuions o hngs in h riod nd ohor lif xny Rfrns Andrv Evguni M Mhod Komonn v Anliz Prodoljilnosy Zjizni. [Th Mhod of Comonns in h Anlysis of Lngh of Lif]. Vsnik Sisiki 9:4-47. Andrv Evguni M. Vldimir Shkolnikov nd Alxndr Z. Bgun. 00. Algorihm for Domosiion of Diffrns Bwn Aggrg Dmogrhi Msurs nd is Aliion o Lif Exnis Gini Coffiins Hlh Exnis Priy-Progrssion Rios nd Tol Friliy Rs. Dmogrhi Rsrh 7: Arrig Edurdo E Msuring nd Exlining h Chng in Lif Exnis. Dmogrhy 1: Bongrs John nd Griffih Fny. 00. How Long Do W Liv? Poulion nd Dvlomn Rviw 81:13-9. Bongrs John Long-Rng Trnds in Adul Morliy: Modls nd Projion Mhods. Dmogrhy 41:3-49. Dmrius Lloyd Rlions Bwn Dmogrhi Prmrs. Dmogrhy 16: Gg Timohy nd Bnn Dyk Prmrizing Abridgd Morliy Tbls: Th Silr Thr-Comonn Hzrd Modl. Humn Biology 58: Goldmn Norn nd Grhm Lord A Nw Look Enroy nd h Lifbl. Dmogrhy 3:75-8. Goldsin Joshu R. nd Knnh W. Whr Gs nd Lgs: Rlionshis Bwn Priod nd Cohor Lif Exny. Unublishd Mnusri Prinon Univrsiy nd Univrsiy of Cliforni Brkly. Hill Grry Th Enroy of h Survivl Curv: An Alrniv Msur. Cndin Sudis in Poulion 0: Hokkr Rlh Lifbl Trnsformions nd Inquliy Msurs: Som Noworhy Forml Rlions. Dmogrhy 4: Humn Morliy Dbs. Univrsiy of Cliforni Brkly USA nd Mx Plnk Insiu for Dmogrhi Rsrh Grmny. Avilbl or d downlodd on [5/1/04]. 80 h://

21 Dmogrhi Rsrh: Volum 13 Aril 3 Kyfiz Nhn Wh Diffrn Dos i Mk if Cnr Wr Erdid? An Exminion of h Tubr Prdox. Dmogrhy 14: Alid Mhmil Dmogrhy. nd d. Nw York: Sringr. Mir S A Shor No on h Tubr Prdox. Dmogrhy 15: Pollrd J. H Th Exion of Lif nd is Rlionshi o Morliy. Journl of h Insiu of Auris 109: On h Domosiion of Chngs in Exion of Lif nd Diffrnils in Lif Exny. Dmogrhy 5: Prss Rolnd Conribuion ds érs d Morlié r Ag l Différn ds Vis Moynns. Poulion 4-5: Prson Smul H. Prik Huvlin nd Mihl Guillo Dmogrhy: Msuring nd Modling Poulion Prosss. Oxford: Blkwll Publishrs. Shon Robr nd Vldimir Cnuds-Romo Chnging Morliy nd Avrg Cohor Lif Exny. Pr rsnd h worksho on Tmo Effs on Morliy Novmbr Nw York. Shon Robr Sfn H. Jonsson nd Pul Tufis A Poulion wih Coninully Dlining Morliy. Working Pr Poulion Rsrh Insiu Pnnsylvni S Univrsiy Univrsiy Prk PA. Silr Willim A Coming-Risk Modl for Animl Morliy. Eology 604: Unid Nions Lvls nd Trnds of Morliy Sin 1950 Sudy 74. Nw York: Unid Nions; D. of Inrnionl Eonomi nd Soil Affirs. Vul Jms W How Chng in Ag-Sifi Morliy Affs Lif Exny. Poulion Sudis 40: Vul Jms W. nd Vldimir Cnuds-Romo Domosing Chng in Lif Exny: A Bouqu of Formuls in Honor of Nhn Kyfiz's 90 h Birhdy. Dmogrhy 40: Whi KM. 00. Longviy Advns in High-Inom Counris Poulion nd Dvlomn Rviw 81: Woods RI PA Wrson nd JH Woodwrd Th Cus of Rid Infn Morliy Dlin in Englnd nd Wls Pr II Poulion Sudis 431: h:// 81

22 Cnuds-Romo & Shon: Ag-sifi onribuions o hngs in h riod nd ohor lif xny Woods RI PA Wrson nd JH Woodwrd Th Cus of Rid Infn Morliy Dlin in Englnd nd Wls Pr I. Poulion Sudis 43: h://