On the decomposition of life expectancy and limits to life
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1 On th dcomposition of lif xpctancy and limits to lif Ls Mayhw and David Smith Faculty of Actuarial Scinc Cass Businss School Longvity 10 Sptmbr 2014 Santiago Chil
2 Som ky dmographic issus What do trnds in lif xpctancy in diffrnt countris tll us about limits to lif xpctancy? Ar thr altrnativs to th us of mortality as a basis for forcasting lif xpctancy? Why dos lif xpctancy in som countris go down as wll as up? Why is th US falling bhind othr major countris?
3 Comparativ trnds in lif xpctancy in thr countris 52 lif xpctancy at ag Japan E&W Poland yar Mal trnds in lif xpctancy at ag 30 in Japan, England and Wals and Poland using quadratic functions (Sourc HMD)
4 Is thr vidnc for convrgnc in England and Wals data? ag to which givn % surviv ag by which givn prcntag ar dad th Prcntil 90th Prcntil 80th Prcntil 70th Prcntil 60th Prcntil 50th Prcntil 40th Prcntil 30th Prcntil 20th Prcntil 10th Prcntil lif xpctancy at lif xpctancy at ag 30 In th convrgnt cas lif xpctancy procds to a maximum. If w tak th priod 1840 to 1939 thr is clar vidnc for lif xpctancy to b on a convrgnt track although it has a long way to run. In both mal and fmal cass this is 67.5 at ag 30.
5 Is thr vidnc for convrgnc in England and Wals data? ag to which givn % surviv Aftr 1939 thr was a clar chang of trnd lif xpctancy at 30 In th convrgnt cas lif xpctancy procds to a maximum. If w tak th priod 1840 to 1939 thr is clar vidnc for lif xpctancy to b on a convrgnt track although it has a long way to run. In both mal and fmal cass this is 67.5 at ag 30.
6 Forcasting lif xpctancy basd on pr-war convrgnt trnd lif xpctancy at ag 30 (mal) mal actual 1941 to 1939 forcast yar Th trnd prdictd from 1939 suggsts that a maximum would b approach from about 2050 whn progrss would lvl out lif xpctancy at ag 30 (mal) mal actual 1941 to 1939 mal actual 1950 to 2009 forcast yar In fact, th actual trnd is svrly rtardd from about 1950 to 1975 bfor rsuming its stp climb. Howvr, convrgnt bhaviour is rplacd by paralll bhaviour. Th sam occurs in fmals but th rtardation ffct is lss. So hardr to stimat uppr limit.
7 Altrnativ mthod basd on Motivation partial lif xpctancy Crat known limits by dividing lif cours into ag intrvals Idntity trnds within ach basd on known uppr limits Aggrgat ag intrvals to obtain lif xpctancy btwn any dsird ag intrval (.g ) Isolat and focus attntion on ag intrvals whr trnd ar hardr to stablish (.g. >100)
8 Partial lif xpctancy lx 1 lx 2 population lx 3 lx 4 x 1 x 2 3 ag x x x 4 5
9 Partial Lif Expctancy Dfin x as th futur xpctd lif of somon n x n: x m currntly agd x n btwn th ags of x n and x m. Hnc And x 1 x1 : x 3 lx l 2 x l 1 x l 2 x l 3 x l 2 x3 lx x3 1 1 l l l lx y x y x x x 1 x3: x 5 lx l 4 x l 3 x l 4 x l 5 x l 4 x5 lx 2 2 x5 1 1 l l l lx y x y x x 3 5 So : : x x x x x x x
10 Aggrgation of partial lif xpctancy l l : : :110 l30 l30 W can add partial lif xpctancis togthr to obtain ovrall lif xpctancy if w wish. Sinc w know that lif xpctancy cannot xcd tn yars in a tn yar intrval w can assss which ag groups hav rachd thir limit and which hav not. In principl this mans w can pin-point whr th gratst uncrtainty lis and thus focus our attntion on th ag rangs whr futur incrass in lif xpctancy will com from
11 Mal partial lif xpctancy by lading 30(30:40) 40(40:50) 50(50:60) 60(60:70) 70(70:80) 80(80:90) 90(90:100) 100(100: 110) country Swdn E&W E&W E&W Japan Swdn Swdn Swdn Swdn E&W E&W Japan Swdn Swdn Swdn Swdn Swdn Japan Japan Swdn Swdn Swdn Swdn Swdn Japan Japan Swdn Swdn Swdn Swdn Swdn Japan Japan Japan Swdn Swdn Swdn Swdn Japan Japan Japan Japan US US Swdn US Japan Japan Japan US US US US US Japan Japan (LC) 30 Swdn Swdn Swdn Japan Japan Japan Japan Tabl showing th lading country by tn yar ag group in ach dcad from 1950 onwards in E&W, Franc, Japan, Swdn and th US
12 Mal partial lif xpctancy by lagging country (30:40) 40(40:50) 50(50:60) 60(60:70) 70(70:80) 80(80:90) 90(90:100) 100(100: 110) Japan Japan US US US US US Japan US US Franc Franc Franc US Japan US US Franc Franc Franc US Japan US US E&W US US US Japan Japan E&W E&W E&W E&W US Japan Japan Japan E&W E&W E&W Swdn Japan Japan Japan Japan E&W Swdn Swdn Japan Japan Japan Japan Franc Swdn Swdn (LC) 30 Japan Japan US Franc US US US Tabl showing th lagging country by tn yar ag group in ach dcad from 1950 onwards in E&W, Franc, Japan, Swdn and th US
13 30(30:40) 40(40:50) 50(50:60) Fmal partial lif xpctancy by 60(60:70) 70(70:80) 80(80:90) 90(90:100) 100(100: 110) lading country Swdn Swdn Swdn Japan Japan Swdn Swdn Swdn Swdn Swdn Japan Japan Swdn Swdn Swdn Swdn Swdn Japan Japan Japan Japan Swdn Swdn Swdn Japan Japan Japan Japan Swdn Swdn Swdn Japan Japan Japan Japan US US Swdn Franc Japan Japan Japan US US US US US Japan Japan US US US US US Japan Japan (LC) 30 Swdn Swdn Swdn Franc Japan Japan Japan Tabl showing th lading country by tn yar ag group in ach dcad from 1950 onwards in E&W, Franc, Japan, Swdn and th US
14 30(30:40) 40(40:50) 50(50:60) 60(60:70) 70(70:80) 80(80:90) 90(90:100) 100(100: 110) Fmal partial lif xpctancy by lagging country Japan Japan US US US US US Japan Japan US US US US US Japan Japan US US US US US Japan Japan US US US US US Japan Japan Japan E&W E&W US US Japan Japan Japan E&W E&W US US Japan Japan Japan Japan E&W E&W Swdn Japan Japan Japan Japan Swdn Swdn Swdn 30 Japan Japan Japan E&W E&W US US Tabl showing th lagging country by tn yar ag group in ach dcad from 1950 onwards in E&W, Franc, Japan, Swdn and th US
15 Empirical rlationship btwn probability of survival and 10-yar lif xpctancy Probability of survival in th nxt tn yars vrsus lif xpctancy in th nxt tn yars: Ky A from ag 30 to 60 a gratr than 85% of surviving a dcad; B from ag 70 to 80 ~ 70% chanc; C from ag 80 to 90 ~ 35% chanc; D from ag 90 to 100 ~ 5% chanc
16 Partial lif xpctancis for Japans fmals From ag (30:40) 30(40:50) 30(50:60) 30(60:70) 30(70:80) 30(80:90) 30(90:100) ( ) Tabl shows 10-yar partial lif xpctancis for Japans fmals from1950 with forcasts for 2030 and Bottom row shows full lif xpctancy at ag 30
17 Fitting trnd lins to partial lif Th trnd lins for Japans fmals ar basd on th following quations: fi ( t) A yi fi ( t) 1 xpctancis f ( t) i a i b t i Th quation fits most of th sris considrd vry accuratly although this is not th only variant
18 Yars Contribution from ach dcad of lif to Japans fmal lif xpctancy at Calndar Yar
19 How trnd lins compar lif xpctancy at 30 (fmals) B D A C A comparison of trnds in Japans fmal lif xpctancy at ag 30 basd on thr forcasting approachs: th quadratic, straight lin and limiting modls. yar Ky: A quadratic trnd; B basd on limiting modl with uppr limit of D; C basd on a straight lin trnd.
20 Conclusions Lif xpctancy is a crucial masur of human dvlopmnt but whn making forcasts trnd lins ar unboundd and can bcom unralistic Partial lif xpctancis offr a way around this, at last in part Rtrospctiv analysis of trnds in partial lif xpctancy show important stratgic shifts with th US falling to th bottom and Japan rising to th top
On the decomposition of life expectancy and limits to life
On th dcomposition of lif xpctancy and limits to lif Ls Mayhw and David Smith Faculty of Actuarial Scinc Cass Businss School ARC Confrnc 2014 Santa Barbara Som ky dmographic issus What do trnds in lif
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