A Ratio Method for Old Age Mortality Projection Based on Incomplete Data: The Case in Taiwan

Mortality projection for the elderly plays a critical role in designing welfare policies for them. Most prevailing projection methods perform well when there is sufficient mortality information. However, the projection power of these methods is uncertain when the mortality profile is incomplete. In this paper, we propose a ratio method, which includes techniques used in regression and time series analyses that utilize the relationship between the old-age group and their younger counterpart to compensate for the lack of mortality information on the former. A simulation demonstrates how this method reduces projection errors. In addition, we compare this new method to three prevailing projection methods (Lee-Carter, SOA, and Pollard). Based on the mortality data on the elderly in Taiwan between 1950 and 1997 and using the data between 1950 and 1992 as pilot data and that between 1993 and 1997 as test data, we evaluate the prediction power of these methods and find that the ratio method is the best for predicting female mortality rates in terms of the absolute and squared errors. Key Words: projection, old age mortality, incomplete data, simulation, ratio method ! " # $ % & ' (*),+ . /1032 4 5 76 8*9 : ;=<3>,?@ @A B C D,E F G H I=JLK M N 5 O Associate Professor, Department of Statistics, National Chengchi University P Q R S TVUXWVY ZV[ ** Assistant Professor, Department of Economics, National Taiwan University \^]XR S _ ` W^aVb ZV[ *** Master of Department of Statistics, National Chengchi University P Q R S TVUVcXd^eVf g Jack C. Yue , Yu-Whuei Hu & Cheng-Peng Chang 6 8 9 :*; < @A B@ F*G 0 ) < "! # ' (%$'&)(@ *B+* <-, .)/* @ 010 B3234 5 637 8 9 ; :); <37 8 A B=< # 4 N 5 O>=@? > 6 8 A B3C+D E F '3G H 5 O I : &)(@)KJ JL 3M , N3O 7 P Q R &K;( B SUT V W @ 3X Y 0 Z)[ < , \U]_^a`cbedX fg^h`i`ejX * N 5 k 76 8 lU m n o 3v A B =@wLxyx{z}|'~a€‚xh„ƒ†…ˆ‡ ‰ ŠŒ‹Ži ~a’‘'D 2 “ &)A=<•” – — n39 ˜@A3X Y lU™ šU› œ ; < &)(*B,  ž Ÿ ¡ ¢¤£ ¥ ¦ § ̈3© a «U¬g­ ®U ̄ °2± 33 ́¶μ ̧· 1 o1⁄4»"1⁄2>μ13⁄4 ¿ À Á3¶μÄà ŶμÇÆ)È É ® ̄ ° ± 3 ́ μ · 1 o » 1⁄2 μ 3⁄4 ¿ À Á  μ à Šμ Æ È É ® ̄ ° ± 3 ́ μ · 1 o » 1⁄2 μ 3⁄4 ¿ À Á  μ à Šμ Æ È É ® ̄ ° ± 3 ́ μ · 1 o » 1⁄2 μ 3⁄4 ¿ À Á  μ à Šμ Æ È É