40 206 Vol. 40 No. January 206 22 Population Research * Lee-Carter 958 ~ 96 Lee-Carter 958 ~ 96 4 4339 ~ 4385 624 ~ 2337 980 Lee-Carter 30058 An Assessment of Abnormal Deaths during the Great Leap Forward Using a Modified Lee-Carter Model Mi Hong Jia Ning Abstract There is a lack of official report by the Chinese government regarding the exact number of abnormal deaths during the Great Leap Forward.Using a modified Lee-Carter mortality prediction model this study conducts reverse prediction based on China s official age-specific mortality data to reconstruct and calculate the single-year-age mortality rate and the normal deaths assuming that there was no great famine.then we estimate the abnormal deaths during the Great Leap Forward occurring between 958 and 96.If there had been no famine there would have been 43. 39 to 43. 85 million normal deaths.with famine abnormal deaths are estimated to be between 6. 24 and 23. 37 million. Our results suggest that the medium estimation of the abnormal deaths during the Great Leap Forward stands at no more than 9. 8 million. Keywords The Great Leap Forward Reverse Prediction Lee-Carter Model Death Authors Mi Hong is Professor School of Public Affairs Zhejiang University Executive Director of Institute of Population &Development Studies.E-mail spsswork@ 63.com.Jia Ning is PhD Candidate Institute of Population and Development Studies School of Public Affairs Zhejiang University.E-mail 222043@ zju.edu.cn. * 7490732 730322 2& ZD099 LEPP
23 958 ~ 96 Dik tter 200 953 964 982 2005 Chen 204 Background Notes China October 997 958 ~ 96 600 ~ 2700 960 000 990 J. Bannister 2987. 39. 5 606. 6 J. Banister 985 PAA Ansley Coale 982 959 ~ 96 248 3068. 3 5549. 3 958 ~ 963 2680 G. Calot 958 ~ 962 2850. 9 4 397. 85 6048. 8 G. Calot 985 959 ~ 96 Eder 960 ~ 96 2300 Mosle 960 00 ~ 3000 Hill 958 ~ 962 3000 3300 Kane 988 Luo Sheng 988 Brass - Logit 3 3 953 ~ 982 Coale Bannister 3 953 ~ 964 05 964 ~ 982 06 959 ~ 963 2889 Luo 988 982 98 953 964 982 958 ~ 963 700 a 986 b 986 959 ~ 96 958 ~ 96 3245. 8 2005 Coale 2200 Lee-Carter
24 40 2 2. 994 ~ 2006 2007 ~ 200 2000 953 964 982 987 995 2005 2009 2 995 00 5 90 + 996 85 + 2005 00 + 3 5 2 3 Eilers Delwarde et al. 2007 4 2. 2 Lee-Carter 2. 2. Lee-Carter Lee-Carter ARIMA Lee and Carter 992 Carter and Prskawetz 200 3 ln m x t = α x + β x k t + ε x t m x t x t α x β x k t k t k t t ε x t 0 δ 2 ξ { β x = all x k t = 0 j t = i 2 i j
25 2. 2. 2 Lee-Carter Lee-Carter Lee-Carter x m x t m x t = exp a x + β x k t 3 0 x = 0 m 0 t = exp a 0 + β 0 k t 4 m 0 t k t t a 0 β 0 t k t k t lim m x - exp x 0 0 t 0 Lee-Carter Lee-Carter 20 2 Lee-Carter Lee-Carter k t lim m x t = lim exp a x + β x k t 0 t - x - lim t + m x t = lim exp a x + β x k t + lim m x t = lim exp a x + β x k t > x + t + x + 2. 2. 3 Logistic 0 Logistic 3 Lee-Carter 2 3 Lee-Carter-MY m x t = γ + e a x + β x k t + ε x t 5
26 40 a x β x k x ARIMA γ γ β x γ - γ = e ax + βxkt 6 m x t ln( - γ m x t ) = a x + β x k t 7 Lee-Carter 2 γ = α x k t β x γ x β x α x α x k t γ = 5 m x t = + e a x + β x k t Lee-Carter S 7 t t = j ln [ ( - t = i m x t ) ] = j a x + j β x k t 9 t = i t = i i j j = 0 k t t = i a x = t = j t = i ln [ ( - ) ] m x t n n 2 k t ln [ ( - all x m x t ) - ax ] = β x k t all x t k t 00 β x x = 0 = [ ( ) ] k t = 00 - - ax x = 0 ln m x t 3 β x 8 0 2
27 /m x t - exp a x = exp β xk t exp a x k t β x γ = a x k t β x γ β x R-square β x R-square Sum R-square 2 γ γ γ = a x β x k t 5 m x 3 t γ + e γ x t γ a x + β x k t x t γ x t = - exp a m x + β x k t 4 x t t γ 2 = j t = i n γ x t γ 2 8 γ γ x β x γ x x γ k t 0 Lee-Carter 0 0 2. 2. 4 20 Luo Sheng 988 953 ~ 982 5 Coale Bannister Coale Bannister Lee-Carter 953 Luo Luo Lee-Carter-MY Luo
28 40 98 Table Comparison of the Estimated Age-Specific Mortality in 98 Luo Luo 0 50. 4 47. 4 54. 4 4. 3 5. 9 5. 2 5. 3. 3. 2 0. 3. 5. 6 5 0. 3 0. 5 20. 2. 25. 82 3. 3 2. 30. 9 0. 8 2. 6 35 2. 3. 9 2. 7 40 3. 3 2. 2 2 45 4. 9 2 2. 50 7. 5 7. 7 8. 4 55. 8 3. 3 0. 4 60 22 23. 6. 65 33. 3 37. 3 25. 8 70 55. 64. 2 50 75 84. 7 4. 9. 80 40. 8 9. 64. 6 85 90. 3 90 236. 2 95 270. 3 00 3. 9 Luo S 988 2 982 Luo Lee-Carter-MY 986 Luo 988 67. 32 67. 88 Luo 66. 47 3 20 20 30 50 5 5 2009 ~ 994 993 ~ 989 2009 ~ 989 988 ~ 984 950 ~ 4
29 a x k t β x γ x a x U U Lee-Carter-MY k t k t 2 a x 2 k t Figure Fitted Value of a x Figure 2 Fitted Value of k t β x 0 β x 85 β x 3 3 β x 4 γ x Figure 3 Fitted Value of β x Figure 4 Fitted Value of γ x γ x a x U γ x
30 40 4 2 β x R-Square 0. 6 95 R-Square 0. 7 70 Lee-Carter-MY 5 6 5 953 ~ 993 Figure 5 Mortality Rate of Single Age Group from 953 to 993 6 0 60 Figure 6 Trends in Life Expectancy at ages 0 and 60 4 958 ~ 96 4.
3 2 = - 5 = - 6 3 4 958 ~ 96 958 ~ 96 958 ~ 96 958 ~ 963 4. 2 953 953 996 953 2 953 ~ 964 953 964 996 954 ~ 963 40. 5 05 3 953 953 ~ 964 4 958 ~ 963 958 ~ 96 5 958 ~ 963 958 ~ 96 4. 3 4. 3. 2 958 ~ 963 958 ~ 96
32 40 2 Table 2 Comparison of Annual Total Population in Our Work and Previous Studies Coale Bannister Calot 953 58800 954 60200 60300 955 6400 6400 60700 6400 6500 956 62600 62600 6900 62700 62600 957 63700 63900 63300 64500 63900 958 64900 64500 63900 65800 64800 959 6600 65200 6500 66300 65500 960 67300 64900 65300 65300 65200 96 68600 64600 64800 65000 64900 962 69900 65500 65300 66400 66800 963 7200 68700 67400 68000 68700 2 Coale 984 Bannister 985 Calot 985 986 4 2 2 3-6 958 959 96 962 96 ~ 962 962 958 959 960 96 3 958 ~ 96 4. 3. 2 2 = 7 3 D t = 00 i = 0 P i t q i t 8 D t t P i t t i q i t t i 3
33 Table 3 3 953 ~ 964 Annual Natural Deaths and Crude Death Rate During 953-964 Assuming no Great Famine 953 594350000 669052 9. 63 954 604377430 53532 9. 09 955 647055 426000 8. 59 956 62556702 33894 8. 3 957 63695594 25785 7. 67 958 648748888 03846 7. 2 959 660895459 04075 6. 7 960 673276278 0962556 6. 28 96 685899625 074494 5. 66 962 69887305 0532090 5. 07 963 7243248 033994 4. 5 964 726569955 009475 3. 89 958 ~ 96 4385347 Coale 4 4 Table 4 Estimated Annual Crude Death Rate by Previous Studies Bannister Coale Calot 954 24. 2 29. 9. 96 955 22. 33 22. 4 22. 3 7. 23 956 20. 20. 8 6. 85 6. 77 957 8. 2 9 3. 24 6. 55 958 20. 65 20. 4 5. 98 7. 25 959 22. 06 23. 3 9. 2 8. 96 960 44. 6 38. 8 40. 76 3. 25 96 23. 0 20. 5 27. 03 24. 57 962 4. 02 3. 7 8. 28 8. 08 963 3. 8 3 2. 22 6. 72 964 2. 45 3. 5 20. 82 3. 03 Coale 984 J. Banister 985 G. Calot 985 b 986 99 5
34 40 5 Table 5 Comparison of Total Actual Deaths Coale Bannister Calot 958 23702 26074 46063 290479 959 27944 095876 35064 68540 960 076662 078932 0797299 07804 96 0307882 0340929 037589 0365035 962 033692 00669 02709 032784 963 002460 999865 000648 05408 958 ~ 96 43389500 433448 43948885 4360468 958 ~ 963 63625652 6337294 64230444 6404748 958 ~ 963 6 6 958 ~ 963 Table 6 Annual Total Deaths in 958-963 Coale Bannister Calot 958 362488 392253 055799 0065 959 5200454 4350030 2736320 232380 960 2563740 290500 26633807 20470000 96 3236440 4904728 7567878 5953792 962 897485 959266 236458 8404 963 8925930 930702 443745 303222 958 ~ 96 667632 75485 67453804 59848667 958 ~ 963 84663237 9008478 9402773 8299230 4. 3. 3 Coale 958 ~ 963 7 7 958 ~ 963 Table 7 Correction of Previous Calculations 958-963 Coale 8466 8466 8299 6363 6462 6405 203 2004 894 2 Coale 984 998 a 986 99 958 ~ 963 =
35 958 ~ 96 Coale Coale 958 ~ 96 958 ~ 963 coale 962 963 96 22 963 47 96 20. 5 963 3 Coale 962 963 962 963 958 ~ 96 Coale 958 ~ 963 962 963 Coale Lee-Carter 958 ~ 96 Coale 958 ~ 96 958 ~ 96 4 4339 ~ 4385 624 ~ 2337 5 953 Lee-Carter Lee-Carte-MY Lee-Carter-MY Lee-Carter-MY 2 Lee-Carter-MY 953 953 48. 43 959 52. 23 964 55. 24 962 ~ 963 7. 3 958 ~ 96 958 959 960 96 962 963 958 ~ 963 624 ~ 2337 958 ~ 96 958 ~ 963 894 ~ 203 962 963 Lee-Carter-MY 958 ~ 96 4339 ~ 4385 3 Coale 958 ~ 96
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