~ 96 Dik tter Chen 204 Background Notes China October ~ ~ J. Bannister

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1 Vol. 40 No. January Population Research * Lee-Carter 958 ~ 96 Lee-Carter 958 ~ ~ ~ Lee-Carter 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 to million normal deaths.with famine abnormal deaths are estimated to be between and 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. spsswork@ 63.com.Jia Ning is PhD Candidate Institute of Population and Development Studies School of Public Affairs Zhejiang University @ zju.edu.cn. * & ZD099 LEPP

2 ~ 96 Dik tter Chen 204 Background Notes China October ~ ~ J. Bannister J. Banister 985 PAA Ansley Coale ~ ~ G. Calot 958 ~ G. Calot ~ 96 Eder 960 ~ Mosle ~ 3000 Hill 958 ~ Kane 988 Luo Sheng 988 Brass - Logit ~ 982 Coale Bannister ~ ~ ~ Luo ~ a 986 b ~ ~ Coale 2200 Lee-Carter

3 ~ ~ Eilers Delwarde et al Lee-Carter Lee-Carter Lee-Carter ARIMA Lee and Carter 992 Carter and Prskawetz 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

4 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 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

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 = ax x = 0 ln m x t 3 β x 8 0 2

6 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 Luo Sheng ~ Coale Bannister Coale Bannister Lee-Carter 953 Luo Luo Lee-Carter-MY Luo

7 Table Comparison of the Estimated Age-Specific Mortality in 98 Luo Luo Luo S Luo Lee-Carter-MY 986 Luo Luo ~ ~ ~ ~ ~ 4

8 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

9 β x R-Square R-Square Lee-Carter-MY ~ 993 Figure 5 Mortality Rate of Single Age Group from 953 to Figure 6 Trends in Life Expectancy at ages 0 and ~ 96 4.

10 3 2 = - 5 = ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 96

11 Table 2 Comparison of Annual Total Population in Our Work and Previous Studies Coale Bannister Calot Coale 984 Bannister 985 Calot ~ ~ = 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

12 33 Table ~ 964 Annual Natural Deaths and Crude Death Rate During Assuming no Great Famine ~ Coale 4 4 Table 4 Estimated Annual Crude Death Rate by Previous Studies Bannister Coale Calot Coale 984 J. Banister 985 G. Calot 985 b

13 Table 5 Comparison of Total Actual Deaths Coale Bannister Calot ~ ~ ~ ~ 963 Table 6 Annual Total Deaths in Coale Bannister Calot ~ ~ Coale 958 ~ ~ 963 Table 7 Correction of Previous Calculations Coale Coale a ~ 963 =

14 ~ 96 Coale Coale 958 ~ ~ 963 coale Coale ~ 96 Coale 958 ~ Coale Lee-Carter 958 ~ 96 Coale 958 ~ ~ ~ ~ Lee-Carter Lee-Carte-MY Lee-Carter-MY Lee-Carter-MY 2 Lee-Carter-MY ~ ~ ~ ~ ~ ~ ~ Lee-Carter-MY 958 ~ ~ Coale 958 ~ 96

15 Coale ~ Coale 958 ~ ~ Coale 958 ~ ~ /References Carter L. R. and A. Prskawetz Examining Structural Shifts in Mortality Using the Lee-Carter Method. Mpidr Working Papers Chen Y The Great Famine in China A Documentary History. Historian AJ Coale J Rapid Population Change in China Washington D. C National Academy Press Dik tter F Mao sgreat Famine the History of China s most Devastating Catastrophe Library Journal Eilers P. H. C. A. Delwarde and M. Denuit Smoothing the Lee-Carter and Poisson Log-bilinear Models for Mortality Forecasting A Penalized Likelihood Approach. Statistical Modelling Kane P Famine in China Demographic and Social Implications. Macmillan Press. 7 Lee R. D. and L. R. Carter 992. Modeling and Forecasting U. S. Mortality. Journal of the American Statistical Association Luo S Reconstruction of Life Tables and Age Distributions for the Population of China by Year from 953 to 982 Phd Dissertation University of Pennsylvania. 9 J. Banister.. IUSSP J. Banister Surprising and Confirmation of the Results of China s Census. Collected Papers of IUSSP 985 Florence Conference Cao Shuji China s Population Death During and Its Causes. Chinese Journal of Population Science G. G. Calot.. IUSSP France G. Calot Suggestions on China s Demographic Data Analysis. Collected Papers of IUSSP 985 Florence

16 37 Conference. 2 a Jiang Zhenghua and Li Nan Parameter Correction of China s Population Dynamics. Journal of Xi an Jiao Tong University b Jiang Zhenghua and Li Nan Methodology and Results of China s Population Dynamics Estimation. Demographic Yearbook of China. Economic Management Press ~ Jiang Zhenghua Mi Hong and Zhang Yougan Estimation of Population Migration from Chinese Mainland to Taiwan and Overseas During 946 and 949. Population Science of China Li Chengrui Population Change Led by the Big Leap. Population Research ~ Roderick Macfarquhar John King Fairbank Xie Langsheng Cambridge Chinese History Volume Rise of Revolutionary China Yang Mingxu. 20. Method Innovation and Empirical Study of Mortality Reverse Prediction. Master Thesis 0384 Xiamen University Yuan Yongxi. 99. On China s Population. Finance and Economic Publishing Houseof China Zhu Wei and Chen Bingzheng Prediction of China s Urban Population Mortality. Application of Statistics and Management

~ 10 2 P Y i t = my i t W Y i t 1000 PY i t Y t i W Y i t t i m Y i t t i 15 ~ 49 1 Y Y Y 15 ~ j j t j t = j P i t i = 15 P n i t n Y

~ 10 2 P Y i t = my i t W Y i t 1000 PY i t Y t i W Y i t t i m Y i t t i 15 ~ 49 1 Y Y Y 15 ~ j j t j t = j P i t i = 15 P n i t n Y * 35 4 2011 7 Vol. 35 No. 4 July 2011 3 Population Research 1950 ~ 1981 The Estimation Method and Its Application of Cohort Age - specific Fertility Rates Wang Gongzhou Hu Yaoling Abstract Based on the