* 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 period age - specific fertility rate this paper has proposed an estimation method of the cohort age - specific fertility rate and uses data of the birth cohort of 1950-1981 to explain its feasibility and reliability.this method can be applied to analyze the pattern of parity progression and related issues particularly for the adjustment of Chinese family planning policy.using this method this paper has estimated the quantity and structure of women with one child and women who are allowed to have two children by the current family planning policy but have had only one child.this would have implications for family planning policy research. Keywords Cohort Age - specific Fertility Rates Fertility Level Estimation Methods Authors Wang Guangzhou Researcher Institute of Population and Labor Economics CASS. E - mail wangguangzhou@ 126.com Hu Yaoling Post - doctor Institute of Population and Labor Economics CASS. * YZDA2010-15
4 35 1 5 ~ 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 1 2 3 Y
4 5 n j t n j t = j i = 15P n i t i 2 j t = 1 j t - 2 j t = j i = 15P 1 i t - j i = 15P 2 i t 3 3. 1 t t - Y Y t - Y 5 ~ 10 5 ~ 10 15 ~ 49 40 r t Y s r < s < t i r i t i s r t 1 r i t i s i P i s = P i r + s - r t - r P i t - P i r Y P n i s = P n i r + s - r t - r P n i t - P n i r 3. 2 Y - 1 i i + 1 Y i + 1 Y - 1 i i + 1 P Y - 1 i. P Y - 1 i + 1. Y i i + 1 P Y i. P Y i + 1. 1
6 35 PY i + 1. P Y i. = PY - 1 i + 1. P Y - 1. PY i + 1. = P Y - 1 i + 1. PY i. P Y - 1 i. Y i + 2 i + 3 49 1 4 1982 1 1950 ~ 1981 1929 ~ 1956 1929 21 ~ 49 1950 ~ 1978 21 ~ 49 1930 20 ~ 49 1950 ~ 1979 20 ~ 49 1955 1965 1975 1955 1960 1965 1970 1975 1929 ~ 1956 stata 4. 1 15 ~ 49 35 1929 ~ 1956 35 1950 ~ 1981 1929 ~ 1956 11 ~ 32 11 ~ 32 t 1929 ~ 1948 p 0. 05 95% 1949 ~ 1956 p 0. 05 1 1929 ~ 1948 p 0. 05 95% 1949 ~ 1956 p 0. 05 2 1949 ~ 1956 i 1
4 7 5 Table 1 1 Method One Test the Difference between the True Value and the Estimates t p t p t p t p 1930 30-1. 4546 0. 1565 1. 6892 0. 1019 0. 1077 0. 9150 0. 1358 0. 8929 1935 32 0. 8670 0. 3926 2. 0438 0. 0498-0. 7813 0. 4405 0. 4230 0. 6753 1940 27 0. 3600 0. 7218 2. 3229 0. 0283-1. 3133 0. 2006 0. 4806 0. 6348 1945 22-0. 7754 0. 4467 1. 1870 0. 2485-1. 1452 0. 2650-1. 0921 0. 2871 1950 17-2. 2834 0. 0364-2. 9428 0. 0096 2. 2611 0. 0380 0. 7802 0. 4466 1955 12-2. 2995 0. 0421-1. 5029 0. 1610 2. 0288 0. 0674-2. 0551 0. 0644 Table 2 2 Method Two Test the Difference between the True Value and the Estimates t p t p t p t p 1930 30 1. 1953 0. 2417 1. 7612 0. 0888-1. 0283 0. 3123 0. 3064 0. 7615 1935 32-0. 0855 0. 9324-0. 7393 0. 4653-0. 8389 0. 4080-0. 7673 0. 4487 1940 27-1. 7311 0. 0953 0. 5097 0. 6145 1. 0433 0. 3064-0. 8519 0. 4020 1945 22-0. 7142 0. 4829-0. 1351 0. 8938-0. 9959 0. 3306-1. 3103 0. 2042 1950 17 0. 9390 0. 3617-2. 3113 0. 0345 2. 3526 0. 0318 1. 6095 0. 1271 1955 12-2. 4297 0. 0334-1. 6383 0. 1296 1. 2374 0. 2417-2. 2593 0. 0451 4. 2 1929 ~ 1956 28 3 1953 ~ 1956 0. 9 1 1 1953 ~ 1956 0. 9 15 1953 ~ 1956 1929 ~ 1952 4 1 1 1 1 b 1929 ~ 1952
8 35 0. 9333 0. 9939 0. 9510 1. 0165 0. 9694 1. 0384 0. 9590 1. 0498 1 ± 0. 05 Table 3 3 Method Two The Correlation Coefficient between the True Value and the Estimates 1929 0. 9917 0. 9587 0. 9406 0. 9123 1943 0. 9453 0. 9964 0. 9936 0. 9840 1930 0. 9939 0. 9588 0. 9536 0. 9253 1944 0. 9411 0. 9926 0. 9908 0. 9860 1931 0. 9907 0. 9594 0. 9630 0. 9306 1945 0. 9686 0. 9930 0. 9883 0. 9902 1932 0. 9772 0. 9720 0. 9766 0. 9501 1946 0. 9350 0. 8717 0. 9101 0. 8254 1933 0. 9862 0. 9784 0. 9779 0. 9528 1947 0. 9868 0. 9887 0. 9935 0. 9945 1934 0. 9923 0. 9888 0. 9758 0. 9660 1948 0. 9887 0. 9837 0. 9943 0. 9949 1935 0. 9928 0. 9826 0. 9781 0. 9662 1949 0. 9903 0. 9902 0. 9892 0. 9946 1936 0. 9860 0. 9788 0. 9869 0. 9723 1950 0. 9930 0. 9950 0. 9894 0. 9938 1937 0. 9717 0. 9815 0. 9854 0. 9625 1951 0. 9745 0. 9856 0. 9856 0. 9909 1938 0. 9473 0. 9797 0. 9935 0. 9704 1952 0. 9429 0. 9639 0. 9874 0. 9876 1939 0. 9326 0. 9889 0. 9963 0. 9770 1953 0. 8832 0. 9584 0. 9978 0. 9778 1940 0. 9150 0. 9860 0. 9955 0. 9729 1954 0. 7682 0. 9322 0. 9931 0. 9495 1941 0. 9003 0. 9952 0. 9972 0. 9749 1955 0. 6368 0. 9132 0. 9934 0. 9227 1942 0. 9316 0. 9906 0. 9952 0. 9823 1956 0. 5986 0. 9200 0. 9851 0. 8961 Table 4 4 Regression Results of the True Value of Cohort Age - Specific Fertility Rate on Estimated Value 1930 1935 1940 1945 0. 9860 0. 9806 0. 9915 0. 9669 0. 9533 0. 9805 0. 9747 0. 9490 1. 0004 0. 9999 0. 9837 1. 0161 0. 8851 0. 8751 0. 8952 1. 0102 0. 9949 1. 0255 1. 0075 0. 9898 1. 0251 1. 0080 0. 9674 1. 0486 1. 0101 0. 9513 1. 0689 1. 0286 1. 0045 1. 0527 1. 0186 0. 9817 1. 0554 1. 0338 0. 9774 1. 0903 1. 0132 0. 9913 1. 0352 1. 0263 0. 9960 1. 0566 1. 0393 0. 9911 1. 0874 1. 0176 0. 9851 1. 0501 1950 0. 8645 0. 8044 0. 9245 1. 0236 0. 9622 1. 0851 0. 9901 0. 9752 1. 0049 1% 95% 0. 9801 0. 9161 1. 0441 5
4 9 Figure 1 1 The True Value of Real Cohort Age - specific Fertility Rate and the Estimates
10 35 2 Figure 2 Trend of Four Cohort Age - specific Fertility Rates 5. 1 1950 ~ 1984 1980 20 ~ 29 1950 30
4 11 26 1950 ~ 1984 1995 2005 1950 ~ 1986 1950 1960 1970 1980 1 2 21 100 21 120 1950 1960 1970 1980 248 243 189 138 26 1950 1960 1980 27 1980 1970 2003 1980 23 1 10 29 1950 1960 1970 1980 1950 1960 1970 25 1980 31 1950 1960 78 1970 1980 40 5 1950 1960 1970 1980 20 14 9 0 1980 4. 7 1950 1960 1970 1980 73 61 14 4. 6 2 1950 1960 1970 1980 1950 1960 1970 1980 25 25 27 29 1950 34 1960 1970 1980 1860 1343 1291 3 1950 1960 1970 1980 800 28 28 30 29 29 1950 1960 1970 1980 501 491 312 208 29 1950 1980 32 1950 538 1970 101 1980 50 1950 ~ 1984
12 35 1950 2179 1968 1502 38 1969 ~ 1984 1500 1381 1456 4 Figure 3 3 The Changes of Cumulative Age - Specific Fertility Rate of Four Bith Cohorts
4 13 4 Figure 4 1950 ~ 1984 Lifetime Fertility Rate of 1950-1984 Cohort 5. 2 1 2 5 15 ~ 27 15 ~ 27 1950 1960 1970 1980 384 383 488 623 28 ~ 40 40 1950 1960 1970 1980 302 265 374 432 82 118 114 191 40 2 5 1950 1960 1970 1980 301 265 370 421 5 Figure 5 Changes of Women with One Child of Four Birth Cohorts 5. 3
14 35 1 49 25% 50% 75% 100% 2012 1981 ~ 1986 2012 6679525 10. 89% 5 0. 25 25% 2012 129. 43 8% 0. 50 0. 75 1. 00 2012 258. 86 388. 29 517. 72 16% 24% 32% 0. 50 2. 0 0. 25 0. 50 1 ~ 3 5 2012 Table 5 Total New Birth Estimation after Family Planning Policy Adjustment 2012 1981 1982 1983 1984 1985 1986 9370801 11316732 9789371 9845225 9830866 11166366 1283725 1541872 1234739 1013239 806580 799368 825. 38 803. 53 781. 79 762. 24 735. 21 685. 51 0. 25 264890 309735 241327 193083 148251 136994 0. 50 529780 619470 482654 386166 296502 273988 0. 75 794670 929205 723981 579249 444753 410982 1. 00 1059560 1238940 965308 772332 593004 547976 1
4 15 6 5 ~ 10 Y - 1 i i + 1 Y i + 1 1950 ~ 1981 1955 1965 1975 1955 1960 1965 1970 1975 1929 ~ 1956 1929 ~ 1956 stata 1 1 1929 ~ 1952 0. 9333 0. 9939 0. 9510 1. 0165 0. 9694 1. 0384 0. 9590 1. 0498 /References 1... 1992 89 ~ 94 United Nations Department of International Economic and Social Affairs Population Division. 1992. The National Bureau
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