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36 2 2012 3 Vol. 36 No. 2 March 2012 71 Population Research 2008 130062 2010 100191 Spatial Econometric Research on Regional Spillover and Distribution Difference of Population Aging in China Zhao Ruyu Liu Chang Zhang Feng Abstract This paper bringing the spatial factor into the framework of ageing study examines patterns of spatial distribution of the regional population aging in China using exploratory spatial data analysis and explores the determinants and their relative importance with Spatial Econometrics theory and spatial error model.in addition to the population aging inertia and population growth the paper places emphasis on the regional spillover mechanism of population aging revealing that the spillover effects are significant.the findings from this research broadens perspectives of ageing research in light of space dimension which has important implications for theoretical research and policy formulation on population aging in China. Keywords Regional Spillover Mechanism Spatial Heterogeneity Spatial Correlation Population Structure Inertia Spatial Error Model Authors Zhao Ruyu is Professor and Deputy Director Center of Northeast Asia Studies Jilin University of China Liu Chang and Zhang Feng are PhD Students Academy of Northeast Asia Studies Jilin U- niversity of China.Email zhaoruyu@ yahoo.com.cn

72 36 1 20 90 29 69 54 134 1995 2000 1999 2008 65 1. 1 2009 1988 1990 1 1999 ~ 2009 2 20 90 1990 20 90 1996 2001 21 2000 1991 ~ 1995 6 2000 20 80 90 2007 2008 1999 ~ 2009 1

2 73 3 3. 1 65 7% Empirical Bayes Method 2000 ~ 2010 0 ~ 14 65 3. 2 3. 2. 1 1 1999 2004 2009 1999 31. 9% 102. 4% 68. 0% 50% 2004 44. 4% 1999 39. 2% 6. 8% 1999 ~ 2004 1999 2004 100% 81% 60% 2009 57. 6% 2004 29. 7% 5. 4% 100% 184% 80% 70% 2004 ~ 2009 3. 2. 2 1999 ~ 2009 1999 ~ 2004 2004 ~ 2009 2

74 36 1 1999 ~ 2009 Table 1 National and Regional Ratio of Older to Child 1999 ~ 2009 % 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 0. 3188 0. 3040 0. 3480 0. 3835 0. 4184 0. 4436 0. 4640 0. 4980 0. 5234 0. 5508 0. 5760 0. 6801 0. 5698 0. 7152 0. 9371 1. 0541 1. 1089 1. 0511 1. 1188 1. 0534 1. 0546 1. 0138 0. 4991 0. 4625 0. 5305 0. 7341 0. 7788 0. 8178 0. 7646 0. 8687 0. 9505 1. 1346 1. 0897 0. 2731 0. 3009 0. 3651 0. 3606 0. 3938 0. 4576 0. 4624 0. 5107 0. 5288 0. 5442 0. 5366 0. 2413 0. 2421 0. 2790 0. 0008 0. 3096 0. 3333 0. 3621 0. 3481 0. 3741 0. 4330 0. 4691 0. 2639 0. 2543 0. 3268 0. 3662 0. 4188 0. 4367 0. 4650 0. 4803 0. 5205 0. 5442 0. 5942 0. 4223 0. 4373 0. 5015 0. 5158 0. 6595 0. 6796 0. 6860 0. 8443 0. 8379 0. 9332 1. 0399 0. 3646 0. 3091 0. 3566 1. 3172 0. 4623 0. 5362 0. 5294 0. 6286 0. 6712 0. 7452 0. 7296 0. 2628 0. 2877 0. 3291 0. 3741 0. 4195 0. 4675 0. 5133 0. 5758 0. 6792 0. 7170 0. 7019 1. 0237 0. 8558 1. 1510 1. 2462 1. 8434 1. 7351 1. 3285 1. 7656 1. 7743 1. 6379 1. 8486 0. 4914 0. 4421 0. 5388 0. 5259 0. 6663 0. 6565 0. 6994 0. 7384 0. 7817 0. 8527 0. 8786 0. 5018 0. 4829 0. 5914 0. 6777 0. 7129 0. 6262 0. 6652 0. 6690 0. 7247 0. 7593 0. 7989 0. 2944 0. 2921 0. 3347 0. 3404 0. 3754 0. 3927 0. 4370 0. 4786 0. 5033 0. 5342 0. 5271 0. 3125 0. 2849 0. 3542 0. 3604 0. 3719 0. 4416 0. 4735 0. 5211 0. 5723 0. 5633 0. 5875 0. 2524 0. 2372 0. 2692 0. 3002 0. 2998 0. 3720 0. 3362 0. 3466 0. 3953 0. 3696 0. 3674 0. 4015 0. 3837 0. 4014 0. 4514 0. 4938 0. 5380 0. 6248 0. 6251 0. 6322 0. 6254 0. 6222 0. 2709 0. 2687 0. 2958 0. 3089 0. 3562 0. 3832 0. 3899 0. 3857 0. 3718 0. 3944 0. 4638 0. 2842 0. 2762 0. 3003 0. 3818 0. 3734 0. 4250 0. 4856 0. 5766 0. 6291 0. 6896 0. 7032 0. 3442 0. 3279 0. 3680 0. 4215 0. 4638 0. 4738 0. 5412 0. 5860 0. 6155 0. 6303 0. 6490 0. 2838 0. 2512 0. 2813 0. 3068 0. 3052 0. 3147 0. 3459 0. 3515 0. 3849 0. 4092 0. 4315 0. 2928 0. 2725 0. 3313 0. 3908 0. 4219 0. 4024 0. 4024 0. 4043 0. 4195 0. 4281 0. 4380 0. 2340 0. 2492 0. 2774 0. 2949 0. 3254 0. 3157 0. 3606 0. 3907 0. 4161 0. 4170 0. 4308 0. 3828 0. 3573 0. 4364 0. 4659 0. 4908 0. 5482 0. 5305 0. 5882 0. 6170 0. 6287 0. 6294 0. 3538 0. 3281 0. 3632 0. 4099 0. 4332 0. 4463 0. 4996 0. 5681 0. 5739 0. 6596 0. 7085 0. 2152 0. 1944 0. 2287 0. 2541 0. 2932 0. 2956 0. 2896 0. 2957 0. 3052 0. 3130 0. 3340 0. 2484 0. 2324 0. 2549 0. 2883 0. 2857 0. 3439 0. 3121 0. 3318 0. 3310 0. 3562 0. 4001 0. 1231 0. 1919 0. 2309 0. 2560 0. 2291 0. 2637 0. 2262 0. 2672 0. 3119 0. 3103 0. 3606 0. 2718 0. 2396 0. 2750 0. 3587 0. 3709 0. 3864 0. 4411 0. 4828 0. 5550 0. 5829 0. 6247 0. 2055 0. 1904 0. 2169 0. 2610 0. 2907 0. 2997 0. 3087 0. 3398 0. 3783 0. 3963 0. 4421 0. 2017 0. 1875 0. 1850 0. 2133 0. 2404 0. 2552 0. 2511 0. 3113 0. 2940 0. 3185 0. 3370 0. 1586 0. 1817 0. 1790 0. 1804 0. 2186 0. 2223 0. 2328 0. 2499 0. 2689 0. 2859 0. 3212 0. 1740 0. 1737 0. 1901 0. 2472 0. 2204 0. 2843 0. 2753 0. 2960 0. 3183 0. 3442 0. 3151 2000 ~ 2010 1999 ~ 2004 6. 8% 2004 ~ 2009 5. 4% 9% 7%

2 75 2 Table 2 Annual Growth Rate of the National and Regional Ratio of Older to Child % 1999 ~ 2009 6. 1 11. 3 10. 3 9. 5 9. 4 8. 7 8. 5 8. 1 8. 0 7. 3 7. 2 7. 2 7. 0 6. 9 6. 5 6. 5 1999 ~ 2004 6. 8 16. 5 12. 2 8. 4 10. 0 7. 3 10. 6 10. 4 7. 8 7. 0 4. 8 8. 0 10. 9 6. 7 6. 6 7. 2 2004 ~ 2009 5. 4 6. 5 8. 5 10. 6 8. 9 10. 1 6. 4 5. 9 8. 1 7. 6 9. 7 6. 4 3. 2 7. 1 6. 5 5. 9 1999 ~ 2009 6. 3 6. 1 6. 1 6. 0 6. 0 5. 5 5. 3 5. 1 4. 9 4. 8 4. 5 4. 5 4. 3 4. 1 4. 1 3. 8 1999 ~ 2004 6. 2 10. 3 11. 1 5. 9 6. 0 7. 2 4. 8 7. 4 6. 7 4. 5 6. 6 6. 0 2. 1 6. 6 10. 3 8. 1 2004 ~ 2009 6. 4 2. 1 1. 3 6. 1 6. 0 3. 9 5. 7 2. 8 3. 1 5. 0 2. 5 3. 0 6. 5 1. 7-1. 8-0. 2 1 3. 2. 3 1999 ~ 2009 6. 8% 5. 4% 1999 ~ 2004 2004 ~ 2009 3. 3 ESDA 1999 ~ 2009 3. 3. 1 Moran Ι n n i = 1 n w ij x i - x 珋 x j - x 珋 j = 1 I = = n i = 1j n w ij n x i - x 珋 2 = 1 i = 1 n i = 1j 1 n w ij x i - x 珋 x j - x 珋 s 2 n i = 1 n j = 1 w ij 1

76 36 n w ij 1 x i x j = 1 n x i - x 珋 2 x i i i j x 珋 = 1 n n i = 1 x i x i s 2 Moran Ι -1 1 0 rook contiguity GeoDa 1999 ~ 2009 3 2000 2002 Moran Ι 0. 4009 0. 2228 1999 ~ 2009 1999 ~ 2004 2004 ~ 2009 4 1999 ~ 2009 1999 ~ 2004 2004 ~ 2009 Moran Ι 0. 1438 0. 1044 0. 0343 3 1999 ~ 2009 Moran Ι Table 3 The Value of Moran Ι Global Spatial Correlation of the Regional Ratio of Older to Child in China 1999-2009 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 \ Moran Ι 0. 3522 0. 4009 0. 3842 0. 2228 0. 2933 0. 2839 0. 3681 0. 2861 0. 3090 0. 3472 0. 2940 1 4 Table 4 Moran Ι The Value of Moran Ι Global Spatial Correlation of the Annual Growth Rate of the Regional Ratio of Older to Child \ 1999 ~ 2009 1999 ~ 2004 2004 ~ 2009 Moran Ι 0. 1438 0. 1044 0. 0343 1 3. 3. 2 LISA Moran Ι I i = x i - x 珋 ω s 2 ij x j - x 珋 2 i j I i - - - - rook contiguity GeoDa 1999 ~ 2009 5 - - - - 5% 1 1 0

2 77 5 1999 ~ 2009 Table 3 Cluster Analysis of the Local Spatial Correlation the Regional Ratio of Older to Child in China 1999-2009 1999 ~ 2000 2001 2002 2003 ~ 2004 2005 ~ 2007 2008 2009 - - - - 1 3. 4 3. 4. 1 3. 4. 1. 1 SAR y = ρwy + Xβ + ε 3 ε ~ N 0 σ 2 In 3. 4. 1. 2 SEM y = Xβ + δ δ = λwδ + ε 4 ε ~ N 0 σ 2 In 3 4 y n X n k n k W n n ρ λ β X k δ ε n 1 2010 3. 4. 1. 3 OLS LM - Error LM - Lag Luc Anselin et. al. 2005 LM - Error LM - Lag OLS LM - Error LM - Lag LM - Error LM - Lag LM - Error LM - Lag Robust LM - Error Robust LM - Lag Robust LM - Error Robust LM - Lag 1999 LnEBROC99 1999 ~ 2009

78 36 LnRNG9909 1 2009 LnE- BROC09 OLS 1999 ~ 2009 R 2 adjusted R 2 0. 95 95% F F - statistic 280 Log likelihood 30. 9 Akaike info criterio Schwarz criterion - 55. 8-51. 5 3 Anselin L. 1998 LnEBROC99 1999 ~ 2009 LnRNG9909 0. 4036 0. 2516-0. 4241 1% 1999 ~ 2009 LM - Error 1% LM - Lag 3. 4. 2 LnEBROC09 i = α + λ W δ i j + β 1 LnEBROC99 i + β 2 LnRNG9909 i + ε i ε i ~ N 0 σ 2 In 5 5 α LnEBROC99 i LnRNG9909 i LnEBROC09 i i 1999 1999 ~ 2009 2009 δ i ε i W λ - 1 1 β 1 β 2 R 2 0. 95 0. 97 Log likelihood 30. 9 36. 8 Akaike info criterion - 55. 8-67. 5 Schwarz criterion - 51. 5-63. 2 α LnE- BROC99 β 1 λ LnRNG9909 β 2 1% α β 1 0. 4035811 0. 4372895 0. 2516492 0. 2660422 β 2-0. 4240538-0. 4319766 Likelihood Ratio Test 11. 72762 1% LnEBROC09 = 0. 4373-0. 9003 W δ + 0. 2660 LnEBROC99-0. 4320 LnRNG9909 + ε 0. 00 0. 00 0. 00 0. 00 R 2 = 0. 97 Log likelihood = 36. 76 Akaike info criterion = - 67. 5Schwarz criterion = - 63. 2 LnEBROC99 β 1 0. 2660 1999 1 2000 ~ 2010 2000

2 79 1% 2009 0. 266% LnRNG9909 β 2-0. 4320 1999 ~ 2009 1% 2009 0. 4320% 20 W δ λ - 0. 9003-1 1% W δ 1% 0. 9003% 0. 266% 0. 4320% 4 4. 1 1999 ~ 2004 2004 ~ 2009 0. 2660-0. 4320

80 36 3 4. 2

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