: 3 ( 100084) :, 1990 UNDP, Spearman HDI,,, ( ), 1990,,,,,, : 1990 (UNDP), ( Human Development Index, HDI), HDI :, ;, ;, GDP(PPP ) (UNDP, 2004) HDI 1 - - HDI ( ), GDP UNDP GDP ( ), 1, HDI ( ) 85 25 ( %), 2Π3 100 0 ( %), 1Π3 100 0 GDP(PPP ) 40000 100 Log 2 ( GDP) 1513 616 60 100 30900 :UNDP (2004), Human Development Report 2004 : Cultural Liberty in Today s Diverse World 817 3 (70403009) (2Π3 ) (1Π3 ) 1997, GDP, 4
2005 7 HDI 0 1,,,UNDP 2004, 175, HDI,,,UNDP ( Indrayan et al. 1999 ; Tang 1999 ; Lai, 2003 ;,2004),,UNDP 3 (1997, 1999, 2002), 2005, 4, 1990 1995 1997 1999 2002,,,, (Ravallion, 1997 ; Sagar and Najam, 1998 ; Srinviasan, 1994), ( Kelly, 1991), (Noorbakhsh, 1998 ; Luchters and Menkhoff, 2000),,,, (Carducci and Pisano, 1995 ; Lind, 1992, 1993 ; Lai, 2001, 2003) (Noorbakhash, 1998 ; Lai, 2001) HDI, (Noorbakhash, 1998 ; Lai, 2001, 2003), (Principal Component Analysis, PCA),, Lai (2001) HDI, HDI, (Lai, 2003), Lai (2001,2003),,,, 1999, (CV = 010669) GDP (CV = 011586),, GDP,,, UNDP, 11 (PCA),, CV(Coefficient of Variation) :, 5
:, Vires (2001),,, (Rao, 1965),,, (principal component), p, X = ( X 1, X 2,, X p ), X i = ( x 1 i, x 2 i,, x ni ), x ni n i ( i = 1,2,, p), i : a 2 1 i + a 2 2 i + + a 2 pi = 1 P i P j ( i j, i, j = 1,2,, p) Var( P i ) > Var( P i + 1 ) Π i = 1,2,, p - 1 P i = a 1 i X 1 + a 2 i X 2 + + a pi X p (1) i P i X 1,, X p i, ( a 1 i, a 2 i,, a pi ) X ( ) i, ( ), ( R),,, X i ( i = 1,2,, p), X i (mean2corrected) ;, X i,,,, 0 1, 21Spearman Spearman Pearson,, ( X Y) ( ),, Spearman : = i - gr) ( S i - gs ) ( i = 1,2,, p) (2) ( R i - gr) 2 2 ( S i - gs ) : R i X i, S i Y i, gr,gs R i S i,, Spearman UNDP, HDI 31 HDI, 31, UNDP 1997 2002, UNDP GDP(PPP ), Atkinson ( ) GDP (UNDP, 1997) 1999 UNDP 1997, Atkinson, GDP(PPP ) (UNDP, 1999) 6 1990 1995 30,
2005 7, 1990 1995 1997 Atkinson GDP(PPP ),,, 1990 1995 1997 GDP HDI, 1999 2003 UNDP HDI HDI, 1,,,HDI ( = - - ) 0 1, 0 1, HDI,,,,,,,,,,,,,,,,, ( ),,,,,,,, ( a 1 i, a 2 i,, a pi ),,,,,,Sharma (1996),,,,, HDI,,,, 11, UNDP ( ) 5,, 2 1999, (Principal Component) : P 1999 = 013775 X 1 + 016163 X 2 + 016912 X 3, 77161 %, 77161 %,, 80 % ( 2),, (Principal Component Index, PCI), 7
: 2 3 ( a 1 ) ( a 2 ) GDP(PPP) ( a 3 ) HDI Spearman P 1990 014241 017789 014621 017937 0199110 P 1995 014169 016637 016211 018291 0199422 P 1997 014429 015840 016803 017865 0199758 P 1999 013775 016163 016912 017761 0199153 P 2003 013944 015423 017419 017824 0199627 3,, PCI = a 1 X 1 + a 2 X 2 + a 3 X 3, X 1 X 2 X 3, ( ) HDI,PCI 0,,PCI ( ), 0, 0,HDI, UNDP, PCI,,, PCI 3 1999 3 PCI, (01277) ( - 01313), UNDP HDI,PCI,, ; (01002) ( - 01003) HDI PCI,, PCI HDI,, 3, HDI PCI,,, 3,HDI PCI Spearman 0199 ( P < 010001) ( 2 ),,, Lai (2003),,,Spearman 019708 (1990 ) 019730 (1997 ) HDI PCI, 0 1 HDI PCI 0 1, HDI, HDI PCI, 1 5 1 HDI PCI ( 1990 ) 8
2005 7 3 (1999 ) GDP HDI 0 1 PCI 0 1 PCI2HDI 0186 0192 0176 01845 2 01976 01254 2 01961 0 0181 0187 0172 01801 3 01843 01179 3 01834 0 0178 0180 0158 01723 11 01608 01032 11 01586 0 0179 0182 0152 01710 14 01569 01002 15 01535 1 0172 0177 0154 01679 22 01476-01038 20 01466-2 0179 0186 0165 01764 5 01732 01111 5 01718 0 0174 0185 0157 01720 12 01599 01036 10 01592-2 0177 0183 0160 01732 9 01636 01054 9 01622 0 0184 0188 0183 01853 1 1 01277 1 1 0 0181 0179 0166 01750 7 01690 01082 7 01669 0 0181 0179 0168 01758 6 01714 01097 6 01696 0 0177 0174 0152 01675 23 01464-01058 25 01432 2 0178 0176 0166 01733 8 01639 01056 8 01627 0 0171 0179 0152 01673 24 01458-01048 22 01450-2 0181 0174 0162 01724 10 01611 01030 12 01582 2 0177 0176 0153 01686 17 01497-01038 19 01467 2 0173 0179 0157 01697 16 01530-01003 16 01526 0 0170 0181 0153 01683 19 01488-01027 17 01485-2 0182 0182 0167 01771 4 01753 01118 4 01731 0 0175 0179 0150 01680 20 01479-01047 21 01451 1 0179 0177 0157 01711 13 01572 01007 14 01542 1 0173 0180 0152 01684 18 01491-01033 18 01476 0 0173 0177 0151 01671 25 01452-01057 24 01434-1 0169 0171 0141 01602 30 01244-01181 30 01223 0 0168 0171 0151 01632 27 01334-01115 27 01335 0 0164 0142 0150 01521 31 0-01313 31 0 0 0176 0178 0150 01680 20 01479-01048 23 01450 3 0171 0171 0148 01632 27 01334-01126 28 01317 1 0169 0166 0152 01625 29 01313-01133 29 01306 0 0176 0171 0151 01660 26 01419-01084 26 01389 0 0174 0181 0157 01707 15 01560 01013 13 01553-2 : HDI 2002, 9
: 2 HDI PCI ( 1995 ) 3 HDI PCI ( 1997 ) 4 HDI PCI ( 1999 ) 1 5, PCI HDI,,,PCI HDI HDI PCI,Spearman 0 1, HDI PCI,, PCI, 10 21
2005 7 5 HDI PCI ( 2003 ), HDI PCI = a 1 X 1 + a 2 X 2 + a 3 X 3, X 1, X 2, X 3, HDI,,,PCI HDI ( a i ) PCI,, PCI, HDI, PCI, PCI (weight structure), : (1), PCI ( ),,,?,? (2),, ( ),,,?,, ( dynamic weight structure) 4 ( a 1 ) ( a 2 ) GDP(PPP) ( a 3 ) PCI 1990 014241 017789 014621 PCI 1995 014169 016637 016211 PCI 1997 014429 015840 016803 PCI 1999 013775 016163 016912 PCI 2003 013944 015423 017419 4 PCI 11
:, 015774,,, ( GDP ) 1, ( ) 1990, PCI 1990 = 014241 X 1 + 017789 X 2 + 014621 X 3,,, 017789, 1990,, 4, PCI, GDP, PCI 1990 014621 2003 017419,, 1990,,, ;, 5 ( %) GDP(PPP ) ( %) ( % 3 ) ( %) ( %) 1990 0173 010034 (19135 %) 0168 010093 (52182 %) 0148 010049 (27183 %) 010176 (100 %) 1995 0173 010034 (17109 %) 0173 010086 (43110 %) 0155 010079 (39181 %) 010199 (100 %) 1997 0172 010035 (19147 %) 0173 010065 (36152 %) 0158 010078 (44101 %) 010178 (100 %) 1999 0176 010026 (13194 %) 0177 010075 (40171 %) 0158 010083 (45134 %) 010184 (100 %) 2003 0179 010026 (14119 %) 0181 010064 (35135 %) 0166 010091 (50146 %) 010180 (100 %) 3 5 1990 0173 2003 0179, 0106 ; 0168 0181, 0113 ; GDP 0148 0166, 0118 1990,, GDP 1990 010049 2003 010091, 27183 % 50146 %,, a 2 1 + a 2 2 + a 2 3 = 1, 1Π3 = 015774 12
2005 7 1990 010093 2003 010064, 52182 % 35135 %,,,,,,,,,,,, ( HDI > 018) 1997 2002, 6 6 ( a 1 ) ( a 2 ) GDP(PPP) ( a 3 ) HDI Spearman PCI 1997 015637 016206 015451 018482 0199951 PCI 1998 015830 015689 015800 018624 0199971 PCI 1999 015813 015887 015618 018621 0199973 PCI 2000 015839 015827 015652 018482 0199969 PCI 2001 016245 015574 015470 018367 0199951 PCI 2002 016227 015476 015589 018298 0199960 6,,, 82 %, 85 %, PCI HDI Spearman 9919 %, PCI HDI, PCI 1998, 015830,015689 015800, 015774,,, 1997 015637 2002 016227,,, PCI, : (1) 1990, ;, (2) 1990, GDP,, 31, 31 HDI,1 15,,, 7 13
: 7 HDI ( a 1 ) ( a 2 ) GDP ( a 3 ) PCI 1990 PCI 1995 PCI 1997 PCI 1999 PCI 2003 (1 15) 013569 014969 017910 017611 (16 30) 013729 019278-10129 018755 (1 15) 014076 013709 018345 018431 (16 30) 013829 019097 011605 019000 (1 15) 013451 012777 018965 018298 (16 30) 013753 019066 011930 018422 (1 15) 012911 013401 018942 018069 (16 30) 012619 019596 011028 018461 (1 15) 012795 013142 019073 018909 (16 30) 013504 019311 011011 018454 7,,,, GDP 1990 017910 2003 019073,, 8 ( ) GDP(PPP ) 1990 0177 010018 (2215 %) 3 0169 010023 (1714 %) 0174 010022 (2715 %) 0162 010101 (7615 %) 0153 010040 (5010 %) 0143 010008 (611 %) 1995 0177 010018 (2015 %) 0169 010023 (1616 %) 0178 010016 (1812 %) 0168 010105 (7515 %) 0162 010053 (6012 %) 0149 010011 (719 %) 1997 0176 010013 (1414 %) 0168 010022 (1812 %) 0177 010016 (1718 %) 0169 010085 (7012 %) 0165 010061 (6718 %) 0152 010013 (1017 %) 1999 0180 010011 (1018 %) 0172 010013 (1116 %) 0182 010023 (2215 %) 0173 010088 (7816 %) 0164 010068 (6617 %) 0151 010011 (918 %) 2003 0183 010009 (915 %) 0176 010018 (1517 %) 0185 010016 (1618 %) 0178 010086 (7418 %) 0174 010070 (7317 %) 0160 010012 (1014 %) : 3, 14
2005 7 8, GDP 1990 0153 2003 0174, 0121, 0111 0106,, GDP 1990 010040 2003 010070, 50 % 7317 %,,, ( ) ( ) 7, ( ),, 1997 011930,, 0190 8,, 0101, 75 %, GDP 01001, 10 %,,,, 2003 0148, 0178,,, HDI, GDP 1999 2003 012561 ( P = 013384) 012104 ( P = 013384),, GDP,,, : (1),,,,,, (2),,,, ;, ( ),, (3) (1) (2),,,,, 5, UNDP, HDI, : (1), Spearman, HDI, (2), UNDP HDI,, ( ),,, 15
:,,, HDI (3),,,,, UNDP 5, 1990,1990,,,,, ;,,,,,,,,,,,,,,,, ;,,, ( ),,,,,,,,,,,,,1997 : 1997 :,,1999 : 1999 :,,2002 : 2002 :,,,2005 : 2005 : ( ),2004 :, 11 Carlucci, F1 and S1 Pisani, 1995, A Multiattribute Measure of Human Development, Social Indicators Research, 361 Kelly, A. C., 1991, The Human Development Index : Handle with Care, Population and Development Review, 17. Lai, D., 2001, Temporal Analysis of Human Development Indicators : Principal Component Approach, Social Indicator Research, 51. Lai, D., 2003, Principal Component Analysis on Human Development Indicators of China, 61. Lind, N. C., 1992, Some Thoughts on the Human Development Index, Social Indicators Research, 27. Lind, N. C., 1993, A Compound Index of National Development, Social Indicators Research, 28. Luchters, G. and L. Menkhoff, 2000, Chaotic Signals from HDI Measurement, Applied Economics Letter, 7. Noorbakhash, F., 1998, The Human Development Indices : Some Technical Issues and Alternative Indice, Journal of International Development, 10. 16
2005 7 Rao, C. R., 1965, The Use and Interpretation of Principal Component Analysis in Applied Research, Sankhya A, 26. Ravallion, M., 1997, Good and Bad Growth : the Human Development Reports, World Development, 25. Sagar, A. D. and A. Najam, 1998, The Human Development Index, a Critical Review, Ecological Economics, 25. Sharma, S., 1996, Applied Multivariate Techniques, John Wiley & Sons, Inc. Srinivasan, T. N., 1994, Human Development : a New Paradigm or Reinvention of the Wheel?, American Economic Review, Papers and Proceedings, 84. Tang, K. L., 1999, Social Development in China : Progress and Problems, Journal of Contemporary Asia, 29. UNDP, 1997, China Human Development Report, Oxford University Press, New York. UNDP, 1999, China Human Development Report, Oxford University Press, New York. UNDP, 2002, China Human Development Report, Oxford University Press, New York. UNDP, 2004, Human Development Report 2004 : Cultural Liberty in Today s Diverse World. De Vires, W. F. M., 2001, Meaningful Measures : Indicators on Progress, Progress on Indicators, International Statistical Review, 69. An Alternative to Human Development Index with Principal Component Analysis Yang Yongheng, Hu Angang and Zhang Ning (Center for National Condition Study, School of Public Policy & Management,Tsinghua University) Abstract : In this study, we used the Covariance2based Principal Component Analysis ( PCA) to measure and analyze the progress of human development in Chinese provinces since 1990. The association of the main principal component obtained from our study and the China human development index reported by the United Nations Development Programme was estimated by the Spearman s rank correlation coefficient. This study suggested that PCA can be used as an effective alternative to traditional HDI technique. In addition, by examining the dynamic weight structure derived from PCA, we can track the changing roles of different aspects, like longevity, knowledge and decent standard of living, in the overall human development progress. Also found is that in China, seriously unbalanced developments have been found among the three aspects of human development, and the overall regional disparities of China have being increasingly attributed to regional economic disparities. The key to eliminate the unbalanced developments is to emphasize more on the role of government in public service delivery, and facilitate government transition towards service orientation. Key Words :China Human Development Index ; Principal Component Analysis ; Dynamic Weight Structure ; Disparity Patterns of Human Development JEL Classification :O180,I290,L190 ( : ) ( : ) 17