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Principal Component Analysis on Human Development Indicators of China Author(s): Dejian Lai Reviewed work(s): Source: Social Indicators Research, Vol. 61, No. 3 (Mar., 2003), pp. 319-330 Published by: Springer Stable URL: http://www.jstor.org/stable/27527078. Accessed: 12/12/2012 22:54 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at. http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Springer is collaborating with JSTOR to digitize, preserve and extend access to Social Indicators Research. http://www.jstor.org

DEJIAN LAI PRINCIPAL COMPONENT ANALYSIS ON HUMAN DEVELOPMENT INDICATORS OF CHINA (Accepted 2 July, 2002) ABSTRACT. In this study, we used the weighted principal component analysis to measure and analyze the progress of human development in Chinese provinces since 1990. The trends of the human development in the period of market transi tion in several provinces of China were discussed in terms of the impact on public health as well as economic development. The association of the main principal component obtained from our study and the human development index reported by the United Nations Development rank correlation coefficient. Programme was estimated by the Spearman's KEY WORDS: China, human development index, principal components, quality of life INTRODUCTION Since the first publication of the yearly Human Development Reports in 1990 by the United Nations Development Programme (UNDP, 1990-2001), the human development index (HDI) provided by the UNDP has been widely used in measuring the relative human development in all nations. Countries are ranked according to the HDI frequently in the literature and general public. The human development index is a composite number that values between 0 and 1. The greater value of the HDI indicates a relatively better human development. The HDI is computed as the average of the measurement in three dimensions: i) longevity index based on life expectancy, ii) educational attainment index based on the percentage of the literacy of the adult population and the children's school enrollment and iii) resource index based on the per capita GDP in the dollars of purchasing power parity ($PPP) (UNDP, 1990-2001). The merits and weaknesses have been a continuous debating topic in the literature (Ravallion, 1997; Sagar and Najam, * Social Indicators Research 61: 319-330,2003.? 2003 Kluwer Academic Publishers. Printed in the Netherlands.

320 DEJIANLAI 1998; Srinivasan, 1994). There are many modifications and exten sions proposed for the human development index (Kelly, 1991; McGillivray, 1991; Luchters and Menkhoff, 2000; Noorbakhsh, 1998a, 1998b). The human development index was initially used for moni toring the development of countries around the world. Later, the method has been applied to regions within a country for the purpose of quantifying the regional differences by the UNDP (http://www.undp.org) and scholars outside the United Nations agencies (Indrayan, Wysocki Chawla, Kumar and Singh, 1999; Tang, 1999). The UNDP has published two human development reports on China (UNDP, 1997, 1999). In the 1999's report on China, the HDIs were reported together with the related indicators for two years (1990 and 1997) for all 30 provinces in 1990 and 31 provinces in 1997 (three municipalities directly under the State Council in 1990 and four in 1997, twenty-two provinces and five autonomous regions) on the Chinese mainland. In computing the HDI of Chinese provinces, the life expectancy from the 1990 popu lation census were used for both years of 1990 and 1997 since there is a lack of yearly mortality data besides the data from the population census. It is well known that the three dimensional indicators of longevity (life expectancy), education (knowledge) and resource (standard of living) used in constructing the HDI are highly correlated (Noorbakhash, 1998b; Lai, 2000). In contrast to the simple average of each index for the three dimensions of human development, a multivariate analysis tool called the principal component method (Noorbakhash, 1998b; Lai, 2000) was used for finding an optimal linear combination of these indicators (Rao, 1965; Anderson, 1984). In the official publications of the UNDP and most of the scholarly articles in the literature, the values of these indicators were treated as if they were realizations of independent and identically distri buted random variables. However, in a recently article, a principal component analysis (PCA) weighted by the population size of each country was used to analyze the three dimensional data from each of the country published by the UNDP (Lai, 2000). Because, as it was pointed out in Lai (2000), one year increase of life expectancy at birth in a larger population such as that of China or India accounts

PRINCIPAL COMPONENT ANALYSIS IN CHINA 321 greater impact on the human development than that with a smaller population such as that of Gambia or New Zealand, the weighted principal component analysis is logically a better method in synthe sizing the multivariate data from widely varied population sizes of different regions. Another feature of using the principal component analysis (weighted or unweighted) is that the values of the prin cipal components are not confined into the interval of (0,1). Hence the PCA may be better than the HDI in measuring the differences between the areas with higher human development and the areas with lower human development. In this article, we applied the weighted principal component analysis on the data published in the 1999 Human Development Report of China by the UNDP (UNDP, 1999). The results from the weighted principal component analysis were compared to the HDI of each province in China using Spearman's rank correlation coefficient. The temporal trend of the values as well as the range of the first principal from 1990 to 1997 on several Chinese provinces were discussed. MATERIALS AND METHODS The UNDP's 1999 Human Development Report on China contains the data of the three dimensions of the human development for all the provinces on the Chinese mainland. We selected the life expec tancy, the adult literacy rate and the per capita GDP in purchasing power parity dollars ($PPP) for our principal component analysis. The same life expectancy in 1990 was used for both 1990 and 1997 since China can only provide the comprehensive mortality data for each province based on the population census. It is not an easy task to compare measurements of multiple dimensions. In our example, we want to compare the multi dimensional human development indicators of each province. For this purpose we need to synthesize the multi-dimensional meas urements into a one dimensional variable without losing much of the information. The principal component analysis has been used widely for this type of purpose (Rao, 1965). We summerize the technique as follows with the human development data of China in mind. Let X = (X\,..., be the Xp) p measurements for provinces

322 DEJIANLAI in China. For example, we may let X\ be the life expectancy, X2 be the adult literacy rate and X3 be the GDP per capita. The principal components are linear combinations of X\,..., The Xp. g-th prin cipal component is the (standardized) eigenvector corresponding to the q-th largest eigenvalue of the covariance matrix of the measure ments (Anderson, 1984). The correlation matrix is used when the measurements are in different scales such as the human development indicators. For the weighted principal component analysis, we used the weighted correlation matrix based on the weighted means and the weighted variances. In our study, the population province at 1990 (SSB, 1993) was used as the weight. size of each RESULTS To perform the weighted principal component analysis on the human development for the Chinese we provinces, computed the weighted correlation coefficients among the three indicators (life expectancy at birth, adult literacy rate and the per capita GDP in the purchasing power parity dollars). The weighted means of these three indicators were 68.66 (years), 78.08 (percent), 1730.63 ($PPP) and 68.66 (years), 83.77 (percent), 3249.82 ($PPP) for 1990 and 1997 respectively. The weighted means of the life expectancy were the same in 1990 and 1997 since the same life expectancy was used for both years. The weighted mean (68.66) of the life expectancy was very closed to 68.96, the life expectancy computed directly from life table (SSB, 1995). It would be better to use the life expectancy from the life table as the mean, however, for consistency with the other two indicators and the classic formula in computing the correla tion coefficient, we selected the weighted mean in our principal component analysis. It is also worth noting that the life expectancy at birth for China in 1990 was reported as 70 in the UNDP's 1990 human development report, whereas it was 68.9 in its 1997's report. The first principal component of the Chinese human development indicators in 1990 and 1997 were: and (1) P90 = 0.5819Xi,9o + 0.5357X2,90 + 0.6119X3,90, (2) P97 = 0.6402Xi,97 + 0.4345X2,97 + 0.6356X3,97,

PRINCIPAL COMPONENT ANALYSIS IN CHINA 323 respectively. Here Xij denotes the i-th indicator of the human development measured at the j-th year in the standardized form. The first principal component accounted for 68% and 64% of the total variation of the three human development indicators in 1990 and 1997 respectively. The standardization of the indicators was achieved by subtracting the weighted mean from the measurement and then dividing the remaining by the weighted standard deviation of the corresponding measurement. The rankings from the human development index and from the main principal component are highly correlated, although there were some discrepancies between these two rankings. The values of the Spearman's p were 0.9708 and 0.9730 for 1990 and 1997 respec tively. All autonomous regions (Xinjiang, Guangxi, Ningxia, Nei Mongol and Xizang (Tibet)) as well as provinces with high minority concentration and non coastal inland provinces were ranked after 15 with Xizang at the last by both methods. The human develop ment index increased for all provinces between 1990 and 1997. The ranges of the HDI and the main principal component were narrowed from 0.454 to 0.425 and from 10.813 to 8.997 respectively. For the two coastal provinces, Guangdong province (near by Hong Kong) and Fujian province (close to Taiwan), the open door policy was adopted right after the economic reform in the late 1970s and their speed of the human development index increase was faster than other provinces. The rank of the HDI for Fujian province increased from 14th in 1990 to 8th in 1997. Similar increase in the rank based on the main principal component was also observed for these two provinces. However, the relative positions of the human develop ment for the three industrious provinces (Heilongjiang, Liaoning and Jilin) in the northeast of China were lowered from 1990 to 1997. The detail results are given in Table I. The location of the provinces is provided in Figure 1. DISCUSSION In this article, we applied the weighted principal component analysis on the indicators of the human development for the Chinese provinces. This method was applied to analyze the progress of the human development for all countries reported in the United Nations'

324 DEJIANLAI TABLE I The Human Development Indicators of China: (a) Human Development Index, (b) Rank of the Human Development Index, (c) Main Principal Component, (d) Rank of the Main Principal Component (1990,1997) Province Pop. (1000) 1990 1997?) (b) (c) (d)l?) (b) (c) (d) Shanghai 13342 Tianjin 8785 Beijing 10819 Liaoning 39460 Guangdong 62830 Zhejiang 41446 Jiangsu 67057 Heilongjiang 35216 Jilin 24660 Shandong 84392 Shanxi 28759 Fujian 30048 Hainan 6558 Hebei 61083 Xinjiang 15157 Hubei 53970 Nei Mongol 21457 Hunan 60658 Guangxi 42245 Henan 85534 Shaanxi 32882 Sichuan 107218 Chongqing - Jiangxi 37710 Anhui 56181 Ningxia 4655 Gansu 22371 Qinghai 4457 Yunnan 36973 Guizhou 32391 Xizang 2196 0.861 1 4.881 1 0.788 2 3.635 2 0.769 3 3.419 3 0.701 4 2.269 4 0.681 5 2.162 5 0.640 6 1.173 6 0.637 7 1.076 7 0.625 8 0.627 9 0.612 9 0.612 10 0.608 10 0.602 11 0.601 11 0.690 8 0.593 12 0.077 14 0.592 13 0.396 12 0.584 14 0.261 13 0.573 15-0.892 21 0.570 16-0.410 18 0.560 17-0.734 19 0.556 18-0.378 17 0.554 19-0.041 15 0.549 20-0.237 16 0.544 21-0.878 20 0.530 22-0.977 22 0.527 23-1.205 24 0.527 23-1.137 23 0.535 25-1.413 25 0.499 26-2.157 26 0.494 27-3.143 29 0.490 28-2.596 27 0.466 29-2.837 28 0.387 30-5.932 30 0.877 1 2.975 1 0.852 3 2.314 4 0.867 2 2.634 2 0.831 5 1.870 5 0.843 4 2.356 3 0.821 6 1.493 6 0.817 7 1.309 7 0.766 10 0.617 10 0.710 12 0.361 13 0.770 9 0.573 11 0.679 16 0.221 14 0.802 8 0.761 8 0.709 13 0.468 12 0.730 11 0.664 9 0.685 15-1.089 22 0.707 14-0.217 16 0.645 21-1.140 23 0.662 17-0.420 18 0.649 19-0.374 17 0.661 18 0.021 15 0.617 25-1.087 21 0.617 24-1.295 24 0.635 22 0.635 22-0.878 20 0.646 20-0.568 19 0.603 26-1.754 25 0.570 28-2.049 26 0.528 29-4.690 29 0.583 27-2.551 27 0.516 30-3.013 28 0.452 31-6.022 30

PRINCIPAL COMPONENT ANALYSIS IN CHINA 3 25 Figure 1. The 1997 Human Development Index of China. Human Development Reports (Lai, 2000). As in the analysis of the world human development for the countries (Lai, 2000), we found similar strong correlation between the main principal component and the human development index for the Chinese provinces. For an easy reference, Figure 1 provides the location and the human development index in 1997 of the provinces on the Chinese mainland. It shows that the human development index was generally higher in the coastal regions than that of other inland provinces. The quantification of this spatial pattern is under further investigation. China has a very distinct administrative classification of its popu lation into two groups: agricultural and non-agricultural population. The non-agricultural population are mostly residing in cities with much better infrastructure for health care, education and employ ment. People in the cities enjoyed relatively higher level of standard of living, whereas, the agricultural population with about 80% of the total population are mostly living in rural areas with very primi tive or no infrastructure for modern health care and education. The employment opportunities for the agricultural people are generally restricted to farming. The health care and the education system in the rural areas in China have been improved greatly since the establish ment of the People's Republic of China in 1949. For example, the

326 DEJIANLAI barefoot-doctor system was created for most rural areas in the 60's and 70's. However, this system has disappeared in almost all rural areas since the reform. The number of elementary and secondary schools in the rural areas has been reduced also in favor of larger schools in big townships and cities following the reform. Nowadays, there exists a great disparity between the agricultural and non agricultural population in China. More studies on the differences of the human development between these two populations are needed. Up to now, the official information on the proportion of the poor in the rural areas is still not publicly available. But, according the author's personal communication to a senior official from the State Statistical Bureau of China, the survey results on the urban poor of China will be available to the public thanks to the assistance by the Asian Development Bank. With the limited arable land and increasing population, unem ployment or under employment is higher in rural China. Prior to the economic reform, the migration of agricultural population to the cities was forbidden. However, after the reform, this policy has been changed gradually. In the last decade, there have been large migra tion from the rural areas to the cities and from the inland provinces to the coastal areas. This migration has created a great effect on the quality of life of both agricultural and non-agricultural population and posed a challenge to the Chinese government and scholars in the academic. Since the increase of life expectancy and the strict family plan ning policy in China, the population is aging quickly (Lai, 1999). It is expected that the burden of taking care of the elderly will impact on other dimensions of the China's human development. Table II provides the percentages of the agricultural, 0-14 years and 65+ years population for each provinces according to the 1990 popula tion census (SSB, 1993) together with the life expectancy, the adult literacy rate and the GDP per capita in purchasing power parity extracted from the UNDP's China Human Development Report (UNDP, 1999). How to measure the multi-dimensional progress of human devel opment requires delicate and thorough understanding of the indi cators in various aspects because human beings live in a complex and dynamical social and environmental system. The measure

PRINCIPAL COMPONENT ANALYSIS IN CHINA 327 TABLE II The Human Development Indicators of China (continued): (a) Life Expectancy in 1990, (b) Adult Literacy (%) in 1990, (c) Adult Literacy (%) in 1997, (d) GDP Per Capita ($PPP) in 1990, (e) GDP Per Capita ($PPP) in 1990, (f) Agricultural Population (%) in 1990, (g) Young Population (0-14, %) in 1990, (h) Elderly Population (65+, %) in 1990 Province (a) (b) (c) (d) (e) (f) (g) (h) Shanghai 74.90 86.70 89.83 4771.17 4886.81 34.99 18.22 9.24 Tianjin 72.32 88.41 90.16 3907.06 4799.71 45.27 22.77 6.48 Beijing 72.86 89.19 92.36 3478.70 4826.34 41.09 2048 642 Liaoning 70.22 88.76 91.79 2911.14 4709.19 58.56 23.27 5.69 Guangdong 72.52 84.65 90.39 2584.21 4757.45 78.44 29.97 6.98 Zhejiang 71.78 77.53 81.62 2289.64 4758.86 84.24 23.29 6.87 Jiangsu 71.37 77.71 80.72 2269.14 4736.42 81.23 23.70 6.79 Heilongjiang 66.97 85.60 90.82 2188.21 4070.42 59.33 26.62 3.82 Juin 67.95 86.21 91.87 1883.93 3093.13 62.24 26.26 4.53 Shandong 70.57 77.62 77.36 1958.39 426542 86.55 26.90 6.23 Shanxi 68.97 87.09 90.13 1648.71 2661.53 79.04 28.27 5.54 Fujian 68.57 76.96 82.55 1929.25 4734.33 83.79 31.30 5.00 Hainan 70.01 7949 85.89 1714.53 3202.16 80.96 33.50 5.47 Hebei 70.35 78.37 85.70 1580.74 3416.27 86.26 29.08 5.08 Xinjiang 62.59 81.59 88.48 1941.12 3317.93 71.74 32.85 3.86 Hubei 67.25 77.48 84.95 1678.92 3315.12 80.98 28.41 546 Nei Mongol 65.68 78.85 83.22 1594.76 2636.24 69.76 28.37 4.01 Hunan 70.15 77.35 88.73 1325.01 2609.27 85.60 28.04 5.63 Guangxi 68.72 84.34 84.88 1150.21 2447.98 87.02 33.21 543 Henan 70.15 77.35 85.12 1177.19 2489.57 87.82 29.27 5.82 Shaanxi 67.40 75.04 82.66 1342.28 2083.26 82.33 28.94 5.18 Sichuan 66.33 78.64 82.00 1192.30 2264.21 85.78 23.17 5.74 Chongqing 66.33 - - - - - - - Jiangxi 66.11 76.04 87.53 1217.11 2335.02 82.74 31.75 5.08 Anhui 69.48 6647 79.83 1275.38 2467.09 86.45 28.41 5.38 Ningxia 66.94 67.52 74.17 1503.05 2261.97 76.65 33.54 3.38 Gansu 67.24 60.84 73.23 1185.82 1762.93 83.95 28.29 4.09 Qinghai 60.57 61.45 56.38 1681.08 2285.01 72.18 31.15 3.13 Yunnan 6349 6440 74.78 1320.70 2271.52 87.81 31.76 4.87 Guizhou 64.29 64.32 74.12 873.90 1244.78 88.09 32.53 4.64 Xizang 59.64 31.74 45.92 1376.80 1794.96 87.29 35.18 4.70

328 DEJIANLAI ments of the human development by the UNDP have inspired many researchers for proposing better and more effective index (Carducci and Pisano, 1995; Lind, 1992,1993; Noorbakhsh, 1998a). For synthesizing the multi-dimensional measurement of the human development index into a single indicator, the United Nations Reports used the equal weights for all indicators. This approach may be subjective. The principal component method is more objective since it selects the weights from an optimal criterion based on the correlation structure of the multi-dimensional indicator (Rao, 1965). The principal component method was used to analyze the regional inequality in Hungary (Quadrado, Heijman and Folmer, 2001). Recently, an extensive review on statistical indicators on social progress including the human development index was given by de Vires (2001). The weighted principal component analysis in our study used the population size of each province as the weights on the obser vations. We did not weight the variable in constructing the principal components since it is difficult to have an universally acceptable prior determination of the weighting scheme for these variables. However, the resulting principal components based on the equal weights of the variables would have unequal coefficients (weights) on the indicators. ACKNOWLEDGMENT The author thanks Dr. Chieh-Wen Hsu for his help in producing Figure 1 and his valuable comments. REFERENCES Anderson, T.W.: 1984, An introduction to multivariate statistical analysis (Wiley, New York). Carlucci, F and S. Pisani: 1995, 'A multiattribute measure of human develop ment', Social Indicators Research 36, pp. 145-176. de Vires, W.F.M.: 2001, 'Meaningful measures: indicators on progress, progress on indicators', International Statistical Review 69, pp. 313-331.

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330 DEJIANLAI United Nations Development Programme (UNDP): 1990-2001, Human develop ment report (Oxford University Press, New York). United Nations Development Programme (UNDP): 1997, 1999, China human development report (Oxford University Press, New York). International and Family Health Module School of Public Health University of Texas Health Science Center at Houston Houston, TX 77030 USA E-mail: dlai@sph.uth.tmc.edu