CHIP CHIP CHIP quantile method % 51.88% UTGI GDP 41.0% CHIP *1
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- たしろう ごみぶち
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1 DISCUSSION PAPER SERIES 灰 色 収 入 の 推 計 中 国 家 計 調 査 データによる 検 証 岑 智 偉 青 木 芳 将 土 居 潤 子 No 京 都 産 業 大 学 大 学 院 経 済 学 研 究 科 京 都 市 北 区 上 賀 茂 本 山 Graduate School of Economics Kyoto Sangyo University Motoyama-Kamigamo, Kita-ku, Kyoto, , Japan 2014/12/01
2 CHIP CHIP CHIP quantile method % 51.88% UTGI GDP 41.0% CHIP * % 50% JSPS Asia-Pacific Economic Association, Seoul, Korea, September 18-19, 2014 Kar-yiu Wong Corresponding author: cen25@cc.kyoto-su.ac.jp. *1 CHIP 3 1
3 GDP 29.5% CHIP CHIP
4 2010 (2010) 2010 *2 CHIP2007 *3 ( ) Ỹi i Y i i i C a C b C i = C a,i + C b,i S i i Ỹ i Y i + G i = C i + S i + G i (1) = C i + S i. 1 G i C i = C a,i + C b,i S i C a C b *4 β i β i β i = C a,i C i, β i = C a,i C i. (2) i z i z i G i ξ i (1 ξ i ) 1 * * % % % % % % % *4 A 3
5 Ỹ i = Y i + G i, = C a + C b + S i + z i G i + (1 z i ) G i, = (C a + ξ i z i G i ) + (C b + (1 ξ i )z i G i ) + (S i + (1 z i ) G i ), = C a,i + C b,i + (S i + (1 z i ) G i ) = C i + S i. (3) 1 2 Ỹi Y i β i 3 2 Ỹ i = C i + S i, = C a,i + (S i + (1 z i ) G i ), β i ( ) ( Ca,i ξ i z i + (1 z i ) = + S i + β ) i G i, β i β i ( ) Ca,i = + S i + ω i G i. (4) β i Y i 4 5 Ỹ i Y i = = = ( Ca,i Y i = C a,i β i + S i. (5) ) + S i + ω i G i β i C ) a,i + ω i G i, β i β i ( Ca,i ( β i β i β i β i ) ( Ca,i β i + S i ), C a,i + ω i G i. (6) 2010 Ỹi Y i Ỹi Y i β i = β i β i = β i ω i = 1 *5 G i 2.2 *6 *5 B * setp1 7 Per Capita Annual Living Expenditure of Urban Households 7 β 1 β 7 step2 e β 1 = β 1,, e β 7 = β 7 7 step3 7 ey 1 ( e β 1 = β 1 ),, ey 7 ( e β 7 = β 7 ) step4 y i ey i 4
6 ( ) * ,462 32, , ,577 ( 15,269 ) % 90.43% CHIP CHIP CHIP CHIP Chinese Household Income Project 1988 Keith Griffin Carl Riskin John Knight CHIP 2007 CHIP CHIP2007 * CHIP urban rural 2 urban *9 *7 6 step1 step4 1 Estimation Value (a) e β i = β i 1 Estimation Value (b) Estimation Value (a) Estimation Value (b) eβ i = β i 6 2 * CHIP 2008 CHIP 2007 CHIP *
7 ( 2 ) 2 CHIP2007 * 10 ( 3-a ) ( 3-b ) CHIP2007 CHIP2007 CHIP CHIP a Engel s coeffecient CHIP a Obs CHIP CHIP CHIP CHIP b 1 ( 1 ) CHIP *10 step Per Capita Annual Living Expenditure of Urban Households 7 7 step2 step1 7 CHIP step3 7 CHIP2007 step4 Step3 ey i y i 6
8 ( 4 ) 4 2 ( 2 ) % 1975 CHIP2007 CHIP i U i = C µ a,i a,i C µ b,i b,i. 1 * 11 β i = C a,i µ a,i =. C i µ a,i + µ b,i µ a,i,µ b,i * 12 β i = β i k( ) l β i,k = β i,l 4 µ a,ik,µ b,ik,µ a,il,µ b,il * 13 CHIP2007 CHIP β i,k = β i,l β i,k = β i,l *11 A *12 A *13 A 7
9 2010 β i = β i CHIP β i = β i i Ỹi β i β i ω i 1 6 Ỹ i = ( β i β i β i β i ) C a,i + Y i + ω i G i, Q i Ỹi Θ i = Y i + ω i G i (7) Θ i ( βi β i β i β i ) C a,i β i β i β i β i β i β i Θ i Q i Y i = ω i G i Q i CHIP i Ỹi Θ i * 14 7 Q i Y i i = 1 7 * 15 Q i Step1 CHIP Ỹi Step2 Step1 β i, i = 1 7 β i β i i Step3 Step4 Step1 Ỹi i Q Q i Y i 5a 5b ( 5-a ) *14 β i > e β i Θ i ey i β i < e β i Θ i ey i *15 > 0 β i > e β i Q i < ey i < 0( β i < e β i ) Q i > ey i 8
10 ( 5-b ) 5a Step1 Ỹi Y i 5a 5-a 3 ( 3 ) 3 CHIP2007 i Q i Ỹi i 5-b Ỹi i Q i Y i 5-b 4 ( 4 4 5b a 5-b CHIP Ỹi a Q i b Ỹi Q i Q i 98.48% Q i % 6a 6b 2010 β i = β i 1 Ỹi 2010 Q i 2010 * 16 ( 6-a ( 6-b GDP 17.5% 29.5% (1) 7 Per Capita Disposable Income * 17 (2) Total Disposable Income of Urban Households (3) Total Disposable *16 4 *17 (1) 9
11 Income * 18 ( Urban Total Gray Income UTGI Aggregate Gray Income AGI UTGI= - AGI= - Total Estimation Income of Urban Households 5 6 Ỹi Q i Total Estimation Income of Households Total Net Income of Rural Households 7 1 Annual Per Capita Net Income of Rural Households AGI UTGI AGI 7a 7b Ỹi Q i 1 UTGI AGI GDP ( 7-a ( 7-b 7-a 7-b CHIP UTGI Ỹi 7-a GDP 33.3 % 41.2% Q i 7-b GDP 41.0% 48.7% * 19 2 AGI Ỹi 7-a GDP 18.8% 26.7% Q i 7-b GDP 26.5% 34.2%% (3) AGI UTGI 2 1 AGI UTGI Total Disposable Income of Urban Households 9.0 Total *18 (1) Basic Conditions of Urban Households 7 Per Capita Annual Income (3) Flow of Funds Accounts Physical Transaction Total Disposable Income (2) Basic Statistics on People s Living Conditions Annual Per Capita Disposable Income of Urban Households *19 /
12 Disposable Income AGI UTGI 4 Discussion 3 5-b CHIP2007 i (i = 1,, 7) 7 Q i Ỹi 5-a Q i 7 G i ω i β i β i ω i 1 CHIP2007 β i > β i ω i > 1 * 20 ω i > 1 CHIP ω i > 1 β i > β i * CHIP *20 B *
13 3 CHIP2007 CHIP % UTGI GDP 41.0% CHIP CHIP G i ω i G i ω i ω i 2 CHIP 6 References 1. Wang, Xiaolu 2007 Gray icome and income difference National Economic Research Institute, China Reform Foundation Wang,Xiaolu 2010 Gray income and distribution of national income Comparative Studies, No Wang,Xiaolu 2011 Gray income has been exaggerated? Comparative Studies, No Wang,Xiaolu 2012 Gray income and development trap, CITIC Press Group. 12
14 5. Li,Shi(1993), The income distribution of China s economic development, Peking University Press. 6. Li Shi, Renwei Zhao and Ping Zhang (1998) Changes in income distribution in China s economic reform Management World, No.1, Li Shi and Zhao Renwei(1999) The residents income distribution in China Economic Research Journal, No Wang,Xiaolu and Fan Gang (2005) China s income gap trend and influence factors analysis Economic Research Journal, No.10, Luo Chuliang Ximing Yue and Shi Li 2011 A Question about Gray income estimation of Wang Xiaolu Comparative Studies, No.52. A. G ( ) µa ( ) µb Max U = Ca Cb, s.t. y + G S = Ca + C b, (µ a, µ b ) (0, 1) C a, C b C a C b 1 y + G S = s y + G), s * 22 y G C a C b ( ) µa C a = (1 s) (y + G), µ a + µ b ( ) µb C b = (1 s) (y + G). µ a + µ b C = C a + C b β = ( ) C a µa (1 s) (y + G) C a + C = b µ a + µ b (1 s) (y + G), = µ a µ a + µ b. (A1) *22 13
15 A1 G µ a, µ b B i β i β i β i β i = C a,i C i C a,i C i = C a,i Ỹ i S i C a,i Y i S i = = (C a,i + ξ i z i G i ) (Y i S i ) (Y i + z i G i S i ) C a,i (Y i + z i G i S i ) (Y i S i ) C a,i Y i + G i (S i + (1 z i ) G i ) C a,i Y i S i, = ξ iz i G i (Y i S i ) z i G i C a,i (Y i + z i G i S i ) (Y i S i ), = (ξ i (Y i S i ) C a,i ) z i G i (Y i + z i G i S i ) (Y i S i ) = (ξ i β i ) (Y i S i ) z i G i (Y i + z i G i S i ) (Y i S i ). (A2) A2 β i β i ξ i β i β i ξ i β i. (A3) ξ i Y i β i ξ i ξ i > β i β i > β i ξ i β i = β i A3 ξ i = β i = β i 4 ω i ω i = ξ iz i + (1 z i ) β i β i = 1, 14
16 15 Figure1 Per capita income estimated by the method of Engel s coefficient(by table 3-b) 50,000 40,000 The value by NBSC Estimation Value Difference 30,000 20,000 10, group 2-group 3-group 4-group 5-group 6-group 7-group -10,000 Figure 2 Per capita income estimated by the method of Engel s coefficient(by table 4) Estimation Value The value by NBSC Difference other 1-group 2-group 3-group 4-group 5-group 6-group 7-group
17 16 Figure 3 Per capita income estimated by decile and quintile (by table5a) 90,000 80,000 70,000 60,000 50,000 40,000 30,000 20,000 10, decile 2-decile 2- quintile 3- quintile 4- quintile 9-decile 10-decile Per Capita Annual Income(NBSC) Engel s coeffecient(nbsc,right) Per Capita Annual Income(EV) Engel s coeffecient(ev,right) Figure 4 Per capita income estimated by decile and quintile (by table5b) 120,000 The value by NBSC Adjusted estimated value Difference 100,000 80,000 60,000 40,000 20, decile (10%) 2-decile (10%) 2- quintile (20%) 3- quintile (20%) 4- quintile (20%) 9-decile (10%) 10-decile (10%)
18 17 Table1 Estimates of the "gray income" of Wang (2010) Engel s coeffecient (a) Estimated value (a) (b) Estimated value (b) (c) The value by NBSC (d) a-c (e) b-c di Σdi*100 ei Σei*100 1-decile(10%) ,685 5,350 4, decile(10%) ,646 7,430 7,363 1, quintile(20%) ,392 11,970 10,196 3,196 1, quintile(20%) ,941 17,900 13,984 6,957 3, quintile(20%) ,910 27,560 19,254 10,656 8, decile(10%) ,772 54,900 26,250 21,522 28, decile(10%) , ,000 43, ,420 95, Average ,462 32,154 16,885 18,577 15,269 sum 164, , Note: The NBSC is an abbreviation of National Bureau of Statistics of People's Republic of China
19 18 Table2 Basic statistics of the CHIP2007 Variable Obs Mean Std.Dev. Min Max Per Capita Annual Income of Urban Households Consumption Expenditure Food Expenditure Engel's Coefficient Table 3-a Estimates of the "estimated income" by the Engel coefficient method using CHIP2007 (calculation method) Engel s coeffecient Per Capita Annual Income of Urban Households(RMB) Mean Obs Percentage of observations Min Max
20 19 Table3-b Estimates of the "estimated income" and "gray income" by the Engel coefficient method using CHIP2007 (estimation results) Estimated value The value by NBSC (c) Difference The ratio of deviation Engel s coeffecient (a) Per capita annual income of urban households Number of observations Engel's coefficient (b) Per capita annual income of urban households (a-b) c b (%) ci Σci (%) 1-group group group group group group group Average Sum
21 20 Table 4 Estimates of the "estimated income" and "gray income" by Engel's coefficient method using CHIP2007 (incomplete estimation results) Estimated value The value by NBSC (c) Difference The ratio of deviation Engel s coeffecient (a) Per capita annual ncome of urban households Percentage of observation Engel's coefficient (b) Per capita annual income of urban households (a-b) c b (%) ci Σci (%) other group group group group group group group Average Sum
22 21 Table5a Estimates of the "estimated income" and "gray income" by quantile method using CHIP2007 Estimated value The value by NBSC (c) Difference The ratio of deviation Engel s coeffecient (a) Per capita annual income of urban households Percentage of observations Engel's coefficient (b) Per capita annual income of urban households (a-b) c b (%) ci Σci (%) 1-decile(10%) decile(10%) quintile(20%) quintile(20%) quintile(20%) decile(10%) decile(10%) Average Sum decile /Tota (%) decile/Total (%)
23 22 Table5b Estimates of the "adjusted estimated income "and "gray income" by quantile method using CHIP2007 Engel s coeffecient Estimated value (a) Per capita annual income of urban households Percentage of observations The value by NBSC Engel's coefficient (b) Per capita annual income of urban households (c)food expenditure (d)gap of Engel's coefficient (e) Adjusted estimated value (f) Difference (e-b) The ratio of deviation 1-decile(10%) decile(10%) quintile(20%) quintile(20%) quintile(20%) decile(10%) decile(10%) Average Sum decile /Tota (%) f b (%) fi Σfi (%) 10-decile/Total (%) Note: (d) is calculated as( β i β i β i βi ) C a,i, (e) is calculated as equation (9).
24 23 Table6a Estimates of the "estimated income"and "gray income" by the income class classification of Wang (2010) using the CHIP2007 Estimated value The value by NBSC (c) Difference The ratio of deviation Engel s coeffecient (a) Per capita annual income of urban households Percentage of observations Engel's coefficient (b) Per capita annual income of urban households Percentage of observations (a-b) c b (%) ci Σci (%) y y y y y y y Average Sum y 7000 Total (%) y Total (%)
25 24 Table6b Estimates of the "adjusted estimated income "and "gray income" by the income class classification of Wang (2010) using the CHIP2007 Engel s coeffecient Estimated value (a) Per capita annual income of urban households Percentage of observations The value by NBSC Engel's coefficient (b) Per capita annual income of urban households (c)food expenditure (d)gap of Engel's coefficient (e) Adjusted estimated value (f) Difference (e-b) The ratio of deviation y y y y y y y Average Sum y 7000 Total (%) y Total (%) Note: (d) is calculated as( β i β i β i β i ) C a,i (e) is calculated as equation (9). f b (%) fi Σfi (%)
26 25 Table7a Estimation results of size of "gray income" using the "estimated income" Estimation(1) (by table 5) Estimation(2) (by table 6) Estimates of Wang (by table1(a)) Estimates of Wang (by table1(b)) (1) Total Net Income of Rural Households (100 million yuan) (a b) a. Annual Per Capita Net Income of Rural Households (yuan) b.rural Population(100 million persons) (2) Total Disposable Income of Urban Households (yuan) (c d) (3) Total Estimation Income of Urban Households (100 million yuan) (e d) c.annual Per Capita Disposable Income of Urban Households (yuan) d.urban Population(100 million persons) e.annual Per Capita Estimation Income of Urban Households (yuan) (4) Total Income of Households (100 million yuan) (1+2) (5) Total Estimation Income of Households (100 million yuan) (1+3) (6) Total Disposable Income(100 million yuan) (7) Urban Total Gray Income (UTGI, 100 million yuan) (3-2) (8) Aggregate Gray Income (AGI, 100 million yuan) (5-6) (9) GDP(100 million yuan) (10) Urban Total Gray Income (UTGI) to GDP ratio(%) (7 9) (11) Aggregate Gray Income(AGI) to GDP ratio(%) (8 9) Note: a ~ d, (6), (9) is the published data of China Statistical Bureau, others are calculated in this paper. In addition, e in Table 9a is the estimated value of Table 5a and Table 7a.
27 26 Table7b Estimation results of size of "gray income" using "adjusted estimated income" Estimation(1) (by table 5) Estimation(2) (by table 7) Estimates of Wang (by table1(a)) Estimates of Wang (by table1(b)) (1) Total Net Income of Rural Households (100 million yuan) (a b) a. Annual Per Capita Net Income of Rural Households (yuan) b.rural Population(100 million persons) (2) Total Disposable Income of Urban Households (yuan) (c d) (3) Total Estimation Income of Urban Households (100 million yuan) (e d) c.annual Per Capita Disposable Income of Urban Households (yuan) d.urban Population(100 million persons) e. Adjusted Annual Per Capita Estimation Income of Urban Households (yuan) (4) Total Income of Households (100 million yuan) (1+2) (5) Total Estimation Income of Households (100 million yuan) (1+3) (6) Total Disposable Income(100 million yuan) (7) Urban Total Gray Income (UTGI, 100 million yuan) (3-2) (8) Aggregate Gray Income (AGI, 100 million yuan) (5-6) (9) GDP(100 million yuan) (10) Urban Total Gray Income (UTGI) to GDP ratio(%) (7 9) (11) Aggregate Gray Income(AGI) to GDP ratio(%) (8 9) Note: a ~ d, (6), (9) is the published data of China Statistical Bureau, others are calculated in this paper. In addition, e in Table 9b is the estimated value of Table 5b and Table 7b.
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