26 3 :,,,,,,,,, :,:,,,,,,(995) (999,p. 49) :,;,,,, (,24 ;,999 ;,2 ;,995) (24),, 33. 3 %2 %, 5 % 2 %,:,, 33. 3 %, ;(,24) (22,p. 26 29), 988 998 3,,872, : chengyonghong @mparuc. edu. cn,, 5&ZD49 ;,;,,,, 9 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net
:,,,,, Sundrum, R. M(99,p. 5), : G P, G 2 2 P 2,, G : G = P 2 G + P 2 2 2 G 2 + P P 2 2 -, :,,995, 26 % % (,22),, Sundrum,(24) Sundrum,,, Cowell (2) :,,,: G = n W i G i + I b + ( f i ) i =, G ; G i i ( i =,2,, n), W i G i,i ; I b,;( f i ),f i,,, ( f i ) = Silber (989),Yao, Shujie (999) (23) ( ),,,, :Mookherjee and Shorrocks (982) ; Silber (989) Lambert and Aronson (993),, :,,, (,998),,,,,; ;, ;,99,; G, () : 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net
26,I,, I,: P{ I < t} = F( t) () :t F ( t),,, (997) ; (998) : x = F( t) (2) y = L ( x) : y = N t tdf( t) (3) W,, y = L ( x), N, W x = F( t) t ( N) x ; t N ; y N ;y (3),y W : W = yw = t N tdf( t) (4) (),L ( x) y = x a : :,L ( x) y y [, ] S (2) : (3) : S = xdy (5) x = F( t) (6) dy = N W tdf( t) (7) :y = t ;y = t,, (6) (7) (5),, :, : S = N W S = N W 2 t F2 ( t) - F( t) tdf( t) (8) 2 F 2 ( t) dt (9) F() F ( ), : ; (,) ;, ;(, ) ; :, ΠN ;, ; N -, - ΠN,,t =,: lim F( t) = F( - ) =, () t - lim F( t) = F( + ) = ΠN () t +,, ΠN ;,, t > F( t) ; N -, - ΠN,, 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net
: t =,: lim F( t) = F( + ) = (2) t + lim t - F( t) = F( - ) = - ΠN (3), N, F(), ; F( ), () (2) (9), : S = N W 2 - y = x a : a = S - () a G : 2 = N W 2-2 F 2 ( t) dt (4) 2, G a : F 2 ( t) dt - G = 2 a = N - W F 2 ( t) dt - (6) Kendall and Stuart (977) Dorfman(979) Yizhaki (982) Lambert (989) (,23),, : W, (3) F( - ) : 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net 2 (5) = F - ( - ΠN ) (7) (4),W W t =,,(4) : (8) (6), : F( t) dt = A, W = N tdf( t) = N G = - - F 2 ( t) dt F( t) dt F 2 ( t) dt = B, (9) : G = u, (8) : - B - A - = A - B - A - F( t) dt (8) - (9) u = W ΠN = - F( t) dt = - A (2),,,, 2 (2)
26 () G : : (), G, G, (2) G, : = G dg d = daπd - dbπd) ( - A) - ( A - B) ( - daπd) ( G ( - A) 2 A B : daπd = F( ), dbπd = F 2 ( ),, : = G [ F( ) - F2 ( ) ] ( - A) - ( A - B) ( - F( ) ) ( - A) 2 = G ( - F( ) ) F( ) - ( A - B)Π( - A) - A (2) (2) : ( A - B)Π( - A) = G, - A = u, : = G ( - F( ) ) F( ) - G u (2) (3) F( t) t = (22a) F( ), : = G N - G u = - G W G (22b), G.,( - G)ΠG <,W,ΠW,, G,, G (22a) (22b) (6),,,,,,,F ( t) F 2 ( t) ; N N 2 ; I I 2 N, N = N + N 2 ;I, F( t) ;,, = max(, ) :, t F ( t), N F ( t) ;, t F 2 ( t), N 2 F 2 ( t) ;, t M = N F ( t) + N 2 F 2 ( t), MΠN = ( N F ( t) + N 2 F 2 ( t) )ΠN, : P{ I < t} = N F ( t) + N 2 F 2 ( t) N : F( t) = N F ( t) N + N 2 F 2 ( t) N (23) N ΠN =, N 2 ΠN =,,, 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net 3
:,+=, : F( t) = F ( t) + F 2 ( t) (24) (24) (6),G n ( >, = max(, ) =, max(, ) ) : G n = - (F - (F + F 2 ) 2 dt + F 2 ) dt, : F dt = A, t >, F 2 ( t) =, F 2 dt = A 2, F 2 dt = B, F 2 dt = -, F 2 2 dt = F 2 dt = F 2 2 dt + - (25) F 2 2 dt = B 2, F 2 2 dt = -, : F 2 2 dt = B 2 + ( - ), F 2 dt + (25),(26),: F 2 dt = A 2 + ( - ) G n = - [ 2 B + 2 B 2 + 2 C + 2 ( - ) ] - [+ A 2 + ( - ) ] A F F 2 dt = C (26) - (27),G n,,,,, G n,(,24), u u 2 u, (2) (2) : - [ A + A 2 +( - ) ] = u,a - B = u G,A 2 - B 2 = u 2 G 2 (27) : G n = ( A - 2 B ) + ( A 2-2 B 2 ) + [( - ) - 2 ( - ) ] - 2 C u += A - B = u G, A - 2 B : A - 2 B = ( A - ( - ) B ) = ( A - B + B ) = u G,(27a) : A 2-2 B 2 = ( A 2 - ( - ) B 2 ) = ( A 2 - B 2 + B 2 ) = u 2 G 2 ( (27b) (27d) (27a), : 4 + B + B 2 (27a) (27b) (27c) - ) - 2 ( - ) = ( - ) ( - ) = ( - ) (27d) G n = u u G + u 2 u G 2 + ( B + B 2-2 C + - ) u 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net (28)
(26) B B 2 F 2 ( t) :, C, : F 2 2 dt = -, B + B 2-2 C : B + B 2-2 C = (28a) (28b) (28), : ( F 2 + F 2 2-2 F F 2 ) dt - G n F 2 2 dt = F 2 2 dt = F 2 2 dt - F 2 2 dt ; t > ( F - F 2 ) 2 dt - ( - ) (28a) D = ( F - F 2 ) 2 dt (28b) = u u G + u 2 u G 2 + u D (29) u = W ΠN, u 2 = W 2 ΠN 2, u = W ΠN (29) : G n = W W G + W 2 W G 2 + u D (3), W ΠW W 2 ΠW,W ΠW, W 2 ΠW -,, (3) : 26 G n = G + ( - ) G 2 + D u (3) G n D :,( ),, ( ; ) ;, :, F F 2,,, F F 2,() () ( ),;,,,:,,, F F 2 (F F 2, ), (, t ),,,, (Johnson, G., 22),;, ( ),,,, ( ) 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net 5
:, D D (28b), D = F F 2, D > F F 2,, D,D,F F 2, D ( ), D F F 2 ( ;, F - F 2 ( F - F 2 ) 2, ) F F 2 ( a ),F > F 2 (F < F 2 ), () ( ) ( ) ( ), ( F - F 2 ) 2 t ; D ( ), F F 2, D F F 2 ( b ),D :, D () (),, D () (), ( ), F F 2, D, F F 2, D,D, D ( ) ( ),,( b ),,( ),, D, ( ) (,25) Cowell (2) :, D,,D, ;D u, DΠu,,,,, : DΠu = G 3,(3) : G n = G + ( - ) G 2 + G 3 (3a), (3) : 6 Sundrum, R. M(99,p. 5),, 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net
26 G G2 :, : D, D,,,, (Dollar, D. and Kraay, A., 2 ;,24),, 99 : (), F F 2 99,,( ) 99 t F t F 2 t F t F 2. 45 72. 738 6. 5589 44. 5656 5. 39 84. 39 8. 7445 56. 6452 2. 359 96. 24. 849 68. 795 3. 38 8. 288 5. 952 8. 7776 4. 2752 2. 3755 2. 9823 5. 4263 32. 4739 : 99 (,99,p276 294),, ;,,,,,, t. 5,, : F( t) = Π( + ae - bt. 5 ) (32), a b, F F 2 t, a b,,,(32),: : (33) : ln (ΠF - ) = ln a - bt. 5 (33) ln (ΠF - ) = y, - b = p, ln a = q, t. 5 = x (34) y = px + q (35), p q, y x F t (34) Matlab y x 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net 7
:, p q,(34) (32) a b 2 p q, a b R 2, 2 99 q p R 2 Adj2R 2 SSE a b 63. 7-45. 95. 9995. 9995. 4267 2. 788E + 27 45. 95 8. 9-57. 3. 9999. 9999. 8 3. 746E + 35 57. 3 (),, A A 2 B B 2 C,Gn :,,,,,,,, (7) (32), : = F - - = F - 2 - = ln a + ln ( N - ) N b = ln a 2 + ln ( N 2 - ) N 2 b 2,a b, a 2 b 2, F F 2,, (26), Matlab,A A 2 B B 2 C, 3, (27) (3) G n (27) 3, (3) 4 6,(3) 3 (27) 4 2 2, (3) N 753 8626 34. 583 756. 845 A 659. 499 743. 45268 B 447. 2983 73773. 57588 u 68. 9 479. 639 G. 355. 2487 =. 672 =. 3298 C 986. 7879 G n. 354368 u 68. 5 479. 58 =. 672 =. 3298 =. 4833 - =. 567 G. 355. 2487 u 944. 3555 D 336. 7966 G n. 354368 : u : N N 2 99 (,99) (p276 294) (p79) ; N N 2 8 :,= u N Π( u N + u 2 N 2 ),,, u u 2 ; N N 2, ; : 99 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net
26 () 4 (3a), G G 2 G 3, G n r r 2 r 3 : r = 42. 49 %, r 2 = 35. 27 %, r 3 = 22. 24 %,(Lee,2,:,25 ;,996), (24 25) :,, 85 %,,, :,,,,,,,, :,,,,,, :,,,,24 :, 8,2 :, 7,22 :, 5,22 :,,998 :,,24 :, 5,24 :, 9,995 :,,23 :,2 2,2 :, 7,22 :, 5,999 :, 4,998 :, 4,997 :, :,999 :,, :,25 :, 3,24 ::,,2 :, 8,996 :,,23 :,2 4 9 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net
: Holland.,999 :, Cowell, A., 2, Measurement of Inequality, in Handbook of Income Distribution, eds by A. Atkinson and F. Bourguignon, North Brown, J. A. C. and Mazzarino, G., 984,Drawing the Lorenz Curve and Calculating the Gini Concentration Index from Grouped Data by Computer. Oxford Bulletin of Economics and Statistics. Oxford : Aug 984. Vol. 46, Iss. 3 ; pg. 273. Dollar, D. and Kraay, A., 2, Growth is Good for the Poor, Mimeo, World Bank, Washington D. C., Policy Research Working Paper, 2587, 9. Griffin. Dorfman, Robert, 979,A Formula for the Gini Coefficient, Review of Economics and Statistics, 6, 46 49. Johnson, G., 22,978,?, 3 Kendall, Maurice G., and Alan Stuart, 977, the Advanced heory of Statistics, Vol., Distribution heory, 4th ed. London : Charles Lambert, Peter, J., 989, the Distribution and Redistribution of Income : A Mathematical Analysis, Cambridge, Massachusetts : Basil Blackwell Inc. Lambert, Peter J. and J. Richard Aronson, 993,Inequality Decomposition Analysis and the Gini Coefficient Revisited, he Economic Journal, 3, 22 227. Lee, J, 2,Changes in the source of Chinaπs Regional Inequality, China Economic Review, (3),pg232 45. Ogwang, omson, 2,A Convenient Method of Computing the Gini Index and its Standard Error. Oxford Bulletin of Economics and Statistics. Oxford : Feb 2. Vol. 62, Iss. ; pg. 23. Sundrum, R. M, 99, Income Distribution in Less Developed Countries, Routledge, Londen and New York. Silber, Jacques, 989,Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality. he Review of Economics and Statistics, Vol. 7,No. (Feb., 989), pg 5. Yao, shujie, 999, On the Decomposition of Gini Coefficients by Population Class and Income Source : a Spreadsheet Approach and Application,Applied Economics, 999,3,249 264. 85. Yizhaki, Shlomo, 982,Stochastic Dominance, Mean Variance and Giniπs Mean Difference,American Economic Review,982,72,78 Calculation and Decomposition of the Overall Gini Coefficient in Dual Economies Cheng Yonghong ( Institute of Social Security, School of Public Administration, Renmin University of China) Abstract :he calculating methods of Gini Coefficient have been very abundant, but it has not been settled that how to calculate the overall Gini Coefficient including city and country in dual economies, which blocks deeply researches in the countrywide income distribution. his paper sets up a new calculating method of the overall Gini Coefficient, and gives a new decomposition method of the overall Gini Coefficient. Moreover, we put forward and reason a new index about the disparity between the rural and the urban. hen, we analyzed some theoretical questions by use of the new decomposition method. At last, we calculated and decomposed the overall Gini Coefficient of individual year in China to test the validity of the new method. Key Words : the Overall Gini Coefficient Including City and Country ;Decomposition of the Overall Gini Coefficient ;Relative Index of Disparity Between City and Country JEL Classification :D63, D3 ( :) ( : ) 2 994-2 China Academic Journal Electronic Publishing House. All rights reserved. http://www.cnki.net