r/s and wavelet analysis on evolutionary process of regional economic disparity in china during past...

8/13/2019 R/S and wavelet analysis on evolutionary process of regional economic disparity in China during past 50 years

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CH1NESE GEOGRAPH ICAL SCIENCEVolume 14, Num ber 3, pp. 193-201, 2004Science Press, Beijing, China

R S A N D W A V E L E T A N A L Y S IS O N E V O L U T I O N A R YP R O C E S S O F R E G I O N A L E C O N O M I C D I S P A R I T YI N C H I N A D U R I N G P A S T 5 0 Y E A R S

X U J i a n - h u a 1 L U Y a n 3, S U F a n g - l i n ~, A I N a n - s h a n 4(1. Department of Geography, Ea st China Normal University, Shanghai 200062, P. R. China; 2. Institute of

Geographic Science s and N atural Resources Research, Chinese Academy of Sciences, Beijing 100 101, P. R. China;3. Sch ool of Environment Wa ter Conservancy, Zhengzhou University, Zhengzhou 450 052 , P. R. China;

4. Architecture Environment College, Sich uan University, Chengdu 6100 65, P. R. C hina)

A B S T R A C T This paper shows the dynam ic process of regional dispari ty of economic development in C hina in thepast 50 years from a new insight by using the rescaled range statistic (R/S) analysis and wav elet analysis of the Theilindex sequen ce with different time scales. The main conclusion s are: 1) The regional disparity o f econom ic deve lop-ment in China, including the inter-provincial disparity, inter-regional disparity and intra-regional disparity, has exist-ed for man y years. Theil index by the comparative price has revealed the true trend for comparative dispari ty o f re-gional economic dev elopment from 1952 to 200 0.2 ) Decomposit ion of Theil index indicates that the dynamic trendof comp arative inter-provincial d isparity in the coastal region is in line with dyna mic trend o f inter-provincial dispa r-i ty in the whole China. 3) The R/S analysis results tell us that during 1966-1978, the Hurst exponent H =0 .50 4~ 0.5 ,which indicates that in that period the evolution o f comparative inter-provincial disparity o f economic developm entshowed a random characterist ic, and in the other periods, i .e. 1952 -1965, 1979-1990 and 199 1-2000, the Hurst ex-ponen t H>0.5, which indicates that in those periods the evolution of the comparative inter-provincial disparity of e-conom ic developmen t in China had a long-end uring characteristic. 4) By using wave let analysis at different timescale, we arrived at a conclusion that the evolutionary process o f the disparity of economic development of China isnot a simple inverted U shape but a compound of several U shapes. The result tells us that the evolutionary plot ofinter-provincial disparity in China follows the inverted U on the who le at the higher scale, 24 (16 years). Th at is tosay, the dispari ty tends to rise in the first stage of economic development, and fal l slowly over the peak in the secondstage of economic development. However, i f we shorten the time scale to 23 (8 years), then a l ink of several Ushapes will appear.K E Y W O R D S China; regional economic disparity; Theil index; R/S analysis; wavelet analysisCLC number: TP79; F124 Docum ent code: A Article ID: 1002-0063(2004)03-0193-09

1 I N T R O D U C T I O NT h e r e h a v e b e e n m a n y l i t e r a t u r e s a b o u t t h e r e g i o n a ld i s p a r i ty o f e c o n o m i c d e v e l o p m e n t i n C h i n a s i n c e t h el a t e 1 9 7 0 s . S o m e s c h o l a r s a r g u e t h a t d i s p a r i t y o f r e -g i o n a l d e v e l o p m e n t i n C h i n a h a s b e e n e x p a n d e d s i n c e1 9 7 8 , b u t o t h e r s f i n d i t h a s r e d u c e d s i n c e 1 9 7 8 . T h ef i n d in g s o f s o m e s c h o l a r s s h o w t h a t th e e v o l u t i o n a r yp r o c e s s o f t h e d i s p a ri ty o f re g i o n a l e c o n o m i c d e v e l o p -m e n t i n C h i n a f o l l o w s t h e i n v e r te d U s h a p e , b u t s o m eo t h e r s d o n o t th i n k s o . W h a t i s th e t r u e t e n d e n c y , a n di s i t r e a l l y i n v e r t e d U s h a p e ? H o w d i d th e d i s p a r i t y o fr e g io n a l e c o n o m i c d e v e l o p m e n t i n C h in a e v o l v e d u r -

i n g t h e p a s t 5 0 y e a r s f r o m 1 9 5 2 - 2 0 0 0 ? T h i s p a p e r a t -t e m p t s t o a n s w e r t h e q u e s t i o n s i n a n e w i n s i g h t o fr e s c a l e d r a n g e s ta t is t ic ( R / S ) a n d w a v e l e t a n a l y s i s o fT h e i l i n d e x s e q u e n c e a n a l y s i s . F i r s t l y , T h e i l i n d e x i sc a lc u la t ed a n d d e c o m p o s e d f r o m 1 9 5 2 - 2 0 0 0 b y th ec o m p a r a t i v e p r i c e i n 1 9 7 8 , w h i c h r e v e a l s t h e c h a n g eo f i n t e r - p r o v i n c i a l d i s p a r i t y i n w h o l e C h i n a , c o a s t a l ,m i d d l e a n d w e s t e r n r e g i o n , a n d t h e d i s p a r i t y b e t w e e nt h e l a t te r t h r e e r e g i o n s . S e c o n d l y , R / S a n d w a v e l e ta n a l y s i s i s u s e d t o p r o d u c e T h e i l i n d e x s e q u e n c e b yd i f fe r e n t t i m e s c a l e s , w h i c h s h o w s t h e d y n a m i c p r o -c e s s o f re g i o n a l d i s p a ri t y o f e c o n o m i c d e v e l o p m e n t i nC h i n a d u r i n g t h e p a s t f i v e d e c a d e s .

Received date: 2003-10-08Foundation i tem: Under the auspices o f National Philosophy and Social Sciences Foundation o f China (No. 00BJL0 51, 03BJL02 7)Biography: XU Jian-hua (19 65 -), male, a native o f Heshui County o f Gansu Province, professor, specialized in GIS and Geo-c om -putation. E-mail : [email protected]


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194 XU Jian-hua LU Yan2 M E T H O D O L O G Y A N D D A T A2 . 1 D i v i s i o n o f S p a t i a l U n i tThe re is usual ly a spat ial cr i ter ion for s tudies on reg ion-al d ispari ty . Wh at spat ial cr i ter ion should we cho ose forresearches? I t depends on s tudy purposes and spec i fi cobject ives . The pur pose o f th is pape r is to reveal provin-cial d ispari ty , regiona l dispari ty in eco nom ic deve lop-me nt f rom 1952-2 000 a nd the i r evo lu t ion . Prov inc ia ladminis t rat ive uni t i s a pol i t ical and economic regionwi th an in t eg ra ted func t ion , and each wi th a com ple tesystem of s tat is tical data, wh ich is readi ly avai lable.Thus , w e choose the p rov inc ia l reg ion (p rov inces , m u-nicipal i t ies and autonomous regions) as basic spat ial u-ni t for th is analysis , and also choose the threesupra-p rov inc ia l reg ions : coas t al , midd le and wes te rnregion as m ore overal l spatial uni ts . The coastalp rov inces a re Bei j ing , T ian j in , Hebei , L iaon ing , S hang-ha i , J i angsu , Zhej i ang , Fu j i an , Shandong , Guangdong ,Guangx i and Hainan . The m idd le p rov inces a re Shanx i ,Inne r M ongo l ia, J i lin , Hei long j iang, Anhu i , J iangxi ,Henan , Hubei and Hunan . The wes te rn p rov inces a reYunna n , Guizhou , S ichuan , Chongq ing , T ibe t , Shaanx i,Gansu , Q inghai, N ingx ia and X in j iang .

SU Fang l in e t d .2 . 2 S e l e c t i o n o f S t a t is t i ca l I n d i c a t o r s a n d S a m p l eD a t aAs fo r s tudy o f dynam ic evo lu t ion o f reg iona l d i spar ityin Ch ina , per cap it a GDP o f each p rov ince m ay be ap -p ropr i a te . Per cap i t a GD P i s wide ly used because i t isthe bes t approx imat ion and c an w el l re f l ec t t he overa l ldeve lopm ent l eve l and peo p le ' s wel l be ing . Mo reover ,the t ime series data in per capi ta GDP in each provinceare com ple te and can be used fo r spa ti al and t emp ora lcompar i son . Therefo re , we choose 31 p rov inces (mu-nicipal i t ies , autono mo us region s) in Ch ina as spatialsamples , the per iod 1952-20 00 as tempora l samples .

The p r imary da ta a re main ly f rom Nat iona l Bureau o fStatist ics of China (NB SC , 1997, 1 999, 2001, 2002). Ina genera l wa y, the data are credi table and authori tat ivetheore t ica l ly . How ever , s evera l years ' da t a such asthose dur ing the Grea t Leap Forward per iod a re d i s -to r ted because o f none-e conom ic fac tors , wh ich isprov ed by Gini and Thei l index in sect ion 3 .1 in this pa-per . C onsequen t ly , these da ta a re no t so c red ib le and theresu l t ca l cu la t ed by us ing them i s no t so p reci se . How -ever , as we s tudy reg iona l econ om ic d i spari ty in Ch inain a long per iod , t he p r imary da ta can on ly be f rom Na-t ional Bure au o f Stat is tics of China.

Xinjiaag

Tibet

Legend[ - - ] oasta|region~ Middle egion

Wos e rogioo o ~ 4o 960 1po ~oo ~

Sichuan

Yunnaa

- ~ . Jiangsu

0

Fig. 1 D ivision of the spatial unit of C hina


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R/S and W avelet Analysis on Evolutionary Process of Regional Econom ic Disparity in China D uring Past 50 Years2 . 3 D at a P r oc e s s in g M e t h od f or E l im in at in g In f lue n c e o f P r i c e sI f t h e p r i c e o f p ro d u c t s a n d s e r v i c e s d o e s n o t c h a n g e a ta l l , w e c a n i g n o r e t h e i n f l u e n c e f r o m p r i c e c h a n g e .C h i n a i s , h o w e v e r , a l a r g e c o u n t r y w i t h a b i g s p a t i a ld i f fe r e n c e . D u r i n g i ts p a s t 5 0 y e a r s o f e c o n o m i c d e v e l -o p m e n t , C h i n a h a s u n d e r g o n e s e v e r a l d i f fe r e n t s t a g e sw h e n t h e c o m p r e h e n s i v e p r i c e i n d e x a n d i n f l a t i o n r a t ew a s c o n s t a n t l y c h a n g i n g i n d i ff e r e n t p e r i o d s a n d a t d i f -f e r en t p l a c es . T h e r e f o r e , i f w e d i s c u s s r e g i o n a l d e v e l -o p m e n t d i sp a r i ty u s in g p r e s e n t p r i c e , w e m a y h a v e af a l s e c o n c l u s i o n . I n o r d e r to a c c u r a t e l y r e f l e c t t h e d is -p a r i ty a n d it s e v o l u t i o n , w e m u s t c o n s i d e r th e i n fl u -e n c e o f th e p r i c e f ac t o r. S o w e c o n v e r t a l l G D P d a t a o fe a c h r e g i o n i n to p r e s e n t v a l u e b y u s i n g p r i c e i n d e x ( 1 )a s fo l l o w s ( H U a n d Z O U , 2 0 0 0 ) .

X. t )=Xi to)X . [3 t ) (1)w h e r e X i t ) i s t h e r e a l G D P d a t a o f t h e r e g i o n i a t t h et t h y e a r , X i t o ) i s t h e r e a l G D P d a t a o f t h e r e g i o n i a tt h e f ir s t p e r i o d ( t h e t0 th y e a r ) , [ 3 ,( t ) is t h e G D P g r o w -t h e x p o n e n t o f t h e r e g i o n i f r o m t h e b a s e y e a r ( th e t 0 thy e a r ) t o t h e t t h y e a r .

I n t h i s a r t i c l e , t h e y e a r 1 9 7 8 i s t h e b a s e y e a r , a n d t h eG D P d a t a o f e a c h y e a r w e r e t h e r e al d a t a c o n v e r t e d i nt e r m o f c o m p a r a b l e p r i c e .2.4 Quant i tat ive Analys is Methods2 . 4 . 1 Q u a n t i t a t i v e i n d i c a t o r sT h e r e a r e s o m a n y q u a n t i t a ti v e e x p o n e n t s u s e d t o d e -s c r ib e r e g i o n a l d i s p a r it y ( B O R T S a n d S T E 1 N , 1 9 6 4 ;D U N F O R D , 1 99 3; D O W R I C K a nd N G U Y E N , 1 98 9) ,s u c h a s e x t r e m e d e v i a t i o n , s t a n d a rd d e v i a t i o n , c o e f f i -c i e n t o f v a r i a t i o n , E n g e l c o e f f i c i e n t , G i n i c o e f f i c i e n t ,l o c a t i o n e n t r o p y a n d s o o n . B e c a u s e i t n o t o n l y i sp r e f e r a b l e t o d e s c r i b e t h e r e l a t i v e d i s p a r i t y a m o n g r e -g i o n s , b u t a l s o c a n b e d e c o m p o s e d i nt o s u b - r e g i o n s ,T h e i l i n d e x w a s c h o s e n a s m a i n q u a n t i t a t i v e i n d i c a t o rf o r a n a l y s i s a n d G i n i c o e f f i c i e n t a s c i r c u m s t a n t i a l e v i -d e n c e .

T h e f t i n d e x is a l s o c a l l e d T h e i l e n t ro p y , w h i c h w a sp r o p o s e d b y T H E I L ( 1 9 6 7 ) . T h e i l i n d e x (T ) is d e f i n e di n t h e f o l l o w i n g w a y : x y

T = ~ .~ Y i l o g ~ 7 ( 2 )t = l

w h e r e N is t h e n u m b e r o f a r e a s, Y , is t h e G D P s h a reo f r e g i o n i i n t o t a l o n e i n t h e w h o l e c o u n t r y , P i i s t h ep o p u l a t i o n s h a re o f r e g i o n i in t o t a l o n e in th e w h o l ec o u n t r y .

I f T i s b i g g e r , d i s p a r i ty i n e c o n o m i c d e v e l o p m e n t a -m o n g v a r i o u s r e g i o n s w i l l b e b i g g e r . O t h e r w i s e , d i s -p a r i t y w i l l b e c o m e s m a l l e r .

195A n o t h e r c h a r a c t e r is t i c o f T h e i l i n d e x i s th a t i t m a y

b e d e c o m p o s e d i n to t w o p a r ts : i n t e r - g ro u p d i s p a r i tya n d i n t r a -g r o u p d i s p a ri t y , w h i c h m a k e u s m o r e c le a ra b o u t t h e e v o l u t i o n o f b o t h i n t e r -g r o u p a n d i n t r a - g r o u pd i s p a r i t i e s a n d t h e i r r e s p e c t i v e i m p o r t a n c e i n o v e r a l ld i s p a r i t y . I n C h i n a , f o r i n s t a n c e , T h e i l i n d e x c a n b ed e c o m p o s e d i n t o i n t e r - r e g i o n a l d i s p a r i t y a n d i n t r a - r e -g i o n a l d i s p a r i t y ( Z H O U , 1 9 9 9 ) a s f o l l o w s :

=Ti,,er+T~n,ra= Y l o g + Y~ [ ~ Y 0 1 o g ~ ]i= i= l j q

3 )w h e r e i ( i = 1 , 2 , 3 ) i s o n e o f t h r e e s u p r a - p r o v in c i a l r e g i o n s( c o a s ta l , m i d d l e o r w e s t e r n r e g io n ) , a n d w h e n i = 1 , j = l ,2 . . . . . 1 2 , w h i c h r e s p e c t i v e l y c o r r e s p o n d t o 1 2 p r o v i n c e s i nc o a s t a l r e g i o n ; w h e n i = 2 , j = l , 2 , .. ., 9 , w h i c h r e s p e c t i v e l yc o r r e s p o n d t o 9 p r o v i n c e s i n m i d d l e r e g i o n ; w h e n i = 3 ,

j = 1 , 2 , . .. , 1 0 , w h i c h r e s p e c t i v e l y c o r r e s p o n d t o 1 0 p r o v i n -c e s in we s te r n r e g io n . Y , i s th e GD P s h a re o f s u p r a -p r o v in c ia l r e g io n i i n n a t io n a l o n e ; P ~ i s th e p o p u la t io ns h a r e o f s u p r a - p r o v in c ia l r e g io n i in n a t io n a l o n e ; Y o is theG D P s h a r e o f p r o v i n c e j i n o v e r a l l o n e o f s u p r a - p ro v i n c i a lr e g io n i ; P , j i s th e p o p u la t io n s h a r e o f p r o v in c e j i n to ta lo n e & s u p r a - p r o v i n c i a l r e g i o n i .2 . 4 . 2 R / S a n a l y s i sAl l s t a t i s t ic a l m e th o d s a s s u m e th a t a l l d a ta o f t ime s e r i e sb e in d e p e n d e n t ( i . e . f i t f o r Ga u s s d i s t r ib u t io n ) , h e n c e th es e r i e s i s s t o c h a s t i c . W h e n H U R S T ( 1 9 5 1 , 1 9 5 5 ) , a B r i t i s hp h y s i c i s t , a n a l y z e d w a t e r l e v e l o f th e N i l e R i v e r , h e f o u n dth a t s u c h t ime s e r i e s l ik e r iv e r wa te r l e v e l wa s n o t f i t f o rG a u s s d i s t r i b u t io n , s h o w i n g a c h a r a c t e r is t i c o f d i sc o n t i n u -i t y a n d d u ra b i l it y . B a s e d o n t h e e m p i r i c a l f i n d i n g s o f H EH U R S T , B B M A N D E L B R O T m a d e a b r ea k th r ou g h onf u n d a m e n t a l t h e o r i e s o f tr a d i ti o n a l s t a ti s ti c a l m e t h o d s . H ed i v i d e d ti m e s e ri e s i n t o t w o c a t e g o ri e s : d i s c o n t i n u e a n dd u r a b l e , o f w h i c h t h e f o r m e r is c a l l e d N o a h E f f e c t s a n dt h e la t t e r i s c a l l e d J o s e p h E f f e c ts , b o t h o r i g i n a ti n g f r o mG e n e s i s 6 o f O l d T e s t a m e n t a s . . .w e r e a l l t h e fo u n t a i n o ft h e g re a t d e e p b r o k e n u p , a n d t h e w i n d o w o f h e a v en w e r eo p e n e d . A n d t h e r a in w a s u p o n t h e e a r th f o r f o r ty d a y s a n df o r ty n ig h t s . T h e to r r e n t i a l r a in l a s tin g f o r 4 0 d a y s a n dn ig h t s p r e s e n t s a c h a r a c te r i s t i c o f u n e v e n n e s s in r a in f a lla n d d i s c o n t i n u i ty i n t i m e . T h e s t o r y o f J o s e p h i n G e n e s i s4 1 r e a d s li k e . .. t h e re c a m e s e v e n y e a r s o f g re a t p l e n t yt h r o u g h o u t t h e la n d o f E g y p t . A n d t h e r e s h a ll a r is e a ft e rt h e m s e v e n y e a r s o f f a m i n e s h o w i n g th e p e r i o d i c a l o c -c u r r e n c e o f h u m i d i t y a n d a r i d i t y w i t h a c h a r a ct e r is t i c o fd u r a b i li t y . T h e i d e a w a s p r o p o s e d i n h i s s p e e c h n a m e d

N e w f o r m s o f c h a n c e i n t h e s c i e n c e s a n d r e c o r d e d inr e fe re n c es o f M A N D E L B R O T a n d W A L L I S ( 1 9 6 8) a n dM A N D E L B R O T ( 1 97 3 ) . U n d e r t he e ff e ct o f N o a h E f -f e c t s a n d J o s e p h E f f e c t s , t i m e s e r ie s n o l o n g e r p r e s e n t sa r a n d o m B r o w n i a n m o v e m e n t u n r e l a te d t o th e p as t ,


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196 X U J i a n - h u a , L U Y a h ,but show s a charac ter i st i c o f long- term cor r e la t ion( C O M T E an d R E N A U L T , 1 99 6) , w h i ch w as ca l ledf B M ( f r act i on a l B r o w n i an M o v em en t ) b y B B M A N -D E L B R O T an d co u l d b e s t u d i ed b y r e s ca l ed r an g estat is t ic (R/S) analysis . The R/S analysis , as a non- l in-ear method fo r fo recas t , has been widely used in manyr e s ea r ch es ( C H E N e t a l l . , 1992) .

The p r inc ip le o f R/S analys is is as fo l lows : Cons id -er ing the t ime ser ies { ~ (t ) } ( t= l , 2 , . . - ) o f Thei l indexvar iat ion, for any posi t ive integ er z >~ 1, the me an v al-ue ser ies i s def ined as

T@ ~ : + 2 ~ ( t) =1 , 2 , -

t = ]The accumula t ive dev ia t ion i s

X ( t , ~ )= ~ ( ~ (u) - (~),) 1 ~ t ~ -cu = l

The ex t r eme dev ia t ion i sR ( ~ ) = m ax X ( t , ) - rain X ( t , ) =-1, 2, - ' .

1 ~ < t ~ T ] ~ < t ~ TThe s tandard dev ia t ion i s

I

1 z = 1 , 2 , -t = l

Wh en analyz ing the s ta ti s ti c ru le o f R ( ) / S ( ~ ) R / S , H U R S T d i s co v e r ed a r e la t io n a l ex p r e s s io n

R / S ~ ( ~ ) 4 )I t shows there i s Hur s t phenomenon in t ime ser ies ,and H i s ca l led the Hurs t exponen t . Acco rd ing to ( z ,R / S ) , H can b e o b t a i n ed b y l e a st s q u ar e m e t h o d ( L S M )in log- log g rid. HU RS T e t a/ . (1965) once p roved tha ti f { ~ (t )} i s independen t ly r andom ser ies w i th l imi tedv a r ian ce , t h e ex p r e s si o n H = 0 .5 , H ( 0 < H < I ) i s d ep en -den t o f an inc idence funct ion C( t ):

C( t)=22 - ' - 1 (5)When H>0.5 , C( t )>0 , i t means tha t the fu tu re t r end o f

t ime ser ies w i l l be cons i s ten t w i th the pas t. I n o therwords , i f the pas t d i spar i ty o f reg ional e conom ic devel -opm ent has been en larged , the d i spar ity in the fu tu rewi l l a l so be en larged . T he p rocess o f r eg ional econ om -ic develo pme nt w i l l assum e a d ivergen t t r end . W henH< 0.5 , C( t )


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R/S and W avelet Analysis on E volutionary Process of R egional Economic Disparity in C hina D uring Past 50 Y earsof r e f inement . The cor r espond ing mul t i - r eso lu t ion de-co m p o s i t i o n o f T ( t ) i s g iv en b y { I , D j , D I _ ~ . . . . D j , . . . , l ) ~ } .

The m ain in teres t o f th i s r esearch i s in the approx ima-t ions o f time ser ies by t ime sca le . The ob jec t ive i s to ex -amine the ex ten t to an a l lowance fo r d i f f er en t e f fec t s byscale, and to have an insight into the total var iat ion ofthe s ignal over t ime. We choose the Symmlet as the ba-s ic wavele t , des ignated S 8 . W e exper imen ted wi tha l te rna t ive ch o ices o f sca l ing funct ions and o f wavele t ,bu t the qual i t a t ive r esu l t s were very robus t to suchchanges and the in it ia l cho ice o f wav ele t seem ed to bethe bes t on ba lance . In a ll cases , the leve ls ana lyzed arerestr icted to $4, $3, and $2 to represe nt the t rend ele-ments .

1 9 73 R E S U L T S A N D D I S C U S S I O N3 1 T h e i l I n d ex a n d I t s D eco m p o s i t i o nWith r ef erence to F ig . 2 , we can see tha t Thei l indexand Gin i coef f ic ien t r evealed the same t r end o f the evo-lu t ionary p rocess o f in ter -p rov inc ia l d i spari ty . From1952 to 1978, exc ept for several unusual data in theGreat Leap Forward per iod , the d ispar i ty assum ed the

upw ard trend on the who le; f rom 1979 to 1990 the dis-par i ty assum ed the s lowly dow nwa rd t r end . Bu t f rom1991 to 2000 the d i spar i ty assume d the s low ly upw ardtrend again. In other word s, while the s trategy to bal-ance r eg ional development befo re the r efo rm and open-ing up has no t succeeded in r educing compara t ive d i s -

0 . 4 00 . 3 50 . 3 00 . 2 50 . 2 00 . 1 50 . 1 00 . 0 50 . 0 0

G i n i c o e f f i c i e n t , - ,, i ,m T h e i l i n e x

Fig. 2 Sam e trend of Theil index and Gini coefficientpar i ty in Ch ina ' s r eg ional econ om ic developm ent , thelops ided development s t r a tegy af te r 1978 a l so has no tenlarged dispar i ty .

Deco mpo s i t ion o f Thei l index can fu r ther r eveal r e -g ional r easons o f d ispar i ty evo lu t ion f rom a r eg ionalper spect ive and e vo lu t ion o f in t r a-r eg ional d i spari ty .Fig. 3 revea ls the evolut ion o f regional dispar i ty and in-t r a - reg ional d i spari ty . The d ynam ic t r end o f in ter-provincial dispar i ty in the coastal region is consis tentwi th the dynam ic t r end o f the overa l l na t ional d i spar i ty .The d i spar i ty be tween the p rov inces in the midd le r e-g ion and tha t in wes tern r emains smal l , and the evo lu -t ion i s r a ther s low. Dev elopm ent d i spar ity be tw een theth ree supra-p rov inc ia l r eg ions has been co n t inuous ly onthe increase and wa s even g rea ter s ince the 1990s .

I t is evide nt f rom Fig. 4 that the intra- regional dis-par i ty be tween the th ree supra-p rov inc ia l r eg ionscon t r ibu tes more and more to China ' s overa l l d i spar i ty .Over h a l f o f the d i spar i ty r esu l ts f rom in ter -p rov inc ia ld i spar i ty in the coas ta l r eg ion . The con t r ibu t ion o fco as ta l r eg io n r ed u ced f r o m 6 3 .4 2 % ( 1 9 5 2 ) t o 5 1 .1 5 %(2000) and the ones o f midd le and wes tern reg ionsr e s p ec t iv e l y r ed u ced f r o m 1 6 .3 2 % , 2 .8 3 % ( 1 9 5 2 ) t o5 .95% , 2 .74% (2000) . The con t r ibu t ion o f the d i spar i ty

betwe en th ree supra-p rov inc ia l r eg ions howev erincreased f rom 14 .31% (1952) to 27 .25% (1990) , andto 43 .27% (2000) .3 2 R / S A n a l y s i s R es u l t s o f T h e i i I n d ex S eq u en ceWhile scho lar s bo th in China and abroad s tudy d i spar ityin r eg ional econo mic developm ent o f Ch ina , they haveb een co n ce r n ed ab o u t a co m m o n i s s u e , i. e ., w h e t h e r e -cono mic d evelop men t in d i ff er en t r eg ions o f Ch ina wi l lconverge , o r whether the income level in each r eg ionw i l l h av e a co n v e r g en ce? B as ed o n t h e S o l o w G r o w t hM o d e l , C H E N an d F L E I S H E R ( 1 9 9 6 ) s t u d i ed C h i n a ' sr eg ional d i spar ity by us ing per cap i ta GDP , and d i scov-ered tha t r eg ional economic d i spar i ty f rom 1978 to1993 in China showed a cond i t ional convergence , i . e . ,i t depen ded on the share o f phys ica l cap i ta l , em ploy-ment g rowth , inves tment in human cap i ta l , f o r e ign d i -r ec t inves tment and loca t ion . On the con t r ary , YA Oan d Z H A N G ( 2 0 0 1 ) an a l y zed co n v e r g en ce o f C h i n a ' sr eg ional economy f rom 1952 to 1997 wi th per cap i taGDP . The r esu l t ind ica tes reg ional d i spar i ty o f econo m-ic develop men t in Ch ina would expand . Wh at is thet rue tendency o f the evo lu t ionary p rocess on the r eg ion-a l economic d i spar i ty in Ch ina dur ing the pas t 50


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1980.140.120.1o

0 0 8~ 0.06

0.040.020

X U J i a n - h u a L U Y a h S U F a n g - l in e t a l.

WholeC h i n aCoastal regionMiddle egion

- . l - - Wes te rn eg ionAmong h r e e r e g i o n s

Y e a r

Fig . 3 The i l index and i t s decompos i t ion f rom 1952 to 2000

70 . Coa stal egion60

~ 5.~ [ ~ + Middle egion40~ 30 ~ + Western egiont.) 20

10 & Am ong hree regions0

YearF ig . 4 Cont r ibu t ions o f in te r - reg iona l and in t ra - reg iona l d i spa r it i e s to the d i spa r i ty in w hole C hina

years? T he fo l lowing i s ou r R/S ana lys i s on th is i s sue .Tak ing Thei l ind ices f rom 1952 to 2000 ob ta ined in

fo rmer parag raphs as t ime series ~ ( t ) , we have ca lcu -la ted the Hurs t expo nen t H accord ing to t empora l char-ac te r i s t i cs o f econ omic deve lopm en t in Ch ina . The re -sul t is in Ta ble 1 .

W i th re ference to Tab le 1 , we may reach the fo l low-

ing conclus ions :(1 ) In t h e p e r i o d 1 9 5 2 -1 9 6 5 , t h e Hu r s t e x p o n e n t

H= 0 .67 0>0 .5 , wh ic h ind icates tha t in th is per iodevo lu t ion o f compara t ive in te r -p rov inc ia l d i spar i ty o fe c o n o m i c d e v e l o p m e n t s h o we d a l o n g -e n d u r i n gcharac te r is t i c . In the per iod 196 6-19 78 , the Theil indexassumed an increas ing t rend , wh ich has conf i rmed th i s

Table 1 Hurst exponent of Theil exponent series of per capita GDP in C hina from 1952 to 2000Period 1952-1966 1967-1978 1979-1990 1991-2000 1952-2000Hurst expon ent 0.670 0.504 0.722 0.730 0.545

conclus ion .(2 ) In t h e p e r i o d 1 9 6 6 -1 9 7 8 , t h e Hu r s t e x p o n e n t

H = 0 .5 0 4 ~ 0 .5 , wh i c h in d i ca t e s t h at i n t h is p e r i o d t h eevo lu t ion o f compara t ive in te r -p rov inc ia l d i spar i ty o fe c o n o m i c d e v e l o p m e n t s h o we d a r a n d o m c h a ra c t e r i s -t ic . I t i s in the per iod o f the Grea t Cu l tu ra l Re vo lu -

t ion , so conclus ion was ver i f i ed .(3 ) In t h e p e ri o d 1 9 7 9 -1 9 9 0 , t h e Hu r s t e x p o n e n t

H--0 .772> 0 .5 , wh ich ind ica tes tha t in th i s per iod theevo lu t ion o f the com para t ive in te r -p rov inc ia l d i spar i tyo f e c o n o m i c d e v e l o p m e n t b e t w e e n p ro v i n c e s i n C h i n ahas a long-endur ing charac te r i s t i c , in the per iod 1991-


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R/S and W ave|et Analysis on E volutionaryProcess of Regional Econom ic Disparity n C hina During Past 50 Years2 0 0 0 H u r s t ex p o n en t H = 0 .7 3 0 > 0 .5 , w h i ch h a s a l s over i f ied the conclus ion .3 . 3 M u l t i r e s o l u t io n A p p r o x i m a t i o n o f T i m e S e r ie so f T h e i l I n d e xFig . 5 and 6 ar e t ime- ser ies p lo t s o f the approx ima t ionfor Thei l index in whole China and the coas ta l r eg ionat l eve l $4 & $3 r espect ive ly . F ig . 5 shows tha t thed ispar i ty in whole China fo l lows the inver ted U on thewhole a t l eve l $4 , namely a t the t ime sca le o f 16 year s .That is to say that the disp ar i ty tends to r ise in the f i rs ts t age o f e co n o m i c d ev e l o p m en t , an d fa l l s l o w l y o v e rt h e p eak i n t h e s eco n d s t ag e o f e co n o m i c d ev e l o p m en t .How ever , i f we r esca le the t ime sca le to 23 (8 year s ) ,then a l ink o f severa l U shapes w i l l be seen a t l eve l$3 . There are two loca l ma x im um po in ts in 1958 and1959 at level $3, i .e . , the regiona l dispar i ty in Chinaincreased in the Grea t Leap Forward per iod (19 58 -1960). C h ina ' s eco nom y recov ered f rom 1961 to 1966 ,which led to a decrease in the r eg ional d i spar i ty . Thei lindex r eached a loca l min imum po in t in 1965 a t l eve l$3 . The d i spar i ty be tween r eg ions increased con t inual -l y d u r in g 1 9 6 6 - 1 9 7 6 , w h i ch l ed t o t h e T h e i l i n d exreac hed i ts pea k in 1976. This suggests that the s trate-g y o f r eg i o n al b a l an ced d ev e l o p m en t b e f o r e t h e r e f o rmand open ing up d id no t b r ing us a r educt ion in com-para t ive d i spari ty o f r eg ional econom ic develop me ntbu t increased the d ispar i ty . W i th the changes o f eco-nom ic po l ic ies , the d i spar i ty be tw een r eg ions r educe daf ter the r efo rm and open ing up , which i s in accor -d an ce w i t h co n c l u s io n s d r aw n b y Y A N G ( 1 9 9 4 ). I nadd i t ion , F ig . 5 a l so shows tha t the d i spar i ty be tweenprov inces r educes f rom 1978 to 1990 , bu t w idens af te r1990 a t l eve l $3 . The same conclus ions were a l sodrawn by Y ING (1999) . Therefo re , the conclus ionsd r aw n b y Y A N G ( 1 9 9 4 ) , Y 1 N G ( 1 9 9 9 ) a r e t h e s p eci a lcase a t l eve l $3 , the lo wer t ime sca le . F ig . 6 a l soshow s tha t the same conclus ion as F ig . 5, i .e . , therei s on ly one inver ted U shape a t l eve l $4 and a l ink o fsevera l U shapes a t l eve l $3 . The approx im at ions fo rThei l index a t l eve l $4 and $3 ind ica te tha t the dy-namic t r end o f the d i spar i ty in the coas ta l r eg ion i s inl ine w i th dyn amic t r end o f the d i spar i ty in whole Chi -na.

Fig. 7 and Fig. 8 are t ie ser ies plots of the approxi-mat ion fo r Thei l index in the midd le r eg ion a t l eve l$4 , $3 , and $2 r espect ive ly . The d i spar ity in themidd le r eg ion fo l lows the inver ted U on the whole a tleve l $4 . The economic d i spar i ty in midd le r eg ion haswidened s ince 1952 and r eached i t s ver tex dur ing the

Great Leap Forward . Af terwards , the d i spar i ty began

(a)[S4lo 1 2 /0 111

~ 0 .10o o 9 [0.08[0 .0 7 ' . . . . . . . .1950 1960 1970 1980 1990Year

(b)[S3]0.161 -

O.lO[g o o 8 [0 .0 6 ' . . . . . . . .

199

2000

1950 1960 1970 1980 1990 2000Year

F i g . 5 T i m e s e r i e s p l o t s o f t h e a p p r o x i m a t i o n f o rTheft index in the w hole China

(a)[S4lo.o8 I0.07[0 .0 6 [0.05 /1950 1960 1970 1980 1990 2000Year

(b)[s3]0,10 / . . . . . . . . . 9 t t.-'~ 0 .0 7 [ ~ / ~ t~ 0 . 061 / v

0 ' 5 o ' 1 ; 6 0 ' 1 ; 7 0 ' 1 ; 8 0 ' 1 ; 9 0 ' 2 ; 00Year

Fig. 6 Time series plots of the approximation forTheil index in the coa stal region

to r educe . I f we r esca le the t ime sca le to 8 year s , then al ink o f severa l U shapes w i l l be seen in F ig . 7 . Tw olocal max imum po in ts appeared in 1978 and 1990 .W hen w e r esca le the t ime sca le to 4 (22 ) ye ar s fo rfu r ther de ta i l s , Thei l index r each ed i t s ver tex dur ing the

Great Leap Forward per iod , and began decreas ing t il l1975 , and then increased befo re 1978 a t l eve l $2 . Af tert h e r e f o rm an d o p en i n g u p p o li cy , t h e eco n o m i c p o l i cyfavor s the eas tern r eg ion , and the midd le r eg ion layss t r ess on deve lopm ent o f energy , r aw mater ia l andsupp l ied the coas ta l w i th p r imary p roduct , which led toan increase o f d i spar ity dur ing the 7 th F ive Yea r P lan( 1 9 8 6 - 1 9 9 0 ) . H o w ev e r , t h e d i s pa r it y r ed u ced a f te r1991 due to the ad jus tment o f the po l icy dur ing t l~e 8 thFive Year P lan .


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200 XU Jian-hua LU Ya h SU F~m g-lin et ~d.(a) IS4]

~, 10

1950 1960 197 0 1980 1990 2000Yearb) [S31

b 10

1 9 5 0 1 ; 6 0 1 ; 7 0 1 ; 8 0 1 9 9 0 2 0 0 0Year

X.~lO81? 6 t

I~ 2 /

Fig. 7 T ime-series plots of the approxima tion lbrTheil index in the m iddle region

1950 1960 1970 1980 1990 2000Year

Fig. 8 Time-seriesplots o f the approximation forTheft index in the middle region at level $2

Fig. 9 show s that regional dispar i ty in the wes ternreg ion a t l eve l $4 and $3 r espect ive ly . The d i spar i ty inthe wes tern r eg ion a lmos t fo l lows the inver ted U onthe whole a t l eve l $4 wi th a max imum po in t in 1974 .There i s a loca l max imum po in t in 1990 and a l ink o fseveral U shapes at level $3. I t is clear that the yea rr each ing maxim um is qu i te d i s t inc t in the coas ta l , themidd le , the wes tern r eg ions as wel l as the who lecoun t ry . T ime ser ies p lo t t ing fo r the Thei l index o famong the th ree supra-p rov inc ia l r eg ions a t l eve l $4and $3 are omi t ted , and the d i spari ty amon g the th reesupra-p rov inc ia l r eg ions i s expand ing . In conclus ion ,us ing wav ele t by d i f f er en t t imes sca le in coas ta l ,midd le , w es tern r eg ions as wel l as th r ee supra-p rov in -c ia l r eg ions , f ind ings show tha t r eg ional develop men tw h i ch i s b a s ed o n t h e d eco m p o s i t i o n an d ap p r o x im -at ion o f Thei l index i s d i f fer en t . Therefo re , we d rawa conclus ion tha t the e vo lu t ionary p rocess o f thed ispar i ty o f econ omic developm ent in Ch ina is no t as imple inver ted U shape bu t a compo und o f severa l Ushapes .

(a)[S4]3.4

g 3.23.02.8 . . . . . .1950 1960 1970 1980 1990 2000

o 3 6 f.43.23.02.82.61950 1960 1970 1980 1990

e a rFig. 9 Time-series plots of the approximation forTheft index in the western region

Y~ar(b)[S3]

2000

4 C O N C L U S I O N SFrom above research r esu l ts , we e l ic it the fo l lowingconclus ions .

(1 ) Reg ional d ispar i ty in econ omic developm ent inChina, including the inter -provincial dispar i ty , inter - re-gional dispar i ty and intra- regional d ispar i ty , has exist-ed fo r many year s . Thei l index have r evealed a dynam-ic t r end fo r compara t ive d i spar i ty in economic devel -opm ent be tw een p rov inces in China . From 1952 to1978 , excep t fo r G rea t Leap Forward per iod , com -para t ive d i spar i ty bas ica l ly assumed an upward t r endand i t assume d a s lowly dow nw ard t r end f rom 1979 to1990 . Af terwards f rom 1991 to 2000 the d i spari ty as -sume d a s lowly upw ard tr end again . In o ther words ,the compara t ive d i spar i ty o f r eg ional econ om y hadbeen n e i ther decreased b y the s t r a tegy o f r eg ional ba l -an ced d ev e l o p m en t b e f o r e t h e r e f o rm an d o p en i n g u p ,n o r w i d en ed b y t h e l o p s id ed d ev e l o p m en t s t ra t eg y inChina s ince then.

(2 ) Dec om pos i t ion o f Thei l index ind ica tes tha t thedynamic t r end o f compara t ive in ter -p rov inc ia l d i spar i tyin coastal region is in l ine w ith dynam ic trend of in-ter -provincial dispar i ty in the wh ole China. In otherwords , in ter-p rov inc ia l d i spar i ty g radual ly expandedfrom 1952 to 1978 and then began to reduce unti l 1990.The in ter -p rov inc ia l d i spar i ty in midd le and w es tern r e-g ions has r educed a ll the t ime, bu t a t a s low pace , anddur ing the who le per iod 195 2-20 00 , d i spar i ty in eco-nomic development among the th ree supra-p rov inc ia lr eg ions was con t inuous ly on the increase , espec ia l ly inthe 1990s dispar i ty among the three supra-provincial re-g ions r ap id ly expanded .


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R / S a n d W a v e l e t A n a l y s is o n E v o l u t i o n a r y P r o c e s s o f R e g i o n a l E c o n o m i c D i s p a r i t y i n C h i n a D u r i n g P a s t 5 0 Y e a r s( 3 ) T h e R / S a n a l y s i s r e s u lt s t el l u s t h a t d u r i n g 1 9 6 6 -

1 97 8 , t he H u r s t e x p o n e n t H = 0 . 5 0 4 ~ 0 . 5 , w h i c h i nd i -c a t e s t h a t in th i s p e r i o d t h e e v o l u t i o n o f c o m p a r a t i v e i n -t e r - p ro v i n c i a l d i s p a ri t y o f e c o n o m i c d e v e l o p m e n ts h o w e d a r a n d o m c h a r a c t e r i s t i c , a n d i n t h e o t h e r p e r i -o d s , i .e ., 1 9 5 2 - 1 9 6 5 , 1 9 7 9 - 1 9 9 0 a n d 1 9 9 1 - 2 0 0 0 , t h eH u r s t e x p o n e n t H > 0 . 5 , w h i c h i n d i c a t e s t h a t i n t h o s ep e r i o d s t h e e v o l u t i o n o f t he c o m p a r a t i v e i n t e r - p ro v i n -c ia l d i sp a r i ty o f e c o n o m i c d e v e l o p m e n t i n C h i n a h a d al o n g - e n d u r i n g c h a r a c t e r i s t i c .

( 4 ) B a s e d o n t h e d e c o m p o s i t i o n a n d a p p r o x i m a t i o no f T h e i l i n d e x , u s i n g w a v e l e t b y d i ff e r e n t t i m e s c a l e , w ea r r i v e d a t a c o n c l u s i o n t h a t t h e e v o l u t i o n a r y p r o c e s s o ft h e d i sp a r i ty o f e c o n o m i c d e v e l o p m e n t o f C h i n a i s n o t as i m p l e i n v e r t e d U s h a p e b u t a c o m p o u n d o f se v e r a l Us h a p e s . T h e r e s u l t t e ll s u s t h e e v o l u t i o n a r y p l o t o f i n -t e r - p r o v i n c i a l d i s p a r i t y i n C h i n a f o l l o w s t h e i n v e r t e d Uo n t h e w h o l e a t t h e h i g h e r s c a l e , 2 4 ( 1 6 y e a r s ) . T h a t i s t os a y , t h e d i s p a r i t y t e n d s t o r i s e in t h e f i r s t s t a g e o f e c o -n o m i c d e v e l o p m e n t , a n d f a l l s l o w l y o v e r t he p e a k i n t h es e c o n d s t ag e o f e c o n o m i c d e v e l o p m e n t . H o w e v e r , i f w es h o r t e n t h e t i m e s c a l e t o 2 3 (8 y e a r s ) , t h e n a l in k o f se v -e r a l U s h a p e s w i l l a p p e a r .R E F E R E N E S

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