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Bonnie Collins
6 years ago
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1 Ole Ope cce pblhg plaf f Maagee Reeach Cpgh 00 ll gh eeed Iegaed Pblhg aca Reeach cle ISSN c e f wegh dea eae effcec ad Idef pdc chage Fahad Hezadeh Lf l Paa Reza N Depae f Maheac Scece ad Reeach Bach Ilac zad Ue Teha Ia Depae f Maheac Zaheda Bach Ilac zad Ue Zaheda Ia paa_az@ah.c BSTRCT Th pape de lzg c e f wegh (CSW) appach deee pdc chage b Malq Pdc Ide (MPI). I c ehd f bag he cpe f MPI whch ae he effcec f dec akg (DMU) dffee ped daa eelpe aal (DE) del ch a CCR del BCC del ad ae ed. The effcec f DMU DE eaed he fae a ela he DMU. Hece ealc (pc) ce ae aged he MPI. Oe f ppe ehd f eal h pble DE peeg a geeal dec ab p ad p wegh whch led CSW appach. I h pape a f a ew CSW del ggeed ba he p ad p wegh. Se fac ela he del ae peeed b hee. Baed he pped del ad b he daa a each ped he cepdg CSW deeed. The CSW f a ped ae he ed f eala DMU dffee ped ad he MPI calclaed. De he ae f CSW ehd he MPI baed CSW e elable ha ha b he clac DE ehd. Mee he pped ehd h pape eakable f he cpaal p f ew. la he appach cpaed wh DE g a ecal eaple. Kewd: Daa eelpe aal (DE) C e f wegh (CSW) Effcec Pdc chage Malq pdc de (MPI).. Idc Daa eelpe aal (DE) e f he b bache f pea eeach whch wa ceaed b Chae e al. (978). Th echqe eae he elae peface f hgee dec akg (DMU) whch e eeal dce called p pdce he eeal dce called p. DE ha bee wdel appled all bache f cece ch a healh d aagee ad. hgh eew p DE 009 wa de b Ck ad Sefd (009). lhgh clac DE del ae eeel ed he a dea f he eae he effcec ce f a ealag DMU a pc apec cpa he he DMU. Th decl pac calclag baed DE pdc chage. Cpg he pdc chage b he effcec eae wa f dced b Cae e al. (98) ad deelped b Fae e al. (99). Malq pdc de (MPI) baed DE wa ggeed b Fae e al. (994) ba he pdc chage. The MPI 405 Vle Ie 0

2 c e f wegh dea eae effcec ad def pdc chage Fahad Hezadeh Lf l Paa Reza N eae he pdc chage e he e ad a pdc f echcal effcec chage ad echlgcal chage. Seeal applca f he MPI hae bee eped he leae. F eaple Chag e al. (008) lzed he MPI eae he chage pdc f US accg f befe ad afe Sabae l c. L ad Wag (008) appled lake baed eae (SBM) (Te 00) eae he MPI Tawaee ecdc cpae. Feg ad Sele (008) ded he echcal chage lage US bak. Cpe f MPI ae he effcec ce f DMU dffee ped whch ae baed b he clac DE del a CCR (Chae e al. 978). eed abe he effcec ce f a ealag DMU b hee ehd eaed he fae p cpa he he DMU ha flece he MPI ad lead cec edc ab he ae f he pdc chage. Oe dea ece h dffcl g a e f wegh eae he effcec f DMU. Th appach called c e f wegh (CSW) ehd. B ea h appach he h (h) wegh ca f he h p (h p) f all DMU ad eflec f he h p (h p) eag he effcec f all DMU alke. Th eag he effcec b h ehd e cadd ha ha b he clac DE del. We ppe e he CSW baed a ped eae he effcec f DMU dffee ped pdce he MPI. The f CSW ehd wa ggeed b Rll e al. (99). The f he a eeache ch a Jahahahl e al. (005) L ad Peg (008) ad Wag e al. (0) egaed bag he CSW ealae DMU. Th pape ppe a ew del ba he CSW whch ha accdace wh lea pgag CCR del (LP CCR). The baed he pped del ad b he daa ped ad + he CSW f ped ad + ae deeed. I ca hee CSW ae ed ba he effcec ce f DMU w ped. F eaple he effcec f a ealag DMU ped ela ped + deeed b he weghed f p ha f p whch he wegh ae baed f ped + ad p ad p ae f ped. a el he cpa f he pped ehd f defg he MPI le ha ha b he clac DE ehd whch he beef f g he CSW eae he MPI. The pape fld a fllw. I ec a ew CSW ehd ggeed ad e fac ela he pped ehd ae eed. Sec 3 decbe lzg he CSW f eag he MPI. I ec 4 a ecal eaple pded llae he pped ehd cpe he MPI ad cpae wh baed CCR MPI. The la ec ae ccl.. C e f wegh ehd Cde DMU each DMU wh p ad p. Le > 0 (... ) ad > 0 (... ) ae epecel he ale f p ad p f DMU (... ). Fllwg lea pgag pble wa ggeed b Chae e al. (978) f eag he peface f DMU ela he he DMU whch called LP CCR a: Ma.. Vle Ie 0 406

3 c e f wegh dea eae effcec ad def pdc chage Fahad Hezadeh Lf l Paa Reza N 0... ε () whee ε he chedea be ad (... ) ad (... ) ae he aged wegh f he h p ad h p epecel. Cde a lea pgag pble a: Ma ε () Thee. The lea pgag pble () ad () ae eqale. Pf: Cde S ad S ae he feable eg f () ad () epecel. We hae S S. The he pal ale f () geae ha eqal he pal ale f (). O he he had f ( ) S he hee θ ad ( θ θ ) S. The ale f he bece fc f () f ( ) S geae ha eqal he ale f he bece fc f () f ( θ θ ) S. a el he pal ale f () geae ha eqal ha f (). Theefe he pal ale f pble () ad () ae eqal ad w pble ae eqale. a dea f bag he CSW accdg () he weghed f p f all DMU be lael azed de he cd ha he weghed f p f each DMU le ha eqal e. Theefe he fllwg lple bece lea pgag ggeed ba he CSW a: Ma ε (3) Ug he weghed ehd f lg lple bece pgag pble whch he wegh f he bece ae eqal e pble (3) ceed a lea pga a fllw: Ma..... (4 ) 0... (4 ) ε (4) Vle Ie 0 407

4 c e f wegh dea eae effcec ad def pdc chage Fahad Hezadeh Lf l Paa Reza N The pal l f h pble cdeed a he c wegh. Thee. Thee ε > 0 ch ha pble (4) feable. Pf: Le ε (... ) ad ε (... ) whee ε ad ε ε. Baed he def f ε we hae ε (... ). I he de accdg he def f ε ε (... ). Th 0 ε (... ) l f pble 4.. Cdeg { ε ε } ε we w hae ( ) Thee3. lea e f he ca (4 ) bdg pal. a a feable Pf: Le ( ) he pal l f pble (4). Wh ca pe ap cde < (... ). Th hee θ > ad θ (... ). If we cde θ { } θ B we hae ) θ he θ > ad θ (... ). 0 whch el θ ( θ 0 (... ). I h a ( θ... θ θ... θ ) a feable l f pble (4). Bede > ( cpleed. θ.th ha cadc wh pal ). Theefe e f he ca (4 ) bdg pal ad pf Thee4. lea e f he ca (4 ) bdg pal. Pf: Cde ( ) pe ap le he pal l f pble (4). B ca < 0 (... ). Th hee h > 0 whch + h 0 (... ). Sppe h { h } h > 0. Theefe + h 0 (... ). We hae. We w defe ( + h... + h... ) whch a feable l f pble (4) ad we hae ( + > h )... (. Th ha cadc wh pal... ). Theefe a lea e f he ca (4 ) bdg pal. Thee5. B g he CSW f del (4) he elae effcec f DMU eaed. Vle Ie 0 408

5 c e f wegh dea eae effcec ad def pdc chage Fahad Hezadeh Lf l Paa Reza N Pf: The ca 0 (... ) ewe a pble (4) ca be (... ). Le ( ) he pal l f (4). Thee 4 gaaee ha hee a {... } a ad. Hece f each {... } a Th hw ha he effcec f DMU eaed b he pal wegh f pble (4) he elae effcec f he. 3. Malq pdc de b c e f wegh ehd ad The MPI eae he pdc chage f DMU ped ad + b: M D ( DMU ) D D ( DMU ) D + ( DMU ) ( DMU ) / p q whee D ( DMU ) he effcec ce f DMU ped q ela ped p. Th ce ca be eaed b lg he fllwg pble: Ma.. q q p p 0... ε (5) Whe M + h gfe a pdc ga; whe M + h gfe a pdc > l; ad whe M + hee chage pdc (Ck ad Sefd 009). Th eae ca be decped w cpe echcal effcec chage ad echlgcal chage ad ca be ewe a: < M D ( DMU ) D ( DMU ) ( DMU ) + D D D ( DMU ) D ( DMU ) ( DMU ) / Vle Ie 0 409

6 c e f wegh dea eae effcec ad def pdc chage Fahad Hezadeh Lf l Paa Reza N whee he a de f he backe he echcal effcec chage ad he geec ea afe h a he echlgcal chage. The cpe f he MPI ae he effcec f DMU dffee ped ha ae baed b LP CCR del (5). I h del he fae wegh ae aged f he ealag DMU ad a deal effcec apppaed he ealag DMU. Th a flece he MPI ad cec ce a be baed f he MPI. We ppe e he CSW appach f calclag he MPI ha a effece ehd f fa aee f DMU (ehe pc pec). The cpe f he MPI clac DE ae baed b cdeg he echlg a ped ad he ealag DMU ha ahe ped. I he wd b g he echlg a ped he effcec f he ealag DMU ha ahe ped eaed. The CSW appach e a e f wegh eae he effcec f a e f DMU. Th eaable ha f calclag he MPI baed he CSW appach we ba he wegh f a ped ad e he f eag he effcec f a e f DMU ha ahe ped Le ( ) ad ( ) ae epecel he CSW ped ad + whch ae baed b lg he fllwg lea pgag pble a: Ma.. p p... p p 0... ε (6) ( p + ) The he peface f DMU ped q ela ped p eaed b: p q p q p q D ( DMU ) { + }. p q Th he MPI g he CSW ehd ca be calclaed a: M Necal eaple I h ec we eae a ecal eaple b he pped ehd. The el f ehd eae he MPI cpaed wh he baed MPI b he CCR del. Hee hee DMU wh e p ad w p ae cdeed w ped ad +. The daa ae epecel he daa + ae pded Table whch ( ) ad ( ) ped ad +. The daa wa pel ded b Ka (00). / Vle Ie 0 40

7 c e f wegh dea eae effcec ad def pdc chage Fahad Hezadeh Lf l Paa Reza N Table : DMU' daa w ped DMU B C Daa ped Daa ped The cpe f he MPI f hee hee DMU ad baed he CCR del ad he pped CSW del ae peeed Table ad 3 epecel. Cpag he el f Table ad 3 he effcec f each DMU Table 3 le ha eqal cepdg ce Table. The ea ha he DMU he clac DE ch a CCR ae ealaed he pc pepece ad he baed effcec f DMU bee ha ha b a he ehd ch a he CSW ehd. Table : Cpe f he MPI b he CCR ehd DMU D ( DMU ) ( DMU + D ) D + ( DMU + + ) D ( DMU ) B C Table 3: Cpe f he MPI b he CSW ehd DMU D ( DMU ) ( DMU + D ) D + ( DMU + + ) D ( DMU ) B C ccdg he effcec f DMU w dffee ped whch wa peeed Table ad 3 he MPI baed he CCR ehd ad he CSW ehd deaed Table 4. We ee ha he calclaed MPI b hee w ehd ae dffee. DMU baed he CCR ehd ha ege he pdc wheea baed he CSW ehd ha pge. Th ae cee f DMU C. DMU B b bh ehd ha ege he pdc. Thee dffeece ca be epeed a fllw. F eaple cde DMU. Thee ce D ( DMU ) ( DMU D ) ad D ( DMU ) calclae he MPI ae ccded b bh D + ( DMU ehd. ) b he CCR ehd eqal.0563 wheea b he CSW ehd eqal We e ha h ce he dea f he a f calclag he MPI. Th he e ha ale f D + ( DMU ) he le ha ale f MPI. Theefe he baed ale f MPI f DMU b he CSW ehd e ha ha b he CCR ehd. Sla dc ca be aed f DMU C. DMU Table 4: he MPI wh he CCR ad CSW ehd MPI (CSW) MPI (CCR) B C Vle Ie 0 4

8 5. Ccl c e f wegh dea eae effcec ad def pdc chage Fahad Hezadeh Lf l Paa Reza N I h acle he CSW appach a a ealc ehd f eag he effcec f DMU (ehe pc pec) wa eeded f cpg he pdc chage b he MPI. f a ew CSW ehd ha ce wh he LP CCR wa pped ba he wegh f dce. The wegh baed dffee ped wee he ed calclae he cpe f he MPI. The eaple peeed h pape hwed ha he el f eag he MPI baed he CCR del ad he ggeed CSW del ca be qe dffee. The ea ha he cpe f he MPI baed he clac DE del ae eaed he pc cd whch lead ealc ce f he MPI wheea hee cpe he CSW ehd ae e ealc. Mee he e f he CSW ehd adaage f he cpaal p f ew. 6. Refeece. Cae D.W. Chee L.R. Dewe W.E (98) The ecc he f de be ad he eaee f p p ad pdc Ececa 50(6) pp Chae. Cpe W.W. Rhde E (978) Meag he effcec f dec akg Epea Jal f Opeaal Reeach (6) pp Ck W.D. Sefd L.M (009) Daa eelpe aal (DE) Th ea Epea Jal f Opeaal Reeach 9() pp Fae R. Gkpf S. Ldge B. R P (99) Pdc chage Swedh phaace : paaec alq appach The Jal f Pdc al 3 pp Fae R. Gkpf S. N M. Zhag Z (994) Pdc gwh echcal pge ad effcec chage dalzed ce The eca Ecc Reew 84() pp Feg G. Sele (008) Pdc ed U.S. afacg: Edece f he NQ ad IM c fc Jal f Ecec 4() pp Jahahahl G.R. Meaa. Hezadeh Lf F. Reza H (005) e e f DE del ad fdg effcec ad cplee akg g c e f wegh ppled Maheac ad Cpa 66() pp Ka C (00) Malq pdc de baed c wegh DE: The cae f Tawa fe afe egaza Oega 38(6) pp L F.H.F. Peg H.H (008) Rakg f he DE fe wh c wegh Cpe & Opea Reeach 35(5) pp Vle Ie 0 4

9 c e f wegh dea eae effcec ad def pdc chage Fahad Hezadeh Lf l Paa Reza N 0. L F.H.F. Wag P.H (008) DE alq pdc eae: Tawaee ecdc cpae Ieaal Jal f Pdc Ecc pp Rll Y. Ck W. Gla B (99) Cllg fac wegh daa eelpe aal IIE Taac 3() pp 9.. Te K (00) lack baed eae f effcec daa eelpe aal Epea Jal f Opeaal Reeach 30(3) pp Wag Y.M. L Y. La Y.X (0) C wegh f fll akg dec akg b ege aal Epe Se wh pplca 38(8) pp Vle Ie 0 43

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