Incorporating Undesirable Outputs into Malmquist TFP Index: Environmental Performance Growth of Chinese Coal-Fired Power Plants

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Incorporating Undesirable Outputs into Malmquist TFP Index: Environmental Performance Growth of Chinese Coal-Fired Power Plants"

Transcription

1 Inorporaing Undsirabl Oupus ino Malmquis TFP Indx: Enironmnal Prforman Growh of Chins Coal-Fird Powr Plans Hongliang Yang and Mihal Polli Spmbr 2007 CWPE 0740 and EPRG 076

2 Inorporaing Undsirabl Oupus ino Malmquis TFP Indx: Enironmnal Prforman Growh of Chins Coal-Fird Powr Plans Hongliang Yang * and Mihal Polli ** Absra In his aril w xamin h ffs of undsirabl oupus on h Malmquis TFP indis. Our mpirial work uss an unbaland panl whih ors 796 uiliy and non-uiliy oal-fird powr plans in China during In ordr o m h rquirmn of a baland panl for alulaing h Malmquis indis, an innoai fak uni approah has bn inrodud. Our final rsuls show ha () h growh of h Chins lriiy haily dpnds upon an inras of rsour inpu; and (2) hug ponial rmains wih rgards o h ffiiny impromn and missions onrol in Chins oal-fird powr plans. Kywords: Malmquis indiis, oal faor produiiy, Chins lriiy, powr plan ffiiny JEL lassifiaion: D24, L94. Inroduion Alhough i is widly aknowldgd in ffiiny analysis liraur ha analyss should onsidr h ffs of undsirabl oupus, in sudis of produiiy hang analysis, ry fw publishd paprs ha akn hs ffs ino onsidraion. As nironmnal onrn inrass, hr is a mor urgn nd for us o onsidr suh ffs. Following a disussion of prious liraur on h Malmquis TFP indx, his papr amps o onribu o h disussion of his onrn in hr ways. Firsly, i amps o inorpora undsirabl oupus ino produiiy hang masurmn by inroduing a nw mission-inorporad Malmquis TFP indx. Sondly, his papr ris o dfin a pur nironmnal prforman indx basd on prious sudis on aribu-inorporad Malmquis indis. Thirdly, his rsarh amps o proid a rlaily obji analysis of prforman growh in Chins oal-fird powr plans. Lam and Shiu (2004) rpord a 2.% annual TFP growh of h Chins lriiy gnraion sor bwn 995 and 2000, using a DEA bnhmarking approah. Howr, hir papr rprsnd mor of a snapsho of h Chins lriiy indusry, rahr han a ompl insigaion. This is baus h numbr of obsraions mad was qui small. Th daa usd inludd annually aggrgad figurs in rms of adminisrai proins, and only 30 DMUs wr sudid. Also, hy only onsidrd radiional inpus and oupus, laing missions rsuling from lriiy gnraion * Judg Businss Shool, Unirsiy of Cambridg, **Judg Businss Shool, Unirsiy of Cambridg, Th auhors ar boh mmbrs of h ESRC Elriiy Poliy Rsarh Group whos finanial suppor is aknowldgd. Commns on an arlir draf by Prof. Sphn Lilhild and Prof. Emmanul Thanassoulis ar also aknowldgd. Thy ha bnfid from ommns rid a prsnaions in Cambridg Unirsiy. All rmaining rrors ar hir own. 2

3 unonsidrd. Howr, h larg shar of oal-fird gnraing apaiy has ausd srious onomi and nironmnal problms in China. So h inorporaion of missions ino produiiy hang aluaion boms nssary. Th panl daa sampl usd in his rsarh ors 796 uiliy and non-uiliy oal-fird powr plans, disribud hroughou 2 proins in h mainland of China bwn 996 and Th oal gnraing apaiy of h sampl was abou 04GW in Calulaing h Malmquis indx normally rquirs a baland panl daa sampl. Howr, during h rpor priod many nw powr plans wr buil whil old powr plans wr shu down on an annual basis. Apparnly, i is hrfor ry hard o m his baland rquirmn. In ordr o sol his problm, his rsarh inrodus an innoai fak dision-making uni approah. To h auhors knowldg, no ohr publishd paprs on TFP hang ha usd his mhod bfor. In his papr, sion 2 riws prious liraur on boh h radiional Malmquis TFP and h aribu-inorporad Malmquis indis. Sion 3 oulins h rsarh mhodology. Boh an mission-inorporad Malmquis TFP indx and a pur nironmnal prforman indx ar dfind in his sion. Sion 4 dsribs h rsarh daa, and also summarizs hniqus for inroduing a fak uni ino h DEA-rlad Malmquis modl. Sion 5 rpors h mpirial rsuls and sion 6 onluds h papr. 2. Liraur Riw 2. Tradiional Produiiy Chang Indx Analysis using indx numbrs o masur h TFP hang of arious produion prosss has bn ondud for many yars. Nishimizu and Pag (982) proposd a mhod o dompos TFP hang ino hnial hang (TECHCH) and hnial ffiiny hang (EFFCH) whn xamining produiiy hang in Yugoslaia bwn 965 and 978. TECHCH was dfind as hang in h bs prai produion fronir, whil EFFCH was dfind o inlud all ohr produiiy hang, inluding larning by doing, diffusion of nw hnologial knowldg, improd managrial prai, and so on. In Nishimizu and Pag s domposiion, h oal TFP hang is h sum of TECHCH and EFFCH. Baur (990) xndd h domposiion of TFP hang by showing how hangs in os ffiiny migh aff TFP growh. Gnrally, h abo xploraions rquir h arbirary slion of a funional form for produion hnology, whras h mhods usd blow nail a non-paramri DEA approah. Far al. (994) alulad h TFP indx as h gomri man of wo Malmquis produiiy indis, h lar of whih was inrodud by Cas al. (982a, 982b). Assum ha h produion hnology S a im an b wrin as x y inpus S = { (, ) : x an b usd o produ y }, N whr x R + dnos inpu bundls and y R + rfrs o oupu bundls for im ( =,, T). Far al. (994) hn dfind h oupu disan funion a im as D ( x, y ) = Inf { θ : ( x, y θ ) S }, whr D ( x, y ) if and only if ( x, y ) S undr CRS assumpion. Similarly, h oupu disan funion a im + an also b dfind. To alula h rlad Malmquis 3

4 indx, wo mor disan funions ha o b dfind wih rsp o wo diffrn im + + priods. On is o masur h disan of produion ( x, y ) rlai o hnology a im, and h ohr is ha of produion ( x, y ) rlai o hnology a im +. Figur : Oupu Disan Funion and h Malmquis TFP Chang Indx Y f S + h d j i b g a O B + B A (x, y ) x x + A + (x +, y + ) S S + S X Figur shows h alulaion of oupu disan funions. In Figur S rprsn CRS produion fronirs, whil S + and S + and S rprsn VRS produion fronirs, a ims + and rspily. Undr CRS, h masurs of arious oupu disan funions ar: D ( x, y ) = Inf { θ : ( x, y / θ ) S } = oa () ob D + ( x +, y + ) = Inf { θ : ( x +, y + / θ ) S + } = o (2) of D ( x, y ) = Inf { θ : ( x, y θ ) S } = o (3) o and D + ( x, y ) = Inf { θ : ( x, y θ ) S + } = oa (4) od 4

5 Far al. s Malmquis TFP hang indx M x y x y Far + + (,,, ) an hn b dfind as Far + + D ( x, y ) D ( x, y ) (,,, ) = + D ( x, y ) D ( x, y ) M x y x y D ( x, y ) D ( x, y ) D ( x, y ) = D ( x, y ) D ( x, y ) D ( x, y ) EFFCH ( TECHCH ) ( ) o ob of od = of oa o ob / 2 / 2 / 2 (5) Th raio ousid h braks in Equaion (5) is dfind as hnial ffiiny hang (EFFCH) and h raio insid h braks as hnial hang (TECHCH). EFFCH D ( x, y ) o ob = = D x y of oa (, ) (5a) TECHCH + + (, ) (, ) / 2 / 2 D x y D x y of od = = D ( x, y ) D ( x, y ) o ob (5b) Normally, if VRS is assumd hn hr is D ( x, y) = D ( x, y) SE( x, y) (6) whr SE rprsns h sal ffiiny. Basd on Equaion (6), Far al. furhr domposd h EFFCH rm ino wo mor omponns undr h VRS fronir: pur hnial ffiiny hang (PEFFCH) and sal ffiiny hang (SCH). D ( x, y ) D ( x, y ) SE ( x, y ) = D ( x, y ) D ( x, y ) SE ( x, y ) ( PEFFCH ) ( SCH ) (7) In rms of Figur h raio forms of following raio forms: PEFFCH and SCH an b wrin in h PEFFCH D ( x, y ) o og = = D x y oh oa (, ) (7a) SCH SE ( x, y ) oh ob = = SE ( x, y ) of og (7b) Finally hn, Far al. s Malmquis TFP hang indx M x y x y Far + + (,,, ) is 5

6 domposd as: Far + + M ( x, y, x, y ) = PEEFCH SCH TECHCH (8) Ray and Dsli (997) poind ou ha Far al. s (994) domposiion in Equaion (8) posd a problm of inrnal inonsisny. Thy argud ha Far al. s masur of TECHCH, whih is dfind in Equaion (5b), orrly masurs hnial hang only whn CRS is assumd. Howr, if his is h as undr CRS hn no sal inffiiny xiss by dfiniion. In ohr rms, if sal inffiiny dos xis and lads o h VRS assumpion, hn Far al. s masur of hnial hang is flawd baus i dos no masur h shif in h VRS fronir. Ray and Dsli s argumn is ry srong. Thy hn proposd hir domposiion of h Malmquis TFP indx basd on VRS fronirs. Howr, Ray and Dsli s domposiion is no wihou problms. Firsly, as Far al. (997) poind ou, alhough Ray and Dsli proidd diffrn spifiaions for h TECHCH and SCH omponns basd on VRS rfrn hnology, hir orall Malmquis TFP indx was sill ompud in rms of a CRS bnhmark. Thrfor, Ray and Dsli s orall masur of Malmquis TFP is in ssn idnial o Far al. s (S Appndix). Sondly, Ray and Dsli (997) also rognizd ha highs arag produiiy ould only b ahid a h angn poin of VRS and CRS fronirs. Th problm hn boms whhr or no w bli ha h VRS fronir an rprsn bs prai in h indusry. If no, hn hr is no ground for us o us h shif of VRS fronir o rprsn hnial hang orrspondingly. Thirdly, Grifll-Taj and Loll (995) poind ou ha whn VRS is assumd, h Malmquis TFP indx dfind in Equaion (5) proids an inaura masur of TFP hang. This inauray is sysmai and dpnds on h magniud of sal onomis. All hs rasons qusion h raionaliy of using h VRS fronir as a bnhmarking hnology for alulaing h Malmquis TFP indis. Thrfor, his papr adops h CRS fronir as a bnhmarking hnology. Howr, in rogniion of Ray and Dsli s inonsisny argumn agains Far al. s domposiion, h auhor only domposs h Malmquis TFP indx ino wo omponns, namly hnial ffiiny hang (EFFCH) and hnial hang (TECHCH), as dfind in Equaion (5). 2.2 Inorporaing Emissions ino Malmquis Indis On of h prsisn diffiulis in h masurmn of produiiy is how o xplain h ff of rain aribus of h produion pross. Currn liraur on aribu-inorporad Malmquis indis mainly fouss on h xamining pross and h qualiy faurs of a produion. This sion amps o dlop an mission-inorporad Malmquis TFP indx basd on h disussion of urrn liraur. Fixlr and Zihang (992) showd how h Malmquis produiiy indx an b usd o aoun for hangs in inpus, oupus and pross and qualiy aribus. Dno inpus by x R +, oupus by y R + and aribus by a R + for im priod ( =,..., T ). Thn h produion hnology S a im boms x y a inpus S = { (,, ) : x an b usd o produ y and a }. Th disan funions wih rsp o diffrn im priods an hn b dfind. For xampl, h inpu disan funion inorporaing aribus a R + a im is dfind as 6

7 { ρ ρ } D ( x, y, a ) = Sup : ( x /, y, a ) S Fixlr and Zihang (992) dfind hir aribu-inorporad, inpu-orind produiiy indx as Equaion (9), whih is ssnially xndd from Equaion (5) o inlud h aribu or a: D ( x, y, a ) D ( x, y, a ) + Fixlr D ( x, y, a ) D ( x, y, a ) a (,,,,, ) = M x y a x y a / 2 (9) Following Fixlr and Zihang, Far al. (995) proposd a nw Malmquis indx o inorpora h non-markabl aribus of produion whn masuring h sri qualiy of Swdish pharmais: D ( x, y, a ) D ( x, y, a ) (0) Far D ( x, y, a ) D ( x, y, a ) a (,,,,, ) = + M x y a x y a Far ( M ) a / 2 Far al. s dfiniion is aually a riproal of Fixlr and Zihang s. Sin Far al. (995) usd inpu disan funions o dfin h Malmquis produiiy indx, a alu of lss han on hrfor orrsponds o prforman impromn, whras a alu grar han on rfls prforman drioraion. This is an unhlpful rprsnaion of produiiy growh, whih w will rurn o lar. Basd on h sam logi as ha apparn in Equaion (5), Equaion (0) an b domposd ino wo faors. Ths ar M D ( x, y, a ) D ( x, y, a ) D ( x, y, a ) (0a) ( EFFCH ) ( TECHCH ) Far a = D ( x, y, a ) D ( x, y, a ) D ( x, y, a ) a a / 2 Far al. also dfind a qualiy (or qualiy hang) indx for h hnology bwn im and +: Q x y a x y a (,,,,, ), + ( Qa ) / 2 (,, ) (,, ) (,, ) (,, ) D x y a D x y a = D x y a D x y a () Th abo hr faors, inluding EFFCH a, non-sparabl indis in Far al. (995). TECHCH a and Q +, wr rpord as, a From h abo, Equaion (0) an also b arrangd as: Far D ( x, y, a ) D ( x, y, a ) a = (,,,,, ) + + M Q x y a x y a D ( x, y, a ) D ( x, y, a ) /2, (2) 7

8 whr Q x y a x y a (,,,,, ) is dfind as in Equaion (). If w an assum ha h disan funion is mulipliaily sparabl in aribus and inpus/oupus, ha is, if D ( x, y, a ) = A ( a ) D ( x, y ), (3) hn h sond faor on h righ hand sid of Equaion (2) boms / 2 (,, ) (,, ) + + D ( x, y, a ) D ( x, y, a ) D x y a D x y a D x y A a D x y A a = (, ) ( ) (, ) ( ) D ( x, y ) A ( a ) D ( x, y ) A ( a ) D ( x, y ) D ( x, y ) = + D ( x, y ) D ( x, y ) = M, + / 2. (4) If h sparabiliy assumpion of Equaion (3) is hld, h aribu-inorporad Malmquis indx M an hrfor b wrin as Far a M = Q M Far, +, + a a = Q EFFCH TECHCH, +, +, + a (5) Th hr faors on h righ-hand sid of Equaion (5) ar idnifid by Far al. (995) as sparabl indis. Th rsuls of Far al. (995) showd ha qualiy aribus do mak a diffrn in masurd produiiy hang, bu h sparabiliy assumpion mad in Equaion (3) may no b appropria. Following Far al. (995), Giannakis al. (2005) usd a similar dfiniion of h qualiy-inorporad Malmquis indx on a bnhmarking sudy of lriiy disribuion uiliis in h UK bwn 99/92 and 998/99. Compard wih Far al. (995), Giannakis al. s onribuions ar wofold. Firsly, diffrnly from Far al. (995), in whih qualiy rfrs o aribus whih rquir h us of mor rsours, Giannakis al. (2005) usd h numbr of minus los and h numbr of inrrupions as aribus of qualiy. Thrfor, alhough h rm qualiy is sill usd, hs aribus ar aually h undsirabl oupus of disribuion uiliis. Baus undsirabl oupus xis xnsily in many produion sysms, Giannakis al. s xnsion on Far al. s qualiy-inorporad Malmquis indx an hus b usd for a grar playing fild. Sondly, Giannakis al. (2005) usd h Malmquis indx as dsribd in Thanassoulis (200), in whih DEA ffiiny sors, rahr han disan funions, ar usd o dfin h Malmquis indx. Baus in CRS DEA h alu of an inpu-orind disan funion is qual o h riproal of h DEA ffiiny sor 2, Thanassoulis dfiniion is aually in In raliy, h qualiy faor A (.) an b ompud rsidually by aking raions of wo rlad disan funions. 2 Th inpu-orind hnial ffiiny is qual o h inrs of h inpu disan funion, whil oupu-orind hnial ffiiny is qual o h oupu disan funion. Also, undr h CRS 8

9 lin wih Fixlr and Zihang s (992) dfiniion (whih an b sn in Equaion (9)). By his dfiniion, a alu grar han on rfls prforman growh and a alu lss han on orrsponds wih prforman dgradaion. Giannakis al. (2005) also rpord an inonsisny bwn non-sparabl and sparabl Malmquis indis. Howr, Giannakis al. (2005) did no noi h inrnal inonsisny problm of Far al. (994), whih was xplaind in h prious sion. Thir final domposiion of h qualiy-inorporad Malmquis indis sill inludd a sal omponn whn masuring TECHCH undr h CRS fronir. Som of hir final rsuls may hrfor b mislading. To summariz, Fixlr and Zihang (992) sussfully showd how h Malmquis produiiy indis an b usd o aoun for hangs in inpus, oupus and pross and qualiy aribus. Far al. (995) suggsd ha qualiy aribus do mak a diffrn in masuring Malmquis produiiy hang. Also, hir rsarh rsuls showd ha h sparabiliy assumpion is no onsisn wih h aribu-inorporad disan funion. Giannakis al. (2005) xndd h aribu-inorporad Malmquis indx o inlud undsirabl oupus as qualiy aribus. This xnsion nlargd h playing fild of h aribu-inorporad Malmquis indis. Addiionally, as xplaind abo, Far al. s masurmn is no in lin wih h daily usom of h popl. Fixlr and Zihang (992) and Giannakis al. (2005) ha sapd his problm by using a diffrn sing for h Malmquis produiiy indx. Basd on h abo, his papr will firsly, dfin an mission-inorporad Malmquis indx following Fixlr and Zihang (992) and Giannakis al. (2005). Sondly, alhough inonsisn idn for a sparabiliy assumpion (for hir sampls) is rpord in boh Far al. (995) and Giannakis al. (2005), baus som nw faurs will b assignd o ariabls in h Malmquis indis in his papr, h auhors will s h sparabiliy assumpion again bfor formally rjing i - so as o no mak an arbirary onlusion. 3. Mhodology I is widly aknowldgd ha ignoring undsirabl oupus in ffiiny analyss may bring mislading rsuls. Thrfor, i is nssary o xamin h ffs of undsirabl oupus on produiiy hang or im. 3. Inorporaing Emissions ino h Malmquis Produiiy Indx Assum ha w ha N (homognous) dision making unis (DMUs), ah using M inpus M d P u S x R + o produ P dsirabl oupus y R + and S undsirabl oupus y R +. Th produion hnology S a im ( =, 2,...,T ) an b wrin as d, u, S = { (,, ) : x y y inpus x an b usd o produ d, y and u, y }. Undr h CRS fronir, h inpu disan funion inorporaing undsirabl oupus is dfind as u, { ρ x y ρ ρ } D x y y = Sup y S d, u, d, (,, ) : (,, ) fronir, h inpu orind hnial ffiiny is qual o h oupu orind hnial ffiiny. For dails, plas rfr o (Colli al., 2005). 9

10 Similarly, disan funions wih rsp o diffrn im priods an also b dfind. Following Fixlr and Zihang (992), w an hn dfin h missions-inorporad, inpu-orind Malmquis TFP indx ( M + ) as D ( x, y, y ) D ( x, y, y ) d, u, + d, u,, + + d, + u, + d, u, D ( x, y, y ) D ( x, y, y ) (,,,,, ) = + d, + u, d, + u, + M x y y x y y /2 (6) As mniond abo, Equaion (6) is aually qual o Equaion (7), whih is similar o hos dfind in Giannakis al. (2005). M + d, + u, d, + u, +, + TE ( x, y, y ) TE ( x, y, y ) = d, u, + d, u, TE ( x, y, y ) TE ( x, y, y ) / 2 (7) In Equaion (7), for xampl, TE x y y + d, + u, + (,, ) rprsns a firm s hnial ffiiny sor undr h CRS fronir a im, using inpu and oupu bundls a im +. Basd on h sam logi as Equaion (5), h missions-inorporad inpu-orind Malmquis indx dfind in Equaion (6) an b domposd as follows: M D x y y D x y y D x y y D ( x, y, y ) D ( x, y, y ) D ( x, y, y ) (8), EFFCH ( TECHCH + ) d, u, + + d, + u, + + d, u,, + (,, ) (,, ) (,, ) = + + d, + u, + + d, + u, + d, u,, + ( ) / 2 No ha h abo quaions inorporad undsirabl oupus. M +,, EFFCH +, and TECHCH +, ha alrady Following Far al. (995), a similar pur nironmnal prforman Malmquis indx is dfind as Q D ( x, y, y ) D ( x, y, y ) d, u, + + d, + u,, + D ( x, y, y ) D ( x, y, y ) = d, u, d, + u, + TE x y y TE x y y = TE x y y TE x y y d, u, d, + u, + (,, ) (,, ) d, u, + + d, + u, (,, ) (,, ) / 2 / 2 (9) Apparnly, if w allow sparabiliy assumpion in h domposiion, basd on h sam logi as Equaion (5), h mission-inorporad Malmquis indx an b domposd as follows: M = Q EFFCH TECHCH (20), +, +, +, + I is worh rpaing ha, as xplaind in h prious sion, in h non-sparabl modl, Q +, is no a omponn of M +,. In fa, in mos ass M + is no qual o h 0

11 mulipliaion of Q +,, EFFCH + and, TECHCH +., 3.2 Compuaion of Disan Funions Th ompuaion of boh M, + and Q + is similar o hos disussd in Far al. (995), and Giannakis al. (2005). Th only diffrn is ha boh of hm assum ha all inpus, oupus and aribus ar frly disposabl. This papr uss diffrn disposabiliy assumpions for diffrn undsirabl oupus in ordr o rfl h siuaion in rms of h polluion abamn hnologis usd (Yang, 2007). Du o his similariy, only wo of h disan funions whih nr ino h Malmquis indx dfind in Equaion (6) ar prsnd. Ths masur h disan of d, u, produion ( x, y, y ) rlai o h hnology a im and im + rspily. Dno undsirabl oupus wih wak disposabiliy by y u w, whil undsirabl oupus wih u srong disposabiliy by y s. Th orrsponding rfrn hnology saisfying his assumpion is hn as follows: S x y y y y Y λ y Y λ y Y λ x X λ λ R+ d, u, u, d, d, u, u, u, u, = {(,, w, s ) :, w = w, s s,, } Baus in DEA h alu of h inpu disan funion is qual o h inrs of h inpu-orind hnial ffiiny, hrfor, h alulaion of disan funion for firm j a im rlai o h hnology a im is as follows: s.. d, u, u, j (,, w, s ) = min D x y y y y Y d, d, j λ θ θ y = Y u, u, w, j w λ (2) θ y θ x u, u, s, j s j λ R Y X λ + λ Similarly, h alulaion of disan funion for firm j a im, rlai o h hnology a im + is as follows.

12 d, d, + j + d, u, u, D j ( x, y, yw, ys ) = minθ s.. y Y λ θ y = Y u, u, + w, j w λ (22) θ y θ x u, u, + s, j s j Y X λ R + + λ λ For a furhr xampl of h disan funions whih nr ino h nironmnal prforman Malmquis indx dfind in Equaion (9), w lis h following: s.. d, u, + u, + j (,, w, s ) = min D x y y y y Y d, d, j λ θ θ y = Y u, + u, w, j w λ (23) θ y θ x u, + u, s, j s j λ R Y X λ + λ 3.3 Domposiion of Nwly Dfind Malmquis Indis In rms of h disan funions dfind in Equaions (2)-(23), w hn prod o, alula M +, whih is dfind in Equaion (8) in h following modifid forma whih disinguishs srongly and wakly disposabl undsirabl oupus: M /2 d, u, u, + + d, + u, + u, + + d, u, u,, + D ( x, y, ys, y ) w D ( x, y, ys, yw ) D ( x, y, ys, y ) w = + + d, + u, + u, + + d, + u, + u, + d, u, u, D ( x, y, ys, yw ) D ( x, y, ys, yw ) D ( x, y, ys, yw ), +, + ( EFFCH ) ( TECHCH ) (24) Similarly, w alula h pur nironmnal prforman indx whih is modifid from Equaion (9): Q + in Equaion (25),, Q (,,, ) (,,, ) d, u, u, + + d, + u, u,, + D ( x, y, ys, yw ) D ( x, y, ys, yw ) = d, u, + u, d, + u, + u, + D x y ys yw D x y ys yw / 2 (25) Th abo hr indis M +,, EFFCH +, and TECHCH +, ar rpord as 2

13 non-sparabiliy indis whih ha inorporad undsirabl oupus. If assuming sparabiliy, M, + an hn b domposd as follows: M = Q EFFCH TECHCH, (26), +, +, +, +, whr Q + is as dfind in Equaion (25) and as in Equaion (5)., EFFCH + and, TECHCH + ar dfind To failia an xplanaion of nwly dfind indis, radiional Malmquis TFP indis ar also alulad for h purpos of omparison. Two kinds of omparisons an b prformd in his papr basd on h indis rpord. Th firs omparison is bwn h radiional, Malmquis produiiy indx ( M + ), dfind in Equaion (5), and h nw, missions-inorporad Malmquis produiiy indx ( M + ). This omparison shows h raionaliy of h nw Malmquis produiiy indx. Th sond omparison is bwn h sparabiliy and non-sparabiliy rsions of h nw Malmquis indis. A wo-sampl T-s is usd o xamin whhr h rsul diffrn bwn h sparabiliy and non-sparabiliy indis is signifian. This omparison illusras whhr or no h sparabiliy assumpion in Equaion (3) is rasonabl. 4. Panl Daa and Variabls 4. Panl Daa Th panl daa usd ors 796 uiliy and non-uiliy oal-fird powr plans disribud hroughou 2 proins in h mainland of China, inluding Hnan, Hubi, Hunan, Jiangxi, Hilongjiang, Jilin, Liaoning, Innr Mongolia, Bijing, Tianjin, Hbi and Shanxi, and nompassing h ara irld by h hik lin in Figur 2. Figur 2: Corag of Panl Daa Sampl 3

14 Th majoriy of h sampl powr plans ar ry small low-paramr powr plans wih an insalld apaiy lss han 50MW. For alulaion simpliiy, whn h proinial aggrgad daa of hs small inffiin powr plans is aailabl, h aggrgad daa is usd as a larg DMU in h modl. Two rasons suppor h us of his aggrgad daa. Firsly, baus DEA is an xrm poin mhod, hs small and inffiin powr plans an nr aff h posiion of h produion fronir. So h us of aggrgad daa dos no ha any ai influn on h final prforman masurmn. Sondly, in gnral h majoriy of small powr plans ha bn onrolld by hir ownrs lss ffily han h big powr plans 3. Using aggrgad daa an hrfor hlp o limina som sampling rrors. Tabl shows h raio of sampl oal o oal insalld apaiy in China during h rpor priod, and also h numbr of obsraions mad in ah rpor yar. During h rpor priod som ass ronfiguraions ourrd in h sampl powr plans. For xampl, som powr plans wih mulipl unis wr spli up ino smallr powr plans and som small powr plans wr mrgd oghr o form largr ons. All of h daa in h sampl has bn ronfigurd o rfl h indusry s sruur by h nd of Tabl also shows ha h larg unbaland daa panl usd in his papr inluds 626 ral obsraions in oal. Tabl : Prnag of Panl Sampl Toal o China Toal Rpor yar Sampl oal apaiy (GW) China oal apaiy (GW) Prnag (%) No. of obsraions Th daa from ah powr plan, suh as insalld apaiy, annual oil and oal onsumpion, annual numbr of mploys, annual lriiy gnraion, and qualiy of ful, was mainly olld during h auhor s fildwork in China bwn 2005 and Daa on h qualiy of ful is omplmnd by h CED (2004). Thr ar som mris in using plan-ll panl daa o analys h produiiy growh of Chins oal-fird powr plans. Firsly, i prmis h analysis of produiiy hang for ah indiidual plan. Sondly, baus sampl powr plans rmain h sam a diffrn poins during h rpor priod, i is saisially adanagous for us o find and limina sampling rrors. 4.2 Slion of Variabls Th radiional ariabls usd inlud lriiy gnrad, apial, labour, and ful. d Elriiy gnrad is usd as dsirabl oupu ( Y ), and is masurd by h uni MWh. Tradiional inpus ( X ) inlud apial, labour and ful. Capial is masurd by insalld apaiy (MW). Labour is masurd by h numbr of mploys, his bing h arag yarly numbr during h rpor priod. Qualiy of labour an b ry diffrn in rms of duaion, raining, xprin,. Howr, baus i is hard o masur, w simply assum in his rsarh ha hr is no noiabl diffrn in labour qualiy. Ful is masurd by nrgy (or ha) 3 This is baus in China h majoriy of larg oal-fird powr plans ar dirly onrolld by nral gornmn firms, and small powr plans ar largly onrolld by loal auhoriis. 4

15 inpu. Baus in almos all Chins oal-fird powr plans oil-fird (somims gas-fird) quipmn is also insalld for boilr-prhaing and sandby purposs, gin h rain load of a boilr, h mor oil or gas i uss, h lss oal is onsumd. In ordr o mak h final ffiiny aluaion aura and h omparison bwn powr plans maningful, i is hrfor nssary o onr all kinds of fossil ful onsumpion ino h sam uni in his papr, namly h rajoul (TJ). u Undsirabl ariabls ( Y ) rfr o missions rsuling from h lriiy gnraion pross. Emissions from oal ombusion mainly ompris CO 2, SO 2, CH 4, N 2 O, NO x, CO, and Non-mhan olail organi ompounds (NMVOC). An aura sima of hs missions dpnds on haing knowldg of sral inrrlad faors, inluding ombusion ondiions, hnology, and mission onrol poliis, as wll as ful hararisis. In gnral, h idnifiaion and quanifiaion of missions by ful yp is ssnial for h prforman aluaion of powr plans in his rsarh. Diffrn mhods an b usd o sima missions. Th mhods usd hr ar basd on h IPCC Rfrn Approah 4. In his papr, only SO 2 missions ar inludd as an undsirabl oupu 5. Following Yang and Polli (2007), srong disposabiliy is assumd for SO 2 missions. Th summary saisis of h ariabls sld ar shown in Tabl 2. For lariy, only daa olld in 996 and 2002 is rpord hr. Variabls ha bn groupd in ordr o rfl hir hararisis. Yar Tabl 2: Summary Saisis of Variabls Usd Annual Insalld No. of Enrgy gnraion apaiy Variabls mploys inpu (TJ) (MWh) (MW) d Y X SO2 Emissions (onn) u Y Toal Maximum Minimum Sandard diaion Man Toal Maximum Minimum Sandard diaion Man For mor dail, plas rfr o Risd 996 IPCC Guidlins for Naional Grnhous Gas Innoris: Rfrn Manual. 5 On h basis of urrnly aailabl daa rsours, CO 2 and NO x missions an also b simad. Howr, baus so far hr isn any CO 2 mission onrol in us in h oal-fird lriiy gnraion, i is ry hard o say whhr hr has bn any hnial impromn in CO 2 missions onrol. A similar siuaion is also h as for NO x onrol in Chins oal-fird powr plans. 5

16 4.3 Daa Compilaion Th qualiy of h daa usd ould ponially ha a srious ff on h final rsuls. Th qualiy of h daa is mainly affd by wo ss of faors, namly h prsn of oulirs in obsraions and h spial rquirmns of h rsarh. Hair al. (998) and Colli al. (2005) boh proidd good disussions on h rasons of h prsn of oulirs and h mhods usd for liminaing hir influn. Whil h prsn of oulirs mainly rsuls from saisial inauray, h spial rquirmns of h rsarh bing undrakn ar largly didd by wha w ar doing. In ordr o alula h Malmquis indis dfind abo, h panl daa usd has o b baland. Tha is, all DMUs mus b obsrd aross all im priods. This spial rquirmn ras an obious diffiuly wih rgards o alulaion. During h 7 yar rpor priod nw powr plans oninud o b buil, whil old plans oninud o b shu down. Sin 980 h Chins adminisraion has implmnd is nrgy onsraion program for h rduion of nrgy wasag. This implmnaion was pariularly idn during h rpor priod. In 998, whn h srious lriiy shorag was mporarily hald, many small and wasful gnraing unis wr shu down and rplad by largr and mor hnially ffiin failiis (Yang, 2006). Thrfor, i is ry hard o balan h daa panl using h ral obsrd daa, as in ah rpor yar som mpy daa nris always appar. On way of daling wih h unbaland daa panl, and hrfor bing abl o m h baland rquirmn for h Malmquis indx alulaion, is o find ou hos DMUs whih ar obsrd in all of h rpor yars. Howr, wo faors prn us from using his mhod. Firsly, in China s as his mans ha w ha o graly rdu h siz of h rsarh sampl. Th final rsuls will hn bom lss omprhnsi. Sondly, baus all powr plans whih mrg or disappar wihin a rpor yar anno b onsidrd in h modl, h final rsuls ar mor a masurmn of h rmaining sampl rahr han a gnral rflion of h whol indusry. This sudy inrodus an innoai approah in ordr o irumn his problm. Essnially, a fak uni is rad o fill in any mpy daa nry and hrfor mak h unbaland daa panl balan. As a guidlin, his fak uni uss a ry larg amoun of ah of h inpus o produ a ry small amoun of ah of h dsirabl oupus and a ry larg amoun of ah of h undsirabl oupus. In gnral, h fak uni xhibis h following faurs: () Similariy - i uss h sam kinds of inpus and produs and h sam kinds of dsirabl and undsirabl oupus as ohr ral DMUs do. (2) Inffiiny - h amoun of inpu i uss is no lss han ha of any ohr DMU in h sampl. Also, h amoun of dsirabl oupu i produs is no mor han, and h amoun of undsirabl oupu i produs is no lss han, hos of any ohr DMU in h sampl. (3) Bing omissibl - is ff on h final alulaion should b asy o pinpoin and dl. Th firs faur of h fak uni nsurs ha i an b usd as a subsiu in h alulaion. Baus h basi bnhmarking hnology usd is DEA, whih is an xrm poin mhod, h sond faur nsurs ha h prsn of h fak uni in h alulaion dos no aff h posiion of h produion fronir. Th hird faur nsurs ha baus h fak uni is rad for alulaing purposs only, is prsn should no aff h orrnss of alulaions for all of h ral obsraions. Essnially, h fak uni approah inrodus an unbaland panl onp ino DEA Malmquis indis. Th us of h fak uni influns h final alulaion of Malmquis indis in wo ways in his sudy. Firsly, in h as of a powr plan whih is shu down during a rpor yar, baus ral obsraions ha bn usd up o ha rpor yar, i is hrfor xpd ha in 6

17 h alulaion h powr plan will ha a larg ffiiny dras on yar afr. In rms of h kind of fak uni rad, his dras an b sral hundrd ims lss han a normal alu. Sondly, in h as of a powr plan whih is nwly buil during a rpor yar, baus ral obsraions ar usd afr ha rpor yar, i is hrfor xpd ha in h alulaion h powr plan will ha a larg ffiiny inras on yar afr. Similarly, in rms of wha kind of fak uni is rad, his inras an b sral hundrd or n sral housand ims mor han a normal alu. So boh ass ar apparnly ry asy o pinpoin in h final rsuls. Calulaions whih ar inflund by h prsn of h fak uni an hn b asily dld. Thrfor, h final rsuls for all of h ral obsraions an b rliably uphld as orrly rfling prforman. 5. Rsuls Rsuls ar alulad using modls and quaions as dfind abo. Alhough our alulaions yild powr plan-spifi Malmquis indis, gin h larg numbr of obsraions, mor aggrga rsuls ar proidd. Rsuls ar rpord blow in wo diffrn ways, namly, indiidual DMU and diffring rpor yars. Th produiiy indx is domposd ino wo omponns: EFFCH and TECHCH. 5. Indis Calulad in Trms of Indiidual DMU Tabl 3 displays hos rsuls alulad for h radiional, non-sparabiliy, and sparabiliy modls. Th alus prsnd for indiidual DMUs ar h gomri mans of Malmquis produiiy indis or h rpor priod. Gin h larg numbr of sampl powr plans, only sral xampls and man alus for all DMUs ar lisd. From Tabl 3, TFP growh an firs b obsrd in all hr modls during h rpor priod. Th TFP growh indis in h radiional and non-sparabiliy modls ar slighly largr han 3%, whil h TFP growh indx in h sparabiliy modl is only 0.8%. Sondly, in boh modls whih onsidr h ffs of missions, h alu of h, nironmnal prforman indx Q + is lss han on. This indias a dras in h nironmnal prforman of Chins powr plans during h rpor priod. Th abo finding shows ha h ff of h ndaour of Chins auhoriis o impro missions onrol in h lriiy indusry is no lar during h rpor priod. Thirdly, Tabl 3 displays h main sour of TFP growh. In all hr modls w an s ha TFP growh mainly oms from hnial hang (TECHCH). This indias ha h fronir shif onribud mor o TFP growh during h rpor priod. Thr is an approxima inras of 3% in h TECHCH indis aross all hr modls. This rsul orrsponds wih wo hings whih ourrd in China during h rpor priod. Abo all, many nw larg gnraing unis wih high hnial paramrs wr insalld annually bwn 996 and Tabl rfls som of h faurs of his rnd. For xampl, hr was a 07 GW oal-fird gnraing apaiy growh in China bwn 996 and 2002, h majoriy of whih am from larg gnraing unis wih a sal of no lss han 300 MW. This ould possibly bring h hnial fronir forwards. Also, whn h srious lriiy shorag in China was mporarily rmdid in 998, h Chins gornmn sard a nw round of lriiy rform ha fousd on building an ffiin lriiy indusry. Many small and inffiin oal-fird powr plans wr shu down. All of hs ffors ar xpd o ha som posii ffs on h prforman impromn of Chins oal-fird powr plans. 7

18 Tabl 3: Gomri Man of h Malmquis Produiiy Indis Or Rpor Priod in Trms of Indiidual DMU Powr plans,, M + Tradiional Non-sparabiliy Sparabiliy EFFCH + TECHCH, +, EFFCH +, TECHCH +, M +, Q + M, +, EFFCH + TECHCH, +, Man Q + Tabl 4: Gomri Man of h Malmquis Produiiy Indis in Trms of Diffrn Rpor Yar Tradiional Non-sparabiliy Sparabiliy Yar, M +, EFFCH + TECHCH, +, EFFCH + TECHCH, +, M +, Q + M, +, EFFCH +, TECHCH +, Man Q + 8

19 Fourhly, whil h ffiin fronir has xprind a posii shif, h prforman gap bwn ffiin and inffiin powr plans has rmaind largly unhangd. In all hr modls h EFFCH indis ar qual o.00, whih indias ha no apparn ffiiny ah-up ff an b obsrd in h indusry during h rpor priod. Las bu no las, h rsul diffrn bwn h non-sparabiliy and sparabiliy modls shows h inonsisny of h sparabiliy assumpion. A wo-sampl T-s by STATA rjs h hypohsis ha boh modls ha qual man alus a h 0.% signifian ll. Thrfor, w didd no o pursu a sparabiliy rsion of Malmquis indx domposiion any furhr in h sudy. This agrs wih h findings in Far al. (995) and Giannakis al. (2005). 5.2 Indis Calulad in Trms of Diffrn Rpor Yars Tabl 4 displays h gomri mans of h Malmquis produiiy indis of all h powr plans obsrd in ha rpor yar. Similar rsuls o hos in Tabl 3 an b found in Tabl 4. Firsly, TFP growh is on again obsrd in all hr modls. Th TFP growh indis in h radiional and non-sparabiliy modls ar 2.2%, whil in h sparabiliy modl his figur is approximaly 0.4%. Th TFP growh indis in h radiional and non-sparabiliy modls ar qui similar o hos rpord by Lam and Shiu (2004), in whih a 2.% annual TFP growh was nod in h Chins lriiy gnraion sor bwn 995 and Sondly, a lss-han-on nironmnal prforman indx is ahid. Thirdly, h main sour of TFP growh oms from hnial hang. Fourhly, almos no ffiiny ah-up is prsn in h indusry. This again indias ha h fronir shif onribud mor o TFP growh during h rpor priod han h ah-up ffs. Finally, h inonsisny bwn h non-sparabiliy and sparabiliy modls is obsrd on again. In gnral, h rsuls in Tabl 4 onfirm hos in Tabl 3. From Tabls 3 and 4, i is firs of all ry lar ha h rsuls of hr modls ha ry similar hang parns. This suppors our missions-inorporad Malmquis produiiy indx. Sondly, i is worh noing ha h TFP Malmquis indis ahid in Tabl 3 ar slighly largr han hos in Tabl 4. This is probably du o h fa ha afr h fak uni has bn inrodud h numbr of obsraions in h alulaion of Tabl 3 boms diffrn o h numbr of obsraions in h alulaion of Tabl 4. In Tabl 3 h numbr of obsraions is 278 hroughou h rpor priod. Howr, in Tabl 4 h numbr aris in rms of diffrn rpor yars. For xampl, h numbr is 205 in 996 and 256 in 2002 (Tabl ). As hr wr mor nw ffiin powr plans in h lar par of h rpor priod, i is xpd ha hy will xr mor of an influn on h final gomri man whn making h alulaions for Tabl Corrlaion of Malmquis Indis bwn Modls Tabl 5 xhibis h orrlaion offiins of h gomri man of h Malmquis indis 9

20 bwn h non-sparabiliy and radiional modls. Gnrally spaking, a high orrlaion offiin bwn wo ss of daa indias a high onsisny in boh ss of daa. Tabl 5: Corrlaion of Malmquis Indis Corrlaion Emissions-inorporad Malmquis Tradiional Malmquis M EFFCH TECHCH Q M EFFCH TECHCH M.0000 Emissions inorporad Malmquis EFFCH TECHCH Q Tradiional Malmquis M EFFCH TECHCH Firs of all, h orrlaion bwn Malmquis indis in h missions-inorporad modl and hos in radiional modl is ry high. This suppors our dfiniion of missions-inorporad Malmquis TFP indis and orrsponds wih h rsuls ahid in h prious sion. Sondly, in boh missions-inorporad and radiional modls h orall produiiy indis ar mor orrlad o EFFCH indis han o TECHCH indis. This suggss ha alhough h fronir shif (TECHCH) onribus mor o an inras in produiiy growh, i is lss orrlad wih ha growh han is ffiiny hang. A similar finding on h orrlaion bwn produiiy growh, ffiiny hang and hnial hang an also b sn in Giannakis al. (2005). Thirdly, in boh modls h orrlaion offiins bwn EFFCH and TECHCH ar qui low, whih implis ha h hang in ffiiny is indpndn of h hnial fronir shif and i rsa. Tha is, an obsrd TECHCH indx inras dos no nssarily man an inras in h EFFCH indx. Finally, h nironmnal prforman indx Q has boh low and ngai orrlaion offiins wih boh missions-inorporad and radiional Malmquis produiiy indis. This is inonsisn wih our inuiion. As h rsuls of h radiional and non-sparabiliy modls ar highly orrlad, his suggss o som xn ha during h rpor priod h impromn in gnraion prforman has om a h xpns of nironmnal 20

21 prforman (a las wih rsp o sulphur dioxid). A possibl hypohsis for his inonsisny is ha h nironmnal prforman indx, as dfind in Equaion (25) using Far al. s (995) forma, is ihr inorr or inappropria on his oasion (if for xampl, ohr dimnsions of nironmnal prforman nd o b inludd). A dfinii xaminaion of his is byond h sop of his papr. 6. Conlusion Numrous analyss rgarding h us of h Malmquis indx o masur h TFP hang ha bn ondud. Y o our knowldg, hr ar fw publishd paprs whih ak h undsirabl oupus of DMUs ino onsidraion whn aluaing produiiy hang or im. Prious sudis of h prforman of DMUs show ha h ignoran of undsirabl oupus migh yild mislading rsuls (Kopp al., 982; Far al., 989). I is hrfor nssary o s h ffs of undsirabl oupus on h TFP hang of DMUs. In his papr, prious liraur rgarding TFP hang has bn xamind and summarizd. Th srnghs of xising paprs ha hn bn ombind in ordr o sr our amp o dfin an missions-inorporad Malmquis indx. Somhing worhy of no is ha, firsly, his papr dfins a nw missions-inorporad Malmquis TFP indx o masur h orall TFP hang of Chins oal-fird powr plans. This papr adops CRS as h bnhmarking hnology. Howr, in rogniion of Ray and Dsli s (997) inonsisny argumn agains Far al. s (994) domposiion, h auhor only domposs h final alulaion of Malmquis TFP indx ino wo omponns, namly, hnial ffiiny hang (EFFCH) and hnial hang (TECHCH). Sondly, his papr also dfins a pur nironmnal prforman indx in ordr o masur h prforman impromn of h onrol of missions in Chins oal-fird powr plans. Th final rsuls suppor h auhors dfiniion of missions-inorporad Malmquis TFP indis. Thirdly, in ordr o m h rquirmn of a baland panl daa sampl for alulaing h Malmquis indis, an innoai fak uni approah has bn inrodud in his papr. This approah maks possibl h alulaion of a Malmquis indx wih an unbaland daa panl. Th mhodology in h papr ould asily b xndd o inorpora mor missions ariabls, suh as CO 2, as daa allows. Bsids onribuing o rsarh mhodology, his papr also nails poliy impliaions. Th rsuls show ha during h rpor priod h TFP growh mainly am from hnial hang. This rsul suppors h Chins gornmn s ffors o build a mor ffiin lriiy indusry. Howr, h rsuls also india ha h growh of Chins oal-fird powr sor oday sill haily dpnds upon an inras of rsour inpu. This is idn from h fa ha, a bs, h annual TFP growh of h sampl oal-fird powr plans bwn 996 and 2002 only arags abou 2%. Y during h priod of our sudy ( ) h annual inras of h sampl powr plans was 6.8% in oal-fird apaiy and 0.29% in oal-fird gnraion (CED, 2004). Furhrmor, no apparn ffiiny ah-up ffs or improd nironmnal prforman indis an b found in our rsuls. This, oupld wih rsuls in Yang and Polli (2007), whih shows arag inffiiny afr adjusing for opraing ondiions of around 0%, suggss ha hug ponial rmains wih rgards o h 2

22 impromn of ffiiny and onrol of missions in h Chins oal-fird powr plans. Tha is o say, for h Chins auhoriis, h oninuaion of is ffors in h onsraion of nrgy and h inrasing of nrgy ffiiny sill ha a ry ruial rol o play. I is imporan o poin ou howr ha our sudy only xamins h TFP growh a xising plans, sin Malmquis indiis anno apur h produiiy growh (or indd nironmnal prforman impromn) rsuling from h losur of old plans and hir rplamn wih nwr ons. Hn w migh xp aggrga TFP growh o show fasr TFP growh han wha w find. Our analysis dos inlud h posii TFP ffs of ramping up nw plans o full ffiiny in hir arly yars of opraion. This would nga h old o nw rplamn ff o som xn. Howr gin ha missions ar srongly orrlad wih aual lrial oupu (rahr han apaiy) a a gin plan h nw for old ff migh rmain signifian on nironmnal prforman. W will insiga his furhr in subsqun rsarh. 22

23 Appndix: Ray and Dsli s Domposiion of Malmquis TFP Indx Following h paramrizaion of sion 2, Ray and Dsli s domposiion an b sard from h masurmn of oupu disan funions undr VRS. In rms of Figur, VRS disan funions an b wrin as and D ( x, y ) = oa og (A) D ( x, y ) = o oh (A2) D x + + (, y ) = o (A3) oi + D ( x, y ) = oa (A4) oj Ray and Dsli hn dfind h TFP hang indx M x y x y Ray + + (,,, ) as / Ray + + D x y D x y D x y (,,, ) = D ( x, y ) D ( x, y ) D ( x, y ) M x y x y whr SE rprsns h sal ffiiny (s A5 ), and (, ) (, ) (, ) / 2 (, ) (, ) + (, ) (, ) SE x y SE x y SE x y SE x y (A5) TECHCH PEFFCH SCH + + (, ) (, ) / 2 / 2 D x y D x y oj oh = = D ( x, y ) D ( x, y ) og oi D ( x, y ) o og = = D x y oa oh (, ) SE x y SE x y SE ( x, y ) SE ( x, y ) (, ) (, ) = + / 2 (A5a) (A5b) (A5) Normally, if VRS is assumd h sal ffiiny (SE) is h quoin of CRS ffiiny or VRS ffiiny. Thn Equaion (A5) an b wrin as SCH ( +, + ) + ( +, + ) + / 2 / 2 SE x y SE x y oi ob oh od = = SE ( x, y ) SE ( x, y ) o og of oj (A5 ) Clarly, h only domposiion faor whih is qual in boh Far al. s and Ray and Dsli s domposiion is h faor PEFFCH. 23

24 If using h raio forms of arious indis as dfind in Equaion (A5a), (A5b) and (A5 ) o rpla h orrsponding pars in Equaion (A5), w g / 2 / 2 Ray + + oj oh o og oi ob oh od M ( x, y, x, y ) = og oi oa oh o og of oj o ob od = oa o of / 2 o ob of od = of oa o ob / 2 (A6) Clarly, h righ-hand sid of Equaion (A6) is qual o ha of Equaion (5) in sion 2. Tha is, Ray + + Far + + M ( x, y, x, y ) = M ( x, y, x, y ) (A7) This mans ha h orall masurs of h Malmquis TFP indx in Far al. (994) and Ray and Dsli (997) ar idnial. 24

25 Rfrns Baur, P. Domposing TFP Growh in h Prsn of Cos Inffiiny, Nononsan Rurns o Sal, and Thnologial Progrss, Th Journal of Produiiy Analysis, Vol. (990), pp Cas, D., Chrisn, L., and Diwr, W. Mulilaral Comparisons of Oupus, Inpus, and Produiiy Using Suprlai Indx Numbrs, Th Eonomi Journal, Vol. 92 (982a), pp Cas, D., Chrisn, L., and Diwr, W. Th Eonomi Thory of Indx Numbrs and h Masurmn of Inpu, Oupu, and Produiiy, Eonomria, Vol. 50 (982b), pp CED, China Enrgy Daabook (V6.0), Lawrn Brkly Naional Laboraory, CA, Colli, T., Rao, D., O Donnll, C., and Bas, G. An Inroduion o Effiiny and Produiiy Analysis, Springr: Nw York, Far, R., Grosskopf, S., Loll, K., and Pasurka, C. Mulilaral Produiiy Comparisons Whn Som Oupus Ar Undsirabl: A Nonparamri Approah, Th Riw of Eonomis and Saisis, Vol. 7 (989). Far, R., Grosskopf, S., Norris, M., and Zhang, Z. Produiiy Growh, Thnial Progrss, and Effiiny Chang in Indusrial Counris, Th Amrian Eonomi Riw, Vol. 84 (994), pp Far, R., Grosskopf, S., and Roos, P. Produiiy and Qualiy Changs in Swdish Pharmais, Inrnaional Journal of Produion Eonomis, Vol. 39 (995), pp Far, R., Grosskopf, S., and Tya, D. An Aiiy Analysis Modl of h Enironmnal Prforman of Firms Appliaion o Fossil-ful-fird Elri Uiliis, Eonlogial Eonomis, Vol. 8 (996), pp Fixlr, D. A Commrial Bank Oupu Pri Indx, BLS Working Papr 79, Washingon, D.C., 988. Fixlr, D. and Zishang, K. Inorporaing Anillary Masurs of Pross and Qualiy Chang ino a Suprlai Produiiy Indx, Th Journal of Produiiy Analysis, Vol. 2 (992), pp Giannakis, D., Jamasb, T., and Polli, M. Bnhmarking and Inni Rgulaion of Qualiy of Sri: An Appliaion o h UK Elriiy Disribuion Nworks, Enrgy Poliy, Vol. 33 (2005), pp Grifll-Taj, E. and Loll, C. A No on h Malmquis Produiiy Indx, Eonomis Lrs, Vol. 47 (995), pp

26 Hair, J., Andrson, R., Taham, R., and Blak, W. Muliaria Daa Analysis (5 h Prni Hall: Nw Jrsy, 998. d.), Kopp, R., Smih, V., and Vaughan, W. Sohasi Cos Fronirs and Prid Thnial Inffiiny. In Smih, K., ds., Adans in Applid Miro-Eonomis, 2, JAI Prss, 982. Lam, P. and Shiu, A. Effiiny and Produiiy of China s Thrmal Powr Gnraion, Riw of Indusrial Organizaion, Vol. 24 (2004), pp Nishimizu, M. and Pag, J. Toal Faor Produiiy Growh, Thnologial Progrss and Thnial Effiiny Chang: Dimnsions of Produiiy Chang in Yugoslaia, , Th Eonomi Journal, Vol. 92 (982), pp Oha, M. A No on h Dualiy bwn Produion and Cos Funions: Ras of Rurn o Sal and Ras of Thnial Progrss, Eonomi Sudis Quarrly, Vol. 25 (974), pp Ray, S. and Dsli, E. Produiiy Growh, Thnial Progrss, and Effiiny Chang in Indusrializd Counris: Commn, Th Amrian Eonomi Riw, Vol. 87 (997), pp Sa Enironmnal Proion Adminisraion of China (SEPAC) China Forum of Enironmnal Journaliss (8 Augus), Thanassoulis, E. Inroduion o h Thory and Appliaion of Daa Enlopmn Analysis: A Foundaion Tx wih Ingrad Sofwar, Kluwr Aadmi Publishrs: Boson, 200. Tya, D. On h Masurmn of h Enironmnal Prforman of Firms A Liraur Riw and A Produi Effiiny Prspi, Journal of Enironmnal Managmn, Vol. 46 (996), pp Tya, D. Linar Programming Modls for h Masurmn of Enironmnal Prforman of Firms Conps and Empirial Rsuls, Journal of Produiiy Analysis, Vol. 8 (997), pp Yang, H. and Polli, M., Inorporaing Boh Undsirabl Oupus and Unonrollabl Variabls ino DEA: h Prforman of Chins Coal-Fird Powr Plans, Working Papr no. EPRG072, Cambridg Elriiy Poliy Rsarh Group, Cambridg Unirsiy, UK, Yang, H. Th Enironmnal Prforman of h Chins Elriiy Indusry, PhD dissraion, Judg Businss Shool, Cambridg Unirsiy, UK,