:Malmquist 47 [4 ],,, Malmquist : ; Malmquist,t t + x t r = ( x t r, x t r,, x t rn ) T, y t r = ( y t r, y t r,, y t rm ) T,x t r R n +, y t

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1 8 00 Chinese Journal of Management Science : (00) , No. Vol. Feb., 00 Malmquist,, (., ;., 00080) :Malmquist,, , Malmquist,Malmquist, :Malmquist ; ; : F4. 7 :A Sten Malmquist (953),, [ ],Malmquist Caves, Christensen Diewert ( CCD,98), [ ] Fgre, Grosskopf, Lindgren Roos ( F GL R,994) CCD Farrell (957), Malmquist, [3 ] Ray Desli (997) RD Malmquist [4 ] ; Si mar Wilson (998,999),,, Malmquist [5, 6 ] Nikolaos Maniadakis (004) Malmquist [ 7 ] : ; : : (708500) ; ( TJ U - YFF - 08B09) :(98 - ), ( ),,,, :, (008), Malmquist [8 ],, ;,,,,,,, Hjalmarsson Veiderpass ( 99 ) Malmquist [9 ] Pollitt (995) D EA SFA, 0 [0 ] : Hattori (00, 005) [ ] [ ] Delmas Tokat (005) [3 ] Tsut sui Goto (009) DEA 转载

2 :Malmquist 47 [4 ],,, Malmquist : ; Malmquist,t t + x t r = ( x t r, x t r,, x t rn ) T, y t r = ( y t r, y t r,, y t rm ) T,x t r R n +, y t r R m +, t r ; ( x t r, y t r) L t, L t t, D t ( x t, y t ) t D EA [5 ] D t ( x t, y t ), ; D t ( x t, y t ), [6 ] [7 ] t t + Malmquist M I [ 7 ] : M I = Dt ( y t+, x t+ ) D t ( y t, x t ) M I Dt+ ( y t+, x t+ ) D t+ ( y t, x t ) () >,, x t+ x t, t t + Malmquist ( Techni cal Efficiency Change : T E ) ( Techno logical Change : TC ) : T E = Dt+ ( y t+, x t+ ) D t ( y t, x t ) TC = D t ( y t+, x t+ ) D t+ ( y t+, x t+ ) Dt ( y t, x t ) D t+ ( y t, x t ) () (3), ;, t t +,,, TC 3 Malmquist Malmquist, [ ],,, ;,,,,Malmquist [8 ] 3. r : u t r ( y t r) R m +, r =,,, N, DEA D EA r, r r N -,,, r : ur t ( y r t ) = r- N j = j = r + uj t ( y j t ) N t : R t ( x t, u t ) = max{ u t r ( y t r) : y t r L t ( x t r), u t r > y t r 0}, r =,,, N (4) u t r ( y t r) / R t ( x t r, u t r) u t r ( y t r) R t ( x t r, u t r),r t ( x t, u t ),,,,, r t t + Malmquist : MU = ut ( y t+ ) / R t ( x t+, u t ) u t ( y t ) / R t ( x t, u t ) ut+ ( y t+ ) / R t+ ( x t+, u t+ ) u t+ ( y t ) / R t+ ( x t, u t+ ) (5), Malmquist,, 3. Malmquist Malmquist, Malmquist,

3 48 00, Malmquist IsoL t ( x t ), IsoR t ( y t, u t ),(5) : MU = OB / OF OG/ OA OB / OE OG/ OC Malmquist (6) (6) Malmquist :(Overall Efficiency Change : ciency Change) ( A E : Allocative Effi ciency Change) T E, Malmquist A E, : OEC = T E A E = T E = Dt+ ( y t+, x t+ ) D t ( y t, x t ) OB / OE OG/ OA = OB / OM OG/ ON (0) () A E = ut+ ( y t+ ) / [ R t+ ( x t+, u t+ ) D t+ ( y t+, u t+ ) ] u t ( y t ) / [ R t ( x t, u t ) D t ( y t, u t ) ] [ OB / OE ]/ [ OB / OM ] OM / OE OEC ) ( UtilityTechnical = = () [ OG/ OA ]/ [ OG/ ON ] O N / OA Change : U T C ) U T C t t +, MU = OEC U T C (7) x t x t+ OEC = ut+ ( y t+ ) / R t+ ( x t+, u t+ ) (8) Malmqist u t ( y t ) / R t ( x t, u t ), u t ( y t+ ) / R t ( x t+, u t ) U T C = ( u t+ ( y t+ ) / R t+ ( x t+, u t+ TC : technical ) ut ( y t ) / R t ( x t, u t change) ( OS E : Out side System ) u t+ ( y t ) / R t+ ( x t, u t+ ) (9) Effect) TC Malmquist, t t + OEC t t +, OS E,, : ( T E : Technical Effi U T C = TC OS E = = OE O F OC OA TC = D t ( x t+, y t+ ) D t+ ( x t+, y t+ ) OB / OF OB / OE D t ( x t, y t ) D t+ ( x t, y t ) OG/ OA OG/ OC (3)

4 :Malmquist 49 OS E = = OB / O H OB / OM OG/ ON OG/ OZ = OM O H OZ O N (4) u t ( y t+ ) / [ R t ( x t+, u t ) D t ( x t+, y t+ ) ] u t+ ( y t+ ) / [ R t+ ( x t+, u t+ ) D t+ ( x t+, y t+ ) ] ut ( y t ) / [ R t ( x t, u t ) D t ( x t, y t ) ] u t+ ( y t ) / [ R t+ ( x t, u t+ ) D t+ ( x t, y t ) ] = = [OB/ OF]/ [OB/ OH ] OA ]/ [OG/ ON ] [OG/ [OB/ OE]/ [OB/ OM ] [OG/ OC]/ [OG/ OZ] O H/ OF OM / OE ON / OA O Z/ OC (5),Malmquist : MU = OEC U T C = ( T E A E) ( TC OS E) = ( T E TC) ( A E OS E) = M I A E OS E (6),Malmquist Malmquist, ,,, Malmquist D EA, 4, : 0, : A 4. :,, ;,,, ;,, ; :, (7) u t r ( y t r) = ( y t max - y t min) + ( y t r - ymin t ) ( y t ymax t - ymin t max - ymin) t y t max = max{ y t j } ymin t = min{ y t j } j =,,, N j j (7) y t max, y t min t 4, Wind ( ) 007 ( ) DEA : : N = 4 >. 5 4 = 0 ; 0, ; :, ;, ,; 006,007,, 4. 3 DEA

5 50 00,DEA, Malmquist Malmquist Malmquist M I MU M I MU T E A E OEC TC OS E U T C M ,, T E 07 ;,,, T E,0. 943,,, A E 50,0. 84 ;, OEC 0. 80,. 053,,, OEC, 007,, TC ,, TC, ,, 30,,. 74 %,,,, OS E ,. 4,Malmquist U T C 57. 7,. 89, T E, TC A E, U T C,, A E, U T C Malmquist : MU,,, 007,, Malmquist Malmquist, Malquist Malmuist,, 5 Malmquist,, Malmquist, MU,, Malmquist,,,,Malmquist Malmquist,,

6 :Malmquist 5 :Malmquist, Malmquist, : [ ] Sten, M.. Index numbers and indifference surfaces [J ]. Trabajos de Estadistica, 953, 4 : [ ] Caves, D. W., Christensen, L. R., Diewert, W. E.. The economic theory of index numbers and the measure ment of input, output, and productivity [J ]. Economet rica, 98, 50 (6) : [3 ] F R, Grosskopf, S., Lindgren, B., et al. Productivity development s in swedish hospitals : A Malmquist output index approach [J ]. Data Envelopment Analysis : Theo ry, Methodology and Applications, 994 : [ 4 ] Grifelltatje, E., Lovell, C. A.. Profits and productivity [J ]. Management Science, 999, 45 (9) : [5] Simar, L., Wilson, P. W.. Sensitivity analysis of efficien cy scores : How to bootstrap in nonparametric frontier mod els [J ]. Management Science, 998, 44 () : [6 ] Simar, L., Wilson, P. W.. Estimating and bootstrap ping Malmquist indices [J ]. European Journal of Opera tional Research, 999, 5 (3) : [ 7 ] Nikolaos Maniadakis, E. T.. A cost Malmquist produc tivity index [J ]. European Journal of Operation al Re search, 004, 54 () : [8 ],,. Malmquist [J ]., 008, 8 () : [ 9 ] Hjalmarsson, L., Veiderpass, A.. Productivity in Swedish electricity retail distribution [ J ]. Scandinavian Journal of Economics, 99, 94 : [ 0 ] Pollitt, M.. Ownership and Performance in Electric U tilities [ M ]. Oxford : Oxford University Press, 995. [ ] Hattori, T.. Relative performance of U. S. and J apa nese electricity distribution : An application of stochas tic f rontier analysis [J ]. Journal of Productivity Analy sis, 00, 8 : [ ] Hattori, T., Jamasb, T., Pollitt, M.. Electricity dis tribution in the U K and Japan : A comparative efficien cy analysis [ J ]. The Energy Journal, 005, 6 () : [ 3 ] Delmas, M., Tokat, Y.. Deregulation, governance structures, and efficiency : The U. S. electric utility sector [J ]. Strategic Management Journal, 005, 6 : [4 ] Tsutsui, M., Goto, M.. A multidivision efficiency e valuation of U. S. electric power companies using a weighted slacksbased measure [ J ]. SocioEconomic Planning Sciences, 009, 43 : [5 ] Shephard, R. W.. Theory of Cost and Production Func tions [ M]. NJ : Princeton University Press, 970. [ 6 ] Lovell, C. A. K.. The Measurement of Productive Efficiency : Techniques and Application [ M ]. Oxford : Oxford University Press, 993 : [ 7 ] Banker, R. D.. Maximum likelihood, consistency and Data Envelopment Analysis : A statistical foundation [J ]. Management Science, 993, 39 ( 0 ) : [ 8 ] Tortosaausina, E., Grifelltatje, E., Carmen Arme ro, D. C.. Sensitivity analysis of efficiency and Malmquist productivity indices : An application to Spanish savings banks [J ]. European Journal of Opera tional Research, 008, 84 : Util ity Malmquist Index and Listed Thermal Power Corporations Empirical Analysis XIE Baichen,,DU Gang (. School of Management, Tianjin University, Tianjin 30007, China ;. Center for Energy and Environmental Policy, Institute of Policy and Management, Chinese Academy of Science, Beijing 00080, China) Abstract : This paper develop a utilit y Malmquist p roductivit y index based o n distance f unctio n. The index, which is defined in terms of maximizing expected utility rather t han outp ut, is decomposed into : technical efficiency change, technical change, allocative efficiency change and o ut side system effect. This met hod is suitable for oligopolistic industry or p ublic goods sectors whose decision needs to integrate economic and social factors. Finally, t he paper gives an empirical analysis by evaluating t he listed coal electricity corpo rations from 006 to 007. The result s indicates t hat the utility approach fit s more close to t he practice t han the inp ut approach, and can give more reasonable economic explanation. Key words : Malmquist index ; utility f unction ; coal power industry

,, ( ) ( ) Farell (1957),, (2003) (1999) DEA DEA, 14 (2000) DEA , (2001) (2001) 5 (2002) DEA Malmquist, , (2003) (2003) DEA (2004) D

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