An allocation productivity indicator: Application in Taiwanese banks

Transcription

1 Journal of Applied Finance & Banking, vol. 8, no. 5, 2018, ISSN: (prin version), (online) Scienpress Ld, 2018 An allocaion produciviy indicaor: Applicaion in Taiwanese banks Xiang Chen 1 Absrac This sudy applies he non-parameric approach and combine he he Luenberger produciviy indicaor and he allocaive efficiency (Chamber e al., 1996) o develop an allocaion Luenberger indicaor. The allocaion Luenberger indicaor can be decomposed ino he allocaive efficiency change and he allocaive echnical change. We also invesigae wheher here is a relaionship in he proposed allocaion indicaor, profi Luenberger indicaor (Juo e al., 2015) and he Luenberger produciviy indicaor. For he empirical applicaion, we use he 31 Taiwanese banks o measure profi Luenberger produciviy indicaor, Luenberger produciviy indicaor and allocaion Luenberger indicaor, and also compare hese indicaors and heir componens by he financial holding company and non-financial holding company. JEL classificaion numbers: G14,D24,G21 Keywords: Daa Envelopmen Analysis; profi produciviy; allocaion Luenberger indicaor; banks 1 Inroducion Financial insiuions play an imporan role in he economy, especially for Banks, which mainain public and privae savings and heir inermediaion aciviies o allocae invesmens ha conribue o he developmen of a counry (Oliveira, 2008). The Taiwanese banking marke also eperienced some changes: Governmen decided 1 Deparmen of Economics, College of Business, Soochow Universiy, Taipei, Taiwan. Aricle Info: Received: March 4, Revised : March 26, 2018 Published online : Sepember 1, 2018

2 20 Xiang Chen o allow overseas invesors in 1991 ino he local banking marke. Differen ypes of financial insiuions, such as invesmen and rus Companies, credi unions, small and medium-sized enerprises are allowed o reinven hemselves as commercial Banks. The governmen cu is value-added a rae from 5% o 2% and rela he rules on he merger of financial insiuions and allowing he esablishmen of financial holding companies (FHCs). However, afer hese changes, are Taiwanese banks performing beer or worse? Do heir profis increase or decrease? This sudy will invesigae he performance of Taiwanese banks by he efficiency and produciviy. Efficiency and produciviy analysis of Decision Making Unis (DMUs) have been applied in many fields since Charnes e al. (1978) inroduced Daa Envelopmen Analysis (DEA) as a non-parameric model (Emrouznejad, e al., 2008). The widely used produciviy-malmquis produciviy inde inroduced by Caves e al. (1982) and refined by Fare e al. (1992) is o measure he change in produciviy over ime, and i can be decomposed ino echnical change efficiency change. However, he Malmquis inde should be made eiher an oupu or inpu orienaion under he assumpion of eiher revenue maimizaion or cos minimizaion (Boussemar e al, 2003). The Luenberger produciviy indicaor which is a difference-based indicaor can well avoid he above limiing assumpion (Chamber e al., 1996). From he Chambers e al.(2002), hese Luenberger indicaors are novel because hey are based on a ranslaion represenaion of he echnology and, hus, are all specified in difference (no raion) from. I also provides a possibiliy of measuring produciviy growh by he direcion of inpu conracions and oupu epansions simulaneously wihin goal of profi maimizaion. Juo e al. (2015) adap he profi efficiency which defined by he Chamber e al. (2002) o replace he direcional disance funcion wihin he Luenberger produciviy indicaor o develop a profi oriened Luenberger produciviy indicaor (PLPI) under he assumpion ha profi maimizaion and he prices of oupus and inpus are available. They decomposed he PLPI ino he profi efficiency change (PEC) and profi echnology change (PTC), and furher decomposed he PEC and he PTC ino he echnical efficiency change (TEC), allocaive efficiency change (AEC), he echnical change (TC) and price effec (PE). The decomposiion can be shown as follows: PLPI=PEC+PTC =TEC+AEC+TC+PE In his sudy, following he sudy of Juo e al. (2015), a concep of an Allocaion Luenberger indicaor (ALI) is proposed and hree ypes of Luenberger indicaors wih heir relaionships in he framework of organizaion managemen are discussed. The profi Luenberger produciviy indicaor can be decomposed ino he Luenberger

3 An allocaion produciviy indicaor: Applicaion in Taiwanese banks 21 produciviy indicaor (LPI) and he Allocaion Luenberger indicaor (ALI). Our proposed Allocaion Luenberger indicaor and is decomposiion of various componens are based on he assumpion of variable reurns o scale. For an empirical illusraion, his sudy applies he proposed Allocaion indicaor wih he mehod of he daa envelopmen approach and uses 31 Taiwanese banks in he sample period of o empirically measure and compare he produciviy changes and profi Luenberger decomposiion componens. Our main findings are ha Taiwanese banks show on average posiive profi produciviy growh from 2010 o The growh mainly comes from he conribuion of Luenberger produciviy improvemen which enough offse he decrease from he Allocaion Luenberger. We also showed ha he allocaion Luenberger indicaor of he Taiwanese banking indusry regresses due o he allocaion echnology decreases. The allocaion echnology regress is more influenial han he allocaion efficiency increase o he allocaion Luenberger indicaor. Finally, we find he profi produciviy growh in financial holding companies is faser han ha in non-financial holding companies, however he former s allocaion indicaor is reducing and he. The res of he paper is organized as follows. The mehodology is discussed in Secion 2. In his secion we also inroduce he concep of Allocaion Malmquis Inde and is decomposiion. Secion 3 presens daa and variables. Secion 4 shows he resuls and discussion and Secion 5 concludes his paper. 2 Mehodology 2.1 Technology, profi funcions and allocaive inefficiency This sudy considers he panel daa of he j-h (j=1, 2,, J) DMUs. Assume ha he DMUs use he inpu vecor ( R N + ) o produce oupu vecor y (y R M + ). For he j-h DMU, his sudy defines is producion echnology se as follow: S = {(, y ): can produce y } where S is assumed o be conve and closed. This sudy follows Chambers e al. (1997) and defines he direcional disance funcion (DDF) by D (, y ; g, g y ) = sup{β: ( βg, y + βg y ) S } (1) Where he direcional vecor g ( g, g ), y g and N R g y M R, denoes his funcion shifs by simulaneously conracing inpus and epanding oupus, so as o reach he producion fronier. Thus, he D (, y ; g, g y ) also represens he degree

4 22 Xiang Chen of he echnical inefficiency (TI). The profi funcion is defined for he echnology S as π (p, w) = sup{p y w : (, y) S }. (2) The Eq. (2) implies π (p, w) p y w Since (, y) S y + D (, y ; g, g y )g y is feasible wihin D (, y ; g, g y )g π (p, w) p [y + D (, y ; g, g y )g y ] w [ D (, y ; g, g y )g ] π (p, w) p y w + (p g y + w g )D (, y ; g, g y ) πi = π (p,w) (p y w ) p g y +w g The profi inefficiency (πi) is defined as D (, y ; g, g y ) (3) πi = π (p,w) (p y w ) p g y +w g (4) TheπI, he difference beween he maimal profi and obversed profi normalized by he sum p g w g which means he firm size, is called he Nerlovian profi y efficiency measured in Chambers e al. (1998). Thus, he πi uni of measure. is independen of he The righ hand side of Eq. (3) measures he echnical inefficiency. The gap in he inequaliy Eq. (3) reflecs he residual inefficiency of profi. And he allocaive inefficiency is defined as AI = π (p,w) (p y w ) p g y +w g The AI D (, y ; g, g y ) (5) reflecs he disance from he maimal profi o he acual profi. In general, AI <0 indicaes he DMU under he assessmen comparing wih oher DMUs, is allocaively inefficien, since is producion is aken place in an inappropriae inpu-oupu mied, given he inpu and oupu prices. If AI =0 indicaes he DMU is allocaive efficien, i have reached he maimal profi. Rearranging he Eq. (5), he profi inefficiency can be decompose ino he wo sources as follows: AI = πi TI (6) From he above Eq. (6), i can be known ha he allocaive inefficiency is a difference of profi inefficiency and echnical inefficiency. The allocaive inefficiency resuls from he wrong oupu-inpu mi in ligh of heir given prices.

5 An allocaion produciviy indicaor: Applicaion in Taiwanese banks The Luenberger produciviy indicaor The Luenberger produciviy inde (LPI) ha is inroduced by Chambers e al. (1996) which used o evaluaing a difference-based produciviy change. This indicaor is defined and calculaed by he quaniy disance funcion. Following Chambers (1996), he Luenberger produciviy indicaor for and +1 as followed: LPI = 1 [D (, y ; g 2, g y ) D +1 (, y ; g, g y ) + D ( +1, y +1 ; g +1, g +1 y ) D +1 ( +1, y +1 ; g +1, g +1 y )] (7) The produciviy indicaor is consruced as he arihmeic mean of he produciviy change measured by he echnology a and he produciviy change measured by he echnology a +1. I indicaes he produciviy change by posiive value and negaive value. Furhermore, i also can be decomposed ino wo componens, namely echnical efficiency change (TEC) and echnical change (TC) as followed: LPI = D (, y ; g, g y ) D +1 ( +1, y +1 ; g +1, g +1 y ) (TEC) + 1 {[D +1 (, y ; g 2, g y ) D (, y ; g, g y )] + [D +1 ( +1, y +1 ; g +1, g +1 y ) D ( +1, y +1 ; g +1, g +1 y )]} (TC) (8) Where he TEC = D (, y ; g, g y ) D +1 ( +1, y +1 ; g +1, g +1 y ) denoes he change of he echnical efficiency from o +1. The funcions of TEC and TC are indicaed by he posiive values and negaive values. For eample, if TEC>0, i means an improved echnical efficiency, TEC<0 indicaes he echnical efficiency decreases and TEC=0 shows a consan efficiency. In he Eq. (7), he TC which is in he second bracke means he shif of he producion echnology beween period and +1. When TC >0, i means echnical improve, TC<0 indicaes echnical regress and TC=0 is he echnology is consan in and +1. This decomposiion has been implemened in Chambers e al. (1996). 2.3 Profi-oriened Luenberger indicaor In he lieraure, he non-parameric profi Luenberger produciviy indicaor (PLPI) inroduced by Juo e al. (2015) is measured in erms of maimum-profi boundaries. Compared wih he convenional Luenberger produciviy, hey use he profi inefficiency o replace he echnical inefficiency, and define i as followed: PLPI = 1 2 {[π (p,w ) (p y w ) p g y +w g π (p,w ) (p y +1 w +1 ) p g +1 y +w g+1 ] +

6 24 Xiang Chen [ π+1 (p +1,w +1 ) (p +1 y w +1 ) p +1 g y +w +1 g π +1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g +1 y +w +1 g+1 ]} (9) This is measure a profi-oriened produciviy. I is defined by he arihmeic means of wo erms (brackes) ha are composed of he own-period and cross-period profi inefficiencies defined by Fare and Primon (2003). Similarly, his profi produciviy improvemen also are indicaed by posiive values and negaive values. If he value of profi produciviy is less han 0, i means he profi produciviy decreases, If he value of is grea han 0, i indicaes an improved profi produciviy, if he value of is 0, i shows a consan produciviy. Furhermore, he profi-oriened Luenberger indicaor also can be decomposed ino he profi efficiency change (PEC) and profi echnology change (PTC) as follows: PLPI = [ π (p,w ) (p y w ) p g y +w g {[π+1 (p +1,w +1 ) (p +1 y w +1 ) p +1 g y +w +1 g [ π+1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g y +1 +w +1 g +1 π +1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g +1 y +w +1 g+1 ] (PEC) π (p,w ) (p y w ) p g y +w g ] + π (p,w ) (p y +1 w +1 ) p g +1 y +w g+1 ]} (PTC) The PEC is he erm in he firs bracke, i shows he degree of cach-up wih he profi boundary cross wo periods. The PTC is he second erm in he brace i is he profi echnology change of he DMU beween period and +1 and measures shif of he profi boundary from, 1 1 y o, y (10). The values of he PEC and PTC greaer han 0 indicaes he improvemens, while he values less han 0 means recession. Moreover, he profi-oriened produciviy can be furher decomposed ino changes in echnical efficiency, allocaive efficiency, echnology change, and price effec. 2.4 Allocaion Luenberger indicaor In he spiri of he works of Chambers e al. (1996a, 1996b), Chambers e al. (1998) and Juo e al. (2015), his sudy defines he allocaion produciviy indicaor ( ALI ) as ALI = 1 2 {[(π+1 (p +1,w +1 ) (p +1 y w +1 ) p +1 g y +w +1 g D ( +1, y +1 ; g +1, g y +1 )) ( π+1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g y +1 +w +1 g +1 D +1 ( +1, y +1 ; g +1, g y +1 ))] + [( π (p,w ) (p y w ) p g y +w g D (, y ; g, g y )) ( π (p,w ) (p y +1 w +1 ) p g +1 y +w g+1 D +1 (, y ; g, g y ))]} (11)

7 An allocaion produciviy indicaor: Applicaion in Taiwanese banks 25 This indicaor in above Eq. (11) can be applied o make resource allocaion managemen wihin he assumpion he inpu and oupu prices are known. The value of he allocaion Luenberger indicaor greaer han 0 means progress, he value less han 0 indicaes regress, and he value equals 0 shows consan. Followed decomposiion in he Chambers e al. (1996) and Juo e al. (2015), his allocaion indicaor also can be decomposed ino he allocaive efficiency change (AEC) and allocaive echnical change (ATC) as follows: ALI = [( π (p,w ) (p y w ) p g y +w g D (, y ; g, g y )) ( π+1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g y +1 +w +1 g +1 D +1 ( +1, y +1 ; g +1, g y +1 ))] (AEC) {[(π+1 (p +1,w +1 ) (p +1 y w +1 ) p +1 g y +w +1 g D ( +1, y +1 ; g +1, g y +1 )) ( π (p,w ) (p y +1 w +1 ) p g y +1 +w g +1 D +1 (, y ; g, g y ))] + [( π+1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g y +1 +w +1 g +1 D +1 ( +1, y +1 ; g +1, g y +1 )) ( π (p,w ) (p y w ) p g y +w g D (, y ; g, g y ))]} (ATC) The AEC is he change of he allocaive efficiency beween period and +1. I indicaes he een of cach-up wih he opimum oupu-inpu mi over ime. AEC = [( π (p,w ) (p y w ) p g y +w g D (, y ; g, g y )) ( π+1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g y +1 +w +1 g +1 D +1 ( +1, y +1 ; g +1, g y +1 ))] (13) The ATC is he shif of he allocaion echnology of he DMU beween period and +1, and measures he change of he producion boundary evaluaed a, y 1 1, and profi boundary evaluaed a he prices, ATC = 1 2 {[(π+1 (p +1,w +1 ) (p +1 y w +1 ) p +1 g y +w +1 g ( π (p,w ) (p y +1 w +1 ) p g y +1 +w g +1 D +1 (, y ; g, g y ))] + [( π+1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g y +1 +w +1 g +1, 1 1 p w and p, w. D ( +1, y +1 ; g +1, g y +1 )) D +1 ( +1, y +1 ; g +1, g y +1 )) (12) y and

8 26 Xiang Chen ( π (p,w ) (p y w ) p g y +w g D (, y ; g, g y ))]} (14) The erm of he ATC is in he sudy of Juo e al. (2015) defined as he price effec. Here, we prefer o call his erm as he allocaion-echnology change. The values of AEC and ATC greaer han 0 denoe improvemen, while he values less han 0 indicae he deerioraion. The Luenberger produciviy indicaor, profi Luenberger produciviy indicaor and allocaion Luenberger indicaor and heir decomposiions are illusraed in Figure 1. As shown in Juo e al. (2015), he profi Luenberger produciviy indicaor and is following decomposiion are esimaed under he assumpion of variable reurns o scale (VRS). y ( p, w ) 1 S h 1 1 g p y w 1 1 p y w p g w g 1 1 y h 0 e 0 d 0 e 1 d 1 ( p, w ) b 1 S p y w 1 1 p y w p g w g y g b p y w p y w (, a ) 0 y a y ( 1, 1 ) 1 o Figure 1: The decomposiion of he indicaors LPI, ALI, PLPI The allocaion Luenberger indicaor can be presened in erms of he disances as follows: API = 1 [(b 2 0d 0 /0g e 0 h 0 /0g) + (b 1 d 1 /0g e 1 h 1 /0g)] AEC = (b 0 d 0 /0g e 1 h 1 /0g) ATC = 1 [(b 2 1d 1 /0g b 0 d 0 /0g) + (e 1 h 1 /0g e 0 h 0 /0g)] The profi-oriened Luenberger indicaor can be presened in erms of he disances as follows: PLPI = 1 [(a 2 0d 0 /0g a 1 d 1 /0g) + (a 0 h 0 /0g a 1 h 1 /0g)]

9 An allocaion produciviy indicaor: Applicaion in Taiwanese banks 27 PEC = (a 0 d 0 /0g a 1 h 1 /0g) PTC = 1 (d 2 0h 0 /0g + d 1 h 1 /0g) The Luenberger indicaor can be presened in erms of he disances as follows: LPI = 1 [(a 2 0b 0 /0g a 1 b 1 /0g) + (a 0 e 0 /0g a 1 e 1 /0g)] TEC = (a 0 b 0 /0g a 1 e 1 /0g) TC = 1 [(a 2 0e 0 /0g a 0 b 0 /0g) + (a 1 e 1 /0g a 1 b 1 /0g)] 2.5 Relaionship of LPI, ALI, PLPI I is well known ha any DMU should have a good managemen wih bes use of producion and resource, for obaining a maimum-profi, herefore, i has o use available resources efficienly. Now, we will show he relaionships among he LPI, ALI, PLPI in he framework of organizaion managemen. According o Chambers e al. (1996), he profi inefficiency ( PI ) can be decomposed ino echnical inefficiency ( TI ) and allocaive inefficiency ( AI ): PI=TI+AI. Combined wih Eq. (7)-(14), he relaionship in, LPI, ALI, PLPI ha is, LPI+ ALI=PLPI is shown as PLPI = 1 2 {[π (p,w ) (p y w ) p g y +w g π (p,w ) (p y +1 w +1 ) p g +1 y +w g+1 ] + [ π+1 (p +1,w +1 ) (p +1 y w +1 ) p +1 g y +w +1 g 1 π +1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g +1 y +w +1 g+1 ]} = 2 [D (, y ; g, g y ) D +1 (, y ; g, g y ) + D ( +1, y +1 ; g +1, g y +1 ) D +1 ( +1, y +1 ; g +1, g y +1 )] {[(π (p +1,w +1 ) (p +1 y w +1 ) p +1 g y +w +1 g D ( +1, y +1 ; g +1, g +1 y )) ( π+1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g y +1 +w +1 g +1 D +1 ( +1, y +1 ; g +1, g y +1 ))] + [( π (p,w ) (p y w ) p g y +w g D (, y ; g, g y )) ( π h (p,w ) (p y +1 w +1 ) p g +1 y +w g+1 D +1 (, y ; g, g y ))]} = LPI + ALI (15) Furhermore, hese indicaors componen s also have he relaionship: PEC =

10 28 Xiang Chen [D (, y ; g, g y ) D +1 ( +1, y +1 ; g +1, g y +1 )] + [( π (p,w ) (p y w ) p g y +w g D (, y ; g, g y )) ( π+1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g y +1 +w +1 g +1 D +1 ( +1, y +1 ; g +1, g y +1 ))] = TEC + AEC (16) Therefore, i can be conduced: PTC = {[π (p +1,w +1 ) (p +1 y w +1 ) p +1 g y +w +1 g π (p,w ) (p y w ) p g y +w g ] + [ π+1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g y +1 +w +1 g +1 = 1 π (p,w ) (p y +1 w +1 ) p g +1 y +w g+1 ]} 2 {[D +1 (, y ; g, g y ) D (, y ; g, g y )] + [D +1 ( +1, y +1 ; g +1, g y +1 ) D ( +1, y +1 ; g +1, g y +1 )]} {[(π+1 (p +1,w +1 ) (p +1 y w +1 ) p +1 g y +w +1 g D ( +1, y +1 ; g +1, g y +1 )) ( π (p,w ) (p y +1 w +1 ) p g y +1 +w g +1 D +1 (, y ; g, g y ))] + [( π+1 (p +1,w +1 ) (p +1 y +1 w ) p +1 g y +1 +w +1 g +1 ( π (p,w ) (p y w ) p g y +w g D (, y ; g, g y ))]} D +1 ( +1, y +1 ; g +1, g y +1 )) = TEC + AEC (17) The profi Luenberger indicaor can be furher decomposed as follows: PLPI=PEC+PTC Where: = (AEC+TEC) + (TC+ATC) = (TEC+TC) + (AEC+ ATC) = LPI + ALI (18) PEC= profi efficiency change PTC= profi echnology change AEC= allocaive efficiency change TEC= echnical efficiency change TC= echnical change ATC= allocaion-echnology change

11 An allocaion produciviy indicaor: Applicaion in Taiwanese banks Implemening he decomposiion In order o implemen he decomposiion of he profi Luenberger produciviy indicaor, we use he DEA approach wihin he direcional disance funcions, depending on he measure of he Nerlovian profi inefficiency. Suppose ha in he ime period ( =1,2,...,T ), he j h ( j =1,2,...,J ) DMU in he employs a vecor of N inpus j = ( j1, j2,, jn ) o generae a vecor of M oupus y j = (y j1, y j2,, y jm ). For he j h DMU in he h h group, we assume is direcional vecor in each ime period is a vecor ha equals he values of he DMU s own oupus and inpus each year, namely, g = ( g, +g y ) = ( j, y j ). Technical inefficiency gives he epansion in oupus and conracion in inpus in erms of he direcional vecor. The group-specific disance funcion D j ( j, y j ; g, g y ) can be compued by using only he group s observaions from he following mahemaical programming: D j ( j, y j ; j, y j ) = maβ j J j=1 λ hj y hj y jm β j y j m = 1,, M J λ j j jn β j=1 j j n = 1,, N J λ j=1 j = 1 λ j 0; j = 1,, J (19) Here, D j ( j, y j ; j, y j ) represens his direcional disance funcion in he j h DMU in he h h group seeking he maimum raio of he increase in oupus and he decrease in inpus. This will produce a projeced poin on he surface of he producion fronier along he direcion of he epansion of oupus and he conracion J of inpus. The consrain, j=1 λ j = 1, imposes a variable reurns o scale (VRS) echnology in he above linear programming problem. We now compue he cross-period direcional disance funcion as follows: D hj ( +1 j, y +1 j ; +1 j, y +1,+1 j ) = ma β j J j=1 λ j y j y +1 jm + β,+1 +1 j y j m = 1,, M J λ j j +1 jn β,+1 +1 j=1 j j n = 1,, N

12 30 Xiang Chen J j=1 λ j = 1 λ j 0; j = 1,, J (20) The oher direcional disance funcions, D j +1 ( j +1, y j +1 ; g +1, g y +1 ) and D j +1 ( j, y j ; g, g y ), can be compued using he above wo linear programs by inerchanging he ime periods and +1. For DMU j, we denoe he observed profi in period a he prevailing oupu price and inpu price vecors, p jm = (p j1, p j2,, p jm ) and w jn = (w j1, w j2,, w jn ), as p y w = M m=1 p jm y jm N w n=1 jn jn. Similarly, we denoe he oher observed profis as: p +1 y +1 w = M m=1 p jm y jm N w n=1 jn jn, p +1 y w +1 = M p m=1 jm y jm N w +1 n=1 jn jn and p y +1 w +1 = M m=1 p jm y jm N w +1 n=1 jn jn. Because g = ( hj, y hj )., he normalized facors denoe proies for he firm producion size, and hey are defined as p g y + w g = M m=1 p jm y jm + N w n=1 jn jn and. p +1 g +1 y + w +1 g +1 y = M m=1 p jm y jm + N w n=1 jn jn We hen compue he maimum profi π hj he following linear programming model: π j (p j, w j ) = ma(p j y m w j n ) J λ j y j=1 j y m m = 1,, M J λ j j=1 j n n = 1,, N J λ j=1 j = 1 (p hj, w hj ) for DMU j in group h from λ j 0; j = 1,, J (21) J Imposing VRS, j=1 λ j = 1, in his model implies a non-perfecly compeiive marke, and hence profi-maimum may no be zero. Given he price vecor and he echnology, he maimal profi (benchmark) is compued by he choosing quaniy vecor of oupus and inpus ( n, y m ). We also compue π j +1 (p j +1, w j +1 ) using he above linear program by inerchanging he ime periods and +1.

13 An allocaion produciviy indicaor: Applicaion in Taiwanese banks 31 3 Daa and variables The sample daa consis of 31 Taiwanese banks over he period The daa se in his sudy has been eraced from he Condiion and Performance of Domesic Banks published by he Cenral Bank of China (Taiwan) and he Taiwan Economic Journal (TEJ) 2. This sudy follows he inermediaion approach for he specificaion of inpus and oupus. This approach assumes ha he bank collecs deposis o ransform hem wih labor and capial ino loans and oher earning asses. According o Berger and Humphrey (1997), his sudy considers wo oupus: financial invesmens (y1) and oal loans (y2). The invesmens are defined as oher earning asses, Including financial asses, securiies, and equiy invesmens. The corresponding uni price of he invesmens (p1) is he raio of he income from invesmens o he invesmens. Toal loans consis of all ypes of loans issued ha generae a given amoun of ineres income. The corresponding uni price of loans (p2) is he raio of he raised amouns of ineres income o he oal loans. Table 1: Specificaion of variables Variable Name Definiion Inpu variables 1 Financial funds Including deposis and borrowed funds (uni: millions of NTD) 2 Labour Number of employees 3 Physical capial Ne amoun of fied asses (uni: millions of NTD) Oupu variables y1 Invesmens Including financial asses, securiies, and equiy invesmens (uni: millions of NYD) y2 Loans Including loans and discouns (uni: millions of NTD) Inpu price variables w1 Price of funds Ineres epenses divided by oal deposi w2 Price of labour personal epenses divided by number of employee w3 Price of physical Toal operaional epenses ne of personal epenses capial divided by fied asse 2 The Condiion and Performance of Domesic Banks was downloaded from hp://

14 32 Xiang Chen Oupu price variables p1 Price of invesmens Revenue from invesmens divided by invesmen p2 Price of loans Revenue from loans divided by loans This sudy specifies hree inpus o model he coss. The inpu vecor includes financial funds (1), labor (2), and physical capial (3). Financial funds are defined as deposis and borrowed funds. This inpu always accouns for he highes percenage of banks oal coss, while i also generaes ineres and oher financial epenses. Thus, he corresponding uni price (w1) is calculaed as he raio of financial epenses o financial funds. Labor is defined as he number of employees, while he corresponding uni price (w2) is calculaed as a raio of personal epenses o he oal number of employees. The las inpu, physical capial, corresponds o he bank s fied asses, whose uni price (W3) is obained as a raio of associaed coss (non-labor operaional epenses, which are non-ineres epenses minus personal epenses). Tables 1 define all he variables and presen summary saisics and Table 2 presens summary saisics of all variables for Taiwanese banks from 2010 o Table 2: Summary saisics of variables from 2010 o 2014 Variables Y1: Invesmen mean 42,423 37,709 41,629 43,435 44,834 SD 46,760 42,800 44,120 44,244 44,863 Y2: Loans mean 129, , , , ,045 SD 120, , , , ,285 X1:Financial funds mean 174, , , , ,716 SD 158, , , , ,910 X2: Labour mean 3,879 3,958 3,969 4,037 4,104 SD 2,450 2,507 2,529 2,657 2,667 X3: Physical capial mean 2,841 2,791 2,881 2,741 2,717 SD 3,317 3,753 3,916 3,677 3,593

15 An allocaion produciviy indicaor: Applicaion in Taiwanese banks 33 P1:Price of invesmens mean SD P2:Price of loans mean SD W1: Price of financial funds mean SD W2: Price of labour mean SD W3: Price of physical capial mean SD Table 2 shows ha Taiwanese banks have slowly increase for he oupus and inpus. The share of he loans (y2) o he invesmens (y1) nearly is 3:1. I means he Taiwanese banks focus heir business in he Loans. In erms of he prices, here is an opposie change for he oupu prices, he price of invesmen (p1) eperiences a decrease from o , and he price of he loan (p2) shows a slighly increase from o For he inpu prices, alhough hey all show a growh over all sample period, he inpu prices of financial fund (w1) and physical capial (w3) have a sudden decrease beween 2012 and Resuls and discussion Table 3 firsly presens he relaionship among he profi-oriened Luenberger indicaor (PLPI), Luenberger (LPI) and allocaion Luenberger indicaor (ALI) in he Taiwanese banks. I can be conduced ha he Taiwanese banking indusry have a profi performance growh beween 2010 and This is because of he posiive conribuions in Luenberger indicaor (0.0493) can offse he negaive conribuions in he allocaion indicaor ( ). From he value of he median, i is conduced ha he mos of he Taiwanese banks have a posiive improvemen among PLPI, LPI and ALI, respecively wih , and We also find ha he allocaion indicaor dominaes Luenberger indicaor for all banks. For he managers in he banks

16 34 Xiang Chen whose profi performance is negaive, he mos imporan job is o adjus heir operaing inpu-oupu mies o boos heir profis. Table 3: The PLPI, LPI and ALI in Taiwanese banks from 2010 o 2014 DMU Bank PLPI LPI ALI DMU 1 Bank of Taiwan DMU 2 Firs Bank DMU 3 Hua Nan Bank DMU 4 Mega Bank DMU 5 Bank SinoPac DMU 6 E. Sun Bank DMU 7 Taishin Bank DMU 8 China Trus Bank DMU 9 Taipei Fubon Bank DMU 10 Cahay Unied Bank DMU 11 Shin Kong Bank DMU 12 Jih Sun Bank DMU 13 Yuan Ta DMU 14 Bank of Kaohsiung DMU 15 Land Bank DMU 16 Chang Hwa Bank DMU 17 Ciibank Taiwan DMU 18 Shanghai Bank DMU 19 Union Bank DMU 20 Far Easern Bank DMU 21 Ta Chong Bank DMU 22 EnTie Bank DMU 23 Sunny Bank DMU 24 Bank of Panhsin DMU 25 Taiwan Business Bank DMU 26 Sandard Charered Bank (Taiwan) DMU 27 Taichung Bank DMU 28 King's Town Bank DMU 29 HWATAI Bank DMU 30 COTA Bank DMU 31 Bank of Taipei Mean Median

17 An allocaion produciviy indicaor: Applicaion in Taiwanese banks 35 Ma Min In he following, we use he decomposiion in he Eq. (18) o eplain he reasons behind he produciviy changes of he PLPI, LPI and ALI in Taiwanese banks. Table 4 which presens he average produciviy changes of he PLPI, LPI and ALI, and heir decomposed componens over he periods of From he mean value, i can be seen he PLPI, LPI and ALI have a relaionship as follows: = ( ) = ( ) + [ ( )] = ( ) + [( ( )) (22) = ( ) This is in line wih he Eq. (18). Table 4: The resuls of PLPI, LPI and ALI in he 31 Taiwanese banks from 2010 o 2014 PLPI = LPI + ALI PLPI = PEC+ PTC LPI = TEC + TC ALI = AEC + ATC DMU PLPI PEC PTC LPI TEC TC AL AEC ATC DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU

18 36 Xiang Chen DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU DMU mean From he profi managemen poin of view, he reason of he improved profi produciviy of he Taiwanese banks can be considered a he profi efficiency change and he profi echnology shif. I also is because he profi efficiency growh (0.2078) can offse he profi echnology reducion ( ). Furhermore, from he decomposiion PEC=TEC + AEC and PTC=TC+ATC, he profi efficiency growh comes from he increases in he echnical efficiency and allocaive efficiency, and he reducion in he profi echnology is because he posiive conribuion in he echnology canno offse he negaive shif in he allocaion echnology. From he indicaor measuremen poin of view, he profi indicaor increases is due o he posiive impac of Luenberger indicaor is greaer han he negaive effec of he allocaion indicaor. I is urn o he producion managemen poin of view, he Luenberger produciviy of he Taiwanese banking indusry increases from 2010 o 2014 is due o boh echnical efficiency increases (0.0145) and he echnical growh (0.0347). The conribuion in echnical growh is more influenial han he echnical efficiency o he Luenberger produciviy. When i comes o he resource allocaion managemen, he allocaion indicaor of he banking indusry regress is mainly resuled from he allocaion echnology regress ( ) hough he allocaive efficiency progress (0.2574) offers a posiive

19 An allocaion produciviy indicaor: Applicaion in Taiwanese banks 37 conribuion o he allocaion indicaor. Specifically for he DMUs, like DMU 1, i have a negaive profi produciviy from 2010 o By he decomposiion in he profi indicaor, i can be eplained ha he negaive effec in profi echnology is more funcional han he profi efficiency increasing effec. For he produciviy managemen of he DMU 1, i can be known ha i have an increasing produciviy which mainly comes from he conribuion in he producion echnology progress, however, from he allocaion indicaor managemen, i have an adverse effec in allocaion abiliy. Alhough he allocaive efficiency increases from 2010 o 2014, he reducion in allocaion echnology severely limis he abiliy o he resource allocaion, yielding he allocaion indicaor regresses. Therefore, for DMU 1, he op prioriy is o manage he inpu-oupu allocaion, and improve he profi echnology. Regarding o he DMU 4, i have a posiive profi produciviy. This is due o he conribuion in he produciviy can offse he impac in he negaive allocaion. In oher words, he funcion of he produciviy is more han ha of he resource allocaion, yielding he profi growh. As a resul, we also can conclude ha he raio of he profi loss is no only from he produciviy, bu also from he resource allocaion managemen. For any DMU, especially for he moribund DMU, i is imporan o focus on he allocaion and producion managemen. Table 5 shows he panel resuls of he PLPI, LPI and ALI beween 2010 and For overall baking indusry, he average change of he profi performance due o he changes in produciviy and resource allocaion increases by over he period The profi efficiency change is he posiive source (0.0770) and he profi echnology change is he negaive and dominan source ( ). From he produciviy poin of view, for he indusry, we find ha he Luenberger produciviy of he Taiwanese banking indusry have an increase wih This is due o boh of he echnical efficiency progress and echnical growh. However, from he allocaion managemen poin of view, alhough he allocaive efficiency increases from 2010 o 2014, he allocaion echnology reduces severely, yielding he decrease in he allocaion indicaor. For he corporae srucure, he financial holding company (FHC) and non-financial holding company (NFHC) have a posiive profi produciviy growh. The profi growh in FHC is faser han ha in NFHC, maybe his is he FHC have a divergen invesmen or a more profi increasing poin. By he decomposiion of he profi indicaor, i is found ha he profi effec growh in he NFHC is greaer han ha in he FHC, and he profi echnology

20 38 Xiang Chen Table 5: The resuls of decomposiion of PLPI, LPI and ALI by bank ypes PLPI FHC NFHC OVERALL PEC FHC NFHC OVERALL PTC FHC NFHC OVERALL LPI FHC NFHC OVERALL TEC FHC NFHC OVERALL TC FHC NFHC OVERALL ALI FHC NFHC OVERALL AEC FHC NFHC OVERALL ATC FHC NFHC OVERALL

21 An allocaion produciviy indicaor: Applicaion in Taiwanese banks 39 5 Conclusion In his paper, following he sudy of Juo e al. (2004), a concep of an allocaion Luenberger is proposed. Three kinds of produciviy indicaors of producion, profi and allocaion wih heir relaionships in he framework of organizaion managemen are discussed. I is shown ha he profi Luenberger produciviy indicaor (PLPI) can be decomposed ino he Luenberger produciviy indicaor (LPI) and allocaion Luenberger indicaor (ALI). The LPI can furher be decomposed ino he echnical change (TC) and echnical efficiency change (TEC), and he ALI also can furher be decomposed ino he allocaive efficiency change (AEC) and he allocaive echnology change (ATC). To illusrae an applicaion of he proposed indicaors, we adop an empirical eperimen wihin Taiwanese banking indusry. This sudy employs panel daa from 31 Taiwanese banks during he period o measure he profi Luenberger produciviy indicaor, Luenberger produciviy indicaor and allocaion Luenberger indicaor. The empirical evidence here finds ha Taiwanese banks show on average posiive profi produciviy growh. The growh mainly comes from he conribuion of Luenberger produciviy improvemen which enough offse he decrease from he Allocaion Luenberger. This indicaes ha producion produciviy is he main source for reducing any profi loss for Taiwanese banks. In erms of produciviy change, he decomposiions of he hree ypes of Luenberger indicaors illusrae he reasons of he produciviy change of he Taiwanese banking indusry from 2010 o We found ha he profi Luenberger produciviy of he Taiwanese banking indusry progresses since he value of he profi efficiency increase is more influenial han he value of he profi echnology regress, he profi efficiency growh is he main facor o cause he profi produciviy growh. We also showed ha he allocaion Luenberger indicaor of he Taiwanese banking indusry regresses due o he allocaion echnology decreases. The allocaion echnology regress is more influenial han he allocaion efficiency increase o he allocaion Luenberger indicaor. Finally, we find he profi produciviy growh in financial holding companies is faser han ha in non-financial holding companies, however he former s allocaion indicaor is reducing and he laer s is increasing. References [1] Baese GE, Rao DSP, O Donnell CJ, A mea-fronier producion funcion for esimaion of echnical efficiencies and echnology gaps for firms operaing under differen echnologies. Journal of Produciviy Analysis, 21, (2004),

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