Bank Branch Operating Efficiency: A DEA Approach

Transcription

1 Poceedings of the Intenational MultiConfeence of Enginees and Compute Scientists 2009 Vol II IMECS 2009, Mach 18-20, 2009, Hong Kong Bank Banch Opeating Efficiency: A DEA Appoach Zijiang Yang Abstact In today s economy and society, pefomance analyses in the sevices industies attact moe and moe attention. his pape pesents an evaluation of 240 banches of one big Canadian bank in Geate oonto Aea using Data Envelopment Analysis (DEA). Special emphasis was placed on how to pesent the DEA esults to management so as to povide moe guidance to them on what to manage and how to accomplish the changes. Finally the potential management uses of the DEA esults wee pesented. Index ems Data Envelopment Analysis (DEA), Linea pogamming, Banking, Efficiency I. INRODUCION he banking industy is one of Canada s leading industies. Canadians enjoy 19 domestic banks, 23 foeign bank subsidiaies and 21 foeign bank banches, which manage ove $1.8 tillion in assets. hey seve Canadians with 249,000 employees, moe than 8,000 banches and 15,950 Automated Banking Machines (ABMs) [1]. he majo five Canadian banks (Bank of Monteal, Canadian Impeial Bank of Commece, Royal Bank of Canada, ScotiaBank and the oonto Dominion Bank and Canada ust), opeate vey lage nationwide banch netwoks in all makets, fom small towns to lage metopolitan aeas. hey ae not only essential fo the secuity and stength of the financial system, but also make significant contibutions to the economy acoss the county. hey continue to pusue all the oppotunities available to enhance thei poductivity and competitiveness. Consequently, poductivity analysis in the banking industy has become pat of thei management pactices. op bank management wants to identify and eliminate the undelying causes of inefficiencies, thus helping thei fims to gain competitive advantage, o, at least, meet the challenges fom othes. aditionally, banks have focused on vaious pofitability measues to evaluate thei pefomance. Usually multiple atios ae selected to focus on the diffeent aspects of the opeations. Howeve, atio analysis povides elatively insignificant amount of infomation when consideing the effects of economies of scale, the identification of benchmaking policies, and the estimation of oveall pefomance measues of fims. As altenatives to taditional bank management tools, fontie efficiency analyses allow management to objectively identify best pactices in complex Manuscipt eceived Decembe 13, Zijiang Yang is with School of Infomation echnology, Atkinson Faculty of Libeal & Pofessional Studies, Yok Univesity, EL 3049, 4700 Keele Steet, oonto, Ontaio, Canada, M3J 1P3 ( zyang@mathstat.yoku.ca ) opeational envionments. Compaed to othe appoaches, Data Envelopment Analysis (DEA) is a bette way to oganize and analyze data since it allows efficiency to change ove time and equies no pio assumption on the specification of the best pactice fontie. In addition, it pemits the inclusion of andom eos if necessay. Since the intoduction of DEA technology, a consideable numbe of eseaches have applied it in financial sevice industy. Cook et al. [2] investigated the use of quantitative vaiable in bank banch evaluation using DEA. Paadi and Schaffnit [3] evaluated the pefomance of the commecial banches of a lage Canadian bank. hey intoduce non-discetionay factos to eflect specific aspects of the envionment a banch is opeating in. Asmild et al. [4] evaluate the pefomance of Canadian banking industy ove time. Bala and Cook [5] incopoate expet knowledge within the DEA famewok. hey fist apply a disciminant o classification tool to quantify the functional elation that best captues the expet's mental model fo pefomance. he outcome of this fist phase is an oientation of vaiables to aid in the definition of inputs and outputs. he esulting oientation then defines the DEA model that makes up the second phase of the model. Camanho and Dyson [6] investigated the bank banch pefomance unde pice uncetainty. Halkos and Salamouis [7] measued the Geek bank pefomance using DEA. Isik and Kabi [8] utilize a DEA-type Malmquist otal Facto Poductivity Change Index to examine poductivity gowth, efficiency change, and technical pogess in ukish commecial banks duing the deegulation of financial makets in ukey. In addition, Guan and Dipinde [9], Athanassopoulos and Giokas [10], Devaney and Webe [11], Pille and Paadi [12], Mecan al at. [13], Penny [14], also studied the use of DEA in financial institutions, to mention a few. his pape pesents an evaluation of 240 banches of one big Canadian bank in Geate oonto Aea using DEA. he est of the pape is oganized as follows. Section 2 gives a bief eview of DEA. Section 3 povides the models and methodology utilized in this pape. Section 4 pesents the DEA esults and the potential use of the DEA esults. Finally, the conclusions ae given. II. DEA BASICS Poduction pocess can be defined as a pocess that can tun a set of esouces into desiable outcomes by poduction units. Duing this pocess, efficiency is used to measue how well a poduction unit is pefoming in utilizing its esouces to geneate the deived outcomes. Each of the vaious DEA models seeks to detemine which of the n decision making units (DMUs) define an envelopment suface that epesents the best pactice, efeed to as the empiical poduction

2 Poceedings of the Intenational MultiConfeence of Enginees and Compute Scientists 2009 Vol II IMECS 2009, Mach 18-20, 2009, Hong Kong function o the efficient fontie. Units that lie on the suface ae deemed efficient in DEA while those units that do not, ae temed inefficient. DEA povides a compehensive analysis of elative efficiencies fo multiple input-multiple output situations by evaluating each DMU and measuing its pefomance elative to an envelopment suface composed of othe DMUs. hose DMUs foming the efficiency efeence set ae known as the pee goup fo the inefficient units. As the inefficient units ae pojected onto the envelopment suface, the efficient units closest to the pojection and whose linea combination compises this vitual unit fom the pee goup fo that paticula DMU. he tagets defined by the efficient pojections give an indication of how this DMU can impove to be efficient. Conside n DMUs to be evaluated, DMU j (j=1,2 n) consumes amounts X j ={x ij } of inputs (i=1, 2,, m) and poduces amounts Y j ={y j } of outputs (=1,, s ). he efficiency of a paticula DMU 0 can be obtained fom the following linea pogams (input-oiented BCC model [15]). 1 + min z0 = θ ε s ε 1s (1) θ, λ, s+, s s. t. Yλ - s + = Y0 θx 0 Xλ s = 0 1λ = 1 λ, s +, s 0 Pefoming a DEA analysis actually equies the solution of n linea pogamming poblems of the above fom, one fo each DMU. he optimal vaiable θ is the popotional eduction to be applied to all inputs of DMU 0 to move it onto the fontie. A DMU is temed efficient if and only if the optimal value θ* is equal to 1 and all the slack vaiables ae zeo. his model allows vaiable etuns to scale. he dual pogam of the above fomulation is illustated by: max µ,, ν s. t. w0 = µ Y0 + u0 v X 0 = 1 µ Y v X + u µ ε 1 v ε 1 u 0 fee If the convexity constaint ( 1 λ = 1 ) in (1) and the vaiable u 0 in (2) ae emoved, the feasible egion is enlaged, which esults in the eduction in the numbe of efficient DMUs, and all DMUs ae opeating at constant etuns to scale. he esulting model is efeed to as the CCR model. he eade is advised to consult the textbook by Coope, Seifod and one [16] fo a compehensive teatment of DEA theoy and application methodology. (2) impotant two appoaches ae the poduction appoach and the financial intemediation appoach. Unde the poduction appoach, banks ae viewed as institutions making use of vaious labou and capital esouces to povide diffeent poducts and sevices to customes. hus, the esouces being consumed such as labou and opeating cost ae deemed as inputs while the poducts and the sevices such as loans and deposits ae consideed as outputs of the banks. his model measues the cost efficiency of the banks. Unde the financial intemediation appoach, banks ae viewed as financial intemediaies which collect deposits and othe loanable funds fom depositos and lend them as loans o othe assets to othes fo pofit. he diffeent foms of funds that can be boowed and the cost associated with pefoming the pocess of intemediation ae consideed as inputs. he foms in which the funds can be lent ae outputs of the model. his model measues the economic viability of the banks. his pape intoduces an opeational efficiency model which adopts a poduction appoach. his model examines how well diffeent banches combine thei esouces to suppot the lagest amount of possible sevices. he vaiables wee selected based on taditional pefomance atios, liteatue models, availability of the data and expets opinion. hee wee fou inputs (sales FE, sevice FE, suppot FE and othe FE) and nine outputs ( to set up new vaiable ate consume loan, to open new inteest beaing cuent accounts, No. of tansactions to open a new menu account, to pocess banch deposit to Menu accounts, No. of tansactions to pocess withdawal fom menu accounts, No. of tansactions to update passbook fom menu accounts in banch, to tansfe funds in banch, No. of tansactions to pocess visa cash advance, to pocess commecial deposits) in the DEA model. he diagam fo the DEA model is povided in figue 1. Input oientation (the LP is oiented to minimize inputs) was selected fo the DEA models in this eseach. I point out that management was moe inteested in minimizing the consumption of inputs subject to attaining the desied output levels. BCC model is utilized in ode to conside the size effect. III MODELS AND MEHODLOGY A numbe of diffeent appoaches can be used fo modeling the banking pocesses. Each of them is used to obtain a diffeent aspect of efficiency measues. he most

3 Poceedings of the Intenational MultiConfeence of Enginees and Compute Scientists 2009 Vol II IMECS 2009, Mach 18-20, 2009, Hong Kong Inputs Sales FE Sevice FE Suppot FE Othe FE Bank Banch Figue 1. DEA model IV RESULS AND DISCUSSIONS Outputs to set up new vaiable ate consume loan to open new inteest beaing cuent accounts to open a new menu account to pocess banch deposit to Menu accounts to pocess withdawal fom menu accounts to update passbook fom menu accounts in banch to tansfe funds in banch to pocess visa cash advance In this analysis, 240 banches of a big Canadian bank in Geate oonto Aea ae evaluated. Summay statistics fo the inputs and outputs ae epoted in able 1. Fom the table one may find some input and output vaiables have zeo values. No futhe action is taken since ou softwae can deal with nonpositive values. It is also obseved that the vaiations among the banches ae quite big. ABLE 1 SUMMARY SAISICS OF OUPUS AND INPUS Max Min Aveage Standad Deviation Inputs Sales FE Sevice FE Suppot FE Othe FE Outputs to set up new vaiable ate consume loan to open new inteest beaing cuent accounts to open a new menu account to pocess banch deposit to Menu accounts to pocess withdawal fom menu accounts to update passbook fom menu accounts in banch to tansfe funds in banch to pocess visa cash advance to pocess commecial deposits he degee of coelation between inputs and outputs is an impotant issue that has geat impact on the obustness of the DEA model. hus, a coelation analysis is impeative to establish appopiate inputs and outputs. On the one hand, if vey high coelations ae found between an input vaiable and any othe input vaiable (o between an output vaiable and any of the othe output vaiables), this input o output vaiable may be thought of as a poxy of the othe vaiables. heefoe, this input (o output) could be excluded fom the model. On the othe hand, if an input vaiable has vey low coelation with all the output vaiables (o an output vaiable has vey low coelation with all the input vaiables), it may indicate that this vaiable does not fit the model. Coelation analyses wee done fo each pai of vaiables and the following table pesents the details.

4 Poceedings of the Intenational MultiConfeence of Enginees and Compute Scientists 2009 Vol II IMECS 2009, Mach 18-20, 2009, Hong Kong able 2 CORRELAION COEFFICIENS BEWEEN HE INPUS AND OUPUS I1 I2 I3 I4 O1 O2 O3 O4 O5 O6 O7 O8 O9 I I I I O O O O O O O O O I1:Sales FE I2: Sevice FE I3:Suppot FE I4:Othe FE O1: to set up new vaiable ate consume loan O2: to open new inteest beaing cuent accounts O3: to open a new menu account O4: to pocess banch deposit to Menu accounts O5: to pocess withdawal fom menu accounts O6: to update passbook fom menu accounts in banch O7: to tansfe funds in banch O8: to pocess visa cash advance O9: to pocess commecial deposits I did not find any evidence of vey high coelation between any one input vaiable and any othe (no between output vaiables) and any one input vaiable having vey low coelation with any of the output vaiables (no between output vaiable and input vaiables) in the above five tables. his is a easonable validation of my DEA models. Othewise, the sensitivity analysis on the impact of including and excluding diffeent vaiables on the efficiency should be pefomed. he input oiented BCC model is un and able 3 summaises the esults fo the model. ABLE 3 DEA RESULS BCC Aveage Scoe 0.89 Standad Deviation 0.14 Maximum Efficiency Scoe 1.00 Minimum Efficiency Scoe 0.49 Numbe (and %) of Efficient 113(47%) DMUs # Efficient DMUs exhibiting 4 IRS # Efficient DMUs exhibiting 66 CRS # Efficient DMUs exhibiting 43 DRS Fom this table, we can conclude that BCC model identified 89% technical efficiency on aveage. he issue of scale inefficiencies is exploed with geate detail by consideing etuns-to-scale (RS) indicatos. Among 113 efficient banches, 4 banches opeate unde inceasing etuns-to-scale, 66 banches opeate unde constant etuns-to-scale, and the emaining 43 banches opeate unde deceasing-etuns-to-scale. he efficiency scoe distibution is given in Figue Efficiency Scoe Distibution Figue 2 Efficiency scoe distibution he distibution of efficiency scoes is skewed towads the highe efficiency scoes. Geneally speaking, this model identified potential savings fo the 240 banches in GA fom the indicated pefomance impovements. he aveage efficiency scoe of 0.89 implies that the bank banches could use about 11 pecent less labou and expenses to poduce thei outputs. It is vey impotant to pesent esults in an easy to undestand manne. hus, we split the banches into goups based on the efficiency scoes in ode to find futhe insights [17]: he obustly efficient units that will appea in many efeence sets and ae likely to emain efficient unless thee wee majo shifts in thei fotunes. he weakly efficient units that will typically appea in only one o two efeence sets and may well dop below 1.0 if thee was even a small dop in the value of an output vaiable (o a small incease in the value of an input vaiable). he maginally inefficient units will have an efficiency ating in excess of 0.9 (but less than 1.0) and could aise thei scoe towads 1.0 with a elatively small amount of impovement in thei opeating esults. Medium inefficient units that have an efficiency scoe between 0.7 and

5 Poceedings of the Intenational MultiConfeence of Enginees and Compute Scientists 2009 Vol II IMECS 2009, Mach 18-20, 2009, Hong Kong Distinctively inefficient units. If the efficiency scoe of a unit is less than 0.7, then this unit would have significant difficulties making themselves efficient in the shot tem. he units in the obustly efficient goup could be examples fo those inefficient units, as they manage thei esouces bette. Figue 3 shows the distibution of the banches in each categoy. Banches Distibution Figue 3 Banches distibution obustly efficient weakly efficient maginally inefficient Medium inefficient Distinctively inefficient DEA esults also highlight the easons fo both favouable and poo use/poduction of esouces/outcomes involved in the unit s pefomance factos that contibuted to o detacted fom the DMUs efficiency ating. Nevetheless, one of the most poweful pieces of infomation that is obtained by a DEA analysis is the set of taget values fo those assessed as inefficient. he efeence set povides stong indications of what type and amounts of inputs and outputs ae needed to make the inefficient units efficient. Since input oiented DEA models ae used in the analysis, thee will be taget input values that the inefficient units could use to achieve an efficiency scoe of 1.0. able 4 povides DEA efficiency scoes and efeence sets fo some of the DMUs in this analysis. Fo example, in ode fo DMU 4302 to become efficient, it should educe each of its input esouces including sales FE, sevice FE, suppot FE and othe FE by 16%. Moe specifically, based on the efeence sets DMU 4302 should consume X 1842 * X 7142 * X 9282 *0.42 (X i is the input vecto fo DMU i) amount of input to geneate its obseved output level. In addition, the DEA scoes can be used to estimate the potential savings fom pefomance impovements. If all the banches can pefom efficiently, by using the taget input and output values, the bank could save as much as 11% of its esouces fom a theoetical point of view. In pactice, the saving will almost cetainly be substantially less. ABLE 4. DEA EFFICIENCY SCORES AND REFERENCE SES. DMU No BCC Scoe Refeence set (lambda) V CONCLUSIONS his pape adopts DEA to evaluate the banch pefomance in GA fo a lage Canadian bank. he banches opeate faily efficiently on the whole although thee is still oom fo impovement. Special emphasis was placed on how to pesent the DEA esults to management so as to povide moe guidance to them on what to manage and how to accomplish the changes. Finally, ecommendations to management s use of DEA esults wee given. REFERENCE [1]. Canadian Bank Facts, Canadian Bankes Association, 2005 Edition. [2]. Cook, W.D., Hababou, M. and uente, H.J., Multicomponent Efficiency Measuement and Shaed Inputs in Data Envelopment Analysis: an Application to Sales and Sevice Pefomance in Bank Banches, Jounal of Poductivity Analysis 14, , [3]. Paadi, J.C. and Schaffnit Claie, Commecial Banch Pefomance Evaluation and Results Communication in a Canadian Bank - a DEA Appoach, Euopean Jounal of Opeational Reseach 156, No. 3, , [4]. Asmild Mette, Paadi J. C., Aggawall Vanita, and Schaffnit Claie, Combining DEA Window Analysis with the Malmquist Index Appoach in a Study of the Canadian Banking Industy, Jounal of Poductivity Analysis 21, No. 1, 67-89, [5]. Bala, Kamel and Cook, Wade D., Pefomance Measuement with Classification Infomation: an Enhanced Additive DEA Model, Omega 31, No. 6, pp , [6]. Camanho A.S., Dyson and R.G., Cost Efficiency Measuement with Pice Uncetainty: a DEA Application to Bank Banch Assessments, Euopean Jounal of Opeational Reseach 161, No. 3, , [7]. Halkos, G.E. and Salamouis, D.S., Efficiency Measuement of the Geek Commecial Banks with the Use of Financial Ratios: a Data Envelopment Analysis Appoach, Management accounting Reseach 15, No. 2, , [8]. Isik, Ihsan and Kabi Hassan, M, Financial Deegulation and otal Facto Poductivity Change: An Empiical Study of ukish Commecial Banks, Jounal of Banking and Finance 27, No. 8, , [9]. Guan, H.L. and Dipinde, S.R., Competition, Libealization and Efficiency: Evidence fom a wo-stage Banking Model on Banks in Hong Kong and Singapoe, Manageial Finance 31, No. 1, 52-77, [10]. Athanassopoulos, A.D. and Giokas, D., he Use of Data Envelopment Analysis in Banking Institutions: Evidence fom the Commecial Bank of Geece, Intefaces, Vol 30, no 2, 81-95, [11]. Casu, B., Giadone, C., and Molyneux, P., Poductivity Change in Euopean Banking: a Compaison of Paametic and Non-Paametic Appoaches, Jounal of Banking and Finance 28, No. 10, , [12]. Pille. P., and Paadi, J.C., Financial Pefomance Analysis of Ontaio (Canada) Cedit Unions: An Application of DEA in the

6 Poceedings of the Intenational MultiConfeence of Enginees and Compute Scientists 2009 Vol II IMECS 2009, Mach 18-20, 2009, Hong Kong Regulatoy Envionment, Euopean Jounal of Opeational Reseach 139, No. 2, , [13]. Mecan, M., Reisman A., Yolalan, R., and Emel, A.B., he effect of Scale and Mode of Owneship on the Financial Pefomance of the ukish Banking Secto: Results of a DEA-Based Analysis, Socio-economic Planning Sciences 37, No. 3, , [14]. Neal, Penny, X-Efficiency and Poductivity Change in Austalian Banking, Austalian Economic Papes, Vol 43, Issue 2, , 2004 [15]. R. D. Banke, A. Chanes and W. W Coope, "Models fo Estimating echnical and Scale Efficiencies in DEA", Management Science 30(9): pp , [16]. Coope, W.W., L.M. Seifod and K. one, Data Envelopment Analysis: A Compehensive ext with Models, Applications, Refeences, Kluwe Academic Publishes, Boston, [17]. Noman, M and Stoke, B, Data Envelopment Analysis: he Assessment of Pefomance, John Wiley & Sons Publishes, 1991.