STOCHASTIC FRONTIER MODEL AND DATA ENVELOPMENT ANALYSIS FOR COST AND PROFIT EFFICIENCY OF BANKS IN BANGLADESH

Transcription

1 Jurnal Karya Asl Lorekan Ahl Matematk Vol. 6 No.1 (213) Page Jurnal Karya Asl Lorekan Ahl Matematk STOCHASTIC FRONTIER MODEL AND DATA ENVELOPMENT ANALYSIS FOR COST AND PROFIT EFFICIENCY OF BANKS IN BANGLADESH Md. Azzul Baten School of Quanttatve Scences, Unverst Utara Malaysa, 161 UUM Sntok Kedah Malaysa baten_math@yahoo.com; md.azzul@uum.edu.my Abstract : Ths study formulates the specfcaton form of both stochastc cost and proft fronter models and constant return to scale Cost and Proft data envelopment analyss (CRS Cost-DEA and CRS Proft-DEA) models. It examnes the cost and proft effcency of Natonal Commercal Banks and Prvate Banks n Bangladesh. The cost neffcency and proft effcency are observed slghtly hgher for prvate banks than natonal commercal banks n case of both stochastc fronter analyss (SFA) and DEA type models. The coeffcents of advance and off-balance sheet tems are found sgnfcant that postvely nfluence the banks n stochastc cost fronter model. The advance, other earnng assets, prce of borrowed fund are observed sgnfcant and negatve effects on the banks n stochastc proft fronter model. The average cost neffcency and average proft effcency were recorded wth 16.3% and 91% respectvely. The lowest cost neffcency s observed for Unted Commercal Bank Lmted whle the hghest cost neffcency s found for Janata Bank. The lowest proft effcency s recorded for Janata Bank whle the hghest proft effcency s observed for Eastern Bank Lmted. The average techncal and allocatve effcency (neffcency) are 68.8% (45.3%) and 35.9% (178.5%), respectvely n case of CRS cost-dea model. The average techncal and allocatve effcency are 7.3% and 31.8% respectvely n case of CRS proft- DEA model. The average cost neffcency s recorded 6.3% by SFA whereas average cost effcency s recorded 24.5% by DEA, that showed less effcent. The average proft effcency s found 91% by SFA whle average proft effcency s found 22.1% by DEA, so SFA method shows better effcency than DEA n terms of banks n Bangladesh. Key Words: Cost and Proft effcency models, Stochastc Fronter Analyss, Data Envelopment Analyss, Natonal commercal banks and Prvate Banks, Bangladesh. 1. Introducton The bankng ndustry of Bangladesh s a mxed one comprsng natonalzed, prvate and foregn commercal banks. These banks are the man vehcles for moblzng nvsble funds and channelng those funds to faster the growth of the productve sectors of the economy. After the lberaton war 1971, Bangladesh Government natonalzed all the commercal banks and fnancal nsttutons functonng n the East Pakstan. But durng , the government allowed commercal banks to operate n prvate sector sde by sde wth the publc sector banks to start a meanngful and constructve competton n the bankng sector. About two decades n Bangladesh that banks are operatng under both publc and prvate sector. Queston arses how successfully the natonal and prvate commercal banks are servng the country, how far they have acheved ther desred goals? To measure cost and proft effcency of natonal commercal banks and prvate banks usng stochastc fronter analyss and data envelopment analyss s mportant for at least two reasons. Frst, effcency measures are ndcators of success, by whch the performance of ndvdual banks, and the bank ndustry as a whole, can be gauged. Second, banks has been faced growng competton, both from other banks and from frms and markets outsde the ndustry (Wheelock and Wlson, 1993) and presumably banks wll be more successful n mantanng ther busness f they operate effcently. Stochastc fronter analyss (SFA) has become a popular tool for producton analyss. One partcular advantage of SFA s the ablty to model the producton relatonshp and the determnants of neffcency n one stage. The orgnal specfcaton of stochastc fronter producton for cross-secton 213 Jurnal Karya Asl Lorekan Ahl Matematk Publshed by Pustaka Aman Press Sdn. Bhd.

2 Md. Azzul Baten data was ndependently proposed by Agner, Lovell and Schmdt (1977), Battese and Corra (1977) and Meeusen and van den Broeck (1977). DEA s a lnear Programmng technque developed by Charnes, Cooper and Rhodes (1978), that allows calculatng relatve effcency of a busness unt wthout knowng ( a pror) whether any relatonshp s exst among the varables. In most of them, t s very dffcult to obtan the nput prce due to unavalablty of data nformaton (prce data s necessary n order to perform econometrc approach). Essentalty for that reason, ths study uses the non-parametrc approach (DEA) to nvestgate the effcency of banks. There has been a wdespread dscusson about lack of cost and proft effcency of banks n developng countres compare to the world wde by usng stochastc fronter cost and proft models. Favero and Pap (1995) measured techncal effcency and scale effcency n the Italan bankng sector usng a non-parametrc approach. Canhoto, and Dermne (23) consdered the mpact of foregn bank entry on bankng effcency n Australa usng DEA and SFA, they found foregn banks more effcent than domestc banks, whch however dd not result n superor profts. The measurement of bank techncal effcency and scale effcency studes are avalable usng DEA by several researchers (for eg., Wahda, 211; Bengul and Ergec, 21; Pardeep and Gan, 21; Dels et al., 29; Tahr et al., 29; Al-Delam and Al-An, 26; Lyroud and Angelds, 26; Dlruba, 25; Shanmugam and Dasz, 24). Interested readers can refer to Vu and Turnell (211), Aknloye et al. (21), Tahr et al. (21), Cadet (28), Dacanay (27), Vander (22), and Berger et al. (1993) for works of cost and proft effcency models. We buld on ths strng of the lterature, but study the effects on banks cost and proft effcency, usng effcent fronters rather than fnancal ratos measurng performance (Berger and Humphrey, 1997). Some of above researchers summarze the exstng lterature on cross-country comparsons of bankng effcency usng SFA and DEA ndependently. In ths paper, by contrast, we concentrate n estmatng cost and proft effcency of banks usng both SFA and DEA smultaneously. Furthermore, we use panel data over the perod 21 to 21 rather than cross-secton data at one pont n tme. Because, t s argued that effcency s better studed and modeled wth panels (Kumbhakar, 1993; Coell et al., 1999; Carbo et al., 22), and the use of panel data over cross-secton provdes more degrees of freedom n the estmaton of the parameters. A few studes are avalable n measurng bank effcency usng only SFA n Bangladesh (Baten and Kaml, 21, 211). Rahman and Islam (211) nvestgated relatve cost and proft effcency of dfferent branches of Islamc Bank Bangladesh Lmted (IBBL) usng only parametrc technque, but the comparsons wth NCBs and PBs usng non-parametrc technque lke DEA s not avalable at ther study. Moreover, Maudos and Poster (21) and Maudos et al., (22) ponted out that the estmaton of proft effcency and ts comparson wth cost effcency, where the avalable evdence on bank effcency s very lmted. Ths study contrbutes n fllng ths gap. Ths study deals to estmate frst cost and proft effcency of Natonal Commercal Banks and Prvate Banks n Bangladesh. Second, t measures year wse techncal effcency of the bankng sector n Bangladesh by SFA. Thrd, t measures both Cost and Proft effcency of banks ndvdually by usng CRS Cost DEA and CRS Proft DEA. Fnally, t compares cost and proft effcency by usng both SFA and DEA. 2. Methodology 2.1 Stochastc Cost Fronter Model Followng Agner et al. (1977) and Meeusen and Broeck (1977), cost effcency model can be defned as: C f y, p, ), 1,......, N..(1) ( k where, N stands for the number of banks; C stands for the bank s total operatonal costs of -th banks; y represents the vector of output quanttes of the -th banks; p k s the vector of prce nputs 17

3 Jurnal KALAM Vol. 6, No. 1, Page of the -th banks; and s a composte error term, through whch the cost functon vares stochastcally. The term can be parttoned nto two parts as follows: v u.(2) The equaton (1) s represented n natural logs: ln C f ( y, p k ) ln v ln u.(3) 18 v refers to endogenous factors and u where, refers to exogenous factors, whch mpact the cost of the bank producton. Thus the term v denotes a rse n the cost of bank producton due to the neffcency factor that may result from the mstakes of the management, such as non-optmal employment of the quantty or mx of nputs gven ther prce. u represents a temporary rse or fall n the bank s costs due to the random factor that may stem from a data/measurement error, or unexpected/uncontrollable factors such as weather, luck, labor strkes, war, etc., that are not under the u nfluence of the management. are assumed to be dentcally dstrbuted as normal varates and 2 neffcency scores are derved from a normal dstrbuton, N (, v ). The relatve effcency of a bank can be estmated by means of the rato, v. u The specfcaton of translog cost fronter model can be expressed n terms of banks as multoutput and mult-nput banks as follows: ln C ln y ln y ln y ln p j j k k 2 j k km ln pp k m k ln y ln pk v u...(4) 2 k m k where, ln s natural logarthm;, j are parameter to be estmated for the fronters of output; km are parameter to be estmated for nput prce of fronter model; k for nteracton effect. 2.2 Stochastc Proft Fronter Model k, s parameter to be estmated Suppose the th bank has a vector of x ndependent nputs that determne proft. Then, the stochastc proft effcency model s defned as: x v u, 1,2,..., N; (5) where s the logarthm of proft of the th bank; x s a vector of nput quanttes; s are unknown parameters to be estmated; v s corresponds to the random fluctuatons, and s assumed to 2 follow a symmetrc normal dstrbuton around the fronter.e., N (, v ) and ndependent of u ; for proft functon, u ( for hghest proft) accounts for bank s neffcency and s assumed here 2 to follow a truncated normal dstrbuton.e., N, u. The proft effcency s measured as the rato between observed proft P to the * correspondng proft fronter P,.e. PE P. After obtanng the estmates of u P the proft effcency of -th bank ndustry s gven by:

4 Md. Azzul Baten PE p * exp( u)..(6) p In log form, alternatve proft functon can be wrtten as follows: ln( a) ln f ( x, p, ) v u (7) k where, represent net proft after tax of the -th banks; x represent vector of nput quantty of -th banks; a s a constant added to the profts of each bank so that natural log s taken of a postve number snce mnmum profts are typcally negatve; p k represent vector of k-th nput prce of banks. The specfcaton form of alternatve translog proft fronter model can be expressed as shown below: ln( a) ln x k ln pk j ln xln xj 1 k1 2 1 j kl ln pk ln pl k ln pk ln x v u (8) 2 k1 l1 k1 1 where,, estmated for nput prce of fronter model; j are parameter to be estmated for the fronters of nput; 2.3 Data Envelopment Analyss Method k, kl are parameter to be k s parameter to be estmated for nteracton effect. CRS Proft DEA Let us consder n DMUs (decson makng unt) or banks, each one producng dfferent output (y) and usng dfferent nputs (x). The proft effcency of the bank assumng constant return scale (CRS), s measured as follows: Maxu, v ( u y / vx ), Subject to u y vx, j 1,2,..., N,...(9) j u, v. j where x s a vector of -th bank nputs. y j s a vector of bank j-th output gven the nputs. u s the weghted relatve vector assocated to output. v s the weghted relatve vector assocated to nput. CRS Cost DEA Imperfect competton, constran n fnance, etc. may cause a bank to be not operatng at optmal scale, n ths case the CRS assumpton s not approprate because t assumes that banks are operatng at optmal scale. In ths case, Banker, Charnes and Cooper (1984) suggested an extenson of the above model to take nto account the varable return to scale (VRS). The dual form of the above problem s: Mn,, St y Y, x X,.(1), 19

5 Jurnal KALAM Vol. 6, No. 1, Page where X s m n nput matrx, Y s s n output matrx, s an n 1 vector of constant and s a scalar. The value of obtaned wll be the effcency score for the -th bank. It wll satsfy 1, wth a value of 1 ndcatng a pont on the fronter and hence a techncal effcency bank. 3. Data and Defnton of Varables We consder two categores of banks () Natonal Commercal Banks (NCBs), () Prvate Banks (PBs) of Bangladesh over the tme perod from 21 to 21. Most of the data are collected from the annual reports of the specfc banks of Bangladesh and annual accounts of Scheduled Commercal Banks publshed by Bangladesh Bank, the central bank of Bangladesh. All varables except for the nput prce and output are measured n mllons of Bangladesh taka. The output vectors nclude (1) Cost s measured as total cost, s defned by all expenses of bank such as salary and allowances, Rent, taxes, Insurance, Lghtng, Statonary, Managng Drector s remuneraton, Deprecaton cost of bank. (2) Proft s measured as total proft after tax. (3) Advance s measured as total loan and advance mnus loan. (4) Other earnng assets s measured by total other assets. (5) Off-balance Sheet Items are measured by total Off-balance Sheet tems ncludng contngent labltes. All nput prces nclude (1) Prce of fxed assets s measured as total reparng cost of fxed assets. (2) Prce of labors s measured as total salary and allowances. (3) Prce of Borrowed fund s measured by total borrowed ncludng nsde and outsde of Bangladesh. All nput quantty ncludes (1) Fxed Assets s measured by number of fxed assets such as buldng, furnture, fxture, offce applance, and motor vehcles etc, multpled by number of branch. (2) Number of labor s measured as full-tme equvalents of bank s person who has agreed by contract to perform specfed servces for another, the employer, n exchange for money. (3) Borrowed fund s collected from nsde and outsde of Bangladesh. 4. Results and Dscusson Summary statstcs of output, nput quantty and nput prces are presented n Table 1. The maxmum lkelhood estmates of the stochastc fronter cost and proft models of the selected bank n Bangladesh are reported n Table-2. A sgnfcant postve or negatve coeffcent for any varable suggests that t ncreases or decreases the bank s cost and proft effcency. The advance and off-balance sheet tems are found sgnfcant and postve effects on the cost effcency of the banks. The coeffcent of advance 1 (.334) s hghly sgnfcant at 1% level and the coeffcent of off-balance sheet tems 3 (.339) s sgnfcant at 5% level of sgnfcant. Both results postvely nfluenced the banks n terms of stochastc cost fronter model. These results suggest that the output varable advance s postvely affected total operatng cost. Other earnng assets and prce of borrowed fund are observed to be nsgnfcant and negatve. In case of proft fronter model, the advance (ADV), other earnng assets (OEA), prce of borrowed fund (PBF) are observed to be sgnfcant and have negatve effects on the banks at 1% level. Besdes, Off-balance sheet tems (OBS), Prce of fxed assets (PFA), Prce of labor (POL) are found to be sgnfcant and have postve effects on the sampled banks. The results of varous hypothess tests of the cost and proft effcency models were presented n Table-3. The frst null hypothess s H :, whch specfy that there s no techncal effcency effect n the cost and proft effcency model. The hypothess s accepted n terms of cost fronter model so we can conclude that there s no techncal effcency effect n the model. But n case of proft effcency model, t s rejected, so t s concluded that there exsts a techncal effcency effect n the model. The second null hypothess s H : j, whch specfes that both Cobb-Douglas stochastc fronter cost and proft models are more preferable than Translog stochastc cost and proft fronter models. From the result t s observed that the null hypothess s rejected so Translog Cost and Proft models are more preferable than Cobb-Douglas stochastc cost and proft fronter models. 2

6 Md. Azzul Baten The evaluaton of techncal effcency, allocatve effcency cost effcency and proft effcency for the selected sample banks s presented n Table-4 for both cost DEA and proft DEA. The average techncal and allocatve effcency are 68.8% and 35.9%, respectvely for cost DEA. The techncal effcency s always greater than allocotve effcency for the selected banks. However, n the selected banks, techncal effcency s observed smaller than the allocatve effcency n case of AB Bank, Bank Asa and BRAC Banks. The results of techncal effcency and allocatve effcency, these two measures are combned to provde a measure of total cost effcency n case of cost DEA. The lowest cost effcency s 1.8% for AB Bank and hghest cost effcency s 1% for Mutual Trust Bank and One Bank n terms of cost DEA. In case of proft DEA, the average techncal and allocatve effcency are 7.3% and 31.8%, respectvely. The techncal effcency s observed hgher than the allocatve effcency for all sample banks expect AB Bank, Bank Asa, Dutch Bangla Bank and Mutual Trust Bank. The measurements of techncal effcency and allocatve effcency are combned to provde a measure of total proft effcency n case of proft DEA. The lowest proft effcency s 1.4% for AB Bank and the hghest proft effcency 1% for One Bank n case of proft DEA. The average cost and proft effcency s recorded at 24.5% and 22.1% respectvely n case of both Cost-DEA and Proft-DEA. Cost and Proft effcency comparson n between SFA and DEA are gven n Table-5. The average cost neffcency s found to be 6.3% by SFA and average cost effcency s recorded at 24.5% by DEA, showed less effcent. No banks are shown cost effcent by SFA but Mutual Trust Bank and One Bank are shown exactly effcent by DEA. The most cost neffcency s observed for Janata Bank wth the value of 44.7%. The less neffcency s recorded at 5.3% for Unted Commercal Bank by SFA and less effcency 1.8% n case of DEA for AB Bank. The average proft effcency s observed 91% by SFA and average proft effcency s found 22.1% by DEA, so SFA s better technque n measurng effcent than DEA. In case of SFA, Janata Bank s found to be less proft effcent wth the value of 75.9% than all other banks and most proft effcent s recorded for Eastern Bank wth the value of 94.9%. On the other hand n case of DEA, less proft effcent s found for AB Bank and exact effcent s for One Bank wth the values of 1.4% and 1% respectvely. Most of the banks are recorded above 9% effcent by SFA on the other hand most of the banks are found below 2% effcent by DEA. The bank wse cost and proft effcency scores are llustrated n Fgure-1. The average proft effcency (91%) and average cost neffcency (16.3%), respectvely, are reported for the selected banks. Eastern Bank proft effcency (94.5%) s observed hgher than others banks. On the other hand Janata Bank proft effcency (76.9%) s very low comparng to others banks. From Fgure 1, we observed that Janata Bank s less effcent n case of proft model; on the other hand ths Janata Bank s most neffcent for cost model. UCBL s less neffcent for cost model but proft effcency s hgh for Brac Bank, NBL Bank, and Prme Bank. Cost neffcency s (5.3%) very low for UCBL, on the other hand cost neffcency (44.7%) s very hgh for Janata Bank. The proft effcences of Bank Asa, BRAC Bank, Dhaka Bank, DBBL, Eastern Bank, Mercantle Bank, MTB, Natonal Bank, One Bank, Prme Bank and Pubal Bank are found almost stable, on the other hand DBBL, Mercantle Bank, MTB, Natonal Bank, One Bank, Prme Bank, Pubal Bank and Uttara Bank are almost stable n terms of cost neffcency. Year-wse cost and proft effcency of Natonal Commercal Banks (NCBs) and Prvate Banks (PBs) usng SFA and DEA are presented n Table-6. The average cost neffcency s recorded at 34.6% for NCB and 15.2% for PB by SFA, on the other hand average cost effcency s found to be 28.2% for NCB and 82.4% for PB by DEA. The NCB cost neffcency s doubled than PB cost neffcency n case of SFA, on the other hand PB cost effcency s one thrd of NCB cost effcency n case of DEA. In case of SFA, the average cost neffcency s found to be hgh n the year of 22 for NCB whle average cost neffcency s recorded hgh n the year of 23 for PB but cost neffcency s found less neffcnt n the year of 21 for NCB and cost neffcency s recorded less neffcent n the year of 27 for PB. In the year of 21 cost neffcency s observed 59.2% for NCB and 13.1% for PB, whch are less neffcent than NCB. In the year of 26 the cost neffcency s recorded 57.6% for NCB and 11.9% for PB, t s also less neffcent than NCB. In case of SFA, average proft 21

7 Jurnal KALAM Vol. 6, No. 1, Page effcency s more effcent n the year of 29 wth the value of 89.1% and less effcent n the year of 25 wth the value of 71.1% for NCB. Average proft effcency s more effcent n the year of 21 wth the value of 94.5% and less effcent n the year of 23 wth the value of 89% for PB. In case of DEA, the cost effcency s most effcent n the year of 29 wth the value of 67.9% for NCB and most effcent wth 91.9% n the year of 24 for PB. It s less effcent n the year of 24 wth the value of 8.4% for NCB and less effcent n the year of 26 wth the value of 76.2% for PB. The average proft effcency 8.4% for NCB and 92.5% for PB whle the average proft effcency 27.1% for NCB and 77.5% for PB. The PB s more effcent than NCB n case of both SFA and DEA. In case of DEA, the average proft effcency s more effcent n the year of 26 wth the value of 68.7% and less effcent n the year of 25 wth the value of 9.5% for NCB; on the other hand, average proft effcency s more effcent n the year of 22 wth the value of 87.8% and less effcent n the year of 26 wth the value of 69.3% for PB. The overall proft effcency of PB s more effcent than NCB n case of both SFA and DEA. Year-wse the proft and cost effcency scores for the selected banks are llustrated n Fgure- 2. From the result, we observed that the trend for proft effcency s ncreasng by year. It s observed that the proft effcency 87.5% n 23 whch ncrease to 93.7% n 29, but proft effcency decreases from 22 to 23. On the other hand n the year 23, low proft effcency s observed, but n the year 21, t slghtly decrease compared to the year 29. The trend for cost neffcency scores ncrease from 19% to 28% from 21 to 23, and then jump from 28% to 12% durng 23 to 25, and then ncrease from 12% to 17% n 26 and then decrease from 17% to 11% durng 28 and Concluson Ths study formulated stochastc cost and proft fronter models and CRS Cost-DEA and CRS Proft-DEA to examne cost and proft effcency of Natonal Commercal Banks and Prvate Banks n Bangladesh. In cost neffcency model, the estmated coeffcent of Prce of borrowed fund (PBF) wth -.18 ndcated that the level of neffcency was decreased by prce of borrowed fund. Advance (ADV) and Off-balance sheet tems (OBS) were found sgnfcant wth postve values that showed ncreasng the value of neffcency. In proft effcency model, the estmated coeffcent of Advance (ADV), Other earnng assets (OEA) and Prce of borrowed fund were recorded hghly sgnfcant wth negatve values represented decreasng level of effcency. But Off-balance sheet tems (OBS), Prce of fxed assets (PFA) and Prce of labor (POL) were found sgnfcant wth postve values represented ncreasng level of effcency. Bank wse average proft effcency and cost neffcency were found to be.91 and 1.63 respectvely. Most proft effcent bank was found Eastern Bank wth score of.949 and less proft effcent bank was found Janata Bank wth score of.769 for proft model. Most cost neffcent bank was Janata Bank wth score of.447 and less cost neffcent bank was Unted Commercal Bank wth score of.53 for cost model. In case of CRS cost DEA, bank-wse techncal effcency, allocatve effcency and cost effcency were.688,.359 and.245 respectvely; and n case of CRS proft DEA, techncal effcency, allocatve effcency and proft effcency were.73,.318 and.221 respectvely. Bank wse average cost and proft effcency usng SFA and DEA were (6.3% and 24.5%) for cost model and (91% and 22.1%) for proft model respectvely; we conclude that SFA effcency s better than DEA effcency. Year-wse proft effcency of prvate banks s recorded most effcent (92.5%) comparng to the natonal commercal banks (8.4%). Besdes, year-wse average cost neffcency of prvate banks occurred wth the value of (15.2%) along wth natonal commercal banks (34.6%). Natonal commercal banks cost and proft effcency were found always less effcent than prvate banks n case of DEA. 22

8 Md. Azzul Baten Appendx Table-1: Summary Statstcs of Output, Input Quantty and Input Prce varables Varable Descrpton Mean Std. Devaton Mnmum Maxmum Output Cost Total Cost Proft Proft after Tax ADV Advance OEA Other Earnng Assets OBS Off-balance Sheet tems Input Prce PFA Prce of Fxed Assets POL Prce of Labor PBF Prce of Borrowed Fund Input Quantty FIA Fxed Assets BOF Total Borrowed Fund NLA Number of Labor Table-2: Maxmum Lkelhood Estmates of Translog Stochastc Cost Fronter Model Cost Proft Varable Parameter Coeffcent T-rato Coeffcent T-rato *** ADV OEA OBS PFA POL PBF.334 *** *** *** ** *** *** *** *** ADV OEA OBS PFA POL PBF ADV*OBS OEA*OBS PFA*POL PFA*PBF POL*PBF ADV*PFA ADV*POL

9 Jurnal KALAM Vol. 6, No. 1, Page ADV*PBF OEA*PFA OEA*POL OEA*PBF OBS*PFA OBS*POL OBS*PBF SIGMA-SQUARED GAMMA Lkelhood functon *** Sgnfcant at the.1 level, ** Sgnfcant at the.5 level, *Sgnfcant at the.1 means nsgnfcant. Table-3: Generalzed Lkelhood-Rato Test of Hypothess of Stochastc Cost and Proft Fronter Model Cost Log-Lkelhood Test Statstcs Null Hypothess Crtcal Value Functon * Decson H : Accept H H : j Reject H Proft H : Reject H H : j Reject H Notes: All crtcal values are at 5% level of sgnfcance. *The crtcal value are obtaned from table of Kodde and Palm (1986). The null hypothess whch ncludes the restrcton that s zero does not have a ch-square dstrbuton, because the restrcton defnes a pont on the boundary of parameter space. 24 Table-4: Bank-wse Cost and Proft Effcency by Data Envelopment Analyss (DEA) Name of the Banks Seral Cost Effcency Proft Effcency No. TE AE CE TE AE PE AB Bank Bank Asa BRAC Bank Dhaka Bank Dutch Bangla Bank Eastern Bank Mercantle Bank Mutual Trust Bank Natonal Bank One Bank Prme Bank Pubal Bank South East Bank Sonal Bank Unted Commercal Uttara Bank Janata Bank Mean TE=Techncal Effcency, AE= Allocatve Effcency, CE= Cost Effcency, PE= Proft Effcency.

10 Md. Azzul Baten Table-5: Bank-wse Cost and Proft Effcency Usng SFA and DEA Methods Name of the Banks Cost proft SFA DEA SFA DEA AB Bank Bank Asa BRAC Bank Dhaka Bank Dutch Bangla Bank Eastern Bank Mercantle Bank Mutual Trust Bank Natonal Bank One Bank Prme Bank Pubal Bank South East Bank Sonal Bank Unted Commercal Bank Uttara Bank Janata Bank Mean Table-6: Year-wse Natonal Commercal Bank and Prvate Bank Effcency by SFA and DEA Year Natonal Commercal Bank Prvate Bank Cost Effcency Proft Effcency Cost Effcency Proft Effcency SFA DEA SFA DEA SFA DEA SFA DEA Mean

11 Jurnal KALAM Vol. 6, No. 1, Page Fgure-1: Average Cost and Proft Effcency of Selected Banks for Stochastc Fronter Analyss Fgure-2: Year-wse Average Cost and Proft Effcency of Banks 26

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