Economies of scale and scope in Macau s banking sector

Transcription

1 Bans and Ban Systes, Volue 6, Issue 4, 2011 Maggie X. Fu (China), Eily U. Sio (China) Econoies of scale and scoe in Macau s baning sector Abstract This aer uses a araetric aroach within a translog cost function fraewor to estiate the econoies of scale and scoe in Macau s baning sector fro 1995 to The results indicate significant diseconoies of scale and econoies of scoe for Macau bans throughout the sale eriod regardless of their size and ownershi. Further analysis rovides evidence of significant roduct-secific econoies of scale and scoe, which vary according to ban size and ownershi. The findings suggest that Macau bans should diversify their asset ortfolios to gain greater cost advantage. However, exansion in size should be discouraged under current technology because it aears to be cost ineffective. In addition, our findings lend strong suort to the ileentation of the universal baning odel in Macau. Keywords: Macau baning sector, econoies of scale and scoe, araetric ethodology. JEL Classification: G21. Introduction Bans are currently exeriencing substantial coetitive ressure doestically and internationally as a result of the global trend towards liberalizing financial services and increasing use of advanced technologies. In resonse to these coetitive ressures, bans have atteted to adot alternative strategies to reduce their roduction costs by exloiting econoies of scale and scoe. In theory, the resence of econoies of scale eans that large bans have a cost advantage over sall bans, while evidence of econoies of scoe ilies that ulti-roduct bans are ore efficient than financial boutiques. A large aount of research has estiated the roduction econoies of the baning sector over the ast decade. However, as ost of these studies are devoted to the baning sectors of develoed econoies, little attention has been aid to bans in the eerging arets 1. China is one of the largest eerging econoies. It has two Secial Adinistrative Regions (SARs) which had been colonized by Portugal and the United Kingdo, resectively, for over a century. However, there are substantial differences between the baning sectors of these two regions. First, Hong Kong is an international financial center with around 150 licensed bans and a well-develoed financial aret. In contrast, Macau is an oen but sall econoy with only 24 bans with full licenses and no stoc aret. Second, bans in Hong Kong are larger than bans in Macau in ters of asset size. The average asset size of the Hong Kong bans is around 24 ties of the average asset size of the Macau bans. Third, in coarison to Macau bans, Hong Kong bans have develoed ore colicated roducts to both satisfy the needs of their general custoers and irove their ris anageent echaniss. Macau bans tyically offer traditional baning roducts to their custoers (e.g., current and savings accounts, loans, and ban cards). A few of the rovide very liited investent services, such as foreign exchange trading and share broerage services. In contrast, Hong Kong bans frequently offer securities, unit trusts, bonds, and various fors of structured roducts to satisfy custoer investent needs. Over the ast decade, Macau benefited fro the strong econoic growth of Mainland China and the rogress of econoic integration with neighboring regions. Such a favorable business environent boosted deand for ore colicated baning services, articularly in retail credit, roject finance, wealth anageent as well as ayent and settleent services. At the sae tie, bans ade considerable efforts to strengthen cororate governance and enhance internal control rocesses. Therefore, it is worth to investigate the resence of econoies of scale and scoe in Macau s baning sector in view of the surging deand for baning services by the counity. On the other hand, the research has already been done to estiate this iortant issue for bans in Mainland China and Hong Kong. Thus, this aer coleents the existing studies on roduction econoies by evaluating the roduction erforance of the baning sector in Macau and sheds soe light on enhancing the erforance of Macau s bans through oerational secialization/diversification and size exansion/reduction. The baning industry, which is one of the four ey industries driving econoic develoent in Macau, accounted for, on average, around eight ercent of Macau s GDP between 1995 and Excet for two offshore bans, all of the bans in Macau are retail bans with full baning licenses. In March 2010, there were 24 fully licensed bans in Macau 2. Ten were locally incororated and 14 were branches of foreign Maggie X. Fu, Eily U. Sio, For details, see Berger and Huhrey (1997) and Fu and Heffernan (2008). 2 The ostal savings office is excluded. 90

2 Bans and Ban Systes, Volue 6, Issue 4, 2011 bans, with total ban deosits and assets of around MOP300 billion and MOP440 billion, resectively. The Monetary Authority of Macau (AMCM), which was created in 1989, is resonsible for the forulation and ileentation of onetary olicy and the oversight of financial institutions in Macau. The Financial Syste Act was introduced in 1993 along with a nuber of baning refors to ensure the soundness of the baning syste. The Act adoted the recoendations of the Basle Coittee and various rules have been introduced since it was assed into law. For exale, all Macau bans ust eet iniu caital adequacy and liquidity ratios of 8.0% and 20.0%, resectively. The AMCM also issued a series of guidelines and rules concerning internal ban control and ris anageent in the 2000s to hel Macau bans safely and rudently irove their financial erforance, ensure their ability to aintain stability and enhance their caacity to cobat ris. On the other hand, the Financial Syste Act favors the introduction of the universal baning odel. The Act allows bans in Macau to rovide a wide range of roducts and services to their custoers. These include acceting deosits and other reayable funds fro the ublic; roviding loans, guarantees and other coitents, financial leasing and factoring, and oney transission services; issuing and adinistering eans of ayent; conducting trading for their own account or for the account of their custoers in oney, financial and foreign exchange aret instruents, and financial futures and otions; articiating in the issue and laceent of securities and the rovision of other services related to such issues; oerating in interban arets; as well as ortfolio safeeeing, anageent of other assets, financial consultancy, safe custody services, and the sale of insurance contracts 1. This aer eloys the rando effects anel data aroach within a translog cost function fraewor to test for the resence of econoies of scale and scoe in Macau s baning sector and to assess whether any of the findings can be exlained by differences in ban size and/or ownershi. The aer is organized as follows. Section 1 reviews revious studies and section 2 discusses the ethodologies eloyed and the data set. The results are reviewed in section 3. The final section discusses ey conclusions and olicy ilications of the findings. 1. Literature review There are two tyes of roduction econoies that ay be achieved by any fir econoies of scale and scoe. Econoies of scale are related to fir size and exist if average roduction costs decrease as outut increases. Conversely, a fir dislays diseconoies of 1 For details, refer to the official website of the AMCM ( scale if average roduction costs increase with outut. Econoies of scoe are resent if a fir can jointly roduce two or ore roducts and/or services at a lower cost than if they are roduced searately. The cost of joint roduction is higher if there are diseconoies of scoe (Bauol et al., 1982). As indicated by Clar (1998), there are two otential sources of econoies of scale and scoe in baning. The first is the sreading of fixed costs. If excess caacity exists, fixed or quasi-fixed branch costs, labor costs, or couter and telecounications equient costs ay be sread over large aounts of outut and/or joint usage of these fixed resources. Inforation roduction is the second basis for econoies of scale and scoe. For exale, the inforation collected fro servicing a custoer s deosits and loans ay be reused. As the cost of reusing inforation is usually less than the indeendent cost of its roduction, reuse ay hel reduce the increental costs of extending additional services. According to Berger et al. (1987), there are two further sources of econoies of scoe: ris reduction and custoer cost econoies. Theoretically, asset diversification and asset-liability aturity atching can reduce ortfolio and interest rate riss. To reduce ris in their revenue streas, bans ay be willing to incur extra costs. In addition, when ban services are situated jointly, custoerincurred baning costs ay be reduced due to transortation cost savings, and ease of inter-account fund transfers, etc. The literature contains extensive research on the econoies of scale and scoe of bans in develoed countries (Benston et al., 1982; Ki, 1986; Berger et al., 1987; Clar, 1988; Hunter and Tie, 1989; Shaffer, 1991; Berger and Huhrey, 1991; Mester, 1992; Zardoohi and Kolari, 1994; Wheeloc and Wilson, 2001; Rie and Stiroh, 2003). The results of these studies suggest that econoies of scale exist only for sall- and ediu-sized bans. However, the findings for scoe econoies are inconclusive. Studies of eerging econoies show, for exale, econoies of scale for sall bans and econoies of scoe for all bans in the Uraine (Mertens and Urga, 2001) and Singaore (Rezvanian and Mehdian, 2002). While the Paistani baning industry exhibits econoies of scale and scoe, scale econoies diinish for large bans. In addition, coared with ublic bans, rivate bans in eerging econoies oerate with relatively large econoies of scale but sall econoies of scoe (Iii, 2004). The results of Fu and Heffernan (2008) indicate the resence of constant returns to scale and significant econoies of scoe for ost joint-stoc bans in China. 2. Methodology and data 2.1. Methodology. Bans are ulti-roduct firs eloying a vector of inuts to roduce a vector of 91

3 Bans and Ban Systes, Volue 6, Issue 4, 2011 oututs. Under duality theory, the ulti-roduct cost function dual to the roduction function can be defined as: Following coon ractice, this study eloys a araetric aroach with a translog secification. The translog cost function taes the following for: C = f (Y, W), (1) where C is total cost, Y is a vector of oututs, W is a vector of inut rices. 1 ln C 0 ln y ln w q ln y ln yq 2 q 1 n ln w ln wn ln y ln w, 2 n where C is the total cost, y is the th outut, w is the th inut rice, is the norally distributed rando error ter. Standard syetry ( q q, n n) is iosed during estiation. To iose linear hoogeneity restrictions on the function, all of the cost and inut rice ters are noralized by the last inut rice. Shehard s lea 1 is not alied for either aroach because it would iose the undesirable assution that there are no allocative inefficiencies (Berger, 1993). Overall scale econoies (SCALE), also called ray scale econoies, is develoed by Bauol et al. (1982). SCALE is the elasticity of cost with resect to an outut, holding outut ix constant. It is defined as follows: SCALE( Y ) ln C( Y )/ ln y, (3) where C(Y) is the ultile-outut cost function, Y is the vector of oututs [ y 1... y ], are the indexes of different roducts. SCALE easures the ercentage change in cost due to a one ercent change in all oututs, a change that alters the scale of outut but not outut ix. SCALE WPSSE where IC ~ y ( y (2) < 1 ilies econoies of scale because costs increase roortionally less than oututs increase, while SCALE > 1 ilies diseconoies of scale. SCALE is useful in cases where bans grow by changing their scales but not their outut ix. Obviously, SCALE does not allow for a change in outut ix. Bauol et al. (1982) suggest an additional easure to illustrate how costs change when the outut of one roduct changes while the quantities of all other roducts are held constant. Product-secific scale econoies (PSSE) is resent if an increase in the roduction of a secific roduct results in a decline in the average cost, holding the other oututs constant. However, Berger et al. (1987) argue that PSSE requires evaluation of the cost function at y near zero, which is generally far outside the sale over which the cost function is estiated. To reedy this roble, Mester (1992) defines a new easure of roduct-secific econoies of scale, which is called within-sale roduct-secific scale econoies (WPSSE). The within-sale degree of econoies of scale secific to outut is: ) [ IC ( ~ y ) / C ] /[ ln C ( Y ) / ln y ] (4) ( ) [ C( y,..., y ) C( y,..., y, y, y,..., y )], where y is the sale iniu of y. Thus, WPSSE( y ) > 1 ( WPSSE( y ) < 1) ilies econoies (diseconoies) 1 of scale in the roduction 1 Shehard s Lea was first introduced by R.W. Shehard in The cost function C is differentiable with resect to the coonents of the inut rice vector, w. Then the solution S to the cost iniization roble is unique and S C / w, = 1,, N; i.e., the cost iniizing deand for the th inut is equal to the artial derivative of the cost function with resect to the th inut rice. This result is nown as the derivative roerty of the cost function, or Shehard s Lea, as Shehard (1953) is the first to obtain the result. of the th outut 2. Bauol et al. (1982) also develo overall scoe econoies (SCOPE), which easures the cost saving fro joint versus secialized roduction. However, as the translog cost function is undefined for the zero outut level required by SCOPE, Mester (1992) suggests a new easure where the iniu outut within the sa- 2 For soe ban grous, the iniu levels of ban investents and non-interest incoe are zero. Following Mester (1992), in this section the iniu values of these oututs are the sae as the conventional easures (0.001). 92

4 le is substituted for the zero level inherent in SCOPE. Therefore, for the case of three oututs, the Bans and Ban Systes, Volue 6, Issue 4, 2011 within-sale scoe econoies (WSCOPE) are defined as follows: WSCOPE( Y ) [ C( y 3 y, y, y ) C( y, y 3 y, y ) C( y, y, y 3 y ) C( y, y, y )]/ C( y, y, y ), where B B B B B B B B B B y is the iniu value of y in the sale 1. WSCOPE easures the ercentage increase in the cost of dividing the oututs into relative secialized bans, though none ore secialised than the ost secialized ban in the sale. WSCOPE > 0, WSCOPE < 0, and WSCOPE = 0 suggest the resence of withinsale scoe econoies, scoe diseconoies and scoe neutrality resectively. WSCOPE is useful in cases where extree roduct secialization is a viable business strategy (Mitchell and Onvural, 1996). 1 1 (5) Another easure of econoies of scoe is roductsecific scoe econoies (PSCO). PSCO exists if the cost of jointly roducing one articular outut with the existing outut bundle is saller than the su of the cost of roducing the outut and the rest of the outut bundle searately. To avoid the extraolation inherent in the easure of PSCO, Mester (1992) suggests a new aroach where the iniu outut within the sale is substituted for the zero level of outut. Thus, within-sale roduct-secific econoies of scoe (WPSCO) is develoed and defined as: WPSCO( y) [ C( y1,..., y 1, y, y 1,..., y) C( y1,..., y 1, y y, y 1,..., y ) C( y,..., y )] / C( y,..., y ), (6) where y sale. is the iniu level of outut within the Therefore, WPSCO is said to exist in the roduction of y when WPSCO (y ) > 0, whereas WPSCO (y ) < 0 indicates within-sale roduct-secific diseconoies of scoe Data. The data set used in this study is collected fro the annual financial stateents of bans. The sale consists of 24 bans registered in Macau between 1995 and Their aret share in ters of total assets was over 98% at the end of The interediation aroach is used to odel the roduction rocess of the baning fir. Three oututs are identified, including total loans (y 1 ), investents (y 2 ), and other non-interest incoe (y 3 ) as a roxy for off-balance-sheet (OBS) activities. These oututs are roduced using two inuts: borrowed funds (x 1 ) and other inuts (x 2 ) 2. The unit rice of funds (w 1 ) is couted by dividing the annual interest exenses by x 1. The rice of other in uts (w 2 ) is calculated as the ratio of total noninterest exenses to x 2. Table 1 resents the descritive statistics of these variables. In details, Panel A shows the statistics for all sale bans. Panel B and Panel C illustrate the statistics for doestic and foreign bans, resectively. Doestic bans refer to bans incororated in Macau. Foreign bans refer to bans incororated outside Macau. There were 10 doestic bans and 14 foreign bans in Macau at the end of Focusing on the differences between Panel B and Panel C, it shows that the doestic bans roduced slightly ore oututs than their foreign counterarts in all three areas. However, the doestic bans could enjoy lower costs than those foreign bans on average. Finally, for doestic bans, the average unit rice of funds was lower, whereas the average unit rice of other inuts (e.g., fixed assets and labors) was higher coaring to the foreign layers. Therefore, Table 1 resents a ixed icture on roduction econoies of Macau bans. Table 1. Descritive statistics of Macau bans 1 2 Variable Mean Min Max Panel A: All bans Total cost 960, ,672, Loans 2,485, ,599, Investents 1,347, ,523, Other non-interest Incoe 37, , B B In this aer, ( y 3 y ) in equation (5) is substituted by ( y ) y because, for the outut vector y 1 (loans) and y 2 (investents), the value calculated by the forer equation is negative, and hence cannot be used in the translog function to obtain costs. This ay overestiate the costs of roducing searately, or underestiate the costs of joint roduction. Hence, the results of WSCOPE should be interreted with regards to this ossible bias. 2 Other inuts ainly include hysical caital (fixed assets). Labor inut is not considered because the nuber of eloyees is not available. 93

5 Bans and Ban Systes, Volue 6, Issue 4, 2011 Table 1 (cont.). Descritive statistics of Macau bans Variable Mean Min Max Panel A: All bans Unit rice of funds Unit rice of other inuts Panel B: Doestic bans Total cost 833, , Loans 2,697, ,599, Investents 1,413, ,523, Other non-interest Incoe 40, , Unit rice of funds Unit rice of other inuts Panel C: Foreign bans Total cost 1,164, ,672, Loans 2,132, ,644,732.4 Investents 1,262, ,640, Other non-interest Incoe 33, ,993.5 Unit rice of funds Unit rice of other inuts Notes: All easures are in Macau ataca (thousands), excet for unit costs. 3. Eirical results Aendix to this aer reorts the coefficients for estiating the translog cost function (equation (2)) using the rando effects anel data aroach. The use of these estiated coefficients together with the original data set roduces different easures of econoies of scale and scoe. The results are resented in Table 2. Colun (1) shows that overall scale econoies (SCALE) and within-sale scoe econoies (WSCOPE) for the entire sale are statistically lower than one and higher than zero, resectively. This indicates that, on average, Macau bans have overall diseconoies of scale and econoies of scoe. This finding suggests that, while bans in Macau can generally obtain significant cost advantages through diversifying their asset ortfolio, increasing size ay lead to cost ineffectiveness. Coluns (2) to (4) rovide inforation on the scale and scoe econoies for different size categories. Macau bans are divided into three grous in ters of total assets, including sall, ediu and large bans. As shown in Table 2, sall and ediu-sized bans exhibit decreasing returns to scale, whereas constant returns to scale cannot be rejected for large bans. This finding suggests the sall and ediu-sized bans should not exand their size under current techonology, whereas large bans have alost achieved their otial scale, i.e., no ore cost saving can be generated fro exansion. In addition, the results indicate that there are scoe econoies for bans in each of the three size categories. The agnitude of the scoe easure, however, is greater for saller bans than larger bans. This ilication is consistent with revious studies of other countries (Rezvanian and Mehdian, 2002; Lii, 2004). That is, on average, Macau bans can reduce their cost of roduction through roduct diversification. The level of cost saving through ortfolio diversification is larger for saller bans than larger bans. We further divide the sale bans into doestic and foreign bans. Bans are categorized as doestic bans if they are incororated in Macau. Otherwise, they are labelled as foreign bans. Coluns (5) and (6) show that doestic and foreign bans exhibit significant diseconoies of scale and econoies of scoe. The difference in the agnitude of the scoe easures suggests that the cost saving via asset diversification is larger for foreign bans than doestic bans. Turning to the roduct-secific econoies of scale (WPSSE) and scoe (WPSCO), Colun (1) shows that there are roduct-secific econoies of scale with resect to total loans and diseconoies of scale with resect to other non-interest incoe, which is a roxy for OBS activities. This finding suggests that the arginal cost of roducing loans falls short of its average cost. This further ilies that the exansion of bans by increasing their loans is cost effective. The reverse is true for OBS activities. 94

6 Tyes of scale and scoe econoies Descritions Table 2. Econoies of scale and scoe (1) All bans (2) Sall bans (3) Mediu bans Bans and Ban Systes, Volue 6, Issue 4, 2011 (4) Large bans (5) Doestic bans (6) Foreign bans SCALE Overall scale econoies 0.79*** 0.56*** 0.77*** *** 0.72*** WSCOPE Within-sale scoe econoies 4.39*** 7.41*** 4.15*** 2.71*** 3.23*** 5.29*** WPSSE(y1) WPSSE(y2) WPSSE(y3) WPSCO(y1) WPSCO(y2) WPSCO(y3) Within-sale scale econoies secific to y1 (total loans) Within-sale scale econoies secific to y2 (investents) Within-sale scale econoies secific to y3 (other non-interest incoe) Within-sale scoe econoies secific to y1 (total loans) Within-sale scoe econoies secific to y2 (investents) Within-sale scoe econoies secific to y3 (other non-interest incoe) 4.17*** *** 5.82* 2.47** 5.46** *** ** ** * 7.64*** 37.85** 1.84** 1.77*** 19.31** 17.42** 8.89*** 48.95** 8.35*** 5.93*** 26.22* 19.59** 14.59*** 47.86** 9.50*** 8.01*** 28.45** NUMBER Nuber of observations Notes: Values with ***, ** and * are (1) statistically different fro one for the easures of econoies of scale (e.g., SCALE and WPSSE) and (2) statistically different fro zero for the easures of econoies of scoe (e.g., WSCOPE and WPSCO) at 1%, 5% and 10% levels of significance, resectively. Sall bans refer to bans with assets less than MOP1.2 billion. Mediu bans refer to bans with assets ranging between MOP1.2 billion and MOP6.5 billion. Large bans refer to bans with assets over MOP6.5 billion. Doestic bans refer to bans incororated in Macau. Foreign bans refer to bans incororated outside Macau. Focusing on bans of different sizes, Coluns (2) to (4) show that large and ediu-sized bans exhibit significant roduct-secific econoies of scale with resect to loans, whereas there are significant roduct-secific econoies of scoe with resect to investent and OBS activities for sall bans. These findings ily that large and ediu-sized bans can save costs by increasing their loans. For sall bans, however, exansion by increasing investents and OBS activities is cost ineffective. Finally, Coluns (1) to (6) also show that there are significant roduct-secific econoies of scoe with resect to all three oututs regardless of ban size and ownershi. This suggests that roducing all oututs jointly is less costly than roducing each outut indeendently for all inds of bans in Macau. The differences in the agnitudes of various roductsecific scoe easures further indicate that ediu bans and foreign bans ay enjoy greater cost advantage through asset diversification. Conclusions This aer is the first study to use baning data to exaine the current econoies of scale and scoe in the Macau s baning sector. Using data collected for the eriod fro 1995 to 2006, the rando effects odel with a anel data set is eloyed to estiate a translog cost function. Three ajor conclusions eerge fro this study. First, in general, Macau bans exhibit diseconoies of scale and econoies of scoe. In articular, sall and ediu-sized bans face significantly decreasing returns to scale, while constant returns to scale is not rejected for large bans. On the other hand, econoies of scoe are greater for salland ediu-sized bans than large bans. These findings suggest that bans in Macau should diversify their asset ortfolios to gain greater cost advantages, esecially the sall- and ediusized bans. Meanwhile, it aears that oerational exansion of these saller bans should be discouraged under current technology because it is cost ineffective. Second, large- and ediu-sized bans exhibit significant roduct-secific econoies of scale with resect to loans and there are significant roduct-secific econoies of scoe with resect to investents and OBS activities for sall bans. Therefore, to save costs, larger bans should increase their loan assets in a safe and rudent anner and saller bans should enhance their investents and OBS activities. Finally, our results show significant roduct-secific econoies of scoe with resect to all three oututs, regardless of ban size and ownershi. This level of cost advantage is found to be greater for ediu bans and foreign bans. These findings lend suort to the ileentation of the universal baning odel in Macau, and the diversification of ban asset ortfolios shoud be encouraged. Overall, given the highly coetitive environent in the baning sector and the increasing deand for diversified roducts and services by the custoers, Macau olicyaers shall encourage bans to ae ore efforts to broaden their sources of incoe in 95

7 Bans and Ban Systes, Volue 6, Issue 4, 2011 References several ways. Fee-based services should be further develoed and enhanced, including utual funds, unit trusts, securities, structured roducts, wealth anageent and other custoized services for secific custoers. Autoated baning services in for of Internet baning, hone baning and obile baning shall be widely alied to coleent traditional baning services. Finally, besides the basic baning services (e.g., deosits, reittances and currency exchange) which have already been ade available to the ublic, bans shall be encouraged to develo ore services regarding Reninbi businesses in Macau. 1. Bauol, W.J., J.C. Panzar, and R.D. Willig (1982). Contestable Marets and the Theory of Industry Structure, New Yor: Harcourt Brace Jovanovich, Inc. 2. Benston, J.G., G.A. Hanwec, and D.B. Huhrey (1982). Scale of Econoies in Baning: A Reconstruction Reassessent, Journal of Money, Credit and Baning, Vol. 14, Berger A.N., G.A. Hanwec, and D.B. Huhrey (1987). Coetitive Viability in Baning: Scale, Scoe, and Product Mix Econoies, Journal of Monetary Econoics, Vol. 20, Berger, A.N. and D.B. Huhrey (1991). The Doinance of Inefficiencies over Scale and Product Mix Econoies in Baning, Journal of Monetary Econoics, Vol. 28, Berger, A.N. (1993). Distribution-free Estiates of Efficiency in the U.S. Baning Industry and Tests of the Standard Distributional Assutions, Journal of Productivity Analysis, Vol. 4, Berger, A.N. and D.B. Huhrey (1997). Efficiency of Financial Institutions: International Survey and Directions for Future Research, Euroean Journal of Oerational Research, Vol. 98, Clar, J.A. (1988). Econoies of Scale and Scoe at Deository Financial Institutions: A Review of the Literature, Econoic Review, FRB of Kansas City, Fu, X. and S.A. Heffernan (2008). Econoies of Scale and Scoe in China's Baning Sector, Alied Financial Econoics, Vol. 18, Hunter, C.W. and S.G. Tie (1989). Does Multiroduct Production in Large Bans Reduce Costs, Federal Reserve Ban of Atlanta Econoic Review, Iii, A. (2004). Baning Sector Refors in Paistan: Econoies of Scale and Scoe, and Cost Coleentarities, Journal of Asian Econoics, Vol. 15, Ki, H. (1986). Econoies of Scale and Econoies of Scoe in Multiroduct Financial Institutions: Further Evidence fro Credit Unions, Journal of Money, Credit and Baning, Vol. 18, Mertens, A. and G. Urga (2001). Efficiency, Scale and Scoe Econoies in the Urainian Baning Sector in 1998, Eerging Maret Review, Vol. 2, Mester, L.J. (1992). Traditional and Nontraditional Baning: An Inforation-theoretic Aroach, Journal of Baning and Finance, Vol. 16, Mitchell, K. and N.M. Onvural (1996). Econoies of Scale and Scoe at Large Coercial Bans: Evidence fro the Fourier Flexible Function For, Journal of Money, Credit and Baning, Vol. 28, No. 2, Rezvanian, R. and S. Mehdian (2002). An Exaination of Cost Structure and Production Perforance of Coercial Bans in Singaore, Journal of Baning and Finance, Vol. 26, Rie, B. and K.J. Stiroh (2003). The Perforance of Universal Bans: Evidence fro Switzerland, Journal of Baning and Finance, Vol. 27, Shaffer, S. (1991). Econoies of Suerscale in Coercial Baning, Alied Econoics, Vol. 9, Shehard, R.W. (1953). Cost and Production Functions, Princeton University Press. 19. Wheeloc, D.C. and P.W. Wilson (2001). New Evidence on Returns to Scale and Product Mix Aong U.S. Coercial Bans, Journal of Monetary Econoics, Vol. 47, Zardoohi, A. and J. Kolari (1994). Branch Baning Econoies of Scale and Scoe: Evidence fro Saving Bans in Finland, Journal of Baning and Finance, Vol. 18, Aendix Table 1A. Paraeter estiates of the translog cost function Variable Coefficients Std. error z-value Constant *** ln y ln y ln y *** ln w *** ln y1 ln y1 / ln y ln y ln y1 ln y *** ln y2 ln y2 / *** ln y2 ln y

8 Table 1A (cont.). Paraeter estiates of the translog cost function Bans and Ban Systes, Volue 6, Issue 4, 2011 Variable Coefficients Std. error z-value ln y3 ln y3 / *** ln w1 ln w 1/ ln y1 ln w *** ln y2 ln w *** ln y3 ln w R Note: To iose linear hoogeneity restrictions on the function, all of the cost and inut rice ters are noralized by the last inut rice, w 2. 97