Analysing Productivity Changes Using the Bootstrapped Malmquist Approach: The Case of the Iranian Banking Industry

Transcription

1 Volume 5 Issue 3 Australasan Accountng Busness and Fnance Journal Australasan Accountng, Busness and Fnance Journal Analysng Productvty Changes Usng the Bootstrapped Malmqust Approach: The Case of the Iranan Bankng Industry Amr Arjomand Unversty of Wollongong, amra@uow.edu.au Abbas Valadkhan Unversty of Wollongong, abbas@uow.edu.au Charles Harve Unversty of Wollongong Artcle 4 Follow ths and addtonal works at: Copyrght 2011 Australasan Accountng Busness and Fnance Journal and Authors. Recommended Ctaton Arjomand, Amr; Valadkhan, Abbas; and Harve, Charles, Analysng Productvty Changes Usng the Bootstrapped Malmqust Approach: The Case of the Iranan Bankng Industry, Australasan Accountng, Busness and Fnance Journal, 5(3), 2011, Research Onlne s the open access nsttutonal repostory for the Unversty of Wollongong. For further nformaton contact the UOW Lbrary: research-pubs@uow.edu.au

2 Analysng Productvty Changes Usng the Bootstrapped Malmqust Approach: The Case of the Iranan Bankng Industry Abstract Ths study employs varous bootstrapped Malmqust ndces and effcency scores to nvestgate the effects of government regulaton on the performance of the Iranan bankng ndustry over the perod An alternatve decomposton of the Malmqust ndex, ntroduced by Smar and Wlson (1998a), s also appled to further decompose techncal changes nto pure techncal change and changes n scale effcency. A combnaton of these approaches facltates a robust and comprehensve analyss of Iranan bankng ndustry performance. Whle ths approach s more approprate than the tradtonal Malmqust approach for bankng effcency studes, t has not prevously been appled to any developng country s bankng system. The results show that although, n general, the regulatory changes had dfferent effects on ndvdual banks, the effcency and productvty of the overall ndustry declned after regulaton. We also fnd that productvty had postve growth before regulaton, manly due to mprovements n pure technology, and that government ownershp had an adverse mpact on the effcency level of state-owned banks. The bootstrap approach demonstrates that the majorty of estmates obtaned n ths study are statstcally sgnfcant. Keywords Regulaton; Productvty; Bankng; Data envelopment analyss; Bootstrap; Malmqust ndces Ths artcle s avalable n Australasan Accountng, Busness and Fnance Journal:

3 Analysng Productvty Changes Usng the Bootstrapped Malmqust Approach: The Case of the Iranan Bankng Industry * Amr Arjomand 1, Abbas Valadkhan 1 and Charles Harve 1 Abstract Ths study employs varous bootstrapped Malmqust ndces and effcency scores to nvestgate the effects of government regulaton on the performance of the Iranan bankng ndustry over the perod An alternatve decomposton of the Malmqust ndex, ntroduced by Smar and Wlson (1998a), s also appled to further decompose techncal changes nto pure techncal change and changes n scale effcency. A combnaton of these approaches facltates a robust and comprehensve analyss of Iranan bankng ndustry performance. Whle ths approach s more approprate than the tradtonal Malmqust approach for bankng effcency studes, t has not prevously been appled to any developng country s bankng system. The results show that although, n general, the regulatory changes had dfferent effects on ndvdual banks, the effcency and productvty of the overall ndustry declned after regulaton. We also fnd that productvty had postve growth before regulaton, manly due to mprovements n pure technology, and that government ownershp had an adverse mpact on the effcency level of state-owned banks. The bootstrap approach demonstrates that the majorty of estmates obtaned n ths study are statstcally sgnfcant. Keywords: Regulaton; Productvty; Bankng; Data envelopment analyss; Bootstrap; Malmqust ndces JEL codes: C02, C14, C61; G21 Acknowledgements: We wsh to thank two anonymous referees and the edtor, Dr Corstan Smark, for ther constructve comments on an earler verson of ths artcle. The vews expressed n ths paper do not necessarly reflect the vews of the referees and the edtor. 1 School of Economcs, Unversty of Wollongong. Correspondng author: Abbas Valadkhan, Emal: abbas@uow.edu.au 35

4 AAFBJ Volume 5, no. 3, Introducton Over the last decade the Iranan bankng ndustry has undergone many substantal changes, such as lberalsaton, government regulaton and technologcal advances, whch have resulted n extensve restructurng of the ndustry. These changes n polcy have affected both government-owned banks (ncludng commercal banks and specalsed banks) and prvate banks. The former have been the most successful n acqurng market share; n contrast, most prvate banks only joned the market after 2001 and have not yet caught up n market share wth the government-owned banks. However, t seems that government-owned banks were affected more notceably after government regulaton ntatves launched n 2005 that oblged all banks to reduce depost and loan nterest rates consderably. The government also mposed dfferent nterest rates and condtons on publc and prvate banks, and mposed oblgatons on government-owned banks to assgn hgher prorty n ther lendng operatons to areas such as advanced technology projects, small and medum enterprses, and housng projects for low-ncome earners. As a result, the level of non-performng loans (NPLs) from government-owned banks ncreased dramatcally after Accordng to the Central Bank of Iran, CBI (2006), the annual growth rate of government-owned banks NPLs was less than 30% before 2005; however, ths fgure ncreased markedly to 129% n CBI (2006) also stated that the hghest share of NPLs belongs to the manufacturng and mnng (20.1%) and constructon (19.5%) sectors. Thus, t s mportant to nvestgate the effect of government polces on the productvty of the Iranan bankng ndustry. Feth and Pasouras (2010), n a comprehensve survey coverng 196 studes usng operatonal research and artfcal ntellgence technques to assess bank performance, revealed that almost all studes that obtaned estmates of total factor productvty growth employed a DEA 2 -type Malmqust ndex. In other words, the Malmqust ndex s n wdespread use for examnng total factor productvty growth. Intally, Caves, Chrstensen and Dewert (1982) ntroduced the Malmqust productvty ndex as a theoretcal ndex. Färe et al. (1992) later merged Farrell s (1957) measurement of effcency wth Caves et al. s (1982) measurement of productvty to develop a new Malmqust ndex of productvty change. Färe et al. (1992) subsequently demonstrated that the resultng total factor productvty (TFP) ndces could be decomposed nto effcency-change and techncal-change components. Färe, Grosskopf, Norrs and Zhang(FGNZ) (1994b) further decomposed effcency change nto pure techncal effcency change and changes n scale effcency, a development that has made the Malmqust ndex wdely popular as an emprcal ndex of productvty change. However, Smar and Wlson (1998a) stated that the FGNZ model does not provde a useful measure of techncal change. Ther emprcal results show that all the estmated means for techncal change are nsgnfcant: many of the naccuraces n FGNZ may be attrbuted to ther confuson between unknown quanttes and estmates of these quanttes (p.4). Moreover, they concluded that Wthout a statstcal nterpretaton, t s not meanngful 2 Data Envelopment Analyss (DEA) s one of the most popular non-parametrc approaches to fronter effcency and productvty methods n the lterature. The major advantage of the DEA approach s that one does not need to adopt a functonal form and ts assocated coeffcents for the producton functon. Accordng to Boussofane, Martn and Parker (1997) and Guan et al. (2006), frms effcency can be measured by the DEA approach wthout any need to know the weghts for the dfferent nputs and outputs n the producton process. 36

5 Arjomand, Valadkhan & Harve: Analysng Productvty Changes to draw nferences from results obtaned wth these methods as t s otherwse mpossble to know whether the numbers reflect real economc phenomena or merely samplng varaton (p.18). Instead, they proposed an alternatve decomposton of the Malmqust ndex: they estmated changes n technology by changes n the varable returns to scale (VRS) estmate, and further decomposed the techncal changes nto pure techncal change and changes n the scale of effcency. The DEA approach for estmatng dstance functons when constructng Malmqust ndces s problematc. As DEA s a non-parametrc approach, t does not allow for random errors and does not have any statstcal foundaton, hence makng t nadequate for testng statstcal sgnfcance of the estmated dstance functons, or for conductng senstvty analyses to examne ther asymptotc propertes; see Coell et al.(2005), Lovell (2000) and Smar and Wlson (1998b; 1999; 2000). The nherent problem wth manstream DEA analyss s that dstances to the fronter are underestmated f the most effcent frms wthn the populaton are not ncluded n the sample. Analyss n ths stuaton leads to based fronter estmaton from the sample, whch n turn affects measurement of dstances to all other unts. Undoubtedly, uncertanty s carred through to parameters, such as the Malmqust ndces of TFP changes, that are estmated from DEA dstance functons. To solve ths problem, Smar and Wlson (1998b; 2000) defned a statstcal model, the bootstrap smulaton method, whch allows for determnng the statstcal propertes of the non-parametrc estmators n the mult-nput and mult-output case, and hence for constructng confdence ntervals for DEA effcency scores. In a later study, Smar and Wlson (1999) demonstrated that the bootstrap technque can also be employed to estmate confdence ntervals for Malmqust ndces. The most mportant practcal mplcaton of ther concluson s that statstcal nference becomes possble for Malmqust ndces. In ths study, we employ the Smar and Wlson (1998a) approach to measure the Malmqust ndex and ts components changes n pure techncal effcency, changes n scale effcency, pure changes n technology and changes n scale of technology to provde a more nclusve and robust analyss of productvty and techncal change n the bankng ndustry of Iran. For the frst tme, we also employ the bootstrap smulaton method (Smar & Wlson 1998b; 2000) n the context of a developng country to determne whether the computed changes n productvty are real or not. The remander of ths paper s structured as follows: Secton 2 presents a lterature revew of the bootstrapped Malmqust ndces. Sectons 3 and 4 descrbe the methodology of Malmqust ndces and the bootstrap technque, respectvely. Secton 5 explans the data and Secton 6 dscusses the results, followed by some concludng remarks. 2. Lterature Revew of Bootstrapped Malmqust Studes Despte a large body of lterature surroundng the tradtonal (FGNZ) Malmqust ndex, there s lttle wrtten about usng the bootstrapped Malmqust. Only a small number of studes have appled the statstcal propertes of the Malmqust estmates; see Balcombe, Davdova and Latruffe (2008), Galdeano-Gómez (2008), Hoff (2006) and Latruffe Davdova and Balcombe (2008) 3. The excepton s Tortosa-Ausna et al. (2008), who used both the FGNZ model and the bootstrap technque to nvestgate the productvty of the Spansh bankng system over the 3 Hoff (2006) appled bootstrapped Malmqust to the fsheres sector for assessng TFP changes for the fleet of Dansh seners operatng n the North Sea and the Skagerrak. Galdeano-Gómez (2008) appled ths technque n the feld of marketng cooperatves. Balcombe et al. (2008) and Latruffe et al. (2008) estmated bootstrapped Malmqust ndces for samples of Polsh farms. 37

6 AAFBJ Volume 5, no. 3, 2011 post-deregulaton perod They found that the productvty growth that occurred was manly attrbutable to an mprovement n producton possbltes (techncal changes). Ther bootstrap analyss also revealed that productvty changes for most of the frms were not statstcally sgnfcant. Our study s, therefore, unque n the sense that the bootstrap technque has not prevously been appled to the alternatve decomposton of Malmqust ndces n the evaluaton of a developng country s bankng system. Glbert and Wlson (1998) and Wheelock and Wlson (1999) analysed the bankng systems of developed countres wth a focus on the US, and Korea, respectvely. Wheelock and Wlson (1999), usng the alternatve decomposton of the Malmqust productvty ndex, showed that the growng neffcency of US banks n the perod can be largely attrbuted to the general falure of banks to adopt technologcal mprovements. Glbert and Wlson (1998) studed the effect of deregulaton on the productvty of Korean banks between 1980 and The ndex of changes n pure technology ndcated that after deregulaton Korean banks altered ther mx of nputs and outputs consderably, leadng to mprovements n productvty. The ndex of change n the scale of technology suggested that the most effcent scale sze was ncreasng over tme. Whle t seems that n many emprcal applcatons the bootstrap approach s more approprate than the tradtonal Malmqust, t has not been wdely used n other appled studes, presumably due to the lack of user-frendly software. In ths study we apply the FEAR (Fronter Effcency Analyss wth R) software package, whch was ntroduced by Wlson (2006) to estmate techncal effcency, the dfferent components of the Malmqust productvty ndex and ther confdence ntervals. 3. Productvty Measurement Usng the Malmqust Index To measure productvty change between perods t 1 and t 2, consder N frms that produce q outputs usng p nputs over T tme perods. A generc frm n perod t 1 employs nput x to t 1 produce output y, whereas n perod t t 1 2 quanttes of nput and output are x and y, t 2 t 2 respectvely. The producton-possbltes set at tme t s: S x, y x can produce y at tme t, (1) t n m where x s an nput vector, x and y s an output vector, y at tme t. Ths can be descrbed n terms of ts sectons. For example: y ( x ) y m ( x, y) S (2) t2 t1 t s ts correspondng output feasblty set. Based on Shephard (1970), the output dstance functon for frm at tme t 1 s: o t1t2 t1 t2 t1 D nf 0 y / y ( x ). (3) o The dstance functon D measures the dstance from the th frm's poston n the nputoutput space at tme t 1 t1 t2 to the boundary of the producton set at tme t 2, where nputs reman constant and θ s a scalar equal to the effcency score. When t 1 and t2 are equal, t s a o measure of effcency relatve to technology at the same tme, and D 1. When t t t 1 and t 2 are o not equal, D can be <, > or =1. t1 t2 38

7 Arjomand, Valadkhan & Harve: Analysng Productvty Changes Based on Färe et al. (1992) the Malmqust ndex between perods t 1 and t 2 can be defned as: M D D (4) oc oc o t1t2 t2 t2 oc oc D D t1t1 t2 t1 whch s a geometrc mean of two Malmqust productvty ndces for t 1 and t 2, as defned by Caves et al. (1982). If M 1, there has been postve total factor productvty change between perods t 1 and t 2. If M 1, there have been negatve changes n the total factor productvty. M 1 ndcates no change n productvty. However, Smar and Wlson (1999) argued that the producton possblty set S t s never observed and, consequently, that all dstances defned are unobserved. Hence, the Malmqust productvty ndex and the dstance functons mentoned above must be estmated. Ths, n sequence, requres estmaton of the producton set, S t, and the output feasblty set, yx. ( ) Burgess and Wlson (1995) wrote the estmated producton set as: (, ),, 1 1, m n N St x y yyt x Xt (5) where Yt y1 t, y2t,..., ynt X x, x,..., x, yt denotes ( m1) vector of observed outputs, t 1t 2t Nt and xt denotes ( n 1) vector of observed nputs. 1 and are a vector of one and an ntensty varable, respectvely. Hence, the correspondng output feasblty sets can be descrbed as: c m N yt ( x) y yyt, x Xt,, and (6). (7) v m N yt ( x) y yyt, x Xt, 1 1, Substtutng c yt ( x) and v yt ( x) for yt ( x) n Equaton 2 leads to computng estmators of the dstance functons by solvng the followng lnear programs: oc 1 N D y 1 2 t Y 1 t t t 2 xt X 1 t 2 ( ) max,, (8) ( ) max,, 1 1, ov 1 N D y 1 2 t Y 1 t t t 2 xt X 1 t 2 (9) where oc D features the assumpton of constant returns to scale and ov D allows for varable t1t2 t1t2 returns to scale. Gven estmates of the dstance functons, estmates of the Malmqust ndex can be constructed by substtutng the estmators for the correspondng true dstance functon values n Equaton 4: 39

8 AAFBJ Volume 5, no. 3, 2011 M oc oc D D oc oc D D t1t1 t2 t1 (10) o t t t t Alternatvely, followng Färe et al. (1992), ths total factor productvty change can be decomposed nto two components: oc oc oc D D D o t2 t2 t1t2 t1t1 M oc oc oc D D D t1t1 t2 t2 t2 t1 Eff Tech (11) where the term outsde the square root sgn, Eff, s an ndex of relatve techncal effcency change, and shows how much closer (or farther away) a frm gets to the best-practce fronter. It can be >, < or = unty dependng on whether the consdered frm mproves, stagnates or declnes. The second component, Tech, s the techncal-change component, whch measures how much the fronter shfts, and ponts out whether the best-practce frm s mprovng, stagnatng, or deteroratng, permttng a comparson to the evaluated frm. It can be >, < or = unty dependng on whether the techncal change s postve, zero or negatve. Färe et al. (1994a) demonstrated that the techncal-change component can be decomposed nto two factors: pure techncal effcency change and changes n scale effcency: ov oc ov oc oc D D / D D D o t2 t2 t2 t2 t2 t2 t1t2 t1t1 M ov oc / ov oc oc D D D D D t1t1 t1t1 t1t1 t2 t2 t2 t1 PureEff Scale Tech (12) where PureEff and Scale are measures of pure effcency change and change n scale effcency, respectvely, and Eff PureEff Scale. Tech remans unchanged from Equaton 11, and gves a measure of change n technology. Whle Tech sgnfes that the Constant Returns to Scale (CRS) fronter shfts over tme, pure effcency change and scale effcency change correspond to VRS fronters from two dfferent perods. On the other hand, Smar and Wlson (1998a) stated that f a generc frm's poston n the nput-output space remans fxed between tme t 1 and t 2, and the only change that happens s n the VRS estmate of technology (e.g., shft upward), the Tech presented n Equaton 12 wll be equal to unty, ndcatng no change n technology. The only way that the Tech n Equaton 12 would show a change n technology s f the CRS estmate of the technology changes. Hence, t s concluded by the authors that n such a crcumstance, the CRS estmate of the technology s statstcally nconsstent. Snce the VRS estmator s always consstent under the assumptons of Knep et al. (1996), they propose an alternatve decomposton of the Malmqust ndex to estmate changes n technology ( Tech ) by changes n the VRS estmate: 40

9 Arjomand, Valadkhan & Harve: Analysng Productvty Changes ov oc ov D D / D o t2 t2 t2 t2 t2 t2 M ov oc / ov D D D t1t1 t1t1 t1t1 PureEff Scale ov ov oc ov D D D / D oc ov D / D t1t2 t1t1 t1t2 t1t2 t ov ov D D D 1 t 1 t 1 t 1 oc ov oc ov t2 t2 t2 t1 / D D / D t2t2 t2t2 t2t1 t2t1 PureTech ScaleTech (13) where Tech s further decomposed nto pure techncal changes PureTech and changes n the scale of technology ScaleTech, and Tech PureTech ScaleTech. PureTech measures pure changes n technology and s the geometrc mean of two ratos that measure the shft n the VRS fronter estmate relatve to the bank's poston at tmes t 1 and t 2. When PureTech s greater than unty, t ndcates an expanson n pure technology. Specfcally, t shows an upward shft of the VRS estmate of the technology. ScaleTech provdes nformaton regardng the shape of the technology by descrbng the change n returns to scale of the VRS technology estmate at two fxed ponts, whch are the frm s locatons at tmes t 1 and t 2. When ScaleTech s greater than unty, ths ndcates that the technology s movng farther from constant returns to scale and the technology s becomng more and more convex. When ths ndex s less than unty t suggests that the technology s movng toward constant returns to scale; and when equal to unty suggests no changes n the shape of the technology. A smlar decomposton of the Malmqust ndex was also proposed by Ray and Desl (1997). They combned changes n the scale of effcency and the scale of technology nto a sngle term (SCH). However, Smar and Wlson (1999) stated that Ray and Desl s SCH confuses changes n the shape of the technology and n scale effcency experenced by the producton unt. Färe, Grosskopf and Norrs (1997) agreed that Ray and Desl s alternatve decomposton of Malmqust ncorrectly measures changes n scale effcency. Other knds of decompostons and components of the Malmqust ndex were descrbed by Fred, Lovell and Schmdt (2008), who concluded that the choce of approprate decompostons depends on the research queston. Accordngly, n ths study, the comprehensve decomposton of Smar and Wlson (1998a) s employed wth the am of provdng addtonal nsght nto productvty and techncal change n the bankng ndustry n Iran. 4. Formulaton of the Bootstrap Smar (1992) and Smar and Wlson (1998b) poneered usng the bootstrap n fronter models to obtan non-parametrc envelopment estmators. The dea behnd bootstrappng s to approxmate a true samplng dstrbuton by mmckng the data-generatng process. The procedure s based on constructng a pseudo-sample and re-solvng the DEA model for each DMU wth the new data. Repeatng ths process many tmes bulds a good approxmaton of the true dstrbuton. Smar and Wlson (1998b) showed that the statstcally consstent estmaton of such confdence ntervals very much depends on the consstent replcaton of a data-generatng process. In other words, the most mportant problem of bootstrappng n fronter models relates to the consstent mmckng of the data-generatng process. 4 They argued that ths problem refers to the bounded nature of the dstance functons. Snce the dstance estmaton values are close to unty, resamplng drectly from the set of orgnal data 4 See Smar and Wlson (2000) for a thorough analyss based on Monte Carlo evdence. 41

10 AAFBJ Volume 5, no. 3, 2011 (the so-called nave bootstrap) to construct pseudo-samples wll provde an nconsstent bootstrap estmaton of the confdence ntervals. To overcome ths problem, they proposed a smoothed bootstrap procedure. They used a unvarate kernel estmator of the densty of the orgnal dstance functon estmates (for effcency scores n that case), and constructed the pseudo-data from ths estmated densty. However, to estmate the Malmqust ndces, ths study uses panel data nstead of a sngle cross-secton of data wth the possblty of temporal correlaton. Smar and Wlson (1999), n adaptng the bootstrappng procedure for Malmqust ndces, proposed a consstent method usng a bvarate kernel densty estmate va the covarance matrx of data from adjacent years. However, the estmated dstance functons D and D usng a kernel estmator are t1 t1 t t 2 2 bounded from above unty; Smar and Wlson noted (1999) that a bvarate kernel estmator value under ths condton s based and asymptotcally nconsstent. To account for ths ssue, Smar and Wlson (1998b, 1999) adapted a unvarate reflecton method proposed by Slverman (1986). 5 Therefore, to acheve consstent replcaton of the data-generatng procedure that takes all these features nto account, one must use the smoothed bootstrap. Repeatedly resamplng from the Malmqust ndces va the smoothed bootstrap mmcs the samplng dstrbuton of the orgnal dstance functons (a set of bootstrap Malmqust ndces), from whch confdence ntervals can be constructed. On the whole, ths process can be summarsed as follows: 1. Calcuatng the Malmqust ndex M o for each bank ( 1,..., N) n each tme ( t 1 and t 2 ) by solvng the lnear programmng models n Equatons 8 and 9 and ther reversals. * * 2. Constructng the pseudo-data set xt, yt ; 1,..., N; t 1,2 to create the reference bootstrap technology usng the bvarate kernel densty estmaton and adapton of the reflecton method proposed by Slverman (1986). 3. Calculatng the bootstrap estmate of the Malmqust ndex * M o for each bank ( 1,..., N) by applyng the orgnal estmators to the pseudo-sample attaned n step Repeatng steps 2 and 3 for a large number of B tmes (n ths study B=2000) to facltate B sets of estmates for each frm. 5. Constructng the confdence ntervals for the Malmqust ndces. The basc dea desgned for constructon of the confdence ntervals of the Malmqust ndces s that the dstrbuton of o o M M s unknown and can be approxmated by the dstrbuton of * o o o M M, where M s the true unknown ndex, o M ( t1, t 2) s the estmate of the Malmqust ndex and * M o s the bootstrap estmate of the ndex. Hence, a and b defnng the (1 ) confdence nterval: o o Pr( b M M a) 1 (14) * * can be approxmated by estmatng the values a and b gven by: * * o o * Pr( b M M a) 1 (15) 5 Ths method s founded on the dea of reflectng the probablty mass lyng beyond unty where, n theory, no probablty mass should exst. 42

11 Arjomand, Valadkhan & Harve: Analysng Productvty Changes Thus, an estmated (1 ) percentage confdence nterval for the th Malmqust ndex s gven by: * * M o ( 1, 2) o ( 1, 2) o t t a M t t M b (16) A Malmqust ndex for the th frm s sad to be sgnfcantly dfferent from unty (whch would ndcate no productvty change) at the % level, f the nterval n Equaton 16 does not nclude unty. It should be mentoned that usng the calculated bootstrap value n step 4, we can also correct for any fnte-sample bas n the orgnal estmators of the Malmqust ndces wth the applcaton of a smple procedure outlned by Smar and Wlson (1999): The bootstrap bas estmate for the orgnal estmator M o s: B o 1 * o o bas B M B M ( b) M b1 Thus, a bas-corrected estmate of M o can be computed as: (17) o o o M M bas B M B o 1 * 2 ( o M t1, t2) B M ( b). b1 (18) However, as explaned by Smar and Wlson (1999), ths bas-corrected estmator may have a hgher mean-square error than the orgnal estmator, and hence t wll be less relable. Overall, the bas-corrected estmator should only be consdered f the sample varance * s 2 of * the bootstrap values o M ( t, t )( b) s less than one-thrd of the squared bootstrap bas 1 2 b1,..., B estmate for the orgnal estmator; that s: 2 * 2 1 o s bas B M 3. (19) Ths procedure can be acheved usng commands malmqust.components and malmqust n the FEAR software program. The above methodology for Malmqust ndces can be easly adapted to effcency scores. Only the tme-dependence structure of the data taken nto account for the Malmqust ndces must be changed (by replacng t 1 and t2 wth the perod consdered). The procedure can be done usng command boot.sw98 n the FEAR program. 5. The Data To facltate measurement of effcency scores and productvty change, we ntally had to specfy sets of nputs and outputs for the banks n our sample. However, there s no consensus as to how to specfy nputs and outputs. In ths study, focusng on bank servces, we employed the ntermedaton approach. In ths approach banks are vewed as fnancal ntermedares wth outputs measured n local currency, and wth labour, captal and varous fundng sources as nputs. Ths approach has several varants: asset, value-added and user- 43

12 AAFBJ Volume 5, no. 3, 2011 cost vews. Sealey and Lndley (1977) focused on the role of banks as fnancal ntermedares between depostors and fnal users of bank assets; they also classfed deposts and other labltes, together wth real resources (labour and captal), as nputs, and only bank assets such as loans as outputs. Berger, Hanweck and Humphrey (1987) classfed loans and all types of deposts as "mportant" outputs, snce these balance-sheet categores contrbute to bank's value added, and classfed labour, captal and purchased funds as nputs. Alternatvely, Aly et al. (1990) and Hancock (1991) mplemented a user-cost framework to determne whether a fnancal product s an nput or an output dependng on ts net contrbuton to bank revenue. In ths approach a bank asset can be categorsed as an output f the fnancal return on the asset exceeds the opportunty cost of the nvestment, and a lablty can be categorsed as an output f the fnancal cost of the lablty s less than ts opportunty cost. As our measurement of productvty depends on a mutually exclusve dstncton between nputs and outputs, followng Aly et al. (1990), Burgess and Wlson (1995) and Wheelock and Wlson (1999), we classfy nputs and outputs on the bass of the user-cost approach. We nclude three nputs: labour ( x 1) measured by the number of full-tme equvalent employees on the payroll at the end of each perod; physcal captal ( x2) measured by the book value of premses and fxed assets; and purchased funds ( x 3) ncludng all tme and savngs deposts and other borrowed funds (not ncludng demand deposts). We nclude three outputs: total demand deposts ( y 1) ; publc sector loans( y 2), ncludng loans for agrculture, manufacturng, mnng and servces; and non-publc loans ( y 3). Snce the prvate banks joned the market effectvely from 2003, and sgnfcant technologcal changes and economc reforms took place n 2004 and 2005, the sample perod was deemed approprate. Due to the unavalablty of the data, the sample expanson was not feasble. All data were obtaned from Iran s Central Bank archves (CBI 2005; 2008). We consdered all banks operatng n the Iranan bankng ndustry except three banks that are not homogenous n nput and output mxes. The study uses balanced panel data for 14 banks and sx years ( ). 6. Emprcal Results 6.1 Estmated Output-Orented Techncal Effcency Scores To estmate output-orented techncal effcency for the banks, the lnear programmng problems n Equaton 9 must be solved for each bank n each perod. When D ov s equal to t t unty t ndcates that the th frm les on the boundary of the producton set of perod t, and accordngly s techncally effcent. When D ov s below unty t ndcates that the frm s t t postoned under the fronter and s techncally neffcent. Table 1 summarses annual mean effcency for the bankng ndustry over the perod Column 2 lsts the mean effcency estmates, and columns 3 through 6 lst the bas-corrected estmates, the bootstrap bas estmates and the effcency s lower and upper bounds for the 95% confdence ntervals (annual means), respectvely, for each year. Table 1 shows that although the ndustry s neffcent over all years, the ndustry effcency level mproves over the perod , and declnes consderably after Note that n all cases the mean of estmated effcency les to the rght of the estmated confdence ntervals; ths result reflects the theory behnd the constructon of the confdence ntervals presented by Smar and Wlson (1998b). 44

13 Arjomand, Valadkhan & Harve: Analysng Productvty Changes In addton, the estmates of techncal effcency dffer from the bas-corrected estmates. In some perods ths dfference (the bas) s qute small. For nstance, the dfference was less than 0.03 between 2004 and 2007, whle n 2003 the dfference was about The means of the estmated confdence ntervals, whch defne the statstcal locaton of the true effcency, were qute narrow over 2005, 2006 and The mnor bas of VRS estmates and the relatvely smaller confdence ntervals n these years mply that the results are relatvely stable. However, results from ths table are very general and do not help us to dstngush between the performance of ndvdual banks. Hence, the bootstraps of the effcency scores for ndvdual banks are dsplayed n three major categores commercal, specalsed and prvate banks n Tables 2 and 3. For the sake of brevty, these tables present only the bootstrap of effcency scores for the years 2003 and 2008, respectvely 6. Table 1 Bootstrap estmates (Annual average) Year Estmated Eff Bas-Corrected Bas Lower Bound Upper Bound Mean Source: Authors' calculatons. A comparson of Table 2 and Table 3 shows that the specalsed banks were the most effcent banks n both years. The results are mxed for commercal and prvate banks. A number of banks show smlar effcences n both perods, but a few banks show substantal dspartes over the perods. For nstance, among the commercal banks, Natonal Bank and Trade Bank were effcent n both perods, whereas Bank Refah, whch was qute neffcent n 2003, became effcent n On the other hand, the stuaton of Export Bank worsened n 2008, and ts effcency deterorated from 0.95 n 2003 to 0.74 n Prvate banks also show smlar dspartes: Parsan Bank and EN Bank appear to be qute effcent n both perods. Karafarn Bank mproved ts effcency sgnfcantly n 2008 to an effcency score of 1.0, but Saman Bank performed exactly the opposte. Accordng to Tables 2 and 3, n 2003 and 2008 specalsed banks and prvate banks were the most effcent, respectvely, and commercal banks (.e., Bank Sepah, Export Bank and Trade Bank) were the most neffcent banks n the market. However, these results only provde a general gude to dentfy the most and the least techncally effcent banks n the market. A comprehensve nvestgaton of why some banks are more effcent than others wll requres a further n-depth analyss of changes n government or banks polces wthn a hstorcal perspectve. 6 Results for all years are avalable from the authors upon request. 45

14 AAFBJ Volume 5, no. 3, 2011 Table 2 Bootstrap of effcency scores, 2003 Bank Estmated Eff Bas-Corrected Bas Lower Bound Upper Bound - Government-owned Banks: Commercal Banks: Natonal Bank Bank Sepah Export Bank Trade Bank Bank Mellat Bank Refah Specalzed Banks: Agrcultural Bank Housng Bank Export development Bank (ED Bank) Bank of Industry and Mnes (BIM) Prvate Banks: Karafarn Bank Saman Bank Parsan Bank Bank Eghtesad Novn (EN Bank) Mean Source: Authors' calculatons. As stated by Smar and Wlson (1998b), relatve comparsons of the performance among frms based on the estmated effcency scores should be made wth cauton. Of specal note s the fndng that Housng Bank was effcent n both perods (as ts estmated effcency was 1.0 for both), and ts estmated confdence ntervals for 2003 and 2008 overlap. However the estmated lower bound n 2008 was much hgher than that of 2003, suggestng that ts true effcency may have mproved n In ths case bas-corrected effcency scores can be very helpful n dstngushng between decson unts. For nstance, the bas-corrected effcency of Housng Bank ncreased from n 2003 to n 2008, suggestng that ths bank was not equally effcent n 2003 and The bas for some banks s very small; hence, ther bas-corrected effcency score s very close to the orgnal estmate (e.g., Saman Bank n 2008), but a few banks show large dfferences (e.g., Bank Mellat n 2003). The bas estmates, n general, are hgher for the most effcent banks (wth the estmated effcency of 1.0) n both years. There are also substantal dssmlartes between banks confdence ntervals: Tables 2 and 3 both show that a number of estmated confdence ntervals are qute wde (e.g., Housng Bank and EN Bank n Table 2 and BIM and Parsan n Table 3 Bootstrap of effcency scores, 2008 Bank Estmated Eff Bas-Corrected Bas Lower Bound Upper Bound - Government-owned Banks: Commercal Banks: Natonal Bank Bank Sepah Export Bank Trade Bank Bank Mellat Bank Refah Specalzed Banks: Agrcultural Bank Housng Bank Export development Bank (ED Bank) Bank of Industry and Mnes (BIM) Prvate Banks: Karafarn Bank Saman Bank Parsan Bank Bank Eghtesad Novn (EN Bank) Mean Source: Authors' calculatons.

15 Arjomand, Valadkhan & Harve: Analysng Productvty Changes Table 3), whle others are rather narrow (e.g., Bank Refah and Karafarn Bank n Table 2 and Bank Refah and Saman Bank n Table 3). In general, the wdths of confdence ntervals appear to be narrower and the bas-corrected effcences tend to reach hgher values n The Decomposton of the Malmqust Index Concentratng only on effcency estmates can provde an ncomplete vew of the performance of banks over tme. Changes n dstance-functon values over tme could be caused by ether 1) movement of banks wthn the nput-output space (effcency changes) or 2) progress/regress of the boundary of the producton set over tme (technologcal changes). The decomposton of the Malmqust ndex, as explaned n Secton 2, makes t possble to dstngush changes n productvty, effcency and technology. Table 4 reports varous estmates of productvty changes for banks n the three categores over fve pars of years between 2003 and Almost all of the estmates are sgnfcantly dfferent from unty at the 90% or 95% level of sgnfcance. Only BIM s nsgnfcantly dfferent from unty for one par of years ( ). Over the perod after the prvate banks came nto exstence based on all 14 estmates of productvty changes only fve banks showed productvty gans. In ths perod, two of the specalsed banks, Agrcultural Bank and Housng Bank, had the hghest levels of productvty losses. On average, the ndustry showed an 11% productvty loss (.e., 0.98 productvty changes). The results for the three pars of years, however, were qute the opposte. Durng the perod all of the banks (wth two exceptons) showed moderate gans, and all specalsed banks showed productvty expansons. In the perod the results ndcate sgnfcant gans for ten banks, and sgnfcant decreases n productvty for four banks (two specalsed banks and two prvate banks). All commercal banks showed rather large productvty gans over ths perod. Durng the perod the ndustry showed a sgnfcant ncrease n productvty: about 28% on average. All banks but one showed productvty gans, and among these banks two of the specalsed banks ED Bank and BIM demonstrated massve productvty advances of 2.29 and 2.67, respectvely. The results for , however, were qute dfferent. Most of the banks experenced large productvty losses and none of the commercal banks were productve. BIM, whch showed the hghest level of productvty gan n , exhbted a 33% productvty loss n Ths pattern was also true for some of the commercal and prvate banks (Export Bank, Trade Bank, Bank Mellat and EN Bank). Usng the four components explaned n Secton 2, we can now trace the man causes of the productvty changes over the sample perod. Tables 5 and 6 present estmates of the changes n pure effcency, scale effcency, pure technology and scale of technology, respectvely. 47

16 AAFBJ Volume 5, no. 3, 2011 Table 4 Estmates of Malmqust ndexes (changes n productvty) Bank 2003/ / / / / Government-owned Banks: Commercal Banks: Natonal Bank * * * * * Bank Sepah ** * * * * Export Bank * * * * * Trade Bank * * * * * Bank Mellat * * * * * Bank Refah * * * * * Specalzed Banks: Agrcultural Bank * * * * * Housng Bank * * * * * Export development Bank (ED Bank) * * * * * Bank of Industry and Mnes (BIM) * * * * Prvate Banks: Karafarn Bank * * * * ** Saman Bank * * * * * Parsan Bank * * * * * Bank Eghtesad Novn (EN Bank) * * * * * Mean Note: Numbers greater than unty ndcate mprovements, and those less than unty ndcate declnes. Sngle astersk (*) denotes sgnfcant dfferences from unty at 90%; double astersk (**) denotes sgnfcant dfferences from unty at 95%. Source: Authors' calculatons. Table 5 Estmates of change n pure effcency Bank 2003/ / / / / Government-owned Banks: Commercal Banks: Natonal Bank 1.00* 1.00* 1.00* 1.00* 1.00* Bank Sepah * * * * Export Bank * 1.00* * * * Trade Bank * 1.00* 1.00* 1.00* * Bank Mellat 1.00* 1.00* 1.00* 1.00* 1.00* Bank Refah * 1.00* 1.00* 1.00* 1.00* Specalzed Banks: Agrcultural Bank 1.00* 1.00* 1.00* * * Housng Bank * * * * * Export development Bank (ED Bank) 1.00* 1.00* 1.00* 1.00* 1.00* Bank of Industry and Mnes (BIM) 1.00* 1.00* 1.00* 1.00* 1.00* - Prvate Banks: Karafarn Bank * * 1.00* 1.00* 1.00** Saman Bank * 1.00* 1.00* * * Parsan Bank 1.00* 1.00* 1.00* 1.00* 1.00* Bank Eghtesad Novn (EN Bank) 1.00* 1.00* * * 1.00* Mean Note: Numbers greater than unty ndcate mprovements, and those less than unty ndcate declnes. Sngle astersk (*) denotes sgnfcant dfferences from unty at 90%; double astersk (**) denotes sgnfcant dfferences from unty at 95%. Source: Authors' calculatons. 48

17 Arjomand, Valadkhan & Harve: Analysng Productvty Changes Table 6 Estmates of change n scale effcency Bank 2003/ / / / / Government-owned Banks: Commercal Banks: Natonal Bank * 1.00* * * * Bank Sepah * * * * * Export Bank * * * * * Trade Bank * * * * * Bank Mellat * * * * * Bank Refah * 1.00** *** 1.00*** Specalzed Banks: Agrcultural Bank * * * * * Housng Bank * * * * * Export development Bank (ED Bank) 1.00* * * * * Bank of Industry and Mnes (BIM) Prvate Banks: Karafarn Bank * * * * * Saman Bank * * 1.00* * * Parsan Bank 1.00*** * 1.00* Bank Eghtesad Novn (EN Bank) 1.00* 1.00* * * * Mean Note: Numbers greater than unty ndcate mprovements, and those less than unty ndcate declnes. Sngle astersk (*) denotes sgnfcant dfferences from unty at 90%; trple astersk (***) denotes sgnfcant dfferences from unty at 99%. Source: Authors' calculatons. Table 5 reports estmated changes n pure effcency. For consecutve years, out of the 70 estmates of changes n pure effcency, only 24 estmates dffered from unty, and all were statstcally sgnfcant. A number of banks showed no changes n pure effcency for all reported years (Natonal Bank, Bank Mellat, ED Bank, BIM, and Parsan Bank). Durng and (.e., n the post regulaton era) when nterest rates and the allocaton of drect lendng facltes were regulated, the number of banks wth losses n pure effcency ncreased to four and fve banks, respectvely. Hence, the ndustry, on average, showed negatve changes n techncal effcency as a result of napproprate polces. Table 6 reveals the estmated changes n scale effcency and as can be seen all changes from unty are statstcally sgnfcant Results for BIM are not sgnfcant n any of the reported perods. The results for , and are mxed. Over these three perods most of the banks experenced negatve changes n scale effcency (.e., the estmates are less than unty) or very low levels of postve changes. Over the perod , the results deterorated, wth only two banks showng some mprovements n scale effcency (ED Bank and EN Bank). Other banks ether experenced negatve changes or kept ther scale effcency more or less unchanged (for example, Bank Refah, BIM and Parsan Bank). These results, n conjuncton wth those for changes n pure effcency, ndcate that the consderable changes n bank productvty for cannot be attrbutable to effcency change components (pure effcency change or scale effcency change); they can be explaned only by technologcal changes. In nearly all of the government-owned banks showed consderable postve changes n scale effcency. However, the stuaton for prvate banks deterorated. As can be seen by the last row of Table 6, only the fnal perod shows postve changes n scale effcency, suggestng that scale neffcency was a major source of neffcency among the Iranan banks. Tables 7 and 8 show the estmated changes n pure technology for producton possbltes and scale of technology, respectvely. The estmated changes are sgnfcantly 49

18 AAFBJ Volume 5, no. 3, 2011 dfferent from unty n all cases at dfferent sgnfcance levels. In a number of cases changes for specalsed banks and prvate banks could not be computed due to the constrants mposed n the lnear programmng to estmate cross-perod dstance functons. We have ndcated these cases by INF n Tables 7 and 8, ndcatng that they were nfeasble to compute. 7 The results from Table 7 reveal that n technology among the government-owned banks shfted nwards for all but Export Bank. However, n , and , the estmated changes n pure technology were greater than unty for nearly all frms, wth the only excepton beng Export Bank n ; these results suggest an overall technologcal progress n the ndustry. Ths s most probably due to the technologcal advances n the bankng ndustry startng n 2004, such as ncreased numbers of automated teller machnes (ATM), credt cards, debt cards and onlne branches. However, almost all banks showed large decreases n technology for the perod Table 7 Estmates of change n pure technology Bank 2003/ / / / / Government-owned Banks: Commercal Banks: Natonal Bank * * * * * Bank Sepah * * * ** * Export Bank * * * *** * Trade Bank * * * * * Bank Mellat * * * * * Bank Refah * * * *** * Specalzed Banks: Agrcultural Bank * * * ** * Housng Bank * * * ** * Export development Bank (ED Bank) INF INF INF *** INF Bank of Industry and Mnes (BIM) INF INF INF INF INF - Prvate Banks: Karafarn Bank INF INF INF INF INF Saman Bank INF *** *** INF * Parsan Bank INF * * * * Bank Eghtesad Novn (EN Bank) INF INF INF ** * Mean Note: Estmates greater than unty ndcate an ncrease n pure technology, and estmates less than unty ndcate a decrease n pure technology. INF=Infeasble to compute. Sngle astersk (*) denotes sgnfcant dfferences from unty at 90%; double astersk (**) denotes sgnfcant dfferences from unty at 95%; trple astersk (***) denote sgnfcant dfferences from unty at 99%. Source: Authors' calculatons. 7 Ths dffculty was also experenced by Glbert and Wlson (1998). 50

19 Arjomand, Valadkhan & Harve: Analysng Productvty Changes Table 8 Estmates of change n scale of technology Bank 2003/ / / / / Government-owned Banks: Commercal Banks: Natonal Bank * * * * * Bank Sepah * * * * * Export Bank * * * * * Trade Bank * * * * * Bank Mellat * * * * * Bank Refah * * * * * Specalzed Banks: Agrcultural Bank * * * * * Housng Bank * * * * * Export development Bank (ED Bank) INF INF INF * INF Bank of Industry and Mnes (BIM) INF INF INF INF INF - Prvate Banks: Karafarn Bank INF INF INF INF INF Saman Bank INF INF * * * Parsan Bank INF * * * * Bank Eghtesad Novn (EN Bank) INF INF INF INF * Mean Note: Estmates greater than unty show that the technology s movng farther from constant return to scale, and estmates less than unty ndcate that the technology s movng toward constant returns to scale. INF=Infeasble to compute. Sngle astersk (*) denotes sgnfcant dfferences from unty at 90%. Source: Authors' calculatons. Fnally, Table 8 presents the estmated changes n the scale of technology. The estmated changes n the prvate banks are sgnfcantly less than unty n almost every case, ndcatng that between 2004 and 2008 the technologcal regon of these banks n the nputoutput space was movng toward constant returns to scale. Among the government-owned banks the results are the opposte n , and , meanng that returns to scale of technology were becomng ncreasngly convex and more varable. Gven that the prvate banks are much smaller than the government-owned banks, these results seem to mply that the most effcent scale sze decreased over these perods. However, the technology faced by government-owned banks n the last perod moved toward constant returns to scale, as the estmated changes showed values less than unty for most of them. In bref, the results n Tables 6 and 8 emphasse that the porton of the technology confrontng government-owned banks seems to have moved substantally further from constant returns to scale, and the banks have performed under decreasng returns to scale for a long perod. In general, the results n Tables 4 to 8 ndcate that whle government ownershp resulted n large advances n the technology of commercal and specalsed banks over tme, t also caused scale neffcences and kept the most effcent scale sze smaller than t otherwse would have been. Government-owned banks showed no postve changes n pure techncal effcency durng the sample perod. Also, after regulaton, three of the largest commercal banks became consderably neffcent. Ths may be attrbuted to the sgnfcant growth of NPLs snce However, the technology advances of government-owned banks offset the ncrease n scale and pure techncal neffcences over , , and , and hence, productvty ncreases n almost all government-owned banks. But large ncreases n the scale effcency of these banks over the perod dd not offset the rse n pure techncal neffcency and the reducton n pure technology (n producton possbltes). Hence, on average, ther productvty deterorated consderably over tme. 51