Cardiff Economics Working Papers

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1 Cardff Economcs Workng Papers Workng Paper No. E2007/5 Ratonal Ineffcency and non-performng loans n Chnese Bankng: A non-parametrc Bootstrappng Approach. Kent Matthews, Janguang Guo and Nna Zhang February 2007 Cardff Busness School Aberconway Buldng Colum Drve Cardff CF10 3EU Unted Kngdom t: +44 (0) f: +44 (0) busness.cardff.ac.uk Ths paper can be downloaded from econpapers.repec.org/repec:cdf:wpaper:2007/5 Ths workng paper s produced for dscusson purpose only. These workng papers are expected to be publshed n due course, n revsed form, and should not be quoted or cted wthout the author s wrtten permsson. Cardff Economcs Workng Papers are avalable onlne from: econpapers.repec.org/paper/cdfwpaper/ and busness.cardff.ac.uk/research/academc-sectons/economcs/workng-papers Enqures: EconWP@cardff.ac.uk

2 Ratonal Ineffcency and non-performng loans n Chnese Bankng: A non-parametrc Bootstrappng Approach Kent Matthews*, Janguang Guo**, Nna Zhang*** *Cardff Busness School, Cardff Unversty, Wales **Central Unversty of Fnance and Economcs, Bejng ***Ctgroup, Shangha November Abstract The exstng Chnese bankng system was born out of a state-plannng framework focussed on the fundng of state-owned enterprses. Despte the development of a modern bankng system, numerous studes of Chnese bankng pont to ts hgh level of average neffcency. Much of ths neffcency relates to the hgh level of non-performng loans held on the banks books. Ths study argues that a sgnfcant component of neffcency relates to a defunct bureaucratc ncentve structure. Usng bootstrap non-parametrc technques the paper decomposes cost-neffcency nto X-neffcency and ratonal neffcency caused by bureaucratc rent seekng. In contrast to other studes of the Chnese bankng sector, the paper argues that a change n the ncentve structure and the compettve threat of the openng up of the bankng market n 2007 has produced reduced neffcency and mproved performance. Keywords : Bank Effcency, Chna, X-neffcency; DEA. Bootstrappng JEL codes: D23, G21, G28 Correspondng author: K Matthews Cardff Busness School Colum Drve, Cardff, CF10 3EU Wales, UK E-mal address: MatthewsK@cf.ac.uk Tel.: +44(0) Paper prepared for the All Chna Economcs Internatonal Conference December 2006, Department of Economcs & Fnance, Cty Unversty of Hong Kong. We gratefully acknowledge the fnancal support of the Brtsh Academy SG-41928(IR) and Chnese Educaton Mnstry projects for research on Humanty and Socal Scence No.04JZD0013. Comments welcome.

3 1. Introducton Studes of bank effcency n Chna have been n vogue among Chnese scholars for a number of years 1. These studes have been partly prompted by the mpendng openng up of the bankng system to foregn competton at the end of The advent of greater foregn competton has galvansed the bankng authortes nto a strategy of recent and planned IPO lstngs of the major state banks and ncreased stake holdngs by foregn banks of the smaller commercal banks. The strategy of allowng a larger stake holdng n the Chnese bankng system by foregn banks as a means of mprovng effcency has a good academc pedgree. The lnk between prvatzaton and effcency mprovement n former government owned enterprses s now very much an establshed fndng (Meggnson and Netter, 2001). The lnk between prvatzaton of bankng and effcency mprovement s an emergng research area (see Meggnson, 2005 for a survey). Gven the mpendng lstng of the major state owned banks and the tact acceptance of larger stakes by foregn banks n the smaller commercal banks, t s not surprsng that bank effcency n Chna has become a popular subject of research n recent years. A number of studes of Chnese bankng effcency have been n publshed n Chnese scholarly journals but to date there have been only a few studes that are avalable to non-chnese readers 2. Ineffcency relatve to 'best practce' s usually blamed on bad management and poor motvaton. In the parlance of Lebensten (1966), ths effcency gap s termed 'Xneffcency'. The Chnese bankng sector has only recently begun to open up to foregn competton. In the context of a bankng sector that was formerly an organ of the state system of plannng, ths paper argues that the measure of bank neffcency represents the outcome of a ratonal process and s less symptomatc of a manageral malase. In other words ths paper 1 For example Qng and Ou, (2001); Xu, Junmn, and Zhensheng, (2001); We and Wang, (2000); Xue and Yang, (1998) and Zhao (2000) have used non-parametrc methods whle 2 A recent excepton s a study usng non-parametrc methods by Chen et. al. (2005) and parametrc methods by Fu and Heffernan (2005)

4 argues that neffcency s symptomatc of rent seekng behavour and not just X- neffcency n the tradtonal sense. Ths research has three objectves. Frst t ams to deal wth the problem caused by non-performng loans n the use of loans as a measure of bank output. Former studes of bank effcency n Chna have used the stock of loans as one of the measures of output. The large amount of non-performng loans (NPLs) and the dvestture of large tranches of NPLs from the balance sheets of the state-owned banks nto the asset management companes have dstorted ths partcular output measure. As a means of dealng wth ths dstorton, we subtract all NPLs from the book value of loans as a measure of output. An alternatve measure of output we use, that does not nvolve the dstorton caused by NPLs s nterest earnngs. Second, the paper decomposes the measure of Cost effcency (CE) n Chnese banks nto techncal effcency (TE), and allocatve effcency (AE). Proponents of the X-effcency (XE) vew argue that TE s consstent wth XE. However, wth reference to the mnmum cost pont of operaton, overall effcency must be measured n terms of cost effcency. Ths paper argues that whle the underutlzaton of factors s consstent wth the noton of X- neffcency, the wrong factor-mx s ndcatve of ratonal decson makng and 'rent-seekng'. The decomposton of cost neffcency nto X-neffcency (techncal neffcency) and rentseekng neffcency allows us to examne ther evoluton over the sample perod. Thrd, ths paper ams to provde an nferental capablty to the pont-estmates of effcency through the use of bootstrappng methods. The queston ths part of the analyss poses s, are the measures of relatve effcency sgnfcantly dfferent from the benchmark? Are the measures of X-neffcency and 'rent-seekng' statstcally sgnfcant? The threat of entry of foregn banks nto the Chnese market wll lead to mproved management, whch wll result n mproved techncal effcency and lower cost-neffcency as ncumbent banks

5 attempt to cut costs and consoldate ther balance sheets. How can the mprovement n effcency be evaluated? Ths paper s organzed on the followng lnes. The next secton dscusses the lterature and outlnes the non-parametrc method of estmatng bank effcency. Secton 3 dscusses the measurement of neffcency and dscusses the dfference between X- neffcency and rent-seekng neffcency. Secton 4 dscusses the data and methodology of bootstrappng as appled to the non-parametrc method. Secton 5 dscusses the results and secton 6 concludes. 2. Methodology and Lterature Revew Most studes of bankng effcency have focussed on the developed economes 3. Whle there have been some studes of other Far Eastern economes 4, the number s small n comparson. Indeed, Berger and Humphrey's (1997) survey of 130 studes of fronter analyss n 21 countres, only 8 were about developng and Asan countres (ncludng 2 n Japan). Studes on US fnancal nsttutons were the most common, accountng for 66 out of 116 sngle country studes. The bass of the non-parametrc method of Data Envelope Analyss (DEA) s the extenson by Charnes et al. (1978) (CCR) 5 of the sngle nput-output model of Farrell (1957) to a multple nput-output generalsaton. Techncal effcency (TE) s measured as the rato of projected output (on the effcent fronter) to actual nput used. There are a number of papers that descrbe the methodology of DEA as appled to bankng 6, what follows s a bref descrpton. 3 Drake and Hall (2003), Cavallo and Ross (2002), Elyasan and Rezvanan (2002), Maudos et al. (2002), Drake (2001) Altunbas and Molyneux (1996) and Molyneux and Forbes (1993) 4 See Rezvanan and Mehdan (2002), Hardy and d Patt (2001), Karm (2001), Laevan (1999), Katb and Matthews (1999), Chu and Lm (1998), Bhattacharyya et al. (1997) and Fukuyama (1995) 5 Charnes et. al (1978) popularsed the DEA method. Tavares (2002) produces a bblography of DEA ( ). There are 3203 DEA authors whose studes cover a wde range of felds. Banxa.com also comples DEA papers from 1978 to the present. 6 The most recent beng Drake (2004)

6 Let us say that there are N banks. Let x represent the nput matrx of the th bank, and y represent ts output matrx. Let the KxN nput matrx be denoted X and the MxN output matrx be denoted Y. The effcency measure of each of the N banks s maxmsed by the DEA searchng for the rato of all weghted outputs over all weghted nputs, where the weghts are selected from the dual of the lnear programmng problem specfed as: mn θ,λ θ subject to y θx φ 0 + Yφ 0 Xφ 0 (1) where φ s an Nx1 vector of constants θ s a scalar and s the economc effcency score of the th bank (0 < θ < 1). The estmaton of cost effcency nvolves the comparson of mnmum cost at the optmal factor nputs to actual cost at the observed factor nputs. The mnmsaton exercse becomes: mn, z ω λ x * subject to y x * + Yφ 0 Xφ 0 (2) where ω s a vector of nput prces for the th bank and * x s the cost mnmsng vector of nputs for the th bank. A graphcal llustraton helps to dfferentate the two concepts n the case of constant returns to scale technology (CRS). Fgure 1 shows an soquant qq producng a gven output wth factor nputs x 1 and x 2 and socost ww, whch traces the rato of factor prces. The effcent cost mnmsng poston s shown at e where ww s tangental to qq. Employng a factor combnaton shown by pont c, whch s to the rght of the soquant qq ndcates that the frm s techncally neffcent. Effcency s decomposed nto techncal effcency and allocatve effcency (AE).

7 Fgure 1: Techncal Effcency and Allocatve Effcency x 2 w w' q w'' e a c b q w'' O w w' x 1 Techncal effcency (TE) s measured by the rato Oa/Oc. The cost to the frm s shown by w''w'' whch s parallel to ww and passes through pont c. Cost effcency (CE) s measured by Ob/Oc and Ob/Oa gves allocatve effcency (AE). It can be seen therefore from ths decomposton that under constant returns to scale (CRS); CE AE = (3) TE However, the CCR model under the assumpton of CRS s only approprate when all banks are at the optmal scale. Ths requres that the Decson Makng Unts (DMUs) operate on the flat porton of the long run average cost curve. However, scale neffcency can be estmated for by alterng the CCR model to allow for varable returns to scale (VRS). Banker et. al (1984) (BCC) accounts for scale effects by estmatng the most productve scale sze for each DMU whle dentfyng ts techncal effcency 7. Therefore techncal effcency s further 7 Coell (1996) shows that the use of the CRS specfcaton when some of the banks are not operatng at the optmal scale wll result n measures of techncal effcency that are mxed up wth scale effcency.

8 decomposed nto measures of pure techncal effcency (PTE) and scale effcency (SE). Hauner (2005) demonstrates that under the assumpton of VRS, cost effcency (CE) can be further decomposed by the formula; CE = AE.SE.TE (4) DEA constructs a non-parametrc fronter of the best practce amongst the decsonmakng unts (DMUs). An effcency score for each DMU s measured n relaton to ths fronter. An effcency score s constructed under both CRS and VRS. If the effcency score of each bank produced by these models dffer sgnfcantly, then the banks are sad to experence varable returns to scale (Avkran, 1999). In the case of VRS, a model can be orentated ether by usng nput mnmsaton (effcency gan through nput reducton nput orentaton) or output maxmsaton (effcency gan from output expanson output orentaton). DEA s relatvely nsenstve to model specfcaton (nput or output orentaton) and functonal form 8, however the results are senstve to the choce of nputs and outputs. The weakness of the DEA approach s that t assumes data are free from measurement errors. Furthermore, snce effcency s measured n a relatve way, ts analyss s confned to the sample used. Ths means that an effcent DMU found n the analyss cannot be compared n a straghtforward way wth other DMUs outsde of the sample. A small but growng ndustry of effcency studes of Chnese banks has emerged n recent years that have used DEA to measure relatve effcency 9. The consensus of fndng from the DEA studes s threefold. Frst, because of a contnued bankng reform programme techncal neffcency has been declnng over tme. Second, average bank effcency s lower n the state owned banks (SOBs) than n the jont stock banks. Thrd, the gap between the two has been narrowng n recent years. 8 Hababou (2002) and Avkran (1999) provde a relatvely thorough dscusson of the merts and lmts of the DEA. 9 In addton to the papers cted n footnote 1, other studes by Chnese scholars that have used non-parametrc technques nclude Xu, Junmn and Zhennsheng (2001), Zhang and L (2001), Fang et. al. (2004).

9 3. Ratonal neffcency Berger, Hunter and Tmme (1993) argue that X-neffcency consttutes 20% or more of bank costs. Proponents of the theory of X-effcency suggest that the famlar average cost curve of a frm s a thck band rather than a thn lne. The band defnes a range of costs per gven level of output, whch wll depend on the applcaton of pressure and motvaton on the personnel employed 10. Poor motvaton and weak pressure resultng n under utlzaton of factors of producton, s part of what Lebensten (1975) descrbes as organsatonal entropy. X-neffcency arses as a result of low pressure for performance. Some nsttutons would be protected by government regulaton that would reduce the external pressure of competton. But even wth a hgher degree of pressure from the envronment, frms may have organsatonal defcences so that management sgnals and ncentves are lost n the herarchy of the organsaton. Studes of bank effcency have used the terms techncal effcency and X-effcency nterchangeably as f they were the same thng. Whle smlar n concept they are not necessarly the same. The concept of techncal effcency derves ts bass from the neoclasscal theory of the frm and assumed proft maxmsng behavour. A frm or a bank may be techncally neffcent for techncal reasons such as low tranng or human captal levels of managers and workers, or the use of nferor or out-of-date technology. The dffuson of new technology s not nstantaneous and some frms or banks may lag behnd others n the acquston and utlsaton of new technology. Wth further tranng and updatng of captal, the frm or bank can expect to move towards the effcent fronter. X-neffcency s not caused by the varablty of sklls or the tme varablty of technology dffuson but by the use and organsaton of such sklls and technology. 10 See for example Franz (1988)

10 Lebensten and Matal (1992) suggest that X-neffcency and ts composton can be measured through the use of DEA analyss. The parttonng of the effcency scores enables the dfferentaton between motvatonal factors and management defcency. Lebensten and Matal (1992) argue that the slack analyss of effcency s a means of separatng the proxmate causes of X-neffcency ncludng management performance 11. The two man scalars produced by DEA analyss s theta (?), whch measures that porton of X-neffcency that could be elmnated by the proportonal reducton of nputs. However, even after reducng nputs, some nputs may stll exhbt slack 12 whch s measured by ota (?). Iota measures the total amount of X-neffcency and therefore the drect management defcency s measured by??. A slacks based measure of effcency has been proposed by Tome (2001) whch specfcally ncorporates the slacks nto the objectve functon. Ths procedure amounts to recognsng that n the case of the nput-orented measure of DEA, some organsatons may be on the flat part of the soquant of Fgure 1 that s parallel to the axs, so that a further reducton n nput could be obtaned wthout sacrfcng output 13. Formally, the system descrbed by (1) s replaced by; + mn, ι = θ ε ( S + S ) ι λ Subject to y θx + Yφ S Xφ + S + λ 0,0 < ε < (5) Where S - and S + are nput and outputs slacks respectvely. The exstence of nput slacks s a volaton of the neo-classcal assumptons of dmnshng returns n producton n 11 Chen (2001) uses the decomposton to dentfy management X-neffcency n Tawan s banks. 12 See Zhu (2003) pp Ths procedure has been appled to the examnaton of banks n Hog Kong by Drake et al (2006)

11 the output orented case and dmnshng margnal productvty of factor nputs n the nput orented case. An alternatve nterpretaton of slacks n producton s rent seekng n the sense of Buchanan (1980) and Tullock (1967, 1980). Rent seekng n ts basc form s the appropraton of surplus n the process of producton or exchange wthout any real contrbuton to the process of ether. Where there are government regulatons on enterprse, barrers to entry and other ant-compettve rules, offcals have the opportunty to extract rents through the mechansm of brbery and corrupton. Therefore the term rent seekng has been generally assocated wth extorton, brbery and corrupton. Whle t s generally accepted that corrupton s farly wdespread n the fnancal sector n Chna, a number of hgh profle cases have made ths subject a matter of contemporary concern 14. The fall-out from a number of well-publczed cases could have the effect of reducng actvty n ths partcular area. However, a hdden but much more pervasve type of rent seekng s the extracton of larger budgets for bureaucraces and what results n the non-pecunary rewards to workers n government owned enterprses (Tullock, 1967 and McKenze and Tullock 1981). The prestge of the senor bureaucrats s enhanced f the sze of the workforce s expanded to be larger than necessary to meet producton targets. Smlarly, offces are more grandose, holdays are longer, and benefts are greater and so on. Bogetoft and Hougaard (2003) suggest that the exstence of slacks n producton s the outcome of a ratonal decson makng process that represents on-the-job compensaton to managers. Whereas X-neffcency s vewed by Lebensten (1966, 1978) as non-maxmsng behavour, Stgler (1976) argues that ts exstence s symptomatc of frms maxmsng ther ndvdual utlty functons. Bogetoft and Hougaard (2003) propose that the slacks be part of 14 The former Governor of the Constructon Bank of Chna Wang Xuebng was sentenced to 12 years jal for acceptng brbes of 1.15 mllon Yuan. The Vce-Presdent of the Bank of Chna receved a suspended death sentence for embezzlng 14.5 mllon Yuan and acceptng brbes of 1.4 mllon Yuan. See also Fan, Ru and Zhao (2006)

12 the preference set of managers rather than the technology of producton. Faced wth a target level of output, a gve set of nputs and factor prces, the bureaucrat mnmses costs subject to a utlty functon that ncludes n t arguments the level of output and a subset of factor nputs. In other words for the th bank, gven the K factor nputs, the bureaucrat mnmses costs to meet a utlty functon whch contans the M outputs and a subset J of factor nputs, gven standard neo-classcal technology. Subject to mn D = ω λ y m, f ( U U ( y x ) k x k, 0 m,, j, ( x ), m = 1,2,..., M f > 0, f < 0, k = 1,2,... K k = k k, (6) The frst order condtons are: D = ω x j D = ω x z D λ = U 0 j z + λ( U + λ( U U m m f + U j ) = 0, j = 1,2,... K J f ) = 0, z = K J + 1,..., K 1, K z ( f ( x ), x ) = 0, k = 1,2,... K k, j, x, j The FOC show that an allocatve neffcency s created that favours factors nputs x j above that mpled by the optmal factor mx. In the context of fgure 1, the ray from the orgn to the tangency pont e on fgure 1 defnes the optmal factor mx. At pont 'a' the DMU s techncally effcent but s allocatvely neffcent. A bank can organse ts nput factors to be on ts producton fronter but be usng the wrong factor mx. Rent seekng n monopolstc publc utltes nvolves over-staffng, 'elaborate offces and a lot of trps to mportant conferences' or 'expensve subsdsed restaurants' (McKenze and Tullock, 1981). The wrong factor mx n the case of the Chnese bankng sector can be nterpreted as excess staffng 15. The management of the banks may reduce techncal effcency (X-neffcency as t has been 15 In the case of pre-reform Chna, the bureaucratc bank manager would have been nstructed to employ a quota of graduates from the central bank sponsored unverstes, and schools as well as retrees from the Peoples Army Offcer Corps.

13 sometmes nterpreted) by movng the cost fronter from w''w'' to w'w', but would stll reman cost neffcent as shown by the gap ab/oc. The gap between the mnmum cost optmal factor mx and the techncally effcent mnmum cost assocated wth the effcent producton fronter wth the sub-optmal factor mx (or allocatve neffcency) can be nterpreted as the neffcency assocated wth 'rent seekng' Data and Bootstrappng Ths study employs annual data ( ) for 15 banks; the four state-owned banks, ten jont-stock commercal banks and one jont-venture bank. Data for one of the jont-stock banks was unavalable for 2004 (Chna Everbrght) and n that year 14 banks data was used. The total sample conssted of 119 bank year observatons. The man source of the data was Ftch/Bankscope and the Almanac of Chna s Fnance and Bankng (varous). The choce of banks was based on the fact that they face a common market and compete natonwde. The one jont-venture bank n the sample s an example of a bank that has strong foregn nterventon and would accordng to the consensus of evdence, be expected to exhbt a hgh level of effcency, even though t can be argued that as a regonal bank t would not necessarly be competng n the same markets as the other banks n the sample. Two approaches are normally taken n determnng what consttutes bank nput and output. Under the ntermedaton approach, bank assets measure outputs and labltes measure nputs. In contrast, nputs n the producton approach are physcal enttes such as labour and captal and the outputs are the flows of ncome generated from the dfferent channels of bank servces. In ths study, we consder two sets of outputs. Frst, we use three nputs and three outputs selected under the ntermedaton approach for the estmaton of techncal effcency. Tradtonally the ntermedaton approach would use as nputs the 16 Cran and Zardkooh (1980) suggest that X-neffcency and rent seekng co-exst and that changes to X-neffcency are offset by equal changes n rent seekng, so that there s a trade-off between one type of neffcency aganst another.

14 number of employees (LAB), fxed assets (FA) and total deposts (DEP), and outputs would be total loans, other earnng assets (OEA), and other operatng ncome (NII). However, the operaton of the Asset Management Companes n strppng out large tranches of NPLS from the state-owned banks dstorts the use of loans as a vald output measure. We therefore consder the qualty of the loan portfolo by strppng out non-performng loans (NPLs) from the stock of loans for each bank (LOANSQ). The argument for adjustng loans for NPLs s to mtgate the effect of the large loan portfolos held by the bg-4 SOBs on the effcency calculaton. The unadjusted loan portfolo would bas the effcency score upwards for the SOBs whch have the largest share of loans but also the hghest proporton of NPLs. The nputs for the constructon of cost-effcency addtonally requre the factor prces of the relevant nputs above. We dstngush between the prce of labour (PL), prce of fxed captal (PK) and the prce of funds (PF). The prce of labour s obtaned as the rato of personnel expenses dvded by employees. The prce of fxed captal s operatng expenses less personnel expenses dvded by fxed assets (less deprecaton). The second of the set of outputs used s nterest ncome (II) and non-nterest ncome (NII). The advantage of these measures s that are relatvely uncontamnated by the NPL problem. Interest ncome wll represent the ncome generated from actve loans and not NPLs. Whle non-nterest ncome s relatvely undeveloped n Chna, t s selected to reflect the growng contrbuton of ths channel to bank s total ncome. The avalablty of unform and comparable data on Chnese bankng s a very recent development. Researchers have typcally made a number of workng assumptons to fll the gaps n data. In general, balance sheet data s avalable although the data revsons alter the fgures from year to year and up untl recently the accountng standards of Chnese banks dffered from nternatonal standards (Ng and Turton 2001). The number of employees are avalable for the bg four state owned banks but not for all of the jont-stock banks over all

15 years. Smlarly, the avalablty of personnel expenses vares across banks. In the years that personnel expenses were not avalable, the rato of personnel expenses to total operatng expenses n the adjacent year to the mssng was appled. In the years where the number of employees was not avalable, the rato of labour to fxed assets n the most recent year avalable was appled 17. Where there were no personnel expenses avalable, t was assumed that the bank faced the same captal costs as banks of comparable sze, whch gave personnel costs as a resdual. Table 1 presents the summary statstcs of the nput and output data for 2004 as a snapshot ndcator of the scale of the varables used. The hgh standard devaton s an ndcaton of the domnance of the 4 state owned banks. Table 1: Output-Input Varables 2004 (mllon RMB) Varable Descrpton Mean Standard Devaton LOANSQ Loans adjusted for NPLs 861, OEA Other Earnng Assets 572, NII Non-nterest ncome 3, II Interest Income 49, ,974.9 LAB Number employed (labour) 110, DEP Total Deposts 1,403, FA Fxed Assets (less deprecaton) 23, PL Prce of labour PF Prce of funds PK Prce of fxed assets Sources: Ftch/Bankscope, Almanac of Chna's Fnance and Bankng (varous) and author calculatons from web sources. One of the crtcsms levelled at the DEA approach s that t produces estmates of effcency that are not open to statstcal nference. In other words f a DMU has a score of 0.95, n what statstcal sense s t 5% neffcent relatve to the benchmark? Wthout the capablty for statstcal nference, non-parametrc methods would be weak alternatves to parametrc methods of estmatng effcency. However, uncertantes also exst n the 17 Fu and Heffernan (2005) assume that the employee growth matches the growth of total assets and they use the average wage pad by state-owned and other types of fnancal nsttutons to estmate labour cost.

16 estmaton of effcency usng DEA. The most obvous uncertanty s what comes from measurement error. Measurement error n the context of data on Chnese banks s partcularly acute. There are three potental sources of error. Frst, dfferences between local bank's accountng procedures and those of nternatonal bodes, second dfferences between local bank's accountng conventons and thrd, researcher assumptons relatng to the generaton of mssng observatons. Other uncertantes arse from the estmaton of the effcency fronter; changes to the nputs and/or outputs can cause large dfferences n the resultng scores. Furthermore there may be errors n the samplng varaton caused by the dffculty n obtanng a suffcently large and consstent samplng frame. Smar and Wlson (1998, 2000a, 2000b) propose a bootstrap procedure for nonparametrc fronter models. Bootstrappng s based on the noton that f the data can be vewed as a random sample from an underlyng populaton under a model (data generatng process - DGP), then the process of contnuous random draws from the sample under the model generates also random draws from the populaton. The random draw can be vewed as a pseudo-sample and as a group of new benchmarks to compute the effcency score for a gven pont. Followng the Smar-Wlson method, 1000 bootstrap values of the ndvdual DMU for all types of effcency scores are generated n each year 18. It s not the ntenton of ths paper to gve a detaled explanaton of the Smar-Wlson bootstrappng method but a bref descrpton of the method and algorthm s provded below. Followng Smar and Wlson (1998, 2000a, 2000b). The effcency scores calculated wth the orgnal data are used to construct pseudo data. The bootstrap procedure s based on the dea that there exsts a DGP, whch can be determned by Monte Carlo smulaton. By usng the estmated dstrbuton of the DGP to generate a large number of random samples, a set of pseudo estmates of the effcency scores θˆ are obtaned. However ths 'nave' 18 Recent bootstrappng applcatons to DEA have been conducted by Löthgren and Tambour (1999); n the case of bankng effcency by Casu and Molyneux (2005); and n the case of Chnese rural credt cooperatves, Dong and Featherstone (2004).

17 bootstrap yelds nconsstent estmates (Smar and Wlson, 2000a). A homogeneous bootstrap procedure that produces consstent values of θˆ from a kernel densty estmate s gven n Smar and Wlson (2000b). The bootstrap algorthm s summarsed n the followng steps 19. Step 1. Compute the orgnal DEA effcency scores usng the lnear programmng model (equaton 1) and let δˆ = 1/ θˆ ; Step 2. Snce radal dstances are used, we wll refer to the polar coordnate of the nput vector of each DMU x defned by ts modulus ω = ω( x ) = x x and ts angle K 1 π η = η( x) 0, 2 where for j=1,, K-1, η = arctan( x j+ 1 / x1) f x 1 > 0 and π η = f 2 x 1 = 0. Then translate the data nto polar coordnates: ( y,, ˆ η δ ), = 1,..., K. And form the L =, L ~ = L R augmented matrx L ~ by: L = [ y η δˆ ], L R [ y η 2 δˆ ] Step 3. Compute the estmated covarance matrces ˆΣ 1, ˆΣ 2 of L and L R by Σ ˆ 1 S = S S S Σ ˆ 1 S = S S S where S 11 s ( M + N 1) ( M + N 1), S 12 = S 21 s ( M + N 1) 1and S 22 s a scalar, and compute the lower trangular matrces L 1 and L 2 such that Σ ˆ 1 = L 1L1 and Σ ˆ 2 = L 2 L2 va the Cholesky decomposton. Step 4. Choose an approprate bandwdth h as descrbed n Smar and Wlson (2000b) usng the nformaton n L ~, ˆΣ 1, ˆΣ 2. Step 5. Draw K rows randomly, wth replacement from the augmented matrx L ~ and denote the result by the K ( M + N) matrx ~ * L ; compute * z, the 1 K row vector contanng the means of each column of ~ * L. 19 The algorthm s run on MATLAB and the codes are avalable from the authors on request.

18 Step 6. Use a random number generator to generate a K ( M + N) matrx ε of..d. standard normal pseudo-random varates; let ε. denote the th row of ths matrx. Then compute the K ( M + N) matrx * ε wth the th row * ε. gven by * ε so that ε ~ (0, ˆ. NM + N Σ j) *. = ε. L j where j=1 f the th row of ~ * L was drawn from rows 1,..., K of L ~, or j=2 f the th row of ~ * L was drawn from rows (K + 1),..., 2K of L ~. Step 7. Compute the K ( M + N) matrx Γ = ~ 2 1/ 2 * * * ( 1 + h ) ( ML + hε ) + K z where M = I K ( 1/ K) K K s the usual K K centrng matrx wth I K denotng an dentty matrx of order K, K an K 1 vector of ones, and denotes the Kronecker product. Step 8. Partton Γ so that Γ = [ γ γ γ ] 1 2 3, where K 1 γ, γ [ 0, π / ] and M 1 R γ 3 (, + ) for = 1,..., K. Defne the K ( M + N) matrx of bootstrap pseudo-data * L such that the the row * z of * L s gven by z * ( γ = ( γ 1 1 γ γ 2 2 γ 3 2 γ ) 3 ) γ 3 1 otherwse Step 9. Translate the polar coordnates n * L to Cartesan coordnates. Ths yelds the x } K y 1 * * bootstrap sample {(, ). = Step 10. For the gven pont (x, y), compute θ ˆ* ( x, y) by solvng the DEA program takng * * { } K, y ) ( x = 1 as the benchmarks and compute the bas-corrected effcency scores ~ θ ( x, y) = θˆ / θ 2 ˆ* Step 11. Repeat Steps 5~11, obtan another group of bas-corrected effcency scores, reducng the nput vector of each DMU x ntoθ ~ x. Compute the cost effcency scores usng equaton(2) from the reduced nputs and outputs. Step 12. Smlar to Step 11, obtan rent-seekng-effcency scores (the dfference between cost-effcency score and techncal (X)-effcency score)

19 Step 13. Repeat Steps 5~12 B (=1000) tmes to obtan a set of bootstrap estmates ~ { } B b (, y) b θ and cost effcency scores and x-effcency scores. x = Emprcal Results Table 2 presents the results of the bootstrap estmaton. For reasons of brevty we present the results for fve years and for CRS only but the relatvely small sample n each year could bas the scale effcency estmates, whch rases doubts about the VRS assumpton 20. Furthermore the evdence of scale economes n bankng s mxed. Early studes tended to confrm the exstence of constant returns to scale 21, however more recent fndngs suggest that there are sgnfcant scale economes for large banks 22. Fnally, the bootstrap estmates under the VRS assumpton showed mplausbly low levels of cost effcency and no dfference between the estmates of cost effcency and techncal effcency (no scale or allocatve neffcency) for all but two of the JSBs (for both types of output). The SOBs had mplausbly hgh scores for cost and techncal effcency. In favour of the CRS measure, the estmates of cost effcency obtaned ths way are smlar to the fndngs of Fu and Heffernan (2005) for roughly the same sample perod usng stochastc fronter methods. 20 The cluster of four large state-owned banks bases the scale effcency estmates for the bg See Hunter and Tmme (1986) and Berger et. al. (1987). 22 Berger and Mester (1997) and Altunbas and Molyneux (1996).

20 Table2 Bootstrap Estmates of Ineffcency: , (%) CRS Bank Output ABOC BOC CCB ICBC BCom CITIC CMB CMBC EVBRT FSB GDB HXIA IBCL SDB SPB X Rent X Rent X Rent X Rent X Rent NPL 51.7 *** 20.3 *** 49.1 *** 29.6 *** 48.4 *** 22.1 *** 33.7 *** 35.0 *** 35.7 *** 27.4 *** Prod 43.7 *** 17.5 *** 41.7 *** 22.4 *** 25.3 *** 29.8 *** 38.5 *** 26.0 *** 40.1 *** 20.9 *** NPL 23.2 *** 13.8 ** 19.6 *** 27.8 *** 18.6 *** *** *** 0 Prod 23.1 *** *** *** *** *** 0 NPL 38.7 *** 23.7 *** 40.3 *** 18.4 *** 33.1 *** 23.0 *** 10.0 *** 44.2 *** 14.2 *** 35.1 *** Prod 42.1 *** 4.4 *** 41.9 *** 15.9 *** 18.8 *** 24.5 *** 18.2 *** 31.4 *** 27.0 *** 23.4 *** NPL 45.7 *** 15.6 *** 44.0 *** 10.6 *** 28.7 *** 24.6 *** 26.9 *** 26.6 *** 31.6 *** 22.6 *** Prod 35.9 *** 15.3 *** 44.2 *** 7.1 *** 14.8 *** 22.1 *** 37.1 *** 15.3 *** 29.1 *** 22.9 *** NPL 38.1 *** *** *** 21.4 *** 14.9 *** 33.6 *** 16.3 *** 29.1 *** Prod 30.0 *** *** *** 17.5 *** 34.5 *** 16.2 *** 36.0 *** 5.7 *** NPL 30.6 *** 20.2 *** 25.2 *** 21.4 *** 34.4 *** *** 15.3 *** 26.7 *** 8.9 ** Prod 20.4 *** 8.0 *** 20.0 *** 31.1 *** 22.7 *** 5.8 *** 26.6 *** 16.9 *** 34.8 *** 4.4 ** NPL 18.7 *** 30.7 *** 27.5 *** 12.9 ** 41.2 *** *** *** 0 Prod 34.0 *** 5.3 *** 16.1 *** 34.5 *** 23.6 *** *** 13.0 ** 45.6 *** 0 NPL 12.6 *** 29.4 *** 14.0 *** 29.3 *** 13.1 *** 21.1 *** 17.8 *** 8.5 ** 14.7 *** 15.0 *** Prod 15.1 *** 26.6 *** 11.3 *** 26.9 *** 6.5 *** 21.0 *** 21.9 *** *** 16.5 *** NPL 33.6 *** 15.3 *** 28.9 *** 17.2 *** 34.9 *** 8.5 *** 28.0 *** 11.0 *** - - Prod 29.5 *** 17.0 ** 24.3 *** 20.3 *** 21.0 *** 8.4 *** 25.9 *** 10.6 ** - - NPL 46.1 *** *** *** *** *** 0 Prod 42.4 *** *** *** *** ** 0 NPL 28.1 *** 28.3 *** 24.5 *** 20.6 *** 22.4 *** 22.8 *** 16.6 *** 19.8 *** 27.9 *** 14.4 *** Prod 21.6 *** 30.3 *** 26.8 *** 22.5 *** 9.6 *** 7.7 * 19.9 *** 10.6 *** 18.7 *** 19.8 *** NPL 23.3 *** 29.2 *** 27.5 *** 24.6 *** 26.6 *** 10.2 *** 12.6 ** 28.1 *** 19.7 *** 20.0 *** Prod 25.7 *** 34.6 *** 16.7 *** 35.2 *** 14.4 ** 14.4 *** 30.7 *** 12.4 *** 35.2 *** 11.6 *** NPL 18.8 *** 34.6 *** 23.5 *** *** 16.1 *** 14.8 *** 22.7 *** 33.5 *** 0 Prod 34.8 *** 26.1 *** 19.5 *** 29.6 *** 16.1 ** 9.2 ** 22.9 *** 9.9 *** 26.2 *** 13.8 ** NPL 27.3 *** 34.8 *** 17.3 *** 25.9 *** 14.3 *** 23.9 *** 13.5 *** 24.8 *** 8.8 *** 30.6 *** Prod 20.4 *** 36.7 *** 21.2 *** 30.7 *** 13.3 *** 10.3 ** 24.6 *** 10.6 *** 19.0 *** 13.9 * NPL 25.3 *** 40.0 *** 26.0 *** 28.4 *** 31.8 *** 5.9 * 32.6 *** *** 0 Prod 26.3 *** 32.9 *** 24.5 *** 29.3 *** 28.8 *** *** 9.8 * 32.9 *** 0 *** sgnfcant at the 1%, ** sgnfcant at the 5%, * sgnfcant at the 10% The sgnfcant pattern than can be gleaned from Table 2 s the general declne n both types of measured neffcency over tme. Other patterns that emerge from careful observaton s the frequency of concdence of zero cells n the rent-seekng neffcency boxes for both measures of output and the frequency of commonalty of the estmates. However, t s not easy to glean patterns from smply eye-ballng the data. Table 3 summarses the average of the bootstrapped DEA scores for the full sample broken down nto X-neffcency and Rent seekng neffcency for the state-owned banks (SOB) and Jontstock banks (JSB), for the two dfferent sets of outputs.

21 Table 3 Mean neffcency, NPL adjusted loans and Producton method (CRS) X-neffcency Rent-Seekng Ineffcency SOB NPL adjusted output 36.4% 30.6% JSB NPL adjusted output 31.3% 18.8% t statstc for dfference n 1.70* 3.90*** mean SOB producton method 30.6% 30.2% output JSB producton method 25.7% 20.3% output t statstc for dfference n 2.39** 2.89*** mean Correlaton coeffcent all *** *** banks Spearman s Rank correlaton all banks *** *** *** sgnfcant at the 1%, ** sgnfcant at the 5%, * sgnfcant at the 10% The frst two rows of Table 3 show the mean neffcency estmates for the full sample for the SOBs and JSBs. The thrd row shows that the dfferences n the means are statstcally sgnfcant. Smlarly, the mean neffcency scores for the SOBs and JSBs usng the producton method are shown rows four and fve. Agan the t test shows sgnfcant dfference n means. So n contrast to the consensus of fndng, Table 3 shows that the SOBs have a sgnfcantly hgher level of X-neffcency and rent-seekng neffcency than the JSBs. The two output sets produce remarkably smlar measures of neffcency. A correlaton over the full sample shows a sgnfcant relaton (row 7) and the rankng of banks effcency by the dfferent output methods show a sgnfcant commonalty (row 8). However, the mportant queston s how do these relatve measures of effcency evolve over tme? We address ths queston by regressng the change n the respectve measure of neffcency on ts lagged value. The estmated coeffcent on the lagged value of neffcency can be treated as the parameter of adjustment. A sgnfcant negatve value

22 ndcates that neffcency s declnng (effcency mprovng). The larger the absolute value of the parameter, the faster the speed of adjustment. The regressons are conducted as a panel of the form wth heteroscedastc adjustment of the standard errors. Y, t = α + βy, t 1 + ε, t The results are shown n Table 4 below. Table 4: Beta value Ineffcency adjustment, CRS Ineffcency Bank Group β - NPL t value β - t value adjusted producton method X- neffcency Rentseekng SOB *** *** JSB *** *** All Banks # -8.13*** *** SOB *** *** JSB *** *** All Banks *** *** # wth SOB ntercept dummy, *** sgnfcant at the 1% The most mportant result of Table 4 s that under both defntons of output there s strong statstcal evdence of a negatve trend n both types of neffcency. In ths respect, the results of ths paper dffer from the fndngs of Chen et. al. (2005) who fnd no dscernble trend mprovement n cost effcency 23. The speed of declne n X-neffcency (mprovement n techncal effcency) s less for the SOBs than the JSBs, on both measures but t s partcularly marked n the case of the NPL adjusted Loans. One can nfer that once NPLs have been removed the bg 4 collectvely are much closer to the fronter than the JSBs and thus the speed of reducton of neffcency s commensurately lower. There s a faster speed of declne of rent-seekng neffcency by the SOBs n the NPL adjusted case but no sgnfcant dfference n the speed of declne of rent-seekng neffcency n the producton case. Whle the results are mxed relatng to the dfferences n the speed of adjustment of the 23 Chen et. al (2005) uses a wder data frame of banks, ncludng regonal jont-stock banks and nternatonal trust and nvestment companes. It can be argued that the use of DMUs that do not compete n the same geographcal market or product s a volaton of the homogenety requrement of DEA.

23 two sets of banks, the common fndng s that both types of neffcency has declned sgnfcantly durng ths perod for all the banks n the sample. Usng parametrc methods, Fu and Heffernan (2005) fnd cost neffcency n the order of 50% over the perod These fndngs are consstent wth the bootstrap estmates obtaned here and also the broad fndngs of Chnese scholars cted n ths paper. Such fndngs have typcally generated a consensus of pessmsm about the future of Chnese bankng. Our fndngs suggest grounds for optmsm n that n terms of relatve effcency, Table 3 shows that the trend s towards mproved performance. 6.0 Concluson Ths paper argues that cost neffcency can be parttoned nto X-neffcency and rent-seekng neffcency. If ths decomposton s accepted then t follows that part of the cost-neffcency of Chnese banks s not due to manageral malase but ratonal decson makng. It s the case then that the mplcaton for the current thrust of offcal bank polcy n Chna s postve. Accordng to Lebensten (1966), X-effcency s mproved through manageral motvaton and external pressure. Impendng competton and the deregulaton of the Chnese bankng market can be expected to motvate managers to mprove performance and utlse exstng factors of producton fully. Competton for well-qualfed staff between the dfferent bankng frms wll rase rewards and attract the best graduates. The potental outflow of the best staff to the hgher payng nsttutons wll motvate a greater focus on tranng, modernzaton and effcency. Bureaucratc rent seekng s a ratonal response to a partcular set of ncentves based on the dctates of plannng polcy. It would be no surprse to learn that over the years of protected growth, as the banks were vessels for the channellng of unproftable loans to stateowned enterprses, the response of the bankng sector was to develop rent seekng strateges and act as employment sponges for the educated youth n Chna. It can be expected that the

24 dsmantlng of protecton and the nvtaton to lst the state-owned banks and the jont stock banks wll alter the ncentve structure for managers and consequently there should be a trend reducton n rent-seekng neffcency. Ths paper has used non-parametrc methods to conduct an analyss of neffcency n a sample of Chnese banks. The estmates of bank neffcency were buttressed wth bootstrappng technques to enable statstcal nference. In general, the estmates from bootstrappng support the vew that relatve effcency has mproved. However, these results must stll be nterpreted wth cauton. The mprovement n effcency s n terms of the benchmark banks, whch are themselves 'best-practce' Chnese banks. The real benchmarks should be foregn banks competng on an equal footng or foregn banks operatng n ther home countres under smlar condtons of development and rsk. It s not the ntenton of ths paper to pant a rose hued pcture of the state of Chnese bankng. Manageral problems and corporate governance ssues stll bedevl bankng n Chna. However, the argument of ths paper s that the threat of an open market to foregn banks has resulted n sgnfcant mprovements n bank effcency, wth faster mprovements beng shown by the JSBs. The man message of ths paper s that a change n the ncentve structure has motvated Chnese bank managers to up ther game. Consequently, Chnese banks are n better shape than they have ever been.

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