Scale Economies, Bank Mergers, and Electronic Payments: A Spline Function Approach

Humph ey, Da id B.; Vale, Ben Wo king Pape Scale Economies, Bank Me ge s, and Elec onic Paymen s: A Spline Func ion App oach Wo king Pape , No. 2003/5 P o ided in Coope a ion wi h: No ges Bank, Oslo Sugges ed Ci a ion: Humph ey, Da id B.; Vale, Ben (2003) : Scale Economies, Bank Me ge s, and Elec onic Paymen s: A Spline Func ion App oach, Wo king Pape , No. 2003/5, ISBN 82-7553-213-2, No ges Bank, Oslo, h ps://hdl.handle.ne /11250/2498622 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/209819 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. 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Humph ey and Ben Vale ISSN 0801-2504 ISBN 82-7553-213-2 Wo king pape s om No ges Bank can be o de ed by e-mail: pos en@no ges-bank.no o om No ges Bank, Subsc ip ion se ice, P.O.Box. 1179 Sen um N-0107 Oslo, No way. Tel. +47 22 31 63 83, Fax. +47 22 41 31 05 Wo king pape s om 1999 onwa ds a e a ailable as pd - iles on he bank’s web si e: www.no ges-bank.no, unde “Publica ions”. No ges Bank’s wo king pape s p esen esea ch p ojec s and epo s (no usually in hei inal o m) and a e in ended in e alia o enable he au ho o bene i om he commen s o colleagues and o he in e es ed pa ies. Views and conclusions exp essed in wo king pape s a e he esponsibili y o he au ho s alone. Wo king pape s a No ges Bank kan bes illes o e e-pos : [email p o ec ed] elle ed hen endelse il: No ges Bank, Abonnemen sse ice Pos boks 1179 Sen um 0107 Oslo Tele on 22 31 63 83, Tele aks 22 41 31 05 F a 1999 og sene e e publikasjonene ilgjengelige som pd - ile på www.no ges-bank.no, unde “Publikasjone ”. Wo king pape s inneholde o skningsa beide og u edninge som anlig is ikke ha å sin endelige o m. Hensik en e blan anne a o a e en kan mo a kommen a e a kollege og and e in e esse e. Synspunk e og konklusjone i a beidene s å o o a e nes egning. SCALE ECONOMIES, BANK MERGERS, AND ELECTRONIC PAYMENTS: A SPLINE FUNCTION APPROACH∗ Da id B. Humph ey Flo ida S a e Uni e si y Ben Vale No ges Bank (The cen al bank o No way)† May 20, 2003 Abs ac This pape demons a es he impo ance o using a lexible cos unc ion speci ica ion when analyzing economies o scale and es ima ing he cos effec o banking me ge s. The in lexibili y o he anslog cos unc ion is illus a ed and esul s a e compa ed o mo e lexible spline and Fou ie cos unc ions. Using hese diffe en app oaches we p edic he ex an e effec on a e age cos om me ge s o e 1987-1998 using a balanced panel o 130 No wegian banks. On a e age me ge s a e p edic ed o lowe cos s. P edic ions using he Fou ie o spline app oach a e in o e all ag eemen wi h compu ed ac ual a e age me ge -cos changes ex pos . Cos effec s o elec onic paymen s a e also es ima ed and exceed cos educ ions associa ed wi h me ge s. JEL code: G21, L11 Keywo ds: Economies o scale, unc ional o m, me ge s. ∗Thanks o Øy ind Ei heim, Claudia Gi a done, Øy ind Ho eid, Kje s i-G o Lindquis , Jon Williams, an anonymous e e ee, semina pa icipan s a No ges Bank, Bank o Finland, Uni e si y o Gö ebo g, pa icipan s a he 39 h Bank S uc u e Con e ence a he Fede al Rese e Bank o Chicago, and a he EARIE 2001 con e ence in Dublin o help ul commen s o p e ious e sions o he pape . Views and conclusions exp essed in his pape a e hose o he au ho s and canno be a ibu ed o any o he pe sons o ins i u ions men ioned abo e. †Co esponding au ho : Ben Vale, No ges Bank, C51, Box 1179, Sen um, N-0107 Oslo, No - way. Fax: +47 22 42 40 62. E-mail: ben . ale@no ges-bank.no 1. In oduc ion. The as majo i y o he pas g ow h o la ge banking ins i u ions in he U.S. and Eu ope has been achie ed h ough me ge s and acquisi ions (c. ., Rhoades (1985), o he U.S.). This me hod o expansion is iewed as being cheape han de no o en y and quicke han elying on demand-de e mined g ow h. The ecen emo al o es ic ions on na ionwide b anching in he U.S., he opening up o domes ic and c oss-bo de banking and inancial ma ke s in Eu ope, and he oppo uni y o mo ing o mo e cos -efficien elec onic se ice deli e y me hods — wi h inhe en ly mo e scale economies1— ha e accele a ed his his o ical end o me ge -dependen g ow h. Public s a emen s by me ging banks in a iably ocus on hei expec ed cos sa - ings, planned expansions in hei se ice mix, and he need o ha e a sufficien ly la ge p esence in ce ain ma ke s o compe e effec i ely wi h o he domes ic o in- e na ional playe s. These posi i e ex an e s a emen s con as sha ply wi h ex pos analyses ha : (a) compa e p e- and pos -me ge cos s o me ging banks (Rhoades (1993)); (b) assess me ge - ela ed changes in on ie cos efficiency le els o ank- ings (Be ge (1998); Be ge and Humph ey (1992)); o (c) summa ize case s udies o indi idual me ging banks (Rhoades (1998)). Ex pos s udies o banking me ge s consis en ly ind ha uni cos s o efficiency le els a e essen ially unchanged o he a e age banking me ge almos ega dless o b anch ma ke o e lap (whe e he expec a ion o cos sa ings is highes ). While some banks expe ience educ ions in uni cos , o he s expe ience inc eases. Fo he small subse o me ge s ha u n ou o be ”success ul”, howe e , uni cos s may all by up o 5%.2 Equi y ma ke e en s udies o Eu ope (Cybo-O one and Mu gia (2000)), bu no he U.S. (Hawawini and Swa y (1990); Hannan and Wolken (1989)), ind sig- ni ican ly posi i e abno mal equi y e u ns associa ed wi h me ge announcemen s. Equi y e en s udies should e lec he po en ial o signi ican cos educ ions as well as possible inc eases in ma ke powe and p o i s. Pe haps due o diffe en ma - 1See o ins ance Lindquis (2002), who documen s inc eased scale economies in banking ol- lowing he adop ion o elec onic paymen s echnology. 2Reduc ions in o al expenses, common in me ge announcemen s, need o be adjus ed o associa ed educ ions in asse s. This is why uni cos is a mo e use ul me ic. 2 ke s uc u es and an i us en o cemen , he expec ed me ge bene i s ha e been posi i e o Eu ope. So a , when examined a e he ac , his expec a ion has no been ealized in he ew ex pos Eu opean s udies ha ha e been done (e.g., Ca bo, Humph ey, and Fe nandez (2003)). Appea ances o he con a y, a 5% educ ion in uni cos om a success ul me ge is consis en wi h s anda d p ojec ions by banking consul an s o o e all cos sa ings in a me ge co esponding o 30% o 40% o an acqui ed bank’s ope a ing cos . Since bank ope a ing expenses (depending on he in e es a e cycle) a e a ound o y pe cen o o al cos s and he a e age acqui ed bank comp ises a ound one- hi d o he consolida ed o ganiza ion, a 30% o 40% educ ion in ope a ing cos o an acqui ed ins i u ion ansla es in o a 4% o 5% educ ion in uni cos (e.g., 40% × .40 ×.33 = 5.3%) o heme ged i m.O e hal o hecos educ ionachie edina success ul me ge is due o educing employmen (Rhoades (1998)) while addi ional sa ings come om closing edundan b anch offices. In some coun ies, howe e , public opposi ion o bank me ge s has led managemen o p omise ha labo o ce educ ions and b anch closings will be limi ed, which educes p e iously announced expec ed gains om a me ge . Al hough a 5% educ ion in uni cos (which only applies o success ul me ge s) may sound small, i can ansla e in o a 23% o 35% imp o emen in e u n on asse s.3 In his pape we i s show ha a mo e de ailed analysis o scale effec s in banking can lead o mo e accu a e p edic ions ega ding he po en ial cos effec s o me ge s. This is achie ed by compa ing he es ima ed scale economies om a es ic i e speci ica ion like he anslog o he mo e lexible speci ica ions o a spline o a Fou ie unc ion. The anslog speci ica ion will in mos cases p edic a e age cos as a s anda d U-shaped quad a ic cu e whe e scale economies a e exhaus ed o all bu ela i ely small o medium-sized banks. By cons uc ion a quad a ic unc ion can only ha e one u ning poin , hence he ypical U-shape o a anslog cos unc ion can in many cases be conside ed an a i ac . Ne e heless, his has been he s anda d unc ional o m used in mos bank cos s udies. In con as 3A 5% educ ion in uni cos implies ha he a io o o al cos o o al asse s (which a e ages .07) will all by .0035. Since he e u n on asse s o en anges be ween a ound .01 o .015, a cos educ ion o .0035 (i en i ely e lec edinap o i inc ease) sugges s ha e u n on asse s (ROA) could ise by 35% o 23%, espec i ely. 3 o he anslog, bo h he spline and he Fou ie speci ica ions—whichbo hallow mo e han one u ning poin — indica e ha p edic ed a e age cos is no quad a ic. Indeed, ins ead o a ypical U-shaped a e age cos cu e, he spline and Fou ie o ms bo h show some hing simila o an M-shaped cu e so ha economies and diseconomies exis o bo h smalle and la ge banks.4 In o de o p edic he cos effec o me ge s, we ma ch me ging ins i u ions wi h hei p e- and pos -me ge bank-speci ic scale measu es a he ime hey me ged o de e mine he likely effec on cos o each me ge indi idually and as a g oup. These esul s a e epo ed using he anslog, spline, and Fou ie cos unc ions. On a e age, he anslog p edic s ha a e age cos will all by less han a i h o one pe cen while he Fou ie and spline unc ions p edic a wo o h ee pe cen dec ease. F equency dis ibu ions o hese se s o p edic ions show ha all h ee unc ions p edic bo h cos inc eases and dec eases o indi idual me ge s, wi h mo e dec eases o he spline and Fou ie o ms. These me ge cos p edic ions a e compa ed o how a e age cos has ac ually changed p e- and pos -me ge a acqui ing banks ela i e o he es o he indus y. This cos change ela ed o me ge s is hen con as ed wi h cos sa ings esul ing om ad ances in paymen echnology which educe back office ope a ing cos s and se ice deli e y expenses. The accu acy o ou analysis in p edic ing he di ec ion o change in a e age cos is on pa wi h ha o me ge pa icipan s who in a iably p edic cos educ ions bu , due o un o eseen e en s, ealize his goal only abou hal he ime. The alue o ou app oach lies in p o iding a mo e accu a e es ima e o he a e age effec o me ge s on cos . This gi es an expec ed alue which compe i ion au ho i ies may use o assess he likelihood ha me ge cos sa ings announced by pa icipan s may in ac be ealized. Fo his ask, he spline and Fou ie unc ions gi e mo e eliable esul s han he anslog. In wha ollows, sec ion 2 ou lines ou use o spline and Fou ie unc ions o mo e accu a ely de e mine a ia ions in scale economies ac oss all banks. This 4This poin was demons a ed on a da a se o U.S. banks by McAllis e and McManus (1993). Also, in a special case, Shaffe (1998) shows ha es ima ing a anslog cos unc ion can esul in a spu iously U-shaped a e age cos cu e when da a a e gene a ed om a p ocess wi h declining a e age cos s. The cos unc ion sugges ed as a eplacemen , howe e , has lexibili y p oblems o i s own. 4 analysis is illus a ed by i s applying a single ou pu model o a balanced panel o 131 No wegian banks o e 1987-1998 (12 yea s), gi ing 1,572 obse a ions. These esul s a e con as ed wi h hose ob ained using a anslog cos unc ion, p o iding a benchma k o assessing he imp o emen in iden i ying scale economy and me ge cos effec s. Then ou single ou pu model is expanded in o a wo-ou pu model whe e we addi ionally con ol o he ansi ion om pape based o elec onic pay- men s. In sec ion 3 his wo-ou pu model is applied o p edic cos effec s om bank me ge s. These p edic ions a e con as ed in sec ion 4 wi h es ima es o he ac ual me ge - ela ed cos change. The pu pose is o de e mine how accu a e ou ex an e me ge cos p edic ions a e ela i e o me ge analyses which ely on ex pos da a. In sec ion 5, he effec on bank expenses om he shi o lowe cos elec onic paymen s is es ima ed and compa ed o he me ge cos effec . Sec ion 6 con ains a summa y and conclusions. 2. Spline and Fou ie Func ion Measu es o Scale Economies. In his sec ion we i s discuss how o bes a ange he da a in o de o cap u e effec s om scale economies. Then we demons a e he impo ance o he choice o unc ional o m when scale economies a e o be e alua ed using an econome ically es ima ed cos unc ion. To acili a e a g aphic illus a ion o his issue we use single ou pu models. Nex , howe e , we expand ou models o con ain wo ou pu s — business loans and consume loans — and con ol o he e olu ion in paymen echnology ha ook place du ing ou sample pe iod. This wo-ou pu model is he model applied in sec ion 3 when we p edic me ge cos effec s ex an e. 2.1. A anging he Da a o Bes Cap u e Scale Effec s. Scale effec s ha e been es ima ed using c oss-sec ion and panel da a. Wi h panel da a, i can make a diffe ence how he da a a e a anged. The a e age cos igu e below illus a es wo ways o doing his when bank a( he la ge o he wo banks) acqui es bank b, o ming he new bank a+b. The usual way is o c ea e a balanced panel by backwa d agg ega ing all p e- me ge da a on banks aand bp io o hei me ge , gene a ing poin 3 in he Figu e 2.1. Once he me ge occu s, yielding poin 4, he ou pu le el will no change by 5 1234567891011 6 6.5 7 7.5 8 8.5 9 9.5 10 Bank b (acqui ed bank) Bank a (acqui ing bank) Me ged bank a+b (pos -me ge ) Me ged bank a+b (p e-me ge ) o AVERAGE COST OUTPUT 1 2 3 4 Figu e 2.1: much (since he banks ha e al eady been a i icially me ged) bu cos s may change i he e a e scale economies. This is a common app oach and we ha e done i ou sel es. Upon e hinking he issue, we eel a mo e de ensible app oach (and he one adop ed below) would be o ins ead use he obse ed p e-me ge da a poin 2 along wi h poin 4. Wi h hisda aa angemen ,when2iscompa ed o4inapanel eg ession bo h cos and ou pu a e allowed o change in esponse o he me ge . The me ge p ocess is hus ep esen ed as a se ies o ou pu and cos ”jumps” which is how i is also iewed by he me ge pa icipan s. 2.2. App oxima ing he Cu a u e o A e age Cos . A spline unc ion is a eg ession-based me hod de eloped o i a polynomial equa- ion o a gi en o de o a sca e plo o da a poin s. A one ex eme, he polynomial i ed can be a s aigh line equal o wha is ob ained wi h a simple linea eg es- sion. A he o he ex eme, a se ies o line segmen s would connec each poin in a sca e plo . The bene i o a spline is ha i can ep esen nume ous cu a u es in e media e o hese wo ex emes a he disc e ion o he esea che , which is how i is applied he e. Take hecaseo as anda da e agecos (AC)cu e. I ACislinea ,loglinea , 6 o m. As elec onic bill paymen s and pay oll disbu semen s a e au oma ed and debi ca ds subs i u e o cash a he poin o sale (Snellman, Vesala, and Humph ey (2000)), he e is less need o di ec bank- o-cus ome in e ac ion, allowing banks o educe he numbe and size o b anch offices and hus lowe se ice deli e y expenses. This apid change o echnology ook place wi hin he pe iod co e ed by ou sample, and con olling o i in es ima ing a cos unc ion is impo an gi en he cos sa ings i has implied. No e ha he a iable ELE only a ies ac oss ime no ac oss banks. As all banks in No way a e connec ed o he same clea ing sys em o e ail paymen s, ELE ep esen s a common change in echnology affec ing all banks. Econome ically his implies ha o he indi idual bank his a iable can be conside ed as exogenous. In o de o assess he use ulness o ou spline unc ion model, he scale economy, paymen echnology, and me ge cos effec s om he spline unc ion a e compa ed wi h simila esul s om anslog and Fou ie speci ica ions es ima ed join ly wi h he cos sha es: T anslog Cos Func ion: lnTC =α0+ 2 X i=1 αilnQi+1/2 2 X i=1 αi,i(lnQi)2+A0+B+γ1lnELE +γ21/2(lnELE)2 Sk=βk+ 4 X m=1 βk,mlnPk+ 2 X i=1 δi,klnQi(2.2) Fou ie Cos Func ion:14 lnTC =T anslog Cos Func ion + 2 X i=1 (τ1isin(lnQ∗ i)+τ2isin(2lnQ∗ i)+τ3isin(3lnQ∗ i)) + 2 X i=1 (τ4icos(lnQ∗ i)+τ5icos(2lnQ∗ i)+τ6icos(3lnQ∗ i)) +τ7sin(lnQ∗ i+lnQ∗ j)+τ8cos(lnQ∗ i+lnQ∗ j) +τ9sin(2lnQ∗ i+lnQ∗ j)+τ10 cos(2lnQ∗ i+lnQ∗ j) +τ11 sin(lnQ∗ i+2lnQ∗ j)+τ12 cos(lnQ∗ i+2lnQ∗ j) Sk=βk+ 4 X m=1 βk,mlnPk+ 2 X i=1 δi,klnQi(2.3) 14The e ms lnQ∗ iand lnQ∗ ja e compu ed as de ined ea lie in sec ion 2.2 13 F om he es ima ion o he h ee cos unc ion speci ica ions (2.1) o (2.3) he scale elas ici ies, o he elas ici ies o o al cos w. . . o al loans (consume loans plus business loans), can be calcula ed as: ETC = 2 X i=1 Ei,T C , whe e Ei,T C is he elas ici y o o al cos w. . . ou pu i. The scale elas ici ies ETC o se en diffe en sub-samples acco ding o bank size15 a e epo ed in Table 2.1 as sample means.16 Table 2.1: Elas ici ies o o al cos s o o al loans To al asse s, Size class NOK billions T anslog Fou ie Spline N 1 0—0.25 0.92 0.93 0.93 255 20.25—0.5 0.94 0.92 0.91 458 3 0.5 — 1.0 0.95 0.96 0.96 403 4 1.0 — 5.0 0.96 0.97 0.95 265 55.0—10.0 1.00 1.04 1.10 55 6 10.0 — 25.0 1.01 1.05 0.97 62 725.0— 1.04 0.94 0.92 50 To al sample 0.95 0.95 0.94 1548 In es ima ing he scale elas ici ies in Table 2.1, we ha e con olled o (a) cos changes associa ed wi h he inc eased use o elec onic paymen s (by speci ying he a io o elec onic o o al non-cash ansac ions) and (b) he e ogenei y be ween business and consume loans (by speci ying wo sepa a e ou pu s). These scale elas ici ies show a simila pa e n as ha ep esen ed by he cu es in Figu e 2.2 using only one ou pu ( o al asse s) and no sepa a ely con olling o changes in paymen echnology. Wi h he wo-ou pu (business and consume loans) anslog speci ica ion and con olling o changes in paymen s echnology, scale economies a e seen o be ully ealized o almos all banks wi h an asse size o only NOK 10 (1.3 Eu os) billion o la ge . In sec ion 2.2 whe e we used a single ou pu ( o al asse s — 15These se en size classes a e based on he alue o o al asse s and co epond o he se en segmen s used in es ima ing he spline unc ion illus a de in Figu e 2.2. 16Two banks om ou o iginal sample o 131 banks did no epo loans by bo owe ca ego ies. Hence when es ima ing models wi h wo ou pu s we a e le wi h 129 banks and a o al o 1548 obse a ions. 14 a he han wo loan ca ego ies), scale economies we e ully ealized o banks wi h an asse size i e imes la ge (NOK 50 billion) in he anslog speci ica ion. This diffe ence e lec s he ac ha among banks wi h o al asse s la ge han NOK 10 billion, loans — a labo in ensi e asse — cons i u e a smalle ac ion o a bank’s asse s he la ge is he bank. As in sec ion 2.2 a log likelihood a io es o he Fou ie speci ica ion e sus he mo e es ic ed anslog speci ica ion indica ed ha he added igonome ic e ms in he Fou ie a e join ly signi ican .17 Thus, econome ically he Fou ie speci ica ion is clea ly p e e able o e he anslog.18 Bo h he Fou ie and he spline speci ica ions show economies o scale o many smalle banks, some diseconomies o medium-sized ins i u ions, and (qui e diffe en ly om he anslog) scale economies o la ge banks. Ou pu speci ic cos elas ici ies as well as ma ginal cos s o business and con- sume loans a e shown in Table 2.2. On a e age o e he whole sample, expanding business loans by 10% gene a es a 2.3% ise in associa ed o al cos s while a 10% expansion in consume loans gene a es a 7.1% ise ( i s wo columns in Table 2.2). This diffe en ial cos effec e e s only o he diffe en slopes o he implied business and consume loan a e age cos cu es — no o hei le el. O e he whole sample, o each ex a NOK 100 o business loans ex ended NOK 16 goes o co e he ma - ginal in e es , capi al, and ope a ing expenses while a simila ex ension o consume loans gene a es NOK 12 o ex a expenses (las wo columns in Table 2.2). Business loans usually in ol e mo e sc eening and moni o ing han do consume loans, and hence a e mo e cos ly on he ma gin. The app oxima e M-shaped a e age cos cu e seen o he Fou ie and spline unc ions in Figu e 2.2 is also seen when he spline unc ion is es ima ed wi h wo loan ou pu s in Figu e 2.3.19 The igu e plo s he diffe en p edic ed a e age cos s 17The log likelihood a io s a is ics is 56.122 wi h 18 deg ees o eedom, gi ing a p- alue less han 0.001. 18Since he spline and he anslog a e no nes ed, we canno es he spline e sus he anslog using a log-likelihood a io es . Ins ead we ha e ouseanon-nes ed es p ocedu elike heJ- es . Howe e ,as equen lycanhappenwi h heJ- es , i was inconclusi e. I was e en inconclusi e be ween he Fou ie and he anslog, indica ing he es has low powe . In addi ion we calcula ed he Akaike in o ma ion c i e ion, which (al hough i has no i m basis in s a is ical heo y) indica ed ha he spline is mo e in o ma i e han he anslog. 19The i ed Fou ie o m wi h wo loan ou pu s is simila o he spline and is hus no shown. 15 10 11 12 13 14 15 16 17 18 19 0.09 0.10 0.11 0.12 0.13 0.14 0.15 P edic ed a e age cos Fi ed cubic spline (solid line) ln(business loans + consume loans) Figu e 2.3: Poin s : P edic ed a e age cos s o he wo-ou pu spline cos unc ion, using sample mean alues o inpu p ices and ELE, plo ed agains log o loans. Solid line: a i ed cubic spline o he poin s. Table 2.2: Ou pu -Speci ic Cos Elas ici ies and Ma ginal cos s, Business and Con- sume Loans To al asse s, Cos elas ici ies Ma ginal cos s NOK billions Business Consume Business Consume 0 — 0.25 0.16 0.77 0.188 0.140 0.25 — 0.5 0.21 0.70 0.157 0.114 0.5 — 1.0 0.22 0.75 0.158 0.111 1.0 — 5.0 0.25 0.70 0.151 0.105 5.0 — 10.0 0.38 0.72 0.143 0.157 10.0 — 25.0 0.29 0.67 0.103 0.114 25.0 — 0.55 0.37 0.146 0.102 To al sample 0.23 0.71 0.158 0.117 Ma ginal cos s a e millions o NOK in inc eased o al cos s pe millions o NOK in inc eased lending. In calcula ing he elas ici ies and ma ginal cos s all ou inpu p ices and he a io o elec onic paymen s a e se a hei ac ual alues. Only esul s om he spline speci ica ion a e shown. The Fou ie speci ica ion gi es simila esul s. 16 agains he log o business plus consume loan alues (on he X-axis).20 The solid line shown in he igu e is a cubic spline i ed o hese p edic ed alues. As seen, he esul is simila o a M-shaped a e age cos cu e. Fo he small banks wi h loans be ween NOK 40 millions and NOK 100 millions ( hose wi h he log o loans be ween 10.6 and 11.25), he solid line ises showing ini ial diseconomies o scale. The eason o hese ini ial diseconomies is wo- old. Fi s , as no ed abo e, business loans cos mo e o p oduce han he same alue o consume loans. Second, as hese small banks become la ge , hey s a o issue mo e business loans. The shi owa d p oducing mo e o he mo e expensi e business loans gene a es he ini ial scale diseconomies seen in he igu e. Bu as hese banks become la ge s ill, g ea e scale economies o business loans s a o domina e. The la e ”humps” in a e age cos shown in he igu e a e associa ed wi h high ma ginal cos s o consume loans o he medium sized banks, banks wi h loans la ge han NOK 5 billions. Finally, he educ ion in a e age cos seen o he e y la ges banks is he di ec esul o signi ican ly smalle ma ginal cos s o consume loans o hese la ge ins i u ions, as shown in Table 2.2. This indica es ha he smalle banks and in pa icula he la ge banks ha e been able o ex end consume loans a low cos s.21 No ice also ha he ma ginal cos o business lending is highe o he la ges banks, almos as la ge as i is o small banks. The highe cos s associa ed wi h la ge banks can be due o mo e complex moni o ing and sc eening o he la ge i ms ha ypically bo ow a la ge banks. Fu he mo e, he la ge co po a e cus ome s o la ge banks usually pu chase ela ed inancial se ices such as o eign exchange, sho - e m in es men s, and inancial de i a i es om hei banks. These se ices equi e physical inpu s ha a e epo ed as highe o al cos s in ou model, bu we can no speci y hese addi ional se ices as ou pu s due o a lack o da a. 20All inpu p ices and he sha e o elec onic paymen s a e held cons an a hei mean alues. 21One explana ion o his pa e n in consume lending is ha small and ai ly local banks ha e good in o ma ion abou hei consume bo owe s and need no spend a lo o esou ces on sc een- ing and moni o ing hese loans. Once banks each a medium size and encompass egions a he han communi ies, hese local in o ma ion ad an ages a e educed as loan equi emen s become mo e s anda dized and less pe sonal. Hence hey ha e o spend mo e esou ces on sc eening and moni o ing he consume loans hey make. Al hough e y la ge na ionwide banks also ha e he same in o ma ion disad an age, hey a e geog aphically much mo e di e si ied and can o some deg ee subs i u e di e si ica ion o in ensi e moni o ing. Fu he mo e, mos o he moni o ing and sc eening o consume loans can be done h ough hese banks’ IT-sys ems, sys ems associa ed wi h la ge ‘ ixed’ cos s making hem mo e a ac i e o la ge banks han o smalle banks. 17 While scale economies exis , scope economies do no . Indeed, sepa a e p oduc- ion o consume and business loans appea s o ha e ma ginally lowe cos s han does join p oduc ion. The a e age scope economy alue wi h he Fou ie o m was -0.01 while i was -0.12 wi h he anslog.22 Thus he join p oduc ion we obse e in p ac ice is mo e likely due o e enue bene i s han cos educ ions. In any case, ew me ging banks ac ually changed hei composi ion o business and consume loans p e- o pos -me ge and so e en i scope economies we e posi i e (indica ing lowe cos s) he effec would ha e been small.23 In he nex sec ion pa ame e es ima es om he h ee cos unc ion speci ica- ions (2.1) o (2.3) a e used o gi e ex an e p edic ions o he cos sa ings om 26 bank me ge s ha ac ually occu ed in ou da a se be ween 1988 and 1997.24 As ou scale es ima es a e independen o back office cos educ ions associa ed wi h changes in paymen echnology — by he e m con olling o his echnological change — so (app op ia ely) a e ou p edic ed cos effec s om me ge s. 3. P edic ing Me ge Cos Effec s Ex An e. When banks aand bme ge in o bank a+bin yea , by bank aacqui ing bank b in ha yea , he da a we use o yea will con ain he balance shee i ems, cos , and income s a emen s o he new la ge bank, bank a+b.Fo yea −1and all p e ious yea s he epo ed da a con ains sepa a e in o ma ion o bank aand bank bas hey we e p io o hei me ge . In o de o p edic ex an e he cos effec s o his me ge we a i icially me ge banks aand bin only yea −1in a 22The o m o he spline unc ion makes i e y difficul o de i e a scope measu e and one is no p esen ed. In unc ional no a ion, ou scope calcula ion was: SCOPE =[C(0.9∗Q1,0.1∗Q2) +C(0.1∗Q1,0.9∗Q2)−C(Q1,Q 2)] /C(Q1,Q 2)whe e Q1(Q2)=business (consume ) loans and C(·)is he es ima ed cos unc ion e alua ed wi h ou pu le els as shown bu wi h all inpu p ices and he sha e o elec onic paymen s held cons an a hei mean alues. As is now known, de e mining scope economies om a loga i hmic cos unc ion should no be done wi h comple e o almos comple e specializa ion in p oduc ion. Hence ou use o 0.9and 0.1poin s o e alua ion a he 1.0and 0.0o 0.99 and 0.01). O he mo e sub le biases also exis , c. . Pulley and Humph ey (1993). 23Fo he 26 me ging banks, he a e age a io o business o o al loans was .36 and he a e age pe cen age poin change in his a io p e- o pos -me ge was .011 (wi h a s anda d de ia ion o .036). 24Ou da a co e s 1987-1998 bu we need a leas one obse a ion bo h one yea p io o a me ge and one yea a e a me ge o calcula e and con as ou p edic ed and ac ual change in me ge - ela ed a e age cos . This elimina es some me ge s ha occu ed in 1987. 18 sepa a e da a se . We hen compa e he p edic ed a e age cos om each o he h ee cos unc ions o a bank wi h ou pu le els he size o bank ain yea −1 o he p edic ed a e age cos o bank abu using he sum o ou pu o bank aand bank bin yea −1. Mo e o mally, his cos compa ison can be s a ed as ollows: Le (·)be he symbol o an es ima ed mapping o inpu p ices, ou pu s, and he paymen echnol- ogy con ol a iable ELE o he o al cos o a bank he size o bank aalone in yea −1and hen o hesizeo bankaand bank bas i hey had me ged in o bank a+bin yea −1. Using his es ima ed mapping he p edic ed a e age cos s a e: ACa, −1= (Q1,a,, −1,Q 2,a, −1,Pa, −1,ELE −1) Q1,a,, −1+Q2,a, −1 ACa+b, −1= (Q1,a,, −1+Q1,b,, −1,Q 2,a, −1+Q2,b,, −1,Pa, −1,ELE −1) (Q1,a,, −1+Q1,b,, −1)+(Q2,a, −1+Q2,b,, −1). The pe cen change in a e age cos p edic ed o be associa ed wi h he scale effec o a me ge is: PCAC =(ACa+b, −1−ACa, −1)/ACa, −1·100 (3.1) whe e Qi,h, −1,i=1,2,h=a, b, is he he quan i y o ou pu io bank hin yea −1, and Pa, −1is he ec o o inpu p ices o bank ain yea −1. Hence ACa, −1is he p edic ed a e age cos o bank abe o e he me ge , and ACa+b, −1is he p edic ed a e age cos o bank aassuming i —one yea ahead o he ac ual me ge —had eached he join size o he wo me ging banks. In calcula ing bo h ACa, −1and ACa+b, −1 we use he inpu p ice ec o Pa, −1and so dis ega d any effec on inpu p ices om he me ge due o inc eased ma ke powe o change in unding composi ion. Thus wha we conside he e is a pu e economies o scale effec . PCAC is calcula ed using each o he h ee cos unc ion speci ica ions, anslog, Fou ie , and spline. Nega i e alues p edic a educ ion in a e age cos while posi i e alues p edic a ise. Ou da a se con ains usable da a on 26 (ou o 33) bank me ge s ha occu ed o e 1987-1998.25 Fo hese 26 me ge s we calcula e he p edic ed pe cen change in a e age cos o all me ging banks as a g oup due o scale effec s (PCAC)as desc ibed in equa ion (3.1). Ou a e age esul s a e epo ed in Table 3.1.26 25Asse enme ge soccu edin he i s yea o he da a se (1987), we a e unable o p edic 19 Table 3.1: P edic ed cos effec om me ge s (PCAC) T anslog Fou ie Spline Pc . change AC (PCAC) (ACa+b−ACa)/ACa−0.16% −2.06% −3.09% No. AC inc ease (+) 16 11 7 No. AC dec ease (-) 10 15 19 Pc . change o al cos 28.8% 26.3% 25.0% Pc . change o al loans 29.0% 29.0% 29.0% Ma ginal scale economy .99 .91 .86 The p edic ed pe cen change in weigh ed a e age cos (AC) due o scale effec s om all 26 me ge s oge he is shown in he i s ow (calcula ed om (ACa+b, −1−ACa, −1)/ACa, −1.Thenumbe o nega i e (posi i e) changes indica e he numbe o bank me ge s ha a e p edic ed o educe (inc ease) a e age cos . Pe cen changes in o al cos and o al business and consume loans e e o he sum o all 26 me ge s. Di iding he o me by he la e gi es a ma ginal scale economy alue ha e e s o he p edic ed o e all me ge effec . As may be expec ed om he ea lie almos L-shaped a e age cos cu e in Figu e 2.2 and scale economy alues epo ed in Table 2.1 o he anslog speci- ica ion, only a sligh educ ion in a e age cos (-.16%) is p edic ed as a weigh ed a e age o all me ge s in Table 3.1.27 Ou o 26 me ge s, 10 a e p edic ed o lowe a e age cos . As he p edic ed change in o al cos (28.8%) is sligh ly lowe han he change in o al business and consume loans (29.0%), he scale economy effec o hese me ge s as a g oup is .99. On balance, use o he anslog o m sugges s ha me ge s in No way would yield some hing close o cons an a e age cos wi h li le bene i o cos o use s o banking se ices. In con as , bo h he Fou ie and spline unc ions sugges ha me ge s would gene a e la ge educ ions in a e age cos o all me ge s oge he . The p edic ed educ ions ange om -2.06% (Fou ie ) o -3.09% (spline) wi h co esponding scale hei cos effec one yea p io o hei me ge . 26To e lec he diffe en p edic ed o al cos (TC) and ou pu le els (Q) among me g- ing banks, he weigh ed a e age cos in Table 3.1 is compu ed om a a io o a e ages: (P26 =1 TC a+b, −1, /P26 =1 Qa+b, −1, )−(P26 =1 TCa, −1, /P26 =1 Qa, −1, ) (P26 =1 TC a, −1, /P26 =1 Qa, −1, )whe e e e s o he me ge num- be . A simple a e age o 26 a e age cos alues (an a e age o a ios as in P26 =1[(ACa+b, −1, − ACa, −1, )/ACa, −1, ]/26 ) would weigh all me ging banks equally e en hough hei impac on indus y cos is diffe en . 27A simple a e age o he p edic ed pe cen changes in a e age cos o he 26 me ge s sugges s ha hese cos s would ise (no all) by 0.27% using he anslog o m. 20 Table 3.2: P edic ed cos effec o 26 indi idual me ge s Pc . change 0-10% 10-20% 20-50% 50-100% >100% o al loans 10 8 4 3 1 F equency: Pe cen T anslog Fou ie Spline 6 o11 1 2 o6 22 2 1 o2 23 1 0 o1 12 5 4 0 o-1 911 9 -1 o -2 12 5 -2 o -6 3 -6 o -11 22 economies o .91 and .86, espec i ely.28 He e om 15 o 19 me ge s a e expec ed o educe cos compa ed o only 10 wi h he anslog. On balance, use o ei he he Fou ie o he spline unc ion p edic s ha me ge s in No way could bene i use s o banking se ices.29 In la ge coun ies (such as he U.S.) he a e age banking me ge inc eased he size o he acqui ing bank by 50% o mo e (Be ge and Humph ey (1992)). Thus he acqui ed bank accoun s o one- hi d o mo e o he consolida ed ins i u ion. Table 3.2 shows he size dis ibu ion o acqui ed banks in No way in e ms o hei p e-me ge expec ed change in loan ou pu .30 Fully 18 o he 26 me ge s we e compa a i ely small and we e no expec ed o inc ease he size o he acqui ing bank by mo e han 20%. Only 4 me ge s inc eased he size o he acqui ing bank by 50% o mo e. Wi h so many ela i ely small me ge s we would also expec ha he p edic ed impac on indi idual banks’ a e age cos would also be ela i ely small. The equency dis ibu ion o he p edic ed pe cen change in a e age cos 28Using simple a e ages sugges s ha a e age cos would ise by a miniscule 0.02% wi h he Fou ie o m bu all by 1.07% wi h he spline. 29O cou se, lowe a e age cos s would be passed on o businesses and consume s only i he ma ke is compe i i e. I so, use s o banking se ices could expec o see ma ginally lowe p ices a e a lag o o expe ience a smalle ise o e ime han would o he wise occu . 30This is om [(Q1,a +Q1,b +Q2,a +Q2,b)/(Q1,a +Q2,a)]−1and ep esen s he pe cen change in loan ou pu expec ed om he me ge i no hing else changes. The usual si ua ion wi h a me ge , howe e , is ha a ew bo owe s swi ch banks while o he s may no ha e hei loans enewed so he simple sum in he nume a o he e may o e s a e somewha he ac ual change in loan ou pu . 21 shown in Table 3.2 con i ms his esul . Indeed, ou o 26 me ge s, 21 ( anslog), 16 (Fou ie ), and 13 (spline) a e p edic ed o change a e age cos —ei he up o down—by less han 1%. As small me ge s will likely ha e ela i ely small effec s on banking cos s, ou ocus will be on he ew bank me ge s ha a e la ge o his is whe e he g ea es impac on he banking indus y and po en ially on hei cus ome s will be. 4. Es ima ing Me ge Cos Effec s Ex Pos . One difficul y in es ima ing he ac ual cos effec o me ge s lies in sepa a ing he effec o he me ge om possible concu en cos changes affec ing he banking indus y as a whole. Such concu en changes include (cos push) effec s om changes in in e es a es and wages, effec s om he shi o elec onic paymen s, and (demand pull) effec s due o changes in he business cycle ha may affec p oduc i i y and al e cos s pe uni o ou pu o e longe pe iods o ime. We app oach his h ee ways, al hough each me hod has i s own p oblems. 4.1. Compa ing P e- and Pos -Me ge Cos Effec s o Indi idual Me g- e s. We i s looka howa e agecos a ame gingbankhaschangedoneyea p io o and one yea a e hei me ge , excluding he me ge yea i sel . Use o such a sho pe iod should minimize cos changes un ela ed o me ge s. The pe cen change in a e agecos o heme gingbankis hencompa ed o he pe cen change in a e age cos o he banking indus y as a whole o e he same h ee yea s. I a e age cos a a me ging bank alls by 5% (say du ing a pe iod when in e es a es a e alling) while a e age cos o he indus y as a whole alls by 3% hen i is p esumed ha ac ual a e age cos a he me ging bank expe ienced a ne educ ion o 2% (ac ually, wo pe cen age poin s). The assump ion is ha changes in cos s expe ienced by he indus y will also be expe ienced o an equal deg ee by he me ging bank. This p ocedu e has been applied o each me ge o e he 8 diffe en yea s ha hese me ge s occu ed. The equency dis ibu ion o he es ima ed ac ual change in a e age cos is shown in Table 4.1, along wi h he equency dis ibu ions o he p edic ed changes om he anslog, Fou ie and spline unc ions.31 While he 31As he ange o he ac ual changes is la ge han he ange o he p edic ed changes, he 22 — due o poo planning, poo execu ion, managemen con lic , o o he p oblems — do no expe ience signi ican cos educ ions. Academics poin o (selec ed) s udies o bank scale economies which show ha scale economies exis and sugges ha expec ed me ge cos sa ings may be simila o he a e age scale effec es ima ed. Ou goal is o demons a e an imp o ed way o es ima e bank scale economies and o de elop mo e accu a e p edic ions o expec ed me ge cos effec s. Following he wo k o McAllis e and McManus (1993), we demons a e he im- po ance o using a cos unc ion speci ica ion ha is mo e lexible han he anslog o m when es ima ing scale economies. Bo h a linea spline and a Fou ie cos unc- ionp o ideamo eaccu a e ep esen a iono howa e agecos a iesbysizeo bank han does he anslog o m and hus imp o es he accu acy o p edic ions o hecos effec o me ge s.44 Using a balanced panel o 131 No wegian banks o e 12 yea s (1987-1998), he anslog o m effec i ely yields an L-shaped a e age cos cu e while he linea spline and Fou ie o ms gi e an M-shaped cu e. Ins ead o anslog-de e mined scale economies o only smalle banks and cons an a e age cos s o only la ge ins i u ions, he spline and Fou ie models show economies and diseconomies o bo h smalle and la ge ins i u ions. This occu s when o al asse s a e used as a single measu e o banking ou pu as well as a wo-ou pu case using business and consume loans. Al hough business loans ha e a highe ma ginal cos han consume loans, hey also ha e g ea e scale economies and hus a g ea e po en ial o uni cos educ ions om a me ge . Using h ee cos unc ions, we compu ed he p edic ed change in a e age cos o each o 26 me ge s. When bank a( he la ge bank) acqui es bank b o o m he me ged bank a+b, he p edic ed change in a e age cos equals he p edic ed a e age cos o a bank he size o bank aone yea p io o i s me ge minus he p edic ed a e age cos o a bank he size o bank a+balso one yea p io o he me ge . Fo all me ge s oge he , he anslog p edic ion is o a e age cos o all sligh ly by -0.16% while la ge cos educ ions a e p edic ed wi h he Fou ie (-2.06%) and spline (-3.09%) models. The o e all change in ac ual a e age cos o all yea s p e-me ge o all yea s pos -me ge o ou 26 me ge e en s was -2.81%. 44Howe e , i one is only in e es ed in he mean scale effec and no conce ned wi h how cos s a y wi h size, hen any one o hese h ee o ms may be used since hey all gi e almos iden ical mean scale economy alues. 29 In con as wi h o he s udies, bank me ge s in No way ha e — on a e age — esul ed in lowe cos s. In he U.S., he a e age acqui ed bank is hal he size o he acqui ing ins i u ion. In No way, he a e age me ge is smalle : in 18 o 26 me ge s he acqui ed bank is less han one- i h he size o he acqui ing ins i u ion. Indeed, he dis ibu ion is qui e skewed. One me ge accoun s o hal o he o al change in he alue o loan ou pu om me ge s while he six la ges me ge s accoun o 87% o his change. Fo hese six me ge s, he accu acy o he di ec ion o he ou p edic ed change in a e age cos is less han one-hal wi h he Fou ie o spline unc ions. This sounds like a poo showing un il i is compa ed o he accu acy o me ge pa icipan s hemsel es. Me ge pa icipan s almos always p edic ha hei me ge will educe cos bu ex pos analyses ypically ind ha his occu s in hal o less han hal o he cases. O e all, ou ex an e cos p edic ions o indi idual me ge s a e abou as good (o poo ) as hose o me ge pa icipan s hemsel es. The e is g ea e ag eemen when he a e age o p edic ed ex an e cos effec s (-3.09% o he spline) a e compa ed wi h he a e age o ex pos changes (-2.81%). Thus he es ima ed expec ed alue o he cos effec om a me ge can play a use ul ole in assessing he likelihood ha cos sa ing es ima es by me ge pa icipan s may be ealized in a p obabilis ic sense. In his a ea, he spline and Fou ie unc ions gi e mo e eliable esul s han he anslog. We also es ima ed how bank a e age cos has been affec ed by he on-going shi om expensi e pape -based paymen ins umen s (checks, pape gi o ansac ions) o lowe cos elec onic paymen subs i u es (debi ca ds, elec onic gi o paymen s). This swi ch om pape o elec onic paymen s has been subs an ial. The sha e o elec onic paymen s in all non-cash ansac ions ose om 16% in 1987 o 74% in 1998. This shi is associa ed wi h a mean yea ly educ ion in all bank a e age cos o 1.3%, o -13% o he indus y o e ou 12 yea pe iod. This cos educ ion exceeds ha o all 26 me ge s and, in e ms o consume and bank bene i s, policies ha encou age elec onic paymen s a e p e e ed o e hose associa ed wi h me ge s. 30 Re e ences Be ge , A. N. (1998): “The efficiency effec s o bank me ge s and acquisi ions: A p elimina y look a he 1990s da a,” in Bank Me ge s and Acquisi ions,ed.by Y. Amihud, and G. Mille . Kluwe Academic, Bos on, MA. Be ge , A. N., and D. B. 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