Testing for Market Power in the Swedish Banking Oligopoly

Transcription

1 Testng for Market Power n the Swedsh Bankng Olgopoly Gabrel C. Oxensterna * Centre for Bankng and Fnance, CeFn and Department of Economcs Stockholm Unversty S Stockholm gabrel.oxensterna@sh.se October 3, 1999 ABSTRACT The purpose of ths paper s to examne the degree and art of competton n a domestc bank market. It s the frst attempt to use the olgopoly model developed n Oxensterna (1998) n emprcal research. A quas mult-product (loans and deposts) bankng applcaton of that paper s basc game theoretc model s developed, allowng for asymmetres n cost levels and two dfferent types of product dfferentaton. The model s then solved for dfferent theoretcal equlbra. The model has enough structure for drect use n the emprcal applcaton - n ths case n an analyss of competton n the Swedsh bank olgopoly. All market parameters are derved from estmatng n bank-specfc demand equatons and an aggregate market demand equaton for each market. Snce all behavoural equatons are provded n the theoretcal model there s no need for econometrcal estmaton of bank-level conduct. Results show that there was sgnfcant market power n both the loan market and the depost market, although wth a strongly tme-varyng pattern. The overall pcture of conduct, s that prcng polces are less compettve n the depost market. The economc cost level consttutes a bottom level for prcng polces n the loan market, and attempts to establsh hgher spreads are not sustanable n the long run. It was also possble to evaluate the conduct of ndvdual banks. Fnally, welfare losses to the socety from noncompettve prcng were calculated. They are around 1.1% of GDP as a yearly average durng the samplng perod ( ). The paper also analyses the emprcal transmsson of money market rates nto loan and depost rates, and fnds evdence of sgnfcant stckness manly n the loan market. * I thank Marcus Asplund for valuable comments, and Phl Molyneux for helpful dscussons and help wth data. I am also grateful to the Rksbank for help wth data and to the Swedsh Competton Authorty for fnancal support.

2 1 Introducton The frst purpose of ths essay s to examne the degree and art of competton n a domestc bank market, where entry has not been free due to legal or economc entry barrers. The paper also ams at developng the new methodology for emprcal work n the study of olgopoly markets set out n Oxensterna (1998). A full-fledged asymmetrc olgopoly model based on non-cooperatve game theory s employed and ts applcaton s demonstrated n a quas mult-product analyss of the Swedsh bankng markets (deposts and loans). Not only the market performance can be analysed over tme, but also the conduct of ndvdual banks. The ndvdual banks emprcal conducts are related to an analytcally deducted scale of game theoretc optmal conducts, and welfare consequences of the conducts found can be evaluated as quantfed changes n consumer surpluses. As ponted out by Berg and Km (1994), any study of performance, or effcency n scale or scope n bankng, should preferably be based on an analyss of market structure and conduct. The reason for ths s that neffcences have been shown to sgnfcantly domnate over economes of scale or scope n recent emprcal studes of bankng ndustres, see, e.g., Berger and Humphrey (1992). Ths mples that the latter are of secondary mportance for economc polcy n the feld of bankng. Ths study ams to advance the understandng of the mportance of market structure and conduct n the bankng ndustry, thus establshng a better bass for emprcal studes of performance and effcency. Many authors, usually usng a model formulaton wth conjectural varatons n Cournot competton have modeled the hypothess of olgopolstc nteracton n bankng. 1 In Oxensterna (1998), motves are gven for basng emprcal ndustral organsaton research on a full-fledged game-theoretc model, as compared to conjectural varatons models. The bankng model developed n ths paper reflects specfc bankng features n that t s a mult-product, asymmetrc olgopoly model. It s concurrently asymmetrc between banks n terms of ther cost functons, and n two dfferent types of product dfferentaton. The advantage of ths approach s that: The econometrc work regardng estmaton of the market s compettve structure s smplfed n comparson to conjectural varatons models: It only requres estmaton of aggregate market parameters for a lnear market demand functon 2, and n frm-specfc demand functons. 3 The behavoural equatons 1 The conjectural varaton s defned as the reacton a frm conjectures about the output of ts compettors f t was to change ts own output. 2 For the olgopsonstc market of deposts, the supply equaton s estmated. 2

3 are all provded as dfferent theoretcally deducted game-theoretc equlbra, and requre no estmaton. Wth n frms n the market, only (n + 1) parameters have to be estmated econometrcally n order to completely defne the market s compettve structure (assumng that the szes of banks can be establshed by drect observaton). Indvdual bank conduct s evaluated over tme and related to dfferent regmes. Indvdual conduct can dffer between banks. Evaluatons of welfare aspects are based on the concept of consumer surplus and are also provded for on frm level n the theoretcal model. Welfare evaluatons thus requre no addtonal econometrc work. In secton 2 of ths essay a quas mult-product model of olgopolstc competton n non-symmetrc bank markets s elaborated, bult on a base verson of the olgopoly model worked out n Oxensterna (1998). In secton 3, a method for emprcal applcaton of the model n a domestc bankng market s proposed, and appled n an analyss of on-balance sheet conduct and performance of Swedsh banks. There s also a separate analyss of the emprcal transmsson of money market rates nto loan and depost rates. In secton 4 some conclusons are drawn. 2 A Mult-product Asymmetrc Olgopoly Bankng Model A model of the basc bankng markets, deposts and loans, should frst of all recognse the mult-product character of the bank s actvtes. The gross margn a bank earns has to be allocated n parts, each representng the opportunty cost of the asset or lablty n queston. One way of dong ths s to peg the bank as a fnancal ntermedary around an (nternal) transfer nterest rate, normally equal to the short-term money market nterest rate or the nterbank nterest rate. Ths market rate then represents a market valuaton of the opportunty cost of lqudty operatng n the bank. Furthermore, the bankng model should correctly handle the dual character of depost labltes. These are frst of all an output,.e. a product sold n a market. But they are also the major part of the fundng, needed to sell loan products. The frst aspect has mplcatons for the specfcaton of demand functons, and the second aspect affects the defnton of cost functons and the method of ther estmaton (see further secton 2.1). 3 In the specfc case of bankng, the banks operatng costs must also be dsaggregated between the market for loans and the market for deposts. Ths s due to the mult-product character of bankng, and the lack of dsaggregated cost data from banks annual reports. See further secton

4 Sx fundamental assumptons referrng to both markets alke are made n the model: 1. Banks are assumed to operate n markets that can be charactersed as asymmetrc olgopoly markets. Three types of asymmetry are consdered; banks may dffer n:. The relatve sze of the market pertanng to each bank, reflectng a sze component of product dfferentaton,. A relatve prce component of product dfferentaton, and. Banks cost levels. All these asymmetres nfluence the strategc nteracton. 2. Both types of output (depost labltes and loans) are assumed to be dfferentated between the banks,.e. customers do not perceve the servces provded as homogenous. 3. The banks nteract strategcally when they make decsons about nterest rate levels. In so dong, they are assumed to be proft maxmsers accordng to the condtons gven by the dfferent market structures and conducts. 4. Banks are prce takers n the money market and n the nput markets. 5. There are no explct demand nterrelatonshps between the loan market and the depost market. Any nteracton between the two markets s transmtted only through the money market and the nterest rate set there. Internally n each bank, there s a non-strategc opportunty cost relatonshp between the two markets, snce the money market nterest rate consttutes a common opportunty cost of lqudty. 6. There are no cost complementartes n the cost functon,.e. no economes of scope. The cost functon s further assumed to be lnear n the short term,.e., C (q ) = c q wthn each perod for each of the two markets. Ponts 1, 2 and 3 ndcate that we mght encounter market power n the bank output markets. Assumptons 4, 5 and 6 make t possble to separate the analyss of the two output markets, except for the jont money market nterest rate. Further comments to these assumptons and addtonal assumptons referrng to the specfc markets and the cost functons are made n the next secton. There are two possble sources of market power: Non-compettve conduct and/or product dfferentaton. In bankng, the underlyng product mght seem to be homogenous ( money ), whch could lead to a model formulaton where market power s wrongly attrbuted to conduct, when t n fact stems from product dfferentaton. An emprcal bankng model should therefore test for product dfferentaton. Product dfferentaton ncludes such factors as the strength of the bank s brand name, the general character of the establshment, effcency, and all the personal lnks that attach the customers. In so far as these and other ntangble factors vary from bank to bank, the servce provded n each case s dfferent- 4

5 ated from the customers pont of vew. Banks also actvely buld relatonshps wth customers n order to generate (prvate) nformaton whch s crucal to the bank n the loan market and s costly to duplcate by other banks (Damond (1984), Boyd and Prescott (1986)), or n order to cross-sell products. Relatonshps tend to grow stronger over tme (Petersen and Rajan (1994), Berger and Udell (1995)), although prcng conduct tend to shorten the lfe-length of the relatonshp (Greenbaum et al. (1989)). Also from the customer s pont of vew the relatonshp-buldng mght have a value, n whch case t wll ncrease product dfferentaton. 2.1 The treatment of demand nterrelatonshps In the lterature on mult-product olgopoly t has been observed that demand nterrelatonshps and/or cost complementartes between the markets can gve rse to strategc lnkages across markets (Bulow, Geanakoplos and Klemperer, 1985). In bankng, demand nterrelatonshps may emanate from revenue economes of scope, meanng that customers can lower ther transacton, transportaton and search costs by consumng the varous fnancal servces jontly from the same bank. Such customer benefts wll be observed ether drectly by a wllngness to pay hgher nterest rates or fees for the jontly provded servces, or ndrectly by acceptng lower nterest rates on deposts. In ths way, banks can ncrease ther revenues, or lower ther fundng costs, by supplyng ther servces jontly rather than separately. Here the market nterrelatonshps have been modelled dfferently, by abstractng from drect demand nterrelatonshps for the two markets. Market nterrelaton takes place only through the nterbank money market whch establshes a jont opportunty cost for both markets, equal to the money market nterest rate. There are two justfcatons for ths smplfyng assumpton:. emprcal tests for crossprce relatonshps between the two markets are unable to establsh any statstcally sgnfcant exstence of such effects n Swedsh bankng, ether on any of the two aggregated markets, or for any of the fve ndvdual banks, see further secton and Appendx 2;. Berger et al. (1996) found no evdence of statstcally sgnfcant revenue economes of scope n US bankng for any of a number of varous model specfcatons and data sets. 4 4 Berger et al. (1996) s the only known such study. Ther modellng approach does not allow them to dstngush between the exstence of market power and the exstence of revenue economes of scope. The non-exstence of the latter does not rule out market power n each separate market, only that market power s not exercsed through extractng hgher prces for jont producton. 5

6 2.2 The Market Structures In the prevous sectons the bank has been conceptualsed as a fnancal ntermedary, separatng ts decson-takng n the deposts and loans markets. Here ths vew wll be pursued by buldng a model of the market structure where any nteracton between the two markets s transmtted only through the exogenously gven money market nterest rate, p M. The model s a statc, dfferentated goods olgopoly model, wth asymmetres between banks n the levels of operatng costs and product dfferentaton, where the latter has one relatve sze component and one relatve prce component. Loans Defne p as the net nterest rate charged for loans, p p pm, where p M s the money market nterest rate. Specfcally, the depost market nterest rate s defned net of the money market nterest rate: ~ p pm p. Let the amount Deposts of loans demanded from the th bank be gven by: L s p p p, (1) and let the amount of deposts suppled to the th bank be gven by: where: j1 ~ ~ D ~ s ~ ~ p ~ ~ p p, (2) p s j p j s the weghted average loan nterest rate of the n banks so that p - p s the devaton between own prce and the weghted average prce., are parameters for the lnear aggregated market demand functon for loans. s the ntercept and s the slope. s assumed to be postve, so that L s a negatve functon of p. s an exogenous parameter that measures the level of substtutablty for bank (.e. the degree of product dfferentaton) between ts product and the products offered by the other banks n the market, as related to prce dfferentals. By assumpton, > 0. s s an exogenous parameter for the relatve sze of the market of frm. 0 < s < 1 and s j = 1. As seen from (1), s s a shft parameter for the level of quantty demanded and represents a sze component of product dfferentaton. n s the number of banks n the market. Varables and parameters wth a tlde (~) on top are for the depost market, and are defned n an analogous way to the loan market. 6

7 2.2.1 Theoretcal equlbra and welfare effects The full dervaton of the dfferent game theoretc equlbra for the basc market structures (1) and (2) n the model used here s provded n Oxensterna (1998). The model s solved for dfferent game-theoretc equlbra 5, whch nclude both prce-settng behavour and quantty-settng behavour. In ths way any confuson whether banks are prce-setters or quantty-setters s avoded. In emprcal studes of the loan market, banks are often thought of as quantty setters. 6 In perods of rapd asset growth, e.g. lke the second half of the 1980s n Sweden, banks seemed to compete for market shares by actvely sellng loans. Also, durng perods of bankng crss charactersed by a credt crunch, banks seem to operate manly as quantty setters. It s therefore clearly relevant to nclude the noncooperatve quanttatve settng equlbrum n comparson wth other equlbra. The only dfferences to the base model n Oxensterna (1998) le n the above gven defntons of prces, whch are calculated net of the money market nterest rate, and n the defnton of costs. For the loan market, the cost ncludes the opportunty cost of equty captal, as reflected n the captal adequacy rato, so that total costs are the sum of operatng costs allocated to loans, costs for expected loan losses, and equty costs. For the depost market the costs nclude the operatng costs allocated to deposts and the opportunty cost arsng from reserve requrement on deposts. Frm-specfc costs and the market nterest rate level p M wll be reflected wth a postve sgn n the varous optmal nterest rate levels, that are gven by the dfferent market regmes Dscusson of the model s aptness n the general bankng context, and to the Swedsh bankng markets n partcular Prces are usually seen as the major nstrument of transmttng nformaton about market condtons or product qualty. However, t s easy to fnd examples of markets where quanttes, n the form of relatve frm szes or market shares, are of major mportance n nfluencng consumers choce. Retal bankng markets seem to dsplay that knd of consumer behavour, where a bank s sze sgnals confdence, or smply avalablty through branch networks to the customers and thus, seemngly, nfluence ther very preferences. The model defned above s de- 5 Nash equlbrum wth respect to competton n prces, Nash equlbrum wth respect to competton n quanttes, the jont maxmsaton of profts (monopoly prce and quantty), and compettve prcng. Also a best reply to the monopoly prce s deducted, although ths s not an equlbrum soluton. 6 See, e.g., Berg and Km (1994) and Berg and Km (1998). Berger et al. (1996) and Humphrey and Pulley (1997) take the opposte vew. 7

8 sgned to capture these effects by lettng demand beng nfluenced by relatve frm sze. Recent methodologcal developments n the emprcal study of olgopoly markets address the ssue of product dfferentaton n detal. Berry (1994), develops a statc olgopoly model where there s a range of observable product characterstcs, as well as a range of unobservables. 7 In the study of servce markets, lke bankng, and most product markets, rch data sets on product characterstcs and on demand data (prces and quanttes) related to these are rarely avalable. One of the few observable characterstcs n offcal data sets that dstngushes retal banks n terms of product dfferentaton s ther relatve szes. These are hghly correlated to the sze of the branch networks of Swedsh banks, snce all the fve banks have natonwde coverage. They also offer very smlar product sets to consumers. Furthermore, payments servces that are offered to customers, such as gro systems and automatc teller machnes, are not a dstngushng factor between Swedsh banks, snce they are provded by jontly owned organsatons. For these reasons, the models and methods developed by Berry and others are not very sutable n a bankng context, where the typcal data set contans only prces, quanttes and cost varables. Another ssue s whether the derved model s a sutable tool for testng competton n Swedsh bank markets, apart from the fact that t accords well wth the avalable data (prces, quanttes, relatve szes, and costs). Some characterstcs of Swedsh bankng mght help to answer that queston. The retal bankng markets n Sweden are deregulated snce The prevous regulatons comprsed a lmt on the total amount of lendng; a lqudty quota that forced the banks to hold large amounts of government and housng bonds; and a regulaton of lendng rates (Englund, 1990). The abolshment of these regulatons meant that the banks were free to decde both the composton of ther balance sheets and ther nterest rates wthout nterference from the Rksbank (the Swedsh central bank). Untl recently, entry to the bank market was severely restrcted due to charter requrements. Only snce 1994 a number of small home-banks have been establshed. The Swedsh bankng system s hghly concentrated wth a concentraton rato for the fve bggest frms of more than 86 percent n both markets. After a deep bankng crss n the begnnng of the 1990s, there were fve major Swedsh banks, see Table 1 n Oxensterna (1999). 8 Each of them has naton-wde branch networks. Each of them can be charactersed as a unversal bank that offers a full 7 Vesala (1998) s the frst known attempt to apply ths modellng technque n a theoretcal model to bankng. 8 Lately, they have become four, snce Swedbank and Förenngsbanken decded to merge n Sprng However, ths event falls outsde the sample perod, whch s from 1989:1 1997:2. 8

9 set of retal servces for ndvduals and corporatons, and a full set of wholesale servces for major corporatons. Another feature s that they all have centralsed fnancal management and treasury functons. On bass of the busness they do and how they operate, t would not be mproper to characterse them all also as commercal banks, even though two of them have ther roots n the long tradtons of savngs banks (Swedbank) and cooperatve banks (Förenngsbanken). Addtonally, there are fundamental asymmetres between the banks. The fve major banks dffer n market shares from about 10% (Förenngsbanken) to about 25% (Swedbank). Cost levels range from about 1.5% to about 3.2%, defned as operatng costs./.total assets (fgures from annual reports 1995). Swedsh banks operate wth a spread between depost and loan nterest rates that s larger than economc costs, see Fg. 1. It s mmedately evdent from the fgure that the dramatc changes n spread over tme cannot be explaned by changes n economc costs, snce the latter are farly constant durng the sample perod. Ths fact mght ndcate that banks exercse ther market power. - Based on these short characterstcs we can conclude that the partcular game theory based olgopolstc model developed above mght ndeed be sutable for an analyss of competton n the Swedsh bankng markets. 3. Testng for Competton n the Swedsh Bankng Olgopoly 3.1 The method of emprcal applcaton The model developed above can be used for a test of competton n a domestc bankng market. The method of applyng the model emprcally comprses the followng steps: 1. Obtan data on output volumes and nterest rates, both regardng banks nterest rates and p M, as well as bank cost data. See secton Estmate the margnal costs, c and c~ respectvely, from a mult-product cost functon augmented wth estmated equty costs and operatng costs for expected loan losses. See secton Estmate the loan market demand functon, as well as the n frm-specfc loan demand equatons. Wth these, and the drectly observed frm szes, the product dfferentaton parameters as well as the market equaton parameters, for (1) are calculated,.e. all market demand parameters are determned. The process s replcated for the depost market. We can specfcally note that 9

10 snce all behavoural equatons are provded n the theoretcal model there s no need for emprcal estmaton of bank-level conduct. See secton Calculate the theoretcal equlbra for all ndvdual banks, usng the estmated parameter values. See secton Compare the observed prces wth the theoretcally predcted prces. Evaluate whch conduct best descrbes the emprcally observed behavour, e.g. by constructng mnmum-squared-error terms. See secton and Calculate welfare effects of devatons from effcent prcng usng the estmated parameter values. See secton Obtanng nterest rate data. Determnng pm Bankng ndustry data are hghly comparable because of the unform regulatory and fnancal reportng requrements. Furthermore, the supervsory actvtes exercsed by regulatory bodes gve some assurance as to the qualty and ntegrty of the data. The Rksbank collects balance sheet data and nterest rate data from all Swedsh banks on a quarterly bass. 9 Data were collected from 1989:1, and the last observaton used here s from 1997:2. Each bank reports balance sheet volumes and nterest rates for three categores of customers: Corporate customers (excludng loans to /from banks and other fnancal corporatons), households (ncludng entrepreneurs wth one-person busnesses), and other customers (ncludes muncpaltes). Each customer category has eght types of accounts. Each bank reports the current nterest rate n percent on each account on the last day of the quarter. Thereafter, the nterest rates are weghted accordng to the balance on each account. However, n ths study, whch s the frst competton study utlsng ths data set, I wll not explot the rchness of the full data set, but aggregate the base data nto two products: Deposts and Loans, respectvely. The calculaton of nterest rates for the aggregates are done wth weghtng accordng to the volumes,.e. wth the same method that s used when the base data are compled. From ths pont of vew, the aggregated nterest rates are comparable between banks. 9 The data comprses only accounts denomnated n the domestc currency and are publshed only as market averages for the fve bggest banks. However, ndvdual bank data have been made avalable for ths study by the Rksbank, on the condton that the dentty of ndvdual banks must reman concealed. There was a change n methodology n the collecton of nterest rate data for deposts from 1993:4, causng a mnor dscontnuty. Further comments on the data set are n Oxensterna (1999). 10

11 Intervews conducted wth fnancal management offcers verfy that banks use a basket of short-term nterest rates to calculate p M, rangng from overnght rates to 3-month money market rates. 10 I have used the 3-month T-bll nterest rate daly averages, compounded to quarterly averages, to calculate p M. 11 Smoothng correctons of p M were undertaken wth a movng average process to adjust for apparent rgdtes n the adaptaton of banks loan stocks and depost stocks to rapdly changng market nterest rates, see Fg. 2. The reason for ths s that parts of stocks have long maturtes, e.g. fxed nterest rate loans. Especally durng the bankng crss n these rgdtes n some quarters lead to an apparently unrealstc dvson of the total spread between loans and deposts Estmatng margnal costs There are sx aspects of the treatment of costs that requre specal comments, snce they wll nfluence the specfcaton of the functons to be estmated:. the possblty that cost complementartes between the two markets can gve rse to strategc lnkages across markets;. the practce of cross-subsdsaton of depost related servces;. that fundng costs are lkely to be nfluenced by market power n depost markets; v. the treatment of loan losses as part of operatng costs; v. the necessty to nclude equty costs n the cost functon; and v. the possblty of rent sharng. 1. The assumpton made above of the absence of cost complementartes s based on emprcal cost studes of banks n varous countres. 12 In Oxensterna 10 Intervews conducted n two Swedsh banks n November 1996 by the author. Intervews conducted by Bergendahl (1989, p 390) ndcate that 3-month money market rates were the prevalent choce by that tme n 11 major Swedsh and UK banks. 11 The Swedsh nterbank market started n 1980 when the frst CDs were ssued. In 1982 the frst T-blls were ssued, whch was the frst step n a development towards a market based fundng of the state debt. A secondary market was establshed and n 1983 the formal regulatons of nterest rates were abolshed n the money market. See Blomberg (1994). One reason for usng the T-bll rate, s that t s less volatle than the nterbank rates. Levels of 3-month T-bll rates and 3-month nterbank rates are qute the same throughout the samplng perod. The tme seres data were obtaned from The Rksbank Statstcal Yearbook. 12 See Vesala (1993, App. 6) for an overvew. The general fndng of the lsted studes s that there s no unanmous evdence of economes of scope. See also Clark (1996) for a contemporary emprcal cost study. He specfcally studes economes of scope, whch are found to be nsgnfcant regardless of bank sze or relatve effcency of banks. In a recent applcaton of the Bulow et al. (1985) model on the bankng ndustry, Vesala (1995, Ch. 4) develops a mult-product conjectural varatons duopoly bankng model wth cost complementartes but ndependent demand functons. In an emprcal applcaton on the Fnnsh bankng ndustry he fnds evdence of postve cost complementartes. 11

12 (1999), there was some evdence presented of slght ds-economes of scope (about 1.5 per cent) n the Swedsh bankng market, whch s of specal relevance here, snce ths paper utlses the same dataset as n that study. 2. One specfc problem n bankng studes s the treatment of costs n the analyss of the banks fund-rasng actvtes. It has been frequently observed that banks don t charge customers the real user costs for depost related servces, e.g. payments servces and ancllary servces. Ths was a behavour that was encouraged by depost nterest rate celngs set by regulatory authortes, common n many countres untl recently. Berger and Humphrey (1992) call ths practce commnglng of mplct revenues, whch are dffcult to dsentangle n emprcal research. 13 The practce of commnglng has lead some researchers to estmate the depost market parameters not on the bass of nterest rates or nterest pad, but on the bass of some quanttatve proxy for the actvty level, such as the volume of transactons, or the number of accounts. 14 The commnglng problem s not necessarly a problem n the model approach used here, snce t s a phenomenon connected wth (sub-)optmsng behavour due to prce regulaton n depost markets, whereas Swedsh bank markets were unregulated n ths respect durng the perod of nvestgaton ( ). 3. In general, when estmatng cost functons, t s assumed that nput markets are compettve, so that nput prces are exogenous. We wll assume that ths s the case for labour costs and other operatng costs. Those cost studes of bankng ndustres, whch defne deposts as an nput, often nclude also depost nterest costs as an nput prce. Snce ths paper ntends to test for competton n the depost market by separatng the output market for depost labltes from the output market for loans, depost nterest rates wll not be ncluded n the estmated cost functon. 4. Loan losses wll here be treated as a normal feature of bankng. In reference to the prcng of loans, ths means that there s a perceved level of expected losses on loan assets,.e. a mean asset rsk, whch s prced nto the loan nterest rate. Ths rsk level s unque for each bank, and for each loan product marketed. Analytcally t forms part of the operatng costs for loans, and need not be ncluded as a separate tem n the statstcal cost functon snce t s by 13 As noted by Fxler and Zeschang (1992), a 100% reserve requrement would force the bank to charge explctly for ts depost related servces. But the reserve requrement s usually a few percentage ponts, whch means that the bank can lend on deposts and rase revenues. These revenues can be pad n the form of a depost nterest rate, or used to subsdse depost-related operatng costs. 14 See, e.g., Berger, Hanweck, and Humphrey (1987); Suomnen (1994); and Vesala (1995). 12

13 defnton allocated to the loan output. As wth other components of the operatng cost, we wll assume that the margnal cost of loan losses s bankspecfc, and constant n the short run. Swedsh banks allocate operatng costs for loan losses as well as equty costs only between loan products 15, therefore they wll be subsequently added to the estmated operatng costs for loans. Ths procedure reduces the number of parameters to be estmated and thus helps to remedy problems caused by a lack of data, snce there are only 33 observatons per bank. 5. An estmate of equty costs s needed,.e. the rsk premum to nvestors for runnng the bank as such. Ths rsk premum s an opportunty cost of captal and reflects the rsk of unexpected losses on assets as a varance of asset rsk, e.g. measured as a varance of asset prcng. Equty costs wll also not need to be ncluded as a separate tem n the statstcal cost functon, snce both the bankng practce and the banks regulators defne the amount of equty as related only to the amount of loans. The calculated equty costs wll consequently also be added to the estmated loan cost functon n a subsequent step Rents earned because of market power leadng to hgh ntermedaton margns,.e. hgh spread between depost and lendng nterest rates, do not necessarly mply a hgh proftablty as measured by some accountng based rato lke return on equty. A hgh spread mght well be accompaned by a low operatng effcency or rent sharng wth labour, whch would result n excess staffng or excess wages, both leadng to hgh operatng costs. In the emprcal applcaton to the fve Swedsh banks below, I wll therefore estmate operatng costs ndvdually, assumng only that there s a common technology n the bankng ndustry. Consderng these remarks, the task s here to determne margnal costs for the dfferent products. In order to do so, a translog cost functon s estmated for the nputs that are not already allocated among the outputs. The ordnary translog cost functon developed by Chrstensen, Jorgenson and Lau (1973) s a second order Taylor expanson seres n output quanttes and nput prces. Usng ths 15 The regulatory practce of allocatng equty costs only among loan products s confrmed also as a bankng practce n Matten (1996) as well as n ntervews conducted by the author wth fnancal management offcers n two major Swedsh banks. 16 See Oxensterna (1999), where the captal asset prcng model (CAPM) s used as a way to measure the rsk premum for nvestors n bank equty, r, by evaluatng a total opportunty cost of equty, pm rm pm. s the stock market beta for the bank s stock, p M s the rsk-free market return for assets of the same duraton as the bank s stock and r M s the return to the aggregate market portfolo of stocks. See Clark (1996) for another emprcal applcaton. 13

14 methodology, the cost structure of mult-product banks can be modelled wth maxmum flexblty, gvng explct recognton to each of the outputs. A translog statstcal cost functon was hence specfed n accordance wth the specfcatons made above: lnoc k1 1 k lnq ln w k j1 2 2 k1 l1 j kl lnq ln w lnq k j ln w l 3 1 k1 2 k lnq ln w k (3) where OC s operatng cost, and j are output ndces for the three outputs, k and l are nput ndces for the two nputs and s the error term. The two major cost tems that are not allocated to ether of the output quanttes are labour costs and other operatng costs 17. The outputs are:. loans n SEK,. deposts n SEK, and. other assets than loans n SEK ( securtes ). Even though securtes gve rse to very low operatng costs compared to other assets, they are ncluded as a separate output for the followng reasons:. they consttute a consderable part of total assets, see Table 1 n Oxensterna (1999);. they contrbute substantally to banks earnngs;. they have a crtcal role n managng fnancal rsks whch means that they can be expected to have a strong mpact on economc costs,.e. opportunty costs for equty captal. Off-balance sheet products are excluded from the outputs snce there s a profound lack of data on them; they are only reported as a net revenue tem n annual and quarterly reports. On the other hand, they comprse a substantal and ncreasngly mportant actvty n Swedsh banks, wth revenues comparable n sze wth the net nterest revenue from on-balance sheet products n later years. In order to approxmate the margnal costs for on-balance products we have to estmate the cost functon for the part of operatng costs that are allocated to produce them. In the absence of data ndcatng otherwse, we wll assume that off-balance sheet products command operatng costs n the same proporton to revenues, as on-balance sheet products,.e. a smlar cost/revenue rato. Ths would be the optmal resource allocaton f banks use the same technology to produce both on- and off-balance sheet products. Hunter et al. (1990) and Hunter and Tmme (1991) do smlar ad hoc allocatons of total costs Other operatng costs (w 2 ) comprses rents, marketng costs, deprecaton allowances and wrtedown of tangble and ntangble fxed assets, IT costs, etc. 18 For a further dscusson on the output vector, see Oxensterna (1999). 14

15 Symmetry requres that j = j for all and j, and kl = lk for all k and l. The followng homogenety restrctons must be mposed on the cost functon n order to get lnear homogenety n the nput prces: 2 k1 k 1; 2 l1 kl 0, k; 2 k1 k 0,. Factor share equatons for the two nputs are obtaned by dfferentatng the cost functon wth respect to nput prces, and usng Shephard s lemma: S k 3 k lnq k 1 2 lnw (4) l kl l where S k s the share of factor costs for nput k of total costs OC. 15

16 The tradtonal statstcal tests used for nference testng requre the underlyng tme seres to be statonary snce regresson wth non-statonary tme seres can gve spurous results. Testng for statonarty was done wth the augmented Dckey-Fuller (ADF) test. Results are reported n Table A2.1 from whch t s evdent that all seres are I(1). All seres were therefore dfferenced once and then brought back to ther mean levels. 19 After addng an error term to (3) and attachng the share equatons, the full dual system s estmated wth the teratve seemngly unrelated regresson (SUR) technque. One of the share equatons s omtted at the estmaton snce the system of share equatons s sngular because of the addng-up constrant, S k = 1. The estmated parameters and ther standard errors and t-statstcs are gven n Table A2.2. Goodness-of-ft measurements for the cost equatons are n Table A2.3. Margnal operatng costs are derved from (3): MOC 3 2 OC OC jq j k lnwk (5) q q j1 k The calculated margnal operatng costs based on the obtaned parameter estmates are reported as averages over tme n Table 1 and as tme seres n Fgures 3 6. For the loan market, the margnal costs are augmented wth normalsed operatng costs for ex ante loan losses from new loans, and wth opportunty costs for equty captal, n accordance wth the specfcatons made above. The methods of estmatng these tems are worked out n Oxensterna (1999). Snce that essay uses the same data set as ths one, the numercal values for these tems are taken from there. As expected, the operatng cost allocated to other assets (q 3 ) s very low. 19 As an alternatve to the more smple technque of dfferencng, Berndt (1991, ch 9) proposes a vector autoregressve process specfcaton n the presence of autocorrelaton. Ths nvolves applyng an autocovarance matrx to the cost functon (4) as well as to the factor share equatons (5). However, the sngularty of the factor share system mposes severe dentfcablty and dagonalty constrants on the autocovarance matrx (p. 478), n essence that all equatons n the whole system have the same lag coeffcent for all lagged varables. Snce ths s a very strong restrcton (op ct), I have refraned from usng the VAR specfcaton n ths case. 16

17 A number of alternatve estmatons were also conducted to check the robustness of the results. (1) Excludng the thrd output from the cost functon nfluenced the ensung margnal cost estmates wth less than plus 5% for the depost market and had a neglgble effect on the loan market estmates. (2) Excludng the cost share equatons from estmaton nfluenced the ensung margnal cost estmates wth between plus 5 to 10% for the two-output model, and wth mnus 5 to 10% for the three-output model. However, the sgnfcance of estmated parameters was lowered. Loan MOC, excl. pred. loan losses Predcted MOC for loan losses MEC for equty captal MEC for loans; sum of col. 2-4 MEC for deposts MOC for other assets Bank Bank Bank Bank Bank Table 1. Margnal costs reported as yearly averages over tme n percent of the amount of total loans, total deposts, and other assets, respectvely. MOC = margnal operatng cost, MEC = margnal economc cost. Values n columns 2, 6 and 7 are calculated from (5) usng the estmated parameter values from (3) and (4). Values n columns 3 and 4 are estmated n Oxensterna (1999) Estmatng demand equatons. Determnng market parameters. The frst stage s to estmate the market demand equatons for the two markets, loans and deposts. 20 The resultng estmates wll allow us to determne the market equaton parameters and for each of the markets. When estmatng loan demand and depost lablty demand functons from tme seres, we agan test for statonarty of all varables wth the ADF test. Results are reported n Table A2.1, from whch t s evdent that all seres are I(1). Addtonally, p M and other seres ncluded n the estmates below are also all I(1). 20 It should be noted, that I estmate demand equatons and not demand elastctes. The reason s that tme seres data wll yeld tme-dependent, unstable values for structural parameters f the parameter estmates from lnear demand equatons are used frst to calculate elastctes and then to deduct parameter values for the theoretcal model. The only alternatve would be to estmate a constant elastcty functon, but that would presuppose a specfc functonal form for market demand, whch s not compatble wth the lnear form of the market demand equatons (1) and (2). 17

18 Economc theory tells us that quantty s the dependent varable n the market demand relatonshp. Ths assumpton was tested wth the Granger causalty test. For both the loan market and the depost market, results are that we can reject the null hypothess that the prce does not Granger cause the market quantty. We are also unable to reject the reverse null hypothess, that the market quantty does not Granger cause the market prce, on the 5 per cent level of sgnfcance (F -test) for both markets. 21 Snce t s clear from both economc theory and from these Granger causalty tests that quanttes are the dependent varables n both markets, I wll follow the Engle and Granger (1987) two step method n order to establsh co-ntegratng vectors and error correcton mechansms (ECM). 22 Economc theory, and the model used here, defnes the demand functon as havng quantty as the dependent varable and own-prce as one of the ndependent varables. Apart from that, there s no theoretcal prescrpton on how a snglemarket demand functon mght be consttuted, for what reason t seems advsable to apply a general to specfc modellng approach. 23 The general model s n an autoregressve dstrbuted lag (ADL) form, where the dependent varable s a functon of ts own lagged values and the contemporary and lagged values of all explanatory varables. For a generalsed demand functon, we get the followng ADL(m,n:k) formula, where m,n are the numbers of lags, k s the number of exogenous varables and the error term u t IID(0, 2 ): q m k n 0 t j 1 j10 q x u (6) t j, t Estmaton technque and results In the current settng, the theoretcal model n Oxensterna (1998) defnes four dfferent equlbrum prce equatons (supply relatonshps), but does not provde any obvous lnk between them that can be used n the estmaton. There s on the other hand no need to make a systems estmaton of the demand equaton and the 21 The tests were made wth one lag for the depost market and four lags for the loan market. There are 33 observatons and the F statstcs are 3.77 for the loan market and 7.13 for the depost market. 22 An alternatve would be the more demandng Johansen (1989) method, bult on the vector autoregressve (VAR) methodology, prmarly desgned for problems where there are no a pror exogenous varables. 23 The general to specfc modellng s proceedng from a farly unrestrcted dynamc model, whch s subsequently tested and reduced n sze by testng dfferent restrctons, see Charemza and Deadman (1997). 18

19 prce equaton smultaneously, snce all parameters that are needed to feed the theoretcal model are defned ether n the demand equaton or n the exogenously determned cost equaton. 24 Demand parameters can be consstently estmated n the presence of unobserved demand factors va the use of tradtonal nstrumental varables methods, such as the two stage least squares method (TSLS), or the generalsed method of moments (GMM). Correlaton between the prce varable and the error term suggests the use of nstruments for prces, assumng that the demand error s uncorrelated wth the nstrument. Demand s specfed to have a nonzero dsturbance, whch s assocated wth unobserved determnants of demand that are correlated across consumers n the market. If these dsturbances are known to the supplers and the consumers (and f demand depends upon them, one expects ths to be so), then equlbrum quanttes and prces wll depend upon the dsturbances. The smultanety problem and the need for alternatves to ordnary least squares estmaton technques arses from ths relatonshp between the dsturbance and prce. Predetermned (.e. exogenous and lagged endogenous) varables and cost functon varables are thus used as supply-shftng nstruments for endogenous prces n order to dentfy demand. Addtonally, t seems relevant to take nto consderaton the possblty that the market conduct has been changng durng the sample perod, snce spread levels have dsplayed a specfc pattern over tme, cf. Fg 1. In order to control for ths, I have added a Lerner ndex, lagged one perod, as a proxy for changes n the market conduct, to the lst of nstrument varables. 25 The loan market ADL structure was tested wth m, n = 5 and the followng extensve range of canddates for exogenous varables: the own-prce (p L, whch s net of the money market rate), the depost market net nterest rate, the short-term money market rate (p M ), the bond market rate for 5-year government bonds (p obl ), the GDP (Y ), the stock market ndex, the consumer prce ndex, and household 24 However, t mght be possble to estmate a smple mark-up supply relatonshp smultaneously wth the demand equaton, n order to mprove the sgnfcance of demand parameter estmates. But snce estmates obtaned from estmatng the demand equatons separately are hghly sgnfcant for all 12 equatons, ths has been deemed not necessary. 25 The Lerner ndex s defned as (p MC)/p. All estmatons were also executed wthout the lagged Lerner ndex as nstrument varable. Results were not much nfluenced: The value of the estmated prce parameter declned wth 2% for the loan market and ncreased wth 3% for the depost market. Another attempt to control for changes n conduct was made by ncludng a market concentraton varable (CR5) as an nstrument varable. Ths had a neglgble effect on the estmates. Also the level of credt losses were tred as an nstrument varable, the dea beng that non-normal credt losses durng the bankng crss would nfluence conduct. Also ths had a neglgble effect on the estmates. 19

20 debts as a percentage of dsposable ncome (Z). The latter varable captures the fact that households lowered ther debt levels from around 140% debt to dsposable ncome n 1989, down to 85% n 1996,.e. a deep change of preferences for havng debt. The lowered household debt levels durng the 1990s are due to some abstruse structural changes takng place n the early 1990 s (see Berg, 1997), wth. a tax reform that together wth other factors rased loan rates after tax wth ca seven percentage ponts from 1990 to 1995,. a credt crunch durng the bankng crss n ,. worsened economc outlooks for households, and v. demographcal changes. The stock of household debt thus dmnshed from 990 bllon SEK n 1989 to 730 bllon SEK n The debt level was n 1997 back at the rato t had before the great expanson of credts commencng n the mddle of the 1980 s. Non-fnancal frms also show a declnng trend of bank loans as a proporton of ther total debt, from around 39% n 1989 to around 29% n Ths trend largely reflects the credt crunch durng the bankng crss, ncludng wrte-offs of bad debt. The declne entrely affects the credt lnes to corporatons, whereas fxed amount loans dsplay a stable growth. There s a steady trend n banks loan portfolos towards more of corporate loans (from 20% of total loans n 1989 to 45% n 1997), whereas corporate credts are declnng somewhat (from 15% of total loans n 1989 to 11% n 1997). Nedersjö (1995) notes that large credt-worthy corporatons ncreasngly have rased fnancal captal drectly on the fnancal markets, leavng banks wth a larger share of comparatvely smaller and possbly rsker corporatons n ther loan portfolos. She suggests that ths could explan the ncreasng (loan) nterest rate spread from , snce corporate credts command a somewhat hgher nterest rate than corporate loans. However, there are no data avalable on the sze dstrbuton of banks corporate loan portfolos. The nterest rate spread s also on the same level n 1997 as t was n 1989, see Fg. 1. I conclude that t s unlkely that structural changes n banks corporate loan portfolos are an mportant factor n explanng the loan prcng conduct durng the samplng perod. Estmaton was done wth TSLS on varables n levels. Predetermned varables were ncluded based on the analyss of varance (ANOVA) technque. The followng ADL structure resulted, wth all parameters beng sgnfcant on the 1% level, except p obl, whch s sgnfcant on the 5% level (wth t -statstcs n parentheses): 26 Data for ths and for the household savngs rato used n the depost equaton below were obtaned from Natonalräkenskaperna and Fnansräkenskaperna. A thorough statstcal and econometrcal analyss of these trends s found n Berg (1997). 20

21 L t L Lt pt 2.38pt 7.11pt 32.5Zt (5.45) (6.84) ( 5.75) (2.18) ( 8.22) (5.48) R 2 =0.92, R 2 adj = 0.91, DW = 1.77 obl M (7) The depost demand functon was tested n a smlar fashon, wth m,n=5 and the followng canddates for exogenous varables: the money market rate mnus the own-prce (p D ), the loan market nterest rate, the short-term money market rate (p M ), the bond market rate for 5-year government bonds (p obl ), the GDP (Y ), the stock market ndex (AFGX), the consumer prce ndex (KPI ), and the household savngs rato (savngs as a percentage of dsposable ncome, X ). The latter ncreases from 5 per cent n 1989 to +8 per cent n 1992, and declnes from The ncrease n savngs s largely due to the factors dscussed above that caused the amount of household debt to declne dramatcally. Estmaton was done wth TSLS on varables n levels, usng predetermned varables, cost functon varables and the lagged Lerner ndex as nstruments. Predetermned varables were ncluded based on ANOVA analyss, after whch the followng ADL structure resulted, wth the prce varable beng sgnfcant on the 1% level (wth t -statstcs n parentheses): D t D (1.20) (2.44) AFGX ( 1.24) t p ( 2.81) t1 D t 4.01X (1.67) 4.38p (1.15) R 2 =0.93, R 2 adj = 0.91, DW = 2.51 t M t Y (2.67) 3.11p (1.78) t3 obl t5 (8) It should be noted, that t was not possble to establsh sgnfcant cross prce effects wth the other market for any of the two markets Co-ntegratng vectors and ndvdual bank markets The concept of co-ntegraton makes t possble to formulate the exstence of an equlbrum, or statonary, relatonshp among tme-seres, although each of them s ndvdually non-statonary. Tme seres contanng unt roots are sad to be contegrated f there exsts a lnear combnaton of them that lacks a unt root. As a consequence, testng for co-ntegraton s to test for a unt root n the resduals of equatons (7) and (8), respectvely, rather than n the consttutng tme seres taken by themselves,.e. the resduals have to be statonary. The hypothess of no co-ntegraton could be rejected for both equatons, wth ADF t -values sgnfcant on the 10 percent level. 21