Working Paper The value of risk: Measuring the service output of U.S. commercial banks

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1 econsor Der Open-Access-Publikaionsserver der ZBW Leibniz-Informaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Basu, Susano; Inklaar, Rober; Wang, J. Chrisina Working Paper The value of risk: Measuring he service oupu of U.S. commercial banks Working paper series // Federal Reserve Bank of Boson, No Provided in Cooperaion wih: Federal Reserve Bank of Boson Suggesed Ciaion: Basu, Susano; Inklaar, Rober; Wang, J. Chrisina (2008) : The value of risk: Measuring he service oupu of U.S. commercial banks, Working paper series // Federal Reserve Bank of Boson, No This Version is available a: hp://hdl.handle.ne/10419/55661 Nuzungsbedingungen: Die ZBW räum Ihnen als Nuzerin/Nuzer das unengelliche, räumlich unbeschränke und zeilich auf die Dauer des Schuzrechs beschränke einfache Rech ein, das ausgewähle Werk im Rahmen der uner hp:// nachzulesenden vollsändigen Nuzungsbedingungen zu vervielfäligen, mi denen die Nuzerin/der Nuzer sich durch die erse Nuzung einversanden erklär. Terms of use: The ZBW grans you, he user, he non-exclusive righ o use he seleced work free of charge, erriorially unresriced and wihin he ime limi of he erm of he propery righs according o he erms specified a hp:// By he firs use of he seleced work he user agrees and declares o comply wih hese erms of use. zbw Leibniz-Informaionszenrum Wirschaf Leibniz Informaion Cenre for Economics

2 08 4 The Value of Risk: Measuring he Service Oupu of U.S. Commercial Banks Susano Basu, Rober Inklaar, and J. Chrisina Wang Absrac: Raher han charging direc fees, banks ofen charge implicily for heir services via ineres spreads. As a resul, much of bank oupu has o be esimaed indirecly. In conras o curren saisical pracice, dynamic opimizing models of banks argue ha compensaion for bearing sysemaic risk is no par of bank oupu. We apply hese models and find ha beween 1997 and 2007, in he U.S. Naional Accouns, on average, bank oupu is overesimaed by 21 percen and GDP is overesimaed by 0.3 percen. Moreover, compared wih curren mehods, our new esimaes imply more plausible esimaes of he share of capial in income and he reurn on fixed capial. JEL Classificaions: E01, E44, O47 Susano Basu is a professor of economics a Boson College and a research associae a he NBER, Rober Inklaar is an assisan professor in he faculy of economics and business a he Universiy of Groningen, and J. Chrisina Wang is a senior economis in he research deparmen a he Federal Reserve Bank of Boson. Their addresses are, respecively, susano.basu@bc.edu, r.c.inklaar@rug.nl, and chrisina.wang@bos.frb.org. We would like o hank Barry Bosworh, Erwin Diewer, John Fernald, Alice Nakamura, Marshall Reinsdorf, Paul Schreyer, Kevin Siroh, Jack Triple, Frank Wykoff and paricipans a he 2006 NBER/CRIW Summer Insiue workshop, for helpful conversaions and commens on he issues addressed in his paper. This paper, which may be revised, is available on he web sie of he Federal Reserve Bank of Boson a hp:// The views expressed in his paper are solely hose of he auhors and are no hose of he Federal Reserve Sysem or he Federal Reserve Bank of Boson. This version: May ; Firs draf: July 12, 2006

3 I. Inroducion Services are an increasingly imporan par of modern economies, boh in erms of size and for heir conribuion o economic growh. However, he oupu daa for many of hese services is nooriously weak, and his is paricularly he case for banking. 1 This makes i hard o deermine he sources of economic growh and even he size of he economy. A major barrier o progress in his area has been he inadequacy of producion models for banks. Wang, Basu, and Fernald (2004, WBF henceforh) propose a generalequilibrium model of ineracions beween banks, firms, and consumers o remedy his problem. 2 In his paper we esimae he value of oupu of U.S. banks, following he prescripions of he WBF model for he period We find ha hese new esimaes differ considerably from hose based on curren Naional Accouns mehods: bank oupu is reduced by 21 percen and GDP is reduced by 0.3 percen. We argue ha hese new oupu esimaes imply a more plausible capial share in income and inernal rae of reurn on fixed capial han curren esimaes. Measuring he value of bank oupu is challenging, since much of bank service oupu is no explicily priced. Insead, he implici charges for financial services are bundled wih ineres flows beween banks and heir cusomers, chiefly borrowers and deposiors. WBF show how implici service revenue can be unbundled from gross ineres flows by applying sandard heories of financial inermediaion and asse pricing. In paricular, he WBF model adops he esablished view ha he main service provided by banks in making loans is reducing asymmeric informaion beween borrowers and lenders. To ha end, banks evaluae he risk characerisics of each loan and monior he borrower. Insead of receiving an upfron fee for he services, an opimizing bank can charge a higher ineres rae han he rae available on a marke securiy wih oherwise he same risk aribues. 1 See, for example, Griliches (1992, 1994), Triple and Bosworh (2004), Diewer (2008), and Inklaar, Timmer, and van Ark (2008). 2 WBF (2004) build on he banking model of Wang (2003) and pu i in a general equilibrium framework. 1

4 These models hus make clear he role of risk in inferring banks income from services. The implici revenue from screening and monioring services should equal he spread of he gross loan ineres rae over he yield on an equally risky fixed income securiy, no a risk free securiy such as a Treasury bill or bond. This accouning mehod in essence reas he loan risk premium as par of he borrowing firms cos of capial and hence as par of households capial income heir compensaion for bearing risk. Tha is, he risk premium on loans is only a ransfer, hrough banks, of propery income from borrowers o savers, and is no par of banks value added. A key advanage of his mehod is ha i leads o a uniform reamen of risk premia on all deb insrumens, so ha nonfinancial firms oupu is invarian o heir source of deb finance markes or banks. The risk premium on marke deb (for example, corporae bonds) has always been accouned for as par of he producing firms cos of capial, and hence households capial income. The risk premium on bank loans should be reaed in he same way. This conrass wih he ypical saisical pracice in OECD counries. According o curren naional accouns guidelines, banks implici revenue from lending services (per uni of loan balance) equals he spread beween he gross loan ineres rae and a risk free rae. 3 This in effec reas loan risk premia as par of banks insead of as he borrowing firms value added. A producing firm s measured oupu will hus fall if i swiches from marke deb o bank loans, or will appear o rise if i sars issuing bonds raher han borrowing from banks. The conras wih he curren pracice can also be seen from he user cos perspecive. This model implied accouning mehod is shown o be fully consisen wih he user cos of capial framework in fac, i is shown o be an exension of ha framework o ake explici accoun of uncerainy. 4 The yield on he equally risky deb can be regarded as he user cos of funds, he so called reference rae. In conras, ypical naional accouns currenly use a risk free reference rae. 3 See SNA (1993, 6.128). 4 Diewer (1974) was one of he firs o inroduce his framework. 2

5 In his paper, we implemen he new model implied measure of bank oupu for U.S. commercial banks. To highligh he role of risk, his paper focuses on new esimaes of he nominal value of services associaed wih loans. 5 This is where our risk based, user cos approach differs subsanially from curren pracice. We also esimae he nominal oupu of services o deposiors. No surprisingly, our resul coincides wih ha of he naional accouns for he bulk of deposis in he Unied Saes, for which deposi insurance makes a risk free reference rae appropriae. 6 Our empirical esimaes use daa for U.S. commercial banks from 1997 o Implemening he model implied oupu measure calls for informaion on boh he acual ineres rae on bank loans and he ineres rae on marke securiies wih he mos comparable risk characerisics. In pracice, maching bank loans o marke securiies is far from perfec. Given he many daa limiaions, we srive o be conservaive wih our esimaes of he risk premia; his approach should yield a relaively generous esimae of nominal bank oupu. Despie his conservaive approach, we show ha impued bank oupu is oversaed by 45 percen on average in he U.S. naional income and produc accouns (NIPA). This ranslaes ino an oversaemen of oal bank oupu of 21 percen, since services associaed wih originaing loans ha remain on bank balance shees comprise only par of bank oupu. 7 Neing ou he lending services o nonfinancial firms, which are couned as inermediae inpu, his finding implies ha U.S. GDP would have been 0.3 percen lower on average over he period of 1997 o 2007 if bank oupu had been measured correcly. Finally, reducing he impued value of bank lending services o businesses also implicily correcs nominal value added in indusries where 5 Also, we consider only radiional loan making and deposi aking aciviies, bu none of he novel aciviies such as securiizaion and he underwriing of derivaives. See Inklaar and Wang (2007) for an accouning of real bank oupu from all aciviies. 6 In mos counries, deposis up o a cerain amoun ($100,000 in he Unied Saes) are insured by he governmen, so risk is no a facor; see, for example, Gropp and Vesala (2001). However, our reasoning dicaes a differen approach in he case of uninsured deposis, such as jumbo cerificaes of deposi. 7 Nowadays, many loans are securiized and sold o ouside invesors. In 2007, securiizaion oupu was equal o abou half of radiional loan oupu. 3

6 firms borrow from banks almos every indusry since our measuremens imply ha borrowing indusries are using fewer inermediae inpus. Models ha consider risk explicily are more plausible han hose ha do no, especially when he models concern he operaions of financial inermediaries, whose chief ask is assessing and miigaing he riskiness of heir porfolios. This is our main argumen for preferring our new measure of bank oupu over curren saisical pracice. Moreover, a number of plausibiliy checks also argue in favor of our oupu measure. In paricular, we compare he share of capial in banks value added wih he share of capial in he oal privae economy and oher indusries. Under curren pracice, banks show up as more (fixed) capial inensive han peroleum refining, whereas our esimaes sugges a capial share closer o he share of capial in he overall privae secor. In addiion, curren pracice implies an inernal rae of reurn on fixed asses ha is 8 percenage poins higher han he rae in he privae secor as a whole. 8 Our new esimaes imply an inernal rae ha is, on average, slighly lower han he rae in he overall privae secor. This is more consisen wih he basic principle ha he inernal rae of reurn on fixed asses should no vary much across indusries as long as capial is mobile. The res of his paper proceeds as follows. We begin wih a brief review of he heoreical analysis underlying he new oupu measure, focusing on he role of risk. We hen discuss daa and presen our resuls. We conclude wih a summary, and discuss direcions for fuure research. II. The Economic Model of Banks This secion reviews briefly he heory of banking oupu based on dynamic sochasic opimizing models. Ineresed readers who wish o pursue he heoreical issues in greaer deail are referred o Wang (2003), WBF (2004), and Basu and Wang (2007). 8 Differences in sysemaic risk beween indusries can explain differences in he inernal rae of reurn; see Secion II. However, our loan risk premium esimaes and sock marke beas sugges ha a 10 percen risk premium is exreme. 4

7 II.A Implici Services in Bank Lending Before aemping o measure a concep, one mus firs define i accuraely. So, wha is he oupu of banks ha corresponds o he asse side of heir balance shee? Wang (2003) and WBF (2004) answer his quesion wih dynamic models of opimal bank operaions under uncerainy. 9 By embedding bank operaions wihin he conex of compeiive financial markes, hese papers show ha he value added of banks lies solely in resolving informaion problems and processing ransacions. In paricular, key o bank lending is screening and monioring aciviies ha miigae adverse selecion and moral hazard problems, respecively, wih regard o borrowers crediworhiness. 10 All of hese services are generaed hrough a producion process ha uses primary inpus of labor and capial, as well as inermediae inpus (such as office supplies and uiliies). More imporanly, Wang (2003) demonsraes he separabiliy beween he flow of financial services and he sock of financial insrumens. By naure, financial services are inangible; financial insrumens such as loans are ofen he mos angible manifesaion of hose services. However, Wang (2003) and Basu and Wang (2007) show ha here is lile heoreical basis for an invarian value mapping beween flows of bank services and socks of heir asse holding, le alone a fixed proporionaliy beween he wo. This conclusion holds wheher he sock is measured by book value or by marke value. The separabiliy of service flows from asse balances is becoming increasingly eviden as more financial firms provide financial services wihou holding he associaed securiies, and vice versa. For insance, finance companies such as GMAC specialize in loan originaion, as well as providing bookkeeping and paymen services o boh he 9 WBF (2004) exend Wang s parial equilibrium model o a general equilibrium seing, and demonsrae ha all he qualiaive resuls in Wang (2003), summarized in his paper, coninue o hold. 10 Banks role in resolving informaion asymmery is well recognized. For example, Fixler (2004, p. 223) observes ha hese [financial] services have o do wih overcoming he problems of asymmeric informaion, a view ha is widely acceped in he financial economics lieraure. The role of banks as a lender arises ou of he privae naure of he lending ransacion he bank reduces he problem of adverse selecion [and] he problem of moral hazard. These are he financial services ha Fama (1985) and ohers idenified when hey argued ha banks were special. 5

8 borrowers and he holders of asse backed securiies, wihou holding much, if any, of he underlying loans on heir balance shees. On he oher hand, a growing number of small and medium size banks hire specialized firms o originae and service heir residenial morgage loans (Bergquis, 2002). The fundamenal disincion beween service flows and asse balances may be less obvious in radiional bank lending, where he inermediary boh performs he services and holds he asses. Bu i is no less inuiive, once we focus on he underlying services. For insance, originaing a $1 million residenial morgage almos cerainly involves much less han 10 imes he services involved in originaing a $100,000 morgage, given he ready availabiliy of individuals credi scores. Fixed proporionaliy beween services and balances is even harder o defend in he case of ransacion services o deposiors. The lieraure on paymen services suggess ha he amoun of work involved in clearing checks is independen of he dollar figure of he check or he accoun balance. 11 The same is rue for many oher deposior services (for example, issuing money orders, ransferring funds, ec). II.B Bank Loan Ineres Raes and he Role of Risk One cenral elemen of he service cenric noion of bank oupu in Wang (2003) and WBF (2004) is ha he flow of services is disinc from he pure reurns ha accrue o he sock of financial asses. This pure reurn is he user cos of funds, defined as he (risky) fuure payoff from invesmen ha compensaes suppliers of funds solely for he forgone curren consumpion and no for any aached services. This can be viewed as an exension of he concep of user cos of money à la Barne (1978) ha akes accoun of he fac ha he reward o mos invesmen is uncerain. Tha is, in a world wih risk, he so called opporuniy cos of money is comparable across securiies only afer adjusing for risk. So he reurn on a risk free securiy is no he appropriae opporuniy cos for risky securiies. 11 See, for example, Kimball and Gregor (1995) and Radecki (1999); boh presen indusry daa on he average and marginal cos of processing a paymen via various means ha make no reference o he size of he paymen. 6

9 The implicaion for he measuremen of bank oupu is ha, o esimae he nominal value of he services provided bu no explicily charged for, he pure cos of funds mus be need ou of a bank s oal income, which is a combinaion of he wo income sreams. To impue he pure cos of funds on a loan, one should use he rae of reurn on a deb securiy subjec o he same risk, bu wihou any services aached. Wha deermines his risk adjused rae of pure reurn ha invesors expec on a financial securiy? Applying sandard heories of asse pricing, Wang (2003) and WBF (2004) show ha he pure reurn depends posiively on he correlaion beween a securiy s reurn and sysemaic facors (such as he represenaive consumer s marginal uiliy in he consumpion capial asse pricing model (CAPM)). 12 For fixed income securiies such as loans, his means ha he expeced rae of reurn demanded by a lender depends on how a deb s prepaymen risk, defaul risk, ec. covary wih macroeconomic condiions. The ineres rae ha he borrower mus promise in he conrac o pay if he remains solven ex pos, however, is higher, and rises wih he probabiliy of his defaul boh he sysemaic and he idiosyncraic componens in order o offse he posiive odds of oucomes where he borrower becomes insolven ex pos. The disincion beween expeced rae of reurn and he promised yield on a deb is imporan, so we shall elaborae somewha. 13 The former is he mean rae of reurn required by a lender given her ex ane expecaion of he deb s payoff; i should on average equal ex pos realized reurns. The laer is he ineres rae a borrower promises ex ane in he deb conrac (also referred o below as he conracual rae) and is obligaed o pay if solven ex pos. 12 A no so obvious implicaion is ha, if a securiy s reurn does no vary wih sysemaic facors, hen is expeced rae of reurn is he risk free rae, no maer how volaile is reurn. This is of course predicaed on he assumpion ha he markes are complee once he asymmeric informaion problems are resolved. Oherwise idiosyncraic risk also maers for a securiy s expeced rae of reurn. 13 See Wang (2003) for a more deailed explanaion of he disincion beween he wo conceps, which is also shown o be equivalen o he disincion beween defaul and risk premia. 7

10 M Le R n, denoe he yield o mauriy promised a ime on a marke deb securiy wih mauriy n and no services aached. Then, i can in general be expressed as: 14 R = r + r + d, (1) M F P e n, n, n, n, F where r n, is he yield on a deb of he same mauriy bu no subjec o defaul risk, nor wih any embedded opions. 15 U.S. Treasurys are he bes example. They are ypically F considered risk free in ha hey earn a guaraneed reurn, r n, P r n,, if he deb is held unil mauriy. 16 This reurn only compensaes he lender for sacrificing curren for fuure consumpion. In addiion o he risk free reurn, he yield on deb wih posiive defaul e r n, d n, risk also conains a premium for risk, P, and a premium for defaul,, which is he exra reurn ha mus be promised o invesors because hey are paid in full only when here is no defaul ex pos. If he probabiliy of defaul or loss upon defaul correlaes wih he risk facors priced in he marke, invesors will also demand ha he average reurn received ex pos exceed he defaul free yield; ha spread is for more deails.) in (1). 17 (See Wang, 2003, So he expeced rae of reurn required on his marke deb, denoed as M r, equals: 18 r = r + r = R d M F P M M, e. (2) 14 To be precise, his equaion is exac only for insananeous reurns under coninuous compounding. In coninuous ime models, he yield o mauriy should equal he inegral of insananeous yields over he mauriy of he deb securiy; see Duffie and Singleon (2003), a sandard reference for pricing defaulable deb securiies. Wang (2003) and WBF (2004) apply a simple discree ime version. 15 Yields on bonds mus be adjused for he embedded opion o be comparable wih hose on opion free deb insrumens. Bonds wih prepaymen risk, such as morgage based securiies, are essenially bonds wih an embedded call opion, as borrowers are graned he opion o pay off he deb (ha is, call he bond) before mauriy. 16 Noe ha even for his ype of deb here is sill ineres rae risk, ha is, he reurn is almos surely uncerain if one sells i prior o he mauriy dae. 17 Under cerain condiions, his is equivalen o he drif adjusmens of he defaul inensiy s diffusion sae variables in coninuous ime models, see Jarrow, Lando, and Yu (2005). 18 For breviy of exposiion, from now on we omi he subscrip denoing mauriy, unless confusion is likely. 8

11 Now consider he decision facing an opimizing bank ha is considering wha ineres rae o charge when making a loan wih he same (sysemaic) risk profile as he above marke deb. In addiion o covering he cos of funds, he bank needs o charge implicily for he services i performs (for example, screening and monioring). As shown in Wang (2003), he opimal required rae of reurn on a loan ( service charge, is: A M S F P A r ), including he implici r = r + r = r + r + r S S, and r A = cμ, (3) where S r represens wha we shall call he service spread, ha is, he rae incremen defining he exra ineres ha mus be charged o compensae he bank for processing he loan. The opimal S r saisfies he condiion ha he exra ineres receip (ha is, S r imes he loan balance A) equals he marginal processing cos of a loan, c, imes he opimal markup, μ (deermined by compeiion in he loan marke). Then, he reference rae for a porfolio comprising N loans of varying mauriies and made in various periods, is a weighed average of he reference raes of he individual loans: 19 r ω r τ n τi, (4) M N Mi = 1,,0, i i τi n = i i i where ωi is he porfolio weigh of loan i, τi is he period when loan i s ineres rae was se, and ni is he mauriy of he loan. Empirically, (4) is especially relevan for loan ypes ha ypically have long mauriies, such as real esae loans. The opimizing bank hen ses he conracual ineres rae, A M S A, e M, e ( ) A R, accordingly: 20 R = R + r + d d. (5) This highlighs he fac ha he reference marke securiies are only required o have he same sysemaic risk as he loans; he securiies can have a differen expeced probabiliy of defaul or prepaymen han he loans. We will see ha he accuracy of our empirical esimaes varies posiively wih he degree o which each caegory of loans and he 19 See WBF (2004) for discussions of he iming mismach beween screening services and loan ineres flow. 20 S A M A A, e M M, e This is because r = r r = ( R d ) ( R d ). 9

12 reference securiies used have he same sysemaic risk despie he securiies generally lower defaul probabiliy. II.C The value of bank oupu The derivaions in he previous secion imply ha, on average, a bank s nominal oupu of implici lending services o borrowers can be impued as 21 ( ) A S A M Y = r A = r r A. (6) According o he nomenclaure of he 1993 Sysem of Naional Accouns (SNA93), M r is he reference rae. Previous discussions make i clear why he reference rae should be risk adjused. Consequenly, he reference rae varies, depending on risk characerisics of he financial securiy or porfolio of securiies associaed wih he services considered. However, he U.S. Naional Income and Produc Accouns (NIPA) currenly impue bank services o borrowers using a nearly risk free rae as he reference rae: ( ) ( ) A F P S A P r r A = r + r A = Y + r A. (7) The value of oupu impued according o (7) will oversae he acual value of service oupu. The informal jusificaion for (7) is ha r A P is regarded as compensaion for rendering a so called risk bearing service. Wang and Basu (2007, secion 3.4) discuss a lengh why risk bearing is no a producive service according o he concepual framework of SNA93 and, more imporanly, why he NIPA s impuaion resuls in inconsisen accouning of he fund using firms oupu, by making i depend on heir source of funding (ha is, he public deb marke versus banks), even given idenical underlying rue oupu. The value of implici deposior services can be impued in a similar manner o he new way we impued he value of implici lending services. Le D denoe he deposi balance, D r he ineres rae paid, and m r he corresponding reference rae (ha is, he reurn on a marke securiy wih he same risk). Then nominal oupu of deposior services is 10

13 ( ) D m D Y = r r D. (8) For insured deposis in he Unied Saes (up o $100,000 per individual per bank), he relevan marke rae is he risk free (Treasury) rae, r m = r. For he remaining, F uninsured, deposis porfolios. r m > r F, because he holders are exposed o some risk in bank asse Noe ha equaion (6) implies ha here are zero implici services provided o asse issuers (ha is, Y A = 0), if a bank passively holds marke securiies in is invesmen porfolio, since r A = r M. Likewise, (8) implies zero implici services (ha is, Y D = 0) provided o holders of bank erm liabiliies (commercial paper, marke bonds, and privaely placed bonds), since he ineres rae paid equals he reference rae ( r D m = r ). Also noe ha under virually all circumsances (ha is, whenever here are equiy holders), r M in (6) is greaer han m r in (8), because bank asses are ypically riskier han bank liabiliies. In oher words, he reference raes for impuing lending and deposior services almos always differ by a posiive margin. Figure 1 illusraes he impued nominal oupu value of implici bank services. Noe ha only par of a bank s ne ineres income consiues nominal oupu of bank services; he remainder corresponding o he risk premium, ( r M F r )A is excluded. 22 This is precisely because he reference rae for lending services generally exceeds ha for deposior services. The risk premium, along wih acual ineres expenses on bank liabiliies, consiues a pure ransfer of capial income. I is par of he facor income generaed by he capial used in he borrowing firms producion or in he consumpion of consumers. This facor income is hen ransferred from he end users of funds o he ulimae suppliers of funds he bank shareholders. Only when all invesors are risk neural or all risk is idiosyncraic will his risk premium disappear. Figure 1 illuminaes 21 See WBF (2004) for a deailed discussion of how he acual value in each period deviaes from his average. 22 As is shown, he balance of loans exceeds ha of deposis, wih bank equiy making up he difference. Also noe ha his figure is a simplified version of Figure 1 in Wang (2003), as i ignores risk premia on deposis due o deposi insurance or uninsured deposis. Tha is, i ses m r = r F, and oversaes deposior services. 11

14 how our model based oupu measure differs from he NIPA s curren measure, which uses a (nearly) risk free rae as he single reference rae (see Fixler, Reinsdorf, and Smih, 2003). As we have argued, he NIPA s measure oversaes bank oupu by he amoun of he risk premium. In he remainder of his paper, we discuss how o esimae he risk premium and is quaniaive impac on he measured oupu of he U.S. commercial banking indusry. III. Daa and Empirical Esimaes of Bank Service Income III.A Daa Sources Accouning daa for individual commercial banks come from he Consolidaed Repors of Condiion and Income (he Call Repors). 23 These are quarerly financial saemens filed by banks o heir regulaors and made available by he Federal Reserve Bank of Chicago. Our empirical esimaes use daa from he second quarer of 1997 o he fourh quarer of 2007, mosly because some of he necessary variables are no available for earlier years. The Call Repors daa are used o esimae he average ineres rae earned by banks on each caegory of loans and deposis. The Call Repors also provide daa on he repricing period of various caegories of loans. Yields on U.S. Treasury securiies of varying mauriies are from he Federal Reserve Board, 24 as are yields on commercial paper of he op wo iers of raings; yields on he remaining iers are from Bloomberg. Yields on morgage and asse backed securiies are based on indices consruced by Ciigroup Global Markes and Merrill Lynch. Finally, ineres raes charged on 23 These correspond o he forms FFIEC ; see for deails. 24 Release H.15; see hp:// We use he consan mauriy series. 12

15 commercial and indusrial (C&I) loans for cliens wih various risk profiles come from he Federal Reserve Survey of Terms of Business Lending. 25 III.B Implemenaion Overview The Call Repors afford no direc observaion of eiher he expeced rae of reurn ( he promised yield on loans ( R ). Wha can be compued is he average ineres rae A acually received by banks on each individual caegory of loans and securiies, ha is, A R d +, where d + 1 is he acual rae of loan defaul in period Rearranging (5), A A 1 can be expressed as S A A M M, e A A, e A r ) or r = ( R d ) ( R d ) + ( d d ). (9) Thus, he service spread can be inferred from he realized loan ineres rae and he mached marke yield, afer correcing for he deviaion of he acual from he expeced rae of loan defaul. This is our basic formula for impuing he value of implicily priced services o borrowers. The reference ineres rae for he loan porfolio associaed wih each ype of borrower services is approximaed using he expeced rae of reurn ( r = R d M M M, S r e ) on marke deb wih he mos similar risk. The Call Repors daa dicae ha we can mach loans wih securiies in only a few broad caegories: residenial morgages wih morgage backed securiies (MBS), consumer loans wih asse backed securiies (ABS), and C&I loans wih commercial paper. Each M r we use is a (noisy) proxy for he rue reference rae on he mached caegory of bank loans, since we observe none of he risk composiion and only limied informaion abou he mauriy of he loans and hus canno assess he accuracy of he mach. Neverheless, using marke deb reurns almos 25 Release E.2; see hp://federalreserve.gov/releases/e2/. For more informaion on banks inernal risk raing, see daa repored in Form FR2028a/s, available from 1997 onward (see Appendix A for furher deails): hp:// a/s. 26 This expression is sricly correc only for one period bonds, oherwise he realized reurn also includes a erm reflecing he change in bond price due o flucuaions in yield. See furher discussion below and chaper 10 of Campbell, Lo, and MacKinlay (1997). 13

16 surely underesimae he rue risk premium on loans, since marke securiies on average have much lower realized defaul raes and are herefore likely o command lower risk premia as well (see deails in he nex subsecion). 27 Anoher issue is ha in each period we observe only he average ineres rae earned by a bank on is porfolio of a given ype of loans, regardless of when he loans were priced. In paricular, for loans wih long periods of fixed raes, like morgages, his loan porfolio will also include loans ha were priced years ago. Comparing his average rae wih curren marke raes o impue he service spread is obviously no correc. Unforunaely, he daa necessary for a proper maching gross flows of new loans originaed and old loans paid off or rese a a new ineres rae in each period are no available. So, raher han rying o make rough assumpions abou he composiion of he loan porfolios, we compare he average ineres rae o he curren marke reference raes in our baseline esimaes. 28 The one excepion is C&I loans, because we can use daa from he Survey of Terms of Business Lending, which provides daa on he ineres rae charged on new C&I loans originaed by commercial banks in he survey week. In his case, we can mach he iming of bank loan ineres raes and he marke rae. While sill no perfec, his maching likely provides a more accurae esimae of acual service spreads han could be obained by using he difference beween average bank loan raes earned and curren marke reference raes. Esimaing deposior services according o equaion (8) is sraighforward, especially once we assume m r = r F. This assumpion is necessary, because he Call Repors do no provide adequae daa for esimaing he risk premium on uninsured deposis, whose share is, forunaely, modes. The following subsecions deail he esimaion of implici incomes from bank services. 27 I is possible, bu unlikely, ha he sysemaic componen of risk, which deermines he risk premium, is sill he same for loans and he mached securiies. 28 This means ha we esimae a marke rae ha would be he heoreically correc reference rae if all he loans in he porfolio had been (re)priced during he curren period. 14

17 III.C Esimaes of Risk Premia To faciliae comparison wih he NIPAs curren measure of bank oupu, we esimae separaely he wo componens he risk free rae and he risk premium of each reference rae for loans. Rearranging equaion (2), he risk premium on a reference securiy can be expressed as r = r r = R r d P M F M F M, e. (10) Daa indicae ha he uncondiional esimae of d M, e, equal o he long erm average of realized d s, is exremely low for cerain caegories of marke deb, such as commercial paper. 29 For example, according o Moody s, he hisorical average defaul raes of commercial paper wih he op wo raing grades (P 1 and P 2) are basically nil. 30 So, for cerain caegories of loans, when such corporae deb is used as he reference securiies, a reasonable esimae of P r is simply he yield spread beween such deb and he mauriymached Treasury securiies (ha is, R M r F ); he upward bias from ignoring d M, e should be negligible. We compue he respecive risk premium on C&I loans and consumer loans, as follows: Firs, o gauge he defaul risk and mauriy composiion of C&I loans and find he bes mach of marke securiies, we rely on he Federal Reserve s Survey of Terms of Business Lending (STBL). 31 Daa from his survey indicae ha abou 70 percen of C&I loans are repriced in less han a monh and over 90 percen less han a year. This suggess ha commercial paper is a more appropriae ype of reference securiy han corporae bonds. On he oher hand, using he yields on commercial paper likely resuls in 29 e The condiional esimae of d is procyclical. 30 For a 180 day period, hese risks are esimaed o be 0.00 percen for P 1, 0.02 percen for P 2, 0.12 percen for P 3, and 0.43 percen for No Prime (NP) I is possible ha he loans covered in he survey are sill no represenaive of he banking indusry as a whole, or a all imes. Bu his is he bes micro daa source available, and here is no reason o suspec sysemaic bias. 15

18 conservaive esimaes of he risk premium on C&I loans, since C&I loans end o have boh longer average mauriies and greaer defaul risk han commercial paper. 32 Among he four risk caegories repored in he STBL, wo have readily available reference marke securiies. Firs, he minimal risk classificaion explicily requires ha he loans be o cusomers wih a bond raing of AA or higher; such firms generally also carry a P 1 shor erm raing by Moody s. Second, he low risk caegory requires cusomers o have a BBB bond raing, which maps ino a P 2 raing by Moody s. 33 However, he reference securiies for he oher wo, relaively higher, risk caegories, moderae risk and oher, are no as clear. So we assume ha he higher ineres rae relaive o he low risk caegory is enirely due o greaer risk bu no o exra implici service revenue. 34 Wih esimaes of he risk premium for each of he four caegories of C&I loans, we calculae a weighed average premium using he volume of new loans in each caegory, and we subrac his from he overall C&I loan ineres rae obained from he STBL. The risk premia of consumer insallmen and credi card loans are esimaed using Merrill Lynch s (ML) asse backed securiies (ABS) indices for fixed rae auo and credi card loans, respecively. A weighed average yield is compued based on he share of credi cards versus all oher loans in he porfolio. The average raing of he ABS underlying he wo indices should be beween BBB and AA, since boh hese indices are componens of ML s ABS maser index. 35 Following his procedure almos cerainly 32 I does no improve he mach o use asse backed commercial paper (ABCP) as he reference for hose bank loans ha are secured. The yields on ABCP and on regular nonfinancial CP are virually he same unil July, 2007, when he subprime induced financial urmoil broke ou in he Unied Saes. See Figure A.3 for a comparison of risk premium esimaes using corporae bonds versus commercial paper as he reference securiies. 33 AA and BBB are bond raings by S&P, equivalen o raings of Aa2 and Baa2 by Moody s. The mapping beween long and shor erm raings can be found a hp://federalreserve.gov/releases/cp/abou.hm. 34 This will likely oversae he risk premium, since common sense suggess ha riskier loans require more screening and monioring, and he cos of servicing hese riskier loans mus be recouped. 35 We choose no o use a general index for he ABS marke because, beween 2003 and he firs half of 2007, a rapidly growing share of he marke comprised securiies backed by subprime and 16

19 yields a raher conservaive esimae of he average risk premium on he consumer loans held on he books of banks because o receive invesmen grade raings, he ABS invariably mus obain credi enhancemen o ensure ha heir holders will be subjec o minimal credi risk. 36 Moreover, even a he original loan level, he loans kep on banks books may be riskier han he ones ha are securiized. 37 In erms of mauriy, however, no daa are available o gauge how well on average he indices consiuen bonds mach consumer loans held by banks. 38 To esimae he risk premium on residenial morgage loans, we use he mauriyweighed redempion yields on MBS issued by governmen sponsored enerprises (GSEs, such as Fannie Mae and Freddy Mac) as he reference rae. The mauriy daa are available in he Call Repors (schedule RC C) since he second quarer of Again, his reference rae likely gives a conservaive esimae of he risk premium on hese loans, since agency MBS are no subjec o defaul risk bu only o prepaymen risk: morgage holders may repay heir loans in par or in full ahead of schedule. 39 More imporanly, for his reference rae o be a good proxy for he pure (risky) reurn in he loan raes, a subsanial fracion of he morgage porfolio mus be repriced in he period of Al A morgage loans from less han 20 percen in 2003 o over 30 percen in 2006, according o he Securiies Indusry and Financial Markes Associaion. 36 Credi enhancemen can be obained in a variey of ways. I can be purchased from hird paries such as insurance companies, or creaed inernally by forming a sufficien loss absorbing cushion of junior claims wihin he ranche srucure wrapped around a pool of asses in a manner ha enables he issued ABS can obain senior raings. 37 Using securiizaion o save on capial requiremens is a form of regulaory arbirage. This may no be a major concern; for example, Calomiris and Mason (2004) find lile evidence of his moivaion in banks ha securiize credi card loans. 38 Since hese are indices for fixed rae ABS, heir average mauriy may exceed ha of he underlying consumer loans, some of which carry floaing raes. 39 All conforming residenial morgages ha back he agency MBS carry no prepaymen penalies. This, in essence, grans he borrowers an implici call opion ha allows a borrower o buy back (ha is, o pay off) he loan a face value. The opion is mos likely o be exercised when a loan s marke value exceeds is face value, ha is, when he curren period morgage rae falls below he loan s conracual ineres rae. See, for example,. Dunn and McConnell (1981) or Kau e al. (1992) for he magniude and deerminans of prepaymen risk. 17

20 consideraion. This iming requiremen is made clear in equaion (9): he reference rae should be for he period when a loan s ineres rae was se or las rese. 40 To gauge he exen o which he above baseline esimaes are affeced by he ineres rae iming mismach, a problem ha we suspec is paricularly acue for longerm, fixed rae loans, such as many residenial morgages, we also compue he risk premium on morgage loans using a series of moving averages of curren and pas (up o five years) marke raes. For he period , he average service spread on morgage loans using curren marke raes is 0.80 percen, while ha using he 5 year moving average raes is 0.69 percen. Service spreads esimaed using shorer moving averages lie in beween. A maximum effec of 0.11 percenage poins seems modes compared wih he size of he service spreads. I herefore seems ha he problem of iming mismach beween bank loan raes and he marke reference raes is no a major concern. For each caegory of loans, we now have an esimae of he risk premium, namely, he difference beween he reference marke rae and Treasury yield of he same mauriy. 41 The spread beween he laer and he 3 monh Treasury yield is he usual erm premium. We use he 3 monh Treasury yield as he reference rae on ransacion deposis shor erm and largely defaul risk free claims and refer o i as he risk free rae in he subsecion below on he empirical resuls. The reference rae for savings and ime deposis, on he oher hand, includes he perinen average erm risk premium. So, by and large, he gap, in erms of reference rae, beween loans and deposis includes boh risk and erm premia. III.D New Esimaes of he Value of Borrower and Deposior Services Given he reference rae for each caegory of loans, we now esimae borrower and deposior services. Table 1 is a deailed exposiion using he esimaes for he fourh quarer of 2007, comparing our model based, service flow measure of bank oupu wih 40 There are, of course, iming issues regarding when he screening or monioring is done versus when he implici revenue is recognized. See WBF (2004) for an in deph discussion. 18

21 he measure according o NIPA s curren mehodology. In oal, i liss five ypes of services o holders of wo ypes of deposi accouns and borrowers of hree ypes of loans. 42 Oher caegories of asses and liabiliies, such as invesmen securiies and subordinaed deb, are excluded because, as explained in Secion II, heir holders do no receive financial services creaed by banks. Table 1 shows ha for 2007:, he risk adjused reference raes on he hree ypes of loans are a leas one percenage poin higher han he risk free rae. Using he riskadjused reference raes lowers he impued value of borrower services by $116.8 billion, o $88.2 billion. To gauge he impac on GDP, we ne ou he value of borrower services o businesses (ha is, services relaed o commercial real esae loans and C&I loans). 43 Accordingly, GDP in 2007: would be $52.9 billion, or 0.4 percen poins, lower using our risk adjused bank oupu measure. We suspec ha his figure is on he low end because, as deailed above, we have adoped conservaive esimaes of risk premia o adjus he reference raes for risk. Figure 2 plos he respecive average risk adjused reference raes for deposis and loans from 1997: o 2007:. Throughou he sample period, he risk plus erm premium says posiive, so he average reference rae for loans consisenly exceeds ha for deposis. For comparison, Figure 2 also plos he acual average ineres rae paid on deposis and received on loans, respecively. The quarerly average rae is calculaed as he ineres received or paid during a quarer over he average balance of he corresponding insrumens for he quarer. 44 I is clear ha he ineres raes paid on 41 The daa in Call Repors refer o he amoun of ime unil mauriy or nex repricing of he loans, which is he economically relevan informaion for comparing wih marke securiies. 42 Among he loan caegories covered in he Call Repors, we consider only hose for which reasonably similar reference securiies can be found in he marke. So, lease financing receivables are excluded. Moreover, we include only loans and deposis made in banks domesic offices, since aciviies in foreign offices do no conribue o U.S. GDP. In sum, he four caegories in Table 1 accoun for 90 percen of he oal balance of loans and leases in We infer he former from oal services relaed o real esae loans, based on he simplifying assumpion ha he share of services o commercial cusomers is proporional o he share of commercial loan balances in oal real esae loans. 44 Table A.1 in he Appendix liss he specific daa iems used in calculaing he average ineres rae on each caegory of securiies, loans, and deposis. Table A.2 summarizes major changes, in 19

22 deposis are, on average, more inerial han he risk free reference rae, a well documened, sylized fac in empirical banking sudies (for example, Berger and Hannan, 1989). Likewise, he ineres raes received on loans are on average less volaile han he reference marke raes. Figure 2 also shows ha he average loan rae consisenly exceeds he average loan reference rae, implying a posiive service spread on average. By conras, beween lae 2001 and early 2004, he average deposi rae, in fac, rose above he deposi reference rae. Flannery (1982) explains such occurrences as reflecing he quasi fixed naure of deposi relaionships. Tha is, deposiors are o some degree locked ino a bank accoun because of he ransacion cos ha hey would incur o swich banks; in reurn, banks implicily commi o smoohing deposi ineres raes. There may also be subsiuions beween headline ineres raes and various direc charges and fees on deposi accouns a such imes. In Figure 3 we plo he service spreads for deposis and loans direcly. No surprisingly, he wo spreads frequenly move in opposie direcions, since heir formulae carry negaive signs (see (6) and (8)), while boh acual raes are more inerial han he respecive reference rae. Furhermore, he spreads appear o comove wih he business cycle: he deposi service spread narrows, while he loan service spread widens following moneary easing in economic downurns, and vice versa. Variaions in he loan service spread can mosly be raced o C&I and consumer loans, as he service spread on real esae loans remains fairly sable hroughou he period. One explanaion for his paern is ha bank C&I loans become riskier relaive o commercial paper in periods of economic weakness, possibly because smaller or riskier firms are more likely o draw on heir credi lines in bad imes. If his is he case, hen our empirical resuls underesimae he risk premium on C&I loans in such periods. erms of reporing requiremens and variable definiions, in he Call Repors beween 1997 and 2007 and he way hey are handled o arrive a harmonized ime series. 20

23 Figure 4 depics he impued bank service income and he compensaion for risk. 45 Compensaion for erm risk and for he risk of defaul represens he difference beween our new model implied measure of bank oupu and he NIPA s curren measure. Variaions across ime in income from he wo services echo hose in he wo service spreads depiced in Figure 3. The erm risk compensaion is ime varying as well; i rises as he yield curve seepens, and falls as he yield curve becomes less seep. In comparison, he defaul risk compensaion is more sable over ime. Especially worh noing are he las wo quarers of Boh he defaul and he erm risk compensaion increased sharply because of he urmoil in financial markes and he moneary easing ha followed in response. III.E Plausibiliy Checks So far, we have made he case for using our measure of bank oupu on heoreical grounds, ha is, we have explained why he reference rae used o impue he value of bank service oupu should be adjused for he risk of he associaed financial insrumen. By removing he risk premium, his new measure of oupu reduces banks operaing surplus. 46 We now examine wheher or no he lower surplus is implausibly small, as Fixler and Reinsdorf (2006, foonoe 6) have assered in arguing agains risk adjused reference raes. We focus on wo indicaors, he capial share in value added and he inernal rae of reurn on fixed capial, since he range of values of each indicaor in oher indusries can be viewed, under cerain condiions, as he plausible benchmark for comparison. The capial share, defined as he share of operaing surplus in indusry value added, gives an indicaion of he capial inensiy of producion in ha indusry. The inernal rae of reurn (IRR) is he reurn an indusry or a firm would need o earn on 45 Loan services in he figure corresponds o Y A in equaion (6), and Deposi services o Y D in (8). Defaul risk compensaion corresponds o he erm r A A in equaion (7). Term risk compensaion denoes he reurn due o mauriies longer han hree monhs. 46 Operaing surplus is defined as value added ne of labor compensaion and indirec axes. As explained above, par of he excess bank operaing surplus should be reallocaed o nonfinancial firms ha purchase bank services, while he remainder should be reallocaed o ineres paymens and receips of households. 21

24 is fixed capial asses, such as buildings and compuers, o exacly cover he renal cos of fixed capial. We mus noe he close link beween he IRR and he user cos of funds. The laer is, in fac, simply he former ne of depreciaion (consising of boh obsolescence and physical wear and ear). The concep of a risk adjused user cos in he case of fixed capial has long been an inegral par of invesmen heories. The IRR in some indusries is consisenly higher han in ohers, even afer conrolling for depreciaion and expeced changes in he price of capial goods precisely because invesing in hose indusries incurs greaer sysemaic risk. Invesors hus demand a higher rae of payoff on average, so long as capial is mobile and he no arbirage condiion holds. The risk based user cos measure is also rouinely used in indusry level growh accouning sudies. 47 We calculae he IRR using he sandard Jorgensonian framework (for example, Jorgenson, Gollop, and Fraumeni, 1987), and capial includes fixed reproducible asses, such as buildings and machinery, as well as land and invenories. The firs sep is o gauge by how much our new measure would revise downward oal nominal oupu of all deposiory insiuions. Toal oupu equals he sum of explici bank service charges (comprising he bulk of non ineres income) and implici revenue from services (ha is, our esimae of borrower and deposior service oupu in Table 1 and Figure 3). 48 While impued bank oupu is oversaed by 45 percen on average, oal banking oupu is oversaed by only 21 percen on average over he sample period 1997: 2007:. Nex, we obain a new oupu esimae for all deposiory insiuions (ha is, he credi inermediaion indusry as defined in he NIPA Indusry Accoun) by assuming ha oupu of he res of he indusry is oversaed by he same percenage as ha of commercial banks in each year. 49 Obviously i would be preferable o have direc 47 See, for example,. Jorgenson, Gollop, and Fraumeni (1987). 48 Noe ha we exclude he rading income elemens of non ineres income, since we argue ha i is also no oupu bu ransfer of propery income; see Inklaar and Wang (2007) for furher discussion. 49 This indusry (NAICS 521 and 522) comprises commercial banks, he Federal Reserve, savings banks, and credi unions. Commercial banks accoun for more han half of he employmen. Savings banks, he second larges caegory, end o have a larger share of real esae loans han 22