Commets Welcome Baks, Taxes, ad Nobak Competitio * by George Peacchi Departmet of Fiace Uiversity of Illiois 4041 BIF, Box 25 505 E. Gregory Drive Champaig, IL 61820 Phoe: (217) 244-0952 Email: gpeacc@illiois.edu First Draft: November 2014 This Draft: March 2015 Abstract This paper models markets for fiacial services to study baks equilibrium capital structure ad iterest rates o loas ad deposits whe baks may be subject to corporate taxes ad obak competitio. I a market with rich ledig opportuities but limited retail deposits, retail borrowers bear the burde of baks corporate taxes. I the absece of taxes, baks may choose high equity capital. I the opposite case of a market with limited ledig opportuities but pletiful retail deposits, depositors may bear the burde of corporate taxes ad baks miimize capital. Whe baks face greater obak deposit competitio, equilibrium loa rates ted to icrease, ecouragig etry from obak loa providers. The model s predictios are cosistet with broad chages i U.S. bakig over the past two ceturies. A emergig empirical literature examiig how taxes affect bak behavior also supports the model. * I am grateful for valuable commets provided by participats of semiars at Louisiaa State Uiversity, Uiversità Cattolica, ad the Uiversity of Oxford.
Baks, Taxes, ad Nobak Competitio I. Itroductio I may coutries, a variety of itermediaries compete for similar fiacial services. This paper takes a idustrial orgaizatio approach to aalyze competitio betwee bakig ad obakig istitutios that provide ledig ad savigs/trasactios services to retail customers. It focuses o how differeces i govermet support, regulatio, ecoomies of scope, ad corporate icome taxes determie the market shares of these differet istitutios. Baks, defied as itermediaries that primarily make loas ad fud them maily with deposits, have faced differeces i regulatio, taxatio, ad competitio over the last two ceturies. I preset a cost of fudig-based model that explais how baks ad obaks evolved durig this chagig eviromet. The aalysis focuses the role that taxes play i determiig baks equilibrium iterest rates o retail loas ad deposits, their capital structures, ad the icetives for obaks to eter the market for fiacial services. Depedig o regulatio ad the structure of the market where a bak operates, taxes ca affect either the equilibrium retail loa rates charged by the bak or the equilibrium retail deposit rates paid by the bak. Hece, the model determies the coditios uder which retail borrowers bear a tax burde versus the coditios uder which retail depositors bear a tax burde. The model also shows that i the absece of taxes, baks will operate with miimal equity capital uder some market coditios but high equity capital uder others. The paper also aalyzes how the itroductio of obak leders ad obak savigs/ trasactios accout providers affects baks market shares ad their equilibrium retail loa ad deposit rates. The model icludig obaks, also kow as shadow baks, emphasizes two mai ways i which they differ from traditioal baks. First, obaks do ot simultaeously make loas ad issue retail deposits. Rather loas are fuded with competitively-priced debt ad equity by oe set of obak istitutios. Aother set of obak itermediaries issue
savigs/trasactios accouts ad ivest the proceeds i marketable, competitively-priced debt securities rather tha retail loas. Cosequetly, obaks do ot beefit from ecoomies of scope from the joit provisio of loas ad deposits. The secod mai differece betwee these obaks ad baks is that the obaks are almost always structured to be exempt from corporate icome taxes. This tax exemptio ca give obaks a cost of fudig advatage that, i some circumstaces, may overcome their ecoomy of scope disadvatage. The curret paper is related to DeAgelo ad Stulz (2013) who examie baks optimal capital structure whe loas ad deposits ca be priced differetly from competitively-priced debt. They argue that whe baks are able to provide liquidity (savigs/trasactio accout) services to idividuals who lack access to capital markets, high leverage is optimal for baks. Like them, the curret paper assumes baks serve retail loa ad deposit customers. However, while their aalysis assumes retail loa ad deposit rates have exogeously-fixed spreads relative to similar competitively-priced securities, the curret paper s model derives these spreads i the cotext of a equilibrium loa ad deposit market. Allowig these spreads to be edogeous shows that, uder some market coditios, bak will wat to miimize equity capital. However, i the absece of taxes, bak may wat to operate with high equity capital uder other market coditios. Hece, the existece of corporate taxes ca be importat for baks operate with high leverage. I markets where retail loa demad exceeds retail deposit supply, retail borrowers bear some of the burde of corporate taxes ad, at the margi, loas are beig fuded with competitively priced debt ad equity. I this case, corporate taxes are ecessary to give baks a preferece for debt at the margi. I cotrast, i markets where retail deposit supply is relatively larger tha loa demad, retail depositors bear the burde of higher bak corporate icome taxes. Retail deposits are fudig a bak s security purchases at the margi. Here, with a equity capital requiremet, the effect of higher corporate taxes is to reduce security purchases with o effect o equilibrium retail loa rates. Rather, retail depositors bear the brut of corporate taxes. 2
I also itroduce two sets of obak fiacial itermediaries ito the model, obak loa ivestors ad obak savigs/trasactios accout providers. Nobak loa ivestors ca take the form of securitizatio vehicles that pool loas ad issue asset-backed securities or, alteratively, mutual fuds that ivest i corporate loas. The mai example of obak savigs/trasactios providers are moey market mutual fuds. The exteded model shows that i a market where retail savigs domiate retail ledig, depositors bear the burde of corporate icome taxes which creates a icetive for moey market fuds to eter. But as moey fuds reduce baks retail deposits relative to their retail loas, at the margi bak loas are fuded with equity ad competitively-priced debt ad the corporate tax burde is shifted to borrowers. Cosequetly, a icetive for etry by obak loa ivestors is created, ad subsequetly securitizatio reduces baks share of retail loas. Ha, Park, ad Peacchi (2014) derive related results, but their model is of a sigle bak. They take the bak s demad for retail loas ad supply of retail deposits as exogeous. The curret paper derives these demads ad supplies based o a market equilibrium that explicitly models competitio with other baks ad obaks. The pla of the paper is as follows. Sectio II outlies the basic model assumptios ad solves for equilibrium retail loa ad deposit rates whe oly baks populate a market. The model is used to help explai the evolutio of U.S. bakig from the early 1800 s to aroud 1970. Sectio III itroduces obak competitio ad shows how, i equilibrium, loa rates ad deposit rates differ betwee obaks ad baks, as well as across baks. This sectio also outlies the coditios uder which obaks would fid it profitable to eter how this correspods to the rise of obak competitio from the 1970s to the preset. Sectio IV surveys recet empirical research related to the model s predictios. Sectio V cocludes. II. A Model with Oly Baks The foudatio of the paper s model is the Salop (1979) circular city model applied to the 3
bakig idustry. Chiappori, Perez-Castrillo, ad Verdier (1995) ad, i particular, Park ad Peacchi (2009) are otable applicatios of this type of model. The curret paper s model solves for equilibrium iterest rates ad market shares for a retail fiacial services market. What defies such a market ca vary across coutries. For example, i the Uited States differet metropolita statistical areas (MSAs) or rural couties ted to costitute idividual retail markets. I other coutries, the etire atio might correspod to a sigle retail market. II.A Assumptios The basic model assumes a sigle period over which fuds are itermediated. Baks operate i a market that has two types of retail customers: savers ad borrowers. There is a cotiuum of these customers uiformly located aroud a circle of uit circumferece. Let D equal the total volume of retail savers fuds to be ivested, which is the product of the market s desity of savers ad each saver s ivestible fuds, which is assumed fixed. Also let L be the total volume of potetial retail loas, which is equal to the product of the market s desity of borrowers ad each borrower s fixed loa amout. As a startig poit, let there be differet baks located equidistatly aroud the market of uit circumferece, so that the distace betwee each bak is 1/. Baks are assumed to have idetical productio fuctios for fiacial services at margial operatig costs of c D per uit of savigs accout balace ad c L per uit of loas, where c D icludes accout admiistrative costs ad c L combies the cost of screeig a borrower s credit, of moitorig the borrower, ad expected default losses. It is assumed that there is a ecoomy of scope i that issuig retail deposits reduces a bak s cost of screeig ad moitorig a retail borrower. Specifically, if a particular bak, say bak i, issues retail deposits i amout D i, the its per uit loa cost satisfies c L (D i )/ D i 0. This assumptio is based o Black (1975) ad Fama (1985) who argue that iformatio obtaied from deposit trasactios reduces the cost of moitorig borrowers. Empirical evidece i Mester et al. (2007) supports the view that baks are special because they simultaeously make loas ad issue deposits. 4
The source of a idividual bak s market power is modeled by retail customers icurrig liear costs of travelig to a particular bak, equal to t D for savers ad t L for borrowers. Retail customers are assumed to obtai sufficiet gross surplus from cosumig fiacial services such that they are always willig to icur these trasportatio costs. 1 These costs give a comparative advatage to the bak located closest to a give customer, ad therefore each bak directly competes with the two eighborig baks that are closest to it. What determies a customer s closeess to a give bak eed ot be limited to physical or geographic distace, but could iclude the distace betwee the particular attributes of a idividual bak s fiacial services ad a idividual s product prefereces. Deote the retail loa rate offered by bak i as r L,i, so that r L,i-1 ad r L,i+1 are the loa rates offered by its two eighborig baks. If a borrower is a distace x - [0, 1/] from bak i ad a distace (1/ - x - ) from bak i-1, this borrow will be idifferet betwee obtaiig the loa from these baks if 1 r + tx = r + t x Li, L Li, 1 L (1) Aother borrower located betwee bak i ad bak i+1 ad who is a distace x + [0, 1/] from bak i is idifferet betwee obtaiig the loa from bak i ad bak i+1 if 1 r + tx = r + t x Li, L + Li, + 1 L + (2) For the distaces satisfyig (1) ad (2), bak i s total loa demad is (x - + x + )L L i or r + r L L = ( + ) = + 2 tl Li, 1 Li, + 1 Li x x+ L rli, (3) Recall that c L combies the per uit of loa cost of screeig a borrower s credit, of moitorig the borrower, ad expected default losses. While screeig ad moitorig the borrower is efficiet i reducig expected default losses, it is assumed to ot affect the lowest 1 Thus, i equilibrium all customers are served: the total volume of loas made by fiacial services firms equals L ad the total volume of savigs accouts issued equals D. 5
(miimum) ed-of-period rate of retur o ay bak s portfolio of loas, equal to a proportioal loss of r low per uit of loa. 2 Besides makig loas to retail borrowers, baks may ivest i default-free moey market securities that ear the iterest rate r M. Assume, for ow, that retail savers face o default risk whe ivestig their savigs i the baks deposit accouts. Later, the parametric coditios for which deposits are riskless will be give. Deote the iterest rate paid by bak i o a deposit accout as r D,i. The if y - ad y + [0, 1/] are distaces where savers are just idifferet to supplyig fuds to bak i, this bak faces the savigs supply curve, defied as D i, of the form: D ( y y ) D r r + r D D Di, 1 Di, + 1 i = + + = Di, + 2 td (4) Besides retail deposits, baks ca also obtai fuds i a wholesale deposit market. Deote by W i the amout of wholesale fuds borrowed by bak i. If there is o risk of default o wholesale deposits, the bak must pay iterest equal to the default-free moey market iterest rate, r M. If W i < 0, the this deotes a situatio where the bak chooses to ivest, rather tha borrow, fuds at the moey market iterest rate. I additio to retail ad wholesale deposits, bak i ca fud its assets by issuig shareholders equity i the amout E i. Besides providig a source of fudig, bak equity ca prevet rus by retail ad wholesale depositors ad may also make these deposits default-free. Bak rus are assumed to be costly because they force the bak to liquidate borrower s projects/loas prior to the ed of the period at a proportioal loss of r ru > r low. Thus, as i Diamod ad Dybvig (1983), rus are assumed to be especially disruptive i that loas liquidated prior to maturity have a value less tha their miimum ed-of-period value. Note that at the start of the period, bak i s balace sheet equatio is 2 For example, for each uit loa made to a retail borrower, 1-r low is the ed-of-period value of the borrower s project if it fails. Credit screeig ad moitorig decrease, but do ot completely elimiate, the probability of project failure, thereby reducig expected default losses but ot the miimum project retur. 6
Li = Di + Wi + Ei (5) Iitially, it is assumed that deposits are uisured ad, if savers withdraw their deposit fuds prior to the ed of the period, they are serviced sequetially ad etitled to receive their iitial cotributio but o iterest. I this case, a bak ru equilibrium exists wheever 3 ( 1 r ) L < D + W (6) i ru i i Cosequetly, comparig (5) ad (6), the bak ru equilibrium ca be ruled out wheever E Lr (7) i i ru which requires sufficiet equity to cover the losses o loas due to early liquidatio from rus. 4 For simplicity, it is assumed that this cost of rus is sufficietly high that bak owers choose adequate equity to elimiate the icetive to ru. If bak i has equity that satisfies (7), it is also assumed that sice r ru > r low the ( 1 r ) ( 1 ) ( 1 ) E + L D + r + W + r (8) i i low i D, i i M I other words, sufficiet equity to rule out a bak ru is eough to esure there is o default o the ed-of-period promised paymets to depositors. If coditio (7) holds, the coditio (8) holds whe ( r r ), L > Dr + Wr (9) ru low i i D i i M The iterpretatio of coditio (9) is that the relatively greater loss o loas from rus exceeds the iterest paid o retail ad wholesale deposits. If W i < 0, the the greater loss o loas from rus plus security iterest icome exceeds the iterest paid o retail deposits. Of course L i, D i, ad the retail deposit iterest rate, r D,i, are determied i equilibrium based o other parameters of the model. Oce this is doe, parameter restrictios for which coditio (9) holds ca be stated 3 If W i < 0, so that the bak ivests i moey market securities, it is assumed that these securities ca be liquidated at their iitial values. I other words, moey market securities are ot costly to liquidate. 4 Note that iequality (7) accouts for the possibility that the bak may hold liquid securities (W i < 0) to reduce liquidatio costs. 7
precisely. I the iterim, this restricted parameter space is assumed, so that bak i s equity is sufficiet to both rule out rus ad make its deposits default-free. Bak equity is risky due to possible loa defaults, but let r E be the certaity equivalet rate of retur required by equity ivestors. Like the rate of retur o moey market istrumets (wholesale debt), r M, it is assumed that r E is a fixed competitive rate of retur set i atioal or global fiacial markets. Baks (ad later obaks) take these rates as give. Moreover, r E ad r M are assumed to be rates of retur after persoal icome taxes paid by the margial equity ad debt ivestors. Hece, r E ad r M may be uequal if the margial equity ivestor is more or less heavily taxed at the persoal level tha the margial debt ivestor. 5 Baks are assumed to be subject to corporate icome taxes at the costat margial tax rate of τ. As i most coutries, a bak s iterest expese o debt is assumed to be deductible prior to calculatig taxable icome. Moreover, it is assumed that r M (1-τ) < r E, a coditio which implies the total tax burde, both persoal ad corporate, o equity exceeds that of debt. Much empirical evidece, such as Graham (2000), supports this iequality assumptio. Lastly, baks are assumed to choose retail loa ad deposit rates, shareholders equity, ad wholesale deposits/ivestmets to maximize the after tax certaity-equivalet retur o equity. Ha, Park, ad Peacchi (2014) show how this objective fuctio ca be derived whe loas are default risky but markets are complete. 6 II.B Model Derivatio Bak i s maximizatio problem ca be writte as r, r, E, W Li, Di, i i ( ( )) ( ),, ( τ ) Max L r c D D r + c Wr 1 Er L i L i i i D i D i M i E (10) 5 For example, if all ivestors were idetical ad had margial persoal icome tax rates for debt ad equity equal to τ D ad τ E, respectively, the i equilibrium r M = r E (1-τ E )/(1-τ D ). 6 They show that objective fuctio (10) holds if deposits have default risk but are paid a fair risk premium (credit spread) or deposits are isured but the bak pays fairly-priced deposit isurace. 8
subject to the balace sheet equality (5) ad the capital costrait (7). Let λ be the Lagrage multiplier associated with the capital costrait. The Appedix shows that the first order coditios are rli, 1 + rli, + 1 re tl 2rL, i + cl ( Di ) + + λ( 1 rru ) = 0 2 1 t ( ) r + r t c D Di, 1 Di, + 1 2 D L i E rdi, + + cd+ Li + λ = 0 2 Di 1 t r (11) (12) Substitutig for λ i (11) ad (12), oe fids ( ) r + r /1 τ λ = 0 (13) M E 1 r + r r t r r = c D r 2 + + + 2 1 t 1 t ( ) ( 1 r ) Li, 1 Li, + 1 E L E L, i L i M ru ( ) r 1 r = + r t c c L D + r Di, 1 Di, + 1 D L i Di, D i M 2 2 Di (14) (15) I a symmetric Bertrad-Nash equilibrium where r L,i = r L,i-1 = r L,i+1, r D,i = r D,i-1 = r D,i+1, D i = D/, ad L i = L/, the equilibrium loa ad deposit rates are re re tl rl, i = rm ( 1 rru ) + cl ( Di ) + 1 t 1 t re tl = rm ( 1 rru ) + rru + cl ( Di ) + 1 t D rdi, = rm cd t L cl D ( D ) i i (16) (17) Equatio (16) shows that the profit maximizig loa rate reflects a weighted average of the margial cost of wholesale fudig, r M, ad the tax-adjusted cost of equity fudig, r E /(1-τ), with the weight o equity, r ru, equalig the miimum amout required to avoid rus. Equatio (17) idicates that the bak optimally raises the retail deposit rate util it equals the wholesale rate less operatig costs, the margial loss of market power, plus the margial beefit from lower loa 9
costs from greater retail deposits. Sice c L / D i 0, ecoomies of scope i deposit-takig ad loa makig result i a higher equilibrium deposit rate. Two types of equilibria ca be classified based o the sig of W i. Sice E i = L i r ru = (L/) r ru, the balace sheet idetity (5) implies (L/)(1-r ru ) = D i + W i = D/ + W i. The implicatio is that W i > 0 whe D < L(1-r ru ). I other words, whe the market s equilibrium amout of deposits is less tha the proportio of loas ot fuded with equity, the bak uses wholesale deposits to fud the remaider. This type of equilibrium where W i = (L/)(1-r ru ) - D/ > 0, i = 1,, characterizes a loa rich, deposit poor market. I cotrast, whe W i < 0 which occurs whe D > L(1-r ru ), the market ca be characterized as loa poor, deposit rich. I this market, the profitable retail deposits i excess of loas are ivested i moey market securities earig the wholesale retur r M. Note that eve if τ = 0 ad r E = r M, so that competitively priced equity ad debt are taxed the same, the loa poor, deposit rich equilibrium where W i < 0 ad the bak ivests the excess of deposits ito securities cotiues to hold. The equity capital costrait E i = L i r ru = (L/)r ru cotiues to bid. However, the loa rich, deposit poor equilibrium may o loger be characterized by a bidig equity capital costrait. I this situatio, a bak would be idifferet betwee issuig additioal equity or issuig wholesale deposits i order to fud its profitable loas i excess of retail deposits. This case is a couterexample to the geeral coclusio of DeAgelo ad Stulz (2013) that baks specialess i providig retail deposits implies that they will choose high leverage. Such a loa rich, deposit poor eviromet may have described the geeral situatio of U.S. baks prior to the start of corporate icome taxatio i 1909. Figure 1 Pael A shows that baks equity capital to asset ratios were geerally much higher durig this period. At the same time, at least util the Natioal Bakig Acts of 1863 ad 1864, cash ad securities holdigs of baks were ot a large proportio of total assets. See Figure 2. However, these Acts passed 10
durig the U.S. Civil War required that atioal baks hold federal ad state govermet bods to back the atioal bak otes (currecy) which the baks issued. Requirig this collateral for issuig bak otes artificially raised the demad for govermet securities. After baks bega payig corporate icome taxes, the model predicts that the establishmet of a govermet leder of last resort, whose missio is to provide fuds to a solvet bak experiecig a ru, reduces the amout of relatively expesive equity fiacig. This result follows from coditio (9) that assumes the amout of equity capital eeded to esure solvecy is less tha the amout of equity capital eeded to rule out the possibility of a bak ru. Figure 1 Pael B is cosistet with this predictio. Whe the Federal Reserve Act of 1913 established a leder of last resort to provide a elastic currecy, average equity capital ratios of baks declied from 18.7 % i 1913 to 11.8% i 1920. However, the Federal Reserve s leder of last resort fuctio was uable to prevet widespread bak rus at the start of the Great Depressio of the early 1930s, arguably because the Federal Reserve did ot led freely eough (Friedma ad Schwartz (1963)) ad because bak opacity preveted depositors from gaugig the solvecy of idividual baks. I respose, the Bakig Act of 1933 established the Federal Deposit Isurace Corporatio (FDIC). Federal deposit isurace was successful i stoppig rus ad, as show i Figure 1 Pael B, baks capital ratios also fell cosiderably followig its implemetatio. Also as show i Figure 2, bak ledig declied substatially durig the Great Depressio of the 1930s, both i absolute terms ad as a proportio of total bak assets. 7 However, with the start of FDIC isurace, there was a flight to quality as retail deposits flowed ito baks. 8 This iflow of deposits ad reductio i loas is reflected i the substatial buildup of securities i bak portfolios, leadig to a loa poor, deposit rich type of equilibrium. 7 Total loas of all U.S. baks fell by 46% from 1929 to 1940. 8 Total deposits of all U.S. baks rose by 70.0% from 1933 to 1940. 11
The 1930s bakig regulatio did ot establish miimum umerical capital ratio requiremets but relied o bak supervisors subjective assessmets of whether capital was adequate. 9 This policy of regulatory discretio was icreasigly questioed durig the late 1970s. As show i Figure 1 Pael B, average equity capital to assets ratios had bee fallig sice the early 1960s ad stayed below 6% from 1977 through 1982. At the same time, Figure 2 idicates that baks asset portfolios were shiftig out of cash ad securities ito loas. Together with icreasig loa losses ad bakig idustry weakess, formal umerical capital requiremets were implemeted by federal bakig regulators begiig i 1981. Over the ext decade, (primary) equity capital to asset ratio requiremets betwee 5% ad 6%, depedig o the type of bak, were established. I 1991, the U.S. implemeted the 1988 Basel Accord which created more detailed capital requiremets. While recogizig that implicit or explicit regulatory capital requiremets varied sice the establishmet of FDIC isurace, a leverage -type equity capital requiremet ca be modeled as: reg E r i Di max ( Wi,0) 1 r + reg (18) where r reg is the miimum required equity capital to asset ratio, so that r reg /(1-r reg ) is the miimum equity-to-debt ratio. Let us resolve the bak s profit maximizatio problem i (10) but with the costrait (18) replacig the previous o-ru equity capital costrait. It is straightforward to show that for a loa rich, deposit poor market where D < L(1-r reg ) so that W i 0, the equilibrium loa ad deposit rates satisfy: re tl rl, i = ( 1 rreg ) rm + rreg + cl ( Di ) + 1 t (19) 9 See Burhouse, Feid, Frech, ad Ligo (2003) for a summary of capital regulatio ad regulatory developmets durig this period. 12
D rdi, = rm cd t L cl D ( D ) i i (20) which is the same as (16) ad (17) but with r reg replacig r ru. Similarly, for a loa poor, deposit rich market where D > L(1-r reg ) so that W i < 0, the equilibrium loa ad deposit rates satisfy: ( ) t L rli, = rm + cl Di + (21) t r r r = r c + r + L c ( D ) D reg E L i Di, M D M i 1 rreg 1 t Di (22) Here, the loa rich, deposit poor case of (19) ad (20) is very similar to the prior case where equity was costraied to equal a level that would prevet bak rus. The effect of corporate icome taxes is passed o to borrowers but ot depositors. However, with r reg < r ru, equilibrium loa rates are lower sice they reflect a weighted cost of debt ad equity fiace but with a lower weight o the relatively expesive tax-adjusted cost of equity. The equilibrium retail deposit rate is uchaged. As metioed earlier, i the absece of a corporate icome tax ad where r E = r D, the regulatory capital costrait would ot be bidig. The case of a loa poor, deposit rich market differs because previously it was assumed that equity was held to cushio possible losses from loa liquidatios due to rus. Now, a miimum required equity capital to total asset ratio meas that capital must also be issued to fud security ivestmets, ot oly loas. Sice baks hold securities i a loa poor, deposit rich market, equity fudig is based o total assets, ot just loas. The corporate tax wedge implies that depositors are affected because, at the margi, baks do ot bid as aggressively for retail deposits to fud security ivestmets. If, istead, the required capital ratio was based o riskweighted assets ad securities had a zero risk weight, the the loa ad deposit rates i (19) ad (20) would also characterize the loa poor, deposit rich market. These results are summarized i the followig propositio. 13
Propositio I: Uder a leverage costrait where r reg is the miimum required equity capital to asset ratio, retail borrowers bear the burde of higher corporate icome taxes ad higher capital requiremets whe market loa demad is relatively high, L(1-r reg )> D. Coversely, uder this leverage costrait but whe market deposit supply is relatively high, D > L(1-r reg ), retail depositors bear the burde of higher corporate taxes ad capital requiremets. Uder a risk-based capital requiremet where securities have a zero risk weight, retail borrowers always bear the burde of higher corporate taxes. For a give umber of baks i the market, our results show that either retail borrowers (i the loa rich, deposit poor case) or retail depositors (i the loa poor, deposit rich case) bear the burde of corporate taxes. Effectively, either retail borrowers or retail depositors bear the higher cost of fudig assets with required outside equity capital. However, bak owers (iside equity) also bear some of the tax burde. Similar to other Salop (1979)-type models, the Appedix shows that each bak ower s profit is ( D ) L t D t L c Di L + D + L i ( 1 t ) (23) where i equilibrium D i = D/. The after tax profits i (23) hold for both the loa rich, deposit poor case ad the loa poor, deposit rich case. Profits are lower i proportio to the tax rate compared to what they would be i the absece of taxes. I a more geeral equilibrium where the umber of baks i the market,, is edogeous ad each bak must pay a fixed cost to eter, the a zero profit etry coditio where (23) equals this fixed etry cost would determie. Obviously, the higher the tax rate, τ, the lower is the equilibrium. I this log ru case, oe sees that from the equilibrium retail loa ad deposit rates (19), (20), (21), ad (22) that higher taxes, by reducig, are bore by both retail borrowers ad retail depositors. Higher corporate taxes icrease market cocetratio which raises the moopoly ret eeded to compesate baks for operatig i the market. 14
III. Baks ad Nobak Competitio This sectio itroduces obak savigs accout providers ad obak leders operatig i the same market as baks. Nobak savigs accout providers are modeled as moey market mutual fuds (MMFs) which ivest purely i moey market securities (wholesale debt) that pay the default-free iterest rate r M. They issue retail savig accout shares that have a margial operatig cost of c D per uit of savigs accout balace, which is assumed to be the same costat margial operatig cost as a bak deposit. However, because obak savigs providers have a mutual fud structure, they have little leeway i settig the rate of retur paid to retail savers. They must pass through the returs o their assets less operatig expeses to their shareholders. 10 Deote the retur paid by obak savigs provider i as r S,i. Sice its mutual fud structure exempts it from corporate icome taxes, it must pay the retur r S,i = r M - c D. Nobak leders are modeled as either special purpose vehicle (SPV) securitizatios or loa-holdig mutual fuds. Nobak leders ca make loas, but they differ from baks because they do ot have access to deposit fudig. Rather, all of their fudig is at wholesale rates, havig a cost of fudig equal to r M for debt ad r E for equity. Also, ulike baks, these obak leders are exempt from payig corporate icome taxes. Examples of such corporate tax-exempt itermediaries are SPVs whose assets are mortgages, cosumer loas, or corporate loas ad whose liabilities are debt ad equity traches, variously referred to as mortgage-backed securities (MBS), asset-backed securities (ABS), or collateralized loa obligatios (CLOs). Also some mutual fuds, which are corporate tax-exempt ad typically issue oly equity shares, ca have assets very similar to baks. Mutual fuds kow as prime rate fuds specialize i holdig corporate sydicated loas. 11 A particular type of closed-ed mutual fud, called a busiess 10 O this poit, see Gorto ad Peacchi (1993) who ote that MMF advisors are limited to chargig reasoable fees, ad there have bee several istaces where advisors have bee sued by MMF shareholders whe fees were alleged to be excessive. 11 These fuds ca be both ope-ed ad closed-ed mutual fuds. Stadard & Poor s (2014) reports that total assets i these prime rate fuds exceeded $170 billio i March 2014. 15
developmet compay (BDC), ivests i small ad medium-sized eterprises (SMEs), ca issue debt up to 50% of its assets, ad yet is corporate tax exempt. 12 As i Ha, Park, ad Peacchi (2014), this paper models obak leders as havig a corporate tax advatage relative to baks. However, they have a disadvatage from ot issuig deposits, so that obak leder i s margial cost of per uit of loas is c L (D i ) = c L (0) c * L. For simplicity, let us take a special case of the previous sectio s assumptio ad assume that for baks which issue ay positive amout of retail deposits, they have a costat margial loa cost of c L < c * L. I other words, it is assumed that oce bak i has established a retail brach etwork, ay additio issuace of deposits does ot further reduce margial loa operatig costs. Hece, at the margi, c L / D i = 0 ad ay further margial declie i loa costs from issuig additioal retail deposits ca be igored. Suppose that there are a total of fiacial service providers i the market, ad idex these idividual fiacial service providers by i = 1,,. It is assumed i the begiig that i both the retail loa market ad i the retail deposit market there are k obak fiacial service providers, so that k are baks. Later, it will be straightforward to show that the model ca be modified to allow a differet umber of obak providers i the loa market versus the umber of obak providers i the deposit market. Cosider, first, the case of k = 1, ad assume this obak is fiacial service provider i = 1, so that the baks are idexed by i = 2,,. This situatio is depicted i Figure 3 for the case of = 8 fiacial service providers, with k = 1 obak ad - k = 7 baks. A symmetric equilibrium is assumed such that baks that are equidistat from the obak set the same loa ad deposit rates. However, baks that differ i their distace from the obak will ot, i geeral, set equivalet loa ad deposit rates. 12 Beltratti, Bock, Jewsikow, ad Nelso (2014) review BDCs ad their stock retur performace. 16
To solve for the market s equilibrium loa ad savigs accout rates, cosider the profit maximizatio problems of the obak ad each bak. As was just metioed, obak providers of savigs accouts are assumed to have o discretio i settig the rates they pay customers. They simply pass through their ivestmet returs less expeses so that r D,1 = r S, i = r M - c D is fixed. Nobak leders have more discretio. Nobak leder i = 1 will make total loas give by equatio (3), ad its profit maximizatio problem is Max r, W L,1 1 * ( ) L r c Wr Er (24) 1 L,1 L 1 M 1 E subject to the o-ru costrait (7) ad the balace sheet costrait L 1 = E 1 + W 1. The profit fuctio (24) reflects the obak s higher cost of ledig due to the absece of a deposit etwork ad its tax-exempt status. The Appedix shows that whe obak leder 1 s eighborig baks set loa rates equal to r L, 2 = r L,, the obak leder 1 s optimal loa rate, r L,1, satisfies 1 * tl rl,1 = rl,2 cl re rru Mi ( re, rm )( 1 rru ) 2 + + + + (25) The obak leder fiaces its loas with all equity whe r E < r M ad fiaces its loas with a proportio r ru of equity ad (1- r ru ) of wholesale debt whe r E > r M. The optimizatio problem for baks i the market is similar to our earlier solutio. Cosider the case of a loa rich, deposit poor market where retail ledig opportuities sigificatly exceed retail savigs, L >> D. The Appedix shows that the profit maximizig loa rate ad savigs rates for bak i are r t r = ( 1 δ ) ( 1 r ) r + r + c + + δ r 1 t E L L, i i, / k reg M reg L i, / k L,1 t r = r c + r c td = rm cd ( 1 δik, / ) D ( 1 δ ) δ ( ) Di, ik, / M D ik, / M D (26) (27) 17
where for the case that is a eve umber 13 δ i k ( 2+ 3) + ( 2 3) k ( 2+ 3) + ( 2 3) + 1 + 1 i 2 2k i, / k 2 2k (28) Equatios (26) ad (27) show that baks loa ad deposit rates are a weighted average of the equilibrium rates they would have set i the absece of a obak ad the rates set by the obak. The variable δ i,/k < 1, i = 2,,, is the weight o the obak s rate ad reflects the impact of obak competitio. Baks closer to the obak are more affected by its rates: δ i,/k is a decliig fuctio of i over the rage from i = 2 to i = /2 + 1, the mid-poit of the circle, ad it satisfies the symmetry coditios: δ 2,/k =δ,/k, δ 3,/k =δ -1,/k,, δ /2,/k =δ /2+2,/k. Moreover, for a give umber of bak itervals i, i= 1,, away from the obak, a bak s rates are less sesitive to the obak s rate the greater is the total umber of fiacial service providers i the market; that is, δ i,/k / (/k) < 0. I particular, sice a obak savigs accout provider is assumed to pay a competitive rate less accout operatig costs, r M c D, oe sees from (27) that bak deposit rates are always greater tha what would occur i the absece of the obak, with baks closest to the obak payig relatively greater rates. To fully solve for the obak ad baks equilibrium loa rates, first substitute (26) for the case if i = 2 ito (25) ad rearrage to obtai: re tl rl,1 = ( 1 rreg ) rm + rreg + cl + 1 t 2 L δ 2, k / (29) r L 1 rreg rm + rreg + cl rrure + 1 rru Mi re, rm + c L 1 τ is the E * where ( ) ( ) ( ) obak s et fudig ad operatig cost advatage. Thus, if L > 0 because regulatory capital 13 The Appedix discusses the case of beig a odd umber. 18
requiremets ad corporate taxes are sufficietly high to offset the obak s operatig cost disadvatage, the obak loa rate will be less tha what baks would have charged i its absece. Substitutig (29) ito (26), bak i s equilibrium loa rate is re t δik, / L L rl, i = ( 1 rreg ) rm + rreg + cl + 1 t 2 δ 2, k / (30) Cosequetly, if L > 0, a bak s equilibrium loa rate is lower the closer it is to the obak. The equilibrium rates o deposits ad loas for this case of a sigle obak ad several baks exteds to the case of k > 1 obaks whe these obaks are symmetrically located aroud the deposit ad loa markets. Figure 4 shows a example of a market with k = 2 obaks with a total of = 8 total fiacial service providers ad, therefore, 6 baks. The Appedix outlies why formulas (27) ad (30) for equilibrium bak deposit ad loa rates ad formula (29) for the obaks equilibrium loa rate cotiue to hold for the case of k > 1. The logic is that i this more geeral case, each cluster of oe obak separated by /k - 1 baks face the idetical profit maximizatio problem previously ecoutered i a market with oe obak ad -1 baks. Util ow, competitio betwee obaks ad baks have assumed a loa rich, deposit poor market where L >> D. Let us ow cosider the case of a retail loa poor, deposit rich market where L << D. Recall that whe such a market has o obaks, equatios (21) ad (22) obtai for bak s equilibrium loa ad deposit rates i the absece of obaks. Usig a similar derivatio, it is straightforward to show that for a loa poor, deposit rich market, the obak s equilibrium loa rate is: 14 * tl L rl,1 = rm + cl + (31) 2 δ 2, k / 14 As before, the aalysis is simplified by assumig that baks have a fixed margial loa operatig cost advatage, c L < c L * whe they issue ay positive amout of retail deposits. This allows us to assume the term L i c L / D i i equatio (22) equals zero. 19
where [ ] r ( 1 r ) Mi (, ) * * L rm + cl rure + ru re rm + c L is the differece betwee the obak ad baks cost of fudig. The Appedix also shows that bak i s equilibrium loa ad deposit rates are * tl ik, / Li, = M + L+ (32) 2 δ2, k / r r c δ L t r r r = r c ( 1 δ ) + r D reg E Di, M D ik, / M 1 rreg 1 t (33) Sice if r M r E, because c * L > c, it is likely that L * < 0. The implicatio is that i this loa poor, L deposit rich market, baks will charge lower rates o retail loas compared to obaks. Hece, oe would ot expect etry by obak leders due to their higher et operatig costs. I equatio (33), baks retail deposit rates reflect their corporate tax disadvatage so that depositors bear the tax burde. However, baks retail deposit rates are higher tha i a loa poor, deposit rich market with o obaks, equatio (22). The competitive effects of obak savigs accout providers higher rates forces baks to icrease their deposit rates. As a cosequece of the geerality of the derived loa ad deposit rates to the case of k > 1 obaks, a comparative statics exercise ca determie the effects o competitio from holdig the total umber of fiacial service providers fixed but icreasig the relative proportio of obaks. Doig so leads to the followig propositio: Propositio 2: For a market with a fixed umber of fiacial service providers, icreasig the proportio of obak providers raises baks deposit iterest rates. Whe L >> D ad r E = r D so that L > 0, a greater proportio of obak leders lowers baks retail loa rates. Whe L << D ad r E = r D so that L * < 0, a greater proportio of obak leders raises baks retail loa rates. The above derivatio of bak ad obak competitio assumes equal proportios of obaks i both retail loa ad retail deposit markets. However, sice obak leders 20
maximizatio problem is separable from that of obak savigs accout providers, the model results geeralize to differet umbers of obaks i the two markets. Cosider the case i which k = 0 i the retail loa market but k 1 i the retail deposit market. For the loa poor, deposit rich case, equatio (32) cotiues to characterize baks equilibrium loa rate but with δ i,/k = 0, i = 1,,. This is the same loa poor, deposit rich equilibrium loa rate set by baks i the absece of obaks, equatio (21). I a sigificatly rich retail deposit market with k 1 of the savigs accout providers beig obaks, bak deposit rates are give by equatio (33) ad, sice 0 < δ i,/k < 1, strictly higher tha for the case of o obaks. Note that this loa poor, deposit rich equilibrium cotiues to hold as log as D i > L i (1-r reg ) for every bak so that it is optimal for each bak to ivest i securities rather tha issue wholesale deposits. However, if oly obak savigs providers eter without obak leders, L i would remai at L/ for baks but D i for baks would be strictly less tha D/(-k) as obak savigs accout providers pay higher savigs accout rates ad capture proportioally more market share. This would ted to switch baks effective market equilibrium from beig loa poor, deposit rich to loa rich, deposit poor. Historically, this may have occurred i the U.S. durig startig i the 1970s ad lastig util 2001 as MMF competitio led to disitermediatio. Figure 5 shows the MMF share, defied as the ratio of total MMF assets to the sum of total bak deposits plus MMF assets. It also shows the Retail MMF share, defied as the ratio of retail MMF assets to the sum of isured bak deposits plus retail MMF assets. 15 Fially, the figure shows the ratio of baks holdigs of cash plus securities assets to total bak assets. It is apparet that from the late 1970s util aroud 2001, the MMF share of total savigs/trasactios accouts was risig as baks ivestmets i cash ad securities were decliig. This is cosistet with the hypothesis that greater competitio by MMFs reduced baks 15 Moey market fuds are classified as retail fuds or istitutioal fuds, with the latter caterig to wholesale ivestors. 21
retail deposits, turig from what was previously a loa poor, deposit rich market equilibrium to a loa rich, deposit poor equilibrium. Uder this sceario, the corporate tax burde shifts from baks retail depositors to their retail borrowers. Assumig o obak leders, baks equilibrium retail loa rates would rise from equatio (21) to equatio (19). However, the higher bak retail loa rates satisfyig equatio (19) would ow create icetives for obak leders to eter. That is because i this situatio, equilibrium obak leder loa rates are less tha those of baks. Cosequetly, with k of leders beig obaks, obak ad bak retail loa rates satisfy equatios (29) ad (30), respectively. I particular, oe ow expects that i this loa rich, deposit poor market that baks corporate taxatio creates a ledig disadvatage that makes securitizatio via special purpose vehicles relatively more profitable. Evidece cosistet with this shift is give i Figure 6. It shows the MBS ad ABS share, defied as the ratio, i percet, of outstadig MBS ad ABS securities to the sum of outstadig MBS ad ABS securities plus outstadig bak loas. 16 Of course, there may be additioal reasos outside the scope of our model for obaks to hold loas previously held by baks. Baks may have bee discouraged from holdig particular types of loas for risk maagemet reasos. 17 I additio, ot every type of loa experieced the same degree of securitizatio. Baks ted to specialize i relatioship loas made to opaque borrowers that require moitorig of the borrower s cashflow, rather tha moitorig of a borrower s asset value (collateral). A example of such loas is a usecured lie of credit. Relative to obaks, baks brach etwork gives them a advatage i makig such loas due to their ability to have a etwork of braches that 16 The measure of outstadig bak loas iclude real estate-related loas, agriculture loas, commercial ad idustrial loas, loas to idividuals, ad leases. Excluded are loas to depository istitutios ad other loas. 17 For example, durig the 1970s high ad volatile iterest rates caused losses o the log duratio mortgages held by may baks, precipitatig the savigs ad loa istitutio crisis. Bak regulators ecouraged mortgage securitizatio, i part via govermet sposored eterprises such as Faie Mae ad Freddie Mac. 22
simultaeously beefit retail deposit collectio ad retail loa moitorig. Both retail borrowers ad retail depositors ted to choose baks that are physically close. 18 Usecured loas, particularly those made to opaque small busiesses, may typically be harder to securitize. I cotrast, collateralized loas with well-established uderwritig stadards, such as mortgages ad automobile loas rated by credit scores, may be easier. I terms of our model, the differece betwee obaks ad baks operatig ad credit loss costs, c * L c, are L smaller for these loas relative to relatioship loas. IV. Survey of Prior Evidece Relatig to the Model Our model has aalyzed two mai dimesios of corporate taxes. How they affect baks choice of equity capital ratios ad how corporate taxes may ecourage obak etry, particularly i the form of tax-exempt securitizatio vehicles. This sectio examies empirical evidece o these two issues. IV.A Corporate Taxes ad Baks Choice of Equity Capital The paper s model assumes that baks must meet a miimum equity capital to asset ratio. I practice, regulators ofte require multiple miimum capital ratios, such as Tier 1 ad Tier 2 risk-weighted capital ratios ad a leverage ratio (equity capital to total uweighted asset ratio). I some istaces, baks ca meet a particular capital requiremet usig either subordiated debt or equity capital. Ashcraft (2008) focuses o how the mix of subordiated debt to shareholders equity capital i meetig a capital costrait affects risk-takig by U.S. baks. As a istrumet for baks o-risk-related icetive to use subordiated debt, he uses the corporate icome tax rate paid by commercial baks. A bak s total icome tax rate depeds o where it operates i the 18 Park ad Peacchi (2009) report that the Federal Reserve s 2004 Survey of Cosumer Fiace idicates that the media distace betwee a household ad its bak is 2 miles for checkig accouts ad 3 miles for savigs accouts ad Certificates of Deposit. Based o the 2003 Federal Reserve Survey of Small Busiess Fiaces, for bak loas made i the 1970s, 1980s, 1990s, ad 2000-2003, the media distaces were 2, 2, 4, ad 9 miles, respectively. Oe might coclude that distaces from their baks are becomig less importat for small busiesses but ot for depositors. 23
Uited States because idividual states may add state-level corporate icome taxes o to the federal corporate icome tax. If a bak ca meet its capital requiremet by issuig competitively-priced subordiated debt, rather tha equity, the curret paper s model would predict it should do so because iterest o subordiated debt is tax-deductible. A bak s icetive to substitute subordiated debt for equity is greater the higher is the corporate icome tax rate it faces. Ideed, Ashcraft s (2008) empirical evidece supports this predictio. He fids a statistically ad ecoomically sigificat positive relatioship betwee a commercial bak s proportio of subordiated debt to equity ad the effective state corporate icome tax rate that it pays. Schadlbauer (2014) also uses variatio i U.S. states corporate icome tax rates to test whether higher rates affect leverage. Usig a differece-i-differece approach that compares similar baks i geographically close states, he fids that, o average, baks icrease their odeposit debt by 5.9% i the year before a corporate tax icrease is eacted i the state where the bak operates. Thus, baks appear to raise their leverage ratios i aticipatio of a higher tax rate. The icrease i debt is the greatest for better-capitalized baks. Baks facig a tax icrease also reduce loa growth by 2.3%, cosistet with the curret paper s predictio that higher taxes lead baks to lose market share to obaks. This slowig of loa growth occurs primarily with worse-capitalized baks. I 2006, Belgium iitiated a otioal iterest deductio for a corporatio s shareholders equity equal to the 10-year govermet bod rate. This tax policy chage, to a close approximatio, equalized the corporate icome tax treatmet for debt ad equity. Schepes (2014) aalyzes whether this reductio i the corporate tax disadvatage of equity chaged the equity capital ratios of Belgia baks. His test matches 35 Belgia baks to other Europea baks based o a earest eighbor propesity score. He fids that implemetatio of this tax policy icreased Belgium baks equity ratios by 14% o average relative to the cotrol group of baks. Moreover, this rise i the equity capital ratio occurred via a icrease i bak s absolute amout 24
of equity, ot by a reductio of debt ad bak assets. Hece, this policy s effective decrease i the tax rate o equity supports the curret paper s model predictio that baks should expad their market share. IV.B Corporate Taxes ad the Icetive to Securitize Loas Recall that the model predicts that higher corporate tax rates, by makig a bak s obalace sheet equity fiacig more expesive, icreases the likelihood that loas will be securitized. I other words, off-balace sheet fiacig where a corporate tax-exempt special purpose vehicle holds loas fuded by debt ad equity, becomes more profitable. The icetive for SPV fudig is greatest whe a bak operates i a loa rich, deposit poor market. Ha, Park, ad Peacchi (2014) test this model predictio by examiig U.S. baks decisio to retai or sell the mortgages they origiate. This paper uses Home Mortgage Disclosure Act (HMDA) data o baks operatig i differet U.S. Metropolita Statistical Areas (MSA) over the period 2001 to 2008. A MSA is characterized as loa rich, deposit poor if it has relatively large umbers of youg people compared to those over age 65. I cotrast, a MSA is characterized as loa poor, deposit rich if there is a relatively large umber of people over age 65. 19 As the model predicts, they fid that baks that operate i higher tax states ted to sell relatively more of their mortgages, but oly whe these baks also operate i a MSA with relatively youg people (loa rich, deposit poor). For baks i relatively youg MSAs, a oestadard deviatio icrease i the state corporate icome tax rate raises mortgage sales by 24.6%. Gog ad Ligthart (2014) aalyze the same issue but i a multi-coutry settig. They examie the securitizatio activities of 4,423 baks headquartered i 19 OECD coutries over the period 1999 to 2006. Based o ABS Alert data, 265 of these baks had sposored at least oe MBS or ABS deal. They classify a bak as operatig i a loa rich, deposit poor eviromet if 19 Categorizig markets by age is based o the idea that youger people are more likely to take out loas while older people are more likely to be savers. I particular, after age 65 may people ivest heavily i bak certificates of deposit. This cocept of associatig older (youger) MSAs with more (less) savigs origiates with Becker (2007). 25
it has a relatively high loa to deposit ratio. Based o the effective margial corporate icome tax rate of the coutry i which the bak is headquartered, they fid that baks i high tax coutries were more likely to securitize loas, but oly if they had a relatively high ratio of loas to deposits. For these loa rich, deposit poor baks, a oe stadard deviatio rise i the corporate tax rate icreased securitizatio itesity by 1.12 percet. I closig this sectio, it should be ackowledged that corporate taxes ca distort baks decisios i other ways that are outside the scope of this paper s model. For example, i may coutries a bak s taxable icome is recorded oly whe capital gais o its securities holdigs are realized. The ability to defer corporate icome taxes o urealized capital gais creates icetives for baks to maitai their holdigs of appreciated securities. Vo Beschwitz ad Foos (2014) documet that, due to a 50% capital gais tax, Germa baks maitaied their owership of appreciated stocks of corporatios to which they also let. After this tax was repealed i 2000, baks divested 86% of their equity stakes i the followig six years but also icreased their ledig to these same corporatios by 60%. This behavior is cosistet with capital gais taxes creatig excess exposure to corporate risk that ihibits baks desire to make corporate loas. V. Cocludig Remarks This paper developed a model of a fiacial services market to study the determiats of baks equilibrium retail loa ad retail deposit rates. The model cosidered the effect of corporate icome taxes o equilibrium iterest rates. Whe baks are subject to a miimum ratio of equity capital to total assets, retail depositors bear a corporate tax burde i the form of lower deposit rates if the market structure is oe of limited ledig opportuities but rich amouts of retail deposits. I this situatio, baks use excess retail deposits to ivest i securities. I cotrast, retail borrowers bear a corporate tax ito burde i the form of higher loa rates if the market structure is oe of rich ledig opportuities but limited retail deposits. I this settig, baks use competitively-priced wholesale debt to help fud the high demad for loas. I the absece of 26
corporate icome taxes, equity capital requiremets may ot be bidig i this latter case, a situatio that appears to characterize U.S. baks durig some periods prior to the eactmet of corporate icome taxes i 1909. The model was exteded to cosider obak fiacial service firms. If a obak savigs/trasactios accout provider i the form of a corporate tax-exempt MMF ow competes, baks are forced to raise their retail deposit iterest rates ad will ted to lose market share. Cosequetly, there would be a tedecy to for baks to switch from a situatio of rich deposits to poor deposits so that loas would eed to be fuded, at the margi, with competitively priced bak debt. The model predicts that such a situatio would icrease retail loa rates so that a corporate tax burde is shifted from retail depositors to retail borrowers. I tur, these higher bak loa rates create profitable opportuities for obak ledig i vehicles holdig securitized loas. Such a rise i MMF competitio coicidet with rapid growth i securitizatio characterizes the U.S. situatio durig the past 40 years. A empirical literature examiig the effects of corporate icome taxes o bak ad obak behavior has recetly emerged. Several studies support the theoretical predictios that higher corporate taxes give baks a icetive to reduce equity capital ad, i loa rich - deposit poor eviromets, to icrease obak ledig activity. What policy reforms might remedy these tax-iduced distortios? Clearly, repealig the corporate icome tax is a obvious remedy, though implemetig such a reform is likely to be politically difficult. A more idirect chael for reducig the tax disadvatage of bak equity might permit a Belgium-like tax deductio for a otioal retur o equity. Aother alterative is to allow issuace of appropriately-desiged cotiget covertible (CoCo) securities. 20 Such CoCos take the form of tax-deductible debt whe a bak is fiacially healthy but covert to stabilizig equity capital at the oset of bak distress. 20 Calomiris ad Herrig (2013) ad Peacchi, Vermaele, ad Wolff (2014) propose particular desigs for goig-cocer CoCos. 27
Appedix A. Equilibrium with Oly Baks Substitutig i for E i i the maximizatio problem (10) usig the balace sheet equality E i = L i D i W i, it ca be writte Max r r r L 1 i rl, i c D L i Di rd, i + cd Wi rm τ 1 τ 1 τ 1 τ r, r, W Li, Di, i which is equivalet to maximizig Max r, r, W Li, Di, i subject to the o-ru costrait: E E E ( ) ( ) re re re Li rl, i c ( D ) L i Di rd, i + cd Wi rm 1 τ 1 τ 1 τ ( 1 r ) i ru i i (A.1) (A.2) L D + W (A.3) Let λ be the Lagrage multiplier for costrait (A.3) ad the substitute equatios (3) ad (4) for L i ad D i ito (A.2) ad (A.3). The first order coditio for r L,i is L re rli, 1 + rli, + 1 L L L rli, c ( D ), ( 1 ) 0 L i + rli + λ rru = (A.4) tl 1 t 2 tl tl which simplifies to equatio (11). The first order coditio for r D,i is ( ) r, 1 + r, 1 c D D D r D D D L r + c r = L i E Di Di+ i Di, D Di, λ 0 Di td td 1 t 2 td td (A.5) which simplifies to equatio (12). The first order coditio for W i is equatio (13). B. Equilibrium with a Regulatory Capital Leverage Requiremet The problem is to maximize (A.2) subject to costrait (18) which ca be rewritte as Di + Wi if Wi 0 1 rreg Li (A.6) Di + Wi if Wi < 0 1 rreg Let λ be the Lagrage multiplier for costrait (A.6) ad the substitute equatios (3) ad (4) for L i ad D i ito (A.2) ad (A.6). The first order coditio for r L,i simplifies to rli, 1 + rli, + 1 re tl 2rLi, + cl( Di) + + λ = 0 (A.7) 2 1 t The first order coditio for r D,I simplifies to ( ) r + r t c D Di, 1 Di, + 1 2 D L i E rdi, + + cd+ Li + = 0 2 Di 1 t 1 rreg r λ (A.8) 28
The first order coditio for W i is λ rm + re / ( 1 τ ) = 0 if Wi 0 1 r ( τ) reg r + r / 1 λ = 0 if W < 0 M E i If W i 0, substitutig i for λ = re /1 ( τ) rm ( 1 rreg ) i (A.7) ad (A.8) gives (A.9) 1 r + r r t r r = c D r 2 + + + 2 1 t 1 t ( ) ( 1 r ) Li, 1 Li, + 1 E L E L, i L i M reg ( ) r 1 r = + r t c c L D + r Di, 1 Di, + 1 D L i Di, D i M 2 2 Di (A.10) (A.11) I a symmetric Bertrad-Nash equilibrium where r L,i = r L,i-1 = r L,i+1, r D,i = r D,i-1 = r D,i+1, D i = D/, ad L i = L/, the equilibrium loa ad deposit rates i (A.10) ad (A.11) become equatios (19) ad (20). If W < 0, substitutig i for λ r /1 ( τ) = E r M i (A.7) ad (A.8) gives rli, 1 + rli, + 1 tl 2rLi, + cl( Di) + + rm = 0 (A.12) 2 ( ) r + r t c D ( r ) Di, 1 Di, + 1 2 D L i E rd, i + + cd + Li + rreg rm /1 reg = 0 2 Di 1 t r (A.13) I a symmetric Bertrad-Nash equilibrium where r L,i = r L,i-1 = r L,i+1, r D,i = r D,i-1 = r D,i+1, D i = D/, ad L i = L/, the loa ad deposit rates i (A.12) ad (A.13) become equatios (21) ad (22). C. A Bak s Profit i a Market with Oly Baks From (A.1), the profits of a bak s iside ower (equityholder) equal L r D r r rli, c D, 1 L i rdi + cd Wi rm 1 τ 1 τ 1 τ E E E ( ) ( τ ) (A.13) Sice the regulatory capital costrait is bidig, whe W i 0 oe ca substitute W i = (L/)(1-r reg ) D/ to obtai L r r D r r rl, i c D L i reg rm rd, i + cd rm 1 τ 1 τ 1 τ 1 τ E E E E ( ) ( 1 r ) ( 1 τ) The substitutig i for r L,i ad r D,i from (19) ad (20) ito (A.14) leads to profits of ( D ) L t D t L c Di L + D + L i ( 1 t ) (A.14) (A.15) Whe W i < 0, oe ca substitute ito (A.13) the bidig costrait W i = (L/) (D/)/(1-r reg ) ad r L,i ad r D,i from (21) ad (22). Doig so also leads to (A.15). 29
D. Nobak Leder s Maximizatio Problem Substitutig i E 1 = L 1 - W 1 i the objective fuctio (23), the profit maximizatio problem is Max r, W L,1 1 * ( ) ( ) L r c Wr L W r (A.16) 1 L,1 L 1 M 1 1 E subject to L ( δ ) 1 1 ru W1. Note that L assumptio that r L,2 = r L,.Thus (A.16) becomes r + r L L = r + 2 tl L, L,2 1 L,1 ad from the symmetry Max r, W Li, 1 L t * ( rl,2 rl,1 ) + ( rl,1 cl re) W1 ( rm re) L L (A.17) L L rl,2 rl,1 + ru W1. Let λ be the Lagrage multiplier o this costrait. tl subject to ( ) ( 1 δ ) The the first order coditio with respect to r L,1 simplifies to * tl rl,2 2rL,1 + cl + re + λ( 1 δru ) = 0 (A.18) The first order coditio with respect to W 1 is ( r r ) λ W1 0 = M E (A.19) Thus, if W 1 > 0, λ = re rm. Therefore whe r E > r M, the capital costrait is bidig. If r E r M, it is ot ad λ = 0. Cosequetly from (A.18) oe see that equatio (25) holds. E. Baks Maximizatio Problem The derivatio is almost exactly the same as Park ad Peacchi (2009). The optimizatio problem for baks i a market cotaiig obaks is similar to our earlier solutio. For the case of a loa rich, deposit poor market, the profit maximizig loa rate ad deposit rates for bak i satisfy equatios similar to (14) ad (15): 1 r r Li, 1 + Li, + 1 E L L, i ( 1 reg ) r t r = r rm rreg cl 2 + + + + 2 1 t (A.20) 1 rdi, 1 + rdi, + 1 td rdi, = rm cd 2 + 2 (A.21) First, cosider (A.20). It ca be rewritte i the form of the secod-order differece equatio ( r ) r ( t) rli, + 1 4rLi, + rli, 1+ 2 1 reg rm regre /1 cl tl/ + + + = 0 (A.22) 30
For shorthad, defie ( r ) r ( t) r = 1 r + r / 1 + c + t /, which would be the L reg M reg E L L equilibrium loa rate i the market if there were oly baks. Equatio (A.22) ca be re-writte usig the backward operator as 2 ( ) 1 4 B+ B r + 2 r = 0 (A.23) Li, for i = 3,,. The roots to the quadratic equatio for the backward operator are B = 2± 3. L Also, ote that a particular solutio to equatio (A.23) is rli, = r. Therefore, the geeral solutio L to (A.23) takes the form r ( 2 3) i i + α ( 2 3) = α + + r (A.24) Li, 1 2 where the costats α 1 ad α 2 are determied subject to two boudary coditios. Oe boudary coditio results from the rate set by the obak i=1, which, iitially, we take as exogeous: r ( 2+ 3) α ( 2 3) = α + + r (A.25) L,1 1 2 The secod boudary coditio is the symmetry property for the oe or two baks that are most distat from the obak. Whe is eve, the oe farthest bak is i = /2 + 1, ad symmetry implies that the loa rates of its two eighbors, r L i-1 ad r L,i+1, are the same. Hece, equatio (A.22) is 1 1 r r r L, 1 L, L 2 2 L = 2 + 2, eve. (A.26) + Whe is a odd umber, there are two baks farthest away from the obak, baks i = (+1)/2 ad i = (+1)/2 + 1. If equatio (A.22) is writte dow for each of these two baks, ad the symmetry coditio r + 1 = r + 1 is imposed, the solvig these two equatios for 1 results i L, + 2 L, 1 2 2 1 2 r r r L, + 1 L, 1 1 L 2 2 + L r L, + 2 = 3 + 3, odd. (A.27) It what follows, we derive the solutio assumig that is eve. 21 Therefore, i additio to (A.25), the secod boudary coditio is based o (A.26). Substitutig (A.24) ito (A.26), simplifyig, ad otig that( 2 3) = ( 2+ 3) 1, leads to a proportioal relatioship betwee α 1 ad α 2 : ( + ) + 2 α 2 3 2 = α1 (A.28) Usig (A.28) to substitute for α 2 i boudary coditio (A.25), oe fids the solutio for α 1 to be 21 The case of odd is similar but uses coditio (A.14) rather tha (A.13). 31
α = 1 ( / ) r r + c + t L,1 E L L ( 2+ 3 ) 1+ ( 2+ 3) Usig (A.28) ad (A.29) to substitute for α 1 ad α 2 i (A.25), we obtai the solutio ( δ ) Li, i, L i, L,1 (A.29) r = 1 r + δ r, i = 1,..., (A.30) which shows that r L,i is a weighted average of rates with the weight o obak 1 s rate beig i ( 2+ 3) + ( 2 3) ( 2+ 3) + ( 2 3) + 1 + 1 i 2 2 δ i, 2 2 Note that (A.31) satisfies the symmetry coditios: δ 2, =δ,, δ 3, =δ -1,,, δ /2, =δ /2+2,. Its derivative with respect to i is ( 2+ 3) ( 2+ 3) + ( 2 3) δ l 1 i 1 i i. 2 2 = ( 2 3) + ( 2 3 ) + + i 2 2 (A.31) (A.32) Sice 0< ( 2 3) < 1< ( 2+ 3), δ i, / i < 0 over the rage from i = 2 to i = /2 + 1, the midpoit of the circle. This implies that a bak rate s weight o obak 1 s rate declies the further is its distace from obak 1. The derivative of (A.31) with respect to is ( 2+ 3) δ l i 1 i 1 i, = 2 ( 2 3) ( 2+ 3 ) 2 2 ( 2+ 3) + ( 2 3) (A.32) Sice i =2,, for the baks, δ i, / < 0. This meas that the rate charged by a bak of a give distace i 1 from obak 1 will have a smaller weight o obak 1 s rate the less cocetrated is the market. I other words, keepig distace costat, obak 1 s rate has less impact o a bak s rate the greater is the umber of baks i the market. For the geeral case of a market with total fiacial service providers havig k 1 obaks located symmetrically aroud the circle, let the umber of baks betwee ay two obaks, (/k) 1, be a odd iteger. The the same derivatio as above applies to each (/k) 1 group of baks bordered by two obaks. 22 A bak s rate is give by equatio (A.30) except that δ i, is replaced with δ i,/k, where δ i,/k is give by equatio (A.31) but with (/k) replacig. This is exactly equatios (26) ad (28). Sice δ i,/k / (/k) = δ i, / < 0, oe obtais δ i,/k / k = - 22 Note that sice obaks are idetical ad are assumed to set rates symmetrically, (A.25) cotiues to be a boudary coditio because the two obaks borderig a group of baks set the same rates. 32
(/k 2 ) [ δ i,/k / (/k)] > 0. This implies that give, baks rates place greater weight o the rate of the obaks the greater is the umber of obaks i the market. Each obak s rate settig problem is the same as i the k = 1 case, such that its equilibrium loa rate equals (25) ad, isertig this back ito its eighborig bak s loa rate oe obtais equatio (30). The same derivatio is used to fid baks deposit rates. 33
Refereces Ashcraft, A. 2008. Does the Market Disciplie Baks? New Evidece from Regulatory Capital Mix. Joural of Fiacial Itermediatio 17, 543-561. Becker, B. 2007. Geographical Segmetatio of U.S. Capital Markets. Joural of Fiacial Ecoomics 85, 151-178. Beltratti, A., J. Bock, R. Jewsikow, ad G. Nelso. 2014. BDCs - The Most Importat Commercial Leders You ve Never Heard About. Mimeo, Boccoi Uiversity ad Wells Fargo Securities. Black, F. 1975. Bak Fuds Maagemet i a Efficiet Market. Joural of Fiacial Ecoomics 2, 323-339. Burhouse, S., J. Feid, G. Frech, ad K. Ligo. 2003. Basel ad the Evolutio of Capital Regulatio: Movig Forward, Lookig Back. A Update o Emergig Issues i Bakig. Federal Deposit Isurace Corporatio. Available at https://www.fdic.gov/bak/aalytical/fyi/2003/011403fyi.html. Calomiris, C., ad R. Herrig. 2013. How to Desig a Cotiget Covertible Debt Requiremet that Helps Solve Our Too-big-to-fail Problem. Joural of Applied Corporate Fiace 25(2), 39-62. Chiappori, P.-A., D. Perez-Castrillo, ad T. Verdier. 1995. Spatial Competitio i the Bakig System: Localizatio, Cross Subsides ad the Regulatio of Deposit Rates. Europea Ecoomic Review 39: 889-918. DeAgelo, H., ad R. Stulz. 2013. Liquid-claim Productio, Risk Maagemet, ad Bak Capital Structure: Why High Leverage is Optimal for Baks. Joural of Fiacial Ecoomics (forthcomig). Diamod, D. 1984. Fiacial Itermediatio ad Delegated Moitorig. Review of Ecoomic Studies 51: 393-414. Diamod, D., ad P. Dybvig. 1983. Bak Rus, Deposit Isurace, ad Liquidity. Joural of Political Ecoomy 91: 401-419. Fama, E. 1985. What's Differet About Baks? Joural of Moetary Ecoomics 15, 29-40. Friedma, M., ad A. Schwartz. 1963. A Moetary History of the Uited States: 1867-1960. Priceto Uiversity Press, Priceto, NJ. Gog, D., ad J. Ligthart. 2014. Does Corporate Icome Taxatio Affect Securitizatio? Joural of Fiacial Services Research (forthcomig). Gorto, G., ad G. Peacchi. 1993. Moey Market Fuds ad Fiace Compaies: Are They the Baks of the Future? i M. Klauser ad L. White, eds. Structural Chage i Bakig. Busiess Oe Irwi, Homewood, Illiois. Graham, J. 2000. How Big Are the Tax Beefits of Debt? Joural of Fiace 55, 1901-1941. 34
Ha, J., K. Park, ad G. Peacchi. 2014. Corporate Taxes ad Securitizatio. Joural of Fiace (forthcomig). Mester, L., L. Nakamura, ad M. Reault. 2007. Trasactios Accouts ad Loa Moitorig. Review of Fiacial Studies 20, 529-556. Park, K., ad G. Peacchi. 2009. Harmig Depositors ad Helpig Borrowers: The Disparate Impact of Bak Cosolidatio. Review of Fiacial Studies 22, 1-40. Peacchi, G., T. Vermaele, ad C. Wolff. 2014. Cotiget Capital: The Case of COERCs. Joural of Fiacial ad Quatitative Aalysis, forthcomig. Salop, S. 1979. Moopolistic Competitio with Outside Goods. Bell Joural of Ecoomics 10: 141-56. Schepes, G. 2014. Taxes ad Bak Capital Structure. Workig paper, Natioal Bak of Belgium ad Departmet of Fiacial Ecoomics, Ghet Uiversity. Shadlbauer, A. 2014. How Do Fiacial Istitutios React to a Tax Icrease? Workig paper, Viea Graduate School of Fiace. Stadard & Poor s. 2014. Leveraged Loa Primer. Available at http://www.leveragedloa.com/primer/. Vo Beschwitz, B., ad D. Foos. 2014. Baks Equity Stakes ad Ledig: Evidece from a Tax Reform. Workig paper, Federal Reserve Board of Goverors ad Deutsche Budesbak. 35
Figure 1 Pael A: Ratio of Equity Capital to Assets of All U.S. Commercial Baks, 1834 to 2013 60 50 40 Ratio (%) 30 20 10 0 1834 1844 1854 1864 1874 1884 1894 1904 1914 1924 1934 1944 1954 1964 1974 1984 1994 2004 Pael B: Ratio of Equity Capital to Assets of All U.S. Commercial Baks, 1900 to 2013 Sources: U.S. Statistical Abstract ad FDIC Call Reports 36
Figure 2 Aggregate Cash, Securities, ad Loas as a Percetage of Commercial Bak Assets, 1834 to 2013 Sources: U.S. Statistical Abstract ad FDIC Call Reports 37
Figure 3 Market with Oe Nobak Nobak r L,1 or r D,1 = r M - c D Bak r L,2, r D,2 Bak r L,8 = r L,2, Rate Symmetry r D,8 = r D,2 Bak r L,3, r D,3 Bak r L,7 = r L,3, r D,7 = r D,3 Bak r L,4, r D,4 Bak r L,5, r D,5 Bak r L,6 = r L,4, r D,6 = r D,4 38
Figure 4 Market with Two Nobaks Nobak r L,1 or r D,1 = r M - c D Bak r L,2, r D,2 Bak r L,8 = r L,2, Rate Symmetry r D,8 = r D,2 Bak r L,3, r D,3 Rate Symmetry Bak r L,7 = r L,3, r D,7 = r D,3 Bak r L,4 = r L,2, r D,4 = r D,2 Nobak r L,5 = r L,1 or r D,6 = r D,1 = r M - c D Bak r L,6 = r L,4, r D,6 = r D,4 39
Figure 5 Moey Market Mutual Fud Share of Savigs/Trasactios Accout Balaces Sources: Ivestmet Compay Istitute ad FDIC 40
Figure 6 MBS ad ABS Share of All Loas Sources: Securities Idustry ad Fiacial Markets Associatio, FDIC, ad Ivestmet Compay Istitute 41