Bank Lending, Durable Goods and Spreads

Transcription

1 Bank Lending, Durable Goods and Spreads Aqib Aslam y Universiy of Cambridge Emiliano Sanoro z Universiy of Copenhagen Firs Draf: h May 28 This Draf: 22nd May 29 Absrac We inegrae a pro -maximizing ineres rae-seing banking secor ino a general equilibrium model of households wih heerogeneiy of ime preference, durable goods and collaeral consrains. Banks se he ineres rae on loans, lend o and borrow from agens in he economy, and are he means by which changes in he moneary policy rae are ransmied. The assumpion of monopolisic compeiion amongs nancial inermediaries induces an endogenous seady sae spread beween loan and savings raes. This spread increases wih concenraion in he banking secor, and crucially modi es he classical ampli caion mechanism in models of privae lending and collaeralized borrowing. We isolae an aenuaion of he e ecs of a moneary policy shock on he accumulaion of durables by collaerallyconsrained impaien households, due o changes in he user cos of durable goods induced by he divergence in ineres raes in he economy. This modi caion occurs irrespecive of he degree of rigidiy in ineres rae-seing. However, as he degree of sickiness in loan rae adjusmen increases, aenuaion is furher magni ed. JEL classi caion: E32; E43; E5 Keywords: Bank Lending, Durable Goods, Credi, Collaeral Consrains, Banking Aenuaor We would like o hank David Aikman, Piergiorgio Alessandri, Alexis Anagnosopoulos, Jim Bullard, Jagji Chadha, James Cloyne, Luisa Corrado, Domenico Delli Gai, Marin Ellison, Andrea Fracasso, Chryssi Giannisarou, Marvin Goodfriend, Sean Holly, Henrik Jensen, Alber Marce, Tommaso Monacelli, van Perella, Sefano Schiavo, Robero Tamborini, Dimirios Tsomocos, and ohers a he Bank of England for heir invaluable commens and suggesions, as well as paricipans a he 4h nernaional Compuing in Economics and Finance Conference in Paris, 26h June 28; he Macroeconomics Workshop, Universiy of Cambridge, he EPRU seminar, Universiy of Copenhagen, and he Macroeconomics Seminar, Universiy of Treno. All errors are our own. y Universiy of Cambridge, Faculy of Economics, Unied Kingdom, maa49@cam.ac.uk. z Universiy of Copenhagen, Deparmen of Economics, Denmark, emiliano.sanoro@econ.ku.dk.

2 nroducion Recen nancial and macroeconomic evens have led academics and cenral bankers alike o reconsider he core componens of he ubiquious New Neoclassical Synhesis (NNS) framework. Furhermore, hese evens have se ou he addiional ingrediens ha any micro-founded dynamic general equilibrium framework for he macroeconomy should ideally inegrae a he simples level: liquidiy-consrained households, durable goods such as housing, and ineres rae spreads generaed by a pro -maximizing ineres raeseing banking secor wih balance shee consideraions. The sandard NNS is ulimaely resriced since he ransmission mechanism of moneary policy remains limied o a single real ineres rae channel on aggregae demand. This means ha a number of ineresing issues are auomaically excluded, namely ineres rae spreads, as well as he ineracion of such spreads wih oher modeling assumpions such as credi marke imperfecions, collaeral and wealh e ecs linked o he evoluion of asse prices, and household heerogeneiy in saving raes. The model developed is populaed by wo ypes of consumers which are di ereniaed by he discoun facors applied o heir expeced fuure sream of insananeous uiliy. Boh classes of agens derive uiliy from consuming durable and non-durable goods. The relaively impaien agen mus also borrow o nance consumpion, using he discouned presen value of his expeced sock of durable good from he nex period as collaeral. To his we add a pro -maximizing monopolisically compeiive banking secor which ses he ineres rae charged on loans o impaien households and hrough which policy rae changes feed ino he res of he economy via he rae of ineres ha banks use o lend o one anoher. 2 Two compeing forces are highlighed: (i) an ampli caion mechanism, induced by he presence of impaien households collaeralized borrowing (agains durable goods), and (ii) a banking modi er, which arises because he direc provision of credi o borrowers by savers is replaced by he inroducion of pro -maximizing nancial inermediaries. More speci cally, we recover boh analyically and numerically a banking aenuaor on he accumulaion of durable goods for borrowers. As banks skim a margin for heir pro s, he level of loans exended o impaien households for he purposes of consuming boh nondurable and durable goods is less han in he absence of hese insiuions. The divergence The balance shee would appear o be a crucial par of any speci caion of he banking secor, as i is an imporan roue for boh inroducing and undersanding porfolio managemen and liquidiy consideraions. 2 There is an imporan assumpion underlying his paricular use of he inerbank rae as he policy rae: changes o he policy rae have a one-o-one e ec on he inerbank lending rae. As is very clear in recen macroeconomic developmens, here is an obvious divergence beween cenral bank policy raes and inerbank raes. However, as his paper is concerned wih he e ecs of inroducing an ineres raeseing banking secor ino he NNS framework, his issue is emporarily side-sepped. is assumed ha moneary auhoriies can inervene direcly in inerbank markes o soak up excess supply and demand using open marke operaions, and subsequenly se he inerbank rae.

3 beween loan and policy raes, which depends upon he degree of concenraion in he banking secor, alers impaien households marginal rae of subsiuion beween durable and non-durable goods. Therefore, he inraemporal and ineremporal allocaion of funds is disored beyond he e ecs induced by collaerally-consrained borrowing in heerogeneous agens seings. The inroducion of marke power in he banking secor is suppored by a large number of conribuions considering local, naional and inernaional markes. 3 A number of recen sudies have also repored ha shifs in money-marke raes and he policy rae are no compleely passed hrough o reail lending raes. 4 This inheren feaure of he banking secor has been negleced by he micro-founded models employed for policy analysis. The aim of his sudy is o address his issue as well as oher broader quesions which he addiion of monopolisically compeiive banks raise. For insance, wha are he implicaions for durable and non-durable consumpion in he presence of margins in banking? Wha does he inroducion of opimizing banks add o he ransmission mechanism highlighed by he lieraure on he nancial acceleraor? How does he real economy reac o he presence of imperfec pass-hrough from policy o bank lending raes? The connecion beween collaerally-consrained households and durable goods has been explored in a number of sudies. Kiyoaki and Moore (997) build a general equilibrium model wih wo ypes of agens (borrowers and savers), and inroduce heerogeneiy via di erenial paience raes. Agens rade privae deb ineremporally and collaeral requiremens are moivaed by he presence of limied enforcemen. Building on Kiyoaki and Moore s work, acoviello (25) acively links heir framework wih he NNS, showing how he role of nominal deb and asse prices are cenral for propagaion of moneary policy shocks. Monacelli (29) furher invesigaes he role of durable goods in sicky price models. He shows ha inroducing nancial marke imperfecions in economies where agens have heerogeneous discoun facors and privaely raded deb reconciles he wo-secor New Keynesian model wih VAR sudies reporing evidence of co-movemen 5 beween durable and non-durable spending following a moneary policy 3 Sha er (993), Molyneux e al. (994), De Band and Davis (999), and Bikker and Haaf (22) are noeworhy examples. 4 Some recen sudies include Mojon (2),Weh (22), Angeloni e al. (23), Gambacora (24), de Bond e al. (25), Kok Sorensen and Werner (26), and Gropp e al. (27). Kobayashi (28) provides a horough review of he recen lieraure. 5 Erceg and Levin (26) and Barsky e al. (27) show how sandard sicky-price models incorporaing secoral heerogeneiy in price sickiness (usually in he form of sicky non-durable goods prices and exible durables prices) are a odd wih he daa, as hey canno generae co-movemen beween value added in he wo secors. Monacelli (29) explains ha a baseline wo-secor New Keynesian model canno replicae such e ecs, since asymmeric price sickiness in he wo secor model means ha whenever consumpion conracs in one secor following a moneary ighening, i would expand in he oher. This is due o he fac ha wih perfec markes he shadow value of durables (i.e. he discouned sream of marginal uiliies of durables) is roughly consan. As a resul, durable spending is highly sensiive o variaions in he user cos. 2

4 shock. 6 The model se ou in his paper di ers imporanly in one respec from hese preceding conribuions feauring collaeralized borrowing - household deb no longer re ecs ineremporal rading beween an impaien borrower and a paien saver. nsead here is a role for banks as explici pro -maximizing ineres rae-seing agens ha inermediae funds, balancing loans and deposis via heir balance shee. This paper also di ers in a number of respecs from oher recen lieraure examining he moneary ransmission mechanism in seings where lending raes deviae from he shor erm policy rae conrolled by he cenral bank. Goodfriend (25) and Goodfriend and McCallum (27) embed a fully-speci ed (perfecly compeiive) banking secor ino a dynamic sochasic general equilibrium framework. 7 These papers implemen RBCsyle loan producion funcions and price-aking banks, where loan raes emerge due o arbirage relaions wih he endogenous variables of he sysem. Valuable insigh is gained by showing ha he e ecs of exogenous shocks can be ampli ed or aenuaed due o changes in he exernal nance premium (EFP). Compared o he seady sae evidence provided by Goodfriend and McCallum (27), where ineres rae di erenials are a eced by he marginal value of collaeral, he seady sae ineres rae spread generaed by our model depends upon he degree of compeiive pressure in he banking secor (hrough he elasiciy of subsiuion beween bank loans). Curdia and Woodford (28) invesigae ime-varying spreads beween he lending and saving raes by inroducing an inermediaion echnology ino a heerogeneous agens framework. They show ha he inroducion of ineres rae spreads does no qualiaively a ec opimal moneary policy prescripions, alhough hey can have a non-negligible quaniaive impac. is worh poining ou ha in his paper we absrac from consideraions relaed o opimal moneary policy design, as he main focus is on he ineracion beween durables accumulaion and bank lending. Gerali e al. (28) develop a dynamic general equilibrium model wih banks and bank capial along he lines of acoviello (25). As in our paper, hey also produce evidence of a banking aenuaor e ec, which hey aribue o he presence of sicky ineres rae-seing for boh he deposi and he loan rae. Our framework di ers from his model in wo imporan respecs: rsly, we show ha banking aenuaion applies only o a resriced sub-se of variables, especially o nancially consrained agens durable accumulaion; secondly, we show ha banking aenuaion in his class of models is fun- 6 Speci cally, nancial marke imperfecions, capured by he presence of collaeralized borrowing by impaien agens, generae co-movemen for wo reasons: rsly, he shadow value of durables is now linked o he shadow value of borrowing (i.e. a marginal uni of durables allows o expand borrowing hrough he collaeral consrain); secondly, he abiliy o borrow depends on asse prices (i.e. a marginal increase in he price of durables allows o expand borrowing hrough he collaeral consrain). 7 Goodfriend and McCallum (27) highligh he role of collaeralized and uncollaeralized exernal nance premia as signi can facors in driving business cycle ucuaions. n his paper all borrowing is collaeralized, and here can be no uncollaeralized borrowing by consrained households. 3

5 damenally driven by he inroducion of a monopolisically compeiive banking secor, which generaes an endogenous seady-sae spread beween policy and lending raes, and no by he assumpion of loan rae sickiness. Therefore, we conclude ha o isolae an aenuaion of durables accumulaion in he presence of nancially-consrained agens and bank lending, he degree of sluggishness in loan rae adjusmens is neiher a su - cien nor a necessary condiion, bu only helps a reconciling he numerical performance of his class of models wih he empirical evidence. The remainder of he paper is laid ou as follows: Secion 2 provides a brief background o some of he key issues and characerisics addressed in he model and examines why hey are imporan o inegrae ino he framework; Secion 3 inroduces he core heoreical seing and he deails of he banking secor; Secion 4 discusses he key mechanism highlighed in he paper, namely he aenuaion of he nancial acceleraor e ec on he accumulaion of durable goods induced by he inroducion of a pro - maximizing banking secor; Secion 5 looks a he dynamics of he model economy under di eren shocks, wih coninued emphasis on he comparison beween banking and non-banking economies. The nal secion concludes. 2 Financial nermediaion and neres Raes By modeling lending aciviies as he oucome of opimizing behavior, we can inroduce ineres raes beyond he single bond rae prevalen in sandard NNS models. Banks will be modeled along he lines of he simple ndusrial Organizaion (O) models of banking as se ou in Freixas and Roche (997). The problem is one of consrained opimizaion, where he pro s for he jh bank are calculaed as ineres income earned from loans B ne of ineres paid on deposis. n he simples seing, pro s, j;, are de ned as: B j; Rj;L L j; + R B Bj; B R D D j; ; () where L j; represen morgage loans, Bj; B capures inerbank (ne) lending o oher banks, and D j; are deposis made a he jh bank by paien households. R B is he inerbank lending rae and will be he policy rae in he model, while Rj; L is he bank-deermined loan rae facing borrowers, and R D is he deposi rae paid by savers. Maximizaion is subjec o he consrain ha he bank balances is asses and liabiliies. The former comprises he various loans made o households as well as o oher banks, while he laer includes deposis. This consrain is formally referred o as he bank balance shee: L j; + B B j; = D j; : (2) Wihin his pro -maximizing seing, we speci cally implemen a monopolisically compeiive banking framework. Banks are monopolisically compeiive only wih re- 4

6 spec o he loan rae hey se on he loans o ered o borrowers, and no he deposi rae. Conrol of he laer rae could be inroduced wih lile addiional complicaion. is clear ha our model feaures deposis as he only source of funding for he lending aciviies of he whole banking secor. Therefore, a moneary policy ighening necessarily acs hrough a quasi-bank lending channel (which we laer re-chrisen he bank balance shee channel), by deermining an equal reducion in deposis and household deb in he form of loans (morgages). As o he process of ineres rae-seing in he banking secor, iniially we explore he impac of a consan mark-up beween he loan rae and he deposi rae (his is referred o as exible loan rae-seing ). We show laer in Secion 4.2 ha such a markup beween he win raes facing borrowers and lenders leads o a modi caion of he e ecs of shocks on he sysem s core variables. We hen enrich he loan rae adjusmen process by implemening Calvo-ype saggered ineres rae adjusmen. Once sickiness is inroduced, he spread beween loan and deposi raes can vary over ime. Kobayashi (28) explois an analogous mechanism, based on widespread evidence of imperfec pass-hrough from policy o bank lending raes. de Bond e al. (25) summarize pas empirical evidence ha documens ha he shor erm adjusmen (3 monhs) of reail bank raes o basis poins change in money marke ineres raes in he EURO area lies in a range of 8-32 basis poins for shor-erm consumer loans, of 2-4 basis poins for morgage raes, and of basis poins for shor-erm loans o rms. As he focus of his paper is on he ineracion beween nancially consrained agens accumulaion of durables and bank lending, i seems appropriae o explore furher how he ineres rae on loans o households reacs o changes in he policy rae. To assess he impac of moneary policy shocks we esimae a quarerly VAR model for he US economy of he form: Z = A (L) Z + + " Z (3) where Z is a vecor of endogenous variables, is a vecor of consan erms and " Z is a vecor of error erms ha are assumed o be whie noise. The vecor Z comprises real GDP, he GDP de aor, he federal funds rae, and he 3-Year Convenional morgage rae. Based on he VAR model, we generae impulse responses of he variables in Z o a moneary policy shock, which is ideni ed by imposing a riangular orhogonalizaion. The ordering of he variables implies ha an innovaion in he shor-erm rae a ecs he oupu level and he price level wih a lag of one quarer, while he loan rae responds conemporaneously. Figure displays he impulse responses of he variables o a moneary policy shock, which is re eced by a one-sandard-deviaion shock o he shor-erm rae. The simulaion horizon covers 2 quarers. The solid lines denoe impulse responses. The doed lines are approximae 95% error bands ha are derived from a boosrap rouine wih 5

7 2 replicaions. nser Figure here The impulse responses show sandard resuls for in aion and GDP o a moneary policy shock. n aion falls following a lag while oupu begins o fall in he following quarer. Crucially, here is incomplee pass-hrough from he Fed Funds rae o he morgage rae se by banks for convenional 3-Year loan producs. Furhermore, he loan rae displays higher persisence han he policy rae. This, ogeher wih he evidence cied above, moivaes our inroducion of Calvo-ype sickiness in he loan rae. 3 The Model This secion ses ou he model o be discussed in he paper. As o he demand side, here are wo ypes of consumer: paien households and impaien households, which are di ereniaed by he discoun facors applied o heir fuure sream of insananeous uiliy. 8 The supply side is populaed by monopolisically compeiive rms producing inermediae goods, as well as by a perfecly compeiive nal goods producion secor. Moreover, here is a nancial inermediaion secor, specializing in exending loans o collaerally-consrained impaien households, and a monopolisically compeiive banking secor, which provides lendable resources o he inermediaries. 3. Consumers There are wo households in he economy:. Paien households, who are nancially unconsrained and behave sandard permanen income households would. They choose how much o deposi wih banks (save) and receive all residual pro s from he monopolisically compeiive inermediae goods producers and monopolisically compeiive banks; 2. mpaien households, who are credi-consrained and borrow from nancial inermediaries using heir holdings of durable goods as collaeral. They also earn wages from rening heir labor o he inermediae goods secor. n his model, paien households savings in he form of deposis and he amoun of borrowing by impaien households are linked hrough he aggregae balance shee 8 Ramsey (928) posulaes ha if wo dynasies have di eren discoun raes and a loan marke is in operaion, hen "equilibrium would be aained by a division of sociey ino wo classes, he hrif enjoying bliss and he improviden a he subsisence level". Becker (98) and Becker and Foias (987) con rm his conjecure, and design dynamic general equilibrium frameworks where wo classes of agens coexis and di er wih respec o heir discoun facor. 6

8 of he banking secor. This crucial link provides an explici role for monopolisically compeiive ineres rae-seing banks o inermediae funds across he economy. The dynamic opimizaion problem for each household is brie y se ou below, and he rs order condiions are repored in Appendix A. 3.. Paien Households The preferences of he represenaive paien household are de ned over a non-durable consumpion good (C P ), durable goods services (H P ), labor (N P ) and real money balances ( M P P uiliy: ). These households maximize he presen discouned value of heir expeced where U P C P ; H P ; M P P E X = P U P C P ; H P ; M P P ; N P M P ; N P = log C P +" P log H P +% P log ; (4) P P (N P ) +' P +' P and P is he discoun facor. Parameer ' P denoes he inverse of he elasiciy of subsiuion beween work and leisure. Maximizaion is subjec o he following sequence of (nominal) budge consrains: P C P + Q H X P + D + M P = R D D + M P + W P N P + B + G + T P ; (5) where P is he price of non-durable goods, D indicaes end-of-period deposis which earn an ineres R D, payable a he sar of period +, Q H is he nominal price of durables B G (housing), and and are dividends (pro s) remied o paien households by he banking and goods secors respecively: Z B = B i;di, Z G = G i;di: (6) Furhermore, X P denoes he purchase of new durables: X P = H P H P (7) where we assume ha here is perfec durabiliy, i.e. durable goods do no depreciae over ime. Paien households ener each period wih M P nominal money balances, receive ransfers from he cenral governmen, T P = M P M P, and earn W P labor inpu o he goods secor. for heir 3..2 mpaien Households Preferences of he represenaive impaien household are de ned over consumpion of he nal non-durable good (C ), durable goods services (H ), labor (N ) and real money 7

9 balances ( M P ). mpaien households maximize he expeced presen discouned value of uiliy: X E U C ; H ; M ; N ; (8) P = where U C ; H ; M M P ; N = log C + " log H + % log N +', and P + ' ( P > ) is he ineremporal discoun facor. Parameer ' is as for he paien agens. Maximizaion is subjec o he following sequence of (nominal) budge consrains: P C + Q H X + R L L + M = L + W N + M + T : (9) mpaien households ener period wih L unis of nominal deb, pay R L gross nominal ineres on his deb a he sar of, and earn W N from working in he goods secor. Paien consumers receive ransfers from he governmen, T = M M, and accumulae durables according o H = X + H, where X denoes he purchase of new durable goods. Borrowing is resriced by he addiional collaeral consrain: R L L E Q H + H ; () ha is, he maximum amoun of borrowable resources is equal o a fracion of he value of durable goods holdings available a he sar of period. Parameer denoes he fracion of he durable good value ha canno be used as a collaeral. This consrain can be raionalized in erms of limied enforcemen. Alhough he borrower could in principle defaul on his deb obligaions, loosing he curren value of he asse acs as a deerren. 3.2 Financial nermediaion We now urn o he speci cs of he banking secor and he sysem of nancial inermediaion. The key elemen of our modeling sraegy emerges in he inermediae banking secor, which is made up of a coninuum of monopolisically compeiive banks who maximize pro s subjec o a balance shee consrain Final Banking Secor The nal banking secor can be viewed as he ulimae loan provider, where banks are aken o be perfecly compeiive and ac o aggregae loans o impaien households using a sandard CES aggregaor: Z L = (L j; ) L L L L dj. () 8

10 The degree of subsiuabiliy beween hese di eren loans is capured by he parameer L >. These loan producs are bundled ino an aggregae loan package for he collaerally-consrained household and his process is akin o how morgage reailers (he nal banking secor) obain funds from muliple sources on wholesale nancial markes when designing and o ering loans o cusomers. This Dixi-Sigliz srucure is ulimaely useful in allowing for ineres rae-seing by banks even if he heerogeneiy in banks is expressed via he producs hey o er and no heir acual risk pro les, which would oherwise be accouned for by heerogenous ineres raes. Pro maximizaion leads o a familiar loan demand funcion: L j; =! L RL j; R L L 8j; (2) where R L = R R L L j; dj L nermediae Banking Secor We nex derive he opimal relaions for loan supply by pro -maximizing banks ha choose ineres raes subjec o a binding balance shee consrain. We explicily inroduce a general framework which allows for di eren degrees of loan rae sickiness while sill generaing an endogenous seady sae spread beween raes. banks face nominal fricions as in Calvo (983). wih a probabiliy adjusmen. The average loan rae is given by: To do his we assume Each bank reses is loan rae only each period, independenly of he ime elapsed since he las R L = h R L L + ( ) R L L i L ; (3) where R L is he loan rae chosen by banks who are able o adjus. The jh bank maximizes pro s by choosing a sequence Rj;; L D j; ; Bj; B discouned sream of pro s o be:, aking he X E s= s ;+s ( X ) B j;+s = E s ;+s R L j;+s L j;+s + R+sB B j;+s B R+sD D j;+s : (4) s= where ;+s is he sochasic discoun facor derived from paien households maximizaion problem. Maximizaion is subjec o he bank balance shee consrain: L j; + B B j; + H j; = X CB j; + D j; ; (5) 9

11 where H j; is high-powered money, iself de ned as: H j; = j; ; (6) where j; are cash reserves ransferred by bank j on is accoun a he Cenral Bank, i.e. he bank-speci c amoun of fracional reserves. j; ypically bears no ineres and is herefore opimally chosen a is minimal level de ned by he regulaor: j; = D j; ; ; (7) where is he reserve requiremen. 9 Therefore we can rewrie he balance shee consrain as: L j; + B B j; = X CB j; + ( ) D j; : (8) Therefore, he jh bank can nance is aciviy in hree ways: (i) i receives cash injecions (Xj; CB ) from he moneary auhoriy; (ii) i can obain funds on he inerbank marke, where he ne posiion of he jh bank on he inerbank marke is denoed by Bj; B ; (iii) i receives deposis from paien households. The loan demand curve (2) from he nal banking secor also serves as an addiional consrain for maximizaion and he inerbank rae R B and deposi rae, R D, are boh aken as given by he banking secor. Afer denoing wih B he Lagrange muliplier associaed o he balance shee ideniy, we rerieve he following rs order condiions: R D = B ( ) ; (9) E 8 < X s ;+s : s= L RB +s Rj; L R B = B ; (2)! 9 L = + L R L j; R L +s L +s = ; (2) ; where Rj; L is he opimal rese loan rae of he jh bank. The inerbank rae equals he deposi rae scaled by he facor = ( ): R B = RD : (22) Furhermore, in he case of perfec exibiliy in loan rae adjusmen ( = ), he loan 9 n he lieraure, is a regularly-commened on, bu lile-used, ool of moneary policy. As he speci caion sands, has no been endogenized. However, o do so would require lile complicaion and is endogenizaion is saved for fuure work.

12 rae is a consan mark-up over he deposi rae (and herefore he policy rae): R L = L L RD : (23) Therefore, when we move away from exible ineres rae-seing ( > ), he mark-up beween R L and R D is no longer consan, bu becomes ime-varying. We will see in Secion 5 how saggered ineres rae-seing alers our key qualiaive resuls furher. When linearized, price-aking behavior by banks wih respec o he deposi rae, means ha he deposi and inerbank raes are equal ( ^R B = ^R D ), and so changes in he policy rae ranslae one-o-one o changes in he deposi rae. Linearizing (2) and combining i wih he aggregae loan rae (3) produces he New Keynesian ineres rae-seing curve for he loan rae: ^R L = P E h ^R L + i P ( ) ^RL ^R B : (24) Under exible ineres raes ^R L = ^R B. 3.3 Goods Secor 3.3. Final Good Producers The aggregae non-durable good is produced by perfecly compeiive rms and requires he assembly of a coninuum of inermediae goods, indexed by i 2 [; ], via he following echnology: Y = (Y i;) R di, where denoes he elasiciy of subsiuion beween di ereniaed goods. Pro maximizaion leads o he ypical demand funcion: R where P = (P i;) di earning null pro s. Y i; = Pi; P Y 8i; (25) is he price index consisen wih he nal good producer nermediae Goods Producion and Pricing A coninuum of rms produces inermediae goods. Shares of hese rms are owned by paien households. Each rm i 2 [; ] employs labor (supplied by paien and impaien households) in a consan-reurn-o scale producion funcion: Y i; = A Ni; P N i; ; (26)

13 where A is a oal facor produciviy shifer, N P i; is he rm-speci c oal demand for paien household labor, and N i; is he rm-speci c oal demand for impaien household labor. Price seing behavior in his secor is deailed below. Each rm acing in he inermediae goods secor has monopolisic power in he producion of is own variey and herefore has leverage in seing he price. n so doing 2 i faces a quadraic cos equal o = Pi; 2 P i; Y, rs proposed by Roemberg (982), where is he seady sae in aion rae and where he parameer measures he degree of nominal price rigidiy. 3.4 The Governmen-Moneary Auhoriy The governmen ses he nominal inerbank ineres rae according o a sandard Taylor rule: R B R B = R B R B rr r ry Y Y rr " R (27) where " R is a moneary policy innovaion. As is sandard in he lieraure, he governmen achieves such rules via open marke operaions (OMOs). These operaions are nanced by lump-sum cash ransfers, X CB, o he banking secor as well as wih money ransfers o he wo households, T P and T, such ha any de cis are equal o zero. 3.5 Marke Clearing and Aggregaion This secion liss he marke-clearing condiions. The aggregae resource consrain covers he goods marke clearing: Y = C P Y ; (28) P where C = C + C P. The supply of durable goods is held xed for he analysis ha follows. n paricular, he oal supply of durable goods, H, is se equal o, such ha H P + H = : (29) As he focus of he paper is on he inerplay beween bank lending raes and durable goods accumulaion by nancially consrained agens, inroducing durable goods producion would only complicae he analysis wihou adding any subsanial insigh, as shown in he nex secion. Equilibrium in he labor marke imposes ha: Z N i;di N ; Z N P i;di N P : (3) 2

14 ndividual bank balance shees from he inermediae secor are aggregaed o replace he radiional iner-household lending-borrowing clearing condiion in models wihou banks: L = D : (3) This aggregae bank balance shee embodies he noion of he banking secor inermediaing funds beween agens in he economy. mplicily, funds in he inerbank marke mus balance a he end of every period: Z B B j; dj B B = : (32) 4 The Model wih and wihou Banks The full linearized sysem is repored in Appendix C. We can decompose he model ino simpler varians which can be used o analyze how he inroducion of addiional secors and assumpions aler he radiional responses of major macroeconomic variables. The naural progression, herefore, will be: () a model of collaeralized borrowing wihou banks, (2) he same model wih banks which se loan raes exibly, and (3) a model wih banks in he presence of sicky loan rae adjusmen. n he absence of banks, households reurn o he familiar paern of rading deb ineremporally beween one anoher, and here is no divergence in ineres raes such ha he deposi rae for paien savers equals he loan rae for impaien borrowers. Boh households borrow and save a he same rae of ineres, R, which is se by he moneary auhoriy via OMOs. This is he same as he single aggregae ineres rae speci caion of he sandard NNS. Equilibrium borrowing and lending beween boh ypes of household is now simply b P = b, where b P denoes (real) paien saving and b denoes (real) impaien borrowing. This is used insead of he equilibrium (real) bank balance shee: l = d. 4. Deerminisic Seady Sae and he Collaeral Consrain in a Model wih Banking The deerminisic seady sae of he sysem can be solved for analyically, and is laid ou in Appendix D. n paricular, we are able o recover seady sae expressions for he ineres raes in he sysem. As discussed above, we nd ha he loan rae is a mark-up over he inerbank rae in he seady sae: R L = L L RB = L ( L ) ( ) RD = A lis of he linearized variables is repored in Appendix B.. L P ( ) ( L ) ; (33) 3

15 where he mark-up erm decreases in he degree of subsiuabiliy beween di eren loans and increases in he reserve requiremen. An imporan poin o urn o in his secion is how our seup guaranees posiive consumpion by boh agens as well as a unique, deerminae level of deb held by he impaien borrower in he seady sae. urns ou he combinaion of di erenial discoun raes, where he borrower is more impaien han he saver, and he presence of binding collaeral consrains ensures ha boh hese characerisics are presen. Becker (98) and Becker and Foias (987) iniially se ou how he long-run seady sae of he income disribuion in a heerogeneous agens model, where heerogeneiy is characerized by di eren discoun raes across households, is deermined by he household wih he lowes discoun rae. Furhermore, if discoun raes are equal hen he seady sae income disribuion would be indeerminae. This noion also appeared as he uni roo problem in he lieraure for small open economies wih incomplee inernaional asse markes, which has been addressed by Schmi-Grohe and Uribe (23) among ohers. Deerminacy imposes cerain resricions for he parameers in our model. From he rs order condiion (65), he collaeral consrain will be binding in he seady sae if and only if < =R L, since: = R L R L ; (34) where and are he seady-sae mulipliers associaed wih he budge consrain and he collaeral consrain faced by impaien households, respecively. 2 f his resricion is no sais ed he consrain would no bind and he level of borrowing by impaien households would be indeerminae and no always posiive in he seady sae. Therefore, a resricion needs o be imposed so ha he muliplier on he collaeral consrain is posiive in he seady sae: < R = L ( ) P < P = L L R : (35) D Condiion (35) shows how he righ hand-side inequaliy is he resul of bank-deermined ineres rae spreads, and he lef hand inequaliy arises due o he binding collaeral n addiion, as Campbell and Hercowiz (25) explain, in a model of heerogeneous discoun raes bu no consrains o borrowing, he impaien household s deb o he lender increases over ime o he maximum level he borrower can service via labor income. The inroducion of binding collaeral consrains resrics he level of deb such ha he economy possesses a unique seady sae wih posiive consumpion by boh households. Therefore a combinaion of deerminae deb under di eren discoun raes, enhanced by posiive seady sae consumpion when collaeral consrains are deployed, serve o reurn a unique, deerminae and sable seady sae pah for deb and consumpion by boh households. 2 See Appendix A. 4

16 consrain. 3 Thus, he relaive size of he discoun facors, as well as he elasiciy of subsiuion, L, are all imporan when imposing ha he collaeral consrain muliplier is posiive. 4.2 Ampli caion and Aenuaion in he Presence of Banking n general, loose moneary policy in models wih collaeralized borrowing booss he relaive price of durables which in urn increases he collaeral value of he sock of durables held by nancially consrained agens. Access o credi rises and his acs as an ampli er o he iniial impulse, allowing consrained agens o increase boh durable and non-durable consumpion. This rise in durables accumulaion is faciliaed by a decrease in he user cos of durable goods, which is a posiive funcion of he ex-ane real ineres rae and of he shadow value of borrowing. Therefore, a sofening of he collaeral consrain (i.e. a fall in he shadow value of borrowing) lowers he user cos, producing a subsiuion from non-durables owards durable goods consumpion. When borrowing akes place in he absence of nancial inermediaries, and credi ows direcly beween privae agens, he loan rae is ypically equal o he savings rae. However, when ineres rae-seing pro maximizing banks are inroduced, an endogenous seady sae spread is generaed beween lending and borrowing raes (see equaion 35) which will be shown below o aenuae he e ec of he iniial policy impulse on he marginal rae of subsiuion beween durables and non-durables. This aenuaion occurs regardless of he naure of ineres rae-seing, which can be expressed by varying degrees of rigidiy in loan rae adjusmen. The aenuaion mechanism is such ha he impac of a moneary policy loosening (ighening) - ceeris paribus - in a model wih banking decreases (increases) he user cos of durable goods by less han wha is observed in models wihou banks. Therefore, subsiuion from durable (non-durable) owards non-durable (durable) consumpion is reduced. n order o undersand how he collaeral consrain channel is modi ed in he presence of banks, we examine he dynamic sysem of equaions facing impaien households. Firs we look a he ineremporal e ecs on consumpion of non-durable goods. The linearized non-durable consumpion Euler of he impaien household reads as: ^C = ^R i h i L + R L E h^+ + R L E ^C + R L C {z } ^ : (36) > 3 We also carry ou simulaions o explore he sign of he muliplier. We recover a broad range of parameers for which he muliplier is posiive in he seady sae and we use his resul o con rm ha locally he collaeral consrain is binding. n e ec, he collaeral consrain may bind only occasionally. However, i always binds if he economy remains close o is nonsochasic seady sae; so following Campbell and Hercowiz (25) sandard rs-order approximaion echniques, speci cally log-linearizaion, can characerize he equilibrium of he model in he presence of small disurbances and low uncerainy. 5

17 As he muliplier increases and he collaeral consrain ighens (^ "), impaien household demand for non-durable goods falls, ceeris paribus. n he model wihou banks he linearized Euler reads as: ^C NB; = ^R i h i NB; + E P h^nb;+ + E P ^C NB;+ NB C NB ^ NB;: (37) {z P } > where subscrip "N B" denoes variables in he economy wihou banks. A ighening of he consrain (an increase in he muliplier) leads o a lower fall in consumpion in he presence of banks if R L > P, which is always sais ed when he collaeral consrain is binding in he seady sae. Nex we can uncover how he marginal rae of subsiuion (MRS) beween durables and non-durables for impaien households, UH; =U C;, varies in he presence of banks. Saring wih he impaien household demand for durable goods, we can assume ha he muliplier associaed o he collaeral consrain ( ) can be decomposed ino he muliplier on he budge consrain ( ) and a second muliplier,! : =!. 4 n addiion, we can rewrie some erms in he Euler in erms of asse price (durable good) in aion, H + = Q H +=Q H. This gives: U H; U C; = q H! E H + " U C;+ E q H UC; + # : (38) We can see how he presence of he muliplier increases he MRS and de-links i from asse price movemens. n he absence of he collaeral consrain we would have a oneo-one relaionship beween he relaive price of durables, q H, and he MRS. 5 The Euler equaions describing he dynamics of borrowers durable and non-durable consumpion can be combined o rerieve he following equaion for he user cos of durables, : = q H! E H + E R L! + q H R L + : (39) We can now see how he user cos capures he down paymen required o purchase a uni of durable (services). This equals he di erence beween he collaeral-adjused relaive price of durables and he e ecive collaeral-adjused amoun ha can be borrowed agains he addiional uni of durables. Linearizing (39) gives us an expression for he 4 See Monacelli (29). 5 Under perfec nancial markes (! = ) movemens in he user cos are dominaed by (curren and expeced) variaions in he asse price q. As explained by Monacelli (29), his is a he roo of he co-movemen puzzle. The presence of a binding collaeral consrain de-links his mechanism. 6

18 user cos: ^ = R L! ^q H + R E L H E ^q + +!! h ^RL ^ + i + (4) ^!! E h^h + i +! E h^+ i ; where = =R L +!. From he non-durable Euler, we know ha in he seady sae! = =R L. Equaion (4) herefore becomes: ^ = where: 6 ( R L R L ^q H R L + h R E L ^RL H R E ^q L + + ^! R L = + R L R L R L R L ^ + i + (4) E h ^H + ^+ i ) ; > : (42) Therefore, a ighening of he collaeral consrain, capured via an increase in he muliplier, ^!, increases he marginal user cos of durables, since R L and so we see a subsiuion away from durables o non-durables. > ; (43) n he absence of banks =R L = P, and here is only one ineres rae in he economy (R L = R D = R). Consequenly,! NB = P and NB = P + P > : (44) Noice ha i is always he case ha NB <. Therefore, he inroducion of banks aenuaes he increase in he MRS which arises from a ighening in he collaeral consrain, since P NB > R L > : (45) This demonsraes how he spread in ineres raes generaed by he presence of monopolisically compeiive banks can a ec he response of he MRS o variaions in he muliplier. n he model wih direc credi ows beween households he e ec of changes in he shadow value of borrowing on he user cos of durables is scaled by a facor ha de- 6 We can see ha is always greaer han zero, since R L >, < and R L >. 7

19 pends on he relaive degree of impaience of he wo agens, P. NB n our model he scale facor is reduced by he inroducion of a wedge beween he degree of impaience of borrowers and he ineres rae on loans (recall ha < =R L < P ). This wedge is he seady sae spread beween he win borrowing and saving raes in he sysem. Given expression (4) for he impaien household s MRS, we can also show how he e ec of a moneary policy ighening is aenuaed in he presence of a monopolisically compeiive banking secor. From (4), he marginal e ec of ^R L on ^ is equal o: R L = (R L ) + ( ) RL > : (46) This is always greaer han zero (R L > and > R L ). For analogous argumens, a rise in ^! (a ighening of he collaeral consrain) means ha he user cos rises. The following responses can be compued in each case (recall ha in he model wih banks ^R B ^R ^ ^R NB; = + ( ) P > ; ^ ^R B = L P ( L ) + ( ) h P i > : (48) L ( L ) f we impose ha he wo responses such ^ NB; can be rerieved: which is always sais ^R ^ ^R B, he following inequaliy L < ; (49) L The presence of monopolisically compeiive banks means ha he subsiuion away from durables o non-durables is relaively lower when moneary policy is conracionary. As subsiuabiliy increases beween he loans of each bank in he inermediae banking secor, he mark-up erm ( L = L ) ends o one, and he wedge ^ ^R and ^ vanishes. Therefore, he aenuaion e ec of nancial inermediaion iself ^R B as L increases. As shown, his aenuaion occurs irrespecive of he degree of sickiness in he ineres rae-seing mechanism. 5 Numerical Analysis n his secion, we explore he dynamic implicaions for moneary policy and he economy agains a backdrop of bank lending and collaerally-consrained households. To his end we invesigae wo shocks in he conex of he dual-household framework wih and 8

20 wihou banks. The rs is a sandard moneary policy shock, while he second is a shock o he loan-o-value raio. Then we consider a shock emanaing from he banking secor iself. Firs, we discuss he calibraion of he model. 5. Calibraion Given he complexiy of he model, various ranges around some of he more radiional parameerizaons were esed. This simple sensiiviy analysis reveals ha cerain parameers exered lile e ec a he exrema of each range, and so i was safe for hem o vary more han ohers. Appendix B.2 records he speci c calibraion used o generae impulse responses. Key parameer calibraions are discussed here. The savers discoun rae is se o :99, and ha of he borrowers a :97. laer is chosen o ensure ha he collaeral consrain binds in he seady sae, namely he Lagrange muliplier associaed wih he collaeral consrain is greaer han zero. The Frisch elasiciies of subsiuion in labor supply, ' P The and ', are se o 2. n he goods secor, he facor share of paien labor,, is :4. Following acoviello (25), he preference parameer for durable goods is assumed o be : for boh agens. For he bank elasiciy of subsiuion parameer L, here was lile guidance in he lieraure. f we le s R RL denoe he spread (margin) beween he wo ineres raes R D faced by he household, we can use (33) o derive he following condiion: s R = Therefore, we can nd he appropriae calibraion for L : L ( L ) ( ) : (5) L = sr s R (5) where we have implicily assumed ha! (i.e. negligible or zero reserve requiremen). The (ne) spread beween he deposi rae and he loan rae in he seady sae is se o 2:68%. n order o ful ll condiion (35) and o be consisen wih he calibraed discoun facors, L is se o 5. We iniially calibrae he Calvo parameer governing he frequency of loan rae adjusmen o :36. This value implies an average duraion of approximaely one and a half quarers and follows from he empirical lieraure repored in Secion 2. We herefore consider a broad range of loan rae sickiness when exploring he dynamics of he model following a cos-push shock in he banking secor. We follow he lieraure when assigning a value for he loan-o-value raio. Speci cally, = :75. This value is used in boh acoviello (25) and Calza e al. (27), and suggess ha borrowers can secure heir loans agains hree-quarers of he value of heir collaeral. 9

21 Given he inclusion of money in he sysem, i is also necessary o calibrae he share of real money balances in uiliy. Once again, he lieraure was scarce in suggesed values. We choose a value greaer han or equal o he share of durable goods in uiliy. Given ha durable goods are no converible as a medium of exchange, as money is, i seems plausible o presume ha households prefer o hold more money, he mos liquid asse, relaive o oher asses in heir porfolios. We op for % P = :6. As for he moneary policy rule, we se r R = :8, r Y = :, r = :4. These are broadly consisen wih he values used in he lieraure on sandard Taylor rules. The moneary policy innovaion is assumed o be iid wih uni variance. 5.2 The E ecs of Adding a Banking Secor n his secion we compare he oupu for he benchmark model wih banks o one wihou a banking secor The E ecs of a Moneary Policy Tighening Figure 2 shows he e ecs of a one-sandard-deviaion moneary policy innovaion. nser Figure 2 here n he model wih banks and exible ineres-rae seing an increase in he policy rae leads o an immediae increase in he ex-ane real ineres rae on loans and deposis. The inroducion of Calvo-ype ineres rae-seing deermines an imperfec pass-hrough from he policy rae o he ineres rae on loans, whereas he deposi rae perfecly co-moves wih he policy rae. n general, he rise in ineres raes induces boh ses of households o pospone curren consumpion of non-durable goods. The responses show ha despie heir impaience o shif consumpion forward, impaien households reduce consumpion relaively more han paien households, since heir abiliy o borrow falls wih he increase in he ex-ane real ineres rae. Furhermore, he ighening of borrowing condiions for impaien households from he conracion in he discouned value of heir collaeral is exacerbaed by he fall in house prices, which follows he moneary policy conracion. Real loans fall, as well as he demand for boh durables and non-durables. Therefore, he presence of a collaeral consrain leads o complemenary e ecs on impaien households consumpion of boh ypes of good. 8 We also observe perfec co-movemen beween paien consumers non-durable consumpion and he relaive price of durables, boh in he model wih and wihou banks. 7 All gures repor percenage deviaions from he seady sae. 8 Given a xed supply of durables (housing), paien durable consumpion is always direcly opposie o ha of impaien households. Despie he responses of durable goods consumpion for boh households being deermined simulansously in equilibrium, he unconsrained paien households are seen o ake up he slack in he housing marke. 2

22 This e ec, documened by Barsky e al. (27), is a characerisic feaure of models wih durable goods and perfec nancial markes ha can be beer undersood by referring o he marginal rae of subsiuion beween paien agens durable and non-durable consumpion. Repeaed forward subsiuion yields: 9 U P C;q H = X j= P j E U P H;+j : (52) Barsky e al. (27) noe ha in he case of durables wih low depreciaion raes, 2 he righ hand-side of (52) is heavily in uenced by he marginal uiliies of durable service ows in he disan fuure. When shocks hiing he economy (and heir e ecs) are emporary, he forward-looking erms in (52) do no deviae from heir seady-sae values, and so even signi can variaion in he rs few erms only have a small impac on he presen value. As Barsky e al. (27) poin ou, his means he presen value remains consan (or invarian) even in he face of subsanial emporary movemens in U P H;+j.2 Given ha he righ hand side of (52) remains fairly consan, any variaion in asse prices immediaely impacs on he marginal uiliy of consumpion. Speci cally, as asse prices rise, UC; P mus fall, which means ha paien non-durable consumpion will rise. n our seing, assuming a logarihmic uiliy in non-durables consumpion deermines perfec co-movemen. As o he impaien households, he presence of a collaeral consrain (i.e. imperfec nancial markes) de-links asse prices from he user cos of durables. The collaeral consrain e ec is such ha as he relaive price of durables falls he user cos in fac rises. We also recover an invered deb-de aion e ec, as in aion falls. This implies a ransfer of wealh from impaien households (borrowers) o he paien households (savers) as he real cos of curren borrowing increases, as well as he real reurn o curren deposis. As a main resul, once nancial inermediaion is inroduced, we nd ha banks induce an aenuaion of collaeral e ecs on he accumulaion of durable goods, as discussed in Secion 4.2. This aenuaion occurs regardless of he naure of ineres rae-seing, which can be expressed by varying degrees of rigidiy in loan rae adjusmen. An even sronger aenuaion occurs as he degree of ineres rae sickiness increases. The mechanism is such ha he impac of he moneary policy ighening in he model wih banking increases he user cos of durable goods by less han wha is observed in he model wihou banks. Therefore, he subsiuion from durables o non-durables is no as severe, 9 Ux; P denoes he parial derivaive of paien uiliy wih respec o variable x P a ime. 2 Recall ha assuming a zero depreciaion rae for durable goods (perfec durabiliy) implies an in nie sock- ow raio. 2 This approximaion is equivalen o saying ha he demand for durable goods displays an almos in nie elasiciy of ineremporal subsiuion. Even a small rise in he price of he durable oday relaive o omorrow would cause people o delay heir purchases. 2

23 and impaien households cu back relaively more on non-durable consumpion, given heir overall diminished capaciy o borrow due o lower collaeral values. The responses o he moneary policy ighening also show ha he presence of banks has no real e ec on he longeviy of he shock. The rae of he decay of he shock o each variable is no signi canly alered when moneary policy changes are inermediaed hrough banks. Therefore, banks do no appear o a ec he propagaion of he shock beyond aenuaing (or acceleraing in he case of non-durable consumpion) he exising e ecs. However, an increasing degree of sickiness in loan rae-seing does miigae furher he e ecs of a policy-induced shock on durable goods consumpion The E ecs of a Loosening of he Collaeral Consrain Figure 3 shows he e ecs of a emporary shock o he loan-o-value raio, which can be assumed o follow a log-saionary process: ^ = ^ + e ; (53) where e is an iid (; ) disurbance. n his case we allow for some persisence in he innovaion by seing = :5. nser Figure 3 here A posiive shock o he loan-o-value raio raises he amoun of loans he borrower can ge for a given value of collaeral. n order o fund his increase in loans, banks mus arac deposis, which requires an increase in he deposi rae. The increase in loans means ha impaien households experience a loosening of heir collaeral consrain. Subsequenly, heir consumpion of boh durables and non-durables increases. These responses once again re ec he complemenariy beween he consumpion of boh ypes of good ha a relaxaion or ighening of he collaeral consrain induces. The rise in deposis (savings) by paien households means ha hey pospone heir consumpion of durables and non-durables, which boh fall in he face of he shock. Due o he loosening of he collaeral consrain and o a higher marginal propensiy o consume, he fall in paien consumers non-durable consumpion exceeds he rise in impaien agens non-durable consumpion. This resuls in an overall increase in aggregae nondurable consumpion. Furhermore, in response o an increase in ineres raes, asse prices fall. And as raes begin o fall following he iniial impulse, asse prices rise once again. There is an elemen of overshooing as prices adjus o ensure ha he marke for durables clears. n aion also spikes as aggregae demand is boosed by he posiive shif in he demand for loans. 22