House Prices, Heterogeneous Banks and Unconventional Monetary Policy Options

Transcription

1 House Prices, Heerogeneous Banks and Unconvenional Moneary Policy Opions Andrew Lee Smih Deparmen of Economics The Universiy of Kansas Lawrence, KS This version: November 8, 213 Firs Draf: May 5, 213 Absrac This paper develops a financial mechanism which fully inegraes housing and financial markes ino an oherwise sandard Real Business Cycle model. The financial secor feaures heerogeneous banks whereby Too Big o Fail insiuions emerge naurally in equilibrium. By incorporaing housing-secured deb ino he financial markes, I show how a change in primiives, such as preferences over housing, can se off a financial firesorm which urns a ypical recession ino a deep, proraced crisis. This amplificaion effec emerges from he heerogeneiy in he financial secor. When home prices fall, he big banks leverage consrain endogenously ighens and housing-secured asses shif o smaller, less producive banks seing off an asse price spiral. As defauls moun, he share of bank-owned homes increases, which depresses home prices ino he fuure and prolongs he recession. This financial srucure is able o quaniaively capure he empirical relaionship beween finance premiums and home prices, oupu and invesmen; a relaionship he celebraed Bernanke, Gerler, and Gilchris (1999) model fails o capure. I also compare he qualiaive predicions of he model agains an esimaed VAR. I conclude by examining he abiliy of Quaniaive Easing policies and equiy injecions ino he Too Big o Fail banks o miigae a housing generaed recession. Alhough boh are effecive, he nuances of he policies are imporan. A prolonged asse purchase program is preferable o a shor-erm equiy injecion. Keywords: Financial Crises, Financial Fricions, Housing, Unconvenional Moneary Policy JEL Codes: E32, E44, G1, G21 asmih5@ku.edu PhD Candidae, Universiy of Kansas, Deparmen of Economics, 146 Jayhawk Blvd. Lawrence, KS I would like o hank paricipans in he Macroeconomics Research Seminar a he Universiy of Kansas for heir commens and feedback. Addiionally, hanks o paricipans a he 213 Midwes Economerics Group Meeings a Indiana Universiy and he 213 Missouri Valley Economics Associaion Conference for helpful quesions. I would also like o hank Shu Wu and Joe Haslag for insighful conversaions regarding his paper. Finally, I would like o hank my Disseraion Advisor, John Keaing, for his suppor and encouragemen. 1

2 1 Inroducion The firs drop in U.S. home prices since he Grea Depression resuled in he 28 Financial Crisis, forcing policy makers o Fly Blind, and ake he excepional acions of injecing equiy ino he larges U.S. financial firms and making a myriad of asse purchases wihou a playbook from economiss. Lile was known regarding he exac financial mechanisms linking home prices o he res of he economy, and o dae, many quesions remain. Why did a drop in home prices se off a financial panic ha forced he larges commercial banks o shed relaively more asses han heir smaller couner-pars? Wha is he ransmission mechanism and wha are he effecs of equiy injecions ino hese big banks and large-scale asse purchases amids a housing cenered credi crunch? In his paper, I propose an empirically moivaed financial mechanism which provides an answer o boh of hese quesions. I embed his financial srucure ino an oherwise sandard Real Business Cycle model o illusrae is abiliy o generae salien feaures of he U.S. economy. Quaniaively, he model maches empirical correlaions ha he radiional financial acceleraor mechanism (Bernanke, Gerler, and Gilchris, 1999) (BGG) fails o capure, including he correlaion of finance premiums wih home prices, invesmen and oupu. I hen es he model s qualiaive predicions agains an esimaed VAR. The resuls of hese empirical comparisons suppor he model s financial srucure. I am no alone in my effors o adap exising financial acceleraor frameworks o simulae he effecs of unconvenional moneary policy in ligh of he financial crisis. However, hese models ypically rely on Financial shocks o generae a crisis scenario and quadraic invesmen adjusmen coss o propagae he downurn (Gerler and Karadi, 211). In such models, no disincion is made beween housing secured deb and oher asses. I ake he alernaive viewpoin ha housing, and housing secured deb insrumens, played a paricularly imporan role in he crisis. In paricular, he housing and financial secor in he model I develop are highly inegraed a feaure ha allows for a financial crunch o originae from a change in primiives such as preferences over housing. Moreover, he use of housing as an ulimae source of collaeral for financial asses provides a naural source o propagae downurns as opposed o quadraic invesmen adjusmen coss. Upon defaul, he liquidaion of housing a durable increases he sock of homes and herefore decreases prices ino he fuure. Furhermore, he ime lag beween defaul and liquidaion leads o hump-shaped impulse response funcions of oupu, an empirical feaure used o jusify he inclusion of quadraic adjusmen coss (cf Chrisiano, Eichenbaum, and Evans (25)). Besides reaing he housing and he financial secor as independen, oher models ha have been used o analyze unconvenional moneary policy fail o provide an answer regarding he effecs, and desirabiliy, of equiy injecions ino Too Big o Fail banks. These papers assume eiher: (i) All banks are he same in erms of size and efficiency (Gerler and Kiyoaki, 21) or (ii) Banks differ in erms of size and efficiency, bu banks face no agency problems (Hafsead and Smih, 212). 2

3 However, boh of hese assumpion are a odds wih he empirical evidence. Recen esimaes of scale efficiency in he financial secor, including off-balance shee aciviies, have found ha Bigger is Beer (Wheelock and Wilson, 212; Bos and Kolari, 213). As for he laer assumpion, Demirguc-Kun, Deragiache, and Merrouche (213) find ha bank capial is an imporan deerminan for he performance of banks, mos markedly for big banks empirical suppor for over-urning he Modigliani-Miller heorem. 1 Wih his empirical evidence in mind, I incorporae bank heerogeneiy ino he financial secor. Big banks naurally arise in equilibrium due o heir superior efficiency inermediaing off-balance shee (housing-secured) asses, relaive o small banks. The only quesion is: Why do small banks operae a all in his marke if hey are echnologically dis-advanaged? This is where eschewing he assumpion ha banks face no agency problems is key. The big/producive banks in he model face a moral-hazard problem. They are oo producive in he sense ha hey have an incenive o falsely claim defaul on he secured-deb and abscond wih he collaeral. The only recourse for borrowers, he vicims of he fraud, is o sue he bank and ake he common-equiy. Therefore, he amoun of housing-secured asses he producive bank can hold is deermined by is capial. In his sense, bank-capial is key for he operaion of big/producive banks, consisen wih he empirical evidence. By capuring he rich ineracion beween he housing marke and he heerogeneous financial secor, he model is able o offer an explanaion as o why he concenraion of asses in he bigges commercial banks decreased wih home prices, as illusraed below Real Home Prices (Lef) Large Bank Share of Ne Credi Exposure (Righ) Figure 1: Real home prices (normalized o pre-recession peak) and he share of oal off-balance shee credi exposure held by he larges commercial banks. The financial mechanism I propose is capable of endogenously generaing he above comovemen. Beyond simply capuring a correlaion, he model provides he insigh ha he above redisribuion is no causal (from home prices o asse concenraion or vice-versa), bu insead a muually re-enforcing feedback relaionship which served o increase he severiy and lengh of he Grea Recession. However, he same feedback mechanism provides racion for boh equiy injecions ino large U.S. banks and large-scale asse purchase programs. 1 The Modigliani-Miller heorem saes ha how a firm chooses o fund iself (deb vs. equiy) is irrelevan. 3

4 2 A DSGE Model wih Inegraed Housing and Financial Markes In his secion I develop a general equilibrium model capable of capuring he asse redisribuion beween big and small banks ha occurs when home prices change. The model implies ha bank heerogeneiy amplifies ypical business cycles when large banks are leverage consrained. To he exen hese large financial firms can more efficienly inermediae secured-deb, he asse concenraion ha occurs during an upswing moves he economy closer o a Pareo oucome. The oher side of his coin however implies ha slumps can be made more severe due o his redisribuion. 2.1 Relaed Models and How his Model Differs The noion ha heerogeneiy beween agens can lead o amplificaion effecs is no new. Kiyoaki and Moore (1997) (hereafer KM) show ha an asse price spiral may occur if producive agens are borrowing consrained and he ighness of his consrain depends on asse prices. If an adverse shock resuls in decreased oupu for he producive agen, hey have fewer asses o borrow agains which resuls in unproducive agens absorbing hese asses, which hey are willing o do so only a reduced prices. However, since he producive agens binding consrain depends on he price of he asse, he decrease in price only furher ighens he collaeral consrain - saring he process over. The model I presen here builds on he keen insigh of his amplificaion effec, however he KM model is silen wih regards o defaul raes since agens in he model never defaul. This aspec was criical during he recen crisis where home prices and MBS fell in value in large par due o rising defauls on risky sub-prime loans. However, Bernanke, Gerler, and Gilchris (1999) (hereafer BGG) develop a financial fricion where risky projecs are financed and each period some share of financed projecs will fail resuling in no repaymen and hence defaul. However, BGG feaures no illiquid collaeral, insead all asses are already moneary. This feaure of he model misses he role of marke liquidiy (or illiquidiy) which is eleganly capured by KM. Moreover, BGG and KM don explicily include banks. 2 To he exen ha deposis and bank capial are perfec subsiues, he financial secor can be lef in he background as household s can hen direcly fund projecs wih deposis. On he oher hand, if bank capial serves a special role in miigaing financial fricions faced by he bank (on he supply side), hen hese agens mus be explicily modeled. Gerler and Kiyoaki (21) presen a model wih financial inermediaries where bank capial faciliaes bank s abiliy o obain funds. Banks in heir model face fricions in raising loanable funds however, here are no demand side fricions, so ha all loans face 2 In KM he agens can simply be re-inerpreed as banks wih invesmen opporuniies and his would capure supply side financial fricions. However, o he exen ha here are also demand side financial fricions his single banker/invesor model would undersae he role of collaeral values in miigaing his fricion. 4

5 zero defaul risk. Addiionally, here is no clear disincion beween big banks and small banks. Banks in heir model differ in erms of heir invesmen opporuniies bu no heir efficiency in inermediaing loans. Therefore, building on Hafsead and Smih (212), I include heerogeneous banks wih marke power - creaing bank capial in he model. Banks in his environmen differ in size due o differences wih regards o heir efficiency. Along his dimension, my work resembles Adrian and Shin (21) who model supply side financial heerogeneiy in erms of financial firms abiliy o value asses. Finally, in conrass o hese previous conribuions, I follow Iacoviello (25) and Iacoviello and Neri (21) who explicily model a housing marke. In paricular, I do no inerpre asse prices generally, bu insead I model asses whose underlying value as collaeral is ied o home prices. Alhough my inclusion of demand side and supply side financial fricions in erms of large producive banks and small unproducive banks is novel, his is one of he cleares conribuions of his paper. By focusing exclusively on asses whose values are ied o house prices, I am able o generae financial marke deerioraion from changes in primiives such as echnology and preferences. 2.2 Model Descripion The model consiss of a household, a housing producer, a coninuum of enrepreneurs who produce he final consumpion good, a banking secor wih 2 ypes of banks (producive and unproducive), boh of whom finance invesmen for goods producers and lasly a cenral bank is modeled. In his secion I will describe he behavior of each agen in urn. Many of he deails including he full se of model equaions are in he appendix as o no disrac from he basic mechanism a work in he model. I follow he convenion hroughou he model ha lower case variables are nominal and uppercase variables are in real erms - including ineres raes Household The household earns wages by rening labor o goods producers L and home builders L H. Addiionally, hey earn non-labor income from banks in he form of dividends p Div, ransfer paymens p T rans and principal plus ineres paymens p 1 D 1 r D 1 on las periods deposis. The moneary auhoriy may ransfer any revenue back o he household in lumpsum form via p T. This income can be saved in he form of bank deposis p D or spen on consumpion p C and housing p H H. Also, any non-depreciaed housing sock, (1 δ) H 1, can be resold a he marke price p H. The resuling budge consrain in any period =, 1, 2,... is given by, p C +p H [ H ( 1 δ H) H 1 ] +p D w L +w H L H +p 1 D 1 r D +p Div +p T rans +p T. Alhough I follow Iacoviello (25) and Iacoviello and Neri (21) by modeling a housing marke, I do no include home equiy borrowing consrains on he household side. Where hey focus on he wealh effecs of housing price changes in erms of financing consumpion, 5

6 I focus more so on real-esae as collaeral for invesmen and he ineracion of house prices and off-balance shee asse prices. Tha being said, in general equilibrium changes in home prices can impac consumpion via radiional income and subsiuion effecs, bu no hrough he home equiy channel highlighed by Iacoviello (25). The household maximizes heir lifeime expeced uiliy subjec o he flow budge consrain above. The household s lifeime expeced uiliy is specified by U = E {ln (C +i ) + η+iln H (H +i ) + η L ln (1 L +i ) + η LH ln ( 1 L+i) } H, i= where η H represens a shif in he elasiciy of demand for housing. I specify his as an exogenous process following a firs order auo-regressive process, in line wih Iacoviello and Neri (21). ln ( η H ) ( ) = 1 ρη H η H + ρ η Hln ( η 1) H + ε η H ε ηh N ( ), σ η H (1) Goods Producion The goods producing secor is comprised of a coninuum of enrepreneurs. Enrepreneurs have limied resources o finance capial required o produce he final good so hey mus borrow from banks. A financial fricion arises whereby enrepreneurs borrow funds from banks his period o purchase capial used in producion nex period. Their oupu nex period is subjec o idiosyncraic produciviy disurbances only observable by banks afer paying a monioring cos. Enrepreneur s Deb Conrac: The Demand Side Financial Fricion A coninuum of enrepreneurs j R + supply wholesale goods o reailers using capial and labor. Enrepreneurs only live for 2 periods and only care abou heir second period uiliy. In he firs period hey have no endowmen and no echnology bu hey have a uni of labor supply. In he second period of heir lives hey are endowed wih 1 uni of an asse which can be narrowly hough of as land, N, which can be ransformed ino housing only by enrepreneurs and banks. However, capial mus be purchased his period o be useful omorrow. Denoe he quaniy of capial purchased in period by enrepreneur j by K j and denoe he period price of capial by q. To purchase his capial he enrepreneur will receive financing from he banking secor. More specifically, he enrepreneur uses las period s wages p W E and pledges omorrows endowmen N j as collaeral for a secured loan in he amoun p N N j and he remaining porion of he capial purchase is financed wih an unsecured loan in he amoun p B j. More concreely, is enrepreneur j s budge consrain. q K j = p N N j + p B j + p W E (2) 6

7 Wihou defaul, disinguishing beween secured and unsecured loans is rivial. However, in he second period of heir life, enrepreneurs are subjeced o an idiosyncraic produciviy shock ω j +1 which is i.i.d. across home builders and ime. I assume hroughou he analysis ( (σ ω ) 2 ) ( in his paper, ω j +1 lnn, σ ω 2 wih CDF a ime denoed by F ω j +1). The choice of parameers implies E { ω+1} j = 1 so ha in he aggregae his idiosyncraic shock has no direc impac on producion, bu he exisence of uncerainy a he firm level impacs aggregae oupu hrough financial imperfecions (BGG). To capure exogenous increases in he cross-secional dispersion of idiosyncraic produciviy shocks I allow σ ω o vary over ime. I posi he simple auo-regressive process, ln (σ ω ) = (1 ρ σ ω) σ ω + ρ σ ωln ( σ ω 1 ) + ε σ ω ε σω N (, σ σ ω) (3) for his demand-side risk shock. Chrisiano, Moo, and Rosagno (213) show ha such shocks have played a significan role in shaping he U.S. business cycle. Moreover, hese shocks prove useful in he empirical analysis of he paper as hey provide a srucural inerpreaion for exogenous increase in he exernal finance premium. Since projecs are financed before he idiosyncraic produciviy shock can be observed by eiher he enrepreneur or he bank, enrepreneurs who receive a low produciviy value will defaul upon heir loan. Denoe he real gross ineres rae on unsecured loans by R L,j and denoe he gross real reurn on capial common o all enrepreneurs by R+1. K Then for any enrepreneur j, we can define he cu-off value of ω j +1 by he equaion ω j +1R K +1K j q = p B j R L,j. (4) This equaion defines he minimum level of produciviy needed o pay back he unsecured loan. For enrepreneur j, he loan will be repaid if ω j +1 ω j +1 and will oherwise be defauled upon. However, he bank can no observe he level of produciviy wihou paying an audiing cos in proporion µ (, 1) o he enrepreneur s revenue. 3 Banks who do no pay for audiing never find ou if he enrepreneur acually received a low produciviy draw or if hey simply chose o renege on heir loan. Given his arrangemen, he opimal debconrac dicaes ha banks will audi only defauling home builders and only enrepreneurs who receive a bad-draw will defaul on heir loans. To make maers more explici I define he expeced revenue o he bank for loaning p B j o enrepreneur j in (5). This expeced revenue is comprised of 2 erms, he firs of which is non-defauling loan revenue and he second is revenue ne of audiing coss on non-performing loans. ( 1 F ( ω +1) ) ω j j p B j R L +1 + (1 µ) ω }{{} +1dF j (ω+1)r j +1K K j q Non-Defauling Payoff }{{} Defauling Payoff (5) 3 This follows from Townsend (1979), bu has been popularized in his conex by Carlsrom and Fuers (1997) and BGG. 7

8 For he bank o be willing o make his loan, his expeced pay-off mus be a leas equal o bank s cos of making he loan. In BGG he cos of making he loan is simply he cos of obaining he funds via deposis - p B j R D. However since he banking secor in his model has marke power his is no longer he case. For he ime being simply define he real cos per dollar loaned by R E. 4 Then he incenive compaibiliy consrain can be expressed as, p B j R E = ( 1 F ( ω j +1) ) p B j R L + (1 µ) ω j +1 ω j +1dF (ω j +1)R K +1K j q. (6) We can simplify his expression (and he resuling enrepreneur s opimizaion problem) by defining he following erms. Firs le G ( ω +1) j be defined as he expeced produciviy value for defauling enrepreneurs. G ( ω j +1) = ω j +1 ω j +1dF (ω j +1) (7) Also le Γ ( ω j +1) be defined as he expeced share of enrepreneurial profis going o he bank gross of audiing coss. Γ ( ω j +1) = ( 1 F ( ω j +1) ) ω j +1 + G ( ω j +1) (8) Now I can combine (6) wih (4), (7) and (8) o rewrie he bank s incenive compaibiliy as, p B j R E = ( Γ ( ω j +1) µg ( ω j +1) ) R K +1K j q. (9) We can now formally sae he problem faced by enrepreneur j. To keep he deb-conrac racable, I assume he enrepreneur is risk-neural wih regards o aggregae consumpion. In paricular, I assume hey seek o maximize heir income and hen allocae ha income beween consumpion and housing services. Enrepreneur j herefore seeks o maximize oal income 5 subjec o he bank s IC consrain. ( 1 Γ ( ω +1) ) j R+1K K j q max K j, ωj +1 subjec o [ q K j p N N j p W E ] R E = ( Γ ( ω j +1) µg ( ω j +1) ) R K +1K j q The soluion o his opimizaion problem pins down he cu-off value ω j +1 and he enrepreneur s demand for capial K j. 6 The problem is idenical in naure o he problem enrepreneurs face in BGG who show he opimal deb conrac has he propery ha he defaul rae and exernal finance premium move inversely wih ne-worh. In his model, he ne-worh componen is replaced wih he collaeral value, implying ha ω +1/ p j N < - finance premiums and defaul raes will move in he opposie direcion of collaeral prices. 4 R E is explicily defined in he descripion of he banking secor in he appendix using he approach laid ou in Hafsead and Smih (212) 5 Noice he enrepreneur s income can be re-wrien as ω ω j j +1 df (ωj +1 )RK +1K j q +1 (1 F ( ω j +1 ) ) R L B j = (1 Γ ( ω j +1 ) ) R K +1K j q where I use (4) and (8). 6 The firs order condiions for his problem are in he appendix. 8

9 Aggregae Goods Producion The previous secion describes he firm-level behavior in he goods producing secor, specifically i describes he deb-conrac problem faced by each producer. In his secion, I describes he indusry wide behavior. Each enrepreneur (in he second period of heir ( K j 1 ) αg ( L G,j ) life) has access o he producion echnology, Y j = ω j 1 αg, which can be aggregaed over due o consan reurns o scale. The aggregae goods producion echnology in any given period is specified as Y = Z G ( K 1 ) αg ( L G ) 1 αg (1) where Z G is an exogenous echnology process which affecs all enrepreneurs equally. I assume his echnology follows a firs-order auoregressive process. ln ( Z G ) = (1 ρz G) Z G + ρ Z Gln ( Z G 1) + ε Z G ε ZG N (, σ Z G) (11) The gross aggregae real reurn on holding a uni of capial from period 1 o period is defined by R K = α G Y K 1 + (1 δ K )Q, (12) Q 1 where I uilize he aggregae marginal produc of capial from he Cobb-Douglas specificaion Y above - MP K = α G K 1. The labor aggregae in he producion funcion is a composie of labor supplied by he household, L,and labor supplied by his periods young enrepreneurs, L E, L G = ( L E ) αe ( L ) 1 αe. (13) This implies he wage paid o he household s labor and he wage paid o enrepreneurial labor are given by, W = (1 α G )(1 α E ) Y L (14) W E = (1 α G )α E Y L E I calibrae α E =.1 so ha in equilibrium he household receives he majoriy of wages and variaions in collaeral values are he primary sources of movemen in enrepreneur s balance shees. The aggregae income of enrepreneurs in period is (1 Γ 1 ( ω )) R K K 1 q 1. I assume enrepreneurs, like he household, receive uiliy from consuming boh he consumpion good and housing services. Unlike households, enrepreneurs have he abiliy o ransform heir endowmen of land - N j - ino non-radeable housing. Recall however, his endowmen was leveraged las period o secure a loan in he amoun p N 1N j. Hence, enrepreneurs who are able, choose o payback he secured loan wih ineres p N 1N j r D 1 and hen conver N j 9 (15)

10 ino housing services one for one. If hey don payback he secured loan hen hey defaul on his conrac and he bank akes possession of he collaeral N j. I assume in he aggregae, all he enrepreneurs who did no defaul on heir unsecured loan, payback heir secured loan and use he res of heir income on he consumpion good. Those who defauled on he unsecured loan have los all income and hence do no consume anyhing. More specifically, he aggregae real consumpion of enrepreneurs is given by C E = (1 Γ 1 ( ω )) R K K 1 Q 1 (1 F 1 ( ω )) P N 1N j R D 1. (16) Wha micro-level preferences would give rise o his aggregae consumpion behavior? is an ineresing quesion. In he appendix I describe one possible micro-srucure ha would lead o his aggregae consumpion behavior. An appealing aspec of his descripion is he exisence of a single defaul rae in he economy New Housing Producion I assume new housing is produced in a purely compeiive marke and free from financial fricions. In paricular, housing producers combine labor L H wih housing specific echnology, Z H in he producion echnology, H New = Z H ( L H ) 1 αh (17) where ln ( Z H ) = (1 ρz H) Z H + ρ Z Hln ( Z H 1) + ε Z H ε ZH N (, σ Z H). (18) I model housing specific echnology independen of echnology in he goods producing secor since much of he economics growh over he las wo decades has been IT-driven and housing producion is a non IT-inensive indusry. Moreover, his specificaion allows for goods echnology process, Z G, o play a significan role in deermining oupu wihou implying a counerfacual negaive correlaion beween home prices and GDP (see for example Davis and Heahcoe (25)). The resuling demand for labor from he housing secor akes he form W H = (1 α H )P H H New. (19) L H Banking Secor: The Supply Side Financial Fricion There are a uni measure of banks in he model each belonging o one of wo ypes. I disinguish bank ypes by a superscrip P for producive banks and a superscrip U for unproducive banks (who make up ν share of he populaion). Producive banks represen he Large commercial banks in he daa. These banks are more producive wih repossessed collaeral pledged by enrepreneurs o secure loans and hence value hese Off-balance shee asses more han heir unproducive counerpars. However, his efficiency creaes a 7 Tha is o say, he defaul rae on unsecured loans is he same as he defaul rae on secured loans. I choose his as a saring poin alhough his assumpion can be relaxed. 1

11 moral hazard problem for borrowers due o he possibiliy of producive banks wrongfully repossessing collaeral and absconding wih he profis. If his occurs, he enrepreneur s only recourse is o ake he producive banks accumulaed capial. To his exen, bankcapial miigaes he moral hazard concerns and allows he producive banks o hold more of hese collaeralized asses. An amplificaion effec emerges from he endogenous ighening and loosening of his moral hazard consrain which forces producive banks o adjus heir holding of collaeralized asses in response o movemens in home prices. For ease of exposiion I describe facors common o boh ypes of bank before describing each ype s opimizing behavior. In paricular, all banks have some degree of marke power, face a balance shee consrain and remi a fracion of profis each period back o he household in he form of dividends and various ransfers. In wha follows I generically refer o bank i o reference one of he infiniely many idenical banks wihin eiher ype. Each bank possesses a degree of marke power which is capured by assuming a Dixi- Sigliz ype aggregaor funcion. As Hafsead and Smih (212) poin ou, his has he simplifying feaure ha all banks serve all enrepreneurs and herefore face he same ex-ane and ex-pos defaul raes. More specifically, aggregae loans are a CES index ( 1 B = ) θb B (i) θ B 1 θ B 1 θ B where θ B is he elasiciy of subsiuion beween differen bank loans and is calibraed o mach aggregae lending raes. The corresponding price index which is dual 8 o his quaniy index is given by ( 1 ) 1 r B = r B (i) 1 θ 1 θ B B. (21) This specificaion of he aggregae indexes implies each bank i of ype T {P, U} faces he downward sloping demand for loans, ( ) B T r B,T θb (i) (i) = B. (22) r B Each bank i mus no only saisfy heir demand for loans, bu hey mus also abide o he balance shee consrain, (2) p B T (i) + p N N T (i) = p D T (i) + p 1 BK T 1(i) (23) which simply saes ha asses (bank loans) mus equal liabiliies (bank deposis) plus bank capial, respecively. Since banks use share holder s reained earnings o fund risky loans, I assume shareholders (households) require compensaion. More specifically, each period he bank is allowed (by 8 Dualiy here refers o he price and quaniy indexes which saisfy Fisher s facor reversal es, 1 rb (i)b (i)di = r B B. 11

12 he cenral bank) o expose a fracion ψ of bank capial o cover expeced losses on unsecured defauled loans. Each period, he fracion of loans ha acually defaul is given by F 1 ( ω ). Hence, each period he bank ransfers he nominal paymen p T rans T (i) = F 1 ( ω )p 1 ψ 1 BK T 1(i) (24) o shareholders in order o compensae hem for he capial ha was exposed o covering losses on loans originaed in period 1. In his sense, he ransfer o shareholders occurs only on realized, or ex-pos, loan losses. Combining his ransfer paymen wih dividend paymens, bank capial evolves according o he following law of moion. p BK T (i) = γ T p Π T (i) p T rans T (i) + (1 δ BK )p 1 BK T 1(i) (25) To summarize his, banks of ype T pay ou a ime varying fracion γ T of period profis as dividends and inves he remaining fracion in bank capial. Addiionally, banks compensae shareholders for exposing reained earnings o poenial losses via p T rans T and lose a fracion of bank capial o depreciaion. Following Gerali, Neri, Sessa, and Signorei (21), I assume bank invesmen decisions are made independenly from bank profi maximizaion, however, I assume his fracion is ime varying. In paricular, I assume ha γ T = γt p Π so T ha each period a consan amoun of new equiy is injeced ino he banks from shareholders. This implies realisically ha banks respond o falling profis by paying ou a smaller share of profis in dividends. Before proceeding o a specific descripion of each ype of bank s problem, i useful o summarize hese ransfers by defining ne invesmen in he banking secor. I BK = { ( ) s T γ T p Π T p T rans T ν if T = U where s T = (26) 1 ν if T = P T {P,U} Producive Bank The producive bank eners each period wih inflows consising of mauring unsecured loans r B,P 1 (i)p B 1(i) P and mauring secured loans p N 1N 1r P 1, D of which, (1 F 1 ( ω )) will be repaid in full. Denoe he real income of all borrowers who are unable o repay las periods loan by Φ 1 ( ω ). The producive bank will receives he fracion BP 1 (i) B 1 of φ 1 ( ω ) ne of audiing coss µ for he unsecured loan defauls. Addiionally, he producive bank repossesses F 1 ( ω )N 1(i), P which is he collaeral posed on he secured loans who defauled. This repossessed collaeral is ransformed in o housing using he echnology common o all banks, H R (i) = Z R N 1(i). P Finally, he producive bank also has incoming deposis oaling p D P (i). A he same ime, he producive bank has ouflows of newly originaed unsecured and secured loans oaling p B P (i)+p N N P (i) and mauring deposis from period 1 oaling p 1 D 1(i)r P 1. D This is saed more concisely below in (3) which defines he producive 12

13 bank s period nominal profis. p Π P (i) = (1 F 1 ( ω )) r B,P 1 (i)p B P 1(i) + (1 µ) BP 1(i) B 1 p Φ 1 ( ω ) + (1 F 1 ( ω )) p N 1N P 1(i)r D 1 + F 1 ( ω )p H Z R N P 1(i) (27) p B P (i) p N N P (i) p 1 D P 1(i)r D 1 + p D (i) The producive bank s abiliy o liquidae repossessed collaeral - N P a zero marginal cos raises a moral hazard. In paricular, if he producive bank were o claim defaul on all he secured loans originaed in period and repossess { he collaeral he} following period, hey would earn a gross real reurn oaling N P Z E R P+1 H (1 F( ω +1)R DP N ). The firs erm P N represens income from he selling he unlawfully repossessed collaeral and he second erm subracs he foregone income ha would have been received from enrepreneurs paying back heir loans. I assume a fracion of his reurn will be los when aken so ha producive banks only ne a fracion ψ N,P of his reurn. This varies sochasically according o he AR(1) process. ( ) ln = ( ) ( ) 1 ρ ψ N,P ψ N,P + ρ ψ N,P ln + ε ψn,p ε ψn,p N ( ), σ ψ N,P (28) ψ N,P ψ N,P 1 These disurbances provide a model equivalen o he large bank share shock from ha will be analyzed in he VAR. If he producive bank chooses o abscond wih he asses, enrepreneurs are eniled o he remaining equiy of he bank afer preferred shareholders (households) receive heir risk premium. Hence, enrepreneurs would be eniled o a claim of (1 ψ F ( ω +1 )) BK P (i). Thus, he incenive for producive banks o claim defaul and abscond wih hese off-balance shee asses is eliminaed when he equiy claims of exploied enrepreneurs exceeds he gross reurn on unlawful liquidaions. (1 ψ F ( ω +1 )) BK P (i) }{{} Equiy Claim of Exploied Enrepreneurs N P E { Z R P H +1 (1 F ( ω +1 )R D P N P N ) } ψ N,P } {{ } Gross Reurn on Unlawful Repossessions When (29) holds wih equaliy, he producive bank will be limied in how many offbalance shee asses i can hold. Moreover, his consrain will endogenously loosen and ighen in response o various macroeconomic shocks which affec home prices or defaul raes. Le Λ denoe he household s sochasic discoun facor used for valuing fuure real paymens. The problem faced by he producive bank is hen defined below. max {r B,P +j (i),bp +j (i),n P +j (i),dp +j (i)} j= j= E { Λ+j Π P +j(i) } subjec o (22), (23), (29) Due o he complicaions ha arise from solving a model wih an occasionally binding consrain, I calibrae he model so ha he producive bank s moral hazard consrain binds in he non-sochasic seady-sae. 13 (29)

14 Unproducive Bank The unproducive bank is idenical o he producive bank wih one noiceable excepion - hey are less producive. To make maers more concree, when a secured loan defauls he unproducive bank repossesses collaeral F 1 ( ω )N U 1(i). Unlike heir producive counerpars, he unproducive bank liquidaes his collaeral while bearing an increasing marginal cos. On defauled secured loans, he unproducive bank ransforms repossessed collaeral ino housing yielding revenue p H Z R N U 1(i) a a resource cos of p µ R,U ( N U 1(i) ) χ R,U. This capures he heerogeneiy beween commercial banks (described in secion??) wih regards o heir abiliy o evaluae and rade off-balance shee asses. Mos noably, as unproducive banks increase heir holding of hese asses, he value of he asses will fall due o he increasing marginal cos. Hence, he marke liquidiy of such asses depends on who is holding hem. A poin firs made by KM and applied o here o housing backed securiies wihin his model. Wih his excepion, he unproducive bank s profi funcion is very similar o he producive bank s saed below. p Π U (i) = (1 F 1 ( ω )) r B,U 1 (i)p B U 1(i) + (1 µ) BU 1(i) B 1 p Φ 1 ( ω ) + (1 F 1 ( ω )) p N 1N 1(i)r U D,U 1 (3) + F 1 ( ω ) [p H Z R N U 1(i) p µ ( R,U N U 1(i) ) ] χ R,U p B U (i) χ B,U B U (i) p N N U (i) p 1 D U 1(i)r D 1 + p D U (i) Noice he lack of produciviy spills over o unsecured loans. The parameer χ B,U is calibraed o mach he average share of resources allocaed o financial inermediaion. The increasing resource cos of repossessing collaeral implies he unproducive bank is no subjec o a moral hazard consrain. In paricular, if any single unproducive bank i aemped o purchase a large amoun of hese asses a a given marke price p N and falsely claim defaul, heir cos of liquidaing he asses would exceed wha hey paid for hem. Therefore he exisence of hese increasing marginal cos eliminaes any incenive o seal away hese asses. Le Λ denoe he household s sochasic discoun facor used for valuing fuure real paymens. The problem faced by he unproducive bank is hen defined below. max {r B,U +j (i),bu +j (i),n U +j (i),du +j (i)} j= { E Λ+j Π U +j(i) } subjec o (22), (23) j= Cenral Bank The cenral bank is charged wih seing a macroprudenial policy rule and a moneary policy rule. The macroprudenial policy insrumen is he regulaory maximum share of 14

15 capial ha can be allocaed o loan losses. This essenially conrols he amoun of owners equiy he bank can allocae o cover loan losses. Here, I assume he cenral bank simply ses his o a consan level. ψ = ψ (31) As for he moneary policy insrumen I assume he cenral bank follows he simple ineres rae rule whereby he rae on one-period deposis adjuss o he inflaion rae where π = Marke Clearing ( ) r D r = D p p 1. ( ) φπ π (32) π Secions describe he opimal behavior of all agens in he economy. A symmeric compeiive equilibrium is defined as a sequence of quaniies, prices and Lagrange mulipliers (shadow prices) which saisfy all opimaliy condiions, policy rules and marke clearing condiions. In paricular, he demand for housing mus equae he supply of housing on he marke which consiss of newly buil homes, repossessed collaeral being liquidaed on he housing marke and non-depreciaed housing from las period. Pu more simply, H = H New + F 1 ( ω )Z R ( νn U 1 + (1 ν)n P 1) + (1 δ H )H 1. (33) The above expression can be furher simplified by noing ha he marke for secured lending (or more narrowly, land) clears when N = νn U + (1 ν)n P, (34) where he lef hand side is he aggregae endowmen of enrepreneurs. By he ex-ane symmery among enrepreneurs his is required o equal N = N j for all home builders j. Similarly, his ex-ane symmery also implies he demand for capial by enrepreneurs is idenical, or K = K j for all enrepreneurs j. I assume ha capial can be ransformed one for one from he final good and depreciaes a rae δ K. Therefore, capial evolves according o, K = I + (1 δ K )K 1. (35) Since I do no include adjusmen coss, he price of capial equals he price of he final good a all imes, q = p. Adjusmen coss in he producion of capial could easily be added, as in BGG. However, in his model, hey are no needed o generae an amplificaion effec. Insead, he asse price spirals occur from he redisribuion of asses beween agens as in KM. Wih his descripion of he model, he goods marke clearing condiion is saisfied whenever, Y = C + C E + I + I BK + µφ 1 ( ω ) + νµ R,U ( N U 1(i) ) χ R,U + νχ B,U B U, (36) which sipulaes ha he consumpion good mus be eiher consumed by he household or he enrepreneur, invesed in bank capial, or used o audi or repossess he collaeral of 15

16 defauling enrepreneurs. I is useful for he purpose of calibraion and model inference o define GDP in his muli-secor model. 2.3 Calibraion GDP = C + I + P H H New (37) The model is calibraed o mach characerisics of he U.S. economy from 1998 o 212 and each ime period is inerpreed as one quarer. In order o numerically solve he model, here are 23 non-shock parameers and 15 shock parameers which mus firs be assigned values. Beginning wih he household s parameers I calibrae β =.99 as o mach up he seady sae deposi rae in he model wih he average rae on 3-Monh U.S. Treasury Bills. I se he uiliy on non-housing leisure and housing leisure, η LH = 7.43 and η L = 1.88 which maches he share of labor supplied in housing equal o 5%, he U.S. average using daa from he BLS and he oal share of ime spen working equal o 1/3. Finally, he las of he preference parameers η H =.2352 calibraes he seady sae real price of housing so ha consumpion s share of GDP = C =.79, which is he average raio of personal GDP consumpion expendiures o personal consumpion expendiures and privae invesmen for he U.S. Similarly, seing δ H =.21 implies he share of housing wealh o annual GDP, P H H = GDP On he producion side, I se he share of income going o labor in he goods producing secor, 1 α G =.7 and he same share in he housing secor 1 α H =.8 following Iacovello and Neri (21). I normalize he land endowmen of enrepreneurs, N = 1.As for he financial acceleraor parameers, I collecively se µ M =.14 and σ ω =.21. The audiing cos parameer falls beween he value from Chrisiano, Moo, and Rosagno (213) and BGG and he seady sae value of he variance of he idiosyncraic produciviy shock implies an annual seady sae defaul rae of F ( ω) =.1 which is he average defaul rae on C & I loans secured by real-esae using dae obained from he S. Louis Fed s FRED daabase. Wih regards o he banking secor, I se he share of capial allocaed o loan losses, ψ =.25, he average of loan-loss allocaions o he equiy of commercial banks over his period according o daa obained from FRED. I normalize each bank s share of he populaion o be equal by seing ν = 1. The depreciaion rae on capial is se a 2 δbk =.8 for a baseline calibraion, following Gerali, Neri, Sessa, and Signorei (21). The value for νχ B,U =.4954 is obained from Hafsead and Smih (212) who creae a ime series of banking produciviy in loan inermediaion. I se he seady-sae rae of reurn on enrepreneurial loans equal o he average prime loan rae, r E = This pins down he elasiciy of subsiuion beween bank loans, θ B = There is lile agreemen over he real reurn on capial, I se i equal o equal o 1% per annum which is slighly below he real reurn on capial in he U.S. esimaed by Oulon and Rincon-Aznar (29). 1 This 9 Hafsead and Smih (212) find a similarly high value for θ B = Oulon and Rincon-Aznar (29) esimae he average annual real reurn on capial o be 13%, however 16

17 value also maches he annualized reurn on small-cap socks, represening firms who are likely o be financially consrained, using daa from Morningsar. I se γ P =.3 and γ U =.1. These values simply ensure he ransfers made o he household for exposing equiy o loan losses, is made up for wih equiy injecions sufficien o guaranee a posiive seady-sae level of bank capial. Similarly, seing ψ N,P =.12 implies in seady sae, he share of Off-balance shee asses held by he producive banks, =.92, he average share of oal credi exposure concenraed in large banks, as explained in Secion (3.2). Addiionally, I se χ R,U = 1.6, implying sricly convex cos of repossessing/liquidaing collaeral for he unproducive bank. This value is adjused in he simulaions below. This ogeher wih seing µ R,U =.2755 calibraes he seady sae price of he Off-balance shee asses so ha P N N+B = 2.5, or he average raio of C&I loans P N N plus oal credi exposure o oal credi exposure. Finally, normalizing Z R = 1 and seing Z H F ( ω)z = 1.14 implies he real-esae owned share, or REO share, R N =.1775 which F ( ω)z R N+H New is he value in he daa according o RealyTrac. N P N P +N U As for he remaining policy parameers, seady sae gross inflaion is se equal o uniy and φ π = 2. following an OLS esimaion of (32) using daa on he effecive federal funds rae and he percen change of he core personal consumpion expendiure s deflaer. The resuls are essenially unchanged if Taylor s (1993) value of φ π = 1.5 is used. The remaining shock parameers can no be pinned down by maching seady sae values. The exogenous process,, which governs he producive bank s moral hazard consrain is used o highligh he impac of asse redisribuion beween banks, and is largely no srucural. Therefore, I se ρ ψ N,P =.9 and σ ψ N,P =.1. ψ N,P The remaining exogenous processes are calibraed using a momens maching exercise. In paricular, I choose ρ Z G =.9338, σ Z G =.157, ρ Z H=.6998, σ Z H =, ρ η H =.8959, σ η H =.665, ρ σ ω.8898 and σ σ ω =.455 o mach he model s sandard deviaion and firs-order auocorrelaion of: he exernal finance premium (proxied by he spread beween BAA corporae bond-rae and 1-year reasuries), real GDP 11, real privae invesmen and real home prices. This exercise no only pins down values for he model s driving shocks, bu since I do no resric he calibraion sraegy o mach he model s implied correlaion marix, i allows for an empirical examinaion of he model s performance. The model fis he daa reasonably well wih all momens in he confidence inerval. Comparing his model o he baseline BGG model augmened wih a housing secor, i becomes clear why he celebraed BGG financial acceleraor mus be adjused o analyze he financial crisis. The BGG financial conrac assumes he borrowers wealh is liquid, herefore (real-esae) secured deb is absen in he model. This explains why BGG has hey acknowledge his esimae is poenially biased upwards. Therefore, I follow Hafsead and Smih (212) and se he annual reurn o 1%. 11 Real GDP is measured as he model equivalen. Hence, I sum personal consumpion expendiures and privae invesmen and deflae he resuling series by he civilian populaion over he age of 16 and he personal consumpion expendiures excluding food and energy price deflaor. 17

18 Table 1: Cyclical Properies of he Model Correlaion 5 Percen Median 95 Percen Model BGG (1999) EFP, GDP EFP, P H EFP, Invesmen GDP, P H GDP, Invesmen P H, Invesmen a The daa correlaions and confidence inervals are compued using Jeffery s Prior and 5 draws from he resuling poserior disribuion of an esimaed VAR(2). difficuly capuring he dynamics beween he EFP and boh P H and Invesmen. BGG s counerfacual correlaion beween GDP and he EFP sems largely from he documened puzzle ha BGG s deb-conrac generaes an increases in he EFP following a posiive echnology shock. (Shen, 211). These issues are absen in he model presened here since housing secured deb, and herefore home prices, play a criical role in he financial conrac. 2.4 The Model s Amplifying Effec of Asse Redisribuion In his secion I analyze he behavior of he following four variables: 1. Exernal Finance Premium (EFP) = µ φ 1( ω ) B 1 2. Real GDP = GDP 3. Real house prices = P H 4. The share of off-balance shee asses held by large banks = (1 ν)n P N in response o he model s srucural shocks. For each se of impulse response funcions, I presen he model s response when he producive bank s moral hazard consrain binds (he solid lines) and when his consrain is relaxed (he dashed lines). Noice ha when he consrain is relaxed, he producive banks hold all of he Off-balance shee asses since hey are significanly more producive. Hence, for his model, he Large Bank Share variable is consan. Figure 2 displays he equilibrium model s response of he endogenous variables o a derimenal risk shock, posiive echnology and housing demand shocks and an increase in he share of off-balance shee asses held by he producive banks. The dynamics are noiceably differen when he moral hazard consrain binds compared o he efficien allocaion whereby large banks hold all of he off-balance shee asses. In paricular, he response of all he variables are amplified. Changes in he risk-characerisics of borrowers or he household s preferences owards housing are magnified by a facor of 2 when asses are redisribued beween large and small banks. Even echnology shocks raise GDP by 25% more 18

19 No Moral Hazard Consrain Moral Hazard Consrain EFP (Risk) Shock Technology Shock Housing Demand Shock Large Bank Share Shock % Change 5 EFP GDP EFP GDP EFP GDP 5 EFP GDP % Change Real House Prices Real House Prices Real House Prices Real House Prices % Change % Change Large Bank Share Quarers Large Bank Share Quarers Large Bank Share Quarers Large Bank Share Quarers Figure 2: Impulse response funcions from he equilibrium model. The solid lines denoe he dynamic responses when he producive bank s moral hazard consrain binds and he dashed lines are he dynamics when his consrain is relaxed. a peak when large banks are able o expand heir off-balance shee asse holdings. The key facor driving hese changes are movemens in home prices, which are hemselves amplified. I highligh his amplificaion effec in figure 3 which illusraes he differences beween he wo models simulaed in he IRFs. The diagram shows he effec of a drop in home prices on he price of N. In paricular, he equaion deermining he price of Off-balance shee asses is given by he unproducive banks firs order condiion for N U, P N = 1 R D { E Z R P+1 H χ R,U µ R,U N U(χ R,U 1) } (38) 19

20 which for χ R,U > 1 looks like a ypical demand curve. If expeced home prices fall, his will shif down he demand curve for hese asses. Wihou any redisribuion effec, asse prices fall from P1 N o P N 1 - his is he dynamic capured in he figure on he lef. P N P N P N 1 P N 1 P N 1 N U 1 P H D U D U N P N 1 P N 2 N1 U N2 U D U D U N N P 1 N P 2 Figure 3: The graph on he lef illusraes he impac on asse prices when home prices drop, wihou any redisribuion effec. The graph on he righ highlighs he addiional fall in asse prices ha resuls when he producive bank mus reduce is share of off-balance shee secured asses due o he endogenously ighening moral hazard consrain. To undersand he amplificaion effec semming from he redisribuion of off-balance shee asses, noice wo hings. (i) Firs, due o he posiive marginal cos of liquidaing collaeral, asse prices fall by more (in percenage erms) han expeced home prices. Tha is, E P N,E {P H +1} > 1. E P N,E {P+1} = P { N } E H E P H +1 { P H +1 } P N = Z R E { P H +1 } { } Z R E P H 1) +1 χ R,U µ R,U N U(χR,U > 1 (39) (ii) Second, he deb conrac described in secion shows ha as he value of he enrepreneur s pledgeable asses falls, he probabiliy of defaul increases. 12 F ( ω j +1) P N = F ( ω j +1) ω j +1 ω j +1 P N > (4) These wo effecs, (i) and (ii) (Eqs. 39 and 4 ), boh ac o ighen he binding moral hazard consrain for he producive bank (Eq. (29)) and hence he large bank share falls. 12 The firs parial derivaive is posiive due o he monooniciy of CDFs and he second parial derivaive is posiive due o he srucure of he opimal deb conrac. 2

21 This is illusraed in he graph on he righ of figure 3. In paricular, a drop in home prices induces no only a direc fall in asse prices from P1 N o P N 1 bu a furher drop o P2 N due o an endogenous reducion in N P (and he downward sloping demand for N U due o he sricly convex { } coss). This is he beginning a muliplier effec of sors. As P N falls by more han E P H +1, he moral hazard consrain ighens furher inducing furher reducions in N P. All he while, as hese forces ac o push down he value of secured deb, borrower s face an increasing exernal finance premium. This is he amplificaion effec highlighed by he difference beween he 2 ses of IRFs in figure 2. This saic muliplier effec from asse redisribuion may be easies o spo when I exogenously increase he share of asses held by he producive bank. The dynamics following his exogenous shock are shown in he he las column of IRFs in figure 2. Alhough, he shock is se o increase N P by only 1% he period he shock his, N P increase more han 5 imes as much, above 5%. Again, his amplified response is driven by he asse redisribuion illusraed in figure 3. When N P increases here are wo immediae effecs, as explained by equaions 39 and 4, boh of which ac o expound his increase in he producive bank s share of off-balance shee asses. One common hem hrough all he impulse response funcions is an amplificaion effec semming from asse redisribuion. Alhough, I have highlighed he saic amplificaion, here is also a dynamic feaure a work which makes he moral-hazard consrained model more persisen. Since repossessed collaeral ulimaely is liquidaed on he real-esae marke, his increase in supply lowers home prices ino he fuure o he exen ha housing does no depreciae immediaely. These effecs re-enforce one anoher over ime. Ulimaely hough, hese dynamic amplificaion effecs are powered by resaring, period by period, he engine ha drives he saic muliplier. 3 A Facor Srucural VAR In his secion, I esimae a VAR o examine he empirical plausibiliy of he model s predicions. Included in he VAR are he same variables examined in he model s impulse response funcions: he exernal finance premium, real GDP, real home prices and he share of oal credi exposure concenraed in large banks. All variables are available a a quarerly frequency from 1998:Q2 o 212:Q4. 13 As specified in log-levels, he Schwarz Bayesian informaion crierion selecs 2 lags for he VAR. In wha follows I firs lay-ou he model s esable predicions, hen I go on o describe he daa and he srucural idenificaion before presening he impulse response funcions. 3.1 The Model s Empirical Implicaions The DSGE model developed in he previous secion posis an amplificaion effec semming from he redisribuion of asses beween large and small banks. In paricular, he 13 The ime series is limied by he availabiliy of ne credi exposure daa from he OCC s Quarerly Derivaives Repor. However, for he removal of ime-rends, I use daa going back o 1975:Q1 21