Subprime Borrowers, Securitization and the Transmission of Business Cycles

Transcription

1 SVERIGES RIKSBANK 317 WORKING PAPER SERIES Subprime Borrowers, Securiizaion and he Transmission of Business Cycles Anna Grodecka March 2016

2 WORKING PAPERS ARE OBTAINABLE FROM Sveriges Riksbank SE Sockholm Fax inernaional: Telephone inernaional: The Working Paper series presens repors on maers in he sphere of aciviies of he Riksbank ha are considered o be of ineres o a wider public. The papers are o be regarded as repors on ongoing sudies and he auhors will be pleased o receive commens. The opinions expressed in his aricle are he sole responsibiliy of he auhor(s) and should no be inerpreed as reflecing he views of Sveriges Riksbank.

3 Subprime Borrowers, Securiizaion and he Transmission of Business Cycles Anna Grodecka Sveriges Riksbank Working Paper Series No. 317 March 2016 Absrac A growing lieraure (i.e. Jaffee, Lynch, Richardson, and Van Nieuwerburgh, 2009, Acharya and Schnabl, 2009) argues ha securiizaion improves financial sabiliy if he securiized asses are held by capial marke paricipans, raher han financial inermediaries. I consruc a quaniaive macroeconomic model wih a novel specificaion for morgage-backed securiies (MBS) o evaluae his claim for subprime securiizaion during he Grea Recession. I find ha oupu in he U.S. would have dropped by only abou a hird and house prices by only a half of wha we acually observed, if subprime MBS had been purchased by non-financial agens, raher han held by banks. This is because banks are subjec o capial requiremens and if MBS remain wihin he banking sysem, he fall in heir value pus a srain on banks balance shees. The subsequen deleveraging amplifies business cycles. My findings sugges ha he exisence of he securiizaion marke sabilizes he economy under he condiion ha financial inermediaries do no engage in he acquisiion of securiized asses. Keywords: Subprime Borrowers, Securiizaion, Financial Inermediaion, Grea Recession JEL Classificaion: E32, E44, G01, G13, G21, R21 I would like o hank Jürgen von Hagen and Gerno Müller for heir insighful commens. I also hank Nuno Coimbra, Chrisopher M. Gunn, Michael Evers, Isaiah Hull, Ehan Ilzezki, Philip Jung, Florian Kirsch, Alexander Kriwoluzky, Johannes Pfeifer, Raùl Razo-Garcia and Kevin Sheedy, as well as seminar paricipans a he Macro and Finance Workshop a Bonn Universiy, he Macro PHD work-in-progress workshop a he LSE, he EDP Jamboree 2012 in Florence, EEA-ESEM 2014 in Toulouse, he EDP Jamboree 2014 in Paris, he VfS- Jahresagung 2014 in Hamburg, he 46. Konsanz Seminar on Moneary Theory and Policy. Financial suppor by he Deusche Forschungsgemeinschaf (DFG) hrough he Bonn Graduae School of Economics (BGSE) is graefully acknowledged. The views expressed in his paper are solely he responsibiliy of he auhor and should no be inerpreed as reflecing he views of Sveriges Riksbank. Sveriges Riksbank, anna.grodecka@riksbank.se. 1

4 1. Inroducion A common poin of deparure for researchers analyzing he Grea Recession is ofen he relaively small subprime morgage marke in he U.S. ha may have been one of he roos of he prolonged downurn, and he securiizaion of subprime loans. Deparing from here, his paper invesigaes poenial sources of he amplificaion mechanism during he recen crisis in he U.S. marke. I provides a numerical inerpreaion o he claim by Jaffee, Lynch, Richardson, and Van Nieuwerburgh (2009) (p.71) who conclude: The financial crisis occurred because financial insiuions did no follow he business model of securiizaion. Raher han acing as inermediaries by ransferring he risk from morgage lenders o capial marke invesors, hey became he invesors. They pu skin in he game. A counerfacual exercise, presened in he paper, shows ha if only financial insiuions had followed he business model of securiizaion, he U.S. oupu fall in he Grea Recession would accoun only o abou one hird of he observed. These resuls hold even if we assume ha he subprime defauls are a he pre-crisis level. This is because non-financial agens can cushion subprime defauls beer han capialconsrained financial inermediaries. Banks ha hold MBS ranches whose value is falling in a downurn deleverage o mee heir capial requiremens. As a consequence, he reduced lending o households and corporaions pus a srain on economy s oupu. As such, my findings sugges ha he exisence of he securiizaion marke dampens business cycles under he condiion ha financial inermediaries do no engage in he acquisiion of securiized asses. This paper presens a calibraed model in a linear New-Keynesian Dynamic Sochasic General Equilibrium (DSGE) framework ha builds on models wih credi fricions, paricularly collaeral consrains (á la Iacoviello, 2005). The focus is on he role of subprime morgages and securiizaion in he recen crisis, and he imporance of he bank lending channel in he presence of binding capial requiremens. The model incorporaes some aspecs of financial modeling (morgage-backed securiies, MBS) ino a sandard macroeconomic framework, which is he main conribuion of his paper. Three differen versions of he model are compared: a benchmark model wihou securiizaion, a model wih securiizaion in which only nonfinancial agens buy securiized asses, and a model wih securiizaion in which also financial inermediaries acquire asse backed securiies. The laer model can be seen as he mos realisic descripion of he crisis, while he former wo are counerfacuals. I leave aside he modeling of he porfolio decisions of agens. The aim of he exercise is much more modes; assuming ha securiizaion ook place and securiized producs were bough by differen agens in he economy, I wan o invesigae wheher here is any difference in he reacion of he economy o differen shocks, depending on who is he ulimae bearer of he subprime risk. I urns ou ha he securiizaion of subprime morgages may have caused an amplificaion of he crisis hrough he balance shee effecs of banks ha were holding he securiized 2

5 producs. If MBS were held by non-banks, securiizaion would have had a posiive effec of risk-spreading, leading o a smooher response of oupu o differen shocks. Securiizaion iself hus canno be blamed for he severiy of he crisis. The resuls of his paper suppor he proposiion ha in principle, securiizaion, even of he dangerous subprime risk, makes sense, because differen marke paricipans have differen invesmen horizons and may be beer able o bear he credi risk han he originaor. Ideally, securiized producs would end up in he porfolios of insiuions such as pension funds ha can cushion shor-erm losses beer han financial inermediaries. The problem occurs if banks hemselves engage in such ransacions, because hey mainly rely on shor-erm funding and play he role of financial inermediary in he economy. IMF (2009) repors ha, a he end of 2006, banks accouned for ca. 51% of oal financial insiuions (banks, hedge funds, insurance companies, finance companies, muual funds, pension funds) exposure o he subprime marke, eiher direcly or indirecly (see Acharya, Schnabl, and Suarez, 2013). 1 The presen model shows ha, if banks facing capial requiremens buy MBS ranches, which lose value in he downurn, he capial requiremen ges igher, so he whole inermediaion process is disruped. Through he deleveraging process, lending o oher agens in he economy declines, causing a credi crunch, parial erminaion of producion and a fall in oupu. The model demonsraes he relevance of his process in a general equilibrium framework and offers a heoreical explanaion for he negaive correlaion beween subprime defauls and commercial lending observed for U.S. banks during he crisis. I is imporan o noe ha, alhough his paper is moivaed by he evens in he subprime securiizaion marke and hence, I model specifically he securiizaion of adjusablerae morgages, he main mechanism hrough which securiizaion impacs he economy in he model is he balance shee dynamics of financial inermediaries. Therefore, he model is also applicable o he securiizaion of differen ypes of asses, no only morgages. The presen paper relaes o hree main srands of he lieraure. I is an exension of Iacoviello (2005) ha relies on he seminal paper by Kiyoaki and Moore (1997). In boh models, he imporance of collaeral consrains and he imperfec enforcemen of lenders righs ha lead o he esablishmen of a cerain loan o value raio are emphasized. Iacoviello (2005) focuses on loans backed by real esae, which makes his model a naural saring poin for my exercise invesigaing he role of subprime securiizaion. I exend he model by adding he wo-secor banking indusry and considering he securiizaion of subprime loans. The balance shee effecs discussed in he paper resemble dynamics occurring in Iacoviello (2014) ha models he consequences of an exogenous fall in banks equiy. The second srand of lieraure imporan for his paper is mainly represened by Adrian and Shin (2010) and Adrian and Shin (2011) ha focus on he balance shees of financial inermediaries and he empirical proper- 1 Due o he Rule 114A, adoped in 1990, allowing unregisered release of cerain securiies o so-called qualified insiuional buyers, i is very difficul o assess he financial secors exposure o he subprime risk. 3

6 ies of he behavior of banks. Lasly, he empirical evidence on he recen crisis delivers many insighs. The presen paper mainly relies on a comprehensive sudy of Goron (2008), who describes in deail he subprime morgage marke in he U.S. and he securiizaion of subprime morgages. Anoher imporan reference is Goron and Souleles (2007) who describe he basics of he securiizaion process. Hellwig (2009) also delivers an exensive descripive analysis of he evens leading o he Grea Recession. When i comes o he modeling of securiizaion in a general equilibrium macroeconomic model, o my knowledge only hree aemps have been made, and all of hem focus on he problem of asymmeric informaion. Faia (2011) models he secondary marke for bank loans in a model in which several economic agens face a moral hazard problem. On he one hand, capial producers ha obain funds from banks may choose o exer low effor, which undermines he success probabiliy of heir projec, bu provides hem wih a privae benefi. On he oher hand, he incenive o monior he projecs decreases for bankers, once a secondary marke for loans exiss. Faia (2011) concludes ha he exisence of secondary markes amplifies he dynamics of macro variables. Hobijn and Ravenna (2010) model securiizaion in a seup wih banks ha have access o cosly screening which provides hem wih informaion abou he credi score of borrowers. Borrowing households are eiher hones or dishones, which leads o defaul evens. Hobijn and Ravenna (2010) demonsrae ha securiizaion reduces he equilibrium ineres raes, and he decline is mos pronounced for riskier, subprime borrowers who gain he mos from he securiizaion process. The auhors examine he response of financial variables, such as ineres rae spreads, o a moneary and financial shock and conclude ha wih securiizaion he reacion of financial variables is amplified in comparison o a sandard New- Keynesian model. Lasly, Kuncl (2014) analyzes he role of asymmeric informaion in he secondary loan marke, in a seup in which firms wih profiable invesmen opporuniies sell he cash-flows from heir projecs o firms wih low or no invesmen opporuniies. Alhough all hree papers deal wih securiizaion, he focus and modeling devices applied in hese papers differ considerably from he seup in his paper. Firsly, I focus on he real esae marke, which is no described in any of he discussed papers. Secondly, in his paper, he inermediaion role of banks (absen in Kuncl, 2014) plays an imporan par, as well as he inerbank marke. Finally, while informaion asymmery is a he hear of analysis of he oher hree papers, in his work i appears only indirecly hrough he exisence of borrowing and capial consrains. Why is i imporan o consider recen developmens in a general equilibrium macro framework when he finance and microeconomics lieraure deliver a fairly good descripion of economic agens incenives and amplificaion processes caused by financial fricions? The general equilibrium macroeconomic seup is especially useful for examining he posiive aspecs of securiizaion hrough iner-marke linkages and quanifying hem. To show why securiizaion may smooh ou he business cycle, I explicily model he inerbank secor. When disinc finan- 4

7 cial inermediaries are conneced hrough loan and deposi conracs (i.e. asses of one banking insiuion correspond o liabiliies of anoher banking insiuion), changes in he balance shee of one of hem will auomaically lead o changes in he balance shee of he second inermediary. Securiizaion of subprime loans releases he pressure on he subprime loan originaors balance shees, which, hrough he inerbank marke, has a posiive effec on he balance shees of oher financial inermediaries in he economy, since hey finance subprime lenders wih deposis. This posiive aspec of securiizaion is presen in all versions of he model wih securiizaion ha I consider. However, he overall impac of securiizaion on he economy depends on oher endogenously arising processes. I urns ou ha he effec on business cycle flucuaions may be amplifying, if he deleveraging effec, presen in he model wih banks invesing in MBS, is sronger han he posiive effec of securiizaion. Moreover, deleveraging may lead o a vicious circle of falls in asse prices and furher deleveraging (Adrian and Shin, 2010), leading even o insabiliy of he sysem, if capial requiremens imposed on banks are very low. Low capial requiremens lead o higher leverage and subsequenly, more pronounced deleveraging, when a negaive shock his he economy. The model presened in his paper is complex, as i incorporaes agens differing in heir impaience level, wo ypes of bankers, as well as diverse collaeral consrains. Ye, he main mechanism presened in he paper is simple - binding collaeral consrains faced by financial inermediaries may lead o disrupions in he lending marke and may amplify losses from an exogenous negaive shock, leading o a decline in oupu. I show ha o undersand he impac of securiizaion on he financial inermediaion marke, one has o ake ino accoun he heerogeneiy among banks and heir effecively differen capial requiremens resuling from differen porfolios. The analysis of he banking and he inerbank marke is very imporan, as i maers no only wheher he securiized producs are being held by he banking or he nonbanking secor, bu also which bank holds which kind of producs. In wha follows, I describe he peculiariies of he subprime marke (Secion 2.1) and some empirical relaions beween he MBS and commercial loans observed in he daa during he crisis (Secion 2.2), which will make he inerpreaion of chosen assumpions and modeling devices easier. Secion 3 presens he baseline model and Secion 4 is is exension wih securiizaion. The main resuls are presened in Secion 5, and Secion 5.3 presens he resuls of he experimen, which provides he counerfacual for he crisis. Secion 6 presens sensiiviy analysis. The main conclusions of he paper are summarized in Secion 7. 5

8 2. Sylized Facs 2.1. Subprime Morgage Marke I is remarkable ha he evens in he subprime morgage marke are imporan for he undersanding of he roos of he crisis, because subprime borrowing accouns for only a small percenage of he whole morgage marke (he share of subprime originaions is depiced in Figure 1). Alhough here is no exac definiion of a subprime borrower or marke, here are cerain feaures common o all subprime loan conracs. Compared o prime borrowers, subprime borrowers have lower crediworhiness, as hey someimes even lack income or collaeral (so called NINJAs - No Income, No Job or Asses, see Jovanovi`c, 2013). Their LTV raios are higher han in he case of prime borrowers. 2 Since subprime borrowers ofen do no have well-documened asses or income, i poses a challenge o creae a loan conrac ha will enable hem o pay he insallmens. The soluions o his problem were hybrid adjusable rae morgages of ype 2/28 or 3/27, in which he firs period s (2 or 3 years) ineres rae was fixed and he res (28 or 27 years respecively) was varying. The shif from he fixed ineres rae o he adjusable one occurred a a previously specified rese dae. As Kliff and Mills (2007) noe, before he oubreak of he crisis, hese hybrid morgages made up abou wo hirds of all ARM (adjusable rae morgage) originaions and were basically shor-erm fixed rae morgages ha convered ino an adjusable rae morgage afer he iniial period. Goron (2008) explains how his kind of conrac can be inerpreed as a shor-erm conrac, whose condiions depended on he changes in housing prices. In line wih ha inerpreaion, Amromin and Paulson (2010) provide evidence of a high sensiiviy of defauls o changes in home prices among subprime borrowers already in he years before he crisis, compared o a very low sensiiviy among prime borrowers (for 2004: for subprime borrowers and for prime borrowers). The shor-erm characerisics of subprime loans as well as heir high sensiiviy o housing prices observed in he daa enable me o model he subprime loan conrac as a one-period conrac wih he possibiliy of defaul linked o changes in house prices. How do developmens in he subprime morgage marke relae o he economic performance of he U.S.? Figure 1 presens subprime loans originaions as a share of he oal marke, nonagency securiizaion aciviy (RMBS - residenial morgage backed securiies - and securiies based on home equiy loans), as well as he real GDP growh rae. The peak of subprime originaions coincided wih he peak in non-agency securiizaion aciviies and boh of hem almos dried ou in 2008 (furher daa for subprime originaions no available). This reflecs 2 More deails on comparison beween prime and subprime borrowers and heir defaul and foreclosure saisics, boh for adjusable and fixed ineres rae loans, are provided in Appendix A. 6

9 Securiies issuance (bn USD) Subprime morgage originaions and securiizaion versus real U.S. GDP growh % 20% % 10% 5% 0% Non-agency RMBS and homeequiy securiies issuance (bn USD) Subprime originaions as % of oal Real GDP growh (%) 00-5% Source: SIMFA, NIPA able , Financial Crisis Inquiry Commission Repor, p.70 Figure 5.2 Figure 1: Subprime marke and real GDP (annual daa) he fac ha securiizaion was he main financing mehod for subprime originaions. 3 The majoriy of subprime morgages were pooled ogeher and sold in he financial marke as MBS, which were ofen a base for a furher securiizaion insrumen - a collaeralized deb obligaion (CDO). 4 Subprime originaions peaked in 2006, while he 4h quarer of 2006 denoes he peak in he U.S. house price index (USSTHPI). The developmens in he housing and morgage marke led he changes in U.S. GDP growh MBS and Commercial Loan Holdings by Banks As he banking secor and is holdings of MBS are crucial in his paper, I invesigae he asse side of he balance shees of U.S. banks. Figure 2 presens he fracion of MBS holdings, commercial real esae loans and commercial loans (all loans o firms, including real esae) in all bank asses over ime. 5 I is visible ha he fracions of MBS and commercial real esae loans wen ino opposie direcions from ca The divergence in he fracions of MBS and commercial real esae loans is preceded by a large surge in subprime defaul raes ha sared 3 A more deailed descripion of securiizaion process in provided in he Appendix B. 4 The raio of securiized subprime/al-a morgages rose from 46% in 2001 o 93% in 2007 (Geihner, 2011, p.11). Al-A morgages are morgages wih characerisics ha places hem beween prime and subprime morgages. 5 The graph is generaed using daa for large domesically-charered commercial banks ha are a good proxy for all U.S. banks and are chosen due o he beer availabiliy of daa. A deailed daa descripion is available in Appendix D. 6 An analogous graph for lending levels ha exhibis he same paern can be found in Appendix C (Figure 16). 7

10 Commercial loans and oal MBS holdings as % of oal bank asses large U.S. banks 30% 25% 20% 15% 10% Commercial real esae loans Commercial loans Toal MBS 5% 0% Source: FRB Table H.8 Asses and Liabiliies of Commercial Banks Figure 2: Composiion of large banks balance shees in 2006 and coincided wih he beginning of he fall in housing prices (see Figure 15 in he Appendix C). The fracion of MBS and commercial real esae loans were approximaely equal when expressed as a percenage of U.S. bank asses unil he subprime defaul raes began o increase. Only wih an increase in subprime delinquencies did he fracion of oal MBS rise and he fracion of commercial real esae loans fall, suggesing ha securiized asses experiencing a fall in value may have crowded ou lending o enrepreneurs. The correlaion beween he fracion of commercial real esae loans on he asse side of he bank and he subprime defaul raes for he crisis period is clearly negaive (see Figure 17 in Appendix C). The negaive correlaion does no imply any causal effecs, bu his paper offers an explanaion for he empirical facs. Rising subprime defaul raes lead o a fall in he value of subprime loans or securiized producs backed by hese loans. This pus a srain on banks balance shees and forces hem o deleverage, which reduces lending o firms. Why does he fracion of held MBS increase during he crisis despie he rising defaul raes on hese securiies? The banks, even if hey waned, could no sell he oxic asses as he marke for hem dried ou when he scale of he crisis was made public: subprime MBS suddenly became illiquid. 7 7 The omnipresen illiquidiy promped he Federal Reserve o inroduce some of is programs aimed a increasing liquidiy, seehp:// fed-sars-program-o-buy-illiquid-morgage-asses, bu he firs acquisiions of oxic asses in 2009 were focused on guaraneed agency morgages whose boom and bus was less pronounced han developmens in he non-agency morgage marke. In fac, i urns ou ha he role of governmen is decisive for he shape of he graph shown in Figure 2. Figures 19 and 20 in he Appendix C provide more empirical evidence on ha. 8

11 3. The Benchmark Model The model economy is inhabied by households ha differ in heir degree of impaience. All households offer labor services o enrepreneurs producing inermediae oupu. Households consume final goods and derive uiliy from housing services. Paien households save in he form of deposis kep a commercial banks ha gran loans o enrepreneurs and offer loans on he inerbank marke. I is assumed ha all impaien borrowers have subprime characerisics: hey borrow from a subprime lender agains housing collaeral. 8 The collaeral consrains faced by borrowers deermine he amoun hey can borrow from he bank, while bankers se he ineres raes on loans, aking ino accoun differen borrowing consrains and defaul probabiliies. The deb conracs in he economy are wrien in nominal erms, as in Iacoviello (2005). The financial connecions of he agens are shown in Figure 3. There is a cenral bank in he economy implemening a Taylor rule and choosing he ineres rae on deposis. Reailers, who produce a final good ou of he inermediary good, are he source of nominal sickiness in he economy Paien Households: Savers The problem of paien households ( savers ) is idenical o he one in Iacoviello (2005) wih one difference: insead of providing loans o households and enrepreneurs, hey save in he form of one-period deposis held a banks. Paien households consume, work and accumulae housing. Their opimizaion problem and he Firs Order Condiions (FOCs) are presened in Appendix E Impaien Households: Subprimers Impaien households are borrowers in he model economy. The feaure ha disinguishes hem from impaien households modeled in Iacoviello (2005) is ha hey may defaul on heir loan obligaion, wih he defaul rae sensiive o house prices, which reflecs he adjusable-rae feaure observed in he daa. Impaien subprime households have he following uiliy funcion: b Sub max E 0,h Sub,L Sub =0 β Sub, ( log c Sub + j log h Sub LSub η Sub η Sub ), (3.1) 8 Previous versions of he paper (Grodecka, 2013, Grodecka, 2014, chaper 1 in Grodecka, 2015) included also he exisence of prime borrowers who may borrow for long-erm and do no defaul on heir loan obligaions. The exisence of prime borrowers has a quaniaive impac on he resuls of he paper (i dampens he responses o he shocks shown in he paper), bu does no change hem qualiaively. Given he complexiy of he paper and he fac ha his feaure is no crucial for he paper s main resul, in his version of he paper I leave he discussion of prime borrowers ou. 9

12 PATIENT HOUSEHOLDS Save in form of deposis face capial requiremens COMMERCIAL BANKERS - Collec deposis - Lend o enrepreneurs and subprime lenders face capial requiremens SUBPRIME LENDERS - Collec deposis from he commercial bank - Lend o subprime borrowers face collaeral consrains ENTREPRENEURS - Borrow agains housing collaeral - Produce using housing sock and labor IMPATIENT HOUSEHOLDS SUBPRIME BORROWERS Borrow agains housing collaeral (defaul rae sensiive o house prices) face collaeral consrains Figure 3: Financial connecions in he benchmark model where c Sub denoes he subprimers consumpion of he final good, j is he marginal uiliy of housing subjec o random disurbances (following Iacoviello, he disurbance is common o paien and impaien households, and is a proxy for a housing demand or housing preference shock), h Sub is he housing sock held by subprime households, L Sub denoes labor supply of impaien subprime households. The budge consrain of he impaien subprime household in real erms is: c Sub + q (h Sub h Sub 1) + (1 δ s, )R s, 1 b Sub 1/π = b Sub + w Sub L Sub, (3.2) where R s, is he nominal ineres rae on subprime loans b Sub, q = Q /P denoes he real housing price, π = P /P 1 is inflaion and δ s, = δ s φ s,h (q Q) (3.3) is he defaul rae on loans (δ s denoes he posiive seady sae value of defaul rae, Q is he seady sae value of housing prices, 9 φ s,h denoes subprimers defaul sensiiviy o house price changes). The dependence on house prices is chosen o capure he high sensiiviy of he hy- 9 The price level in he seady sae (P) equals 1. 10

13 brid subprime morgage conrac o changes in housing prices and is gamble characerisics. 10 Subprime lenders be on an increase in house prices because hey may hen expec a lower han prediced defaul rae and hus, faser repaymen of he loan. 11 Noe ha he deb conracs in his model are wrien in nominal erms (following Iacoviello, 2005), which reflecs he majoriy of loan conracs in low-inflaion counries. Impaien households may borrow agains he fuure value of heir housing collaeral: R s, b Sub where m Sub deermines he LTV raio for subprime borrowers. m Sub E (q +1 π +1 )h Sub, (3.4) The FOCs of subprime borrowers are presened in Appendix E.2. I is imporan o noe ha, alhough he collaeral consrain of subprime borrowers does no refer o heir possible defaul, he ineres rae paid on heir subprime loans includes he defaul premium. They pay a higher ineres rae reflecing heir ex ane probabiliy of defaul. The subprime ineres rae is deermined by he subprime lenders opimizaion problem, see equaion Enrepreneurs The problem of enrepreneurs is similar o ha in Iacoviello (2005) wih he exclusion of capial accumulaion and invesmen conduced by firms. 12 They produce inermediae oupu priced a P w, using housing sock and labor provided by households, and sell i o reailers. They borrow shor-erm o cover heir expendiures, facing a collaeral consrain analogous o he one faced by households. Their opimizaion problem and he FOCs are presened in Appendix E Reailers The problem of reailers is idenical o ha in Iacoviello (2005). They are he source of price sickiness in he economy. I presen he equaions concerning he reailer secor in Appendix E Forlai and Lamberini (2011) consider a model wih risky morgages and endogenous defaul rae arising from idiosyncraic shocks o households housing invesmen, which is also a proxy for modeling negaive home equiy and is consequences. However, in heir model firms do no borrow capial from financial inermediaries, so one imporan ransmission channel of he crisis is excluded. 11 Given he formulaion in equaion 3.3, heoreically, when a large shock occurs, he defaul rae can urn negaive. However, he posiive seady sae rae of defaul, as well as he fac ha in a log-linearized model only shocks of a small ampliude can be considered, preven his from happening in he curren seup. 12 Capial and invesmen were par of he model in he earlier version of his paper, Grodecka (2013), and heir inclusion does no change he resuls qualiaively, so for simpliciy reason hey were lef ou from his analysis. 11

14 3.5. Bankers Commercial Bankers Commercial bankers collec deposis from paien households and issue loans o enrepreneurs. They also provide inerbank loans for subprime lenders ha operae as a bank. 13 Commercial bankers maximize uiliy from heir consumpion c b (as in Iacoviello, 2014): 14 max c b, E 0 βb(log c b, ), (3.5) =0 where β b is assumed o be lower han he discoun facor of paien households (necessary condiion for he capial requiremen o be binding - see Iacoviello, 2014). The budge consrain of bankers is: c b, + R d, 1d 1 π + bb + b e, = d + R b, 1bb 1 π + R e, 1b e, 1 π, (3.6) where R d, is he ineres rae on deposis d, bb denoes inerbank lending and R b, is he inerbank ineres rae, b e, are he loans o enrepreneurs and R e, 1 is he ineres rae on corporae loans. The commercial banker s balance shee looks as follows: Asses Inerbank loans: bb Loans o enrepreneurs: b e, Liabiliies Deposis d Equiy eq Thus, a Basel-ype capial requiremen, given exogenously, has he form: τ bb + b e, d χ Inb bb + χ F irm b e,, (3.7) 13 The disincion beween commercial and subprime bankers is no necessary for he benchmark version of he model, bu becomes imporan once securiizaion is inroduced ino he model economy. The evidence from he U.S. suggess ha here were several banks and financial inermediaries ha specialized specifically in he subprime marke. 14 Noe ha his formulaion considers a risk-averse banker. Alhough financial inermediaries are ofen considered o be risk-neural, here is some evidence of heir risk-aversion (see Rai, 1980 and Angelini, 2000). More recenly, examining ineres raes for differen deposi mauriies for a se of U.S. banks, Nishiyama (2007) concludes ha individual banks relaive risk aversion coefficiens fall beween 0 and 1 (mos likely around 0.2), which means ha hey are slighly risk averse. The log-uiliy funcion is characerized by he decreasing absolue risk aversion and consan relaive risk aversion of order 1, i is hus higher han he esimaes of Nishiyama (2007). However, in he curren seup he degree of risk-aversion does no maer. As he model is solved using he log-linearizaion echnique, i has he feaure of cerainy equivalence: wha maers for he soluion are he firs order-momens of variables, bu no higher-order momens, such as variance. Since uncerainy does no play a role under he firs-order-approximaion, he soluion of he model would no change if I assumed he risk-neuraliy of bankers. 12

15 where χ Inb < χ F irm are risk weighs of asses and τ denoes an equiy raio se by a regulaor. The condiion saes ha he raio of equiy (defined as asses minus deposis) o risk weighed asses has o exceed some exogenously chosen number. The FOCs of he bankers problem deermine he ineres raes paid on deposis and differen ypes of loans (G denoes he Lagrangian muliplier on he capial requiremen): w.r.. bb ( ) 1 Rb, = β b E + (1 τχ Inb )G, (3.8) c b, c b,+1 π +1 w.r.. b e, ( ) 1 Re, = β b E + (1 τχ F irm )G, (3.9) c b, c b,+1 π +1 w.r.. d ( ) 1 Rd, = β b E + G. (3.10) c b, c b,+1 π +1 The inerpreaion of equaions 3.8 o 3.10 is crucial for undersanding he main resul of he paper. The equaions wihou considering he Lagrangian muliplier on he capial requiremen represen ypical Euler equaions, saying ha he banker mus be indifferen beween consuming one uni of consumpion oday, and lending one uni oday and consuming i omorrow. The capial requiremen of bankers inroduces a wedge beween he cos and marginal gain from lending. Is bindingness influences he bankers decisions beween consumpion and borrowing/lending and gives rise o he process of deleveraging. This resuls in a shrinking balance shee in he face of a negaive shock, as bankers are impaien and prefer o consume raher han raise equiy or increase heir lending Subprime Lenders Subprime lenders operae as financial inermediaries ha collec deposis bb from he inerbank marke and issue subprime loans b Sub. Their opimizaion problem is: max c bb, E 0 βbb(log c bb, ), (3.11) =0 s.. c bb, + b Sub + R b, 1 bb 1 /π = bb + R s, 1 (1 δ s, )b Sub 1/π, (3.12) where c bb, denoes subprime lenders consumpion. I assume ha subprime lenders hold a reserve for fuure losses, aking ino accoun he ex ane (seady sae) defaul rae. The subprime banker s balance shee is: 13

16 Asses Loans o subprime borrowers: b Sub Loss reserve δ s b Sub Liabiliies Inerbank deposis bb Equiy eq Thus, a Basel-ype capial requiremen, given exogenously, has he form: τ Sub (1 δ s)b Sub bb, (3.13) χ Sub (1 δ s )b Sub where he risk weigh on subprime loans is denoed by χ Sub and τ Sub is he capial raio imposed on subprime lenders by he regulaor. The FOCs of he subprime bankers problem (GG denoes he Lagrangian muliplier on he capial requiremen of subprime lenders) are: w.r.. b Sub ( ) 1 Rs, (1 δ s,+1 ) = β bb E + (1 τ Sub χ Sub )(1 δ s )GG, (3.14) c bb, c bb,+1 π +1 w.r.. bb ( ) 1 Rb, = β bb E + GG. (3.15) c bb, c bb,+1 π +1 Equaion 3.14 deermines he ineres rae paid on subprime loans and makes clear ha when pricing he subprime loan, he subprime lender akes ino accoun he defaul probabiliy of he borrowers. As a consequence, he seady sae ineres rae on subprime loans is higher han ha of loans wih a zero defaul probabiliy Cenral Bank The cenral bank implemens a Taylor ype ineres rae rule (idenical o Iacoviello, 2005). I is assumed ha he ineres rae se by he cenral bank equals he ineres rae paid on deposis (disregarding reserve requiremens): ( R d, = (R d, 1 ) r R π 1+rπ Marke Clearing Condiions ( Y 1 Y ) ry 1 rre e rr) R,. (3.16) Following Iacoviello (2005), I assume ha real esae is fixed in he aggregae. The marke clearing condiion for he housing marke is: 1 = h Savers + h Sub + h e,. (3.17) 14

17 The goods marke clearing condiion is given by: Y = c Savers + c Sub + c e, + c b, + c bb,. (3.18) The marke clearing condiions for labor are defined by equaions E.5 and E.15 for he paien households labor supply and demand, and by equaions E.8 and E.16 for he impaien subprime households. The lending o differen agens is deermined hrough heir collaeral consrains, while he marke clearing condiions for he loan and deposis markes are given by he capial requiremens of he bankers (equaion 3.7 and 3.13). 4. Model wih Securiizaion of Subprime Loans The daa provides evidence for he imporance of securiizaion in subprime lending. The majoriy of subprime loans have been securiized, firs in he form of a RMBS, which ofen was a building block of CDO srucures. Usually, differen subprime borrowers have differen defaul probabiliies, so securiizaion may be a way o average he risk on subprime exposure. In he presen model, all subprime borrowers have he same defaul rae, which can be inerpreed as a defaul rae represening he mean of he aggregae disribuion over all subprime borrowers, who differ in heir defaul sensiiviy a an individual level. Typically, an MBS srucure consiss of hree ranches: senior, mezzanine and equiy. To simplify he compuaion, I assume ha he model s RMBS consiss only of wo ranches: senior and equiy. Figure 4 illusraes he payoff funcions of invesors in he RMBS. Senior ranche A raed Equiy ranche C raed Aachmen poin f Figure 4: A wo-ranche MBS (face value wrien in nominal erms) The securiy is a pass-hrough securiy, which means ha he nominal loan proceeds are redisribued o he MBS invesors. The smaller he loss on he underlying loan porfolio (de- 15

18 ermined by he defaul rae), he larger is he payoff of equiy ranche invesors. The size of he equiy ranche, deermined by he parameer f, called he aachmen poin in he CDO jargon, defines he maximum risk exposure of equiy ranche invesors. 15 If here is a loss on he underlying loan porfolio, he equiy ranche invesors ge he difference beween he size of he equiy ranche and he loss. However, if he loss exceeds he size of he ranche, he equiy ranche invesors simply ge nohing from heir invesmen, and he senior ranche invesors begin o suffer. Their payoff funcion is a minimum funcion. They eiher ge back he ranche size, or he difference beween he face value of he MBS and he loss (in he case where losses are bigger han he size of he equiy ranche). P s, = min(s fs, S Loss ) denoes he payoff of senior ranche buyers, and P e, = max(fs Loss, 0) denoes he payoff of equiy ranche buyers, where he principal of he MBS is (in real erms) S = R s, 1 b Sub 1/π, and loss equals δ s, S. 16 To quanify he imporance of he engagemen of commercial banks in he securiizaion process, I consider wo cases. In he firs case, I assume ha he generaed MBS ranches are bough by paien households (because hey are more paien, hey acquire claims on he senior ranche) and enrepreneurs (because of heir degree of impaience, hey are more prone o acquire claims on he equiy ranche). In he second case, I assume ha he commercial bankers buy he senior ranche of MBS and he enrepreneurs inves in he equiy ranche. 17 In boh cases, subprime lenders reain a verical fracion of he issued securiy (equivalen o reaining a percenage of cash flows). 18 Why migh commercial bankers buy claims on MBS? One reason may be he diversificaion of heir credi risk and he exposure o a differen credi marke. Also, hey may be as opimisic as subprime borrowers are, and believe ha housing prices will coninue o rise. Moreover, 15 Goron (2008) argues ha subprime securiizaion differs from he securiizaion of oher asses because he ranche sizes are no fixed. There is dynamic ranching as a funcion of excess spread and prepaymens, so he whole srucure is sensiive o house prices. A he beginning of he exisence of a subprime MBS, he equiy ranches are usually very hin and along wih repaymens of he subprime loans hey reach heir arge level. However, if house prices decline from he very beginning, he equiy ranche remains very hin and hus senior ranche holders are subjec o a very large subprime risk (ha was he case for MBS issued in 2006 and laer). This works as anoher amplificaion mechanism in he design of subprime securiy. Including varying ranche sizes in he model would hus amplify he effecs of shocks in he economy. 16 The payoffs of equiy and senior ranche holders resemble payoffs from invesmen in European opions. More informaion on he opion characerisics of MBS ranches is given in Appendix F. In order o solve he model wih he non-linear payoff funcions for he MBS ranches, I use he piecewise linear perurbaion soluion as presened in Guerrieri and Iacoviello (2015). Grodecka (2015) uses he logisics approximaion of he maximum funcion, which delivers he same qualiaive and very similar quaniaive resuls, bu is less accurae. 17 One could also assume ha one and he same agen buys boh ranches. In ha case, he conclusions of he paper hold: if only non-financial agens in he economy buy MBS ranches, securiizaion resuls in a dampending of business cycles, bu whenever also commercial banks buy MBS ranches, securiizaion resuls in an amplificaion of business cycles. 18 In general, he lieraure discusses hree main ypes of reenion: verical slice reenion, horizonal slice reenion, and an equivalen exposure of he securiized pool, discussed furher in Geihner (2011). In he presen model s case, verical slice reenion generaes he same payoff for he bank as equivalen exposure. 16

19 senior ranches usually have he highes possible raing, so he risk weigh on hem is very low and he purchase has a posiive impac on he balance shee of banks. The regulaory capial arbirage is he reason why subprime lenders may wan o conduc securiizaion and why commercial bankers may wan o buy cerain ranches, as described in Jones (2000). Why migh paien households and enrepreneurs buy MBS ranches? For hem, his invesmen is jus anoher possibiliy o smooh heir consumpion. I is reasonable o assume ha oher agens han banks were mosly exposed o losses on equiy ranches of MBS, given ha he residual ranches of securiized asses had much larger risk-weighs han he senior ranches afer he inroducion of he so-called recourse rule by Fed in As such, banks had much more incenives o hold senior MBS ranches. I assume ha cerain agens in he economy inves in MBS securiies, and I do no model heir decision as a porfolio choice decision, which allows me o use he firs order approximaion o solve he model. 19 For answering he research quesion of his paper his approach is sufficien, as I do no aim o explain how he securiized asses were disribued among he invesors. Securiizaion changes he capial requiremen faced by originaors of he subprime loans, as hey may remove par of he risk from he balance shee due o he repackaging and sale of he asses. In he case of enrepreneurs and paien households who buy MBS ranches, heir budge consrain changes o include he new asse acquired, and he FOC wih respec o he new asse deermines is price. When commercial bankers inves in MBS ranches, apar from a changed budge consrain, he capial requiremen of he bankers also changes in order o include he new asse ino he balance shee of he invesor. The following subsecions 4.1 and 4.2 presen he equaion ha are changed in he model wih securiizaion wih respec o he bechmark model presened in secion 3. If no saed oherwise, all remaining equaions remain exacly he same as in he benchmark model Firs Version: Paien Households and Enrepreneurs Inves in MBS Tranches In he firs version of he model wih securiizaion of subprime loans, paien households inves in he senior ranche, and enrepreneurs in he equiy ranche. The budge consrains of invesors change and a new erm describing invesmen in he derivaive securiy appears. Firs, denoe he payoff of he senior ranche E [min(s +1 fs +1, S +1 δ s,+1 S +1 )] as MBS s, and he price of he senior ranche by p s,. Then, he budge consrain of he paien household is (remember ha subprime lenders reain porion 19 For he deerminaion of he porfolio choice, higher-order soluions have o be used, as under he firs order approximaion, he equilibrium porfolio is no deermined (Devereux and Suherland, 2010). 17

20 of every ranche): c Savers + q (h Savers h Savers 1 ) + d + (1 )p s, MBS s, = R d, 1 d 1 /π + w Savers L Savers + F + (1 )MBS s, 1. (4.19) In each period, he paien household ges revenue from invesing in he senior ranche and buys a claim on fuure proceedings from invesmen in MBS. The FOCs of prime households do no change, bu here is a new equaion deermining he price of he new claim: β 1 c Savers +1 = p s, 1 c Savers. (4.20) Analogously, denoe he erms describing he invesmen in he equiy ranche E [max(fs +1 δ s,+1 S +1, 0)] as MBS e, and max(fs δ s, S, 0) as MBS e, 1 and he price of he equiy ranche by p e,. Then, he budge consrain of he enrepreneur is: Y X + b e, + (1 )MBS e, 1 = c e, + q (h e, h e, 1 ) + R e, 1 π The FOC w.r. o he new claim is: b e, 1 + w Savers L Savers + w Sub L Sub + (1 )p e, MBS e,. (4.21) γ 1 c e,+1 = p e, 1 c e,. (4.22) Along wih he opimizaion problems of agens invesing in he securiy, he problem of subprime lenders also changes in he wake of securiizaion of subprime loans. They have now o include only he reained proporion of subprime loans in heir balance shee: Asses Loans o subprime borrowers: b Sub Loss reserve δ s b Sub Liabiliies Inerbank deposis bb Thus, a Basel-ype capial requiremen, given exogenously, is now given by: τ Sub (1 δ s)b Sub bb. (4.23) χ Sub (1 δ s )b Sub The budge consrain of subprime lenders changes. Noe ha when i comes o he ransfer of already realized cashflows, i holds ha: 18

21 (1 )[min(s fs, S δ s, S ) + max(fs δ s, S, 0)] = (1 )[S (1 δ s, )] = (1 )[R s, 1 b Sub 1(1 δ s, )/π ]. Ye, in he case of claims purchases on fuure proceedings, his shorcu canno be made because he prices of boh ranches differ, since he agens ha buy hem have differen discoun facors. Thus, he budge consrain of he subprime lender is: c bb, + b Sub + R b, 1 bb 1 /π (1 )[p s, MBS s, + p e, MBS e, ] = The prices of he ranches are deermined by equaions 4.20 and bb + R s, 1 (1 δ s, )b Sub 1/π. (4.24) 4.2. Second Version: Commercial Bankers and Enrepreneurs Inves in MBS Tranches In he second version of he model wih securiizaion, commercial bankers inves in he senior ranche, whereas enrepreneurs, as in he firs case, buy claims on he equiy ranche. The problem of he enrepreneurs does no change wih respec o he version of he model when paien households and enrepreneurs buy MBS ranches. The budge consrain of commercial bankers changes, as well as heir balance shee and capial requiremen. I assume here ha he risk weigh on he senior ranche is as high as in he case of inerbank deposis (since i is highly raed), whereas he risk weigh on he equiy ranche equals he risk weigh of subprime loans. The commercial bankers balance shee is: Asses Inerbank loans : bb Loans o enrepreneurs: b e, Liabiliies Deposis d Equiy eq MBS securiy - senior ranche: (1 )MBS s, Thus, a Basel-ype capial requiremen, given exogenously, has he form: τ bb + b e, + (1 )MBS s, d χ Inb bb + χ F irm b e, + χ In (1 )MBS s,. (4.25) The budge consrain of commercial bankers is now: c b, + R d, 1 d 1 /π + bb + b e, + (1 )p s, MBS s, = d + R b, 1 bb 1 /π + R e, 1 b e, 1 /π + (1 )MBS s, 1. (4.26) 19

22 New FOC: w.r.. MBS s, β b 1 c b,+1 = p s, 1 c b, + (1 τχ In )G. (4.27) The problem of subprime lender is analogous o he case where paien households and enrepreneurs buy MBS ranches. 5. Calibraion and Resuls 5.1. Calibraion The model is log-linearized around he seady sae. The log-linearized equaions presen variables in he form of percen deviaions from he seady sae, which makes he inerpreaion of model variables easier. For he versions of he model wih securiizaion (presened in he secion 4.1 and 4.2), I use he "occbin" oolki presened in Guerrieri and Iacoviello (2015) applying a piecewise linear perurbaion soluion. All equaions describing he benchmark model (also shock processes) are given in Appendix E I calibrae he model using parameer values from he lieraure, as well as empirical papers (see Table 1). Following Iacoviello (2005), I assume ha paien households have he highes discoun facor, followed by enrepreneurs and boh ypes of bankers. The mos impaien agens in he economy are subprime borrowers. The choice of discoun facors assures ha he collaeral consrains in he model are always binding. The parameer J conrols he sock of residenial housing over annual oupu in he seady sae, J = 0.09 fixes his raio around 150%, which is in line wih he daa from he Flow of Funds accouns (able B.100, row 4). The LTV raios for firms and subprime borrowers are se a 0.99, which is a high value, bu is consisen wih he lieraure (Iacoviello, 2014). Parameer η is chosen o fix he Frisch labor supply elasiciy a 1. The chosen value lies beween he esimaes provided by microeconomic sudies (0-0.54) and by macroeconomic sudies (2-4) (see Peerman, 2012). The seady sae gross markup is a value aken from Iacoviello (2005). The paien households wage share of 0.87 corresponds o he conclusions of Jappelli (1990) who finds ha 19% of U.S. families are raioned in credi markes and hey accoun for 12.7% of oal wage income. The value of 0.55 for he parameer θ describing he price rigidiy is consisen wih he evidence of Dhyne e al. (2006) who show ha he average price duraion in he Unied Saes equals 6.7 monhs. 20 A lis of he log-linearized equaions for he exended version of he model (including capial and invesmen, as well as impaien prime borrowers), may be found in he previous working paper version of his model, Grodecka (2013). 20

23 Descripion Parameer Value Discoun facor of paien households β Discoun facor of impaien households β Sub 0.93 Discoun facor of enrepreneurs γ 0.96 Discoun facor of commercial bankers β b 0.97 Discoun facor of subprime lenders β bb 0.95 Weigh on housing services J 0.09 Loan o value enrepreneurs m 0.99 Loan o value subprime households m Sub 0.99 Labor supply aversion η Savers = η Sub 2 Housing share in producion funcion ν 0.15 Seady sae gross markup X 1.05 Paien households wage share α 0.87 Probabiliy fixed price θ 0.55 Capial adjusmen coss φ 2 Risk weigh of inerbank loans χ Inb 0.2 Risk weigh on commercial loans χ F irms 1.5 Risk weigh of subprime loans χ Sub 4.5 Commercial bankers capial requiremen τ 0.13 Subprime lenders capial requiremen τ Sub 0.2 Subprimers defaul sensiiviy o house price changes φ sh Seady sae subprime defaul rae δ s 0.05 Weigh of policy response o ineres rae r R 0.73 Weigh of policy response o inflaion r π 0.27 Weigh of policy response o oupu r y 0.13 Auocorrelaion of preference shock ρ j 0.95 Sandard deviaion of preference shock σ εj 1 Sandard deviaion of moneary shock σ εr 1 Tranche reenion by banks 0.01 Aachmen poin of senior ranche f 0.2 Table 1: Calibraed parameers 21

24 Parameers describing he risk weighs of differen ypes of loans are based on U.S. regulaions of he Federal Deposi Insurance Corporaion (Code of Federal Regulaions - Tile 12: Banks and Banking, 12 CFR Appendix A o Par Saemen of Policy on Risk-Based Capial). Inerbank loans have he lowes risk weigh, followed by he risk weigh on commercial loans (he facor for risky loans has been applied). The risk weigh on subprime loans has a very high value, which is consisen wih he Expanded Guidance for Subprime Lending Programs, 21 saing ha an insiuion would hold capial agains subprime porfolios in an amoun ha is one and a half o hree imes greaer han wha is appropriae for non-subprime asses of a similar ype. The capial raio for commercial bankers corresponds o he average regulaory capial o risk-weighed asses for he Unied Saes before he crisis, repored in he FRED daabase. 22 The capial raio for subprime lenders is higher han for commercial bankers, which again, corresponds o he Expanded Guidance for Subprime Lending Programs: Insiuions wih subprime programs affeced by his guidance should have capial raios ha are well above he averages for heir radiional peer groups or oher similarly siuaed insiuions ha are no engaged in subprime lending. (...) insiuions ha underwrie higher-risk subprime pools, such as unsecured loans or high loan-o-value second morgages, may need significanly higher levels of capial, perhaps as high as 100% of he loans ousanding depending on he level and volailiy of risk. The sensiiviy of subprime households o housing price changes has been chosen according o he pre-crisis daa. Over ime, he sensiiviy changed and i was much higher jus before he oubreak of he crisis, bu on average one can assume ha i did no exceed 20% (Amromin and Paulson, 2010). The subprime defaul rae is chosen o be 5% in he seady sae. According o he daa presened in Demyanyk and Hemer (2011), in he decade preceding he crisis, he defaul rae on subprime hybrid loans oscillaed around 10%. However, usually when a household defauls on is morgage, he bank seizes and sells he propery, receiving some foreclosure value. The presen model does no have his feaure, hus he seady sae defaul rae is half of ha in he daa. Also, a higher seady sae defaul rae would resul in an unreasonably high seady sae value for he ineres rae on subprime loans. The Taylor rule coefficiens are aken from Iacoviello (2005). The shocks are assumed o be persisen, wih he auocorrelaion coefficien equal o I consider a 1 percen shock in each case. For he parameers governing he securiizaion process, evidence suggess ha on average, reenion of securiized asses is higher in Europe han in he U.S. Whereas originaors usually held around 5% of issued securiies in Europe, he reenion rae was ofen a 0% and rarely exceeded 1% for MBS in he U.S. Reenion percenages for CDOs and ABS (Asse Backed Securiies) were usually higher, bu in he years , on average hey did no exceed 7% (Global Financial 21 hp:// 22 Series DDSI05USA156NWDB 22