Mortgage Defaults, Expectation-Driven House Prices and Monetary Policy. ECO 2017/09 Department of Economics

Transcription

1 ECO 2017/09 Deparmen of Economics Morgage Defauls, Expecaion-Driven House Prices and Moneary Policy Selios Bekiros, Rachaar Nilavongse, Gazi S. Uddin

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3 European Universiy Insiue Deparmen of Economics Morgage Defauls, Expecaion-Driven House Prices and Moneary Policy Selios Bekiros, Rachaar Nilavongse, Gazi S. Uddin EUI Working Paper ECO 2017/09

4 This ex may be downloaded for personal research purposes only. Any addiional reproducion for oher purposes, wheher in hard copy or elecronically, requires he consen of he auhor(s), edior(s). If cied or quoed, reference should be made o he full name of he auhor(s), edior(s), he ile, he working paper or oher series, he year, and he publisher. ISSN Selios Bekiros, Rachaar Nilavongse, Gazi S. Uddin, 2017 Prined in Ialy European Universiy Insiue Badia Fiesolana I San Domenico di Fiesole (FI) Ialy cadmus.eui.eu

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6 MORTGAGE DEFAULTS, EXPECTATION-DRIVEN HOUSE PRICES AND MONETARY POLICY STELIOS BEKIROS a * RACHATAR NILAVONGSE b GAZI S. UDDIN c a European Universiy Insiue (EUI), Florence, Ialy b Uppsala Universiy, Uppsala, Sweden c Linköping Universiy, Linköping, Sweden ABSTRACT We conribue o he lieraure on dynamic sochasic general equilibrium models wih housing collaerals by including shocks o house price expecaions. We incorporae endogenous morgage defauls which are rarely included in DSGE models wih housing collaerals. We show ha our heoreical model of morgage defaul is consisen wih empirical evidence. We use his paricular DSGE seup o sudy he effecs of variaions in house price expecaions on macroeconomic dynamics and heir implicaions for moneary policy. Exensive model simulaions show ha an increase in expeced fuure house prices leads o a decline in morgage defaul raes as well as in ineres raes on loans, whereas i leads o an increase in house prices, household deb, bank leverage raios and economic aciviy. As opposed o previous sudies we find ha inflaion is low during a house price boom. Finally, we demonsrae ha alhough moneary policy ha reacs o household credi growh improves he sabiliy of he real economy and enhances financial sabiliy, ye i jeopardizes price sabiliy. JEL classificaion: E32; E44; E52 Keywords: House price expecaions; Inflaion dynamics; Moneary policy; Morgage defauls We are graeful o faculy members of he Uppsala Universiy, Sveriges Riksbank, Sockholm Universiy, European Universiy Insiue (EUI), Bocconi Universiy, and Universiy College Dublin (UCD) for helpful discussions. We paricularly hank Mikael Bask and Nils Gofries a he Deparmen of Economics of Uppsala Universiy, Jesper Lindé a Sveriges Riksbank and Paul Klein a he Deparmen of Economics of Sockholm Universiy. The usual disclaimer applies. * Corresponding auhor: a Deparmen of Economics, Villa La Fone, Via delle Fonanelle, 18, I-50014, Florence, Ialy; Tel.: ; Fax: ; address: selios.bekiros@eui.eu b Deparmen of Economics, Uppsala Universiy, 513, SE , Uppsala, Sweden; Tel.: ; Fax: ; address: rachaar.nilavongse@nek.uu.se c Deparmen of Managemen and Engineering, Linköping Universiy, SE Linköping, Sweden; Tel.: ; Fax: ; address: gazi.uddin@liu.se 1

7 1. INTRODUCTION Flucuaions in house prices can have a grea impac on he real economy as i was clearly demonsraed by he burs of he U.S real esae bubble in 2006 as well as he burs of he Japanese housing bubble in he early 1990s. Indeed, Shiller (2007) noe righ before he burs ha he U.S. experienced he bigges house price boom in is hisory. In Figure 1, which displays he real house prices for he U.S., i is eviden ha he boom sared in 1997 and ended in 2006, when house prices suddenly collapsed and hereafer enered is wors recession since he 1930s. In heir survey of homebuyers Case and Shiller (2003) find ha in 2003 a large share of home buyers expeced fuure house prices o rise over he nex several years. Shiller (2007) and Case e al. (2012) find ha expecaions of a boos in fuure house prices played an imporan role in deermining he upcoming U.S. house price boom. Piazzesi and Schneider (2009) demonsrae ha a fracion of households whose opimism reflecs price appreciaions grew during he U.S. boom and generaed an afer-effec on house price dynamics. Lamberini e al. (2013) using daa on expecaions abou fuure propery prices by he Michigan Survey of Consumers, show via a VAR model ha he expecaions of rising house prices explain a large par of business cycle oscillaions during he U.S. price boom. Addiionally, Ling e al. (2015) find ha nonfundamenal componens of he U.S. housing marke senimen can predic price flucuaions above and beyond movemens in fundamenals. Towbin and Weber (2015) afer esimaing a VAR model for he U.S. economy, illusraed ha shocks o house price expecaions are he mos imporan drivers of house prices, as hey generae a significan persisence componen in he GDP. All he aforemenioned sudies indicae ha expecaions play an imporan role as he driving forces of house prices. Ineresingly hough, shocks o house price expecaions are mosly absen in DSGE models including a housing collaeral. Such examples can be encounered in he works of Iacoviello (2005), Gerali e al. (2010), Iacoviello and Neri (2010), Forlai and Lamberini (2011), Liu e al. (2013) and Iacoviello (2015). Hence, unlike he models repored in hose sudies, our seup incorporaes shocks o house price expecaions under a DSGE framework wih housing collaerals. The purpose of his paper is o sudy he role of house price expecaions and he implicaions for macroeconomic dynamics and moneary policy under a DSGE model wih housing collaerals. Our model includes many secors, e.g., household, business, enrepreneur, reail, banking secor and a cenral bank. In paricular, he household secor is comprises wo ypes: financially unconsrained and financially consrained households. Boh ypes consume, work and buy houses. The financially consrained households use heir housing sock as collaeral o obain loans from he banking secor o buy houses. The business secor consiss of enrepreneurs who 2

8 use labor, capial and housing sock o produce inermediae goods. Enrepreneurs are financially consrained agens uilizing heir housing sock as collaeral o obain loans from he banking secor. The laer secor is represened by commercial banks which collec deposis from financially unconsrained households and provide funds o financially consrained households and enrepreneurs. The commercial banks face a capial requiremen. Furhermore, he reail secor consiss of monopolisic reailers who ransform inermediae goods ino final goods; his secor is he source of price sickiness in he economy. Lasly, he cenral bank conducs moneary policy. We include wo feaures ha are no ypically included in a DSGE model wih housing collaerals, namely shocks o house price expecaions and endogenous morgage defauls. In our model, a posiive shock o price expecaions leads o an increase in prices and consequenly he boom is caused by opimisic expecaions abou fuure propery prices. The decision of morgage defaul is endogenous in he sense ha financially consrained households defaul when he value of heir houses is lower han he sipulaed morgage loan repaymen. Furhermore, he commercial bank s lending decisions are influenced by he bank capial posiion which is affeced by house prices. The commercial bank also akes ino accoun expeced morgage defauls when making loans o financially consrained households. While Kollmann e al. (2011) and Iacoviello (2015) also include a banking secor under a similar seup, noably hey do no model loan defauls as exogenous shocks. In addiion, hese works do no include shocks o house price expecaions, as opposed o ours. Accordingly, alhough Forlai and Lamberini (2011) include endogenous morgage defauls and variaions in morgage defauls wih he laer depending on variaions in morgage risk, in our modeling framework morgage defauls derive from variaions in expeced fuure house prices. As such, he models by Forlai and Lamberini (2011) and Iacoviello (2015) imply ha variaions in morgage defauls lead movemens in house prices, so a decline in morgage defauls leads o an increase in house prices. In conras o he aforemenioned works, our heoreical model of defauls implies ha a rise in opimisic expecaions abou fuure house prices leads o an increase in house prices, which in urn leads o a decline in morgage defauls. Hence, our morgage defaul componen behaves consisenly wih economeric evidence which shows ha variaions in house prices lead movemens in morgage defauls, ye no vice versa. On he whole, we use our proposed DSGE model wih endogenous morgage defauls o examine he effecs of shocks o house price expecaions on he real economy and financial aciviies i.e., household deb, business deb, bank leverage raio, morgage defaul rae, ineres raes on household and business loans. We also invesigae he effecs of shocks o house price expecaions on inflaion dynamics and provide evidence ha our DSGE model may explain why inflaion is low during a house 3

9 price boom. Ineresingly, we also demonsrae he mechanism according o which he reacion of moneary policy o household credi growh can reduce he volailiy of oupu and inflaion. We conribue o he relevan lieraure in he following manner: we embed shocks o house price expecaions ino a DSGE model wih housing collaerals, and we include endogenous morgage defauls which depend on variaions in expeced fuure house prices. Evenually, he DSGE model allows for an inerplay beween he household secor and he banking secor hrough he house price and expeced morgage defaul channels. We learn ha opimisic expecaions abou fuure propery price appreciaions can generae a housing marke boom and a credi boom, ye a he same ime we observe a period of low inflaion. Moneary policy ha reacs o household credi growh reduces he volailiy of oupu and dampens he credi boom, bu hese effecs lead o higher inflaion volailiy. Consequenly, he cenral bank when i includes financial sabiliy consideraions in is moneary policy decisions, migh miss is inflaion arge in he shor-run. Furhermore, he main findings from he DSGE model simulaions are as follows: firsly, we see ha a posiive house price expecaion shock leads o a rise in prices, housing demand, household deb, business deb and bank leverage raio, whils i leads o a decline in morgage defaul rae and ineres raes on household and business loans. The posiive shock generaes an increase in he real economic indicaors and in financial/banking aciviies. The inuiion behind our resuls is ha a rise in expecaions abou fuure house prices increases he expeced value of housing collaerals and he expeced resale value of houses. Hence, hese effecs evenually induce financially consrained households o increase heir demand for houses, which in urn leads o an increase in household deb. The rise in house prices leads o a rise in home equiy whereas a he same ime i projecs a decline in morgage defaul rae, which is in accordance wih economeric evidence in he relevan lieraure. The increase in house prices induces commercial banks o expand loan supply, which drives down ineres raes on household and business loans, bu his effec increases he bank leverage raio. The increase in loan supply o financially consrained households and enrepreneurs simulaes he real economy. As a side effec also he rise in house prices relaxes enrepreneurs collaeral consrains, which encourages he enrepreneurs o increase capial invesmen. Our second finding is ha inflaion ends o be low during a house price boom and amid a credi boom, whereas previous sudies such as by Bernanke and Gerler (2000), Forlai and Lamberini (2011) and Badarau and Popescu (2014) repor ha inflaion ends o be higher during asse price booms in general. This resul has imporan ramificaions for moneary policy and financial sabiliy. Specifically, he cenral bank observes a downward pressure on inflaion and 4

10 responds o he shock o house price expecaions by reducing he policy rae. This furher magnifies he rise in real esae demand, household deb and bank leverage raios, herefore i increases financial insabiliy. Obviously, he real economy becomes more vulnerable o a housing marke meldown. For example, Chrisiano e al. (2010) argued ha during he Japanese sock marke boom in he 1980s, he Bank of Japan cu he policy rae o simulae inflaion which in urn amplified he sock marke boom 1. Ulimaely, asse prices collapsed and he Japanese economy underwen a severe recession. Thirdly, we find ha moneary policy which reacs o household credi growh, dampens he response of he real economy o house price expecaion shocks, ye i amplifies he response of inflaion in he shor-run. Moneary policy ha akes ino accoun credi growh reduces he volailiy of oupu bu increases he volailiy of inflaion. Moreover, by reacing o household credi growh, he exercised moneary policy reduces housing demand, household deb and bank leverage raio, hence i enhances real economy and financial sabiliy, albei o he cos of price sabiliy. Our proposed seup is relaed o DSGE modeling wih collaeral consrains as already menioned, and in paricular is based on he framework of Kiyoaki and Moore (1997) and Iacoviello (2005) wherein he amoun economic agens can borrow is ied o he value of heir collaeral. Similarly in our model, he amoun of loans ha financially consrained households can obain are ied o he value of heir houses. The collaeral consrain framework has been applied also by Monacelli (2009), Iacoviello and Neri (2010), Jermann and Quadrini (2012), Calza e al. (2013), Lamberini e al. (2013), Liu e al. (2013) and Walenin (2014). Neverheless, as opposed o our DSGE model, heir models do no include deb defauls. Unlike Kollmann e al. (2011) and Iacoviello (2015) who rea loan defauls as exogenous shocks, we model morgage defauls as an endogenous process, in a way ha households defaul when he value of heir houses is lower han he morgage loan repaymen. Furhermore, in conras o he model of Kollmann e al. (2011) and Iacoviello (2015) our model has sicky prices, so we can direcly analyze he effecs of variaions in house price expecaions upon inflaion dynamics. Our banking secor accommodaes differen ineres raes under a perfec banking compeiion framework wih a represenaive bank facing capial requiremens (Kollmann e al., 2011). 2 Overall, all aforemenioned sudies do no include shocks o house price expecaions in heir models. 1 The Japanese economy experienced boh a sock marke boom and a house price boom in he 1980s. 2 Oher DSGE sudies incorporaing a financial inermediary or a banking secor can be found in Gerali e al. (2010), Andrés and Arce (2012), Gambacora and Signorei (2014), Verona e al. (2014) and Bekiros and Paccagnini (2016). 5

11 The paper is organized as follows: secion 2 presens empirical findings vis-à-vis he relaionship beween house prices and morgage defaul raes. Secion 3 inroduces a DSGE model wih endogenous morgage defauls, whils secion 4 displays he impac of sochasic processes for shocks o house price expecaions. Secion 5 presens he calibraion of our model parameers and secion 6 highlighs he quaniaive resuls from exensive model simulaions. Secion 7 discusses implicaions for moneary policy and secion 8 conducs a sensiiviy analysis. Secion 9 concludes. 2. EMPIRICAL ANALYSIS OF HOUSE PRICES AND MORTGAGE DEFAULT RATES In his secion, we presen our empirical findings regarding he link beween house prices and morgage defaul raes. We conduc a Granger causaliy analysis and hen we examine he effecs of a posiive shock o real house prices on morgage defaul rae under a bivariae VAR model for he U.S uilizing quarerly daa from 1991 Q1 o 2015 Q4. 3,4 The lag order (four) is deermined using he Schwarz informaion crierion. Table 1 presens he Granger causaliy es resuls, which indicae ha real house prices Granger cause morgage defauls. Hence, real house prices carry significan informaion for morgage defaul raes, bu no vice versa. This economeric evidence suppors our assumpion ha flucuaions in real house prices lead hose in morgage defauls, as opposed o Forlai and Lamberini (2011) and Iacoviello (2015) who boh imply ha variaions in morgage defauls lead movemens in house prices. 5 Figure 2 displays he impulse responses in he morgage defaul raes and real house prices o posiive house price shocks. We use a Cholesky decomposiion o idenify he srucural VAR following an ordering where he morgage defaul rae comes firs and he house prices are las, implying ha i) a house price shock has an immediae impac on house prices and ii) his price shock does no affec he morgage defaul raes conemporaneously. These assumpions are realisic aking ino accoun ha households do no defaul immediaely as heir housing value becomes less han he loan repaymen. Furhermore, we wan o show ha even hough a house price shock does no impac morgage defaul raes immediaely, ineresingly he house price shock generaes a srong persisence in morgage raes. In addiion, Figure 2 clearly indicaes ha a posiive house price shock has a negaive effec on defaul raes and a posiive shock o house prices leads o a srongly persisen morgage defaul rae, alhough heir inerrelaionship is no 3 Morgage defaul rae is measured as he delinquency rae on residenial morgages. For more deails please see Appendix II. 4 All variables are deviaed from linear rend. The saring dae for our economeric model is refleced by daa availabiliy wih respec o he morgage defaul rae. 5 The comprehensive version of our heoreical model - which incorporaes morgage defauls - is included in secion

12 conemporaneous. Our specific ordering of house prices before he morgage defaul rae does no change he qualiaive response o house price shocks, however when i is reversed he effecs of house price shocks on morgage defaul rae become slighly sronger. In general, he aforemenioned economeric resuls suppor our assumpion ha an increase in house prices causes a decline in morgage defauls. In he nex secion, we elaborae on he concep of endogenous morgage defauls and hereby we incorporae endogenous morgage defauls and house price expecaion shocks ino a novel DSGE model. 3. DSGE MODEL We incorporae a morgage defaul channel, a banking secor and house price expecaion shocks in our DSGE model. The economy is composed of six ypes of agens, i.e., financially unconsrained and consrained households, enrepreneurs, commercial banks, monopolisic reailers and he cenral bank. Boh ypes of households supply heir labor supply o enrepreneurs, consume and hen buy houses. Financially consrained households ake loans from a commercial bank and borrow in accordance wih he value of heir house. The financially consrained households defaul when he value of heir house is lower han he sipulaed morgage loan repaymen. Enrepreneurs produce inermediae goods and perceive he price of inermediae goods as given. Also, enrepreneurs are credi consrained and pay back all loans which means ha hey do no defaul on heir loans. The mauriy of loans o he financially consrained households and enrepreneurs is one-period. Commercial banks obain deposis from financially unconsrained households and provide loans o financially consrained households as well as o enrepreneurs. Commercial bank asses comprise household and business loans. Moreover, commercial banks face capial requiremens while heir balance shees are affeced by morgage defauls and house prices. Monopolisic reailers ransform inermediae goods o final goods and he reail secor is he source of price rigidiy in he economy. Lasly, he cenral bank conducs moneary policy. Below we describe each agen in deail. 3.1 Financially Unconsrained Household The expeced uiliy of a represenaive financially unconsrained household is E 0 =0 β U lnc U, + ν h lnh U, N U, η+1 (1) where β U represens he discoun facor, C U, he curren consumpion, H U, denoes he holding of housing sock, N U, he labor hours, ν h he weigh on housing and η he inverse Frisch labor supply elasiciy. η+1 7

13 The financially unconsrained household receives he gross ineres income upon las period deposis i.e., R 1 D 1 π, where R 1 is he gross nominal ineres rae on deposis, D 1 he las period deposis and π he inflaion. The household earns he real wage rae W U, for supplying N U, hours o an enrepreneur. The real house prices are denoed by q. The financially unconsrained household uses income for consumpion C U, buys houses a q H U, H U, 1 and makes deposis D a a commercial bank. As he owner of a reail firm, he financially unconsrained household receives he lump-sum profi F. The budge consrain is expressed as follows C U, + D + q H U, H U, 1 = R 1 π D 1 + W U, N U, + F (2) The financially unconsrained household chooses C U,, D, H U,, and N U, o maximize equaion (1) subjec o (2); he firs-order condiions are and 1 = β C U E 1 U, C U,+1 R π +1 (3) q C U, = ν h H U, + β U E q +1 C U,+1 (4) W U, C U, η = N U, Equaion (3) is a sandard consumpion Euler equaion ha capures he household s ineremporal choice beween curren and fuure consumpion. Curren consumpion depends negaively on he real deposi ineres rae E (R π +1 ). Equaion (4) is he opimal holding of housing sock. The lef-hand side capures he marginal cos of acquiring an addiional uni of house q C U,, whereas he righ-hand side depics he marginal benefi of purchasing an exra uni of house, which comprises he marginal uiliy of having a house ν h H U, and he expeced resale value of he house β U E q +1 C U,+1. The opimal hours worked are deermined by equaion (5). 6 (5) 3.2 Financially Consrained Household The expeced uiliy of a represenaive financially consrained household is given by E 0 =0 β F lnc F, + ν h lnh F, N F, η+1 (6) The discoun facor of he financially consrained household is symbolized as β F. C F, is he consumpion while H F, denoes he holding of housing sock, N F, he labor hours, ν h he weigh on housing and η similarly o equaion (1), he inverse Frisch labor supply elasiciy. η+1 6 The exac derivaion of firs order condiions can be found in Appendix I. 8

14 This ype of household receives he real wage rae W F, for supplying N F, hours o he enrepreneur, and he obains new loans L F, from a commercial bank. The financially consrained household buys houses q H F, H F, 1. Furhermore, he amoun of deb ha he financially consrained household has agreed o pay back is R F, 1 L F, 1 π, where R F, 1 is he gross nominal ineres rae on one-period morgage loans (including repaymen) and R F, 1 represens he gross real ineres on morgage loans. However, he financially consrained household can defaul on is loans by paying back less han he conracual obligaions, hence Z F, is he amoun of morgage defauls which will be deermined below. The budge consrain is expressed as C F, + q H F, H F, 1 + R F, 1 L π F, 1 Z F, = L F, + W F, N F, (7) The financially consrained household canno borrow more han a fracion m F of he expeced value of he house. The collaeral consrain is wrien similarly as in Iacoviello (2005), namely E R F, L π F, m F E q +1 H F, (8) +1 Thereafer we explain he mechanism of endogenous morgage defaul; he financially i consrained household consiss of many members i who all purchase houses H F,. The oal housing sock of he household is H F, = 1 i=0 i H F, 9 di. In each period, each member s house value is subjec o an idiosyncraic iid shock ω i i such ha he value of he house becomes q H F, 1 + ω i. The household member defauls when he value of he house is lower han he morgage loan i repaymen i.e., R F, 1 L F, 1 π > q H F, 1 + ω i. Le ω be he hreshold value of he shock for which he member will pay back he morgages, hus ω = R F, 1L F, 1 1. If he household π q H F, 1 member draws an ω lower han ω, he member will defaul. Le ω be he lower bound of he disribuion where ω > 0 and f(ω) he probabiliy densiy funcion of ω. The amoun of morgage defauls Z F, is deermined by he following inegral Z F, = R F, 1 L F, 1 1 π q H F, 1 ω R F, 1L F, 1 π q H F, 1 (1 + ω) f(ω)dω (9) The inuiion behind equaion (9) is he following: he household defauls on he loans if he iid shock ranges beween is lowes possible value and he criical value of he shock a which he defaul occurs. In he case of defaul, he amoun of morgage defauls is he promised repaymen of he loan minus he value of he house ha is aken over by he commercial bank. Z F, is he realized morgage defauls. To simplify, we assume ha f(ω) is consan in he relevan inerval such ha f(ω) = f. By evaluaing he inegral, we can obain he following amoun of morgage defauls π

15 2 Z F, = f q H F, 1 R F, 1L F, 1 (1 ω ) 2 π q H F, 1 (10) We now ake he derivaive of Z F, wih respec o L F, 1 and H F, 1 and Z F, L F, 1 = f R F, 1 π R F, 1L F, 1 π q H F, 1 (1 ω ) > 0 (11) Z F, = f R F, 1L F, 1 (1 ω ) R F, 1L F, 1 H F, 1 2H F, 1 π q H F, 1 π f 2H F, 1 R F, 1L F, 1 π q H F, 1 (1 ω ) (1 ω ) q H F, 1 < 0 (12) Equaion (11) implies ha one more uni of loans will lead o more morgage defauls given ha he holding of he housing sock is consan. Equaion (12) implies ha an addiional uni of houses leads o less morgage defauls given ha he uni of loans is consan. 7 The financially consrained household chooses C F,, L F,, H F, and N F, o maximize (6) subjec o (7), (8) and (10). The firs-order condiions are as follows and 1 = β C F E 1 R F, + λ F, C F,+1 π F, E R F, β +1 π F E 1 Z F,+1 (13) +1 C F,+1 L F, q C F, = ν h H F, + β F E q +1 C F,+1 + λ F, m F E (q +1 ) + β F E 1 C F,+1 Z F,+1 H F, (14) W F, C F, η = N F, Equaion (13) is he Euler condiion for consumpion wih collaeral consrain and endogenous loan defaul. λ F, is he muliplier on he collaeral consrain (8). Evidenly, equaion (13) implies ha when he household maximizes uiliy, he marginal uiliy of consuming one more uni of goods oday (1 C F, ) is equal o he marginal uiliy of consuming one more uni of goods in he nex period, aking ino accoun ineres rae β F E 1 C F,+1 R F, π +1 plus wo erms: he firs of hese erms is λ F, E R F, π +1, which reflecs he fac ha he more financially consrained he household (15) is, he less i will consume oday. The las erm β F E 1 Z F,+1 C F,+1 L F, arises because for a given invesmen in houses, one more uni of loans increases he expeced defaul probabiliy. This effec reduces he repaymen of he loan, which in urn reduces he cos of consumpion and obviously increases consumpion. 7 The derivaion of he morgage defaul condiions is analyzed in Appendix I. 10

16 Moreover, equaion (14) deermines he opimal holding of houses. The lef-hand side is he marginal cos of purchasing an exra uni of house. As he household buys one more uni of houses, he household reduces consumpion. The righ-hand side conains four componens: he direc uiliy gain of having a house ν h H F,, he expeced resale value of he house β F E q +1 C F,+1, he expeced marginal benefi of using house as collaeral λ F, m F E (q +1 ), and he expeced morgage defauls β F E 1 C F,+1 Z F,+1 H F,. The housing collaeral channel erm λ F, m F E (q +1 ) implies ha a more relaxed collaeral consrain signifies lower λ F,, which sequenially induces he household o buy more houses. The expeced morgage defaul erm β F E 1 C F,+1 Z F,+1 H F, implies ha by holding more houses he financially consrained household can borrow more, which in urn provides he household wih an incenive o buy more houses. However, holding more houses for given loans reduces he expeced defauls, which makes i less aracive o buy more houses. Finally, he labor supply decision for he financially consrained household is deermined by equaion (15). 3.3 Enrepreneur An enrepreneur has he following objecive funcion E 0 =0 β E lnc E, (16) where β E is her discoun facor and C E, he enrepreneur s consumpion. She produces an inermediae good Y E, and sells he inermediae good o a reailer a a price P W. The reailer ransforms he inermediae good wihou coss ino a final good and hen he reailer sells he final good o oher agens, namely o he enrepreneur, o he financially unconsrained and consrained households and o he banker a he reail price of P. The markup of he final good over he inermediae good is defined as X = P W P. The enrepreneur uses capial, houses and labor o produce an inermediae good. The producion funcion is given by Y E, = K μ 1 ν H E, 1 N α(1 μ ν) (1 α)(1 μ ν) U, N F, where K 1 is he capial ha depreciaes a rae δ, H E, 1 he housing inpu, and N U, and N F, respecively are he financially unconsrained and consrained household labor inpus. The parameer α deermines he labor income share of he financially unconsrained household and he parameers μ and ν represen he capial and housing shares in he producion funcion. The consrain assumpion for he flow of funds is given by C E, + q H E, H E, 1 + R E, 1 L π E, 1 + W U, N U, + W F, N F, + I + ξ K, = Y E, + L X E, (18) (17) 11

17 Wage paymens o he households are esimaed as W U, N U, + W F, N F,, and capial invesmen is denoed I. The enrepreneur faces capial adjusmen coss ξ K, = (ψ k 2δ) I δ 2 K K 1, 1 where ψ k is a capial adjusmen cos parameer. The capial accumulaion is K = (1 δ)k 1 + I. The enrepreneur invess in he housing sock q H E, H E, 1 and obains loans L E, from a commercial bank. The enrepreneur pays back he loans R E, 1 L E, 1 π o he commercial bank, where R E, 1 is he gross nominal ineres rae on business loans. Nex, he enrepreneur faces a collaeral consrain and she canno borrow more han a fracion m E of he expeced value of housing sock E q +1 H E,. The collaeral consrain is wrien as E R E, π +1 L E, m E E q +1 H E, (19) The enrepreneur chooses C E,, L E,, K, I, N U,, N F,, H E, o maximize he objecive funcion (16) subjec o equaions (17), (18) and (19). The firs-order condiions are calculaed as follows 1 = β C E E 1 R E, + λ E, C E,+1 π E, E R E, (20) +1 π +1 q C E, = E β E C E,+1 ν Y E,+1 X +1 H E, + q +1 + λ E, m E E (q +1 ) (21) μ E, = 1 C E, 1 + ψ k δ I K 1 δ (22) 1 μ E, = β E E ψ k C E,+1 δ I +1 μy E,+1 K 12 δ I +1 K ψ 2 k 2δ I +1 δ K +β E E + μ C E,+1 X +1 K E,+1 (1 δ) (23) α(1 μ ν) Y E, X = W U, N U, (24) (1 α)(1 μ ν) Y E, X = W F, N F, (25) The enrepreneur s Euler consumpion condiion is given by equaion (20), where λ E, is he muliplier on her borrowing consrain (19). The opimal invesmen in he housing marke is deermined by equaion (21) and he marginal cos of holding an exra uni of he house is q. The marginal benefi of an addiional invesmen in he housing marke comprises he C E, expeced fuure marginal produc of house E β E C E,+1 νy E,+1 X +1 H E,, he expeced resale value of house β E E q +1 C E,+1 and he marginal benefi of using house as collaeral m E E λ E, q +1. A more relaxed collaeral consrain implies ha λ E, is lower; his increases he marginal benefi of having houses as collaeral, which in urn increases he incenive o buy more houses. The decision on capial invesmen is given by equaions (22) and (23). Equaions (24) and (25) are labor demand equaions.

18 3.4 Commercial Bank For he banker he preference is defined as E 0 =0 β B lnc B, (26) where her discoun facor is β B and C B, he banker s consumpion. The commercial bank s asses comprises loans o he financially consrained household L F, as well as loans o he enrepreneur L E,. The commercial bank obains deposis D from he financially unconsrained household o finance is loan operaions. The commercial bank capial is expressed as K B, = L F, + L E, D (27) We follow Kollmann e al. (2011) in assuming ha a commercial bank faces a capial o asse raio requiremen γ. When a commercial bank deviaes from a required or desired capial raio he bank faces a φ cos, which is a funcion of bank s excess capial X B,. The bank excess capial X B, is defined as he difference beween he bank capial K B, and a fracion γ of he bank s asses (L F, + L E, ) as X B, = K B, γ(l F, + L E, ) (28) where φ = φ(x B, ) is a convex funcion wih he following properies: he firs derivaive is φ < 0 and he second derivaive is posiive φ > 0. The firs derivaive implies ha a higher excess capial reduces he cos of deviaing from he required capial raio, while he second derivaive implies ha a higher excess capial reduces he cos bu a a decreasing rae. Using equaions (27) and (28), he commercial bank s excess capial can be rewrien as X B, = (1 γ) L F, + L E, D (29) We now consider he commercial bank s flow of funds. The expendiure side of he banker includes curren consumpion, he ineres paymen R 1 D π 1 o he financially unconsrained household, new loans o he financially consrained household L F, (household loans) and o he enrepreneur L E, (business loans), as well as he cos of deviaing from he required capial raio φ X B,. The flow of income includes he household deposis, he repaymen of loans by he enrepreneur R E, 1 L π E, 1 and he repaymen of loans by he financially consrained household R F, 1 L π F, 1. However, he financially consrained household can defaul on he morgage loans and he amoun of morgage defauls is Z F,. An increase in Z F, has a negaive impac on he banker s flow of income. The consrain of her flow of funds is expressed as C B, + R 1 π D 1 + L E, + L F, + φ X B, = D + R E, 1 L π E, 1 + R F, 1 L π F, 1 Z F, (30) 13

19 The bank chooses C B,, D, L E,, and L F, o maximize (26) subjec o (10), (29) and (30). The firs-order condiions are β B E R π +1 = E C B,+1 C B, 1 + φ X B, (31) and β B E R E, π +1 = E C B,+1 C B, 1 + (1 γ)φ X B, (32) β B E R F, π +1 = E C B,+1 C B, 1 + (1 γ)φ X B, + β B E Z F,+1 L F, (33) Equaion (31) defines he opimal holding of deposis, whils equaion (32) deermines he opimal loan supply o he enrepreneur. Equaion (33) deermines he opimal loan supply o he financially consrained household. Therefore, he main difference beween equaion (32) and (33) is ha he expeced morgage defaul channel E Z F,+1 L F, is incorporaed ino he opimal loan supply for he financially consrained household. Furhermore, equaion (32) implies ha a rise in he bank s excess capial reduces he cos of deviaing from he capial raio requiremen, which in urn induces he bank o increase he loan supply. This effec leads o a decrease in he ineres rae on business loans. In he absence of he capial requiremen γ he ineres raes on deposis and loans would be he same, and variaions in he bank capial would have a small impac on he borrowing cos for he enrepreneur. Thus, a posiive shock o house price expecaions leads o an increase in he bank s excess capial which in urn leads o a decline in ineres rae on business loans. Then, equaion (33) implies ha an increase in he excess capial reduces he cos of deviaing from he capial raio requiremen; hereby his reducion induces he banker o increase loans o he financially consrained household which leads o a decline in he ineres rae on household loans. Consequenly, a posiive shock o house price expecaions leads o an increase in bank capial and excess capial, ha will lead o a decline in household loan raes given he expeced morgage defauls. On he oher hand, for a given uni of houses an increase in he uni of loans o he financially consrained household leads o a rise in he expeced morgage defauls, and in urn dampens an expansion of he supply of loans o he financially consrained household and slows down he decline in he ineres rae on household loans. In summary, he commercial bank s lending decisions are influenced by he bank capial posiion which is affeced by house prices. The commercial bank also akes ino accoun he expeced morgage defauls when making loans o he financially consrained household. 14

20 3.5 Reailer We now urn o he reail secor which inroduces price sickiness ino he model (Iacoviello, 2005). The model feaures a coninuum of reailers indexed by zε[0,1] where hey ransform an inermediae good ino a final good. Each reailer z purchases inermediae goods from enrepreneurs a a price P W and each reailer ransforms hem wihou cos ino he differeniaed goods Y (z), sold a a price P (z). The differeniaed goods are hen aggregaed ino oal final goods Y as such 1 0 Y = Y (z) (ε 1) ε dz (34) ε (ε 1) where ε > 1 is he price elasiciy of demand for goods z. The aggregae price index P is defined as 1 0 P = P (z) 1 ε dz Each reailer faces he following demand curve (35) 1 (1 ε) Y (z) = (P (z)/p ) ε Y (36) We assume ha here is a Calvo price-seing mechanism and a reailer can se her price wih probabiliy (1 θ), and wih θ mus keep he price unchanged. P (z) is he price ha he reailer is able o change. Each reailer maximizes he following expeced profi k=0 θ k E Λ,k P (z) X Y P +k X +k (z) (37) +k where Y +k (z) = (P (z)/p +k ) ε Y +k. Recall ha, he financially unconsrained household is he owner of he reail secor, herefore Λ,k = β U C U, C U,+k represens he financially unconsrained household s sochasic discoun facor. X is he markup of final over inermediae goods and her seady sae is X = ε (ε 1). The Calvo price evolves as ε P = [θp 1 + (1 θ)(p ) 1 ε ] ε (1 ε) (38) Combining (37) and (38) and hen log-linearizing, we obain he following Phillips curve π = β U E π +1 κx (39) where κ = (1 θ)(1 β U θ)/θ. Equaion (39) indicaes ha inflaion depends negaively on he markup X and posiively on expeced inflaion Cenral Bank The cenral bank follows a Taylor rule ha reacs o inflaion, oupu and household credi growh R = ρ i R 1 + (1 ρ i ) ρ π π + ρ y Y + ρ F L F, L F, 1 (40) 8 The (^) ha variables denoe percenage changes from he seady sae. 15

21 where 0 ρ i 1 is he parameer associaed wih ineres rae ineria and ρ π 0, ρ y 0 and ρ F 0 measure he response of he policy rae o curren inflaion, oupu and household credi growh respecively. Equaion (40) is referred o as an augmened Taylor rule, in which he cenral bank reacs o he deviaions of inflaion from is seady sae, he deviaions of oupu from is seady sae and household credi growh. Wih ρ F = 0, we have a sandard Taylor rule where he cenral bank reacs o inflaion and oupu. 4. STOCHASTIC PROCESSES In his secion we discuss he sochasic processes associaed wih a shock o house price expecaions. A house price expecaion shock can be defined as a shif in expecaions abou fuure house prices. In our paper, house price expecaion shocks only affec financially consrained households and he main reasons are as follows: firsly, as Piazzesi and Schneider (2009) repor, here is a heerogeneiy in households view abou he housing marke so here is a cluser of households ha believe i is a good ime o purchase a house because hey believe house prices will rise in he fuure. Households opimism reflecs changes in heir house price expecaions and some of he households are more opimisic han ohers. Moivaed by Piazzesi and Schneider (2009), we assume ha households have differen perspecives abou fuure price increases. Hence, we model financially consrained households o be opimisic abou price appreciaions by incorporaing expecaion shocks o he financially consrained households housing demand equaion. Noe ha unconsrained households are no direcly affeced by house price expecaion shocks. Secondly, he fac ha house price expecaion shocks only affec he financially consrained households, creaes a housing marke boom and a credi boom and a he same ime a period of low inflaion in our model simulaions; his is beer demonsraed in he relevan secion where we also ouline how his oucome has imporan ramificaions for macroeconomic and financial sabiliy. In paricular, he sochasic process of a house price expecaion shock ε follows an AR(1) process: lnε = ρ q lnε 1 + u q,, where 0 < ρ q < 1 and u q, follows a whie noise process wih mean zero and variance σ q 2. The shock is incorporaed ino he financially consrained household housing demand equaion. In fac, he housing demand equaion (14) now is rewrien as q C F, = ν h H F, + β F E ε q +1 C F,+1 + λ F, m F E (ε q +1 ) + β F E 1 C F,+1 Z F,+1 H F, (41) and he expeced morgage defaul becomes Z F,+1 = f R F, L F, (1 ω ) R F,L F, H F, 2H F, π +1 ε q +1 H F, π +1 16

22 f R F, L F, (1 ω ) (1 ω ) ε 2H F, π +1 ε q +1 H q +1 H F, < 0 F, Equaion (41) implies ha a shock o expeced fuure house prices will have a direc impac on he demand for housing hrough he expeced resale value of he house β F E ε q +1 C F,+1, he expeced collaeral value λ F, m F E (ε q +1 ) and he expeced morgage defaul channel E Z F,+1 H F,. 5. CALIBRATION AND PARAMETERIZATION We calibrae he baseline model o mach U.S. daa, hus mos of he values of model parameers are derived by Iacoviello (2005) and Finocchiaro and Heideken (2013). The model economy is log-linearized around is deerminisic seady sae. Table 2 summarizes he calibraion. The financially unconsrained household s discoun facor β U is se o o obain a seady-sae ineres rae on deposis R approximaely 3 % on annual basis. We se he financially consrained household s discoun facor β F and he enrepreneur s discoun facor β E o 0.95, which is smaller han he financially unconsrained household s discoun facor, because i) we wan he financially consrained household and he enrepreneur o borrow in equilibrium and ii) he collaeral consrains o be binding. The value of he weigh on housing in he households uiliy funcion ν h is se o , which implies ha he raio of residenial housing o annual oupu is approximaely 145 % in line wih he U.S. uilized daase. The housing share ν in he producion funcion is se o i.e., so ha he raio of commercial real esae o annual oupu of 70 % remains in line wih he U.S. daa as well. The household loan-o-value (LTV) raio m F is 0.83, and he business LTV raio m E is se o These values indicae ha he household secor is more leveraged han he business secor, as documened in Cecchei e al. (2011). The values of he banking parameers are based on Kollmann e al. (2011). The discoun facor of banker β B is se o 0.97, he cos parameer φ o 0.25, while he bank capial raio γ is se o 0.05 in accordance wih he empirical findings of D Hulser (2009), ha he capial raios of he major European and U.S. invesmen banks range beween 3 % and 5 % over he period Furhermore, following D Hulser (2009) he U.S. regulaor recommends a minimum leverage raio of 5 % in order for a bank o be considered well-capialized prior o he financial crisis. The parameer on he magniude of losses ω is se o 0.61 o obain a seady-sae ineres rae on household loans R F of approximaely 5 % on annual basis. The higher ω is, i will increase he magniude of morgage defauls in he seady sae, hus increase he seady-sae ineres rae on 17

23 household loans. f measures he sensiiviy of he morgage defaul o housing prices. A higher f will make morgage defauls more sensiive o house prices. We se f o 0.83, which implies ha he annual morgage defaul rae is approximaely 2.5 %, in line wih U.S. evidence (Forlai and Lamberini, 2011). Recall ha he deposi rae R is approximaely 3 % annually. The lending rae on household loans R F is higher han he deposi rae R because he parameers ha capure he possibiliy of defaul (ω and f) are included in he ineres rae on household loans. The annualized seady-sae ineres rae on business loans (i.e., he ineres rae for lending o enrepreneurs) R E is approximaely 3.12 %, which is slighly higher han he deposi rae because his lending rae on business loans does no include he possibiliy of defaul. We already menioned ha moneary policy reacs o quarerly inflaion and oupu. So, for he moneary policy parameers we se ρ i = 0.7, ρ y = 0.125, and ρ π = 1.8, based on he U.S. esimaed values indicaed by Finocchiaro and Heideken (2013). Under he sandard Taylor rule, we se ρ F = 0. In he nex secion, we vary he credi growh coefficien in he augmened Taylor rule. According o our daa, he auocorrelaions of he linearly derended U.S. real house prices are approximaely Thereby, we se he persisence of he house price expecaion shock ρ q o MODEL SIMULATIONS We simulae he response of he economy o a posiive shock o house price expecaions. Figure 3 shows he impulse response funcions o a posiive house price expecaion shock. All values are expressed in percenage deviaions from seady sae values, and one period represens one quarer in his model. The cenral bank follows a sandard Taylor rule in which he policy rae responds o inflaion and oupu. Toal consumpion comprises consumpion of financially unconsrained households, financially consrained households, enrepreneurs and he banker. For illusraive purpose, we se an one-sandard deviaion shock o house price expecaions. Figure 3 shows ha a posiive house price expecaion shock yields an increase in oal consumpion, invesmen, employmen, housing demand, household loans, household deb, business loans and bank leverage raio, whereas i yields a reducion in inflaion, morgage defaul rae, ineres raes on household and business loans. A rise in expecaions abou fuure house prices induces financially consrained households o increase heir demand for housing, also riggering a rise in household loans and household deb. The rise in expeced fuure house prices relaxes he collaeral consrain, which furher encourages he financially consrained households o borrow more, leading o even higher household deb. 18

24 The increase in expeced fuure house prices leads o a rise in curren house prices and a boom. The rise in curren house prices increases he value of houses beyond he household deb, and as a resul he morgage defaul rae declines. This is consisen wih he empirical evidence shown in secion 2. The increase in curren house prices expands he commercial bank s balance shee by increasing he value of bank asses (household and business loans) relaive o he liabiliies (household deposis). The posiive house price expecaion shock generaes a rise in bank asses and leverage raio (i.e., bank asses o capial raio). The rise in house prices leads o a rise in bank capial and he bank s excess capial, which in urn boh reduce he cos of deviaing from he capial o asse raio requiremen. This effec induces he bank o increase loans o he business secor, hence accordingly he ineres rae on business loans decline. Likewise, he rise in bank capial and he excess capial leads he commercial bank o increase loans o financially consrained households, which in urn causes a decline in he ineres rae on household loans. On he oher hand, a rise in he amoun of loans o financially consrained households augmens he expeced morgage defauls given he housing sock. The bank akes ino accoun he expeced morgage defauls when making a decision on lending o financially consrained households. Consequenly, a grow in he defauls ends o dampen down he expansion of loans o financially consrained households and weakens he decline of ineres raes on household loans. The inerplay beween he household and he banking secor occurs hrough he house price and expeced morgage defaul channels. The increase in house prices causes he ineres rae on household loans o decrease, while he rise in expeced morgage defauls booss he ineres raes on loans o financially consrained households. Ineresingly, he house price channel is sronger han he expeced morgage defaul one, and as a resul he ineres rae on household loans declines. Moreover, he rise in expeced fuure house prices induces financially consrained households o cu consumpion goods and leisure o inves more in housing. Noneheless, financially unconsrained households consume more, increase leisure and buy less houses. As house prices increase, he collaeral consrains of enrepreneurs are relaxed, which in urn induces he enrepreneurs o increase invesmen and consumpion. Also, business loans and business deb boh increase, and oal consumpion rises during a house price boom as well. Now we discuss he effec of a shock o house price expecaions on inflaion dynamics. The response of inflaion rae is negaive and persisen. Noably, i is he desire o inves in housing ha causes financially consrained households o cu consumpion of goods and leisure so as o inves more. The increase in he labor supply by financially consrained households leads o a rise in oal employmen, ha creaes downward pressure on he wage rae and he marginal cos of producion. This oucome leads o an increase in he markup of final goods over inermediae 19

25 goods and places downward pressure on inflaion. An increase in he markup ends o pu downward pressure on inflaion indicaed by equaion (39), which describes he Phillips curve. Thus, a posiive shock creaes a negaive response in inflaion. The cenral bank responds o a decline in inflaion by lowering he policy rae, which leads o lower loan raes and in urn encourages financially consrained households o ake on more deb. Hence, he lower policy rae may increase he risk of financial crisis and insabiliy, in ha he economy becomes more sensiive o shocks o house price expecaions and a collapse of house prices. In conclusion, our resuls complemen he sudy of Chrisiano e al. (2010), who show ha i is possible for a DSGE model o generae a fall in inflaion while he economy experiences a sock marke boom. In heir model, firms receive a signal abou a new cos-saving echnology ha will be available in he fuure. The anicipaion of he new echnology leads o an increase in invesmen and a boom in sock prices because firms believe his new echnology will improve producion and lower he marginal cos of producion. The fall in he marginal cos of producion creaes downward pressure on inflaion. In our seup, we showed ha a posiive shock o house price expecaions yields an increase in house prices (a housing marke boom) and a decline in inflaion a he same ime. 7. HOUSE PRICE EXPECTATIONS AND IMPLICATIONS FOR MONETARY POLICY This secion discusses house price expecaion shocks and heir implicaions for moneary policy. In paricular, we invesigae wheher moneary policy reacing o household credi growh can dampen he responses of he economy o house price expecaion shocks and reduce he volailiy of oupu and inflaion. We conduc wo exercises: in he firs one, we compare he responses of he economy under he sandard Taylor rule, and under he augmened Taylor rule wherein he cenral bank reacs o household credi growh. Under he sandard Taylor rule regime, he cenral bank reacs o he deviaions of inflaion and oupu from heir seady sae. Under he augmened Taylor rule, he cenral bank reacs o he deviaions of inflaion and oupu from heir seady sae, ye also from household credi growh. For illusraive purposes, under he augmened Taylor rule, he household credi growh coefficien ρ F in he generalized rule equaion (40) is se o be greaer han zero, i.e., In he second exercise, we vary he household credi growh coefficien in he Taylor rule beween 0 and 2. We apply a Mone Carlo simulaion mehod where our model is simulaed imes, and compue he sandard deviaions for oupu and inflaion. 7.1 Firs Exercise Figure 4 shows he responses of he economy under he wo differen Taylor rule cases. Specifically, he solid line demonsraes he responses o a posiive house price expecaion shock 20