Too Much Skin-in-the-Game? The Effect of Mortgage Market Concentration on Credit and House Prices

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1 Too Muh Skin-in-the-Game? The Effet of Mortgage Market Conentration on Credit and House Pries Deeksha Gupta January 28, 2019 Abstrat During the housing boom, a small number of institutions - the government-sponsored enterprises GSEs) and a few banks - held large shares of US mortgage risk I develop a theory where suh onentration of mortgage risk an explain key features of the housing risis In the model, lenders with many outstanding mortgages have inentives to extend risky redit to prop up house pries At the onset of downturns, large lenders will ontinue risky lending for a short period of time This an explain evidene doumenting high-risk lending by the GSEs during the bust The expetation of ontinued risky lending during busts, worsens lending standards during preeding booms through a feedbak effet More onentrated mortgage market exposure leads to larger and riskier redit booms and busts Keywords: Conentration, GSEs, housing booms and busts, mortgage redit JEL Classifiations: G01, G21, L11, L25, R21, R31 The Tepper Shool, Carnegie Mellon University I am deeply indebted to my dissertation ommittee: Itay Goldstein, Vinent Glode, Benjamin Keys, David Musto, and Christian Opp for their insightful omments, guidane, and support I am also thankful to Anna Cororaton, Ayan Corum, Tetiana Davydiuk, Mehran Ebrahimian, Ronel Elul, Joao Gomes, Daniel Greenwald, Maro Grotteria, Ben Hyman, Jessia Jeffers, Mete Kili, Tim Landvoigt, Doron Levit, Priila Maziero, Thien guyen, Giorgia Piaentino, Sam Rosen, ikolai Roussanov, Hongxun Ruan, Lin Shen, Jan Starmans, and seminar partiipants at Carnegie Mellon, the Carnegie-LAEF onferene, Emory University, the Federal Reserve Bank of ew York, the Federal Reserve Bank of Philadelphia, Georgetown University, HEC Paris, ISEAD, Ohio State University, Oxford University, the Soiety for Eonomi Dynamis Meetings, Tulane University, UCLA, University of Mihigan, University of orth Carolina, University of Washington, the Western Finane Assoiation Meetings and the Wharton Shool for their helpful feedbak I also thank the Rodney L White Center for Finanial Researh for finanial support on this projet

2 In 2007, US housing markets were in deline - house pries were falling and there was a spike in mortgage defaults At this time, small, private seuritizers withdrew from the market for risky mortgage lending However, the GSEs ontinued, and in some ases, even inreased their risky mortgage ativity purhasing loans made to borrowers with low-fico sores at high loan-to-value LTV) ratios Bhutta and Keys 2017), Elul, Gupta, and Musto 2017)) These new mortgages were assoiated with high default rates and ex-post did not seem to be profitable for the agenies 1 What motivated this high-risk, seemingly unprofitable lending at a time of falling house pries? By 2007, the GSEs and a few banks had amassed a large onentration of mortgage risk The agenies share of the US mortgage market was about 40% and was as high as 88% in some MSAs 2 Additionally, about 50% of all holdings of AAA rated non-gse mortgage-baked seurities were onentrated amongst a few large omplex finanial institutions LCFIs) Aharya et al 2011)) In this paper, I develop a theory of how suh onentration of mortgage risk an explain high-risk lending in downturns and other important harateristis of the housing boom and bust The key idea of the model is that if redit affets house pries and house pries in turn affet the severity of default, large mortgage lenders internalize their effet on house pries and onsequently on default probabilities and losses when making lending deisions 3 More speifially, prevailing house pries affet the profitability of previously issued mortgages sine borrowers are less likely to default when house pries are high and upon default their house, whih is ollateral for lenders, is worth more Lenders with a large amount of mortgages on their books therefore have an inentive to keep house pries high when they are due mortgage repayments If lenders an influene house pries through inreasing their supply of redit, they may find it optimal to extend redit to low-quality, high-risk borrowers not beause of the return they expet to make on the loan itself, but beause of the boost in house pries that omes from redit provision Lenders trade off the loss they make on the issuane of mortgages to these borrowers with the profits they make by keeping house pries high whih 1 These high-risk mortgage loans made by the agenies did not perform well Fannie Mae and Freddie Ma were plaed into government onservatorship in September 2008 At this time their shareholder equity was negative Aharya, Rihardson, ieuwerburgh, and White 2011)) Following the risis of 2007, many private seuritizers went out of business whih was widely blamed on similarly risky mortgages that they had made during the boom Banks suh as Lehman Brothers and Bear Sterns ollapsed or had to be bailed out due to their exposure to suh loans 2 Appendix D plots the GSEs market share of and total dollar exposure to the US mortgage market from See Elul et al 2017) for variation in the GSE share aross MSAs The GSEs exposure to mortgages ame in the form of portfolio holdings of their own loans about half of whih they held on to) and insurane guarantees on the seuritized mortgages that they sold Additionally, the agenies were the single largest investors in the private seuritization market purhasing about 30% of the total dollar volume of private-label MBSes between Aharya et al 2011)) and Adelino, Frame, and Gerardi 2016) 3 There is a large amount of empirial support for these assumptions Many papers have found a onnetion 1

3 helps mortgages that are due for repayment Conentration impats both the quantity and quality of mortgage redit In the model, banks ompete in a ournot-style framework - they deide how many mortgage loans to make taking into aount their effet on house pries In most models of industrial organization, as onentration inreases, agents behave less like prie-takers and the aggregate quantity supplied of the good in question dereases 4 While this Cournot effet is present in the model, there is a seond effet of hanges in onentration that is new, the propping-up effet In more onentrated markets, individual lenders have larger market shares whih reates an inentive to extend more redit to prop up house pries If the propping-up effet dominates the Cournot effet, the aggregate supply of redit inreases as mortgage markets beome more onentrated Furthermore, redit in more onentrated markets is generally riskier than redit in less onentrated markets In the model, I show that it is possible for two areas with different levels of onentration to have the same level of redit provision However, the area with higher onentration will have lower quality redit with higher default rates The area with low onentration has redit provision due to a relatively strong Cournot effet while the area with high onentration has a weak Cournot effet but a strong propping-up effet The marginal loan made in the area with higher onentration is riskier sine banks ompromise on the return they earn from the expeted loan repayment due to the benefit they get from the resulting inrease in house pries If parameter values allow for equal redit provision under two different levels of onentration, in the presene of ostly default a soial planner would always prefer to make markets less onentrated The model an explain key empirial features of the reent housing risis In partiular, at the onset of a bust, lenders in onentrated markets who have aumulated a large outstanding mortgage exposure during the boom ontinue to make high-risk loans expetation of ontinued lending during the bust affets lending inentives during the redit boom through a feedbak effet The Speifially, the expetation of relatively higher future house pries if a bust ours, dereases the quality of the marginal mortgage loan made during the boom This feedbak effet auses redit quality to worsen over the life of the boom as the propping-up effet grows stronger as outstanding mortgage exposure builds up over the boom The worsening redit quality in turn auses more defaults during downturns Longer redit booms therefore lead to deeper busts The model an thus explain the timing between house pries and default See Foote, Gerardi, and Willen 2008), Haughwout, Peah, and Tray 2008), Palmer 2013), Ferreira and Gyourko 2015) Further, many papers also provide evidene that the availability of redit affets house pries See Himmelberg, Mayer, and Sinai 2005), Khandani, Lo, and Merton 2009), Hubbard and Mayer 2009), Mayer 2011), Griffin and Maturana 2015), Landvoigt, Piazzesi, and Shneider 2015), An and Yao 2016) and Favilukis, Ludvigson, and ieuwerburgh 2017) 4 See Tirole 1988) 2

4 of high-risk lending during the redit boom as mortgage lending got suessively riskier from It also explains the ontinuation of high-risk ativity by the GSEs in 2007 one mortgage markets began to slow down This timing is diffiult for other theories of the risis to explain as arguably house prie expetations were low in 2007 and the demand for mortgage baked seurities had dereased at this time 5 This paper ontributes to maro-prudential poliy disussion in the aftermath of the rises From a poliy perspetive, it is ruial to understand the different fores that an drive housing booms and busts With respet to the finanial risis, while steps have been taken to address the issue of seuritization leading to a lak of skin-in-the game, with the Dodd-Frank at requiring a minimum level of risk retention by lenders, onentration in the mortgage market has not been disussed muh by regulators and has inreased sine the risis In 2016, The Eonomist reported that the GSEs and Federal Housing Assoiation were funding about 65-80% of new mortgages Further, the new regulations faed by banks have made them move out of mortgage lending As a result, mortgage origination has beome highly onentrated with new, independent firms Quiken Loans and Freedom Mortgage originating roughly half of all new mortgages 6 At least some of these mortgages appear to be highly risky and of questionable quality, with the report stating that 20% of all loans sine 2012 have LTV ratios of over 95% Moreover, house pries have been rising rapidly and have surpassed their peak during the boom These patterns ould be ause for onern and this paper illustrates a hannel that may be driving this This paper puts forward a theory that an explain the deterioration in lending standards and its link to the growth of the seondary market beause there was onentration in the holdings of seuritized loans Papers by Ben-David 2011), Carrillo 2013), Garmaise 2015) and Piskorski, Seru, and Witkin 2015) have shown that mortgage originators were lowering underwriting standards, beoming more lax in loan sreening and not monitoring loans arefully in the years leading up to the 2008 risis Keys, Mukherjee, Seru, and Vig 2011) onnet this phenomenon to the development of the seondary market for mortgages 7 While seuritization did reate a new seurity with potential information fritions and moral hazard onerns, it also resulted in a large onentration of mortgage market exposure with seondary market partiipants In partiular, the rise of seuritization ourred after 5 For theoretial models of how seuritization an lead to a lak of skin-in-the-game see Parlour and Plantin 2008) and Vanaso 2017) Cheng, Raina, and Xiong 2014), Shiller 2014) and Glaeser and athanson 2015) show that high house prie expetation an derease lending standards 6 Briefing: Housing in Ameria 2016 Comradely Capitalism The Eonomist 7 Keys et al 2011) find that loan performane was signifiantly worse for borrowers with a FICO sore of just above 620 whih onformed to a rule-of-thumb that made loans with a FICO sore of 620 and above easier to seuritize, than those just below Also see Elul 2011) and Griffin and Maturana 2016) 3

5 Salomon Brothers reated a mortgage trading operation and found investors for MBS Investor interest in MBS allowed the GSEs and some banks to grow their share of the mortgage market by beoming the key players in MBS issuane The agenies share alone inreased from about 7% of the US mortgage market in the 1980s to over 40% in the 2000s This seond effet of seuritization has been largely overlooked by researh into the housing rises I show that in the presene of a propping-up effet, an exogenous inrease in market power of mortgage providers an generate a redit boom even without any hanges to underlying eonomi fundamentals Many reent papers provide support for the theory that large lenders were driving risky lending In a paper testing this theory, Elul et al 2017) find that in 2007 as small private seuritizers were withdrawing from the risky lending, the GSEs inreased high-ltv mortgage purhases in MSAs in whih they had high outstanding mortgage exposure Additionally, Favara and Giannetti 2017) find that mortgage lenders in more onentrated markets internalize house prie drops oming from forelosure externalities and are less likely to forelose on delinquent households Dell Ariia, Igan, and Laeven 2012) find that the deline in lending standards was driven by large lenders and that loan denial rates were lower in areas that had a smaller number of ompeting lenders Adelino et al 2016) find that when private seuritizers designed MBS pools for the agenies, loans in GSE pools were riskier based on observable risk harateristis than loans in non-gse pools adauld and Sherlund 2013) find that seuritization of sub-prime mortgages inreased 200% between 2003 and 2005 and was driven primarily by the five largest broker/dealer banks resulting in a lowering of lending standards in the primary market 8 This paper also ontributes to an important debate on whether the housing risis was driven by distortions in the supply of redit or by high house prie expetations by lenders and borrowers Two entral papers in this debate by Mian and Sufi 2009) and Adelino, Shoar, and Severino 2016) examine the relationship between inome growth and the growth in mortgage redit during the housing boom to address this question In support of the reditsupply view, Mian and Sufi 2009) find that inome growth deoupled from the growth in mortgage redit in the US at the ZIP ode-level They point to innovations in the provision of redit to low-quality borrowers as an explanation for their findings In support of the expetations view, Adelino et al 2016) find that at a borrower-level, inome growth did not deouple from the growth in mortgage redit, indiating that lenders did not fae distorted inentives to lend disproportionately to riskier borrowers Following a shok to onentration, the model an generate different orrelations between inome-growth and the growth in mortgage redit depending on the level of aggregation of 8 Also see Jiang, elson, and Vytlail 2014) 4

6 the variables Following an inrease in mortgage market onentration, the model mortgage redit and inome growth an be negatively orrelated when looking aross areas suh as ZIP odes), while at the same time being positively orrelated when looking aross borrowers In the model, lenders have relatively more market power in affeting housing pries in areas with low inome growth sine in suh areas without the availability of redit there is little else to drive the demand for housing and keep house pries high Therefore, for eah additional mortgage loan, the perentage inrease in house pries and onsequently the return to propping up house pries is high An inrease in onentration an therefore lead to a redit supply shok in areas where inome growth is low, leading to a deoupling of inome growth from the growth in mortgage redit However, banks inentives to lend more to higher-quality borrowers do not fundamentally hange All else equal, a bank would always prefer to make a loan to a high-quality borrower, if possible, as suh a loan would also serve to inrease house pries Therefore when looking at borrower-level data, the growth in inome and mortgage redit an remain positively orrelated 9 While this paper fouses on how the model applies to the housing risis, the mehanism is appliable more generally As disussed above, the model an help explain why we ontinue to see mortgage loans being made at high LTV ratios despite maro-prudential regulation aimed at urbing risky lending Another related appliation of the model is to housing poliy sine 2009 aimed at stabilizing housing markets In the aftermath of the risis, the government took on a large amount of mortgage exposure when the GSEs were taken into onservatorship and the Federal Reserve Bank undertook large-sale purhases of mortgagebaked seurities as part of quantitative easing Many government poliies suh as the Home Affordable Refinane Program HARP), the The Home Affordable Modifiation Program HAMP) and the ontinued purhase of mortgage-baked seurities expliitly stated keeping house pries from falling as one of their goals In 2009, when announing some of these programs, President Obama said that by bringing down forelosure rates, [these poliies] will help to shore up housing pries for everyone 10 put forward in this paper This is in line with propping-up inentives 9 In follow-up papers, Mian and Sufi 2016) and Mian and Sufi 2015), Mian and Sufi argue that some of Adelino et al 2016) results are driven by an improper alulation of total mortgage size and fraudulent inome over-statement In Adelino, Shoar, and Severino 2015), the authors respond to these ritiques and provide evidene that inome over-statement does not drive their results It is not the goal of this paper to take a stane on what empirial fats are valid Rather the paper is meant to highlight a theoretial framework that an help with the eonomi interpretation of the orrelation between inome and mortgage redit growth when looking at more miro versus aggregated data If inome and mortgage redit growth do remain orrelated at a borrower-level, this does not theoretially rule out the possibility of a redit supply shok driving the risis 10 $275 Billion Plan Seeks to Address Housing Crisis The ew York Times, 2009 Also see Bernanke s 2012 FOMC Press Conferene 5

7 I extend the model in various ways First, I inorporate the possibility of banks propping up pries by refinaning borrowers who are lose to default rather than by making loans to new borrowers The same intuition as in the baseline model flows through - banks with large outstanding mortgage exposure may refinane a mortgage by making a loan that is negative PV if the benefit from house prie appreiation is large enough Depending on the expeted repayment a bank an get from existing versus new borrowers, refinaning or new lending an be preferable Seond, I extend the model to allow for lender heterogeneity with a few large lenders making loans alongside smaller, dispersed lenders In this ase, large lenders inrease their share of the mortgage market over time, even if their market power does not hange This is beause as the mortgage holdings of large lenders builds up over a boom period, they are inentivized to make riskier and riskier mortgages in an attempt to prop up pries Suh an effet is not present for smaller lenders who at like prie-takers in the mortgage market Therefore, the market share of large lenders inreases over a boom as they lend relatively more than small lenders This an help explain the rise in the exposure of banks and the GSEs to the mortgage market over the 1990s I additionally show that the model is robust to onentration in the mortgage market at an originator level or at a seondary market level At an originator level, Countrywide Finanial was inreasing its share of the US mortgage market during the boom and aounted for about 15% of all mortgage origination in 2005 In the seondary market, the GSEs were the largest partiipants in the US mortgage market but did not originate mortgages themselves Rather their exposure to the mortgage market was through insurane guarantees on MBS they sold to investors, through portfolio holdings of their own loans, and through the purhase of private-labeled MBS The key mehanism in the model simply requires onentration in mortgage holdings The basi model setup abstrats away from the seondary market However, I provide an equivalent version of the model in whih onentration is present in the seondary market rather than the primary originator market The key mehanism works as long as there is onentration in mortgage holdings at some level and agents with exposure to mortgage payments have some market power If seondary market players own a large share of the mortgage market, they benefit from high house pries If they have market power, they an offer attrative pries on the seondary market for riskier mortgages that will inentivize mortgage originators to then issue mortgages to risky borrowers Holders of these mortgages will suffer losses on these purhases but the inrease in house pries will be profitable for their outstanding mortgage exposure Finally, although the model is very stylized and abstrats away from many aspets of housing markets, I perform a basi alibration of the model to the US housing market The stylized model is able to math some key moments of the housing market 6

8 and demonstrates that hanging onentration an produe signifiant differenes in the likelihood of a redit boom and bust, and the quantity and quality of redit expanded during the redit yle Speifially, when onentration is set to approximately math the GSE market share, the model is able to explain about half of the boom and bust in house pries and over 90% of lending to sub-prime borrowers during the housing boom and bust 11 In a ounterfatual analysis of the alibrated model, I show that dereasing onentration by doubling the number of ompeting lenders in the mortgage market would have redued the fration of sub-prime lending in the housing boom and bust to 0 It would have also resulted in 30% lower growth in house pries during the boom and 80% smaller deline in house pries during the bust This exerise suggests that the model ould be quantitatively signifiant, although preisely estimating the magnitude of propping-up inentives during the housing boom and bust is beyond the sope of this paper The rest of this paper is arranged as follows Setion 1 provides a review of the literature related to this paper Setion 2 desribes the main model setup Setion 3 illustrates the key mehanism of how onentration an affet redit in a simple three-period model Setion 4 disusses the main infinite horizon model and explains how the model generates housing booms and busts Setion 5 extends the model to inorporate onentration in seondary rather than primary markets, refinaning of mortgage loans and lender heterogeneity Setion 6 provides details of the alibration exerise The last setion onludes All proofs are in the appendix 1 Related Literature Although the effet of onentration in markets on resulting pries and quantities is widely studied in eonomis, researh on the effet of onentration in mortgage markets on redit and house pries jointly is relatively sparse Sharfstein and Sunderam 2014), Fuster, Lo, and Willen 2016) and Agarwal, Amromin, Chomsisengphet, Landvoigt, Piskorski, Seru, and Yao 2017) study how ompetition in the mortgage market affets mortgage interest rates, but take house pries as exogenous Poterba 1984) and Himmelberg et al 2005) study 11 In this paper, I fous on the private mandate of the GSEs to maximize profits for shareholders to explain high-risk lending Although the GSEs had private shareholders, they also had a publi mandate to ahieve goals to support housing amongst low- and moderate-inome households and in underserved areas This private/publi nature of the the agenies may mean that their motivations were not purely profitmaximizing Aharya et al 2011) argue that it is hard to explain GSE high-risk ativity beause of their publi mandate alone They report that GSE adherene to their housing targets seemed to be voluntary - the GSEs missed their housing targets on several oasions without any severe santions by regulators Furthermore, the largest housing target inreases for the GSEs took plae in 1996 and 2001, yet the inrease in GSE high-risk ativity did not take plae till later See Elenev, Landvoigt, and Van ieuwerburgh 2016) for a theory of the quasi-government nature of the GSEs 7

9 how mortgage interest rates affet house pries, but assume perfetly ompetitive mortgage markets This paper ombines these ideas and studies redit and house pries when lenders internalize the impat their redit provision has on house pries This paper is related to the literature on how size an affet inentives to take on risk The main theory in this area of researh is too-big-to-fail: large institutions take on exessive risks beause they expet to be bailed out by the government Stern and Feldman 2004)) In my paper, the key variable that auses institutions to take on mortgage risk is the size of their mortgage exposure rather than the size of the institution This yields ross-setional preditions, holding a lender fixed, and is onsistent with empirial evidene In a similar vein, Bond and Leitner 2015) develop a theory in whih buyers with large inventories of assets, an make further asset purhases at loss-making pries beause other market partiipants use pries to infer information about the underlying asset value their model, the buyer inurs a ost when the market value of his inventories falls too low and would therefore like to keep market pries high In my setting, there is no asymmetri information and lenders with large outstanding mortgage make loans that are low-quality based on observable risk This an therefore help explain the rise of sub-prime lending, whih had observably higher LTV and DTI ratios and higher default rates than prime mortgages In related work, there are other papers that have linked size to risk-taking Boyd and ioló 2016) develop a theory in whih banks in onentrated markets make riskier loans as higher interest rates harged by monopolisti banks make default by borrowers more likely due to inreased moral hazard when borrowers fae higher interest rates 12 The paper is also related to the literature on zombie-lending whih douments that large Japanese banks ontinued to provide redit to insolvent borrowers 13 In Aording to this literature, banks may ontinue to extend redit to under performing loans as it is ostly for them to fall below their required apital levels, or beause they wanted to avoid publi ritiism In this literature, a bank may make negative PV loans beause of other externalities assoiated with ontinuing to extend redit In my model, banks similarly have a positive externality when they make new mortgage loans through the effet of redit on house pries The mehanism I propose arises naturally in the mortgage market beause of the durability of housing Jorda, Shularik, and Taylor 2014) and Mian, Sufi, and Verner 2017) show that a buildup in mortgage debt and real estate lending booms predit future finanial rises aross time and ountries This paper points to a speifi feature of mortgages that reates inentive to engage in risky lending and an help explain why real estate assets 12 For empirial evidene of onentration inreasing bank risk taking, see ioló 2001) and ioló, Bartholomew, Zaman, and Zephirin ioló et al) 13 See Hoshi 2006) and Caballero, Hoshi, and Kashyap 2008) 8

10 are entral to periods of booms and busts This paper also ontributes to the reent debate on whether the housing boom and ollapse was driven by a redit supply shok or by high house prie expetations The majority of this debate has been empirial with Mian and Sufi 2009), Favara and Imbs 2015), Griffin and Maturana 2015), Landvoigt et al 2015) providing evidene supporting a redit supply shok and with Glaeser, Gottlieb, and Gyourko 2013) and Adelino et al 2016) arguing that an expetations based explanation fits the data better The theoretial literature reoniling observations from the risis with either view is relatively sparse, and typially requires either irrationality or misinformation to justify the housing boom The expetations-based view often requires that buyers and lenders in housing markets hold overoptimisti views about future housing pries 14 In the ase of a redit supply shok, sine borrowers, seuritizers and the MBS buyers faed large losses in the risis, it is hard to explain why the redit supply shok happened without an overoptimism or misinformation about the benefits of new ways to supply redit This paper adds to this literature by providing a theoretial framework that an reonile many of the empirial findings driving the urrent debate 2 The Model The model is an infinite horizon, disrete time model with overlapping generations A number,, of infinitely lived banks eah with aess to an equal share of borrowers make mortgage loans to households Eah period t a new generation is born that lives for two periods and onsists of a ontinuum [0, 1] of households Households from generation t derive utility from onsuming housing, k t {0, 1}, when they are young, and a onsumption good when they are old Their life-time utility is given by, uk t, t+1 ) = γk t + β t+1 The extent to whih households value housing onsumption is aptured by the preferene parameter, γ, and β < 1 is a disount fator 15 tehnology whih yields a return of 1 Households have aess to a storage There are two types of households: a proportion α nb of households non-borrowers ) reeive their endowment when they are young and the remaining households borrowers ) 14 Arguments in favor of this have been made by Cheng et al 2014), Shiller 2014) and Glaeser and athanson 2015) 15 Green and White 1997), Sekkat and Szafarz 2011) and Sodini, ieuwerburgh, Vestman, and Lilienfeldtoal 2016) provide estimates of the benefits of home-ownership 9

11 reeive their endowment when they are old on-borrowers from generation t are born with an endowment ωt nb at t They reeive a positive endowment, ωt nb = e nb, with probability φ nb s and 0 otherwise where s is a generation-speifi inome shok Borrowers from generation t reeive an endowment ω b t at t + 1 These households therefore need a mortgage to be able to buy a house at t There are two types of borrowers: proportion α bh of households are high-quality borrowers and the remaining are low-quality borrowers, with the former having a greater expeted endowment High and low-quality borrowers reeive a positive endowment ωt b = e b with probability φ bh s and φ bl s < φ bh s ) respetively and 0 otherwise Eah generation t has a generation-speifi shok, s t {R, P }, and an be born rih or poor with q being the probability of a rih generation being born In a rih generation, all agents have a higher expeted endowment than in a poor generation: φ nb P < φnb R, φbh P < φbh R and φ bl P At eah time t, one a generation is born, the expeted endowments of its < φbl R borrowers and non-borrowers are ommon knowledge There is therefore no adverse seletion due to information fritions in the redit market 21 Housing Market The housing stok, h t, depreiates at rate δ per period where 0 < δ < 1 Eah period, ompetitive prie-taking onstrution firms an also produe new housing, n t, to add to the existing stok of housing Firms have a ost of produing houses, h t, whih depends on both the existing stok of housing and new houses produed The ost to firm i of produing n i t new houses is h t n i t This partiular ost funtion delivers tratable solutions and aptures the idea that land availability is an important fator in the ost of housing onstrution Piazzesi and Shneider 2016) show that movements in the value of the residential housing stok are primarily due to movements in the value of land Knoll, Shularik, and Steger 2017) provide evidene that rising land pries explain about 80 perent of global house prie appreiation sine World War II 16 The total supply of housing at time t is therefore given by: h t = 1 δ)h t 1 + n t The demand for housing is given by the number of mortgage loans borrowers get from banks, h b t, and the number of houses purhased by non-borrowers, h nb t I will make parameter restritions outlined at the end of this setion) to ensure that there is some new onstrution every period The prie of housing, P t, is then set to lear the housing market and is given 16 The main results of the model also hold for a more general supply funtion in whih onstrution osts are affeted differentially by new onstrution and by the exisiting stok of housing More generally, the key results of the model require that house pries inrease when redit supply expands 10

12 by a linear funtion: P t = h t Mortgage Loans At time t, a household i borrows k i tp t at an interest rate, r i ts t+1 ), that an be ontingent on the future states of the world At time t + 1, if a household pays bak its loan, it keeps its house whih it an sell to use the proeeds for onsumption If the household defaults on its loan, the bank foreloses on the house and is entitled to the household s endowment In the model, mortgage loans are therefore similar to adjustable rate mortgages with reourse The Household s Problem Eah period t, borrowers and non-borrowers from generation t deide whether to purhase a house Households also have aess to a storage tehnology whih gives a rate of return of 1 at time t + 1 When deiding whether to purhase a house, non-borrowers aount for both the utility they get from housing onsumption and the future prie at whih they expet to sell their home the proeeds of whih are spent on the onsumption good) At time t, a non-borrower with endowment ω nb t P t will buy 1 unit of housing if: γ + β1 δ)e[p t+1 ] βp t Borrower households from generation t reeive their endowment in the future and must borrow from banks at time t to buy housing At time t + 1, a borrower who has suessfully obtained a mortgage will either suessfully repay their mortgage and an then sell their house, or default and lose their endowment and house If a borrower s bank harges him a state-ontingent interest rate of r t s t+1 ), then he will buy 1 unit of housing if: γ + β1 δ)e[p t+1 ] βe[min{p t 1 + r t s t+1 )), ω b t + 1 δ)p t+1 }] The LHS is the utility the household gains from living in the house in period t and the 17 Eah firm solves the following problem, max n i t P t n i t h t n i t In equilibrium, firms will produe housing until P t = h t 18 In a model with reourse, at time t, a household with a mortgage loan from generation t 1, repays its mortgage if its net worth is larger than the repayment amount ω b t δ)p t P t 1 r i t 1s t ) If the household defaults, the bank gets the maximum amount the household an repay, ie, ω b t 1 +1 δ)p t 11

13 proeeds the household gets from selling the house at t + 1 The RHS represents the net ost of purhasing the house to the household If the household does not have enough funds to repay its mortgage, ω b t + 1 δ)p t+1 < P t 1 + r t s t+1 )), then it defaults and loses its endowment and house 24 The Bank s Problem There are infinitely lived banks that an make mortgage loans to households Eah period t, banks observe the inome shok of the urrent generation and deide how many loans to 1 issue and at what interest rate Eah bank has aess to an equal share,, of the mortgage market The mortgage market is thus segmented implying that households borrow from their loal bank and do not shop around for mortgage rates Therefore, eah bank has aess to a group of borrowers without having to ompete with other banks on interest rates 19 Although banks do not ompete diretly on interest rates, they interat strategially with eah other due to the olletive effet of their ations on house pries This gives rise to strategi substitution effets that are similar to those in models of Cournot ompetition I solve the model in both the ase when a bank annot ommit to future lending and in the ase when the bank an ommit to future lending Let V s t, m h t 1, r h t 1, m l t 1, r l t 1, P t 1, s t 1 ) be the value funtion of a bank at time t where s t = {h, l} represents the inome shok of the generation born at time t, m j t 1 represent the number of mortgage loans that the bank has made at time t 1 to borrowers of type j = {h, l} at interest rate r j t 1, and P t 1 is the prie of housing at time t 1 and a funtion of m h t 1 and m l t 1) Then at time t, a bank solves the following problem: 19 Lako and Pappalardo 2007) and Amel, Kennikell, and Moore 2008) provide empirial evidene that supports this assumption They find that onsumers tend to bank loally and do not shop around for mortgage rates 12

14 V s t 1, s t, m h t 1, m l t 1, r h t 1, r l t 1, P t 1 ) = j={h,l} max m h t 0,ml t 0,rh t,rl t m j t 1 φ bj s t min{p t rt 1), j e b + 1 δ)p t } + 1 φ bj s t ) min{p t rt 1), j 1 δ)p t } ) }{{} Repayment m j tp t }{{} j={h,l} ew Lending + βe [ V s t, s t+1, m h t, m l t, r h t, r l t, P t ) ] }{{} Continuation Value st γ + β1 δ)e[p t+1 ] βe[min{p t 1 + r t s t+1 )), ω b t + 1 δ)p t+1 }] m h t 1 αbh m l t 1 1 αbh α nb ) The first term in the bank s payoff is the amount the bank earns on loans made to borrowers from generation t 1 whih are due for repayment at time t House pries at time t affet the bank s payoff from outstanding loans in two ways: they affet borrower net-worth whih determines whether the borrower will repay or not; they also affet the bank s payoff in ase of default The seond term is the ost of new lending and the final term is the bank s expeted ontinuation value The bank faes a borrower purhasing onstraint - that given the repayment shedule hosen by the bank, the borrower wants to get a mortgage The seond and third onstraints are the market share onstraints of the bank Parametri Restritions Given the [0, 1] ontinuum of households born every period, the maximum housing prie is To help understand the following parameter restritions, it is useful to note that given these restritions, the prie of housing in the eonomy will never fall below φ nb P αnb To lose out the model, I make the following parametri restritions 1 The private benefit of housing is large enough, ie, γ β 1 δ)φ nb P αnb ), to guarantee that non-borrowers always demand housing and there is a positive interest rate at whih borrowers demand housing 20 ote that banks are taking into aount the urrent and future lending deisions of all other banks when making their own deision about how many loans to make In a slight abuse of notation, the problem as it is urrently written does not make this expliit Lending by other banks is embedded in the bank s deision when it aounts for urrent and future house pries 13

15 2 on-borrower endowment is large enough, ie, e nb, to guarantee that a nonborrower who reeives a positive endowment an always afford to buy a house Sine non-borrowers in the model are proxying for outside housing demand, this assumption guarantees that redit is never the sole driver of house pries 21 3 In the theoretial results, depreiation is not too low, ie φ nb P αnb > 1 δ, to guarantee that there is at least some new onstrution every period and that the bank s problem is thus ontinuous in house pries In the alibrated version of the model, I do not restrit the parameters to satisfy this assumption 4 Low-quality borrower endowment is small enough, ie, βφ bl Re b + β1 δ) < φ nb P α nb, to guarantee that it is never profitable for banks to lend to low-quality borrowers The assumption on new onstrution every period guarantees that prie never falls below φ nb P αnb This restrition helps to larify the key mehanism of the model sine for any possible sequene of house pries and in any state, any mortgage loan made to low-quality borrowers is PV negative Therefore, there is no reason a bank would ever make loans to low-quality borrowers unless the return from propping up pries is high enough Model Robustness: There are two key requirements for the results First, house pries affet a household s ability or inentive to repay a mortgage suh that higher housing pries redue the probability of default and/or the loss due to default Seond, redit provision has an effet on house pries The model is robust to modeling mortgage loans without reourse and as fixed rate mortgages The model is also robust to other market strutures as long as banks are able to make profits in one period and offset them with losses from another The model an also allow entry and exit so that banks lifetime profits are zero as long as they an make profits or losses period-by-period 3 Three-Period Model To demonstrate the key mehanisms of the model I start by disussing the equilibrium in a simplified three-period setting This highlights how onentration affets both the quantity and quality of redit It also explains how, in onentrated markets, mortgage growth an 21 This also helps simplify the model solution as house pries will always inrease with more redit Banks do not rowd non-borrowers out of the market by making house pries too expensive 14

16 be negatively orrelated with inome growth aross areas and positively orrelated with inome growth aross borrowers Unertainty in future lending opportunities and intraperiod borrower heterogeneity are not neessary to obtain the key results of the model, and therefore I abstrat away from both in this simplified model The full model keeps the intuition of the three-period model and is additionally able to produe boom and bust yles with features that haraterized the reent housing risis In the first period the eonomy is in a rih-state with only non-borrowers and high-quality borrowers, and in the seond period a poor-state hits with ertainty in whih there are only non-borrowers and low-quality borrowers In the final period, no new generation is born and therefore I assume the prie of housing falls to an endogenously speified liquidation value, φ nb P αnb κ 0 Sine no high-quality borrowers are born in the seond period, any t = 2 lending will only be to low-quality borrowers Sine by assumption low-quality loans are negative PV, banks only lend a positive amount at t = 2 if they find it profitable to prop up house pries This setup thus learly demonstrates when a bank is inentivized to sarifie loan quality for the return to keeping house pries high 22 I haraterize the results of the model both when banks annot ommit to a level of t = 2 lending when making loans at t = 1 and when banks an ommit to future lending As I will disuss, in both ases the results are qualitatively similar but the eonomi intuition for why banks want to prop up pries is different In pratie, there are reasons to think that the GSEs were able to ommit, at least in part, to future lending Hurst, Keys, Seru, and Vavra 2016) provide evidene that the GSEs faed politial pressure that did not allow them to make substantial hanges to interest rates These onstraints ould redibly allow the GSEs to ommit to future ativity The three-period model an be solved by bakwards indution Sine no new generation is born in the third period, banks do not lend at t = 3 In the seond period, lending by any given bank, m 2 is stated in the following lemma, where M i 2 is lending by all other banks at t = 2 Lemma 1A In the three-period model, without ommitment to future lending, a bank s period-2 lending, m 2, is given by the following two ases Case 1: If φ bh R eb γ β, { max 0, m 11 δ) φnb P α + M 2 i β φbl P eb + 1 δ)κ 2 } 22 In this three-period model, sine t = 3 values are kappa and low-quality borrowers are only born at t = 2, the fourth parametri restrition an be simplified to βφ bl P eb + β1 δ)κ < φ nb P αnb 15

17 Case 2: If φ bh R eb > γ β, 1 φbh R max {0, )m 11 δ) φnb P α + M 2 i β φbl P eb + 1 δ)κ 2 In the three-period model, with ommitment to future lending, a bank s period-2 lending, m 2, is given by: { max 0, m 11 δ) φnb P α + M 2 i β φbl P eb + 1 δ)κ 2 The loans a bank makes to low-quality borrowers, m 2, is always inreasing in outstanding loans, m 1 When m 1 = 0 and the bank has no outstanding loans on its balane sheet, it will never make any loans at t = 2 to low-quality borrowers and m 2 = 0 23 } } As the amount of outstanding loans inreases, m 2 an beome positive If at t = 1, a bank is unable to ommit to a level of future lending, m 2, then it props up house pries to improve its return on loans that are delinquent - when the borrower is unable to return the full fae-value of the loan By inreasing house pries through redit expansion, a bank is able to earn a higher return on defaulting loans sine it has a laim on the house If a bank is able to ommit to future lending, it props up pries to improve its return on delinquent loans and additionally to inrease the fae-value it an harge on non-delinquent loans With ommitment, a bank therefore has greater inentives to prop up pries 24 Loans to low-quality borrowers, m 2, is also inreasing in the future expeted inome of low-quality borrowers, φ bl P eb It is dereasing in the housing demand oming from nonborrowers and other banks, φ nb P αnb + M2 i A lower φ nb P αnb + M2 i implies that an individual bank effetively has larger market power in influening house pries sine outside soures of demand are lower In other words, a lower φ nb P αnb + M i 2 implies a larger elastiity of house pries to redit 25 This inreases the net benefit that redit expansion by the bank has on house pries At t = 1, a bank takes into aount its lending at time t = 2 when determining how many loans to make In period 1, a bank s lending is stated in the following lemma, where M i 1 is lending by all other banks at t = 1 23 Sine low-quality loans are assumed to be negative PV, φ nb P αnb M2 i + β φbl P eb +1 δ)κ < 0 24 When φ bh R eb γ β, bank lending at t = 2 is idential with and without ommitment In this ase, t = 1 borrowers are willing to repay the bank φ bh R eb + 1 δ)p 2 and by setting a fae-value of the loan slightly above this, banks an redibly raise house pries to improve their return on all outstanding loans at t = 2 by propping up pries For more detail on this, see the appendix 25 The elastiity of house pries is simply defined here as the perentage hange in house pries for the marginal mortgage loan 16

18 Lemma 1B In the three-period model, without ommitment to future lending, a bank s period-1 lending, m 1, is given by the following two ases Case 1: If φ bh R eb γ β, m 1 = max { Case 2: If φ bh R eb > γ β, 0, min { β m 1 = max 0, min φ bh R e b + 1 δ)p 2 ) φ nb β 2 R αnb M1 i ) γ + 1 δ)p β 2 φ nb R αnb M1 i 2 β 1 φbh 2 R )φbh R 1 δ)2) 1 {m2 >0} }}, 1 αnb ), 1 αnb ) In the three-period model, with ommitment to future lending, a bank s period-1 lending, m 1, is given by: ) β min{φ bh R eb, γ } + 1 δ)p β 2 φ nb m 1 = max 0, min 2 R αnb + M1 i, 1 αnb ) In an equilibrium in whih a bank props up house pries, if a bank lends more at t = 1, it also inreases its t = 2 lending This pushes up housing pries at t = 2 P 2 ) in turn inreasing the amount of loans a bank makes at t = 1 There is thus a feedbak loop between t = 1 and t = 2 lending Bank lending is also affeted by the aggregate lending of other banks The number of loans a bank makes at t = 1 is dereasing in the number of loans made by other banks, M i 1, but inreasing in the number of loans made by banks in the future, M i 2 The more loans other banks make at t = 1, the higher is the prie of housing at t = 1, making it more expensive for a bank to make mortgage loans This auses a bank to derease the amount it lends The more loans other banks make at t = 2, the higher is the prie of housing at t = 2, allowing banks to harge a larger interest rate on loans made at t = 1 and inreasing their inentive to lend at t = 1 There is thus strategi substitution in bank lending within period but strategi omplimenterities in bank lending aross periods The full haraterization of the equilibrium is disussed in the following subsetion umerial Example: To help understand the mehanism, I run through a numerial example with = 1 I hoose the following parameters: α nb = 7, δ = 4, e b = $200, 000, φ bh R = 1, φbl P = 7, κ = $100, 000, = $300, 000 Following the seond parametri restrition, e nb For simpliity, I assume no disounting, ie β = 1, and also have no non-borrower inome shoks, ie φ nb R = φnb P = 1 I also assume γ φbh R eb, so that bank lending with and 17

19 without ommitment are equivalent 26 Imagine a bank does not take into aount the effet of house pries on the profitability of its outstanding share of loans Then in the seond period, a bank will not prop-up pries It therefore makes makes no loans at t = 2 sine all loans to low-quality borrowers are negative PV Only non-borrowers will buy housing at t = 2 Therefore, housing demand in the seond period is h d 2 = 7, and resulting house pries are h d 2 = $210, 000 We an hek that loans to low-quality borrowers are negative PV House pries at t = 3 are given by the liquidation value κ = $100, 000 and low-quality borrowers expeted endowment is φ bl P eb = $100, 000 If a bank was to lend to low-quality borrowers, it would have to pay $210, 000 at t = 2 and reeives an expeted repayment of 1 δ)κ + φ bl P eb = $200, 000 at t = 3 If a bank is not propping up house pries, it will make no loans in period 2 first period, the bank will make m 1 = 19 loans 27 In the Resulting house pries at t = 1, will be h d 1 = $268, 000 The ost of making t = 1 loans to a bank is $268, 000 and the expeted repayment from these loans is 1 δ)p 2 + φ bh R eb = $326, 000 The total profits earned by the bank are , , 000) = $11, 213 ow, let s onsider what happens if the bank takes into aount its outstanding share of loans in the seond period and wants to deviate to making t = 2 loans Then if the bank s outstanding share is m 1 = 19, a bank will find it optimal to make m 2 = 04 loans This will inrease t = 2 prie to $222, 400 The bank earns an inreased return of $1, 438 on its outstanding loans while making a loss of $926 on new lending at t = 2 Banks are able to make this gain in profits at the expense of young non-borrowers They are harmed by this inrease in prie and suffer an aggregate loss of α nb $222, 400 $210, 000) = $8, 680 This loss of young non-borrowers is transferred to banks, old non-borrowers, and onstrution firms The inrease in house pries at t = 2, allows banks to make a greater return per loan they make at t = 1 Banks are now able to get an expeted repayment of $333, 440 instead of $326, 000 This makes banks want to lend more at t = 1 This will in turn make the bank want to lend more at t = 2 and so on and so forth Eventually, the bank will inrease t = 1 lending to 21 and t = 2 lending to 05 House pries at t = 2 will be $223, 516 and at t = 1 will be $271, 720 The total profits earned by the banks make from t = 1 loans is $12, 836 an inrease from $11, 213) The bank earns losses on t = 2 lending totaling $1, 059 whih offsets some of these profits Young non-borrowers at t = 2 aount for the 26 In this example, to guarantee that loans to low-quality borrowers are negative PV, it is suffiient that βφ bl P eb + β1 δ)κ < φ nb P αnb 27 Loan amounts an be alulated using Lemma 1 18