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 3, 018 Link to Latest Version Abstrat During the housing boom, mortgage markets beame inreasingly onentrated with the government-sponsored enterprises GSEs) being exposed to over 40 perent of US mortgages in the 000s Researh on the auses of the pre-risis rise in risky lending has largely overlooked this trend I develop a theory where this onentration in mortgage holdings an explain key features of the housing boom and bust In the model, large lenders with many outstanding mortgages have inentives to extend risky redit to prop up house pries An inrease in onentration an lead to a redit boom with worsening redit quality and a subsequent bust with widespread defaults The model an generate a negative orrelation between redit and inome growth aross areas suh as ZIP odes) while maintaining a positive orrelation between them aross borrowers reoniling empirial evidene that has previously seemed ontraditory Keywords: Conentration, GSEs, housing booms and busts, mortgage redit JEL Classifiations: G01, G1, L11, L5, R1, R31 The Wharton Shool, University of Pennsylvania 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, Maro Grotteria, Ben Hyman, Jessia Jeffers, Mete Kili, Tim Landvoigt, Doron Levit, Priila Maziero, Thien guyen, Sam Rosen, ikolai Roussanov, Hongxun Ruan, Lin Shen, Jan Starmans, and seminar partiipants at the Wharton Shool for their helpful feedbak I would also like to thank the Rodney L White Center for Finanial Researh for finanial support on this projet

2 In the 000s, there was an unpreedented surge in risky lending to borrowers with low FICO sores at high debt-to-inome and loan-to-value ratios These mortgages were assoiated with high default rates and ex-post did not seem to be profitable for redit suppliers 1 What motivated this high-risk, seemingly unprofitable lending? A ommon explanation is that dispersion in mortgage holdings driven by seuritization aused moral hazard problems in mortgage origination More speifially, sine redit providers ould sell off mortgages, they no longer had skin-in-the-game in the mortgages they originated and therefore had a redued inentive to monitor and originate quality mortgages This explanation has gained tration in maro-prudential poliy following the risis, with the Dodd-Frank at requiring a minimum level of risk retention by mortgage lenders However, during the housing boom, mortgage markets had a historially high level of onentration if we onsider broader exposure to the mortgage market, suh as mortgage holdings rather than just originations In partiular, the GSEs and a few banks had rising exposure to the mortgage market through the 1990s and amassed a large onentration of mortgage risk in the 000s The agenies share inreased from about 7% of the US mortgage market in the 1980s to over 40% in the 000s 3 In this paper, I develop a theory of how this inrease in onentration of mortgage risk an explain the surge in high-risk lending and other important harateristis of the housing boom and bust The model an explain key empirial features of the reent housing risis In partiular, as mortgage markets beome more onentrated, the model predits a boom in redit haraterized by inreasing house pries and debt-to-inome DTI) ratios Credit quality worsens over the life of the boom A fundamental shok to a onentrated market an lead to a ollapse in real estate pries aompanied by large-sale defaults For a short period after the bust, lenders in onentrated markets ontinue to make high-risk loans Importantly, the model an explain the timing of high-risk lending that started in the 000s after the redit boom had already begun and the ontinuation of high-risk ativity by the GSEs in 007 one mortgage markets began to slow down Bhutta and Keys 017)) 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 1 Following the risis of 007, many private seuritizers went out of business, banks suh as Lehman Brothers and Bear Sterns ollapsed or had to be bailed out due to their exposure to the subprime market, and Fannie Mae and Freddie Ma were plaed into government onservatorship For theoretial models of this mehanism see Parlour and Plantin 008) and Vanaso 017) 3 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, Rihardson, ieuwerburgh, and White 011)) and Adelino, Frame, and Gerardi 016) 1

3 and onsequently on default probabilities and losses when making lending deisions 4 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 on mortgages that are due repayment Conentration impats both the quantity and quality of mortgage redit 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 5 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 As onentration inreases, individual lenders aquire 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 This is beause large banks are willing to ompromise on the return they earn from the expeted loan repayment beause of the benefit they get from the resulting inrease in house pries A alibration of the stylized model mathes key moments of the US housing market during the redit yle 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 4 There is a large amount of empirial support for these assumptions Many papers have found a onnetion between house pries and default See Foote, Gerardi, and Willen 008), Haughwout, Peah, and Tray 008), Palmer 013), Ferreira and Gyourko 015) Further, many papers also provide evidene that the availability of redit affets house pries See Himmelberg, Mayer, and Sinai 005), Khandani, Lo, and Merton 009), Hubbard and Mayer 009), Mayer 011), Griffin and Maturana 015), Landvoigt, Piazzesi, and Shneider 015), An and Yao 016) and Favilukis, Ludvigson, and ieuwerburgh 017) 5 See Tirole 1988)

4 the boom and bust in house pries and over 90% of lending to sub-prime borrowers during the housing boom and bust 6 The model is also able to generate the GSEs inrease in market share 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 paper also ontributes to an important debate on the ause of the housing risis that has entered around two narratives The first is that distortions in the supply of redit led to lax lending standards A key finding in support of this view is by Mian and Sufi 009) who 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 The seond narrative is that the expetation of high future house pries led lenders and borrowers to over-estimate the profitability of mortgage loans Reent evidene in support of this view is presented by Adelino, Shoar, and Severino 016) who find that at a borrower-level, inome growth did not deouple from the growth in mortgage redit This paper an provide a theoretial foundation for the seemingly ontraditory empirial findings by Mian and Sufi 009) and Adelino et al 016) Following an inrease in mortgage market onentration, the model an generate a negative orrelation between mortgage redit and inome growth when looking aross areas suh as ZIP odes), while at the same time maintaining a positive orrelation between them at a borrower-level 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 6 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 011) 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 001, yet the inrease in GSE high-risk ativity did not take plae till later See Elenev, Landvoigt, and Van ieuwerburgh 016) for a theory of the quasi-government nature of the GSEs 3

5 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 remains positively orrelated 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 005 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 mortgage-baked seurities MBS) they sold to investors, through portfolio holdings of their own loans, and through the purhase of private-labeled MBS Additionally, about 50% of all holdings of AAA rated non-gse MBS were onentrated amongst a few large omplex finanial institutions LCFIs) The key mehanism in the model simply requires onentration in mortgage markets 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 sub-prime mortgages that will inentivize mortgage originators to 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 This paper also 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 drove the housing boom and bust 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 The Eonomist reently reported that the GSEs and Federal Housing Assoiation are funding about 65-80% of new mortgages At least some of these mortgages appear to be highly risky and of questionable quality, with the report stating that 0% of all loans sine 01 have LTV ratios of over 95% 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 4

6 Loans and Freedom Mortgage originating roughly half of all new mortgages 7 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 011), Carrillo 013), Garmaise 015) and Piskorski, Seru, and Witkin 015) 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 008 risis Keys, Mukherjee, Seru, and Vig 011) onnet this phenomenon to the development of the seondary market for mortgages 8 While seuritization did reate a new seurity with potential information fritions and moral hazard onerns, it also aused a large inrease in the onentration of mortgage market exposure In partiular, the rise of seuritization ourred after Salomon Brothers reated a mortgage trading operation and found investors for MBS Investor interest in MBS allowed the GSEs to grow their share of the mortgage market by beoming the key players in MBS issuane This seond effet of seuritization has been largely overlooked by researh into the housing rises Many reent papers provide support for the theory that large lenders were driving risky lending In a paper testing my theory, Elul, Gupta, and Musto 017) find that in 007 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 017) 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 01) 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 016) 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 013) find that seuritization of sub-prime mortgages inreased 00% between 003 and 005 and was driven primarily by the five largest broker/dealer banks resulting in a lowering of lending standards in the primary market 9 The rest of this paper is arranged as follows Setion 1 provides a review of the literature related to this paper Setion desribes the main model setup Setion 3 illustrates 7 Briefing: Housing in Ameria 016 Comradely Capitalism The Eonomist 8 Keys et al 011) find that loan performane was signifiantly worse for borrowers with a FICO sore of just above 60 whih onformed to a rule-of-thumb that made loans with a FICO sore of 60 and above easier to seuritize, than those just below Also see Elul 011) and Griffin and Maturana 016) 9 Also see Jiang, elson, and Vytlail 014) 5

7 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 provides an equivalent model to the baseline model with onentration in the seondary mortgage market Setion 6 disusses an extension of the model with lender heterogeneity It also provides details of the model alibration 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 014), Fuster, Lo, and Willen 016) and Agarwal, Amromin, Chomsisengphet, Landvoigt, Piskorski, Seru, and Yao 017) study how ompetition in the mortgage market affets mortgage interest rates, but take house pries as exogenous Poterba 1984) and Himmelberg et al 005) study 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 They 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 004)) 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 015) 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 In 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 Milbradt 01) models how mark-to-market aounting an lead finanial institutions to suspend trading Kumar and Seppi 199) show that uniformed investors have inentives to manipulate the spot prie used to ompute the ash settlement at delivery when they hold futures positions My model fouses instead on how outstanding exposure an inrease inentives to extend redit rather than ause a suspension of trade 6

8 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 009), Favara and Imbs 015), Griffin and Maturana 015), Landvoigt et al 015) providing evidene supporting a redit supply shok and with Glaeser, Gottlieb, and Gyourko 013) and Adelino et al 016) 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 10 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 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 11 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 ) reeive their endowment when they are old on-borrowers from generation t are born with 10 Arguments in favor of this have been made by Cheng, Raina, and Xiong 014), Shiller 014) and Glaeser and athanson 015) 11 Green and White 1997), Sekkat and Szafarz 011) and Sodini, ieuwerburgh, Vestman, and Lilienfeldtoal 016) provide estimates of the benefits of home-ownership 7

9 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 1 Housing Market The housing stok, h t, depreiates at rate δ per period where 0 < δ < 1 Eah period, ompetitive onstrution firms an also produe new housing, n t, to add to the existing stok of housing Firms have a quadrati ost of produing houses, h t, whih depends on both the existing stok of housing and new houses produed This partiular ost funtion delivers tratable solutions and aptures the idea that land availability is an important fator in the ost of housing onstrution 1 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 by a linear funtion: P t = h t 13 1 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 13 To obtain this we an solve the representative onstrution firm s problem, max nt P t n t 1 δ)h t 1 + n t ) 8

10 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 14 3 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 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 The first order ondition yields, P t = 1 δ)h t 1 + n t ) = h t 14 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 9

11 4 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 15 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: 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 ) 15 Lako and Pappalardo 007) and Amel, Kennikell, and Moore 008) provide empirial evidene that supports this assumption They find that onsumers tend to bank loally and do not shop around for mortgage rates 10

12 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 16 5 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 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 17 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, 16 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 17 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 11

13 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 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 = 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 = 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 1

14 I haraterize the results of the model both when banks annot ommit to a level of t = 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 016) 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 is stated in the following lemma, where M i is lending by all other banks at t = Lemma 1A In the three-period model, without ommitment to future lending, a bank s period- lending, m, 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 i + β φbl P eb + 1 δ)κ } Case : If φ bh R eb > γ β, 1 φbh R max {0, )m 11 δ) φnb P α + M i + β φbl P eb + 1 δ)κ In the three-period model, with ommitment to future lending, a bank s period- lending, m, is given by: { max 0, m 11 δ) φnb P α + M i + β φbl P eb + 1 δ)κ The loans a bank makes to low-quality borrowers, m, 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 = to low-quality borrowers and m = 0 18 } } As the amount of outstanding loans inreases, m an beome positive If at t = 1, a bank is unable to ommit to a level of future lending, m, 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 18 Sine low-quality loans are assumed to be negative PV, φ nb P αnb M i + β φbl P eb +1 δ)κ < 0 13

15 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 19 Loans to low-quality borrowers, m, 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 + M i A lower φ nb P αnb + M 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 implies a larger elastiity of house pries to redit 0 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 = 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 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 : If φ bh R eb > γ β, 0, min { β m 1 = max 0, min φ bh R e b + 1 δ)p ) φ nb β R αnb M1 i ) γ + 1 δ)p β φ nb R αnb M1 i β 1 φbh R )φbh R 1 δ)) 1 {m >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: 19 When φ bh R eb γ β, bank lending at t = 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 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 = by propping up pries For more detail on this, see the appendix 0 The elastiity of house pries is simply defined here as the perentage hange in house pries for the marginal mortgage loan 14

16 ) β min{φ bh R eb, γ } + 1 δ)p β φ nb m 1 = max 0, min 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 = lending This pushes up housing pries at t = P ) in turn inreasing the amount of loans a bank makes at t = 1 There is thus a feedbak loop between t = 1 and t = 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 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 =, the higher is the prie of housing at t =, 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 = 3, δ = 3, e b = $100, 000, φ bh R = 1, φbl P = 35, κ = $75, 000, = $300, 000 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 φ bh R eb, so that bank lending with and without ommitment are equivalent 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 = sine all loans to low-quality borrowers are negative PV Only non-borrowers will buy housing at t = Therefore, housing demand in the seond period is h d = 3, and resulting house pries are h d = $90, 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 = $75, 000 and low-quality borrowers expeted endowment is φ bl P eb = $35, 000 If a bank was to lend to low-quality borrowers, it would have to pay $90, 000 at t = and reeives an expeted repayment of 1 δ)κ + φ bl P eb = $87, 500 at t = 3 If a bank is not propping up house pries, it will make no loans in period In the first period, the bank will make m 1 = 1 loans 1 Resulting house pries at t = 1, will be h d 1 = $16, 500 The ost of making t = 1 loans to a bank is $16, 500 and the expeted 1 Loan amounts an be alulated using Lemma 1 15

17 repayment from these loans is 1 δ)p + φ bh R eb = $163, 000 The total profits earned by the bank are 1 163, , 500) = $4441 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 = loans Then if the bank s outstanding share is m 1 = 1, a bank will find it optimal to make m = 04 loans This will inrease t = prie to $101, 55 The bank earns an inreased return of $98 on its outstanding loans while making a loss of $539 on new lending at t = 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 $101, 55 $90, 000) = $3458 This loss of young non-borrowers is transferred to banks, old non-borrowers, and onstrution firms The inrease in house pries at t =, allows banks to make a greater return per loan they make at t = 1 Banks are now able to get an expeted repayment of $171, 068 instead of $163, 000 This makes banks want to lend more at t = 1 This will in turn make the bank want to lend more at t = and so on and so forth Eventually, the bank will inrease t = 1 lending to 14 and t = lending to 04 House pries at t = will be $10, 937 and at t = 1 will be $130, 534 The total profits earned by the banks make from t = 1 loans is $5, 610 an inrease from $4, 441) The bank earns losses on t = lending totaling $667 whih offsets some of these profits Young non-borrowers at t = aount for the rest of the transfer to banks 31 Conentration and Credit When onentration in mortgage holdings is low and eah bank holds a small share of the market, the return to propping up pries for any individual bank is low Banks therefore do not issue any loans to low-quality borrowers As onentration inreases, banks have aess to a larger share of high-quality borrowers at t = 1 In this ase, they will issue loans to risky borrowers to inrease house pries and onsequently the rents that they get from high-quality borrowers Formally, we an establish the following proposition, Proposition 1 The three-period model has a unique equilibrium There exists a utoff,, suh that if, banks do not prop up houses pries and make no negative PV loans If <, banks engage in risky lending to prop up house pries and supply a positive amount of negative PV loans When house pries at t = are high, high-quality borrowers who get a mortgage at t = 1) make larger mortgage repayments to banks This allows banks to earn greater rents from them As the market share of banks inreases, they lend to more high-quality borrowers at t = 1 This inreases the effet of t = house pries on their profitability As onentration 16

18 inreases, banks begin to make low-quality loans at t = sine redit expansion keeps house pries high As onentration dereases, banks begin to at more like prie-takers in the mortgage market and no longer make loans to prop up house pries Despite strategi omplimenterities in bank lending aross time, the equilibrium is unique The uniqueness arises due to intra-temporal strategi substitution in bank lending If other banks pull bak on lending at t =, an individual bank is inentivized to inrease its own lending at t = and not ut bak on its t = 1 lending enough to give arise to multipliity There is therefore a unique equilibrium of the model As onentration inreases aggregate redit an inrease or derease There are two ompeting effets The first is a ontemporaneous prie effet Large lenders internalize their effet on house pries more than small lenders The marginal inrease in prie when making an additional loan affets large lenders ost of total lending more than that of small lenders Lenders in a onentrated market will therefore ut bak on redit more than lenders in a market with many small lenders This effet is similar to a typial mehanism in Cournot ompetition in whih as onentration inreases, the quantity of goods supplied on the market dereases as suppliers internalize prie effets more As the number of banks dereases, this Cournot effet leads to a derease in redit supply However, sine onentration also reates inentives to prop up pries, there is a seond effet of hange in onentration on redit, the propping-up effet Conentration inreases banks inentives to inrease t = pries through redit expansion and if this effet is large enough, it an ause overall lending to inrease The following orollary summarizes the effet of onentration on mortgage lending: Corollary 1 In the unique equilibrium of the three-period model, as dereases, 1 redit extended by any given bank to both high- and low-quality borrowers inreases, if and banks are not propping up pries, aggregate redit dereases, 3 if < and banks are propping up pries, aggregate redit an inrease When and banks are not propping up housing pries, aggregate redit is always dereasing with onentration beause of the Cournot effet As is typial in most models Typially the presene of strategi omplimenterities gives rise to multiple equilibria The typial reason for multipliity is as follows: when banks expet aggregate lending to be high at t =, they lend more at t = 1, and the high t = 1 lending would lead to the high t = lending that banks antiipated Conversely, when banks expet lending at t = to be low, they lend less at t = 1 whih in turn leads to low t = lending as banks antiipated 17

19 of ompetition, as the number of banks dereases, banks behave more like prie-takers and are willing to issue more loans As disussed above, when <, there is a seond effet of onentration on redit, the propping-up effet As banks aquire larger market shares, they issue more loans per bank at t = 1 This inreases the inentive for banks to prop up pries and make negative PV loans at t = Higher t = prie further inrease the inentive to issue t = 1 loans and so on and so forth As onentration inreases, this feedbak loop an ause aggregate lending to inrease Figure 1 illustrates the effet of onentration on house pries As the market beomes more onentrated and the number of banks dereases, banks begin to prop up house pries In this parametrization, redit inreases with onentration in the region in whih banks prop up pries, as the propping-up effet dominates the Cournot effet As onentration dereases and >, banks stop propping up pries and the amount of redit inreases as ompetition in the market auses banks to behave more and more like prie-takers Figure 1: The figure above plots total redit, measured by the number of households who get a mortgage, against the level of onentration in the mortgage market As we move along the x-axis, inreases and onentration dereases The parametrization is as follows: δ = 01, α nb =, φ bl P =, φbh R = 1, φnb P = 7, φ nb R = 1, e b =,κ = 45, γ = 4, = 98 Looking at Figure 1, we an see that it is possible for two areas with different levels of onentration to have the same amount of aggregate redit However, the omposition of this redit is different In partiular, the redit in the area with larger onentration is riskier - a larger fration of lending is to high-risk borrowers Figure overlays the first graph with different redit risk harateristis - debt-to-inome ratios and default rates As Figure illustrates, although two areas with differing onentration an have the same aggregate redit, the redit in the area with higher onentration is riskier When banks are propping up pries, they extend redit to riskier households with high default rates and make 18

20 negative PV mortgage loans If there is an eonomi ost to high mortgage default rates, this result suggests that a safer way to expand homeownership would be through inreased ompetition rather than through reating agenies that onentrate mortgage risk This may however ome at the ost of lower inome and negative PV) households not getting redit Figure : The figures above plot the debt-to-inome ratio and default rates on the right y-axis against onentration As we move along the x-axis, inreases and onentration dereases The parametrization is as follows: δ = 01, α nb =, φ bl P =, φbh R = 1, φnb P = 7, φnb R = 1, e b =,κ = 45, γ = 4, = The Effet of Various Model Primitives A number of fators affet banks inentives to prop up house pries When the expeted inome of low-quality borrowers, φ bl P eb, is high it is relatively more profitable to lend to low-quality borrowers and banks have to take a smaller loss on these loans in their effort to prop up pries Therefore this inreases the inentive to prop up house pries When non-borrower inome growth in the poor state, φ nb P, is low banks have relatively more market power when it omes to affeting house pries, inreasing the inentive to prop up pries Finally, when δ is low, houses are worth more in future periods inreasing how muh banks and households value the future asset value of a house As banks are inentivized to prop up pries more when these primitives hange, the threshold level of onentration neessary for banks to make high-risk loans dereases The following orollary formalizes how hanges with the various primitives of the model Corollary In the three-period model, inreases as the expeted inome of low-quality borrowers inreases, as the depreiation rate dereases, and as non-borrower growth in the poor state dereases Formally, φ bl P eb > 0, δ < 0 and φ nb P < 0 19