Abstract
In 2007, as American housing markets started to decline, the government-sponsored enterprises dramatically increased their acquisitions of low FICO and high loan-to-value mortgages. By 2008, the agencies had reversed course by decreasing their high-risk acquisitions. I develop a theory in which large lenders temporarily increase high-risk activity at the end of a boom. In the model, lenders with many outstanding mortgages have incentives to extend risky credit to prop up house prices. The increase in house prices lessens the losses they make on their outstanding portfolio of mortgages. As the bust continues, lenders slowly wind down their mortgage exposure.
In 2007, the American housing boom had ended and there was heightened risk of a housing crisis. At this time, private-label securitizers withdrew from purchasing high-risk mortgages. The Government-sponsored enterprises (GSEs), on the other hand, increased their acquisitions of risky mortgages dramatically, almost doubling their purchases of low FICO and high loan-to-value (LTV) mortgages (Elul, Gupta, and Musto 2020, Bhutta and Keys Forthcoming). These new mortgages defaulted at high rates and ex post did not seem to be profitable for the agencies.1 Moreover, this surge in high-risk activity was temporary. By the end of the year, the agencies had substantially reduced risky purchases. What motivated this temporary increase in high-risk, seemingly unprofitable acquisitions at a time of low house price expectations?2
By 2007, GSEs had amassed a large concentration of mortgage risk. The agencies’ share of the U.S. mortgage market was as high as 88|$\%$| in some metropolitan statistical areas (MSAs).3 Their market power increased even further when the housing boom ended as private- label securitizers retreated from the mortgage market. In this paper, I develop a theory of how such concentration of mortgage risk can create incentives for institutions to temporarily increase high-risk mortgage activity at the end of a housing boom.
The key idea underlying the model is that if credit affects house prices and house prices in turn affect the severity of default, large mortgage lenders internalize their effect on house prices and consequently on default losses when making lending decisions. More specifically, prevailing house prices affect the profitability of previously issued mortgages since borrowers are less likely to default when house prices are high and upon default their house, which is collateral for lenders, is worth more. Lenders with a large number of mortgages on their books therefore have an incentive to keep house prices high when they are due mortgage repayments. If lenders can influence house prices through increasing their supply of credit, they may find it optimal to extend credit to low-quality, high-risk borrowers not because of the return they expect to make on the mortgage loan itself, but because of the boost in house prices that comes from credit provision. Lenders trade off the loss they make on the issuance of mortgages to these borrowers with the profits they make on mortgages due for repayment by keeping house prices high.
Concentration affects both the quantity and quality of mortgage credit. In the model, banks compete in a Cournot-style framework: they decide how many mortgage loans to make after taking into account their effect on house prices. In most models of industrial organization, as concentration increases, agents behave less like price-takers and the aggregate quantity supplied of the good in question decreases.4 While this “Cournot” effect is present in the model, a second effect of changes in concentration is new, namely, the “propping-up” effect. In more concentrated markets, individual lenders have larger market shares, a situation that creates an incentive to extend credit to prop up house prices. If the propping-up effect dominates the Cournot effect, the aggregate supply of credit increases as mortgage markets become more concentrated. Furthermore, concentration affects the quality of credit due to the propping-up effect. In particular, the marginal loan made by lenders when they prop up house prices, relative to when they do not, is riskier since banks compromise on the return they earn from the expected loan repayment due to the benefit they get from the resultant increase in house prices. In equilibrium, lenders may even benefit from making negative net present value (NPV) loans.
To observe propping up in equilibrium, a set of conditions must be satisfied. In particular, we require (a) that the credit provision affects house prices, (b) that higher prices reduce the probability of default and/or bank losses due to default, (c) concentrated mortgage markets, (d) a large stock of outstanding mortgage exposure in danger of default, (e) a lack of good-quality borrowers, and (f) a set of relatively price-inelastic homebuyers who banks can expropriate surplus from. A large body of empirical work provides evidence that the first two requirements are likely satisfied most of the time.5 The remaining requirements will vary across geographies and time.
The incentives of a concentrated lender to prop up prices are highest at the end of housing booms as the economy is transitioning into a housing bust. In particular, propping-up incentives are increasing in the size of a lender’s outstanding portfolio, the risk of default of outstanding loans and the lender’s market power. These factors are arguably strongest in transitional periods between booms and busts. In 2007, as the housing market slowed and fears of a crisis grew, all three of these forces combined in a way that could generate strong incentives for the GSEs to prop up prices. The agencies had a large exposure to the mortgage market coming out of the credit boom. The default propensity of outstanding mortgage loans increased dramatically between 2006 and 2007 as evidenced by the asset-backed securities index, which saw a jump in the spread of 2006 vintage mortgage loans.6 The private-label market pulled back from mortgage activity significantly in 2007, increasing GSE market power.
The model can generate a temporary increase in high-risk mortgage activity at the beginning of a bust similar to the pattern of GSE acquisitions in 2007. This transitory spike in risky lending does not require the fundamentals of the economy to be different across different periods of the bust. In the model, the economy can experience a rich or a poor state in each period. In a poor state, borrower incomes are lower than in a rich state. A boom-to-bust transition can be represented by a series of rich shocks followed by a series of poor shocks. By design, the incomes of all borrowers are identical in all poor states of the world ensuring that the fundamentals of lending opportunities are identical in all periods of the bust. However, banks have high outstanding portfolios at the end of a boom. This makes the initial poor states at the beginning of a bust distinct from other periods during a downturn as propping-up incentives are heightened due to the large outstanding mortgage exposure banks have built up over the boom. As the bust continues, banks will wind down their outstanding mortgage exposure in response to poor fundamentals and endogenously reduce their incentives to prop up prices.
Propping up is never Pareto improving as banks profit by expropriating surplus from price-inelastic homebuyers in the market. However, propping up can be beneficial under a utilitarian social welfare criterion. If the benefits of homeownership and credit stability over time are relatively high and the social costs of default are relatively low, a benevolent mortgage lender who maximizes aggregate welfare subject to breaking even would like to make some low-quality loans, which are subsidized by higher-quality borrowers. Propping up causes a similar type of cross-subsidization as banks make rents from high-quality borrowers and losses on low-quality loans. Therefore, when the benefits of homeownership and credit stability are high relative to default costs, propping up can improve total welfare. Conversely, if default costs are relatively high and the benefits of homeownership and credit stability are relatively low, propping up is not welfare improving.
A calibration of the stylized model matches key moments of GSE activity from 2006 to 2008 as the economy transitioned from a housing boom to a bust. Specifically, when concentration is set to approximately match the GSE market share during the boom and bust (following the private-label exit), the model is able to replicate the temporary increase in high-risk acquisitions by the agencies in 2007. The GSEs grew the number of high-risk mortgages they were acquiring dramatically by 104|$\%$| between 2006 and 2007. The model is able to generate a 90|$\%$| growth in the level of high-risk acquisitions by the GSEs in the beginning of the bust, that is, in the first poor state that hits the economy relative to the preceding rich state. In subsequent poor states, the model-implied high-risk activity decreases by 15|$\%$|, which captures about half of the magnitude of the decrease in the GSEs’ high-risk acquisitions between 2007 and 2008. The model is also able to match cross-sectional patterns of GSE activity. In particular, a regression using model generated panel data of the growth in GSE high-risk acquisitions on their outstanding share, generates a similar coefficient at the beginning of the housing bust as that in Elul, Gupta, and Musto (2020).
I perform a number of counterfactual analyses using the calibrated model to evaluate how house prices and defaults may have looked different absent propping up. First, I shut down the propping-up channel. This causes high-risk acquisitions to fall to zero in all periods of the bust. Moreover, it also reduces high-risk acquisitions during the boom years because future house price expectations in the event of a poor state are lower absent propping up making low-quality mortgages less profitable. The combined effects of the reduction in high-risk lending cause house prices to decrease by less and mortgage defaults to be lower. However, aggregate credit also decreases substantially. Second, I shut down the propping-up channel but increase house price expectations during the boom. In this case, high-risk acquisitions during the boom are at a similar level as in the benchmark calibration, but there is no high-risk activity once the bust begins. The fall in house prices is now 11|$\%$| higher than with the propping-up channel. However, default rates on mortgage loans made in 2007 are lower since less low-quality loans are made once the bust begins. Finally, I also consider a counterfactual scenario in which the private-label market maintains their market share in the bust. In this case, the model-implied high-risk acquisitions by the GSEs in 2006 are similar to the benchmark calibration because house price expectations in the bust are high as the private-label market continues to lend. However, high-risk acquisitions in 2007 are substantially lower since the GSEs have less market power to influence house prices reducing the return to propping up.
The model is robust to concentration in the mortgage market at an originator level or at a secondary market level. The GSEs were the largest participants in the U.S. mortgage market but did not originate mortgages themselves. Rather, their exposure to the mortgage market was through insurance guarantees on MBSs they sold to investors, through portfolio holdings of their own loans, and through the purchase of private-labeled MBSs. The key mechanism in the model simply requires concentration in mortgage holdings. The basic model setup abstracts away from the secondary market. In an extension to the benchmark model, I provide an equivalent version of the model in which concentration is present in the secondary market rather than the primary originator market. The key mechanism works as long as there is concentration in mortgage holdings at some level and agents with exposure to mortgage payments have some market power. If secondary market players own a large share of the mortgage market, they benefit from high house prices. If they have market power, they can offer attractive prices on the secondary market for riskier mortgages that will incentivize mortgage originators to then issue mortgages to risky borrowers. Holders of these mortgages will suffer losses on these purchases but the increase in house prices will be profitable for their outstanding mortgage exposure.
A few papers provide empirical support for the channel highlighted in the model. In a paper testing this theory, Elul, Gupta, and Musto (2020) exploit variation in the outstanding share of the GSEs across MSAs at the start of 2007. They provide evidence that the GSEs increased high-LTV mortgage purchases in MSAs in which they had high outstanding mortgage exposure. They also document that this effect is stronger in inelastic MSAs in which prices should be more sensitive to credit provision. Additionally, Favara and Giannetti (2017) find that mortgage lenders internalize house price drops coming from foreclosure externalities in markets in which they have a large share of outstanding mortgages.
This paper contributes to macroprudential policy discussion in the aftermath of the crisis. The GSEs are currently in government conservatorship and policy makers are debating whether and how they should emerge from conservatorship. The Dodd-Frank Act did not address the GSEs’ market power and the agencies’ share of the U.S. housing market has grown since the boom. In February 2019, the GSEs accounted for 61|$\%$| of all outstanding U.S. mortgage debt (The Urban Institute 2019). From a macroprudential perspective, the propping-up effect can provide house price stability but at the same time may cause greater financial fragility by increasing housing defaults in later periods during the bust. This dynamic is therefore important to bear in mind when deciding on the future of the agencies.
While this paper focuses on how the model applies to the 2008 housing crisis, the mechanism is applicable more generally. Another possible application of the model is to housing policy since 2009 aimed at stabilizing housing markets. In the aftermath of the crisis, the government took on a large amount of mortgage exposure when the GSEs were taken into conservatorship and the Federal Reserve Bank undertook large-scale purchases of mortgage-backed securities as part of quantitative easing. Many government policies, such as the Home Affordable Refinance Program (HARP), the Home Affordable Modification Program (HAMP), and the continued purchase of mortgage-backed securities, explicitly state keeping house prices from falling as one of their goals. In 2009, when announcing some of these programs, President Obama said that “by bringing down foreclosure rates, [these policies] will help to shore up housing prices for everyone.”7 This is in line with propping-up incentives put forward in this paper.
1. Related Literature
Although the effect of concentration in markets on resultant prices and quantities is widely studied in economics, research on the effect of concentration in mortgage markets on credit and house prices jointly is relatively sparse. Scharfstein and Sunderam (2016), Fuster, Lo, and Willen (2017) and Agarwal et al. (2020) study how competition in the mortgage market affects mortgage interest rates, but take house prices as exogenous. Poterba (1984) and Himmelberg, Mayer, and Sinai (2005) study how mortgage interest rates affect house prices, but assume perfectly competitive mortgage markets. This paper combines these ideas and studies credit and house prices when lenders internalize the impact their credit provision has on house prices.
This paper is closely related to the literature studying lending by the GSEs and their role in the American housing market. Acharya et al. (2011) provide a detailed dive into the agencies and their role in the housing boom and bust. Elenev, Landvoigt, and Nieuwerburgh (2016) develop a model in which they show that underpriced government mortgage guarantees increase financial sector leverage, lead to riskier mortgage origination and can cause financial fragility. Jeske, Karsten, and Mitman (2013) and Gete and Zecchetto (218) study the distributional effects of subsidies provided to households by the GSEs. This paper complements this literature by solely focusing on the market power of the GSEs rather than their particular role in the U. S. housing market due to their public-private nature. The analysis in this paper remains silent on how markets get to be concentrated in the first place. However, it is likely that the special treatment the GSEs received, highlighted by the rest of the literature, allowed them to have the market power required for the mechanism proposed in the paper.
This paper is also more broadly related to the literature on how size can affect incentives to take on risk. The main theory in this area of research focuses on a too-big-to-fail mechanism: large institutions take on excessive risks because they expect to be bailed out by the government (Stern and Feldman 2004). In this paper, the key variable that causes institutions to take on mortgage risk is the size of their mortgage exposure rather than the size of the institution. This yields cross-sectional predictions, holding a lender fixed, and is consistent with the evidence presented in Favara and Giannetti (2017) and Elul, Gupta, and Musto (2020). In a similar vein, Bond and Leitner (2015) develop a theory in which buyers with large inventories of assets can make further asset purchases at loss-making prices because other market participants use prices to infer information about the underlying asset value. In their model, the buyer incurs a cost when the market value of his inventories falls too low and would therefore like to keep market prices high. In the model in this paper, there is no asymmetric information and lenders with large outstanding mortgage exposure make loans that are low-quality based on observable risk. This can therefore help explain high-risk mortgage activity based on observably higher LTV ratios and lower FICO scores. In related work, other papers have linked size to risk-taking. Boyd and Nicoló (2005) develop a theory in which banks in concentrated markets make riskier loans as higher interest rates charged by monopolistic banks make default by borrowers more likely due to increased moral hazard when borrowers face higher interest rates.
The paper is also related to the literature on zombie lending that documents that large Japanese banks continued to provide credit to insolvent borrowers (Hoshi (2006); Caballero, Hoshi, and Kashyap (2008)). According to this literature, banks may continue to extend credit to under performing loans as it is costly for them to fall below their required capital levels, or because they wanted to avoid public criticism. A bank may therefore make negative NPV loans because of other externalities associated with continuing to extend credit. In this paper, banks similarly have a positive externality when they make new mortgage loans through the effect of credit on house prices. Such a mechanism arises naturally in the mortgage market because of the durability of housing.
2. The Model
There are two types of households: a proportion |$\alpha^{nb}_s$| of households (“nonborrowers”) receive their endowment when they are young, and the remaining households (“borrowers”) receive their endowment when they are old. “Nonborrowers” from generation |$t$| are born with an endowment |$e^{nb}$| at |$t$|. “Borrowers” from generation |$t$| receive endowment |$e$| at |$t+1$| with probability |$\phi$|. These households therefore need a mortgage to be able to buy a house at |$t$|.
There are two types of borrowers: a proportion |$\alpha^{bh}_s$| of households are high-quality borrowers and the remaining are low-quality borrowers, with the former having a greater expected endowment. In particular, high- and low-quality borrowers receive an endowment |$e$| with probability |$\phi^{bh}_s$| and |$\phi^{bl}_s(<\phi^{bh}_s)$|, respectively, and zero otherwise. The state of the world is represented by |$s$|. Specifically, each period |$t$|, an aggregate income shock causes borrowers from generation |$t-1$| who are receiving their endowment to be relatively richer or poorer, |$s_t \in \{R,P\}$|. If a rich shock occurs, borrowers from generation |$t-1$| have a higher probability of receiving a positive endowment than when a poor shock occurs, |$\phi^{bh}_P<\phi^{bh}_R$| and |$\phi^{bl}_P<\phi^{bl}_R$|. The shares of nonborrowers and high-quality borrowers can also vary by state. |$Q =[RR,RL;LR, LL]$| is the state transition matrix, where each entry represents the probability of transitioning from the state represented by the first letter to the state represented by the second letter. The probabilities in each row sum to one.
At each time |$t$|, once a generation is born, the expected endowments of its borrowers are common knowledge. Therefore, adverse selection is absent as there are no information frictions in the credit market.
2.1 Housing market
2.2 Mortgage loans
At time |$t$|, a household |$i$| borrows |$k_t^i P_t$| through a loan with face value, |$D^i_t(s_{t+1})$|, that can be contingent on the future states of the world. At time |$t+1$|, if a household pays back its loan, it keeps its house, which it can sell to use the proceeds for consumption. If the household defaults on its loan, the bank forecloses on the house and is entitled to the household’s endowment up to the promised repayment. In the model, mortgage loans are therefore similar to adjustable-rate mortgages with recourse. In the appendix, I confirm the robustness of the mechanism to mortgage loans without recourse.
2.3 The household’s problem
2.4 The bank’s problem
|$N$| infinitely lived banks can make mortgage loans to households. Each period |$t$|, each bank observes the state |$s\in\{R,P\}$| and decides how many loans, |$m^i_t$|, to issue to each type, |$i \in \{h,l\}$|, of borrower and the face value of each loan, |$D^i_t$|. Each bank has access to an equal share, |$\frac{1}{N}$|, of the mortgage market. The mortgage market is therefore segmented implying that households borrow from their local bank and do not shop around for mortgage rates. Therefore, each bank has access to a group of borrowers without having to compete with other banks.11 Although banks do not compete directly, they interact strategically with each other due to the collective effect of their actions on house prices.
The first two terms in the bank’s payoff are the amounts the bank earns on loans made to borrowers from generation |$t-1$| that are due for repayment at time |$t$|. A proportion |$\phi^i_{s_t}$| of borrowers of type |$i$| receive endowment |$e$|. They decide whether to repay the face value of their debt or default. In the event of default, the bank seizes their endowment and their house. A proportion |$1-\phi^i_{s_t}$| receive an endowment of zero and similarly decide whether to repay their loan or default. The third term is the cost of new lending and the final term is the bank’s expected continuation value. The bank faces default constraints given by (7b), borrower rationality constraints given by (7c) and market share constraints given by (7d). Finally, the bank also takes into account it’s affect on equilibrium house prices given by (7e).
2.5 Parametric restrictions
Given the |$[0,1]$| continuum of households born every period, the maximum housing price is |$c$|. To help understand the following parameter restrictions, it is useful to note that given these restrictions, the price of housing in the economy will never fall below |$c: \underline{\alpha^{nb}}$|, where |$\underline{\alpha^{nb}} = \min\{\alpha^{nb}_P, \alpha^{nb}_R\}$|. To close out the model, I make the following parametric restrictions.
The private benefit of housing is large enough, that is, |$\gamma \geq \beta(c- (1-\delta) c \underline{\alpha^{nb}})$|, to guarantee that nonborrowers always demand housing and that there exists a positive interest rate at which borrowers demand housing.
Nonborrower endowment is large enough, that is, |$e^{nb} \geq c$|, to guarantee nonborrowers can always afford to buy a house. Since nonborrowers in the model proxy for outside housing demand, this assumption guarantees that credit is never the sole driver of house prices. This also helps simplify the model solution as house prices will always increase with more credit. Banks do not crowd nonborrowers out of the market by making house prices too expensive.
In the theoretical results, depreciation is not too low, that is, |$\underline{\alpha^{nb}} > 1-\delta$|, to guarantee at least some new construction every period and that the bank’s problem is thus continuous in house prices. In the calibrated version of the model, I do not restrict the parameters to satisfy this assumption.
- In the theoretical results, low-quality borrower endowment is small enough, that is,to guarantee that it is never profitable for banks to lend to low-quality borrowers. This restriction helps to clarify the key mechanism of the model since for any possible sequence of house prices and in any state, any mortgage loan made to low-quality borrowers is NPV negative. Therefore, a bank would never make loans to low-quality borrowers unless the return from propping up prices is high enough. In the calibrated version of the model, I do not restrict the parameters to satisfy this assumption.(8)$$\begin{equation} \beta E_{s}[\omega] + \beta (1-\delta) c < c \underline{\alpha^{nb}} \qquad \forall \, s. \end{equation}$$
3. Three-Period Model
To demonstrate the key mechanisms of the model, I start by discussing the equilibrium in a simplified three-period setting. I first discuss the case of a single bank and then the case with |$N$| banks. Intraperiod borrower heterogeneity and state uncertainty are not necessary to obtain the key results of the model are therefore abstracted away from.
In the three-period model, I assume that in the first period of the economy all borrowers are high-quality, and in the second period all borrowers are low-quality. In the final period, no new generation is born and I assume that the price of housing falls to an exogenously specified liquidation value, |$ \kappa \in [0, c \underline{\alpha^{nb}}]$|. As no high-quality borrowers are born in the second period, any |$t=2$| lending will only be to low-quality borrowers. Since by assumption all loans to low-quality borrowers are negative NPV, banks only lend a positive amount at |$t=2$| if they find it profitable to prop up house prices. This setup thus clearly demonstrates when a bank is incentivized to sacrifice loan quality for the return to keeping house prices high. To reduce the number of variables, I set |$\beta=1$| and assume the fraction of nonborrowers is the same at |$t=1$| and |$t=2$|.
In the notation of the full model, if the first state is a rich state and the second state is poor state, |$\alpha^{nb}_R=\alpha^{nb}_P=\alpha^{nb}$|, |$\alpha^{bh}_{R}=(1-\alpha^{nb})$|, |$\alpha^{bh}_P=0$|, |$Q(RR)= 0$|, |$Q(RP)=1$|. To simplify the notation, since there is only one type of borrower each period and states are deterministic, I only index variables that are different across |$t=1$| and |$t=2$| with a subscript indicating the relevant time period. I therefore drop the indexes associated with borrower type and the state of the economy. Specifically, |$\phi_1 = \phi_R^{bh}$|, |$\phi_2 = \phi_P^{bl}$|, |$D_1 = D_1^h$|, |$D_2 = D_2^l$|, |$m_1 = m_1^h$| and |$m_2 = m_2^l$|.
Bank Repayment: Two possible cases determine the repayment demanded by banks. When |$E[\phi_1] e \geq \gamma$|, the maximum repayment banks can charge high-quality who they lend to at time |$1$| is |$D_1 = \frac{\gamma}{E[\phi_1]} + (1-\delta) P_{2}$|. When |$E[\phi_1] e < \gamma$|, the maximum repayment banks can charge high-quality borrowers who they lend to at time |$1$| is |$D_1 = e + (1-\delta)P_{2}$|. Conceptually, the differences between the two are not particularly interesting and therefore I focus on the former and assume that |$E[\phi_1] e \geq \gamma$|. Together, assumptions 1 (private benefit of homeownership is large enough) and 4 (low-quality borrowers are negative NPV) imply that |$E[\phi_2] e < \gamma$|. Therefore, the maximum face value a bank can charge to a low-quality borrower who they lend to at |$t=2$| is |$D_2 = e + (1-\delta)\kappa$|.
3.1 Equilibrium with a single bank
The optimal lending by the bank is summarized in the following lemma.
The number of loans a bank makes to low-quality borrowers at |$t=2$|, |$m_2$|, is increasing in outstanding loans, |$m_1$|. In particular, when |$m_1=0$| and the bank has no outstanding loans on its balance sheet, it will never make any loans at |$t=2$| to low-quality borrowers and |$m_2=0$|.12 As the amount of outstanding loans increases, |$m_2$| can become positive. |$m_2$| is also increasing in the future expected income of low-quality borrowers, |$E[R_2]$|. Additionally, the loans made at |$t=2$| are increasing in |$(1-\phi_{1})$| or the proportion of borrowers who do not receive a positive endowment. Intuitively, the more loans that are at risk of default, the higher the return from propping-up house prices.
A bank’s lending at |$t=1$|, |$m_1$|, is increasing in the return to |$t=1$| lending, |$E[R_1]$|. In an equilibrium in which a bank props up house prices, if a bank lends more at |$t=1$|, it also increases its |$t=2$| lending. This pushes up housing prices at |$t=2$|. The increase in |$t=2$| house prices increases |$E[R_1]$|. The increase in |$E[R_1]$| in turn increases the number of loans a bank makes at |$t=1$|. Thus, there is a feedback loop between |$t=1$| and |$t=2$| lending.
3.2 N banks
The lemma below summarizes the optimal lending undertaken by any given bank.
With multiple banks, the intuition is similar to the case with a single bank. In addition, an individual bank’s lending is affected by the aggregate lending of other banks. In particular, |$m_2^j$| is decreasing in credit lent out by other banks, |$M_2^{-j}$|. A lower |$M_2^{-j}$| implies that an individual bank effectively has larger market power in influencing house prices since outside sources of housing demand are lower. In other words, a lower |$M_2^{-j}$| implies a larger elasticity of house prices to credit. This increases the net effect that credit expansion by the bank has on house prices.
The number of loans a bank makes at |$t=1$| is decreasing in the number of loans made by other banks in the same period, |$M_1^{-j}$|, but increasing in the number of loans made by other banks in the future, |$M_2^{-j}$|. The more loans other banks make at |$t=1$|, the higher is the price of housing at |$t=1$|, making it more expensive for a bank to make mortgage loans. This causes a bank to decrease the amount it lends. The more loans other banks make at |$t=2$|, the higher is the price of housing at |$t=2$|, allowing banks to charge a higher interest rate on loans made at |$t=1$| and increasing their incentive to lend at |$t=1$|. Thus, there is strategic substitution in bank lending within a period but strategic complimentary in bank lending across periods. The full characterization of the equilibrium is discussed in the following subsection.
3.3 Concentration and credit
When concentration in mortgage holdings is low and each bank holds a small share of the market, the return to propping up prices for any individual bank is low. Banks therefore do not issue any loans to low-quality borrowers. As concentration increases, banks have access to a larger share of high-quality borrowers at |$t=1$|. In this case, each bank has a larger outstanding portfolio of loans at |$t=2$| and greater market power to affect house prices. They will therefore have a greater incentive to issue loans to low-quality borrowers to prop up house prices. The proposition below details equilibrium propping up.
The three-period model has a unique equilibrium. There exists a cutoff, |$\overline{N}$|, such that if |$N\geq \overline{N}$|, banks do not prop up houses prices and make no negative NPV loans. If |$N < \overline{N}$|, banks engage in risky lending to prop up house prices and supply a positive amount of negative NPV loans.
In the model, there are strategic complementarities in bank lending across time. If banks expect aggregate lending at |$t=2$| to be high, they expect future house prices to be high and therefore lend more at |$t=1$|. Despite strategic complementarities in bank lending across time, the equilibrium is unique.13 This uniqueness arises due to intratemporal strategic substitution in bank lending. If other banks pull back on lending at |$t=2$|, an individual bank is incentivized to increase its own lending at |$t=2$| and not cut back on its |$t=1$| lending enough to give arise to multiplicity. Therefore, there is a unique equilibrium of the model.
As concentration increases aggregate credit can increase or decrease. Two effects determine the net response of aggregate credit to concentration. The first is a contemporaneous price effect. Large lenders internalize their effect on house prices more than small lenders. The marginal increase in price when making an additional loan affects large lenders’ cost of total lending more than that of small lenders. Lenders in a concentrated market will therefore cut back on credit more than lenders in a market with many small lenders. This effect is similar to a typical mechanism in Cournot competition in which as concentration increases, the quantity of goods supplied in the market decreases as suppliers internalize price effects more. As the number of banks decreases, this effect leads to a decrease in credit supply. However, since concentration also creates incentives to prop up prices, there is a second effect of concentration on credit, namely, the propping-up effect. Concentration increases banks’ incentives to increase |$t=2$| prices through credit expansion and if this effect is large enough, it can cause overall lending to increase.
The following corollary summarizes the effect of concentration on mortgage credit.
In the unique equilibrium of the three-period model, as |$N$| decreases,
credit extended by any given bank to both high- and low-quality borrowers increases,
if |$N\geq \overline{N}$| and banks are not propping up prices, aggregate credit decreases,
if |$N<\overline{N}$| and banks are propping up prices, aggregate credit can increase.
When |$N \geq \overline{N}$| and banks are not propping up housing prices, aggregate credit is always decreasing with concentration because of the Cournot effect. As is typical in most models of competition, as the number of banks decreases, banks behave more like price-takers and are willing to issue more loans. As discussed above, when |$N < \overline{N}$|, there is a second effect of concentration on credit, namely, the propping-up effect. When banks have larger market shares, they issue more loans per bank at |$t=1$|. This increases the incentive for banks to prop up prices and make negative NPV loans at |$t=2$|. Higher |$t=2$| prices further increase the incentive to issue |$t=1$| loans and so on and so forth. As concentration increases, this feedback loop can cause aggregate lending to increase.
Figure 1 illustrates the effect of concentration on house prices. The left panel plots total credit, measured as the sum of the number of households who get a mortgage at |$t=1$| and |$t=2$|, against the number of banks. As the market becomes more concentrated and the number of banks decreases from |$3$| to |$2$|, banks begin to prop up house prices. In this parametrization, credit increases with concentration in the region in which banks prop up prices, as the propping-up effect dominates the Cournot effect. As concentration decreases, banks stop propping up prices and the amount of credit increases as competition in the market causes banks to behave more like price-takers.
Concentration and credit
The left panel plots total credit, measured by the total number of households who get a mortgage at |$t=1$| and |$t=2$|, against the level of concentration in the mortgage market. The right panel plots the fraction of low-quality loans, measured as |$t=2$| credit divided by total credit, against the level of concentration in the mortgage market. As one moves along the x-axis, |$N$| increases and concentration decreases.
The left panel of Figure 1 shows that it is possible for two areas with different levels of concentration to have the same amount of aggregate credit. However, the composition of this credit is different. In particular, the credit in the area with higher concentration is riskier since a larger fraction of lending is to low-quality borrowers. The right panel of Figure 1 plots the fraction of loans made to low-quality borrowers for different levels of concentration. For a given level of concentration, banks’ incentives to prop up prices are affected by the size of their outstanding portfolio, the number of loans in default, their expected return from |$t=2$| lending and their market power. The following corollary to Proposition 1 summarizes the effect of various model primitives on propping-up incentives.
For a given |$N$|, |$t=2$| lending, |$M_2$|, is increasing in |$\gamma$|, decreasing in |$\phi_1$|, increasing in |$\kappa$|, and decreasing in |$\alpha^{nb}$|.
As |$\gamma$| increases, banks can charge higher interest rates to |$t=1$| borrowers increasing the expected return to lending to them. As a result, banks have more outstanding loans at |$t=2$|, increasing propping-up incentives. As |$\phi_1$| decreases, the default propensity of loans outstanding at |$t=2$| increases. Banks therefore have a stronger incentive to prop up prices as a larger number of loans are in danger of defaulting. As |$\kappa$| increases, the expected return from lending to low-quality borrowers at |$t=2$| increases. Banks therefore have to take a smaller loss on low-quality loans when propping up prices. Finally, as |$\alpha^{nb}$| decreases, banks’ market power increases. Subsequently, the effect any given bank has on house prices for every additional mortgage loan it makes increases, making propping up more profitable.
3.4 Welfare
Propping up never generates a Pareto optimal improvement in welfare. However, under a utilitarian welfare criterion, propping up can be welfare improving.
3.4.1 Pareto optimality
Banks benefit from propping up house prices because they can transfer some surplus from nonborrowers born at |$t=2$| to themselves. In particular, when a bank props up prices, nonborrowers pay higher prices upon buying homes that are part of a bank’s outstanding portfolio of mortgages. As a result, propping up house prices never generates a Pareto improvement since nonborrowers are worse off because of it. The proposition below summarizes these distributional effects of propping up.
An equilibrium in which banks prop up house prices never generates a Pareto improvement relative to an equilibrium in which banks do not prop up house prices. In particular, nonborrowers born at |$t=2$| are always worse off when banks prop up house prices.
3.4.2 Utilitarian social planner
Propping up can be beneficial if a social planner’s objective is to maximize total welfare in the economy since it can increase the total number of households getting access to credit. Because of the private benefits of homeownership, total welfare increases by |$\gamma$| for every additional homeowner. However, propping up also affects aggregate defaults. Since more loans are made to risky borrowers with higher rates of default, propping up increases defaults and can increase financial fragility. I incorporate the social costs of default into the model by assuming some deadweight losses that are not internalized by banks or households but that affect the final utility of households.
The first constraint is the social planner’s break-even constraint. The second constraint is the individual rationality constraint for |$t=1$| borrowers. The assumptions on |$\gamma$|, |$\kappa$| and |$\phi_{2}$| guarantee that the individual rationality constraint is always satisfied for |$t=2$| borrowers. The last term in the planner’s maximization problem (16a) are the social costs of default. |$d$| is a parameter that determines the magnitude of the costs. The case without social costs from default corresponds to |$d=0$|.14|$0 \leq\theta\leq 1$| is a parameter that governs how the distribution of credit and defaults over time affect social welfare. As |$\theta$| decreases, the social planner cares relatively more about maintaining credit access across time. In particular, when |$\theta=1$|, only the total number of defaults affect welfare. Conditional on the number of defaults, their distribution over time, does not matter.15 When |$\theta=0$|, the social planner’s marginal utility from increasing credit access in any given period will be higher when defaults in that period are lower. In this case, the planner prefers to maintain at least some level of credit access every period. |$\theta$| can therefore be interpreted as capturing the social value of the “stability” of the housing market.
The proposition below characterizes the optimal lending by the social planner.
If the benefits of homeownership and the social value of stability are low relative to default costs, that is, when |$\theta>\frac{1-\phi_2}{1-\phi_1}$| and |$\frac{\gamma}{d} \leq \theta (1-\phi_1)(1-\phi_2)(1-\alpha^{nb})$|, the social planner makes no loans to low-quality borrowers, |$m_2^*=0$|. In this case, high-quality borrowers at |$t=1$| are charged a competitive interest rate, that is, |$E[R_1]=P_1$|.
Otherwise, the social planner prefers to make a strictly positive amount of loans to low-quality borrowers, |$m_2^*>0$|. In this case, high-quality borrowers at |$t=1$| are charged a noncompetitive interest rate and cross-subsidize low-quality borrowers, that is, |$E[R_1]>P_1$| and |$E[R_2]<P_2$|.
The social planner values making loans to low-quality borrowers at |$t=2$| when the private benefits from homeownership are high, when the social costs of default are low and when the value of stability in the housing market is high. Since borrowers at |$t=2$| have an expected endowment that is lower than their loan amount, the social planner will need to cross-subsidize |$t=2$| borrowers by charging |$t=1$| borrowers a higher interest rate than the competitive rate.
In the model, banks do not internalize the benefits of homeownership that accrue to households or the social costs of default by design. However, banks that prop up prices subsidize low-quality borrowers and make profits from high-quality borrowers. This cross-subsidization can increase aggregate welfare when the benefits of homeownership are high, default costs are low and the value of stability in the housing market is high.
Otherwise, total welfare is higher with |$N_2$| banks.
It is possible for two regions with different levels of concentration to have the same amount of credit extended to |$t=1$| borrowers. For example, if lending to high-quality borrowers is very profitable, banks may find it beneficial to lend to all |$t=1$| borrowers. When |$N_1<\overline{N}$|, banks additionally lend to low-quality borrowers at |$t=2$| due to the propping-up effect. The left panel of Figure 2 plots the credit to high- and low-quality borrowers in a case where |$\overline{N}=3$|. In this example, all banks make the same amount of loans to |$t=1$| borrowers. Specifically, banks lend to all available high-quality borrowers at |$t=1$|. The loans made to low-quality borrowers at |$t=2$| are decreasing in |$N$| due to the propping-up effect. The right panel of Figure 2 plots total welfare as a function of the number of banks in the economy. The blue (red) lines plot welfare when the benefits of homeownership are high (low) relative to default costs. The solid blue and red lines represent the case in which there is no social value to stability in the housing market, |$\theta=1$|. In this case, when the relative benefits of homeownership are high (low), welfare increases (decreases) as banks prop up prices. The dashed red and blue lines represent the case in which there is social value to stability in the housing market, |$\theta=0$|. In this case, for both parametrizations of the relative benefits of homeownership to the social costs of default, welfare increases as markets become more concentrated.
Concentration and welfare
The left panel plots total high-quality and low-quality credit, measured by the number of households who obtain a mortgage at |$t=1$| and |$t=2$|, respectively, against the level of concentration in the mortgage market. The right panel plots total welfare against the level of concentration in the mortgage market, for two different levels of default costs. As one moves along the x-axis, |$N$| increases and concentration decreases.
Figure 3 illustrates the cross-subsidization across borrowers when banks prop up prices. The two panels plot the interest rate above the price, |$E[R_t]-P_t$|, charged to |$t=1$| borrowers and |$t=2$| borrowers as a function of the number of banks to demonstrate cross-subsidization when banks prop up prices. For purposes of the graph when |$N\geq 3$|, |$E[R_2]$| has been set to zero. However, in this case, no loans are actually made to |$t=2$| borrowers, and, therefore, there is no relevant interest rate. When |$N=1$|, the propping-up effect is the strongest and the degree of cross-subsidization is the highest.
Concentration and borrower repayments
The left panel plots the expected repayment net loan amount of |$t=1$| borrowers, against the level of concentration in the mortgage market. The right panel plots the expected repayment net loan amount of |$t=2$| borrowers, against the level of concentration in the mortgage market. As one moves along the x-axis, |$N$| increases and concentration decreases.
Although propping up achieves cross-subsidization, it will not generally mimic the credit allocation corresponding to the social planner optimum since banks do not internalize the private benefits of housing or default costs. Therefore, to implement the social planner optimum, additional policies, such as subsidies for homebuyers and taxes on banks for mortgage defaults, are necessary. Since propping up is an inefficient way to achieve cross-subsidization, it is likely only useful as a policy tool if constraints (e.g., political partisanship) make it difficult to implement alternative, more direct policies.
4. Infinite Horizon Model
The infinite-horizon model extends the three-period model to incorporate intraperiod heterogeneity, that is, each period has both high- and low-quality borrowers, and uncertainty about the state of the world, that is, each period a rich or a poor state can be realized. In a rich state, borrowers have a higher probability of receiving a positive endowment than in the poor state. The share of nonborrowers, high-quality borrowers and low-quality borrowers can also vary across states.
The path dependency of this problem makes it complicated to solve since in every period banks have to decide how much to lend taking into account outstanding loans and future lending. Furthermore, they also have to account for how the lending decisions of other banks will affect both current and future house prices. Given the model setup, it is possible to simplify a bank’s maximization to get a tractable problem. In particular, if all banks have the same initial loans outstanding, we can exploit the symmetric first order conditions and write an equivalent maximization problem of a representative bank in this economy.16
In the infinite horizon model, similar to the model with three periods, once markets become concentrated banks have incentives to prop up house prices. As in the three-period case, because of intraperiod strategic substitution amongst banks, the economy has a unique equilibrium despite strategic complimenterities in lending across periods.
The infinite-horizon model has a unique equilibrium. There exists a cutoff, |$\overline{N}$|, such that if |$N\geq \overline{N}$|, for any possible sequence of shocks, banks do not make any loans to low-quality borrowers to prop up prices. If |$N < \overline{N}$|, there is a strictly positive number of sequences of shocks in which banks will extend credit to low-quality borrowers to prop up house prices.
The key intuition for this proposition is identical to that in the three-period case. When |$N$| is large, each individual bank has a small amount of loans outstanding in any given period and little market power to influence house prices. Therefore, banks do not benefit from making loans that are unprofitable to push up house prices as the return from propping up prices is low. As |$N$| increases and individual banks acquire larger market shares, increasing house prices allows them to make profits on a greater outstanding portfolio. This increases the return to propping up prices.
4.1 Credit dynamics in boom-to-bust transitions
The infinite horizon model allows us to study credit dynamics as the economy transitions from a credit boom to bust. The key insight is that the propping-up effect can cause a transitory increase in low-quality credit at the end of a boom. A boom-to-bust transition in the model can be represented by a series of rich shocks followed by a series of poor shocks. By design, the share and income of all borrowers and nonborrowers are identical in all poor states of the world. Therefore, the fundamentals of the lending opportunities in all periods of the bust are the same. However, banks have high outstanding portfolios at the end of a boom. This makes the initial poor states at the beginning of a bust distinct from other periods during a downturn as propping-up incentives are heightened due to the large outstanding mortgage exposure banks have built up over the boom. As the bust continues, banks will wind down their outstanding mortgage exposure in response to poor fundamentals and have less incentives to prop up prices.
The increased propping-up incentives can cause a temporary increase in low-quality credit at the beginning of a boom. If poor states also have a lower fraction of high-quality borrowers, this increase in low-quality credit can occur even as total credit decreases. The left panel of Figure 4 plots aggregate credit in blue and low-quality in red during a transition from a boom period (when the economy experiences rich shocks) to a bust (when the economy experiences poor shocks). Loans made to low-quality borrowers spike in the first poor state growing by over 90|$\%$| and then decrease in subsequent poor states as banks wind down their portfolio of outstanding mortgages.
Credit in boom-to-bust transition
The left panel plots total credit and low-quality credit for a series of rich and poor shocks. The right panel plots the fraction of low-quality credit for the same series of shocks. Appendix B contains details about the parametrization.
4.2 Calibration exercise
The main purpose of this model is to clearly illustrate propping-up incentives. In doing so, the model abstracts away from various aspects of mortgage markets, housing choices by households, details of mortgage contracts, etc. A deeper examination of the quantitative implications of concentration on mortgage credit requires a more detailed framework. However, a calibration of the stylized model can help us address two questions. First, can the model produce quantitatively significant credit and house price dynamics that match GSE acquisitions during the housing boom-to-bust transition? Second, would the counterfactual path of credit and house prices look significantly different in the absence of propping-up incentives?
The model is calibrated to the 2006–2008 U.S. housing market, with the key moments of interest being the GSEs’ sudden and temporary increase in high-risk activity in 2007. I measure high-risk as mortgage loans with LTVs of over 80|$\%$|. For this exercise, I assume that the economy experienced rich shocks during the ongoing boom in 2006 followed by a sequence of poor shocks starting in 2007 that initiated the housing bust. The rich and poor shocks are semi-annual and are calibrated to match the change in real median household income from its peak level during the housing boom to its lowest level during the housing bust.
In the calibration, I incorporate private-label securitizers as small mortgage market participants who lend to a share of the housing market. I allow this share to change depending on the state of the economy to match the departure of private-label securitizers from the mortgage market in 2007.17
Table B1 in Appendix B summarizes the benchmark configuration of the model parameters. I choose |$N=2$| to represent the Fannie Mae and Freddie Mac. The fraction of borrowers who the private-label market had access to is chosen to match the share of acquisitions of the private-label market relative to the GSEs during 2006 and 2007. The income shocks of high- and low-quality borrowers in the rich and poor state of the economy are fixed to match the default rates on prime and subprime loans during the boom and bust. The fraction of nonborrowers in the rich and poor state is chosen to match the fraction of cash-only house purchases during 2006 and 2007. The probabilities of the state transition matrix are very persistent. This endogenously implies that, during a rich state, future house price expectations are high and once a poor state occurs future expectations are bleaker. The remaining parameters—the fraction of high-quality borrowers in the rich and poor state, borrower endowment when received, and the construction cost parameter—target the remaining moments reported in Table B2.
Table B2 in Appendix B compares the model-generated quantities to those in the data. The main focus is on explaining the sudden and transitory increase in high-risk activity by the GSEs. The model captures both the rise in the high-risk fraction of GSE acquisitions during the transition from boom to bust and the decrease in this fraction once the housing crisis was in full swing. Focusing on magnitudes, the model predicts a smaller decrease from 2007 to 2008 relative to the data.
In terms of the level of low-quality credit, the GSEs grew the number of high-risk mortgages they were acquiring dramatically by 104|$\%$| between 2006 and 2007. The model is able to generate a 90|$\%$| growth in the level of high-risk acquisitions by the GSEs between 2006 and 2007. This growth was transitory as the GSEs then decreased their high-risk acquisitions by 36|$\%$| between 2007 and 2008. The model captures a similar decrease although the magnitude of the decrease is smaller at 15|$\%$|.
The lower model-generated magnitudes when comparing 2007 and 2008 can be partially attributed to the fact that the model only allows for two possible states; therefore, all the difference in the model-generated GSE acquisitions in 2007 and 2008 comes from the outstanding loan share. If 2008 were modeled as a worse state of the world compared to 2007 in terms of new lending opportunities, the model could generate a larger decrease in high-risk activity. Furthermore, the GSEs were taken into government conservatorship in 2008, a step that would change their acquisition incentives. This feature is not captured in the model.
4.2.1 Counterfactual analyses
Table B3 in Appendix B reports the results of three counterfactual analyses. In the first, I artificially shut down the propping-up channel. In this case, the GSEs acquire no low-quality loans in 2007. Moreover, they also do not purchase low-quality loans in 2006 since the expectation of lower house prices without propping up should a bust occur makes it less profitable to lend to low-quality borrowers during the boom. Shutting down propping up therefore decreases both bust and boom lending to low-quality borrowers. Total defaults are lower under this counterfactual. However, less total credit is available to households.
In the second counterfactual, I incorporate overly optimistic house price expectations during the boom into the model. In particular, I model future house price expectations as being 33|$\%$| higher during the boom than the true model-implied expectation to generate a similar magnitude of low-quality loans in 2006 as in the benchmark calibration. I then shut down the propping-up channel. This exercise essentially allows us to consider how GSE acquisitions in 2007 would have been different in the absence of propping-up incentives if their acquisitions during the boom had not been affected by propping up. It essentially shuts down any quantitative impact of the feedback effect. In this case, there are no high-risk acquisitions in 2007, and, subsequently, the model-implied mortgage defaults on the GSEs’ 2007 vintage are lower. However, lending in 2006 remains at similar levels as in the benchmark calibration due to high house price expectations. The fall in house prices is much larger relative to the benchmark case, that is, 32|$\%$| versus 21|$\%$|. Conditional on outstanding mortgage exposure, propping up therefore leads to house price stabilization.
In the third counterfactual, I consider a situation in which the private-label market continues to have the same market share in 2007 as it did in 2006. Therefore, concentration in 2007 does not increase. This has two effects: the GSEs have relatively less market power during the bust, and, additionally, house prices are not in danger of falling as much because of continued private-label activity. This change substantially reduces the degree of propping up undertaken in 2007. The fraction of high-risk acquisitions in 2007 is only 7|$\%$| relative to 28|$\%$| in the benchmark calibration. The GSEs continued to purchase a similar number of low-quality loans during the boom in 2006 since future house price expectations remain high as a result of continued private-label activity in the event of a bust. Since the GSEs prop up less and make less low-quality loans in 2007, the fraction of their 2007 vintage that defaults is lower.
4.2.2 Welfare
Table B4 in Appendix B compares welfare in the benchmark calibration to that of the social planner. The social planner problem is solved for |$\theta=0$| and therefore the distribution of credit over time and borrower type affects welfare.18 The social planner optimal is calculated for three different levels of default costs, holding the benefits of homeownership constant. The first scenario corresponds to a case of high benefits of homeownership relative to default costs. In the second scenario, default costs are higher than in the first. In particular, the level of default costs is picked so that the social planner’s acquisitions in 2007 match those of the GSEs’ in the benchmark equilibrium. In the third scenario, default costs are higher than in both the first and second scenarios. In particular, the level of default costs is picked so that the social planner’s acquisitions in 2006 match those of the GSEs’ in the benchmark equilibrium. To isolate the effect of propping-up incentives on welfare, the table includes welfare under counterfactual 1 in which propping up is artificially shut down. The last three rows of Table B4 show that the relative welfare gain from propping up increases as the benefit of homeownership relative to default costs increases.
Under the calibrated parameters, the social planner’s acquisitions in general do not correspond to either those in the benchmark calibration or those in counterfactual 1. Figure 5 plots house prices and the fraction of low-quality credit extended in the benchmark equilibrium (solid blue line), counterfactual 1 (dashed blue line) and the three social planner scenarios (red lines). The social planner values some degree of stability in credit over time and borrower type, and, therefore, a positive amount of credit is always extended to low-quality borrowers. Consequently, counterfactual 1 always has an underprovision of credit to low-quality borrowers and house prices are too low.
Welfare
The left panel plots house prices for a series of rich and poor shocks. The right panel plots the fraction of low-quality credit for the same series of shocks. Appendix B contains details about the parametrization.
When the relative benefit of homeownership is high (the solid red line), the social planner prefers to maintain a high level of credit in both the boom and the bust. The fraction of credit extended to low-quality borrowers therefore increases in the bust to maintain a high level of credit in the economy. House prices remain at similar levels in both the boom and the bust. Propping up can generate similar patterns of low-quality credit, although the level of credit remains below that preferred by the social planner. Although house prices do fall under the propping-up equilibrium once the bust begins, they are higher in both the boom and the bust than in a case without propping up. Propping-up incentives therefore lead to welfare gains.
Under scenario 2 (dashed red line), propping up matches the social planner’s optimal credit at the start of the bust by construction. However, there is an underprovision of credit in the propping-up equilibrium during the boom. Additionally, there is an underprovision of credit in later periods of the bust as propping-up incentives weaken. The degree of underprovision of credit is lower in the propping-up equilibrium compared to counterfactual 1. Therefore, propping-up incentives lead to welfare gains. Under scenario 3 (dotted red line), propping up matches the social planner’s optimal credit in the boom by construction. In this case, there is an overprovision of credit during the bust in the propping-up equilibrium. Although the benchmark equilibrium has higher welfare during the boom relative to counterfactual 1, welfare during the bust is lower. The net effect is a slight reduction in welfare due to propping up.
4.2.3 Cross-sectional moments
|$\Delta HRI_{i,t}$| is the increase in the proportion of low-quality mortgages in region |$i$| between period |$t-1$| and |$t$|. |$SHR_{i,t}$| is the GSEs’ outstanding share in region |$i$| in period |$t$|. |$2007H1_t$| is an indicator that equals one in the first half of 2007 and zero otherwise. The coefficient of interest is |$\beta_3$|. The model is able to closely match cross-sectional patterns of GSE acquisitions. In particular, the model delivers a regression coefficient of 0.18 with a standard error of 0.02. In the data, the regression coefficient is 0.19 with a standard error of 0.04.
Cross-sectional analysis
The above figure plots the coefficient of regressing the increase in the proportion of high-risk acquisitions on the GSEs’ outstanding share for various half years using simulated data. Appendix B contains details about the parametrization.
5. Discussion
In this section, I discuss additional features of the theory. In particular, I discuss the robustness of the model, necessary conditions for propping up to take place, the theory’s connection to the Coase conjecture, the differences between propping-up and risk-shifting incentives and evidence in support of propping up.
5.1 Model robustness
In Appendix C, I relax various assumptions of the main analysis to demonstrate robustness of the propping-up mechanism. I show model robustness to a general housing supply function, to general housing demand elasticities, to mortgage loans without recourse and to interest rate competition among banks. I also extend the model to allow for mortgage refinancing.
Additionally, I describe an equivalent setup of the benchmark model to capture the market power of mortgage institutions in the secondary market. The key mechanism works as long as there is concentration in mortgage holdings at some level and agents with exposure to mortgage payments have some market power. If secondary market players own a large share of the mortgage market, they benefit from high house prices. If they have market power, they can offer attractive prices on the secondary market for riskier mortgages that will incentivize mortgage originators to then issue mortgages to risky borrowers. Holders of these mortgages will suffer losses on these purchases but the increase in house prices will be profitable for their outstanding mortgage exposure.
Finally, I discuss how the equilibrium changes if banks can commit to future lending. Commitment unequivocally increases the magnitude of propping up taken by a bank. Banks benefit from committing to propping up house prices more as borrowers are willing to pay a higher interest rate when they expect future house prices to be higher. In practice, there are reasons to think that the GSEs were able to commit, at least in part, to future lending. Hurst et al. (2016) provide evidence that the GSEs faced political pressure that did not allow them to make substantial changes to interest rates. These constraints could credibly allow the GSEs to commit to future activity.
5.2 Conditions required for propping up
While many assumptions in the model are made for tractability purposes and can be relaxed, as discussed above, some conditions are required for propping up to take place. In particular, to observe propping up in equilibrium, we require (a) that credit provision has an effect on house prices, (b) that house prices affect a household’s ability or incentive to repay a mortgage such that higher prices reduce the probability of default and/or the bank’s loss due to default, (c) concentrated mortgage markets, (d) a large stock of outstanding mortgage exposure in danger of default, (e) a lack of good quality borrowers, and (f) a set of relatively price-inelastic homebuyers who banks can expropriate surplus from.
Many papers provide support for the first two requirements. For example, Foote, Gerardi, and Willen (2008), Haughwout, Peach, and Tracy (2008), Ferreira and Gyourko (2015), and Palmer (2015) provide evidence that house prices affect default incentives. Himmelberg, Mayer, and Sinai (2005), Hubbard and Mayer (2011), Mayer (2011), Khandani, Lo, and Merton (2013), Landvoigt, Piazzesi, and Schneider (2015), An and Yao (2016), Favilukis, Ludvigson, and Nieuwerburgh (2016), and Griffin and Maturana (2016) show that the availability of credit affects house prices. The remaining requirements will vary across geographies and time. Importantly, conditions (c)–(e) are likely to be most salient at the end of credit booms.
5.3 Connection to Coase conjecture
Since banks in the model operate like monopolists in the credit market and are exposed to the price of a durable good (housing), the equilibrium credit dynamics may seem surprising because they differ from those implied by the Coase conjecture. The Coase conjecture states that in an infinite horizon model, a durable goods monopolist who faces individuals with different valuations of a good will saturate the market at the start of time and not earn any profits. The key idea is that the monopolist cannot commit to only selling the good to high valuation customers. In the following periods, after high value customers have been sold the good, he will benefit from additionally selling goods to low valuation customers. Because of this lack of commitment, a high valuation customer can simply wait, if he is patient enough, for the price of the good in the future to fall.
The model solution departs from the Coase conjecture because of three key reasons. First, banks in the model are able to price discriminate between different types of borrowers through the interest rate they charge them. For the Coase conjecture to hold, a monopolist cannot price discriminate within period. Second, due to the overlapping generations setup, each borrower only values consuming housing in the period in which they are born. They therefore cannot get the bank to compete with its future self by waiting to get a mortgage loan when interest rates are lower. Finally, collateral on mortgage loans and new credit while complementary assets, are not equivalent to the same good being sold twice as in the Coase conjecture. In the model, the sale of a new home enabled by additional credit that is extended by the bank, increases the value of outstanding collateral. The increased collateral value is beneficial to the bank as it wants old houses to have a higher resale value. In the Coase conjecture, on the other hand, the resale of durable assets hurts the monopolist.
5.4 Distinguishing propping up from risk shifting
Propping-up incentives can help explain the sudden and temporary increase in high-risk acquisitions by the GSEs in the beginning of 2007. An alternative story that delivers similar predictions is one of risk shifting. In this case, due to limited liability or implicit bailout guarantees, if a bank believes that it will be insolvent if house prices fall, it is incentivized to make loans that payoff in the state of the world in which the bank is solvent even if it makes losses in the state in which it is insolvent. Under a risk-shifting story, in the beginning of 2007 if the GSEs believed that they would be insolvent if house prices fell, they would have an incentive to increase high-risk acquisitions only accounting for the payoff of these loans in the states of the world in which they continue to be solvent. Risk-shifting and propping-up incentives are not mutually exclusive, and both may have been active in 2007. Both theories are also consistent with a temporary increase in high-risk activity followed by insolvency and failure. Under risk shifting, if a bad state realizes the lender will fail. This state is rationally anticipated by the lender as a possibility. Under propping up, if the gains on outstanding loan repayments benefit enough from a temporary increase in prices, lenders have an incentive to prop up prices even if they are certain a downturn will realize in the future. To help disentangle the quantitative importance of each channel, I highlight the dimensions along which the two theories deliver different predictions.
Unlike risk shifting, the propping-up theory predicts cross-sectional variation in regional activity within an institution. In particular, the GSEs share of mortgages varied significantly across MSAs at the end of the boom, from 20|$\%$| to 80|$\%$|.19 Propping-up incentives will depend on these regional exposures. Empirically, we should see the GSEs engage in higher-risk activity where they have more outstanding mortgage exposure. Risk-shifting incentives depend on the total outstanding portfolio of the institution since limited liability and bailouts depend on the overall solvency of the institution. The GSEs acquisition decisions, in this case, should be determined by the return they can make on a loan in the good state of the world and not their outstanding regional exposure where the loan is originated. The quantitative results in section 4.2.3 are able to reproduce the cross-sectional results in Elul, Gupta, and Musto (2020) and provide support to the quantitative importance of propping up during the housing bust of 2007.
5.5 Evidence
Elul, Gupta, and Musto (2020) provide evidence that the sudden and temporary increase in the GSEs’ purchases of high LTV and low FICO loans in 2007 can be partially explained by propping up. To try to identify the degree to which the GSEs’ risky activity is driven by propping up, they exploit cross-sectional predictions of the theory. They find that at the MSA-level, the agencies outstanding mortgage share predicts higher growth in risky acquisitions in the first half of 2007. They also find that this effect is stronger in inelastic MSAs where prices are likely to respond more to credit provision.
A recent paper by Bhutta and Keys (Forthcoming) studying the behavior of private mortgage insurance (PMI) at the beginning of the housing downturn also provides some support for propping up. The GSEs were required to get PMI on loans with LTV ratios of above 80|$\%$|. Bhutta and Keys (Forthcoming) document that private mortgage insurers expanded insurance on high-risk mortgages in 2007 and that this growth was primarily in nonjumbo loans. Although PMI companies seemed to be willing to insure both jumbo and nonjumbo loans as evidenced by a fall in the denial rates of both types of loans, there was not much private-label, high-risk activity in 2007. Consequently, the authors attribute the increase in high-LTV conforming loans backed by PMI to the “joint willingness” of the GSEs and PMI companies to take on risk. Propping-up incentives are in line with this pattern of growth as the theory predicts a disproportionate increase in high-LTV acquisitions by the GSEs relative to smaller market participants. Notably, the PMI expansion was concentrated in cities in which industry reports predicted high house price declines.
Finally, evidence from Favara and Giannetti (2017) indicates that, during the housing crisis, lenders were less likely to foreclose on a mortgage if they were exposed to a large fraction of outstanding mortgages in the same area. They find that this reduction in foreclosures has affected local house prices.
6. Conclusion
This paper provides a novel theory of how concentration in mortgage markets can affect both the quantity and the quality of mortgage credit. Lenders with large outstanding mortgage exposure have incentives to extend risky credit to prop up house prices. These propping-up incentives are particularly strong at the end of credit booms when the economy is transitioning into a housing bust.
In the aftermath of the housing crisis, policy makers have wanted to design policy to curb high-risk lending. However, the role that concentration can play in creating incentives to extend risky mortgage credit has been largely overlooked in this process. The GSEs currently have more market power than they did in 2006. From a macroprudential perspective, the propping-up incentives generated by such concentration may or may not be desirable. As this paper demonstrates, propping up can provide house price stability by encouraging credit expansion during busts but can also cause increased defaults. As policy makers discuss whether or not to phase out the GSEs, the desirability of increased risky lending at the start of housing busts is an important consideration.
Appendix A. Theoretical Proofs
Note that the above solution is under the assumption that at |$t=2$| other banks take |$m_2$| as given. This approach assumes that deviations at |$t=1$| from equilibrium are not observable. An alternative approach involves other banks taking |$m_2$| as a function of |$m_1$| at |$t=2$|, in which case at |$t=1$| when a bank chooses |$m_1$|, it would also take into account its affect on |$M_2^{-j}$|. The model solution if equilibrium deviations are observable is similar but less tractable. ■
Since |$m_1$| is decreasing in |$N$|, when |$N<\overline{N}$|, an equilibrium in symmetric strategies in which banks prop up prices exists. By the same argument when |$N \geq \overline{N}$|, an equilibrium in symmetric strategies in which banks do not prop up prices exists. Since all banks face symmetric first order conditions, the equilibrium in symmetric strategies is also the unique equilibrium. ■
The above expression can increase or decrease in |$N$| depending on the value of the various parameters in the model.20 ■
Recall that, |$E[R_1]=\gamma + E[P_2]$| and |$E[R_2]=\phi_2 e + (1-\delta)\kappa$|. From equation (A12a), note that |$m_1$| is increasing in |$\gamma$|, decreasing in |$\alpha^{nb}$| and not affected by |$\phi_1$|. Therefore, from equation (A24), |$M_2$| is increasing in |$\gamma$| (since |$m_1$| is increasing in |$\gamma$|), decreasing in |$\phi_1$|, increasing in |$\kappa$| (since |$E[R_2]$| is increasing in |$\kappa$|), and decreasing in |$\alpha^{nb}$| (since |$m_1$| is decreasing in |$\alpha^{nb}$|). ■
Since when banks prop up prices, |$M_2>0$|, the utility of a nonborrower at |$t=2$| is always lower than the utility of a nonborrower when banks do not prop up prices. Therefore, propping up prices never generates a Pareto improvement. ■
If the above expression does not hold, the social planner will have to lower |$m_2$| until the borrower rationality constraint binds. The first parametric restriction and the continuous choice of |$m_2$| between |$0$| and |$1-\alpha^{nb}$| imply that the social planner can pick an |$m_2>0$| so that both the break-even and borrower rationality constraints hold. ■
The LHS is decreasing as |$N$| increases. Therefore, there exists |$\overline{N}$| s.t. when |$N\geq \overline{N}$|, an equilibrium in which banks do not prop up house prices exists. When |$N<\overline{N}$|, banks will make loans to low-quality borrowers and prop up prices. ■
A.1 Social Planner Problem: Infinite Horizon
Note that as long as an expected repayment schedule exists that satisfies borrower rationality constraints, the exact nature of the repayment schedule does not affect welfare as it is only redistributive.
Appendix B. Model Calibration
B.1 Data Description
GSE and private-label level and share of (defined as LTV |$\geq 80$|) acquisitions is from Elul, Gupta, and Musto (2020). U.S. house price changes are calculated from the Federal Reserve Economic Data (the S|$\&$|P/Case-Shiller U.S. National Home Price Index). Household income levels during the boom and bust are from the Federal Reserve Economic Data (Real Median Household Income in the United States). The default rates on prime and subprime loans are taken from a research report by the U.S. Census Bureau. The fraction of cash-only house purchases comes from RealtyTrac. Data on elasticities come from Favara and Imbs (2015). The private benefit of homeownership is difficult to measure in the data, and, therefore, I choose a parametrization such that |$\gamma$| does not determine any calibrated quantities.
Configuration of the model’s parameters
| Description | Symbol | Value | Target/source |
|---|---|---|---|
| Rich state | |||
| Fraction high-quality borrowers | |$\alpha^{bh}_R$| | 0.33 | Target moments |
| Fraction non-borrowers | |$\alpha^{nb}_{R}$| | 0.14 | Cash-only purchase fraction boom |
| High-quality borrower shock | |$\phi_R^{bh}$| | 0.98 | Default rate prime loans boom |
| Low-quality borrower shock | |$\phi_R^{bl}$| | 0.88 | Default rate sub-prime loans boom |
| Fraction private-label borrowers | |$s_R$| | 0.25 | Private-label share boom |
| Probability rich state transition | |$P$| | 0.90 | Target moments |
| Poor state | |||
| Fraction high-quality borrowers | |$\alpha^{bh}_P$| | 0.25 | Target moments |
| Fraction non-borrowers | |$\alpha^{nb}_{P}$| | 0.21 | Cash-only purchase fraction bust |
| High-quality borrower shock | |$\phi_P^{bh}$| | 0.95 | Default rate prime loans bust |
| Low-quality borrower shock | |$\phi_P^{bl}$| | 0.75 | Default rate sub-prime loans bust |
| Fraction private-label borrowers | |$s_P$| | 0.07 | Private-label share bust |
| Probability poor state transition | |$P$| | 0.99 | Target moments |
| Common parameters | |||
| Discount factor | |$\hat{\beta}$| | 0.94 | Standard |
| Depreciation | |$\delta$| | 0.01 | Standard |
| Borrower endowment | |$e_b$| | 0.95 | Target moments |
| Construction cost | |$c$| | 1.00 | Target moments |
| Number of large lenders | |$N$| | 2.00 | Number of GSEs |
| Description | Symbol | Value | Target/source |
|---|---|---|---|
| Rich state | |||
| Fraction high-quality borrowers | |$\alpha^{bh}_R$| | 0.33 | Target moments |
| Fraction non-borrowers | |$\alpha^{nb}_{R}$| | 0.14 | Cash-only purchase fraction boom |
| High-quality borrower shock | |$\phi_R^{bh}$| | 0.98 | Default rate prime loans boom |
| Low-quality borrower shock | |$\phi_R^{bl}$| | 0.88 | Default rate sub-prime loans boom |
| Fraction private-label borrowers | |$s_R$| | 0.25 | Private-label share boom |
| Probability rich state transition | |$P$| | 0.90 | Target moments |
| Poor state | |||
| Fraction high-quality borrowers | |$\alpha^{bh}_P$| | 0.25 | Target moments |
| Fraction non-borrowers | |$\alpha^{nb}_{P}$| | 0.21 | Cash-only purchase fraction bust |
| High-quality borrower shock | |$\phi_P^{bh}$| | 0.95 | Default rate prime loans bust |
| Low-quality borrower shock | |$\phi_P^{bl}$| | 0.75 | Default rate sub-prime loans bust |
| Fraction private-label borrowers | |$s_P$| | 0.07 | Private-label share bust |
| Probability poor state transition | |$P$| | 0.99 | Target moments |
| Common parameters | |||
| Discount factor | |$\hat{\beta}$| | 0.94 | Standard |
| Depreciation | |$\delta$| | 0.01 | Standard |
| Borrower endowment | |$e_b$| | 0.95 | Target moments |
| Construction cost | |$c$| | 1.00 | Target moments |
| Number of large lenders | |$N$| | 2.00 | Number of GSEs |
The table describes the configuration of the model’s parameters for the calibration exercise.
Configuration of the model’s parameters
| Description | Symbol | Value | Target/source |
|---|---|---|---|
| Rich state | |||
| Fraction high-quality borrowers | |$\alpha^{bh}_R$| | 0.33 | Target moments |
| Fraction non-borrowers | |$\alpha^{nb}_{R}$| | 0.14 | Cash-only purchase fraction boom |
| High-quality borrower shock | |$\phi_R^{bh}$| | 0.98 | Default rate prime loans boom |
| Low-quality borrower shock | |$\phi_R^{bl}$| | 0.88 | Default rate sub-prime loans boom |
| Fraction private-label borrowers | |$s_R$| | 0.25 | Private-label share boom |
| Probability rich state transition | |$P$| | 0.90 | Target moments |
| Poor state | |||
| Fraction high-quality borrowers | |$\alpha^{bh}_P$| | 0.25 | Target moments |
| Fraction non-borrowers | |$\alpha^{nb}_{P}$| | 0.21 | Cash-only purchase fraction bust |
| High-quality borrower shock | |$\phi_P^{bh}$| | 0.95 | Default rate prime loans bust |
| Low-quality borrower shock | |$\phi_P^{bl}$| | 0.75 | Default rate sub-prime loans bust |
| Fraction private-label borrowers | |$s_P$| | 0.07 | Private-label share bust |
| Probability poor state transition | |$P$| | 0.99 | Target moments |
| Common parameters | |||
| Discount factor | |$\hat{\beta}$| | 0.94 | Standard |
| Depreciation | |$\delta$| | 0.01 | Standard |
| Borrower endowment | |$e_b$| | 0.95 | Target moments |
| Construction cost | |$c$| | 1.00 | Target moments |
| Number of large lenders | |$N$| | 2.00 | Number of GSEs |
| Description | Symbol | Value | Target/source |
|---|---|---|---|
| Rich state | |||
| Fraction high-quality borrowers | |$\alpha^{bh}_R$| | 0.33 | Target moments |
| Fraction non-borrowers | |$\alpha^{nb}_{R}$| | 0.14 | Cash-only purchase fraction boom |
| High-quality borrower shock | |$\phi_R^{bh}$| | 0.98 | Default rate prime loans boom |
| Low-quality borrower shock | |$\phi_R^{bl}$| | 0.88 | Default rate sub-prime loans boom |
| Fraction private-label borrowers | |$s_R$| | 0.25 | Private-label share boom |
| Probability rich state transition | |$P$| | 0.90 | Target moments |
| Poor state | |||
| Fraction high-quality borrowers | |$\alpha^{bh}_P$| | 0.25 | Target moments |
| Fraction non-borrowers | |$\alpha^{nb}_{P}$| | 0.21 | Cash-only purchase fraction bust |
| High-quality borrower shock | |$\phi_P^{bh}$| | 0.95 | Default rate prime loans bust |
| Low-quality borrower shock | |$\phi_P^{bl}$| | 0.75 | Default rate sub-prime loans bust |
| Fraction private-label borrowers | |$s_P$| | 0.07 | Private-label share bust |
| Probability poor state transition | |$P$| | 0.99 | Target moments |
| Common parameters | |||
| Discount factor | |$\hat{\beta}$| | 0.94 | Standard |
| Depreciation | |$\delta$| | 0.01 | Standard |
| Borrower endowment | |$e_b$| | 0.95 | Target moments |
| Construction cost | |$c$| | 1.00 | Target moments |
| Number of large lenders | |$N$| | 2.00 | Number of GSEs |
The table describes the configuration of the model’s parameters for the calibration exercise.
Aggregate moments
| Model | Data | |
|---|---|---|
| GSE fraction of high-risk acquisitions 06 | 0.14 | .16 |
| GSE fraction of high-risk acquisitions 07 | 0.28 | .26 |
| GSE fraction of high-risk acquisitions 08 | 0.25 | .20 |
| GSE high-risk acquisition growth 06-07 | 0.90 | 1.04 |
| GSE high-risk acquisition growth 07-08 | |$-$|0.15 | |$-$|.36 |
| House price fall 06-08 | |$-$|0.21 | |$-$|.16 |
| Bust household income/Boom household income | 0.92 | .92 |
| Elasticity 06 | 0.25 | .20 |
| Private-label share 06 | 0.39 | .41 |
| Private-label share 07 | 0.17 | .16 |
| GSE share 06 | 0.61 | .59 |
| GSE share 07 | 0.83 | .84 |
| Cash-only purchases 2006 | 0.18 | .20 |
| Cash-only purchases 2007 | 0.33 | .25 |
| Model | Data | |
|---|---|---|
| GSE fraction of high-risk acquisitions 06 | 0.14 | .16 |
| GSE fraction of high-risk acquisitions 07 | 0.28 | .26 |
| GSE fraction of high-risk acquisitions 08 | 0.25 | .20 |
| GSE high-risk acquisition growth 06-07 | 0.90 | 1.04 |
| GSE high-risk acquisition growth 07-08 | |$-$|0.15 | |$-$|.36 |
| House price fall 06-08 | |$-$|0.21 | |$-$|.16 |
| Bust household income/Boom household income | 0.92 | .92 |
| Elasticity 06 | 0.25 | .20 |
| Private-label share 06 | 0.39 | .41 |
| Private-label share 07 | 0.17 | .16 |
| GSE share 06 | 0.61 | .59 |
| GSE share 07 | 0.83 | .84 |
| Cash-only purchases 2006 | 0.18 | .20 |
| Cash-only purchases 2007 | 0.33 | .25 |
The table compares model-generated moments to those in the data.
Aggregate moments
| Model | Data | |
|---|---|---|
| GSE fraction of high-risk acquisitions 06 | 0.14 | .16 |
| GSE fraction of high-risk acquisitions 07 | 0.28 | .26 |
| GSE fraction of high-risk acquisitions 08 | 0.25 | .20 |
| GSE high-risk acquisition growth 06-07 | 0.90 | 1.04 |
| GSE high-risk acquisition growth 07-08 | |$-$|0.15 | |$-$|.36 |
| House price fall 06-08 | |$-$|0.21 | |$-$|.16 |
| Bust household income/Boom household income | 0.92 | .92 |
| Elasticity 06 | 0.25 | .20 |
| Private-label share 06 | 0.39 | .41 |
| Private-label share 07 | 0.17 | .16 |
| GSE share 06 | 0.61 | .59 |
| GSE share 07 | 0.83 | .84 |
| Cash-only purchases 2006 | 0.18 | .20 |
| Cash-only purchases 2007 | 0.33 | .25 |
| Model | Data | |
|---|---|---|
| GSE fraction of high-risk acquisitions 06 | 0.14 | .16 |
| GSE fraction of high-risk acquisitions 07 | 0.28 | .26 |
| GSE fraction of high-risk acquisitions 08 | 0.25 | .20 |
| GSE high-risk acquisition growth 06-07 | 0.90 | 1.04 |
| GSE high-risk acquisition growth 07-08 | |$-$|0.15 | |$-$|.36 |
| House price fall 06-08 | |$-$|0.21 | |$-$|.16 |
| Bust household income/Boom household income | 0.92 | .92 |
| Elasticity 06 | 0.25 | .20 |
| Private-label share 06 | 0.39 | .41 |
| Private-label share 07 | 0.17 | .16 |
| GSE share 06 | 0.61 | .59 |
| GSE share 07 | 0.83 | .84 |
| Cash-only purchases 2006 | 0.18 | .20 |
| Cash-only purchases 2007 | 0.33 | .25 |
The table compares model-generated moments to those in the data.
Counterfactual analyses
| Benchmark | Counterfactual 1 | |
|---|---|---|
| GSE fraction of high-risk acquisitions 06 | 0.14 | 0.00 |
| GSE fraction of high-risk acquisitions 07 | 0.28 | 0.01 |
| GSE fraction of high-risk acquisitions 08 | 0.25 | 0.01 |
| House price fall 06-08 | |$-$|0.21 | |$-$|0.17 |
| GSE acquisitions 06 | 0.77 | 0.51 |
| GSE acquisitions 07 | 0.70 | 0.51 |
| GSE mortgage defaults 06 vintage | 0.04 | 0.02 |
| GSE mortgage defaults 07 vintage | 0.07 | 0.03 |
| Counterfactual 2 | Counterfactual 3 | |
| GSE fraction of high-risk acquisitions 06 | 0.14 | 0.14 |
| GSE fraction of high-risk acquisitions 07 | 0.00 | 0.10 |
| GSE fraction of high-risk acquisitions 08 | 0.00 | 0.05 |
| House price fall 06-08 | |$-$|0.32 | |$-$|0.13 |
| GSE acquisitions 06 | 0.77 | 0.77 |
| GSE acquisitions 07 | 0.48 | 0.56 |
| GSE mortgage defaults 06 vintage | 0.04 | 0.04 |
| GSE mortgage defaults 07 vintage | 0.02 | 0.04 |
| Benchmark | Counterfactual 1 | |
|---|---|---|
| GSE fraction of high-risk acquisitions 06 | 0.14 | 0.00 |
| GSE fraction of high-risk acquisitions 07 | 0.28 | 0.01 |
| GSE fraction of high-risk acquisitions 08 | 0.25 | 0.01 |
| House price fall 06-08 | |$-$|0.21 | |$-$|0.17 |
| GSE acquisitions 06 | 0.77 | 0.51 |
| GSE acquisitions 07 | 0.70 | 0.51 |
| GSE mortgage defaults 06 vintage | 0.04 | 0.02 |
| GSE mortgage defaults 07 vintage | 0.07 | 0.03 |
| Counterfactual 2 | Counterfactual 3 | |
| GSE fraction of high-risk acquisitions 06 | 0.14 | 0.14 |
| GSE fraction of high-risk acquisitions 07 | 0.00 | 0.10 |
| GSE fraction of high-risk acquisitions 08 | 0.00 | 0.05 |
| House price fall 06-08 | |$-$|0.32 | |$-$|0.13 |
| GSE acquisitions 06 | 0.77 | 0.77 |
| GSE acquisitions 07 | 0.48 | 0.56 |
| GSE mortgage defaults 06 vintage | 0.04 | 0.04 |
| GSE mortgage defaults 07 vintage | 0.02 | 0.04 |
The table compares key moments in the benchmark calibration to those in various counterfactual analyses. Counterfactual 1 shuts down the propping-up channel. Counterfactual 2 shuts down the propping-up channel and incorporates overly optimistic future house price expectations during the boom. Counterfactual 3 assumes there is no private-label exit at the start of the bust.
Counterfactual analyses
| Benchmark | Counterfactual 1 | |
|---|---|---|
| GSE fraction of high-risk acquisitions 06 | 0.14 | 0.00 |
| GSE fraction of high-risk acquisitions 07 | 0.28 | 0.01 |
| GSE fraction of high-risk acquisitions 08 | 0.25 | 0.01 |
| House price fall 06-08 | |$-$|0.21 | |$-$|0.17 |
| GSE acquisitions 06 | 0.77 | 0.51 |
| GSE acquisitions 07 | 0.70 | 0.51 |
| GSE mortgage defaults 06 vintage | 0.04 | 0.02 |
| GSE mortgage defaults 07 vintage | 0.07 | 0.03 |
| Counterfactual 2 | Counterfactual 3 | |
| GSE fraction of high-risk acquisitions 06 | 0.14 | 0.14 |
| GSE fraction of high-risk acquisitions 07 | 0.00 | 0.10 |
| GSE fraction of high-risk acquisitions 08 | 0.00 | 0.05 |
| House price fall 06-08 | |$-$|0.32 | |$-$|0.13 |
| GSE acquisitions 06 | 0.77 | 0.77 |
| GSE acquisitions 07 | 0.48 | 0.56 |
| GSE mortgage defaults 06 vintage | 0.04 | 0.04 |
| GSE mortgage defaults 07 vintage | 0.02 | 0.04 |
| Benchmark | Counterfactual 1 | |
|---|---|---|
| GSE fraction of high-risk acquisitions 06 | 0.14 | 0.00 |
| GSE fraction of high-risk acquisitions 07 | 0.28 | 0.01 |
| GSE fraction of high-risk acquisitions 08 | 0.25 | 0.01 |
| House price fall 06-08 | |$-$|0.21 | |$-$|0.17 |
| GSE acquisitions 06 | 0.77 | 0.51 |
| GSE acquisitions 07 | 0.70 | 0.51 |
| GSE mortgage defaults 06 vintage | 0.04 | 0.02 |
| GSE mortgage defaults 07 vintage | 0.07 | 0.03 |
| Counterfactual 2 | Counterfactual 3 | |
| GSE fraction of high-risk acquisitions 06 | 0.14 | 0.14 |
| GSE fraction of high-risk acquisitions 07 | 0.00 | 0.10 |
| GSE fraction of high-risk acquisitions 08 | 0.00 | 0.05 |
| House price fall 06-08 | |$-$|0.32 | |$-$|0.13 |
| GSE acquisitions 06 | 0.77 | 0.77 |
| GSE acquisitions 07 | 0.48 | 0.56 |
| GSE mortgage defaults 06 vintage | 0.04 | 0.04 |
| GSE mortgage defaults 07 vintage | 0.02 | 0.04 |
The table compares key moments in the benchmark calibration to those in various counterfactual analyses. Counterfactual 1 shuts down the propping-up channel. Counterfactual 2 shuts down the propping-up channel and incorporates overly optimistic future house price expectations during the boom. Counterfactual 3 assumes there is no private-label exit at the start of the bust.
Welfare
| Benchmark | Counterfactual 1 | ||
|---|---|---|---|
| GSE acquisitions 06 | 0.77 | 0.51 | |
| GSE acquisitions 07 | 0.70 | 0.51 | |
| GSE acquisitions 08 | 0.67 | 0.51 | |
| GSE mortgage defaults 06 vintage | 0.04 | 0.02 | |
| GSE mortgage defaults 07 vintage | 0.07 | 0.03 | |
| GSE mortgage defaults 08 vintage | 0.07 | 0.03 | |
| House price fall 06-08 | |$-$|0.21 | |$-$|0.17 | |
| Standard deviation of credit | 0.02 | 0.00 | |
| Standard deviation of house prices | 0.08 | 0.06 | |
| Welfare – high |$\gamma/d$| | 0.66 | 0.45 | |
| Welfare – medium |$\gamma/d$| | 0.63 | 0.44 | |
| Welfare – low |$\gamma/d$| | 0.44 | 0.39 | |
| Social planner 1 | Social planner 2 | Social planner 3 | |
| GSE acquisitions 06 | 1.22 | 1.22 | 0.77 |
| GSE acquisitions 07 | 1.44 | 0.70 | 0.53 |
| GSE acquisitions 08 | 1.44 | 0.70 | 0.53 |
| GSE mortgage defaults 06 vintage | 0.17 | 0.17 | 0.06 |
| GSE mortgage defaults 07 vintage | 0.26 | 0.08 | 0.03 |
| GSE mortgage defaults 08 vintage | 0.26 | 0.08 | 0.03 |
| House price fall 06-08 | 0.00 | |$-$|0.37 | |$-$|0.30 |
| Standard deviation of credit | 0.06 | 0.13 | 0.06 |
| Standard deviation of house prices | 0.00 | 0.19 | 0.12 |
| Welfare – high |$\gamma/d$| | 1.03 | N/A | N/A |
| Welfare – medium |$\gamma/d$| | N/A | 0.80 | N/A |
| Welfare – low |$\gamma/d$| | N/A | N/A | 0.53 |
| Benchmark | Counterfactual 1 | ||
|---|---|---|---|
| GSE acquisitions 06 | 0.77 | 0.51 | |
| GSE acquisitions 07 | 0.70 | 0.51 | |
| GSE acquisitions 08 | 0.67 | 0.51 | |
| GSE mortgage defaults 06 vintage | 0.04 | 0.02 | |
| GSE mortgage defaults 07 vintage | 0.07 | 0.03 | |
| GSE mortgage defaults 08 vintage | 0.07 | 0.03 | |
| House price fall 06-08 | |$-$|0.21 | |$-$|0.17 | |
| Standard deviation of credit | 0.02 | 0.00 | |
| Standard deviation of house prices | 0.08 | 0.06 | |
| Welfare – high |$\gamma/d$| | 0.66 | 0.45 | |
| Welfare – medium |$\gamma/d$| | 0.63 | 0.44 | |
| Welfare – low |$\gamma/d$| | 0.44 | 0.39 | |
| Social planner 1 | Social planner 2 | Social planner 3 | |
| GSE acquisitions 06 | 1.22 | 1.22 | 0.77 |
| GSE acquisitions 07 | 1.44 | 0.70 | 0.53 |
| GSE acquisitions 08 | 1.44 | 0.70 | 0.53 |
| GSE mortgage defaults 06 vintage | 0.17 | 0.17 | 0.06 |
| GSE mortgage defaults 07 vintage | 0.26 | 0.08 | 0.03 |
| GSE mortgage defaults 08 vintage | 0.26 | 0.08 | 0.03 |
| House price fall 06-08 | 0.00 | |$-$|0.37 | |$-$|0.30 |
| Standard deviation of credit | 0.06 | 0.13 | 0.06 |
| Standard deviation of house prices | 0.00 | 0.19 | 0.12 |
| Welfare – high |$\gamma/d$| | 1.03 | N/A | N/A |
| Welfare – medium |$\gamma/d$| | N/A | 0.80 | N/A |
| Welfare – low |$\gamma/d$| | N/A | N/A | 0.53 |
The table compares key moments and welfare in the benchmark calibration, counterfactual 1, and the social planner optimal for three different values of default costs relative to the benefits of homeownership.
Welfare
| Benchmark | Counterfactual 1 | ||
|---|---|---|---|
| GSE acquisitions 06 | 0.77 | 0.51 | |
| GSE acquisitions 07 | 0.70 | 0.51 | |
| GSE acquisitions 08 | 0.67 | 0.51 | |
| GSE mortgage defaults 06 vintage | 0.04 | 0.02 | |
| GSE mortgage defaults 07 vintage | 0.07 | 0.03 | |
| GSE mortgage defaults 08 vintage | 0.07 | 0.03 | |
| House price fall 06-08 | |$-$|0.21 | |$-$|0.17 | |
| Standard deviation of credit | 0.02 | 0.00 | |
| Standard deviation of house prices | 0.08 | 0.06 | |
| Welfare – high |$\gamma/d$| | 0.66 | 0.45 | |
| Welfare – medium |$\gamma/d$| | 0.63 | 0.44 | |
| Welfare – low |$\gamma/d$| | 0.44 | 0.39 | |
| Social planner 1 | Social planner 2 | Social planner 3 | |
| GSE acquisitions 06 | 1.22 | 1.22 | 0.77 |
| GSE acquisitions 07 | 1.44 | 0.70 | 0.53 |
| GSE acquisitions 08 | 1.44 | 0.70 | 0.53 |
| GSE mortgage defaults 06 vintage | 0.17 | 0.17 | 0.06 |
| GSE mortgage defaults 07 vintage | 0.26 | 0.08 | 0.03 |
| GSE mortgage defaults 08 vintage | 0.26 | 0.08 | 0.03 |
| House price fall 06-08 | 0.00 | |$-$|0.37 | |$-$|0.30 |
| Standard deviation of credit | 0.06 | 0.13 | 0.06 |
| Standard deviation of house prices | 0.00 | 0.19 | 0.12 |
| Welfare – high |$\gamma/d$| | 1.03 | N/A | N/A |
| Welfare – medium |$\gamma/d$| | N/A | 0.80 | N/A |
| Welfare – low |$\gamma/d$| | N/A | N/A | 0.53 |
| Benchmark | Counterfactual 1 | ||
|---|---|---|---|
| GSE acquisitions 06 | 0.77 | 0.51 | |
| GSE acquisitions 07 | 0.70 | 0.51 | |
| GSE acquisitions 08 | 0.67 | 0.51 | |
| GSE mortgage defaults 06 vintage | 0.04 | 0.02 | |
| GSE mortgage defaults 07 vintage | 0.07 | 0.03 | |
| GSE mortgage defaults 08 vintage | 0.07 | 0.03 | |
| House price fall 06-08 | |$-$|0.21 | |$-$|0.17 | |
| Standard deviation of credit | 0.02 | 0.00 | |
| Standard deviation of house prices | 0.08 | 0.06 | |
| Welfare – high |$\gamma/d$| | 0.66 | 0.45 | |
| Welfare – medium |$\gamma/d$| | 0.63 | 0.44 | |
| Welfare – low |$\gamma/d$| | 0.44 | 0.39 | |
| Social planner 1 | Social planner 2 | Social planner 3 | |
| GSE acquisitions 06 | 1.22 | 1.22 | 0.77 |
| GSE acquisitions 07 | 1.44 | 0.70 | 0.53 |
| GSE acquisitions 08 | 1.44 | 0.70 | 0.53 |
| GSE mortgage defaults 06 vintage | 0.17 | 0.17 | 0.06 |
| GSE mortgage defaults 07 vintage | 0.26 | 0.08 | 0.03 |
| GSE mortgage defaults 08 vintage | 0.26 | 0.08 | 0.03 |
| House price fall 06-08 | 0.00 | |$-$|0.37 | |$-$|0.30 |
| Standard deviation of credit | 0.06 | 0.13 | 0.06 |
| Standard deviation of house prices | 0.00 | 0.19 | 0.12 |
| Welfare – high |$\gamma/d$| | 1.03 | N/A | N/A |
| Welfare – medium |$\gamma/d$| | N/A | 0.80 | N/A |
| Welfare – low |$\gamma/d$| | N/A | N/A | 0.53 |
The table compares key moments and welfare in the benchmark calibration, counterfactual 1, and the social planner optimal for three different values of default costs relative to the benefits of homeownership.
Cross-sectional moments
| Model | Data | |
|---|---|---|
| GSE outstanding share in 07 - Mean | 0.66 | 0.65 |
| GSE outstanding share in 07 - Standard deviation | 0.12 | 0.09 |
| GSE outstanding share in 07 - Skewness | -0.65 | -0.61 |
| GSE outstanding share in 07 - Kurtosis | 3.08 | 3.82 |
| Regression coefficient | 0.18 | 0.19 |
| Standard error | 0.02 | 0.04 |
| Model | Data | |
|---|---|---|
| GSE outstanding share in 07 - Mean | 0.66 | 0.65 |
| GSE outstanding share in 07 - Standard deviation | 0.12 | 0.09 |
| GSE outstanding share in 07 - Skewness | -0.65 | -0.61 |
| GSE outstanding share in 07 - Kurtosis | 3.08 | 3.82 |
| Regression coefficient | 0.18 | 0.19 |
| Standard error | 0.02 | 0.04 |
The table compares cross-sectional moments generated in the model to those in the data.
Cross-sectional moments
| Model | Data | |
|---|---|---|
| GSE outstanding share in 07 - Mean | 0.66 | 0.65 |
| GSE outstanding share in 07 - Standard deviation | 0.12 | 0.09 |
| GSE outstanding share in 07 - Skewness | -0.65 | -0.61 |
| GSE outstanding share in 07 - Kurtosis | 3.08 | 3.82 |
| Regression coefficient | 0.18 | 0.19 |
| Standard error | 0.02 | 0.04 |
| Model | Data | |
|---|---|---|
| GSE outstanding share in 07 - Mean | 0.66 | 0.65 |
| GSE outstanding share in 07 - Standard deviation | 0.12 | 0.09 |
| GSE outstanding share in 07 - Skewness | -0.65 | -0.61 |
| GSE outstanding share in 07 - Kurtosis | 3.08 | 3.82 |
| Regression coefficient | 0.18 | 0.19 |
| Standard error | 0.02 | 0.04 |
The table compares cross-sectional moments generated in the model to those in the data.
Appendix C. Robustness and Extensions of Benchmark Model
C.1 Propping Up with Commitment
In this case, |$m_2$| is higher than in the case with no commitment. The feedback effect increases |$m_1$|, which further increases |$m_2$|. Therefore, the threshold level of concentration at which propping up is undertaken is lower with a commitment to future lending; that is, |$\overline{N}$| is higher with interest rate competition than without.
C.2 Robustness to Interest Rate Competition
C.3 Robustness to a General Supply Function
Since |$P^{'}_2(m_2)$| is positive, for a large enough |$m_1$|, |$m_2$| will be positive even if |$(-P_2 + E[R_2])$| is negative, which corresponds to the loan itself being negative NPV. Therefore, the mechanism is robust to a general housing supply function.
C.4 Robustness to General Demand Elasticities
As before, the higher |$m_1$|, the more mortgage loans an individual bank will want to make at |$t=2$|. In the benchmark model in the paper, the assumption that nonborrowers get high-enough utility from housing such that they do not exit the market implies |$\epsilon_{d_2,m_2}=1$|. The assumption on the housing supply curve implies |$\epsilon_{P_2,d_2}=c$|. If these values are substituted into the above equation, equilibrium lending is identical to the benchmark model in the paper.
C.5 Robustness to Nonrecourse Loans
This is positive for a large enough |$m_1$| even when loans are negative NPV. Therefore, the mechanism is robust to nonrecourse loans.
C.6 Secondary Market Equivalency
The last constraint is the secondary market price required to incentivize for a lender to originate a mortgage to a borrower of type |$i$| with face value |$D_t^j$|. The mortgage holder will pick |$Y_t(D_t^j)$| so that the originator is just willing to lend to a borrower of type |$j$|, implying that |$Y_t(D_t^j)=P_t$|. Furthermore, they will choose a |$D_t^j$| so that borrowers repay the maximum they are willing to pay. This is equivalent to the problem faced by banks that hold onto the mortgages they originate. The same logic can be applied if mortgages are resold on the secondary market. The key requirement for the mechanism to work is that the final holder of mortgages has some market power.
C.7 Extension to Refinancing
If |$\phi_{12}<\phi_{2}$| a bank would strictly prefer to make new loans rather than refinance existing borrowers. The intuition for this is relatively straightforward. The bank will simply choose whichever option is less negative NPV. This will depend on whether a loan to a new low-quality borrower or the existing borrower in default has higher expected future repayment. The basic intuition is therefore applicable to both refinancing and new loans.
Acknowledgement
I am thankful to Philip Bond, Anna Cororaton, Aycan Corum, Tetiana Davydiuk, Mehran Ebrahimian, Ronel Elul, Itay Goldstein, Vincent Glode, William Fuchs, Joao Gomes, Daniel Greenwald, Marco Grotteria, Ben Hyman, Jessica Jeffers, Benjamin Keys, Mete Kilic, Tim Landvoigt, Doron Levit, Pricila Maziero, David Musto, Thien Nguyen, Christian Opp, Giorgia Piacentino, Sam Rosen, Nikolai Roussanov, Hongxun Ruan, Lin Shen, Jan Starmans, and Stijn Van Nieuwerburgh and seminar participants at Carnegie Mellon, the Carnegie-LAEF conference, Emory University, the Federal Reserve Bank of New York, the Federal Reserve Bank of Philadelphia, Georgetown University, HEC Paris, INSEAD, Ohio State University, Oxford University, the Society for Economic Dynamics Meetings, the Texas Finance Festival, Tulane University, UCLA, UCSD, University of Michigan, University of North Carolina, University of Washington, the Western Finance Association Meetings and the Wharton School for their helpful feedback. I also thank the Rodney L. White Center for Financial Research for financial support on this project.
Footnotes
1These high-risk mortgage loans purchased by the agencies did not perform well: about 30|$\%$| of them experienced a bad termination (Elul, Gupta, and Musto 2020). Furthermore, when Fannie Mae and Freddie Mac were placed into government conservatorship in September 2008, their shareholder equity was negative (Acharya et al. 2011).
2It was common knowledge that the housing downturn was beginning. In March 2007, the New York Times reported that a record number of houses had gone into foreclosure in the last quarter of 2006” (Bajaj 2007). Further, in October 2006, Moody’s released a report stating that the housing market’s downturn was in “full swing” and predicted house price declines across the United States (Zandi, Chen, and Carey 2006). In fact, in an October 2006 interview with the San Francisco Gate Richard Syron, then CEO of Freddie Mac, cautioned against “betting on a turnaround” in house prices and expressed his belief that the housing market would continue to worsen.
3See Elul, Gupta, and Musto (2020) for variation in the GSE share across MSAs. The GSEs’ exposure to mortgages came in the form of portfolio holdings of their own loans (about half of which they held on to) and insurance guarantees on the securitized mortgages that they sold. Additionally, the agencies were the largest investors in the private securitization market purchasing about 30|$\%$| of the total dollar volume of private-label mortgage-backed securities (MBSs) between 2003 and 2007 (Acharya et al. 2011; Adelino, Frame, and Gerardi 2017).
4See Tirole (1998).
5See Himmelberg, Mayer, and Sinai (2005), Foote, Gerardi, and Willen (2008), Haughwout, Peach, and Tracy (2008), Hubbard and Mayer (2011), Mayer (2011), Khandani, Lo, and Merton (2013), Ferreira and Gyourko (2015), Landvoigt, Piazzesi, and Schneider (2015), Palmer (2015), An and Yao (2016), Favilukis, Ludvigson, and Nieuwerburgh (2017), and Griffin and Maturana (2016).
7See Gay Stolberg and Andrews (2011). See also Ben Bernanke’s (2012) FOMC Press Conference.
8Green and White (1997), Sekkat and Szafarz (2011), and Sodini et al. (2016) estimate the benefits of homeownership.
9Each firm solves the following problem:
In equilibrium, firms will produce housing until |$P_t = c h_t$|.
10Piazzesi and Schneider (2016) show that movements in the value of the residential housing stock are primarily due to movements in the value of land. Knoll, Shularick, and Steger (2017) provide evidence that rising land prices explain about 80|$\%$| of global house price appreciation since World War II.
11Lacko and Pappalardo (2007) and Amel, Kennickell, and Moore (2008) provide evidence that supports this assumption. They find that consumers tend to bank locally and do not shop around for mortgage rates.
12Since low-quality loans are assumed to be negative NPV, |$\frac{E[R_2]}{c} - \alpha^{nb} <0$|.
13Typically, the presence of strategic complementarities gives rise to multiple equilibria.
14If there are no costs to default and |$d=0$|, the planner simply wants to maximize the amount of credit available in the economy. In this case, the optimal |$N$| is equal to the number of banks that maximize aggregate credit availability.
15When |$\theta=1$|, the cost function simplifies to |$((1-\phi_1)m_1 + (1-\phi_2)m_2)^2$|.
16The appendix provides details.
17This is equivalent to adjusting |$\alpha^{nb}_{s_t}$| in the benchmark model as long as a feasible interest rate exists such that securitizers break even in expectation.
18Appendix A contains details on the social planner’s optimum in the infinite-horizon model. To keep the solution tractable, I assume that the social planner’s budget constraint is satisfied at its optimal lending level.
20The mathematics of when exactly this expression is increasing and decreasing in |$N$| is tedious and does not add much to understanding the main mechanism in the paper but can be made available on request.
References
The Urban Institute.
