Distributional Implications of Government Guarantees. in Mortgage Markets

Transcription

1 Distributional Implications of Government Guarantees in Mortgage Markets Pedro Gete and Franco Zecchetto This Draft: March 2016 Abstract We analyze the removal of the government guarantees from the mortgage market. We use a quantitative model in which mortgage spreads are endogenously related to borrowers income. The guarantees generate credit subsidies that are heterogeneous across households. The removal of the guarantees leads to higher wealth inequality driven by uneven rises in mortgage spreads and housing costs. Leverage and housing affordability decrease for low and mid-income households while they increase for high-income households. Renters and high leveraged mortgagors with conforming loans, which are low and mid-income households, lose the most welfare from the removal of the guarantees. Keywords: Default, Loan Guarantees, Housing, Inequality, Mortgages, Rents. JEL Classification: E51, H81, G21, R2 We thank Jim Albrecht, Fernando Alvarez, Satyajit Chatterjee, Juan Carlos Conesa, Behzad Diba, Ronel Elul, Martin Evans, W. Scott Frame, Carlos Garriga, Ross J. Hallren, Simon Gilchrist, Mark Huggett, Steven Laufer, Wenli Li, Arvind Krishnamurthy, Paul Willen and participants at the 2015 AREUEA national meetings and 2015 Southern Economic Conference for helpful comments. Pedro Gete gratefully acknowledges the financial support of the Spanish Ministry of Economy and Competitiveness Grant No. ECO Georgetown University and IE Business School. 37th and O Sts., NW Washington, DC, 20057, USA. Telephone: pg252@georgetown.edu. Georgetown University. 37th and O Sts., NW Washington, DC, 20057, USA. Telephone: fz43@georgetown.edu. 1

2 1 Introduction Reforming the Housing Finance System is a pressing policy issue in the U.S. although all recent proposals have failed to gain Congress support. 1 The status quo is that the federal government, directly or indirectly, insures the credit risk of most of the mortgage market. 2 Most policy reforms propose to dramatically reduce the size of the government guarantees. At the same time, the effect of the policy on inequality is a key element of the policy debate. In this paper we analyze the effects of removing the guarantees in a quantitative model in which mortgage spreads are endogenously related to borrowers income and the guarantees reduce the risk of lenders assets. Our main findings are: 1) the guarantees generate credit subsidies that are very heterogeneous across households. The average subsidy of around 30bp estimated in the housing finance literature (and that we match in the model) does not capture this substantial heterogeneity; 2) removing the guarantees will hurt the low and mid-income households that are high leveraged homeowners or renters, it will benefit high-income households borrowing in the jumbo market; 3) The cross-sectional distribution of leverage will change: leverage will decrease for low and mid-income households but it will increase for high income households. We study a general equilibrium model of housing, rental and mortgage markets with incomplete markets. Households are heterogeneous and subject to idiosyncratic shocks to income and house values. We model a house as an asset that provides housing services (which can be rented), serves as collateral and is a risky storage of value (depreciation shocks make house values stochastic). Houses are large relative to income (there is a minimum house size). Our model has two main novelties: 1) Borrower s spread is endogenously related to the income of the borrower. This is the case 1 For example, the U.S. Congress recently failed to approve the Corker-Warner and the Johnson Crapo bills. The Obama administration also made a proposal that was abandoned. 2 For example, in 2014 Fannie Mae and Freddie Mac (the Government-Sponsored Enterprises or GSEs) insured about 50%, while other programs such as the FHA, VA, RD, and PIH loans insured around 20% of the market. 2

3 because we work with recourse mortgages, that is, if the borrower defaults the lender can go after the borrower s house and other assets, and she can sue to have the borrower s income garnished. 3 In a non-recourse mortgage the lender can only go after the house. Therefore, in non-recourse mortgages the borrower s income affects neither the default decision, nor the mortgage rate. The existing literature on housing finance has focused on non-recourse mortgages because it is commonly assumed that the lenient U.S. bankruptcy regime makes all U.S. mortgages nonrecourse. However, Ghent and Kudlyak (2011) and Pence (2006) provide evidence supporting our recourse assumption. First, most U.S. states are recourse states. 4 In those states the lender may be able to collect on debt not covered by the proceedings from a foreclosure sale by obtaining a deficiency judgment. Second, the effect of recourse is not reflected in the frequency of deficiency judgments but, instead, in the way the threat of recourse alters borrower behavior (recourse reduces the probability of default) and allows the lender to obtain concessions from the borrower. Li and Oswald (2016) show that in 2009 lenders tightened their lending standards when Nevada legislated to become a non-recourse state. The empirical evidence suggests that the borrower s income and related variables as the FICO score affect mortgage rates and lending standards. We show that incorporating the link between income and mortgage spreads is key when studying distributional questions, like the effects of mortgage finance reforms or who benefits from credit subsidies. 2) We model the government guarantees as a tax-financed insurance to the mortgage lenders assets. 5 That is, in case of borrower s default the government refunds the lender for a fraction of its credit loss. 6 Since the lenders do not bear the full cost of borrower s default they do not fully price all the credit risk into the mortgage rate (mortgage spread plus risk-free rate). The 3 Another way to link spreads and the income of the borrower is to assume that default costs change with income, for example, because the costs of a bad credit record are larger for high income households. We would obtain the same result than with recourse mortgages: borrower s income is correlated with default propensity. 4 There are twelve non-recourse states: Alaska, Arizona, California, Iowa, Minnesota, Montana, Nevada (since 2009), North Carolina (purchase mortgages), North Dakota, Oregon, Washington, and Wisconsin. See Ghent and Kudlyak (2011). 5 The Congressional Budget Offi ce (CBO) and several authors have shown that the guarantees are underpriced and the CBO inputs the credit subsidies into the federal budget (CBO 2013, Lucas and McDonald 2010). 6 Our model allows for conforming and non-conforming loans. Only conforming loans receive the guarantees, they are subject to caps on LTV and mortgage size following the GSEs conforming limits. 3

4 guarantees are a subsidy that lowers mortgage spreads relative to the market with no guarantees. Our model shows large cross-sectional differences on who benefits from this subsidy. The previous two assumptions link borrower s income to the mortgage subsidy: the subsidy is larger for those households with larger default risk, that is, households with higher debtto-house value (DTV) and debt-to-income (DTI) ratios in the conforming mortgage market. These are mid-income, mid-wealth households because they need more credit to afford a house and because they like to borrow against it to smooth consumption. If the subsidy to credit risk disappears those households will face the largest increase in mortgage spreads and qualification thresholds. Following the removal of the guarantees, households whose borrowings become more expensive reduce their mortgage debt and housing holdings. Some of them move into rental housing. House prices decrease while rents increase. Moreover, deposit rates (the risk-free rate in our model) decrease to discourage savings. Since all households have the same preferences, renters are the low-income households who do not qualify for credit or prefer not to borrow given their credit conditions. These households suffer with the policy change because rents increase, the return on their deposits is lower and their access to mortgage credit is more diffi cult and expensive since they need high DTV and DTI. Mid-income households who are high leveraged mortgagors suffer because their mortgage spreads increase the most and some need to become renters. Higher housing costs (rents or mortgage payments) reduce savings and prevent these households from accumulating wealth. Wealth inequality measured by the Gini Index increases. Most of the increase is accounted for by mid-income households who after the removal of the guarantees do not qualify for credit. They pass from paying a mortgage and accumulating housing wealth to paying rents and not accumulating any wealth. High-income households who borrow in the jumbo market are the main winners from the removal. Their spreads are not affected and their mortgage rates decrease as lenders pass on 4

5 their lower cost of funds (lower deposit rates). Moreover, high-income households bear most of the costs of the guarantees given the progressive tax system. Taxes go down with the removal and this benefits the households in the highest tax brackets. Lower price-to-rent ratios and return on deposits make more attractive to be a landlord. High-income households shift their portfolio towards housing. Leverage and housing affordability move in opposite ways depending on a household s position in the income and wealth distributions. 7 The low and mid-income households whose mortgage spreads increase the most reduce their leverage and see their affordability reduced. However, for high-income households their mortgage rates decrease and the lower price-to-rent ratios encourage them to increase leverage. Thus, removing the guarantees lowers homeownership rates and changes the distribution of leverage. The previous channels imply an uneven distribution of the welfare gains or losses from the policy change. However, there is one channel that is beneficial for everybody: removing the guarantees brings a reduction in default rates and in the deadweight costs from foreclosures. The economy has more output available for consumption. However, this channel is not strong enough to compensate the low and mid-income households who are the losers from removing the guarantees. We find that most households oppose the removal. This result may explain why all proposals to reduce the guarantees have so far failed. In our model, almost all renters and leveraged homeowners are against the removal. The correlation between being favorable to the policy change and income is around 0.6, the correlation with wealth is lower, around 0.4, because the lower deposit rates are bad for the households with largest deposit holdings. To isolate this interest rate effect we do an experiment in which deposit rates are constant (a small open economy setup) and then both income and wealth are strongly correlated with supporting the 7 We define affordability like the ability of a household to cover the mortgage payments on a median size house bought with a 20% downpayment (this is the methodology of the popular index computed by the National Association of Realtors). 5

6 removal. This paper is related to the growing literature which uses models of heterogeneous agents with idiosyncratic labor income risk to study housing and/or mortgage markets. 8 Several papers in this area, like for example Chambers et al. (2009), Floetotto et al. (2015), Gervais (2002), Jeske et al. (2013) or Sommer and Sullivan (2015) analyze distributional effects from housing policies. These papers abstract from the link between income and mortgage rates. 9 In this paper we show that the link between income and mortgage rates is important, especially to analyze the distributional consequences of general equilibrium effects such as lower house prices or lower risk-free rates. For example, low-income households cannot benefit from those effects if the effects occur at the same time as their mortgage spreads are increasing and their access to credit is becoming more diffi cult. Moreover, our model is innovative by integrating several aspects, such as the addition of guarantees, the modeling of the housing tenure choice with both endogenous house prices and rents, and the presence of both conforming and non-conforming mortgages. Through the question that we study, our paper contributes to the literature analyzing housing finance reform and the role of the government in mortgage markets. Frame et al. (2013), Glaeser and Gyourko (2008) and Levitin and Wachter (2013) survey the U.S. housing finance policy. Passmore et al. (2002) and McKenzie (2002) have estimated the average implicit subsidy from the government guarantees. We calibrate the model to match those estimates but our paper highlights that average subsidies hide substantial heterogeneity across households. For example, the average subsidy is 30.3 basis points but the standard deviation is 23.6 basis points. The largest subsidies are for the low and mid-income households with high leverage. To 8 Some examples include Arslan et al. (2014), Chambers et al. (2009), Chatterjee and Eyigungor (2014), Chu (2014), Corbae and Quintin (2014), Diaz and Luengo-Prado (2010), Floetotto et al. (2015), Gervais (2002), Guler (2015), Hatchondo et al. (2014), Jeske et al. (2013), Iacoviello and Pavan (2013), Li et al. (2016), Mitman (2016), Silos (2007), Sommer et al. (2013) and Sommer and Sullivan (2015). Gete and Reher (2016) solve for the closed form solutions of a model with aggregate shocks but deterministic heterogeneity. 9 To our knowledge only Corbae and Quintin (2014), Hatchondo et al. (2015) and Mitman (2016) study default with recourse mortgages. However these papers do not focus on distributional aspects and differ from our model in many other aspects. 6

7 our knowledge, the empirical literature on housing finance has not studied this cross-sectional heterogeneity. Jeske et al. (2013) analyze mortgage guarantees in a model with heterogeneous agents and idiosyncratic risk. They conclude that eliminating the guarantees is a progressive policy that would hurt high-income, high-wealth households. We obtain the opposite distributional results for two reasons: 1) we focus on recourse loans while they study non-recourse mortgages. Thus, only in our model income differences imply differences in mortgage spreads. 2) We model the guarantees as a subsidy to lenders liabilities. In their model the guarantees are a reduction in lenders cost of funds that lowers the cost of credit equally for all borrowers. In their model, high-income households enjoy the subsidy the most because they borrow the most. In our model, it is not the amount of borrowing but the risk of the borrower what determines who gets the largest subsidy. Low-income mortgagors receive the largest subsidy because they have the largest default risk in conforming loans. Elenev et al. (2015) study a general equilibrium model with aggregate shocks, non-recourse mortgages, three sets of agents (borrowers, depositors and bankers) and a government that, in addition to subsidizing mortgage credit risk, provides a bailout guarantee to the banks. Their focus is the interaction between the guarantees and bankers risk taking, not the distributional aspects. They find that removing the guarantees leads to a more stable financial system with borrowers basically indifferent on whether to remove the guarantees, while savers are substantially better off. Thus, virtually nobody opposes the removal of the guarantees. Our results are very different in this regard because in our setup the spreads endogenously depend on income, and because we allow for rental markets. Thus, we take account of the groups who would lose with the policy change: renters and low to mid-income mortgagors whose higher spreads prevent them from enjoying the lower house prices while rents increase. Zhang (2015) uses a partial equilibrium, deterministic assignment model to assess the distributional impact of eliminating the GSEs. He does not model households default. He studies 7

8 the guarantees as a subsidy to the interest rate. He imposes conforming limits on mortgage size. High-wealth households borrow above the conforming limits and cannot enjoy the guarantees. Thus, the guarantees mostly benefit low-income households. The rest of the paper is organized as follows. Section 2 presents the model and Section 3 calibrates it. Section 4 contains the results. Section 5 analyzes an economy with constant deposit rates. Section 6 concludes. The online Appendix discusses the numerical algorithm. 2 Model There is a continuum of infinitely lived households, a continuum of competitive lenders and a government. It is a closed economy model. The model is described recursively. 2.1 Households Preferences. Households derive utility from consumption of the numeraire good (c) and from housing services that we call shelter (s). Housing services can be either owned or rented. Preferences are the expected value of the discounted sum of period utilities: E 0 t=0 β t u(c t, s t ), where β (0, 1) is the discount factor. Endowments. Households supply labor inelastically and receive an idiosyncratic stochastic labor income y Y measured in terms of the numeraire. This shock follows a finite state Markov chain with transition probabilities π(y y) and unique invariant distribution Π(y). 10 The unconditional stationary income mean is ȳ = yπ(y). Because of the law of large numbers, y Y π and Π describe the deterministic fraction of households receiving a particular income shock 10 Here and in what follows, a prime denotes the value at the start of next period. 8

9 while ȳ is the aggregate income. The government taxes labor income to finance the mortgage guarantees. We use a progressive tax system in which the tax rate for a household with income y is τ y. Thus, (1 τ y )y is the disposable income. Markets. There are five markets: owner-occupied housing, rental housing, consumption goods, mortgage credit, and deposits. There are three assets: houses h, deposits d and mortgage debt m. Households can invest in one-period deposits P d d which pay d next period. Thus, the gross risk-free rate is 1 P d. Shelter services can be obtained either from the rental market at price P s, or through homeownership at price P h. The aggregate stock of housing (H) is in fixed supply and can be used for both ownership or rental housing. One unit of housing stock h equals one unit of shelter services s. The household s choices of housing stock and shelter consumption determine whether the household is a renter (h = 0), owner-occupier (h = s), or a landlord (h > s). Landlords lease (h s) to renters at the price P s, thus rental supply is endogenous. The tenure status of a household is denoted by the indicator function I (I = 1 for a homeowner, I = 0 for a renter). There is a minimum house size for ownership h h, but none for rental. This assumption allows to have well-defined renters and owners (with perfectly divisible housing almost everybody would own some housing). Houses are risky assets subject to idiosyncratic depreciation shocks δ such that if a house of size h is bought today, then next period the size of the house is (1 δ )h. We denote the associated cumulative distribution function as F (δ ) with support [ δ, 1] where δ 0. The role of these shocks is to introduce uncertainty about the value of a house. If a household buys a house she can use it as collateral for one-period mortgage debt. We denote by P m m the principal of the loan, and by m the amount to be repaid next period. The mortgage rate 1 P m is determined by perfect competition among lenders and will, in general, depend on the borrower s characteristics, namely the mortgage amount m, the size of the house h used as collateral, deposit holdings d and labor income y, and on whether the loan is insured by the government or not. The gross mortgage interest rate is 1 P m and the mortgage spread is 9

10 s m = 1 P m 1 P d. We consider recourse mortgages. That is, after the idiosyncratic shocks (y, δ ) are realized, a borrower can default on her mortgage at the cost of losing her housing stock, her deposits plus a fraction φ < 1 of her disposable income (1 τ y )y. This assumption, together with mortgages being one-period contracts, imply that a borrower will default whenever her wealth after repaying the mortgage is smaller than the unseizable disposable income: (1 τ y )y + d + P h (1 δ )h m < (1 φ)(1 τ y )y. (1) Therefore, the probability of default is a function of the mortgage m, housing h, deposits d, and current labor income y, which affects the realization of y through π(y y). In the Online Appendix we prove that if the lender has recourse on borrower s deposits, any household facing a positive mortgage spread will not borrow while holding deposits which pay the risk-free rate. 11 Thus, to save notation we omit the dependency of P m on deposits d and denote the mortgage rate function as P m (m, h, y; α), where a positive value for α indicates that the loan is guaranteed by the government. Households can choose between conforming and non-conforming mortgage loans (I c = 1 for conforming, I c = 0 for non-conforming). Conforming loans are insured by the government and subject to a maximum loan size l and loan-to-value cap θ. These are also the criteria that the GSEs require in a conforming mortgage Household s problem Let a denote wealth after the realization of the housing depreciation shocks, that is, disposable income plus the value from all assets brought into the period. Households take the 11 Jeske et al. (2013) shows that with non-recourse mortgages the households both borrow and hold deposits as the deposits are not seizable by the lenders. 12 The conforming limits are realistic and are needed to ensure the existence of stationary equilibria when lenders enjoy government guarantees. Otherwise households demand for credit becomes unbounded. 10

11 price system (P h, P s, P d, P m (.; α), P m (.; 0)) as given. Denoting by V (a, y) the value function, the household s problem in recursive form is: V (a, y) = { max u(c, s) + β π(y y) {c,s,d,m,h} 0,{I,I c} {0,1} y Y subject to 1 δ } V (a, y ) df (δ ) (2) c + P d d + P h h = a + P s (h s) + P m (m, h, y; I c α)m, (3) s h if I = 1, (4) I c P m (m, h, y; I c α)m min { θp h h, l }, (5) a = max { (1 τ y )y + d + P h (1 δ )h m, (1 φ)(1 τ y )y }, (6) h if I = 1, h = 0 if I = 0, h (7) m = 0 if I = 0. (8) Households spend in consumption c, deposits d, house purchases h and shelter services s. The term P s (s h) in equation (3) represents either rental payments by renters (when h = 0), or rental income received by landlords (when h > s). The lending rate is different for conforming 1 loans,, than for non-conforming, 1 P m(m,h,y;α) P m(m. Equation (4) captures that a homeowner,h,y;0) cannot lease more rental space than her housing space. The maximum loan-to-value and loan size on conforming loans are summarized in (5). Equation (6) captures the beginning-of-next period wealth a following the optimal default rule discussed in (1). The first argument in the max operator is the disposable income, plus the return on deposits, plus the value of the depreciated house minus the mortgage payments. The second argument in (6) is the income the household keeps if she defaults. Equation (7) captures that the household decides whether to be a homeowner or a renter. Households may want to own housing because it is an asset that gives housing services and serves as collateral. Renters cannot borrow from mortgage markets (equation (8)). We denote the individual state variables as x = (a, y) and X = A Y is the state space. 11

12 We denote by µ a probability measure over X. Since we focus on stationary equilibria in which µ is constant across time, we omit the dependence of prices on µ. 2.3 Lenders Lenders are risk-neutral and compete loan by loan. Perfect competition implies that lenders expected profits are zero. Lenders are financed through deposits at cost 1 P d costs r w per unit of mortgage issued. 13 to cover in expectation their cost of funds. and face origination Lenders will originate any mortgage that allows them When making their origination decisions, lenders take into account that households may default on their mortgages. Since mortgages are recourse, if the borrower defaults then the lender receives the borrowers assets and a share φ of her labor income. The housing foreclosure technology is ineffi cient and the lender only recovers a fraction γ < 1 of the house value. If a household defaults, the loss for the lender is the difference between the mortgage payments m and the amount the lender really recovers: 14 L(m, h, y, δ ) = m φ(1 τ y )y γp h (1 δ )h. (9) Thus, the loss is a function of borrower s debt, housing stock, income and depreciation shocks. In conforming loans, the government insures a fraction α [0, 1] of the lender s loss. That is, when a borrower defaults on a conforming loan, the lender receives: φ(1 τ y )y + γp h (1 δ )h + αl. When α = 1 the lender faces no credit risk, when α = 0 the lender faces all the credit risk. 13 Positive origination costs (r w > 0) ensure a positive mortgage spread over the deposit rate for households with zero-default risk, which prevents an indeterminacy in the household s maximization problem (if r w = 0 then deposits and zero-default mortgages are perfect substitutes). 14 To ease notation, we are already using the result that, given positive origination costs (r w > 0), borrowers will not hold deposits at the same time that they borrow. 12

13 The depreciation shock threshold function, δ (m, h, y ) captures that according to (1) a borrower owing mortgage repayments m, with house size h and realized labor income y will default whenever she suffers depreciation shocks δ larger than δ (m, h, y ), δ (m, h, y ) = 1 m φ(1 τ y )y. (10) P h h It is important to remark that, since the mortgage is recourse, δ depends on the income level. Given the guarantee α, the mortgage pricing function P m (m, h, y; α) satisfies the lender s expected zero profit condition: (1 + r w )P m (m, h, y; α)m = P d { 1 } π(y y) mf (δ ) + [φ(1 τ y )y + γp h (1 δ )h + αl(m, h, y, δ )] df (δ ). (11) δ y Y The left-hand-side of (11) is the cost of funds for the lender, that is, the amount lent P m (; α)m, augmented by the cost of origination and the cost of the deposits that fund the loan. The right-hand side of (11) is the expected revenue from the borrower. Conditional on an income realization y, the borrower will repay for depreciation shocks below the default threshold δ (m, h, y). For conforming loans, in case of default, the government covers a fraction α of the lender s credit losses. Thus, mortgage guarantees reduce the risk of lenders assets. 2.4 Government We focus on the subsidy implicit in the mortgage guarantees and assume that the guarantees are tax financed. This is consistent with the CBO inputing the cost of the guarantees into the federal government (CBO 2014). The government taxes the households income to finance the 13

14 spending on the guarantees: X [ y Y ] 1 π(y y) I c (x)αl(m (x), h(x), y, δ ) df (δ ) dµ = τ y yπ(y) (12) δ y Y The left-hand side aggregates the guarantees paid to the lenders for those households who default on conforming mortgages. The right-hand side is the tax revenue. 2.5 Market clearing and equilibrium Since one unit of housing provides one unit of housing services, the market for shelter services clears when the demand for shelter equals the aggregate housing stock H, which is in fixed supply: X s(x) dµ = H. (13) Moreover, every house needs to have an owner: h(x) dµ = H. (14) X Equations (14) and (13), together with (4) and (7), allow to write the equilibrium in rental markets as (1 I(x))s(x) dµ = H I(x)s(x) dµ. (15) X X The right hand side of (15) is the supply of rental housing services, that is, the total flow of housing services minus those consumed by homeowners. While the left-hand side of (15) is the demand for those services. The goods market clears when the aggregate endowment of consumption goods (ȳ) equals the consumption by households, plus the gross investment in housing (I h ) that ensures a constant 14

15 housing stock, plus the costs of mortgage origination: c(x) dµ + I h + r w P m (m (x), h(x), y; I c (x)α)m (x) dµ = ȳ. (16) X X I h is the investment to cover both the housing net depreciation and the foreclosure costs: [ δ I h = P h π(y y) δ df (δ ) + X y Y δ 1 δ (1 γ(1 δ )) df (δ ) ] h(x) dµ. (17) I h is multiplied by house prices to convert it into units of numeraire. The credit market clears if the supply of deposits equals the funds requested by the banks to lend: X P d d (x) dµ = (1 + r w ) P m (m (x), h(x), y; I c (x)α)m (x) dµ. (18) X We define a stationary equilibrium as follows: Definition. Given a guarantee rate α, loan-to-value limit θ and loan limit l, a stationary recursive competitive equilibrium is a collection of value and policy functions V, c, s, d, h, m : X R, I, I c : X {0, 1}, house price P h, shelter price P s, deposit interest rate 1 P d, price functions for conforming and non-conforming mortgage P m (; α), P m (; 0) : R 2 + Y R +, flattax rates {τ y } y Y and a probability measure µ over X such that: 1. Given P h, P s, 1 P d, P m (; α), P m (; 0) and {τ y } y Y, the function V (x) solves the household problem (2) and the policy functions are c(x), s(x), d (x), h(x), m (x), I(x) and I c (x). 2. Given P h, 1 P d, P m (; α), P m (; 0) and {τ y } y Y, the lender participation constraint (11) holds for all m, h, y. 3. The tax rates {τ y } y Y satisfy the government budget constraint (12). 4. The measure µ is stationary with respect to the Markov process induced by π(y y) and the policy functions. 15

16 5. All market clearing conditions are satisfied. 3 Calibration Qualitatively the results that we will show in the next section are robust to different calibrations. In this section we discuss how we calibrate the model to derive the quantitative results. We divide the parameters into two groups: firstly, those that we assign exogenously following micro evidence and standard values in the literature. And secondly, those parameters that we calibrate for the model to match some empirical targets. Tables 1 and 2 summarize these two groups of parameters. A period in the model corresponds to a year. A. Parameters calibrated exogenously. We assume a CRRA with a Cobb-Douglas aggregator for non-durable and shelter consumption: 15 u(c, s) = (cη s 1 η ) 1 σ 1 σ (19) where σ > 1. We set η = to obtain an aggregate share of shelter services over total consumption of 0.15, which is the NIPA average share of nominal housing expenditures in total nominal personal consumption expenditures for the period We set the relative risk aversion coeffi cient to σ = 4, which is within the standard range used in the macro literature. For the income process we use a continuous AR(1) process for log earnings: ln y = w + ρ ln y + ε, (20) ε N(0, σ 2 ε). 15 The Cobb-Douglas assumption simplifies the numerical solution of the model as we discuss in the Online Appendix. These preferences imply a unit intratemporal elasticity of substitution. 16 This share has been roughly stable during the last 40 years. The annual average from is 0.148, while during the average is

17 We follow Storesletten et al. (2004) and set the persistence parameter ρ to and the standard deviation of the innovations σ ε to We approximate (20) with a seven-state Markov chain using the method of Rouwenhorst (1995). 17 The Online Appendix reports the values for the income realizations (y), Markov transition matrix π(y y) and invariant distribution Π(y). For the maximum loan-to-value θ we use 0.8 which implies the usual 20% downpayment. We set the origination cost r w to 10 basis points following Jeske et al. (2013). We set the loss in value of a house that goes into foreclosure γ to 0.78 following Pennington-Cross (2006), who estimates that foreclosed properties appreciate on average 22% less than other properties. We set the garnishment parameter φ to In a recourse mortgage, creditors can usually garnish up to 25% of disposable wage earnings under the Federal Wage Garnishment Law. We select the tax progressivity parameters to match the progressivity in tax rates reported by the IRS Income Tax Return Statistical Tables. In 2013 the average tax rate for taxpayers in the bottom 50%, 50-25%, 5-10%, 5-1% and top 1% were 3.3%, 7.3%, 10.1%, 18.4% and 27.1% respectively. Our labor income realizations fall within these ranges. We set τ y = ι i τ for i = 1,.., 7 and we choose ι i to match the tax progressivity in the data, while the tax rate τ is solved in equilibrium to ensure that the government s budget is balanced. B. Parameters calibrated endogenously. Following Jeske et al. (2013), we assume a truncated generalized Pareto distribution for the housing depreciation shock δ. 18 The probability density function with support on [ δ, 1] where δ 0 is f(δ ) = ) 1 + ξ (δ δ) ( 1 +1) ξ σ δ ( ) ξ (1 δ) 1. (21) ξ σ δ ( 1 σ δ The location ( δ), scale (σ δ ) and shape (ξ) parameters, together with the remaining parameters of the model, are calibrated to match the following targets: 17 Kopecky and Suen (2010) show that this method is more reliable than others in approximating highly persistent AR(1) processes and generating accurate model solutions. 18 This functional form is useful for numerical reasons as we discuss in the Online Appendix. 17

18 1) An equilibrium risk-free rate of 1%. 2) A mean implicit interest rate subsidy of 30 basis points. Estimates of the implicit subsidy from the government guarantees usually range between 22 and 30 basis points; although they are sensitive to the methodology (CBO 2014). One way of estimating the benefit to borrowers is comparing the interest rates on mortgages that are eligible for GSE s financing with the rates on loans that are not eligible (controlling for other differences in the characteristics of borrowers and loans). Evidence from the spread between interest rates on jumbo and conforming loans suggests that the implicit federal guarantees lowered mortgage interest rates from less than 25 basis points in normal times to more than 100 basis points at the end of September 2010 (CBO 2010). 3) A share of homeowners with mortgage debt of 65%. Sommer et al. (2013) report that this is the percentage of homeowners with collateral debt according to the American Housing Survey ) A homeownership rate of 65%. The U.S. homeownership rate averaged 65.6% during the period ) A foreclosure rate for mortgagors of 1.25%. According to the National Delinquency Survey of the Mortgage Bankers Association, between 1997 and 2006 the average percentage of mortgage loans in the foreclosure was 1.22%. The share of loans in foreclosure increased since 2007, reaching 4.6% in 2010 and gradually falling to 1.88% in the third quarter of ) Using data from the American Housing Survey from 1983 to 2001, Harding et al. (2007) estimate that the annual depreciation rate of housing is roughly 2.5%. This is the value we use. 7) We target house price volatility of 10% and normalize the price of housing to one. Based on FHDA sales price data, since 1991 the standard deviation of house price growth across states fluctuates within the range 6-10% with a mean of 7.7%. For the period , Cannon et al. (2006) report a volatility of median house price returns of 14.8% across ZIP codes. 18

19 Table 3 compares the empirical targets with the model generated moments. The model can match them very well. Moreover, concerning other moments not directly targeted we obtain: 1) The share of mortgagors with nonconforming mortgages is 23.9%. In the data, nearly 25% of the mortgages originated in 2014 in the U.S. were jumbo loans. 2) The price-to-rent ratio in our benchmark equilibrium equals This value is close to the population-weighted median price-to-rent ratio for the top 30 largest cities in the US, which was 26.1 in ) In the model, the ratio of the average size of owner-occupied to rental housing is 2.6. Floetotto et al. (2015), using data from the 1999 American Housing Survey, estimate a ratio of 2.72 for the U.S. 4 Results In this section we first analyze the reaction of the lenders to removing the tax-financed guarantees. Second, we study the households portfolio and borrowing choices. Then, we analyze the aggregate and affordability implications from the removal of the guarantees. Finally, we compare the welfare changes for households in different positions on the wealth and income distributions. 4.1 Lenders The supply of mortgage credit is characterized by the price function P m (m, h, y) that satisfies equation (11). It can be decomposed into the deposit rate (lender s cost of funds) plus a mortgage spread. Figure 1 plots the mortgage spread with and without government guarantees. The spread is increasing in the debt-to-income (DTI) and the debt-to-house-value (DTV) since these variables increase the probability of default. The guarantees reduce the risk that lenders bear, thus, for the same default risk, lenders charge a lower spread. Interestingly, the difference between the spread with and without the guarantees is increasing in both DTI and DTV. That 19

20 is, the reduction in spreads is larger for riskier loans. Thus, the guarantees reduce the dispersion in the cross-sectional distribution of mortgage spreads because they reduce the spreads more for the high-risk households. Removing the guarantees will increase mortgage spreads the most for the households with highest default risk. 4.2 Households Figure 2 plots the households choices of housing (h), deposits (d ) and mortgage borrowings (m ) as a function of wealth (a) for households with income y 3 (bottom 25% of the income distribution) and with income y 4 (median income). We can classify households into four groups: 1) Renters, that is, households who do not own a house nor have a mortgage (h = m = 0). These households may have some deposits (d 0), but their income and wealth are so low that either they cannot get enough credit to buy the minimum house, or they would face large mortgage spreads and prefer to rent. Most households with low-income are renters. 2) Homeowners with mortgage credit (h m h, > 0). These households do not hold deposits (d = 0) because with recourse mortgages it is suboptimal to borrow while keeping deposits that pay less than the cost of borrowing. We refer to these households as leveraged homeowners. Both panels of Figure 2 show that housing holdings are non-monotonic in wealth for low-wealth homeowners. These households buy extra housing to borrow against it to smooth consumption. As their wealth increases and their consumption smoothing needs are smaller, these households decrease their housing and mortgage holdings. Housing holdings are bounded below by the minimum size of house. This explains why sometimes housing holdings are flat (the household would like a smaller house but it does not exist). 3) Jumbo homeowners. For incomes above the median income some households prefer to borrow non-conforming mortgages (the jumbo market) to avoid the conforming limits on DTV and mortgage size. These are high-income households with low default risk. 4) Households with housing and deposit holdings (h h, d 0) but no mortgage debt (m = 0). We refer to them as homeowners without debt. Figure 20

21 2 shows that as income and wealth increase, households move from being renters to leveraged homebuyers and finally to homebuyers without debt. Figure 3 analyzes credit outcomes for households with median labor income (y 4 ). DTV and DTI are decreasing in wealth. Thus, low-wealth households have higher default risk and mortgage spreads. Figure 3 shows that the credit risk subsidy created by the government guarantees is decreasing in wealth. 19 High-wealth households do not receive much subsidy because either their default risk is small, or they do not use conforming loans. Thus, the benefits from the government guarantees are asymmetrically distributed across households. For example, if we compute the distribution of the implicit subsidies, the bottom 5% is a subsidy of 0.98 basis points while the top 95% receives basis points. Removing the guarantees increases cross-sectional differences in mortgage spreads. In our calibration the average mortgage spread increases by 41.4% and its standard deviation by 24.8%. 4.3 Aggregate effects of removing the guarantees Table 4 summarizes the aggregate effects of removing the guarantees. There is a lower demand for credit (a reduction in the ratio of mortgage debt-to-gdp) that leads to lower deposit rates to discourage households from supplying deposits. 20 More diffi cult access to credit lowers demand for ownership, low-income households either buy less housing or decide not to buy and instead rent. Housing prices decrease and rents increase. Lower return on deposits, cheaper housing prices and higher rents encourage the high-wealth households to rebalance their portfolios from deposits towards housing. 19 We define the implicit mortgage subsidy Υ(m, h, y, I c ) as the difference between the mortgage rate of a non-conforming loan and a conforming loan given the characteristics of the loan and household, that is Υ(m, h, y, I c ) = 1 P m (m, h, y; 0) 1 P m (m, h, y; I c α). 20 We define GDP as aggregate endowment plus the value of shelter services, i.e. GDP = ȳ + P s S where S = s(x) dµ is aggregate shelter. X 21

22 On average, DTV and DTI are lower. This reduces defaults and the foreclosure rate declines by 10.3%. However, Figure 4 shows that the cross-sectional composition of leverage changes. Low and mid-income households reduce leverage while high-income households increase it. This is because the guarantees induce an increase in mortgage spreads but a reduction in deposit rates and housing prices. For example, the share of high-leveraged mortgagors of type y 3 drops by 55.13% and their mean DTV falls by 9.7%. For low and mid-income households the increase in spreads dominates and they reduce leverage when the guarantees are removed. In addition, some low-income households react along the extensive margin and cut their leverage to zero by becoming renters with no mortgage debt. However, for high-income households the reduction in deposit rates and housing prices dominate the increase in spreads. Their mortgage rates decrease and they increase leverage. 4.4 Changes in housing affordability One of the main justifications for the mortgage guarantees is that they may increase housing affordability (Glaeser and Gyourko 2008 or Levitin and Wachter 2013 for example). Here we construct an affordability index inspired by the popular Housing Affordability Index computed by the National Association of Realtors (NAR). 21 That index measures whether a typical household earns enough income to qualify for a mortgage loan on a typical home. Our innovation is to compute the index across the income and wealth distributions. Then we compare how the index changes when the guarantees are removed. To construct our index we follow the NAR index and assume that all households want (ĥ) to buy a house of median size and finance the purchase with a mortgage with a 20% downpayment. We allow the households to be heterogenous in income and wealth. 22 This To infer the wealth associated with an income level we use the stationary distribution of income and wealth. Since the composition of wealth matters for mortgage pricing (housing is risky, deposits are safe) we assume that all households own the median house but input heterogeneous deposits to match the wealth heterogeneity associated with each income in the stationary distribution. For the expression of the mortgage pricing function with deposits d, see the Online Appendix. 22

23 heterogeneity translates into different mortgage rates although we impose all households to borrow the same amount: P m (a, y) m (a, y) = 0.8P h ĥ. Therefore, the mortgage interest payments are [1 P m (a, y)] m (a, y) and are heterogeneous across households. The NAR index is household s income over mortgage interest and principal payments. We compute our index as household s expected income given the current income level over mortgage interest and expected depreciation payments. Like the NAR, we divide income by 4 to normalize the index to 100 for those households spending 25 percent of their income on housing costs: E [y y] /4 Ω(a, y) = 100 [1 P m (a, y)] m (a, y) + P h E [δ ] ĥ. Our goal with the Affordability Index is to measure how changes in prices and mortgage rates affect the ability to pay for a given basket of housing bought using mortgage credit. Increases in the index means that housing is more affordable. Households need less income to consume the same housing. The top panel of Figure 5 shows that when the guarantees are removed the high-wealth households increase their affordability while low-wealth households see their affordability reduced. This is because for low-wealth households the increase in mortgage spreads dominates the lower house prices and the downward pressure in mortgage rates from lower deposit rates. The bottom panel of Figure 5 shows the same result for income. The removal of the guarantees implies less affordability for low-income households while more for high-income households. 4.5 Distributional implications of removing the guarantees Without the guarantees, the distribution of wealth becomes more dispersed, as reflected by an increase of 2.19% in the Gini Index reported in Table 4. Figure 6 plots the stationary 23

24 distribution of wealth in both cases. It suggests that the increase in wealth inequality is due to an increase in the mass of low-wealth households who after the removal of the guarantees do not qualify for credit. These households spend more now in housing rents and their savings and wealth are lower. With the guarantees they received the housing services from homeownership and by repaying the mortgage they built wealth. To analyze the welfare consequences of the policy change we compute the Consumption Equivalent Variation (CEV), ω(a, y), of moving from the steady state of an economy with guarantees to the steady state of an economy without guarantees. That is, the change in perperiod numeraire consumption (c) such that a household is indifferent when moving from an economy with guarantees to one without guarantees. 23 Formally, for each state (a, y) we solve for ω(a, y) such that [ E 0 β t u ( ) ] [ ] (1 + ω(a, y))c t, s t x0 = (a, y) = E 0 β t u(c N t, s N t ) x 0 = (a, y), (22) t=0 t=0 where the superscript N refers to the economy with no guarantees. 24 If ω(a, y) > 0 the household has higher utility when the guarantees are removed, that is, she must be compensated in terms of numeraire consumption to live in the economy with guarantees. Figure 7 plots the CEV as a function of wealth for different levels of income. There is significant heterogeneity on the welfare assessment over both dimensions (a, y). Low-income households (y {y 1, y 2 }) prefer to be in the economy with guarantees. Almost all of these households are renters with deposits. They are worse-off when the guarantees are removed because rental prices rise and the return on deposits falls. 23 Given that in our model there is no physical capital and the supply of housing is fixed, the transition towards the new steady state happens in a few periods. Thus, the welfare gains of the transition path should be very similar to the steady state welfare gains. 24 Given the preferences that we use the CEV has an analytical solution in terms of the value functions: ω(a, y) = [ V N ] 1 η(1 σ) (a, y) 1. V (a, y) 24

25 The welfare consequences for mid-income (y {y 3, y 4, y 5 }) households are highly nonmonotone in wealth. Low-wealth households are renters with deposits and suffer welfare losses from higher rents and lower deposit rates. Welfare losses become much larger for mid-income households with mid or high-wealth because these households are high-leverage homeowners (DTV above median DTV). Their mortgage spreads increase the most and their welfare loss can be as high as 0.47% of CEV for the median income y 4. The welfare losses decrease as wealth increases since households have less leverage and thus benefit less from the subsidy generated by the guarantees. In fact, losses turn into gains when wealth is high enough such that spreads are low and mortgage rates decrease because of lower deposit rates. This benefit is not shared by the wealthiest mid-income households who do not have debt. In fact, the mid-income households with more wealth may experience welfare losses with the policy change because of lower deposit rates. High-income households (y {y 6, y 7 }) benefit the most from the policy change. They can gain as much as 0.45% of CEV. These low-risk mortgagors receive the least amount of implicit subsidy and benefit from the decrease in the deposit rate, the reduction of taxes, and cheaper house prices. As wealth increases and these households start investing in deposits, they lose from the removal of the guarantees since the return of their deposits decreases. To better illustrate the previous effects, Table 5 reports the mean CEV with households classified by housing tenure, leverage, and labor income. The table highlights that the gains and losses from the policy are unevenly distributed. The main winners from the removal are the high-income mortgagors. The main losers are the mid-income high-leverage mortgagors and the renters. Reforming the housing finance system has been in the policy agenda for several years but all proposals have so far failed. Tables 6 and 7 suggest an explanation. The share of households in favor and opposed to the removal are very close. Table 7 shows the share of the population in each of the classifications we used in Table 5. Then Table 6 reports the percentage of each group 25