Mortgage Market Institutions and Housing Market Outcomes Edward Kung UCLA May 2th, 215 Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 1 / 51
Introduction General framework for studying interactions between housing and mortgage markets Focal points of model: Institutional features of mortgage market, including long-term mortgage contracts Equilibrium relationship between housing demand and mortgage credit availability Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 2 / 51
Model Overview Housing demand Demand generated by incoming buyers Buyers have limited wealth Whether to buy a home / type of home affected by mortgage availability Housing supply Supply comes from existing owners who move Movers can either sell house or default In either case, a unit of supply is added to housing market House prices adjust so that housing market clears Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 3 / 51
Model Overview Lenders Risk neutral and competitive lenders Mortgage interest rate set so that expected return = opportunity cost of funds Because of default risk, interest rate depends on house price expectations and leverage ratio Equilibrium when all contracts earn zero net return over opportunity cost Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 4 / 51
Results Overview Model calibrated to data from Los Angeles, 23-21 Many salient features of the data are captured Counterfactuals studied: Impact of disappearing market for non-agency mortgages Figure Effectiveness of government responses Introducing shared appreciation mortgages General equilibrium effects are shown to be important Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 5 / 51
Related Literature Models of the housing and mortgage markets Ortalo-Magne and Rady (26); Campbell and Cocco (214); Favilukis et. al. (215); Landvoigt et. al. (215); Corbae and Quintin (215); Guren and McQuade (215) Empirical literature on interactions between housing and mortgages Himmelberg et. al. (25); Glaeser et. al. (21); Ferreira and Gyourko (211); Mian and Sufi (29); Favara and Imbs (215); Adelino et. al. (214); Kung (215); Hurst et. al. (215) Mortgage design Caplin et. al. (27); Shiller (28); Piskorski and Tchistyi (21); Mian and Sufi (214) Collateral equilibrium Kiyotaki and Moore (1997); Geanakoplos (1996); Geanakoplos and Zame (214) Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 6 / 51
Model (Preliminaries) Discrete time Housing market with two types of housing h =, 1 (vertical quality) Fixed stock µ of each type Price in state s t : p h (s t ) Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 7 / 51
Model (Mortgages) M mortgage types, including m = (no mortgage) Mortgage characterized by z t = (age t, rate t, balance t ) Type determines how z t evolves over time and translates to payments; also determines how much the lender can recover in a default Interest rate on new mortgage origination of type m collateralized by house type h: r m h (b, x it, s t ) Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 8 / 51
Model (Homeowners) Owns / occupies one housing unit Lives in housing unit until moving shock; λ probability each period Moving is terminal state; movers do not re-enter housing market Discussion Homeowners care about: Flow consumption of a numeraire good: u ( θ h c t ) Final wealth at the time of a move: βu (wt ) Homeowners have constant income; can save at risk-free rate rfr t but cannot borrow (except through mortgages) Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 9 / 51
Homeowner decision problem... Last period Enters Period λ Moves Sell w T = y i + w it + p h(s t) b it 1 λ Default w T = y i + w it c D Doesn t Move No refinance Consumption / savings Next period... Refinance Consumption / savings Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 1 / 51
Homeowner Bellman equation Homeowner that stays solves: V stay it = max u ( θ h c ) + δe [ (1 λ) V stay it+1 ] move + λvit+1 subject to: c + 1 1 + rfr t w = { y i + w it pay it y i + w it b it + b pay it c R if no refinance if refinance Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 11 / 51
Potential buyers Buyers are heterogeneous on income y i, initial wealth w i, and outside option v i Present value to buying house type h: V buy h (y i, w i, s t ) = max u ( θ h c ) + δe [ (1 λ) V stay it+1 ] move + λvit+1 subject to: c + 1 1 + rfr t w = y i + w i p h (s t ) + b pay it Buy house type h if: V buy h { } = max V buy, V buy 1, v i Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 12 / 51
Housing demand Housing demand is the integral of individual buyers demands: ˆ ˆ ˆ D h (s t ) = d h (y, w, v; s t ) Γ (y, w, v; s t ) dydwdv y w v Housing market clearing condition: D h (s t ) = λµ for h =, 1 Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 13 / 51
Lenders Lenders correctly anticipate homeowners default and refinance rules Π move it = τ it ψh m (z it, s t ) + (1 τ it ) b it Π stay it = ρ it b it + (1 ρ it ) Π norefi it Π norefi it = pay it + ( 1 1 + rfr t + a m ) E [ λπ move it+1 + (1 λ) Π stay ] it+1 a m is the opportunity cost of funds Can differ by mortgage type to reflect higher liquidity in agency market May be higher than rfrt to reflect better investment opportunities available to lenders than borrowers Mortgage market clearing condition: Π norefi it aget= b = Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 14 / 51
Equilibrium Equilibrium solved via fixed point iteration on three nests Equilibrium objects to solve for: ph (s t) the price of housing in each state (outer nest) r m h (b, x it, s t) the mortgage interest rate menu (middle nest) V stay, Π stay (inner nest) Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 15 / 51
Implementation (Mortgage Types) Two mortgage types: agency and non-agency: Table: Differences in agency and non-agency Agency Lender recovers full loan amount on default Non-Agency Lender recovers φ of collateral value on default Cost of funds a 1 Cost of funds a 2 Cannot exceed 8% of collateral value Payment cannot exceed 5% of income Cannot exceed 1% of collateral value Payment cannot exceed 5% of income Cannot exceed cll t Unavailable if mps t = Contracts are 3-year fixed-rate mortgages Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 16 / 51
Other Implementation Notes Aggregate state variables: risk-free rate conforming loan limit availability of non-agency mortgages unobserved demand shock expected growth or decline of demand shock Ruthless default and no refinancing No savings Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 17 / 51
Calibration Notes Choose parameters to simultaneously fit moments in the data Ownership durations identify λ Price paths identify vt and θ Mortgage interest rates identify a and ϕ Average LTVs identify parameters governing wealth distribution and β Growth of demand shocks identified by requiring consistency between guessed and implied parameters Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 18 / 51
Figure: Model Fit: House Prices 1.9 Low Valued House Price (Simulated) High Valued House Price (Simulated) Low Valued House Price (Data) High Valued House Price (Data).8.7 Price ($millions).6.5.4.3.2 23 24 25 26 27 28 29 21
Table: Model Fit: LTVs of Home Buyers Real Data Simulated Data Year Low-Valued High-Valued Low-Valued High-Valued 23.844.756.882.794 24.849.76.884.816 25.857.76.867.873 26.884.779.82.837 27.842.723.795.86 28.755.617.726.661 29.725.68.698.629 21.723.598.698.629
Figure: Model Fit: Cumulative Default Rates Cumulative Default Rate.1.8.6.4.2 CDR (Simulated) CDR (Data) 24 Cohort Cumulative Default Rate.2.15.1.5 CDR (Simulated) CDR (Data) 25 Cohort 22 24 26 28 21 22 24 26 28 21 Cumulative Default Rate.35.3.25.2.15.1.5 CDR (Simulated) CDR (Data) 26 Cohort Cumulative Default Rate.14.12.1.8.6.4.2 CDR (Simulated) CDR (Data) 27 Cohort 22 24 26 28 21 22 24 26 28 21
Figure: Buyer Value Functions in 27 (Baseline) Low Income Buyers High Income Buyers.4 Low valued housing High valued housing.4 Low valued housing High valued housing.35.35.3.3 Outside Option.25.2 Outside Option.25.2.15.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
Figure: Housing Demand Profile in 27 (Baseline) Low Income Buyers High Income Buyers.4 Low valued housing High valued housing.4 Low valued housing High valued housing.35.35.3.3 Outside Option.25.2 Outside Option.25.2.15.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
Figure: Buyer Value Functions in 28 (Baseline) Low Income Buyers High Income Buyers Low valued housing High valued housing Low valued housing High valued housing.25.25.2.2 Outside Option.15 Outside Option.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
Figure: Housing Demand Profile in 28 (Baseline) Low Income Buyers High Income Buyers Low valued housing High valued housing Low valued housing High valued housing.25.25.2.2 Outside Option.15 Outside Option.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
Figure: Mortgage Demand Profile in 27 (Baseline) Low Income Buyers High Income Buyers.4 No mtg Agency Non Agency.4 No mtg Agency Non Agency.35.35.3.3 Outside Option.25.2 Outside Option.25.2.15.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
Figure: Mortgage Demand Profile in 28 (Baseline) Low Income Buyers High Income Buyers No mtg Agency No mtg Agency.25.25.2.2 Outside Option.15 Outside Option.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
The Impact of Non-Agency Availability In the baseline, non-agency loans disappear in 28 Low wealth buyers are priced out of the housing market What if non-agency loans were made available in 28? Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 28 / 51
Figure: House Prices of Non-Agency Available 28+ 1.9 Low Valued House Price (Counterfactual) High Valued House Price (Counterfactual) Low Valued House Price (Baseline) High Valued House Price (Baseline).8.7 Price ($millions).6.5.4.3.2 23 24 25 26 27 28 29 21
Figure: Housing Demand Profile in 28 (Counterfactual) Low Income Buyers High Income Buyers Low valued housing High valued housing Low valued housing High valued housing.25.25.2.2 Outside Option.15 Outside Option.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
Figure: Mortgage Demand Profile in 28 (Counterfactual) Low Income Buyers High Income Buyers No mtg Agency Non Agency Agency Non Agency.25.25.2.2 Outside Option.15 Outside Option.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
Figure: Mortgage Rates in 28 (Counterfactual) Low Valued Housing High Valued Housing.1 Non Agency Agency.1 Non Agency Agency.9.9.8.8.7.7.6.6 Rate.5 Rate.5.4.4.3.3.2.2.1.1.2.4.6.8 1 LTV.2.4.6.8 1 LTV
Figure: Mortgage Rates in 28 (Baseline) Low Valued Housing High Valued Housing.1 Non Agency Agency.1 Non Agency Agency.9.9.8.8.7.7.6.6 Rate.5 Rate.5.4.4.3.3.2.2.1.1.2.4.6.8 1 LTV.2.4.6.8 1 LTV
Figure: Sensitivity of Prices to Demand Shocks.7 Low Valued Housing Non Agency Available Non Agency Unavailable 1 High Valued Housing Non Agency Available Non Agency Unavailable.6.9.5.8.7.4 Price Price.6.3.5.2.4.1.3.2.4.6.8 v.2.2.4.6.8 v
Figure: Effectiveness of Government Response 1.9 Low Valued House Price (Counterfactual) High Valued House Price (Counterfactual) Low Valued House Price (Baseline) High Valued House Price (Baseline).8.7 Price ($millions).6.5.4.3.2 23 24 25 26 27 28 29 21
Takeaways Availability of non-agency financing is an important driver of housing demand and house prices High leverage loans can reduce house-price volatility Allows more households with inelastic housing demand to afford homes Government policy was effective in manipulating house prices Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 36 / 51
Introducing Shared Appreciation Mortgages Introduce two types of shared-appreciation mortgages from 23 to 27 as a non-agency option FSAM: indexed to house prices on both up and downside PSAM: indexed to house prices on only downside Payments and balances go up or down proportionally with house prices Homeowners are never underwater Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 37 / 51
Figure: House Prices if PSAMs Available 23-27 1.9 Low Valued House Price (Counterfactual) High Valued House Price (Counterfactual) Low Valued House Price (Baseline) High Valued House Price (Baseline).8.7 Price ($millions).6.5.4.3.2 23 24 25 26 27 28 29 21
Figure: Mortgage Demand Profile in 25 (PSAMs Available).5.45 Low Income Buyers No mtg Agency Non Agency SAM.5.45 High Income Buyers No mtg Agency Non Agency.4.4.35.35 Outside Option.3.25.2 Outside Option.3.25.2.15.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
Figure: Interest Rates in 25 (PSAMs Available) Low Valued Housing High Valued Housing.1 SAM Non Agency Agency.1 SAM Non Agency Agency.9.9.8.8.7.7.6.6 Rate.5 Rate.5.4.4.3.3.2.2.1.1.2.4.6.8 1 LTV.2.4.6.8 1 LTV
Figure: Mortgage Demand Profile in 27 (PSAMs Available) Low Income Buyers High Income Buyers.4 No mtg Agency Non Agency.4 No mtg Agency Non Agency.35.35.3.3 Outside Option.25.2 Outside Option.25.2.15.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
Figure: Interest Rates in 25 (PSAMs Available) Low Valued Housing High Valued Housing.1 SAM Non Agency Agency.1 SAM Non Agency Agency.9.9.8.8.7.7.6.6 Rate.5 Rate.5.4.4.3.3.2.2.1.1.2.4.6.8 1 LTV.2.4.6.8 1 LTV
Figure: Cumulative Default Rates (PSAMs Available) Cumulative Default Rate.8.6.4.2 24 Cohort CDR (Counterfactual) CDR (Baseline) Cumulative Default Rate.14.12.1.8.6.4.2 25 Cohort CDR (Counterfactual) CDR (Baseline) 22 24 26 28 21 22 24 26 28 21 Cumulative Default Rate.35.3.25.2.15.1.5 26 Cohort CDR (Counterfactual) CDR (Baseline) Cumulative Default Rate.14.12.1.8.6.4.2 27 Cohort CDR (Counterfactual) CDR (Baseline) 22 24 26 28 21 22 24 26 28 21
Figure: House Prices if FSAMs Available 23-27 1.9 Low Valued House Price (Counterfactual) High Valued House Price (Counterfactual) Low Valued House Price (Baseline) High Valued House Price (Baseline).8.7 Price ($millions).6.5.4.3.2 23 24 25 26 27 28 29 21
Figure: Mortgage Demand Profile in 25 (FSAMs Available).5.45 Low Income Buyers No mtg Agency SAM.5.45 High Income Buyers No mtg Agency SAM.4.4.35.35 Outside Option.3.25.2 Outside Option.3.25.2.15.15.1.1.5.5.2.4.6.8 1 Initial Wealth.2.4.6.8 1 Initial Wealth
Figure: Interest Rates in 25 (FSAMs Available) Low Valued Housing High Valued Housing.1 SAM Non Agency Agency.1 SAM Non Agency Agency.9.9.8.8.7.7.6.6 Rate.5 Rate.5.4.4.3.3.2.2.1.1.2.4.6.8 1 LTV.2.4.6.8 1 LTV
Figure: Cumulative Default Rates (FSAMs Available) Cumulative Default Rate.8.6.4.2 24 Cohort CDR (Counterfactual) CDR (Baseline) Cumulative Default Rate.14.12.1.8.6.4.2 25 Cohort CDR (Counterfactual) CDR (Baseline) 22 24 26 28 21 22 24 26 28 21 Cumulative Default Rate.25.2.15.1.5 26 Cohort CDR (Counterfactual) CDR (Baseline) Cumulative Default Rate.2.15.1.5 27 Cohort CDR (Counterfactual) CDR (Baseline) 22 24 26 28 21 22 24 26 28 21
Takeaways SAMs can be welfare-enhancing Uptake can be positive even if they don t receive the liquidity benefits of the GSEs Uptake depends on expectations on house-price growth, contract design Defaults can go up if not everyone chooses a SAM Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 48 / 51
Figure: Agency and Non-Agency MBS Issuance (USD Billions) 2,5 2, 1,5 1, 5 1994 1996 1998 2 22 24 26 28 21 212 214 Agency MBS Non-Agency RMBS Back
Age profile of house value 25 homeowners Log(Housing Value) 11.8 12 12.2 12.4 12.6 3 4 5 6 7 Age High-school or less College or more Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 5 / 51
Evidence on within-market movers log house_value i = β + β 1 moved_from_within i + β 2 moved_from_outside i + X i β 3 + ɛ i (1) (2) (3) All ages Age<45 Age 45 Moved from within.47*.458*** -.488*** (.26) (.32) (.41) Moved from outside.15***.561*** -.379*** (.27) (.34) (.41) N 2,439,293 685,58 1,753,713 Back Edward Kung (UCLA) Mortgage Market Institutions May 2th, 215 51 / 51