Leverage and the Foreclosure Crisis

Transcription

1 Leverage and the Foreclosure Crisis Dean Corbae and Erwan Quintin University of Wisconsin - Madison April 16, / 69

2 Motivation Until 1998, there was a long period where real house prices were relatively constant and the fraction of low downpayment loans in the stock of loans was low. From 1999 to the end of 2006, house prices boomed and the fraction of low downpayment loans rose dramatically. From 2007, house prices fell back to their pre-boom levels and foreclosure rates more than doubled. Question: How much did changes in the composition of mortgages with respect to leverage contribute to the foreclosure boom? 2 / 69

3 Purchase Loans with CLTV 97% as a fraction of all loans 40.00% 35.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% Source: Pinto, E. (2010) Government Housing Policies in the Lead-up to the Financial Crisis: A Forensic Study, mimeo. Definition 3 / 69

4 The Housing Boom and Bust Real Home Price Index (left axis) Foreclosure starts (right axis) Sources: Case Shiller, National Delinquency Survey (Mortgage Bankers Association). Quarterly foreclosure rates are the fraction of all loans that enter the foreclosure process in a given quarter. Definition 4 / 69

5 A model of housing Heterogeneous agents choose to own or rent, how to finance house purchases, and how to terminate mortgage contracts Mortgage holders may default because: 1. their home equity is negative 2. making the payment reduces nondurable consumption too much Mortgage terms reflect default risk, hence vary with initial income/asset position, as well as loan size priced in competitive market. Changes in house price and approval standards induce important variation in contract selection and the pool of risky borrowers. 5 / 69

6 Quantitative experiment Stage 1: Long period of normal aggregate house prices and mortgage approval standards (pre-1998); Stage 2: House price boom and relaxed approval standards ( ); Stage 3: House price bust (post-2007). All parameters are estimated to match pre-1998 moments only. Our model predicts a 275% rise in foreclosures (256% in post-2007 data). In a counterfactual where approval standards are not relaxed, the same price shock accounts for a 105% increase in foreclosures. Thus, changes in approval standards can account for 62% of the rise in foreclosures. 6 / 69

7 Some Literature 1. Empirical: Gerardi et. al. (2009): Documents that subprime loans have high CLTV Negative net equity is in general necessary but not sufficient for foreclosure. More on empirical approaches 2. Structural: Campbell and Cocco (2013) - Mortgage decision problem with multiple sources of uncertainty (e.g. earnings, house prices, etc.) and default but no contract selection. Chatterjee and Eyigungor (2013) - Endogenize house prices in presence of default so can determine feedback effects. Mitman (2011) - Interaction of recourse and bankruptcy policies with short term mortgages. 7 / 69

8 a) Environment Outline b) Decision Problems and Mortgage Pricing c) Parameterization and Cross-section tests d) Long Run Results Contract Selection Default Hazards across Contracts Distribution of Interest Rates e) Boom-Bust Transition Results f) Policy: Recourse 8 / 69

9 Environment Time is discrete and infinite. Continuum of agents. Young agents become mid-aged with probability ρ M, mid-aged agents become old with probability ρ O, old agents die with probability ρ D. Young or mid-aged agents earn stochastic income y t drawn from a n-state {y η 1..., y η n } Markov process with transition matrix P η where η {Y, M}. Old agents earn y O with certainty. Agents are born with no assets and with an income level drawn from P Y. 9 / 69

10 Agents value consumption and housing services according to: E 0 β t u (c t, h t ) t=0 where c t 0, h t {h 1, h 2, h 3 }, and u(c, h) log c + log[h θ(h)] with θ(h 3 ) = θ(h 2 ) > 1 = θ(h 1 ) so that homeowners h t {h 2, h 3 } enjoy a proportional utility premium θ over renters h t = h 1. Agents can save at gross rate 1 + r in youth and mid-age, and in annuities that pay off (1 + r)/(1 ρ D ) in old age if alive. 10 / 69

11 Housing Agents can rent quantity h 1 of housing capital at rate R t. When agents become mid-aged they can purchase a house for unit price q t where h 3 > h 2 > h 1. House prices follow an exogenous Markov process q t {q L, q N, q H } with transition matrix P q. Homeowners face uninsurable idiosyncratic shocks (e.g. neighborhood effects) to the value of the house that follow a Markov process ɛ t {ɛ b, 1, ɛ g } with transition matrix P ɛ. Housing capital depreciates at rate δ. Agents can sell/foreclose on their house in any period, but are then constrained to be renters for at least one period then receive exogenous option to buy with prob γ. When agents turn old, they must move from their house. 11 / 69

12 Financial Intermediary Stores deposits at rate r 0, issues mortgages, and rebundles existing housing for new rentals and purchases in competitive markets. Mortgages carry administrative cost φ. Intermediary loses fraction χ > 0 of principal in event of default. 12 / 69

13 Mortgages A hh who wants to buy a house of size h t at price q t finances it with a fixed rate mortgage of maturity T with downpayment fraction (leverage choice) ν t {LD, HD}. The mortgage contract stipulates an interest rate r ν t (a t, y t, h t ; q t, α t ) that depends on (at time of origination t): household wealth and income characteristics, house size, downpayment, purchase price, mortgage approval standards α. Mortgage payment function Approval standards: PTI requirement m ν t y t α t (1) 13 / 69

14 Mortgage Termination Households can terminate a mortgage: 1. House Sale. Yields q t+n ɛ t+n h t b ν t,n. 2. Default. Evicted at the end of the period. Intermediary collects Defaulting household receives min{(1 χ)q t+n ɛ t+n h t, b ν t,n} max{(1 χ)q t+n ɛ t+n h t b ν t,n, 0} When homeowners become old and must move, if they have positive (negative) equity it is counted as a sale (foreclosure). 14 / 69

15 1. Youth: Timing Receive age shock and signal of income realization. Make savings decision. 2. Middle-age: 3. Old: Receive age shock and signal of income realization. New mid-aged agents make home-buying and mortgage choice decision. Existing homeowners may receive a depreciation shock and decide whether to default or sell. Make mortgage or rental payments as well as savings decisions. Newly old agents move from house (sale or foreclosure). Receive death shock or income. Make (dis)saving decision. 15 / 69

16 Fixed point of the mapping: Mortgage Market Equilibrium 1. Given prices (including r ν t (a t, y t, h t ; q t, α t )), hh policy functions (savings, house purchases/sales, contract choice (ν t K(a t, y t, h t ; q t, α t )), and default) are optimal across all states. 2. Given hh policy functions, pricing menus rt ν (a t, y t, h t ; q t, α t ) earn zero profits: For each ν t K(a t, y t, h t ; q t, α t ), rt ν (a t, y t, h t ; q t, α t ) is such that W0 ν(a t, y t, h t ; q t, α t ) (1 ν t )q t h t = 0 (i.e. EPDV of mortgage payments equals principal using household optimal default decisions). IP 3. The distributions of household states evolve consistent with shock processes and agent decisions. Dist 16 / 69

17 Parameterization One period = 2 years, T = 15 so consider 30 yr. fixed mortgages. 3 state markov process for aggregate house prices is chosen to match real Case-Shiller index from 1890-present (support is q N (0.7, 1, 1.45)). Graph Markov process for rental rates chosen to match Davis et. al. (2008) calculations. Stochastic process for idiosyncratic housing price shocks is chosen within the model. Informative moments are st. dev. of reported capital gains on homes purchased in 1996 or 1997 from SCF by households whose head is between 35 and 59 years old, the rate of mortgage terminations caused by default prior to / 69

18 Income process From the PSID 1997 and 1999 Split households into quartiles and age groups (21-34 for young, for middle-aged). Transition matrix for each age group calibrated to match mobility patterns across quartiles between 1997 and The incomes of mid-aged agents y M {0.2097, , , } with the median normalized to 1. The transition matrix is [ ] The incomes of young agents y Y {0.1478, , , } with transition matrix ] [ / 69

19 Parameters set independently ρ M Fraction of young agents 1/7 who become mid-aged ρ O Fraction of mid-aged agents 1/12 who become old ρ D Fraction of old agents 1/10 who die r Storage return 8% δ Maintenance rate 5% ν HD High downpayment 20% T Mortgage maturity 15 q L N Low home value level 0.7 q H q N High home value level / 69

20 Parameters set jointly θ Owner-occupied premium (0.386) β Discount rate (0.007) α N (= α L ) PTI level in normal (low) state (0.099) φ Mortgage service cost (0.025) χ Foreclosing costs (0.021) h 1 Size of rental unit (N.A.) h 2 Size of small house (0.035) h 3 Size of large house (0.063) λ Home-value shock probability (0.201) ɛ Size of home value shock (0.000) q N Normal home value level (0.000) 20 / 69

21 Targeted moments Pre-98 Pre-98 Long-term data benchmark moments Home-ownership rate (0.061) Ex-housing asset to income ratio (0.023) Housing expenditure share (0.001) Rent to income ratio (0.001) Homeowner housing share (0.020) Interest rate on HD loans (0.004) Foreclosure rate (0.007) Foreclosure discount (0.052) Recovery rate (0.025) Fraction of LD loans (0.082) Standard error of 2-year capital gains (0.000) 21 / 69

22 Untargeted Cross-Sectional Statistics (2007) LTY High-LTV Data Model Data Model Income Below median (0.06) (0.01) Above median (0.02) (0.01) Asset-to-income Below median (0.04) (0.02) Above median (0.04) (0.01) Age Below (0.04) (0.02) Above (0.04) (0.01) Loan size Below median (0.03) (0.01) Above median (0.04) (0.01) SCF1998 SCF / 69

23 Summary of Untargeted Cross-Sectional Statistics Matches patterns of data from SCF pretty well: LTY falls with income high LTV at bottom of asset distribution 23 / 69

24 Young agents problem State: ω = (a, y) [ V Y (a, y; q) = max u(c, h 1 (1 ρm )V ) + βe Y (a, y ; q ) y c 0,a,q y,q 0 ρ M V M (a, y, n = 0; q ) s.t. c + a = y + a(1 + r) R(q)h 1 ] Mid-aged agents contract choice problem Mid-aged agents default decision problem 24 / 69

25 Endog. Distn. of assets upon entering mid-age Pre 98 benchmark ŷ = y 1 ŷ = y 2 ŷ = y 3 ŷ = y Initial assets (â) Long boom ŷ = y 1 ŷ = y 2 ŷ = y 3 ŷ = y Initial assets (â) Correlation of income and wealth. 25 / 69

26 Selection: Contract type by assets and income Rent LD loan HD loan h 1 h 2 h 3 h 2 h 3 y 1 all a q N y 2 a 0 < a 0 - y 3 - a 0 < a 0 y a 0 < a 0 y 1 a 0 < a 0 < a 0 q H y 2 a 0 < a 0 < a 0 < a 0 y a 0 < a 0 y a 0 < a 0 In normal times, low income and low asset hhs rent while with relaxed approval standards many select small houses and middle class buys bigger houses with LD loans in boom times. 26 / 69

27 Default hazard rates by contract type Pre 1998 hazard rates HD loans LD loans Mortgage age (n) Long boom hazard rates HD loans LD loans Mortgage age (n) Construct hazard rate (fraction of terminations due to default conditional on staying in the home up to date n) from a pseudopanel of 50,000 mortgages drawn from long run distribution of our model economy. Default hazards are uniformly higher for LDs than for HDs due to selection and slower equity accumulation. High-leverage mortgages are not much riskier than HD loans in the pre-boom economy because selection effects are muted by tight approval standards. 27 / 69

28 Default by type Fraction of all defaults Average equity at default Income Moving Neither Income Moving Neither Pre-98 LD loan 17.32% 77.92% 4.76% -5.15% % -5.19% HD loan 9.63% 90.37% 0.00% 6.67% -9.03% N.A. Boom LD loan 62.23% 14.80% 22.93% % % % HD loan 28.85% 71.15% 0.00% % % N.A. Bust LD loan 44.65% 37.85% 17.49% % % % HD loan 27.75% 68.85% 0.00% % % N.A. Income shocks and neither (strategic default to smooth consumption) more important in boom and bust times. Almost all default involves negative equity (one exception happens for low wealth agents who live rent free one period). move cal 28 / 69

29 Determinants of foreclosure 94% of defaults involve negative equity. However, 91% of agents with negative equity choose to continue meeting payments. Thus, negative equity alone is not sufficient for foreclosure in our model. Default occurs with another event like a negative income shock. 29 / 69

30 Interest rate offerings HD interest rate schedule for ĥ3 ŷ = y 1 ŷ = y 2 ŷ = y 3 ŷ = y HD interest rate schedule for ĥ2 ŷ = y 1 ŷ = y 2 ŷ = y 3 ŷ = y Initial assets (â) Initial assets (â) LD interest rate schedule for ĥ3 ŷ = y 1 ŷ = y 2 ŷ = y 3 ŷ = y LD interest rate schedule for ĥ2 ŷ = y 1 ŷ = y 2 ŷ = y 3 ŷ = y Initial assets (â) Initial assets (â) Truncated Rates 30 / 69

31 Equilibrium distribution of interest rates Distribution of interest rates during normal times HD LD Distribution of interest rates during long boom times HD LD Define a high-priced (subprime) loan as one which is 300 basis points above a prime (best-priced) loan. Model makes 2 predictions: coefficient of variation of mortgage rates rise during booms and the fraction of high priced or subprime loans should increase as well, both consistent with data. 31 / 69

32 Main experiment Stage 1: Long period of normal aggregate house prices and mortgage approval standards (pre-1998); Stage 2: House price boom and relaxed approval standards ( ); Stage 3: House price bust (post-2006). 32 / 69

33 The boom-bust home-ownership rates fraction of LD loans 0.3 model model data data % of originations Pre Pre fraction of high-priced loans default rate model model 0.14 MBA subprime count data 0.05 data % of mortgage stock % of mortgage stock Pre Pre / 69

34 Selection Overall default rate D t = ξt LD Dt LD + ξt HD Dt HD where ξt ν is the share of loans of type ν {HD, LD} in the stock in period t while Dt ν is the default rate on those loans. Changes in the pool of borrowers (i.e. (ξ ν t )) and changes in default rates of that pool (i.e. (D ν t )) matter for changes in the overall default rate. 34 / 69

35 Selection - Default rates by Borrower Type pre-1998 LD loans HD loans All loans Fraction of stock (ξt ν ) Default rate (Dt ν ) First period of the crisis Fraction of stock Default rate Incumbents Fraction of stock Default rate Switchers Fraction of stock Default rate N.A New-entrants Fraction of stock Default rate / 69

36 Selection - Summary Almost 10% of LD holders in first period of crisis are entrants (hhs who took an LD loan during the boom and would have been renters in the pre-98 benchmark). They default at nearly 9 times the pace of LD incumbents ( hhs who opted for an LD loan pre-98). Roughly 32% of LD holders at the onset of the crisis are loan-type switchers (hhs who would have opted for an HD loan pre-98). These loan-type switchers default at a 40% higher pace than incumbents do when the crisis strikes. 36 / 69

37 Leverage counterfactuals home-ownership rates model counterfactual fraction of LD loans % of originations Pre Pre fraction of high-priced loans 0.06 default rate % of mortgage stock % of mortgage stock Pre Pre When approval standards are not relaxed, during transition homeownership falls, very few high leverage and subprime loans, foreclosure rate 62% lower. 37 / 69

38 Summary of transition results Data Model Counterfactual Frac of LDs in last period of boom 25% 25% 8.0% Increase in foreclosure rate (pre-98 to peak) 256% 275% 105% In transition, nontargetted model LD originations match data and foreclosure rates within 7% of data In the counterfactual where the PTI requirement remains the same in the boom as during normal times, the rise in the foreclosure rate is only 38% higher than normal times. Thus, the relaxation of approval standards with the same price shock can explain 62% of the rise in foreclosures. bound 38 / 69

39 Other Experiments Income Shocks (prolong foreclosure crisis with an unanticipated decrease in earnings distribution chosen to match estimates by Saez (2013)) Income experiment Lower financing costs (we decrease risk free rate and loan service costs to match values, requiring a change in homeownership premium to match pre-crisis values, but still the change in approval standards explains about 50% of the rise in foreclosures) Income experiment 39 / 69

40 Policy: recourse imposes harsher punishment Anti-deficiency (Non-recourse) laws: borrower is not responsible for any deficiency. Banks cannot attach to the household s assets. Some states have them (AZ,CA,FL... ), others don t. What if all states had recourse? Intermediary Hhs Non-recourse min{(1 χ)qh, b} a + max{(1 χ)qh b, 0} Recourse min{(1 χ)qh + a, b} max{(1 χ)qh + a b, 0} Harsher punishment lowers extensive default margin. Higher repayment lowers intensive loss incidence. 40 / 69

41 Long Run Role of Recourse Moments Benchmark Recourse Home-ownership rate Interest rate on HD loans Interest rate on LD loans Foreclosure discount Recovery rate Fraction of LD loans Foreclosure rate Foreclosure rates are 4.2% lower and HO rates are 16.8% higher with recourse (due to lower interest rates). Ghent and Kudlyak (2009) estimate that at average borrower characteristics, the likelihood of default is 20% lower with recourse. 41 / 69

42 Broader recourse mitigates the crisis home-ownership rates fraction of LD loans model with recourse % of originations Pre Pre fraction of high-priced loans 0.06 default rate % of mortgage stock % of mortgage stock Pre Pre The spike in default rates would be about 20% lower. 42 / 69

43 Summary Question: How much did relaxed mortgage approval standards contribute to the foreclosure boom? Answer: By over 60%. Large effects not a consequence of mispricing. Foreclosure rates would have been 20% lower with recourse in the early stages of the transition. 43 / 69

44 Real home values (CS) in the long-run Back 44 / 69

45 The experiment 1. Calibrate price process to match long-term data 2. Calibrate parameters so that, following a long period of q = q N and using PTI limits of 25% (as they are in the data), the use of low-downpayment mortgages is around 5% 3. Relax underwriting standards for 4 model periods with q = q H 4. Then q H and underwriting standards return to pre-1998 values Preliminary results: The model captures the rise in low-downpayment after 98, the rise in HO rates, and the the foreclosure boom Counterfactual 1: PTI standards not relaxed after 98 Counterfactual 2: No middle stage, price falls from q N to q L Foreclosure rates peak 30% to 50% below benchmark 45 / 69

46 Housing Market Clearing Condition The market for housing capital clears provided h1 {H =1,h(ω)=h}dµ M Ω M h 1 {H =1}P(h ω)dµ M Ω M = Ak In equilibrium the production of new housing capital must equal the housing capital lost to devaluation. Both the rental and owner-occupied markets clear since the intermediary is willing to accommodate any allocation of total housing capital by the arbitrage condition. Back 46 / 69

47 Mortgage payment function Fixed-rate mortgages (HDs) m ν t (at, yt, ht ; qt, αt ) = rt ν (at, yt, ht ; qt, αt ) 1 (1 + rt ν (1 νt )ht qt, n {0, T 1} (at, yt, ht ; qt, αt )) T Back 47 / 69

48 Intermediary s problem The intermediary s value function after n {1,...T 1} periods of the mortgage contract initiated in state κ is given by W (ν,κ) n (a, y, ɛ; s) = (S (ν,κ) + D (ν,κ) )(a, y, ɛ, n; s) min{(1 D (ν,κ) (a, y, ɛ, n; s)χ)q sɛĥ, bν n (κ)}+ [1 (S (ν,κ) + D (ν,κ) ( [ )(a, y, ɛ, n; s)] m ν (κ)+e 1 + r + φ Back to SS def (1 ρ O )W (ν,κ) n+1 (a, y, ɛ ; s ) +ρ O W (ν,κ) O (n + 1, ɛ ; s ) ] ) 48 / 69

49 At time of originationa, if the household meets the downpayment constraint (a νqh) and the PTI constraint α), then: ( mν (κ) y W (ν,κ) 0 (â, ŷ, ɛ = 1; ŝ) = mν (κ) 1 + r + φ +E y,ɛ,s y,1,s (1 ρo ) W (ν,κ) 1 (a,y,ɛ ;s ) 1+r+φ +ρ O W (ν,κ) (1,ɛ ;s ) O 1+r+φ. Back to SS def 49 / 69

50 Truncated Rates The rate is truncated since the household default probability is too high for the bank to break-even at any mortgage rate below the rate at which the mortgage payment in the first period is so high that the budget set is empty. The left truncation can be thought of as an endogenous borrowing constraint associated with different borrower characteristics. In that period (i.e. when n = 0), the budget set is empty when c = a = 0 and m(0; ζ, r ζ ) > y 0 + (a 0 + ι vqh 1 {ζ=hd} )(1 + r). Since m(0; ζ, r ζ, h 0 ) is strictly increasing in r ζ, we know there is an interest rate r ζ that depends on y 0 and a 0 such that for any r > r ζ the bank cannot break even. Back 50 / 69

51 Agents with option to buy a home V M (a, y, n = 0; s) = max c 0,a 0,h {h 1,h 2,h 3 },ν K +β(1 ρ O )E y,ɛ,s y,1,s where if h = h 1, then u(c, h) + βρ O [ E ɛ,s 1,s VO (a + max{q s ɛ h b1 ν (κ), 0}; s ) ] 1 {h=h 1 } +1 {h {h 2,h 3 }} ( (1 γ)v R M (a, y ; s ) ) +γv ( M (a, y, n = 0; s ) ) V (ν,κ) M (a, y, ɛ, n = 1; s s.t. c + a = y + a(1 + r) R sh 1 and if h {h 2, h 3 }, then the following conditions must hold c + a = y + (1 + r) [a νq sh] m ν (κ) δq sh m ν (κ) y a νq sh (2) α s. (3) Back 51 / 69

52 Value functions for a mid-aged agents with a mortgage 1. Sell: V (ν,κ) S (a, y, ɛ, n; s) = max c 0,a 0 u ( c, h 1) + βρ O V O (a ; s ) + β(1 ρ O )V R M (a, y ; s ) s.t. c + a = y + a(1 + r) R sh 1 + (q sɛĥ bν n )(1 + r). 2. Default: ( ) V (ν,κ) D (a, y, ɛ, n; s) = max u c, ĥ + βρ O V O (a ; s ) + β(1 ρ O )V c 0,a M R 0 (a, y ; s ) s.t. c + a = y + a(1 + r) + max{(1 χ)q sɛĥ bν n, 0}(1 + r). 3. Continue: V (ν,κ) H (a, y, ɛ, n; s) = ( ) max c, ĥ c 0,a 0 [ ] + βρ O E ɛ,s ɛ,s V O (a + max{q s ɛ ĥ bn+1 ν (κ), 0}; s ) [ ] +β(1 ρ O )E y,ɛ,s y,ɛ,s V (ν,κ) M (a, y, ɛ, n + 1; s ) s.t. c + a = y + a(1 + r) m ν (κ)1 {n<t } δq sh. Back to young s prob. 52 / 69

53 Definition of default 1. Involuntary default D I (ω) = 1 { H = 1 y + (a + ι)(1 + r) m(n; κ) δh < 0 2. Voluntary default D V (ω) = 1 H = 1 y + (a + ι)(1 + r) m(n; κ) δh 0 qh b(n; κ) < 0 H = 0 Back to default freq. 53 / 69

54 Distribution of young agents The cross sectional distribution µ Y of young agents evolves according to (newborns plus young that did not turn mid-aged): µ t+1 Y (A, y s t ) = µ 0 p 0 (y )1 {0 A )} + (1 ρ M ) 1 {a ω Ω Y Y (ω;s t ) A )}P Y (y y)dµ t Y(ω s t 1 ). Back to SS def 54 / 69

55 Middle-aged renters The cross sectional distribution µ M,R of middle aged renters evolves according to (renters who did not turn old and didn t have opportunity to buy, renters who choose to continue to rent, or mid-aged who just sold or defaulted): µ t+1 M,R (A, y s t ) = (1 ρ O )(1 γ) 1 {a ω M,R (ω;s t ) A )} PM (y y)dµ t M,R (ω st 1 ) +(1 ρ O ) 1 {a {ω:h M,n=0 (ω;s t )=h 1 } M,n=0 (ω;s t ) A )} PM (y y)dµ t M,n=0 (ω st 1 ) +(1 ρ O ) 1 {a {ω:(d+s)(ω;s t )=1} M,n 1 (ω;s t ) A )} PM (y y)dµ t M,n 1 (ω st 1 ). where ω = (a, y). Back to SS def 55 / 69

56 Middle-aged with option to buy The cross sectional distribution µ M,n=0 of middle aged agents with the option to buy evolves according to (mid-aged renters who received the option to buy, just became mid-aged due to age shock): µ t+1 M,n=0 (A, y s t ) = (1 ρ O )γ 1 {a ω M,R (ω;s t ) A )} PM (y y)dµ t M,R (ω st 1 ) + ρ M 1 {a ω Y (ω;s t ) A )} PY (y y)dµ t Y (ω st 1 ) where ω = (a, y). Back to SS def 56 / 69

57 Middle-aged homeowners The cross sectional distribution µ M,n 1 (a, y, ɛ, n, ν, κ) of middle aged homeowners evolves according to (did not age or choose to sell or default, were given the option to buy, took it, and did not change age state): { µ t+1 M,n 1 (A, y, ɛ, n, ν, κ s t ) = (1 ρ O ) 1 Ω (κ,ν) {a M,n 1 (ω;s t ) A,h M,n 1 (ω;s t )=ĥ}pm (y y)p ɛ (ɛ ɛ)dµ t M,n 1 (ω st 1 )+ n 1 } 1 Ω M,n=0 {n =1,a M,n=0 (ω;st ) A,(D+S)(ω;s t )=0,ν M,n=0 (ω;s t )= ν,s t t =ŝ}pm (y y)p ɛ (ɛ 1)dµ t M,n=0 (ω st 1 ) where ω = (a, y, ɛ, n, ν, κ). Back to SS def 57 / 69

58 On calibrating to HDs only before 2003 In Figure 1, we can see the fraction of non-hds accounts for about 15 percent of all mortgages before However, 2/3 of that fraction of non-hds were standard nominally indexed ARM, which look more like traditional mortgages than LDs, until Back 58 / 69

59 Some Steady State Accounting where C + H (R + δ) = Y + r S + H R + X C is goods consumption R H is housing services consumption δ H is investment Y is the aggregate endowment r S is return to storage (or interest payments abroad if S < 0) R H + X is imputed rents plus rental income of persons (i.e. X is the difference between imputed rents and what people actually pay for their housing consumption like mortgage payments plus maintenance for owners) Back 59 / 69

60 Gerardi et. al. s approach 1. Estimate a default/refi competing hazard model with panel mortgage data that includes a proxy for home values (home equity) as an explanatory variable 2. Ask: if 2002 vintage of loans had experienced the same average price shock as 2005 vintage, at what average rate would they have defaulted? 3. Idea: 2002 vintage was written under more typical/stringent leverage and income tests standards 4. Answer: 2002 loans would have defaulted at about half the rate 2005 loans did Back 60 / 69

61 How our approach differs from and complements the econometric approach These numbers are predicated on 1. a specific econometric model, 2. the quality of controls (zip-codes vs actual home values), and 3. the assumption that the 2002 borrower pool is what the 2005 pool would have been with 2002 underwriting standards (no sample selection effects) Our calculations do not require these assumptions but, of course, are conditional on our modeling choices Further, our model can be used to simulate the role of policy, such as recourse statutes Back 61 / 69

62 Definition of high-cltv fraction Fraction of loans with CLTV 97% = Back Volume of loans with CLTV 97% Total volume of loans 62 / 69

63 National Delinquency Survey definitions Fraction of subprime mortgages is the stock of loans lenders report as subprime in NDS divided by the total stock of loans The foreclosure rate is the number of foreclosure starts in the course of a given quarter divided by the total stock of mortgages at the start of the quarter Back 63 / 69

64 Moving Shock Since hhs must move when they become old, ρ O has a direct impact on the median duration of home-ownership. Setting ρ O = 1 12 implies the median duration of home ownership is 7 model periods (=14 years) in our benchmark simulations. Based on American Community Survey data, Emrath (2009) estimates that median duration to range from 12 to 15 years for single family home buyers in the US between 1990 and Thus, the shock is calibrated such that hhs move to match the median duration of home-ownership in US data. Back to default freq. 64 / 69

65 Model with unexpected income shock in second period of the crisis home-ownership rates model counterfactual data fraction of LD loans % of originations Pre Pre fraction of high-priced loans 0.06 default rate % of mortgage stock % of mortgage stock Pre Pre / 69

66 Model with low interest rates during boom home-ownership rates model counterfactual data fraction of LD loans % of originations Pre Pre fraction of high-priced loans 0.06 default rate % of mortgage stock % of mortgage stock Pre Pre / 69

67 Untargeted Cross-Sectional Statistics (1998) LTY High-LTV Data Model Data Model Income Below median (0.04) (0.02) Above median (0.01) (0.01) Asset-to-income Below median (0.02) (0.02) Above median (0.02) (0.01) Age Below (0.03) (0.02) Above (0.02) (0.01) Loan size Below median (0.03) (0.02) Above median (0.02) (0.01) BackSCF 67 / 69

68 Untargeted Cross-Sectional Statistics (2010) LTY High-LTV Data Model Data Model Income Below median (0.06) (0.01) Above median (0.02) (0.01) Asset-to-income Below median (0.03) (0.02) Above median (0.05) (0.01) Age Below (0.04) (0.02) Above (0.04) (0.01) Loan size Below median (0.02) (0.01) Above median (0.05) (0.01) BackSCF 68 / 69

69 Bound Calculation The change in approval standards may have contributed to the increase in house prices. Since we are ignoring this effect in the counterfactual, what we report is in fact a lower bound. To see this, assume that all of the change in prices was caused by a change in approval standards. Then no change in standards, no change in price, no change in foreclosures. In that extreme case approval standards would explain 100% of the crisis. BackSTR 69 / 69