Phasing out the GSEs

Vadim Elenev1 Tim Landvoigt2 Stijn Van Nieuwerburgh3

1NYU Stern

2UT Austin

3NYU Stern, NBER, and CEPR

April 25, 2015

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 1 / 26

Motivation

Large government footprint in mortgage finance. GSE MBS accountfor

I 60% of stock of mortgage debtI 80% of originations in last 5 years

GSEs provide mortgage default insurance at fixed price

I How does their presence affect mortgage and housing markets?I How does it affect the financial sector?

Interaction of GSEs with banking system

I Bailout guarantees / deposit insuranceI Ability of government to provide cushion in crises

Welfare consequences of phase-out: “crowding in” the private sector

I Opinions differ for effect on mortgage stability, house prices, etc.(Mortgage Bankers Association vs Congressional Budget Office)

I Consensus around reform building (Johnson-Crapo bill)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 2 / 26

Motivation

Large government footprint in mortgage finance. GSE MBS accountfor

I 60% of stock of mortgage debtI 80% of originations in last 5 years

GSEs provide mortgage default insurance at fixed priceI How does their presence affect mortgage and housing markets?I How does it affect the financial sector?

Interaction of GSEs with banking system

I Bailout guarantees / deposit insuranceI Ability of government to provide cushion in crises

Welfare consequences of phase-out: “crowding in” the private sector

I Opinions differ for effect on mortgage stability, house prices, etc.(Mortgage Bankers Association vs Congressional Budget Office)

I Consensus around reform building (Johnson-Crapo bill)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 2 / 26

Motivation

Large government footprint in mortgage finance. GSE MBS accountfor

I 60% of stock of mortgage debtI 80% of originations in last 5 years

GSEs provide mortgage default insurance at fixed priceI How does their presence affect mortgage and housing markets?I How does it affect the financial sector?

Interaction of GSEs with banking systemI Bailout guarantees / deposit insuranceI Ability of government to provide cushion in crises

Welfare consequences of phase-out: “crowding in” the private sector

I Opinions differ for effect on mortgage stability, house prices, etc.(Mortgage Bankers Association vs Congressional Budget Office)

I Consensus around reform building (Johnson-Crapo bill)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 2 / 26

Motivation

Large government footprint in mortgage finance. GSE MBS accountfor

I 60% of stock of mortgage debtI 80% of originations in last 5 years

GSEs provide mortgage default insurance at fixed priceI How does their presence affect mortgage and housing markets?I How does it affect the financial sector?

Interaction of GSEs with banking systemI Bailout guarantees / deposit insuranceI Ability of government to provide cushion in crises

Welfare consequences of phase-out: “crowding in” the private sectorI Opinions differ for effect on mortgage stability, house prices, etc.

(Mortgage Bankers Association vs Congressional Budget Office)I Consensus around reform building (Johnson-Crapo bill)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 2 / 26

Model Overview

Houses

(Collateral)

Home

Equity

Mortgages

Equity

Deposits

Own Funds

Borrowers

Risk Takers

Depositors

Gov. Debt

Government

Mortgages

Guarantees Deposits

Gov. Debt

NPV of

Tax

Revenues

Bailouts

Guarantees

Households

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 3 / 26

Preview of Findings1. Effect of guarantees

I Cheap fixed-price guarantees distort mortgage pricing ...F 16 % more mortgage debtF 9% higher house pricesF 2.2 pp higher foreclosure rate

I ... and increase financial fragilityF Risk takers have 10% higher leverageF More frequent financial crises

I Feedback: guarantees ⇒ more bank leverage & mortgage debt⇒ more foreclosures ⇒ more guarantees

2. Welfare and Risk SharingI Aggregate welfare gain of 5% from phase outI Depositors > Risk takers > BorrowersI Negative impact of guarantees due to

F less efficient allocation of riskF foreclosure-induced DWL

3. Interaction of asset and liability guarantees: deposit insuranceamplifies effect of guarantees

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 4 / 26

Preview of Findings1. Effect of guarantees

I Cheap fixed-price guarantees distort mortgage pricing ...F 16 % more mortgage debtF 9% higher house pricesF 2.2 pp higher foreclosure rate

I ... and increase financial fragilityF Risk takers have 10% higher leverageF More frequent financial crises

I Feedback: guarantees ⇒ more bank leverage & mortgage debt⇒ more foreclosures ⇒ more guarantees

2. Welfare and Risk SharingI Aggregate welfare gain of 5% from phase outI Depositors > Risk takers > BorrowersI Negative impact of guarantees due to

F less efficient allocation of riskF foreclosure-induced DWL

3. Interaction of asset and liability guarantees: deposit insuranceamplifies effect of guarantees

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 4 / 26

Preview of Findings1. Effect of guarantees

I Cheap fixed-price guarantees distort mortgage pricing ...F 16 % more mortgage debtF 9% higher house pricesF 2.2 pp higher foreclosure rate

I ... and increase financial fragilityF Risk takers have 10% higher leverageF More frequent financial crises

I Feedback: guarantees ⇒ more bank leverage & mortgage debt⇒ more foreclosures ⇒ more guarantees

2. Welfare and Risk SharingI Aggregate welfare gain of 5% from phase outI Depositors > Risk takers > BorrowersI Negative impact of guarantees due to

F less efficient allocation of riskF foreclosure-induced DWL

3. Interaction of asset and liability guarantees: deposit insuranceamplifies effect of guarantees

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 4 / 26

Related Literature

Quantitative models on causes and consequencesof the housing boom:

I Kiyotaki, Michaelides & Nikolov 2011,Favilukis, Ludvigson & Van Nieuwerburgh 2013,Landvoigt, Piazzesi & Schneider 2015, Chu 2014

I Corbae & Quintin 2014, Garriga & Schlagenhauf 2009,Chetterjee & Eyigungor 2009, Jeske, Kruger, & Mittman 2013,Landvoigt 2013, Arslan, Guler, & Taskin 2013, Hedlund 2014

Financial intermediaries and crises:Brunnermeier & Sannikov 2012, He & Krishnamurthy 2013,Garleanu & Pedersen 2011, Adrian & Boyarchenko 2012Drechsler, Savov, & Schnabl 2014

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 5 / 26

Households and Goods

Households are three types, j = B,D,R:borrowers, depositors and risk-takers

2 goods: housing consumption, nonhousing consumption (numeraire)

Aggregate endowment of numeraire consumption,grows with stochastic trend

Housing tree pays housing services as dividends

Households have preferences over both goodsI Consumption bundle: Cobb-Douglas aggregatorI Epstein-Zin over consumption bundle

with intertemporal elasticity of one, risk aversion σj , discount factor βj

Households get share of income,initial endowment K j of shares in housing tree

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 6 / 26

Borrowers

Large family of households who chooseconsumption, houses, mortgage debt, opt. default threshold

Mortgages are (i) long-term

I Bonds with payment stream (1, δ, δ2, . . .)I Face value of debt at beginning of period

debtt−1 =α

1− δ×# of bonds ≡ F × AB

t−1

(ii) defaultable,

I Each period, borrower i receives idiosyncratic house valuation shock ωi

I Value of house after shock ωiptKBt−1

I Borrowers optimally choose owners of houses who default ⇒threshold ω∗t s.t. default for all ωi < ω∗t

I Lenders seize foreclosed houses, debt secured by houses is erased

and (iii) prepayable

I Option to prepay amount RBt of outstanding debt

at face value F for convex cost Ψ(RBt /A

Bt−1)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 7 / 26

Borrowers

Large family of households who chooseconsumption, houses, mortgage debt, opt. default threshold

Mortgages are (i) long-termI Bonds with payment stream (1, δ, δ2, . . .)I Face value of debt at beginning of period

debtt−1 =α

1− δ×# of bonds ≡ F × AB

t−1

(ii) defaultable,

I Each period, borrower i receives idiosyncratic house valuation shock ωi

I Value of house after shock ωiptKBt−1

I Borrowers optimally choose owners of houses who default ⇒threshold ω∗t s.t. default for all ωi < ω∗t

I Lenders seize foreclosed houses, debt secured by houses is erased

and (iii) prepayable

I Option to prepay amount RBt of outstanding debt

at face value F for convex cost Ψ(RBt /A

Bt−1)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 7 / 26

Borrowers

Large family of households who chooseconsumption, houses, mortgage debt, opt. default threshold

Mortgages are (i) long-termI Bonds with payment stream (1, δ, δ2, . . .)I Face value of debt at beginning of period

debtt−1 =α

1− δ×# of bonds ≡ F × AB

t−1

(ii) defaultable,I Each period, borrower i receives idiosyncratic house valuation shock ωi

I Value of house after shock ωiptKBt−1

I Borrowers optimally choose owners of houses who default ⇒threshold ω∗t s.t. default for all ωi < ω∗t

I Lenders seize foreclosed houses, debt secured by houses is erased

and (iii) prepayable

I Option to prepay amount RBt of outstanding debt

at face value F for convex cost Ψ(RBt /A

Bt−1)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 7 / 26

Borrowers

Large family of households who chooseconsumption, houses, mortgage debt, opt. default threshold

Mortgages are (i) long-termI Bonds with payment stream (1, δ, δ2, . . .)I Face value of debt at beginning of period

debtt−1 =α

1− δ×# of bonds ≡ F × AB

t−1

(ii) defaultable,I Each period, borrower i receives idiosyncratic house valuation shock ωi

I Value of house after shock ωiptKBt−1

I Borrowers optimally choose owners of houses who default ⇒threshold ω∗t s.t. default for all ωi < ω∗t

I Lenders seize foreclosed houses, debt secured by houses is erased

and (iii) prepayableI Option to prepay amount RB

t of outstanding debtat face value F for convex cost Ψ(RB

t /ABt−1)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 7 / 26

Borrowers (contd.)

Housing shock distribution G (ω) with E(ωi ) = µω = 1−depreciationI Default rate ZA(ω∗t ) = G (ω∗t )I 1− Recovery rate of lender = ZK (ω∗t ) =

∫ω>ω∗

tω dG (ω)

Variance σ2ω,t determines aggregate credit risk of borrower debt

ABt = δ(1− ZA(ω∗t ))AB

t−1 − RBt + new borrowing

Budget constraint

(1− τ)Y + qmABt + ZK (ω∗) pKB

t−1 =

C + (1− Z (ω∗))(1− δ)qmABt−1 + FRB

t + Ψ(RBt

ABt−1

) + pKBt

Borrowing constraint: F ABt ≤ φpKB

t

Complete Problem

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 8 / 26

Risk Takers

Risk takers are households that arise as intermediaries betweenborrowers and depositors

Timing of risk taker decisions

1. Bankruptcy choice2. Consumption and portfolio choice

Risk taker bankruptcyI leads to liquidation of assets and liabilitiesI and RTs incur (stochastic) utility penaltyI Government covers shortfall if assets − liabilities < 0

Effectively limited liability and deposit insurance

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 9 / 26

Risk Takers (contd.)Portfolio choice of

I private mortgage bond ARP with payoff MP and price qm

MP = 1− Z (ω∗) +(1− ζ)(µω − ZK (ω∗))pKB

AB

I guaranteed bond ARG with payoff MG and price qm + γ

MG = 1 + δZ (ω∗)F

I Risk free one-period bond BR with price q

No short-sales for both mortgage bonds and leverage constraint

−BR ≤ qm(ξPAP + ξGAG )

Beginning-of-period risk taker wealth

W Rt =[MP,t + δ(1− Z (ω∗t ))− ZR

t (qmt − F )]ARP,t−1

+ [MG ,t + δ(1− Z (ω∗t ))− ZRt (qmt − F )]AR

G ,t−1

+ BRt−1

Complete Problem

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 10 / 26

Depositors and Government

Depositors are very risk averseand only invest in risk free bonds, BD

Government follows passive tax and spending ruleI Revenues

Tt = τBt Y Bt + τSt (Y R

t + Y Dt )− τmt ZA(ω∗t )AB

t + γARt,G

I Expenditures

Gt = (MG ,t −MP,t)ARG ,t − I{R bankruptcy},tW

Rt + GT

t

I Budget constraintBGt−1 + Gt = qtB

Gt + Tt

I Transversality condition to ensure BG stays bounded

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 11 / 26

Competitive Equilibrium

Given realizations {Yt , σω,t}, sequence of choices

{CBt ,K

Bt ,A

Bt ,R

Bt , ω

∗t } for borrower households

{Dt ,CRt ,A

RP,t ,A

RG ,t ,B

Rt } for risk-taker households

{CDt ,B

Dt } for depositor households

and prices {qmt , qt , pt} such that all agents optimize and all asset marketsclear

BGt = BR

t + BDt

ABt = AR

P,t + ARG ,t

KBt = K − KD − KR

Goods market

CBt + CR

t + CDt + Housing maint. + Prepaym. cost = Yt − Forecl. losses

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 12 / 26

State Variables and Solution Method

Exogenous statesI Persistent growth rate of incomeI Mortgage credit risk σω,t

Endogenous states: wealth distribution matters for asset pricesdue to differences in preferences

I Total mortgage debt (borrower wealth)I Risk-taker wealthI Depositor wealthI Government debt

Nonlinear global solution method (policy time iteration)I Wealth distribution between risk-taker and depositor

depends on differences in risk aversionI Collateral constraints not always bindingI Bankruptcy choice

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 13 / 26

Equilibrium Characterization

Borrowers’ optimal default threshold

ω∗t =(1− τm − ψ′ + δqmt )AB

t

ptKBt−1

Risk takers’ demand for private mortgage bonds ...

qmt (1− ξPλRt ) =

Et

[MR

t,t+1

(MP,t+1 + δ(1− Z (ω∗t+1))qmt+1 − ZR

t+1(qmt+1 − F ))]

... and mortgage default insurance (guaranteed bonds)

γ = Et

[MR

t,t+1 (MG ,t+1 −MP,t+1)]

+ λRt qmt (ξG − ξP)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 14 / 26

Equilibrium Characterization

Borrowers’ optimal default threshold

ω∗t =(1− τm − ψ′ + δqmt )AB

t

ptKBt−1

Risk takers’ demand for private mortgage bonds ...

qmt (1− ξPλRt ) =

Et

[MR

t,t+1

(MP,t+1 + δ(1− Z (ω∗t+1))qmt+1 − ZR

t+1(qmt+1 − F ))]

... and mortgage default insurance (guaranteed bonds)

γ = Et

[MR

t,t+1 (MG ,t+1 −MP,t+1)]

+ λRt qmt (ξG − ξP)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 14 / 26

Equilibrium Characterization

Borrowers’ optimal default threshold

ω∗t =(1− τm − ψ′ + δqmt )AB

t

ptKBt−1

Risk takers’ demand for private mortgage bonds ...

qmt (1− ξPλRt ) =

Et

[MR

t,t+1

(MP,t+1 + δ(1− Z (ω∗t+1))qmt+1 − ZR

t+1(qmt+1 − F ))]

... and mortgage default insurance (guaranteed bonds)

γ = Et

[MR

t,t+1 (MG ,t+1 −MP,t+1)]

+ λRt qmt (ξG − ξP)

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 14 / 26

Calibration: Mortgage Risk

1. Jointly estimate mortgage duration δ and face value F = α1−δ

from Barclays MBS index using prepayment model Model

I Auxiliary pricing model to back out duration of data mortgage poolI Match geometric bond’s price-rate relationship to auxiliary model:δ = 0.95, α = 0.52

2. Two states of mortgage risk [σω,lo , σω,hi ]with transition matrix Pω

I to match average loss rates on mortgagesI and frequency and length of mortgage crises

(Jorda, Shularick, and Taylor (2014))

3. Set borrower leverage φ to match mortgage debt/income of“borrower” households in SCF

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 15 / 26

Calibration: Overview

Parameter & Description Value TargetExogenous Shocks

g mean income growth 1.9% Mean rpc GDP gr 1929-2013σg volatility income growth 3.9% Vol rpc GDP gr 1929-2013ρg persistence income growth 0.41 AC(1) rpc GDP gr 1929-2013

µω mean idiosync. house value shock 2.5% Housing depreciation CensusPopulation, Income, and Housing Shares

`i , i ∈ {B,D, R} population shares {47,51,2}% Population shares SCF 1995-2013

Y i , i ∈ {B,D, R} income shares {38,52,10}% Income shares SCF 1995-2013

K i , i ∈ {B,D, R} housing shares {39,49,12}% Housing wealth shares SCF 1995-2013Preferences

σB risk aversion borrower 8 Vol household mortgage debt to GDP 1985-2014

βB time discount factor borrower 0.88 Mean housing wealth to GDP 1985-2014

θB housing expenditure share 0.20 Housing expenditure share NIPA

σD risk aversion depositor 20 Volatility risk-free interest rate 1985-2014

βD = βR time discount factor savers 0.975 Mean risk-free interest rate 1985-2014

σR risk aversion risk taker 4 Financial sector leverage Flow of Funds 1985-2014ν intertemp. elasticity of subst. 1

Government Policy

τS = τB income tax rate 19.83% BEA govmt revenues to trend GDP 1929-2013Go exogenous govmt spending 15.8% BEA govmt spending to trend GDP 1929-2013

GT govmt transfer to HH 3.41% BEA govmt net transfers to trend GDP 1929-2013

τm mortgage interest rate deductibility 0.48 τB See textφ collateral constr 0.65% Mean borrowers’ mortgage debt-to-income SCF 1995-2013

ξG margin guaranteed MBS 1.6% Basel 2/3 regulatory capital charge agency MBSξP margin private MBS 8% Basel 2/3 regulatory capital charge non-agency mortgages

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 16 / 26

Model Simulation: Different G-fees

G-fees 20 bp g-fee 25 bp g-fee 65 bp g-feemean stdev mean stdev mean stdev

PricesRisk free rate -0.001 0.018 0.023 0.031 0.032 0.035Mortgage rate 0.035 0.003 0.039 0.003 0.042 0.003House price 2.121 0.138 2.041 0.100 1.934 0.100

Risk-TakerMarket value of bank assets 0.603 0.027 0.550 0.020 0.507 0.021Market value of private bonds 0.213 0.240 0.494 0.166 0.507 0.021Market value of guaranteed bonds 0.390 0.243 0.056 0.162 0.000 0.000Risk taker leverage 0.955 0.034 0.866 0.048 0.849 0.055Fraction λR > 0 0.922 0.269 0.205 0.404 0.154 0.361Bankruptcy frequency 0.186 0.389 0.002 0.039 0.000 0.014Return on RT wealth (excld. bankr.) 0.131 0.730 0.041 0.226 0.033 0.217

BorrowerMarket value of debt LTV 0.760 0.072 0.724 0.057 0.706 0.058Default rate 0.046 0.102 0.022 0.051 0.018 0.046Rate-induced prepayment rate 0.087 0.025 0.048 0.026 0.029 0.026Loss rate private 0.023 0.054 0.011 0.027 0.009 0.024Loss rate guaranteed (prepaym.) 0.006 0.012 0.002 0.004 0.001 0.003

GovernmentGovernment debt / GDP 0.195 0.179 0.051 0.059 0.021 0.005

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 17 / 26

Model Simulation: Different G-fees

G-fees

20 bp g-fee 25 bp g-fee 65 bp g-feemean stdev mean stdev mean stdev

PricesRisk free rate -0.001 0.018 0.023 0.031 0.032 0.035Mortgage rate 0.035 0.003 0.039 0.003 0.042 0.003House price 2.121 0.138 2.041 0.100 1.934 0.100

Risk-TakerMarket value of bank assets 0.603 0.027 0.550 0.020 0.507 0.021Market value of private bonds 0.213 0.240 0.494 0.166 0.507 0.021Market value of guaranteed bonds 0.390 0.243 0.056 0.162 0.000 0.000Risk taker leverage 0.955 0.034 0.866 0.048 0.849 0.055Fraction λR > 0 0.922 0.269 0.205 0.404 0.154 0.361Bankruptcy frequency 0.186 0.389 0.002 0.039 0.000 0.014Return on RT wealth (excld. bankr.) 0.131 0.730 0.041 0.226 0.033 0.217

BorrowerMarket value of debt LTV 0.760 0.072 0.724 0.057 0.706 0.058Default rate 0.046 0.102 0.022 0.051 0.018 0.046Rate-induced prepayment rate 0.087 0.025 0.048 0.026 0.029 0.026Loss rate private 0.023 0.054 0.011 0.027 0.009 0.024Loss rate guaranteed (prepaym.) 0.006 0.012 0.002 0.004 0.001 0.003

GovernmentGovernment debt / GDP 0.195 0.179 0.051 0.059 0.021 0.005

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 17 / 26

Model Simulation: Different G-fees

G-fees

20 bp g-fee 25 bp g-fee 65 bp g-feemean stdev mean stdev mean stdev

PricesRisk free rate -0.001 0.018 0.023 0.031 0.032 0.035Mortgage rate 0.035 0.003 0.039 0.003 0.042 0.003House price 2.121 0.138 2.041 0.100 1.934 0.100

Risk-TakerMarket value of bank assets 0.603 0.027 0.550 0.020 0.507 0.021Market value of private bonds 0.213 0.240 0.494 0.166 0.507 0.021Market value of guaranteed bonds 0.390 0.243 0.056 0.162 0.000 0.000Risk taker leverage 0.955 0.034 0.866 0.048 0.849 0.055Fraction λR > 0 0.922 0.269 0.205 0.404 0.154 0.361Bankruptcy frequency 0.186 0.389 0.002 0.039 0.000 0.014Return on RT wealth (excld. bankr.) 0.131 0.730 0.041 0.226 0.033 0.217

BorrowerMarket value of debt LTV 0.760 0.072 0.724 0.057 0.706 0.058Default rate 0.046 0.102 0.022 0.051 0.018 0.046Rate-induced prepayment rate 0.087 0.025 0.048 0.026 0.029 0.026Loss rate private 0.023 0.054 0.011 0.027 0.009 0.024Loss rate guaranteed (prepaym.) 0.006 0.012 0.002 0.004 0.001 0.003

GovernmentGovernment debt / GDP 0.195 0.179 0.051 0.059 0.021 0.005

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 17 / 26

Model Simulation: Different G-fees

G-fees

20 bp g-fee 25 bp g-fee 65 bp g-feemean stdev mean stdev mean stdev

PricesRisk free rate -0.001 0.018 0.023 0.031 0.032 0.035Mortgage rate 0.035 0.003 0.039 0.003 0.042 0.003House price 2.121 0.138 2.041 0.100 1.934 0.100

Risk-TakerMarket value of bank assets 0.603 0.027 0.550 0.020 0.507 0.021Market value of private bonds 0.213 0.240 0.494 0.166 0.507 0.021Market value of guaranteed bonds 0.390 0.243 0.056 0.162 0.000 0.000Risk taker leverage 0.955 0.034 0.866 0.048 0.849 0.055Fraction λR > 0 0.922 0.269 0.205 0.404 0.154 0.361Bankruptcy frequency 0.186 0.389 0.002 0.039 0.000 0.014Return on RT wealth (excld. bankr.) 0.131 0.730 0.041 0.226 0.033 0.217

BorrowerMarket value of debt LTV 0.760 0.072 0.724 0.057 0.706 0.058Default rate 0.046 0.102 0.022 0.051 0.018 0.046Rate-induced prepayment rate 0.087 0.025 0.048 0.026 0.029 0.026Loss rate private 0.023 0.054 0.011 0.027 0.009 0.024Loss rate guaranteed (prepaym.) 0.006 0.012 0.002 0.004 0.001 0.003

GovernmentGovernment debt / GDP 0.195 0.179 0.051 0.059 0.021 0.005

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 17 / 26

Model Simulation: Different G-fees

G-fees

20 bp g-fee 25 bp g-fee 65 bp g-feemean stdev mean stdev mean stdev

PricesRisk free rate -0.001 0.018 0.023 0.031 0.032 0.035Mortgage rate 0.035 0.003 0.039 0.003 0.042 0.003House price 2.121 0.138 2.041 0.100 1.934 0.100

Risk-TakerMarket value of bank assets 0.603 0.027 0.550 0.020 0.507 0.021Market value of private bonds 0.213 0.240 0.494 0.166 0.507 0.021Market value of guaranteed bonds 0.390 0.243 0.056 0.162 0.000 0.000Risk taker leverage 0.955 0.034 0.866 0.048 0.849 0.055Fraction λR > 0 0.922 0.269 0.205 0.404 0.154 0.361Bankruptcy frequency 0.186 0.389 0.002 0.039 0.000 0.014Return on RT wealth (excld. bankr.) 0.131 0.730 0.041 0.226 0.033 0.217

BorrowerMarket value of debt LTV 0.760 0.072 0.724 0.057 0.706 0.058Default rate 0.046 0.102 0.022 0.051 0.018 0.046Rate-induced prepayment rate 0.087 0.025 0.048 0.026 0.029 0.026Loss rate private 0.023 0.054 0.011 0.027 0.009 0.024Loss rate guaranteed (prepaym.) 0.006 0.012 0.002 0.004 0.001 0.003

GovernmentGovernment debt / GDP 0.195 0.179 0.051 0.059 0.021 0.005

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 17 / 26

Model Simulation: Different G-fees

G-fees

20 bp g-fee 25 bp g-fee 65 bp g-feemean stdev mean stdev mean stdev

PricesRisk free rate -0.001 0.018 0.023 0.031 0.032 0.035Mortgage rate 0.035 0.003 0.039 0.003 0.042 0.003House price 2.121 0.138 2.041 0.100 1.934 0.100

Risk-TakerMarket value of bank assets 0.603 0.027 0.550 0.020 0.507 0.021Market value of private bonds 0.213 0.240 0.494 0.166 0.507 0.021Market value of guaranteed bonds 0.390 0.243 0.056 0.162 0.000 0.000Risk taker leverage 0.955 0.034 0.866 0.048 0.849 0.055Fraction λR > 0 0.922 0.269 0.205 0.404 0.154 0.361Bankruptcy frequency 0.186 0.389 0.002 0.039 0.000 0.014Return on RT wealth (excld. bankr.) 0.131 0.730 0.041 0.226 0.033 0.217

BorrowerMarket value of debt LTV 0.760 0.072 0.724 0.057 0.706 0.058Default rate 0.046 0.102 0.022 0.051 0.018 0.046Rate-induced prepayment rate 0.087 0.025 0.048 0.026 0.029 0.026Loss rate private 0.023 0.054 0.011 0.027 0.009 0.024Loss rate guaranteed (prepaym.) 0.006 0.012 0.002 0.004 0.001 0.003

GovernmentGovernment debt / GDP 0.195 0.179 0.051 0.059 0.021 0.005

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 17 / 26

Model Simulation: Different G-fees

G-fees

20 bp g-fee 25 bp g-fee 65 bp g-feemean stdev mean stdev mean stdev

PricesRisk free rate -0.001 0.018 0.023 0.031 0.032 0.035Mortgage rate 0.035 0.003 0.039 0.003 0.042 0.003House price 2.121 0.138 2.041 0.100 1.934 0.100

Risk-TakerMarket value of bank assets 0.603 0.027 0.550 0.020 0.507 0.021Market value of private bonds 0.213 0.240 0.494 0.166 0.507 0.021Market value of guaranteed bonds 0.390 0.243 0.056 0.162 0.000 0.000Risk taker leverage 0.955 0.034 0.866 0.048 0.849 0.055Fraction λR > 0 0.922 0.269 0.205 0.404 0.154 0.361Bankruptcy frequency 0.186 0.389 0.002 0.039 0.000 0.014Return on RT wealth (excld. bankr.) 0.131 0.730 0.041 0.226 0.033 0.217

BorrowerMarket value of debt LTV 0.760 0.072 0.724 0.057 0.706 0.058Default rate 0.046 0.102 0.022 0.051 0.018 0.046Rate-induced prepayment rate 0.087 0.025 0.048 0.026 0.029 0.026Loss rate private 0.023 0.054 0.011 0.027 0.009 0.024Loss rate guaranteed (prepaym.) 0.006 0.012 0.002 0.004 0.001 0.003

GovernmentGovernment debt / GDP 0.195 0.179 0.051 0.059 0.021 0.005

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 17 / 26

Sources of Welfare Differences

Welfare is lower in low g-fee economy due to

less efficient allocation of riskI Effect on volatility of consumption through worse insuranceI Effect on mean of consumption through lower interest ratesI Can gauge these effects by looking at ratios of marginal utilities

(complete markets = ratios are constant)

larger deadweight losses from foreclosure: effect on mean ofconsumption

20 bp g-fee 25 bp g-fee 65 bp g-feemean stdev mean stdev mean stdev

Aggregate Welfare 0.309 0.008 0.313 0.008 0.324 0.009Consumption borrower 0.300 0.040 0.296 0.031 0.295 0.030Consumption depositor 0.393 0.018 0.413 0.012 0.420 0.009Consumption risk taker 0.077 0.011 0.075 0.005 0.073 0.004log(MU ratio) borrower/risk taker -0.766 0.226 -0.774 0.139 -0.852 0.116log(MU ratio) risk taker/depositor 1.109 0.154 1.146 0.082 1.174 0.051

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 18 / 26

Sources of Welfare Differences

Welfare is lower in low g-fee economy due to

less efficient allocation of riskI Effect on volatility of consumption through worse insuranceI Effect on mean of consumption through lower interest ratesI Can gauge these effects by looking at ratios of marginal utilities

(complete markets = ratios are constant)

larger deadweight losses from foreclosure: effect on mean ofconsumption

20 bp g-fee 25 bp g-fee 65 bp g-feemean stdev mean stdev mean stdev

Aggregate Welfare 0.309 0.008 0.313 0.008 0.324 0.009Consumption borrower 0.300 0.040 0.296 0.031 0.295 0.030Consumption depositor 0.393 0.018 0.413 0.012 0.420 0.009Consumption risk taker 0.077 0.011 0.075 0.005 0.073 0.004log(MU ratio) borrower/risk taker -0.766 0.226 -0.774 0.139 -0.852 0.116log(MU ratio) risk taker/depositor 1.109 0.154 1.146 0.082 1.174 0.051

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 18 / 26

Sources of Welfare Differences

Welfare is lower in low g-fee economy due to

less efficient allocation of riskI Effect on volatility of consumption through worse insuranceI Effect on mean of consumption through lower interest ratesI Can gauge these effects by looking at ratios of marginal utilities

(complete markets = ratios are constant)

larger deadweight losses from foreclosure: effect on mean ofconsumption

20 bp g-fee 25 bp g-fee 65 bp g-feemean stdev mean stdev mean stdev

Aggregate Welfare 0.309 0.008 0.313 0.008 0.324 0.009Consumption borrower 0.300 0.040 0.296 0.031 0.295 0.030Consumption depositor 0.393 0.018 0.413 0.012 0.420 0.009Consumption risk taker 0.077 0.011 0.075 0.005 0.073 0.004log(MU ratio) borrower/risk taker -0.766 0.226 -0.774 0.139 -0.852 0.116log(MU ratio) risk taker/depositor 1.109 0.154 1.146 0.082 1.174 0.051

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 18 / 26

Role of Limited Liability and Capital RequirementsBenchmark 20 bp High µρ ξG = 92%mean stdev mean stdev mean stdev

PricesRisk free rate -0.001 0.018 0.020 0.032 0.017 0.029Mortgage rate 0.035 0.003 0.039 0.003 0.038 0.003House price 2.121 0.138 2.099 0.101 2.063 0.106

Risk TakerMarket value of bank assets 0.603 0.027 0.572 0.020 0.563 0.019Market value of private bonds 0.213 0.240 0.512 0.175 0.504 0.171Market value of guaranteed bonds 0.390 0.243 0.060 0.172 0.059 0.169Risk taker leverage 0.955 0.034 0.865 0.048 0.869 0.044Fraction λR > 0 0.922 0.269 0.216 0.411 0.243 0.429Bankruptcy frequency 0.186 0.389 0.000 0.000 0.001 0.033Return on RT wealth (excld. bankr.) 0.131 0.730 0.040 0.225 0.055 0.239

BorrowerMarket value of debt LTV 0.760 0.073 0.731 0.058 0.732 0.059Default rate 0.046 0.105 0.024 0.054 0.025 0.057Loss rate private 0.023 0.054 0.012 0.028 0.013 0.030Loss rate guaranteed 0.006 0.012 0.002 0.005 0.002 0.006

GovernmentGovernment debt / GDP 0.195 0.179 0.082 0.092 0.064 0.072

WelfareAggregate Welfare 0.309 0.008 0.318 0.009 0.320 0.009

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 19 / 26

Role of Limited Liability and Capital RequirementsBenchmark 20 bp High µρ ξG = 92%mean stdev mean stdev mean stdev

PricesRisk free rate -0.001 0.018 0.020 0.032 0.017 0.029Mortgage rate 0.035 0.003 0.039 0.003 0.038 0.003House price 2.121 0.138 2.099 0.101 2.063 0.106

Risk TakerMarket value of bank assets 0.603 0.027 0.572 0.020 0.563 0.019Market value of private bonds 0.213 0.240 0.512 0.175 0.504 0.171Market value of guaranteed bonds 0.390 0.243 0.060 0.172 0.059 0.169Risk taker leverage 0.955 0.034 0.865 0.048 0.869 0.044Fraction λR > 0 0.922 0.269 0.216 0.411 0.243 0.429Bankruptcy frequency 0.186 0.389 0.000 0.000 0.001 0.033Return on RT wealth (excld. bankr.) 0.131 0.730 0.040 0.225 0.055 0.239

BorrowerMarket value of debt LTV 0.760 0.073 0.731 0.058 0.732 0.059Default rate 0.046 0.105 0.024 0.054 0.025 0.057Loss rate private 0.023 0.054 0.012 0.028 0.013 0.030Loss rate guaranteed 0.006 0.012 0.002 0.005 0.002 0.006

GovernmentGovernment debt / GDP 0.195 0.179 0.082 0.092 0.064 0.072

WelfareAggregate Welfare 0.309 0.008 0.318 0.009 0.320 0.009

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 19 / 26

Role of Limited Liability and Capital RequirementsBenchmark 20 bp High µρ ξG = 92%mean stdev mean stdev mean stdev

PricesRisk free rate -0.001 0.018 0.020 0.032 0.017 0.029Mortgage rate 0.035 0.003 0.039 0.003 0.038 0.003House price 2.121 0.138 2.099 0.101 2.063 0.106

Risk TakerMarket value of bank assets 0.603 0.027 0.572 0.020 0.563 0.019Market value of private bonds 0.213 0.240 0.512 0.175 0.504 0.171Market value of guaranteed bonds 0.390 0.243 0.060 0.172 0.059 0.169Risk taker leverage 0.955 0.034 0.865 0.048 0.869 0.044Fraction λR > 0 0.922 0.269 0.216 0.411 0.243 0.429Bankruptcy frequency 0.186 0.389 0.000 0.000 0.001 0.033Return on RT wealth (excld. bankr.) 0.131 0.730 0.040 0.225 0.055 0.239

BorrowerMarket value of debt LTV 0.760 0.073 0.731 0.058 0.732 0.059Default rate 0.046 0.105 0.024 0.054 0.025 0.057Loss rate private 0.023 0.054 0.012 0.028 0.013 0.030Loss rate guaranteed 0.006 0.012 0.002 0.005 0.002 0.006

GovernmentGovernment debt / GDP 0.195 0.179 0.082 0.092 0.064 0.072

WelfareAggregate Welfare 0.309 0.008 0.318 0.009 0.320 0.009

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 19 / 26

Dynamics During Mortgage Crisis

2 4 6 8 10-0.02

-0.01

0

0.01

0.02

0.03Risk-free Rate

2 4 6 8 100.034

0.035

0.036

0.037

0.038

0.039

0.04Mortg.Rate

2 4 6 8 101.9

1.95

2

2.05

2.1

2.15House Price

2 4 6 8 100.48

0.49

0.5

0.51

0.52

0.53

0.54

0.55Mortg.Debt

2 4 6 8 100.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9Risk-free Debt

2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

0.3Gov.debt

25 bp20 bp

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 20 / 26

Dynamics During Mortgage Crisis

2 4 6 8 10-0.02

-0.01

0

0.01

0.02

0.03Risk-free Rate

2 4 6 8 100.034

0.035

0.036

0.037

0.038

0.039

0.04Mortg.Rate

2 4 6 8 101.9

1.95

2

2.05

2.1

2.15House Price

2 4 6 8 100.48

0.49

0.5

0.51

0.52

0.53

0.54

0.55Mortg.Debt

2 4 6 8 100.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9Risk-free Debt

2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

0.3Gov.debt

25 bp20 bp

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 20 / 26

Conclusion and Outlook

Underpriced government guarantee leads to pecuniary externalityI Intermediaries stop pricing credit risk in mortgage ratesI More debt and foreclosures

Limited liability and low capital charges of intermediaries greatlyamplify effect

Welfare higher in economy without guaranteesI Intermediaries are constrained less oftenI Better allocation among households with different risk preferences

Next stepsI Allow depositors to hold guaranteed bonds (mutual funds)I Evaluate policy proposal from Corker-WarnerI Production economy: effect of mortgage guarantees on other

productive lending opportunities in economy

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 21 / 26

Borrowers: Complete ProblemBack

V B(KBt−1,A

Bt ,SBt ) = max

{CBt ,K

Bt ,ω

∗t ,R

Bt ,B

Bt }

{(1− βB)

[(CBt

)1−θ (AKK

Bt−1

)θ]1−1/ν

+

+ βBEt

[(egt+1V B(KB

t ,ABt+1,SBt+1)

)1−σB] 1−1/ν

1−σB

1

1−1/ν

subject to

CBt = (1− τBt )Y B

t + GT ,Bt + ZK (ω∗t )ptK

Bt−1 + qmt B

Bt

− (1− τmt )ZA(ω∗t )ABt − ptK

Bt − FRB

t −Ψ(RBt ,A

Bt )

ABt+1 = e−gt+1

[δZA (ω∗t )AB

t − RBt + BB

t

]φptK

Bt ≥ F

[δZA (ω∗t )AB

t − RBt + BB

t

]0 ≤RB

t ≤ δZA (ω∗t )ABt

SBt+1 = h(SBt )

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 22 / 26

Risk Takers: Complete ProblemBack

V R(W Rt , ρt ,SRt ) = max

CRt ,A

Rt+1,P

,ARt+1,P

,BRt

(1− βR)

[(CR

t )1−θ(KRt−1)θ

eρt

]1−1/ν

+βREt

[(egt+1 V R

(W R

t+1,SRt+1

))1−σR] 1−1/ν

1−σR

1

1−1/ν

subject to:

(1− τS )Y Rt + W R

t + GT ,Rt = CR

t + (1− µω)ptKRt−1 + qmt AR

t+1,P + (qmt + γt)ARt+1,G + qft B

Rt ,

W Rt+1 = e−gt+1

[(Mt+1,P + δZA(ω∗t+1)qmt+1)AR

t+1,P + (Mt+1,G + δZA(ω∗t+1)qmt+1)ARt+1,G + BR

t

],

BRt ≥ − qmt (ξPA

Rt+1,P + ξGA

Rt+1,G ),

ARt+1,G ≥ 0,

ARt+1,P ≥ 0,

SRt+1 = h(SRt )

with continuation value

V R(W Rt ,SRt ) = max

D(ρ)Eρ[D(ρ)V R(0, ρ,SRt ) + (1− D(ρ))V R(W R

t , 0,SRt )]

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 23 / 26

G-fees Over TimeBack

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 24 / 26

Prepayment Model: Fit

1985 1990 1995 2000 2005 2010 20150

1

2

3

4

5

6Duration

Data MBS PoolModel MBS Pool

0.02 0.04 0.06 0.08 0.1 0.1275

80

85

90

95

100

105

110

115Price

Model MBS poolModel mortgage

Back

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 25 / 26

Prepayment Model: Error for Different α

0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04Absolute Errors

MeanMin RateMax Rate

0.2 0.3 0.4 0.5 0.6 0.7 0.80.86

0.88

0.9

0.92

0.94

0.96

0.98Delta

Back

Elenev, Landvoigt, Van Nieuwerburgh Phasing out the GSEs April 25, 2015 26 / 26