The Mortgage Credit Channel of Macroeconomic Transmission Daniel L. - - PowerPoint PPT Presentation

The Mortgage Credit Channel of Macroeconomic Transmission

Daniel L. Greenwald (MIT Sloan)

GCFP Annual Conference

September 29, 2016

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 1 / 19

Introduction

◮ Motivation: despite importance of mortgage markets, much to learn about

core mechanisms connecting credit, house prices, economic activity.

◮ Main question: if and how mortgage credit issuance amplifies and

propagates fundamental shocks.

• Mortgage credit channel of transmission.

◮ Approach: General equilibrium framework centered on two important but

largely unstudied features of US mortgage markets:

• 1. Size of new loans limited by payment-to-income (PTI) constraint,

alongside loan-to-value (LTV) constraint.

Underwriting

• 2. Borrowers hold long-term, fixed-rate loans and can choose to prepay

existing loans and replace with new ones.

Prepay Data Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 2 / 19

Main Findings

Main Finding #1: When calibrated to US mortgage microdata, novel features amplify transmission from interest rates into debt, house prices, economic activity.

◮ Initial source: PTI limits are highly sensitive to nominal interest rates.

• Change by ∼ 10% in response to 1% change in nominal rates.

◮ Key propagation mechanism: changes in which constraint is binding for

borrowers move house prices (constraint switching effect).

• Price-rent ratios rise up to 4% after persistent 1% fall in nominal rates.

Main Finding #2: PTI liberalization appears essential to boom-bust.

◮ Changes in LTV standards alone insufficient. PTI liberalization compelling

theoretically and empirically.

◮ Quantitative impact: 38% of observed rise in price-rent ratios, 47% of the

rise in debt-household income from PTI relaxation alone.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 3 / 19

Simple Example

◮ Consider homebuyer who wants large house, minimal down payment. Faces

PTI limit of 28%, LTV limit of 80%.

140 160 180 200 220 240 260 House Price 20 40 60 80 100 Down Payment

Max PTI Price Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 4 / 19

Simple Example

◮ At income of $50k per year, 28% PTI limit =

⇒ max monthly payment of ∼ $1,200.

140 160 180 200 220 240 260 House Price 20 40 60 80 100 Down Payment

Max PTI Price Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 4 / 19

Simple Example

◮ At 6% interest rate, $1,200 payment =

⇒ maximum PTI loan size $160k. Plus 20% down payment = ⇒ house price of $200k.

140 160 180 200 220 240 260 House Price 20 40 60 80 100 Down Payment

Max PTI Price Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 4 / 19

Simple Example

◮ Kink in down payment at price $200k. Below this point size of loan limited

by LTV, above by PTI. Kink likely optimum for homebuyers.

140 160 180 200 220 240 260 House Price 20 40 60 80 100 Down Payment

Down Payment Max PTI Price Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 5 / 19

Simple Example

◮ Interest rates fall from 6% to 5%. Borrower’s max PTI now limits loan to

$178k (rise of 11%). Kink price now $223k, housing demand increases.

140 160 180 200 220 240 260 House Price 20 40 60 80 100 Down Payment

Down Payment Max PTI Price Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 6 / 19

Simple Example

◮ Increasing the maximum PTI ratio from 28% to 31% has a similar effect to

fall in rates, increases max loan size and corresponding price.

140 160 180 200 220 240 260 House Price 20 40 60 80 100 Down Payment

Down Payment Max PTI Price Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 7 / 19

Simple Example

◮ In contrast, increasing maximum LTV ratio from 80% to 90% means that

$160k loan associated with only $178k house. Housing demand falls.

140 160 180 200 220 240 260 House Price 20 40 60 80 100 Down Payment

Down Payment Max PTI Price Max PTI Loan Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 8 / 19

LTV and PTI in the Data

◮ LTV constraint: balance cannot exceed fraction of house value.

• Key property: moves with house prices.
• Clear influence on borrowers: large spikes at institutional limits.

50 60 70 80 90 100 110 0.0 0.1 0.2 0.3 0.4 0.5 0.6

(a) CLTV Histogram: 2014 Q3

10 20 30 40 50 60 70 80 0.00 0.02 0.04 0.06 0.08 0.10

(b) PTI Histogram: 2014 Q3

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 9 / 19

LTV and PTI in the Data

◮ PTI constraint: payment cannot exceed fraction of income.

• Key property: moves with interest rates (elasticity ≃ 10)
• Data consistent with some PTI constrained + search frictions.

50 60 70 80 90 100 110 0.0 0.1 0.2 0.3 0.4 0.5 0.6

(a) CLTV Histogram: 2014 Q3

10 20 30 40 50 60 70 80 0.00 0.02 0.04 0.06 0.08 0.10

(b) PTI Histogram: 2014 Q3

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 9 / 19

LTV and PTI in the Data

◮ PTI bunching larger in cash-out refinances, where no housing search occurs.

• But majority of borrowers probably not PTI constrained.

50 60 70 80 90 100 110 0.0 0.1 0.2 0.3 0.4 0.5 0.6

(a) CLTV Histogram: 2014 Q3

10 20 30 40 50 60 70 80 0.00 0.02 0.04 0.06 0.08 0.10

(b) PTI Histogram: 2014 Q3

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 10 / 19

Constraint Switching Effect

◮ General model includes population heterogeneity.

• Fraction of LTV-constrained borrowers (F ltv) depends on macro state.
• LTV-constrained value housing more, willing to pay premium.

◮ When rates fall, PTI limits loosen.

• Borrowers switch from PTI-constrained to LTV-constrained, increasing F ltv.
• House prices rise, also loosening LTV limits.

Interest Rates PTI Limits LTV Limits F ltv House Prices

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 11 / 19

Comparison of Models

◮ Main Result #1: Strong transmission from interest rates into debt, house

prices, economic activity.

◮ Experiment: consider economies that differ by credit limit and compare

response to interest rate movements:

• 1. LTV Economy: LTV constraint only.
• 2. PTI Economy: PTI constraint only.
• 3. Benchmark Economy: Both constraints, applied borrower by

borrower.

◮ Computation: Linearize model to obtain impulse responses.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 12 / 19

Constraint Switching Effect (Inflation Target Shock)

◮ Response to near-permanent -1% (annualized) fall in nominal rates.

5 10 15 20 Quarters 5 10 Debt

IRF to Infl. Target

5 10 15 20 Quarters 2 2 4 Price-Rent Ratio

IRF to Infl. Target

5 10 15 20 Quarters 1 2 3 F ltv (Level)

IRF to Infl. Target

LTV PTI Benchmark

• Exog. Prepay Version

TFP IRFs Credit Standards IRFs 43% PTI Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 13 / 19

Constraint Switching Effect (Inflation Target Shock)

◮ Debt response of Benchmark Economy closer to PTI Economy even though

most borrowers constrained by LTV (∼ 75% in steady state).

5 10 15 20 Quarters 5 10 Debt

IRF to Infl. Target

5 10 15 20 Quarters 2 2 4 Price-Rent Ratio

IRF to Infl. Target

5 10 15 20 Quarters 1 2 3 F ltv (Level)

IRF to Infl. Target

LTV PTI Benchmark

• Exog. Prepay Version

TFP IRFs Credit Standards IRFs 43% PTI Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 13 / 19

Credit Standards and the Boom-Bust

◮ Main Result #2: PTI liberalization essential to the boom-bust.

• So far, have been treating maximum LTV and PTI ratios as fixed, but credit

standards can change.

• Fannie/Freddie origination data: substantial increase in PTI ratios in boom.

◮ Experiment: unexpectedly change parameters, unexpectedly return to

baseline 32Q later. 1. PTI Liberalization: max PTI ratio from 36% → 54%. 2. LTV Liberalization: max LTV ratio from 85% → 99%.

◮ Computation: nonlinear transition paths.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 14 / 19

Credit Standards and the Boom-Bust

◮ Fannie Mae data: PTI constraints appear to bind after bust but not during

boom.

10 20 30 40 50 60 70 80 0.00 0.02 0.04 0.06 0.08 0.10

(a) PTI Histogram: 2006 Q1

10 20 30 40 50 60 70 80 0.00 0.02 0.04 0.06 0.08 0.10

(b) PTI Histogram: 2014 Q3

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 15 / 19

Credit Standards and the Boom-Bust

◮ Cash-out refi plots even more striking.

10 20 30 40 50 60 70 80 0.00 0.02 0.04 0.06 0.08 0.10

(a) PTI Histogram: 2006 Q1

10 20 30 40 50 60 70 80 0.00 0.02 0.04 0.06 0.08 0.10

(b) PTI Histogram: 2014 Q3

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 16 / 19

Credit Standards and the Boom-Bust

◮ Main Result #2: PTI liberalization essential to the boom-bust.

• So far, have been treating maximum LTV and PTI ratios as fixed, but credit

standards can change.

• Fannie/Freddie origination data: substantial increase in PTI ratios in boom.

◮ Experiment: unexpectedly change parameters, unexpectedly return to

baseline 32Q later.

• 1. PTI Liberalization: max PTI ratio from 36% → 54%.
• 2. LTV Liberalization: max LTV ratio from 85% → 99%.

◮ Computation: nonlinear transition paths.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 17 / 19

Credit Liberalization Experiment

◮ LTV Liberalization generates small rise in debt-to-household income

(19%). House prices, price-rent ratios fall (-2%).

20 40 Quarters 10 10 20 30 Price-Rent Ratio 20 40 Quarters 5 10 15 20 25 Debt 20 40 Quarters 60 70 80 90 100 F ltv (Level)

LTV Liberalized PTI Liberalized

Data More Series LTV Intuition PTI Intuition Preference Shocks Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 18 / 19

Credit Liberalization Experiment

◮ PTI Liberalization generates large boom in house prices, price-rent ratios

(38%), debt-household income (47%).

20 40 Quarters 10 10 20 30 Price-Rent Ratio 20 40 Quarters 5 10 15 20 25 Debt 20 40 Quarters 60 70 80 90 100 F ltv (Level)

LTV Liberalized PTI Liberalized

Data More Series LTV Intuition PTI Intuition Preference Shocks Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 18 / 19

Credit Liberalization Experiment

◮ Macroprudential policy: cap on PTI ratios more effective at limiting

boom-bust cycles.

20 40 Quarters 10 10 20 30 Price-Rent Ratio 20 40 Quarters 5 10 15 20 25 Debt 20 40 Quarters 60 70 80 90 100 F ltv (Level)

LTV Liberalized PTI Liberalized

Data More Series LTV Intuition PTI Intuition Preference Shocks Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 18 / 19

Conclusion

◮ Macro model with two novel features:

• Payment-to-income constraint.
• Endogenous prepayment of long-term debt.

◮ Novel transmission channel from interest rates into credit, house prices,

economic activity.

• Credit, house prices through constraint switching effect.
• Amplification into output through endogenous prepayment (see paper).
• Monetary policy more effective, but may pose tradeoff (see paper).

◮ PTI liberalization appears essential to boom-bust.

• Cap on PTI ratios, not LTV ratios more effective macroprudential policy.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 19 / 19

APPENDIX

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 1 / 61

Literature Review

◮ Empirical Work: Adelino, Schoar, Severino (2015a, 2015b), Aladangady (2014), Anderson, Campbell, Nielsen,

Ramadorai (2014), Di Maggio, Kermani (2015), Keys, Pope, Pope (2014), Mian, Sufi (2008, 2014).

Here: Income-based lending, behavioral prepayment in general equilibrium.

◮ Heterogeneous Agent Models:

Campbell, Cocco (2015), Chatterjee, Eyigungor (2015), Chen, Michaux, Roussanov (2013), Corbae, Quintin (2013), Elenev, Landvoigt, Van Nieuwerburgh (2015), Gorea, Midrigan (2015), Guler (2014), Hedlund (2013), Garriga, Hedlund (2016), Kaplan, Mitman, Violante (2016), Kaplan, Violante (2014), Khandani, Lo, Merton (2013), Landvoigt (2015), Laufer (2013), Wong (2015).

Here: Embed into monetary DSGE, transmission through PTI.

◮ Monetary DSGE Models:

Eggertsson, Krugman (2012), Garriga, Kydland, Sustek (2015), Kiyotaki, Moore (1997), Iacoviello (2005), Iacoviello, Neri (2011), Liu, Wang, Zha (2013), Monacelli (2008).

Here: Realistic mortgage structure, transmission through PTI.

◮ Credit Standards and the Boom-Bust:

Campbell, Hercowitz (2005), Favilukis, Ludvigson, Van Nieuwerburgh (2015), Iacoviello, Pavan (2013), Kermani (2015), Justiniano, Primiceri, Tambalotti (2015).

Here: PTI liberalization critical to boom-bust.

◮ Redistribution Channel: Auclert (2015), Calza, Monacelli, Stracca (2013), Rubio (2011).

Here: Transmission through credit growth, not mortgage payments.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 2 / 61

Model Overview

◮ Borrowing =

⇒ impatient borrowers/patient savers.

• Permanent types with fixed measure χj for j ∈ {b, s}.
• Preferences:

Vj,t = log(cj,t/χj) + ξ log(hj,t/χj) − η (nj,t/χj)1+ϕ 1 + ϕ + βjEtVj,t+1

◮ Mortgage debt =

⇒ durable housing.

• Divisible, cannot change stock without prepaying mortgage.
• Fixed housing stock, saver housing demand.

◮ Realistic mortgage contracts =

⇒ long-term fixed-rate bonds

• Endogenous fraction ρt prepay each period, update balance and interest rate.

◮ Movements in long rates =

⇒ Taylor rule, shock to inflation target π∗

t .

• Any shock to real rates or term premia should activate channel.

◮ Effects on real economy =

⇒ labor supply, sticky prices, TFP shocks.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 3 / 61

Representative Borrower’s Problem

◮ State variables: average principal balance mt−1, mortgage payment payt−1,

housing stock hb,t−1.

◮ Control variables: nondurable consumption cb,t, labor supply nb,t,

prepayment rate ρt, size of new houses h∗

b,t, size of new loans m∗ t .

◮ Budget constraint:

cb,t ≤ ρt

• m∗

t − (1 − ν)π−1 t

mt−1

• new issuance

+ wtnb,t − π−1

t

payt−1 − ρtph

t

• h∗

b,t − hb,t−1

• − δph

t hb,t−1 −

• Cost(ρt) − Rebatet
• m∗

t .

◮ Credit constraint:

m∗

t ≤

• min
• ¯

mltv

i,t , ¯

mpti

i,t

• dΓ(incomei).
• Agg. LOM
• Borr. Optimality

Saver’s Problem

• Eqm. Defn.

Monetary Policy

• Prod. Tech.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 4 / 61

Representative Borrower’s Housing Decision

◮ Housing optimality condition (unconstrained or no LTV):

ph

t =

uh

b,t/uc b,t + (1 − δ)Et

• Λb,t+1ph

t+1

• 1

◮ Λb,t+1 is borrower stochastic discount factor, µt is multiplier on credit

constraint.

◮ Ct (“collateral value”) is marginal value of relaxing constraint via extra $1 of

house value: Ct ≡ µtF ltv

t θltv

◮ Long-term debt: ph

t includes value of collateralizing a new loan, but

probability 1 − ρt+1 will not prepay.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 5 / 61

Representative Borrower’s Housing Decision

◮ Housing optimality condition (one-period debt, LTV only):

ph

t =

uh

b,t/uc b,t + (1 − δ)Et

• Λb,t+1ph

t+1

• 1−µtθltv

◮ Λb,t+1 is borrower stochastic discount factor, µt is multiplier on credit

constraint.

◮ Ct (“collateral value”) is marginal value of relaxing constraint via extra $1 of

house value: Ct ≡ µtF ltv

t θltv

◮ Long-term debt: ph

t includes value of collateralizing a new loan, but

probability 1 − ρt+1 will not prepay.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 5 / 61

Representative Borrower’s Housing Decision

◮ Housing optimality condition (one-period debt, LTV and PTI):

ph

t =

uh

b,t/uc b,t + (1 − δ)Et

• Λb,t+1ph

t+1

• 1−Ct

◮ Λb,t+1 is borrower stochastic discount factor, µt is multiplier on credit

constraint.

◮ Ct (“collateral value”) is marginal value of relaxing constraint via extra $1 of

house value: Ct ≡ µtF ltv

t θltv

◮ Long-term debt: ph

t includes value of collateralizing a new loan, but

probability 1 − ρt+1 will not prepay.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 5 / 61

Representative Borrower’s Housing Decision

◮ Housing optimality condition (Benchmark model):

ph

t =

uh

b,t/uc b,t + (1 − δ)Et

• Λb,t+1ph

t+1

• 1 − (1 − ρt+1)Ct+1
• 1−Ct

◮ Λb,t+1 is borrower stochastic discount factor, µt is multiplier on credit

constraint.

◮ Ct (“collateral value”) is marginal value of relaxing constraint via extra $1 of

house value: Ct ≡ µtF ltv

t θltv

◮ Long-term debt: ph

t includes value of collateralizing a new loan, but

probability 1 − ρt+1 will not prepay.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 5 / 61

Demographics and Preferences

◮ Two types of infinitely lived agents:

◮ Family of borrowers (b) with measure χb. ◮ Family of savers (s) with measure χs = 1 − χb.

◮ Both types provide labor: nt = nb,t + ns,t. ◮ Complete set of contracts over consumption and housing services traded

within each family, but not across families.

◮ Separable, expected utility preferences over consumption, housing services,

and labor supply (for j ∈ {b, s}): Vj,t = log(cj,t/χj) + ξ log(hj,t/χj) − η (nj,t/χj)1+ϕ 1 + ϕ + βjEtVj,t+1

◮ Borrowers are more impatient than savers: βb < βs.

• Motivation to borrow.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 6 / 61

Asset Technology

Housing:

◮ Divisible, owned by both types, requires maintenance cost. ◮ Cannot change housing stock without prepaying mortgage. ◮ Fixed housing stock ¯

H, saver demand ¯ Hs.

• Total collateral value, not price, crucial to constraints.
• Price effects are upper bound.

One-Period Bonds

◮ Nominal risk-free bond in zero net supply with rate Rt. ◮ No short positions/borrowing in one-period bond =

⇒ traded by savers only in equilibrium.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 7 / 61

Asset Technology

Mortgages:

◮ Only source of borrowing in the economy. ◮ Long-term nominal bonds with fixed interest rates.

• See paper for adjustable-rate version.

◮ Originated with principal balance m∗

t , borrower repays fraction ν of principal

each period.

◮ Contract specifies fixed coupon rate q∗

t (interest + principal), saver receives

$(1 − ν)kq∗

t m∗ t

at all t + k until prepayment.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 8 / 61

Demographics and Preferences

◮ Two types of infinitely lived agents:

◮ Family of borrowers (b) with measure χb. ◮ Family of savers (s) with measure χs = 1 − χb.

◮ Both types provide labor: nt = nb,t + ns,t. ◮ Complete set of contracts over consumption and housing services traded

within each family, but not across families.

◮ Separable, expected utility preferences over consumption, housing services,

and labor supply (for j ∈ {b, s}): Vj,t = log(cj,t/χj) + ξ log(hj,t/χj) − η (nj,t/χj)1+ϕ 1 + ϕ + βjEtVj,t+1

◮ Borrowers are more impatient than savers: βb < βs.

• Motivation to borrow.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 9 / 61

Asset Technology

Housing:

◮ Divisible, owned by both types, requires maintenance cost. ◮ Cannot change housing stock without prepaying mortgage. ◮ Fixed housing stock ¯

H, saver demand ¯ Hs.

• Total collateral value, not price, crucial to constraints.
• Price effects are upper bound.

One-Period Bonds

◮ Nominal risk-free bond in zero net supply with rate Rt. ◮ No short positions/borrowing in one-period bond =

⇒ traded by savers only in equilibrium.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 10 / 61

Asset Technology

Mortgages:

◮ Only source of borrowing in the economy. ◮ Long-term nominal bonds with fixed interest rates.

• See paper for adjustable-rate version.

◮ Originated with principal balance m∗

t , borrower repays fraction ν of principal

each period.

◮ Contract specifies fixed coupon rate q∗

t (interest + principal), saver receives

$(1 − ν)kq∗

t m∗ t

at all t + k until prepayment.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 11 / 61

Idiosyncratic Heterogeneity

• 1. Income shocks: An endogenous fraction of borrowers (those with low

enough income draws) are constrained by PTI, the rest by LTV.

• Equivalent to any shock that creates dispersion in house value-to-income

ratio.

Details PTI by Income

• Effect: smooth out constraint, dampen mechanism.
• 2. Prepayment cost shocks: An endogenous fraction of borrowers (those with

low enough costs) prepay their loans.

• Simplifying assumption: borrower must choose whether to prepay based only
• n aggregate state.

Details Redistribution Effects

• Can still respond to: average existing rate vs. new rate, total extractable

equity, forward looking expectations.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 12 / 61

Monetary Policy

◮ Monetary policy follows a Taylor rule with time-varying inflation target.

log Rt = log ¯ πt + φr(log Rt−1 − log ¯ πt−1) + (1 − φr)

• log ¯

Rreal + ψπ(log πt − log ¯ πt)

• for

log ¯ πt = (1 − φ¯

π) log πss + φ¯ π log ¯

πt−1 + ε¯

π,t.

◮ Why consider near-permanent policy shocks?

• ‘‘Level factor” shocks needed to move long-term nominal rates.
• But movements in term premia would also be amplified.
• With ARMs, amplification of transitory monetary policy shocks.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 13 / 61

Productive Technology

◮ Embed in simple New Keynesian environment (e.g., Gali (2008)). ◮ Intermediate goods producers operate the linear production function

yt(i) = atnt(i) where at is productivity, and nt(i) are labor hours.

◮ TFP process at:

log at+1 = φa log at + εa,t+1.

◮ Monopolistic intermediate producers with Calvo price rigidity (can’t reset

price with probability ζp).

Back Details Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 14 / 61

Calibration (Quarterly)

Parameter Name Value Internal Target/Source Fraction of borrowers χ 0.35 N 2001 SCF

• Borr. housing preference

ξ 0.253 Y phhb/wbnb = 8.68 (2001 SCF)

• St. Dev. Incomes

σe 0.411 N Fannie Mae Loan-Level Data Issuance cost mean µκ 0.188 Y

• Avg. FRM prepayment 1994-2015

Issuance cost scale sκ 0.0330 Y Fannie Mae MBS Data Max PTI Ratio θpti 0.28 N Max LTV Ratio θltv 0.85 N Saver discount factor βs 0.993 Y Real rate = 3% Borrower discount factor βb 0.95 N Mortgage amortization ν 1/120 N 30-year duration Taylor rule (inflation) ψπ 1.5 N Taylor rule (output) ψy N Taylor rule (smoothing) φr 0.89 N Campbell et al (2014) Trend infl (pers.) φ¯

π

0.994 N Garriga et al. (2013) TFP (pers.) φa 0.9641 N Garriga et al. (2013) PTI Ratio Offset τ 0.0375 / 4 N 200bp + Taxes, Ins.

Other Params. SCF Income Shocks Issuance Costs Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 15 / 61

Frontloading Effect

◮ PTI constraints deliver transmission into credit, house prices, but need

endogenous prepayment for transmission into output.

◮ Credit issuance can increase demand, but only affects output through sticky

prices if occurs in short run.

◮ Without endogenous prepayment, debt limits increase, but few borrowers

take advantage right away = ⇒ slow issuance.

◮ With endogenous prepayment, get issuance wave when rates fall, frontloaded

spending affects output.

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 16 / 61

Frontloading Effect (TFP Shock)

◮ TFP shock lowers nominal rates (deflationary) and raises labor income =

⇒ loosens PTI limits.

5 10 15 20 0.0 0.5 1.0 1.5

• Avg. Debt Limit

IRF to TFP

5 10 15 20 0.0 0.1 0.2 0.3 New Issuance (Level)

IRF to TFP

5 10 15 20 Quarters 0.0 0.5 Output 5 10 15 20 Quarters 0.0 0.5 1.0 1.5 Prepay Rate (Level)

LTV (Exog Prepay) Benchmark (Exog Prepay) Benchmark

π∗ IRFs 43% PTI Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 17 / 61

Frontloading Effect (TFP Shock)

◮ Effects large: output response to 1% TFP shock increased by 46% (0.52 to

0.76) on impact.

5 10 15 20 0.0 0.5 1.0 1.5

• Avg. Debt Limit

IRF to TFP

5 10 15 20 0.0 0.1 0.2 0.3 New Issuance (Level)

IRF to TFP

5 10 15 20 Quarters 0.0 0.5 Output 5 10 15 20 Quarters 0.0 0.5 1.0 1.5 Prepay Rate (Level)

LTV (Exog Prepay) Benchmark (Exog Prepay) Benchmark

π∗ IRFs 43% PTI Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 17 / 61

Inflation Stabilization (TFP Shock)

◮ Monetary policy experiment: how much does central bank need to move

policy rate to fully stabilize inflation, πt = ¯ π?

5 10 15 20 0.03 0.02 0.01 0.00 Rt

IRF to TFP

5 10 15 20 0.0 0.5 1.0 Debt

IRF to TFP

5 10 15 20 Quarters 0.0 0.5 1.0 Output 5 10 15 20 Quarters 0.0 0.5 1.0 Prepay Rate (Level)

LTV (Exog Prepay) Benchmark

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 18 / 61

Inflation Stabilization (TFP Shock)

◮ Monetary policy “stronger” under Benchmark model: smaller movement in

policy rate required to stabilize.

5 10 15 20 0.03 0.02 0.01 0.00 Rt

IRF to TFP

5 10 15 20 0.0 0.5 1.0 Debt

IRF to TFP

5 10 15 20 Quarters 0.0 0.5 1.0 Output 5 10 15 20 Quarters 0.0 0.5 1.0 Prepay Rate (Level)

LTV (Exog Prepay) Benchmark

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 18 / 61

Inflation Stabilization (TFP Shock)

◮ But smaller movement in policy rate comes with larger movement in debt.

Potential trade-off for policymakers.

5 10 15 20 0.03 0.02 0.01 0.00 Rt

IRF to TFP

5 10 15 20 0.0 0.5 1.0 Debt

IRF to TFP

5 10 15 20 Quarters 0.0 0.5 1.0 Output 5 10 15 20 Quarters 0.0 0.5 1.0 Prepay Rate (Level)

LTV (Exog Prepay) Benchmark

Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 18 / 61

Credit Liberalization Experiment

◮ Experiment liberalizing both LTV and PTI accounts for more than 92% of

rise in debt-household income (but not much more of price-rent).

20 40 10 20 30 Price-Rent Ratio 20 40 10 20 30 40 50 Debt 20 40 Quarters 70 75 80 85 90 95 F ltv (Level) 20 40 Quarters 5 10 15 20 25 Prepay Rate (Level)

Both Liberalized PTI Liberalized

Data More Series Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 19 / 61

Macroprudential Policy: Dodd-Frank Limit

◮ Counterfactual with Dodd-Frank cap, (θltv, θpti) → (0.99, 0.35) substantially

dampens cycle, cuts price-rent ratio rise by 63%.

20 40 10 20 30 Price-Rent Ratio 20 40 10 20 30 40 50 Debt 20 40 Quarters 65 70 75 80 85 F ltv (Level) 20 40 Quarters 5 10 15 20 25 Prepay Rate (Level)

Both Liberalized Dodd-Frank

Data More Series Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 20 / 61

Intensive Margin: Credit Constraints

◮ Actual 2015 underwriting standards from Fannie Mae (“DTI” = PTI).

Transaction Type Number of Units Maximum LTV, CLTV, HCLTV Credit Score/LTV Minimum Reserves Credit Score/LTV Minimum Reserves FRM: 680 if > 75% FRM: 620 if ≤ 75% ARM: 680 if > 75% ARM: 640 if ≤ 75% 700 if > 75% 640 if ≤ 75% 660 if > 75% 6 FRM: 680 if > 75% FRM: 620 if ≤ 75% ARM: 680 if > 75% 2 700 if > 75% 660 if ≤ 75% 6 680 if > 75% 640 if ≤ 75% 12 680 6 660 12 680 if > 75% 660 if ≤ 75% 700 if > 75% 680 if ≤ 75% 640 if ≤ 75% 660 if ≤ 75% 660 if ≤ 75% 640 if ≤ 75% 660 if ≤ 75% 640 if ≤ 75% 1 Unit FRM: 95% ARM: 90% 3-4 Units FRM: 75% ARM: 65% Purchase Limited Cash- Out Refinance FRM: 85% ARM: 75% 640 if ≤ 75% 2 Units

Standard Eligibility Requirements - Manual Underwriting

Excludes: Refi Plus, HomeStyle Renovation, and HomeReady 6 660

Maximum DTI ≤ 36% Maximum DTI ≤ 45%

6 680 if > 75% 640 if ≤ 75% 640 if ≤ 75% Principal Residence

Back to Intro Back to Credit Limits Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 21 / 61

Loan Level Price Adjustments

◮ PTI not priced, strictly a limit.

Table 1: All Eligible Mortgages (excluding MCM) – LLPA by Credit Score/LTV Ratio

Representative Credit Score LTV Range Applicable for all mortgages with terms greater than 15 years < 60.00% 60.01 – 70.00% 70.01 – 75.00% 75.01 – 80.00% 80.01 – 85.00% 85.01 – 90.00% 90.01 – 95.00% 95.01 – 97.00% SFC ≥ 740 0.000% 0.250% 0.250% 0.500% 0.250% 0.250% 0.250% 0.750% N/A 720 – 739 0.000% 0.250% 0.500% 0.750% 0.500% 0.500% 0.500% 1.000% N/A 700 – 719 0.000% 0.500% 1.000% 1.250% 1.000% 1.000% 1.000% 1.500% N/A 680 – 699 0.000% 0.500% 1.250% 1.750% 1.500% 1.250% 1.250% 1.500% N/A 660 – 679 0.000% 1.000% 2.250% 2.750% 2.750% 2.250% 2.250% 2.250% N/A 640 – 659 0.500% 1.250% 2.750% 3.000% 3.250% 2.750% 2.750% 2.750% N/A 620 – 639 0.500% 1.500% 3.000% 3.000% 3.250% 3.250% 3.250% 3.500% N/A < 620 (1) 0.500% 1.500% 3.000% 3.000% 3.250% 3.250% 3.250% 3.750% N/A (1) A minimum required credit score of 620 applies to all mortgage loans delivered to Fannie Mae in accordance with the Selling Guide; exceptions to this requirement are limited to loans in which all borrowers have nontraditional credit.

Back to Intro Back to Credit Limits Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 22 / 61

Prepayment Rates

◮ Fraction prepaying small, but volatile and highly responsive to interest rate

incentives.

1995 2000 2005 2010 2015 0.2 0.4 0.6 0.8

• 2
• 1

1 2 Prepayment Rate Rate Incentive

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 23 / 61

Subprime PTIs

◮ Plot from Foote, Gerardi, Willen (2009) shows subprime PTIs bunch at 50

and 55.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 24 / 61

LTV and PTI in the Data

◮ Individual borrower’s process:

• 1. Given income, interest rates, compute max loan size ¯

mpti

i,t .

• 2. Given max loan size, compute min house price associated with this

loan: ph

t ¯

hi,t = ¯ mpti

i,t /θltv t .

• 3. Search for house such that hi,t ≤ ¯

hi,t.

• 4. Obtain largest possible loan given house value:

m∗

i,t = ¯

mltv

i,t = θltv t ph t hi,t < θltv t ph t ¯

hi,t = ¯ mpti

i,t .

◮ Result: LTV exactly at limit, PTI slightly below. ◮ Why asymmetry? Can choose house price, not income/rates.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 25 / 61

Income Shocks

◮ Want heterogeneity so that endogenous fraction are constrained by PTI. ◮ Idiosyncratic labor efficiency shocks ei,t

iid

∼ Γe, so individual borrower’s income is incomei,t = wtnb,tei,t.

◮ Shocks affect only credit limits, not consumption or labor supply (due to

insurance, timing).

• Equivalent to any shock causing variation in house price/income ratios.

◮ PTI binds for

ei,t ≤ ¯ et ≡ θltvph

t ht

θptiwtnb,t/(q∗

t + τ).

◮ Fraction constrained by LTV:

F ltv

t

= 1 − Γe(¯ et).

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 26 / 61

PTI by Income

◮ PTI appear more binding for low income. High (low) income is top (bottom)

quartile.

10 20 30 40 50 60 70 80 PTI Ratio (%) 0.00 0.02 0.04 0.06 0.08 0.10

Fannie Mae: PTI Ratio, Low Income Buyers

(a) PTIs: 2014 Q3 (Low Income)

10 20 30 40 50 60 70 80 PTI Ratio (%) 0.00 0.02 0.04 0.06 0.08 0.10

Fannie Mae: PTI Ratio, High Income Buyers

(b) PTIs: 2014 Q3 (High Income)

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 27 / 61

PTI by Income

◮ Very high PTIs for low-income borrowers at height of boom.

10 20 30 40 50 60 70 80 PTI Ratio (%) 0.00 0.02 0.04 0.06 0.08 0.10

Fannie Mae: PTI Ratio, Low Income Buyers

(a) PTIs: 2006 Q1 (Low Income)

10 20 30 40 50 60 70 80 PTI Ratio (%) 0.00 0.02 0.04 0.06 0.08 0.10

Fannie Mae: PTI Ratio, High Income Buyers

(b) PTIs: 2006 Q1 (High Income)

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 28 / 61

CLTV by Income

◮ In contrast, CLTVs look very similar across income groups during boom and

bust.

50 60 70 80 90 100 110 CLTV Ratio (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Fannie Mae: CLTV Ratio, Low Income Buyers

(a) CLTVs: 2014 Q3 (Low Income)

50 60 70 80 90 100 110 CLTV Ratio (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Fannie Mae: CLTV Ratio, High Income Buyers

(b) CLTVs: 2014 Q3 (High Income)

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 29 / 61

CLTV by Income

◮ In contrast, CLTVs look very similar across income groups during boom and

bust.

50 60 70 80 90 100 110 CLTV Ratio (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Fannie Mae: CLTV Ratio, Low Income Buyers

(a) CLTVs: 2006 Q1 (Low Income)

50 60 70 80 90 100 110 CLTV Ratio (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Fannie Mae: CLTV Ratio, High Income Buyers

(b) CLTVs: 2006 Q1 (High Income)

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 30 / 61

Prepayment

◮ Prepayment:

• Borrower pays remaining principal to lender, cancels future payments.
• Borrower can immediately take out new loan, adjust housing holdings.

◮ Transaction cost shocks:

• Borrower must pay cost κi,tm∗

t , to obtain a new loan where κi,t iid

∼ Γκ.

• If κi,t ≤ ¯

κi,t, then the borrower executes transaction, prepays.

◮ Timing within the period:

• 1. Borrowers choose labor supply nb,t, threshold transaction cost ¯

κt, target house size h∗

t (conditional on prepaying).

• 2. Borrowers draw κi,t, prepay if κi,t ≤ ¯

κt.

• 3. Borrowers draw ei,t, obtain new loan of size m∗

i,t = min( ¯

mltv

i,t , ¯

mpti

i,t ).

• 4. Insurance claims are paid out, equalizing consumption across borrowers.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 31 / 61

Credit or Redistribution?

◮ Prepayment has two effects:

• Allows borrower to obtain new debt (credit channel).
• Changes payments on existing debt (redistribution channel).

◮ Unlike previous work (Rubio (2011), Calza et al. (2013), Auclert (2015)),

this framework can generate large redistributions in fixed-rate mortgage environment from prepayment.

◮ However, impact on aggregate demand is very small. ◮ Key is persistence of transfers.

• Impatient borrower consumes out of current income, while patient saver

consumes out of permanent income.

• But with FRMs, prepayment leads to constant change in payments each

month for decades.

• Changes in current and permanent income nearly identical =

⇒ offsetting consumption responses.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 32 / 61

Aggregation

◮ Aggregate laws of motion:

mt = ρtm∗

t + (1 − ρt)(1 − ν)π−1 t

mt−1 payt = ρtq∗

t m∗ t + (1 − ρt)(1 − ν)π−1 t

payt−1 hb,t = ρth∗

b,t + (1 − ρt)hb,t−1.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 33 / 61

Borrower Optimality

◮ Labor supply (nb,t) condition:

wt = − un

b,t

uc

b,t

.

◮ New loan size (m∗

t ) condition:

1 = Ωm

b,t + q∗ t Ωpay b,t + µt

where µt is multiplier, Ωm

b,t and Ωpay b,t are marginal continuation costs of

extra unit of face value debt and promised payments: Ωm

b,t = Et

• Λ$

b,t+1

• (1 − ν)ρt+1 + (1 − ν)(1 − ρt+1)Ωm

b,t+1

• Ωpay

b,t = Et

• Λ$

b,t+1

• 1 + (1 − ν)(1 − ρt+1)Ωpay

b,t+1

• and Λ$

b,t+1 is the nominal SDF.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 34 / 61

Borrower Optimality

◮ Prepayment optimality condition:

ρt = Γ

• (m∗

t )−1

• (1 − Ωm

b,t)

• m∗

t − (1 − ν)π−1 t

mt−1

• new debt

− Ωpay

b,t

• q∗

t m∗ t − (1 − ν)π−1 t

payt−1

• new payments

− Ctph

t

• h∗

b,t − (1 − δ)hb,t−1

• cost of collateral
• .

◮ Ωm

b,t and Ωpay b,t are the marginal costs of extra unit of principal balance and

promised payment: Ωm

b,t = Et

• Λ$

b,t+1

• (1 − ν)ρt+1 + (1 − ν)(1 − ρt+1)Ωm

b,t+1

• Ωpay

b,t = Et

• Λ$

b,t+1

• 1 + (1 − ν)(1 − ρt+1)Ωpay

b,t+1

• .

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 35 / 61

Saver’s Problem

◮ Budget constraint:

cs,t ≤ Πt + wtns,t − ρt(m∗

t − (1 − ν)π−1 t

mt−1)

• New Issuance

+ π−1

t

payt−1 − ph

t (hs,t − (1 − δ)hs,t−1) − R−1 t

bt + bt−1.

◮ Optimality conditions:

(b) : 1 = RtEt

• Λ$

s,t+1

• (m∗) :

1 = Ωm

s,t + Ωpay s,t q∗ t

◮ Ωm

s,t and Ωpay s,t are the marginal benefits of extra unit of principal balance and

promised payment: Ωm

s,t = Et

• Λ$

s,t+1

• (1 − ν)ρt+1 + (1 − ν)(1 − ρt+1)Ωm

s,t+1

• Ωpay

s,t = Et

• Λ$

s,t+1

• 1 + (1 − ν)(1 − ρt+1)Ωpay

s,t+1

• .

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 36 / 61

Equilibrium Definition

A competitive equilibrium in this model is defined as a sequence of endogenous states (mt−1, qt−1, hb,t−1, hs,t−1), allocations (cj,t, nj,t, hj,t), mortgage market quantities (m∗

t , ρt), and prices (πt, wt, ph t , Rt, q∗ t ) such that:

• 1. Given prices, (cb,t, nb,t, h∗

b,t, m∗ t , ρt) solve the borrower’s problem.

• 2. Given prices and borrower refinancing behavior, (cs,t, ns,t, hs,t, m∗

t ) solve the

saver’s problem.

• 3. Given wages and consumer demand, πt is the outcome of the intermediate

firm’s optimization problem.

• 4. Given inflation and output, Rt satisfies the monetary policy rule.
• 5. The resource, bond, and housing markets clear:

yt = cb,t + cs,t + xh

t ,

bs,t = 0 ht = ¯ H, hs,t = ¯ Hs.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 37 / 61

Calvo Pricing

Solution to intermediate firm’s problem: yt =

• yt(i)

λ−1 λ di

• λ

λ−1

= atnt ∆t Nt = yt mct mcss

• + ζpEt
• Λs,t+1

πt+1 πss λ Nt+1

• Dt = yt + ζpEt
• Λs,t+1

πt+1 πss λ−1 Dt+1

• ˜

pt = Nt Dt πt = πss 1 − (1 − ζp)˜ p1−λ ζp

• 1

λ−1

∆t = (1 − ζp)˜ p−λ + ζp(πt/πss)λ∆t−1 where Nt and Dt are auxiliary variables, ˜ pt is the ratio of the optimal price for resetting firms relative to the average price, and ∆t is price dispersion.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 38 / 61

Calibration (Quarterly)

Parameter Name Value Internal Target/Source Steady state inflation πss 1.0075 N

• Avg. infl. = 3%

Variety elasticity λ 6.0 N

• Inv. Frisch Elasticity

ϕ 1.0 N Disutility of Labor η 7.935 Y n = 1/3 Price stickiness ζ 0.75 N Average productivity µa 1.098 Y y = 1 Trend infl (std.) σ¯

π

0.0015 N Garriga et al. (2013) TFP (std.) σa 0.0082 N Garriga et al. (2013)

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 39 / 61

Calibration: Fraction of Borrowers

◮ Calibrate borrower/saver division to match 2001 Survey of Consumer

Finances (SCF).

◮ Borrowers in the model: have house and mortgage but no liquid assets, save

in home equity.

• Match to households in 2001 SCF with less than one month’s income in

liquid assets (Kaplan and Violante (2014)) with a mortgage (24.3%).

• Use housing preference ξ to match housing wealth / income for borrowers.

◮ Savers in the model: unconstrained agents with liquid assets.

• Match to households in 2001 SCF with more than one month’s income in

liquid assets (45.4%).

◮ Remove households with no liquid assets and no mortgage (mostly renters)

who are not represented in the model and normalize: χb = 0.35.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 40 / 61

Calibration: Income Shock Distribution

◮ Parameterize ei shocks to be lognormal, only need to calibrate σe.

2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 log value - log income 0.0 0.5 1.0 1.5 2.0

Figure: House Price / Income Ratio: 2000 Q1

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 41 / 61

Calibration: Income Shock Distribution

◮ Choose σe to match cross-sectional dispersion of log valuei,t − log incomei,t

in Fannie Mae loan-level origination data (average over 2000-2014).

• This ratio determines which constraint is binding, given aggregates.

2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 log value - log income 0.0 0.5 1.0 1.5 2.0

Figure: House Price / Income Ratio: 2000 Q1

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 41 / 61

Calibration: Issuance Costs

◮ Choose Γκ so that approx. annualized prepayment rate

cpr t = 4ρt has a logistic functional form:

• cpr t =

1 1 + exp

• − κ−µκ

sκ

.

◮ To calibrate sk, estimate prepayment regression

logit(cpri,t) = γ0,t + γ1(q∗

t − ¯

qi,t−1) + ei,t using pool-level MBS data (Fannie Mae 30-Year FRMs, 1994-2015).

◮ Choose sκ so that model equation

logit( cpr t) = γ0,t − Ωpay

b,t

sκ

• q∗

t − ¯

qt−1 (1 − ν)π−1

t

mt−1 m∗

t

• satisfies Ωpay

b

/sκ = ˆ γ1 in steady state.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 42 / 61

Calibration: Issuance Costs

◮ Given sκ can choose µκ to match average prepayment rates on the same

MBS series.

0.1 0.0 0.1 0.2 0.3 0.4 0.5 1 2 3 4 5 6 7 8 Density

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 43 / 61

Calibration: Issuance Costs

◮ Resulting costs are high (threshold prepayer pays 13.1%, average prepayer

pays 8.1%). Needed to match “inertial” behavior.

0.1 0.0 0.1 0.2 0.3 0.4 0.5 1 2 3 4 5 6 7 8 Density

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 43 / 61

Monetary Policy Shock (Trend Infl.)

◮ Focus on mechanism: exogenous prepayment (ρt = ¯

ρ).

5 10 15 20 5 Debt

IRF to Infl. Target

5 10 15 20 2 4 House Price

IRF to Infl. Target

5 10 15 20 Quarters 1 2 F ltv (Level) 5 10 15 20 Quarters 0.5 0.0 q ∗

t (Level)

LTV (Exog) PTI (Exog) Benchmark (Exog)

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 44 / 61

Constraint Switching Effect (TFP Shock)

◮ TFP shock lowers nominal rates (deflationary) and raises labor income =

⇒ loosens PTI limits.

5 10 15 20 0.0 0.5 1.0 1.5 Debt

IRF to TFP

5 10 15 20 0.0 0.2 0.4 Price-Rent Ratio

IRF to TFP

5 10 15 20 Quarters 0.0 0.2 0.4 F ltv (Level) 5 10 15 20 Quarters 0.10 0.05 0.00 q ∗

t (Level)

LTV PTI Benchmark

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 45 / 61

Credit Liberalization: LTV

◮ For IRFs, assume log θt is AR(1) with persistence 0.9.

5 10 15 20 5 Debt

IRF to LTV Limit

5 10 15 20 5 10 House Price

IRF to LTV Limit

5 10 15 20 Quarters 5 F ltv (Level) 5 10 15 20 Quarters Price-Rent Ratio

LTV PTI Benchmark

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 46 / 61

Credit Liberalization: LTV

◮ Loosening LTV (10%) causes decrease in collateral value, house prices and

price-rent ratios fall in Benchmark model.

5 10 15 20 5 Debt

IRF to LTV Limit

5 10 15 20 5 10 House Price

IRF to LTV Limit

5 10 15 20 Quarters 5 F ltv (Level) 5 10 15 20 Quarters Price-Rent Ratio

LTV PTI Benchmark

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 46 / 61

Credit Liberalization: PTI

◮ Loosening PTI (10%) causes increase in collateral value, house prices and

price-rent ratios rise in Benchmark model.

5 10 15 20 2 4 Debt

IRF to PTI Limit

5 10 15 20 5 House Price

IRF to PTI Limit

5 10 15 20 Quarters 2 4 F ltv (Level) 5 10 15 20 Quarters 1 Price-Rent Ratio

LTV PTI Benchmark

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 47 / 61

Constraint Switching Effect (Monetary Policy Shock)

◮ θpti = 43% (Dodd-Frank): only 13% constrained by PTI.

5 10 15 20 5 10 Debt

IRF to Trend Infl.

5 10 15 20 2 4 Price-Rent Ratio

IRF to Trend Infl.

5 10 15 20 Quarters 1 2 F ltv (Level) 5 10 15 20 Quarters 0.5 0.0 q ∗

t (Level)

LTV PTI Benchmark

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 48 / 61

Frontloading Effect (Monetary Policy Shock)

◮ Large response of output to -1% near-permanent monetary policy shock.

5 10 15 20 2 4 6

• Avg. Debt Limit

IRF to Infl. Target

5 10 15 20 1 2 New Issuance (Level)

IRF to Infl. Target

5 10 15 20 Quarters 0.0 0.5 1.0 1.5 Output 5 10 15 20 Quarters 5 Prepay Rate (Level)

LTV (Exog Prepay) Benchmark (Exog Prepay) Benchmark

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 49 / 61

Frontloading Effect (TFP Shock)

◮ θpti = 43% (Dodd-Frank): only 13% constrained by PTI.

5 10 15 20 1 Debt

IRF to TFP

5 10 15 20 0.0 Price-Rent Ratio

IRF to TFP

5 10 15 20 0.0 0.2 F ltv (Level) 5 10 15 20 0.10 0.05 0.00 q ∗

t (Level)

5 10 15 20 Quarters 0.0 0.5 Output 5 10 15 20 Quarters 1 Prepay Rate (Level)

LTV PTI Benchmark

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 50 / 61

Credit Standards and the Boom-Bust

◮ Large rise in PTI ratios relative to CLTV ratios.

2001 2003 2005 2007 2009 2011 2013 80 82 84 86 88 90 92 94 96

CLTV Ratio, 75th percentile

(a) CLTV: 75th Percentile

2001 2003 2005 2007 2009 2011 2013 40 41 42 43 44 45 46 47 48 49

PTI Ratio, 75th percentile

(b) PTI: 75th Percentile

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 51 / 61

Credit Standards and the Boom-Bust

2001 2003 2005 2007 2009 2011 2013 90 91 92 93 94 95

CLTV Ratio, 90th percentile

(a) CLTV: 90th Percentile

2001 2003 2005 2007 2009 2011 2013 44 46 48 50 52 54 56

PTI Ratio, 90th percentile

(b) PTI: 90th Percentile

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 52 / 61

Credit Standards and the Boom-Bust

Fannie Mae 2007 Selling Guide

◮ Although we have established a benchmark qualifying debt-to-income ratio, we

recognize that often there are legitimate reasons for exceeding this guideline. Therefore, a lender may use a ratio that is higher than our benchmark guideline, as long as its assessment of the comprehensive risk of the mortgage identifies and documents factors that justify the higher ratio...Our benchmark debt-to-income ratio is 36 percent of the borrower’s monthly income.

Fannie Mae 2009 Selling Guide

◮ For manually underwritten loans, Fannie Mae’s benchmark total debt-to-income

ratio is 36% of the borrower’s stable monthly income. The benchmark can be exceeded up to a maximum of 45% with strong compensating factors... For loan casefiles underwritten through DU [Desktop Underwriter], DU determines the maximum allowable debt-to income ratio based on the overall risk assessment of the loan casefile. DU will apply a maximum allowable total expense ratio of 45%, with flexibilities offered up to 50% for certain loan casefiles with strong compensating factors.

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 53 / 61

Credit Standards and the Boom-Bust

“A New Method for Evaluating Your Debt” (Los Angeles Times: January 27, 2002)

◮ “In the 1970s and 1980s, a common rule of thumb was that your mortgage-related

payments shouldn’t eat up more than 25% of your monthly household income. During the late 1980s and into the 1990s, that rule began to stretch into the 31% to 33% range and sometimes higher.”

◮ “In the 1990s, acceptable ratios began creeping above 40%. Late in the decade,

even Freddie Mac confirmed that it no longer had hard and fast rules on total monthly debt to monthly income ratios, and lenders reported selling loans to Freddie with debt-to-income ratios of 55% and higher.”

Back Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 54 / 61

Boom-Bust Paths (Data)

◮ Percent deviations from price-rent trough (1997Q4).

1999 2001 2003 2005 2007 2009 2011 2013 2015 10 10 20 30 40 50 Log Price-Rent (%)

(a) Log Price-Rent

1999 2001 2003 2005 2007 2009 2011 2013 2015 10 10 20 30 40 50 60 Log Debt-Household Income (%)

(b) Log Debt-Household Income

LTV/PTI Both Dodd-Frank Daniel L. Greenwald (MIT Sloan) The Mortgage Credit Channel September 29, 2016 55 / 61

Credit Liberalization Experiment

20 40 5 10 15 20 25

• Avg. Debt Limit

20 40 4 2 2 4 6 New Issuance (Level) 20 40 Quarters 0.2 0.0 logR10Y − logR (Level) 20 40 Quarters 0.5 0.0 0.5 1.0 q ∗

t (Level)

LTV Liberalized PTI Liberalized

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Credit Liberalization Experiment (Intuition)

◮ Changes to LTV standards cannot explain the boom-bust with PTI limits at

traditional levels.

• Direct effect: PTI constraints limit debt boom.
• GE effect: constraint switching limits house price boom.

F ltv House Prices LTV Limits PTI Limits Max LTV

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Credit Liberalization Experiment (Intuition)

◮ Relaxation of PTI standards increases house prices, price-rent ratios through

constraint switching effect.

◮ High house prices relax LTV limits =

⇒ large increase in debt.

Max PTI PTI Limits LTV Limits F ltv House Prices

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Macroprudential Policy: Preference Shocks

◮ Alternative experiment: leave PTI limits fixed at θpti = 0.28, instead

increase housing preference ξ by 10%, return to baseline after 32Q.

20 40 20 15 10 5 5 Price-Rent Ratio 20 40 5 10 15 20 25 Debt 20 40 Quarters 10 10 20 30 40

• Avg. Debt Limit

20 40 Quarters 5 10 15 20 25 Prepay Rate (Level)

LTV Economy Benchmark Economy

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Credit Liberalization Experiment

20 40 10 20 30 40 50

• Avg. Debt Limit

20 40 5 5 10 New Issuance (Level) 20 40 Quarters 0.2 0.0 logR10Y − logR (Level) 20 40 Quarters 1.0 0.5 0.0 0.5 1.0 q ∗

t (Level)

Both Liberalized PTI Liberalized

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Macroprudential Policy: Dodd-Frank Limit

20 40 10 20 30 40 50

• Avg. Debt Limit

20 40 5 5 10 New Issuance (Level) 20 40 Quarters 0.2 0.0 logR10Y − logR (Level) 20 40 Quarters 1.0 0.5 0.0 0.5 1.0 q ∗

t (Level)

Both Liberalized Dodd-Frank

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