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Do Mortgage Subsidies Help or Hurt Borrowers? David Rappoport Federal Reserve Board

WEAI Santiago – January 4, 2017 The opinions expressed here do not necessarily reflect those of the Federal Reserve Board or its staff.

I. Motivation I

I

Debt subsidies are provided in several countries and are economically significant I

interest deduction for mortgages and corporate debt

I

student loans

Current debate in the U.S. about housing and tax policy I

Mortgage Interest Deductions (MID) $70 billion in 2015 (Office of Management and Budget, 2015)

I

Role and design of GSEs in mortgage market

David Rappoport (FRB)

Do Mortgage Subsidies Help or Hurt Borrowers?

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I. Motivation I

I

I

Debt subsidies are provided in several countries and are economically significant I

interest deduction for mortgages and corporate debt

I

student loans

Current debate in the U.S. about housing and tax policy I

Mortgage Interest Deductions (MID) $70 billion in 2015 (Office of Management and Budget, 2015)

I

Role and design of GSEs in mortgage market

Debt subsidies → effective interest rates & asset prices But welfare evaluation using sufficient statistics ignores effect on asset prices



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This paper

I

Mortgage subsidies’ effect, as function of sufficient statistics, w/ both interest rates & house prices respond



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This paper

I

Mortgage subsidies’ effect, as function of sufficient statistics, w/ both interest rates & house prices respond

1. Applied welfare model to describe analytically effects on house prices, economic incidence, and efficiency costs 2. Estimate these effects for 269 metropolitan areas from eliminating MID



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Preview of Analytical Results I

Mortgage subsidies fully distort marginal user cost, acting as a non-linear subsidy I

Households increase LTVs

I

Amplifies the response of house prices

I

First-time buyers can be hurt by mortgage subsidies

I

Financial frictions make LTV key statistic to describe incidence (in addition to demand/supply elasticities)

I

Efficiency Loss (EB): house price movements attenuate EB w/o additional losses (zero-sum redistribution)



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Preview of Estimated Results I

Evaluate elimination of MID using sufficient statistics formulas previously derived

I

Estimate house price decline for 269 MSAs, average 6.9

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Estimate incidence for first-time buyers and owners for 269 MSAs—elasticities, LTV, mortgage rate and term

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Welfare on average reduced by 10% of house value: Owners/buyers loose/less more in more inelastic regions

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Efficiency losses about 5 basis points of housing value



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Related Literature I

Effect of mortgage supply on house prices Himmelberg, Mayer and Sinai (2005 JEP); Glaeser, Gottlieb and Gyourko (2011); Favara and Imbs (2015 AER); Adelino, Schoar and Severino (2015); Di Maggio and Kermani (2015); Kung (2015)

I

Welfare evaluation of housing/mortgage policy using sufficient statistics Laidler (1969); Aaron (1972); Rosen (1979); Rosen (1985); Poterba (1992 AER); Poterba and Sinai (2008 AER)

I

Regional variation of mortgage policy Capozza, Green and Hendershot (1996); Hilber and Turner (2014 REStat); Hurst, Keys, Seru and Vavra (2016 AER)



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Outline

I. Introduction

II. Applied Welfare Analysis of Mortgage Subsidies

III. Estimates of the Effects of Eliminating MID



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II. Applied Welfare Analysis I

Households’ problem

max u(x) + c x,m,c

s.t.

(HhP)

px + T ≤ y + (q + t)m c + m ≤ (1 − δ + π)px x, m, c ≥ 0



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II. Applied Welfare Analysis I

Households’ problem

max u(x) + c

(HhP)

x,m,c

s.t.

px + T ≤ y + (q + t)m c + m ≤ (1 − δ + π)px x, m, c ≥ 0

I

Demand for housing depends on rental rate

ux = [r(t) + δ − π] p uc | {z }

with

r(t) =

user cost



1 −1 q+t 7 / 24

Applied Welfare Analysis (cont’d) I

I

I

Lenders I

Maximize profits (r − rf − ρ)l

I

Assume CRS techonology, so r = rf + ρ, with ρ > 0

Homeowners and house producers I

Owners endowed with stock h, and sell inelastically

I

Producers maximize profits pz − κ(z)

Government I

Collect lump-sum taxe T and give mortgage subsidy t

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Balance budget T = t m



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Notation

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Price elasticity of house supply: εS,p

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Price elasticity of house demand: εD,p

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Mortgage rate semi-elasticity of house demand: ζD,r

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Indirect utility function V(t) ≡ V(p(t), r(t), y)



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Incidence of Mortgage Subsidies

Proposition 1 (Incidence of Mortgage Subsidies)

The incidence of increasing the mortgage subsidy, t, is z dp/dt on house producers, h dp/dt on homeowners, and

dV ≈ uc px ζp,r [r(t) + δ − π] + LTV dt

on homebuyers, with effect on house prices given by

ζp,r =


ζD,r 1 dp 0) pin down the household’s LTV and make it a key statistic to calculate incidence

I

Chain rule imply ζD,r = εD,p /(r(t) + δ − π), then

ζp,r = I

εD,p 1 dp 1 = p dr r(t) + δ − π εS,p − εD,p

Use it to show that buyers can get hurt and house price amplification from LTV increase



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Efficiency Cost of Mortgage Subsidies

Proposition 2 (Efficiency Loss of Mortgage Subsidies)

The efficiency loss of mortgage subsidies equals the triangle produced by the distortion in the mortgage market, while in the housing there is zero-sum redistribution between buyers and sellers (i.e., home producers and home owners).

EB(t) ≈


1 t Δm 2


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Efficiency Loss of Mortgage Subsidies Graphical Representation

(a) Mortgage Market

(b) Housing Market

p

r

r a

S

b

t

r−t e 0


c d

p(t) a p(0) d e

S

b c f

D(t)

M(t)

D(0)

M(0) m(0)

m(t)

M

0


x(0) x(t)

D

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Efficiency Cost of Mortgage Subsidies Discussion I

House price effect: I

introduces regional heterogeneity in efficiency costs

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attenuates response of house and mortgage demand—attenuating efficiency loss

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ˆ Income effects: use compensated mortgage demand Δm

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Pre-existing subsidies: Harberger trapezoid formula

EB(t) = t0 Δm1 +


1 Δt1 Δm1 2


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III. Effect of Eliminating MID by MSA I

McDash Analytics 17.5 million fixed mortgages 2010−15 ri , ii , LTVi , Ti (10, 15, 20, 25, 30 years), and zip code

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Equifax Credit Risk Insight Servicing: first-time buyers if no mortgage account 6 prior to mortgage close, 18.5%



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I


I

Assume house tenure is also Ti years



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I


I

Assume house tenure is also Ti years

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εS,p,j ∈ [0.6, 12.1] with εˉ S,p,j = 1.8 (Saiz, 2010)

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εD,p = −1 (Rosen, 1985; Davis and Ortalo-Magne, 2011)

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ri − τy ii + (1 − τy )τp + δ − π + φ = 5% ⇒ ζˉD,r,i = −15.3 | {z } δ − π = 3.8% τy = 25%, ii = 4.2% (Poterba 1984, Himmelberg et al. 2005, MacDash)



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Measuring the Welfare Effects ζp,r,j =

P

i∈Ij

ωi ζD,r,i

εS,p,j − εD,p

Δpj ≈ pj

and

P

i∈Ij

ωi ζD,r,i τy ii

εS,p,j − εD,p

Proposition 3 (Incidence over multiple periods) The incidence of a permanent elimination of MID, equals zero for lenders, pj zj (Δpj /pj ) for house producers,

ΔVi = uc pj xi −φp (ri (1), Ti ) Δpj /pj − φm (ri (1), Ti ) LTVi

(1)

for household i in metropolitan area j, where Δpj /pj < 0.    T   1−(1−ri (1)−δ+π) i for first time buyers φp (ri (ϕ),Ti )=     −(1−ri (1)−δ+π)Ti for homeowners    τy ii 12Ti 1 φm (ri (ϕ),Ti )=  11/12  1/12 − 12(1+ri (ϕ))


(1+ri (ϕ))

−1

(1+ri (ϕ))1/12 (1+ri (ϕ))Ti −1


 

 .

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Measuring the Welfare Effects (cont’d)

EB(1, 0) ≈

1 X m ˆi 0 −m ˆ i 1 ti (0) + ti (1) 2 i∈I j

=

1X Δm ˆ i ti (1) (2) 2 i∈I j

With

" ! # Δpj 1X ri (1)LTVi Δm ˆi = pj xi (1 + ri (1))εD,p + ζD,r,i − τy ii 2 i∈I pj 1 + ri (1) j {z } | {z } | house price effect >0



mortgage rate effect